Proof with Tarski.
intros.
assert (exists P', Cong_3 B D P D B P').
apply l4_14;Col...
DecompEx H5 P'.
assert (Col D B P').
eapply l4_13;try apply H6;Col...
assert (FSC B D P A D B P' C).
unfold FSC;intuition...
assert (FSC B D P C D B P' A).
unfold FSC;intuition...
assert (Cong P A P' C).
eapply l4_16; try apply H7...
assert (Cong P C P' A).
eapply l4_16; try apply H8...
assert (Cong_3 A P C C P' A).
unfold Cong_3;intuition...
assert (Col C P' A).
eapply l4_13;try apply H11...
assert (P=P').
unfold FSC in *;intuition.
eapply (l6_21 A C B D);Col...
treat_equalities.
assert (C = A \/ is_midpoint P C A).
eapply l7_20;Col...
assert (B = D \/ is_midpoint P B D).
eapply l7_20;Col...
unfold FSC,Cong_3 in *.
intuition;sTarski...
intuition.
unfold is_midpoint,FSC,Cong_3 in *;intuition.
treat_equalities.
clear H13 H21 H26 H2 H4 H5 H6.
unfold Col in H.
intuition.
assert (Bet C C B)...
intuition.
Qed.

Lemma l7_22_aux : forall A1 A2 B1 B2 C M1 M2,
Bet A1 C A2 -> Bet B1 C B2 ->
Cong C A1 C B1 -> Cong C A2 C B2 ->
is_midpoint M1 A1 B1 -> is_midpoint M2 A2 B2 -> le C A1 C A2 ->
Bet M1 C M2.