Fixpoint eqm_bool (x y : Map bool) {struct y} : bool :=
  match x, y with
  | M0, M0 => true
  | M0, M1 _ _ => false
  | M0, M2 _ _ => false
  | M1 _ _, M0 => false
  | M1 a b, M1 c d => Neqb a c && eq_bool b d
  | M1 _ _, M2 _ _ => false
  | M2 _ _, M0 => false
  | M2 _ _, M1 _ _ => false
  | M2 a b, M2 c d => eqm_bool a c && eqm_bool b d
  end.

Lemma eqm_bool_equal : forall x y : Map bool, eqm_bool x y = true -> x = y.