Definition ext_link := ext_link_prog prog.(* Should we really need a concrete user program in order to build enough of an external_specification for the juicy_dry proof? *)
Definition io_ext_spec
  :=
  add_funspecs_rec
    ext_link
    (ok_void_spec IO_itree).(@OK_ty)
    (ok_void_spec IO_itree).(@OK_spec)
    io_specs.Definition getchar_post (m0 m : mem) r (k : int -> IO_itree) (z : IO_itree) :=
  m0 = m /\ - two_p 7 <= Int.signed r <= two_p 7 - 1 /\ z = k r.Definition putchar_post (m0 m : mem) r (c : int) (k : IO_itree) (z : IO_itree) :=
  m0 = m /\ r = c /\ z = k.Program Definition io_dry_spec : external_specification mem external_function IO_itree.Definition dessicate : forall ef (jm : juicy_mem), ext_spec_type io_ext_spec ef -> ext_spec_type io_dry_spec ef.

Lemma nth_nil : forall {A} n (d : A), nth n nil d = d.