proposition: Lemma perp_bisect_cong_2 : forall P Q A B, Perp_bisect P Q A B -> Cong A Q B Q.
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 Q A Q B). apply (per_double_cong Q I A B); eauto with perp. Cong. Qed.
imports: GeoCoq.Tarski_dev.Ch10_line_reflexivity_2