Definition check_pp_int' e1 e2 op t e :=
  match op with
  | Cop.Oeq | Cop.One =>
      tc_andp'
        (tc_test_eq' e1 e2)
        (tc_bool (is_int_type t) (op_result_type e))
  | Cop.Ole | Cop.Olt | Cop.Oge | Cop.Ogt =>
      tc_andp'
        (tc_test_order' e1 e2)
        (tc_bool (is_int_type t) (op_result_type e))
| _ => tc_noproof
end.

Lemma denote_tc_assert_nonzero': forall {CS: compspecs} e, denote_tc_assert (tc_nonzero e) = denote_tc_assert (tc_nonzero' e).