let F be non empty right_complementable add-associative right_zeroed distributive left_unital associative doubleLoopStr ; :: thesis: for V, W being non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital ModuleStr over 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 ModuleStr over 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 Th31

.= 0. F ; :: thesis: verum

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 ModuleStr over 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 Th31

.= 0. F ; :: thesis: verum