reserve B,C,D for Category;

theorem Th43:
  for S being Contravariant_Functor of C,B, c being Object of C
  holds (Obj S*').c = ((Obj S).c) opp
proof
  let S be Contravariant_Functor of C,B, c be Object of C;
  now
    thus (S*').(id c) = id(((Obj S).c) opp) by Lm16;
    let c be Object of C;
    (S*').(id c) = id(((Obj S).c) opp) by Lm16;
    hence ex d being Object of B opp st (S*').(id c) = id d;
  end;
  hence thesis by CAT_1:66;
end;
