End Grid.

Lemma change_grid_sum :
forall O E E' A B C O' A' B' C',
Par_strict O E O' E' ->
Ar1 O E A B C ->
Ar1 O' E' A' B' C' ->
Pj O O' E E' ->
Pj O O' A A' ->
Pj O O' B B' ->
Pj O O' C C' ->
Sum O E E' A B C ->
Sum O' E' E A' B' C'.