let v, w be Vector of V; :: according to BILINEAR:def 25 :: thesis: (f + g) . (v,w) = (f + g) . (w,v)
thus (f + g) . (v,w) = (f . (v,w)) + (g . (v,w)) by Def2
.= (f . (w,v)) + (g . (v,w)) by Def25
.= (f . (w,v)) + (g . (w,v)) by Def25
.= (f + g) . (w,v) by Def2 ; :: thesis: verum