diff options
Diffstat (limited to 'theories/Relations/Relations.v')
| -rw-r--r-- | theories/Relations/Relations.v | 10 |
1 files changed, 4 insertions, 6 deletions
diff --git a/theories/Relations/Relations.v b/theories/Relations/Relations.v index 630b2822..08b7574f 100644 --- a/theories/Relations/Relations.v +++ b/theories/Relations/Relations.v @@ -1,13 +1,11 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2011 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Relations.v 14641 2011-11-06 11:59:10Z herbelin $ i*) - Require Export Relation_Definitions. Require Export Relation_Operators. Require Export Operators_Properties. @@ -16,16 +14,16 @@ Lemma inverse_image_of_equivalence : forall (A B:Type) (f:A -> B) (r:relation B), equivalence B r -> equivalence A (fun x y:A => r (f x) (f y)). Proof. - intros; split; elim H; red in |- *; auto. + 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 : forall (A B:Type) (f:A -> B), equivalence A (fun x y:A => f x = f y). Proof. - split; red in |- *; + split; red; [ (* reflexivity *) reflexivity | (* transitivity *) intros; transitivity (f y); assumption - | (* symmetry *) intros; symmetry in |- *; assumption ]. + | (* symmetry *) intros; symmetry ; assumption ]. Qed. |