proposition: Lemma coplanar_plane1 : forall A B C D X, (Bet A B X \/ Bet B X A \/ Bet X A B) -> (Bet C D X \/ Bet D X C \/ Bet X C D) -> exists p, IncidP A p /\ IncidP B p /\ IncidP C p /\ IncidP D p.
proof: Proof. intros A B C D X H1 H2. apply coplanar_plane0 with X. clear H2; destruct H1 as [|[|]]; Col. clear H1; destruct H2 as [|[|]]; Col. 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