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-rw-r--r--theories/.dir-locals.el4
-rw-r--r--theories/Arith/Arith.v10
-rw-r--r--theories/Arith/Arith_base.v10
-rw-r--r--theories/Arith/Between.v10
-rw-r--r--theories/Arith/Bool_nat.v10
-rw-r--r--theories/Arith/Compare.v10
-rw-r--r--theories/Arith/Compare_dec.v22
-rw-r--r--theories/Arith/Div2.v14
-rw-r--r--theories/Arith/EqNat.v16
-rw-r--r--theories/Arith/Euclid.v10
-rw-r--r--theories/Arith/Even.v10
-rw-r--r--theories/Arith/Factorial.v10
-rw-r--r--theories/Arith/Gt.v10
-rw-r--r--theories/Arith/Le.v28
-rw-r--r--theories/Arith/Lt.v39
-rw-r--r--theories/Arith/Max.v10
-rw-r--r--theories/Arith/Min.v10
-rw-r--r--theories/Arith/Minus.v20
-rw-r--r--theories/Arith/Mult.v34
-rw-r--r--theories/Arith/PeanoNat.v30
-rw-r--r--theories/Arith/Peano_dec.v12
-rw-r--r--theories/Arith/Plus.v24
-rw-r--r--theories/Arith/Wf_nat.v10
-rw-r--r--theories/Bool/Bool.v10
-rw-r--r--theories/Bool/BoolEq.v10
-rw-r--r--theories/Bool/Bvector.v10
-rw-r--r--theories/Bool/DecBool.v10
-rw-r--r--theories/Bool/IfProp.v10
-rw-r--r--theories/Bool/Sumbool.v10
-rw-r--r--theories/Bool/Zerob.v10
-rw-r--r--theories/Classes/CEquivalence.v10
-rw-r--r--theories/Classes/CMorphisms.v10
-rw-r--r--theories/Classes/CRelationClasses.v10
-rw-r--r--theories/Classes/DecidableClass.v10
-rw-r--r--theories/Classes/EquivDec.v10
-rw-r--r--theories/Classes/Equivalence.v10
-rw-r--r--theories/Classes/Init.v10
-rw-r--r--theories/Classes/Morphisms.v10
-rw-r--r--theories/Classes/Morphisms_Prop.v10
-rw-r--r--theories/Classes/Morphisms_Relations.v10
-rw-r--r--theories/Classes/RelationClasses.v10
-rw-r--r--theories/Classes/RelationPairs.v16
-rw-r--r--theories/Classes/SetoidClass.v10
-rw-r--r--theories/Classes/SetoidDec.v10
-rw-r--r--theories/Classes/SetoidTactics.v10
-rw-r--r--theories/Compat/AdmitAxiom.v10
-rw-r--r--theories/Compat/Coq85.v36
-rw-r--r--theories/Compat/Coq86.v10
-rw-r--r--theories/Compat/Coq87.v10
-rw-r--r--theories/FSets/FMapAVL.v16
-rw-r--r--theories/FSets/FMapFacts.v22
-rw-r--r--theories/FSets/FMapFullAVL.v16
-rw-r--r--theories/FSets/FMapInterface.v16
-rw-r--r--theories/FSets/FMapList.v16
-rw-r--r--theories/FSets/FMapPositive.v16
-rw-r--r--theories/FSets/FMapWeakList.v16
-rw-r--r--theories/FSets/FMaps.v16
-rw-r--r--theories/FSets/FSetAVL.v16
-rw-r--r--theories/FSets/FSetBridge.v16
-rw-r--r--theories/FSets/FSetCompat.v16
-rw-r--r--theories/FSets/FSetDecide.v16
-rw-r--r--theories/FSets/FSetEqProperties.v16
-rw-r--r--theories/FSets/FSetFacts.v16
-rw-r--r--theories/FSets/FSetInterface.v16
-rw-r--r--theories/FSets/FSetList.v16
-rw-r--r--theories/FSets/FSetPositive.v16
-rw-r--r--theories/FSets/FSetProperties.v16
-rw-r--r--theories/FSets/FSetToFiniteSet.v16
-rw-r--r--theories/FSets/FSetWeakList.v16
-rw-r--r--theories/FSets/FSets.v16
-rw-r--r--theories/Init/Datatypes.v28
-rw-r--r--theories/Init/Decimal.v163
-rw-r--r--theories/Init/Logic.v31
-rw-r--r--theories/Init/Logic_Type.v18
-rw-r--r--theories/Init/Nat.v68
-rw-r--r--theories/Init/Notations.v37
-rw-r--r--theories/Init/Peano.v30
-rw-r--r--theories/Init/Prelude.v11
-rw-r--r--theories/Init/Specif.v45
-rw-r--r--theories/Init/Tactics.v10
-rw-r--r--theories/Init/Wf.v10
-rw-r--r--theories/Lists/List.v11
-rw-r--r--theories/Lists/ListDec.v10
-rw-r--r--theories/Lists/ListSet.v10
-rw-r--r--theories/Lists/ListTactics.v10
-rw-r--r--theories/Lists/SetoidList.v16
-rw-r--r--theories/Lists/SetoidPermutation.v16
-rw-r--r--theories/Lists/StreamMemo.v10
-rw-r--r--theories/Lists/Streams.v10
-rw-r--r--theories/Logic/Berardi.v10
-rw-r--r--theories/Logic/ChoiceFacts.v24
-rw-r--r--theories/Logic/Classical.v10
-rw-r--r--theories/Logic/ClassicalChoice.v10
-rw-r--r--theories/Logic/ClassicalDescription.v10
-rw-r--r--theories/Logic/ClassicalEpsilon.v12
-rw-r--r--theories/Logic/ClassicalFacts.v10
-rw-r--r--theories/Logic/ClassicalUniqueChoice.v10
-rw-r--r--theories/Logic/Classical_Pred_Type.v10
-rw-r--r--theories/Logic/Classical_Prop.v10
-rw-r--r--theories/Logic/ConstructiveEpsilon.v10
-rw-r--r--theories/Logic/Decidable.v10
-rw-r--r--theories/Logic/Description.v10
-rw-r--r--theories/Logic/Diaconescu.v19
-rw-r--r--theories/Logic/Epsilon.v10
-rw-r--r--theories/Logic/Eqdep.v10
-rw-r--r--theories/Logic/EqdepFacts.v12
-rw-r--r--theories/Logic/Eqdep_dec.v10
-rw-r--r--theories/Logic/ExtensionalFunctionRepresentative.v10
-rw-r--r--theories/Logic/ExtensionalityFacts.v10
-rw-r--r--theories/Logic/FinFun.v10
-rw-r--r--theories/Logic/FunctionalExtensionality.v10
-rw-r--r--theories/Logic/Hurkens.v10
-rw-r--r--theories/Logic/IndefiniteDescription.v10
-rw-r--r--theories/Logic/JMeq.v10
-rw-r--r--theories/Logic/ProofIrrelevance.v10
-rw-r--r--theories/Logic/ProofIrrelevanceFacts.v10
-rw-r--r--theories/Logic/PropExtensionality.v10
-rw-r--r--theories/Logic/PropExtensionalityFacts.v10
-rw-r--r--theories/Logic/PropFacts.v10
-rw-r--r--theories/Logic/RelationalChoice.v10
-rw-r--r--theories/Logic/SetIsType.v10
-rw-r--r--theories/Logic/SetoidChoice.v10
-rw-r--r--theories/Logic/WKL.v10
-rw-r--r--theories/Logic/WeakFan.v10
-rw-r--r--theories/MSets/MSetAVL.v16
-rw-r--r--theories/MSets/MSetDecide.v16
-rw-r--r--theories/MSets/MSetEqProperties.v16
-rw-r--r--theories/MSets/MSetFacts.v16
-rw-r--r--theories/MSets/MSetGenTree.v16
-rw-r--r--theories/MSets/MSetInterface.v16
-rw-r--r--theories/MSets/MSetList.v16
-rw-r--r--theories/MSets/MSetPositive.v16
-rw-r--r--theories/MSets/MSetProperties.v16
-rw-r--r--theories/MSets/MSetRBT.v16
-rw-r--r--theories/MSets/MSetToFiniteSet.v16
-rw-r--r--theories/MSets/MSetWeakList.v16
-rw-r--r--theories/MSets/MSets.v16
-rw-r--r--theories/NArith/BinNat.v175
-rw-r--r--theories/NArith/BinNatDef.v28
-rw-r--r--theories/NArith/NArith.v10
-rw-r--r--theories/NArith/Ndec.v22
-rw-r--r--theories/NArith/Ndigits.v34
-rw-r--r--theories/NArith/Ndist.v10
-rw-r--r--theories/NArith/Ndiv_def.v22
-rw-r--r--theories/NArith/Ngcd_def.v10
-rw-r--r--theories/NArith/Nnat.v64
-rw-r--r--theories/NArith/Nsqrt_def.v20
-rw-r--r--theories/Numbers/BinNums.v10
-rw-r--r--theories/Numbers/Cyclic/Abstract/CyclicAxioms.v10
-rw-r--r--theories/Numbers/Cyclic/Abstract/DoubleType.v10
-rw-r--r--theories/Numbers/Cyclic/Abstract/NZCyclic.v10
-rw-r--r--theories/Numbers/Cyclic/Int31/Cyclic31.v10
-rw-r--r--theories/Numbers/Cyclic/Int31/Int31.v10
-rw-r--r--theories/Numbers/Cyclic/Int31/Ring31.v10
-rw-r--r--theories/Numbers/Cyclic/ZModulo/ZModulo.v10
-rw-r--r--theories/Numbers/DecimalFacts.v143
-rw-r--r--theories/Numbers/DecimalN.v107
-rw-r--r--theories/Numbers/DecimalNat.v302
-rw-r--r--theories/Numbers/DecimalPos.v383
-rw-r--r--theories/Numbers/DecimalString.v265
-rw-r--r--theories/Numbers/DecimalZ.v75
-rw-r--r--theories/Numbers/Integer/Abstract/ZAdd.v10
-rw-r--r--theories/Numbers/Integer/Abstract/ZAddOrder.v10
-rw-r--r--theories/Numbers/Integer/Abstract/ZAxioms.v10
-rw-r--r--theories/Numbers/Integer/Abstract/ZBase.v10
-rw-r--r--theories/Numbers/Integer/Abstract/ZBits.v10
-rw-r--r--theories/Numbers/Integer/Abstract/ZDivEucl.v10
-rw-r--r--theories/Numbers/Integer/Abstract/ZDivFloor.v10
-rw-r--r--theories/Numbers/Integer/Abstract/ZDivTrunc.v10
-rw-r--r--theories/Numbers/Integer/Abstract/ZGcd.v10
-rw-r--r--theories/Numbers/Integer/Abstract/ZLcm.v10
-rw-r--r--theories/Numbers/Integer/Abstract/ZLt.v10
-rw-r--r--theories/Numbers/Integer/Abstract/ZMaxMin.v10
-rw-r--r--theories/Numbers/Integer/Abstract/ZMul.v10
-rw-r--r--theories/Numbers/Integer/Abstract/ZMulOrder.v10
-rw-r--r--theories/Numbers/Integer/Abstract/ZParity.v10
-rw-r--r--theories/Numbers/Integer/Abstract/ZPow.v10
-rw-r--r--theories/Numbers/Integer/Abstract/ZProperties.v10
-rw-r--r--theories/Numbers/Integer/Abstract/ZSgnAbs.v10
-rw-r--r--theories/Numbers/Integer/Binary/ZBinary.v10
-rw-r--r--theories/Numbers/Integer/NatPairs/ZNatPairs.v10
-rw-r--r--theories/Numbers/NaryFunctions.v10
-rw-r--r--theories/Numbers/NatInt/NZAdd.v10
-rw-r--r--theories/Numbers/NatInt/NZAddOrder.v10
-rw-r--r--theories/Numbers/NatInt/NZAxioms.v10
-rw-r--r--theories/Numbers/NatInt/NZBase.v10
-rw-r--r--theories/Numbers/NatInt/NZBits.v10
-rw-r--r--theories/Numbers/NatInt/NZDiv.v10
-rw-r--r--theories/Numbers/NatInt/NZDomain.v10
-rw-r--r--theories/Numbers/NatInt/NZGcd.v10
-rw-r--r--theories/Numbers/NatInt/NZLog.v10
-rw-r--r--theories/Numbers/NatInt/NZMul.v10
-rw-r--r--theories/Numbers/NatInt/NZMulOrder.v10
-rw-r--r--theories/Numbers/NatInt/NZOrder.v10
-rw-r--r--theories/Numbers/NatInt/NZParity.v10
-rw-r--r--theories/Numbers/NatInt/NZPow.v10
-rw-r--r--theories/Numbers/NatInt/NZProperties.v10
-rw-r--r--theories/Numbers/NatInt/NZSqrt.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NAdd.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NAddOrder.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NAxioms.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NBase.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NBits.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NDefOps.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NDiv.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NGcd.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NIso.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NLcm.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NLog.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NMaxMin.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NMulOrder.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NOrder.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NParity.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NPow.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NProperties.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NSqrt.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NStrongRec.v10
-rw-r--r--theories/Numbers/Natural/Abstract/NSub.v10
-rw-r--r--theories/Numbers/Natural/Binary/NBinary.v10
-rw-r--r--theories/Numbers/Natural/Peano/NPeano.v134
-rw-r--r--theories/Numbers/NumPrelude.v10
-rw-r--r--theories/PArith/BinPos.v352
-rw-r--r--theories/PArith/BinPosDef.v65
-rw-r--r--theories/PArith/PArith.v10
-rw-r--r--theories/PArith/POrderedType.v10
-rw-r--r--theories/PArith/Pnat.v70
-rw-r--r--theories/Program/Basics.v10
-rw-r--r--theories/Program/Combinators.v10
-rw-r--r--theories/Program/Equality.v10
-rw-r--r--theories/Program/Program.v10
-rw-r--r--theories/Program/Subset.v10
-rw-r--r--theories/Program/Syntax.v10
-rw-r--r--theories/Program/Tactics.v10
-rw-r--r--theories/Program/Utils.v10
-rw-r--r--theories/Program/Wf.v10
-rw-r--r--theories/QArith/QArith.v10
-rw-r--r--theories/QArith/QArith_base.v10
-rw-r--r--theories/QArith/QOrderedType.v10
-rw-r--r--theories/QArith/Qabs.v10
-rw-r--r--theories/QArith/Qcabs.v10
-rw-r--r--theories/QArith/Qcanon.v10
-rw-r--r--theories/QArith/Qfield.v10
-rw-r--r--theories/QArith/Qminmax.v10
-rw-r--r--theories/QArith/Qpower.v10
-rw-r--r--theories/QArith/Qreals.v10
-rw-r--r--theories/QArith/Qreduction.v14
-rw-r--r--theories/QArith/Qring.v10
-rw-r--r--theories/QArith/Qround.v10
-rw-r--r--theories/Reals/Alembert.v10
-rw-r--r--theories/Reals/AltSeries.v10
-rw-r--r--theories/Reals/ArithProp.v10
-rw-r--r--theories/Reals/Binomial.v10
-rw-r--r--theories/Reals/Cauchy_prod.v10
-rw-r--r--theories/Reals/Cos_plus.v10
-rw-r--r--theories/Reals/Cos_rel.v10
-rw-r--r--theories/Reals/DiscrR.v10
-rw-r--r--theories/Reals/Exp_prop.v10
-rw-r--r--theories/Reals/Integration.v10
-rw-r--r--theories/Reals/MVT.v10
-rw-r--r--theories/Reals/Machin.v10
-rw-r--r--theories/Reals/NewtonInt.v10
-rw-r--r--theories/Reals/PSeries_reg.v10
-rw-r--r--theories/Reals/PartSum.v10
-rw-r--r--theories/Reals/RIneq.v17
-rw-r--r--theories/Reals/RList.v10
-rw-r--r--theories/Reals/ROrderedType.v10
-rw-r--r--theories/Reals/R_Ifp.v10
-rw-r--r--theories/Reals/R_sqr.v10
-rw-r--r--theories/Reals/R_sqrt.v10
-rw-r--r--theories/Reals/Ranalysis.v10
-rw-r--r--theories/Reals/Ranalysis1.v10
-rw-r--r--theories/Reals/Ranalysis2.v10
-rw-r--r--theories/Reals/Ranalysis3.v10
-rw-r--r--theories/Reals/Ranalysis4.v10
-rw-r--r--theories/Reals/Ranalysis5.v72
-rw-r--r--theories/Reals/Ranalysis_reg.v10
-rw-r--r--theories/Reals/Ratan.v10
-rw-r--r--theories/Reals/Raxioms.v10
-rw-r--r--theories/Reals/Rbase.v10
-rw-r--r--theories/Reals/Rbasic_fun.v12
-rw-r--r--theories/Reals/Rcomplete.v10
-rw-r--r--theories/Reals/Rdefinitions.v10
-rw-r--r--theories/Reals/Rderiv.v10
-rw-r--r--theories/Reals/Reals.v10
-rw-r--r--theories/Reals/Rfunctions.v10
-rw-r--r--theories/Reals/Rgeom.v10
-rw-r--r--theories/Reals/RiemannInt.v10
-rw-r--r--theories/Reals/RiemannInt_SF.v10
-rw-r--r--theories/Reals/Rlimit.v10
-rw-r--r--theories/Reals/Rlogic.v14
-rw-r--r--theories/Reals/Rminmax.v10
-rw-r--r--theories/Reals/Rpow_def.v10
-rw-r--r--theories/Reals/Rpower.v35
-rw-r--r--theories/Reals/Rprod.v10
-rw-r--r--theories/Reals/Rseries.v10
-rw-r--r--theories/Reals/Rsigma.v10
-rw-r--r--theories/Reals/Rsqrt_def.v10
-rw-r--r--theories/Reals/Rtopology.v10
-rw-r--r--theories/Reals/Rtrigo.v10
-rw-r--r--theories/Reals/Rtrigo1.v10
-rw-r--r--theories/Reals/Rtrigo_alt.v10
-rw-r--r--theories/Reals/Rtrigo_calc.v10
-rw-r--r--theories/Reals/Rtrigo_def.v10
-rw-r--r--theories/Reals/Rtrigo_fun.v10
-rw-r--r--theories/Reals/Rtrigo_reg.v10
-rw-r--r--theories/Reals/SeqProp.v10
-rw-r--r--theories/Reals/SeqSeries.v10
-rw-r--r--theories/Reals/SplitAbsolu.v10
-rw-r--r--theories/Reals/SplitRmult.v10
-rw-r--r--theories/Reals/Sqrt_reg.v10
-rw-r--r--theories/Relations/Operators_Properties.v10
-rw-r--r--theories/Relations/Relation_Definitions.v10
-rw-r--r--theories/Relations/Relation_Operators.v10
-rw-r--r--theories/Relations/Relations.v10
-rw-r--r--theories/Setoids/Setoid.v10
-rw-r--r--theories/Sets/Classical_sets.v10
-rw-r--r--theories/Sets/Constructive_sets.v10
-rw-r--r--theories/Sets/Cpo.v10
-rw-r--r--theories/Sets/Ensembles.v10
-rw-r--r--theories/Sets/Finite_sets.v10
-rw-r--r--theories/Sets/Finite_sets_facts.v10
-rw-r--r--theories/Sets/Image.v10
-rw-r--r--theories/Sets/Infinite_sets.v10
-rw-r--r--theories/Sets/Integers.v10
-rw-r--r--theories/Sets/Multiset.v14
-rw-r--r--theories/Sets/Partial_Order.v10
-rw-r--r--theories/Sets/Permut.v10
-rw-r--r--theories/Sets/Powerset.v10
-rw-r--r--theories/Sets/Powerset_Classical_facts.v10
-rw-r--r--theories/Sets/Powerset_facts.v10
-rw-r--r--theories/Sets/Relations_1.v10
-rw-r--r--theories/Sets/Relations_1_facts.v10
-rw-r--r--theories/Sets/Relations_2.v10
-rw-r--r--theories/Sets/Relations_2_facts.v10
-rw-r--r--theories/Sets/Relations_3.v10
-rw-r--r--theories/Sets/Relations_3_facts.v10
-rw-r--r--theories/Sets/Uniset.v14
-rw-r--r--theories/Sorting/Heap.v12
-rw-r--r--theories/Sorting/Mergesort.v10
-rw-r--r--theories/Sorting/PermutEq.v10
-rw-r--r--theories/Sorting/PermutSetoid.v10
-rw-r--r--theories/Sorting/Permutation.v10
-rw-r--r--theories/Sorting/Sorted.v10
-rw-r--r--theories/Sorting/Sorting.v10
-rw-r--r--theories/Strings/Ascii.v12
-rw-r--r--theories/Strings/String.v22
-rw-r--r--theories/Structures/DecidableType.v16
-rw-r--r--theories/Structures/DecidableTypeEx.v16
-rw-r--r--theories/Structures/Equalities.v16
-rw-r--r--theories/Structures/EqualitiesFacts.v16
-rw-r--r--theories/Structures/GenericMinMax.v16
-rw-r--r--theories/Structures/OrderedType.v16
-rw-r--r--theories/Structures/OrderedTypeAlt.v16
-rw-r--r--theories/Structures/OrderedTypeEx.v18
-rw-r--r--theories/Structures/Orders.v16
-rw-r--r--theories/Structures/OrdersAlt.v16
-rw-r--r--theories/Structures/OrdersEx.v16
-rw-r--r--theories/Structures/OrdersFacts.v16
-rw-r--r--theories/Structures/OrdersLists.v16
-rw-r--r--theories/Structures/OrdersTac.v16
-rw-r--r--theories/Unicode/Utf8.v10
-rw-r--r--theories/Unicode/Utf8_core.v25
-rw-r--r--theories/Vectors/Fin.v10
-rw-r--r--theories/Vectors/Vector.v10
-rw-r--r--theories/Vectors/VectorDef.v12
-rw-r--r--theories/Vectors/VectorEq.v10
-rw-r--r--theories/Vectors/VectorSpec.v10
-rw-r--r--theories/Wellfounded/Disjoint_Union.v10
-rw-r--r--theories/Wellfounded/Inclusion.v10
-rw-r--r--theories/Wellfounded/Inverse_Image.v10
-rw-r--r--theories/Wellfounded/Lexicographic_Exponentiation.v10
-rw-r--r--theories/Wellfounded/Lexicographic_Product.v10
-rw-r--r--theories/Wellfounded/Transitive_Closure.v10
-rw-r--r--theories/Wellfounded/Union.v10
-rw-r--r--theories/Wellfounded/Well_Ordering.v10
-rw-r--r--theories/Wellfounded/Wellfounded.v10
-rw-r--r--theories/ZArith/BinInt.v186
-rw-r--r--theories/ZArith/BinIntDef.v27
-rw-r--r--theories/ZArith/Int.v22
-rw-r--r--theories/ZArith/Wf_Z.v10
-rw-r--r--theories/ZArith/ZArith.v10
-rw-r--r--theories/ZArith/ZArith_base.v10
-rw-r--r--theories/ZArith/ZArith_dec.v12
-rw-r--r--theories/ZArith/Zabs.v56
-rw-r--r--theories/ZArith/Zbool.v20
-rw-r--r--theories/ZArith/Zcompare.v36
-rw-r--r--theories/ZArith/Zcomplements.v10
-rw-r--r--theories/ZArith/Zdigits.v10
-rw-r--r--theories/ZArith/Zdiv.v28
-rw-r--r--theories/ZArith/Zeuclid.v10
-rw-r--r--theories/ZArith/Zeven.v26
-rw-r--r--theories/ZArith/Zgcd_alt.v10
-rw-r--r--theories/ZArith/Zhints.v10
-rw-r--r--theories/ZArith/Zlogarithm.v10
-rw-r--r--theories/ZArith/Zmax.v62
-rw-r--r--theories/ZArith/Zmin.v48
-rw-r--r--theories/ZArith/Zminmax.v24
-rw-r--r--theories/ZArith/Zmisc.v12
-rw-r--r--theories/ZArith/Znat.v126
-rw-r--r--theories/ZArith/Znumtheory.v72
-rw-r--r--theories/ZArith/Zorder.v96
-rw-r--r--theories/ZArith/Zpow_alt.v10
-rw-r--r--theories/ZArith/Zpow_def.v22
-rw-r--r--theories/ZArith/Zpow_facts.v40
-rw-r--r--theories/ZArith/Zpower.v10
-rw-r--r--theories/ZArith/Zquot.v40
-rw-r--r--theories/ZArith/Zsqrt_compat.v10
-rw-r--r--theories/ZArith/Zwf.v10
-rw-r--r--theories/ZArith/auxiliary.v10
409 files changed, 5177 insertions, 2756 deletions
diff --git a/theories/.dir-locals.el b/theories/.dir-locals.el
deleted file mode 100644
index 4e8830f6c..000000000
--- a/theories/.dir-locals.el
+++ /dev/null
@@ -1,4 +0,0 @@
-((coq-mode . ((eval . (let ((default-directory (locate-dominating-file
- buffer-file-name ".dir-locals.el")))
- (setq-local coq-prog-args `("-coqlib" ,(expand-file-name "..") "-R" ,(expand-file-name ".") "Coq"))
- (setq-local coq-prog-name (expand-file-name "../bin/coqtop")))))))
diff --git a/theories/Arith/Arith.v b/theories/Arith/Arith.v
index 649819878..1cba8fafe 100644
--- a/theories/Arith/Arith.v
+++ b/theories/Arith/Arith.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export Arith_base.
diff --git a/theories/Arith/Arith_base.v b/theories/Arith/Arith_base.v
index 1493deb48..e3a033a4a 100644
--- a/theories/Arith/Arith_base.v
+++ b/theories/Arith/Arith_base.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export PeanoNat.
diff --git a/theories/Arith/Between.v b/theories/Arith/Between.v
index ead08b3eb..25d84a621 100644
--- a/theories/Arith/Between.v
+++ b/theories/Arith/Between.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Le.
diff --git a/theories/Arith/Bool_nat.v b/theories/Arith/Bool_nat.v
index a1eaf02f7..d892542e7 100644
--- a/theories/Arith/Bool_nat.v
+++ b/theories/Arith/Bool_nat.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export Compare_dec.
diff --git a/theories/Arith/Compare.v b/theories/Arith/Compare.v
index 8381be5ce..6778d6a02 100644
--- a/theories/Arith/Compare.v
+++ b/theories/Arith/Compare.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Equality is decidable on [nat] *)
diff --git a/theories/Arith/Compare_dec.v b/theories/Arith/Compare_dec.v
index 1e3237d10..713aef858 100644
--- a/theories/Arith/Compare_dec.v
+++ b/theories/Arith/Compare_dec.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Le Lt Gt Decidable PeanoNat.
@@ -133,11 +135,11 @@ Qed.
See now [Nat.compare] and its properties.
In scope [nat_scope], the notation for [Nat.compare] is "?=" *)
-Notation nat_compare := Nat.compare (compat "8.4").
+Notation nat_compare := Nat.compare (compat "8.6").
-Notation nat_compare_spec := Nat.compare_spec (compat "8.4").
-Notation nat_compare_eq_iff := Nat.compare_eq_iff (compat "8.4").
-Notation nat_compare_S := Nat.compare_succ (compat "8.4").
+Notation nat_compare_spec := Nat.compare_spec (compat "8.6").
+Notation nat_compare_eq_iff := Nat.compare_eq_iff (compat "8.6").
+Notation nat_compare_S := Nat.compare_succ (only parsing).
Lemma nat_compare_lt n m : n<m <-> (n ?= m) = Lt.
Proof.
@@ -198,9 +200,9 @@ Qed.
See now [Nat.leb] and its properties.
In scope [nat_scope], the notation for [Nat.leb] is "<=?" *)
-Notation leb := Nat.leb (compat "8.4").
+Notation leb := Nat.leb (only parsing).
-Notation leb_iff := Nat.leb_le (compat "8.4").
+Notation leb_iff := Nat.leb_le (only parsing).
Lemma leb_iff_conv m n : (n <=? m) = false <-> m < n.
Proof.
diff --git a/theories/Arith/Div2.v b/theories/Arith/Div2.v
index ecb9a5706..42956c475 100644
--- a/theories/Arith/Div2.v
+++ b/theories/Arith/Div2.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Nota : this file is OBSOLETE, and left only for compatibility.
@@ -18,7 +20,7 @@ Implicit Type n : nat.
(** Here we define [n/2] and prove some of its properties *)
-Notation div2 := Nat.div2 (compat "8.4").
+Notation div2 := Nat.div2 (only parsing).
(** Since [div2] is recursively defined on [0], [1] and [(S (S n))], it is
useful to prove the corresponding induction principle *)
@@ -84,7 +86,7 @@ Qed.
(** Properties related to the double ([2n]) *)
-Notation double := Nat.double (compat "8.4").
+Notation double := Nat.double (only parsing).
Hint Unfold double Nat.double: arith.
diff --git a/theories/Arith/EqNat.v b/theories/Arith/EqNat.v
index 722615428..4b51dfc00 100644
--- a/theories/Arith/EqNat.v
+++ b/theories/Arith/EqNat.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import PeanoNat.
@@ -69,10 +71,10 @@ Defined.
We reuse the one already defined in module [Nat].
In scope [nat_scope], the notation "=?" can be used. *)
-Notation beq_nat := Nat.eqb (compat "8.4").
+Notation beq_nat := Nat.eqb (only parsing).
-Notation beq_nat_true_iff := Nat.eqb_eq (compat "8.4").
-Notation beq_nat_false_iff := Nat.eqb_neq (compat "8.4").
+Notation beq_nat_true_iff := Nat.eqb_eq (only parsing).
+Notation beq_nat_false_iff := Nat.eqb_neq (only parsing).
Lemma beq_nat_refl n : true = (n =? n).
Proof.
diff --git a/theories/Arith/Euclid.v b/theories/Arith/Euclid.v
index 6c6bf7fef..29f4d3e23 100644
--- a/theories/Arith/Euclid.v
+++ b/theories/Arith/Euclid.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Mult.
diff --git a/theories/Arith/Even.v b/theories/Arith/Even.v
index f30d05c7a..baf119732 100644
--- a/theories/Arith/Even.v
+++ b/theories/Arith/Even.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Nota : this file is OBSOLETE, and left only for compatibility.
diff --git a/theories/Arith/Factorial.v b/theories/Arith/Factorial.v
index 0625c03da..22f586d7e 100644
--- a/theories/Arith/Factorial.v
+++ b/theories/Arith/Factorial.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import PeanoNat Plus Mult Lt.
diff --git a/theories/Arith/Gt.v b/theories/Arith/Gt.v
index 2d783f9e2..52ecf131b 100644
--- a/theories/Arith/Gt.v
+++ b/theories/Arith/Gt.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Theorems about [gt] in [nat].
diff --git a/theories/Arith/Le.v b/theories/Arith/Le.v
index d95b05770..69626cc10 100644
--- a/theories/Arith/Le.v
+++ b/theories/Arith/Le.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Order on natural numbers.
@@ -26,17 +28,17 @@ Local Open Scope nat_scope.
(** * [le] is an order on [nat] *)
-Notation le_refl := Nat.le_refl (compat "8.4").
-Notation le_trans := Nat.le_trans (compat "8.4").
-Notation le_antisym := Nat.le_antisymm (compat "8.4").
+Notation le_refl := Nat.le_refl (only parsing).
+Notation le_trans := Nat.le_trans (only parsing).
+Notation le_antisym := Nat.le_antisymm (only parsing).
Hint Resolve le_trans: arith.
Hint Immediate le_antisym: arith.
(** * Properties of [le] w.r.t 0 *)
-Notation le_0_n := Nat.le_0_l (compat "8.4"). (* 0 <= n *)
-Notation le_Sn_0 := Nat.nle_succ_0 (compat "8.4"). (* ~ S n <= 0 *)
+Notation le_0_n := Nat.le_0_l (only parsing). (* 0 <= n *)
+Notation le_Sn_0 := Nat.nle_succ_0 (only parsing). (* ~ S n <= 0 *)
Lemma le_n_0_eq n : n <= 0 -> 0 = n.
Proof.
@@ -53,8 +55,8 @@ Proof Peano.le_n_S.
Theorem le_S_n : forall n m, S n <= S m -> n <= m.
Proof Peano.le_S_n.
-Notation le_n_Sn := Nat.le_succ_diag_r (compat "8.4"). (* n <= S n *)
-Notation le_Sn_n := Nat.nle_succ_diag_l (compat "8.4"). (* ~ S n <= n *)
+Notation le_n_Sn := Nat.le_succ_diag_r (only parsing). (* n <= S n *)
+Notation le_Sn_n := Nat.nle_succ_diag_l (only parsing). (* ~ S n <= n *)
Theorem le_Sn_le : forall n m, S n <= m -> n <= m.
Proof Nat.lt_le_incl.
@@ -65,8 +67,8 @@ Hint Immediate le_n_0_eq le_Sn_le le_S_n : arith.
(** * Properties of [le] w.r.t predecessor *)
-Notation le_pred_n := Nat.le_pred_l (compat "8.4"). (* pred n <= n *)
-Notation le_pred := Nat.pred_le_mono (compat "8.4"). (* n<=m -> pred n <= pred m *)
+Notation le_pred_n := Nat.le_pred_l (only parsing). (* pred n <= n *)
+Notation le_pred := Nat.pred_le_mono (only parsing). (* n<=m -> pred n <= pred m *)
Hint Resolve le_pred_n: arith.
diff --git a/theories/Arith/Lt.v b/theories/Arith/Lt.v
index 035c4e466..0c7515c6f 100644
--- a/theories/Arith/Lt.v
+++ b/theories/Arith/Lt.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Strict order on natural numbers.
@@ -23,7 +25,7 @@ Local Open Scope nat_scope.
(** * Irreflexivity *)
-Notation lt_irrefl := Nat.lt_irrefl (compat "8.4"). (* ~ x < x *)
+Notation lt_irrefl := Nat.lt_irrefl (only parsing). (* ~ x < x *)
Hint Resolve lt_irrefl: arith.
@@ -62,12 +64,12 @@ Hint Immediate le_not_lt lt_not_le: arith.
(** * Asymmetry *)
-Notation lt_asym := Nat.lt_asymm (compat "8.4"). (* n<m -> ~m<n *)
+Notation lt_asym := Nat.lt_asymm (only parsing). (* n<m -> ~m<n *)
(** * Order and 0 *)
-Notation lt_0_Sn := Nat.lt_0_succ (compat "8.4"). (* 0 < S n *)
-Notation lt_n_0 := Nat.nlt_0_r (compat "8.4"). (* ~ n < 0 *)
+Notation lt_0_Sn := Nat.lt_0_succ (only parsing). (* 0 < S n *)
+Notation lt_n_0 := Nat.nlt_0_r (only parsing). (* ~ n < 0 *)
Theorem neq_0_lt n : 0 <> n -> 0 < n.
Proof.
@@ -84,8 +86,8 @@ Hint Immediate neq_0_lt lt_0_neq: arith.
(** * Order and successor *)
-Notation lt_n_Sn := Nat.lt_succ_diag_r (compat "8.4"). (* n < S n *)
-Notation lt_S := Nat.lt_lt_succ_r (compat "8.4"). (* n < m -> n < S m *)
+Notation lt_n_Sn := Nat.lt_succ_diag_r (only parsing). (* n < S n *)
+Notation lt_S := Nat.lt_lt_succ_r (only parsing). (* n < m -> n < S m *)
Theorem lt_n_S n m : n < m -> S n < S m.
Proof.
@@ -107,6 +109,11 @@ Proof.
intros. symmetry. now apply Nat.lt_succ_pred with m.
Qed.
+Lemma S_pred_pos n: O < n -> n = S (pred n).
+Proof.
+ apply S_pred.
+Qed.
+
Lemma lt_pred n m : S n < m -> n < pred m.
Proof.
apply Nat.lt_succ_lt_pred.
@@ -122,28 +129,28 @@ Hint Resolve lt_pred_n_n: arith.
(** * Transitivity properties *)
-Notation lt_trans := Nat.lt_trans (compat "8.4").
-Notation lt_le_trans := Nat.lt_le_trans (compat "8.4").
-Notation le_lt_trans := Nat.le_lt_trans (compat "8.4").
+Notation lt_trans := Nat.lt_trans (only parsing).
+Notation lt_le_trans := Nat.lt_le_trans (only parsing).
+Notation le_lt_trans := Nat.le_lt_trans (only parsing).
Hint Resolve lt_trans lt_le_trans le_lt_trans: arith.
(** * Large = strict or equal *)
-Notation le_lt_or_eq_iff := Nat.lt_eq_cases (compat "8.4").
+Notation le_lt_or_eq_iff := Nat.lt_eq_cases (only parsing).
Theorem le_lt_or_eq n m : n <= m -> n < m \/ n = m.
Proof.
apply Nat.lt_eq_cases.
Qed.
-Notation lt_le_weak := Nat.lt_le_incl (compat "8.4").
+Notation lt_le_weak := Nat.lt_le_incl (only parsing).
Hint Immediate lt_le_weak: arith.
(** * Dichotomy *)
-Notation le_or_lt := Nat.le_gt_cases (compat "8.4"). (* n <= m \/ m < n *)
+Notation le_or_lt := Nat.le_gt_cases (only parsing). (* n <= m \/ m < n *)
Theorem nat_total_order n m : n <> m -> n < m \/ m < n.
Proof.
diff --git a/theories/Arith/Max.v b/theories/Arith/Max.v
index d8c6f6528..1727fa371 100644
--- a/theories/Arith/Max.v
+++ b/theories/Arith/Max.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** THIS FILE IS DEPRECATED. Use [PeanoNat.Nat] instead. *)
diff --git a/theories/Arith/Min.v b/theories/Arith/Min.v
index 4826013f0..fcf0b14c8 100644
--- a/theories/Arith/Min.v
+++ b/theories/Arith/Min.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** THIS FILE IS DEPRECATED. Use [PeanoNat.Nat] instead. *)
diff --git a/theories/Arith/Minus.v b/theories/Arith/Minus.v
index 950f985d4..3bf6cd952 100644
--- a/theories/Arith/Minus.v
+++ b/theories/Arith/Minus.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Properties of subtraction between natural numbers.
@@ -46,7 +48,7 @@ Qed.
(** * Diagonal *)
-Notation minus_diag := Nat.sub_diag (compat "8.4"). (* n - n = 0 *)
+Notation minus_diag := Nat.sub_diag (only parsing). (* n - n = 0 *)
Lemma minus_diag_reverse n : 0 = n - n.
Proof.
@@ -87,13 +89,13 @@ Qed.
(** * Relation with order *)
Notation minus_le_compat_r :=
- Nat.sub_le_mono_r (compat "8.4"). (* n <= m -> n - p <= m - p. *)
+ Nat.sub_le_mono_r (only parsing). (* n <= m -> n - p <= m - p. *)
Notation minus_le_compat_l :=
- Nat.sub_le_mono_l (compat "8.4"). (* n <= m -> p - m <= p - n. *)
+ Nat.sub_le_mono_l (only parsing). (* n <= m -> p - m <= p - n. *)
-Notation le_minus := Nat.le_sub_l (compat "8.4"). (* n - m <= n *)
-Notation lt_minus := Nat.sub_lt (compat "8.4"). (* m <= n -> 0 < m -> n-m < n *)
+Notation le_minus := Nat.le_sub_l (only parsing). (* n - m <= n *)
+Notation lt_minus := Nat.sub_lt (only parsing). (* m <= n -> 0 < m -> n-m < n *)
Lemma lt_O_minus_lt n m : 0 < n - m -> m < n.
Proof.
diff --git a/theories/Arith/Mult.v b/theories/Arith/Mult.v
index e4084ba47..4f4aa1837 100644
--- a/theories/Arith/Mult.v
+++ b/theories/Arith/Mult.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Properties of multiplication.
@@ -23,35 +25,35 @@ Local Open Scope nat_scope.
(** ** Zero property *)
-Notation mult_0_l := Nat.mul_0_l (compat "8.4"). (* 0 * n = 0 *)
-Notation mult_0_r := Nat.mul_0_r (compat "8.4"). (* n * 0 = 0 *)
+Notation mult_0_l := Nat.mul_0_l (only parsing). (* 0 * n = 0 *)
+Notation mult_0_r := Nat.mul_0_r (only parsing). (* n * 0 = 0 *)
(** ** 1 is neutral *)
-Notation mult_1_l := Nat.mul_1_l (compat "8.4"). (* 1 * n = n *)
-Notation mult_1_r := Nat.mul_1_r (compat "8.4"). (* n * 1 = n *)
+Notation mult_1_l := Nat.mul_1_l (only parsing). (* 1 * n = n *)
+Notation mult_1_r := Nat.mul_1_r (only parsing). (* n * 1 = n *)
Hint Resolve mult_1_l mult_1_r: arith.
(** ** Commutativity *)
-Notation mult_comm := Nat.mul_comm (compat "8.4"). (* n * m = m * n *)
+Notation mult_comm := Nat.mul_comm (only parsing). (* n * m = m * n *)
Hint Resolve mult_comm: arith.
(** ** Distributivity *)
Notation mult_plus_distr_r :=
- Nat.mul_add_distr_r (compat "8.4"). (* (n+m)*p = n*p + m*p *)
+ Nat.mul_add_distr_r (only parsing). (* (n+m)*p = n*p + m*p *)
Notation mult_plus_distr_l :=
- Nat.mul_add_distr_l (compat "8.4"). (* n*(m+p) = n*m + n*p *)
+ Nat.mul_add_distr_l (only parsing). (* n*(m+p) = n*m + n*p *)
Notation mult_minus_distr_r :=
- Nat.mul_sub_distr_r (compat "8.4"). (* (n-m)*p = n*p - m*p *)
+ Nat.mul_sub_distr_r (only parsing). (* (n-m)*p = n*p - m*p *)
Notation mult_minus_distr_l :=
- Nat.mul_sub_distr_l (compat "8.4"). (* n*(m-p) = n*m - n*p *)
+ Nat.mul_sub_distr_l (only parsing). (* n*(m-p) = n*m - n*p *)
Hint Resolve mult_plus_distr_r: arith.
Hint Resolve mult_minus_distr_r: arith.
@@ -59,7 +61,7 @@ Hint Resolve mult_minus_distr_l: arith.
(** ** Associativity *)
-Notation mult_assoc := Nat.mul_assoc (compat "8.4"). (* n*(m*p)=n*m*p *)
+Notation mult_assoc := Nat.mul_assoc (only parsing). (* n*(m*p)=n*m*p *)
Lemma mult_assoc_reverse n m p : n * m * p = n * (m * p).
Proof.
@@ -83,8 +85,8 @@ Qed.
(** ** Multiplication and successor *)
-Notation mult_succ_l := Nat.mul_succ_l (compat "8.4"). (* S n * m = n * m + m *)
-Notation mult_succ_r := Nat.mul_succ_r (compat "8.4"). (* n * S m = n * m + n *)
+Notation mult_succ_l := Nat.mul_succ_l (only parsing). (* S n * m = n * m + m *)
+Notation mult_succ_r := Nat.mul_succ_r (only parsing). (* n * S m = n * m + n *)
(** * Compatibility with orders *)
diff --git a/theories/Arith/PeanoNat.v b/theories/Arith/PeanoNat.v
index bde6f1bb4..4e4938a99 100644
--- a/theories/Arith/PeanoNat.v
+++ b/theories/Arith/PeanoNat.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
@@ -724,6 +726,26 @@ Definition shiftr_spec a n m (_:0<=m) := shiftr_specif a n m.
Include NExtraProp.
+(** Properties of tail-recursive addition and multiplication *)
+
+Lemma tail_add_spec n m : tail_add n m = n + m.
+Proof.
+ revert m. induction n as [|n IH]; simpl; trivial.
+ intros. now rewrite IH, add_succ_r.
+Qed.
+
+Lemma tail_addmul_spec r n m : tail_addmul r n m = r + n * m.
+Proof.
+ revert m r. induction n as [| n IH]; simpl; trivial.
+ intros. rewrite IH, tail_add_spec.
+ rewrite add_assoc. f_equal. apply add_comm.
+Qed.
+
+Lemma tail_mul_spec n m : tail_mul n m = n * m.
+Proof.
+ unfold tail_mul. now rewrite tail_addmul_spec.
+Qed.
+
End Nat.
(** Re-export notations that should be available even when
diff --git a/theories/Arith/Peano_dec.v b/theories/Arith/Peano_dec.v
index 247ea20a8..9a24c804a 100644
--- a/theories/Arith/Peano_dec.v
+++ b/theories/Arith/Peano_dec.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Decidable PeanoNat.
@@ -19,7 +21,7 @@ Proof.
- left; exists n; auto.
Defined.
-Notation eq_nat_dec := Nat.eq_dec (compat "8.4").
+Notation eq_nat_dec := Nat.eq_dec (only parsing).
Hint Resolve O_or_S eq_nat_dec: arith.
diff --git a/theories/Arith/Plus.v b/theories/Arith/Plus.v
index 600e5e518..b8297c2d8 100644
--- a/theories/Arith/Plus.v
+++ b/theories/Arith/Plus.v
@@ -1,9 +1,11 @@
- (************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Properties of addition.
@@ -27,12 +29,12 @@ Local Open Scope nat_scope.
(** * Neutrality of 0, commutativity, associativity *)
-Notation plus_0_l := Nat.add_0_l (compat "8.4").
-Notation plus_0_r := Nat.add_0_r (compat "8.4").
-Notation plus_comm := Nat.add_comm (compat "8.4").
-Notation plus_assoc := Nat.add_assoc (compat "8.4").
+Notation plus_0_l := Nat.add_0_l (only parsing).
+Notation plus_0_r := Nat.add_0_r (only parsing).
+Notation plus_comm := Nat.add_comm (only parsing).
+Notation plus_assoc := Nat.add_assoc (only parsing).
-Notation plus_permute := Nat.add_shuffle3 (compat "8.4").
