Definition A2P {A} :=
 (fun (pmap : access_map) (a : address * A) =>
      let (a0, _) := a in let (b0, ofs0) := a0 in setPermBlock (Some Writable) b0 ofs0 pmap LKSIZE_nat).

Lemma AMap_remove_add {A} (m : AMap.t A) x y : AMap.find x m = Some y -> AMap.Equal m (AMap.add x y (AMap.remove x m)).