summaryrefslogtreecommitdiff
path: root/theories7/Setoids/Setoid.v
diff options
context:
space:
mode:
Diffstat (limited to 'theories7/Setoids/Setoid.v')
-rw-r--r--theories7/Setoids/Setoid.v73
1 files changed, 0 insertions, 73 deletions
diff --git a/theories7/Setoids/Setoid.v b/theories7/Setoids/Setoid.v
deleted file mode 100644
index f8176f60..00000000
--- a/theories7/Setoids/Setoid.v
+++ /dev/null
@@ -1,73 +0,0 @@
-(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(************************************************************************)
-
-(*i $Id: Setoid.v,v 1.1.2.1 2004/07/16 19:31:38 herbelin Exp $: i*)
-
-Section Setoid.
-
-Variable A : Type.
-Variable Aeq : A -> A -> Prop.
-
-Record Setoid_Theory : Prop :=
-{ Seq_refl : (x:A) (Aeq x x);
- Seq_sym : (x,y:A) (Aeq x y) -> (Aeq y x);
- Seq_trans : (x,y,z:A) (Aeq x y) -> (Aeq y z) -> (Aeq x z)
-}.
-
-End Setoid.
-
-Definition Prop_S : (Setoid_Theory Prop iff).
-Split; [Exact iff_refl | Exact iff_sym | Exact iff_trans].
-Qed.
-
-Add Setoid Prop iff Prop_S.
-
-Hint prop_set : setoid := Resolve (Seq_refl Prop iff Prop_S).
-Hint prop_set : setoid := Resolve (Seq_sym Prop iff Prop_S).
-Hint prop_set : setoid := Resolve (Seq_trans Prop iff Prop_S).
-
-Add Morphism or : or_ext.
-Intros.
-Inversion H1.
-Left.
-Inversion H.
-Apply (H3 H2).
-
-Right.
-Inversion H0.
-Apply (H3 H2).
-Qed.
-
-Add Morphism and : and_ext.
-Intros.
-Inversion H1.
-Split.
-Inversion H.
-Apply (H4 H2).
-
-Inversion H0.
-Apply (H4 H3).
-Qed.
-
-Add Morphism not : not_ext.
-Red ; Intros.
-Apply H0.
-Inversion H.
-Apply (H3 H1).
-Qed.
-
-Definition fleche [A,B:Prop] := A -> B.
-
-Add Morphism fleche : fleche_ext.
-Unfold fleche.
-Intros.
-Inversion H0.
-Inversion H.
-Apply (H3 (H1 (H6 H2))).
-Qed.
-