Definition full_hist h v := exists l, hist_list h l /\ apply_hist (vint 0) l = Some v.
Definition full_hist' h v := exists l, hist_list' h l /\ apply_hist (vint 0) l = Some v.

Lemma full_hist'_nil : forall n l, Forall2 full_hist' (repeat [] n) l -> l = repeat (vint 0) n.