TPTP Problem File: SWW476

TPTP Problem File: SWW476_2.p

%------------------------------------------------------------------------------
% File     : SWW476_2 : TPTP v8.2.0. Released v5.3.0.
% Domain   : Software Verification
% Problem  : Java type soundness line 197, 500 axioms selected
% Version  : Especial.
% English  :

% Refs     : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
%          : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source   : [Bla11]
% Names    : jinja_500_tff_l197 [Bla11]

% Status   : Theorem
% Rating   : 1.00 v5.5.0, 0.75 v5.4.0, 1.00 v5.3.0
% Syntax   : Number of formulae    : 1289 ( 175 unt; 578 typ;   0 def)
%            Number of atoms       : 1705 ( 575 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives : 1324 ( 330   ~;   6   |;  29   &)
%                                         (  96 <=>; 863  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   8 avg)
%            Maximal term depth    :   13 (   2 avg)
%            Number of types       :  213 ( 212 usr)
%            Number of type conns  :  585 ( 340   >; 245   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  365 ( 365 usr;  26 con; 0-6 aty)
%            Number of variables   : 3429 (3335   !;  94   ?;3429   :)
% SPC      : TF0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2011-08-09 17:25:39
%------------------------------------------------------------------------------
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tff(ty_ty_tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooptio,type,
    fun_fu1693644106l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooptio_031,type,
    fun_fu1690035458on_val: $tType ).

tff(ty_ty_tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__,type,
    fun_fu100249073l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List,type,
    fun_fu177229913l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List_032,type,
    fun_fu1718160452on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__O,type,
    fun_Pr252072522l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__O_033,type,
    fun_Pr1713170355l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__O_034,type,
    fun_Pr1899415884al_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_,type,
    fun_Pr680585871l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J__035,type,
    fun_Pr633696065l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J__036,type,
    fun_Pr714818201on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__S,type,
    fun_Pr248118298l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__S_037,type,
    fun_Pr597144499l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__S_038,type,
    fun_Pr2075414204on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J,type,
    fun_Pr1336948301r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_039,type,
    fun_Pr92408125r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_040,type,
    fun_Pr1453773143t_char: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_041,type,
    fun_Pr227936640r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_042,type,
    fun_Pr1794669603r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_043,type,
    fun_Pr743134922t_char: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_I,type,
    fun_Pr565113489r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_I_044,type,
    fun_Pr806764899on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_I_045,type,
    fun_Pr185059443r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_I_046,type,
    fun_Pr1380325635t_char: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_I_047,type,
    fun_Pr1785445921t_char: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod,type,
    fun_Pr315804320l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_048,type,
    fun_Pr357631842on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_049,type,
    fun_Pr788853347l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_050,type,
    fun_Pr1948698346on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__O,type,
    fun_Pr46158268r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__O_051,type,
    fun_Pr1074372915r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__O_052,type,
    fun_Pr141094017t_char: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__O_053,type,
    fun_Pr612024994t_char: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc_,type,
    fun_Pr827765831r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__054,type,
    fun_Pr378536435r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__055,type,
    fun_Pr1504659044t_char: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__056,type,
    fun_Pr1620417347t_char: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__HOL__Obool_J,type,
    fun_Pr2081272681l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__fun_Itc__prod_I,type,
    fun_Pr324760563l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__prod_Itc__Expr_,type,
    fun_Pr1615326228al_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__prod_Itc__prod_,type,
    fun_Pr1637618473al_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I,type,
    fun_Pr1696029455l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_057,type,
    fun_Pr598845249l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_058,type,
    fun_Pr231134077on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_059,type,
    fun_Pr254484106on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_060,type,
    fun_Pr84821017on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc,type,
    fun_Pr897334561l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__,type,
    fun_Pr691271849l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String___061,type,
    fun_Pr220980979l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String___062,type,
    fun_Pr12181427on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String___063,type,
    fun_Pr609382377on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol,type,
    fun_Pr859510977l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol_064,type,
    fun_Pr1511900787l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol_065,type,
    fun_Pr1898553187on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol_066,type,
    fun_Pr807902897on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String_,type,
    fun_Pr908866473r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__067,type,
    fun_Pr1895638121r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis,type,
    fun_Pr1336847023r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun,type,
    fun_Pr235369833l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_It,type,
    fun_Pr1728267013r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr_,type,
    fun_Pr1890037787r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__prod_,type,
    fun_Pr832147423l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_I,type,
    fun_Pr693020585l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
    fun_Pr903661919l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc,type,
    fun_Pr302334223l_bool: $tType ).

tff(ty_ty_tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_J,type,
    produc1645268488al_val: $tType ).

tff(ty_ty_tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__prod,type,
    produc124828825on_val: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc,type,
    produc2061676504on_val: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__Exp,type,
    produc809539159t_char: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__pro,type,
    produc1285161482t_char: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc__Strin,type,
    produc1278157519t_char: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_Itc__Lis,type,
    produc639455274on_val: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Olist_Itc_,type,
    produc220283002t_char: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__List__Ol,type,
    produc662261637t_char: $tType ).

tff(ty_ty_tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J,type,
    product_prod_val_val: $tType ).

tff(ty_ty_tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List_,type,
    produc12694297on_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__,type,
    produc630464863al_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
    produc1102272487on_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__,type,
    produc430140671on_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_,type,
    produc1534059751t_char: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J__068,type,
    produc349695911t_char: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_,type,
    produc1350825965t_char: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__pro,type,
    produc87279271on_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__,type,
    produc1406897475t_char: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc,type,
    produc1826280281t_char: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__prod_Itc__Valu,type,
    produc800118557al_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_,type,
    produc409205479on_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String_,type,
    produc231486621on_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__O,type,
    produc1466422861on_val: $tType ).

