theorem Th18:
  (idt G1)*F1 = idt (G1*F1)
proof
  now
    let a be Object of A;
    thus ((idt G1)*F1)!a = (idt G1)!(F1.a) by Th12
      .= idm(G1.(F1.a)) by FUNCTOR2:4
      .= idm((G1*F1).a) by FUNCTOR0:33
      .= (idt (G1*F1))!a by FUNCTOR2:4;
  end;
  hence thesis by FUNCTOR2:3;
end;
