
theorem Th10:
  for K be non empty ZeroStr, V,W be non empty ModuleStr over K, v
  be Vector of V holds FunctionalFAF(NulForm(V,W),v) = 0Functional(W)
proof
  let K be non empty ZeroStr, V,W be non empty ModuleStr over K, v be Vector
  of V;
  set N = NulForm(V,W);
  now
    let y be Vector of W;
    thus FunctionalFAF(N,v).y = N.(v,y) by Th8
      .= 0.K by FUNCOP_1:70
      .= (0Functional(W)).y by HAHNBAN1:14;
  end;
  hence thesis by FUNCT_2:63;
end;
