proposition: Lemma l13_1 : forall A B C P Q R, ~ Col A B C -> Midpoint P B C -> Midpoint Q A C -> Midpoint R A B -> exists X, exists Y, Perp_at R X Y A B /\ Perp X Y P Q.
proof: Proof. intros. destruct (l13_1_aux A B C P Q R) as [X [Y]]; trivial. spliter. exists X. exists Y. split; assumption. Qed.
imports: GeoCoq.Tarski_dev.Ch12_parallel