(* Lookup tables *)
Definition update_mem_table (s : Sstate) args v :=
  (args, v) :: s.

(* Specifications: *)
Lemma lookup_valid' s args : state_wf s -> forall v, lookup_mem_table s args = Some v -> f args = Some v.
Lemma lookup_valid s args : state_wf s -> if lookup_mem_table s args is Some v then f args = Some v else True.