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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
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(*    //   *    This file is distributed under the terms of the         *)
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(*                                                                          *)
(*                         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.  *)
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Require Export Relations_1.
Definition Complement (U:Type) (R:Relation U) : Relation U :=
fun x y:U => ~ R x y.
Hint Resolve Equiv_from_preorder : core.
Hint Resolve Equiv_from_order : core.
Hint Resolve contains_is_preorder : core.
Hint Resolve same_relation_is_equivalence : core.

Theorem cong_symmetric_same_relation :
forall (U:Type) (R R':Relation U),
same_relation U R R' -> Symmetric U R -> Symmetric U R'.