diff options
author | Stephane Glondu <steph@glondu.net> | 2012-01-12 16:04:54 +0100 |
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committer | Stephane Glondu <steph@glondu.net> | 2012-01-12 16:04:54 +0100 |
commit | 39efc41237ec906226a3a53d7396d51173495204 (patch) | |
tree | 87cd58d72d43469d2a2a0a127c1060d7c9e0206b /theories/Arith/Le.v | |
parent | 5fe4ac437bed43547b3695664974f492b55cb553 (diff) | |
parent | 97fefe1fcca363a1317e066e7f4b99b9c1e9987b (diff) |
Remove non-DFSG contentsupstream/8.4_beta+dfsg
Diffstat (limited to 'theories/Arith/Le.v')
-rw-r--r-- | theories/Arith/Le.v | 11 |
1 files changed, 3 insertions, 8 deletions
diff --git a/theories/Arith/Le.v b/theories/Arith/Le.v index b73959e7..f0ebf162 100644 --- a/theories/Arith/Le.v +++ b/theories/Arith/Le.v @@ -1,13 +1,11 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2011 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Le.v 14641 2011-11-06 11:59:10Z herbelin $ i*) - (** Order on natural numbers. [le] is defined in [Init/Peano.v] as: << Inductive le (n:nat) : nat -> Prop := @@ -84,8 +82,7 @@ Hint Immediate le_Sn_le: arith v62. Theorem le_S_n : forall n m, S n <= S m -> n <= m. Proof. - intros n m H; change (pred (S n) <= pred (S m)) in |- *. - destruct H; simpl; auto with arith. + exact Peano.le_S_n. Qed. Hint Immediate le_S_n: arith v62. @@ -105,11 +102,9 @@ Hint Resolve le_pred_n: arith v62. Theorem le_pred : forall n m, n <= m -> pred n <= pred m. Proof. - destruct n; simpl; auto with arith. - destruct m; simpl; auto with arith. + exact Peano.le_pred. Qed. - (** * [le] is a order on [nat] *) (** Antisymmetry *) |