(** Typechecking soundness **)
Transparent Float.to_intu.
Transparent Float32.to_int.
Transparent Float32.to_intu.

(* Specifications: *)
Lemma isCastR: forall {CS: compspecs} tfrom tto a,
denote_tc_assert (isCastResultType tfrom tto a) =
denote_tc_assert
match classify_cast tfrom tto with
| Cop.cast_case_default => tc_FF  (invalid_cast tfrom tto)
| Cop.cast_case_f2i _ Signed => tc_andp (tc_Zge a Int.min_signed ) (tc_Zle a Int.max_signed)
| Cop.cast_case_s2i _ Signed => tc_andp (tc_Zge a Int.min_signed ) (tc_Zle a Int.max_signed)
| Cop.cast_case_f2i _ Unsigned => tc_andp (tc_Zge a 0) (tc_Zle a Int.max_unsigned)
| Cop.cast_case_s2i _ Unsigned => tc_andp (tc_Zge a 0) (tc_Zle a Int.max_unsigned)
| Cop.cast_case_i2l _ =>
tc_andp (tc_bool (is_int_type tfrom) (invalid_cast_result tfrom tto))
(if is_pointer_type tto then tc_iszero a else tc_TT)
| Cop.cast_case_l2i _ _ =>
tc_andp (tc_bool (is_long_type tfrom) (invalid_cast_result tfrom tto))
(if is_pointer_type tto then tc_iszero a else tc_TT)
| Cop.cast_case_pointer  =>
if eqb_type tfrom tto then tc_TT else
if orb  (andb (is_pointer_type tto) (is_pointer_type tfrom))
(if Archi.ptr64
then (andb (is_long_type tto) (is_long_type tfrom))
else (andb (is_int_type tto) (is_int_type tfrom)))
then tc_TT else
if (andb (eqb_type tto int_or_ptr_type) ((if Archi.ptr64 then is_long_type else is_int_type) tfrom))
then tc_TT else
if (andb (eqb_type tto int_or_ptr_type) (is_pointer_type tfrom))
then tc_TT else
if (andb (eqb_type tfrom int_or_ptr_type) (is_pointer_type tto))
then tc_isptr a else
if (andb (eqb_type tfrom int_or_ptr_type) ((if Archi.ptr64 then is_long_type else is_int_type) tto))
then (if Archi.ptr64 then tc_islong else tc_isint) a
else tc_iszero a
| Cop.cast_case_l2l => tc_bool (is_long_type tfrom && is_long_type tto) (invalid_cast_result tto tto)
| Cop.cast_case_f2bool => tc_bool (is_float_type tfrom) (invalid_cast_result tfrom tto)
| Cop.cast_case_s2bool => tc_bool (is_single_type tfrom) (invalid_cast_result tfrom tto)
| Cop.cast_case_l2bool =>
if is_pointer_type tfrom
then tc_test_eq a (Econst_long Int64.zero (Tlong Unsigned noattr))
else tc_TT
| Cop.cast_case_i2bool =>
if is_pointer_type tfrom
then tc_test_eq a (Econst_int Int.zero (Tint I32 Unsigned noattr))
else tc_TT
| Cop.cast_case_void => tc_noproof
| _ => match tto with
| Tint _ _ _  => tc_bool (is_int_type tfrom) (invalid_cast_result tto tto)
| Tfloat F64 _  => tc_bool (is_anyfloat_type tfrom) (invalid_cast_result tto tto)
| Tfloat F32 _  => tc_bool (is_anyfloat_type tfrom) (invalid_cast_result tto tto)
| _ => tc_FF (invalid_cast tfrom tto)
end
end.
Lemma Z2R_pow_0_lt:
forall e,
0 <= e ->
Rdefinitions.Rlt 0 (Fcore_Raux.Z2R (2 ^ e)).