diff options
Diffstat (limited to 'theories/Numbers/Natural')
28 files changed, 30 insertions, 30 deletions
diff --git a/theories/Numbers/Natural/Abstract/NAdd.v b/theories/Numbers/Natural/Abstract/NAdd.v index 638cfc7e..eecec3ac 100644 --- a/theories/Numbers/Natural/Abstract/NAdd.v +++ b/theories/Numbers/Natural/Abstract/NAdd.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Abstract/NAddOrder.v b/theories/Numbers/Natural/Abstract/NAddOrder.v index 144bce72..9d68a006 100644 --- a/theories/Numbers/Natural/Abstract/NAddOrder.v +++ b/theories/Numbers/Natural/Abstract/NAddOrder.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Abstract/NAxioms.v b/theories/Numbers/Natural/Abstract/NAxioms.v index d300f857..25e285d5 100644 --- a/theories/Numbers/Natural/Abstract/NAxioms.v +++ b/theories/Numbers/Natural/Abstract/NAxioms.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Abstract/NBase.v b/theories/Numbers/Natural/Abstract/NBase.v index 40453214..f949a0f6 100644 --- a/theories/Numbers/Natural/Abstract/NBase.v +++ b/theories/Numbers/Natural/Abstract/NBase.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Abstract/NBits.v b/theories/Numbers/Natural/Abstract/NBits.v index 6f8a8fe5..3dd603e2 100644 --- a/theories/Numbers/Natural/Abstract/NBits.v +++ b/theories/Numbers/Natural/Abstract/NBits.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Abstract/NDefOps.v b/theories/Numbers/Natural/Abstract/NDefOps.v index 892b9266..b3a53617 100644 --- a/theories/Numbers/Natural/Abstract/NDefOps.v +++ b/theories/Numbers/Natural/Abstract/NDefOps.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Abstract/NDiv.v b/theories/Numbers/Natural/Abstract/NDiv.v index fb68c139..84e1219e 100644 --- a/theories/Numbers/Natural/Abstract/NDiv.v +++ b/theories/Numbers/Natural/Abstract/NDiv.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) @@ -137,7 +137,7 @@ Proof. intros; apply mul_succ_div_gt; auto'. Qed. Lemma div_exact : forall a b, b~=0 -> (a == b*(a/b) <-> a mod b == 0). Proof. intros. apply div_exact; auto'. Qed. -(** Some additionnal inequalities about div. *) +(** Some additional inequalities about div. *) Theorem div_lt_upper_bound: forall a b q, b~=0 -> a < b*q -> a/b < q. diff --git a/theories/Numbers/Natural/Abstract/NGcd.v b/theories/Numbers/Natural/Abstract/NGcd.v index a1f4ddf8..1eac134d 100644 --- a/theories/Numbers/Natural/Abstract/NGcd.v +++ b/theories/Numbers/Natural/Abstract/NGcd.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Abstract/NIso.v b/theories/Numbers/Natural/Abstract/NIso.v index c296315d..e6cac0ba 100644 --- a/theories/Numbers/Natural/Abstract/NIso.v +++ b/theories/Numbers/Natural/Abstract/NIso.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Abstract/NLcm.v b/theories/Numbers/Natural/Abstract/NLcm.v index 0fe8e105..3d749799 100644 --- a/theories/Numbers/Natural/Abstract/NLcm.v +++ b/theories/Numbers/Natural/Abstract/NLcm.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Abstract/NLog.v b/theories/Numbers/Natural/Abstract/NLog.v index 605c0aad..0c9da29b 100644 --- a/theories/Numbers/Natural/Abstract/NLog.v +++ b/theories/Numbers/Natural/Abstract/NLog.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Abstract/NMaxMin.v b/theories/Numbers/Natural/Abstract/NMaxMin.v index e0710561..b4c9db91 100644 --- a/theories/Numbers/Natural/Abstract/NMaxMin.v +++ b/theories/Numbers/Natural/Abstract/NMaxMin.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Abstract/NMulOrder.v b/theories/Numbers/Natural/Abstract/NMulOrder.v index c41275d2..a4b52396 100644 --- a/theories/Numbers/Natural/Abstract/NMulOrder.v +++ b/theories/Numbers/Natural/Abstract/NMulOrder.