let K be non empty right_zeroed addLoopStr ; :: thesis: for V, W being non empty VectSpStr of K
for f being Form of V,W holds f + (NulForm V,W) = f
let V, W be non empty VectSpStr of K; :: thesis: for f being Form of V,W holds f + (NulForm V,W) = f
let f be Form of V,W; :: thesis: f + (NulForm V,W) = f
set g = NulForm V,W;

now

let v be Vector of V; :: thesis: for w being Vector of W holds (f + (NulForm V,W)) . v,w = f . v,w
let w be Vector of W; :: thesis: (f + (NulForm V,W)) . v,w = f . v,w
thus (f + (NulForm V,W)) . v,w = (f . v,w) + ((NulForm V,W) . v,w) by Def3
.= (f . v,w) + (0. K) by FUNCOP_1:85
.= f . v,w by RLVECT_1:def 7 ; :: thesis: verum

end;

hence f + (NulForm V,W) = f by BINOP_1:2; :: thesis: verum