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 sum_to_sum3 : forall O E E' A B AB X S, Sum O E E' A B AB -> Sum O E E' AB X S -> sum3 O E E' A B X S.