
theorem Th32:
  for a,b,c being Real st (1 - a) * b + a * c <> 0 holds
    1 - ((a * c) / ((1 - a) * b + a * c)) =
      (1 - a) * b / ((1 - a) * b + a * c)
  proof
    let a,b,c be Real;
    set r = (1 - a) * b + a * c;
    assume (1 - a) * b + a * c <> 0; then
    1 - (a * c) / r = r / r - (a * c) / r by XCMPLX_1:60
                   .= (1 - a) * b / r;
    hence thesis;
  end;
