let F be non empty right_complementable add-associative right_zeroed doubleLoopStr ; :: thesis: for V, W being non empty right_zeroed VectSpStr of F
for f being additiveSAF Form of V,W
for w being Vector of W holds f . ((0. V),w) = 0. F
let V, W be non empty right_zeroed VectSpStr of F; :: thesis: for f being additiveSAF Form of V,W
for w being Vector of W holds f . ((0. V),w) = 0. F
let f be additiveSAF 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
f . ((0. V),v) = f . (((0. V) + (0. V)),v) by RLVECT_1:def 7
.= (f . ((0. V),v)) + (f . ((0. V),v)) by Th27 ;
hence f . ((0. V),v) = 0. F by RLVECT_1:22; :: thesis: verum