proposition: Lemma axiom_plane_existence : forall A B C, ~ Col_H A B C -> exists p, IncidentP A p /\ IncidentP B p /\ IncidentP C p.
proof: Proof. intros A B C HNCol. exists (Plan A B C HNCol). unfold IncidentP; simpl; repeat split; Cop. Qed.
imports: Morphisms GeoCoq.Axioms.hilbert_axioms GeoCoq.Axioms.parallel_postulates GeoCoq.Meta_theory.Parallel_postulates.tarski_playfair GeoCoq.Meta_theory.Parallel_postulates.SPP_ID GeoCoq.Meta_theory.Dimension_axioms.upper_dim_3 GeoCoq.Meta_theory.Parallel_postulates.parallel_postulates GeoCoq.Utils.triples