let F be non empty right_complementable add-associative right_zeroed doubleLoopStr ; :: thesis: for V, W being non empty right_zeroed ModuleStr over 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 ModuleStr over 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 4

.= (f . ((0. V),v)) + (f . ((0. V),v)) by Th26 ;

hence f . ((0. V),v) = 0. F by RLVECT_1:9; :: thesis: verum

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 ModuleStr over 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 4

.= (f . ((0. V),v)) + (f . ((0. V),v)) by Th26 ;

hence f . ((0. V),v) = 0. F by RLVECT_1:9; :: thesis: verum