diff options
Diffstat (limited to 'theories/Numbers')
60 files changed, 0 insertions, 120 deletions
diff --git a/theories/Numbers/BigNumPrelude.v b/theories/Numbers/BigNumPrelude.v index 08da68444..f11fb67b1 100644 --- a/theories/Numbers/BigNumPrelude.v +++ b/theories/Numbers/BigNumPrelude.v @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - (** * BigNumPrelude *) (** Auxillary functions & theorems used for arbitrary precision efficient diff --git a/theories/Numbers/Cyclic/Abstract/CyclicAxioms.v b/theories/Numbers/Cyclic/Abstract/CyclicAxioms.v index af30b0175..0403722cb 100644 --- a/theories/Numbers/Cyclic/Abstract/CyclicAxioms.v +++ b/theories/Numbers/Cyclic/Abstract/CyclicAxioms.v @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(* $Id$ *) - (** * Signature and specification of a bounded integer structure *) (** This file specifies how to represent [Z/nZ] when [n=2^d], diff --git a/theories/Numbers/Cyclic/Abstract/NZCyclic.v b/theories/Numbers/Cyclic/Abstract/NZCyclic.v index b68e89560..0796d9f49 100644 --- a/theories/Numbers/Cyclic/Abstract/NZCyclic.v +++ b/theories/Numbers/Cyclic/Abstract/NZCyclic.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Export NZAxioms. Require Import BigNumPrelude. Require Import DoubleType. diff --git a/theories/Numbers/Cyclic/DoubleCyclic/DoubleAdd.v b/theories/Numbers/Cyclic/DoubleCyclic/DoubleAdd.v index aa798e1c7..81b2c9403 100644 --- a/theories/Numbers/Cyclic/DoubleCyclic/DoubleAdd.v +++ b/theories/Numbers/Cyclic/DoubleCyclic/DoubleAdd.v @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Set Implicit Arguments. Require Import ZArith. diff --git a/theories/Numbers/Cyclic/DoubleCyclic/DoubleBase.v b/theories/Numbers/Cyclic/DoubleCyclic/DoubleBase.v index 23c62740c..bf18c1753 100644 --- a/theories/Numbers/Cyclic/DoubleCyclic/DoubleBase.v +++ b/theories/Numbers/Cyclic/DoubleCyclic/DoubleBase.v @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Set Implicit Arguments. Require Import ZArith. diff --git a/theories/Numbers/Cyclic/DoubleCyclic/DoubleCyclic.v b/theories/Numbers/Cyclic/DoubleCyclic/DoubleCyclic.v index 49a4f950a..a640aaf7f 100644 --- a/theories/Numbers/Cyclic/DoubleCyclic/DoubleCyclic.v +++ b/theories/Numbers/Cyclic/DoubleCyclic/DoubleCyclic.v @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Set Implicit Arguments. Require Import ZArith. diff --git a/theories/Numbers/Cyclic/DoubleCyclic/DoubleDiv.v b/theories/Numbers/Cyclic/DoubleCyclic/DoubleDiv.v index 1ce1e81b0..ae806dd5e 100644 --- a/theories/Numbers/Cyclic/DoubleCyclic/DoubleDiv.v +++ b/theories/Numbers/Cyclic/DoubleCyclic/DoubleDiv.v @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Set Implicit Arguments. Require Import ZArith. diff --git a/theories/Numbers/Cyclic/DoubleCyclic/DoubleDivn1.v b/theories/Numbers/Cyclic/DoubleCyclic/DoubleDivn1.v index 136f96c04..1c4247231 100644 --- a/theories/Numbers/Cyclic/DoubleCyclic/DoubleDivn1.v +++ b/theories/Numbers/Cyclic/DoubleCyclic/DoubleDivn1.v @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Set Implicit Arguments. Require Import ZArith. diff --git a/theories/Numbers/Cyclic/DoubleCyclic/DoubleLift.v b/theories/Numbers/Cyclic/DoubleCyclic/DoubleLift.v index 3405b6f4d..1395caa33 100644 --- a/theories/Numbers/Cyclic/DoubleCyclic/DoubleLift.v +++ b/theories/Numbers/Cyclic/DoubleCyclic/DoubleLift.v @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Set Implicit Arguments. Require Import ZArith. diff --git a/theories/Numbers/Cyclic/DoubleCyclic/DoubleMul.v b/theories/Numbers/Cyclic/DoubleCyclic/DoubleMul.v index 6a2a34449..8b978172c 100644 --- a/theories/Numbers/Cyclic/DoubleCyclic/DoubleMul.v +++ b/theories/Numbers/Cyclic/DoubleCyclic/DoubleMul.v @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Set Implicit Arguments. Require Import ZArith. diff --git a/theories/Numbers/Cyclic/DoubleCyclic/DoubleSqrt.v b/theories/Numbers/Cyclic/DoubleCyclic/DoubleSqrt.v index e2c623201..81df55bd4 100644 --- a/theories/Numbers/Cyclic/DoubleCyclic/DoubleSqrt.v +++ b/theories/Numbers/Cyclic/DoubleCyclic/DoubleSqrt.v @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Set Implicit Arguments. Require Import ZArith. diff --git a/theories/Numbers/Cyclic/DoubleCyclic/DoubleSub.v b/theories/Numbers/Cyclic/DoubleCyclic/DoubleSub.v index a7e556713..a5610fe78 100644 --- a/theories/Numbers/Cyclic/DoubleCyclic/DoubleSub.v +++ b/theories/Numbers/Cyclic/DoubleCyclic/DoubleSub.v @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Set Implicit Arguments. Require Import ZArith. diff --git a/theories/Numbers/Cyclic/DoubleCyclic/DoubleType.v b/theories/Numbers/Cyclic/DoubleCyclic/DoubleType.v index 88cbb484f..da75219a5 100644 --- a/theories/Numbers/Cyclic/DoubleCyclic/DoubleType.v +++ b/theories/Numbers/Cyclic/DoubleCyclic/DoubleType.v @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Set Implicit Arguments. Require Import ZArith. diff --git a/theories/Numbers/Cyclic/Int31/Cyclic31.v b/theories/Numbers/Cyclic/Int31/Cyclic31.v index e2e5b563f..ca73a9f00 100644 --- a/theories/Numbers/Cyclic/Int31/Cyclic31.v +++ b/theories/Numbers/Cyclic/Int31/Cyclic31.v @@ -6,8 +6,6 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id$ i*) - (** * 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 cc224254f..9b4c25e2c 100644 --- a/theories/Numbers/Cyclic/Int31/Int31.v +++ b/theories/Numbers/Cyclic/Int31/Int31.v @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Import NaryFunctions. Require Import Wf_nat. Require Export ZArith. diff --git a/theories/Numbers/Cyclic/Int31/Ring31.v b/theories/Numbers/Cyclic/Int31/Ring31.v index a9c499fb9..01002656d 100644 --- a/theories/Numbers/Cyclic/Int31/Ring31.v +++ b/theories/Numbers/Cyclic/Int31/Ring31.v @@ -6,8 +6,6 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id$ i*) - (** * Int31 numbers defines Z/(2^31)Z, and can hence be equipped with a ring structure and a ring tactic *) diff --git a/theories/Numbers/Cyclic/ZModulo/ZModulo.v b/theories/Numbers/Cyclic/ZModulo/ZModulo.v index da0be5e2a..a2ee248ab 100644 --- a/theories/Numbers/Cyclic/ZModulo/ZModulo.v +++ b/theories/Numbers/Cyclic/ZModulo/ZModulo.v @@ -6,8 +6,6 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(* $Id$ *) - (** * Type [Z] viewed modulo a particular constant corresponds to [Z/nZ] as defined abstractly in CyclicAxioms. *) diff --git a/theories/Numbers/Integer/Abstract/ZAdd.v b/theories/Numbers/Integer/Abstract/ZAdd.v index 5663408d1..123c40428 100644 --- a/theories/Numbers/Integer/Abstract/ZAdd.v +++ b/theories/Numbers/Integer/Abstract/ZAdd.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Export ZBase. Module ZAddPropFunct (Import Z : ZAxiomsSig'). diff --git a/theories/Numbers/Integer/Abstract/ZAddOrder.v b/theories/Numbers/Integer/Abstract/ZAddOrder.v index de12993f8..adc843264 100644 --- a/theories/Numbers/Integer/Abstract/ZAddOrder.v +++ b/theories/Numbers/Integer/Abstract/ZAddOrder.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Export ZLt. Module ZAddOrderPropFunct (Import Z : ZAxiomsSig'). diff --git a/theories/Numbers/Integer/Abstract/ZAxioms.v b/theories/Numbers/Integer/Abstract/ZAxioms.v index 9158a214d..46f7810ac 100644 --- a/theories/Numbers/Integer/Abstract/ZAxioms.v +++ b/theories/Numbers/Integer/Abstract/ZAxioms.