diff options
author | Stephane Glondu <steph@glondu.net> | 2012-08-20 18:27:01 +0200 |
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committer | Stephane Glondu <steph@glondu.net> | 2012-08-20 18:27:01 +0200 |
commit | e0d682ec25282a348d35c5b169abafec48555690 (patch) | |
tree | 1a46f0142a85df553388c932110793881f3af52f /theories/Numbers/NatInt | |
parent | 86535d84cc3cffeee1dcd8545343f234e7285530 (diff) |
Imported Upstream version 8.4dfsgupstream/8.4dfsg
Diffstat (limited to 'theories/Numbers/NatInt')
-rw-r--r-- | theories/Numbers/NatInt/NZAdd.v | 2 | ||||
-rw-r--r-- | theories/Numbers/NatInt/NZAddOrder.v | 2 | ||||
-rw-r--r-- | theories/Numbers/NatInt/NZAxioms.v | 4 | ||||
-rw-r--r-- | theories/Numbers/NatInt/NZBase.v | 2 | ||||
-rw-r--r-- | theories/Numbers/NatInt/NZBits.v | 2 | ||||
-rw-r--r-- | theories/Numbers/NatInt/NZDiv.v | 2 | ||||
-rw-r--r-- | theories/Numbers/NatInt/NZDomain.v | 2 | ||||
-rw-r--r-- | theories/Numbers/NatInt/NZGcd.v | 2 | ||||
-rw-r--r-- | theories/Numbers/NatInt/NZLog.v | 2 | ||||
-rw-r--r-- | theories/Numbers/NatInt/NZMul.v | 2 | ||||
-rw-r--r-- | theories/Numbers/NatInt/NZMulOrder.v | 6 | ||||
-rw-r--r-- | theories/Numbers/NatInt/NZOrder.v | 2 | ||||
-rw-r--r-- | theories/Numbers/NatInt/NZParity.v | 2 | ||||
-rw-r--r-- | theories/Numbers/NatInt/NZPow.v | 2 | ||||
-rw-r--r-- | theories/Numbers/NatInt/NZProperties.v | 2 | ||||
-rw-r--r-- | theories/Numbers/NatInt/NZSqrt.v | 2 |
16 files changed, 19 insertions, 19 deletions
diff --git a/theories/Numbers/NatInt/NZAdd.v b/theories/Numbers/NatInt/NZAdd.v index 8bed3027..83b2d63b 100644 --- a/theories/Numbers/NatInt/NZAdd.v +++ b/theories/Numbers/NatInt/NZAdd.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/NatInt/NZAddOrder.v b/theories/Numbers/NatInt/NZAddOrder.v index ee03e5f9..ed179699 100644 --- a/theories/Numbers/NatInt/NZAddOrder.v +++ b/theories/Numbers/NatInt/NZAddOrder.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/NatInt/NZAxioms.v b/theories/Numbers/NatInt/NZAxioms.v index fcd98787..3a432eaa 100644 --- a/theories/Numbers/NatInt/NZAxioms.v +++ b/theories/Numbers/NatInt/NZAxioms.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) @@ -43,7 +43,7 @@ End IsNZDomain. (** Axiomatization of some more constants Simply denoting "1" for (S 0) and so on works ok when implementing - by nat, but leaves some (Nsucc N0) when implementing by N. + by nat, but leaves some (N.succ N0) when implementing by N. *) Module Type OneTwo (Import T:Typ). diff --git a/theories/Numbers/NatInt/NZBase.v b/theories/Numbers/NatInt/NZBase.v index 65b64635..62b14829 100644 --- a/theories/Numbers/NatInt/NZBase.v +++ b/theories/Numbers/NatInt/NZBase.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/NatInt/NZBits.v b/theories/Numbers/NatInt/NZBits.v index dc97eeb1..8be5d45c 100644 --- a/theories/Numbers/NatInt/NZBits.v +++ b/theories/Numbers/NatInt/NZBits.