%----Explicit typings (366)
tff(sy_c_BigStep_Oeval,type,
    eval: ( list_P1999446415t_char * exp_list_char * produc12694297on_val ) > fun_ex1201926843l_bool ).

tff(sy_c_BigStep_Oevals,type,
    evals: ( list_P1999446415t_char * list_exp_list_char * produc12694297on_val ) > fun_li1372729616l_bool ).

tff(sy_c_BigStep_Ofinal_000tc__List__Olist_Itc__String__Ochar_J,type,
    final_list_char: exp_list_char > bool ).

tff(sy_c_BigStep_Ofinals_000tc__List__Olist_Itc__String__Ochar_J,type,
    finals_list_char: list_exp_list_char > bool ).

tff(sy_c_Conform_Oconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Oc,type,
    conf_P373316194t_char: ( list_P1999446415t_char * fun_na939144002on_val ) > fun_val_fun_ty_bool ).

tff(sy_c_Conform_Ohconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
    hconf_97414254t_char: ( list_P1999446415t_char * fun_na939144002on_val ) > bool ).

tff(sy_c_Conform_Olconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
    lconf_496643946t_char: ( list_P1999446415t_char * fun_na939144002on_val * fun_li1432931796on_val * fun_li688206603ion_ty ) > bool ).

tff(sy_c_Exceptions_OClassCast,type,
    classCast: list_char ).

tff(sy_c_Exceptions_ONullPointer,type,
    nullPointer: list_char ).

tff(sy_c_Exceptions_Oaddr__of__sys__xcpt,type,
    addr_of_sys_xcpt: list_char > nat ).

tff(sy_c_Expr_Obinop,type,
    binop: produc1645268488al_val > option_val ).

tff(sy_c_Expr_Obop_OEq,type,
    c_Expr_Obop_OEq: bop ).

tff(sy_c_Expr_Oexp_OBinOp_000tc__List__Olist_Itc__String__Ochar_J,type,
    binOp_list_char: ( exp_list_char * bop * exp_list_char ) > exp_list_char ).

tff(sy_c_Expr_Oexp_OBlock_000tc__List__Olist_Itc__String__Ochar_J,type,
    block_list_char: ( list_char * ty * exp_list_char ) > exp_list_char ).

tff(sy_c_Expr_Oexp_OCall_000tc__List__Olist_Itc__String__Ochar_J,type,
    call_list_char: ( exp_list_char * list_char * list_exp_list_char ) > exp_list_char ).

tff(sy_c_Expr_Oexp_OCast_000tc__List__Olist_Itc__String__Ochar_J,type,
    cast_list_char: ( list_char * exp_list_char ) > exp_list_char ).

tff(sy_c_Expr_Oexp_OFAcc_000tc__List__Olist_Itc__String__Ochar_J,type,
    fAcc_list_char: ( exp_list_char * list_char * list_char ) > exp_list_char ).

tff(sy_c_Expr_Oexp_OFAss_000tc__List__Olist_Itc__String__Ochar_J,type,
    fAss_list_char: ( exp_list_char * list_char * list_char * exp_list_char ) > exp_list_char ).

tff(sy_c_Expr_Oexp_OLAss_000tc__List__Olist_Itc__String__Ochar_J,type,
    lAss_list_char: ( list_char * exp_list_char ) > exp_list_char ).

tff(sy_c_Expr_Oexp_OSeq_000tc__List__Olist_Itc__String__Ochar_J,type,
    seq_list_char: ( exp_list_char * exp_list_char ) > exp_list_char ).

tff(sy_c_Expr_Oexp_OTryCatch_000tc__List__Olist_Itc__String__Ochar_J,type,
    tryCatch_list_char: ( exp_list_char * list_char * list_char * exp_list_char ) > exp_list_char ).

tff(sy_c_Expr_Oexp_OVal_000tc__List__Olist_Itc__String__Ochar_J,type,
    val_list_char: fun_va223928858t_char ).

tff(sy_c_Expr_Oexp_OWhile_000tc__List__Olist_Itc__String__Ochar_J,type,
    while_list_char: ( exp_list_char * exp_list_char ) > exp_list_char ).

tff(sy_c_Expr_Oexp_Othrow_000tc__List__Olist_Itc__String__Ochar_J,type,
    throw_list_char: exp_list_char > exp_list_char ).

tff(sy_c_Fun_Ocomp_000tc__List__Olist_Itc__Option__Ooption_Itc__Value__Oval_J_J_000t,type,
    comp_l1825390573t_char: ( fun_li1459524056st_val * fun_li1580442732on_val ) > fun_li742655849st_val ).

tff(sy_c_Fun_Ocomp_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__Value__Oval_000t,type,
    comp_o1129292306t_char: ( fun_option_val_val * fun_li1432931796on_val ) > fun_list_char_val ).

tff(sy_c_Fun_Ofun__upd_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooptio,type,
    fun_up424764369ion_ty: ( fun_li688206603ion_ty * list_char * option_ty ) > fun_li688206603ion_ty ).

tff(sy_c_Fun_Ofun__upd_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooptio_069,type,
    fun_up1149430426on_val: ( fun_li1432931796on_val * list_char * option_val ) > fun_li1432931796on_val ).

tff(sy_c_Fun_Ofun__upd_000tc__Nat__Onat_000tc__Option__Ooption_Itc__prod_Itc__List__,type,
    fun_up2041264236on_val: ( fun_na939144002on_val * nat * option1479284511on_val ) > fun_na939144002on_val ).

tff(sy_c_Fun_Ofun__upd_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__,type,
    fun_up204312361on_val: ( fun_Pr806764899on_val * produc1278157519t_char * option_val ) > fun_Pr806764899on_val ).

tff(sy_c_Fun_Ooverride__on_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Oo,type,
    overri2012515291on_val: ( fun_li1432931796on_val * fun_li1432931796on_val * fun_list_char_bool ) > fun_li1432931796on_val ).

tff(sy_c_List_Oappend_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
    append_exp_list_char: ( list_exp_list_char * list_exp_list_char ) > list_exp_list_char ).

tff(sy_c_List_Odistinct_000tc__List__Olist_Itc__String__Ochar_J,type,
    distinct_list_char: list_list_char > bool ).

tff(sy_c_List_Olist_OCons_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
    cons_exp_list_char: ( exp_list_char * list_exp_list_char ) > list_exp_list_char ).

tff(sy_c_List_Olist_OCons_000tc__List__Olist_Itc__String__Ochar_J,type,
    cons_list_char: ( list_char * list_list_char ) > list_list_char ).

tff(sy_c_List_Olist_OCons_000tc__Type__Oty,type,
    cons_ty: ( ty * list_ty ) > list_ty ).

tff(sy_c_List_Olist_OCons_000tc__Value__Oval,type,
    cons_val: ( val * list_val ) > list_val ).

tff(sy_c_List_Olist__all2_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_,type,
    list_a52822260ion_ty: ( fun_ex1708156690y_bool * list_exp_list_char * list_option_ty ) > bool ).

tff(sy_c_List_Olist__all2_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Oop,type,
    list_a1834344429ion_ty: ( fun_li1351943641y_bool * list_list_char * list_option_ty ) > bool ).

tff(sy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Expr__Oexp_,type,
    list_a283687028t_char: ( fun_op14579988r_bool * list_option_ty * list_exp_list_char ) > bool ).

tff(sy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist,type,
    list_a839443437t_char: ( fun_op668690445r_bool * list_option_ty * list_list_char ) > bool ).

tff(sy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Type__Oty,type,
    list_a2039389316_ty_ty: ( fun_op174240306y_bool * list_option_ty * list_ty ) > bool ).

