diff options
author | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2012-07-05 16:56:37 +0000 |
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committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2012-07-05 16:56:37 +0000 |
commit | ffb64d16132dd80f72ecb619ef87e3eee1fa8bda (patch) | |
tree | 5368562b42af1aeef7e19b4bd897c9fc5655769b /theories/Sets/Relations_2_facts.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/Relations_2_facts.v')
-rw-r--r-- | theories/Sets/Relations_2_facts.v | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Sets/Relations_2_facts.v b/theories/Sets/Relations_2_facts.v index 89b98c1f5..bc5960ebe 100644 --- a/theories/Sets/Relations_2_facts.v +++ b/theories/Sets/Relations_2_facts.v @@ -43,13 +43,13 @@ Qed. Theorem Rstar_contains_R : forall (U:Type) (R:Relation U), contains U (Rstar U R) R. Proof. -intros U R; red in |- *; intros x y H'; apply Rstar_n with y; auto with sets. +intros U R; red; intros x y H'; apply Rstar_n with y; auto with sets. Qed. Theorem Rstar_contains_Rplus : forall (U:Type) (R:Relation U), contains U (Rstar U R) (Rplus U R). Proof. -intros U R; red in |- *. +intros U R; red. intros x y H'; elim H'. generalize Rstar_contains_R; intro T; red in T; auto with sets. intros x0 y0 z H'0 H'1 H'2; apply Rstar_n with y0; auto with sets. @@ -58,7 +58,7 @@ Qed. Theorem Rstar_transitive : forall (U:Type) (R:Relation U), Transitive U (Rstar U R). Proof. -intros U R; red in |- *. +intros U R; red. intros x y z H'; elim H'; auto with sets. intros x0 y0 z0 H'0 H'1 H'2 H'3; apply Rstar_n with y0; auto with sets. Qed. @@ -75,7 +75,7 @@ Theorem Rstar_equiv_Rstar1 : forall (U:Type) (R:Relation U), same_relation U (Rstar U R) (Rstar1 U R). Proof. generalize Rstar_contains_R; intro T; red in T. -intros U R; unfold same_relation, contains in |- *. +intros U R; unfold same_relation, contains. split; intros x y H'; elim H'; auto with sets. generalize Rstar_transitive; intro T1; red in T1. intros x0 y0 z H'0 H'1 H'2 H'3; apply T1 with y0; auto with sets. @@ -85,7 +85,7 @@ Qed. Theorem Rsym_imp_Rstarsym : forall (U:Type) (R:Relation U), Symmetric U R -> Symmetric U (Rstar U R). Proof. -intros U R H'; red in |- *. +intros U R H'; red. intros x y H'0; elim H'0; auto with sets. intros x0 y0 z H'1 H'2 H'3. generalize Rstar_transitive; intro T1; red in T1. @@ -97,7 +97,7 @@ Theorem Sstar_contains_Rstar : forall (U:Type) (R S:Relation U), contains U (Rstar U S) R -> contains U (Rstar U S) (Rstar U R). Proof. -unfold contains in |- *. +unfold contains. intros U R S H' x y H'0; elim H'0; auto with sets. generalize Rstar_transitive; intro T1; red in T1. intros x0 y0 z H'1 H'2 H'3; apply T1 with y0; auto with sets. |