reserve B,C,D for Category;

theorem
  for S being Function of the carrier' of C opp,the carrier' of D holds
  *'(/*S) = S
proof
  let S be Function of the carrier' of C opp,the carrier' of D;
  now
    let f be Morphism of C opp;
    thus *'(/*S).f = (/*S).(opp f) by Def10
      .= S.((opp f) opp) by Def8
      .= S.f;
  end;
  hence thesis by FUNCT_2:63;
end;