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Export NZAxioms. Set Implicit Arguments. diff --git a/theories/Numbers/Integer/Abstract/ZBase.v b/theories/Numbers/Integer/Abstract/ZBase.v index 44bb02ecc..ca288e6b2 100644 --- a/theories/Numbers/Integer/Abstract/ZBase.v +++ b/theories/Numbers/Integer/Abstract/ZBase.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Export Decidable. Require Export ZAxioms. Require Import NZProperties. diff --git a/theories/Numbers/Integer/Abstract/ZLt.v b/theories/Numbers/Integer/Abstract/ZLt.v index 849bf6b40..fdb7c77f6 100644 --- a/theories/Numbers/Integer/Abstract/ZLt.v +++ b/theories/Numbers/Integer/Abstract/ZLt.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Export ZMul. Module ZOrderPropFunct (Import Z : ZAxiomsSig'). diff --git a/theories/Numbers/Integer/Abstract/ZMul.v b/theories/Numbers/Integer/Abstract/ZMul.v index 84d840ad2..4a87a54c8 100644 --- a/theories/Numbers/Integer/Abstract/ZMul.v +++ b/theories/Numbers/Integer/Abstract/ZMul.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Export ZAdd. Module ZMulPropFunct (Import Z : ZAxiomsSig'). diff --git a/theories/Numbers/Integer/Abstract/ZMulOrder.v b/theories/Numbers/Integer/Abstract/ZMulOrder.v index 99be58ebd..1952f4e2a 100644 --- a/theories/Numbers/Integer/Abstract/ZMulOrder.v +++ b/theories/Numbers/Integer/Abstract/ZMulOrder.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Export ZAddOrder. Module Type ZMulOrderPropFunct (Import Z : ZAxiomsSig'). diff --git a/theories/Numbers/Integer/Abstract/ZProperties.v b/theories/Numbers/Integer/Abstract/ZProperties.v index 45662d3b6..76451da33 100644 --- a/theories/Numbers/Integer/Abstract/ZProperties.v +++ b/theories/Numbers/Integer/Abstract/ZProperties.v @@ -6,8 +6,6 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id$ i*) - Require Export ZAxioms ZMaxMin ZSgnAbs. (** This functor summarizes all known facts about Z. diff --git a/theories/Numbers/Integer/BigZ/BigZ.v b/theories/Numbers/Integer/BigZ/BigZ.v index aa62ae76b..c0b8074b6 100644 --- a/theories/Numbers/Integer/BigZ/BigZ.v +++ b/theories/Numbers/Integer/BigZ/BigZ.v @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Export BigN. Require Import ZProperties ZDivFloor ZSig ZSigZAxioms ZMake. diff --git a/theories/Numbers/Integer/BigZ/ZMake.v b/theories/Numbers/Integer/BigZ/ZMake.v index 3196f11ea..41b1d6e69 100644 --- a/theories/Numbers/Integer/BigZ/ZMake.v +++ b/theories/Numbers/Integer/BigZ/ZMake.v @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Import ZArith. Require Import BigNumPrelude. Require Import NSig. diff --git a/theories/Numbers/Integer/Binary/ZBinary.v b/theories/Numbers/Integer/Binary/ZBinary.v index bc1dadcd9..aa857f3ca 100644 --- a/theories/Numbers/Integer/Binary/ZBinary.v +++ b/theories/Numbers/Integer/Binary/ZBinary.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Import ZAxioms ZProperties. Require Import BinInt Zcompare Zorder ZArith_dec Zbool. diff --git a/theories/Numbers/Integer/NatPairs/ZNatPairs.v b/theories/Numbers/Integer/NatPairs/ZNatPairs.v index 8b5624cdf..cafcc549e 100644 --- a/theories/Numbers/Integer/NatPairs/ZNatPairs.v +++ b/theories/Numbers/Integer/NatPairs/ZNatPairs.