(* End of proof of lem_rel_union_prop                                      *)

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(* Intersection de deux relations                                          *)
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Definition rel_inter (r1 a1 b1 r2 a2 b2 : E) (rRel1 : rel_sig r1 a1 b1)
  (rRel2 : rel_sig r2 a2 b2) := inter r1 r2.

Lemma lem_rel_inter_prop : forall (r1 a1 b1 r2 a2 b2 : E) (rRel1 : rel_sig r1 a1 b1) (rRel2 : rel_sig r2 a2 b2) (c : E), In c (rel_inter r1 a1 b1 r2 a2 b2 rRel1 rRel2) <-> In c r1 /\ In c r2.