proposition: Lemma perp_bisect_cong_1 : forall P Q A B, Perp_bisect P Q A B -> Cong A P B P.
proof: Proof. intros. apply perp_bisect_equiv_def in H. unfold Perp_bisect_bis in *. elim H;intros I;intros;clear H. decompose [and] H0;clear H0. assert (Cong P A P B). apply (per_double_cong P I A B); eauto with perp. Cong. Qed.
imports: GeoCoq.Tarski_dev.Ch10_line_reflexivity_2