tff(sy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Value__Oval,type,
    list_a1073113293ty_val: ( fun_op1696804347l_bool * list_option_ty * list_val ) > bool ).

tff(sy_c_List_Olist__all2_000tc__Type__Oty_000tc__Option__Ooption_Itc__Type__Oty_J,type,
    list_a1880637950ion_ty: ( fun_ty1580608948y_bool * list_ty * list_option_ty ) > bool ).

tff(sy_c_List_Olist__all2_000tc__Type__Oty_000tc__Type__Oty,type,
    list_all2_ty_ty: ( fun_ty_fun_ty_bool * list_ty * list_ty ) > bool ).

tff(sy_c_List_Olist__all2_000tc__Value__Oval_000tc__Option__Ooption_Itc__Type__Oty_J,type,
    list_a1462908359ion_ty: ( fun_va642468779y_bool * list_val * list_option_ty ) > bool ).

tff(sy_c_List_Olist__all2_000tc__Value__Oval_000tc__Type__Oty,type,
    list_all2_val_ty: ( fun_val_fun_ty_bool * list_val * list_ty ) > bool ).

tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__,type,
    map_ex2109939687t_char: fun_ex1075505132t_char > fun_li218321462t_char ).

tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___070,type,
    map_ex1548475405ion_ty: fun_ex12316946ion_ty > fun_li241576028ion_ty ).

tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___071,type,
    map_ex1598883030on_val: fun_ex1158871131on_val > fun_li690207653on_val ).

tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___072,type,
    map_ex740158547ar_val: fun_ex793263652ar_val > fun_li363341936st_val ).

tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___073,type,
    map_ex230966390t_char: fun_ex360394747t_char > fun_li456535877t_char ).

tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___074,type,
    map_ex840371726on_val: fun_ex1732915347on_val > fun_li1581546589on_val ).

tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___075,type,
    map_ex2031894694on_val: fun_ex1957978155on_val > fun_li1135544693on_val ).

tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__List__Olist_Itc__S,type,
    map_li1333403488t_char: fun_li1751394789t_char > fun_li1898638973t_char ).

tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooption_It,type,
    map_li771939206ion_ty: fun_li688206603ion_ty > fun_li1921893539ion_ty ).

tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooption_It_076,type,
    map_li50976719on_val: fun_li1432931796on_val > fun_li1580442732on_val ).

tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
    map_list_char_val: fun_list_char_val > fun_li742655849st_val ).

tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__List__Ol,type,
    map_li239070063t_char: fun_li1857149300t_char > fun_li1796883468t_char ).

tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__prod_Itc,type,
    map_li1100402823on_val: fun_li2145367436on_val > fun_li1867552164on_val ).

tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__prod_Itc_077,type,
    map_li1925379487on_val: fun_li328275876on_val > fun_li917540924on_val ).

tff(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Expr__Oexp_Itc__Li,type,
    map_op1779340173t_char: fun_op1508857234t_char > fun_li156600670t_char ).

tff(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist_Itc__S,type,
    map_op1924521862t_char: fun_op195029515t_char > fun_li712717783t_char ).

tff(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Option__Ooption_It,type,
    map_op1363057580ion_ty: fun_op1279324977ion_ty > fun_li735972349ion_ty ).

tff(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Type__Oty,type,
    map_option_ty_ty: fun_option_ty_ty > fun_li202512966ist_ty ).

tff(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Value__Oval,type,
    map_option_ty_val: fun_option_ty_val > fun_li1333774223st_val ).

tff(sy_c_List_Omap_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__Value__Oval,type,
    map_option_val_val: fun_option_val_val > fun_li1459524056st_val ).

tff(sy_c_List_Omap_000tc__Type__Oty_000tc__List__Olist_Itc__String__Ochar_J,type,
    map_ty_list_char: fun_ty_list_char > fun_li2094888364t_char ).

tff(sy_c_List_Omap_000tc__Type__Oty_000tc__Option__Ooption_Itc__Type__Oty_J,type,
    map_ty_option_ty: fun_ty_option_ty > fun_li2118142930ion_ty ).

tff(sy_c_List_Omap_000tc__Type__Oty_000tc__Option__Ooption_Itc__Value__Oval_J,type,
    map_ty_option_val: fun_ty_option_val > fun_li1110934555on_val ).

tff(sy_c_List_Omap_000tc__Type__Oty_000tc__Value__Oval,type,
    map_ty_val: fun_ty_val > fun_list_ty_list_val ).

tff(sy_c_List_Omap_000tc__Type__Oty_000tc__prod_Itc__List__Olist_Itc__String__Ochar_,type,
    map_ty1751634702t_char: fun_ty2043669721t_char > fun_li63139771t_char ).

tff(sy_c_List_Omap_000tc__Type__Oty_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List_,type,
    map_ty891785382on_val: fun_ty2028523121on_val > fun_li1883640275on_val ).

tff(sy_c_List_Omap_000tc__Type__Oty_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr,type,
    map_ty1597677374on_val: fun_ty1366122761on_val > fun_li2066832875on_val ).

tff(sy_c_List_Omap_000tc__Value__Oval_000tc__Expr__Oexp_Itc__List__Olist_Itc__String,type,
    map_va1934808527t_char: fun_va223928858t_char > fun_li430210730t_char ).

tff(sy_c_List_Omap_000tc__Value__Oval_000tc__List__Olist_Itc__String__Ochar_J,type,
    map_val_list_char: fun_val_list_char > fun_li1120813347t_char ).

tff(sy_c_List_Omap_000tc__Value__Oval_000tc__Option__Ooption_Itc__Type__Oty_J,type,
    map_val_option_ty: fun_val_option_ty > fun_li1144067913ion_ty ).

tff(sy_c_List_Omap_000tc__Value__Oval_000tc__Option__Ooption_Itc__Value__Oval_J,type,
    map_val_option_val: fun_val_option_val > fun_li1091306514on_val ).

tff(sy_c_List_Omap_000tc__Value__Oval_000tc__Value__Oval,type,
    map_val_val: fun_val_val > fun_li1707879747st_val ).

tff(sy_c_List_Omap_000tc__Value__Oval_000tc__prod_Itc__List__Olist_Itc__String__Ocha,type,
    map_va234578647t_char: fun_va318401314t_char > fun_li1141758898t_char ).

tff(sy_c_List_Omap_000tc__Value__Oval_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__Lis,type,
    map_va527586287on_val: fun_va172965946on_val > fun_li1659202122on_val ).

tff(sy_c_List_Omap_000tc__Value__Oval_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Ex,type,
    map_va787979527on_val: fun_va358894930on_val > fun_li1897585634on_val ).

tff(sy_c_List_Omap_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olis,type,
    map_Pr361633150t_char: fun_Pr1380325635t_char > fun_li1304494141t_char ).

