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19 (*#***********************************************************************)
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 *)
29 (* * GNU Lesser General Public License Version 2.1 *)
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33 (*#***************************************************************************)
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: Relations_1_facts.v,v 1.7.2.1 2004/07/16 19:31:18 herbelin Exp $ i*)
71 include "Sets/Relations_1.ma".
73 inline procedural "cic:/Coq/Sets/Relations_1_facts/Complement.con" as definition.
75 inline procedural "cic:/Coq/Sets/Relations_1_facts/Rsym_imp_notRsym.con" as theorem.
77 inline procedural "cic:/Coq/Sets/Relations_1_facts/Equiv_from_preorder.con" as theorem.
80 Hint Resolve Equiv_from_preorder.
83 inline procedural "cic:/Coq/Sets/Relations_1_facts/Equiv_from_order.con" as theorem.
86 Hint Resolve Equiv_from_order.
89 inline procedural "cic:/Coq/Sets/Relations_1_facts/contains_is_preorder.con" as theorem.
92 Hint Resolve contains_is_preorder.
95 inline procedural "cic:/Coq/Sets/Relations_1_facts/same_relation_is_equivalence.con" as theorem.
98 Hint Resolve same_relation_is_equivalence.
101 inline procedural "cic:/Coq/Sets/Relations_1_facts/cong_reflexive_same_relation.con" as theorem.
103 inline procedural "cic:/Coq/Sets/Relations_1_facts/cong_symmetric_same_relation.con" as theorem.
105 inline procedural "cic:/Coq/Sets/Relations_1_facts/cong_antisymmetric_same_relation.con" as theorem.
107 inline procedural "cic:/Coq/Sets/Relations_1_facts/cong_transitive_same_relation.con" as theorem.