
theorem Th11:
  for K be non empty ZeroStr, V,W be non empty ModuleStr over K, w
  be Vector of W holds FunctionalSAF(NulForm(V,W),w) = 0Functional(V)
proof
  let K be non empty ZeroStr, V,W be non empty ModuleStr over K, y be Vector
  of W;
  set N = NulForm(V,W);
  now
    let v be Vector of V;
    thus FunctionalSAF(N,y).v = N.(v,y) by Th9
      .= 0.K by FUNCOP_1:70
      .= (0Functional(V)).v by HAHNBAN1:14;
  end;
  hence thesis by FUNCT_2:63;
end;
