(** Boolean-valued equality test *)
Definition nmem_beq (nm1 nm2: nmem) : bool :=
match nm1, nm2 with
| NMemDead, NMemDead => true
| NMem stk1 gl1, NMem stk2 gl2 => ISet.beq stk1 stk2 && PTree.beq ISet.beq gl1 gl2
| _, _ => false
end.

(* Specifications: *)
Lemma nmem_beq_sound:
forall nm1 nm2 b ofs,
nmem_beq nm1 nm2 = true ->
(nlive nm1 b ofs <-> nlive nm2 b ofs).