Proof with Tarski.
intros.
unfold le in H0.
DecompExAnd H0 Y.
assert (P<>Y).
unfold not;intro.
(* *)
treat_equalities.
unfold out in H;intuition.
(* *)
assert (Y=A).
eapply l6_11_unicity.
5:apply H.
5:apply H3.
unfold out in H.
intuition.
intuition.
unfold out in *;intuition.
Tarski.
subst Y...
Qed.

Lemma l6_13_2 : forall P A B,
out P A B -> Bet P A B -> le P A P B.