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. *)

(* a + b + c + d = b  c + a + d *)
Lemma sum_abcd : forall O E E' A B C D AB CD BC AD S,
Sum O E E' A B AB -> Sum O E E' C D CD -> Sum O E E' B C BC ->
Sum O E E' A D AD -> Sum O E E' AB CD S ->
Sum O E E' BC AD S.