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