(** 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_16_1 : forall P Q S X, P<>Q -> S<>P -> Col S P Q -> (Col X P Q -> Col X P S).