Open Scope pred.
(* Various utility lemmas *)
Definition instr_approx_rel (n:nat) (i1 i2:instruction) : Prop :=
fmap_instr (K.approx n) i1 = fmap_instr (K.approx n) i2.
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 step_prog_levels : forall t p p' r s r' s',
step t p p' r s r' s' ->
level p' <= level p.