proposition: Lemma same_side_prime__plane : forall A B C D, same_side' A B C D -> exists p, IncidP A p /\ IncidP B p /\ IncidP C p /\ IncidP D p.
proof: Proof. intros. destruct H. destruct (line_existence C D H) as [l]. destruct (same_side__plane A B l) as [p]; spliter; auto. exists p; repeat split; auto. Qed.
imports: Setoid Coq.Classes.Morphisms Coq.Classes.Morphisms_Prop GeoCoq.Axioms.gupta_inspired_variant_axioms GeoCoq.Meta_theory.Models.gupta_inspired_to_tarski GeoCoq.Tactics.Coinc.tactics_axioms GeoCoq.Tactics.Coinc.ColR GeoCoq.Meta_theory.Dimension_axioms.upper_dim_3 GeoCoq.Meta_theory.Parallel_postulates.parallel_postulates GeoCoq.Axioms.hilbert_axioms