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 Th19:
  for F1,F2 be Functor of A,B st F1 is_transformable_to F2 for t
be 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 such that
A1: F1 is_transformable_to F2;
  let t be transformation of F1,F2, G be Functor of B,C, a be Object of A;
A2: Hom(F1.a,F2.a) <> {} by A1;
  thus (G*t).a = (G*t).(a qua set) by A1,Th3,NATTRA_1:def 5
    .= ((G qua Function of the carrier' of B, the carrier' of C)* (t qua
  Function of the carrier of A, the carrier' of B)).a by A1,Def5
    .= G.(t.(a qua set)) by FUNCT_2:15
    .= G.(t.a qua Morphism of B) by A1,NATTRA_1:def 5
    .= G/.(t.a) by A2,CAT_3:def 10;
end;
