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 additiveFAF Form of V,W

for v being Vector of V holds f . (v,(0. W)) = 0. F

let V, W be non empty right_zeroed ModuleStr over F; :: thesis: for f being additiveFAF Form of V,W

for v being Vector of V holds f . (v,(0. W)) = 0. F

let f be additiveFAF 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

f . (v,(0. W)) = f . (v,((0. W) + (0. W))) by RLVECT_1:def 4

.= (f . (v,(0. W))) + (f . (v,(0. W))) by Th27 ;

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

for f being additiveFAF Form of V,W

for v being Vector of V holds f . (v,(0. W)) = 0. F

let V, W be non empty right_zeroed ModuleStr over F; :: thesis: for f being additiveFAF Form of V,W

for v being Vector of V holds f . (v,(0. W)) = 0. F

let f be additiveFAF 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

f . (v,(0. W)) = f . (v,((0. W) + (0. W))) by RLVECT_1:def 4

.= (f . (v,(0. W))) + (f . (v,(0. W))) by Th27 ;

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