Proof with Tarski.
intros.
unfold out.
intuition.
subst A.
assert (Bet P P B)...
subst B.
assert (Bet A P P)...
unfold Col in H0;intuition.
Qed.
(** out reflexivity. *)

(* Specifications: *)
Lemma l6_5 : forall P A, A<>P -> out P A A.
(** out symmetry. *)
Lemma l6_6 : forall P A B, out P A B -> out P B A.
(** out transitivity. *)
Lemma l6_7 : forall P A B C, out P A B -> out P B C -> out P A C.
Lemma l6_11_unicity : forall A B C R X Y,
R<>A -> B<>C ->
out A X R -> Cong A X B C ->
out A Y R -> Cong A Y B C ->
X=Y.