Definition bnd_from_init m := bounded_maps.bounded_map (snd (getMaxPerm m)) /\ (Mem.mem_access m).1 = fun z k => None.

Lemma mem_alloc_bounded_init:
forall m lo hi m1 b,
bnd_from_init m ->
Mem.alloc m lo hi = (m1, b) ->
bnd_from_init m1.