summaryrefslogtreecommitdiff
path: root/theories7/Sets/Finite_sets.v
diff options
context:
space:
mode:
Diffstat (limited to 'theories7/Sets/Finite_sets.v')
-rwxr-xr-xtheories7/Sets/Finite_sets.v74
1 files changed, 0 insertions, 74 deletions
diff --git a/theories7/Sets/Finite_sets.v b/theories7/Sets/Finite_sets.v
deleted file mode 100755
index fb53994d..00000000
--- a/theories7/Sets/Finite_sets.v
+++ /dev/null
@@ -1,74 +0,0 @@
-(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(************************************************************************)
-(****************************************************************************)
-(* *)
-(* Naive Set Theory in Coq *)
-(* *)
-(* INRIA INRIA *)
-(* Rocquencourt Sophia-Antipolis *)
-(* *)
-(* Coq V6.1 *)
-(* *)
-(* Gilles Kahn *)
-(* Gerard Huet *)
-(* *)
-(* *)
-(* *)
-(* Acknowledgments: This work was started in July 1993 by F. Prost. Thanks *)
-(* to the Newton Institute for providing an exceptional work environment *)
-(* in Summer 1995. Several developments by E. Ledinot were an inspiration. *)
-(****************************************************************************)
-
-(*i $Id: Finite_sets.v,v 1.1.2.1 2004/07/16 19:31:39 herbelin Exp $ i*)
-
-Require Ensembles.
-
-Section Ensembles_finis.
-Variable U: Type.
-
-Inductive Finite : (Ensemble U) -> Prop :=
- Empty_is_finite: (Finite (Empty_set U))
- | Union_is_finite:
- (A: (Ensemble U)) (Finite A) ->
- (x: U) ~ (In U A x) -> (Finite (Add U A x)).
-
-Inductive cardinal : (Ensemble U) -> nat -> Prop :=
- card_empty: (cardinal (Empty_set U) O)
- | card_add:
- (A: (Ensemble U)) (n: nat) (cardinal A n) ->
- (x: U) ~ (In U A x) -> (cardinal (Add U A x) (S n)).
-
-End Ensembles_finis.
-
-Hints Resolve Empty_is_finite Union_is_finite : sets v62.
-Hints Resolve card_empty card_add : sets v62.
-
-Require Constructive_sets.
-
-Section Ensembles_finis_facts.
-Variable U: Type.
-
-Lemma cardinal_invert :
- (X: (Ensemble U)) (p:nat)(cardinal U X p) -> Case p of
- X == (Empty_set U)
- [n:nat] (EXT A | (EXT x |
- X == (Add U A x) /\ ~ (In U A x) /\ (cardinal U A n))) end.
-Proof.
-NewInduction 1; Simpl; Auto.
-Exists A; Exists x; Auto.
-Qed.
-
-Lemma cardinal_elim :
- (X: (Ensemble U)) (p:nat)(cardinal U X p) -> Case p of
- X == (Empty_set U)
- [n:nat](Inhabited U X) end.
-Proof.
-Intros X p C; Elim C; Simpl; Trivial with sets.
-Qed.
-
-End Ensembles_finis_facts.