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_assoc : forall O E E' A B C AB BC ABC,
Sum O E E' A B AB ->
Sum O E E' B C BC ->
(Sum O E E' A BC ABC <-> Sum O E E' AB C ABC).