let K be non empty right_complementable add-associative right_zeroed left-distributive doubleLoopStr ; :: thesis: for V, W being non empty VectSpStr of K
for g being Functional of W holds FormFunctional ((0Functional V),g) = NulForm (V,W)
let V, W be non empty VectSpStr of K; :: thesis: for g being Functional of W holds FormFunctional ((0Functional V),g) = NulForm (V,W)
let h be Functional of W; :: thesis: FormFunctional ((0Functional V),h) = NulForm (V,W)

now

let v be Vector of V; :: thesis: for y being Vector of W holds (FormFunctional ((0Functional V),h)) . (v,y) = (NulForm (V,W)) . (v,y)
let y be Vector of W; :: thesis: (FormFunctional ((0Functional V),h)) . (v,y) = (NulForm (V,W)) . (v,y)
thus (FormFunctional ((0Functional V),h)) . (v,y) = 0. K by Th22
.= (NulForm (V,W)) . (v,y) by FUNCOP_1:85 ; :: thesis: verum

end;

hence FormFunctional ((0Functional V),h) = NulForm (V,W) by BINOP_1:2; :: thesis: verum