+Notation plus_permute := Nat.add_shuffle3 (only parsing).
Definition plus_Snm_nSm : forall n m, S n + m = n + S m :=
Peano.plus_n_Sm.
@@ -138,7 +140,7 @@ Defined.
(** * Derived properties *)
-Notation plus_permute_2_in_4 := Nat.add_shuffle1 (compat "8.4").
+Notation plus_permute_2_in_4 := Nat.add_shuffle1 (only parsing).
(** * Tail-recursive plus *)
diff --git a/theories/Arith/Wf_nat.v b/theories/Arith/Wf_nat.v
index c9693dbb4..b02288986 100644
--- a/theories/Arith/Wf_nat.v
+++ b/theories/Arith/Wf_nat.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Well-founded relations and natural numbers *)
diff --git a/theories/Bool/Bool.v b/theories/Bool/Bool.v
index fe050ca26..edf78ed52 100644
--- a/theories/Bool/Bool.v
+++ b/theories/Bool/Bool.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** The type [bool] is defined in the prelude as
diff --git a/theories/Bool/BoolEq.v b/theories/Bool/BoolEq.v
index aaa774904..106a79e8c 100644
--- a/theories/Bool/BoolEq.v
+++ b/theories/Bool/BoolEq.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Cuihtlauac Alvarado - octobre 2000 *)
diff --git a/theories/Bool/Bvector.v b/theories/Bool/Bvector.v
index d697bd86e..aecdb59db 100644
--- a/theories/Bool/Bvector.v
+++ b/theories/Bool/Bvector.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Bit vectors. Contribution by Jean Duprat (ENS Lyon). *)
diff --git a/theories/Bool/DecBool.v b/theories/Bool/DecBool.v
index 78bca1f5e..f84aed191 100644
--- a/theories/Bool/DecBool.v
+++ b/theories/Bool/DecBool.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Set Implicit Arguments.
diff --git a/theories/Bool/IfProp.v b/theories/Bool/IfProp.v
index fea952585..6f99ea1da 100644
--- a/theories/Bool/IfProp.v
+++ b/theories/Bool/IfProp.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Bool.
diff --git a/theories/Bool/Sumbool.v b/theories/Bool/Sumbool.v
index 065c979c9..5333c7411 100644
--- a/theories/Bool/Sumbool.v
+++ b/theories/Bool/Sumbool.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Here are collected some results about the type sumbool (see INIT/Specif.v)
diff --git a/theories/Bool/Zerob.v b/theories/Bool/Zerob.v
index b2fc58f30..2420c0fdc 100644
--- a/theories/Bool/Zerob.v
+++ b/theories/Bool/Zerob.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Arith.
diff --git a/theories/Classes/CEquivalence.v b/theories/Classes/CEquivalence.v
index 6e0f9e014..03e611f54 100644
--- a/theories/Classes/CEquivalence.v
+++ b/theories/Classes/CEquivalence.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Typeclass-based setoids. Definitions on [Equivalence].
diff --git a/theories/Classes/CMorphisms.v b/theories/Classes/CMorphisms.v
index fae132fc6..09b35ca75 100644
--- a/theories/Classes/CMorphisms.v
+++ b/theories/Classes/CMorphisms.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8; coq-prog-args: ("-coqlib" "../.." "-R" ".." "Coq" "-top" "Coq.Classes.CMorphisms") -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Typeclass-based morphism definition and standard, minimal instances
diff --git a/theories/Classes/CRelationClasses.v b/theories/Classes/CRelationClasses.v
index 02baa9114..bc821532f 100644
--- a/theories/Classes/CRelationClasses.v
+++ b/theories/Classes/CRelationClasses.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Typeclass-based relations, tactics and standard instances
diff --git a/theories/Classes/DecidableClass.v b/theories/Classes/DecidableClass.v
index 34ed6f7a4..bffad2b38 100644
--- a/theories/Classes/DecidableClass.v
+++ b/theories/Classes/DecidableClass.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * A typeclass to ease the handling of decidable properties. *)
diff --git a/theories/Classes/EquivDec.v b/theories/Classes/EquivDec.v
index 1278dac64..e9a9d6aff 100644
--- a/theories/Classes/EquivDec.v
+++ b/theories/Classes/EquivDec.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Decidable equivalences.
diff --git a/theories/Classes/Equivalence.v b/theories/Classes/Equivalence.v
index 76c3e768f..5217aedb8 100644
--- a/theories/Classes/Equivalence.v
+++ b/theories/Classes/Equivalence.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Typeclass-based setoids. Definitions on [Equivalence].
diff --git a/theories/Classes/Init.v b/theories/Classes/Init.v
index bddaa44b5..8a04206bb 100644
--- a/theories/Classes/Init.v
+++ b/theories/Classes/Init.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Initialization code for typeclasses, setting up the default tactic
diff --git a/theories/Classes/Morphisms.v b/theories/Classes/Morphisms.v
index 9859fb52f..1858ba76a 100644
--- a/theories/Classes/Morphisms.v
+++ b/theories/Classes/Morphisms.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8; coq-prog-args: ("-coqlib" "../.." "-R" ".." "Coq" "-top" "Coq.Classes.Morphisms") -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Typeclass-based morphism definition and standard, minimal instances
diff --git a/theories/Classes/Morphisms_Prop.v b/theories/Classes/Morphisms_Prop.v
index 24529ff37..8881fda57 100644
--- a/theories/Classes/Morphisms_Prop.v
+++ b/theories/Classes/Morphisms_Prop.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * [Proper] instances for propositional connectives.
diff --git a/theories/Classes/Morphisms_Relations.v b/theories/Classes/Morphisms_Relations.v
index c12b6b7bd..a3e575010 100644
--- a/theories/Classes/Morphisms_Relations.v
+++ b/theories/Classes/Morphisms_Relations.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Morphism instances for relations.
diff --git a/theories/Classes/RelationClasses.v b/theories/Classes/RelationClasses.v
index 63225853d..2ab3af202 100644
--- a/theories/Classes/RelationClasses.v
+++ b/theories/Classes/RelationClasses.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Typeclass-based relations, tactics and standard instances
diff --git a/theories/Classes/RelationPairs.v b/theories/Classes/RelationPairs.v
index 8d1c49822..7af2b0fc4 100644
--- a/theories/Classes/RelationPairs.v
+++ b/theories/Classes/RelationPairs.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Relations over pairs *)
diff --git a/theories/Classes/SetoidClass.v b/theories/Classes/SetoidClass.v
index 628160711..2673a1191 100644
--- a/theories/Classes/SetoidClass.v
+++ b/theories/Classes/SetoidClass.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Typeclass-based setoids, tactics and standard instances.
diff --git a/theories/Classes/SetoidDec.v b/theories/Classes/SetoidDec.v
index 54e54cd89..f6b240bf2 100644
--- a/theories/Classes/SetoidDec.v
+++ b/theories/Classes/SetoidDec.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Decidable setoid equality theory.
diff --git a/theories/Classes/SetoidTactics.v b/theories/Classes/SetoidTactics.v
index 292e8fc2e..3fab3c5a0 100644
--- a/theories/Classes/SetoidTactics.v
+++ b/theories/Classes/SetoidTactics.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Tactics for typeclass-based setoids.
diff --git a/theories/Compat/AdmitAxiom.v b/theories/Compat/AdmitAxiom.v
index 7747b75ed..f6b751bd5 100644
--- a/theories/Compat/AdmitAxiom.v
+++ b/theories/Compat/AdmitAxiom.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Compatibility file for making the admit tactic act similar to Coq v8.4. In
diff --git a/theories/Compat/Coq85.v b/theories/Compat/Coq85.v
deleted file mode 100644
index 56a9130d1..000000000
--- a/theories/Compat/Coq85.v
+++ /dev/null
@@ -1,36 +0,0 @@
-(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
-(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(************************************************************************)
-
-(** Compatibility file for making Coq act similar to Coq v8.5 *)
-
-(** Any compatibility changes to make future versions of Coq behave like Coq 8.6
- are likely needed to make them behave like Coq 8.5. *)
-Require Export Coq.Compat.Coq86.
-
-(** We use some deprecated options in this file, so we disable the
- corresponding warning, to silence the build of this file. *)
-Local Set Warnings "-deprecated-option".
-
-(* In 8.5, "intros [|]", taken e.g. on a goal "A\/B->C", does not
- behave as "intros [H|H]" but leave instead hypotheses quantified in
- the goal, here producing subgoals A->C and B->C. *)
-
-Global Unset Bracketing Last Introduction Pattern.
-Global Unset Regular Subst Tactic.
-Global Unset Structural Injection.
-Global Unset Shrink Abstract.
-Global Unset Shrink Obligations.
-Global Set Refolding Reduction.
-
-(** The resolution algorithm for type classes has changed. *)
-Global Set Typeclasses Legacy Resolution.
-Global Set Typeclasses Limit Intros.
-Global Unset Typeclasses Filtered Unification.
-
-(** Allow silently letting unification constraints float after a "." *)
-Global Unset Solve Unification Constraints.
diff --git a/theories/Compat/Coq86.v b/theories/Compat/Coq86.v
index 34061ddd6..666be207e 100644
--- a/theories/Compat/Coq86.v
+++ b/theories/Compat/Coq86.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Compatibility file for making Coq act similar to Coq v8.6 *)
diff --git a/theories/Compat/Coq87.v b/theories/Compat/Coq87.v
index aeef9595d..89556ee75 100644
--- a/theories/Compat/Coq87.v
+++ b/theories/Compat/Coq87.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Compatibility file for making Coq act similar to Coq v8.7 *)
diff --git a/theories/FSets/FMapAVL.v b/theories/FSets/FMapAVL.v
index 4a790296b..3485b9c68 100644
--- a/theories/FSets/FMapAVL.v
+++ b/theories/FSets/FMapAVL.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(* Finite map library. *)
diff --git a/theories/FSets/FMapFacts.v b/theories/FSets/FMapFacts.v
index 3c5690a72..997059669 100644
--- a/theories/FSets/FMapFacts.v
+++ b/theories/FSets/FMapFacts.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite maps library *)
@@ -24,7 +26,7 @@ Hint Extern 1 (Equivalence _) => constructor; congruence.
Module WFacts_fun (E:DecidableType)(Import M:WSfun E).
-Notation option_map := option_map (compat "8.4").
+Notation option_map := option_map (compat "8.6").
Notation eq_dec := E.eq_dec.
Definition eqb x y := if eq_dec x y then true else false.
@@ -440,7 +442,7 @@ destruct (eq_dec x y); auto.
Qed.
Lemma map_o : forall m x (f:elt->elt'),
- find x (map f m) = option_map f (find x m).
+ find x (map f m) = Datatypes.option_map f (find x m).
Proof.
intros.
generalize (find_mapsto_iff (map f m) x) (find_mapsto_iff m x)
@@ -473,7 +475,7 @@ Qed.
Lemma mapi_o : forall m x (f:key->elt->elt'),
(forall x y e, E.eq x y -> f x e = f y e) ->
- find x (mapi f m) = option_map (f x) (find x m).
+ find x (mapi f m) = Datatypes.option_map (f x) (find x m).
Proof.
intros.
generalize (find_mapsto_iff (mapi f m) x) (find_mapsto_iff m x)
diff --git a/theories/FSets/FMapFullAVL.v b/theories/FSets/FMapFullAVL.v
index b8e362f15..345296782 100644
--- a/theories/FSets/FMapFullAVL.v
+++ b/theories/FSets/FMapFullAVL.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(* Finite map library. *)
diff --git a/theories/FSets/FMapInterface.v b/theories/FSets/FMapInterface.v
index 4d89b562d..38a96dc39 100644
--- a/theories/FSets/FMapInterface.v
+++ b/theories/FSets/FMapInterface.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite map library *)
diff --git a/theories/FSets/FMapList.v b/theories/FSets/FMapList.v
index aadef476d..3e98d1197 100644
--- a/theories/FSets/FMapList.v
+++ b/theories/FSets/FMapList.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite map library *)
diff --git a/theories/FSets/FMapPositive.v b/theories/FSets/FMapPositive.v
index 3e7664929..0fc68b143 100644
--- a/theories/FSets/FMapPositive.v
+++ b/theories/FSets/FMapPositive.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * FMapPositive : an implementation of FMapInterface for [positive] keys. *)
diff --git a/theories/FSets/FMapWeakList.v b/theories/FSets/FMapWeakList.v
index 812409702..673609650 100644
--- a/theories/FSets/FMapWeakList.v
+++ b/theories/FSets/FMapWeakList.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite map library *)
diff --git a/theories/FSets/FMaps.v b/theories/FSets/FMaps.v
index 19b25d95a..ec5076358 100644
--- a/theories/FSets/FMaps.v
+++ b/theories/FSets/FMaps.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
Require Export OrderedType OrderedTypeEx OrderedTypeAlt.
diff --git a/theories/FSets/FSetAVL.v b/theories/FSets/FSetAVL.v
index df627a14b..3c9b6b428 100644
--- a/theories/FSets/FSetAVL.v
+++ b/theories/FSets/FSetAVL.v
@@ -1,11 +1,13 @@
(* -*- coding: utf-8 -*- *)
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * FSetAVL : Implementation of FSetInterface via AVL trees *)
diff --git a/theories/FSets/FSetBridge.v b/theories/FSets/FSetBridge.v
index 97f140b39..0c4ecb1f3 100644
--- a/theories/FSets/FSetBridge.v
+++ b/theories/FSets/FSetBridge.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite sets library *)
diff --git a/theories/FSets/FSetCompat.v b/theories/FSets/FSetCompat.v
index 31bc1cc31..736c85dad 100644
--- a/theories/FSets/FSetCompat.v
+++ b/theories/FSets/FSetCompat.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Compatibility functors between FSetInterface and MSetInterface. *)
diff --git a/theories/FSets/FSetDecide.v b/theories/FSets/FSetDecide.v
index 1db6a71e8..83bb07ffb 100644
--- a/theories/FSets/FSetDecide.v
+++ b/theories/FSets/FSetDecide.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(**************************************************************)
(* FSetDecide.v *)
diff --git a/theories/FSets/FSetEqProperties.v b/theories/FSets/FSetEqProperties.v
index f2f4cc2cc..56844f477 100644
--- a/theories/FSets/FSetEqProperties.v
+++ b/theories/FSets/FSetEqProperties.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite sets library *)
diff --git a/theories/FSets/FSetFacts.v b/theories/FSets/FSetFacts.v
index b240ede4d..f4d281e93 100644
--- a/theories/FSets/FSetFacts.v
+++ b/theories/FSets/FSetFacts.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite sets library *)
diff --git a/theories/FSets/FSetInterface.v b/theories/FSets/FSetInterface.v
index c791f49a6..0926d3ae9 100644
--- a/theories/FSets/FSetInterface.v
+++ b/theories/FSets/FSetInterface.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite set library *)
diff --git a/theories/FSets/FSetList.v b/theories/FSets/FSetList.v
index 9c3ec71ae..2036d360a 100644
--- a/theories/FSets/FSetList.v
+++ b/theories/FSets/FSetList.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite sets library *)
diff --git a/theories/FSets/FSetPositive.v b/theories/FSets/FSetPositive.v
index 507f1cda6..8a93f3816 100644
--- a/theories/FSets/FSetPositive.v
+++ b/theories/FSets/FSetPositive.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** Efficient implementation of [FSetInterface.S] for positive keys,
inspired from the [FMapPositive] module.
diff --git a/theories/FSets/FSetProperties.v b/theories/FSets/FSetProperties.v
index 0041bfa1c..c9cfb94ac 100644
--- a/theories/FSets/FSetProperties.v
+++ b/theories/FSets/FSetProperties.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite sets library *)
diff --git a/theories/FSets/FSetToFiniteSet.v b/theories/FSets/FSetToFiniteSet.v
index 3ac5d9e4a..f8d13ed2b 100644
--- a/theories/FSets/FSetToFiniteSet.v
+++ b/theories/FSets/FSetToFiniteSet.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite sets library : conversion to old [Finite_sets] *)
diff --git a/theories/FSets/FSetWeakList.v b/theories/FSets/FSetWeakList.v
index 9dbea8849..1dacd0568 100644
--- a/theories/FSets/FSetWeakList.v
+++ b/theories/FSets/FSetWeakList.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite sets library *)
diff --git a/theories/FSets/FSets.v b/theories/FSets/FSets.v
index e03fb2236..7e9e7aae7 100644
--- a/theories/FSets/FSets.v
+++ b/theories/FSets/FSets.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
Require Export OrderedType.
Require Export OrderedTypeEx.
diff --git a/theories/Init/Datatypes.v b/theories/Init/Datatypes.v
index 22e10e2e4..05b741f0a 100644
--- a/theories/Init/Datatypes.v
+++ b/theories/Init/Datatypes.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Set Implicit Arguments.
@@ -359,14 +361,14 @@ Definition idProp : IDProp := fun A x => x.
(* Compatibility *)
-Notation prodT := prod (compat "8.2").
-Notation pairT := pair (compat "8.2").
-Notation prodT_rect := prod_rect (compat "8.2").
-Notation prodT_rec := prod_rec (compat "8.2").
-Notation prodT_ind := prod_ind (compat "8.2").
-Notation fstT := fst (compat "8.2").
-Notation sndT := snd (compat "8.2").
-Notation prodT_uncurry := prod_uncurry (compat "8.2").
-Notation prodT_curry := prod_curry (compat "8.2").
+Notation prodT := prod (only parsing).
+Notation pairT := pair (only parsing).
+Notation prodT_rect := prod_rect (only parsing).
+Notation prodT_rec := prod_rec (only parsing).
+Notation prodT_ind := prod_ind (only parsing).
+Notation fstT := fst (only parsing).
+Notation sndT := snd (only parsing).
+Notation prodT_uncurry := prod_uncurry (only parsing).
+Notation prodT_curry := prod_curry (only parsing).
(* end hide *)
diff --git a/theories/Init/Decimal.v b/theories/Init/Decimal.v
new file mode 100644
index 000000000..57163b1b0
--- /dev/null
+++ b/theories/Init/Decimal.v
@@ -0,0 +1,163 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(** * Decimal numbers *)
+
+(** These numbers coded in base 10 will be used for parsing and printing
+ other Coq numeral datatypes in an human-readable way.
+ See the [Numeral Notation] command.
+ We represent numbers in base 10 as lists of decimal digits,
+ in big-endian order (most significant digit comes first). *)
+
+(** Unsigned integers are just lists of digits.
+ For instance, ten is (D1 (D0 Nil)) *)
+
+Inductive uint :=
+ | Nil
+ | D0 (_:uint)
+ | D1 (_:uint)
+ | D2 (_:uint)
+ | D3 (_:uint)
+ | D4 (_:uint)
+ | D5 (_:uint)
+ | D6 (_:uint)
+ | D7 (_:uint)
+ | D8 (_:uint)
+ | D9 (_:uint).
+
+(** [Nil] is the number terminator. Taken alone, it behaves as zero,
+ but rather use [D0 Nil] instead, since this form will be denoted
+ as [0], while [Nil] will be printed as [Nil]. *)
+
+Notation zero := (D0 Nil).
+
+(** For signed integers, we use two constructors [Pos] and [Neg]. *)
+
+Inductive int := Pos (d:uint) | Neg (d:uint).
+
+Delimit Scope uint_scope with uint.
+Bind Scope uint_scope with uint.
+Delimit Scope int_scope with int.
+Bind Scope int_scope with int.
+
+(** This representation favors simplicity over canonicity.
+ For normalizing numbers, we need to remove head zero digits,
+ and choose our canonical representation of 0 (here [D0 Nil]
+ for unsigned numbers and [Pos (D0 Nil)] for signed numbers). *)
+
+(** [nzhead] removes all head zero digits *)
+
+Fixpoint nzhead d :=
+ match d with
+ | D0 d => nzhead d
+ | _ => d
+ end.
+
+(** [unorm] : normalization of unsigned integers *)
+
+Definition unorm d :=
+ match nzhead d with
+ | Nil => zero
+ | d => d
+ end.
+
+(** [norm] : normalization of signed integers *)
+
+Definition norm d :=
+ match d with
+ | Pos d => Pos (unorm d)
+ | Neg d =>
+ match nzhead d with
+ | Nil => Pos zero
+ | d => Neg d
+ end
+ end.
+
+(** A few easy operations. For more advanced computations, use the conversions
+ with other Coq numeral datatypes (e.g. Z) and the operations on them. *)
+
+Definition opp (d:int) :=
+ match d with
+ | Pos d => Neg d
+ | Neg d => Pos d
+ end.
+
+(** For conversions with binary numbers, it is easier to operate
+ on little-endian numbers. *)
+
+Fixpoint revapp (d d' : uint) :=
+ match d with
+ | Nil => d'
+ | D0 d => revapp d (D0 d')
+ | D1 d => revapp d (D1 d')
+ | D2 d => revapp d (D2 d')
+ | D3 d => revapp d (D3 d')
+ | D4 d => revapp d (D4 d')
+ | D5 d => revapp d (D5 d')
+ | D6 d => revapp d (D6 d')
+ | D7 d => revapp d (D7 d')
+ | D8 d => revapp d (D8 d')
+ | D9 d => revapp d (D9 d')
+ end.
+
+Definition rev d := revapp d Nil.
+
+Module Little.
+
+(** Successor of little-endian numbers *)
+
+Fixpoint succ d :=
+ match d with
+ | Nil => D1 Nil
+ | D0 d => D1 d
+ | D1 d => D2 d
+ | D2 d => D3 d
+ | D3 d => D4 d
+ | D4 d => D5 d
+ | D5 d => D6 d
+ | D6 d => D7 d
+ | D7 d => D8 d
+ | D8 d => D9 d
+ | D9 d => D0 (succ d)
+ end.
+
+(** Doubling little-endian numbers *)
+
+Fixpoint double d :=
+ match d with
+ | Nil => Nil
+ | D0 d => D0 (double d)
+ | D1 d => D2 (double d)
+ | D2 d => D4 (double d)
+ | D3 d => D6 (double d)
+ | D4 d => D8 (double d)
+ | D5 d => D0 (succ_double d)
+ | D6 d => D2 (succ_double d)
+ | D7 d => D4 (succ_double d)
+ | D8 d => D6 (succ_double d)
+ | D9 d => D8 (succ_double d)
+ end
+
+with succ_double d :=
+ match d with
+ | Nil => D1 Nil
+ | D0 d => D1 (double d)
+ | D1 d => D3 (double d)
+ | D2 d => D5 (double d)
+ | D3 d => D7 (double d)
+ | D4 d => D9 (double d)
+ | D5 d => D1 (succ_double d)
+ | D6 d => D3 (succ_double d)
+ | D7 d => D5 (succ_double d)
+ | D8 d => D7 (succ_double d)
+ | D9 d => D9 (succ_double d)
+ end.
+
+End Little.
diff --git a/theories/Init/Logic.v b/theories/Init/Logic.v
index 037d37daf..10ca9ecc9 100644
--- a/theories/Init/Logic.v
+++ b/theories/Init/Logic.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Set Implicit Arguments.
@@ -267,6 +269,13 @@ Notation "'exists2' x : A , p & q" := (ex2 (A:=A) (fun x => p) (fun x => q))
format "'[' 'exists2' '/ ' x : A , '/ ' '[' p & '/' q ']' ']'")
: type_scope.
+Notation "'exists2' ' x , p & q" := (ex2 (fun x => p) (fun x => q))
+ (at level 200, x strict pattern, p at level 200, right associativity) : type_scope.
+Notation "'exists2' ' x : A , p & q" := (ex2 (A:=A) (fun x => p) (fun x => q))
+ (at level 200, x strict pattern, A at level 200, p at level 200, right associativity,
+ format "'[' 'exists2' '/ ' ' x : A , '/ ' '[' p & '/' q ']' ']'")
+ : type_scope.
+
(** Derived rules for universal quantification *)
Section universal_quantification.
@@ -542,14 +551,14 @@ Qed.
(* Aliases *)
-Notation sym_eq := eq_sym (compat "8.3").
-Notation trans_eq := eq_trans (compat "8.3").
-Notation sym_not_eq := not_eq_sym (compat "8.3").
+Notation sym_eq := eq_sym (only parsing).
+Notation trans_eq := eq_trans (only parsing).
+Notation sym_not_eq := not_eq_sym (only parsing).
-Notation refl_equal := eq_refl (compat "8.3").
-Notation sym_equal := eq_sym (compat "8.3").
-Notation trans_equal := eq_trans (compat "8.3").
-Notation sym_not_equal := not_eq_sym (compat "8.3").
+Notation refl_equal := eq_refl (only parsing).
+Notation sym_equal := eq_sym (only parsing).
+Notation trans_equal := eq_trans (only parsing).
+Notation sym_not_equal := not_eq_sym (only parsing).
Hint Immediate eq_sym not_eq_sym: core.
diff --git a/theories/Init/Logic_Type.v b/theories/Init/Logic_Type.v
index 567d2c15c..6f10a9399 100644
--- a/theories/Init/Logic_Type.v
+++ b/theories/Init/Logic_Type.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This module defines type constructors for types in [Type]
@@ -66,7 +68,7 @@ Defined.
Hint Immediate identity_sym not_identity_sym: core.
-Notation refl_id := identity_refl (compat "8.3").
-Notation sym_id := identity_sym (compat "8.3").
-Notation trans_id := identity_trans (compat "8.3").
-Notation sym_not_id := not_identity_sym (compat "8.3").
+Notation refl_id := identity_refl (only parsing).
+Notation sym_id := identity_sym (only parsing).
+Notation trans_id := identity_trans (only parsing).
+Notation sym_not_id := not_identity_sym (only parsing).
diff --git a/theories/Init/Nat.v b/theories/Init/Nat.v
index e942ca562..ad1bc717c 100644
--- a/theories/Init/Nat.v
+++ b/theories/Init/Nat.v
@@ -1,13 +1,15 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Notations Logic Datatypes.
-
+Require Decimal.
Local Open Scope nat_scope.
(**********************************************************************)
@@ -134,6 +136,62 @@ Fixpoint pow n m :=
where "n ^ m" := (pow n m) : nat_scope.
+(** ** Tail-recursive versions of [add] and [mul] *)
+
+Fixpoint tail_add n m :=
+ match n with
+ | O => m
+ | S n => tail_add n (S m)
+ end.
+
+(** [tail_addmul r n m] is [r + n * m]. *)
+
+Fixpoint tail_addmul r n m :=
+ match n with
+ | O => r
+ | S n => tail_addmul (tail_add m r) n m
+ end.
+
+Definition tail_mul n m := tail_addmul 0 n m.
+
+(** ** Conversion with a decimal representation for printing/parsing *)
+
+Local Notation ten := (S (S (S (S (S (S (S (S (S (S O)))))))))).
+
+Fixpoint of_uint_acc (d:Decimal.uint)(acc:nat) :=
+ match d with
+ | Decimal.Nil => acc
+ | Decimal.D0 d => of_uint_acc d (tail_mul ten acc)
+ | Decimal.D1 d => of_uint_acc d (S (tail_mul ten acc))
+ | Decimal.D2 d => of_uint_acc d (S (S (tail_mul ten acc)))
+ | Decimal.D3 d => of_uint_acc d (S (S (S (tail_mul ten acc))))
+ | Decimal.D4 d => of_uint_acc d (S (S (S (S (tail_mul ten acc)))))
+ | Decimal.D5 d => of_uint_acc d (S (S (S (S (S (tail_mul ten acc))))))
+ | Decimal.D6 d => of_uint_acc d (S (S (S (S (S (S (tail_mul ten acc)))))))
+ | Decimal.D7 d => of_uint_acc d (S (S (S (S (S (S (S (tail_mul ten acc))))))))
+ | Decimal.D8 d => of_uint_acc d (S (S (S (S (S (S (S (S (tail_mul ten acc)))))))))
+ | Decimal.D9 d => of_uint_acc d (S (S (S (S (S (S (S (S (S (tail_mul ten acc))))))))))
+ end.
+
+Definition of_uint (d:Decimal.uint) := of_uint_acc d O.
+
+Fixpoint to_little_uint n acc :=
+ match n with
+ | O => acc
+ | S n => to_little_uint n (Decimal.Little.succ acc)
+ end.
+
+Definition to_uint n :=
+ Decimal.rev (to_little_uint n Decimal.zero).
+
+Definition of_int (d:Decimal.int) : option nat :=
+ match Decimal.norm d with
+ | Decimal.Pos u => Some (of_uint u)
+ | _ => None
+ end.
+
+Definition to_int n := Decimal.Pos (to_uint n).
+
(** ** Euclidean division *)
(** This division is linear and tail-recursive.
diff --git a/theories/Init/Notations.v b/theories/Init/Notations.v
index 70a6c61e7..72073bb4f 100644
--- a/theories/Init/Notations.v
+++ b/theories/Init/Notations.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** These are the notations whose level and associativity are imposed by Coq *)
@@ -79,6 +81,33 @@ Reserved Notation "{ x & P }" (at level 0, x at level 99).
Reserved Notation "{ x : A & P }" (at level 0, x at level 99).
Reserved Notation "{ x : A & P & Q }" (at level 0, x at level 99).
+Reserved Notation "{ ' pat | P }"
+ (at level 0, pat strict pattern, format "{ ' pat | P }").
+Reserved Notation "{ ' pat | P & Q }"
+ (at level 0, pat strict pattern, format "{ ' pat | P & Q }").
+
+Reserved Notation "{ ' pat : A | P }"
+ (at level 0, pat strict pattern, format "{ ' pat : A | P }").
+Reserved Notation "{ ' pat : A | P & Q }"
+ (at level 0, pat strict pattern, format "{ ' pat : A | P & Q }").
+
+Reserved Notation "{ ' pat : A & P }"
+ (at level 0, pat strict pattern, format "{ ' pat : A & P }").
+Reserved Notation "{ ' pat : A & P & Q }"
+ (at level 0, pat strict pattern, format "{ ' pat : A & P & Q }").
+
+(** Support for Gonthier-Ssreflect's "if c is pat then u else v" *)
+
+Module IfNotations.
+
+Notation "'if' c 'is' p 'then' u 'else' v" :=
+ (match c with p => u | _ => v end)
+ (at level 200, p pattern at level 100).
+
+End IfNotations.
+
+(** Scopes *)
+
Delimit Scope type_scope with type.
Delimit Scope function_scope with function.
Delimit Scope core_scope with core.
diff --git a/theories/Init/Peano.v b/theories/Init/Peano.v
index 571d2f2dd..73c8c5ef4 100644
--- a/theories/Init/Peano.v
+++ b/theories/Init/Peano.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** The type [nat] of Peano natural numbers (built from [O] and [S])
@@ -37,7 +39,7 @@ Hint Resolve f_equal_nat: core.
(** The predecessor function *)
-Notation pred := Nat.pred (compat "8.4").
+Notation pred := Nat.pred (only parsing).
Definition f_equal_pred := f_equal pred.
@@ -79,7 +81,7 @@ Hint Resolve n_Sn: core.
(** Addition *)
-Notation plus := Nat.add (compat "8.4").
+Notation plus := Nat.add (only parsing).
Infix "+" := Nat.add : nat_scope.
Definition f_equal2_plus := f_equal2 plus.
@@ -110,12 +112,12 @@ Qed.
(** Standard associated names *)
-Notation plus_0_r_reverse := plus_n_O (compat "8.2").
-Notation plus_succ_r_reverse := plus_n_Sm (compat "8.2").
+Notation plus_0_r_reverse := plus_n_O (only parsing).
+Notation plus_succ_r_reverse := plus_n_Sm (only parsing).
(** Multiplication *)
-Notation mult := Nat.mul (compat "8.4").
+Notation mult := Nat.mul (only parsing).
Infix "*" := Nat.mul : nat_scope.
Definition f_equal2_mult := f_equal2 mult.
@@ -137,12 +139,12 @@ Hint Resolve mult_n_Sm: core.
(** Standard associated names *)
-Notation mult_0_r_reverse := mult_n_O (compat "8.2").
-Notation mult_succ_r_reverse := mult_n_Sm (compat "8.2").
+Notation mult_0_r_reverse := mult_n_O (only parsing).
+Notation mult_succ_r_reverse := mult_n_Sm (only parsing).
(** Truncated subtraction: [m-n] is [0] if [n>=m] *)
-Notation minus := Nat.sub (compat "8.4").
+Notation minus := Nat.sub (only parsing).
Infix "-" := Nat.sub : nat_scope.
(** Definition of the usual orders, the basic properties of [le] and [lt]
@@ -219,8 +221,8 @@ Qed.
(** Maximum and minimum : definitions and specifications *)
-Notation max := Nat.max (compat "8.4").
-Notation min := Nat.min (compat "8.4").
+Notation max := Nat.max (only parsing).
+Notation min := Nat.min (only parsing).
Lemma max_l n m : m <= n -> Nat.max n m = n.
Proof.
diff --git a/theories/Init/Prelude.v b/theories/Init/Prelude.v
index f0867a034..802f18c0f 100644
--- a/theories/Init/Prelude.v
+++ b/theories/Init/Prelude.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export Notations.
@@ -11,6 +13,7 @@ Require Export Logic.
Require Export Logic_Type.
Require Export Datatypes.
Require Export Specif.
+Require Coq.Init.Decimal.
Require Coq.Init.Nat.
Require Export Peano.
Require Export Coq.Init.Wf.
diff --git a/theories/Init/Specif.v b/theories/Init/Specif.v
index c42cc00b8..b6afba29a 100644
--- a/theories/Init/Specif.v
+++ b/theories/Init/Specif.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Basic specifications : sets that may contain logical information *)
@@ -54,6 +56,15 @@ Notation "{ x : A & P }" := (sigT (A:=A) (fun x => P)) : type_scope.
Notation "{ x : A & P & Q }" := (sigT2 (A:=A) (fun x => P) (fun x => Q)) :
type_scope.
+Notation "{ ' pat | P }" := (sig (fun pat => P)) : type_scope.
+Notation "{ ' pat | P & Q }" := (sig2 (fun pat => P) (fun pat => Q)) : type_scope.
+Notation "{ ' pat : A | P }" := (sig (A:=A) (fun pat => P)) : type_scope.
+Notation "{ ' pat : A | P & Q }" := (sig2 (A:=A) (fun pat => P) (fun pat => Q)) :
+ type_scope.
+Notation "{ ' pat : A & P }" := (sigT (A:=A) (fun pat => P)) : type_scope.
+Notation "{ ' pat : A & P & Q }" := (sigT2 (A:=A) (fun pat => P) (fun pat => Q)) :
+ type_scope.
+
Add Printing Let sig.
Add Printing Let sig2.
Add Printing Let sigT.
@@ -734,16 +745,16 @@ Hint Resolve exist exist2 existT existT2: core.
(* Compatibility *)
-Notation sigS := sigT (compat "8.2").
-Notation existS := existT (compat "8.2").
-Notation sigS_rect := sigT_rect (compat "8.2").
-Notation sigS_rec := sigT_rec (compat "8.2").
-Notation sigS_ind := sigT_ind (compat "8.2").
-Notation projS1 := projT1 (compat "8.2").
-Notation projS2 := projT2 (compat "8.2").
-
-Notation sigS2 := sigT2 (compat "8.2").
-Notation existS2 := existT2 (compat "8.2").
-Notation sigS2_rect := sigT2_rect (compat "8.2").
-Notation sigS2_rec := sigT2_rec (compat "8.2").
-Notation sigS2_ind := sigT2_ind (compat "8.2").
+Notation sigS := sigT (compat "8.6").
+Notation existS := existT (compat "8.6").
+Notation sigS_rect := sigT_rect (compat "8.6").
+Notation sigS_rec := sigT_rec (compat "8.6").
+Notation sigS_ind := sigT_ind (compat "8.6").
+Notation projS1 := projT1 (compat "8.6").
+Notation projS2 := projT2 (compat "8.6").
+
+Notation sigS2 := sigT2 (compat "8.6").
+Notation existS2 := existT2 (compat "8.6").
+Notation sigS2_rect := sigT2_rect (compat "8.6").
+Notation sigS2_rec := sigT2_rec (compat "8.6").
+Notation sigS2_ind := sigT2_ind (compat "8.6").
diff --git a/theories/Init/Tactics.v b/theories/Init/Tactics.v
index 47a971ef0..9e6c26b10 100644
--- a/theories/Init/Tactics.v
+++ b/theories/Init/Tactics.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Notations.
diff --git a/theories/Init/Wf.v b/theories/Init/Wf.v
index 690a3f644..c27ffa33f 100644
--- a/theories/Init/Wf.v
+++ b/theories/Init/Wf.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * This module proves the validity of
diff --git a/theories/Lists/List.v b/theories/Lists/List.v
index eae2c52de..ca5f154e9 100644
--- a/theories/Lists/List.v
+++ b/theories/Lists/List.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Setoid.
@@ -27,7 +29,6 @@ Module ListNotations.
Notation "[ ]" := nil (format "[ ]") : list_scope.
Notation "[ x ]" := (cons x nil) : list_scope.
Notation "[ x ; y ; .. ; z ]" := (cons x (cons y .. (cons z nil) ..)) : list_scope.
-Notation "[ x ; .. ; y ]" := (cons x .. (cons y nil) ..) (compat "8.4") : list_scope.
End ListNotations.
Import ListNotations.
diff --git a/theories/Lists/ListDec.v b/theories/Lists/ListDec.v
index b03461e0b..e7e2cfc87 100644
--- a/theories/Lists/ListDec.v
+++ b/theories/Lists/ListDec.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Decidability results about lists *)
diff --git a/theories/Lists/ListSet.v b/theories/Lists/ListSet.v
index 31970da81..cc7d6f553 100644
--- a/theories/Lists/ListSet.v
+++ b/theories/Lists/ListSet.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** A library for finite sets, implemented as lists *)
diff --git a/theories/Lists/ListTactics.v b/theories/Lists/ListTactics.v
index 0d42b7499..843e38352 100644
--- a/theories/Lists/ListTactics.v
+++ b/theories/Lists/ListTactics.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import BinPos.
diff --git a/theories/Lists/SetoidList.v b/theories/Lists/SetoidList.v
index c95fb4d5c..0c5fe55b2 100644
--- a/theories/Lists/SetoidList.v
+++ b/theories/Lists/SetoidList.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
Require Export List.
Require Export Sorted.
diff --git a/theories/Lists/SetoidPermutation.v b/theories/Lists/SetoidPermutation.v
index cea3e839f..24b96514f 100644
--- a/theories/Lists/SetoidPermutation.v
+++ b/theories/Lists/SetoidPermutation.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
Require Import Permutation SetoidList.
(* Set Universe Polymorphism. *)
diff --git a/theories/Lists/StreamMemo.v b/theories/Lists/StreamMemo.v
index 5fccd0dec..57f558de5 100644
--- a/theories/Lists/StreamMemo.v
+++ b/theories/Lists/StreamMemo.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Eqdep_dec.
diff --git a/theories/Lists/Streams.v b/theories/Lists/Streams.v
index 64e8dffaa..310c651e8 100644
--- a/theories/Lists/Streams.v
+++ b/theories/Lists/Streams.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Set Implicit Arguments.
diff --git a/theories/Logic/Berardi.v b/theories/Logic/Berardi.v
index dac43ad52..c6836a1c7 100644
--- a/theories/Logic/Berardi.v
+++ b/theories/Logic/Berardi.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This file formalizes Berardi's paradox which says that in
diff --git a/theories/Logic/ChoiceFacts.v b/theories/Logic/ChoiceFacts.v
index 78ec8ff24..238ac7df0 100644
--- a/theories/Logic/ChoiceFacts.v
+++ b/theories/Logic/ChoiceFacts.v
@@ -1,10 +1,12 @@
-(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(************************************************************************)
(** Some facts and definitions concerning choice and description in
@@ -26,6 +28,8 @@ intentional type theory, Journal of Symbolic Logic 70(2):488-514, 2005.
[[Werner97]] Benjamin Werner, Sets in Types, Types in Sets, TACS, 1997.
*)
+Require Import RelationClasses Logic.
+
Set Implicit Arguments.
Local Unset Intuition Negation Unfolding.
@@ -123,8 +127,6 @@ Definition DependentFunctionalRelReification_on (A:Type) (B:A -> Type) :=
formulation of choice); Note also a typo in its intended
formulation in [[Werner97]]. *)
-Require Import RelationClasses Logic.
-
Definition RepresentativeFunctionalChoice_on :=
forall R:A->A->Prop,
(Equivalence R) ->
@@ -1308,11 +1310,11 @@ Qed.
(**********************************************************************)
(** * Compatibility notations *)
Notation description_rel_choice_imp_funct_choice :=
- functional_rel_reification_and_rel_choice_imp_fun_choice (compat "8.6").
+ functional_rel_reification_and_rel_choice_imp_fun_choice (only parsing).
-Notation funct_choice_imp_rel_choice := fun_choice_imp_rel_choice (compat "8.6").
+Notation funct_choice_imp_rel_choice := fun_choice_imp_rel_choice (only parsing).
Notation FunChoice_Equiv_RelChoice_and_ParamDefinDescr :=
- fun_choice_iff_rel_choice_and_functional_rel_reification (compat "8.6").
+ fun_choice_iff_rel_choice_and_functional_rel_reification (only parsing).
-Notation funct_choice_imp_description := fun_choice_imp_functional_rel_reification (compat "8.6").
+Notation funct_choice_imp_description := fun_choice_imp_functional_rel_reification (only parsing).
diff --git a/theories/Logic/Classical.v b/theories/Logic/Classical.v
index 044ca2122..72f53a46e 100644
--- a/theories/Logic/Classical.v
+++ b/theories/Logic/Classical.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* File created for Coq V5.10.14b, Oct 1995 *)
diff --git a/theories/Logic/ClassicalChoice.v b/theories/Logic/ClassicalChoice.v
index 27cb59a8f..016fa72f9 100644
--- a/theories/Logic/ClassicalChoice.v
+++ b/theories/Logic/ClassicalChoice.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This file provides classical logic and functional choice; this
diff --git a/theories/Logic/ClassicalDescription.v b/theories/Logic/ClassicalDescription.v
index 304ae59f8..6867c76e2 100644
--- a/theories/Logic/ClassicalDescription.v
+++ b/theories/Logic/ClassicalDescription.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This file provides classical logic and definite description, which is
diff --git a/theories/Logic/ClassicalEpsilon.v b/theories/Logic/ClassicalEpsilon.v
index e660e9566..77af90481 100644
--- a/theories/Logic/ClassicalEpsilon.v
+++ b/theories/Logic/ClassicalEpsilon.v
@@ -1,10 +1,12 @@
-(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(************************************************************************)
(** This file provides classical logic and indefinite description under
diff --git a/theories/Logic/ClassicalFacts.v b/theories/Logic/ClassicalFacts.v
index c90a97612..b06384e99 100644
--- a/theories/Logic/ClassicalFacts.v
+++ b/theories/Logic/ClassicalFacts.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Some facts and definitions about classical logic
diff --git a/theories/Logic/ClassicalUniqueChoice.v b/theories/Logic/ClassicalUniqueChoice.v
index 1309f91a3..841bd1bed 100644
--- a/theories/Logic/ClassicalUniqueChoice.v
+++ b/theories/Logic/ClassicalUniqueChoice.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This file provides classical logic and unique choice; this is
diff --git a/theories/Logic/Classical_Pred_Type.v b/theories/Logic/Classical_Pred_Type.v
index 06c298466..18820d3ba 100644
--- a/theories/Logic/Classical_Pred_Type.v
+++ b/theories/Logic/Classical_Pred_Type.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* This file is a renaming for V5.10.14b, Oct 1995, of file Classical.v
diff --git a/theories/Logic/Classical_Prop.v b/theories/Logic/Classical_Prop.v
index a5ae07b64..9f5a29937 100644
--- a/theories/Logic/Classical_Prop.v
+++ b/theories/Logic/Classical_Prop.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* File created for Coq V5.10.14b, Oct 1995 *)
diff --git a/theories/Logic/ConstructiveEpsilon.v b/theories/Logic/ConstructiveEpsilon.v
index 71ce2a40a..6e3da423e 100644
--- a/theories/Logic/ConstructiveEpsilon.v
+++ b/theories/Logic/ConstructiveEpsilon.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(*i $Id: ConstructiveEpsilon.v 12112 2009-04-28 15:47:34Z herbelin $ i*)
diff --git a/theories/Logic/Decidable.v b/theories/Logic/Decidable.v
index acb34771f..35920d913 100644
--- a/theories/Logic/Decidable.v
+++ b/theories/Logic/Decidable.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Properties of decidable propositions *)
diff --git a/theories/Logic/Description.v b/theories/Logic/Description.v
index 4ab52ae46..5c4f1960f 100644
--- a/theories/Logic/Description.v
+++ b/theories/Logic/Description.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This file provides a constructive form of definite description; it
diff --git a/theories/Logic/Diaconescu.v b/theories/Logic/Diaconescu.v
index c124e7141..3317766c9 100644
--- a/theories/Logic/Diaconescu.v
+++ b/theories/Logic/Diaconescu.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Diaconescu showed that the Axiom of Choice entails Excluded-Middle
@@ -40,6 +42,7 @@
[[Carlström04]] Jesper Carlström, EM + Ext_ + AC_int is equivalent
to AC_ext, Mathematical Logic Quaterly, vol 50(3), pp 236-240, 2004.
*)
+Require ClassicalFacts ChoiceFacts.
(**********************************************************************)
(** * Pred. Ext. + Rel. Axiom of Choice -> Excluded-Middle *)
@@ -54,7 +57,7 @@ Definition PredicateExtensionality :=
(** From predicate extensionality we get propositional extensionality
hence proof-irrelevance *)
-Require Import ClassicalFacts.
+Import ClassicalFacts.
Variable pred_extensionality : PredicateExtensionality.
@@ -76,7 +79,7 @@ Qed.
