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 14.15 *)
(** The choice of E' does not affect sum. *)
Lemma sum_y_axis_change :
forall O E E' E'' A B C,
Sum O E E' A B C ->
~ Col O E E'' ->
Sum O E E'' A B C.