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 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 VectSpStr of 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 Th33
.= 0. F by VECTSP_1:7 ; :: thesis: verum