let F be non empty right_complementable add-associative right_zeroed associative distributive left_unital doubleLoopStr ; :: thesis: for V, W being non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr of F
for f being homogeneousSAF Form of V,W
for w being Vector of W holds f . ((0. V),w) = 0. F
let V, W be non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr of F; :: thesis: for f being homogeneousSAF Form of V,W
for w being Vector of W holds f . ((0. V),w) = 0. F
let f be homogeneousSAF Form of V,W; :: thesis: for w being Vector of W holds f . ((0. V),w) = 0. F
let v be Vector of W; :: thesis: f . ((0. V),v) = 0. F
thus f . ((0. V),v) = f . (((0. F) * (0. V)),v) by VECTSP10:1
.= (0. F) * (f . ((0. V),v)) by Th32
.= 0. F by VECTSP_1:7 ; :: thesis: verum