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 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 VectSpStr of 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 7
.= (f . v,(0. W)) + (f . v,(0. W)) by Th28 ;
hence f . v,(0. W) = 0. F by RLVECT_1:22; :: thesis: verum