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| author |  glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2009-09-17 15:58:14 +0000 |
|---|---|---|
| committer | glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2009-09-17 15:58:14 +0000 |
| commit | 61ccbc81a2f3b4662ed4a2bad9d07d2003dda3a2 (patch) | |
| tree | 961cc88c714aa91a0276ea9fbf8bc53b2b9d5c28 /theories/Sets/Finite_sets_facts.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/Finite_sets_facts.v')
| -rw-r--r-- | theories/Sets/Finite_sets_facts.v | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/theories/Sets/Finite_sets_facts.v b/theories/Sets/Finite_sets_facts.v index 0615c9c9d..fdcc4150f 100644 --- a/theories/Sets/Finite_sets_facts.v +++ b/theories/Sets/Finite_sets_facts.v @@ -72,7 +72,7 @@ Section Finite_sets_facts. Proof. intros X Y H; induction H as [|A Fin_A Hind x]. rewrite (Empty_set_zero U Y). trivial. - intros. + intros. rewrite (Union_commutative U (Add U A x) Y). rewrite <- (Union_add U Y A x). rewrite (Union_commutative U Y A). @@ -98,7 +98,7 @@ Section Finite_sets_facts. Proof. intros A H' X; apply Finite_downward_closed with A; auto with sets. Qed. - + Lemma cardinalO_empty : forall X:Ensemble U, cardinal U X 0 -> X = Empty_set U. Proof. @@ -212,7 +212,7 @@ Section Finite_sets_facts. Proof. intros; apply cardinal_is_functional with X X; auto with sets. Qed. - + Lemma card_Add_gen : forall (A:Ensemble U) (x:U) (n n':nat), cardinal U A n -> cardinal U (Add U A x) n' -> n' <= S n. @@ -279,7 +279,7 @@ Section Finite_sets_facts. intro E; rewrite E; auto with sets arith. apply cardinal_unicity with X; auto with sets arith. Qed. - + Lemma G_aux : forall P:Ensemble U -> Prop, (forall X:Ensemble U, |