Proof with Tarski.
intros.
assert (exists A', Bet A Q A' /\ Cong Q A' A Q)...
DecompExAnd H0 A'.
assert (exists X, Bet A' Q X /\ Cong Q X B C)...
DecompExAnd H0 X.
exists X.
split...
cut (A'<>Q).
intro.
eapply l5_2.
apply H0.
Between.
assumption.
unfold not;intro.
treat_equalities.
auto.
Qed.

Lemma le_trivial : forall A C D, le A A C D .
Proof with Tarski.