diff options
author | Enrico Tassi <gareuselesinge@debian.org> | 2016-01-26 16:56:33 +0100 |
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committer | Enrico Tassi <gareuselesinge@debian.org> | 2016-01-26 16:56:33 +0100 |
commit | 164c6861860e6b52818c031f901ffeff91fca16a (patch) | |
tree | 4f91d20c890c25915e7b28226c663b94a8cfb0d3 /theories/Numbers/Integer/Abstract | |
parent | 91dbeab8eef959c3f64960909ca69d4e68c8198d (diff) |
Imported Upstream version 8.5upstream/8.5
Diffstat (limited to 'theories/Numbers/Integer/Abstract')
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZAdd.v | 2 | ||||
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZAddOrder.v | 2 | ||||
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZAxioms.v | 2 | ||||
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZBase.v | 2 | ||||
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZBits.v | 2 | ||||
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZDivEucl.v | 4 | ||||
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZDivFloor.v | 4 | ||||
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZDivTrunc.v | 4 | ||||
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZGcd.v | 2 | ||||
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZLcm.v | 2 | ||||
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZLt.v | 2 | ||||
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZMaxMin.v | 2 | ||||
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZMul.v | 2 | ||||
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZMulOrder.v | 2 | ||||
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZParity.v | 2 | ||||
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZPow.v | 2 | ||||
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZProperties.v | 2 | ||||
-rw-r--r-- | theories/Numbers/Integer/Abstract/ZSgnAbs.v | 2 |
18 files changed, 21 insertions, 21 deletions
diff --git a/theories/Numbers/Integer/Abstract/ZAdd.v b/theories/Numbers/Integer/Abstract/ZAdd.v index ec8801c4..f7fdc179 100644 --- a/theories/Numbers/Integer/Abstract/ZAdd.v +++ b/theories/Numbers/Integer/Abstract/ZAdd.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/Integer/Abstract/ZAddOrder.v b/theories/Numbers/Integer/Abstract/ZAddOrder.v index e341ea8a..6bf5e9d4 100644 --- a/theories/Numbers/Integer/Abstract/ZAddOrder.v +++ b/theories/Numbers/Integer/Abstract/ZAddOrder.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/Integer/Abstract/ZAxioms.v b/theories/Numbers/Integer/Abstract/ZAxioms.v index 2a9fa539..ad10e65f 100644 --- a/theories/Numbers/Integer/Abstract/ZAxioms.v +++ b/theories/Numbers/Integer/Abstract/ZAxioms.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/Integer/Abstract/ZBase.v b/theories/Numbers/Integer/Abstract/ZBase.v index 6634eab1..9b1b30f8 100644 --- a/theories/Numbers/Integer/Abstract/ZBase.v +++ b/theories/Numbers/Integer/Abstract/ZBase.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/Integer/Abstract/ZBits.v b/theories/Numbers/Integer/Abstract/ZBits.v index 9dd0ec0e..c919e121 100644 --- a/theories/Numbers/Integer/Abstract/ZBits.v +++ b/theories/Numbers/Integer/Abstract/ZBits.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/Integer/Abstract/ZDivEucl.v b/theories/Numbers/Integer/Abstract/ZDivEucl.v index d0df8fb4..278e1bcf 100644 --- a/theories/Numbers/Integer/Abstract/ZDivEucl.v +++ b/theories/Numbers/Integer/Abstract/ZDivEucl.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 *) @@ -391,7 +391,7 @@ rewrite <- (add_0_r (b*(a/b))) at 2. apply add_cancel_l. Qed. -(** Some additionnal inequalities about div. *) +(** Some additional inequalities about div. *) Theorem div_lt_upper_bound: forall a b q, 0<b -> a < b*q -> a/b < q. diff --git a/theories/Numbers/Integer/Abstract/ZDivFloor.v b/theories/Numbers/Integer/Abstract/ZDivFloor.v index d5f3f4ad..310748dd 100644 --- a/theories/Numbers/Integer/Abstract/ZDivFloor.v +++ b/theories/Numbers/Integer/Abstract/ZDivFloor.