Corollary add_items_trace_mono : forall h la h', add_items_trace h la h' ->
  hists_mono h h'.

Lemma get_item_trace_map : forall h k v i h' (Hwf : wf_hists h) (Hlenh : Zlength h = size) (Htrace : get_item_trace h k v i h') (Hk : k <> 0) (Hrepk : repable_signed k) (Hrepv : repable_signed v), wf_hists h' /\ match get (make_map h') k with | Some v' => v' = v /\ map_incl (upd_Znth i (make_map h) (k, v)) (make_map h') | None => v = 0 /\ map_incl (make_map h) (make_map h') end.