(** We need a notion of plane. *)
Definition IncidentP := fun A p => Coplanar (M1 p) (M2 p) (M3 p) A.
(** For every triplet of non collinear points there is a plane containing them. *)

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