(** 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_11_existence : forall A B C R, R<>A -> B<>C -> exists X, out A X R /\ Cong A X B C.