diff options
| author |  letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2009-11-02 13:34:02 +0000 |
|---|---|---|
| committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2009-11-02 13:34:02 +0000 |
| commit | 0d651865b60bfa937e3857ede664938660b29abd (patch) | |
| tree | b935cef55f4ff381e062b5acff9aab4d72df4712 /theories/Relations | |
| parent | 66ea3473632a1b54fd1427e7b39e549213b64da3 (diff) | |
Operators_Properties: avoid to depend on Setoid
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12453 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Relations')
| -rw-r--r-- | theories/Relations/Operators_Properties.v | 11 |
1 files changed, 6 insertions, 5 deletions
diff --git a/theories/Relations/Operators_Properties.v b/theories/Relations/Operators_Properties.v index b3f30ddf2..1976b435c 100644 --- a/theories/Relations/Operators_Properties.v +++ b/theories/Relations/Operators_Properties.v @@ -16,7 +16,6 @@ Require Import Relation_Definitions. Require Import Relation_Operators. -Require Import Setoid. Section Properties. @@ -274,10 +273,12 @@ Section Properties. P z -> (forall x y, R x y -> P y -> clos_refl_trans R y z -> P x) -> forall x, clos_refl_trans R x z -> P x. - intros. - rewrite clos_rt_rt1n_iff in H1. - elim H1 using rt1n_ind_right; auto. - intros; rewrite <- clos_rt_rt1n_iff in *. + intros P z Hz IH x Hxz. + apply clos_rt_rt1n_iff in Hxz. + elim Hxz using rt1n_ind_right; auto. + clear x Hxz. + intros x y Hxy Hyz Hy. + apply clos_rt_rt1n_iff in Hyz. eauto. Qed. |