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 *) @@ -436,7 +436,7 @@ rewrite <- (add_0_r (b*(a/b))) at 2. apply add_cancel_l. Qed. -(** Some additionnal inequalities about div. *) +(** Some additional inequalities about div. *) Theorem div_lt_upper_bound: forall a b q, 0<b -> a < b*q -> a/b < q. diff --git a/theories/Numbers/Integer/Abstract/ZDivTrunc.v b/theories/Numbers/Integer/Abstract/ZDivTrunc.v index de2e99ec..04301077 100644 --- a/theories/Numbers/Integer/Abstract/ZDivTrunc.v +++ b/theories/Numbers/Integer/Abstract/ZDivTrunc.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 *) @@ -404,7 +404,7 @@ Proof. intros. rewrite rem_eq by order. rewrite sub_move_r; nzsimpl; tauto. Qed. -(** Some additionnal inequalities about quot. *) +(** Some additional inequalities about quot. *) Theorem quot_lt_upper_bound: forall a b q, 0<=a -> 0<b -> a < b*q -> a÷b < q. diff --git a/theories/Numbers/Integer/Abstract/ZGcd.v b/theories/Numbers/Integer/Abstract/ZGcd.v index cf6ff79e..30adaeb4 100644 --- a/theories/Numbers/Integer/Abstract/ZGcd.v +++ b/theories/Numbers/Integer/Abstract/ZGcd.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/Integer/Abstract/ZLcm.v b/theories/Numbers/Integer/Abstract/ZLcm.v index 9a1768eb..ef33308c 100644 --- a/theories/Numbers/Integer/Abstract/ZLcm.v +++ b/theories/Numbers/Integer/Abstract/ZLcm.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/Integer/Abstract/ZLt.v b/theories/Numbers/Integer/Abstract/ZLt.v index 6d0cdb01..0c92918d 100644 --- a/theories/Numbers/Integer/Abstract/ZLt.v +++ b/theories/Numbers/Integer/Abstract/ZLt.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/Integer/Abstract/ZMaxMin.v b/theories/Numbers/Integer/Abstract/ZMaxMin.v index 07c78ead..24a47f00 100644 --- a/theories/Numbers/Integer/Abstract/ZMaxMin.v +++ b/theories/Numbers/Integer/Abstract/ZMaxMin.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/Integer/Abstract/ZMul.v b/theories/Numbers/Integer/Abstract/ZMul.v index 2d78d8f3..830c0a7d 100644 --- a/theories/Numbers/Integer/Abstract/ZMul.v +++ b/theories/Numbers/Integer/Abstract/ZMul.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/Integer/Abstract/ZMulOrder.v b/theories/Numbers/Integer/Abstract/ZMulOrder.v index 487aaae1..320c8f35 100644 --- a/theories/Numbers/Integer/Abstract/ZMulOrder.v +++ b/theories/Numbers/Integer/Abstract/ZMulOrder.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/Integer/Abstract/ZParity.v b/theories/Numbers/Integer/Abstract/ZParity.v index 195a0277..952d8e9c 100644 --- a/theories/Numbers/Integer/Abstract/ZParity.v +++ b/theories/Numbers/Integer/Abstract/ZParity.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/Integer/Abstract/ZPow.v b/theories/Numbers/Integer/Abstract/ZPow.v index 87de2c78..02b8501c 100644 --- a/theories/Numbers/Integer/Abstract/ZPow.v +++ b/theories/Numbers/Integer/Abstract/ZPow.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/Integer/Abstract/ZProperties.v b/theories/Numbers/Integer/Abstract/ZProperties.v index 5cfeeb21..1dec3c58 100644 --- a/theories/Numbers/Integer/Abstract/ZProperties.v +++ b/theories/Numbers/Integer/Abstract/ZProperties.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/Integer/Abstract/ZSgnAbs.v b/theories/Numbers/Integer/Abstract/ZSgnAbs.v index b379853e..a10552ab 100644 --- a/theories/Numbers/Integer/Abstract/ZSgnAbs.v +++ b/theories/Numbers/Integer/Abstract/ZSgnAbs.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 *) |