(** We omit lemma 14.26 which states that we have a division ring. *)

Lemma change_grid_prod : 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' ->
Prod O E E' A B C ->
Prod O' E' E A' B' C'.