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 homogeneousFAF Form of V,W

for v being Vector of V holds f . (v,(0. 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 homogeneousFAF Form of V,W

for v being Vector of V holds f . (v,(0. W)) = 0. F

let f be homogeneousFAF Form of V,W; :: thesis: for v being Vector of V holds f . (v,(0. W)) = 0. F

let v be Vector of V; :: thesis: f . (v,(0. W)) = 0. F

thus f . (v,(0. W)) = f . (v,((0. F) * (0. W))) by VECTSP10:1

.= (0. F) * (f . (v,(0. W))) by Th32

.= 0. F ; :: thesis: verum

for f being homogeneousFAF Form of V,W

for v being Vector of V holds f . (v,(0. 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 homogeneousFAF Form of V,W

for v being Vector of V holds f . (v,(0. W)) = 0. F

let f be homogeneousFAF Form of V,W; :: thesis: for v being Vector of V holds f . (v,(0. W)) = 0. F

let v be Vector of V; :: thesis: f . (v,(0. W)) = 0. F

thus f . (v,(0. W)) = f . (v,((0. F) * (0. W))) by VECTSP10:1

.= (0. F) * (f . (v,(0. W))) by Th32

.= 0. F ; :: thesis: verum