proposition: Lemma proj_comm : forall A B P Q, proj A P Q B -> proj A Q P B.
proof: Proof. intros. unfold proj in *. spliter. induction H0; spliter; split; auto. left. repeat split. intro. apply H0. Col. Perp. Col. subst B. right. split; Col. Qed.
imports: GeoCoq.Tarski_dev.Ch12_parallel_inter_dec