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'.