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authorGravatar Samuel Mimram <smimram@debian.org>2006-04-28 14:59:16 +0000
committerGravatar Samuel Mimram <smimram@debian.org>2006-04-28 14:59:16 +0000
commit2c4a6b4efe55a2c6ca9ca7b185723e7909e57269 (patch)
treee1542c8adb83ff297284eefc23a2703461713d9b /theories7/Relations/Relations.v
parent514dce2dfe717e3ed2e37dce6467b56219d451c1 (diff)
parent3ef7797ef6fc605dfafb32523261fe1b023aeecb (diff)
Merge commit 'upstream/8.0pl3+8.1alpha' into 8.0pl3+8.1alpha
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-(************************************************************************)
-(* 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: Relations.v,v 1.1.2.1 2004/07/16 19:31:38 herbelin Exp $ i*)
-
-Require Export Relation_Definitions.
-Require Export Relation_Operators.
-Require Export Operators_Properties.
-
-Lemma inverse_image_of_equivalence : (A,B:Set)(f:A->B)
- (r:(relation B))(equivalence B r)->(equivalence A [x,y:A](r (f x) (f y))).
-Intros; Split; Elim H; Red; Auto.
-Intros _ equiv_trans _ x y z H0 H1; Apply equiv_trans with (f y); Assumption.
-Qed.
-
-Lemma inverse_image_of_eq : (A,B:Set)(f:A->B)
- (equivalence A [x,y:A](f x)=(f y)).
-Split; Red;
-[ (* reflexivity *) Reflexivity
-| (* transitivity *) Intros; Transitivity (f y); Assumption
-| (* symmetry *) Intros; Symmetry; Assumption
-].
-Qed.