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

Lemma make_map_eq : forall h h', Forall2 (fun a b => value_of_hist (fst a) = value_of_hist (fst b) /\ value_of_hist (snd a) = value_of_hist (snd b)) h h' -> make_map h = make_map h'.