reserve B,C,D for Category;

theorem
  for S being Function of the carrier' of C opp,the carrier' of B for f
  being Morphism of C opp holds (/*S).(opp f) = S.f
proof
  let S be Function of the carrier' of C opp,the carrier' of B;
  let f be Morphism of C opp;
  thus (/*S).(opp f) = S.((opp f) opp) by Def8
    .= S.f;
end;
