(** 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_4_1 : forall A B P, out P A B -> Col A P B /\ ~ Bet A P B.