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Diffstat (limited to 'theories7/Relations/Relations.v')
| -rwxr-xr-x | theories7/Relations/Relations.v | 28 |
1 files changed, 0 insertions, 28 deletions
diff --git a/theories7/Relations/Relations.v b/theories7/Relations/Relations.v deleted file mode 100755 index 694d0eec..00000000 --- a/theories7/Relations/Relations.v +++ /dev/null @@ -1,28 +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: 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. |