tff(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
    map_Pr1655409582on_val: fun_Pr12181427on_val > fun_li1479469629on_val ).

tff(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List_,type,
    map_Pr1729094110on_val: fun_Pr1898553187on_val > fun_li1119704125on_val ).

tff(sy_c_List_Oset_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
    set_exp_list_char: list_exp_list_char > fun_ex736065929r_bool ).

tff(sy_c_List_Oset_000tc__List__Olist_Itc__String__Ochar_J,type,
    set_list_char: list_list_char > fun_list_char_bool ).

tff(sy_c_List_Oset_000tc__Option__Ooption_Itc__Type__Oty_J,type,
    set_option_ty: list_option_ty > fun_option_ty_bool ).

tff(sy_c_List_Oset_000tc__Type__Oty,type,
    set_ty: list_ty > fun_ty_bool ).

tff(sy_c_List_Oset_000tc__Value__Oval,type,
    set_val: list_val > fun_val_bool ).

tff(sy_c_List_Oset_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olis,type,
    set_Pr550895038t_char: list_P1916372464t_char > fun_Pr565113489r_bool ).

tff(sy_c_List_Oset_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
    set_Pr1921835862on_val: list_P1439941640on_val > fun_Pr691271849l_bool ).

tff(sy_c_List_Oset_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List_,type,
    set_Pr771975662on_val: list_P507235360on_val > fun_Pr859510977l_bool ).

tff(sy_c_Map_Omap__add_000tc__List__Olist_Itc__String__Ochar_J_000tc__Type__Oty,type,
    map_add_list_char_ty: ( fun_li688206603ion_ty * fun_li688206603ion_ty ) > fun_li688206603ion_ty ).

tff(sy_c_Map_Omap__add_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
    map_ad325961431ar_val: ( fun_li1432931796on_val * fun_li1432931796on_val ) > fun_li1432931796on_val ).

tff(sy_c_Map_Omap__upds_000tc__List__Olist_Itc__String__Ochar_J_000tc__Type__Oty,type,
    map_up891053837har_ty: ( fun_li688206603ion_ty * list_list_char * list_ty ) > fun_li688206603ion_ty ).

tff(sy_c_Map_Omap__upds_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
    map_up1085636310ar_val: ( fun_li1432931796on_val * list_list_char * list_val ) > fun_li1432931796on_val ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_,type,
    size_s1143674878t_char: list_exp_list_char > nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__List__Olist_Itc__String__Och,type,
    size_s2113983095t_char: list_list_char > nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Option__Ooption_Itc__Type__O,type,
    size_s1050794909ion_ty: list_option_ty > nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Option__Ooption_Itc__Value__,type,
    size_s1595297126on_val: list_option_val > nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Type__Oty_J,type,
    size_size_list_ty: list_ty > nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Value__Oval_J,type,
    size_size_list_val: list_val > nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__S,type,
    size_s1010401542t_char: list_P1916372464t_char > nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__prod_Itc__prod_Itc__Expr__Oe,type,
    size_s1699857438on_val: list_P1439941640on_val > nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Ol,type,
    size_s2086378294on_val: list_P507235360on_val > nat ).

tff(sy_c_Objects_Ohext,type,
    hext: ( fun_na939144002on_val * fun_na939144002on_val ) > bool ).

tff(sy_c_Objects_Otypeof__h,type,
    typeof_h: fun_na939144002on_val > fun_val_option_ty ).

tff(sy_c_Option_Ooption_OSome_000tc__Type__Oty,type,
    some_ty: fun_ty_option_ty ).

tff(sy_c_Option_Ooption_OSome_000tc__Value__Oval,type,
    some_val: fun_val_option_val ).

tff(sy_c_Option_Ooption_OSome_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_,type,
    some_P948696889on_val: fun_Pr357631842on_val ).

tff(sy_c_Option_Othe_000tc__Type__Oty,type,
    the_ty: fun_option_ty_ty ).

tff(sy_c_Option_Othe_000tc__Value__Oval,type,
    the_val: fun_option_val_val ).

tff(sy_c_Option_Othe_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc_,type,
    the_Pr431167171on_val: fun_op498348476on_val ).

tff(sy_c_Product__Type_OPair_000tc__Expr__Obop_000tc__prod_Itc__Value__Oval_Mtc__Val,type,
    produc621191550al_val: bop > fun_Pr1615326228al_val ).

tff(sy_c_Product__Type_OPair_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J,type,
    produc1259058957on_val: exp_list_char > fun_Pr231134077on_val ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
    produc379668296on_val: list_exp_list_char > fun_Pr254484106on_val ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_,type,
    produc1147572817t_char: list_list_char > fun_ex303050433t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar__078,type,
    produc921874948t_char: list_list_char > fun_Pr141094017t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__List__Ol,type,
    produc5062597t_char: list_char > fun_li1857149300t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc_,type,
    produc823076510on_val: list_char > fun_fu1718160452on_val ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Type__Oty_J_000tc__prod_Itc__Li,type,
    produc1909267824t_char: list_ty > fun_Pr1504659044t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Value__Oval_J_000tc__Expr__Oexp,type,
    produc1916172923t_char: list_val > fun_ex588373425t_char ).

tff(sy_c_Product__Type_OPair_000tc__Value__Oval_000tc__Value__Oval,type,
    product_Pair_val_val: val > fun_va1923334394al_val ).

tff(sy_c_Product__Type_OPair_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pro,type,
    produc899768717on_val: fun_na939144002on_val > fun_fu1690035458on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_,type,
    produc1924279125al_val: produc1645268488al_val > fun_Pr1899415884al_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
    produc1441475159on_val: produc124828825on_val > fun_Pr714818201on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List_,type,
    produc1611380469on_val: produc2061676504on_val > fun_Pr2075414204on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri,type,
    produc1897818327t_char: produc809539159t_char > fun_Pr1453773143t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri_079,type,
    produc24551831t_char: produc1285161482t_char > fun_Pr743134922t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__,type,
    produc2080520419t_char: produc1278157519t_char > fun_Pr1785445921t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___080,type,
    produc499151895on_val: produc639455274on_val > fun_Pr1948698346on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod,type,
    produc57279289t_char: produc220283002t_char > fun_Pr612024994t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Ex,type,
    produc1299387215t_char: produc662261637t_char > fun_Pr1620417347t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__,type,
    produc1244920211al_val: product_prod_val_val > fun_Pr1637618473al_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooptio,type,
    produc870913623on_val: produc12694297on_val > fun_Pr84821017on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_,type,
    produc1564932627on_val: produc1102272487on_val > fun_Pr609382377on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_,type,
    produc1951691075on_val: produc430140671on_val > fun_Pr807902897on_val ).

