
theorem Th21:
  for K be add-associative right_zeroed right_complementable
left-distributive non empty doubleLoopStr for V,W be non empty ModuleStr over
  K for g be Functional of W, v be Vector of V, w be Vector of W holds
  FormFunctional(0Functional(V),g).(v,w) = 0.K
proof
  let K be add-associative right_zeroed right_complementable left-distributive
  non empty doubleLoopStr;
  let V,W be non empty ModuleStr over K;
  let h be Functional of W, v be Vector of V, y be Vector of W;
  set 0F = 0Functional(V), F = FormFunctional(0F,h);
  thus F.(v,y) = 0F.v * h.y by Def10
    .= 0.K * h.y by FUNCOP_1:7
    .= 0.K;
end;
