let V, W be non empty ModuleStr over F_Complex ; for f, g being Form of V,W holds (f + g) *' = (f *') + (g *')
let f, g be Form of V,W; (f + g) *' = (f *') + (g *')
now for v being Vector of V
for w being Vector of W holds ((f + g) *') . (v,w) = ((f *') + (g *')) . (v,w)let v be
Vector of
V;
for w being Vector of W holds ((f + g) *') . (v,w) = ((f *') + (g *')) . (v,w)let w be
Vector of
W;
((f + g) *') . (v,w) = ((f *') + (g *')) . (v,w)thus ((f + g) *') . (
v,
w) =
((f + g) . (v,w)) *'
by Def8
.=
((f . (v,w)) + (g . (v,w))) *'
by BILINEAR:def 2
.=
((f . (v,w)) *') + ((g . (v,w)) *')
by COMPLFLD:51
.=
((f *') . (v,w)) + ((g . (v,w)) *')
by Def8
.=
((f *') . (v,w)) + ((g *') . (v,w))
by Def8
.=
((f *') + (g *')) . (
v,
w)
by BILINEAR:def 2
;
verum end;
hence
(f + g) *' = (f *') + (g *')
; verum