let v, w be Vector of V; :: according to BILINEAR:def 26 :: thesis: (f + g) . v,w = (f + g) . w,v
thus (f + g) . v,w =
(f . v,w) + (g . v,w)
by Def3
.=
(f . w,v) + (g . v,w)
by Def26
.=
(f . w,v) + (g . w,v)
by Def26
.=
(f + g) . w,v
by Def3
; :: thesis: verum