Instance incidentp_Proper (A:Tpoint) :
Proper (EqP ==>iff) (IncidentP A).

Lemma axiom_plane_uniqueness : forall A B C p q, ~ Col_H A B C -> IncidentP A p -> IncidentP B p -> IncidentP C p -> IncidentP A q -> IncidentP B q -> IncidentP C q -> p =p= q.