diff options
| author |  barras <barras@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2004-10-06 15:31:23 +0000 |
|---|---|---|
| committer | barras <barras@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2004-10-06 15:31:23 +0000 |
| commit | c29aa4ce8fe8090ca1a84d0be020e40787149c38 (patch) | |
| tree | c37bc3c8933438b601ace269d6b77dedbb0c1de5 /theories/Setoids | |
| parent | 3d0c94cd30c5ed2d6d8cb52b3c127ef29d4f3846 (diff) | |
added transitivity
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@6188 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Setoids')
| -rw-r--r-- | theories/Setoids/Setoid.v | 9 |
1 files changed, 9 insertions, 0 deletions
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. |