
theorem Th25:
  for a,b being Real st a <> b holds 1 - (a / (a - b)) = - b / (a - b)
  proof
    let a,b be Real;
    assume a <> b;
    then a - b <> 0;
    then 1 - (a / (a - b)) = (a - b) / (a - b) - a / (a - b) by XCMPLX_1:60
                          .= (a - b - a) / (a - b);
    hence thesis;
  end;
