aboutsummaryrefslogtreecommitdiffhomepage
path: root/theories/Sets/Constructive_sets.v
diff options
context:
space:
mode:
authorGravatar glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7>2009-09-17 15:58:14 +0000
committerGravatar glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7>2009-09-17 15:58:14 +0000
commit61ccbc81a2f3b4662ed4a2bad9d07d2003dda3a2 (patch)
tree961cc88c714aa91a0276ea9fbf8bc53b2b9d5c28 /theories/Sets/Constructive_sets.v
parent6d3fbdf36c6a47b49c2a4b16f498972c93c07574 (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.v12
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.