Inductive stack_approx_rel (n:nat) : stack -> stack -> Prop :=
| stack_approx_nil : stack_approx_rel n nil nil
| stack_approx_cons : forall i i' stk stk',
instr_approx_rel n i i' ->
stack_approx_rel n stk stk' ->
stack_approx_rel n (i::stk) (i'::stk').

Lemma nec_prog_lookup : forall p p' l i,
necR p p' ->
prog_lookup p l = Some i ->
prog_lookup p' l = Some (fmap_instr (K.approx (level p')) i).