
theorem
for R being Ring,
    S being R-homomorphic Ring, T being R-homomorphic S-homomorphic Ring
for f being additive Function of R,S, g being additive Function of S,T
st g * f = id R holds PolyHom(g*f) = id(Polynom-Ring R)
proof
let R be Ring, S be R-homomorphic Ring, T be R-homomorphic S-homomorphic Ring;
let f be additive Function of R,S, g be additive Function of S,T;
assume g * f = id R;
hence id(Polynom-Ring R) = (PolyHom g) * (PolyHom f) by ll2
                        .= PolyHom(g*f) by ll;
end;
