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 proj_preserves_sum :
forall O E E' A B C A' B' C',
Sum O E E' A B C ->
Ar1 O E' A' B' C' ->
Pj E E' A A' ->
Pj E E' B B' ->
Pj E E' C C' ->
Sum O E' E A' B' C'.