(* Proof of lem_couple_propertie_lr                                        *)
intros; elim (lem_couple_propertie al ar bl br); intros; exact (H0 H).
Qed.
(* End of proof of lem_couple_propertie_lr                                 *)

Lemma lem_couple_propertie_rl :
forall al ar bl br : E, al = ar /\ bl = br -> couple al bl = couple ar br.