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/NatInt/NZDiv.v b/theories/Numbers/NatInt/NZDiv.v index bc109ace..4b8a62a8 100644 --- a/theories/Numbers/NatInt/NZDiv.v +++ b/theories/Numbers/NatInt/NZDiv.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/NatInt/NZDomain.v b/theories/Numbers/NatInt/NZDomain.v index 36aaa3e7..4b71d539 100644 --- a/theories/Numbers/NatInt/NZDomain.v +++ b/theories/Numbers/NatInt/NZDomain.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/NatInt/NZGcd.v b/theories/Numbers/NatInt/NZGcd.v index f72023d9..d7e598fb 100644 --- a/theories/Numbers/NatInt/NZGcd.v +++ b/theories/Numbers/NatInt/NZGcd.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/NatInt/NZLog.v b/theories/Numbers/NatInt/NZLog.v index a5aa6d8a..fba91bf3 100644 --- a/theories/Numbers/NatInt/NZLog.v +++ b/theories/Numbers/NatInt/NZLog.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/NatInt/NZMul.v b/theories/Numbers/NatInt/NZMul.v index 2b5a1cf3..117a9621 100644 --- a/theories/Numbers/NatInt/NZMul.v +++ b/theories/Numbers/NatInt/NZMul.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/NatInt/NZMulOrder.v b/theories/Numbers/NatInt/NZMulOrder.v index 97306f93..a1fe4bf5 100644 --- a/theories/Numbers/NatInt/NZMulOrder.v +++ b/theories/Numbers/NatInt/NZMulOrder.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) @@ -271,9 +271,9 @@ Definition mul_eq_0 := eq_mul_0. Definition mul_eq_0_l := eq_mul_0_l. Definition mul_eq_0_r := eq_mul_0_r. -Theorem lt_0_mul : forall n m, 0 < n * m <-> (0 < n /\ 0 < m) \/ (m < 0 /\ n < 0). +Theorem lt_0_mul n m : 0 < n * m <-> (0 < n /\ 0 < m) \/ (m < 0 /\ n < 0). Proof. -intros n m; split; [intro H | intros [[H1 H2] | [H1 H2]]]. +split; [intro H | intros [[H1 H2] | [H1 H2]]]. destruct (lt_trichotomy n 0) as [H1 | [H1 | H1]]; [| rewrite H1 in H; rewrite mul_0_l in H; false_hyp H lt_irrefl |]; (destruct (lt_trichotomy m 0) as [H2 | [H2 | H2]]; diff --git a/theories/Numbers/NatInt/NZOrder.v b/theories/Numbers/NatInt/NZOrder.v index 8cf5b26f..37074aba 100644 --- a/theories/Numbers/NatInt/NZOrder.v +++ b/theories/Numbers/NatInt/NZOrder.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/NatInt/NZParity.v b/theories/Numbers/NatInt/NZParity.v index 29109ccb..0e932378 100644 --- a/theories/Numbers/NatInt/NZParity.v +++ b/theories/Numbers/NatInt/NZParity.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/NatInt/NZPow.v b/theories/Numbers/NatInt/NZPow.v index 58704735..26d5ffef 100644 --- a/theories/Numbers/NatInt/NZPow.v +++ b/theories/Numbers/NatInt/NZPow.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/NatInt/NZProperties.v b/theories/Numbers/NatInt/NZProperties.v index 13c26233..a2eb1996 100644 --- a/theories/Numbers/NatInt/NZProperties.v +++ b/theories/Numbers/NatInt/NZProperties.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) diff --git a/theories/Numbers/NatInt/NZSqrt.v b/theories/Numbers/NatInt/NZSqrt.v index 6e85c689..8146fd01 100644 --- a/theories/Numbers/NatInt/NZSqrt.v +++ b/theories/Numbers/NatInt/NZSqrt.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) |