
theorem Th24:
  for K be non empty multMagma for V,W be non empty ModuleStr over
  K for f be Functional of V, g be Functional of W, v be Vector of V holds
  FunctionalFAF(FormFunctional(f,g),v) = f.v * g
proof
  let K be non empty multMagma, V,W be non empty ModuleStr over K;
  let f be Functional of V, h be Functional of W, v be Vector of V;
  set F = FormFunctional(f,h), FF = FunctionalFAF(F,v);
  now
    let y be Vector of W;
    thus FF.y = F.(v,y) by Th8
      .= f.v * h.y by Def10
      .= (f.v * h).y by HAHNBAN1:def 6;
  end;
  hence thesis by FUNCT_2:63;
end;
