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 14.13 *)
(** Parallel projection on the second axis preserves sums. *)

Lemma sum3_to_sum4 : forall O E E' A B C X ABC S , sum3 O E E' A B C ABC -> Sum O E E' ABC X S -> Sum4 O E E' A B C X S.