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

Lemma Zlog_sup_unique : forall z : Z, 0 < z -> forall i j : Z, 0 <= i -> 0 <= j -> 2 ^ (i - 1) < z -> z <= 2 ^ i -> 2 ^ (j - 1) < z -> z <= 2 ^ j -> i = j.