(** We need a notion of equality over planes. *)

Definition EqP : relation Plane := fun p q => forall X, IncidentP X p <-> IncidentP X q.Infix "=p=" := EqP (at level 70):type_scope.

Lemma eqp_transitivity : forall p q r, p =p= q -> q =p= r -> p =p= r.