Definition hist_incl (h : hist_part) l := forall t e, h t = Some e -> nth_error l t = Some e.
Definition hist_list (h : hist_part) l := forall t e, h t = Some e <-> nth_error l t = Some e.

Lemma hist_list_nil_inv2 : forall h, hist_list h [] -> h = empty_map.
Definition ghost_ref l g := EX hr : hist_part, !!(hist_list hr l) &&
own(RA := ref_PCM map_disj_PCM) g (None, Some hr) NoneP.