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author | glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2009-09-17 15:58:14 +0000 |
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committer | glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2009-09-17 15:58:14 +0000 |
commit | 61ccbc81a2f3b4662ed4a2bad9d07d2003dda3a2 (patch) | |
tree | 961cc88c714aa91a0276ea9fbf8bc53b2b9d5c28 /theories/Sets/Constructive_sets.v | |
parent | 6d3fbdf36c6a47b49c2a4b16f498972c93c07574 (diff) |
Delete trailing whitespaces in all *.{v,ml*} files
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12337 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Sets/Constructive_sets.v')
-rw-r--r-- | theories/Sets/Constructive_sets.v | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Sets/Constructive_sets.v b/theories/Sets/Constructive_sets.v index 65ce03e28..0719365f1 100644 --- a/theories/Sets/Constructive_sets.v +++ b/theories/Sets/Constructive_sets.v @@ -30,7 +30,7 @@ Require Export Ensembles. Section Ensembles_facts. Variable U : Type. - + Lemma Extension : forall B C:Ensemble U, B = C -> Same_set U B C. Proof. intros B C H'; rewrite H'; auto with sets. @@ -52,7 +52,7 @@ Section Ensembles_facts. Proof. unfold Add at 1 in |- *; auto with sets. Qed. - + Lemma Add_intro2 : forall (A:Ensemble U) (x:U), In U (Add U A x) x. Proof. unfold Add at 1 in |- *; auto with sets. @@ -98,15 +98,15 @@ Section Ensembles_facts. Proof. intros B C x H'; elim H'; auto with sets. Qed. - + Lemma Add_inv : forall (A:Ensemble U) (x y:U), In U (Add U A x) y -> In U A y \/ x = y. Proof. - intros A x y H'; induction H'. + intros A x y H'; induction H'. left; assumption. right; apply Singleton_inv; assumption. Qed. - + Lemma Intersection_inv : forall (B C:Ensemble U) (x:U), In U (Intersection U B C) x -> In U B x /\ In U C x. @@ -125,7 +125,7 @@ Section Ensembles_facts. Proof. unfold Setminus at 1 in |- *; red in |- *; auto with sets. Qed. - + Lemma Strict_Included_intro : forall X Y:Ensemble U, Included U X Y /\ X <> Y -> Strict_Included U X Y. Proof. |