proposition: Lemma coplanar_plane : forall A B C D, Coplanar A B 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]|[[H1 H2]|[H1 H2]]]]. apply coplanar_plane1 with X; assumption. destruct (coplanar_plane1 A C B D X) as [p]; [..|spliter; exists p]; repeat split; assumption. destruct (coplanar_plane1 A D B C X) as [p]; [..|spliter; exists p]; repeat split; assumption. 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