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

Lemma add_items_Znth : forall h la h' j, add_items_trace h la h' -> 0 <= j < Zlength la -> exists h1 h2, let '(k, v, i, s) := Znth j la (0, 0, 0, false) in add_item_trace h1 k v i s h2 /\ hists_mono h h1 /\ hists_mono h2 h'.