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'.