Proof with Tarski.
unfold le.
intros.
DecompExAnd H Y.
DecompExAnd H0 Z.
assert (exists B' : Point, Bet E B' Z /\ Cong_3 C Y D E B' Z)...
DecompExAnd H T.
exists T.
split;Between.
unfold Cong_3 in H6;intuition.
eTarski.
Qed.
(** Two crucials lemmas not found in the book *)

(* Specifications: *)
Lemma between_cong : forall A B C,
Bet A C B -> Cong A C A B -> C=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.
Lemma le_anti_symmetry : forall A B C D,
le A B C D -> le C D A B -> Cong A B C D.