Section Grid.
Variable O E E' : Tpoint.
Variable grid_ok : ~ Col O E E'.
(** We are not faithful to Tarski's def because for uniqueness we do not need the assumption that A and B are on line OE as it is implied by the definition of sum. *)
End Grid.

Lemma pj_left_comm : forall A B C D, Pj A B C D -> Pj B A C D.