Proof with finish.
intros A B C X1 X2 X3 HNC HPar1 HPar2 HPar3.
apply cop_npar__inter_exists.
apply coplanar_perm_2, coplanar_trans_1 with C; Col; Cop.
intro HNPar; apply HNC.
assert (HFalsePar : Par B C A C)
by (apply (par_trans B C B X1 A C); finish; apply (par_trans B C A X3 B); finish).
apply par_id_2...
Qed.

Lemma altitude_is_perp_bisect : forall A B C O A1 E F,
A <> O -> E <> F -> Perp A A1 B C -> Col O A1 A -> Col A E F -> Par B C A E -> Midpoint A E F ->
Perp_bisect A O E F.