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Import NProperties. (* The most complete file for N *) Require Export ZProperties. (* The most complete file for Z *) Require Export Ring. diff --git a/theories/Numbers/Integer/SpecViaZ/ZSig.v b/theories/Numbers/Integer/SpecViaZ/ZSig.v index ffa91706f..ab12e584b 100644 --- a/theories/Numbers/Integer/SpecViaZ/ZSig.v +++ b/theories/Numbers/Integer/SpecViaZ/ZSig.v @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Import ZArith Znumtheory. Open Scope Z_scope. diff --git a/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v b/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v index bcecb6a8a..2c4797969 100644 --- a/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v +++ b/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v @@ -6,8 +6,6 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id$ i*) - Require Import ZArith ZAxioms ZDivFloor ZSig. (** * The interface [ZSig.ZType] implies the interface [ZAxiomsSig] diff --git a/theories/Numbers/NaryFunctions.v b/theories/Numbers/NaryFunctions.v index 417463eba..121b33b00 100644 --- a/theories/Numbers/NaryFunctions.v +++ b/theories/Numbers/NaryFunctions.v @@ -8,8 +8,6 @@ (* Pierre Letouzey, Jerome Vouillon, PPS, Paris 7, 2008 *) (************************************************************************) -(*i $Id$ i*) - Local Open Scope type_scope. Require Import List. diff --git a/theories/Numbers/NatInt/NZAdd.v b/theories/Numbers/NatInt/NZAdd.v index 9535cfdb4..37a174c48 100644 --- a/theories/Numbers/NatInt/NZAdd.v +++ b/theories/Numbers/NatInt/NZAdd.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Import NZAxioms NZBase. Module Type NZAddPropSig diff --git a/theories/Numbers/NatInt/NZAddOrder.v b/theories/Numbers/NatInt/NZAddOrder.v index 97c122029..66e9c6ceb 100644 --- a/theories/Numbers/NatInt/NZAddOrder.v +++ b/theories/Numbers/NatInt/NZAddOrder.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Import NZAxioms NZBase NZMul NZOrder. Module Type NZAddOrderPropSig (Import NZ : NZOrdAxiomsSig'). diff --git a/theories/Numbers/NatInt/NZAxioms.v b/theories/Numbers/NatInt/NZAxioms.v index ee7ee159f..7cfa62eab 100644 --- a/theories/Numbers/NatInt/NZAxioms.v +++ b/theories/Numbers/NatInt/NZAxioms.v @@ -8,8 +8,6 @@ (** Initial Author : Evgeny Makarov, INRIA, 2007 *) -(*i $Id$ i*) - Require Export Equalities Orders NumPrelude GenericMinMax. (** Axiomatization of a domain with zero, successor, predecessor, diff --git a/theories/Numbers/NatInt/NZBase.v b/theories/Numbers/NatInt/NZBase.v index 18e3b9b92..9f587a1d0 100644 --- a/theories/Numbers/NatInt/NZBase.v +++ b/theories/Numbers/NatInt/NZBase.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Import NZAxioms. Module Type NZBasePropSig (Import NZ : NZDomainSig'). diff --git a/theories/Numbers/NatInt/NZDomain.v b/theories/Numbers/NatInt/NZDomain.v index eb06cae03..7afbee4a4 100644 --- a/theories/Numbers/NatInt/NZDomain.v +++ b/theories/Numbers/NatInt/NZDomain.v @@ -6,8 +6,6 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id$ i*) - Require Export NumPrelude NZAxioms. Require Import NZBase NZOrder NZAddOrder Plus Minus. diff --git a/theories/Numbers/NatInt/NZMul.v b/theories/Numbers/NatInt/NZMul.v index 296bd095f..c97aa9f3a 100644 --- a/theories/Numbers/NatInt/NZMul.v +++ b/theories/Numbers/NatInt/NZMul.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Import NZAxioms NZBase NZAdd. Module Type NZMulPropSig diff --git a/theories/Numbers/NatInt/NZMulOrder.v b/theories/Numbers/NatInt/NZMulOrder.v index 7b64a6983..acc43fc17 100644 --- a/theories/Numbers/NatInt/NZMulOrder.v +++ b/theories/Numbers/NatInt/NZMulOrder.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Import NZAxioms. Require Import NZAddOrder. diff --git a/theories/Numbers/NatInt/NZOrder.v b/theories/Numbers/NatInt/NZOrder.v index 14fa0bfde..bfbcc2c65 100644 --- a/theories/Numbers/NatInt/NZOrder.v +++ b/theories/Numbers/NatInt/NZOrder.