Section GHist.
(* Ghost histories in the style of Nanevsky *)
Context {hist_el : Type}.
Notation hist_part := (nat -> option hist_el).
Definition hist_sub sh (h : hist_part) hr := sh <> Share.bot /\ if eq_dec sh Tsh then h = hr
else map_incl h hr.
Definition ghost_hist (sh : share) (h : hist_part) g :=
own(RA := ref_PCM map_disj_PCM) g (Some (sh, h), None) NoneP.
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.