(** From proof-irrelevance and relational choice, we get guarded
relational choice *)
-Require Import ChoiceFacts.
+Import ChoiceFacts.
Variable rel_choice : RelationalChoice.
@@ -89,7 +92,7 @@ Qed.
(** The form of choice we need: there is a functional relation which chooses
an element in any non empty subset of bool *)
-Require Import Bool.
+Import Bool.
Lemma AC_bool_subset_to_bool :
exists R : (bool -> Prop) -> bool -> Prop,
@@ -161,6 +164,8 @@ End PredExt_RelChoice_imp_EM.
Section ProofIrrel_RelChoice_imp_EqEM.
+Import ChoiceFacts.
+
Variable rel_choice : RelationalChoice.
Variable proof_irrelevance : forall P:Prop , forall x y:P, x=y.
diff --git a/theories/Logic/Epsilon.v b/theories/Logic/Epsilon.v
index 96f677e43..d8c527c61 100644
--- a/theories/Logic/Epsilon.v
+++ b/theories/Logic/Epsilon.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This file provides indefinite description under the form of
diff --git a/theories/Logic/Eqdep.v b/theories/Logic/Eqdep.v
index ac003bf1a..35bc42259 100644
--- a/theories/Logic/Eqdep.v
+++ b/theories/Logic/Eqdep.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* File Eqdep.v created by Christine Paulin-Mohring in Coq V5.6, May 1992 *)
diff --git a/theories/Logic/EqdepFacts.v b/theories/Logic/EqdepFacts.v
index c9dca432a..d938b315f 100644
--- a/theories/Logic/EqdepFacts.v
+++ b/theories/Logic/EqdepFacts.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* File Eqdep.v created by Christine Paulin-Mohring in Coq V5.6, May 1992 *)
@@ -123,7 +125,7 @@ Proof.
apply eq_dep_intro.
Qed.
-Notation eq_sigS_eq_dep := eq_sigT_eq_dep (compat "8.2"). (* Compatibility *)
+Notation eq_sigS_eq_dep := eq_sigT_eq_dep (compat "8.6"). (* Compatibility *)
Lemma eq_dep_eq_sigT :
forall (U:Type) (P:U -> Type) (p q:U) (x:P p) (y:P q),
diff --git a/theories/Logic/Eqdep_dec.v b/theories/Logic/Eqdep_dec.v
index beb4d0b3d..0560d9ed4 100644
--- a/theories/Logic/Eqdep_dec.v
+++ b/theories/Logic/Eqdep_dec.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Created by Bruno Barras, Jan 1998 *)
diff --git a/theories/Logic/ExtensionalFunctionRepresentative.v b/theories/Logic/ExtensionalFunctionRepresentative.v
index becc9f147..0aac56bbc 100644
--- a/theories/Logic/ExtensionalFunctionRepresentative.v
+++ b/theories/Logic/ExtensionalFunctionRepresentative.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This module states a limited form axiom of functional
diff --git a/theories/Logic/ExtensionalityFacts.v b/theories/Logic/ExtensionalityFacts.v
index 86539544b..02c8998a8 100644
--- a/theories/Logic/ExtensionalityFacts.v
+++ b/theories/Logic/ExtensionalityFacts.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Some facts and definitions about extensionality
diff --git a/theories/Logic/FinFun.v b/theories/Logic/FinFun.v
index 8bdbfe85b..89f5a82a8 100644
--- a/theories/Logic/FinFun.v
+++ b/theories/Logic/FinFun.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Functions on finite domains *)
diff --git a/theories/Logic/FunctionalExtensionality.v b/theories/Logic/FunctionalExtensionality.v
index 82b04d132..95e1af2ea 100644
--- a/theories/Logic/FunctionalExtensionality.v
+++ b/theories/Logic/FunctionalExtensionality.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This module states the axiom of (dependent) functional extensionality and (dependent) eta-expansion.
diff --git a/theories/Logic/Hurkens.v b/theories/Logic/Hurkens.v
index 4590d609d..6c4a8533a 100644
--- a/theories/Logic/Hurkens.v
+++ b/theories/Logic/Hurkens.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Hurkens.v *)
(************************************************************************)
diff --git a/theories/Logic/IndefiniteDescription.v b/theories/Logic/IndefiniteDescription.v
index 10ef72ade..86e81529d 100644
--- a/theories/Logic/IndefiniteDescription.v
+++ b/theories/Logic/IndefiniteDescription.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This file provides a constructive form of indefinite description that
diff --git a/theories/Logic/JMeq.v b/theories/Logic/JMeq.v
index aa6193bc7..9c56b60aa 100644
--- a/theories/Logic/JMeq.v
+++ b/theories/Logic/JMeq.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** John Major's Equality as proposed by Conor McBride
diff --git a/theories/Logic/ProofIrrelevance.v b/theories/Logic/ProofIrrelevance.v
index d11e7c872..134bf649d 100644
--- a/theories/Logic/ProofIrrelevance.v
+++ b/theories/Logic/ProofIrrelevance.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This file axiomatizes proof-irrelevance and derives some consequences *)
diff --git a/theories/Logic/ProofIrrelevanceFacts.v b/theories/Logic/ProofIrrelevanceFacts.v
index f359a2109..10d9dbcda 100644
--- a/theories/Logic/ProofIrrelevanceFacts.v
+++ b/theories/Logic/ProofIrrelevanceFacts.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This defines the functor that build consequences of proof-irrelevance *)
diff --git a/theories/Logic/PropExtensionality.v b/theories/Logic/PropExtensionality.v
index b8bc9a52c..80dd4e850 100644
--- a/theories/Logic/PropExtensionality.v
+++ b/theories/Logic/PropExtensionality.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This module states propositional extensionality and draws
diff --git a/theories/Logic/PropExtensionalityFacts.v b/theories/Logic/PropExtensionalityFacts.v
index 8a1cf9708..2b3035173 100644
--- a/theories/Logic/PropExtensionalityFacts.v
+++ b/theories/Logic/PropExtensionalityFacts.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Some facts and definitions about propositional and predicate extensionality
diff --git a/theories/Logic/PropFacts.v b/theories/Logic/PropFacts.v
index 309539e5c..067870356 100644
--- a/theories/Logic/PropFacts.v
+++ b/theories/Logic/PropFacts.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Basic facts about Prop as a type *)
diff --git a/theories/Logic/RelationalChoice.v b/theories/Logic/RelationalChoice.v
index 668568b03..994f07856 100644
--- a/theories/Logic/RelationalChoice.v
+++ b/theories/Logic/RelationalChoice.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This file axiomatizes the relational form of the axiom of choice *)
diff --git a/theories/Logic/SetIsType.v b/theories/Logic/SetIsType.v
index 19b6f62dd..afa85514e 100644
--- a/theories/Logic/SetIsType.v
+++ b/theories/Logic/SetIsType.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * The Set universe seen as a synonym for Type *)
diff --git a/theories/Logic/SetoidChoice.v b/theories/Logic/SetoidChoice.v
index 62979330d..21bf73356 100644
--- a/theories/Logic/SetoidChoice.v
+++ b/theories/Logic/SetoidChoice.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This module states the functional form of the axiom of choice over
diff --git a/theories/Logic/WKL.v b/theories/Logic/WKL.v
index 7f98d8e91..579800b80 100644
--- a/theories/Logic/WKL.v
+++ b/theories/Logic/WKL.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** A constructive proof of a version of Weak König's Lemma over a
diff --git a/theories/Logic/WeakFan.v b/theories/Logic/WeakFan.v
index 0068f72eb..c9822f47d 100644
--- a/theories/Logic/WeakFan.v
+++ b/theories/Logic/WeakFan.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** A constructive proof of a non-standard version of the weak Fan Theorem
diff --git a/theories/MSets/MSetAVL.v b/theories/MSets/MSetAVL.v
index b30cb6b56..b966f217a 100644
--- a/theories/MSets/MSetAVL.v
+++ b/theories/MSets/MSetAVL.v
@@ -1,11 +1,13 @@
(* -*- coding: utf-8 -*- *)
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * MSetAVL : Implementation of MSetInterface via AVL trees *)
diff --git a/theories/MSets/MSetDecide.v b/theories/MSets/MSetDecide.v
index 9c622fd78..f228cbb3b 100644
--- a/theories/MSets/MSetDecide.v
+++ b/theories/MSets/MSetDecide.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(**************************************************************)
(* MSetDecide.v *)
diff --git a/theories/MSets/MSetEqProperties.v b/theories/MSets/MSetEqProperties.v
index ae20edc87..1ee098cb0 100644
--- a/theories/MSets/MSetEqProperties.v
+++ b/theories/MSets/MSetEqProperties.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite sets library *)
diff --git a/theories/MSets/MSetFacts.v b/theories/MSets/MSetFacts.v
index 4e17618f7..d57a7741e 100644
--- a/theories/MSets/MSetFacts.v
+++ b/theories/MSets/MSetFacts.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite sets library *)
diff --git a/theories/MSets/MSetGenTree.v b/theories/MSets/MSetGenTree.v
index 9fb8e499b..9d2a73ed0 100644
--- a/theories/MSets/MSetGenTree.v
+++ b/theories/MSets/MSetGenTree.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * MSetGenTree : sets via generic trees
diff --git a/theories/MSets/MSetInterface.v b/theories/MSets/MSetInterface.v
index 74a7f6df8..f0e757157 100644
--- a/theories/MSets/MSetInterface.v
+++ b/theories/MSets/MSetInterface.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite set library *)
diff --git a/theories/MSets/MSetList.v b/theories/MSets/MSetList.v
index 05c20eb8f..35fe4cee4 100644
--- a/theories/MSets/MSetList.v
+++ b/theories/MSets/MSetList.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite sets library *)
diff --git a/theories/MSets/MSetPositive.v b/theories/MSets/MSetPositive.v
index be95a0379..a726eebd3 100644
--- a/theories/MSets/MSetPositive.v
+++ b/theories/MSets/MSetPositive.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** Efficient implementation of [MSetInterface.S] for positive keys,
inspired from the [FMapPositive] module.
diff --git a/theories/MSets/MSetProperties.v b/theories/MSets/MSetProperties.v
index 396067b57..3c7dea736 100644
--- a/theories/MSets/MSetProperties.v
+++ b/theories/MSets/MSetProperties.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite sets library *)
diff --git a/theories/MSets/MSetRBT.v b/theories/MSets/MSetRBT.v
index 83a2343dd..eab01a55b 100644
--- a/theories/MSets/MSetRBT.v
+++ b/theories/MSets/MSetRBT.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * MSetRBT : Implementation of MSetInterface via Red-Black trees *)
diff --git a/theories/MSets/MSetToFiniteSet.v b/theories/MSets/MSetToFiniteSet.v
index e8087bc57..f456c407b 100644
--- a/theories/MSets/MSetToFiniteSet.v
+++ b/theories/MSets/MSetToFiniteSet.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite sets library : conversion to old [Finite_sets] *)
diff --git a/theories/MSets/MSetWeakList.v b/theories/MSets/MSetWeakList.v
index 2ac57a932..8df1ff1cd 100644
--- a/theories/MSets/MSetWeakList.v
+++ b/theories/MSets/MSetWeakList.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * Finite sets library *)
diff --git a/theories/MSets/MSets.v b/theories/MSets/MSets.v
index 1ee485cc1..0c9bc20cc 100644
--- a/theories/MSets/MSets.v
+++ b/theories/MSets/MSets.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
Require Export Orders.
Require Export OrdersEx.
diff --git a/theories/NArith/BinNat.v b/theories/NArith/BinNat.v
index 75a8bfdb3..5d3ec5abc 100644
--- a/theories/NArith/BinNat.v
+++ b/theories/NArith/BinNat.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export BinNums.
@@ -956,95 +958,94 @@ Notation "( p | q )" := (N.divide p q) (at level 0) : N_scope.
(** Compatibility notations *)
-(*Notation N := N (compat "8.3").*) (*hidden by module N above *)
Notation N_rect := N_rect (only parsing).
Notation N_rec := N_rec (only parsing).
Notation N_ind := N_ind (only parsing).
Notation N0 := N0 (only parsing).
Notation Npos := N.pos (only parsing).
-Notation Ndiscr := N.discr (compat "8.3").
-Notation Ndouble_plus_one := N.succ_double (compat "8.3").
-Notation Ndouble := N.double (compat "8.3").
-Notation Nsucc := N.succ (compat "8.3").
-Notation Npred := N.pred (compat "8.3").
-Notation Nsucc_pos := N.succ_pos (compat "8.3").
-Notation Ppred_N := Pos.pred_N (compat "8.3").
-Notation Nplus := N.add (compat "8.3").
-Notation Nminus := N.sub (compat "8.3").
-Notation Nmult := N.mul (compat "8.3").
-Notation Neqb := N.eqb (compat "8.3").
-Notation Ncompare := N.compare (compat "8.3").
-Notation Nlt := N.lt (compat "8.3").
-Notation Ngt := N.gt (compat "8.3").
-Notation Nle := N.le (compat "8.3").
-Notation Nge := N.ge (compat "8.3").
-Notation Nmin := N.min (compat "8.3").
-Notation Nmax := N.max (compat "8.3").
-Notation Ndiv2 := N.div2 (compat "8.3").
-Notation Neven := N.even (compat "8.3").
-Notation Nodd := N.odd (compat "8.3").
-Notation Npow := N.pow (compat "8.3").
-Notation Nlog2 := N.log2 (compat "8.3").
-
-Notation nat_of_N := N.to_nat (compat "8.3").
-Notation N_of_nat := N.of_nat (compat "8.3").
-Notation N_eq_dec := N.eq_dec (compat "8.3").
-Notation Nrect := N.peano_rect (compat "8.3").
-Notation Nrect_base := N.peano_rect_base (compat "8.3").
-Notation Nrect_step := N.peano_rect_succ (compat "8.3").
-Notation Nind := N.peano_ind (compat "8.3").
-Notation Nrec := N.peano_rec (compat "8.3").
-Notation Nrec_base := N.peano_rec_base (compat "8.3").
-Notation Nrec_succ := N.peano_rec_succ (compat "8.3").
-
-Notation Npred_succ := N.pred_succ (compat "8.3").
-Notation Npred_minus := N.pred_sub (compat "8.3").
-Notation Nsucc_pred := N.succ_pred (compat "8.3").
-Notation Ppred_N_spec := N.pos_pred_spec (compat "8.3").
-Notation Nsucc_pos_spec := N.succ_pos_spec (compat "8.3").
-Notation Ppred_Nsucc := N.pos_pred_succ (compat "8.3").
-Notation Nplus_0_l := N.add_0_l (compat "8.3").
-Notation Nplus_0_r := N.add_0_r (compat "8.3").
-Notation Nplus_comm := N.add_comm (compat "8.3").
-Notation Nplus_assoc := N.add_assoc (compat "8.3").
-Notation Nplus_succ := N.add_succ_l (compat "8.3").
-Notation Nsucc_0 := N.succ_0_discr (compat "8.3").
-Notation Nsucc_inj := N.succ_inj (compat "8.3").
-Notation Nminus_N0_Nle := N.sub_0_le (compat "8.3").
-Notation Nminus_0_r := N.sub_0_r (compat "8.3").
-Notation Nminus_succ_r:= N.sub_succ_r (compat "8.3").
-Notation Nmult_0_l := N.mul_0_l (compat "8.3").
-Notation Nmult_1_l := N.mul_1_l (compat "8.3").
-Notation Nmult_1_r := N.mul_1_r (compat "8.3").
-Notation Nmult_comm := N.mul_comm (compat "8.3").
-Notation Nmult_assoc := N.mul_assoc (compat "8.3").
-Notation Nmult_plus_distr_r := N.mul_add_distr_r (compat "8.3").
-Notation Neqb_eq := N.eqb_eq (compat "8.3").
-Notation Nle_0 := N.le_0_l (compat "8.3").
-Notation Ncompare_refl := N.compare_refl (compat "8.3").
-Notation Ncompare_Eq_eq := N.compare_eq (compat "8.3").
-Notation Ncompare_eq_correct := N.compare_eq_iff (compat "8.3").
-Notation Nlt_irrefl := N.lt_irrefl (compat "8.3").
-Notation Nlt_trans := N.lt_trans (compat "8.3").
-Notation Nle_lteq := N.lt_eq_cases (compat "8.3").
-Notation Nlt_succ_r := N.lt_succ_r (compat "8.3").
-Notation Nle_trans := N.le_trans (compat "8.3").
-Notation Nle_succ_l := N.le_succ_l (compat "8.3").
-Notation Ncompare_spec := N.compare_spec (compat "8.3").
-Notation Ncompare_0 := N.compare_0_r (compat "8.3").
-Notation Ndouble_div2 := N.div2_double (compat "8.3").
-Notation Ndouble_plus_one_div2 := N.div2_succ_double (compat "8.3").
-Notation Ndouble_inj := N.double_inj (compat "8.3").
-Notation Ndouble_plus_one_inj := N.succ_double_inj (compat "8.3").
-Notation Npow_0_r := N.pow_0_r (compat "8.3").
-Notation Npow_succ_r := N.pow_succ_r (compat "8.3").
-Notation Nlog2_spec := N.log2_spec (compat "8.3").
-Notation Nlog2_nonpos := N.log2_nonpos (compat "8.3").
-Notation Neven_spec := N.even_spec (compat "8.3").
-Notation Nodd_spec := N.odd_spec (compat "8.3").
-Notation Nlt_not_eq := N.lt_neq (compat "8.3").
-Notation Ngt_Nlt := N.gt_lt (compat "8.3").
+Notation Ndiscr := N.discr (compat "8.6").
+Notation Ndouble_plus_one := N.succ_double (only parsing).
+Notation Ndouble := N.double (compat "8.6").
+Notation Nsucc := N.succ (compat "8.6").
+Notation Npred := N.pred (compat "8.6").
+Notation Nsucc_pos := N.succ_pos (compat "8.6").
+Notation Ppred_N := Pos.pred_N (compat "8.6").
+Notation Nplus := N.add (only parsing).
+Notation Nminus := N.sub (only parsing).
+Notation Nmult := N.mul (only parsing).
+Notation Neqb := N.eqb (compat "8.6").
+Notation Ncompare := N.compare (compat "8.6").
+Notation Nlt := N.lt (compat "8.6").
+Notation Ngt := N.gt (compat "8.6").
+Notation Nle := N.le (compat "8.6").
+Notation Nge := N.ge (compat "8.6").
+Notation Nmin := N.min (compat "8.6").
+Notation Nmax := N.max (compat "8.6").
+Notation Ndiv2 := N.div2 (compat "8.6").
+Notation Neven := N.even (compat "8.6").
+Notation Nodd := N.odd (compat "8.6").
+Notation Npow := N.pow (compat "8.6").
+Notation Nlog2 := N.log2 (compat "8.6").
+
+Notation nat_of_N := N.to_nat (only parsing).
+Notation N_of_nat := N.of_nat (only parsing).
+Notation N_eq_dec := N.eq_dec (compat "8.6").
+Notation Nrect := N.peano_rect (only parsing).
+Notation Nrect_base := N.peano_rect_base (only parsing).
+Notation Nrect_step := N.peano_rect_succ (only parsing).
+Notation Nind := N.peano_ind (only parsing).
+Notation Nrec := N.peano_rec (only parsing).
+Notation Nrec_base := N.peano_rec_base (only parsing).
+Notation Nrec_succ := N.peano_rec_succ (only parsing).
+
+Notation Npred_succ := N.pred_succ (compat "8.6").
+Notation Npred_minus := N.pred_sub (only parsing).
+Notation Nsucc_pred := N.succ_pred (compat "8.6").
+Notation Ppred_N_spec := N.pos_pred_spec (only parsing).
+Notation Nsucc_pos_spec := N.succ_pos_spec (compat "8.6").
+Notation Ppred_Nsucc := N.pos_pred_succ (only parsing).
+Notation Nplus_0_l := N.add_0_l (only parsing).
+Notation Nplus_0_r := N.add_0_r (only parsing).
+Notation Nplus_comm := N.add_comm (only parsing).
+Notation Nplus_assoc := N.add_assoc (only parsing).
+Notation Nplus_succ := N.add_succ_l (only parsing).
+Notation Nsucc_0 := N.succ_0_discr (only parsing).
+Notation Nsucc_inj := N.succ_inj (compat "8.6").
+Notation Nminus_N0_Nle := N.sub_0_le (only parsing).
+Notation Nminus_0_r := N.sub_0_r (only parsing).
+Notation Nminus_succ_r:= N.sub_succ_r (only parsing).
+Notation Nmult_0_l := N.mul_0_l (only parsing).
+Notation Nmult_1_l := N.mul_1_l (only parsing).
+Notation Nmult_1_r := N.mul_1_r (only parsing).
+Notation Nmult_comm := N.mul_comm (only parsing).
+Notation Nmult_assoc := N.mul_assoc (only parsing).
+Notation Nmult_plus_distr_r := N.mul_add_distr_r (only parsing).
+Notation Neqb_eq := N.eqb_eq (compat "8.6").
+Notation Nle_0 := N.le_0_l (only parsing).
+Notation Ncompare_refl := N.compare_refl (compat "8.6").
+Notation Ncompare_Eq_eq := N.compare_eq (only parsing).
+Notation Ncompare_eq_correct := N.compare_eq_iff (only parsing).
+Notation Nlt_irrefl := N.lt_irrefl (compat "8.6").
+Notation Nlt_trans := N.lt_trans (compat "8.6").
+Notation Nle_lteq := N.lt_eq_cases (only parsing).
+Notation Nlt_succ_r := N.lt_succ_r (compat "8.6").
+Notation Nle_trans := N.le_trans (compat "8.6").
+Notation Nle_succ_l := N.le_succ_l (compat "8.6").
+Notation Ncompare_spec := N.compare_spec (compat "8.6").
+Notation Ncompare_0 := N.compare_0_r (only parsing).
+Notation Ndouble_div2 := N.div2_double (only parsing).
+Notation Ndouble_plus_one_div2 := N.div2_succ_double (only parsing).
+Notation Ndouble_inj := N.double_inj (compat "8.6").
+Notation Ndouble_plus_one_inj := N.succ_double_inj (only parsing).
+Notation Npow_0_r := N.pow_0_r (compat "8.6").
+Notation Npow_succ_r := N.pow_succ_r (compat "8.6").
+Notation Nlog2_spec := N.log2_spec (compat "8.6").
+Notation Nlog2_nonpos := N.log2_nonpos (compat "8.6").
+Notation Neven_spec := N.even_spec (compat "8.6").
+Notation Nodd_spec := N.odd_spec (compat "8.6").
+Notation Nlt_not_eq := N.lt_neq (only parsing).
+Notation Ngt_Nlt := N.gt_lt (only parsing).
(** More complex compatibility facts, expressed as lemmas
(to preserve scopes for instance) *)
diff --git a/theories/NArith/BinNatDef.v b/theories/NArith/BinNatDef.v
index 6771e57ad..5de75537c 100644
--- a/theories/NArith/BinNatDef.v
+++ b/theories/NArith/BinNatDef.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export BinNums.
@@ -378,4 +380,22 @@ Definition iter (n:N) {A} (f:A->A) (x:A) : A :=
| pos p => Pos.iter f x p
end.
+(** Conversion with a decimal representation for printing/parsing *)
+
+Definition of_uint (d:Decimal.uint) := Pos.of_uint d.
+
+Definition of_int (d:Decimal.int) :=
+ match Decimal.norm d with
+ | Decimal.Pos d => Some (Pos.of_uint d)
+ | Decimal.Neg _ => None
+ end.
+
+Definition to_uint n :=
+ match n with
+ | 0 => Decimal.zero
+ | pos p => Pos.to_uint p
+ end.
+
+Definition to_int n := Decimal.Pos (to_uint n).
+
End N.
diff --git a/theories/NArith/NArith.v b/theories/NArith/NArith.v
index 64eea4419..f3007970b 100644
--- a/theories/NArith/NArith.v
+++ b/theories/NArith/NArith.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Library for binary natural numbers *)
diff --git a/theories/NArith/Ndec.v b/theories/NArith/Ndec.v
index 892bbe7cd..67c30f225 100644
--- a/theories/NArith/Ndec.v
+++ b/theories/NArith/Ndec.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Bool.
@@ -20,11 +22,11 @@ Local Open Scope N_scope.
(** Obsolete results about boolean comparisons over [N],
kept for compatibility with IntMap and SMC. *)
-Notation Peqb := Pos.eqb (compat "8.3").
-Notation Neqb := N.eqb (compat "8.3").
-Notation Peqb_correct := Pos.eqb_refl (compat "8.3").
-Notation Neqb_correct := N.eqb_refl (compat "8.3").
-Notation Neqb_comm := N.eqb_sym (compat "8.3").
+Notation Peqb := Pos.eqb (compat "8.6").
+Notation Neqb := N.eqb (compat "8.6").
+Notation Peqb_correct := Pos.eqb_refl (only parsing).
+Notation Neqb_correct := N.eqb_refl (only parsing).
+Notation Neqb_comm := N.eqb_sym (only parsing).
Lemma Peqb_complete p p' : Pos.eqb p p' = true -> p = p'.
Proof. now apply Pos.eqb_eq. Qed.
@@ -274,7 +276,7 @@ Qed.
(* Old results about [N.min] *)
-Notation Nmin_choice := N.min_dec (compat "8.3").
+Notation Nmin_choice := N.min_dec (only parsing).
Lemma Nmin_le_1 a b : Nleb (N.min a b) a = true.
Proof. rewrite Nleb_Nle. apply N.le_min_l. Qed.
diff --git a/theories/NArith/Ndigits.v b/theories/NArith/Ndigits.v
index 9aadf985d..3ccaa7211 100644
--- a/theories/NArith/Ndigits.v
+++ b/theories/NArith/Ndigits.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Bool Morphisms Setoid Bvector BinPos BinNat PeanoNat Pnat Nnat.
@@ -14,17 +16,17 @@ Local Open Scope N_scope.
(** Compatibility names for some bitwise operations *)
-Notation Pxor := Pos.lxor (compat "8.3").
-Notation Nxor := N.lxor (compat "8.3").
-Notation Pbit := Pos.testbit_nat (compat "8.3").
-Notation Nbit := N.testbit_nat (compat "8.3").
+Notation Pxor := Pos.lxor (only parsing).
+Notation Nxor := N.lxor (only parsing).
+Notation Pbit := Pos.testbit_nat (only parsing).
+Notation Nbit := N.testbit_nat (only parsing).
-Notation Nxor_eq := N.lxor_eq (compat "8.3").
-Notation Nxor_comm := N.lxor_comm (compat "8.3").
-Notation Nxor_assoc := N.lxor_assoc (compat "8.3").
-Notation Nxor_neutral_left := N.lxor_0_l (compat "8.3").
-Notation Nxor_neutral_right := N.lxor_0_r (compat "8.3").
-Notation Nxor_nilpotent := N.lxor_nilpotent (compat "8.3").
+Notation Nxor_eq := N.lxor_eq (only parsing).
+Notation Nxor_comm := N.lxor_comm (only parsing).
+Notation Nxor_assoc := N.lxor_assoc (only parsing).
+Notation Nxor_neutral_left := N.lxor_0_l (only parsing).
+Notation Nxor_neutral_right := N.lxor_0_r (only parsing).
+Notation Nxor_nilpotent := N.lxor_nilpotent (only parsing).
(** Equivalence of bit-testing functions,
either with index in [N] or in [nat]. *)
@@ -249,7 +251,7 @@ Local Close Scope N_scope.
(** Checking whether a number is odd, i.e.
if its lower bit is set. *)
-Notation Nbit0 := N.odd (compat "8.3").
+Notation Nbit0 := N.odd (only parsing).
Definition Nodd (n:N) := N.odd n = true.
Definition Neven (n:N) := N.odd n = false.
@@ -498,7 +500,7 @@ Qed.
(** Number of digits in a number *)
-Notation Nsize := N.size_nat (compat "8.3").
+Notation Nsize := N.size_nat (only parsing).
(** conversions between N and bit vectors. *)
diff --git a/theories/NArith/Ndist.v b/theories/NArith/Ndist.v
index d81c119d3..d9a58c057 100644
--- a/theories/NArith/Ndist.v
+++ b/theories/NArith/Ndist.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Arith.
Require Import Min.
diff --git a/theories/NArith/Ndiv_def.v b/theories/NArith/Ndiv_def.v
index 974e93994..7c9fd8695 100644
--- a/theories/NArith/Ndiv_def.v
+++ b/theories/NArith/Ndiv_def.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import BinNat.
@@ -22,10 +24,10 @@ Lemma Pdiv_eucl_remainder a b :
snd (Pdiv_eucl a b) < Npos b.
Proof. now apply (N.pos_div_eucl_remainder a (Npos b)). Qed.
-Notation Ndiv_eucl := N.div_eucl (compat "8.3").
-Notation Ndiv := N.div (compat "8.3").
-Notation Nmod := N.modulo (compat "8.3").
+Notation Ndiv_eucl := N.div_eucl (compat "8.6").
+Notation Ndiv := N.div (compat "8.6").
+Notation Nmod := N.modulo (only parsing).
-Notation Ndiv_eucl_correct := N.div_eucl_spec (compat "8.3").
-Notation Ndiv_mod_eq := N.div_mod' (compat "8.3").
-Notation Nmod_lt := N.mod_lt (compat "8.3").
+Notation Ndiv_eucl_correct := N.div_eucl_spec (only parsing).
+Notation Ndiv_mod_eq := N.div_mod' (only parsing).
+Notation Nmod_lt := N.mod_lt (compat "8.6").
diff --git a/theories/NArith/Ngcd_def.v b/theories/NArith/Ngcd_def.v
index cfca82eb3..70784d9ce 100644
--- a/theories/NArith/Ngcd_def.v
+++ b/theories/NArith/Ngcd_def.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import BinPos BinNat.
diff --git a/theories/NArith/Nnat.v b/theories/NArith/Nnat.v
index 798ab2828..3488c8b43 100644
--- a/theories/NArith/Nnat.v
+++ b/theories/NArith/Nnat.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import BinPos BinNat PeanoNat Pnat.
@@ -208,30 +210,30 @@ Hint Rewrite Nat2N.id : Nnat.
(** Compatibility notations *)
-Notation nat_of_N_inj := N2Nat.inj (compat "8.3").
-Notation N_of_nat_of_N := N2Nat.id (compat "8.3").
-Notation nat_of_Ndouble := N2Nat.inj_double (compat "8.3").
-Notation nat_of_Ndouble_plus_one := N2Nat.inj_succ_double (compat "8.3").
-Notation nat_of_Nsucc := N2Nat.inj_succ (compat "8.3").
-Notation nat_of_Nplus := N2Nat.inj_add (compat "8.3").
-Notation nat_of_Nmult := N2Nat.inj_mul (compat "8.3").
-Notation nat_of_Nminus := N2Nat.inj_sub (compat "8.3").
-Notation nat_of_Npred := N2Nat.inj_pred (compat "8.3").
-Notation nat_of_Ndiv2 := N2Nat.inj_div2 (compat "8.3").
-Notation nat_of_Ncompare := N2Nat.inj_compare (compat "8.3").
-Notation nat_of_Nmax := N2Nat.inj_max (compat "8.3").
-Notation nat_of_Nmin := N2Nat.inj_min (compat "8.3").
-
-Notation nat_of_N_of_nat := Nat2N.id (compat "8.3").
-Notation N_of_nat_inj := Nat2N.inj (compat "8.3").
-Notation N_of_double := Nat2N.inj_double (compat "8.3").
-Notation N_of_double_plus_one := Nat2N.inj_succ_double (compat "8.3").
-Notation N_of_S := Nat2N.inj_succ (compat "8.3").
-Notation N_of_pred := Nat2N.inj_pred (compat "8.3").
-Notation N_of_plus := Nat2N.inj_add (compat "8.3").
-Notation N_of_minus := Nat2N.inj_sub (compat "8.3").
-Notation N_of_mult := Nat2N.inj_mul (compat "8.3").
-Notation N_of_div2 := Nat2N.inj_div2 (compat "8.3").
-Notation N_of_nat_compare := Nat2N.inj_compare (compat "8.3").
-Notation N_of_min := Nat2N.inj_min (compat "8.3").
-Notation N_of_max := Nat2N.inj_max (compat "8.3").
+Notation nat_of_N_inj := N2Nat.inj (only parsing).
+Notation N_of_nat_of_N := N2Nat.id (only parsing).
+Notation nat_of_Ndouble := N2Nat.inj_double (only parsing).
+Notation nat_of_Ndouble_plus_one := N2Nat.inj_succ_double (only parsing).
+Notation nat_of_Nsucc := N2Nat.inj_succ (only parsing).
+Notation nat_of_Nplus := N2Nat.inj_add (only parsing).
+Notation nat_of_Nmult := N2Nat.inj_mul (only parsing).
+Notation nat_of_Nminus := N2Nat.inj_sub (only parsing).
+Notation nat_of_Npred := N2Nat.inj_pred (only parsing).
+Notation nat_of_Ndiv2 := N2Nat.inj_div2 (only parsing).
+Notation nat_of_Ncompare := N2Nat.inj_compare (only parsing).
+Notation nat_of_Nmax := N2Nat.inj_max (only parsing).
+Notation nat_of_Nmin := N2Nat.inj_min (only parsing).
+
+Notation nat_of_N_of_nat := Nat2N.id (only parsing).
+Notation N_of_nat_inj := Nat2N.inj (only parsing).
+Notation N_of_double := Nat2N.inj_double (only parsing).
+Notation N_of_double_plus_one := Nat2N.inj_succ_double (only parsing).
+Notation N_of_S := Nat2N.inj_succ (only parsing).
+Notation N_of_pred := Nat2N.inj_pred (only parsing).
+Notation N_of_plus := Nat2N.inj_add (only parsing).
+Notation N_of_minus := Nat2N.inj_sub (only parsing).
+Notation N_of_mult := Nat2N.inj_mul (only parsing).
+Notation N_of_div2 := Nat2N.inj_div2 (only parsing).
+Notation N_of_nat_compare := Nat2N.inj_compare (only parsing).
+Notation N_of_min := Nat2N.inj_min (only parsing).
+Notation N_of_max := Nat2N.inj_max (only parsing).
diff --git a/theories/NArith/Nsqrt_def.v b/theories/NArith/Nsqrt_def.v
index 97de41c20..e771fe916 100644
--- a/theories/NArith/Nsqrt_def.v
+++ b/theories/NArith/Nsqrt_def.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import BinNat.
@@ -11,8 +13,8 @@ Require Import BinNat.
(** Obsolete file, see [BinNat] now,
only compatibility notations remain here. *)
-Notation Nsqrtrem := N.sqrtrem (compat "8.3").
-Notation Nsqrt := N.sqrt (compat "8.3").
-Notation Nsqrtrem_spec := N.sqrtrem_spec (compat "8.3").
-Notation Nsqrt_spec := (fun n => N.sqrt_spec n (N.le_0_l n)) (compat "8.3").
-Notation Nsqrtrem_sqrt := N.sqrtrem_sqrt (compat "8.3").
+Notation Nsqrtrem := N.sqrtrem (compat "8.6").
+Notation Nsqrt := N.sqrt (compat "8.6").
+Notation Nsqrtrem_spec := N.sqrtrem_spec (compat "8.6").
+Notation Nsqrt_spec := (fun n => N.sqrt_spec n (N.le_0_l n)) (only parsing).
+Notation Nsqrtrem_sqrt := N.sqrtrem_sqrt (compat "8.6").
diff --git a/theories/Numbers/BinNums.v b/theories/Numbers/BinNums.v
index d7e4185f7..f8b3d9e1d 100644
--- a/theories/Numbers/BinNums.v
+++ b/theories/Numbers/BinNums.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Binary Numerical Datatypes *)
diff --git a/theories/Numbers/Cyclic/Abstract/CyclicAxioms.v b/theories/Numbers/Cyclic/Abstract/CyclicAxioms.v
index 1777743fa..951a4ef2b 100644
--- a/theories/Numbers/Cyclic/Abstract/CyclicAxioms.v
+++ b/theories/Numbers/Cyclic/Abstract/CyclicAxioms.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Cyclic/Abstract/DoubleType.v b/theories/Numbers/Cyclic/Abstract/DoubleType.v
index 73a064acd..fe0476e4d 100644
--- a/theories/Numbers/Cyclic/Abstract/DoubleType.v
+++ b/theories/Numbers/Cyclic/Abstract/DoubleType.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Cyclic/Abstract/NZCyclic.v b/theories/Numbers/Cyclic/Abstract/NZCyclic.v
index 94f860841..64935ffe1 100644
--- a/theories/Numbers/Cyclic/Abstract/NZCyclic.v
+++ b/theories/Numbers/Cyclic/Abstract/NZCyclic.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Cyclic/Int31/Cyclic31.v b/theories/Numbers/Cyclic/Int31/Cyclic31.v
index d2390e2ce..bd4f0279d 100644
--- a/theories/Numbers/Cyclic/Int31/Cyclic31.v
+++ b/theories/Numbers/Cyclic/Int31/Cyclic31.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Int31 numbers defines indeed a cyclic structure : Z/(2^31)Z *)
diff --git a/theories/Numbers/Cyclic/Int31/Int31.v b/theories/Numbers/Cyclic/Int31/Int31.v
index cc359bfdf..9f8da831d 100644
--- a/theories/Numbers/Cyclic/Int31/Int31.v
+++ b/theories/Numbers/Cyclic/Int31/Int31.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Cyclic/Int31/Ring31.v b/theories/Numbers/Cyclic/Int31/Ring31.v
index c076dbd9a..b69352945 100644
--- a/theories/Numbers/Cyclic/Int31/Ring31.v
+++ b/theories/Numbers/Cyclic/Int31/Ring31.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Int31 numbers defines Z/(2^31)Z, and can hence be equipped
diff --git a/theories/Numbers/Cyclic/ZModulo/ZModulo.v b/theories/Numbers/Cyclic/ZModulo/ZModulo.v
index e7658841a..784e81758 100644
--- a/theories/Numbers/Cyclic/ZModulo/ZModulo.v
+++ b/theories/Numbers/Cyclic/ZModulo/ZModulo.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Type [Z] viewed modulo a particular constant corresponds to [Z/nZ]
diff --git a/theories/Numbers/DecimalFacts.v b/theories/Numbers/DecimalFacts.v
new file mode 100644
index 000000000..0f4905277
--- /dev/null
+++ b/theories/Numbers/DecimalFacts.v
@@ -0,0 +1,143 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(** * DecimalFacts : some facts about Decimal numbers *)
+
+Require Import Decimal.
+
+Lemma uint_dec (d d' : uint) : { d = d' } + { d <> d' }.
+Proof.
+ decide equality.
+Defined.
+
+Lemma rev_revapp d d' :
+ rev (revapp d d') = revapp d' d.
+Proof.
+ revert d'. induction d; simpl; intros; now rewrite ?IHd.
+Qed.
+
+Lemma rev_rev d : rev (rev d) = d.
+Proof.
+ apply rev_revapp.
+Qed.
+
+(** Normalization on little-endian numbers *)
+
+Fixpoint nztail d :=
+ match d with
+ | Nil => Nil
+ | D0 d => match nztail d with Nil => Nil | d' => D0 d' end
+ | D1 d => D1 (nztail d)
+ | D2 d => D2 (nztail d)
+ | D3 d => D3 (nztail d)
+ | D4 d => D4 (nztail d)
+ | D5 d => D5 (nztail d)
+ | D6 d => D6 (nztail d)
+ | D7 d => D7 (nztail d)
+ | D8 d => D8 (nztail d)
+ | D9 d => D9 (nztail d)
+ end.
+
+Definition lnorm d :=
+ match nztail d with
+ | Nil => zero
+ | d => d
+ end.
+
+Lemma nzhead_revapp_0 d d' : nztail d = Nil ->
+ nzhead (revapp d d') = nzhead d'.
+Proof.
+ revert d'. induction d; intros d' [=]; simpl; trivial.
+ destruct (nztail d); now rewrite IHd.
+Qed.
+
+Lemma nzhead_revapp d d' : nztail d <> Nil ->
+ nzhead (revapp d d') = revapp (nztail d) d'.
+Proof.
+ revert d'.
+ induction d; intros d' H; simpl in *;
+ try destruct (nztail d) eqn:E;
+ (now rewrite ?nzhead_revapp_0) || (now rewrite IHd).
+Qed.
+
+Lemma nzhead_rev d : nztail d <> Nil ->
+ nzhead (rev d) = rev (nztail d).
+Proof.
+ apply nzhead_revapp.
+Qed.
+
+Lemma rev_nztail_rev d :
+ rev (nztail (rev d)) = nzhead d.
+Proof.
+ destruct (uint_dec (nztail (rev d)) Nil) as [H|H].
+ - rewrite H. unfold rev; simpl.
+ rewrite <- (rev_rev d). symmetry.
+ now apply nzhead_revapp_0.
+ - now rewrite <- nzhead_rev, rev_rev.
+Qed.
+
+Lemma revapp_nil_inv d d' : revapp d d' = Nil -> d = Nil /\ d' = Nil.
+Proof.
+ revert d'.
+ induction d; simpl; intros d' H; auto; now apply IHd in H.
+Qed.
+
+Lemma rev_nil_inv d : rev d = Nil -> d = Nil.
+Proof.
+ apply revapp_nil_inv.
+Qed.
+
+Lemma rev_lnorm_rev d :
+ rev (lnorm (rev d)) = unorm d.
+Proof.
+ unfold unorm, lnorm.
+ rewrite <- rev_nztail_rev.
+ destruct nztail; simpl; trivial;
+ destruct rev eqn:E; trivial; now apply rev_nil_inv in E.
+Qed.
+
+Lemma nzhead_nonzero d d' : nzhead d <> D0 d'.
+Proof.
+ induction d; easy.
+Qed.
+
+Lemma unorm_0 d : unorm d = zero <-> nzhead d = Nil.
+Proof.
+ unfold unorm. split.
+ - generalize (nzhead_nonzero d).
+ destruct nzhead; intros H [=]; trivial. now destruct (H u).
+ - now intros ->.
+Qed.
+
+Lemma unorm_nonnil d : unorm d <> Nil.
+Proof.
+ unfold unorm. now destruct nzhead.
+Qed.
+
+Lemma nzhead_invol d : nzhead (nzhead d) = nzhead d.
+Proof.
+ now induction d.
+Qed.
+
+Lemma unorm_invol d : unorm (unorm d) = unorm d.
+Proof.
+ unfold unorm.
+ destruct (nzhead d) eqn:E; trivial.
+ destruct (nzhead_nonzero _ _ E).
+Qed.
+
+Lemma norm_invol d : norm (norm d) = norm d.
+Proof.
+ unfold norm.
+ destruct d.
+ - f_equal. apply unorm_invol.
+ - destruct (nzhead d) eqn:E; auto.
+ destruct (nzhead_nonzero _ _ E).
+Qed.
diff --git a/theories/Numbers/DecimalN.v b/theories/Numbers/DecimalN.v
new file mode 100644
index 000000000..ef00e2805
--- /dev/null
+++ b/theories/Numbers/DecimalN.v
@@ -0,0 +1,107 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(** * DecimalN
+
+ Proofs that conversions between decimal numbers and [N]
+ are bijections *)
+
+Require Import Decimal DecimalFacts DecimalPos PArith NArith.
+
+Module Unsigned.
+
+Lemma of_to (n:N) : N.of_uint (N.to_uint n) = n.
+Proof.
+ destruct n.
+ - reflexivity.
+ - apply DecimalPos.Unsigned.of_to.
+Qed.
+
+Lemma to_of (d:uint) : N.to_uint (N.of_uint d) = unorm d.
+Proof.
+ exact (DecimalPos.Unsigned.to_of d).
+Qed.
+
+Lemma to_uint_inj n n' : N.to_uint n = N.to_uint n' -> n = n'.
+Proof.
+ intros E. now rewrite <- (of_to n), <- (of_to n'), E.
+Qed.
+
+Lemma to_uint_surj d : exists p, N.to_uint p = unorm d.
+Proof.
+ exists (N.of_uint d). apply to_of.
+Qed.
+
+Lemma of_uint_norm d : N.of_uint (unorm d) = N.of_uint d.
+Proof.
+ now induction d.
+Qed.
+
+Lemma of_inj d d' :
+ N.of_uint d = N.of_uint d' -> unorm d = unorm d'.
+Proof.
+ intros. rewrite <- !to_of. now f_equal.
+Qed.
+
+Lemma of_iff d d' : N.of_uint d = N.of_uint d' <-> unorm d = unorm d'.
+Proof.
+ split. apply of_inj. intros E. rewrite <- of_uint_norm, E.
+ apply of_uint_norm.
+Qed.
+
+End Unsigned.
+
+(** Conversion from/to signed decimal numbers *)
+
+Module Signed.
+
+Lemma of_to (n:N) : N.of_int (N.to_int n) = Some n.
+Proof.
+ unfold N.to_int, N.of_int, norm. f_equal.
+ rewrite Unsigned.of_uint_norm. apply Unsigned.of_to.
+Qed.
+
+Lemma to_of (d:int)(n:N) : N.of_int d = Some n -> N.to_int n = norm d.
+Proof.
+ unfold N.of_int.
+ destruct (norm d) eqn:Hd; intros [= <-].
+ unfold N.to_int. rewrite Unsigned.to_of. f_equal.
+ revert Hd; destruct d; simpl.
+ - intros [= <-]. apply unorm_invol.
+ - destruct (nzhead d); now intros [= <-].
+Qed.
+
+Lemma to_int_inj n n' : N.to_int n = N.to_int n' -> n = n'.
+Proof.
+ intro E.
+ assert (E' : Some n = Some n').
+ { now rewrite <- (of_to n), <- (of_to n'), E. }
+ now injection E'.
+Qed.
+
+Lemma to_int_pos_surj d : exists n, N.to_int n = norm (Pos d).
+Proof.
