
theorem FRA:
  for a be non integer Real holds (frac a) + (frac (-a)) = 1
  proof
    let a be non integer Real;
    frac a = a - [\ a/] & frac (-a) = -a - [\-a/] by INT_1:def 8; then
    (frac a) + (frac (-a)) = -[\a/1/] - [\-a/]
    .= ([\(-a)/1/] + 1) - [\-a/1/] by INT_1:63;
    hence thesis;
  end;
