diff options
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 *) |