(** 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 between_cong_2 : forall A B D E, Bet A D B -> Bet A E B -> Cong A D A E -> D = E.