tff(sy_c_Product__Type_Ocurry_000tc__Expr__Obop_000tc__prod_Itc__Value__Oval_Mtc__Va,type,
    produc1555310053l_bool: fun_Pr252072522l_bool > fun_bo1454185032l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_,type,
    produc1911975310l_bool: fun_Pr680585871l_bool > fun_ex1201926843l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_It,type,
    produc1838470831l_bool: fun_Pr248118298l_bool > fun_li1372729616l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar,type,
    produc288369490r_bool: fun_Pr1336948301r_bool > fun_li221477r_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_081,type,
    produc1574020101r_bool: fun_Pr227936640r_bool > fun_li1024794712r_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__String__Ochar_J_000tc__List__O,type,
    produc95371820r_bool: fun_Pr565113489r_bool > fun_li860735411r_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc,type,
    produc481748255l_bool: fun_Pr315804320l_bool > fun_li823162622l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Type__Oty_J_000tc__prod_Itc__L,type,
    produc156891095r_bool: fun_Pr46158268r_bool > fun_li887890578r_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Value__Oval_J_000tc__Expr__Oex,type,
    produc550034914r_bool: fun_Pr827765831r_bool > fun_li826105035r_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__Value__Oval_000tc__Value__Oval_000tc__HOL__Oboo,type,
    produc886919678l_bool: fun_Pr2081272681l_bool > fun_val_fun_val_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pr,type,
    produc2062775566l_bool: fun_Pr1696029455l_bool > fun_fu100249073l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval,type,
    produc1969754044l_bool: fun_Pr897334561l_bool > fun_Pr1713170355l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Stri,type,
    produc1159035454l_bool: fun_Pr691271849l_bool > fun_Pr633696065l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List,type,
    produc2053127004l_bool: fun_Pr859510977l_bool > fun_Pr597144499l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Str,type,
    produc1295142846r_bool: fun_Pr908866473r_bool > fun_Pr92408125r_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Str_082,type,
    produc17861502r_bool: fun_Pr1895638121r_bool > fun_Pr1794669603r_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_,type,
    produc715708746r_bool: fun_Pr1336847023r_bool > fun_Pr185059443r_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__083,type,
    produc1996970750l_bool: fun_Pr235369833l_bool > fun_Pr788853347l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__pro,type,
    produc1268552608r_bool: fun_Pr1728267013r_bool > fun_Pr1074372915r_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__E,type,
    produc1535899062r_bool: fun_Pr1890037787r_bool > fun_Pr378536435r_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc_,type,
    produc1034940666l_bool: fun_Pr832147423l_bool > fun_Pr324760563l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Oopti,type,
    produc1073654846l_bool: fun_Pr693020585l_bool > fun_Pr598845249l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist,type,
    produc1497005946l_bool: fun_Pr903661919l_bool > fun_Pr220980979l_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp,type,
    produc971707818l_bool: fun_Pr302334223l_bool > fun_Pr1511900787l_bool ).

tff(sy_c_SmallStep_Oblocks,type,
    blocks: produc1285161482t_char > exp_list_char ).

tff(sy_c_SmallStep_Ored,type,
    red: list_P1999446415t_char > fun_Pr691271849l_bool ).

tff(sy_c_SmallStep_Oredp,type,
    redp: ( list_P1999446415t_char * exp_list_char * produc12694297on_val ) > fun_ex1201926843l_bool ).

tff(sy_c_SmallStep_Oreds,type,
    reds: list_P1999446415t_char > fun_Pr859510977l_bool ).

tff(sy_c_SmallStep_Oredsp,type,
    redsp: ( list_P1999446415t_char * list_exp_list_char * produc12694297on_val ) > fun_li1372729616l_bool ).

tff(sy_c_State_Ohp,type,
    hp: produc12694297on_val > fun_na939144002on_val ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__List__Olist_Itc__String__Ochar_J,type,
    transi1395422419t_char: fun_Pr565113489r_bool > fun_Pr565113489r_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__Value__Oval,type,
    transi935034983cl_val: fun_Pr2081272681l_bool > fun_Pr2081272681l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Val,type,
    transi1906258203al_val: fun_Pr897334561l_bool > fun_Pr897334561l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_I,type,
    transi2024712006on_val: fun_Pr691271849l_bool > fun_Pr691271849l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_I,type,
    transi374442731on_val: fun_Pr859510977l_bool > fun_Pr859510977l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__List__Olist_,type,
    transi198989188t_char: fun_Pr908866473r_bool > fun_Pr908866473r_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__List__Olist__084,type,
    transi122195895t_char: fun_Pr1895638121r_bool > fun_Pr1895638121r_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__String__Ocha,type,
    transi1095029602t_char: fun_Pr1336847023r_bool > fun_Pr1336847023r_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__String__Ocha_085,type,
    transi61620055on_val: fun_Pr235369833l_bool > fun_Pr235369833l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_,type,
    transi1257872013t_char: fun_Pr1728267013r_bool > fun_Pr1728267013r_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__Value__Oval_,type,
    transi1789604888t_char: fun_Pr1890037787r_bool > fun_Pr1890037787r_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_,type,
    transi1423755450al_val: fun_Pr832147423l_bool > fun_Pr832147423l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Optio,type,
    transi921647814on_val: fun_Pr693020585l_bool > fun_Pr693020585l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__Lis,type,
    transi910771962on_val: fun_Pr903661919l_bool > fun_Pr903661919l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Ex,type,
    transi208336786on_val: fun_Pr302334223l_bool > fun_Pr302334223l_bool ).

tff(sy_c_TypeRel_OMethod_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__,type,
    method1809630380t_char: ( list_P1999446415t_char * list_char * list_char * list_ty * ty * produc809539159t_char ) > fun_list_char_bool ).

tff(sy_c_TypeRel_Osubcls1_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String_,type,
    subcls851966956t_char: list_P1999446415t_char > fun_Pr565113489r_bool ).

tff(sy_c_TypeRel_Owiden_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
    widen_2090681816t_char: list_P1999446415t_char > fun_ty_fun_ty_bool ).

tff(sy_c_TypeSafe__Mirabelle__dnoescdigw_Osconf,type,
    typeSa525116494_sconf: ( list_P1999446415t_char * fun_li688206603ion_ty ) > fun_Pr1696029455l_bool ).

tff(sy_c_Type_Ois__refT,type,
    is_refT: ty > bool ).

tff(sy_c_Type_Othis,type,
    this: list_char ).

tff(sy_c_Type_Oty_OClass,type,
    class: list_char > ty ).

tff(sy_c_Value_Odefault__val,type,
    default_val: fun_ty_val ).

tff(sy_c_Value_Oval_OAddr,type,
    addr: nat > val ).

tff(sy_c_Value_Oval_OBool,type,
    bool_1: bool > val ).

