diff options
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. |