(** 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).

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).