(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
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(* File: ZFrelations.v                                                     *)
(* auteur: alex@sysal.ibp.fr                                               *)
(* date: 19/10/95                                                          *)
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Require Export axs_fundation.
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(* Une relation est un ensemble de couples                                 *)
(* Nous nous interessons ici aux relations binaires.                       *)
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Definition rel (r : E) :=
forall c : E, In c r -> exists x : E, (exists y : E, c = couple x y).
Definition rel_sig (r a b : E) := inc r (cartesien a b).

(* Specifications: *)
Lemma lem_rel_sig_to_rel : forall r a b : E, rel_sig r a b -> rel r.
unfold rel_sig in |- *; unfold inc in |- *; intros.