+ exists (N.of_uint d). unfold N.to_int. now rewrite Unsigned.to_of.
+Qed.
+
+Lemma of_int_norm d : N.of_int (norm d) = N.of_int d.
+Proof.
+ unfold N.of_int. now rewrite norm_invol.
+Qed.
+
+Lemma of_inj_pos d d' :
+ N.of_int (Pos d) = N.of_int (Pos d') -> unorm d = unorm d'.
+Proof.
+ unfold N.of_int. simpl. intros [= H]. apply Unsigned.of_inj.
+ change Pos.of_uint with N.of_uint in H.
+ now rewrite <- Unsigned.of_uint_norm, H, Unsigned.of_uint_norm.
+Qed.
+
+End Signed.
diff --git a/theories/Numbers/DecimalNat.v b/theories/Numbers/DecimalNat.v
new file mode 100644
index 000000000..5ffe1688b
--- /dev/null
+++ b/theories/Numbers/DecimalNat.v
@@ -0,0 +1,302 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(** * DecimalNat
+
+ Proofs that conversions between decimal numbers and [nat]
+ are bijections. *)
+
+Require Import Decimal DecimalFacts Arith.
+
+Module Unsigned.
+
+(** A few helper functions used during proofs *)
+
+Definition hd d :=
+ match d with
+ | Nil => 0
+ | D0 _ => 0
+ | D1 _ => 1
+ | D2 _ => 2
+ | D3 _ => 3
+ | D4 _ => 4
+ | D5 _ => 5
+ | D6 _ => 6
+ | D7 _ => 7
+ | D8 _ => 8
+ | D9 _ => 9
+end.
+
+Definition tl d :=
+ match d with
+ | Nil => d
+ | D0 d | D1 d | D2 d | D3 d | D4 d | D5 d | D6 d | D7 d | D8 d | D9 d => d
+end.
+
+Fixpoint usize (d:uint) : nat :=
+ match d with
+ | Nil => 0
+ | D0 d => S (usize d)
+ | D1 d => S (usize d)
+ | D2 d => S (usize d)
+ | D3 d => S (usize d)
+ | D4 d => S (usize d)
+ | D5 d => S (usize d)
+ | D6 d => S (usize d)
+ | D7 d => S (usize d)
+ | D8 d => S (usize d)
+ | D9 d => S (usize d)
+ end.
+
+(** A direct version of [to_little_uint], not tail-recursive *)
+Fixpoint to_lu n :=
+ match n with
+ | 0 => Decimal.zero
+ | S n => Little.succ (to_lu n)
+ end.
+
+(** A direct version of [of_little_uint] *)
+Fixpoint of_lu (d:uint) : nat :=
+ match d with
+ | Nil => 0
+ | D0 d => 10 * of_lu d
+ | D1 d => 1 + 10 * of_lu d
+ | D2 d => 2 + 10 * of_lu d
+ | D3 d => 3 + 10 * of_lu d
+ | D4 d => 4 + 10 * of_lu d
+ | D5 d => 5 + 10 * of_lu d
+ | D6 d => 6 + 10 * of_lu d
+ | D7 d => 7 + 10 * of_lu d
+ | D8 d => 8 + 10 * of_lu d
+ | D9 d => 9 + 10 * of_lu d
+ end.
+
+(** Properties of [to_lu] *)
+
+Lemma to_lu_succ n : to_lu (S n) = Little.succ (to_lu n).
+Proof.
+ reflexivity.
+Qed.
+
+Lemma to_little_uint_succ n d :
+ Nat.to_little_uint n (Little.succ d) =
+ Little.succ (Nat.to_little_uint n d).
+Proof.
+ revert d; induction n; simpl; trivial.
+Qed.
+
+Lemma to_lu_equiv n :
+ to_lu n = Nat.to_little_uint n zero.
+Proof.
+ induction n; simpl; trivial.
+ now rewrite IHn, <- to_little_uint_succ.
+Qed.
+
+Lemma to_uint_alt n :
+ Nat.to_uint n = rev (to_lu n).
+Proof.
+ unfold Nat.to_uint. f_equal. symmetry. apply to_lu_equiv.
+Qed.
+
+(** Properties of [of_lu] *)
+
+Lemma of_lu_eqn d :
+ of_lu d = hd d + 10 * of_lu (tl d).
+Proof.
+ induction d; simpl; trivial.
+Qed.
+
+Ltac simpl_of_lu :=
+ match goal with
+ | |- context [ of_lu (?f ?x) ] =>
+ rewrite (of_lu_eqn (f x)); simpl hd; simpl tl
+ end.
+
+Lemma of_lu_succ d :
+ of_lu (Little.succ d) = S (of_lu d).
+Proof.
+ induction d; trivial.
+ simpl_of_lu. rewrite IHd. simpl_of_lu.
+ now rewrite Nat.mul_succ_r, <- (Nat.add_comm 10).
+Qed.
+
+Lemma of_to_lu n :
+ of_lu (to_lu n) = n.
+Proof.
+ induction n; simpl; trivial. rewrite of_lu_succ. now f_equal.
+Qed.
+
+Lemma of_lu_revapp d d' :
+of_lu (revapp d d') =
+ of_lu (rev d) + of_lu d' * 10^usize d.
+Proof.
+ revert d'.
+ induction d; intro d'; simpl usize;
+ [ simpl; now rewrite Nat.mul_1_r | .. ];
+ unfold rev; simpl revapp; rewrite 2 IHd;
+ rewrite <- Nat.add_assoc; f_equal; simpl_of_lu; simpl of_lu;
+ rewrite Nat.pow_succ_r'; ring.
+Qed.
+
+Lemma of_uint_acc_spec n d :
+ Nat.of_uint_acc d n = of_lu (rev d) + n * 10^usize d.
+Proof.
+ revert n. induction d; intros;
+ simpl Nat.of_uint_acc; rewrite ?Nat.tail_mul_spec, ?IHd;
+ simpl rev; simpl usize; rewrite ?Nat.pow_succ_r';
+ [ simpl; now rewrite Nat.mul_1_r | .. ];
+ unfold rev at 2; simpl revapp; rewrite of_lu_revapp;
+ simpl of_lu; ring.
+Qed.
+
+Lemma of_uint_alt d : Nat.of_uint d = of_lu (rev d).
+Proof.
+ unfold Nat.of_uint. now rewrite of_uint_acc_spec.
+Qed.
+
+(** First main bijection result *)
+
+Lemma of_to (n:nat) : Nat.of_uint (Nat.to_uint n) = n.
+Proof.
+ rewrite to_uint_alt, of_uint_alt, rev_rev. apply of_to_lu.
+Qed.
+
+(** The other direction *)
+
+Lemma to_lu_tenfold n : n<>0 ->
+ to_lu (10 * n) = D0 (to_lu n).
+Proof.
+ induction n.
+ - simpl. now destruct 1.
+ - intros _.
+ destruct (Nat.eq_dec n 0) as [->|H]; simpl; trivial.
+ rewrite !Nat.add_succ_r.
+ simpl in *. rewrite (IHn H). now destruct (to_lu n).
+Qed.
+
+Lemma of_lu_0 d : of_lu d = 0 <-> nztail d = Nil.
+Proof.
+ induction d; try simpl_of_lu; try easy.
+ rewrite Nat.add_0_l.
+ split; intros H.
+ - apply Nat.eq_mul_0_r in H; auto.
+ rewrite IHd in H. simpl. now rewrite H.
+ - simpl in H. destruct (nztail d); try discriminate.
+ now destruct IHd as [_ ->].
+Qed.
+
+Lemma to_of_lu_tenfold d :
+ to_lu (of_lu d) = lnorm d ->
+ to_lu (10 * of_lu d) = lnorm (D0 d).
+Proof.
+ intro IH.
+ destruct (Nat.eq_dec (of_lu d) 0) as [H|H].
+ - rewrite H. simpl. rewrite of_lu_0 in H.
+ unfold lnorm. simpl. now rewrite H.
+ - rewrite (to_lu_tenfold _ H), IH.
+ rewrite of_lu_0 in H.
+ unfold lnorm. simpl. now destruct (nztail d).
+Qed.
+
+Lemma to_of_lu d : to_lu (of_lu d) = lnorm d.
+Proof.
+ induction d; [ reflexivity | .. ];
+ simpl_of_lu;
+ rewrite ?Nat.add_succ_l, Nat.add_0_l, ?to_lu_succ, to_of_lu_tenfold
+ by assumption;
+ unfold lnorm; simpl; now destruct nztail.
+Qed.
+
+(** Second bijection result *)
+
+Lemma to_of (d:uint) : Nat.to_uint (Nat.of_uint d) = unorm d.
+Proof.
+ rewrite to_uint_alt, of_uint_alt, to_of_lu.
+ apply rev_lnorm_rev.
+Qed.
+
+(** Some consequences *)
+
+Lemma to_uint_inj n n' : Nat.to_uint n = Nat.to_uint n' -> n = n'.
+Proof.
+ intro EQ.
+ now rewrite <- (of_to n), <- (of_to n'), EQ.
+Qed.
+
+Lemma to_uint_surj d : exists n, Nat.to_uint n = unorm d.
+Proof.
+ exists (Nat.of_uint d). apply to_of.
+Qed.
+
+Lemma of_uint_norm d : Nat.of_uint (unorm d) = Nat.of_uint d.
+Proof.
+ unfold Nat.of_uint. now induction d.
+Qed.
+
+Lemma of_inj d d' :
+ Nat.of_uint d = Nat.of_uint d' -> unorm d = unorm d'.
+Proof.
+ intros. rewrite <- !to_of. now f_equal.
+Qed.
+
+Lemma of_iff d d' : Nat.of_uint d = Nat.of_uint d' <-> unorm d = unorm d'.
+Proof.
+ split. apply of_inj. intros E. rewrite <- of_uint_norm, E.
+ apply of_uint_norm.
+Qed.
+
+End Unsigned.
+
+(** Conversion from/to signed decimal numbers *)
+
+Module Signed.
+
+Lemma of_to (n:nat) : Nat.of_int (Nat.to_int n) = Some n.
+Proof.
+ unfold Nat.to_int, Nat.of_int, norm. f_equal.
+ rewrite Unsigned.of_uint_norm. apply Unsigned.of_to.
+Qed.
+
+Lemma to_of (d:int)(n:nat) : Nat.of_int d = Some n -> Nat.to_int n = norm d.
+Proof.
+ unfold Nat.of_int.
+ destruct (norm d) eqn:Hd; intros [= <-].
+ unfold Nat.to_int. rewrite Unsigned.to_of. f_equal.
+ revert Hd; destruct d; simpl.
+ - intros [= <-]. apply unorm_invol.
+ - destruct (nzhead d); now intros [= <-].
+Qed.
+
+Lemma to_int_inj n n' : Nat.to_int n = Nat.to_int n' -> n = n'.
+Proof.
+ intro E.
+ assert (E' : Some n = Some n').
+ { now rewrite <- (of_to n), <- (of_to n'), E. }
+ now injection E'.
+Qed.
+
+Lemma to_int_pos_surj d : exists n, Nat.to_int n = norm (Pos d).
+Proof.
+ exists (Nat.of_uint d). unfold Nat.to_int. now rewrite Unsigned.to_of.
+Qed.
+
+Lemma of_int_norm d : Nat.of_int (norm d) = Nat.of_int d.
+Proof.
+ unfold Nat.of_int. now rewrite norm_invol.
+Qed.
+
+Lemma of_inj_pos d d' :
+ Nat.of_int (Pos d) = Nat.of_int (Pos d') -> unorm d = unorm d'.
+Proof.
+ unfold Nat.of_int. simpl. intros [= H]. apply Unsigned.of_inj.
+ now rewrite <- Unsigned.of_uint_norm, H, Unsigned.of_uint_norm.
+Qed.
+
+End Signed.
diff --git a/theories/Numbers/DecimalPos.v b/theories/Numbers/DecimalPos.v
new file mode 100644
index 000000000..722e73d96
--- /dev/null
+++ b/theories/Numbers/DecimalPos.v
@@ -0,0 +1,383 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(** * DecimalPos
+
+ Proofs that conversions between decimal numbers and [positive]
+ are bijections. *)
+
+Require Import Decimal DecimalFacts PArith NArith.
+
+Module Unsigned.
+
+Local Open Scope N.
+
+(** A direct version of [of_little_uint] *)
+Fixpoint of_lu (d:uint) : N :=
+ match d with
+ | Nil => 0
+ | D0 d => 10 * of_lu d
+ | D1 d => 1 + 10 * of_lu d
+ | D2 d => 2 + 10 * of_lu d
+ | D3 d => 3 + 10 * of_lu d
+ | D4 d => 4 + 10 * of_lu d
+ | D5 d => 5 + 10 * of_lu d
+ | D6 d => 6 + 10 * of_lu d
+ | D7 d => 7 + 10 * of_lu d
+ | D8 d => 8 + 10 * of_lu d
+ | D9 d => 9 + 10 * of_lu d
+ end.
+
+Definition hd d :=
+match d with
+ | Nil => 0
+ | D0 _ => 0
+ | D1 _ => 1
+ | D2 _ => 2
+ | D3 _ => 3
+ | D4 _ => 4
+ | D5 _ => 5
+ | D6 _ => 6
+ | D7 _ => 7
+ | D8 _ => 8
+ | D9 _ => 9
+end.
+
+Definition tl d :=
+ match d with
+ | Nil => d
+ | D0 d | D1 d | D2 d | D3 d | D4 d | D5 d | D6 d | D7 d | D8 d | D9 d => d
+end.
+
+Lemma of_lu_eqn d :
+ of_lu d = hd d + 10 * (of_lu (tl d)).
+Proof.
+ induction d; simpl; trivial.
+Qed.
+
+Ltac simpl_of_lu :=
+ match goal with
+ | |- context [ of_lu (?f ?x) ] =>
+ rewrite (of_lu_eqn (f x)); simpl hd; simpl tl
+ end.
+
+Fixpoint usize (d:uint) : N :=
+ match d with
+ | Nil => 0
+ | D0 d => N.succ (usize d)
+ | D1 d => N.succ (usize d)
+ | D2 d => N.succ (usize d)
+ | D3 d => N.succ (usize d)
+ | D4 d => N.succ (usize d)
+ | D5 d => N.succ (usize d)
+ | D6 d => N.succ (usize d)
+ | D7 d => N.succ (usize d)
+ | D8 d => N.succ (usize d)
+ | D9 d => N.succ (usize d)
+ end.
+
+Lemma of_lu_revapp d d' :
+ of_lu (revapp d d') =
+ of_lu (rev d) + of_lu d' * 10^usize d.
+Proof.
+ revert d'.
+ induction d; simpl; intro d'; [ now rewrite N.mul_1_r | .. ];
+ unfold rev; simpl revapp; rewrite 2 IHd;
+ rewrite <- N.add_assoc; f_equal; simpl_of_lu; simpl of_lu;
+ rewrite N.pow_succ_r'; ring.
+Qed.
+
+Definition Nadd n p :=
+ match n with
+ | N0 => p
+ | Npos p0 => (p0+p)%positive
+ end.
+
+Lemma Nadd_simpl n p q : Npos (Nadd n (p * q)) = n + Npos p * Npos q.
+Proof.
+ now destruct n.
+Qed.
+
+Lemma of_uint_acc_eqn d acc : d<>Nil ->
+ Pos.of_uint_acc d acc = Pos.of_uint_acc (tl d) (Nadd (hd d) (10*acc)).
+Proof.
+ destruct d; simpl; trivial. now destruct 1.
+Qed.
+
+Lemma of_uint_acc_rev d acc :
+ Npos (Pos.of_uint_acc d acc) =
+ of_lu (rev d) + (Npos acc) * 10^usize d.
+Proof.
+ revert acc.
+ induction d; intros; simpl usize;
+ [ simpl; now rewrite Pos.mul_1_r | .. ];
+ rewrite N.pow_succ_r';
+ unfold rev; simpl revapp; try rewrite of_lu_revapp; simpl of_lu;
+ rewrite of_uint_acc_eqn by easy; simpl tl; simpl hd;
+ rewrite IHd, Nadd_simpl; ring.
+Qed.
+
+Lemma of_uint_alt d : Pos.of_uint d = of_lu (rev d).
+Proof.
+ induction d; simpl; trivial; unfold rev; simpl revapp;
+ rewrite of_lu_revapp; simpl of_lu; try apply of_uint_acc_rev.
+ rewrite IHd. ring.
+Qed.
+
+Lemma of_lu_rev d : Pos.of_uint (rev d) = of_lu d.
+Proof.
+ rewrite of_uint_alt. now rewrite rev_rev.
+Qed.
+
+Lemma of_lu_double_gen d :
+ of_lu (Little.double d) = N.double (of_lu d) /\
+ of_lu (Little.succ_double d) = N.succ_double (of_lu d).
+Proof.
+ rewrite N.double_spec, N.succ_double_spec.
+ induction d; try destruct IHd as (IH1,IH2);
+ simpl Little.double; simpl Little.succ_double;
+ repeat (simpl_of_lu; rewrite ?IH1, ?IH2); split; reflexivity || ring.
+Qed.
+
+Lemma of_lu_double d :
+ of_lu (Little.double d) = N.double (of_lu d).
+Proof.
+ apply of_lu_double_gen.
+Qed.
+
+Lemma of_lu_succ_double d :
+ of_lu (Little.succ_double d) = N.succ_double (of_lu d).
+Proof.
+ apply of_lu_double_gen.
+Qed.
+
+(** First bijection result *)
+
+Lemma of_to (p:positive) : Pos.of_uint (Pos.to_uint p) = Npos p.
+Proof.
+ unfold Pos.to_uint.
+ rewrite of_lu_rev.
+ induction p; simpl; trivial.
+ - now rewrite of_lu_succ_double, IHp.
+ - now rewrite of_lu_double, IHp.
+Qed.
+
+(** The other direction *)
+
+Definition to_lu n :=
+ match n with
+ | N0 => Decimal.zero
+ | Npos p => Pos.to_little_uint p
+ end.
+
+Lemma succ_double_alt d :
+ Little.succ_double d = Little.succ (Little.double d).
+Proof.
+ now induction d.
+Qed.
+
+Lemma double_succ d :
+ Little.double (Little.succ d) =
+ Little.succ (Little.succ_double d).
+Proof.
+ induction d; simpl; f_equal; auto using succ_double_alt.
+Qed.
+
+Lemma to_lu_succ n :
+ to_lu (N.succ n) = Little.succ (to_lu n).
+Proof.
+ destruct n; simpl; trivial.
+ induction p; simpl; rewrite ?IHp;
+ auto using succ_double_alt, double_succ.
+Qed.
+
+Lemma nat_iter_S n {A} (f:A->A) i :
+ Nat.iter (S n) f i = f (Nat.iter n f i).
+Proof.
+ reflexivity.
+Qed.
+
+Lemma nat_iter_0 {A} (f:A->A) i : Nat.iter 0 f i = i.
+Proof.
+ reflexivity.
+Qed.
+
+Lemma to_ldec_tenfold p :
+ to_lu (10 * Npos p) = D0 (to_lu (Npos p)).
+Proof.
+ induction p using Pos.peano_rect.
+ - trivial.
+ - change (N.pos (Pos.succ p)) with (N.succ (N.pos p)).
+ rewrite N.mul_succ_r.
+ change 10 at 2 with (Nat.iter 10%nat N.succ 0).
+ rewrite ?nat_iter_S, nat_iter_0.
+ rewrite !N.add_succ_r, N.add_0_r, !to_lu_succ, IHp.
+ destruct (to_lu (N.pos p)); simpl; auto.
+Qed.
+
+Lemma of_lu_0 d : of_lu d = 0 <-> nztail d = Nil.
+Proof.
+ induction d; try simpl_of_lu; split; trivial; try discriminate;
+ try (intros H; now apply N.eq_add_0 in H).
+ - rewrite N.add_0_l. intros H.
+ apply N.eq_mul_0_r in H; [|easy]. rewrite IHd in H.
+ simpl. now rewrite H.
+ - simpl. destruct (nztail d); try discriminate.
+ now destruct IHd as [_ ->].
+Qed.
+
+Lemma to_of_lu_tenfold d :
+ to_lu (of_lu d) = lnorm d ->
+ to_lu (10 * of_lu d) = lnorm (D0 d).
+Proof.
+ intro IH.
+ destruct (N.eq_dec (of_lu d) 0) as [H|H].
+ - rewrite H. simpl. rewrite of_lu_0 in H.
+ unfold lnorm. simpl. now rewrite H.
+ - destruct (of_lu d) eqn:Eq; [easy| ].
+ rewrite to_ldec_tenfold; auto. rewrite IH.
+ rewrite <- Eq in H. rewrite of_lu_0 in H.
+ unfold lnorm. simpl. now destruct (nztail d).
+Qed.
+
+Lemma Nadd_alt n m : n + m = Nat.iter (N.to_nat n) N.succ m.
+Proof.
+ destruct n. trivial.
+ induction p using Pos.peano_rect.
+ - now rewrite N.add_1_l.
+ - change (N.pos (Pos.succ p)) with (N.succ (N.pos p)).
+ now rewrite N.add_succ_l, IHp, N2Nat.inj_succ.
+Qed.
+
+Ltac simpl_to_nat := simpl N.to_nat; unfold Pos.to_nat; simpl Pos.iter_op.
+
+Lemma to_of_lu d : to_lu (of_lu d) = lnorm d.
+Proof.
+ induction d; [reflexivity|..];
+ simpl_of_lu; rewrite Nadd_alt; simpl_to_nat;
+ rewrite ?nat_iter_S, nat_iter_0, ?to_lu_succ, to_of_lu_tenfold by assumption;
+ unfold lnorm; simpl; destruct nztail; auto.
+Qed.
+
+(** Second bijection result *)
+
+Lemma to_of (d:uint) : N.to_uint (Pos.of_uint d) = unorm d.
+Proof.
+ rewrite of_uint_alt.
+ unfold N.to_uint, Pos.to_uint.
+ destruct (of_lu (rev d)) eqn:H.
+ - rewrite of_lu_0 in H. rewrite <- rev_lnorm_rev.
+ unfold lnorm. now rewrite H.
+ - change (Pos.to_little_uint p) with (to_lu (N.pos p)).
+ rewrite <- H. rewrite to_of_lu. apply rev_lnorm_rev.
+Qed.
+
+(** Some consequences *)
+
+Lemma to_uint_nonzero p : Pos.to_uint p <> zero.
+Proof.
+ intro E. generalize (of_to p). now rewrite E.
+Qed.
+
+Lemma to_uint_nonnil p : Pos.to_uint p <> Nil.
+Proof.
+ intros E. generalize (of_to p). now rewrite E.
+Qed.
+
+Lemma to_uint_inj p p' : Pos.to_uint p = Pos.to_uint p' -> p = p'.
+Proof.
+ intro E.
+ assert (E' : N.pos p = N.pos p').
+ { now rewrite <- (of_to p), <- (of_to p'), E. }
+ now injection E'.
+Qed.
+
+Lemma to_uint_pos_surj d :
+ unorm d<>zero -> exists p, Pos.to_uint p = unorm d.
+Proof.
+ intros.
+ destruct (Pos.of_uint d) eqn:E.
+ - destruct H. generalize (to_of d). now rewrite E.
+ - exists p. generalize (to_of d). now rewrite E.
+Qed.
+
+Lemma of_uint_norm d : Pos.of_uint (unorm d) = Pos.of_uint d.
+Proof.
+ now induction d.
+Qed.
+
+Lemma of_inj d d' :
+ Pos.of_uint d = Pos.of_uint d' -> unorm d = unorm d'.
+Proof.
+ intros. rewrite <- !to_of. now f_equal.
+Qed.
+
+Lemma of_iff d d' : Pos.of_uint d = Pos.of_uint d' <-> unorm d = unorm d'.
+Proof.
+ split. apply of_inj. intros E. rewrite <- of_uint_norm, E.
+ apply of_uint_norm.
+Qed.
+
+End Unsigned.
+
+(** Conversion from/to signed decimal numbers *)
+
+Module Signed.
+
+Lemma of_to (p:positive) : Pos.of_int (Pos.to_int p) = Some p.
+Proof.
+ unfold Pos.to_int, Pos.of_int, norm.
+ now rewrite Unsigned.of_to.
+Qed.
+
+Lemma to_of (d:int)(p:positive) :
+ Pos.of_int d = Some p -> Pos.to_int p = norm d.
+Proof.
+ unfold Pos.of_int.
+ destruct d; [ | intros [=]].
+ simpl norm. rewrite <- Unsigned.to_of.
+ destruct (Pos.of_uint d); now intros [= <-].
+Qed.
+
+Lemma to_int_inj p p' : Pos.to_int p = Pos.to_int p' -> p = p'.
+Proof.
+ intro E.
+ assert (E' : Some p = Some p').
+ { now rewrite <- (of_to p), <- (of_to p'), E. }
+ now injection E'.
+Qed.
+
+Lemma to_int_pos_surj d :
+ unorm d <> zero -> exists p, Pos.to_int p = norm (Pos d).
+Proof.
+ simpl. unfold Pos.to_int. intros H.
+ destruct (Unsigned.to_uint_pos_surj d H) as (p,Hp).
+ exists p. now f_equal.
+Qed.
+
+Lemma of_int_norm d : Pos.of_int (norm d) = Pos.of_int d.
+Proof.
+ unfold Pos.of_int.
+ destruct d.
+ - simpl. now rewrite Unsigned.of_uint_norm.
+ - simpl. now destruct (nzhead d) eqn:H.
+Qed.
+
+Lemma of_inj_pos d d' :
+ Pos.of_int (Pos d) = Pos.of_int (Pos d') -> unorm d = unorm d'.
+Proof.
+ unfold Pos.of_int.
+ destruct (Pos.of_uint d) eqn:Hd, (Pos.of_uint d') eqn:Hd';
+ intros [=].
+ - apply Unsigned.of_inj; now rewrite Hd, Hd'.
+ - apply Unsigned.of_inj; rewrite Hd, Hd'; now f_equal.
+Qed.
+
+End Signed.
diff --git a/theories/Numbers/DecimalString.v b/theories/Numbers/DecimalString.v
new file mode 100644
index 000000000..1a3220f63
--- /dev/null
+++ b/theories/Numbers/DecimalString.v
@@ -0,0 +1,265 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+Require Import Decimal Ascii String.
+
+(** * Conversion between decimal numbers and Coq strings *)
+
+(** Pretty straightforward, which is precisely the point of the
+ [Decimal.int] datatype. The only catch is [Decimal.Nil] : we could
+ choose to convert it as [""] or as ["0"]. In the first case, it is
+ awkward to consider "" (or "-") as a number, while in the second case
+ we don't have a perfect bijection. Since the second variant is implemented
+ thanks to the first one, we provide both. *)
+
+Local Open Scope string_scope.
+
+(** Parsing one char *)
+
+Definition uint_of_char (a:ascii)(d:option uint) :=
+ match d with
+ | None => None
+ | Some d =>
+ match a with
+ | "0" => Some (D0 d)
+ | "1" => Some (D1 d)
+ | "2" => Some (D2 d)
+ | "3" => Some (D3 d)
+ | "4" => Some (D4 d)
+ | "5" => Some (D5 d)
+ | "6" => Some (D6 d)
+ | "7" => Some (D7 d)
+ | "8" => Some (D8 d)
+ | "9" => Some (D9 d)
+ | _ => None
+ end
+ end%char.
+
+Lemma uint_of_char_spec c d d' :
+ uint_of_char c (Some d) = Some d' ->
+ (c = "0" /\ d' = D0 d \/
+ c = "1" /\ d' = D1 d \/
+ c = "2" /\ d' = D2 d \/
+ c = "3" /\ d' = D3 d \/
+ c = "4" /\ d' = D4 d \/
+ c = "5" /\ d' = D5 d \/
+ c = "6" /\ d' = D6 d \/
+ c = "7" /\ d' = D7 d \/
+ c = "8" /\ d' = D8 d \/
+ c = "9" /\ d' = D9 d)%char.
+Proof.
+ destruct c as [[|] [|] [|] [|] [|] [|] [|] [|]];
+ intros [= <-]; intuition.
+Qed.
+
+(** Decimal/String conversion where [Nil] is [""] *)
+
+Module NilEmpty.
+
+Fixpoint string_of_uint (d:uint) :=
+ match d with
+ | Nil => EmptyString
+ | D0 d => String "0" (string_of_uint d)
+ | D1 d => String "1" (string_of_uint d)
+ | D2 d => String "2" (string_of_uint d)
+ | D3 d => String "3" (string_of_uint d)
+ | D4 d => String "4" (string_of_uint d)
+ | D5 d => String "5" (string_of_uint d)
+ | D6 d => String "6" (string_of_uint d)
+ | D7 d => String "7" (string_of_uint d)
+ | D8 d => String "8" (string_of_uint d)
+ | D9 d => String "9" (string_of_uint d)
+ end.
+
+Fixpoint uint_of_string s :=
+ match s with
+ | EmptyString => Some Nil
+ | String a s => uint_of_char a (uint_of_string s)
+ end.
+
+Definition string_of_int (d:int) :=
+ match d with
+ | Pos d => string_of_uint d
+ | Neg d => String "-" (string_of_uint d)
+ end.
+
+Definition int_of_string s :=
+ match s with
+ | EmptyString => Some (Pos Nil)
+ | String a s' =>
+ if ascii_dec a "-" then option_map Neg (uint_of_string s')
+ else option_map Pos (uint_of_string s)
+ end.
+
+(* NB: For the moment whitespace between - and digits are not accepted.
+ And in this variant [int_of_string "-" = Some (Neg Nil)].
+
+Compute int_of_string "-123456890123456890123456890123456890".
+Compute string_of_int (-123456890123456890123456890123456890).
+*)
+
+(** Corresponding proofs *)
+
+Lemma usu d :
+ uint_of_string (string_of_uint d) = Some d.
+Proof.
+ induction d; simpl; rewrite ?IHd; simpl; auto.
+Qed.
+
+Lemma sus s d :
+ uint_of_string s = Some d -> string_of_uint d = s.
+Proof.
+ revert d.
+ induction s; simpl.
+ - now intros d [= <-].
+ - intros d.
+ destruct (uint_of_string s); [intros H | intros [=]].
+ apply uint_of_char_spec in H.
+ intuition subst; simpl; f_equal; auto.
+Qed.
+
+Lemma isi d : int_of_string (string_of_int d) = Some d.
+Proof.
+ destruct d; simpl.
+ - unfold int_of_string.
+ destruct (string_of_uint d) eqn:Hd.
+ + now destruct d.
+ + destruct ascii_dec; subst.
+ * now destruct d.
+ * rewrite <- Hd, usu; auto.
+ - rewrite usu; auto.
+Qed.
+
+Lemma sis s d :
+ int_of_string s = Some d -> string_of_int d = s.
+Proof.
+ destruct s; [intros [= <-]| ]; simpl; trivial.
+ destruct ascii_dec; subst; simpl.
+ - destruct (uint_of_string s) eqn:Hs; simpl; intros [= <-].
+ simpl; f_equal. now apply sus.
+ - destruct d; [ | now destruct uint_of_char].
+ simpl string_of_int.
+ intros. apply sus; simpl.
+ destruct uint_of_char; simpl in *; congruence.
+Qed.
+
+End NilEmpty.
+
+(** Decimal/String conversions where [Nil] is ["0"] *)
+
+Module NilZero.
+
+Definition string_of_uint (d:uint) :=
+ match d with
+ | Nil => "0"
+ | _ => NilEmpty.string_of_uint d
+ end.
+
+Definition uint_of_string s :=
+ match s with
+ | EmptyString => None
+ | _ => NilEmpty.uint_of_string s
+ end.
+
+Definition string_of_int (d:int) :=
+ match d with
+ | Pos d => string_of_uint d
+ | Neg d => String "-" (string_of_uint d)
+ end.
+
+Definition int_of_string s :=
+ match s with
+ | EmptyString => None
+ | String a s' =>
+ if ascii_dec a "-" then option_map Neg (uint_of_string s')
+ else option_map Pos (uint_of_string s)
+ end.
+
+(** Corresponding proofs *)
+
+Lemma uint_of_string_nonnil s : uint_of_string s <> Some Nil.
+Proof.
+ destruct s; simpl.
+ - easy.
+ - destruct (NilEmpty.uint_of_string s); [intros H | intros [=]].
+ apply uint_of_char_spec in H.
+ now intuition subst.
+Qed.
+
+Lemma sus s d :
+ uint_of_string s = Some d -> string_of_uint d = s.
+Proof.
+ destruct s; [intros [=] | intros H].
+ apply NilEmpty.sus in H. now destruct d.
+Qed.
+
+Lemma usu d :
+ d<>Nil -> uint_of_string (string_of_uint d) = Some d.
+Proof.
+ destruct d; (now destruct 1) || (intros _; apply NilEmpty.usu).
+Qed.
+
+Lemma usu_nil :
+ uint_of_string (string_of_uint Nil) = Some Decimal.zero.
+Proof.
+ reflexivity.
+Qed.
+
+Lemma usu_gen d :
+ uint_of_string (string_of_uint d) = Some d \/
+ uint_of_string (string_of_uint d) = Some Decimal.zero.
+Proof.
+ destruct d; (now right) || (left; now apply usu).
+Qed.
+
+Lemma isi d :
+ d<>Pos Nil -> d<>Neg Nil ->
+ int_of_string (string_of_int d) = Some d.
+Proof.
+ destruct d; simpl.
+ - intros H _.
+ unfold int_of_string.
+ destruct (string_of_uint d) eqn:Hd.
+ + now destruct d.
+ + destruct ascii_dec; subst.
+ * now destruct d.
+ * rewrite <- Hd, usu; auto. now intros ->.
+ - intros _ H.
+ rewrite usu; auto. now intros ->.
+Qed.
+
+Lemma isi_posnil :
+ int_of_string (string_of_int (Pos Nil)) = Some (Pos Decimal.zero).
+Proof.
+ reflexivity.
+Qed.
+
+(** Warning! (-0) won't parse (compatibility with the behavior of Z). *)
+
+Lemma isi_negnil :
+ int_of_string (string_of_int (Neg Nil)) = Some (Neg (D0 Nil)).
+Proof.
+ reflexivity.
+Qed.
+
+Lemma sis s d :
+ int_of_string s = Some d -> string_of_int d = s.
+Proof.
+ destruct s; [intros [=]| ]; simpl.
+ destruct ascii_dec; subst; simpl.
+ - destruct (uint_of_string s) eqn:Hs; simpl; intros [= <-].
+ simpl; f_equal. now apply sus.
+ - destruct d; [ | now destruct uint_of_char].
+ simpl string_of_int.
+ intros. apply sus; simpl.
+ destruct uint_of_char; simpl in *; congruence.
+Qed.
+
+End NilZero.
diff --git a/theories/Numbers/DecimalZ.v b/theories/Numbers/DecimalZ.v
new file mode 100644
index 000000000..3a0837963
--- /dev/null
+++ b/theories/Numbers/DecimalZ.v
@@ -0,0 +1,75 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(** * DecimalZ
+
+ Proofs that conversions between decimal numbers and [Z]
+ are bijections. *)
+
+Require Import Decimal DecimalFacts DecimalPos DecimalN ZArith.
+
+Lemma of_to (z:Z) : Z.of_int (Z.to_int z) = z.
+Proof.
+ destruct z; simpl.
+ - trivial.
+ - unfold Z.of_uint. rewrite DecimalPos.Unsigned.of_to. now destruct p.
+ - unfold Z.of_uint. rewrite DecimalPos.Unsigned.of_to. destruct p; auto.
+Qed.
+
+Lemma to_of (d:int) : Z.to_int (Z.of_int d) = norm d.
+Proof.
+ destruct d; simpl; unfold Z.to_int, Z.of_uint.
+ - rewrite <- (DecimalN.Unsigned.to_of d). unfold N.of_uint.
+ now destruct (Pos.of_uint d).
+ - destruct (Pos.of_uint d) eqn:Hd; simpl; f_equal.
+ + generalize (DecimalPos.Unsigned.to_of d). rewrite Hd. simpl.
+ intros H. symmetry in H. apply unorm_0 in H. now rewrite H.
+ + assert (Hp := DecimalPos.Unsigned.to_of d). rewrite Hd in Hp. simpl in *.
+ rewrite Hp. unfold unorm in *.
+ destruct (nzhead d); trivial.
+ generalize (DecimalPos.Unsigned.of_to p). now rewrite Hp.
+Qed.
+
+(** Some consequences *)
+
+Lemma to_int_inj n n' : Z.to_int n = Z.to_int n' -> n = n'.
+Proof.
+ intro EQ.
+ now rewrite <- (of_to n), <- (of_to n'), EQ.
+Qed.
+
+Lemma to_int_surj d : exists n, Z.to_int n = norm d.
+Proof.
+ exists (Z.of_int d). apply to_of.
+Qed.
+
+Lemma of_int_norm d : Z.of_int (norm d) = Z.of_int d.
+Proof.
+ unfold Z.of_int, Z.of_uint.
+ destruct d.
+ - simpl. now rewrite DecimalPos.Unsigned.of_uint_norm.
+ - simpl. destruct (nzhead d) eqn:H;
+ [ induction d; simpl; auto; discriminate |
+ destruct (nzhead_nonzero _ _ H) | .. ];
+ f_equal; f_equal; apply DecimalPos.Unsigned.of_iff;
+ unfold unorm; now rewrite H.
+Qed.
+
+Lemma of_inj d d' :
+ Z.of_int d = Z.of_int d' -> norm d = norm d'.
+Proof.
+ intros. rewrite <- !to_of. now f_equal.
+Qed.
+
+Lemma of_iff d d' : Z.of_int d = Z.of_int d' <-> norm d = norm d'.
+Proof.
+ split. apply of_inj. intros E. rewrite <- of_int_norm, E.
+ apply of_int_norm.
+Qed.
diff --git a/theories/Numbers/Integer/Abstract/ZAdd.v b/theories/Numbers/Integer/Abstract/ZAdd.v
index 9d94ff65d..c4c5174da 100644
--- a/theories/Numbers/Integer/Abstract/ZAdd.v
+++ b/theories/Numbers/Integer/Abstract/ZAdd.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Integer/Abstract/ZAddOrder.v b/theories/Numbers/Integer/Abstract/ZAddOrder.v
index 84bb1a24a..7f5b0df68 100644
--- a/theories/Numbers/Integer/Abstract/ZAddOrder.v
+++ b/theories/Numbers/Integer/Abstract/ZAddOrder.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Integer/Abstract/ZAxioms.v b/theories/Numbers/Integer/Abstract/ZAxioms.v
index 6efb7ea23..4f1ab7752 100644
--- a/theories/Numbers/Integer/Abstract/ZAxioms.v
+++ b/theories/Numbers/Integer/Abstract/ZAxioms.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Integer/Abstract/ZBase.v b/theories/Numbers/Integer/Abstract/ZBase.v
index b2014135f..7fdd018d3 100644
--- a/theories/Numbers/Integer/Abstract/ZBase.v
+++ b/theories/Numbers/Integer/Abstract/ZBase.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Integer/Abstract/ZBits.v b/theories/Numbers/Integer/Abstract/ZBits.v
index 68d27fec9..2da445281 100644
--- a/theories/Numbers/Integer/Abstract/ZBits.v
+++ b/theories/Numbers/Integer/Abstract/ZBits.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import
diff --git a/theories/Numbers/Integer/Abstract/ZDivEucl.v b/theories/Numbers/Integer/Abstract/ZDivEucl.v
index 967b68d36..d7f25a661 100644
--- a/theories/Numbers/Integer/Abstract/ZDivEucl.v
+++ b/theories/Numbers/Integer/Abstract/ZDivEucl.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import ZAxioms ZMulOrder ZSgnAbs NZDiv.
diff --git a/theories/Numbers/Integer/Abstract/ZDivFloor.v b/theories/Numbers/Integer/Abstract/ZDivFloor.v
index a9077127e..a0d1821b6 100644
--- a/theories/Numbers/Integer/Abstract/ZDivFloor.v
+++ b/theories/Numbers/Integer/Abstract/ZDivFloor.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import ZAxioms ZMulOrder ZSgnAbs NZDiv.
diff --git a/theories/Numbers/Integer/Abstract/ZDivTrunc.v b/theories/Numbers/Integer/Abstract/ZDivTrunc.v
index bbb8ad5ae..31e427383 100644
--- a/theories/Numbers/Integer/Abstract/ZDivTrunc.v
+++ b/theories/Numbers/Integer/Abstract/ZDivTrunc.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import ZAxioms ZMulOrder ZSgnAbs NZDiv.
diff --git a/theories/Numbers/Integer/Abstract/ZGcd.v b/theories/Numbers/Integer/Abstract/ZGcd.v
index 1144bd2bf..f0b7bf9d2 100644
--- a/theories/Numbers/Integer/Abstract/ZGcd.v
+++ b/theories/Numbers/Integer/Abstract/ZGcd.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Properties of the greatest common divisor *)
diff --git a/theories/Numbers/Integer/Abstract/ZLcm.v b/theories/Numbers/Integer/Abstract/ZLcm.v
index 4b0f9f978..0ab528de8 100644
--- a/theories/Numbers/Integer/Abstract/ZLcm.v
+++ b/theories/Numbers/Integer/Abstract/ZLcm.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import ZAxioms ZMulOrder ZSgnAbs ZGcd ZDivTrunc ZDivFloor.
diff --git a/theories/Numbers/Integer/Abstract/ZLt.v b/theories/Numbers/Integer/Abstract/ZLt.v
index f43d74d70..726b041c2 100644
--- a/theories/Numbers/Integer/Abstract/ZLt.v
+++ b/theories/Numbers/Integer/Abstract/ZLt.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Integer/Abstract/ZMaxMin.v b/theories/Numbers/Integer/Abstract/ZMaxMin.v
index 40c3980a5..f3f3a861b 100644
--- a/theories/Numbers/Integer/Abstract/ZMaxMin.v
+++ b/theories/Numbers/Integer/Abstract/ZMaxMin.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import ZAxioms ZMulOrder GenericMinMax.
diff --git a/theories/Numbers/Integer/Abstract/ZMul.v b/theories/Numbers/Integer/Abstract/ZMul.v
index 2550ae1c5..120647dcc 100644
--- a/theories/Numbers/Integer/Abstract/ZMul.v
+++ b/theories/Numbers/Integer/Abstract/ZMul.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Integer/Abstract/ZMulOrder.v b/theories/Numbers/Integer/Abstract/ZMulOrder.v
index adea36f0e..cd9523d34 100644
--- a/theories/Numbers/Integer/Abstract/ZMulOrder.v
+++ b/theories/Numbers/Integer/Abstract/ZMulOrder.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Integer/Abstract/ZParity.v b/theories/Numbers/Integer/Abstract/ZParity.v
index db379474b..a5e53b361 100644
--- a/theories/Numbers/Integer/Abstract/ZParity.v
+++ b/theories/Numbers/Integer/Abstract/ZParity.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Bool ZMulOrder NZParity.
diff --git a/theories/Numbers/Integer/Abstract/ZPow.v b/theories/Numbers/Integer/Abstract/ZPow.v
index 478724e2e..a4b964e52 100644
--- a/theories/Numbers/Integer/Abstract/ZPow.v
+++ b/theories/Numbers/Integer/Abstract/ZPow.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Properties of the power function *)
diff --git a/theories/Numbers/Integer/Abstract/ZProperties.v b/theories/Numbers/Integer/Abstract/ZProperties.v
index 4a0ce5e5b..e4b997cfd 100644
--- a/theories/Numbers/Integer/Abstract/ZProperties.v
+++ b/theories/Numbers/Integer/Abstract/ZProperties.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export ZAxioms ZMaxMin ZSgnAbs ZParity ZPow ZDivTrunc ZDivFloor
diff --git a/theories/Numbers/Integer/Abstract/ZSgnAbs.v b/theories/Numbers/Integer/Abstract/ZSgnAbs.v
index b2f77c3f5..dda128726 100644
--- a/theories/Numbers/Integer/Abstract/ZSgnAbs.v
+++ b/theories/Numbers/Integer/Abstract/ZSgnAbs.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Properties of [abs] and [sgn] *)
diff --git a/theories/Numbers/Integer/Binary/ZBinary.v b/theories/Numbers/Integer/Binary/ZBinary.v
index 553bd68ac..bed827fd0 100644
--- a/theories/Numbers/Integer/Binary/ZBinary.v
+++ b/theories/Numbers/Integer/Binary/ZBinary.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Integer/NatPairs/ZNatPairs.v b/theories/Numbers/Integer/NatPairs/ZNatPairs.v
index c640145ba..4b2d5c13b 100644
--- a/theories/Numbers/Integer/NatPairs/ZNatPairs.v
+++ b/theories/Numbers/Integer/NatPairs/ZNatPairs.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/NaryFunctions.v b/theories/Numbers/NaryFunctions.v
index cf0d2e835..ee28628ed 100644
--- a/theories/Numbers/NaryFunctions.v
+++ b/theories/Numbers/NaryFunctions.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Pierre Letouzey, Jerome Vouillon, PPS, Paris 7, 2008 *)
(************************************************************************)
diff --git a/theories/Numbers/NatInt/NZAdd.v b/theories/Numbers/NatInt/NZAdd.v
index 4beab1e1b..bc366c508 100644
--- a/theories/Numbers/NatInt/NZAdd.v
+++ b/theories/Numbers/NatInt/NZAdd.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/NatInt/NZAddOrder.v b/theories/Numbers/NatInt/NZAddOrder.v
index 82e500ca2..99812ee3f 100644
--- a/theories/Numbers/NatInt/NZAddOrder.v
+++ b/theories/Numbers/NatInt/NZAddOrder.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/NatInt/NZAxioms.v b/theories/Numbers/NatInt/NZAxioms.v
index c0851791d..8c364cde7 100644
--- a/theories/Numbers/NatInt/NZAxioms.v
+++ b/theories/Numbers/NatInt/NZAxioms.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Initial Author : Evgeny Makarov, INRIA, 2007 *)
diff --git a/theories/Numbers/NatInt/NZBase.v b/theories/Numbers/NatInt/NZBase.v
index e0d55b893..595b2182a 100644
--- a/theories/Numbers/NatInt/NZBase.v
+++ b/theories/Numbers/NatInt/NZBase.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/NatInt/NZBits.v b/theories/Numbers/NatInt/NZBits.v
index d731de62d..eefa51572 100644
--- a/theories/Numbers/NatInt/NZBits.v
+++ b/theories/Numbers/NatInt/NZBits.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Bool NZAxioms NZMulOrder NZParity NZPow NZDiv NZLog.
