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

Theorem div_approx1 : forall (y : Zpls) (a : Zpls) (b : Zpls) (x : Z_ (a * b + a)), x / a * a / y - 1 <= x / a * (a * b / y) / b <= x / a * a / y.