Proof with Tarski.
intros.
cases_equality A B.
left.
subst B.
apply le_trivial.
assert (exists X : Point, (Bet A B X \/ Bet A X B) /\ Cong A X C D).
eapply (segment_construction_2 B A C D).
auto.
DecompExAnd H0 X.
elim H2;intro.
left.
eapply l5_5_2.
exists X.
auto.
right.
unfold le.
exists X.
sTarski.
Qed.

(* Specifications: *)
Lemma le_zero : forall A B C, le A B C C -> A=B.
Definition lt := fun A B C D => le A B C D /\ ~ Cong A B C D.