Proof with finish.
intros.
apply perp_bisect_equiv_def.
unfold Perp_bisect_bis in *.
exists C...
split...
assert_cols; apply l8_14_2_1b_bis...
Qed.

Lemma perp_bisect_existence_cop : forall A B C,
A <> B -> exists P, exists Q, Perp_bisect P Q A B /\ Coplanar A B C P /\
Coplanar A B C Q.