Global Notation "a # b" := (Maps.PMap.get b a) (at level 1).

Lemma permission_at_alloc_4: forall m m' lo hi nb b ofs (Halloc: Mem.alloc m lo hi = (m', nb)) (Hb: b <> nb), forall k, permissions.permission_at m b ofs k = permissions.permission_at m' b ofs k.