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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/Infinite_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/Infinite_sets.v')
-rw-r--r--theories/Sets/Infinite_sets.v12
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.