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 Th18:
  for G1,G2 be Functor of B,C st G1 is_transformable_to G2 for F
be Functor of A,B, t be transformation of G1,G2, a be Object of A holds (t*F).a
  = t.(F.a)
proof
  let G1,G2 be Functor of B,C such that
A1: G1 is_transformable_to G2;
  let F be Functor of A,B, t be transformation of G1,G2, a be Object of A;
  thus (t*F).a = (t*F).(a qua set) by A1,Th3,NATTRA_1:def 5
    .= ((t qua Function of the carrier of B, the carrier' of C)*Obj F).a by A1
,Def6
    .= t.((Obj F).a qua set) by FUNCT_2:15
    .= t.(F.a) by A1,NATTRA_1:def 5;
end;
