
theorem HTh10:
  for V, W being non empty ModuleStr over INT.Ring, v being Vector of V holds
  FrFunctionalFAF(NulFrForm(V,W),v) = 0FrFunctional(W)
  proof
    let V, W be non empty ModuleStr over INT.Ring, v be Vector of V;
    set N = NulFrForm(V,W);
    now
      let y be Vector of W;
      thus FrFunctionalFAF(N,v).y = N.(v,y) by HTh8
      .= 0.F_Real by FUNCOP_1:70
      .= (0FrFunctional(W)).y by FUNCOP_1:7;
    end;
    hence thesis by FUNCT_2:63;
  end;
