let V, W be non empty ModuleStr over F_Complex ; :: thesis: for f being Form of V,W holds (f *') *' = f

let f be Form of V,W; :: thesis: (f *') *' = f

let f be Form of V,W; :: thesis: (f *') *' = f

now :: thesis: for v being Vector of V

for w being Vector of W holds ((f *') *') . (v,w) = f . (v,w)

hence
(f *') *' = f
; :: thesis: verumfor w being Vector of W holds ((f *') *') . (v,w) = f . (v,w)

let v be Vector of V; :: thesis: for w being Vector of W holds ((f *') *') . (v,w) = f . (v,w)

let w be Vector of W; :: thesis: ((f *') *') . (v,w) = f . (v,w)

thus ((f *') *') . (v,w) = ((f *') . (v,w)) *' by Def8

.= ((f . (v,w)) *') *' by Def8

.= f . (v,w) ; :: thesis: verum

end;let w be Vector of W; :: thesis: ((f *') *') . (v,w) = f . (v,w)

thus ((f *') *') . (v,w) = ((f *') . (v,w)) *' by Def8

.= ((f . (v,w)) *') *' by Def8

.= f . (v,w) ; :: thesis: verum