Definition PMap_eq {A} (m m' : PMap.t (Z -> A)) := forall b' ofs', m !! b' ofs' = m' !! b' ofs'.

Lemma A2PMap_add_outside T b b' ofs ofs' set o :
(@A2PMap T (AMap.add (b, ofs) o set)) !! b' ofs' =
if adr_range_dec (b, ofs) LKSIZE (b', ofs') then
Some Writable
else
(@A2PMap T set) !! b' ofs'.