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| author |  Stephane Glondu <steph@glondu.net> | 2010-07-21 09:48:05 +0200 |
|---|---|---|
| committer | Stephane Glondu <steph@glondu.net> | 2010-07-21 09:48:05 +0200 |
| commit | bbb5e6eb84a46c7e8041e05ab0059994fa0b1a25 (patch) | |
| tree | 7d2930678b27e520c9431739c3d1af9d6475ccd1 /theories/Sets/Infinite_sets.v | |
| parent | 7a998985060742038ba6d2664d159ff2dbcdec3d (diff) | |
| parent | 5b7eafd0f00a16d78f99a27f5c7d5a0de77dc7e6 (diff) | |
Merge branch 'experimental/upstream' into experimental/master
Diffstat (limited to 'theories/Sets/Infinite_sets.v')
| -rw-r--r-- | theories/Sets/Infinite_sets.v | 14 |
1 files changed, 7 insertions, 7 deletions
diff --git a/theories/Sets/Infinite_sets.v b/theories/Sets/Infinite_sets.v index ae2143c8..b63ec1d4 100644 --- a/theories/Sets/Infinite_sets.v +++ b/theories/Sets/Infinite_sets.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Infinite_sets.v 10637 2008-03-07 23:52:56Z letouzey $ i*) +(*i $Id$ i*) Require Export Finite_sets. Require Export Constructive_sets. @@ -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. |