reserve A,B,C,D for Category,
  F for Functor of A,B,
  G for Functor of B,C;
reserve o,m for set;

theorem Th21:
  for F1,F2 be Functor of A,B st F1 is_naturally_transformable_to
  F2 for t be natural_transformation of F1,F2, G be Functor of B,C, a being
  Object of A holds (G*t).a = G/.(t.a)
proof
  let F1,F2 be Functor of A,B;
  assume
A1: F1 is_naturally_transformable_to F2;
  then
A2: F1 is_transformable_to F2;
  let t be natural_transformation of F1,F2, G be Functor of B,C, a be Object
  of A;
  thus (G*t).a = (G*(t qua transformation of F1,F2)).a by A1,Def7
    .= G/.(t.a) by A2,Th19;
end;