tff(sy_c_Value_Oval_ONull,type,
    null: val ).

tff(sy_c_Value_Oval_OUnit,type,
    unit: val ).

tff(sy_c_WellTypeRT_OWTrt,type,
    wTrt: ( list_P1999446415t_char * fun_na939144002on_val * fun_li688206603ion_ty * exp_list_char * ty ) > bool ).

tff(sy_c_WellTypeRT_OWTrts,type,
    wTrts: ( list_P1999446415t_char * fun_na939144002on_val * fun_li688206603ion_ty * list_exp_list_char * list_ty ) > bool ).

tff(sy_c_fFalse,type,
    fFalse: bool ).

tff(sy_c_fTrue,type,
    fTrue: bool ).

tff(sy_c_fequal_000tc__Type__Oty,type,
    fequal_ty: fun_ty_fun_ty_bool ).

tff(sy_c_fequal_000tc__Value__Oval,type,
    fequal_val: fun_val_fun_val_bool ).

tff(sy_c_hAPP_000tc__Expr__Obop_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Ov,type,
    hAPP_b97269396l_bool: ( fun_bo1454185032l_bool * bop ) > fun_Pr2081272681l_bool ).

tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__HOL__,type,
    hAPP_e544220455r_bool: ( fun_ex736065929r_bool * exp_list_char ) > bool ).

tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_I,type,
    hAPP_e1833980889l_bool: ( fun_ex1201926843l_bool * exp_list_char ) > fun_Pr1696029455l_bool ).

tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__prod_,type,
    hAPP_e952791821t_char: ( fun_ex303050433t_char * exp_list_char ) > produc809539159t_char ).

tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__prod__086,type,
    hAPP_e1752110927t_char: ( fun_ex588373425t_char * exp_list_char ) > produc662261637t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar,type,
    hAPP_l2065413838t_char: ( fun_li218321462t_char * list_exp_list_char ) > list_list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_087,type,
    hAPP_l1002225652ion_ty: ( fun_li241576028ion_ty * list_exp_list_char ) > list_option_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_088,type,
    hAPP_l1607890493on_val: ( fun_li690207653on_val * list_exp_list_char ) > list_option_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_089,type,
    hAPP_l1539861698st_val: ( fun_li363341936st_val * list_exp_list_char ) > list_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_090,type,
    hAPP_l1379210717t_char: ( fun_li456535877t_char * list_exp_list_char ) > list_P1916372464t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_091,type,
    hAPP_l1557845365on_val: ( fun_li1581546589on_val * list_exp_list_char ) > list_P1439941640on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_092,type,
    hAPP_l1585742349on_val: ( fun_li1135544693on_val * list_exp_list_char ) > list_P507235360on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_093,type,
    hAPP_l146377954l_bool: ( fun_li1372729616l_bool * list_exp_list_char ) > fun_Pr1696029455l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List,type,
    hAPP_l407174677t_char: ( fun_li1898638973t_char * list_list_char ) > list_list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_094,type,
    hAPP_l1491470139ion_ty: ( fun_li1921893539ion_ty * list_list_char ) > list_option_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_095,type,
    hAPP_l297961988on_val: ( fun_li1580442732on_val * list_list_char ) > list_option_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_096,type,
    hAPP_l1892737211st_val: ( fun_li742655849st_val * list_list_char ) > list_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_097,type,
    hAPP_l1416713636t_char: ( fun_li1796883468t_char * list_list_char ) > list_P1916372464t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_098,type,
    hAPP_l418486716on_val: ( fun_li1867552164on_val * list_list_char ) > list_P1439941640on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_099,type,
    hAPP_l2122855380on_val: ( fun_li917540924on_val * list_list_char ) > list_P507235360on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_,type,
    hAPP_l214204733r_bool: ( fun_li221477r_bool * list_list_char ) > fun_ex736065929r_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun__100,type,
    hAPP_l217977712r_bool: ( fun_li1024794712r_bool * list_list_char ) > fun_Pr46158268r_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Option__Ooption_Itc__Type__Oty_J_J_000tc__List,type,
    hAPP_l330149622t_char: ( fun_li156600670t_char * list_option_ty ) > list_exp_list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Option__Ooption_Itc__Type__Oty_J_J_000tc__List_101,type,
    hAPP_l1368737135t_char: ( fun_li712717783t_char * list_option_ty ) > list_list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Option__Ooption_Itc__Type__Oty_J_J_000tc__List_102,type,
    hAPP_l305548949ion_ty: ( fun_li735972349ion_ty * list_option_ty ) > list_option_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Option__Ooption_Itc__Type__Oty_J_J_000tc__List_103,type,
    hAPP_l1583451544ist_ty: ( fun_li202512966ist_ty * list_option_ty ) > list_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Option__Ooption_Itc__Type__Oty_J_J_000tc__List_104,type,
    hAPP_l336371937st_val: ( fun_li1333774223st_val * list_option_ty ) > list_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Option__Ooption_Itc__Value__Oval_J_J_000tc__Li,type,
    hAPP_l228474410st_val: ( fun_li1459524056st_val * list_option_val ) > list_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__HOL__Obool,type,
    hAPP_list_char_bool: ( fun_list_char_bool * list_char ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__List__Olist_Itc__String,type,
    hAPP_l1074208899t_char: ( fun_li1751394789t_char * list_char ) > list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooption_Itc__Ty,type,
    hAPP_l512744617ion_ty: ( fun_li688206603ion_ty * list_char ) > option_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooption_Itc__Va,type,
    hAPP_l207779698on_val: ( fun_li1432931796on_val * list_char ) > option_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
    hAPP_list_char_val: ( fun_list_char_val * list_char ) > val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__List__Olist_It,type,
    hAPP_l1361600383r_bool: ( fun_li860735411r_bool * list_char ) > fun_list_char_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__fun_Itc__prod_,type,
    hAPP_l465799708l_bool: ( fun_li823162622l_bool * list_char ) > fun_fu177229913l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__List__Olist_I,type,
    hAPP_l2100324114t_char: ( fun_li1857149300t_char * list_char ) > produc1278157519t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__List__Olis,type,
    hAPP_l402740472t_char: ( fun_li2094888364t_char * list_ty ) > list_list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__Option__Oo,type,
    hAPP_l1487035934ion_ty: ( fun_li2118142930ion_ty * list_ty ) > list_option_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__Option__Oo_105,type,
    hAPP_l1014734695on_val: ( fun_li1110934555on_val * list_ty ) > list_option_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__Value__Ova,type,
    hAPP_l1530663448st_val: ( fun_list_ty_list_val * list_ty ) > list_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__prod_Itc__,type,
    hAPP_l1218266887t_char: ( fun_li63139771t_char * list_ty ) > list_P1916372464t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__prod_Itc___106,type,
    hAPP_l1634001311on_val: ( fun_li1883640275on_val * list_ty ) > list_P1439941640on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__prod_Itc___107,type,
    hAPP_l2092195639on_val: ( fun_li2066832875on_val * list_ty ) > list_P507235360on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__fun_Itc__prod_Itc__List__Ol,type,
    hAPP_l1987619678r_bool: ( fun_li887890578r_bool * list_ty ) > fun_Pr827765831r_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__Expr__Oe,type,
    hAPP_l732421366t_char: ( fun_li430210730t_char * list_val ) > list_exp_list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__List__Ol,type,
    hAPP_l922645359t_char: ( fun_li1120813347t_char * list_val ) > list_list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__Option__,type,
    hAPP_l2006940821ion_ty: ( fun_li1144067913ion_ty * list_val ) > list_option_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__Option___108,type,
    hAPP_l761459294on_val: ( fun_li1091306514on_val * list_val ) > list_option_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__Value__O,type,
    hAPP_l273806049st_val: ( fun_li1707879747st_val * list_val ) > list_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__prod_Itc,type,
    hAPP_l1687586302t_char: ( fun_li1141758898t_char * list_val ) > list_P1916372464t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__prod_Itc_109,type,
    hAPP_l382831894on_val: ( fun_li1659202122on_val * list_val ) > list_P1439941640on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__prod_Itc_110,type,
    hAPP_l1134997550on_val: ( fun_li1897585634on_val * list_val ) > list_P507235360on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__fun_Itc__Expr__Oexp_Itc__,type,
    hAPP_l1062423959r_bool: ( fun_li826105035r_bool * list_val ) > fun_ex736065929r_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc,type,
    hAPP_l250787541t_char: ( fun_li1304494141t_char * list_P1916372464t_char ) > list_P1916372464t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olis,type,
    hAPP_l1695428693on_val: ( fun_li1479469629on_val * list_P1439941640on_val ) > list_P1439941640on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oex,type,
    hAPP_l1208602837on_val: ( fun_li1119704125on_val * list_P507235360on_val ) > list_P507235360on_val ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc,type,
    hAPP_n546249108on_val: ( fun_na939144002on_val * nat ) > option1479284511on_val ).

