induction(eq_dec_points D C).
subst D.
apply le_zero in H.
subst B.
eapply le_trivial.
induction(eq_dec_points A B).
subst B.
apply le_trivial.
assert(HH:=segment_construction_3 D C A B H0 H1).
ex_and HH P'.
unfold Out in H2.
spliter.
induction H5.
assert(Le D C A B).
eapply l5_5_2.
exists P'.
split; auto.
apply le_left_comm in H6.
assert(Cong A B C D).
apply le_anti_symmetry.
auto.
auto.
unfold Le.
exists C.
split.
apply between_trivial.
Cong.
unfold Le.
exists P'.
split.
assumption.
Cong.
Qed.

Lemma le_comm : forall A B C D, Le A B C D -> Le B A D C.
intros.