End PerpBisect_2.
Hint Resolve perp_bisect_cong_1 perp_bisect_cong_2 : cong.
Section PerpBisect_3.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

(* Specifications: *)
Lemma perp_bisect_cong2 :
forall P Q A B,
Perp_bisect P Q A B ->
Cong A P B P /\ Cong A Q B Q.
Lemma perp_bisect_cong :
forall A A1 B B1 C C1 O: Tpoint,
~ Col A B C ->
Perp_bisect O A1 B C -> Perp_bisect O B1 A C -> Perp_bisect O C1 A B ->
Cong A O B O -> Cong B O C O ->
Cong A O C O.
Lemma cong_cop_perp_bisect :
forall P Q A B,
P <> Q -> A <> B ->
Coplanar P Q A B ->
Cong A P B P ->
Cong A Q B Q ->
Perp_bisect P Q A B.
Lemma perp_bisect_is_on_perp_bisect :
forall A B C P,
Is_on_perp_bisect P A B ->
Is_on_perp_bisect P B C ->
Is_on_perp_bisect P A C.
Lemma perp_mid_perp_bisect : forall A B C D,
Midpoint C A B -> Perp C D A B ->
Perp_bisect C D A B.