diff options
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. |