reserve B,C,D for Category;

theorem
  for S being Function of the carrier' of C,the carrier' of B for f
  being Morphism of C holds (*'S).(f opp) = S.f
proof
  let S be Function of the carrier' of C,the carrier' of B;
  let f be Morphism of C;
  thus (*'S).(f opp) = S.(opp (f opp)) by Def10
    .= S.f;
end;
