From c29aa4ce8fe8090ca1a84d0be020e40787149c38 Mon Sep 17 00:00:00 2001
From: barras <barras@85f007b7-540e-0410-9357-904b9bb8a0f7>
Date: Wed, 6 Oct 2004 15:31:23 +0000
Subject: added transitivity

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@6188 85f007b7-540e-0410-9357-904b9bb8a0f7
---
 theories/Setoids/Setoid.v | 9 +++++++++
 1 file changed, 9 insertions(+)

(limited to 'theories/Setoids')

diff --git a/theories/Setoids/Setoid.v b/theories/Setoids/Setoid.v
index 1bf729055..bde24eded 100644
--- a/theories/Setoids/Setoid.v
+++ b/theories/Setoids/Setoid.v
@@ -574,6 +574,11 @@ Definition equality_morphism_of_setoid_theory:
  unfold make_compatibility_goal; simpl; split; eauto.
 Defined.
 
+Lemma eq_setoid : forall R, Setoid_Theory (@eq R).
+Proof
+  (fun R =>
+    Build_Setoid_Theory (@eq R) (@refl_equal R) (@sym_eq R) (@trans_eq R)).
+
 (* END OF UTILITY/BACKWARD COMPATIBILITY PART *)
 
 (* A FEW EXAMPLES *)
@@ -612,6 +617,10 @@ Theorem impl_refl: reflexive _ impl.
  hnf; unfold impl; tauto.
 Qed.
 
+Theorem impl_trans: transitive _ impl.
+ hnf; unfold impl; tauto.
+Qed.
+
 (* THE ASYMMETRIC AREFLEXIVE RELATION impl WITH A FEW MORPHISMS *)
 
 Add Relation Prop impl reflexivity proved by impl_refl.
-- 
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