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 sorted_find A a x l l' (sorted : Sorted (AMap.Raw.PX.ltk (elt:=A)) ((a, x) :: l)) (sorted' : Sorted (AMap.Raw.PX.ltk (elt:=A)) ((a, x) :: l')) : (forall y : AMap.key, AMap.Raw.find (elt:=A) y ((a, x) :: l) = AMap.Raw.find (elt:=A) y ((a, x) :: l')) -> forall y : AMap.key, AMap.Raw.find (elt:=A) y l = AMap.Raw.find (elt:=A) y l'.