reserve A,B,C,D for Category,
  F for Functor of A,B,
  G for Functor of B,C;
reserve o,m for set;
reserve F,F1,F2,F3 for Functor of A,B,
  G,G1,G2,G3 for Functor of B,C,
  H,H1,H2 for Functor of C,D,
  s for natural_transformation of F1,F2,
  s9 for natural_transformation of F2,F3,
  t for natural_transformation of G1,G2,
  t9 for natural_transformation of G2,G3,
  u for natural_transformation of H1,H2;

theorem
  F1 is_naturally_transformable_to F2 implies G*s = (id G)(#)s
proof
  assume F1 is_naturally_transformable_to F2;
  then G*F1 is_naturally_transformable_to G*F2 by Th20;
  hence G*s = id(G*F2)`*`(G*s) by NATTRA_1:24
    .= (id G)(#)s by Th30;
end;