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Import NZAxioms NZBase Decidable OrdersTac. Module Type NZOrderPropSig diff --git a/theories/Numbers/NatInt/NZProperties.v b/theories/Numbers/NatInt/NZProperties.v index 125b4f62c..cc7bfe031 100644 --- a/theories/Numbers/NatInt/NZProperties.v +++ b/theories/Numbers/NatInt/NZProperties.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Export NZAxioms NZMulOrder. (** This functor summarizes all known facts about NZ. diff --git a/theories/Numbers/Natural/Abstract/NAdd.v b/theories/Numbers/Natural/Abstract/NAdd.v index 9f0b54a6a..859641280 100644 --- a/theories/Numbers/Natural/Abstract/NAdd.v +++ b/theories/Numbers/Natural/Abstract/NAdd.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Export NBase. Module NAddPropFunct (Import N : NAxiomsSig'). diff --git a/theories/Numbers/Natural/Abstract/NAddOrder.v b/theories/Numbers/Natural/Abstract/NAddOrder.v index 0ce04e54e..67bc80850 100644 --- a/theories/Numbers/Natural/Abstract/NAddOrder.v +++ b/theories/Numbers/Natural/Abstract/NAddOrder.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Export NOrder. Module NAddOrderPropFunct (Import N : NAxiomsSig'). diff --git a/theories/Numbers/Natural/Abstract/NAxioms.v b/theories/Numbers/Natural/Abstract/NAxioms.v index 42016ab10..cd3d8f0a8 100644 --- a/theories/Numbers/Natural/Abstract/NAxioms.v +++ b/theories/Numbers/Natural/Abstract/NAxioms.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Export NZAxioms. Set Implicit Arguments. diff --git a/theories/Numbers/Natural/Abstract/NBase.v b/theories/Numbers/Natural/Abstract/NBase.v index 842f4bcf2..f26f56d0c 100644 --- a/theories/Numbers/Natural/Abstract/NBase.v +++ b/theories/Numbers/Natural/Abstract/NBase.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Export Decidable. Require Export NAxioms. Require Import NZProperties. diff --git a/theories/Numbers/Natural/Abstract/NDefOps.v b/theories/Numbers/Natural/Abstract/NDefOps.v index 22eb2cb34..2302e8d35 100644 --- a/theories/Numbers/Natural/Abstract/NDefOps.v +++ b/theories/Numbers/Natural/Abstract/NDefOps.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Import Bool. (* To get the orb and negb function *) Require Import RelationPairs. Require Export NStrongRec. diff --git a/theories/Numbers/Natural/Abstract/NIso.v b/theories/Numbers/Natural/Abstract/NIso.v index 47bf38cba..12dcd3258 100644 --- a/theories/Numbers/Natural/Abstract/NIso.v +++ b/theories/Numbers/Natural/Abstract/NIso.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Import NBase. Module Homomorphism (N1 N2 : NAxiomsSig). diff --git a/theories/Numbers/Natural/Abstract/NMulOrder.v b/theories/Numbers/Natural/Abstract/NMulOrder.v index a2162b137..29d1838c2 100644 --- a/theories/Numbers/Natural/Abstract/NMulOrder.v +++ b/theories/Numbers/Natural/Abstract/NMulOrder.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Export NAddOrder. Module NMulOrderPropFunct (Import N : NAxiomsSig'). diff --git a/theories/Numbers/Natural/Abstract/NOrder.v b/theories/Numbers/Natural/Abstract/NOrder.v index 090c02ecf..9439e04f5 100644 --- a/theories/Numbers/Natural/Abstract/NOrder.v +++ b/theories/Numbers/Natural/Abstract/NOrder.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Export NAdd. Module NOrderPropFunct (Import N : NAxiomsSig'). diff --git a/theories/Numbers/Natural/Abstract/NProperties.v b/theories/Numbers/Natural/Abstract/NProperties.v index 9fc9b290e..eed7cac18 100644 --- a/theories/Numbers/Natural/Abstract/NProperties.v +++ b/theories/Numbers/Natural/Abstract/NProperties.v @@ -6,8 +6,6 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id$ i*) - Require Export NAxioms NMaxMin. (** This functor summarizes all known facts about N. diff --git a/theories/Numbers/Natural/Abstract/NStrongRec.v b/theories/Numbers/Natural/Abstract/NStrongRec.v index cbbcdbff5..bd666bc8b 100644 --- a/theories/Numbers/Natural/Abstract/NStrongRec.v +++ b/theories/Numbers/Natural/Abstract/NStrongRec.