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

Lemma make_map_no_key : forall h k (Hout : Forall (fun x => make_int (value_of_hist (fst x)) <> k) h), Forall (fun x => fst x <> k) (make_map h).