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

now

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;

hence (f *') *' = f by BINOP_1:2; :: thesis: verum