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - (** This file defined the strong (course-of-value, well-founded) recursion and proves its properties *) diff --git a/theories/Numbers/Natural/Abstract/NSub.v b/theories/Numbers/Natural/Abstract/NSub.v index 1df032ea3..7d3117fdb 100644 --- a/theories/Numbers/Natural/Abstract/NSub.v +++ b/theories/Numbers/Natural/Abstract/NSub.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Export NMulOrder. Module Type NSubPropFunct (Import N : NAxiomsSig'). diff --git a/theories/Numbers/Natural/BigN/NMake_gen.ml b/theories/Numbers/Natural/BigN/NMake_gen.ml index 5442a5626..20cb01b16 100644 --- a/theories/Numbers/Natural/BigN/NMake_gen.ml +++ b/theories/Numbers/Natural/BigN/NMake_gen.ml @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - (*S NMake_gen.ml : this file generates NMake.v *) diff --git a/theories/Numbers/Natural/BigN/Nbasic.v b/theories/Numbers/Natural/BigN/Nbasic.v index 9772e6a1f..9177b8092 100644 --- a/theories/Numbers/Natural/BigN/Nbasic.v +++ b/theories/Numbers/Natural/BigN/Nbasic.v @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Import ZArith. Require Import BigNumPrelude. Require Import Max. diff --git a/theories/Numbers/Natural/Binary/NBinary.v b/theories/Numbers/Natural/Binary/NBinary.v index e8651d47c..ba592507b 100644 --- a/theories/Numbers/Natural/Binary/NBinary.v +++ b/theories/Numbers/Natural/Binary/NBinary.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Import BinPos Ndiv_def. Require Export BinNat. Require Import NAxioms NProperties NDiv. diff --git a/theories/Numbers/Natural/Peano/NPeano.v b/theories/Numbers/Natural/Peano/NPeano.v index 80d434bab..491c33666 100644 --- a/theories/Numbers/Natural/Peano/NPeano.v +++ b/theories/Numbers/Natural/Peano/NPeano.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Import Peano Peano_dec Compare_dec EqNat NAxioms NProperties NDiv. (** Functions not already defined: div mod *) diff --git a/theories/Numbers/Natural/SpecViaZ/NSig.v b/theories/Numbers/Natural/SpecViaZ/NSig.v index 3f60cbf1a..55a6302aa 100644 --- a/theories/Numbers/Natural/SpecViaZ/NSig.v +++ b/theories/Numbers/Natural/SpecViaZ/NSig.v @@ -8,8 +8,6 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Import ZArith Znumtheory. Open Scope Z_scope. diff --git a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v index 49a60916a..8cbd96c1f 100644 --- a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v +++ b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v @@ -6,8 +6,6 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id$ i*) - Require Import ZArith Nnat NAxioms NDiv NSig. (** * The interface [NSig.NType] implies the interface [NAxiomsSig] *) diff --git a/theories/Numbers/NumPrelude.v b/theories/Numbers/NumPrelude.v index 32860cd31..5022c9ae6 100644 --- a/theories/Numbers/NumPrelude.v +++ b/theories/Numbers/NumPrelude.v @@ -8,8 +8,6 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id$ i*) - Require Export Setoid Morphisms. Set Implicit Arguments. diff --git a/theories/Numbers/Rational/SpecViaQ/QSig.v b/theories/Numbers/Rational/SpecViaQ/QSig.v index 10d0189a3..6466fc511 100644 --- a/theories/Numbers/Rational/SpecViaQ/QSig.v +++ b/theories/Numbers/Rational/SpecViaQ/QSig.v @@ -6,8 +6,6 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id$ i*) - Require Import QArith Qpower Qminmax Orders RelationPairs GenericMinMax. Open Scope Q_scope. |