Definition latest_read (h : hist) v :=
  (* initial condition *)
  ((forall t r w, h t = Some (AE r w) -> w = Empty -> r = Empty) /\ v = vint 1) \/
  v <> Empty /\ exists n, h n = Some (AE v Empty) /\
  forall t r w, h t = Some (AE r w) -> w = Empty -> r <> Empty -> (t <= n)%nat.

Lemma Empty_inj : forall i, vint i = Empty -> repable_signed i -> i = -1.