let V, W be non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ModuleStr over INT.Ring ; :: thesis: for f being homogeneousSAF Form of V,W
for w being Vector of W holds f . ((0. V),w) = 0. INT.Ring
let f be homogeneousSAF Form of V,W; :: thesis: for w being Vector of W holds f . ((0. V),w) = 0. INT.Ring
let v be Vector of W; :: thesis: f . ((0. V),v) = 0. INT.Ring
(0. INT.Ring) * (0. V) = 0. V by VS10Th1;
hence f . ((0. V),v) = (0. INT.Ring) * (f . ((0. V),v)) by BLTh31
.= 0. INT.Ring ;
:: thesis: verum