(** 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_3_1 : forall A B P, out P A B -> (A<>P /\ B<>P /\ exists C, C<>P /\ Bet A P C /\ Bet B P C).