theorem Th20:
  F1 is_transformable_to F2 implies (id B) * p = p
proof
  assume
A1: F1 is_transformable_to F2;
  now
    let i be object;
    assume i in the carrier of A;
    then reconsider a = i as Object of A;
A2: <^F1.a,F2.a^> <> {} by A1;
    thus ((id B) * p).i = (id B).(p!a) by A1,Def1
      .= p!a by A2,FUNCTOR0:31
      .= p.i by A1,FUNCTOR2:def 4;
  end;
  hence thesis;
end;
