
theorem
  for V be non empty ModuleStr over F_Complex for f be Functional of V,
  a be Scalar of V holds (a*f)*' = a*' * (f*')
proof
  let V be non empty ModuleStr over F_Complex, f be Functional of V, a be
  Scalar of V;
  now
    let v be Vector of V;
    thus (a*f)*'.v = ((a*f).v)*' by Def2
      .= (a* (f.v))*' by HAHNBAN1:def 6
      .= a*' * (f.v)*' by COMPLFLD:54
      .= a*' *(f*'.v) by Def2
      .= (a*'* (f*')).v by HAHNBAN1:def 6;
  end;
  hence thesis by FUNCT_2:63;
end;
