Corollary last_two_reads_In2 : forall h, In (AE (snd (last_two_reads h)) Empty) (AE (vint 1) Empty :: h).

(* Specifications: *)
Lemma latest_read_Empty : forall h n v, newer h n -> latest_read (map_upd h n (AE Empty Empty)) v <-> latest_read h v.
Lemma latest_read_new : forall h n v, newer h n -> v <> Empty -> latest_read (map_upd h n (AE v Empty)) v.
Lemma make_shares_out : forall b lasts shs (Hb : ~In b lasts) (Hlen : Zlength lasts = Zlength shs), make_shares shs lasts b = shs.