diff --git a/theories/Numbers/NatInt/NZDiv.v b/theories/Numbers/NatInt/NZDiv.v
index 5610eccb7..550aa226a 100644
--- a/theories/Numbers/NatInt/NZDiv.v
+++ b/theories/Numbers/NatInt/NZDiv.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Euclidean Division *)
diff --git a/theories/Numbers/NatInt/NZDomain.v b/theories/Numbers/NatInt/NZDomain.v
index f5ee1351d..3d0c005fd 100644
--- a/theories/Numbers/NatInt/NZDomain.v
+++ b/theories/Numbers/NatInt/NZDomain.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export NumPrelude NZAxioms.
diff --git a/theories/Numbers/NatInt/NZGcd.v b/theories/Numbers/NatInt/NZGcd.v
index f8af97196..c38d1aac3 100644
--- a/theories/Numbers/NatInt/NZGcd.v
+++ b/theories/Numbers/NatInt/NZGcd.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Greatest Common Divisor *)
diff --git a/theories/Numbers/NatInt/NZLog.v b/theories/Numbers/NatInt/NZLog.v
index 239f20a42..794851a9d 100644
--- a/theories/Numbers/NatInt/NZLog.v
+++ b/theories/Numbers/NatInt/NZLog.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Base-2 Logarithm *)
diff --git a/theories/Numbers/NatInt/NZMul.v b/theories/Numbers/NatInt/NZMul.v
index 145f56352..44cbc5171 100644
--- a/theories/Numbers/NatInt/NZMul.v
+++ b/theories/Numbers/NatInt/NZMul.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/NatInt/NZMulOrder.v b/theories/Numbers/NatInt/NZMulOrder.v
index 430f8fd2e..292f0837c 100644
--- a/theories/Numbers/NatInt/NZMulOrder.v
+++ b/theories/Numbers/NatInt/NZMulOrder.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/NatInt/NZOrder.v b/theories/Numbers/NatInt/NZOrder.v
index 37ec46410..60e1123b3 100644
--- a/theories/Numbers/NatInt/NZOrder.v
+++ b/theories/Numbers/NatInt/NZOrder.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/NatInt/NZParity.v b/theories/Numbers/NatInt/NZParity.v
index 626d59d73..93d99f08f 100644
--- a/theories/Numbers/NatInt/NZParity.v
+++ b/theories/Numbers/NatInt/NZParity.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Bool NZAxioms NZMulOrder.
diff --git a/theories/Numbers/NatInt/NZPow.v b/theories/Numbers/NatInt/NZPow.v
index 350047fa1..a1310667e 100644
--- a/theories/Numbers/NatInt/NZPow.v
+++ b/theories/Numbers/NatInt/NZPow.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Power Function *)
diff --git a/theories/Numbers/NatInt/NZProperties.v b/theories/Numbers/NatInt/NZProperties.v
index aee3b6245..fbcf43e88 100644
--- a/theories/Numbers/NatInt/NZProperties.v
+++ b/theories/Numbers/NatInt/NZProperties.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/NatInt/NZSqrt.v b/theories/Numbers/NatInt/NZSqrt.v
index c03107299..c2d2c4ae1 100644
--- a/theories/Numbers/NatInt/NZSqrt.v
+++ b/theories/Numbers/NatInt/NZSqrt.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Square Root Function *)
diff --git a/theories/Numbers/Natural/Abstract/NAdd.v b/theories/Numbers/Natural/Abstract/NAdd.v
index 899fa3933..dc5f8e537 100644
--- a/theories/Numbers/Natural/Abstract/NAdd.v
+++ b/theories/Numbers/Natural/Abstract/NAdd.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Natural/Abstract/NAddOrder.v b/theories/Numbers/Natural/Abstract/NAddOrder.v
index d62903db6..2da3f0bfc 100644
--- a/theories/Numbers/Natural/Abstract/NAddOrder.v
+++ b/theories/Numbers/Natural/Abstract/NAddOrder.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Natural/Abstract/NAxioms.v b/theories/Numbers/Natural/Abstract/NAxioms.v
index d67689dbd..dd09ac5f3 100644
--- a/theories/Numbers/Natural/Abstract/NAxioms.v
+++ b/theories/Numbers/Natural/Abstract/NAxioms.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Natural/Abstract/NBase.v b/theories/Numbers/Natural/Abstract/NBase.v
index 85a015cf2..ad0b3d3d2 100644
--- a/theories/Numbers/Natural/Abstract/NBase.v
+++ b/theories/Numbers/Natural/Abstract/NBase.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Natural/Abstract/NBits.v b/theories/Numbers/Natural/Abstract/NBits.v
index 1e7644eda..e1391f599 100644
--- a/theories/Numbers/Natural/Abstract/NBits.v
+++ b/theories/Numbers/Natural/Abstract/NBits.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Bool NAxioms NSub NPow NDiv NParity NLog.
diff --git a/theories/Numbers/Natural/Abstract/NDefOps.v b/theories/Numbers/Natural/Abstract/NDefOps.v
index e934eda9b..8e1be0d70 100644
--- a/theories/Numbers/Natural/Abstract/NDefOps.v
+++ b/theories/Numbers/Natural/Abstract/NDefOps.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Natural/Abstract/NDiv.v b/theories/Numbers/Natural/Abstract/NDiv.v
index eff27abc5..4c26a071f 100644
--- a/theories/Numbers/Natural/Abstract/NDiv.v
+++ b/theories/Numbers/Natural/Abstract/NDiv.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import NAxioms NSub NZDiv.
diff --git a/theories/Numbers/Natural/Abstract/NGcd.v b/theories/Numbers/Natural/Abstract/NGcd.v
index 943caef63..96fb4247c 100644
--- a/theories/Numbers/Natural/Abstract/NGcd.v
+++ b/theories/Numbers/Natural/Abstract/NGcd.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Properties of the greatest common divisor *)
diff --git a/theories/Numbers/Natural/Abstract/NIso.v b/theories/Numbers/Natural/Abstract/NIso.v
index 2b61f9784..d41d0aff5 100644
--- a/theories/Numbers/Natural/Abstract/NIso.v
+++ b/theories/Numbers/Natural/Abstract/NIso.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Natural/Abstract/NLcm.v b/theories/Numbers/Natural/Abstract/NLcm.v
index 2e7bcf40c..47b74193e 100644
--- a/theories/Numbers/Natural/Abstract/NLcm.v
+++ b/theories/Numbers/Natural/Abstract/NLcm.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import NAxioms NSub NDiv NGcd.
diff --git a/theories/Numbers/Natural/Abstract/NLog.v b/theories/Numbers/Natural/Abstract/NLog.v
index d22510ab9..fe6fcee56 100644
--- a/theories/Numbers/Natural/Abstract/NLog.v
+++ b/theories/Numbers/Natural/Abstract/NLog.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Base-2 Logarithm Properties *)
diff --git a/theories/Numbers/Natural/Abstract/NMaxMin.v b/theories/Numbers/Natural/Abstract/NMaxMin.v
index 1020fe375..3cf4d3f9f 100644
--- a/theories/Numbers/Natural/Abstract/NMaxMin.v
+++ b/theories/Numbers/Natural/Abstract/NMaxMin.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import NAxioms NSub GenericMinMax.
diff --git a/theories/Numbers/Natural/Abstract/NMulOrder.v b/theories/Numbers/Natural/Abstract/NMulOrder.v
index ace1e736e..b7f1c8e45 100644
--- a/theories/Numbers/Natural/Abstract/NMulOrder.v
+++ b/theories/Numbers/Natural/Abstract/NMulOrder.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Natural/Abstract/NOrder.v b/theories/Numbers/Natural/Abstract/NOrder.v
index f05d783ad..acaecad93 100644
--- a/theories/Numbers/Natural/Abstract/NOrder.v
+++ b/theories/Numbers/Natural/Abstract/NOrder.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Natural/Abstract/NParity.v b/theories/Numbers/Natural/Abstract/NParity.v
index fd136ff93..cb89e1d72 100644
--- a/theories/Numbers/Natural/Abstract/NParity.v
+++ b/theories/Numbers/Natural/Abstract/NParity.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Bool NSub NZParity.
diff --git a/theories/Numbers/Natural/Abstract/NPow.v b/theories/Numbers/Natural/Abstract/NPow.v
index d31d67a1c..fc1cc93b1 100644
--- a/theories/Numbers/Natural/Abstract/NPow.v
+++ b/theories/Numbers/Natural/Abstract/NPow.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Properties of the power function *)
diff --git a/theories/Numbers/Natural/Abstract/NProperties.v b/theories/Numbers/Natural/Abstract/NProperties.v
index b753d659a..bcf906cf9 100644
--- a/theories/Numbers/Natural/Abstract/NProperties.v
+++ b/theories/Numbers/Natural/Abstract/NProperties.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export NAxioms.
diff --git a/theories/Numbers/Natural/Abstract/NSqrt.v b/theories/Numbers/Natural/Abstract/NSqrt.v
index 68c06775e..6bffe693e 100644
--- a/theories/Numbers/Natural/Abstract/NSqrt.v
+++ b/theories/Numbers/Natural/Abstract/NSqrt.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Properties of Square Root Function *)
diff --git a/theories/Numbers/Natural/Abstract/NStrongRec.v b/theories/Numbers/Natural/Abstract/NStrongRec.v
index 8e825ef7d..f76d8ae8a 100644
--- a/theories/Numbers/Natural/Abstract/NStrongRec.v
+++ b/theories/Numbers/Natural/Abstract/NStrongRec.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Natural/Abstract/NSub.v b/theories/Numbers/Natural/Abstract/NSub.v
index dce78f610..453b0c0d4 100644
--- a/theories/Numbers/Natural/Abstract/NSub.v
+++ b/theories/Numbers/Natural/Abstract/NSub.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Natural/Binary/NBinary.v b/theories/Numbers/Natural/Binary/NBinary.v
index bdb715f33..c9e1c6401 100644
--- a/theories/Numbers/Natural/Binary/NBinary.v
+++ b/theories/Numbers/Natural/Binary/NBinary.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/Numbers/Natural/Peano/NPeano.v b/theories/Numbers/Natural/Peano/NPeano.v
index 787ef81dc..6000bdcf7 100644
--- a/theories/Numbers/Natural/Peano/NPeano.v
+++ b/theories/Numbers/Natural/Peano/NPeano.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
@@ -18,74 +20,74 @@ Module Nat <: NAxiomsSig := Nat.
(** Compat notations for stuff that used to be at the beginning of NPeano. *)
-Notation leb := Nat.leb (compat "8.4").
-Notation ltb := Nat.ltb (compat "8.4").
-Notation leb_le := Nat.leb_le (compat "8.4").
-Notation ltb_lt := Nat.ltb_lt (compat "8.4").
-Notation pow := Nat.pow (compat "8.4").
-Notation pow_0_r := Nat.pow_0_r (compat "8.4").
-Notation pow_succ_r := Nat.pow_succ_r (compat "8.4").
-Notation square := Nat.square (compat "8.4").
-Notation square_spec := Nat.square_spec (compat "8.4").
-Notation Even := Nat.Even (compat "8.4").
-Notation Odd := Nat.Odd (compat "8.4").
-Notation even := Nat.even (compat "8.4").
-Notation odd := Nat.odd (compat "8.4").
-Notation even_spec := Nat.even_spec (compat "8.4").
-Notation odd_spec := Nat.odd_spec (compat "8.4").
+Notation leb := Nat.leb (only parsing).
+Notation ltb := Nat.ltb (only parsing).
+Notation leb_le := Nat.leb_le (only parsing).
+Notation ltb_lt := Nat.ltb_lt (only parsing).
+Notation pow := Nat.pow (only parsing).
+Notation pow_0_r := Nat.pow_0_r (only parsing).
+Notation pow_succ_r := Nat.pow_succ_r (only parsing).
+Notation square := Nat.square (only parsing).
+Notation square_spec := Nat.square_spec (only parsing).
+Notation Even := Nat.Even (only parsing).
+Notation Odd := Nat.Odd (only parsing).
+Notation even := Nat.even (only parsing).
+Notation odd := Nat.odd (only parsing).
+Notation even_spec := Nat.even_spec (only parsing).
+Notation odd_spec := Nat.odd_spec (only parsing).
Lemma Even_equiv n : Even n <-> Even.even n.
Proof. symmetry. apply Even.even_equiv. Qed.
Lemma Odd_equiv n : Odd n <-> Even.odd n.
Proof. symmetry. apply Even.odd_equiv. Qed.
-Notation divmod := Nat.divmod (compat "8.4").
-Notation div := Nat.div (compat "8.4").
-Notation modulo := Nat.modulo (compat "8.4").
-Notation divmod_spec := Nat.divmod_spec (compat "8.4").
-Notation div_mod := Nat.div_mod (compat "8.4").
-Notation mod_bound_pos := Nat.mod_bound_pos (compat "8.4").
-Notation sqrt_iter := Nat.sqrt_iter (compat "8.4").
-Notation sqrt := Nat.sqrt (compat "8.4").
-Notation sqrt_iter_spec := Nat.sqrt_iter_spec (compat "8.4").
-Notation sqrt_spec := Nat.sqrt_spec (compat "8.4").
-Notation log2_iter := Nat.log2_iter (compat "8.4").
-Notation log2 := Nat.log2 (compat "8.4").
-Notation log2_iter_spec := Nat.log2_iter_spec (compat "8.4").
-Notation log2_spec := Nat.log2_spec (compat "8.4").
-Notation log2_nonpos := Nat.log2_nonpos (compat "8.4").
-Notation gcd := Nat.gcd (compat "8.4").
-Notation divide := Nat.divide (compat "8.4").
-Notation gcd_divide := Nat.gcd_divide (compat "8.4").
-Notation gcd_divide_l := Nat.gcd_divide_l (compat "8.4").
-Notation gcd_divide_r := Nat.gcd_divide_r (compat "8.4").
-Notation gcd_greatest := Nat.gcd_greatest (compat "8.4").
-Notation testbit := Nat.testbit (compat "8.4").
-Notation shiftl := Nat.shiftl (compat "8.4").
-Notation shiftr := Nat.shiftr (compat "8.4").
-Notation bitwise := Nat.bitwise (compat "8.4").
-Notation land := Nat.land (compat "8.4").
-Notation lor := Nat.lor (compat "8.4").
-Notation ldiff := Nat.ldiff (compat "8.4").
-Notation lxor := Nat.lxor (compat "8.4").
-Notation double_twice := Nat.double_twice (compat "8.4").
-Notation testbit_0_l := Nat.testbit_0_l (compat "8.4").
-Notation testbit_odd_0 := Nat.testbit_odd_0 (compat "8.4").
-Notation testbit_even_0 := Nat.testbit_even_0 (compat "8.4").
-Notation testbit_odd_succ := Nat.testbit_odd_succ (compat "8.4").
-Notation testbit_even_succ := Nat.testbit_even_succ (compat "8.4").
-Notation shiftr_spec := Nat.shiftr_spec (compat "8.4").
-Notation shiftl_spec_high := Nat.shiftl_spec_high (compat "8.4").
-Notation shiftl_spec_low := Nat.shiftl_spec_low (compat "8.4").
-Notation div2_bitwise := Nat.div2_bitwise (compat "8.4").
-Notation odd_bitwise := Nat.odd_bitwise (compat "8.4").
-Notation div2_decr := Nat.div2_decr (compat "8.4").
-Notation testbit_bitwise_1 := Nat.testbit_bitwise_1 (compat "8.4").
-Notation testbit_bitwise_2 := Nat.testbit_bitwise_2 (compat "8.4").
-Notation land_spec := Nat.land_spec (compat "8.4").
-Notation ldiff_spec := Nat.ldiff_spec (compat "8.4").
-Notation lor_spec := Nat.lor_spec (compat "8.4").
-Notation lxor_spec := Nat.lxor_spec (compat "8.4").
+Notation divmod := Nat.divmod (only parsing).
+Notation div := Nat.div (only parsing).
+Notation modulo := Nat.modulo (only parsing).
+Notation divmod_spec := Nat.divmod_spec (only parsing).
+Notation div_mod := Nat.div_mod (only parsing).
+Notation mod_bound_pos := Nat.mod_bound_pos (only parsing).
+Notation sqrt_iter := Nat.sqrt_iter (only parsing).
+Notation sqrt := Nat.sqrt (only parsing).
+Notation sqrt_iter_spec := Nat.sqrt_iter_spec (only parsing).
+Notation sqrt_spec := Nat.sqrt_spec (only parsing).
+Notation log2_iter := Nat.log2_iter (only parsing).
+Notation log2 := Nat.log2 (only parsing).
+Notation log2_iter_spec := Nat.log2_iter_spec (only parsing).
+Notation log2_spec := Nat.log2_spec (only parsing).
+Notation log2_nonpos := Nat.log2_nonpos (only parsing).
+Notation gcd := Nat.gcd (only parsing).
+Notation divide := Nat.divide (only parsing).
+Notation gcd_divide := Nat.gcd_divide (only parsing).
+Notation gcd_divide_l := Nat.gcd_divide_l (only parsing).
+Notation gcd_divide_r := Nat.gcd_divide_r (only parsing).
+Notation gcd_greatest := Nat.gcd_greatest (only parsing).
+Notation testbit := Nat.testbit (only parsing).
+Notation shiftl := Nat.shiftl (only parsing).
+Notation shiftr := Nat.shiftr (only parsing).
+Notation bitwise := Nat.bitwise (only parsing).
+Notation land := Nat.land (only parsing).
+Notation lor := Nat.lor (only parsing).
+Notation ldiff := Nat.ldiff (only parsing).
+Notation lxor := Nat.lxor (only parsing).
+Notation double_twice := Nat.double_twice (only parsing).
+Notation testbit_0_l := Nat.testbit_0_l (only parsing).
+Notation testbit_odd_0 := Nat.testbit_odd_0 (only parsing).
+Notation testbit_even_0 := Nat.testbit_even_0 (only parsing).
+Notation testbit_odd_succ := Nat.testbit_odd_succ (only parsing).
+Notation testbit_even_succ := Nat.testbit_even_succ (only parsing).
+Notation shiftr_spec := Nat.shiftr_spec (only parsing).
+Notation shiftl_spec_high := Nat.shiftl_spec_high (only parsing).
+Notation shiftl_spec_low := Nat.shiftl_spec_low (only parsing).
+Notation div2_bitwise := Nat.div2_bitwise (only parsing).
+Notation odd_bitwise := Nat.odd_bitwise (only parsing).
+Notation div2_decr := Nat.div2_decr (only parsing).
+Notation testbit_bitwise_1 := Nat.testbit_bitwise_1 (only parsing).
+Notation testbit_bitwise_2 := Nat.testbit_bitwise_2 (only parsing).
+Notation land_spec := Nat.land_spec (only parsing).
+Notation ldiff_spec := Nat.ldiff_spec (only parsing).
+Notation lor_spec := Nat.lor_spec (only parsing).
+Notation lxor_spec := Nat.lxor_spec (only parsing).
Infix "<=?" := Nat.leb (at level 70) : nat_scope.
Infix "<?" := Nat.ltb (at level 70) : nat_scope.
diff --git a/theories/Numbers/NumPrelude.v b/theories/Numbers/NumPrelude.v
index f01d5880e..7cf13feae 100644
--- a/theories/Numbers/NumPrelude.v
+++ b/theories/Numbers/NumPrelude.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
diff --git a/theories/PArith/BinPos.v b/theories/PArith/BinPos.v
index ff880eefa..8d0896db7 100644
--- a/theories/PArith/BinPos.v
+++ b/theories/PArith/BinPos.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export BinNums.
@@ -1903,180 +1905,180 @@ Notation IsNul := Pos.IsNul (only parsing).
Notation IsPos := Pos.IsPos (only parsing).
Notation IsNeg := Pos.IsNeg (only parsing).
-Notation Psucc := Pos.succ (compat "8.3").
-Notation Pplus := Pos.add (compat "8.3").
-Notation Pplus_carry := Pos.add_carry (compat "8.3").
-Notation Ppred := Pos.pred (compat "8.3").
-Notation Piter_op := Pos.iter_op (compat "8.3").
-Notation Piter_op_succ := Pos.iter_op_succ (compat "8.3").
-Notation Pmult_nat := (Pos.iter_op plus) (compat "8.3").
-Notation nat_of_P := Pos.to_nat (compat "8.3").
-Notation P_of_succ_nat := Pos.of_succ_nat (compat "8.3").
-Notation Pdouble_minus_one := Pos.pred_double (compat "8.3").
-Notation positive_mask := Pos.mask (compat "8.3").
-Notation positive_mask_rect := Pos.mask_rect (compat "8.3").
-Notation positive_mask_ind := Pos.mask_ind (compat "8.3").
-Notation positive_mask_rec := Pos.mask_rec (compat "8.3").
-Notation Pdouble_plus_one_mask := Pos.succ_double_mask (compat "8.3").
-Notation Pdouble_mask := Pos.double_mask (compat "8.3").
-Notation Pdouble_minus_two := Pos.double_pred_mask (compat "8.3").
-Notation Pminus_mask := Pos.sub_mask (compat "8.3").
-Notation Pminus_mask_carry := Pos.sub_mask_carry (compat "8.3").
-Notation Pminus := Pos.sub (compat "8.3").
-Notation Pmult := Pos.mul (compat "8.3").
-Notation iter_pos := @Pos.iter (compat "8.3").
-Notation Ppow := Pos.pow (compat "8.3").
-Notation Pdiv2 := Pos.div2 (compat "8.3").
-Notation Pdiv2_up := Pos.div2_up (compat "8.3").
-Notation Psize := Pos.size_nat (compat "8.3").
-Notation Psize_pos := Pos.size (compat "8.3").
-Notation Pcompare x y m := (Pos.compare_cont m x y) (compat "8.3").
-Notation Plt := Pos.lt (compat "8.3").
-Notation Pgt := Pos.gt (compat "8.3").
-Notation Ple := Pos.le (compat "8.3").
-Notation Pge := Pos.ge (compat "8.3").
-Notation Pmin := Pos.min (compat "8.3").
-Notation Pmax := Pos.max (compat "8.3").
-Notation Peqb := Pos.eqb (compat "8.3").
-Notation positive_eq_dec := Pos.eq_dec (compat "8.3").
-Notation xI_succ_xO := Pos.xI_succ_xO (compat "8.3").
-Notation Psucc_discr := Pos.succ_discr (compat "8.3").
+Notation Psucc := Pos.succ (compat "8.6").
+Notation Pplus := Pos.add (only parsing).
+Notation Pplus_carry := Pos.add_carry (only parsing).
+Notation Ppred := Pos.pred (compat "8.6").
+Notation Piter_op := Pos.iter_op (compat "8.6").
+Notation Piter_op_succ := Pos.iter_op_succ (compat "8.6").
+Notation Pmult_nat := (Pos.iter_op plus) (only parsing).
+Notation nat_of_P := Pos.to_nat (only parsing).
+Notation P_of_succ_nat := Pos.of_succ_nat (only parsing).
+Notation Pdouble_minus_one := Pos.pred_double (only parsing).
+Notation positive_mask := Pos.mask (only parsing).
+Notation positive_mask_rect := Pos.mask_rect (only parsing).
+Notation positive_mask_ind := Pos.mask_ind (only parsing).
+Notation positive_mask_rec := Pos.mask_rec (only parsing).
+Notation Pdouble_plus_one_mask := Pos.succ_double_mask (only parsing).
+Notation Pdouble_mask := Pos.double_mask (compat "8.6").
+Notation Pdouble_minus_two := Pos.double_pred_mask (only parsing).
+Notation Pminus_mask := Pos.sub_mask (only parsing).
+Notation Pminus_mask_carry := Pos.sub_mask_carry (only parsing).
+Notation Pminus := Pos.sub (only parsing).
+Notation Pmult := Pos.mul (only parsing).
+Notation iter_pos := @Pos.iter (only parsing).
+Notation Ppow := Pos.pow (compat "8.6").
+Notation Pdiv2 := Pos.div2 (compat "8.6").
+Notation Pdiv2_up := Pos.div2_up (compat "8.6").
+Notation Psize := Pos.size_nat (only parsing).
+Notation Psize_pos := Pos.size (only parsing).
+Notation Pcompare x y m := (Pos.compare_cont m x y) (only parsing).
+Notation Plt := Pos.lt (compat "8.6").
+Notation Pgt := Pos.gt (compat "8.6").
+Notation Ple := Pos.le (compat "8.6").
+Notation Pge := Pos.ge (compat "8.6").
+Notation Pmin := Pos.min (compat "8.6").
+Notation Pmax := Pos.max (compat "8.6").
+Notation Peqb := Pos.eqb (compat "8.6").
+Notation positive_eq_dec := Pos.eq_dec (only parsing).
+Notation xI_succ_xO := Pos.xI_succ_xO (only parsing).
+Notation Psucc_discr := Pos.succ_discr (compat "8.6").
Notation Psucc_o_double_minus_one_eq_xO :=
- Pos.succ_pred_double (compat "8.3").
+ Pos.succ_pred_double (only parsing).
Notation Pdouble_minus_one_o_succ_eq_xI :=
- Pos.pred_double_succ (compat "8.3").
-Notation xO_succ_permute := Pos.double_succ (compat "8.3").
+ Pos.pred_double_succ (only parsing).
+Notation xO_succ_permute := Pos.double_succ (only parsing).
Notation double_moins_un_xO_discr :=
- Pos.pred_double_xO_discr (compat "8.3").
-Notation Psucc_not_one := Pos.succ_not_1 (compat "8.3").
-Notation Ppred_succ := Pos.pred_succ (compat "8.3").
-Notation Psucc_pred := Pos.succ_pred_or (compat "8.3").
-Notation Psucc_inj := Pos.succ_inj (compat "8.3").
-Notation Pplus_carry_spec := Pos.add_carry_spec (compat "8.3").
-Notation Pplus_comm := Pos.add_comm (compat "8.3").
-Notation Pplus_succ_permute_r := Pos.add_succ_r (compat "8.3").
-Notation Pplus_succ_permute_l := Pos.add_succ_l (compat "8.3").
-Notation Pplus_no_neutral := Pos.add_no_neutral (compat "8.3").
-Notation Pplus_carry_plus := Pos.add_carry_add (compat "8.3").
-Notation Pplus_reg_r := Pos.add_reg_r (compat "8.3").
-Notation Pplus_reg_l := Pos.add_reg_l (compat "8.3").
-Notation Pplus_carry_reg_r := Pos.add_carry_reg_r (compat "8.3").
-Notation Pplus_carry_reg_l := Pos.add_carry_reg_l (compat "8.3").
-Notation Pplus_assoc := Pos.add_assoc (compat "8.3").
-Notation Pplus_xO := Pos.add_xO (compat "8.3").
-Notation Pplus_xI_double_minus_one := Pos.add_xI_pred_double (compat "8.3").
-Notation Pplus_xO_double_minus_one := Pos.add_xO_pred_double (compat "8.3").
-Notation Pplus_diag := Pos.add_diag (compat "8.3").
-Notation PeanoView := Pos.PeanoView (compat "8.3").
-Notation PeanoOne := Pos.PeanoOne (compat "8.3").
-Notation PeanoSucc := Pos.PeanoSucc (compat "8.3").
-Notation PeanoView_rect := Pos.PeanoView_rect (compat "8.3").
-Notation PeanoView_ind := Pos.PeanoView_ind (compat "8.3").
-Notation PeanoView_rec := Pos.PeanoView_rec (compat "8.3").
-Notation peanoView_xO := Pos.peanoView_xO (compat "8.3").
-Notation peanoView_xI := Pos.peanoView_xI (compat "8.3").
-Notation peanoView := Pos.peanoView (compat "8.3").
-Notation PeanoView_iter := Pos.PeanoView_iter (compat "8.3").
-Notation eq_dep_eq_positive := Pos.eq_dep_eq_positive (compat "8.3").
-Notation PeanoViewUnique := Pos.PeanoViewUnique (compat "8.3").
-Notation Prect := Pos.peano_rect (compat "8.3").
-Notation Prect_succ := Pos.peano_rect_succ (compat "8.3").
-Notation Prect_base := Pos.peano_rect_base (compat "8.3").
-Notation Prec := Pos.peano_rec (compat "8.3").
-Notation Pind := Pos.peano_ind (compat "8.3").
-Notation Pcase := Pos.peano_case (compat "8.3").
-Notation Pmult_1_r := Pos.mul_1_r (compat "8.3").
-Notation Pmult_Sn_m := Pos.mul_succ_l (compat "8.3").
-Notation Pmult_xO_permute_r := Pos.mul_xO_r (compat "8.3").
-Notation Pmult_xI_permute_r := Pos.mul_xI_r (compat "8.3").
-Notation Pmult_comm := Pos.mul_comm (compat "8.3").
-Notation Pmult_plus_distr_l := Pos.mul_add_distr_l (compat "8.3").
-Notation Pmult_plus_distr_r := Pos.mul_add_distr_r (compat "8.3").
-Notation Pmult_assoc := Pos.mul_assoc (compat "8.3").
-Notation Pmult_xI_mult_xO_discr := Pos.mul_xI_mul_xO_discr (compat "8.3").
-Notation Pmult_xO_discr := Pos.mul_xO_discr (compat "8.3").
-Notation Pmult_reg_r := Pos.mul_reg_r (compat "8.3").
-Notation Pmult_reg_l := Pos.mul_reg_l (compat "8.3").
-Notation Pmult_1_inversion_l := Pos.mul_eq_1_l (compat "8.3").
-Notation Psquare_xO := Pos.square_xO (compat "8.3").
-Notation Psquare_xI := Pos.square_xI (compat "8.3").
-Notation iter_pos_swap_gen := Pos.iter_swap_gen (compat "8.3").
-Notation iter_pos_swap := Pos.iter_swap (compat "8.3").
-Notation iter_pos_succ := Pos.iter_succ (compat "8.3").
-Notation iter_pos_plus := Pos.iter_add (compat "8.3").
-Notation iter_pos_invariant := Pos.iter_invariant (compat "8.3").
-Notation Ppow_1_r := Pos.pow_1_r (compat "8.3").
-Notation Ppow_succ_r := Pos.pow_succ_r (compat "8.3").
-Notation Peqb_refl := Pos.eqb_refl (compat "8.3").
-Notation Peqb_eq := Pos.eqb_eq (compat "8.3").
-Notation Pcompare_refl_id := Pos.compare_cont_refl (compat "8.3").
-Notation Pcompare_eq_iff := Pos.compare_eq_iff (compat "8.3").
-Notation Pcompare_Gt_Lt := Pos.compare_cont_Gt_Lt (compat "8.3").
-Notation Pcompare_eq_Lt := Pos.compare_lt_iff (compat "8.3").
-Notation Pcompare_Lt_Gt := Pos.compare_cont_Lt_Gt (compat "8.3").
-
-Notation Pcompare_antisym := Pos.compare_cont_antisym (compat "8.3").
-Notation ZC1 := Pos.gt_lt (compat "8.3").
-Notation ZC2 := Pos.lt_gt (compat "8.3").
-Notation Pcompare_spec := Pos.compare_spec (compat "8.3").
-Notation Pcompare_p_Sp := Pos.lt_succ_diag_r (compat "8.3").
-Notation Pcompare_succ_succ := Pos.compare_succ_succ (compat "8.3").
-Notation Pcompare_1 := Pos.nlt_1_r (compat "8.3").
-Notation Plt_1 := Pos.nlt_1_r (compat "8.3").
-Notation Plt_1_succ := Pos.lt_1_succ (compat "8.3").
-Notation Plt_lt_succ := Pos.lt_lt_succ (compat "8.3").
-Notation Plt_irrefl := Pos.lt_irrefl (compat "8.3").
-Notation Plt_trans := Pos.lt_trans (compat "8.3").
-Notation Plt_ind := Pos.lt_ind (compat "8.3").
-Notation Ple_lteq := Pos.le_lteq (compat "8.3").
-Notation Ple_refl := Pos.le_refl (compat "8.3").
-Notation Ple_lt_trans := Pos.le_lt_trans (compat "8.3").
-Notation Plt_le_trans := Pos.lt_le_trans (compat "8.3").
-Notation Ple_trans := Pos.le_trans (compat "8.3").
-Notation Plt_succ_r := Pos.lt_succ_r (compat "8.3").
-Notation Ple_succ_l := Pos.le_succ_l (compat "8.3").
-Notation Pplus_compare_mono_l := Pos.add_compare_mono_l (compat "8.3").
-Notation Pplus_compare_mono_r := Pos.add_compare_mono_r (compat "8.3").
-Notation Pplus_lt_mono_l := Pos.add_lt_mono_l (compat "8.3").
-Notation Pplus_lt_mono_r := Pos.add_lt_mono_r (compat "8.3").
-Notation Pplus_lt_mono := Pos.add_lt_mono (compat "8.3").
-Notation Pplus_le_mono_l := Pos.add_le_mono_l (compat "8.3").
-Notation Pplus_le_mono_r := Pos.add_le_mono_r (compat "8.3").
-Notation Pplus_le_mono := Pos.add_le_mono (compat "8.3").
-Notation Pmult_compare_mono_l := Pos.mul_compare_mono_l (compat "8.3").
-Notation Pmult_compare_mono_r := Pos.mul_compare_mono_r (compat "8.3").
-Notation Pmult_lt_mono_l := Pos.mul_lt_mono_l (compat "8.3").
-Notation Pmult_lt_mono_r := Pos.mul_lt_mono_r (compat "8.3").
-Notation Pmult_lt_mono := Pos.mul_lt_mono (compat "8.3").
-Notation Pmult_le_mono_l := Pos.mul_le_mono_l (compat "8.3").
-Notation Pmult_le_mono_r := Pos.mul_le_mono_r (compat "8.3").
-Notation Pmult_le_mono := Pos.mul_le_mono (compat "8.3").
-Notation Plt_plus_r := Pos.lt_add_r (compat "8.3").
-Notation Plt_not_plus_l := Pos.lt_not_add_l (compat "8.3").
-Notation Ppow_gt_1 := Pos.pow_gt_1 (compat "8.3").
-Notation Ppred_mask := Pos.pred_mask (compat "8.3").
-Notation Pminus_mask_succ_r := Pos.sub_mask_succ_r (compat "8.3").
-Notation Pminus_mask_carry_spec := Pos.sub_mask_carry_spec (compat "8.3").
-Notation Pminus_succ_r := Pos.sub_succ_r (compat "8.3").
-Notation Pminus_mask_diag := Pos.sub_mask_diag (compat "8.3").
-
-Notation Pplus_minus_eq := Pos.add_sub (compat "8.3").
-Notation Pmult_minus_distr_l := Pos.mul_sub_distr_l (compat "8.3").
-Notation Pminus_lt_mono_l := Pos.sub_lt_mono_l (compat "8.3").
-Notation Pminus_compare_mono_l := Pos.sub_compare_mono_l (compat "8.3").
-Notation Pminus_compare_mono_r := Pos.sub_compare_mono_r (compat "8.3").
-Notation Pminus_lt_mono_r := Pos.sub_lt_mono_r (compat "8.3").
-Notation Pminus_decr := Pos.sub_decr (compat "8.3").
-Notation Pminus_xI_xI := Pos.sub_xI_xI (compat "8.3").
-Notation Pplus_minus_assoc := Pos.add_sub_assoc (compat "8.3").
-Notation Pminus_plus_distr := Pos.sub_add_distr (compat "8.3").
-Notation Pminus_minus_distr := Pos.sub_sub_distr (compat "8.3").
-Notation Pminus_mask_Lt := Pos.sub_mask_neg (compat "8.3").
-Notation Pminus_Lt := Pos.sub_lt (compat "8.3").
-Notation Pminus_Eq := Pos.sub_diag (compat "8.3").
-Notation Psize_monotone := Pos.size_nat_monotone (compat "8.3").
-Notation Psize_pos_gt := Pos.size_gt (compat "8.3").
-Notation Psize_pos_le := Pos.size_le (compat "8.3").
+ Pos.pred_double_xO_discr (only parsing).
+Notation Psucc_not_one := Pos.succ_not_1 (only parsing).
+Notation Ppred_succ := Pos.pred_succ (compat "8.6").
+Notation Psucc_pred := Pos.succ_pred_or (only parsing).
+Notation Psucc_inj := Pos.succ_inj (compat "8.6").
+Notation Pplus_carry_spec := Pos.add_carry_spec (only parsing).
+Notation Pplus_comm := Pos.add_comm (only parsing).
+Notation Pplus_succ_permute_r := Pos.add_succ_r (only parsing).
+Notation Pplus_succ_permute_l := Pos.add_succ_l (only parsing).
+Notation Pplus_no_neutral := Pos.add_no_neutral (only parsing).
+Notation Pplus_carry_plus := Pos.add_carry_add (only parsing).
+Notation Pplus_reg_r := Pos.add_reg_r (only parsing).
+Notation Pplus_reg_l := Pos.add_reg_l (only parsing).
+Notation Pplus_carry_reg_r := Pos.add_carry_reg_r (only parsing).
+Notation Pplus_carry_reg_l := Pos.add_carry_reg_l (only parsing).
+Notation Pplus_assoc := Pos.add_assoc (only parsing).
+Notation Pplus_xO := Pos.add_xO (only parsing).
+Notation Pplus_xI_double_minus_one := Pos.add_xI_pred_double (only parsing).
+Notation Pplus_xO_double_minus_one := Pos.add_xO_pred_double (only parsing).
+Notation Pplus_diag := Pos.add_diag (only parsing).
+Notation PeanoView := Pos.PeanoView (only parsing).
+Notation PeanoOne := Pos.PeanoOne (only parsing).
+Notation PeanoSucc := Pos.PeanoSucc (only parsing).
+Notation PeanoView_rect := Pos.PeanoView_rect (only parsing).
+Notation PeanoView_ind := Pos.PeanoView_ind (only parsing).
+Notation PeanoView_rec := Pos.PeanoView_rec (only parsing).
+Notation peanoView_xO := Pos.peanoView_xO (only parsing).
+Notation peanoView_xI := Pos.peanoView_xI (only parsing).
+Notation peanoView := Pos.peanoView (only parsing).
+Notation PeanoView_iter := Pos.PeanoView_iter (only parsing).
+Notation eq_dep_eq_positive := Pos.eq_dep_eq_positive (only parsing).
+Notation PeanoViewUnique := Pos.PeanoViewUnique (only parsing).
+Notation Prect := Pos.peano_rect (only parsing).
+Notation Prect_succ := Pos.peano_rect_succ (only parsing).
+Notation Prect_base := Pos.peano_rect_base (only parsing).
+Notation Prec := Pos.peano_rec (only parsing).
+Notation Pind := Pos.peano_ind (only parsing).
+Notation Pcase := Pos.peano_case (only parsing).
+Notation Pmult_1_r := Pos.mul_1_r (only parsing).
+Notation Pmult_Sn_m := Pos.mul_succ_l (only parsing).
+Notation Pmult_xO_permute_r := Pos.mul_xO_r (only parsing).
+Notation Pmult_xI_permute_r := Pos.mul_xI_r (only parsing).
+Notation Pmult_comm := Pos.mul_comm (only parsing).
+Notation Pmult_plus_distr_l := Pos.mul_add_distr_l (only parsing).
+Notation Pmult_plus_distr_r := Pos.mul_add_distr_r (only parsing).
+Notation Pmult_assoc := Pos.mul_assoc (only parsing).
+Notation Pmult_xI_mult_xO_discr := Pos.mul_xI_mul_xO_discr (only parsing).
+Notation Pmult_xO_discr := Pos.mul_xO_discr (only parsing).
+Notation Pmult_reg_r := Pos.mul_reg_r (only parsing).
+Notation Pmult_reg_l := Pos.mul_reg_l (only parsing).
+Notation Pmult_1_inversion_l := Pos.mul_eq_1_l (only parsing).
+Notation Psquare_xO := Pos.square_xO (compat "8.6").
+Notation Psquare_xI := Pos.square_xI (compat "8.6").
+Notation iter_pos_swap_gen := Pos.iter_swap_gen (only parsing).
+Notation iter_pos_swap := Pos.iter_swap (only parsing).
+Notation iter_pos_succ := Pos.iter_succ (only parsing).
+Notation iter_pos_plus := Pos.iter_add (only parsing).
+Notation iter_pos_invariant := Pos.iter_invariant (only parsing).
+Notation Ppow_1_r := Pos.pow_1_r (compat "8.6").
+Notation Ppow_succ_r := Pos.pow_succ_r (compat "8.6").
+Notation Peqb_refl := Pos.eqb_refl (compat "8.6").
+Notation Peqb_eq := Pos.eqb_eq (compat "8.6").
+Notation Pcompare_refl_id := Pos.compare_cont_refl (only parsing).
+Notation Pcompare_eq_iff := Pos.compare_eq_iff (only parsing).
+Notation Pcompare_Gt_Lt := Pos.compare_cont_Gt_Lt (only parsing).
+Notation Pcompare_eq_Lt := Pos.compare_lt_iff (only parsing).
+Notation Pcompare_Lt_Gt := Pos.compare_cont_Lt_Gt (only parsing).
+
+Notation Pcompare_antisym := Pos.compare_cont_antisym (only parsing).
+Notation ZC1 := Pos.gt_lt (only parsing).
+Notation ZC2 := Pos.lt_gt (only parsing).
+Notation Pcompare_spec := Pos.compare_spec (compat "8.6").
+Notation Pcompare_p_Sp := Pos.lt_succ_diag_r (only parsing).
+Notation Pcompare_succ_succ := Pos.compare_succ_succ (compat "8.6").
+Notation Pcompare_1 := Pos.nlt_1_r (only parsing).
+Notation Plt_1 := Pos.nlt_1_r (only parsing).
+Notation Plt_1_succ := Pos.lt_1_succ (compat "8.6").
+Notation Plt_lt_succ := Pos.lt_lt_succ (compat "8.6").
+Notation Plt_irrefl := Pos.lt_irrefl (compat "8.6").
+Notation Plt_trans := Pos.lt_trans (compat "8.6").
+Notation Plt_ind := Pos.lt_ind (compat "8.6").
+Notation Ple_lteq := Pos.le_lteq (compat "8.6").
+Notation Ple_refl := Pos.le_refl (compat "8.6").
+Notation Ple_lt_trans := Pos.le_lt_trans (compat "8.6").
+Notation Plt_le_trans := Pos.lt_le_trans (compat "8.6").
+Notation Ple_trans := Pos.le_trans (compat "8.6").
+Notation Plt_succ_r := Pos.lt_succ_r (compat "8.6").
+Notation Ple_succ_l := Pos.le_succ_l (compat "8.6").
+Notation Pplus_compare_mono_l := Pos.add_compare_mono_l (only parsing).
+Notation Pplus_compare_mono_r := Pos.add_compare_mono_r (only parsing).
+Notation Pplus_lt_mono_l := Pos.add_lt_mono_l (only parsing).
+Notation Pplus_lt_mono_r := Pos.add_lt_mono_r (only parsing).
+Notation Pplus_lt_mono := Pos.add_lt_mono (only parsing).
+Notation Pplus_le_mono_l := Pos.add_le_mono_l (only parsing).
+Notation Pplus_le_mono_r := Pos.add_le_mono_r (only parsing).
+Notation Pplus_le_mono := Pos.add_le_mono (only parsing).
+Notation Pmult_compare_mono_l := Pos.mul_compare_mono_l (only parsing).
+Notation Pmult_compare_mono_r := Pos.mul_compare_mono_r (only parsing).
+Notation Pmult_lt_mono_l := Pos.mul_lt_mono_l (only parsing).
+Notation Pmult_lt_mono_r := Pos.mul_lt_mono_r (only parsing).
+Notation Pmult_lt_mono := Pos.mul_lt_mono (only parsing).
+Notation Pmult_le_mono_l := Pos.mul_le_mono_l (only parsing).
+Notation Pmult_le_mono_r := Pos.mul_le_mono_r (only parsing).
+Notation Pmult_le_mono := Pos.mul_le_mono (only parsing).
+Notation Plt_plus_r := Pos.lt_add_r (only parsing).
+Notation Plt_not_plus_l := Pos.lt_not_add_l (only parsing).
+Notation Ppow_gt_1 := Pos.pow_gt_1 (compat "8.6").
+Notation Ppred_mask := Pos.pred_mask (compat "8.6").
+Notation Pminus_mask_succ_r := Pos.sub_mask_succ_r (only parsing).
+Notation Pminus_mask_carry_spec := Pos.sub_mask_carry_spec (only parsing).
+Notation Pminus_succ_r := Pos.sub_succ_r (only parsing).
+Notation Pminus_mask_diag := Pos.sub_mask_diag (only parsing).
+
+Notation Pplus_minus_eq := Pos.add_sub (only parsing).
+Notation Pmult_minus_distr_l := Pos.mul_sub_distr_l (only parsing).
+Notation Pminus_lt_mono_l := Pos.sub_lt_mono_l (only parsing).
+Notation Pminus_compare_mono_l := Pos.sub_compare_mono_l (only parsing).
+Notation Pminus_compare_mono_r := Pos.sub_compare_mono_r (only parsing).
+Notation Pminus_lt_mono_r := Pos.sub_lt_mono_r (only parsing).
+Notation Pminus_decr := Pos.sub_decr (only parsing).
