Corollary last_two_reads_fst : forall h, fst (last_two_reads h) <> Empty.

(* Specifications: *)
Lemma find_read_In : forall d h, In (AE (fst (find_read h d)) Empty) (AE d Empty :: h).
Lemma find_read_In : forall d h, In (AE (fst (find_read h d)) Empty) (AE d Empty :: h).