let V, W be non empty right_zeroed ModuleStr over INT.Ring ; for f being additiveFAF Form of V,W
for v being Vector of V holds f . (v,(0. W)) = 0
let f be additiveFAF Form of V,W; for v being Vector of V holds f . (v,(0. W)) = 0
let v be Vector of V; f . (v,(0. W)) = 0
f . (v,(0. W)) =
f . (v,((0. W) + (0. W)))
by RLVECT_1:def 4
.=
(f . (v,(0. W))) + (f . (v,(0. W)))
by BLTh27
;
hence
f . (v,(0. W)) = 0
; verum