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Type__Oty,type,
    hAPP_option_ty_ty: ( fun_option_ty_ty * option_ty ) > ty ).

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__Value__Oval,type,
    hAPP_option_val_val: ( fun_option_val_val * option_val ) > val ).

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J,type,
    hAPP_o1977518472on_val: ( fun_op498348476on_val * option1479284511on_val ) > produc639455274on_val ).

tff(sy_c_hAPP_000tc__Type__Oty_000tc__HOL__Obool,type,
    hAPP_ty_bool: ( fun_ty_bool * ty ) > bool ).

tff(sy_c_hAPP_000tc__Type__Oty_000tc__Option__Ooption_Itc__Type__Oty_J,type,
    hAPP_ty_option_ty: ( fun_ty_option_ty * ty ) > option_ty ).

tff(sy_c_hAPP_000tc__Type__Oty_000tc__Value__Oval,type,
    hAPP_ty_val: ( fun_ty_val * ty ) > val ).

tff(sy_c_hAPP_000tc__Type__Oty_000tc__fun_Itc__Type__Oty_Mtc__HOL__Obool_J,type,
    hAPP_ty_fun_ty_bool: ( fun_ty_fun_ty_bool * ty ) > fun_ty_bool ).

tff(sy_c_hAPP_000tc__Value__Oval_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Och,type,
    hAPP_v834067052t_char: ( fun_va223928858t_char * val ) > exp_list_char ).

tff(sy_c_hAPP_000tc__Value__Oval_000tc__HOL__Obool,type,
    hAPP_val_bool: ( fun_val_bool * val ) > bool ).

tff(sy_c_hAPP_000tc__Value__Oval_000tc__Option__Ooption_Itc__Type__Oty_J,type,
    hAPP_val_option_ty: ( fun_val_option_ty * val ) > option_ty ).

tff(sy_c_hAPP_000tc__Value__Oval_000tc__Option__Ooption_Itc__Value__Oval_J,type,
    hAPP_val_option_val: ( fun_val_option_val * val ) > option_val ).

tff(sy_c_hAPP_000tc__Value__Oval_000tc__fun_Itc__Type__Oty_Mtc__HOL__Obool_J,type,
    hAPP_val_fun_ty_bool: ( fun_val_fun_ty_bool * val ) > fun_ty_bool ).

tff(sy_c_hAPP_000tc__Value__Oval_000tc__fun_Itc__Value__Oval_Mtc__HOL__Obool_J,type,
    hAPP_v1392248405l_bool: ( fun_val_fun_val_bool * val ) > fun_val_bool ).

