theorem Th31:
  G*id F = id(G*F)
proof
  now
    let a be Object of A;
    thus (G*id F).a = G/.(id F.a) by Th21
      .= G/.id(F.a) by NATTRA_1:20
      .= id(G.(F.a)) by NATTRA_1:15
      .= id((G*F).a) by CAT_1:76
      .= (id(G*F)).a by NATTRA_1:20;
  end;
  hence thesis by Th24;
end;
