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. *)

(* (x + y) - (a + b) = (x - a) + (y - b) *)
Lemma sum_diff2_diff_sum2_a : forall O E E' A B C X Y Z dXA dYB dZC,
Sum O E E' A B C -> Sum O E E' X Y Z -> Diff O E E' X A dXA ->
Diff O E E' Y B dYB -> Sum O E E' dXA dYB dZC ->
Diff O E E' Z C dZC.