(** One needs to define a predicate for which MA is uniquely defined. *)
Definition inv O E E' A MA :=
  (A <> O /\ Prod O E E' MA A E) \/ (A = O /\ MA = O).

Lemma inv_uniqueness : forall A B1 B2, inv O E E' A B1 -> inv O E E' A B2 -> B1 = B2.