let K be non empty right_complementable add-associative right_zeroed addLoopStr ; :: thesis: for V, W being non empty VectSpStr of K
for f being Form of V,W holds f - f = NulForm V,W
let V, W be non empty VectSpStr of K; :: thesis: for f being Form of V,W holds f - f = NulForm V,W
let f be Form of V,W; :: thesis: f - f = NulForm V,W

now

let v be Vector of V; :: thesis: for w being Vector of W holds (f - f) . v,w = (NulForm V,W) . v,w
let w be Vector of W; :: thesis: (f - f) . v,w = (NulForm V,W) . v,w
thus (f - f) . v,w = (f . v,w) - (f . v,w) by Def8
.= 0. K by RLVECT_1:28
.= (NulForm V,W) . v,w by FUNCOP_1:85 ; :: thesis: verum

end;

hence f - f = NulForm V,W by BINOP_1:2; :: thesis: verum