
theorem Th19:
  for V be non empty ModuleStr over F_Complex, f be Functional of
  V holds (-f)*'=-(f*')
proof
  let V be non empty ModuleStr over F_Complex, f be Functional of V;
  now
    let v be Vector of V;
    thus (-f)*'.v = ((-f).v)*' by Def2
      .= (-f.v)*' by HAHNBAN1:def 4
      .= -(f.v)*' by COMPLFLD:52
      .= -(f*'.v) by Def2
      .= (-(f*')).v by HAHNBAN1:def 4;
  end;
  hence thesis by FUNCT_2:63;
end;
