Local Notation "'un'" := (@orp _).

Lemma listd_pure_atomd_purei atms s0 s : listd (fun atms : list pure_atom => listd pure_atom_denote inter TT atms) inter TT atms s0 -> join_sub s0 s -> listd (fun atms : list pure_atom => listd pure_atom_denote inter TT atms) inter TT atms s.