
theorem
  for V,W be non empty ModuleStr over F_Complex for f be Form of V,W, a
  be Element of F_Complex holds (a*f)*' = a*' * (f*')
proof
  let V,W be non empty ModuleStr over F_Complex, f be Form of V,W, a be
  Element of F_Complex;
  now
    let v be Vector of V,w be Vector of W;
    thus (a*f)*'.(v,w) = ((a*f).(v,w))*' by Def8
      .= (a* (f.(v,w)))*' by BILINEAR:def 3
      .= a*' * (f.(v,w))*' by COMPLFLD:54
      .= a*' *(f*'.(v,w)) by Def8
      .= (a*'* (f*')).(v,w) by BILINEAR:def 3;
  end;
  hence thesis;
end;
