(* Julien Narboux *)
(* Formalization of *)
(* Tarski's axiomatic *)
Require Export Ch05_between_transitivity_le.
(** The predicate out P A B informally means that P is on the line A B outside the segment A B. *)
Definition out := fun P A B => A<>P /\ B<>P /\ (Bet P A B \/ Bet P B A).

(* Specifications: *)
Lemma l6_2 : forall A B C P,
A<>P -> B<>P -> C<>P -> Bet A P C -> (Bet B P C <-> out P A B).