theorem Th30:
  (id G)*F = id(G*F)
proof
  now
    let a be Object of A;
    thus ((id G)*F).a = id G.(F.a) by Th22
      .= id(G.(F.a)) by NATTRA_1:20
      .= id((G*F).a) by CAT_1:76
      .= id(G*F).a by NATTRA_1:20;
  end;
  hence thesis by Th24;
end;