+Notation Pminus_xI_xI := Pos.sub_xI_xI (only parsing).
+Notation Pplus_minus_assoc := Pos.add_sub_assoc (only parsing).
+Notation Pminus_plus_distr := Pos.sub_add_distr (only parsing).
+Notation Pminus_minus_distr := Pos.sub_sub_distr (only parsing).
+Notation Pminus_mask_Lt := Pos.sub_mask_neg (only parsing).
+Notation Pminus_Lt := Pos.sub_lt (only parsing).
+Notation Pminus_Eq := Pos.sub_diag (only parsing).
+Notation Psize_monotone := Pos.size_nat_monotone (only parsing).
+Notation Psize_pos_gt := Pos.size_gt (only parsing).
+Notation Psize_pos_le := Pos.size_le (only parsing).
(** More complex compatibility facts, expressed as lemmas
(to preserve scopes for instance) *)
diff --git a/theories/PArith/BinPosDef.v b/theories/PArith/BinPosDef.v
index 2b647555c..070314746 100644
--- a/theories/PArith/BinPosDef.v
+++ b/theories/PArith/BinPosDef.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(**********************************************************************)
@@ -557,4 +559,59 @@ Fixpoint of_succ_nat (n:nat) : positive :=
| S x => succ (of_succ_nat x)
end.
+(** ** Conversion with a decimal representation for printing/parsing *)
+
+Local Notation ten := 1~0~1~0.
+
+Fixpoint of_uint_acc (d:Decimal.uint)(acc:positive) :=
+ match d with
+ | Decimal.Nil => acc
+ | Decimal.D0 l => of_uint_acc l (mul ten acc)
+ | Decimal.D1 l => of_uint_acc l (add 1 (mul ten acc))
+ | Decimal.D2 l => of_uint_acc l (add 1~0 (mul ten acc))
+ | Decimal.D3 l => of_uint_acc l (add 1~1 (mul ten acc))
+ | Decimal.D4 l => of_uint_acc l (add 1~0~0 (mul ten acc))
+ | Decimal.D5 l => of_uint_acc l (add 1~0~1 (mul ten acc))
+ | Decimal.D6 l => of_uint_acc l (add 1~1~0 (mul ten acc))
+ | Decimal.D7 l => of_uint_acc l (add 1~1~1 (mul ten acc))
+ | Decimal.D8 l => of_uint_acc l (add 1~0~0~0 (mul ten acc))
+ | Decimal.D9 l => of_uint_acc l (add 1~0~0~1 (mul ten acc))
+ end.
+
+Fixpoint of_uint (d:Decimal.uint) : N :=
+ match d with
+ | Decimal.Nil => N0
+ | Decimal.D0 l => of_uint l
+ | Decimal.D1 l => Npos (of_uint_acc l 1)
+ | Decimal.D2 l => Npos (of_uint_acc l 1~0)
+ | Decimal.D3 l => Npos (of_uint_acc l 1~1)
+ | Decimal.D4 l => Npos (of_uint_acc l 1~0~0)
+ | Decimal.D5 l => Npos (of_uint_acc l 1~0~1)
+ | Decimal.D6 l => Npos (of_uint_acc l 1~1~0)
+ | Decimal.D7 l => Npos (of_uint_acc l 1~1~1)
+ | Decimal.D8 l => Npos (of_uint_acc l 1~0~0~0)
+ | Decimal.D9 l => Npos (of_uint_acc l 1~0~0~1)
+ end.
+
+Definition of_int (d:Decimal.int) : option positive :=
+ match d with
+ | Decimal.Pos d =>
+ match of_uint d with
+ | N0 => None
+ | Npos p => Some p
+ end
+ | Decimal.Neg _ => None
+ end.
+
+Fixpoint to_little_uint p :=
+ match p with
+ | 1 => Decimal.D1 Decimal.Nil
+ | p~1 => Decimal.Little.succ_double (to_little_uint p)
+ | p~0 => Decimal.Little.double (to_little_uint p)
+ end.
+
+Definition to_uint p := Decimal.rev (to_little_uint p).
+
+Definition to_int n := Decimal.Pos (to_uint n).
+
End Pos.
diff --git a/theories/PArith/PArith.v b/theories/PArith/PArith.v
index 66e1ae152..2be3d07cc 100644
--- a/theories/PArith/PArith.v
+++ b/theories/PArith/PArith.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Library for positive natural numbers *)
diff --git a/theories/PArith/POrderedType.v b/theories/PArith/POrderedType.v
index b73ddff82..c454e8afd 100644
--- a/theories/PArith/POrderedType.v
+++ b/theories/PArith/POrderedType.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import BinPos Equalities Orders OrdersTac.
diff --git a/theories/PArith/Pnat.v b/theories/PArith/Pnat.v
index 461967de8..26aba87fb 100644
--- a/theories/PArith/Pnat.v
+++ b/theories/PArith/Pnat.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import BinPos PeanoNat.
@@ -382,36 +384,36 @@ End SuccNat2Pos.
(** For compatibility, old names and old-style lemmas *)
-Notation Psucc_S := Pos2Nat.inj_succ (compat "8.3").
-Notation Pplus_plus := Pos2Nat.inj_add (compat "8.3").
-Notation Pmult_mult := Pos2Nat.inj_mul (compat "8.3").
-Notation Pcompare_nat_compare := Pos2Nat.inj_compare (compat "8.3").
-Notation nat_of_P_xH := Pos2Nat.inj_1 (compat "8.3").
-Notation nat_of_P_xO := Pos2Nat.inj_xO (compat "8.3").
-Notation nat_of_P_xI := Pos2Nat.inj_xI (compat "8.3").
-Notation nat_of_P_is_S := Pos2Nat.is_succ (compat "8.3").
-Notation nat_of_P_pos := Pos2Nat.is_pos (compat "8.3").
-Notation nat_of_P_inj_iff := Pos2Nat.inj_iff (compat "8.3").
-Notation nat_of_P_inj := Pos2Nat.inj (compat "8.3").
-Notation Plt_lt := Pos2Nat.inj_lt (compat "8.3").
-Notation Pgt_gt := Pos2Nat.inj_gt (compat "8.3").
-Notation Ple_le := Pos2Nat.inj_le (compat "8.3").
-Notation Pge_ge := Pos2Nat.inj_ge (compat "8.3").
-Notation Pminus_minus := Pos2Nat.inj_sub (compat "8.3").
-Notation iter_nat_of_P := @Pos2Nat.inj_iter (compat "8.3").
-
-Notation nat_of_P_of_succ_nat := SuccNat2Pos.id_succ (compat "8.3").
-Notation P_of_succ_nat_of_P := Pos2SuccNat.id_succ (compat "8.3").
-
-Notation nat_of_P_succ_morphism := Pos2Nat.inj_succ (compat "8.3").
-Notation nat_of_P_plus_morphism := Pos2Nat.inj_add (compat "8.3").
-Notation nat_of_P_mult_morphism := Pos2Nat.inj_mul (compat "8.3").
-Notation nat_of_P_compare_morphism := Pos2Nat.inj_compare (compat "8.3").
-Notation lt_O_nat_of_P := Pos2Nat.is_pos (compat "8.3").
-Notation ZL4 := Pos2Nat.is_succ (compat "8.3").
-Notation nat_of_P_o_P_of_succ_nat_eq_succ := SuccNat2Pos.id_succ (compat "8.3").
-Notation P_of_succ_nat_o_nat_of_P_eq_succ := Pos2SuccNat.id_succ (compat "8.3").
-Notation pred_o_P_of_succ_nat_o_nat_of_P_eq_id := Pos2SuccNat.pred_id (compat "8.3").
+Notation Psucc_S := Pos2Nat.inj_succ (only parsing).
+Notation Pplus_plus := Pos2Nat.inj_add (only parsing).
+Notation Pmult_mult := Pos2Nat.inj_mul (only parsing).
+Notation Pcompare_nat_compare := Pos2Nat.inj_compare (only parsing).
+Notation nat_of_P_xH := Pos2Nat.inj_1 (only parsing).
+Notation nat_of_P_xO := Pos2Nat.inj_xO (only parsing).
+Notation nat_of_P_xI := Pos2Nat.inj_xI (only parsing).
+Notation nat_of_P_is_S := Pos2Nat.is_succ (only parsing).
+Notation nat_of_P_pos := Pos2Nat.is_pos (only parsing).
+Notation nat_of_P_inj_iff := Pos2Nat.inj_iff (only parsing).
+Notation nat_of_P_inj := Pos2Nat.inj (only parsing).
+Notation Plt_lt := Pos2Nat.inj_lt (only parsing).
+Notation Pgt_gt := Pos2Nat.inj_gt (only parsing).
+Notation Ple_le := Pos2Nat.inj_le (only parsing).
+Notation Pge_ge := Pos2Nat.inj_ge (only parsing).
+Notation Pminus_minus := Pos2Nat.inj_sub (only parsing).
+Notation iter_nat_of_P := @Pos2Nat.inj_iter (only parsing).
+
+Notation nat_of_P_of_succ_nat := SuccNat2Pos.id_succ (only parsing).
+Notation P_of_succ_nat_of_P := Pos2SuccNat.id_succ (only parsing).
+
+Notation nat_of_P_succ_morphism := Pos2Nat.inj_succ (only parsing).
+Notation nat_of_P_plus_morphism := Pos2Nat.inj_add (only parsing).
+Notation nat_of_P_mult_morphism := Pos2Nat.inj_mul (only parsing).
+Notation nat_of_P_compare_morphism := Pos2Nat.inj_compare (only parsing).
+Notation lt_O_nat_of_P := Pos2Nat.is_pos (only parsing).
+Notation ZL4 := Pos2Nat.is_succ (only parsing).
+Notation nat_of_P_o_P_of_succ_nat_eq_succ := SuccNat2Pos.id_succ (only parsing).
+Notation P_of_succ_nat_o_nat_of_P_eq_succ := Pos2SuccNat.id_succ (only parsing).
+Notation pred_o_P_of_succ_nat_o_nat_of_P_eq_id := Pos2SuccNat.pred_id (only parsing).
Lemma nat_of_P_minus_morphism p q :
Pos.compare_cont Eq p q = Gt ->
diff --git a/theories/Program/Basics.v b/theories/Program/Basics.v
index ff0d5b91b..f55093ed4 100644
--- a/theories/Program/Basics.v
+++ b/theories/Program/Basics.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Standard functions and combinators.
diff --git a/theories/Program/Combinators.v b/theories/Program/Combinators.v
index 237d878bf..f78d06b1d 100644
--- a/theories/Program/Combinators.v
+++ b/theories/Program/Combinators.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Proofs about standard combinators, exports functional extensionality.
diff --git a/theories/Program/Equality.v b/theories/Program/Equality.v
index 5e3d0b1a7..cf42ed18d 100644
--- a/theories/Program/Equality.v
+++ b/theories/Program/Equality.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Tactics related to (dependent) equality and proof irrelevance. *)
diff --git a/theories/Program/Program.v b/theories/Program/Program.v
index be8bb26d3..de0a6d5d6 100644
--- a/theories/Program/Program.v
+++ b/theories/Program/Program.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export Coq.Program.Utils.
Require Export Coq.Program.Wf.
diff --git a/theories/Program/Subset.v b/theories/Program/Subset.v
index c68be0d22..1c89b6c3b 100644
--- a/theories/Program/Subset.v
+++ b/theories/Program/Subset.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Tactics related to subsets and proof irrelevance. *)
diff --git a/theories/Program/Syntax.v b/theories/Program/Syntax.v
index a62348716..785b9437e 100644
--- a/theories/Program/Syntax.v
+++ b/theories/Program/Syntax.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Custom notations and implicits for Coq prelude definitions.
diff --git a/theories/Program/Tactics.v b/theories/Program/Tactics.v
index b06562fc4..bc8388184 100644
--- a/theories/Program/Tactics.v
+++ b/theories/Program/Tactics.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This module implements various tactics used to simplify the goals produced by Program,
diff --git a/theories/Program/Utils.v b/theories/Program/Utils.v
index 8d7548803..78c36dc7d 100644
--- a/theories/Program/Utils.v
+++ b/theories/Program/Utils.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Various syntactic shorthands that are useful with [Program]. *)
diff --git a/theories/Program/Wf.v b/theories/Program/Wf.v
index da9020bc1..627879854 100644
--- a/theories/Program/Wf.v
+++ b/theories/Program/Wf.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Reformulation of the Wf module using subsets where possible, providing
the support for [Program]'s treatment of well-founded definitions. *)
diff --git a/theories/QArith/QArith.v b/theories/QArith/QArith.v
index 439006abf..813900822 100644
--- a/theories/QArith/QArith.v
+++ b/theories/QArith/QArith.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export QArith_base.
diff --git a/theories/QArith/QArith_base.v b/theories/QArith/QArith_base.v
index 5996d30f2..467f263be 100644
--- a/theories/QArith/QArith_base.v
+++ b/theories/QArith/QArith_base.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export ZArith.
diff --git a/theories/QArith/QOrderedType.v b/theories/QArith/QOrderedType.v
index cf18ed896..37b4b298a 100644
--- a/theories/QArith/QOrderedType.v
+++ b/theories/QArith/QOrderedType.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import QArith_base Equalities Orders OrdersTac.
diff --git a/theories/QArith/Qabs.v b/theories/QArith/Qabs.v
index ec2ac7832..48be89417 100644
--- a/theories/QArith/Qabs.v
+++ b/theories/QArith/Qabs.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export QArith.
diff --git a/theories/QArith/Qcabs.v b/theories/QArith/Qcabs.v
index 09908665e..f45868a77 100644
--- a/theories/QArith/Qcabs.v
+++ b/theories/QArith/Qcabs.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * An absolute value for normalized rational numbers. *)
diff --git a/theories/QArith/Qcanon.v b/theories/QArith/Qcanon.v
index 0b399febe..e25f69c31 100644
--- a/theories/QArith/Qcanon.v
+++ b/theories/QArith/Qcanon.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Field.
diff --git a/theories/QArith/Qfield.v b/theories/QArith/Qfield.v
index bb1bb2079..6cbb491b8 100644
--- a/theories/QArith/Qfield.v
+++ b/theories/QArith/Qfield.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export Field.
diff --git a/theories/QArith/Qminmax.v b/theories/QArith/Qminmax.v
index 254c5b57f..264b2f928 100644
--- a/theories/QArith/Qminmax.v
+++ b/theories/QArith/Qminmax.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import QArith_base Orders QOrderedType GenericMinMax.
diff --git a/theories/QArith/Qpower.v b/theories/QArith/Qpower.v
index 187bef2ab..3fd78f092 100644
--- a/theories/QArith/Qpower.v
+++ b/theories/QArith/Qpower.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Zpow_facts Qfield Qreduction.
diff --git a/theories/QArith/Qreals.v b/theories/QArith/Qreals.v
index e6f7e7ac9..14ab1700e 100644
--- a/theories/QArith/Qreals.v
+++ b/theories/QArith/Qreals.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export Rbase.
diff --git a/theories/QArith/Qreduction.v b/theories/QArith/Qreduction.v
index 5d055b547..7b08515d2 100644
--- a/theories/QArith/Qreduction.v
+++ b/theories/QArith/Qreduction.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Normalisation functions for rational numbers. *)
@@ -11,8 +13,8 @@
Require Export QArith_base.
Require Import Znumtheory.
-Notation Z2P := Z.to_pos (compat "8.3").
-Notation Z2P_correct := Z2Pos.id (compat "8.3").
+Notation Z2P := Z.to_pos (only parsing).
+Notation Z2P_correct := Z2Pos.id (only parsing).
(** Simplification of fractions using [Z.gcd].
This version can compute within Coq. *)
diff --git a/theories/QArith/Qring.v b/theories/QArith/Qring.v
index 9569348b9..7f972d568 100644
--- a/theories/QArith/Qring.v
+++ b/theories/QArith/Qring.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export Qfield.
diff --git a/theories/QArith/Qround.v b/theories/QArith/Qround.v
index 6e72dd2c2..e4e974972 100644
--- a/theories/QArith/Qround.v
+++ b/theories/QArith/Qround.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import QArith.
diff --git a/theories/Reals/Alembert.v b/theories/Reals/Alembert.v
index 155bf977b..09aad1ecb 100644
--- a/theories/Reals/Alembert.v
+++ b/theories/Reals/Alembert.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/AltSeries.v b/theories/Reals/AltSeries.v
index 9e106f267..c17ad0cfa 100644
--- a/theories/Reals/AltSeries.v
+++ b/theories/Reals/AltSeries.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/ArithProp.v b/theories/Reals/ArithProp.v
index 4cdc035bb..37240eb74 100644
--- a/theories/Reals/ArithProp.v
+++ b/theories/Reals/ArithProp.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Binomial.v b/theories/Reals/Binomial.v
index d608a9359..271100a58 100644
--- a/theories/Reals/Binomial.v
+++ b/theories/Reals/Binomial.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Cauchy_prod.v b/theories/Reals/Cauchy_prod.v
index 61af31e34..306b09dc4 100644
--- a/theories/Reals/Cauchy_prod.v
+++ b/theories/Reals/Cauchy_prod.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Cos_plus.v b/theories/Reals/Cos_plus.v
index 194d6fda2..d046ecf1e 100644
--- a/theories/Reals/Cos_plus.v
+++ b/theories/Reals/Cos_plus.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Cos_rel.v b/theories/Reals/Cos_rel.v
index b5ae76939..f9919278d 100644
--- a/theories/Reals/Cos_rel.v
+++ b/theories/Reals/Cos_rel.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/DiscrR.v b/theories/Reals/DiscrR.v
index 5dc5269c7..f3bc2f22e 100644
--- a/theories/Reals/DiscrR.v
+++ b/theories/Reals/DiscrR.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import RIneq.
diff --git a/theories/Reals/Exp_prop.v b/theories/Reals/Exp_prop.v
index 6666dc3a1..3de131eae 100644
--- a/theories/Reals/Exp_prop.v
+++ b/theories/Reals/Exp_prop.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Integration.v b/theories/Reals/Integration.v
index 3db55efed..1f4fd5764 100644
--- a/theories/Reals/Integration.v
+++ b/theories/Reals/Integration.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export NewtonInt.
diff --git a/theories/Reals/MVT.v b/theories/Reals/MVT.v
index a4b3845e8..717df1b11 100644
--- a/theories/Reals/MVT.v
+++ b/theories/Reals/MVT.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Machin.v b/theories/Reals/Machin.v
index 6ed0658a0..cdf98cbde 100644
--- a/theories/Reals/Machin.v
+++ b/theories/Reals/Machin.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Fourier.
diff --git a/theories/Reals/NewtonInt.v b/theories/Reals/NewtonInt.v
index 405296f72..66918eeed 100644
--- a/theories/Reals/NewtonInt.v
+++ b/theories/Reals/NewtonInt.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/PSeries_reg.v b/theories/Reals/PSeries_reg.v
index dbef02e02..61d1b5afe 100644
--- a/theories/Reals/PSeries_reg.v
+++ b/theories/Reals/PSeries_reg.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/PartSum.v b/theories/Reals/PartSum.v
index 1376c5134..33feeac0c 100644
--- a/theories/Reals/PartSum.v
+++ b/theories/Reals/PartSum.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/RIneq.v b/theories/Reals/RIneq.v
index 7bcd2799a..59a104965 100644
--- a/theories/Reals/RIneq.v
+++ b/theories/Reals/RIneq.v
@@ -1,10 +1,12 @@
-(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(************************************************************************)
(*********************************************************)
@@ -1611,6 +1613,9 @@ Proof.
Qed.
Hint Resolve mult_INR: real.
+Lemma pow_INR (m n: nat) : INR (m ^ n) = pow (INR m) n.
+Proof. now induction n as [|n IHn];[ | simpl; rewrite mult_INR, IHn]. Qed.
+
(*********)
Lemma lt_0_INR : forall n:nat, (0 < n)%nat -> 0 < INR n.
Proof.
@@ -2024,7 +2029,7 @@ Qed.
Lemma R_rm : ring_morph
0%R 1%R Rplus Rmult Rminus Ropp eq
- 0%Z 1%Z Zplus Zmult Zminus Zopp Zeq_bool IZR.
+ 0%Z 1%Z Zplus Zmult Zminus Z.opp Zeq_bool IZR.
Proof.
constructor ; try easy.
exact plus_IZR.
diff --git a/theories/Reals/RList.v b/theories/Reals/RList.v
index f739d1550..e12937c70 100644
--- a/theories/Reals/RList.v
+++ b/theories/Reals/RList.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/ROrderedType.v b/theories/Reals/ROrderedType.v
index e20652aad..ee65ee1d1 100644
--- a/theories/Reals/ROrderedType.v
+++ b/theories/Reals/ROrderedType.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase Equalities Orders OrdersTac.
diff --git a/theories/Reals/R_Ifp.v b/theories/Reals/R_Ifp.v
index 5705eacbd..77e2a1e04 100644
--- a/theories/Reals/R_Ifp.v
+++ b/theories/Reals/R_Ifp.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(**********************************************************)
diff --git a/theories/Reals/R_sqr.v b/theories/Reals/R_sqr.v
index 057a16976..a60bb7cf4 100644
--- a/theories/Reals/R_sqr.v
+++ b/theories/Reals/R_sqr.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/R_sqrt.v b/theories/Reals/R_sqrt.v
index 7a386bd2e..d4035fad6 100644
--- a/theories/Reals/R_sqrt.v
+++ b/theories/Reals/R_sqrt.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Ranalysis.v b/theories/Reals/Ranalysis.v
index 9b0357f03..4bde9b609 100644
--- a/theories/Reals/Ranalysis.v
+++ b/theories/Reals/Ranalysis.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Ranalysis1.v b/theories/Reals/Ranalysis1.v
index 7f7344031..36ac738ca 100644
--- a/theories/Reals/Ranalysis1.v
+++ b/theories/Reals/Ranalysis1.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Ranalysis2.v b/theories/Reals/Ranalysis2.v
index 04ee7a7bf..7a97ca63e 100644
--- a/theories/Reals/Ranalysis2.v
+++ b/theories/Reals/Ranalysis2.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Ranalysis3.v b/theories/Reals/Ranalysis3.v
index 1fa2b6965..301d6d2c5 100644
--- a/theories/Reals/Ranalysis3.v
+++ b/theories/Reals/Ranalysis3.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Ranalysis4.v b/theories/Reals/Ranalysis4.v
index 0ea698d8d..94f1757a8 100644
--- a/theories/Reals/Ranalysis4.v
+++ b/theories/Reals/Ranalysis4.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Ranalysis5.v b/theories/Reals/Ranalysis5.v
index 61c0debb7..afb78e1c8 100644
--- a/theories/Reals/Ranalysis5.v
+++ b/theories/Reals/Ranalysis5.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
@@ -27,46 +29,34 @@ Lemma f_incr_implies_g_incr_interv : forall f g:R->R, forall lb ub,
(forall x , f lb <= x -> x <= f ub -> lb <= g x <= ub) ->
(forall x y, f lb <= x -> x < y -> y <= f ub -> g x < g y).
Proof.
-intros f g lb ub lb_lt_ub f_incr f_eq_g g_ok x y lb_le_x x_lt_y y_le_ub.
- assert (x_encad : f lb <= x <= f ub).
- split ; [assumption | apply Rle_trans with (r2:=y) ; [apply Rlt_le|] ; assumption].
- assert (y_encad : f lb <= y <= f ub).
- split ; [apply Rle_trans with (r2:=x) ; [|apply Rlt_le] ; assumption | assumption].
- assert (Temp1 : lb <= lb) by intuition ; assert (Temp2 : ub <= ub) by intuition.
- assert (gx_encad := g_ok _ (proj1 x_encad) (proj2 x_encad)).
- assert (gy_encad := g_ok _ (proj1 y_encad) (proj2 y_encad)).
- clear Temp1 Temp2.
- case (Rlt_dec (g x) (g y)).
- intuition.
+ intros f g lb ub lb_lt_ub f_incr f_eq_g g_ok x y lb_le_x x_lt_y y_le_ub.
+ assert (x_encad : f lb <= x <= f ub) by lra.
+ assert (y_encad : f lb <= y <= f ub) by lra.
+ assert (gx_encad := g_ok _ (proj1 x_encad) (proj2 x_encad)).
+ assert (gy_encad := g_ok _ (proj1 y_encad) (proj2 y_encad)).
+ case (Rlt_dec (g x) (g y)); [ easy |].
intros Hfalse.
- assert (Temp := Rnot_lt_le _ _ Hfalse).
- assert (Hcontradiction : y <= x).
- replace y with (id y) by intuition ; replace x with (id x) by intuition ;
- rewrite <- f_eq_g. rewrite <- f_eq_g.
- assert (f_incr2 : forall x y, lb <= x -> x <= y -> y < ub -> f x <= f y).
+ assert (Temp := Rnot_lt_le _ _ Hfalse).
+ enough (y <= x) by lra.
+ replace y with (id y) by easy.
+ replace x with (id x) by easy.
+ rewrite <- f_eq_g by easy.
+ rewrite <- f_eq_g by easy.
+ assert (f_incr2 : forall x y, lb <= x -> x <= y -> y < ub -> f x <= f y). {
intros m n lb_le_m m_le_n n_lt_ub.
case (m_le_n).
- intros ; apply Rlt_le ; apply f_incr ; [| | apply Rlt_le] ; assumption.
- intros Hyp ; rewrite Hyp ; apply Req_le ; reflexivity.
- apply f_incr2.
- intuition. intuition.
- Focus 3. intuition.
- Focus 2. intuition.
- Focus 2. intuition. Focus 2. intuition.
- assert (Temp2 : g x <> ub).
- intro Hf.
- assert (Htemp : (comp f g) x = f ub).
- unfold comp ; rewrite Hf ; reflexivity.
- rewrite f_eq_g in Htemp ; unfold id in Htemp.
- assert (Htemp2 : x < f ub).
- apply Rlt_le_trans with (r2:=y) ; intuition.
- clear -Htemp Htemp2. fourier.
- intuition. intuition.
- clear -Temp2 gx_encad.
- case (proj2 gx_encad).
- intuition.
- intro Hfalse ; apply False_ind ; apply Temp2 ; assumption.
- apply False_ind. clear - Hcontradiction x_lt_y. fourier.
+ - intros; apply Rlt_le, f_incr, Rlt_le; assumption.
+ - intros Hyp; rewrite Hyp; apply Req_le; reflexivity.
+ }
+ apply f_incr2; intuition.
+ enough (g x <> ub) by lra.
+ intro Hf.
+ assert (Htemp : (comp f g) x = f ub). {
+ unfold comp; rewrite Hf; reflexivity.
+ }
+ rewrite f_eq_g in Htemp by easy.
+ unfold id in Htemp.
+ fourier.
Qed.
Lemma derivable_pt_id_interv : forall (lb ub x:R),
diff --git a/theories/Reals/Ranalysis_reg.v b/theories/Reals/Ranalysis_reg.v
index f5ebb4c53..e1d4781bf 100644
--- a/theories/Reals/Ranalysis_reg.v
+++ b/theories/Reals/Ranalysis_reg.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Ratan.v b/theories/Reals/Ratan.v
index 8c631dade..ce39d5ffe 100644
--- a/theories/Reals/Ratan.v
+++ b/theories/Reals/Ratan.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Fourier.
diff --git a/theories/Reals/Raxioms.v b/theories/Reals/Raxioms.v
index 947972bd5..6019d4faf 100644
--- a/theories/Reals/Raxioms.v
+++ b/theories/Reals/Raxioms.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(*********************************************************)
diff --git a/theories/Reals/Rbase.v b/theories/Reals/Rbase.v
index 11d5a5b29..b63c8e1c6 100644
--- a/theories/Reals/Rbase.v
+++ b/theories/Reals/Rbase.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export Rdefinitions.
diff --git a/theories/Reals/Rbasic_fun.v b/theories/Reals/Rbasic_fun.v
index 17b3c5099..aa886cee0 100644
--- a/theories/Reals/Rbasic_fun.v
+++ b/theories/Reals/Rbasic_fun.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(*********************************************************)
@@ -609,7 +611,7 @@ Qed.
Lemma Rabs_Zabs : forall z:Z, Rabs (IZR z) = IZR (Z.abs z).
Proof.
- intros z; case z; unfold Zabs.
+ intros z; case z; unfold Z.abs.
apply Rabs_R0.
now intros p0; apply Rabs_pos_eq, (IZR_le 0).
unfold IZR at 1.
diff --git a/theories/Reals/Rcomplete.v b/theories/Reals/Rcomplete.v
index 783b81974..19cbbeca1 100644
--- a/theories/Reals/Rcomplete.v
+++ b/theories/Reals/Rcomplete.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Rdefinitions.v b/theories/Reals/Rdefinitions.v
index c668a708e..857b4ec33 100644
--- a/theories/Reals/Rdefinitions.v
+++ b/theories/Reals/Rdefinitions.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(*********************************************************)
diff --git a/theories/Reals/Rderiv.v b/theories/Reals/Rderiv.v
index 67a06e290..dfa5c7104 100644
--- a/theories/Reals/Rderiv.v
+++ b/theories/Reals/Rderiv.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(*********************************************************)
diff --git a/theories/Reals/Reals.v b/theories/Reals/Reals.v
index 8c4a9727e..b249b519f 100644
--- a/theories/Reals/Reals.v
+++ b/theories/Reals/Reals.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** The library REALS is divided in 6 parts :
diff --git a/theories/Reals/Rfunctions.v b/theories/Reals/Rfunctions.v
index c70ec42ef..77e531474 100644
--- a/theories/Reals/Rfunctions.v
+++ b/theories/Reals/Rfunctions.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(*i Some properties about pow and sum have been made with John Harrison i*)
diff --git a/theories/Reals/Rgeom.v b/theories/Reals/Rgeom.v
index a7002e959..6c2f3ac6e 100644
--- a/theories/Reals/Rgeom.v
+++ b/theories/Reals/Rgeom.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/RiemannInt.v b/theories/Reals/RiemannInt.v
index f8617b01e..f7d98fca8 100644
--- a/theories/Reals/RiemannInt.v
+++ b/theories/Reals/RiemannInt.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rfunctions.
diff --git a/theories/Reals/RiemannInt_SF.v b/theories/Reals/RiemannInt_SF.v
index 0829dac52..ceac021ef 100644
--- a/theories/Reals/RiemannInt_SF.v
+++ b/theories/Reals/RiemannInt_SF.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Rlimit.v b/theories/Reals/Rlimit.v
index d769593a4..b14fcc4d3 100644
--- a/theories/Reals/Rlimit.v
+++ b/theories/Reals/Rlimit.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(*********************************************************)
diff --git a/theories/Reals/Rlogic.v b/theories/Reals/Rlogic.v
index 4ad3339ec..04f13477c 100644
--- a/theories/Reals/Rlogic.v
+++ b/theories/Reals/Rlogic.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This module proves some logical properties of the axiomatic of Reals.
@@ -63,7 +65,7 @@ destruct (Rle_lt_dec l 0) as [Hl|Hl].
now apply Rinv_0_lt_compat.
now apply Hnp.
left.
-set (N := Zabs_nat (up (/l) - 2)).
+set (N := Z.abs_nat (up (/l) - 2)).
assert (H1l: (1 <= /l)%R).
rewrite <- Rinv_1.
apply Rinv_le_contravar with (1 := Hl).
@@ -75,7 +77,7 @@ assert (HN: (INR N + 1 = IZR (up (/ l)) - 1)%R).
rewrite inj_Zabs_nat.
replace (IZR (up (/ l)) - 1)%R with (IZR (up (/ l) - 2) + 1)%R.
apply (f_equal (fun v => IZR v + 1)%R).
- apply Zabs_eq.
+ apply Z.abs_eq.
apply Zle_minus_le_0.
apply (Zlt_le_succ 1).
apply lt_IZR.
diff --git a/theories/Reals/Rminmax.v b/theories/Reals/Rminmax.v
index 57e485cb7..7f73f7c18 100644
--- a/theories/Reals/Rminmax.v
+++ b/theories/Reals/Rminmax.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Orders Rbase Rbasic_fun ROrderedType GenericMinMax.
diff --git a/theories/Reals/Rpow_def.v b/theories/Reals/Rpow_def.v
index 6279e1f16..0d9213031 100644
--- a/theories/Reals/Rpow_def.v
+++ b/theories/Reals/Rpow_def.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rdefinitions.
diff --git a/theories/Reals/Rpower.v b/theories/Reals/Rpower.v
index a646104cd..c6fac951b 100644
--- a/theories/Reals/Rpower.v
+++ b/theories/Reals/Rpower.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(*i Due to L.Thery i*)
@@ -431,9 +433,9 @@ Proof.
Qed.
Theorem Rpower_lt :
- forall x y z:R, 1 < x -> 0 <= y -> y < z -> x ^R y < x ^R z.
+ forall x y z:R, 1 < x -> y < z -> x ^R y < x ^R z.
Proof.
- intros x y z H H0 H1.
+ intros x y z H H1.
unfold Rpower.
apply exp_increasing.
apply Rmult_lt_compat_r.
@@ -488,11 +490,13 @@ Proof.
Qed.
Theorem Rle_Rpower :
- forall e n m:R, 1 < e -> 0 <= n -> n <= m -> e ^R n <= e ^R m.
+ forall e n m:R, 1 <= e -> n <= m -> e ^R n <= e ^R m.
Proof.
- intros e n m H H0 H1; case H1.
- intros H2; left; apply Rpower_lt; assumption.
- intros H2; rewrite H2; right; reflexivity.
+ intros e n m [H | H]; intros H1.
+ case H1.
+ intros H2; left; apply Rpower_lt; assumption.
+ intros H2; rewrite H2; right; reflexivity.
+ now rewrite <- H; unfold Rpower; rewrite ln_1, !Rmult_0_r; apply Rle_refl.
Qed.
Theorem ln_lt_2 : / 2 < ln 2.
@@ -707,13 +711,18 @@ intros x y z x0 y0; unfold Rpower.
rewrite <- exp_plus, ln_mult, Rmult_plus_distr_l; auto.
Qed.
-Lemma Rle_Rpower_l a b c: 0 <= c -> 0 < a <= b -> Rpower a c <= Rpower b c.
+Lemma Rlt_Rpower_l a b c: 0 < c -> 0 < a < b -> a ^R c < b ^R c.
+Proof.
+intros c0 [a0 ab]; apply exp_increasing.
+now apply Rmult_lt_compat_l; auto; apply ln_increasing; fourier.
+Qed.
+
+Lemma Rle_Rpower_l a b c: 0 <= c -> 0 < a <= b -> a ^R c <= b ^R c.
Proof.
intros [c0 | c0];
[ | intros; rewrite <- c0, !Rpower_O; [apply Rle_refl | |] ].
intros [a0 [ab|ab]].
- left; apply exp_increasing.
- now apply Rmult_lt_compat_l; auto; apply ln_increasing; fourier.
+ now apply Rlt_le, Rlt_Rpower_l;[ | split]; fourier.
rewrite ab; apply Rle_refl.
apply Rlt_le_trans with a; tauto.
tauto.
diff --git a/theories/Reals/Rprod.v b/theories/Reals/Rprod.v
index 2cda84a58..17736af65 100644
--- a/theories/Reals/Rprod.v
+++ b/theories/Reals/Rprod.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Compare.
diff --git a/theories/Reals/Rseries.v b/theories/Reals/Rseries.v
index 4ed943070..3521a476b 100644
--- a/theories/Reals/Rseries.v
+++ b/theories/Reals/Rseries.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Rsigma.v b/theories/Reals/Rsigma.v
index 91b1a979a..83c60751d 100644
--- a/theories/Reals/Rsigma.v
+++ b/theories/Reals/Rsigma.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Rsqrt_def.v b/theories/Reals/Rsqrt_def.v
index 584ba125d..6a3dd9765 100644
--- a/theories/Reals/Rsqrt_def.v
+++ b/theories/Reals/Rsqrt_def.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Sumbool.
diff --git a/theories/Reals/Rtopology.v b/theories/Reals/Rtopology.v
index 91b742978..171dba552 100644
--- a/theories/Reals/Rtopology.v
+++ b/theories/Reals/Rtopology.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Rtrigo.v b/theories/Reals/Rtrigo.v
index db1c46e9c..ffc0adf50 100644
--- a/theories/Reals/Rtrigo.v
+++ b/theories/Reals/Rtrigo.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Rtrigo1.v b/theories/Reals/Rtrigo1.v
index 32b5cb694..bf00f736f 100644
--- a/theories/Reals/Rtrigo1.v
+++ b/theories/Reals/Rtrigo1.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Rtrigo_alt.v b/theories/Reals/Rtrigo_alt.v
index f03ba549b..71b90fb45 100644
--- a/theories/Reals/Rtrigo_alt.v
+++ b/theories/Reals/Rtrigo_alt.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Rtrigo_calc.v b/theories/Reals/Rtrigo_calc.v
index 3cffaee6c..7cbfc6303 100644
--- a/theories/Reals/Rtrigo_calc.v
+++ b/theories/Reals/Rtrigo_calc.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Rtrigo_def.v b/theories/Reals/Rtrigo_def.v
index 88b72f0df..d2faf95bc 100644
--- a/theories/Reals/Rtrigo_def.v
+++ b/theories/Reals/Rtrigo_def.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase Rfunctions SeqSeries Rtrigo_fun Max.
diff --git a/theories/Reals/Rtrigo_fun.v b/theories/Reals/Rtrigo_fun.v
index 4b4423726..744a99a12 100644
--- a/theories/Reals/Rtrigo_fun.v
+++ b/theories/Reals/Rtrigo_fun.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/Rtrigo_reg.v b/theories/Reals/Rtrigo_reg.v
index a0ae73770..456fb6a71 100644
--- a/theories/Reals/Rtrigo_reg.v
+++ b/theories/Reals/Rtrigo_reg.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/SeqProp.v b/theories/Reals/SeqProp.v
index 62a954ce8..38b0b3c4b 100644
--- a/theories/Reals/SeqProp.v
+++ b/theories/Reals/SeqProp.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/SeqSeries.v b/theories/Reals/SeqSeries.v
index 667164d22..ccd205e23 100644
--- a/theories/Reals/SeqSeries.v
+++ b/theories/Reals/SeqSeries.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Reals/SplitAbsolu.v b/theories/Reals/SplitAbsolu.v
index 3dc6ca1f3..aa67b6774 100644
--- a/theories/Reals/SplitAbsolu.v
+++ b/theories/Reals/SplitAbsolu.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbasic_fun.
diff --git a/theories/Reals/SplitRmult.v b/theories/Reals/SplitRmult.v
index ab656440f..a8ff60b07 100644
--- a/theories/Reals/SplitRmult.v
+++ b/theories/Reals/SplitRmult.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(*i Lemma mult_non_zero :(r1,r2:R)``r1<>0`` /\ ``r2<>0`` -> ``r1*r2<>0``. i*)
diff --git a/theories/Reals/Sqrt_reg.v b/theories/Reals/Sqrt_reg.v
index 04062fbbd..d6b386f10 100644
--- a/theories/Reals/Sqrt_reg.v
+++ b/theories/Reals/Sqrt_reg.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Rbase.
diff --git a/theories/Relations/Operators_Properties.v b/theories/Relations/Operators_Properties.v
index e8d80f469..e82a67344 100644
--- a/theories/Relations/Operators_Properties.v
+++ b/theories/Relations/Operators_Properties.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(************************************************************************)
diff --git a/theories/Relations/Relation_Definitions.v b/theories/Relations/Relation_Definitions.v
index 2198ab165..53def4741 100644
--- a/theories/Relations/Relation_Definitions.v
+++ b/theories/Relations/Relation_Definitions.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Section Relation_Definition.
diff --git a/theories/Relations/Relation_Operators.v b/theories/Relations/Relation_Operators.v
index fb6f11158..529e4d08e 100644
--- a/theories/Relations/Relation_Operators.v
+++ b/theories/Relations/Relation_Operators.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(************************************************************************)
diff --git a/theories/Relations/Relations.v b/theories/Relations/Relations.v
index 403e69238..61344974e 100644
--- a/theories/Relations/Relations.v
+++ b/theories/Relations/Relations.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export Relation_Definitions.
diff --git a/theories/Setoids/Setoid.v b/theories/Setoids/Setoid.v
index 2bc0bc3b2..af06bcf47 100644
--- a/theories/Setoids/Setoid.v
+++ b/theories/Setoids/Setoid.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export Coq.Classes.SetoidTactics.
diff --git a/theories/Sets/Classical_sets.v b/theories/Sets/Classical_sets.v
index 68ef08e60..b68022f8f 100644
--- a/theories/Sets/Classical_sets.v
+++ b/theories/Sets/Classical_sets.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Constructive_sets.v b/theories/Sets/Constructive_sets.v
index 823b5cb84..f2475af12 100644
--- a/theories/Sets/Constructive_sets.v
+++ b/theories/Sets/Constructive_sets.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Cpo.v b/theories/Sets/Cpo.v
index a6208ebb2..3977097e8 100644
--- a/theories/Sets/Cpo.v
+++ b/theories/Sets/Cpo.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Ensembles.v b/theories/Sets/Ensembles.v
index cb340f260..c37132078 100644
--- a/theories/Sets/Ensembles.v
+++ b/theories/Sets/Ensembles.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Finite_sets.v b/theories/Sets/Finite_sets.v
index 8934a322a..5c42cbe67 100644
--- a/theories/Sets/Finite_sets.v
+++ b/theories/Sets/Finite_sets.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Finite_sets_facts.v b/theories/Sets/Finite_sets_facts.v
index 714de75ac..1c191613f 100644
--- a/theories/Sets/Finite_sets_facts.v
+++ b/theories/Sets/Finite_sets_facts.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Image.v b/theories/Sets/Image.v
index 27ce2d4dc..3e28bbe91 100644
--- a/theories/Sets/Image.v
+++ b/theories/Sets/Image.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Infinite_sets.v b/theories/Sets/Infinite_sets.v
index 845861d70..bdeeb6a7c 100644
--- a/theories/Sets/Infinite_sets.v
+++ b/theories/Sets/Infinite_sets.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Integers.v b/theories/Sets/Integers.v
index 1471a44e1..225e388b1 100644
--- a/theories/Sets/Integers.v
+++ b/theories/Sets/Integers.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Multiset.v b/theories/Sets/Multiset.v
index 01805fe92..a79ddead2 100644
--- a/theories/Sets/Multiset.v
+++ b/theories/Sets/Multiset.v
@@ -1,14 +1,17 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* G. Huet 1-9-95 *)
Require Import Permut Setoid.
+Require Plus. (* comm. and ass. of plus *)
Set Implicit Arguments.
@@ -67,9 +70,6 @@ Section multiset_defs.
unfold meq; unfold munion; simpl; auto.
Qed.
-
- Require Plus. (* comm. and ass. of plus *)
-
Lemma munion_comm : forall x y:multiset, meq (munion x y) (munion y x).
Proof.
unfold meq; unfold multiplicity; unfold munion.
diff --git a/theories/Sets/Partial_Order.v b/theories/Sets/Partial_Order.v
index a9f136eff..17fc0ed25 100644
--- a/theories/Sets/Partial_Order.v
+++ b/theories/Sets/Partial_Order.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Permut.v b/theories/Sets/Permut.v
index 48d2248da..86a500dfd 100644
--- a/theories/Sets/Permut.v
+++ b/theories/Sets/Permut.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* G. Huet 1-9-95 *)
diff --git a/theories/Sets/Powerset.v b/theories/Sets/Powerset.v
index a98b4aca2..88bcd6555 100644
--- a/theories/Sets/Powerset.v
+++ b/theories/Sets/Powerset.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Powerset_Classical_facts.v b/theories/Sets/Powerset_Classical_facts.v
index 66cc44fbd..7975a0269 100644
--- a/theories/Sets/Powerset_Classical_facts.v
+++ b/theories/Sets/Powerset_Classical_facts.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Powerset_facts.v b/theories/Sets/Powerset_facts.v
index 209c22f71..81b475ac6 100644
--- a/theories/Sets/Powerset_facts.v
+++ b/theories/Sets/Powerset_facts.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Relations_1.v b/theories/Sets/Relations_1.v
index 7f1b03cf3..1ed745995 100644
--- a/theories/Sets/Relations_1.v
+++ b/theories/Sets/Relations_1.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Relations_1_facts.v b/theories/Sets/Relations_1_facts.v
index 679525bf4..296ec42ad 100644
--- a/theories/Sets/Relations_1_facts.v
+++ b/theories/Sets/Relations_1_facts.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Relations_2.v b/theories/Sets/Relations_2.v
index 8d19eab8c..cc839506f 100644
--- a/theories/Sets/Relations_2.v
+++ b/theories/Sets/Relations_2.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Relations_2_facts.v b/theories/Sets/Relations_2_facts.v
index 1fc5a2f10..36da36844 100644
--- a/theories/Sets/Relations_2_facts.v
+++ b/theories/Sets/Relations_2_facts.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Relations_3.v b/theories/Sets/Relations_3.v
index 292cdbb5d..de3212e2e 100644
--- a/theories/Sets/Relations_3.v
+++ b/theories/Sets/Relations_3.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Relations_3_facts.v b/theories/Sets/Relations_3_facts.v
index 59a987f15..0c1f670d0 100644
--- a/theories/Sets/Relations_3_facts.v
+++ b/theories/Sets/Relations_3_facts.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(****************************************************************************)
(* *)
diff --git a/theories/Sets/Uniset.v b/theories/Sets/Uniset.v
index 8406c049e..7940bda1a 100644
--- a/theories/Sets/Uniset.v
+++ b/theories/Sets/Uniset.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Sets as characteristic functions *)
@@ -11,7 +13,7 @@
(* G. Huet 1-9-95 *)
(* Updated Papageno 12/98 *)
-Require Import Bool.
+Require Import Bool Permut.
Set Implicit Arguments.
