reserve B,C,D for Category;

theorem
  for F1 being Function of the carrier' of C,the carrier' of B for F2
being Function of the carrier' of B,the carrier' of D holds *'(F2*F1)*' = (*'F2
  *')*(*'F1*')
proof
  let F1 be Function of the carrier' of C,the carrier' of B;
  let F2 be Function of the carrier' of B,the carrier' of D;
  now
    let f be Morphism of C opp;
    thus (*'(F2*F1)*').f = ((F2*F1).(opp f)) opp by Lm17
      .= (F2.(F1.(opp f))) opp by FUNCT_2:15
      .= (*'F2*').((F1.(opp f)) opp) by Th44
      .= (*'F2*').((*'F1*').f) by Lm17
      .= ((*'F2*')*(*'F1*')).f by FUNCT_2:15;
  end;
  hence thesis by FUNCT_2:63;
end;
