diff options
| author |  letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2012-07-05 16:56:37 +0000 |
|---|---|---|
| committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2012-07-05 16:56:37 +0000 |
| commit | ffb64d16132dd80f72ecb619ef87e3eee1fa8bda (patch) | |
| tree | 5368562b42af1aeef7e19b4bd897c9fc5655769b /theories/Sets/Image.v | |
| parent | a46ccd71539257bb55dcddd9ae8510856a5c9a16 (diff) | |
Kills the useless tactic annotations "in |- *"
Most of these heavyweight annotations were introduced a long time ago
by the automatic 7.x -> 8.0 translator
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15518 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Sets/Image.v')
| -rw-r--r-- | theories/Sets/Image.v | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/theories/Sets/Image.v b/theories/Sets/Image.v index 24facb6f6..440e636cb 100644 --- a/theories/Sets/Image.v +++ b/theories/Sets/Image.v @@ -55,7 +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. @@ -72,7 +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. @@ -102,7 +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. @@ -153,7 +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. @@ -180,7 +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); |