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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/Infinite_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/Infinite_sets.v')
-rw-r--r-- | theories/Sets/Infinite_sets.v | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Sets/Infinite_sets.v b/theories/Sets/Infinite_sets.v index 6b02e8383..b63ec1d47 100644 --- a/theories/Sets/Infinite_sets.v +++ b/theories/Sets/Infinite_sets.v @@ -50,7 +50,7 @@ Hint Resolve Defn_of_Approximant. Section Infinite_sets. Variable U : Type. - + Lemma make_new_approximant : forall A X:Ensemble U, ~ Finite U A -> Approximant U A X -> Inhabited U (Setminus U A X). @@ -61,7 +61,7 @@ Section Infinite_sets. red in |- *; intro H'3; apply H'. rewrite <- H'3; auto with sets. Qed. - + Lemma approximants_grow : forall A X:Ensemble U, ~ Finite U A -> @@ -101,7 +101,7 @@ Section Infinite_sets. apply Defn_of_Approximant; auto with sets. apply cardinal_finite with (n := S n0); auto with sets. Qed. - + Lemma approximants_grow' : forall A X:Ensemble U, ~ Finite U A -> @@ -121,7 +121,7 @@ Section Infinite_sets. apply cardinal_finite with (n := S n); auto with sets. apply approximants_grow with (X := X); auto with sets. Qed. - + Lemma approximant_can_be_any_size : forall A X:Ensemble U, ~ Finite U A -> @@ -135,7 +135,7 @@ Section Infinite_sets. Qed. Variable V : Type. - + Theorem Image_set_continuous : forall (A:Ensemble U) (f:U -> V) (X:Ensemble V), Finite V X -> @@ -230,7 +230,7 @@ Section Infinite_sets. rewrite H'4; auto with sets. elim H'3; auto with sets. Qed. - + Theorem Pigeonhole_ter : forall (A:Ensemble U) (f:U -> V) (n:nat), injective U V f -> Finite V (Im U V A f) -> Finite U A. |