theorem Lm2:
  [.0, (k+1)/t .[ \/ [. (k+1)/t, (k+2)/t .[ = [. 0, (k+2)/t .[
  proof
    0 <= (k+1)/t & (k+1)/t <= (k+2)/t
    proof
      k+1 <= (k+1) + 1 by XREAL_1:31;
      hence thesis by XREAL_1:64;
    end;
    hence thesis by XXREAL_1:168;
  end;
