Proof with Midpoint.
intros.
assert (Cong P B P' B).
eapply l7_13...
assert (exists B', is_midpoint A B B')...
DecompEx H2 B'.
assert (Cong P' B P B').
eapply l7_13.
apply H.
Midpoint.
(* *)
assert (Cong P B P B').
eTarski.
assert (Cong P B P' B').
eapply l7_13.
apply l7_2.
apply H.
Midpoint.
(* *)
assert (Cong P' B P' B').
eTarski.
(* *)
assert (Bet P B P').
unfold is_midpoint in *;intuition.
assert (B=B').
eapply l4_19.
apply H7.
sTarski.
sTarski.
treat_equalities.
eapply l7_3...
Qed.

Lemma l7_20 : forall M A B,
Col A M B -> Cong M A M B -> A=B \/ is_midpoint M A B.