reserve B,C,D for Category;

theorem Th40:
  for S being Functor of C,B, c being Object of C holds (Obj S*').
  c = ((Obj S).c) opp
proof
  let S be Functor of C,B, c be Object of C;
  now
    thus (S*').(id c) = id(((Obj S).c) opp) by Lm14;
    let c be Object of C;
    (S*').(id c) = id(((Obj S).c) opp) by Lm14;
    hence ex d being Object of B opp st (S*').(id c) = id d;
  end;
  hence thesis by CAT_1:66;
end;