@@ -138,8 +140,6 @@ Hint Resolve seq_right.
(** Here we should make uniset an abstract datatype, by hiding [Charac],
[union], [charac]; all further properties are proved abstractly *)
-Require Import Permut.
-
Lemma union_rotate :
forall x y z:uniset, seq (union x (union y z)) (union z (union x y)).
Proof.
diff --git a/theories/Sorting/Heap.v b/theories/Sorting/Heap.v
index eaadb440f..d9e5ad676 100644
--- a/theories/Sorting/Heap.v
+++ b/theories/Sorting/Heap.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This file is deprecated, for a tree on list, use [Mergesort.v]. *)
@@ -134,7 +136,7 @@ Section defs.
(munion (list_contents _ eqA_dec l1) (list_contents _ eqA_dec l2)) ->
(forall a, HdRel leA a l1 -> HdRel leA a l2 -> HdRel leA a l) ->
merge_lem l1 l2.
- Require Import Morphisms.
+ Import Morphisms.
Instance: Equivalence (@meq A).
Proof. constructor; auto with datatypes. red. apply meq_trans. Defined.
diff --git a/theories/Sorting/Mergesort.v b/theories/Sorting/Mergesort.v
index 51e34f42d..824d000d2 100644
--- a/theories/Sorting/Mergesort.v
+++ b/theories/Sorting/Mergesort.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** A modular implementation of mergesort (the complexity is O(n.log n) in
diff --git a/theories/Sorting/PermutEq.v b/theories/Sorting/PermutEq.v
index 90f64beec..97297f7ef 100644
--- a/theories/Sorting/PermutEq.v
+++ b/theories/Sorting/PermutEq.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Relations Setoid SetoidList List Multiset PermutSetoid Permutation Omega.
diff --git a/theories/Sorting/PermutSetoid.v b/theories/Sorting/PermutSetoid.v
index 3ccf15d5e..08bc400f0 100644
--- a/theories/Sorting/PermutSetoid.v
+++ b/theories/Sorting/PermutSetoid.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Omega Relations Multiset SetoidList.
diff --git a/theories/Sorting/Permutation.v b/theories/Sorting/Permutation.v
index 301548a1d..7b99b3626 100644
--- a/theories/Sorting/Permutation.v
+++ b/theories/Sorting/Permutation.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(*********************************************************************)
diff --git a/theories/Sorting/Sorted.v b/theories/Sorting/Sorted.v
index 2e99f0d6b..89e9c7f3e 100644
--- a/theories/Sorting/Sorted.v
+++ b/theories/Sorting/Sorted.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Made by Hugo Herbelin *)
diff --git a/theories/Sorting/Sorting.v b/theories/Sorting/Sorting.v
index 1152c1118..c2be14616 100644
--- a/theories/Sorting/Sorting.v
+++ b/theories/Sorting/Sorting.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export Sorted.
diff --git a/theories/Strings/Ascii.v b/theories/Strings/Ascii.v
index 0f0e760c7..5154b75b3 100644
--- a/theories/Strings/Ascii.v
+++ b/theories/Strings/Ascii.v
@@ -1,10 +1,12 @@
-(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(************************************************************************)
(** Contributed by Laurent Théry (INRIA);
diff --git a/theories/Strings/String.v b/theories/Strings/String.v
index c39b47fb1..2be6618ad 100644
--- a/theories/Strings/String.v
+++ b/theories/Strings/String.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Contributed by Laurent Théry (INRIA);
@@ -163,6 +165,18 @@ intros n0 H; apply Rec; simpl; auto.
apply Le.le_S_n; auto.
Qed.
+(** *** Concatenating lists of strings *)
+
+(** [concat sep sl] concatenates the list of strings [sl], inserting
+ the separator string [sep] between each. *)
+
+Fixpoint concat (sep : string) (ls : list string) :=
+ match ls with
+ | nil => EmptyString
+ | cons x nil => x
+ | cons x xs => x ++ sep ++ concat sep xs
+ end.
+
(** *** Test functions *)
(** Test if [s1] is a prefix of [s2] *)
diff --git a/theories/Structures/DecidableType.v b/theories/Structures/DecidableType.v
index d811f04ef..24333ad81 100644
--- a/theories/Structures/DecidableType.v
+++ b/theories/Structures/DecidableType.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
Require Export SetoidList.
Require Equalities.
diff --git a/theories/Structures/DecidableTypeEx.v b/theories/Structures/DecidableTypeEx.v
index 163a40f2e..8dd2e7103 100644
--- a/theories/Structures/DecidableTypeEx.v
+++ b/theories/Structures/DecidableTypeEx.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
Require Import DecidableType OrderedType OrderedTypeEx.
Set Implicit Arguments.
diff --git a/theories/Structures/Equalities.v b/theories/Structures/Equalities.v
index 747d03f8a..5f60a979c 100644
--- a/theories/Structures/Equalities.v
+++ b/theories/Structures/Equalities.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
Require Export RelationClasses.
Require Import Bool Morphisms Setoid.
diff --git a/theories/Structures/EqualitiesFacts.v b/theories/Structures/EqualitiesFacts.v
index cee3d63f0..7b6ee2eac 100644
--- a/theories/Structures/EqualitiesFacts.v
+++ b/theories/Structures/EqualitiesFacts.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
Require Import Equalities Bool SetoidList RelationPairs.
diff --git a/theories/Structures/GenericMinMax.v b/theories/Structures/GenericMinMax.v
index ac52d1bbb..05edc6ccd 100644
--- a/theories/Structures/GenericMinMax.v
+++ b/theories/Structures/GenericMinMax.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
Require Import Orders OrdersTac OrdersFacts Setoid Morphisms Basics.
diff --git a/theories/Structures/OrderedType.v b/theories/Structures/OrderedType.v
index 93ca383b2..f6fc247d5 100644
--- a/theories/Structures/OrderedType.v
+++ b/theories/Structures/OrderedType.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
Require Export SetoidList Morphisms OrdersTac.
Set Implicit Arguments.
diff --git a/theories/Structures/OrderedTypeAlt.v b/theories/Structures/OrderedTypeAlt.v
index b054496e9..278046a89 100644
--- a/theories/Structures/OrderedTypeAlt.v
+++ b/theories/Structures/OrderedTypeAlt.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
Require Import OrderedType.
(** * An alternative (but equivalent) presentation for an Ordered Type
diff --git a/theories/Structures/OrderedTypeEx.v b/theories/Structures/OrderedTypeEx.v
index 3c6afc7b2..f2a9a5691 100644
--- a/theories/Structures/OrderedTypeEx.v
+++ b/theories/Structures/OrderedTypeEx.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
Require Import OrderedType.
Require Import ZArith.
@@ -55,7 +57,7 @@ Module Nat_as_OT <: UsualOrderedType.
Definition compare x y : Compare lt eq x y.
Proof.
- case_eq (nat_compare x y); intro.
+ case_eq (Nat.compare x y); intro.
- apply EQ. now apply nat_compare_eq.
- apply LT. now apply nat_compare_Lt_lt.
- apply GT. now apply nat_compare_Gt_gt.
diff --git a/theories/Structures/Orders.v b/theories/Structures/Orders.v
index 724690b42..42756ad33 100644
--- a/theories/Structures/Orders.v
+++ b/theories/Structures/Orders.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
Require Export Relations Morphisms Setoid Equalities.
Set Implicit Arguments.
diff --git a/theories/Structures/OrdersAlt.v b/theories/Structures/OrdersAlt.v
index 5dd917a71..ad6a38763 100644
--- a/theories/Structures/OrdersAlt.v
+++ b/theories/Structures/OrdersAlt.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(* Finite sets library.
* Authors: Pierre Letouzey and Jean-Christophe Filliâtre
diff --git a/theories/Structures/OrdersEx.v b/theories/Structures/OrdersEx.v
index 89c563882..93168f7df 100644
--- a/theories/Structures/OrdersEx.v
+++ b/theories/Structures/OrdersEx.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(* Finite sets library.
* Authors: Pierre Letouzey and Jean-Christophe Filliâtre
diff --git a/theories/Structures/OrdersFacts.v b/theories/Structures/OrdersFacts.v
index 0115d8a54..87df6b479 100644
--- a/theories/Structures/OrdersFacts.v
+++ b/theories/Structures/OrdersFacts.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
Require Import Bool Basics OrdersTac.
Require Export Orders.
diff --git a/theories/Structures/OrdersLists.v b/theories/Structures/OrdersLists.v
index bf8529bc7..abdb9eff0 100644
--- a/theories/Structures/OrdersLists.v
+++ b/theories/Structures/OrdersLists.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
Require Export RelationPairs SetoidList Orders EqualitiesFacts.
diff --git a/theories/Structures/OrdersTac.v b/theories/Structures/OrdersTac.v
index 475a25a41..ebd8ee8fc 100644
--- a/theories/Structures/OrdersTac.v
+++ b/theories/Structures/OrdersTac.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
Require Import Setoid Morphisms Basics Equalities Orders.
Set Implicit Arguments.
diff --git a/theories/Unicode/Utf8.v b/theories/Unicode/Utf8.v
index a8b512a8f..6cc9ea09d 100644
--- a/theories/Unicode/Utf8.v
+++ b/theories/Unicode/Utf8.v
@@ -1,10 +1,12 @@
(* -*- coding:utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export Utf8_core.
diff --git a/theories/Unicode/Utf8_core.v b/theories/Unicode/Utf8_core.v
index a0545c0a4..5a8931a8c 100644
--- a/theories/Unicode/Utf8_core.v
+++ b/theories/Unicode/Utf8_core.v
@@ -1,19 +1,23 @@
(* -*- coding:utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* Logic *)
-Notation "∀ x .. y , P" := (forall x, .. (forall y, P) ..)
- (at level 200, x binder, y binder, right associativity) : type_scope.
-Notation "∃ x .. y , P" := (exists x, .. (exists y, P) ..)
- (at level 200, x binder, y binder, right associativity) : type_scope.
+Notation "∀ x .. y , P" := (forall x, .. (forall y, P) ..)
+ (at level 200, x binder, y binder, right associativity,
+ format "'[ ' ∀ x .. y ']' , P") : type_scope.
+Notation "∃ x .. y , P" := (exists x, .. (exists y, P) ..)
+ (at level 200, x binder, y binder, right associativity,
+ format "'[ ' ∃ x .. y ']' , P") : type_scope.
Notation "x ∨ y" := (x \/ y) (at level 85, right associativity) : type_scope.
Notation "x ∧ y" := (x /\ y) (at level 80, right associativity) : type_scope.
@@ -25,5 +29,6 @@ Notation "¬ x" := (~x) (at level 75, right associativity) : type_scope.
Notation "x ≠ y" := (x <> y) (at level 70) : type_scope.
(* Abstraction *)
-Notation "'λ' x .. y , t" := (fun x => .. (fun y => t) ..)
- (at level 200, x binder, y binder, right associativity).
+Notation "'λ' x .. y , t" := (fun x => .. (fun y => t) ..)
+ (at level 200, x binder, y binder, right associativity,
+ format "'[ ' 'λ' x .. y ']' , t").
diff --git a/theories/Vectors/Fin.v b/theories/Vectors/Fin.v
index 2955184f6..4088843a1 100644
--- a/theories/Vectors/Fin.v
+++ b/theories/Vectors/Fin.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Arith_base.
diff --git a/theories/Vectors/Vector.v b/theories/Vectors/Vector.v
index 19d749fc8..08158769f 100644
--- a/theories/Vectors/Vector.v
+++ b/theories/Vectors/Vector.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Vectors.
diff --git a/theories/Vectors/VectorDef.v b/theories/Vectors/VectorDef.v
index c49451776..f6f3cafa2 100644
--- a/theories/Vectors/VectorDef.v
+++ b/theories/Vectors/VectorDef.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Definitions of Vectors and functions to use them
@@ -305,12 +307,10 @@ End VECTORLIST.
Module VectorNotations.
Delimit Scope vector_scope with vector.
Notation "[ ]" := [] (format "[ ]") : vector_scope.
-Notation "[]" := [] (compat "8.5") : vector_scope.
Notation "h :: t" := (h :: t) (at level 60, right associativity)
: vector_scope.
Notation "[ x ]" := (x :: []) : vector_scope.
Notation "[ x ; y ; .. ; z ]" := (cons _ x _ (cons _ y _ .. (cons _ z _ (nil _)) ..)) : vector_scope.
-Notation "[ x ; .. ; y ]" := (cons _ x _ .. (cons _ y _ (nil _)) ..) (compat "8.4") : vector_scope.
Notation "v [@ p ]" := (nth v p) (at level 1, format "v [@ p ]") : vector_scope.
Open Scope vector_scope.
End VectorNotations.
diff --git a/theories/Vectors/VectorEq.v b/theories/Vectors/VectorEq.v
index 04c570731..317f3f1c6 100644
--- a/theories/Vectors/VectorEq.v
+++ b/theories/Vectors/VectorEq.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Equalities and Vector relations
diff --git a/theories/Vectors/VectorSpec.v b/theories/Vectors/VectorSpec.v
index 869d0fb5a..34dbaf36a 100644
--- a/theories/Vectors/VectorSpec.v
+++ b/theories/Vectors/VectorSpec.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Proofs of specification for functions defined over Vector
diff --git a/theories/Wellfounded/Disjoint_Union.v b/theories/Wellfounded/Disjoint_Union.v
index 693b0892a..10d902743 100644
--- a/theories/Wellfounded/Disjoint_Union.v
+++ b/theories/Wellfounded/Disjoint_Union.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Author: Cristina Cornes
diff --git a/theories/Wellfounded/Inclusion.v b/theories/Wellfounded/Inclusion.v
index 7fba5ef8d..ff233ef9c 100644
--- a/theories/Wellfounded/Inclusion.v
+++ b/theories/Wellfounded/Inclusion.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Author: Bruno Barras *)
diff --git a/theories/Wellfounded/Inverse_Image.v b/theories/Wellfounded/Inverse_Image.v
index b743edc2b..4a4ab87d9 100644
--- a/theories/Wellfounded/Inverse_Image.v
+++ b/theories/Wellfounded/Inverse_Image.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Author: Bruno Barras *)
diff --git a/theories/Wellfounded/Lexicographic_Exponentiation.v b/theories/Wellfounded/Lexicographic_Exponentiation.v
index 83a4926e4..684efeebe 100644
--- a/theories/Wellfounded/Lexicographic_Exponentiation.v
+++ b/theories/Wellfounded/Lexicographic_Exponentiation.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Author: Cristina Cornes
diff --git a/theories/Wellfounded/Lexicographic_Product.v b/theories/Wellfounded/Lexicographic_Product.v
index 0b09ada9f..37fd2fb23 100644
--- a/theories/Wellfounded/Lexicographic_Product.v
+++ b/theories/Wellfounded/Lexicographic_Product.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Authors: Bruno Barras, Cristina Cornes *)
diff --git a/theories/Wellfounded/Transitive_Closure.v b/theories/Wellfounded/Transitive_Closure.v
index b7a8e63e5..59068623a 100644
--- a/theories/Wellfounded/Transitive_Closure.v
+++ b/theories/Wellfounded/Transitive_Closure.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Author: Bruno Barras *)
diff --git a/theories/Wellfounded/Union.v b/theories/Wellfounded/Union.v
index cf897afd7..9e671651f 100644
--- a/theories/Wellfounded/Union.v
+++ b/theories/Wellfounded/Union.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Author: Bruno Barras *)
diff --git a/theories/Wellfounded/Well_Ordering.v b/theories/Wellfounded/Well_Ordering.v
index aab864e83..fd363d02c 100644
--- a/theories/Wellfounded/Well_Ordering.v
+++ b/theories/Wellfounded/Well_Ordering.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Author: Cristina Cornes.
diff --git a/theories/Wellfounded/Wellfounded.v b/theories/Wellfounded/Wellfounded.v
index 17b3138e4..bfe09e40b 100644
--- a/theories/Wellfounded/Wellfounded.v
+++ b/theories/Wellfounded/Wellfounded.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export Disjoint_Union.
diff --git a/theories/ZArith/BinInt.v b/theories/ZArith/BinInt.v
index e6fd0f22e..cf7397b57 100644
--- a/theories/ZArith/BinInt.v
+++ b/theories/ZArith/BinInt.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export BinNums BinPos Pnat.
@@ -1565,94 +1567,94 @@ End Z2Pos.
(** Compatibility Notations *)
-Notation Zdouble_plus_one := Z.succ_double (compat "8.3").
-Notation Zdouble_minus_one := Z.pred_double (compat "8.3").
-Notation Zdouble := Z.double (compat "8.3").
-Notation ZPminus := Z.pos_sub (compat "8.3").
-Notation Zsucc' := Z.succ (compat "8.3").
-Notation Zpred' := Z.pred (compat "8.3").
-Notation Zplus' := Z.add (compat "8.3").
-Notation Zplus := Z.add (compat "8.3"). (* Slightly incompatible *)
-Notation Zopp := Z.opp (compat "8.3").
-Notation Zsucc := Z.succ (compat "8.3").
-Notation Zpred := Z.pred (compat "8.3").
-Notation Zminus := Z.sub (compat "8.3").
-Notation Zmult := Z.mul (compat "8.3").
-Notation Zcompare := Z.compare (compat "8.3").
-Notation Zsgn := Z.sgn (compat "8.3").
-Notation Zle := Z.le (compat "8.3").
-Notation Zge := Z.ge (compat "8.3").
-Notation Zlt := Z.lt (compat "8.3").
-Notation Zgt := Z.gt (compat "8.3").
-Notation Zmax := Z.max (compat "8.3").
-Notation Zmin := Z.min (compat "8.3").
-Notation Zabs := Z.abs (compat "8.3").
-Notation Zabs_nat := Z.abs_nat (compat "8.3").
-Notation Zabs_N := Z.abs_N (compat "8.3").
-Notation Z_of_nat := Z.of_nat (compat "8.3").
-Notation Z_of_N := Z.of_N (compat "8.3").
-
-Notation Zind := Z.peano_ind (compat "8.3").
-Notation Zopp_0 := Z.opp_0 (compat "8.3").
-Notation Zopp_involutive := Z.opp_involutive (compat "8.3").
-Notation Zopp_inj := Z.opp_inj (compat "8.3").
-Notation Zplus_0_l := Z.add_0_l (compat "8.3").
-Notation Zplus_0_r := Z.add_0_r (compat "8.3").
-Notation Zplus_comm := Z.add_comm (compat "8.3").
-Notation Zopp_plus_distr := Z.opp_add_distr (compat "8.3").
-Notation Zopp_succ := Z.opp_succ (compat "8.3").
-Notation Zplus_opp_r := Z.add_opp_diag_r (compat "8.3").
-Notation Zplus_opp_l := Z.add_opp_diag_l (compat "8.3").
-Notation Zplus_assoc := Z.add_assoc (compat "8.3").
-Notation Zplus_permute := Z.add_shuffle3 (compat "8.3").
-Notation Zplus_reg_l := Z.add_reg_l (compat "8.3").
-Notation Zplus_succ_l := Z.add_succ_l (compat "8.3").
-Notation Zplus_succ_comm := Z.add_succ_comm (compat "8.3").
-Notation Zsucc_discr := Z.neq_succ_diag_r (compat "8.3").
-Notation Zsucc_inj := Z.succ_inj (compat "8.3").
-Notation Zsucc'_inj := Z.succ_inj (compat "8.3").
-Notation Zsucc'_pred' := Z.succ_pred (compat "8.3").
-Notation Zpred'_succ' := Z.pred_succ (compat "8.3").
-Notation Zpred'_inj := Z.pred_inj (compat "8.3").
-Notation Zsucc'_discr := Z.neq_succ_diag_r (compat "8.3").
-Notation Zminus_0_r := Z.sub_0_r (compat "8.3").
-Notation Zminus_diag := Z.sub_diag (compat "8.3").
-Notation Zminus_plus_distr := Z.sub_add_distr (compat "8.3").
-Notation Zminus_succ_r := Z.sub_succ_r (compat "8.3").
-Notation Zminus_plus := Z.add_simpl_l (compat "8.3").
-Notation Zmult_0_l := Z.mul_0_l (compat "8.3").
-Notation Zmult_0_r := Z.mul_0_r (compat "8.3").
-Notation Zmult_1_l := Z.mul_1_l (compat "8.3").
-Notation Zmult_1_r := Z.mul_1_r (compat "8.3").
-Notation Zmult_comm := Z.mul_comm (compat "8.3").
-Notation Zmult_assoc := Z.mul_assoc (compat "8.3").
-Notation Zmult_permute := Z.mul_shuffle3 (compat "8.3").
-Notation Zmult_1_inversion_l := Z.mul_eq_1 (compat "8.3").
-Notation Zdouble_mult := Z.double_spec (compat "8.3").
-Notation Zdouble_plus_one_mult := Z.succ_double_spec (compat "8.3").
-Notation Zopp_mult_distr_l_reverse := Z.mul_opp_l (compat "8.3").
-Notation Zmult_opp_opp := Z.mul_opp_opp (compat "8.3").
-Notation Zmult_opp_comm := Z.mul_opp_comm (compat "8.3").
-Notation Zopp_eq_mult_neg_1 := Z.opp_eq_mul_m1 (compat "8.3").
-Notation Zmult_plus_distr_r := Z.mul_add_distr_l (compat "8.3").
-Notation Zmult_plus_distr_l := Z.mul_add_distr_r (compat "8.3").
-Notation Zmult_minus_distr_r := Z.mul_sub_distr_r (compat "8.3").
-Notation Zmult_reg_l := Z.mul_reg_l (compat "8.3").
-Notation Zmult_reg_r := Z.mul_reg_r (compat "8.3").
-Notation Zmult_succ_l := Z.mul_succ_l (compat "8.3").
-Notation Zmult_succ_r := Z.mul_succ_r (compat "8.3").
-
-Notation Zpos_xI := Pos2Z.inj_xI (compat "8.3").
-Notation Zpos_xO := Pos2Z.inj_xO (compat "8.3").
-Notation Zneg_xI := Pos2Z.neg_xI (compat "8.3").
-Notation Zneg_xO := Pos2Z.neg_xO (compat "8.3").
-Notation Zopp_neg := Pos2Z.opp_neg (compat "8.3").
-Notation Zpos_succ_morphism := Pos2Z.inj_succ (compat "8.3").
-Notation Zpos_mult_morphism := Pos2Z.inj_mul (compat "8.3").
-Notation Zpos_minus_morphism := Pos2Z.inj_sub (compat "8.3").
-Notation Zpos_eq_rev := Pos2Z.inj (compat "8.3").
-Notation Zpos_plus_distr := Pos2Z.inj_add (compat "8.3").
-Notation Zneg_plus_distr := Pos2Z.add_neg_neg (compat "8.3").
+Notation Zdouble_plus_one := Z.succ_double (only parsing).
+Notation Zdouble_minus_one := Z.pred_double (only parsing).
+Notation Zdouble := Z.double (compat "8.6").
+Notation ZPminus := Z.pos_sub (only parsing).
+Notation Zsucc' := Z.succ (compat "8.6").
+Notation Zpred' := Z.pred (compat "8.6").
+Notation Zplus' := Z.add (compat "8.6").
+Notation Zplus := Z.add (only parsing). (* Slightly incompatible *)
+Notation Zopp := Z.opp (compat "8.6").
+Notation Zsucc := Z.succ (compat "8.6").
+Notation Zpred := Z.pred (compat "8.6").
+Notation Zminus := Z.sub (only parsing).
+Notation Zmult := Z.mul (only parsing).
+Notation Zcompare := Z.compare (compat "8.6").
+Notation Zsgn := Z.sgn (compat "8.6").
+Notation Zle := Z.le (compat "8.6").
+Notation Zge := Z.ge (compat "8.6").
+Notation Zlt := Z.lt (compat "8.6").
+Notation Zgt := Z.gt (compat "8.6").
+Notation Zmax := Z.max (compat "8.6").
+Notation Zmin := Z.min (compat "8.6").
+Notation Zabs := Z.abs (compat "8.6").
+Notation Zabs_nat := Z.abs_nat (compat "8.6").
+Notation Zabs_N := Z.abs_N (compat "8.6").
+Notation Z_of_nat := Z.of_nat (only parsing).
+Notation Z_of_N := Z.of_N (only parsing).
+
+Notation Zind := Z.peano_ind (only parsing).
+Notation Zopp_0 := Z.opp_0 (compat "8.6").
+Notation Zopp_involutive := Z.opp_involutive (compat "8.6").
+Notation Zopp_inj := Z.opp_inj (compat "8.6").
+Notation Zplus_0_l := Z.add_0_l (only parsing).
+Notation Zplus_0_r := Z.add_0_r (only parsing).
+Notation Zplus_comm := Z.add_comm (only parsing).
+Notation Zopp_plus_distr := Z.opp_add_distr (only parsing).
+Notation Zopp_succ := Z.opp_succ (compat "8.6").
+Notation Zplus_opp_r := Z.add_opp_diag_r (only parsing).
+Notation Zplus_opp_l := Z.add_opp_diag_l (only parsing).
+Notation Zplus_assoc := Z.add_assoc (only parsing).
+Notation Zplus_permute := Z.add_shuffle3 (only parsing).
+Notation Zplus_reg_l := Z.add_reg_l (only parsing).
+Notation Zplus_succ_l := Z.add_succ_l (only parsing).
+Notation Zplus_succ_comm := Z.add_succ_comm (only parsing).
+Notation Zsucc_discr := Z.neq_succ_diag_r (only parsing).
+Notation Zsucc_inj := Z.succ_inj (compat "8.6").
+Notation Zsucc'_inj := Z.succ_inj (compat "8.6").
+Notation Zsucc'_pred' := Z.succ_pred (compat "8.6").
+Notation Zpred'_succ' := Z.pred_succ (compat "8.6").
+Notation Zpred'_inj := Z.pred_inj (compat "8.6").
+Notation Zsucc'_discr := Z.neq_succ_diag_r (only parsing).
+Notation Zminus_0_r := Z.sub_0_r (only parsing).
+Notation Zminus_diag := Z.sub_diag (only parsing).
+Notation Zminus_plus_distr := Z.sub_add_distr (only parsing).
+Notation Zminus_succ_r := Z.sub_succ_r (only parsing).
+Notation Zminus_plus := Z.add_simpl_l (only parsing).
+Notation Zmult_0_l := Z.mul_0_l (only parsing).
+Notation Zmult_0_r := Z.mul_0_r (only parsing).
+Notation Zmult_1_l := Z.mul_1_l (only parsing).
+Notation Zmult_1_r := Z.mul_1_r (only parsing).
+Notation Zmult_comm := Z.mul_comm (only parsing).
+Notation Zmult_assoc := Z.mul_assoc (only parsing).
+Notation Zmult_permute := Z.mul_shuffle3 (only parsing).
+Notation Zmult_1_inversion_l := Z.mul_eq_1 (only parsing).
+Notation Zdouble_mult := Z.double_spec (only parsing).
+Notation Zdouble_plus_one_mult := Z.succ_double_spec (only parsing).
+Notation Zopp_mult_distr_l_reverse := Z.mul_opp_l (only parsing).
+Notation Zmult_opp_opp := Z.mul_opp_opp (only parsing).
+Notation Zmult_opp_comm := Z.mul_opp_comm (only parsing).
+Notation Zopp_eq_mult_neg_1 := Z.opp_eq_mul_m1 (only parsing).
+Notation Zmult_plus_distr_r := Z.mul_add_distr_l (only parsing).
+Notation Zmult_plus_distr_l := Z.mul_add_distr_r (only parsing).
+Notation Zmult_minus_distr_r := Z.mul_sub_distr_r (only parsing).
+Notation Zmult_reg_l := Z.mul_reg_l (only parsing).
+Notation Zmult_reg_r := Z.mul_reg_r (only parsing).
+Notation Zmult_succ_l := Z.mul_succ_l (only parsing).
+Notation Zmult_succ_r := Z.mul_succ_r (only parsing).
+
+Notation Zpos_xI := Pos2Z.inj_xI (only parsing).
+Notation Zpos_xO := Pos2Z.inj_xO (only parsing).
+Notation Zneg_xI := Pos2Z.neg_xI (only parsing).
+Notation Zneg_xO := Pos2Z.neg_xO (only parsing).
+Notation Zopp_neg := Pos2Z.opp_neg (only parsing).
+Notation Zpos_succ_morphism := Pos2Z.inj_succ (only parsing).
+Notation Zpos_mult_morphism := Pos2Z.inj_mul (only parsing).
+Notation Zpos_minus_morphism := Pos2Z.inj_sub (only parsing).
+Notation Zpos_eq_rev := Pos2Z.inj (only parsing).
+Notation Zpos_plus_distr := Pos2Z.inj_add (only parsing).
+Notation Zneg_plus_distr := Pos2Z.add_neg_neg (only parsing).
Notation Z := Z (only parsing).
Notation Z_rect := Z_rect (only parsing).
diff --git a/theories/ZArith/BinIntDef.v b/theories/ZArith/BinIntDef.v
index 443667f48..db4de0b90 100644
--- a/theories/ZArith/BinIntDef.v
+++ b/theories/ZArith/BinIntDef.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Export BinNums.
@@ -299,6 +301,23 @@ Definition to_pos (z:Z) : positive :=
| _ => 1%positive
end.
+(** Conversion with a decimal representation for printing/parsing *)
+
+Definition of_uint (d:Decimal.uint) := of_N (Pos.of_uint d).
+
+Definition of_int (d:Decimal.int) :=
+ match d with
+ | Decimal.Pos d => of_uint d
+ | Decimal.Neg d => opp (of_uint d)
+ end.
+
+Definition to_int n :=
+ match n with
+ | 0 => Decimal.Pos Decimal.zero
+ | pos p => Decimal.Pos (Pos.to_uint p)
+ | neg p => Decimal.Neg (Pos.to_uint p)
+ end.
+
(** ** Iteration of a function
By convention, iterating a negative number of times is identity.
diff --git a/theories/ZArith/Int.v b/theories/ZArith/Int.v
index 72021f2e4..2f3bf9a32 100644
--- a/theories/ZArith/Int.v
+++ b/theories/ZArith/Int.v
@@ -1,10 +1,12 @@
-(***********************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
-(* \VV/ *************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(***********************************************************************)
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
(** * An light axiomatization of integers (used in MSetAVL). *)
@@ -452,7 +454,7 @@ Module Z_as_Int <: Int.
Proof. reflexivity. Qed.
(** Compatibility notations for Coq v8.4 *)
- Notation plus := add (compat "8.4").
- Notation minus := sub (compat "8.4").
- Notation mult := mul (compat "8.4").
+ Notation plus := add (only parsing).
+ Notation minus := sub (only parsing).
+ Notation mult := mul (only parsing).
End Z_as_Int.
diff --git a/theories/ZArith/Wf_Z.v b/theories/ZArith/Wf_Z.v
index f6583a335..864342088 100644
--- a/theories/ZArith/Wf_Z.v
+++ b/theories/ZArith/Wf_Z.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import BinInt.
diff --git a/theories/ZArith/ZArith.v b/theories/ZArith/ZArith.v
index 5f7b571d9..0842920bb 100644
--- a/theories/ZArith/ZArith.v
+++ b/theories/ZArith/ZArith.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Library for manipulating integers based on binary encoding *)
diff --git a/theories/ZArith/ZArith_base.v b/theories/ZArith/ZArith_base.v
index 9135f5591..3d6bcddcd 100644
--- a/theories/ZArith/ZArith_base.v
+++ b/theories/ZArith/ZArith_base.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Library for manipulating integers based on binary encoding.
diff --git a/theories/ZArith/ZArith_dec.v b/theories/ZArith/ZArith_dec.v
index 0ee233a35..9bcdb73af 100644
--- a/theories/ZArith/ZArith_dec.v
+++ b/theories/ZArith/ZArith_dec.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Sumbool.
@@ -32,7 +34,7 @@ Lemma Zcompare_rec (P:Set) (n m:Z) :
((n ?= m) = Eq -> P) -> ((n ?= m) = Lt -> P) -> ((n ?= m) = Gt -> P) -> P.
Proof. apply Zcompare_rect. Defined.
-Notation Z_eq_dec := Z.eq_dec (compat "8.3").
+Notation Z_eq_dec := Z.eq_dec (compat "8.6").
Section decidability.
diff --git a/theories/ZArith/Zabs.v b/theories/ZArith/Zabs.v
index d4a46930a..0d8450e36 100644
--- a/theories/ZArith/Zabs.v
+++ b/theories/ZArith/Zabs.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Binary Integers : properties of absolute value *)
@@ -27,17 +29,17 @@ Local Open Scope Z_scope.
(**********************************************************************)
(** * Properties of absolute value *)
-Notation Zabs_eq := Z.abs_eq (compat "8.3").
-Notation Zabs_non_eq := Z.abs_neq (compat "8.3").
-Notation Zabs_Zopp := Z.abs_opp (compat "8.3").
-Notation Zabs_pos := Z.abs_nonneg (compat "8.3").
-Notation Zabs_involutive := Z.abs_involutive (compat "8.3").
-Notation Zabs_eq_case := Z.abs_eq_cases (compat "8.3").
-Notation Zabs_triangle := Z.abs_triangle (compat "8.3").
-Notation Zsgn_Zabs := Z.sgn_abs (compat "8.3").
-Notation Zabs_Zsgn := Z.abs_sgn (compat "8.3").
-Notation Zabs_Zmult := Z.abs_mul (compat "8.3").
-Notation Zabs_square := Z.abs_square (compat "8.3").
+Notation Zabs_eq := Z.abs_eq (compat "8.6").
+Notation Zabs_non_eq := Z.abs_neq (only parsing).
+Notation Zabs_Zopp := Z.abs_opp (only parsing).
+Notation Zabs_pos := Z.abs_nonneg (only parsing).
+Notation Zabs_involutive := Z.abs_involutive (compat "8.6").
+Notation Zabs_eq_case := Z.abs_eq_cases (only parsing).
+Notation Zabs_triangle := Z.abs_triangle (compat "8.6").
+Notation Zsgn_Zabs := Z.sgn_abs (only parsing).
+Notation Zabs_Zsgn := Z.abs_sgn (only parsing).
+Notation Zabs_Zmult := Z.abs_mul (only parsing).
+Notation Zabs_square := Z.abs_square (compat "8.6").
(** * Proving a property of the absolute value by cases *)
@@ -68,11 +70,11 @@ Qed.
(** * Some results about the sign function. *)
-Notation Zsgn_Zmult := Z.sgn_mul (compat "8.3").
-Notation Zsgn_Zopp := Z.sgn_opp (compat "8.3").
-Notation Zsgn_pos := Z.sgn_pos_iff (compat "8.3").
-Notation Zsgn_neg := Z.sgn_neg_iff (compat "8.3").
-Notation Zsgn_null := Z.sgn_null_iff (compat "8.3").
+Notation Zsgn_Zmult := Z.sgn_mul (only parsing).
+Notation Zsgn_Zopp := Z.sgn_opp (only parsing).
+Notation Zsgn_pos := Z.sgn_pos_iff (only parsing).
+Notation Zsgn_neg := Z.sgn_neg_iff (only parsing).
+Notation Zsgn_null := Z.sgn_null_iff (only parsing).
(** A characterization of the sign function: *)
@@ -86,13 +88,13 @@ Qed.
(** Compatibility *)
-Notation inj_Zabs_nat := Zabs2Nat.id_abs (compat "8.3").
-Notation Zabs_nat_Z_of_nat := Zabs2Nat.id (compat "8.3").
-Notation Zabs_nat_mult := Zabs2Nat.inj_mul (compat "8.3").
-Notation Zabs_nat_Zsucc := Zabs2Nat.inj_succ (compat "8.3").
-Notation Zabs_nat_Zplus := Zabs2Nat.inj_add (compat "8.3").
-Notation Zabs_nat_Zminus := (fun n m => Zabs2Nat.inj_sub m n) (compat "8.3").
-Notation Zabs_nat_compare := Zabs2Nat.inj_compare (compat "8.3").
+Notation inj_Zabs_nat := Zabs2Nat.id_abs (only parsing).
+Notation Zabs_nat_Z_of_nat := Zabs2Nat.id (only parsing).
+Notation Zabs_nat_mult := Zabs2Nat.inj_mul (only parsing).
+Notation Zabs_nat_Zsucc := Zabs2Nat.inj_succ (only parsing).
+Notation Zabs_nat_Zplus := Zabs2Nat.inj_add (only parsing).
+Notation Zabs_nat_Zminus := (fun n m => Zabs2Nat.inj_sub m n) (only parsing).
+Notation Zabs_nat_compare := Zabs2Nat.inj_compare (only parsing).
Lemma Zabs_nat_le n m : 0 <= n <= m -> (Z.abs_nat n <= Z.abs_nat m)%nat.
Proof.
diff --git a/theories/ZArith/Zbool.v b/theories/ZArith/Zbool.v
index 407aef3b6..632d41b6a 100644
--- a/theories/ZArith/Zbool.v
+++ b/theories/ZArith/Zbool.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import BinInt.
@@ -33,10 +35,10 @@ Definition Zeven_odd_bool (x:Z) := bool_of_sumbool (Zeven_odd_dec x).
(**********************************************************************)
(** * Boolean comparisons of binary integers *)
-Notation Zle_bool := Z.leb (compat "8.3").
-Notation Zge_bool := Z.geb (compat "8.3").
-Notation Zlt_bool := Z.ltb (compat "8.3").
-Notation Zgt_bool := Z.gtb (compat "8.3").
+Notation Zle_bool := Z.leb (only parsing).
+Notation Zge_bool := Z.geb (only parsing).
+Notation Zlt_bool := Z.ltb (only parsing).
+Notation Zgt_bool := Z.gtb (only parsing).
(** We now provide a direct [Z.eqb] that doesn't refer to [Z.compare].
The old [Zeq_bool] is kept for compatibility. *)
@@ -87,7 +89,7 @@ Proof.
apply Z.leb_le.
Qed.
-Notation Zle_bool_refl := Z.leb_refl (compat "8.3").
+Notation Zle_bool_refl := Z.leb_refl (only parsing).
Lemma Zle_bool_antisym n m :
(n <=? m) = true -> (m <=? n) = true -> n = m.
diff --git a/theories/ZArith/Zcompare.v b/theories/ZArith/Zcompare.v
index f823c41a2..c8432e27b 100644
--- a/theories/ZArith/Zcompare.v
+++ b/theories/ZArith/Zcompare.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Binary Integers : results about Z.compare *)
@@ -181,18 +183,18 @@ Qed.
(** Compatibility notations *)
-Notation Zcompare_refl := Z.compare_refl (compat "8.3").
-Notation Zcompare_Eq_eq := Z.compare_eq (compat "8.3").
-Notation Zcompare_Eq_iff_eq := Z.compare_eq_iff (compat "8.3").
-Notation Zcompare_spec := Z.compare_spec (compat "8.3").
-Notation Zmin_l := Z.min_l (compat "8.3").
-Notation Zmin_r := Z.min_r (compat "8.3").
-Notation Zmax_l := Z.max_l (compat "8.3").
-Notation Zmax_r := Z.max_r (compat "8.3").
-Notation Zabs_eq := Z.abs_eq (compat "8.3").
-Notation Zabs_non_eq := Z.abs_neq (compat "8.3").
-Notation Zsgn_0 := Z.sgn_null (compat "8.3").
-Notation Zsgn_1 := Z.sgn_pos (compat "8.3").
-Notation Zsgn_m1 := Z.sgn_neg (compat "8.3").
+Notation Zcompare_refl := Z.compare_refl (compat "8.6").
+Notation Zcompare_Eq_eq := Z.compare_eq (only parsing).
+Notation Zcompare_Eq_iff_eq := Z.compare_eq_iff (only parsing).
+Notation Zcompare_spec := Z.compare_spec (compat "8.6").
+Notation Zmin_l := Z.min_l (compat "8.6").
+Notation Zmin_r := Z.min_r (compat "8.6").
+Notation Zmax_l := Z.max_l (compat "8.6").
+Notation Zmax_r := Z.max_r (compat "8.6").
+Notation Zabs_eq := Z.abs_eq (compat "8.6").
+Notation Zabs_non_eq := Z.abs_neq (only parsing).
+Notation Zsgn_0 := Z.sgn_null (only parsing).
+Notation Zsgn_1 := Z.sgn_pos (only parsing).
+Notation Zsgn_m1 := Z.sgn_neg (only parsing).
(** Not kept: Zcompare_egal_dec *)
diff --git a/theories/ZArith/Zcomplements.v b/theories/ZArith/Zcomplements.v
index eb1e17180..adf72a6ac 100644
--- a/theories/ZArith/Zcomplements.v
+++ b/theories/ZArith/Zcomplements.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import ZArithRing.
diff --git a/theories/ZArith/Zdigits.v b/theories/ZArith/Zdigits.v
index f80494c5e..d1eef6131 100644
--- a/theories/ZArith/Zdigits.v
+++ b/theories/ZArith/Zdigits.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Bit vectors interpreted as integers.
diff --git a/theories/ZArith/Zdiv.v b/theories/ZArith/Zdiv.v
index fa1ddf56f..15d0e4874 100644
--- a/theories/ZArith/Zdiv.v
+++ b/theories/ZArith/Zdiv.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Euclidean Division *)
@@ -18,16 +20,16 @@ Local Open Scope Z_scope.
(** The definition of the division is now in [BinIntDef], the initial
specifications and properties are in [BinInt]. *)
-Notation Zdiv_eucl_POS := Z.pos_div_eucl (compat "8.3").
-Notation Zdiv_eucl := Z.div_eucl (compat "8.3").
-Notation Zdiv := Z.div (compat "8.3").
-Notation Zmod := Z.modulo (compat "8.3").
+Notation Zdiv_eucl_POS := Z.pos_div_eucl (only parsing).
+Notation Zdiv_eucl := Z.div_eucl (compat "8.6").
+Notation Zdiv := Z.div (compat "8.6").
+Notation Zmod := Z.modulo (only parsing).
-Notation Zdiv_eucl_eq := Z.div_eucl_eq (compat "8.3").
-Notation Z_div_mod_eq_full := Z.div_mod (compat "8.3").
-Notation Zmod_POS_bound := Z.pos_div_eucl_bound (compat "8.3").
-Notation Zmod_pos_bound := Z.mod_pos_bound (compat "8.3").
-Notation Zmod_neg_bound := Z.mod_neg_bound (compat "8.3").
+Notation Zdiv_eucl_eq := Z.div_eucl_eq (compat "8.6").
+Notation Z_div_mod_eq_full := Z.div_mod (only parsing).
+Notation Zmod_POS_bound := Z.pos_div_eucl_bound (only parsing).
+Notation Zmod_pos_bound := Z.mod_pos_bound (only parsing).
+Notation Zmod_neg_bound := Z.mod_neg_bound (only parsing).
(** * Main division theorems *)
diff --git a/theories/ZArith/Zeuclid.v b/theories/ZArith/Zeuclid.v
index 3839d1d77..dc75db131 100644
--- a/theories/ZArith/Zeuclid.v
+++ b/theories/ZArith/Zeuclid.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Morphisms BinInt ZDivEucl.
diff --git a/theories/ZArith/Zeven.v b/theories/ZArith/Zeven.v
index 42a6a8ee3..00a58b517 100644
--- a/theories/ZArith/Zeven.v
+++ b/theories/ZArith/Zeven.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Binary Integers : Parity and Division by Two *)
@@ -58,8 +60,8 @@ Proof (Zodd_equiv n).
(** Boolean tests of parity (now in BinInt.Z) *)
-Notation Zeven_bool := Z.even (compat "8.3").
-Notation Zodd_bool := Z.odd (compat "8.3").
+Notation Zeven_bool := Z.even (only parsing).
+Notation Zodd_bool := Z.odd (only parsing).
Lemma Zeven_bool_iff n : Z.even n = true <-> Zeven n.
Proof.
@@ -130,17 +132,17 @@ Qed.
Hint Unfold Zeven Zodd: zarith.
-Notation Zeven_bool_succ := Z.even_succ (compat "8.3").
-Notation Zeven_bool_pred := Z.even_pred (compat "8.3").
-Notation Zodd_bool_succ := Z.odd_succ (compat "8.3").
-Notation Zodd_bool_pred := Z.odd_pred (compat "8.3").
+Notation Zeven_bool_succ := Z.even_succ (only parsing).
+Notation Zeven_bool_pred := Z.even_pred (only parsing).
+Notation Zodd_bool_succ := Z.odd_succ (only parsing).
+Notation Zodd_bool_pred := Z.odd_pred (only parsing).
(******************************************************************)
(** * Definition of [Z.quot2], [Z.div2] and properties wrt [Zeven]
and [Zodd] *)
-Notation Zdiv2 := Z.div2 (compat "8.3").
-Notation Zquot2 := Z.quot2 (compat "8.3").
+Notation Zdiv2 := Z.div2 (compat "8.6").
+Notation Zquot2 := Z.quot2 (compat "8.6").
(** Properties of [Z.div2] *)
diff --git a/theories/ZArith/Zgcd_alt.v b/theories/ZArith/Zgcd_alt.v
index 3a460a563..cced1190c 100644
--- a/theories/ZArith/Zgcd_alt.v
+++ b/theories/ZArith/Zgcd_alt.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** * Zgcd_alt : an alternate version of Z.gcd, based on Euclid's algorithm *)
diff --git a/theories/ZArith/Zhints.v b/theories/ZArith/Zhints.v
index 424b35a43..bfcc60edd 100644
--- a/theories/ZArith/Zhints.v
+++ b/theories/ZArith/Zhints.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** This file centralizes the lemmas about [Z], classifying them
diff --git a/theories/ZArith/Zlogarithm.v b/theories/ZArith/Zlogarithm.v
index 28a2e287e..24412e943 100644
--- a/theories/ZArith/Zlogarithm.v
+++ b/theories/ZArith/Zlogarithm.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(**********************************************************************)
diff --git a/theories/ZArith/Zmax.v b/theories/ZArith/Zmax.v
index b52da8563..7f595fcfd 100644
--- a/theories/ZArith/Zmax.v
+++ b/theories/ZArith/Zmax.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** THIS FILE IS DEPRECATED. *)
@@ -16,32 +18,32 @@ Local Open Scope Z_scope.
