(** Predicates to compare segment lengths. *)
  
Definition le := fun A B C D =>
   exists y, Bet C y D /\ Cong A B C y.Definition ge := fun A B C D => le C D A B.

Lemma l5_5_1 : forall A B C D, le A B C D -> exists x, Bet A B x /\ Cong A x C D.