let V, W be non empty ModuleStr over INT.Ring ; :: thesis: for f being FrFunctional of V holds FrFormFunctional (f,(0FrFunctional W)) = NulFrForm (V,W)
let f be FrFunctional of V; :: thesis: FrFormFunctional (f,(0FrFunctional W)) = NulFrForm (V,W)

now :: thesis: for v being Vector of V
for y being Vector of W holds (FrFormFunctional (f,(0FrFunctional W))) . (v,y) = (NulFrForm (V,W)) . (v,y)

let v be Vector of V; :: thesis: for y being Vector of W holds (FrFormFunctional (f,(0FrFunctional W))) . (v,y) = (NulFrForm (V,W)) . (v,y)
let y be Vector of W; :: thesis: (FrFormFunctional (f,(0FrFunctional W))) . (v,y) = (NulFrForm (V,W)) . (v,y)
thus (FrFormFunctional (f,(0FrFunctional W))) . (v,y) = 0. INT.Ring by HTh20
.= (NulFrForm (V,W)) . (v,y) by FUNCOP_1:70 ; :: thesis: verum

end;

hence FrFormFunctional (f,(0FrFunctional W)) = NulFrForm (V,W) ; :: thesis: verum