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

now :: thesis: for v being Vector of V
for y being Vector of W holds (FormFunctional (f,(0Functional W))) . (v,y) = (NulForm (V,W)) . (v,y)

let v be Vector of V; :: thesis: for y being Vector of W holds (FormFunctional (f,(0Functional W))) . (v,y) = (NulForm (V,W)) . (v,y)
let y be Vector of W; :: thesis: (FormFunctional (f,(0Functional W))) . (v,y) = (NulForm (V,W)) . (v,y)
thus (FormFunctional (f,(0Functional W))) . (v,y) = 0 by BLTh20
.= (NulForm (V,W)) . (v,y) by FUNCOP_1:70 ; :: thesis: verum

end;

hence FormFunctional (f,(0Functional W)) = NulForm (V,W) ; :: thesis: verum