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 VectSp-like 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 VectSp-like 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 VECTSP10:2
.= (0. F) * (f . v,(0. W)) by Th33
.= 0. F by VECTSP_1:39 ; :: thesis: verum