proposition: Lemma not_par_inter_exists : forall A1 B1 A2 B2, ~ Par A1 B1 A2 B2 -> exists X, Col X A1 B1 /\ Col X A2 B2.
proof: Proof. intros A1 B1 A2 B2. apply cop_npar__inter_exists. apply all_coplanar. Qed.
imports: GeoCoq.Meta_theory.Parallel_postulates.parallel_postulates GeoCoq.Meta_theory.Parallel_postulates.par_trans_NID