theorem Th21:
  G1 is_transformable_to G2 implies q * id B = q
proof
  assume
A1: G1 is_transformable_to G2;
  now
    let i be object;
    assume i in the carrier of B;
    then reconsider a = i as Object of B;
    thus (q * id B).i = q!((id B).a) by A1,Def2
      .= q!a by FUNCTOR0:29
      .= q.i by A1,FUNCTOR2:def 4;
  end;
  hence thesis;
end;
