reserve A for non empty AltCatStr,
  B, C for non empty reflexive AltCatStr,
  F for feasible Covariant FunctorStr over A, B,
  G for feasible Covariant FunctorStr over B, C,
  M for feasible Contravariant FunctorStr over A, B,
  N for feasible Contravariant FunctorStr over B, C,
  o1, o2 for Object of A,
  m for Morphism of o1, o2;
reserve A, B, C, D for transitive with_units non empty AltCatStr,
  F1, F2, F3 for covariant Functor of A, B,
  G1, G2, G3 for covariant Functor of B, C,
  H1, H2 for covariant Functor of C, D,
  p for transformation of F1, F2,
  p1 for transformation of F2, F3,
  q for transformation of G1, G2,
  q1 for transformation of G2, G3,
  r for transformation of H1, H2;

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;
