diff options
Diffstat (limited to 'theories/Sets/Image.v')
| -rw-r--r-- | theories/Sets/Image.v | 16 |
1 files changed, 7 insertions, 9 deletions
diff --git a/theories/Sets/Image.v b/theories/Sets/Image.v index e5eae17e..bdb7c077 100644 --- a/theories/Sets/Image.v +++ b/theories/Sets/Image.v @@ -1,6 +1,6 @@ (************************************************************************) (* 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 *) @@ -24,8 +24,6 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Image.v 14641 2011-11-06 11:59:10Z herbelin $ i*) - Require Export Finite_sets. Require Export Constructive_sets. Require Export Classical_Type. @@ -57,7 +55,7 @@ Section Image. Proof. intros X x f. apply Extensionality_Ensembles. - split; red in |- *; intros x0 H'. + split; red; intros x0 H'. elim H'; intros. rewrite H0. elim Add_inv with U X x x1; auto using Im_def with sets. @@ -74,7 +72,7 @@ Section Image. intro f; try assumption. apply Extensionality_Ensembles. split; auto with sets. - red in |- *. + red. intros x H'; elim H'. intros x0 H'0; elim H'0; auto with sets. Qed. @@ -104,7 +102,7 @@ Section Image. forall f:U -> V, ~ injective f -> exists x : _, (exists y : _, f x = f y /\ x <> y). Proof. - unfold injective in |- *; intros f H. + unfold injective; intros f H. cut (exists x : _, ~ (forall y:U, f x = f y -> x = y)). 2: apply not_all_ex_not with (P := fun x:U => forall y:U, f x = f y -> x = y); trivial with sets. @@ -155,7 +153,7 @@ Section Image. apply cardinal_unicity with V (Add _ (Im A f) (f x)); trivial with sets. apply card_add; auto with sets. rewrite <- H1; trivial with sets. - red in |- *; intro; apply H'2. + red; intro; apply H'2. apply In_Image_elim with f; trivial with sets. Qed. @@ -182,7 +180,7 @@ Section Image. cardinal U A n -> forall n':nat, cardinal V (Im A f) n' -> n' < n -> ~ injective f. Proof. - unfold not in |- *; intros A f n CAn n' CIfn' ltn'n I. + unfold not; intros A f n CAn n' CIfn' ltn'n I. cut (n' = n). intro E; generalize ltn'n; rewrite E; exact (lt_irrefl n). apply injective_preserves_cardinal with (A := A) (f := f) (n := n); @@ -202,4 +200,4 @@ Section Image. End Image. -Hint Resolve Im_def image_empty finite_image: sets v62.
\ No newline at end of file +Hint Resolve Im_def image_empty finite_image: sets v62. |