diff options
| author |  letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2005-02-03 14:44:34 +0000 |
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| committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2005-02-03 14:44:34 +0000 |
| commit | 62e7a0f9679f501f2bc9ff7343c8128a341da37c (patch) | |
| tree | e237c519c79639fda9d05c9914756dc8a3482909 /theories/Arith/Le.v | |
| parent | 551f14d9540c4c5ec05ddd482295f52fceb68bac (diff) | |
legere simplification des preuves de le_S_n et pred_le
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@6669 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Arith/Le.v')
| -rwxr-xr-x | theories/Arith/Le.v | 7 |
1 files changed, 3 insertions, 4 deletions
diff --git a/theories/Arith/Le.v b/theories/Arith/Le.v index b87f545a8..1f265b8f5 100755 --- a/theories/Arith/Le.v +++ b/theories/Arith/Le.v @@ -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 *) |