diff options
| author |  letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2010-02-17 13:44:25 +0000 |
|---|---|---|
| committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2010-02-17 13:44:25 +0000 |
| commit | e9ccfc401c610ce4df6b06f48c611070a26f89d7 (patch) | |
| tree | 4fc33ceb1a3151a599906fa3640cbe1678460384 /theories/Arith/Le.v | |
| parent | fbaa8cdc94dd62f5c138bee1eeabbf0ba6b696ff (diff) | |
Arith's min and max placed in Peano (+basic specs max_l and co)
This allow for instance to remove the dependency of List.v toward Min.v
To prove max_l and co, we push Le.le_pred and Le.le_S_n into Peano.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12784 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Arith/Le.v')
| -rw-r--r-- | theories/Arith/Le.v | 7 |
1 files changed, 2 insertions, 5 deletions
diff --git a/theories/Arith/Le.v b/theories/Arith/Le.v index d85178dea..6140eeb5a 100644 --- a/theories/Arith/Le.v +++ b/theories/Arith/Le.v @@ -84,8 +84,7 @@ 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 +104,9 @@ 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 *) |