Corollary newer_out : forall h t, newer h t -> h t = None.

(* Specifications: *)
Lemma add_new_inj : forall h h' t t' v v' (Ht : newer h t) (Ht' : newer h' t'), map_upd h t v = map_upd h' t' v' -> h = h' /\ t = t' /\ v = v'.
Lemma hist_incl_lt : forall h l, hist_incl h l -> newer h (length l).