Definition classify_binarith' (ty1: type) (ty2: type) :=
  match stupid_typeconv ty1, stupid_typeconv ty2 with
  | Tint i1 s1 _, Tint i2 s2 _ => bin_case_i 
    match i1, s1, i2, s2 with
    | I32, Unsigned, _, _ => Unsigned
    | _, _, I32, Unsigned => Unsigned
    | _, _, _, _ => Signed
    end
  | Tint _ _ _, Tlong s _ => bin_case_l s
  | Tlong s _, Tint _ _ _ => bin_case_l s
  | Tlong s1 _, Tlong s2 _ => bin_case_l
    match s1, s2 with
    | Signed, Signed => Signed
    | _, _ => Unsigned
    end
  | Tfloat F32 _, Tfloat F32 _ => bin_case_s
  | Tfloat _ _, Tfloat _ _ => bin_case_f
  | Tfloat F64 _, (Tint _ _ _ | Tlong _ _) => bin_case_f
  | (Tint _ _ _ | Tlong _ _), Tfloat F64 _ => bin_case_f
  | Tfloat F32 _, (Tint _ _ _ | Tlong _ _) => bin_case_s
  | (Tint _ _ _ | Tlong _ _), Tfloat F32 _ => bin_case_s
  | _, _ => bin_default
  end.Definition binarithType' t1 t2 ty deferr reterr : tc_assert :=
  match classify_binarith' t1 t2 with
  | Cop.bin_case_i sg =>  tc_bool (is_int32_type ty) reterr
  | Cop.bin_case_l sg => tc_bool (is_long_type ty) reterr
  | Cop.bin_case_f   => tc_bool (is_float_type ty) reterr
  | Cop.bin_case_s   => tc_bool (is_single_type ty) reterr
  | Cop.bin_default => tc_FF deferr
  end.

(* Specifications: *)
Lemma classify_binarith_eq: classify_binarith = classify_binarith'.
Lemma binarithType_eq: binarithType = binarithType'.
Lemma den_isBinOpR: forall {CS: compspecs} op a1 a2 ty, denote_tc_assert (isBinOpResultType op a1 a2 ty) = let e := (Ebinop op a1 a2 ty) in let reterr := op_result_type e in let deferr := arg_type e in denote_tc_assert match op with | Cop.Oadd => match classify_add' (typeof a1) (typeof a2) with | Cop.add_case_pi t _ => tc_andp' (tc_andp' (tc_andp' (tc_isptr a1) (tc_bool (complete_type cenv_cs t) reterr)) (tc_int_or_ptr_type (typeof a1))) (tc_bool (is_pointer_type ty) reterr) | Cop.add_case_ip _ t => tc_andp' (tc_andp' (tc_andp' (tc_isptr a2) (tc_bool (complete_type cenv_cs t) reterr)) (tc_int_or_ptr_type (typeof a2))) (tc_bool (is_pointer_type ty) reterr) | Cop.add_case_pl t => tc_andp' (tc_andp' (tc_andp' (tc_isptr a1) (tc_bool (complete_type cenv_cs t) reterr)) (tc_int_or_ptr_type (typeof a1))) (tc_bool (is_pointer_type ty) reterr) | Cop.add_case_lp t => tc_andp' (tc_andp' (tc_andp' (tc_isptr a2) (tc_bool (complete_type cenv_cs t) reterr)) (tc_int_or_ptr_type (typeof a2))) (tc_bool (is_pointer_type ty) reterr) | Cop.add_default => tc_andp (binarithType' (typeof a1) (typeof a2) ty deferr reterr) (tc_nobinover Z.add a1 a2) end | Cop.Osub => match classify_sub' (typeof a1) (typeof a2) with | Cop.sub_case_pi t _ => tc_andp' (tc_andp' (tc_andp' (tc_isptr a1) (tc_bool (complete_type cenv_cs t) reterr)) (tc_int_or_ptr_type (typeof a1))) (tc_bool (is_pointer_type ty) reterr) | Cop.sub_case_pl t => tc_andp' (tc_andp' (tc_andp' (tc_isptr a1) (tc_bool (complete_type cenv_cs t) reterr)) (tc_int_or_ptr_type (typeof a1))) (tc_bool (is_pointer_type ty) reterr) | Cop.sub_case_pp t => tc_andp' (tc_andp' (tc_andp' (tc_andp' (tc_andp' (tc_andp' (tc_andp' (tc_andp' (tc_samebase a1 a2) (tc_isptr a1)) (tc_isptr a2)) (tc_int_or_ptr_type (typeof a1))) (tc_int_or_ptr_type (typeof a2))) (tc_bool (is_ptrofs_type ty) reterr)) (tc_bool (negb (Z.eqb (sizeof t) 0)) (pp_compare_size_0 t))) (tc_bool (complete_type cenv_cs t) reterr)) (tc_bool (Z.leb (sizeof t) Ptrofs.max_signed) (pp_compare_size_exceed t)) | Cop.sub_default => tc_andp (binarithType' (typeof a1) (typeof a2) ty deferr reterr) (tc_nobinover Z.sub a1 a2) end | Cop.Omul => tc_andp (binarithType' (typeof a1) (typeof a2) ty deferr reterr) (tc_nobinover Z.mul a1 a2) | Cop.Omod => match classify_binarith' (typeof a1) (typeof a2) with | Cop.bin_case_i Unsigned => tc_andp' (tc_nonzero' a2) (tc_bool (is_int32_type ty) reterr) | Cop.bin_case_l Unsigned => tc_andp' (tc_nonzero' a2) (tc_bool (is_long_type ty) reterr) | Cop.bin_case_i Signed => tc_andp' (tc_andp' (tc_nonzero' a2) (tc_nodivover' a1 a2)) (tc_bool (is_int32_type ty) reterr) | Cop.bin_case_l Signed => tc_andp' (tc_andp' (tc_nonzero' a2) (tc_nodivover' a1 a2)) (tc_bool (is_long_type ty) reterr) | _ => tc_FF deferr end | Cop.Odiv => match classify_binarith' (typeof a1) (typeof a2) with | Cop.bin_case_i Unsigned => tc_andp' (tc_nonzero' a2) (tc_bool (is_int32_type ty) reterr) | Cop.bin_case_l Unsigned => tc_andp' (tc_nonzero' a2) (tc_bool (is_long_type ty) reterr) | Cop.bin_case_i Signed => tc_andp' (tc_andp' (tc_nonzero' a2) (tc_nodivover' a1 a2)) (tc_bool (is_int32_type ty) reterr) | Cop.bin_case_l Signed => tc_andp' (tc_andp' (tc_nonzero' a2) (tc_nodivover' a1 a2)) (tc_bool (is_long_type ty) reterr) | Cop.bin_case_f => tc_bool (is_float_type ty) reterr | Cop.bin_case_s => tc_bool (is_single_type ty) reterr | Cop.bin_default => tc_FF deferr end | Cop.Oshl | Cop.Oshr => match classify_shift' (typeof a1) (typeof a2) with | Cop.shift_case_ii _ => tc_andp' (tc_ilt' a2 Int.iwordsize) (tc_bool (is_int32_type ty) reterr) | Cop.shift_case_il _ => tc_andp' (tc_llt' a2 (Int64.repr 32)) (tc_bool (is_int32_type ty) reterr) | Cop.shift_case_li _ => tc_andp' (tc_ilt' a2 Int64.iwordsize') (tc_bool (is_long_type ty) reterr) | Cop.shift_case_ll _ => tc_andp' (tc_llt' a2 Int64.iwordsize) (tc_bool (is_long_type ty) reterr) | _ => tc_FF deferr end | Cop.Oand | Cop.Oor | Cop.Oxor => match classify_binarith' (typeof a1) (typeof a2) with | Cop.bin_case_i _ =>tc_bool (is_int32_type ty) reterr | Cop.bin_case_l _ =>tc_bool (is_long_type ty) reterr | Cop.bin_case_f => tc_FF deferr | Cop.bin_case_s => tc_FF deferr | Cop.bin_default => tc_FF deferr end | Cop.Oeq | Cop.One | Cop.Olt | Cop.Ogt | Cop.Ole | Cop.Oge => match classify_cmp' (typeof a1) (typeof a2) with | Cop.cmp_default => tc_bool (is_numeric_type (typeof a1) && is_numeric_type (typeof a2) && is_int_type ty) deferr | Cop.cmp_case_pp => tc_andp' (tc_andp' (tc_int_or_ptr_type (typeof a1)) (tc_int_or_ptr_type (typeof a2))) (check_pp_int' a1 a2 op ty e) | Cop.cmp_case_pi si => tc_andp' (tc_int_or_ptr_type (typeof a1)) (check_pp_int' a1 (Ecast a2 size_t) op ty e) | Cop.cmp_case_ip si => tc_andp' (tc_int_or_ptr_type (typeof a2)) (check_pp_int' (Ecast a1 size_t) a2 op ty e) | Cop.cmp_case_pl => tc_andp' (tc_int_or_ptr_type (typeof a1)) (check_pp_int' a1 (Ecast a2 size_t) op ty e) | Cop.cmp_case_lp => tc_andp' (tc_int_or_ptr_type (typeof a2)) (check_pp_int' (Ecast a1 size_t) a2 op ty e) end end.
Lemma denote_tc_assert'_andp'_e: forall {CS: compspecs} a b rho m, denote_tc_assert' (tc_andp' a b) rho m -> denote_tc_assert' a rho m /\ denote_tc_assert' b rho m.
Lemma cast_int_long_nonzero: forall s i, Int.eq i Int.zero = false -> Int64.eq (cast_int_long s i) Int64.zero = false.