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Abstract/NOrder.v b/theories/Numbers/Natural/Abstract/NOrder.v index 90053a73..60e955f5 100644 --- a/theories/Numbers/Natural/Abstract/NOrder.v +++ b/theories/Numbers/Natural/Abstract/NOrder.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Abstract/NParity.v b/theories/Numbers/Natural/Abstract/NParity.v index b3526c9a..e1f573f6 100644 --- a/theories/Numbers/Natural/Abstract/NParity.v +++ b/theories/Numbers/Natural/Abstract/NParity.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) @@ -8,7 +8,7 @@ Require Import Bool NSub NZParity. -(** Some additionnal properties of [even], [odd]. *) +(** Some additional properties of [even], [odd]. *) Module Type NParityProp (Import N : NAxiomsSig')(Import NP : NSubProp N). diff --git a/theories/Numbers/Natural/Abstract/NPow.v b/theories/Numbers/Natural/Abstract/NPow.v index 9cc23004..c9b2177f 100644 --- a/theories/Numbers/Natural/Abstract/NPow.v +++ b/theories/Numbers/Natural/Abstract/NPow.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Abstract/NProperties.v b/theories/Numbers/Natural/Abstract/NProperties.v index cb3501d4..819a5be9 100644 --- a/theories/Numbers/Natural/Abstract/NProperties.v +++ b/theories/Numbers/Natural/Abstract/NProperties.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Abstract/NSqrt.v b/theories/Numbers/Natural/Abstract/NSqrt.v index 8dc66884..4ae41407 100644 --- a/theories/Numbers/Natural/Abstract/NSqrt.v +++ b/theories/Numbers/Natural/Abstract/NSqrt.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Abstract/NStrongRec.v b/theories/Numbers/Natural/Abstract/NStrongRec.v index 896ffc18..fa3a5351 100644 --- a/theories/Numbers/Natural/Abstract/NStrongRec.v +++ b/theories/Numbers/Natural/Abstract/NStrongRec.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Abstract/NSub.v b/theories/Numbers/Natural/Abstract/NSub.v index 18ebe77b..21f12037 100644 --- a/theories/Numbers/Natural/Abstract/NSub.v +++ b/theories/Numbers/Natural/Abstract/NSub.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/BigN/BigN.v b/theories/Numbers/Natural/BigN/BigN.v index f7f4347b..29a1145e 100644 --- a/theories/Numbers/Natural/BigN/BigN.v +++ b/theories/Numbers/Natural/BigN/BigN.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/BigN/NMake.v b/theories/Numbers/Natural/BigN/NMake.v index bdcdd5ca..98949736 100644 --- a/theories/Numbers/Natural/BigN/NMake.v +++ b/theories/Numbers/Natural/BigN/NMake.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/BigN/NMake_gen.ml b/theories/Numbers/Natural/BigN/NMake_gen.ml index 6de77e0a..601fa108 100644 --- a/theories/Numbers/Natural/BigN/NMake_gen.ml +++ b/theories/Numbers/Natural/BigN/NMake_gen.ml @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/BigN/Nbasic.v b/theories/Numbers/Natural/BigN/Nbasic.v index 8fe9ea92..18d0262c 100644 --- a/theories/Numbers/Natural/BigN/Nbasic.v +++ b/theories/Numbers/Natural/BigN/Nbasic.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Binary/NBinary.v b/theories/Numbers/Natural/Binary/NBinary.v index d54bedd1..037b10d9 100644 --- a/theories/Numbers/Natural/Binary/NBinary.v +++ b/theories/Numbers/Natural/Binary/NBinary.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/Peano/NPeano.v b/theories/Numbers/Natural/Peano/NPeano.v index 96eb7b35..58b1b018 100644 --- a/theories/Numbers/Natural/Peano/NPeano.v +++ b/theories/Numbers/Natural/Peano/NPeano.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/SpecViaZ/NSig.v b/theories/Numbers/Natural/SpecViaZ/NSig.v index 1049c156..258e0315 100644 --- a/theories/Numbers/Natural/SpecViaZ/NSig.v +++ b/theories/Numbers/Natural/SpecViaZ/NSig.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v index 11569b3f..355da4cc 100644 --- a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v +++ b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) |