Definition control_as_safe {Espec: OracleKind} ge n ctl1 ctl2 :=
 forall (ora : OK_ty) (ve : env) (te : temp_env) (m : juicy_mem) (n' : nat),
     n' <= n ->
     jsafeN (@OK_spec Espec) ge n' ora (State ve te ctl1) m ->
     jsafeN (@OK_spec Espec) ge n' ora (State ve te ctl2) m.Fixpoint prebreak_cont (k: cont) : cont :=
  match k with
  | Kloop1 s e3 :: k' => k
  | Kseq s :: k' => prebreak_cont k'
  | Kloop2 s e3 :: k' => k
  | Kswitch :: k' => k
  | _ =>  nil (* stuck *)
  end.

Lemma control_as_safe_bupd {Espec: OracleKind}: forall ge n ctl1 ctl2, control_as_safe ge n ctl1 ctl2 -> forall (ora : OK_ty) (ve : env) (te : temp_env) (m : juicy_mem) (n' : nat), n' <= n -> jm_bupd ora (jsafeN (@OK_spec Espec) ge n' ora (State ve te ctl1)) m -> jm_bupd ora (jsafeN (@OK_spec Espec) ge n' ora (State ve te ctl2)) m.