(* Proof of lem_rel_Comp_rel_sig                                           *)
unfold rel_sig in |- *; unfold rel_Comp in |- *; unfold Comp in |- *;
unfold inc in |- *; intros.
elim (axs_comprehension (fun y : E => ~ In y r) (cartesien a b) v0); intros;
generalize (H0 H); clear H H0 H1; intros; elim H;
clear H; intros; auto with zfc.
Qed.
(* End of proof of lem_rel_Comp_rel_sig                                    *)
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(* Reunion de relations                                                    *)
(***************************************************************************)
Definition rel_union (r1 a1 b1 r2 a2 b2 : E) (rRel1 : rel_sig r1 a1 b1)
(rRel2 : rel_sig r2 a2 b2) := union r1 r2.

Lemma lem_rel_union_rel_sig :
forall (r1 a1 b1 r2 a2 b2 : E) (rRel1 : rel_sig r1 a1 b1)
(rRel2 : rel_sig r2 a2 b2),
rel_sig (rel_union r1 a1 b1 r2 a2 b2 rRel1 rRel2)
(union a1 a2) (union b1 b2).