diff options
Diffstat (limited to 'theories/Arith/Le.v')
| -rw-r--r--[-rwxr-xr-x] | theories/Arith/Le.v | 9 |
1 files changed, 4 insertions, 5 deletions
diff --git a/theories/Arith/Le.v b/theories/Arith/Le.v index a5378cff..e95ef408 100755..100644 --- a/theories/Arith/Le.v +++ b/theories/Arith/Le.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Le.v,v 1.14.2.1 2004/07/16 19:31:00 herbelin Exp $ i*) +(*i $Id: Le.v 8642 2006-03-17 10:09:02Z notin $ i*) (** Order on natural numbers *) Open Local Scope nat_scope. @@ -62,15 +62,14 @@ 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 |- *. -elim H; simpl in |- *; auto with arith. +destruct H; simpl; auto with arith. Qed. Hint Immediate le_S_n: arith v62. Theorem le_pred : forall n m, n <= m -> pred n <= pred m. Proof. -induction n as [| n IHn]. simpl in |- *. auto with arith. -destruct m as [| m]. simpl in |- *. intro H. inversion H. -simpl in |- *. auto with arith. +destruct n; simpl; auto with arith. +destruct m; simpl; auto with arith. Qed. (** Comparison to 0 *) |