Corollary add_items_trace_wf : forall h la h', add_items_trace h la h' ->
  wf_hists h -> wf_hists h'.

(* Specifications: *)
Lemma wf_empty : wf_hists empty_hists.
Lemma add_items_length : forall h la h', add_items_trace h la h' -> Zlength h' = Zlength h.