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 :
forall A B, A <> B -> exists P, exists Q, Perp_bisect P Q A B.