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

Lemma approx_m1_two : forall y a b x : Z, 0 < y -> 0 < a -> a <= y -> 0 < b -> 0 <= x -> x / y - 1 <= x / a * a / y.