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_sub_list_incl : forall sh h h' l (Hsub : hist_sub sh h h') (Hlist : hist_list h' l),
hist_incl h l.