Definition Zlog_sup (M : Z) :=
  match M with
  | Zpos p => log_sup p
  | _ => 0
  end.

Lemma div_r'_i : forall a m : Z, 0 < m -> a mod 2 ^ Zlog_sup m / m = 0 \/ a mod 2 ^ Zlog_sup m / m = 1.