(* End of proof of lem_sym_so_rdom_eq_rImg                                 *)

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(* Transitivite                                                            *)
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Definition transitivity (r a : E) (rRel : rel_sig r a a) :=
  forall x y z : E,
  In (couple x y) r -> In (couple y z) r -> In (couple x z) r.

(* Specifications: *)
Lemma lem_Vide_rel_sig : forall a : E, rel_sig Vide a a.
Lemma lem_Vide_dom : forall a : E, rdom Vide a a (lem_Vide_rel_sig a) = Vide.
Lemma lem_Vide_Img : forall a : E, rImg Vide a a (lem_Vide_rel_sig a) = Vide.