(** Exact compatibility *)
-Notation Zmax_case := Z.max_case (compat "8.3").
-Notation Zmax_case_strong := Z.max_case_strong (compat "8.3").
-Notation Zmax_right := Z.max_r (compat "8.3").
-Notation Zle_max_l := Z.le_max_l (compat "8.3").
-Notation Zle_max_r := Z.le_max_r (compat "8.3").
-Notation Zmax_lub := Z.max_lub (compat "8.3").
-Notation Zmax_lub_lt := Z.max_lub_lt (compat "8.3").
-Notation Zle_max_compat_r := Z.max_le_compat_r (compat "8.3").
-Notation Zle_max_compat_l := Z.max_le_compat_l (compat "8.3").
-Notation Zmax_idempotent := Z.max_id (compat "8.3").
-Notation Zmax_n_n := Z.max_id (compat "8.3").
-Notation Zmax_comm := Z.max_comm (compat "8.3").
-Notation Zmax_assoc := Z.max_assoc (compat "8.3").
-Notation Zmax_irreducible_dec := Z.max_dec (compat "8.3").
-Notation Zmax_le_prime := Z.max_le (compat "8.3").
-Notation Zsucc_max_distr := Z.succ_max_distr (compat "8.3").
-Notation Zmax_SS := Z.succ_max_distr (compat "8.3").
-Notation Zplus_max_distr_l := Z.add_max_distr_l (compat "8.3").
-Notation Zplus_max_distr_r := Z.add_max_distr_r (compat "8.3").
-Notation Zmax_plus := Z.add_max_distr_r (compat "8.3").
-Notation Zmax1 := Z.le_max_l (compat "8.3").
-Notation Zmax2 := Z.le_max_r (compat "8.3").
-Notation Zmax_irreducible_inf := Z.max_dec (compat "8.3").
-Notation Zmax_le_prime_inf := Z.max_le (compat "8.3").
-Notation Zpos_max := Pos2Z.inj_max (compat "8.3").
-Notation Zpos_minus := Pos2Z.inj_sub_max (compat "8.3").
+Notation Zmax_case := Z.max_case (compat "8.6").
+Notation Zmax_case_strong := Z.max_case_strong (compat "8.6").
+Notation Zmax_right := Z.max_r (only parsing).
+Notation Zle_max_l := Z.le_max_l (compat "8.6").
+Notation Zle_max_r := Z.le_max_r (compat "8.6").
+Notation Zmax_lub := Z.max_lub (compat "8.6").
+Notation Zmax_lub_lt := Z.max_lub_lt (compat "8.6").
+Notation Zle_max_compat_r := Z.max_le_compat_r (only parsing).
+Notation Zle_max_compat_l := Z.max_le_compat_l (only parsing).
+Notation Zmax_idempotent := Z.max_id (only parsing).
+Notation Zmax_n_n := Z.max_id (only parsing).
+Notation Zmax_comm := Z.max_comm (compat "8.6").
+Notation Zmax_assoc := Z.max_assoc (compat "8.6").
+Notation Zmax_irreducible_dec := Z.max_dec (only parsing).
+Notation Zmax_le_prime := Z.max_le (only parsing).
+Notation Zsucc_max_distr := Z.succ_max_distr (compat "8.6").
+Notation Zmax_SS := Z.succ_max_distr (only parsing).
+Notation Zplus_max_distr_l := Z.add_max_distr_l (only parsing).
+Notation Zplus_max_distr_r := Z.add_max_distr_r (only parsing).
+Notation Zmax_plus := Z.add_max_distr_r (only parsing).
+Notation Zmax1 := Z.le_max_l (only parsing).
+Notation Zmax2 := Z.le_max_r (only parsing).
+Notation Zmax_irreducible_inf := Z.max_dec (only parsing).
+Notation Zmax_le_prime_inf := Z.max_le (only parsing).
+Notation Zpos_max := Pos2Z.inj_max (only parsing).
+Notation Zpos_minus := Pos2Z.inj_sub_max (only parsing).
(** Slightly different lemmas *)
diff --git a/theories/ZArith/Zmin.v b/theories/ZArith/Zmin.v
index d9e3ab19e..6bc72227b 100644
--- a/theories/ZArith/Zmin.v
+++ b/theories/ZArith/Zmin.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** THIS FILE IS DEPRECATED. *)
@@ -16,24 +18,24 @@ Local Open Scope Z_scope.
(** Exact compatibility *)
-Notation Zmin_case := Z.min_case (compat "8.3").
-Notation Zmin_case_strong := Z.min_case_strong (compat "8.3").
-Notation Zle_min_l := Z.le_min_l (compat "8.3").
-Notation Zle_min_r := Z.le_min_r (compat "8.3").
-Notation Zmin_glb := Z.min_glb (compat "8.3").
-Notation Zmin_glb_lt := Z.min_glb_lt (compat "8.3").
-Notation Zle_min_compat_r := Z.min_le_compat_r (compat "8.3").
-Notation Zle_min_compat_l := Z.min_le_compat_l (compat "8.3").
-Notation Zmin_idempotent := Z.min_id (compat "8.3").
-Notation Zmin_n_n := Z.min_id (compat "8.3").
-Notation Zmin_comm := Z.min_comm (compat "8.3").
-Notation Zmin_assoc := Z.min_assoc (compat "8.3").
-Notation Zmin_irreducible_inf := Z.min_dec (compat "8.3").
-Notation Zsucc_min_distr := Z.succ_min_distr (compat "8.3").
-Notation Zmin_SS := Z.succ_min_distr (compat "8.3").
-Notation Zplus_min_distr_r := Z.add_min_distr_r (compat "8.3").
-Notation Zmin_plus := Z.add_min_distr_r (compat "8.3").
-Notation Zpos_min := Pos2Z.inj_min (compat "8.3").
+Notation Zmin_case := Z.min_case (compat "8.6").
+Notation Zmin_case_strong := Z.min_case_strong (compat "8.6").
+Notation Zle_min_l := Z.le_min_l (compat "8.6").
+Notation Zle_min_r := Z.le_min_r (compat "8.6").
+Notation Zmin_glb := Z.min_glb (compat "8.6").
+Notation Zmin_glb_lt := Z.min_glb_lt (compat "8.6").
+Notation Zle_min_compat_r := Z.min_le_compat_r (only parsing).
+Notation Zle_min_compat_l := Z.min_le_compat_l (only parsing).
+Notation Zmin_idempotent := Z.min_id (only parsing).
+Notation Zmin_n_n := Z.min_id (only parsing).
+Notation Zmin_comm := Z.min_comm (compat "8.6").
+Notation Zmin_assoc := Z.min_assoc (compat "8.6").
+Notation Zmin_irreducible_inf := Z.min_dec (only parsing).
+Notation Zsucc_min_distr := Z.succ_min_distr (compat "8.6").
+Notation Zmin_SS := Z.succ_min_distr (only parsing).
+Notation Zplus_min_distr_r := Z.add_min_distr_r (only parsing).
+Notation Zmin_plus := Z.add_min_distr_r (only parsing).
+Notation Zpos_min := Pos2Z.inj_min (only parsing).
(** Slightly different lemmas *)
@@ -46,7 +48,7 @@ Qed.
Lemma Zmin_irreducible n m : Z.min n m = n \/ Z.min n m = m.
Proof. destruct (Z.min_dec n m); auto. Qed.
-Notation Zmin_or := Zmin_irreducible (compat "8.3").
+Notation Zmin_or := Zmin_irreducible (only parsing).
Lemma Zmin_le_prime_inf n m p : Z.min n m <= p -> {n <= p} + {m <= p}.
Proof. apply Z.min_case; auto. Qed.
diff --git a/theories/ZArith/Zminmax.v b/theories/ZArith/Zminmax.v
index 7e62d6689..06919642f 100644
--- a/theories/ZArith/Zminmax.v
+++ b/theories/ZArith/Zminmax.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Orders BinInt Zcompare Zorder.
@@ -12,11 +14,11 @@ Require Import Orders BinInt Zcompare Zorder.
(*begin hide*)
(* Compatibility with names of the old Zminmax file *)
-Notation Zmin_max_absorption_r_r := Z.min_max_absorption (compat "8.3").
-Notation Zmax_min_absorption_r_r := Z.max_min_absorption (compat "8.3").
-Notation Zmax_min_distr_r := Z.max_min_distr (compat "8.3").
-Notation Zmin_max_distr_r := Z.min_max_distr (compat "8.3").
-Notation Zmax_min_modular_r := Z.max_min_modular (compat "8.3").
-Notation Zmin_max_modular_r := Z.min_max_modular (compat "8.3").
-Notation max_min_disassoc := Z.max_min_disassoc (compat "8.3").
+Notation Zmin_max_absorption_r_r := Z.min_max_absorption (only parsing).
+Notation Zmax_min_absorption_r_r := Z.max_min_absorption (only parsing).
+Notation Zmax_min_distr_r := Z.max_min_distr (only parsing).
+Notation Zmin_max_distr_r := Z.min_max_distr (only parsing).
+Notation Zmax_min_modular_r := Z.max_min_modular (only parsing).
+Notation Zmin_max_modular_r := Z.min_max_modular (only parsing).
+Notation max_min_disassoc := Z.max_min_disassoc (only parsing).
(*end hide*)
diff --git a/theories/ZArith/Zmisc.v b/theories/ZArith/Zmisc.v
index a6f29936b..c46241cee 100644
--- a/theories/ZArith/Zmisc.v
+++ b/theories/ZArith/Zmisc.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Wf_nat.
@@ -18,7 +20,7 @@ Local Open Scope Z_scope.
(** [n]th iteration of the function [f] *)
-Notation iter := @Z.iter (compat "8.3").
+Notation iter := @Z.iter (only parsing).
Lemma iter_nat_of_Z : forall n A f x, 0 <= n ->
Z.iter n f x = iter_nat (Z.abs_nat n) A f x.
diff --git a/theories/ZArith/Znat.v b/theories/ZArith/Znat.v
index be712db6b..5c960da1f 100644
--- a/theories/ZArith/Znat.v
+++ b/theories/ZArith/Znat.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Binary Integers (Pierre Crégut, CNET, Lannion, France) *)
@@ -951,65 +953,65 @@ Definition inj_gt n m := proj1 (Nat2Z.inj_gt n m).
(** For the others, a Notation is fine *)
-Notation inj_0 := Nat2Z.inj_0 (compat "8.3").
-Notation inj_S := Nat2Z.inj_succ (compat "8.3").
-Notation inj_compare := Nat2Z.inj_compare (compat "8.3").
-Notation inj_eq_rev := Nat2Z.inj (compat "8.3").
-Notation inj_eq_iff := (fun n m => iff_sym (Nat2Z.inj_iff n m)) (compat "8.3").
-Notation inj_le_iff := Nat2Z.inj_le (compat "8.3").
-Notation inj_lt_iff := Nat2Z.inj_lt (compat "8.3").
-Notation inj_ge_iff := Nat2Z.inj_ge (compat "8.3").
-Notation inj_gt_iff := Nat2Z.inj_gt (compat "8.3").
-Notation inj_le_rev := (fun n m => proj2 (Nat2Z.inj_le n m)) (compat "8.3").
-Notation inj_lt_rev := (fun n m => proj2 (Nat2Z.inj_lt n m)) (compat "8.3").
-Notation inj_ge_rev := (fun n m => proj2 (Nat2Z.inj_ge n m)) (compat "8.3").
-Notation inj_gt_rev := (fun n m => proj2 (Nat2Z.inj_gt n m)) (compat "8.3").
-Notation inj_plus := Nat2Z.inj_add (compat "8.3").
-Notation inj_mult := Nat2Z.inj_mul (compat "8.3").
-Notation inj_minus1 := Nat2Z.inj_sub (compat "8.3").
-Notation inj_minus := Nat2Z.inj_sub_max (compat "8.3").
-Notation inj_min := Nat2Z.inj_min (compat "8.3").
-Notation inj_max := Nat2Z.inj_max (compat "8.3").
-
-Notation Z_of_nat_of_P := positive_nat_Z (compat "8.3").
+Notation inj_0 := Nat2Z.inj_0 (only parsing).
+Notation inj_S := Nat2Z.inj_succ (only parsing).
+Notation inj_compare := Nat2Z.inj_compare (only parsing).
+Notation inj_eq_rev := Nat2Z.inj (only parsing).
+Notation inj_eq_iff := (fun n m => iff_sym (Nat2Z.inj_iff n m)) (only parsing).
+Notation inj_le_iff := Nat2Z.inj_le (only parsing).
+Notation inj_lt_iff := Nat2Z.inj_lt (only parsing).
+Notation inj_ge_iff := Nat2Z.inj_ge (only parsing).
+Notation inj_gt_iff := Nat2Z.inj_gt (only parsing).
+Notation inj_le_rev := (fun n m => proj2 (Nat2Z.inj_le n m)) (only parsing).
+Notation inj_lt_rev := (fun n m => proj2 (Nat2Z.inj_lt n m)) (only parsing).
+Notation inj_ge_rev := (fun n m => proj2 (Nat2Z.inj_ge n m)) (only parsing).
+Notation inj_gt_rev := (fun n m => proj2 (Nat2Z.inj_gt n m)) (only parsing).
+Notation inj_plus := Nat2Z.inj_add (only parsing).
+Notation inj_mult := Nat2Z.inj_mul (only parsing).
+Notation inj_minus1 := Nat2Z.inj_sub (only parsing).
+Notation inj_minus := Nat2Z.inj_sub_max (only parsing).
+Notation inj_min := Nat2Z.inj_min (only parsing).
+Notation inj_max := Nat2Z.inj_max (only parsing).
+
+Notation Z_of_nat_of_P := positive_nat_Z (only parsing).
Notation Zpos_eq_Z_of_nat_o_nat_of_P :=
- (fun p => eq_sym (positive_nat_Z p)) (compat "8.3").
-
-Notation Z_of_nat_of_N := N_nat_Z (compat "8.3").
-Notation Z_of_N_of_nat := nat_N_Z (compat "8.3").
-
-Notation Z_of_N_eq := (f_equal Z.of_N) (compat "8.3").
-Notation Z_of_N_eq_rev := N2Z.inj (compat "8.3").
-Notation Z_of_N_eq_iff := (fun n m => iff_sym (N2Z.inj_iff n m)) (compat "8.3").
-Notation Z_of_N_compare := N2Z.inj_compare (compat "8.3").
-Notation Z_of_N_le_iff := N2Z.inj_le (compat "8.3").
-Notation Z_of_N_lt_iff := N2Z.inj_lt (compat "8.3").
-Notation Z_of_N_ge_iff := N2Z.inj_ge (compat "8.3").
-Notation Z_of_N_gt_iff := N2Z.inj_gt (compat "8.3").
-Notation Z_of_N_le := (fun n m => proj1 (N2Z.inj_le n m)) (compat "8.3").
-Notation Z_of_N_lt := (fun n m => proj1 (N2Z.inj_lt n m)) (compat "8.3").
-Notation Z_of_N_ge := (fun n m => proj1 (N2Z.inj_ge n m)) (compat "8.3").
-Notation Z_of_N_gt := (fun n m => proj1 (N2Z.inj_gt n m)) (compat "8.3").
-Notation Z_of_N_le_rev := (fun n m => proj2 (N2Z.inj_le n m)) (compat "8.3").
-Notation Z_of_N_lt_rev := (fun n m => proj2 (N2Z.inj_lt n m)) (compat "8.3").
-Notation Z_of_N_ge_rev := (fun n m => proj2 (N2Z.inj_ge n m)) (compat "8.3").
-Notation Z_of_N_gt_rev := (fun n m => proj2 (N2Z.inj_gt n m)) (compat "8.3").
-Notation Z_of_N_pos := N2Z.inj_pos (compat "8.3").
-Notation Z_of_N_abs := N2Z.inj_abs_N (compat "8.3").
-Notation Z_of_N_le_0 := N2Z.is_nonneg (compat "8.3").
-Notation Z_of_N_plus := N2Z.inj_add (compat "8.3").
-Notation Z_of_N_mult := N2Z.inj_mul (compat "8.3").
-Notation Z_of_N_minus := N2Z.inj_sub_max (compat "8.3").
-Notation Z_of_N_succ := N2Z.inj_succ (compat "8.3").
-Notation Z_of_N_min := N2Z.inj_min (compat "8.3").
-Notation Z_of_N_max := N2Z.inj_max (compat "8.3").
-Notation Zabs_of_N := Zabs2N.id (compat "8.3").
-Notation Zabs_N_succ_abs := Zabs2N.inj_succ_abs (compat "8.3").
-Notation Zabs_N_succ := Zabs2N.inj_succ (compat "8.3").
-Notation Zabs_N_plus_abs := Zabs2N.inj_add_abs (compat "8.3").
-Notation Zabs_N_plus := Zabs2N.inj_add (compat "8.3").
-Notation Zabs_N_mult_abs := Zabs2N.inj_mul_abs (compat "8.3").
-Notation Zabs_N_mult := Zabs2N.inj_mul (compat "8.3").
+ (fun p => eq_sym (positive_nat_Z p)) (only parsing).
+
+Notation Z_of_nat_of_N := N_nat_Z (only parsing).
+Notation Z_of_N_of_nat := nat_N_Z (only parsing).
+
+Notation Z_of_N_eq := (f_equal Z.of_N) (only parsing).
+Notation Z_of_N_eq_rev := N2Z.inj (only parsing).
+Notation Z_of_N_eq_iff := (fun n m => iff_sym (N2Z.inj_iff n m)) (only parsing).
+Notation Z_of_N_compare := N2Z.inj_compare (only parsing).
+Notation Z_of_N_le_iff := N2Z.inj_le (only parsing).
+Notation Z_of_N_lt_iff := N2Z.inj_lt (only parsing).
+Notation Z_of_N_ge_iff := N2Z.inj_ge (only parsing).
+Notation Z_of_N_gt_iff := N2Z.inj_gt (only parsing).
+Notation Z_of_N_le := (fun n m => proj1 (N2Z.inj_le n m)) (only parsing).
+Notation Z_of_N_lt := (fun n m => proj1 (N2Z.inj_lt n m)) (only parsing).
+Notation Z_of_N_ge := (fun n m => proj1 (N2Z.inj_ge n m)) (only parsing).
+Notation Z_of_N_gt := (fun n m => proj1 (N2Z.inj_gt n m)) (only parsing).
+Notation Z_of_N_le_rev := (fun n m => proj2 (N2Z.inj_le n m)) (only parsing).
+Notation Z_of_N_lt_rev := (fun n m => proj2 (N2Z.inj_lt n m)) (only parsing).
+Notation Z_of_N_ge_rev := (fun n m => proj2 (N2Z.inj_ge n m)) (only parsing).
+Notation Z_of_N_gt_rev := (fun n m => proj2 (N2Z.inj_gt n m)) (only parsing).
+Notation Z_of_N_pos := N2Z.inj_pos (only parsing).
+Notation Z_of_N_abs := N2Z.inj_abs_N (only parsing).
+Notation Z_of_N_le_0 := N2Z.is_nonneg (only parsing).
+Notation Z_of_N_plus := N2Z.inj_add (only parsing).
+Notation Z_of_N_mult := N2Z.inj_mul (only parsing).
+Notation Z_of_N_minus := N2Z.inj_sub_max (only parsing).
+Notation Z_of_N_succ := N2Z.inj_succ (only parsing).
+Notation Z_of_N_min := N2Z.inj_min (only parsing).
+Notation Z_of_N_max := N2Z.inj_max (only parsing).
+Notation Zabs_of_N := Zabs2N.id (only parsing).
+Notation Zabs_N_succ_abs := Zabs2N.inj_succ_abs (only parsing).
+Notation Zabs_N_succ := Zabs2N.inj_succ (only parsing).
+Notation Zabs_N_plus_abs := Zabs2N.inj_add_abs (only parsing).
+Notation Zabs_N_plus := Zabs2N.inj_add (only parsing).
+Notation Zabs_N_mult_abs := Zabs2N.inj_mul_abs (only parsing).
+Notation Zabs_N_mult := Zabs2N.inj_mul (only parsing).
Theorem inj_minus2 : forall n m:nat, (m > n)%nat -> Z.of_nat (n - m) = 0.
Proof.
diff --git a/theories/ZArith/Znumtheory.v b/theories/ZArith/Znumtheory.v
index 5dfc37095..f5444c31d 100644
--- a/theories/ZArith/Znumtheory.v
+++ b/theories/ZArith/Znumtheory.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import ZArith_base.
@@ -25,20 +27,20 @@ Open Scope Z_scope.
- properties of the efficient [Z.gcd] function
*)
-Notation Zgcd := Z.gcd (compat "8.3").
-Notation Zggcd := Z.ggcd (compat "8.3").
-Notation Zggcd_gcd := Z.ggcd_gcd (compat "8.3").
-Notation Zggcd_correct_divisors := Z.ggcd_correct_divisors (compat "8.3").
-Notation Zgcd_divide_l := Z.gcd_divide_l (compat "8.3").
-Notation Zgcd_divide_r := Z.gcd_divide_r (compat "8.3").
-Notation Zgcd_greatest := Z.gcd_greatest (compat "8.3").
-Notation Zgcd_nonneg := Z.gcd_nonneg (compat "8.3").
-Notation Zggcd_opp := Z.ggcd_opp (compat "8.3").
+Notation Zgcd := Z.gcd (compat "8.6").
+Notation Zggcd := Z.ggcd (compat "8.6").
+Notation Zggcd_gcd := Z.ggcd_gcd (compat "8.6").
+Notation Zggcd_correct_divisors := Z.ggcd_correct_divisors (compat "8.6").
+Notation Zgcd_divide_l := Z.gcd_divide_l (compat "8.6").
+Notation Zgcd_divide_r := Z.gcd_divide_r (compat "8.6").
+Notation Zgcd_greatest := Z.gcd_greatest (compat "8.6").
+Notation Zgcd_nonneg := Z.gcd_nonneg (compat "8.6").
+Notation Zggcd_opp := Z.ggcd_opp (compat "8.6").
(** The former specialized inductive predicate [Z.divide] is now
a generic existential predicate. *)
-Notation Zdivide := Z.divide (compat "8.3").
+Notation Zdivide := Z.divide (compat "8.6").
(** Its former constructor is now a pseudo-constructor. *)
@@ -46,17 +48,17 @@ Definition Zdivide_intro a b q (H:b=q*a) : Z.divide a b := ex_intro _ q H.
(** Results concerning divisibility*)
-Notation Zdivide_refl := Z.divide_refl (compat "8.3").
-Notation Zone_divide := Z.divide_1_l (compat "8.3").
-Notation Zdivide_0 := Z.divide_0_r (compat "8.3").
-Notation Zmult_divide_compat_l := Z.mul_divide_mono_l (compat "8.3").
-Notation Zmult_divide_compat_r := Z.mul_divide_mono_r (compat "8.3").
-Notation Zdivide_plus_r := Z.divide_add_r (compat "8.3").
-Notation Zdivide_minus_l := Z.divide_sub_r (compat "8.3").
-Notation Zdivide_mult_l := Z.divide_mul_l (compat "8.3").
-Notation Zdivide_mult_r := Z.divide_mul_r (compat "8.3").
-Notation Zdivide_factor_r := Z.divide_factor_l (compat "8.3").
-Notation Zdivide_factor_l := Z.divide_factor_r (compat "8.3").
+Notation Zdivide_refl := Z.divide_refl (compat "8.6").
+Notation Zone_divide := Z.divide_1_l (only parsing).
+Notation Zdivide_0 := Z.divide_0_r (only parsing).
+Notation Zmult_divide_compat_l := Z.mul_divide_mono_l (only parsing).
+Notation Zmult_divide_compat_r := Z.mul_divide_mono_r (only parsing).
+Notation Zdivide_plus_r := Z.divide_add_r (only parsing).
+Notation Zdivide_minus_l := Z.divide_sub_r (only parsing).
+Notation Zdivide_mult_l := Z.divide_mul_l (only parsing).
+Notation Zdivide_mult_r := Z.divide_mul_r (only parsing).
+Notation Zdivide_factor_r := Z.divide_factor_l (only parsing).
+Notation Zdivide_factor_l := Z.divide_factor_r (only parsing).
Lemma Zdivide_opp_r a b : (a | b) -> (a | - b).
Proof. apply Z.divide_opp_r. Qed.
@@ -91,12 +93,12 @@ Qed.
(** Only [1] and [-1] divide [1]. *)
-Notation Zdivide_1 := Z.divide_1_r (compat "8.3").
+Notation Zdivide_1 := Z.divide_1_r (only parsing).
(** If [a] divides [b] and [b] divides [a] then [a] is [b] or [-b]. *)
-Notation Zdivide_antisym := Z.divide_antisym (compat "8.3").
-Notation Zdivide_trans := Z.divide_trans (compat "8.3").
+Notation Zdivide_antisym := Z.divide_antisym (compat "8.6").
+Notation Zdivide_trans := Z.divide_trans (compat "8.6").
(** If [a] divides [b] and [b<>0] then [|a| <= |b|]. *)
@@ -734,7 +736,7 @@ Qed.
(** we now prove that [Z.gcd] is indeed a gcd in
the sense of [Zis_gcd]. *)
-Notation Zgcd_is_pos := Z.gcd_nonneg (compat "8.3").
+Notation Zgcd_is_pos := Z.gcd_nonneg (only parsing).
Lemma Zgcd_is_gcd : forall a b, Zis_gcd a b (Z.gcd a b).
Proof.
@@ -767,8 +769,8 @@ Proof.
- subst. now case (Z.gcd a b).
Qed.
-Notation Zgcd_inv_0_l := Z.gcd_eq_0_l (compat "8.3").
-Notation Zgcd_inv_0_r := Z.gcd_eq_0_r (compat "8.3").
+Notation Zgcd_inv_0_l := Z.gcd_eq_0_l (only parsing).
+Notation Zgcd_inv_0_r := Z.gcd_eq_0_r (only parsing).
Theorem Zgcd_div_swap0 : forall a b : Z,
0 < Z.gcd a b ->
@@ -798,16 +800,16 @@ Proof.
rewrite <- Zdivide_Zdiv_eq; auto.
Qed.
-Notation Zgcd_comm := Z.gcd_comm (compat "8.3").
+Notation Zgcd_comm := Z.gcd_comm (compat "8.6").
Lemma Zgcd_ass a b c : Z.gcd (Z.gcd a b) c = Z.gcd a (Z.gcd b c).
Proof.
symmetry. apply Z.gcd_assoc.
Qed.
-Notation Zgcd_Zabs := Z.gcd_abs_l (compat "8.3").
-Notation Zgcd_0 := Z.gcd_0_r (compat "8.3").
-Notation Zgcd_1 := Z.gcd_1_r (compat "8.3").
+Notation Zgcd_Zabs := Z.gcd_abs_l (only parsing).
+Notation Zgcd_0 := Z.gcd_0_r (only parsing).
+Notation Zgcd_1 := Z.gcd_1_r (only parsing).
Hint Resolve Z.gcd_0_r Z.gcd_1_r : zarith.
diff --git a/theories/ZArith/Zorder.v b/theories/ZArith/Zorder.v
index ff8e22029..a1ec4b35e 100644
--- a/theories/ZArith/Zorder.v
+++ b/theories/ZArith/Zorder.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Binary Integers : results about order predicates *)
@@ -38,9 +40,9 @@ Qed.
(**********************************************************************)
(** * Decidability of equality and order on Z *)
-Notation dec_eq := Z.eq_decidable (compat "8.3").
-Notation dec_Zle := Z.le_decidable (compat "8.3").
-Notation dec_Zlt := Z.lt_decidable (compat "8.3").
+Notation dec_eq := Z.eq_decidable (only parsing).
+Notation dec_Zle := Z.le_decidable (only parsing).
+Notation dec_Zlt := Z.lt_decidable (only parsing).
Theorem dec_Zne n m : decidable (Zne n m).
Proof.
@@ -64,12 +66,12 @@ Qed.
(** * Relating strict and large orders *)
-Notation Zgt_lt := Z.gt_lt (compat "8.3").
-Notation Zlt_gt := Z.lt_gt (compat "8.3").
-Notation Zge_le := Z.ge_le (compat "8.3").
-Notation Zle_ge := Z.le_ge (compat "8.3").
-Notation Zgt_iff_lt := Z.gt_lt_iff (compat "8.3").
-Notation Zge_iff_le := Z.ge_le_iff (compat "8.3").
+Notation Zgt_lt := Z.gt_lt (compat "8.6").
+Notation Zlt_gt := Z.lt_gt (compat "8.6").
+Notation Zge_le := Z.ge_le (compat "8.6").
+Notation Zle_ge := Z.le_ge (compat "8.6").
+Notation Zgt_iff_lt := Z.gt_lt_iff (only parsing).
+Notation Zge_iff_le := Z.ge_le_iff (only parsing).
Lemma Zle_not_lt n m : n <= m -> ~ m < n.
Proof.
@@ -121,18 +123,18 @@ Qed.
(** Reflexivity *)
-Notation Zle_refl := Z.le_refl (compat "8.3").
-Notation Zeq_le := Z.eq_le_incl (compat "8.3").
+Notation Zle_refl := Z.le_refl (compat "8.6").
+Notation Zeq_le := Z.eq_le_incl (only parsing).
Hint Resolve Z.le_refl: zarith.
(** Antisymmetry *)
-Notation Zle_antisym := Z.le_antisymm (compat "8.3").
+Notation Zle_antisym := Z.le_antisymm (only parsing).
(** Asymmetry *)
-Notation Zlt_asym := Z.lt_asymm (compat "8.3").
+Notation Zlt_asym := Z.lt_asymm (only parsing).
Lemma Zgt_asym n m : n > m -> ~ m > n.
Proof.
@@ -141,8 +143,8 @@ Qed.
(** Irreflexivity *)
-Notation Zlt_irrefl := Z.lt_irrefl (compat "8.3").
-Notation Zlt_not_eq := Z.lt_neq (compat "8.3").
+Notation Zlt_irrefl := Z.lt_irrefl (compat "8.6").
+Notation Zlt_not_eq := Z.lt_neq (only parsing).
Lemma Zgt_irrefl n : ~ n > n.
Proof.
@@ -151,8 +153,8 @@ Qed.
(** Large = strict or equal *)
-Notation Zlt_le_weak := Z.lt_le_incl (compat "8.3").
-Notation Zle_lt_or_eq_iff := Z.lt_eq_cases (compat "8.3").
+Notation Zlt_le_weak := Z.lt_le_incl (only parsing).
+Notation Zle_lt_or_eq_iff := Z.lt_eq_cases (only parsing).
Lemma Zle_lt_or_eq n m : n <= m -> n < m \/ n = m.
Proof.
@@ -161,11 +163,11 @@ Qed.
(** Dichotomy *)
-Notation Zle_or_lt := Z.le_gt_cases (compat "8.3").
+Notation Zle_or_lt := Z.le_gt_cases (only parsing).
(** Transitivity of strict orders *)
-Notation Zlt_trans := Z.lt_trans (compat "8.3").
+Notation Zlt_trans := Z.lt_trans (compat "8.6").
Lemma Zgt_trans n m p : n > m -> m > p -> n > p.
Proof.
@@ -174,8 +176,8 @@ Qed.
(** Mixed transitivity *)
-Notation Zlt_le_trans := Z.lt_le_trans (compat "8.3").
-Notation Zle_lt_trans := Z.le_lt_trans (compat "8.3").
+Notation Zlt_le_trans := Z.lt_le_trans (compat "8.6").
+Notation Zle_lt_trans := Z.le_lt_trans (compat "8.6").
Lemma Zle_gt_trans n m p : m <= n -> m > p -> n > p.
Proof.
@@ -189,7 +191,7 @@ Qed.
(** Transitivity of large orders *)
-Notation Zle_trans := Z.le_trans (compat "8.3").
+Notation Zle_trans := Z.le_trans (compat "8.6").
Lemma Zge_trans n m p : n >= m -> m >= p -> n >= p.
Proof.
@@ -240,8 +242,8 @@ Qed.
(** Special base instances of order *)
-Notation Zlt_succ := Z.lt_succ_diag_r (compat "8.3").
-Notation Zlt_pred := Z.lt_pred_l (compat "8.3").
+Notation Zlt_succ := Z.lt_succ_diag_r (only parsing).
+Notation Zlt_pred := Z.lt_pred_l (only parsing).
Lemma Zgt_succ n : Z.succ n > n.
Proof.
@@ -255,8 +257,8 @@ Qed.
(** Relating strict and large order using successor or predecessor *)
-Notation Zlt_succ_r := Z.lt_succ_r (compat "8.3").
-Notation Zle_succ_l := Z.le_succ_l (compat "8.3").
+Notation Zlt_succ_r := Z.lt_succ_r (compat "8.6").
+Notation Zle_succ_l := Z.le_succ_l (compat "8.6").
Lemma Zgt_le_succ n m : m > n -> Z.succ n <= m.
Proof.
@@ -295,10 +297,10 @@ Qed.
(** Weakening order *)
-Notation Zle_succ := Z.le_succ_diag_r (compat "8.3").
-Notation Zle_pred := Z.le_pred_l (compat "8.3").
-Notation Zlt_lt_succ := Z.lt_lt_succ_r (compat "8.3").
-Notation Zle_le_succ := Z.le_le_succ_r (compat "8.3").
+Notation Zle_succ := Z.le_succ_diag_r (only parsing).
+Notation Zle_pred := Z.le_pred_l (only parsing).
+Notation Zlt_lt_succ := Z.lt_lt_succ_r (only parsing).
+Notation Zle_le_succ := Z.le_le_succ_r (only parsing).
Lemma Zle_succ_le n m : Z.succ n <= m -> n <= m.
Proof.
@@ -334,8 +336,8 @@ Qed.
(** Special cases of ordered integers *)
-Notation Zlt_0_1 := Z.lt_0_1 (compat "8.3").
-Notation Zle_0_1 := Z.le_0_1 (compat "8.3").
+Notation Zlt_0_1 := Z.lt_0_1 (compat "8.6").
+Notation Zle_0_1 := Z.le_0_1 (compat "8.6").
Lemma Zle_neg_pos : forall p q:positive, Zneg p <= Zpos q.
Proof.
@@ -375,10 +377,10 @@ Qed.
(** ** Addition *)
(** Compatibility of addition wrt to order *)
-Notation Zplus_lt_le_compat := Z.add_lt_le_mono (compat "8.3").
-Notation Zplus_le_lt_compat := Z.add_le_lt_mono (compat "8.3").
-Notation Zplus_le_compat := Z.add_le_mono (compat "8.3").
-Notation Zplus_lt_compat := Z.add_lt_mono (compat "8.3").
+Notation Zplus_lt_le_compat := Z.add_lt_le_mono (only parsing).
+Notation Zplus_le_lt_compat := Z.add_le_lt_mono (only parsing).
+Notation Zplus_le_compat := Z.add_le_mono (only parsing).
+Notation Zplus_lt_compat := Z.add_lt_mono (only parsing).
Lemma Zplus_gt_compat_l n m p : n > m -> p + n > p + m.
Proof.
@@ -412,7 +414,7 @@ Qed.
(** Compatibility of addition wrt to being positive *)
-Notation Zplus_le_0_compat := Z.add_nonneg_nonneg (compat "8.3").
+Notation Zplus_le_0_compat := Z.add_nonneg_nonneg (only parsing).
(** Simplification of addition wrt to order *)
@@ -570,9 +572,9 @@ Qed.
(** Compatibility of multiplication by a positive wrt to being positive *)
-Notation Zmult_le_0_compat := Z.mul_nonneg_nonneg (compat "8.3").
-Notation Zmult_lt_0_compat := Z.mul_pos_pos (compat "8.3").
-Notation Zmult_lt_O_compat := Z.mul_pos_pos (compat "8.3").
+Notation Zmult_le_0_compat := Z.mul_nonneg_nonneg (only parsing).
+Notation Zmult_lt_0_compat := Z.mul_pos_pos (only parsing).
+Notation Zmult_lt_O_compat := Z.mul_pos_pos (only parsing).
Lemma Zmult_gt_0_compat n m : n > 0 -> m > 0 -> n * m > 0.
Proof.
@@ -624,9 +626,9 @@ Qed.
(** * Equivalence between inequalities *)
-Notation Zle_plus_swap := Z.le_add_le_sub_r (compat "8.3").
-Notation Zlt_plus_swap := Z.lt_add_lt_sub_r (compat "8.3").
-Notation Zlt_minus_simpl_swap := Z.lt_sub_pos (compat "8.3").
+Notation Zle_plus_swap := Z.le_add_le_sub_r (only parsing).
+Notation Zlt_plus_swap := Z.lt_add_lt_sub_r (only parsing).
+Notation Zlt_minus_simpl_swap := Z.lt_sub_pos (only parsing).
Lemma Zeq_plus_swap n m p : n + p = m <-> n = m - p.
Proof.
diff --git a/theories/ZArith/Zpow_alt.v b/theories/ZArith/Zpow_alt.v
index e1220dcee..983405acb 100644
--- a/theories/ZArith/Zpow_alt.v
+++ b/theories/ZArith/Zpow_alt.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import BinInt.
diff --git a/theories/ZArith/Zpow_def.v b/theories/ZArith/Zpow_def.v
index a768868bd..2b099671f 100644
--- a/theories/ZArith/Zpow_def.v
+++ b/theories/ZArith/Zpow_def.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import BinInt Ring_theory.
@@ -14,12 +16,12 @@ Local Open Scope Z_scope.
(** Nota : this file is mostly deprecated. The definition of [Z.pow]
and its usual properties are now provided by module [BinInt.Z]. *)
-Notation Zpower_pos := Z.pow_pos (compat "8.3").
-Notation Zpower := Z.pow (compat "8.3").
-Notation Zpower_0_r := Z.pow_0_r (compat "8.3").
-Notation Zpower_succ_r := Z.pow_succ_r (compat "8.3").
-Notation Zpower_neg_r := Z.pow_neg_r (compat "8.3").
-Notation Zpower_Ppow := Pos2Z.inj_pow (compat "8.3").
+Notation Zpower_pos := Z.pow_pos (only parsing).
+Notation Zpower := Z.pow (only parsing).
+Notation Zpower_0_r := Z.pow_0_r (only parsing).
+Notation Zpower_succ_r := Z.pow_succ_r (only parsing).
+Notation Zpower_neg_r := Z.pow_neg_r (only parsing).
+Notation Zpower_Ppow := Pos2Z.inj_pow (only parsing).
Lemma Zpower_theory : power_theory 1 Z.mul (@eq Z) Z.of_N Z.pow.
Proof.
diff --git a/theories/ZArith/Zpow_facts.v b/theories/ZArith/Zpow_facts.v
index 3ea3ae4ab..a9bc5bd09 100644
--- a/theories/ZArith/Zpow_facts.v
+++ b/theories/ZArith/Zpow_facts.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import ZArith_base ZArithRing Zcomplements Zdiv Znumtheory.
@@ -29,17 +31,17 @@ Proof. now apply (Z.pow_0_l (Zpos p)). Qed.
Lemma Zpower_pos_pos x p : 0 < x -> 0 < Z.pow_pos x p.
Proof. intros. now apply (Z.pow_pos_nonneg x (Zpos p)). Qed.
-Notation Zpower_1_r := Z.pow_1_r (compat "8.3").
-Notation Zpower_1_l := Z.pow_1_l (compat "8.3").
-Notation Zpower_0_l := Z.pow_0_l' (compat "8.3").
-Notation Zpower_0_r := Z.pow_0_r (compat "8.3").
-Notation Zpower_2 := Z.pow_2_r (compat "8.3").
-Notation Zpower_gt_0 := Z.pow_pos_nonneg (compat "8.3").
-Notation Zpower_ge_0 := Z.pow_nonneg (compat "8.3").
-Notation Zpower_Zabs := Z.abs_pow (compat "8.3").
-Notation Zpower_Zsucc := Z.pow_succ_r (compat "8.3").
-Notation Zpower_mult := Z.pow_mul_r (compat "8.3").
-Notation Zpower_le_monotone2 := Z.pow_le_mono_r (compat "8.3").
+Notation Zpower_1_r := Z.pow_1_r (only parsing).
+Notation Zpower_1_l := Z.pow_1_l (only parsing).
+Notation Zpower_0_l := Z.pow_0_l' (only parsing).
+Notation Zpower_0_r := Z.pow_0_r (only parsing).
+Notation Zpower_2 := Z.pow_2_r (only parsing).
+Notation Zpower_gt_0 := Z.pow_pos_nonneg (only parsing).
+Notation Zpower_ge_0 := Z.pow_nonneg (only parsing).
+Notation Zpower_Zabs := Z.abs_pow (only parsing).
+Notation Zpower_Zsucc := Z.pow_succ_r (only parsing).
+Notation Zpower_mult := Z.pow_mul_r (only parsing).
+Notation Zpower_le_monotone2 := Z.pow_le_mono_r (only parsing).
Theorem Zpower_le_monotone a b c :
0 < a -> 0 <= b <= c -> a^b <= a^c.
@@ -231,7 +233,7 @@ Qed.
(** * Z.square: a direct definition of [z^2] *)
-Notation Psquare := Pos.square (compat "8.3").
-Notation Zsquare := Z.square (compat "8.3").
-Notation Psquare_correct := Pos.square_spec (compat "8.3").
-Notation Zsquare_correct := Z.square_spec (compat "8.3").
+Notation Psquare := Pos.square (compat "8.6").
+Notation Zsquare := Z.square (compat "8.6").
+Notation Psquare_correct := Pos.square_spec (only parsing).
+Notation Zsquare_correct := Z.square_spec (only parsing).
diff --git a/theories/ZArith/Zpower.v b/theories/ZArith/Zpower.v
index 6dcbdbdee..fa6905355 100644
--- a/theories/ZArith/Zpower.v
+++ b/theories/ZArith/Zpower.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Wf_nat ZArith_base Omega Zcomplements.
diff --git a/theories/ZArith/Zquot.v b/theories/ZArith/Zquot.v
index efb56c469..e93ebb1ad 100644
--- a/theories/ZArith/Zquot.v
+++ b/theories/ZArith/Zquot.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import Nnat ZArith_base ROmega ZArithRing Zdiv Morphisms.
@@ -31,21 +33,21 @@ Local Open Scope Z_scope.
exploiting the arbitrary value of division by 0).
*)
-Notation Ndiv_Zquot := N2Z.inj_quot (compat "8.3").
-Notation Nmod_Zrem := N2Z.inj_rem (compat "8.3").
-Notation Z_quot_rem_eq := Z.quot_rem' (compat "8.3").
-Notation Zrem_lt := Z.rem_bound_abs (compat "8.3").
-Notation Zquot_unique := Z.quot_unique (compat "8.3").
-Notation Zrem_unique := Z.rem_unique (compat "8.3").
-Notation Zrem_1_r := Z.rem_1_r (compat "8.3").
-Notation Zquot_1_r := Z.quot_1_r (compat "8.3").
-Notation Zrem_1_l := Z.rem_1_l (compat "8.3").
-Notation Zquot_1_l := Z.quot_1_l (compat "8.3").
-Notation Z_quot_same := Z.quot_same (compat "8.3").
-Notation Z_quot_mult := Z.quot_mul (compat "8.3").
-Notation Zquot_small := Z.quot_small (compat "8.3").
-Notation Zrem_small := Z.rem_small (compat "8.3").
-Notation Zquot2_quot := Zquot2_quot (compat "8.3").
+Notation Ndiv_Zquot := N2Z.inj_quot (only parsing).
+Notation Nmod_Zrem := N2Z.inj_rem (only parsing).
+Notation Z_quot_rem_eq := Z.quot_rem' (only parsing).
+Notation Zrem_lt := Z.rem_bound_abs (only parsing).
+Notation Zquot_unique := Z.quot_unique (compat "8.6").
+Notation Zrem_unique := Z.rem_unique (compat "8.6").
+Notation Zrem_1_r := Z.rem_1_r (compat "8.6").
+Notation Zquot_1_r := Z.quot_1_r (compat "8.6").
+Notation Zrem_1_l := Z.rem_1_l (compat "8.6").
+Notation Zquot_1_l := Z.quot_1_l (compat "8.6").
+Notation Z_quot_same := Z.quot_same (compat "8.6").
+Notation Z_quot_mult := Z.quot_mul (only parsing).
+Notation Zquot_small := Z.quot_small (compat "8.6").
+Notation Zrem_small := Z.rem_small (compat "8.6").
+Notation Zquot2_quot := Zquot2_quot (compat "8.6").
(** Particular values taken for [a÷0] and [(Z.rem a 0)].
We avise to not rely on these arbitrary values. *)
diff --git a/theories/ZArith/Zsqrt_compat.v b/theories/ZArith/Zsqrt_compat.v
index cccd970da..bd0904540 100644
--- a/theories/ZArith/Zsqrt_compat.v
+++ b/theories/ZArith/Zsqrt_compat.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import ZArithRing.
diff --git a/theories/ZArith/Zwf.v b/theories/ZArith/Zwf.v
index ca4b386dc..a71ea4f30 100644
--- a/theories/ZArith/Zwf.v
+++ b/theories/ZArith/Zwf.v
@@ -1,9 +1,11 @@
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import ZArith_base.
diff --git a/theories/ZArith/auxiliary.v b/theories/ZArith/auxiliary.v
index 494cb30dd..306a85638 100644
--- a/theories/ZArith/auxiliary.v
+++ b/theories/ZArith/auxiliary.v
@@ -1,10 +1,12 @@
(* -*- coding: utf-8 -*- *)
(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(** Binary Integers (Pierre Crégut, CNET, Lannion, France) *)