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Diffstat (limited to 'theories7/Setoids/Setoid.v')
-rw-r--r-- | theories7/Setoids/Setoid.v | 73 |
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. - |