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 homogeneousFAF Form of V,W
for v being Vector of V holds f . (v,(0. W)) = 0. INT.Ring
let f be homogeneousFAF Form of V,W; :: thesis: for v being Vector of V holds f . (v,(0. W)) = 0. INT.Ring
let v be Vector of V; :: thesis: f . (v,(0. W)) = 0. INT.Ring
(0. INT.Ring) * (0. W) = 0. W by VS10Th1;
hence f . (v,(0. W)) = (0. INT.Ring) * (f . (v,(0. W))) by BLTh32
.= 0. INT.Ring ;
:: thesis: verum