assert(A' <> B').
intro.
apply H.
assert(Cong A' B' A B).
eapply l7_13.
apply H0.
assumption.
apply cong_symmetry in H4.
subst B'.
apply cong_identity in H4.
assumption.
assert(HH0:= H0).
assert(HH1:= H1).
unfold Midpoint in HH0.
unfold Midpoint in HH1.
spliter.
assert(Col M A A').
apply bet_col in H6.
Col.
assert(Col M B B').
apply bet_col in H4.
Col.
induction(eq_dec_points B B').
subst B'.
apply l7_3 in H1.
subst M.
Col5.
assert(Col A A' B').
assert(Col B M A).
eapply col_transitivity_1.
apply H10.
Col.
Col.
assert(Col A M B').
eapply col_transitivity_1.
apply H.
Col.
Col.
induction(eq_dec_points A M).
subst M.
apply cong_symmetry in H7.
apply cong_identity in H7.
subst A'.
Col.
eapply col_transitivity_1.
apply H13.
Col.
Col.
repeat split;
Col.
induction(eq_dec_points A B').
subst B'.
assert(A'=B).
eapply l7_9.
2: apply H1.
apply l7_2.
assumption.
subst A'.
Col.
ColR.
Qed.

Lemma midpoint_par : forall A B A' B' M, A <> B -> Midpoint M A A' -> Midpoint M B B' -> Par A B A' B'.
intros.