proposition: Lemma par_perp__perp : forall A B C D P Q, Par A B C D -> Perp A B P Q -> Perp C D P Q.
proof: Proof. intros A B C D P Q HPar HPer. assert (HCop := all_coplanar C D P Q). apply (cop_par_perp__perp A B); assumption. Qed.
imports: GeoCoq.Meta_theory.Parallel_postulates.parallel_postulates GeoCoq.Meta_theory.Parallel_postulates.par_trans_NID