
theorem
  for V be non empty ModuleStr over F_Complex holds
  (0Functional(V))*' = 0Functional(V)
proof
  let V be non empty ModuleStr over F_Complex;
  set f= 0Functional(V);
  now
    let v be Vector of V;
    thus f*'.v = (f.v)*' by Def2
      .= 0.F_Complex by COMPLFLD:47,HAHNBAN1:14
      .= f.v by HAHNBAN1:14;
  end;
  hence thesis by FUNCT_2:63;
end;
