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21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
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27 (* // * This file is distributed under the terms of the *)
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37 (* Naive Set Theory in Coq *)
43 (* Rocquencourt Sophia-Antipolis *)
61 (* Acknowledgments: This work was started in July 1993 by F. Prost. Thanks *)
63 (* to the Newton Institute for providing an exceptional work environment *)
65 (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *)
67 (*#***************************************************************************)
69 (*i $Id: Ensembles.v,v 1.7.2.1 2004/07/16 19:31:17 herbelin Exp $ i*)
76 cic:/Coq/Sets/Ensembles/Ensembles/U.var
79 inline procedural "cic:/Coq/Sets/Ensembles/Ensemble.con" as definition.
81 inline procedural "cic:/Coq/Sets/Ensembles/In.con" as definition.
83 inline procedural "cic:/Coq/Sets/Ensembles/Included.con" as definition.
85 inline procedural "cic:/Coq/Sets/Ensembles/Empty_set.ind".
87 inline procedural "cic:/Coq/Sets/Ensembles/Full_set.ind".
89 (*#* NB: The following definition builds-in equality of elements in [U] as
92 This may have to be changed if we replace [U] by a Setoid on [U]
93 with its own equality [eqs], with
94 [In_singleton: (y: U)(eqs x y) -> (In (Singleton x) y)]. *)
96 inline procedural "cic:/Coq/Sets/Ensembles/Singleton.ind".
98 inline procedural "cic:/Coq/Sets/Ensembles/Union.ind".
100 inline procedural "cic:/Coq/Sets/Ensembles/Add.con" as definition.
102 inline procedural "cic:/Coq/Sets/Ensembles/Intersection.ind".
104 inline procedural "cic:/Coq/Sets/Ensembles/Couple.ind".
106 inline procedural "cic:/Coq/Sets/Ensembles/Triple.ind".
108 inline procedural "cic:/Coq/Sets/Ensembles/Complement.con" as definition.
110 inline procedural "cic:/Coq/Sets/Ensembles/Setminus.con" as definition.
112 inline procedural "cic:/Coq/Sets/Ensembles/Subtract.con" as definition.
114 inline procedural "cic:/Coq/Sets/Ensembles/Disjoint.ind".
116 inline procedural "cic:/Coq/Sets/Ensembles/Inhabited.ind".
118 inline procedural "cic:/Coq/Sets/Ensembles/Strict_Included.con" as definition.
120 inline procedural "cic:/Coq/Sets/Ensembles/Same_set.con" as definition.
122 (*#* Extensionality Axiom *)
124 inline procedural "cic:/Coq/Sets/Ensembles/Extensionality_Ensembles.con".
127 Hint Resolve Extensionality_Ensembles.
135 Hint Unfold In Included Same_set Strict_Included Add Setminus Subtract: sets
140 Hint Resolve Union_introl Union_intror Intersection_intro In_singleton
141 Couple_l Couple_r Triple_l Triple_m Triple_r Disjoint_intro
142 Extensionality_Ensembles: sets v62.