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.

(* Specifications: *)
Lemma cong_cop2_perp_bisect_col : forall A B C D E,
Coplanar A C D E ->
Coplanar B C D E ->
Cong C D C E ->
Perp_bisect A B D E ->
Col A B C.
Lemma perp_bisect_cop2_existence : 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.
Lemma perp_bisect_existence :
forall A B, A <> B -> exists P, exists Q, Perp_bisect P Q A B.
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.