reserve B,C,D for Category;

theorem Th44:
  for F being Function of the carrier' of C,the carrier' of D for
  f being Morphism of C holds *'F*'.(f opp) = (F.f) opp
proof
  let F be Function of the carrier' of C,the carrier' of D;
  let f be Morphism of C;
  thus *'F*'.(f opp) = (F.(opp(f opp))) opp by Lm17
    .= (F.f) opp;
end;
