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