Program Definition is_w w: pred rmap := fun w' => necR w w'.

Lemma join_singleton_inv: forall k a b RA c v pp, join a b (singleton k (existT _ RA (exist _ (core c) v), pp)) -> a = singleton k (existT _ RA (exist _ (core c) v), pp) \/ b = singleton k (existT _ RA (exist _ (core c) v), pp).