(** We need a notion of plane. *)

Record Plane := Plan {M1; M2; M3; NCol : ~ Col_H M1 M2 M3}.(** We need a notion of plane. *)

Record Plane := Plan {M1; M2; M3; NCol : ~ Col_H M1 M2 M3}.(** We need a notion of plane. *)

Record Plane := Plan {M1; M2; M3; NCol : ~ Col_H M1 M2 M3}.(** We need a notion of plane. *)

Record Plane := Plan {M1; M2; M3; NCol : ~ Col_H M1 M2 M3}.(** We need a notion of plane. *)

Record Plane := Plan {M1; M2; M3; NCol : ~ Col_H M1 M2 M3}.(** We need a notion of plane. *)

Record Plane := Plan {M1; M2; M3; NCol : ~ Col_H M1 M2 M3}.Definition IncidentP := fun A p => Coplanar (M1 p) (M2 p) (M3 p) A.

Lemma axiom_plane_existence : forall A B C, ~ Col_H A B C -> exists p, IncidentP A p /\ IncidentP B p /\ IncidentP C p.