reserve B,C,D for Category;

theorem
  for S being Function of the carrier' of C,the carrier' of B for T
  being Function of the carrier' of B,the carrier' of D holds *'(T*S) = T*(*'S)
proof
  let S be Function of the carrier' of C,the carrier' of B;
  let T be Function of the carrier' of B,the carrier' of D;
  now
    let f be Morphism of C opp;
    thus (*'(T*S)).f = (T*S).(opp f) by Def10
      .= T.(S.(opp f)) by FUNCT_2:15
      .= T.(*'S.f) by Def10
      .= (T*(*'S)).f by FUNCT_2:15;
  end;
  hence thesis by FUNCT_2:63;
end;