tff(sy_c_hAPP_000tc__Value__Oval_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J,type,
    hAPP_v852496844al_val: ( fun_va1923334394al_val * val ) > product_prod_val_val ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_,type,
    hAPP_f1033709212l_bool: ( fun_fu1693644106l_bool * fun_li1432931796on_val ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__111,type,
    hAPP_f1727192346on_val: ( fun_fu1690035458on_val * fun_li1432931796on_val ) > produc12694297on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol,type,
    hAPP_f1175813647l_bool: ( fun_fu100249073l_bool * fun_na939144002on_val ) > fun_fu1693644106l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__,type,
    hAPP_f1715346603l_bool: ( fun_fu177229913l_bool * fun_Pr806764899on_val ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___112,type,
    hAPP_f900686428on_val: ( fun_fu1718160452on_val * fun_Pr806764899on_val ) > produc639455274on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__Ova,type,
    hAPP_P943837928l_bool: ( fun_Pr252072522l_bool * produc1645268488al_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__Ova_113,type,
    hAPP_P323054207l_bool: ( fun_Pr1713170355l_bool * produc1645268488al_val ) > fun_Pr252072522l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__Ova_114,type,
    hAPP_P2123720426al_val: ( fun_Pr1899415884al_val * produc1645268488al_val ) > produc630464863al_val ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt,type,
    hAPP_P1708370145l_bool: ( fun_Pr680585871l_bool * produc124828825on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_115,type,
    hAPP_P1116729363l_bool: ( fun_Pr633696065l_bool * produc124828825on_val ) > fun_Pr680585871l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_116,type,
    hAPP_P1886180715on_val: ( fun_Pr714818201on_val * produc124828825on_val ) > produc1102272487on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str,type,
    hAPP_P71593144l_bool: ( fun_Pr248118298l_bool * produc2061676504on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_117,type,
    hAPP_P1183008383l_bool: ( fun_Pr597144499l_bool * produc2061676504on_val ) > fun_Pr248118298l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_118,type,
    hAPP_P658340954on_val: ( fun_Pr2075414204on_val * produc2061676504on_val ) > produc430140671on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M,type,
    hAPP_P2014166431r_bool: ( fun_Pr1336948301r_bool * produc809539159t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_119,type,
    hAPP_P1939418767r_bool: ( fun_Pr92408125r_bool * produc809539159t_char ) > fun_Pr1336948301r_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_120,type,
    hAPP_P1342907945t_char: ( fun_Pr1453773143t_char * produc809539159t_char ) > produc1534059751t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_121,type,
    hAPP_P92196306r_bool: ( fun_Pr227936640r_bool * produc1285161482t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_122,type,
    hAPP_P1928969845r_bool: ( fun_Pr1794669603r_bool * produc1285161482t_char ) > fun_Pr227936640r_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_123,type,
    hAPP_P1539798428t_char: ( fun_Pr743134922t_char * produc1285161482t_char ) > produc349695911t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc,type,
    hAPP_P449474095r_bool: ( fun_Pr565113489r_bool * produc1278157519t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc_124,type,
    hAPP_P2094403585on_val: ( fun_Pr806764899on_val * produc1278157519t_char ) > option_val ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc_125,type,
    hAPP_P663876415r_bool: ( fun_Pr185059443r_bool * produc1278157519t_char ) > fun_Pr565113489r_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc_126,type,
    hAPP_P760138657t_char: ( fun_Pr1380325635t_char * produc1278157519t_char ) > produc1278157519t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc_127,type,
    hAPP_P1657265855t_char: ( fun_Pr1785445921t_char * produc1278157519t_char ) > produc1350825965t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I,type,
    hAPP_P1235399154l_bool: ( fun_Pr315804320l_bool * produc639455274on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I_128,type,
    hAPP_P1510515380on_val: ( fun_Pr357631842on_val * produc639455274on_val ) > option1479284511on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I_129,type,
    hAPP_P416784693l_bool: ( fun_Pr788853347l_bool * produc639455274on_val ) > fun_Pr315804320l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I_130,type,
    hAPP_P330218428on_val: ( fun_Pr1948698346on_val * produc639455274on_val ) > produc87279271on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Oli,type,
    hAPP_P1907982426r_bool: ( fun_Pr46158268r_bool * produc220283002t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Oli_131,type,
    hAPP_P1214880255r_bool: ( fun_Pr1074372915r_bool * produc220283002t_char ) > fun_Pr46158268r_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Oli_132,type,
    hAPP_P767818445t_char: ( fun_Pr141094017t_char * produc220283002t_char ) > produc1285161482t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Oli_133,type,
    hAPP_P1333668416t_char: ( fun_Pr612024994t_char * produc220283002t_char ) > produc1406897475t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__L,type,
    hAPP_P2118621157r_bool: ( fun_Pr827765831r_bool * produc662261637t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__L_134,type,
    hAPP_P357098431r_bool: ( fun_Pr378536435r_bool * produc662261637t_char ) > fun_Pr827765831r_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__L_135,type,
    hAPP_P1392904962t_char: ( fun_Pr1504659044t_char * produc662261637t_char ) > produc220283002t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__L_136,type,
    hAPP_P1220989409t_char: ( fun_Pr1620417347t_char * produc662261637t_char ) > produc1826280281t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__HOL__Obool,type,
    hAPP_P929938951l_bool: ( fun_Pr2081272681l_bool * product_prod_val_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_Itc__prod_I,type,
    hAPP_P1815899455l_bool: ( fun_Pr324760563l_bool * product_prod_val_val ) > fun_Pr2081272681l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__prod_Itc__Expr_,type,
    hAPP_P929466802al_val: ( fun_Pr1615326228al_val * product_prod_val_val ) > produc1645268488al_val ).

tff(sy_c_hAPP_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__prod_Itc__prod_,type,
    hAPP_P47773639al_val: ( fun_Pr1637618473al_val * product_prod_val_val ) > produc800118557al_val ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc,type,
    hAPP_P159683425l_bool: ( fun_Pr1696029455l_bool * produc12694297on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_137,type,
    hAPP_P1988153107l_bool: ( fun_Pr598845249l_bool * produc12694297on_val ) > fun_Pr1696029455l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_138,type,
    hAPP_P604205461on_val: ( fun_Pr231134077on_val * produc12694297on_val ) > produc124828825on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_139,type,
    hAPP_P1963616220on_val: ( fun_Pr254484106on_val * produc12694297on_val ) > produc2061676504on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_140,type,
    hAPP_P291613419on_val: ( fun_Pr84821017on_val * produc12694297on_val ) > produc409205479on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__,type,
    hAPP_P738987199l_bool: ( fun_Pr897334561l_bool * produc630464863al_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc,type,
    hAPP_P282169671l_bool: ( fun_Pr691271849l_bool * produc1102272487on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_141,type,
    hAPP_P2062527807l_bool: ( fun_Pr220980979l_bool * produc1102272487on_val ) > fun_Pr691271849l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_142,type,
    hAPP_P918220497on_val: ( fun_Pr12181427on_val * produc1102272487on_val ) > produc1102272487on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_143,type,
    hAPP_P1486793863on_val: ( fun_Pr609382377on_val * produc1102272487on_val ) > produc231486621on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis,type,
    hAPP_P1333315679l_bool: ( fun_Pr859510977l_bool * produc430140671on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis_144,type,
    hAPP_P220718911l_bool: ( fun_Pr1511900787l_bool * produc430140671on_val ) > fun_Pr859510977l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis_145,type,
    hAPP_P1439304705on_val: ( fun_Pr1898553187on_val * produc430140671on_val ) > produc430140671on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis_146,type,
    hAPP_P1758592847on_val: ( fun_Pr807902897on_val * produc430140671on_val ) > produc1466422861on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
    hAPP_P1002912327r_bool: ( fun_Pr908866473r_bool * produc1534059751t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O_147,type,
    hAPP_P824029447r_bool: ( fun_Pr1895638121r_bool * produc349695911t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List_,type,
    hAPP_P2010574925r_bool: ( fun_Pr1336847023r_bool * produc1350825965t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_I,type,
    hAPP_P124632071l_bool: ( fun_Pr235369833l_bool * produc87279271on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc_,type,
    hAPP_P1240100515r_bool: ( fun_Pr1728267013r_bool * produc1406897475t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__O,type,
    hAPP_P1183499705r_bool: ( fun_Pr1890037787r_bool * produc1826280281t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__prod_It,type,
    hAPP_P2123002749l_bool: ( fun_Pr832147423l_bool * produc800118557al_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc,type,
    hAPP_P1221872711l_bool: ( fun_Pr693020585l_bool * produc409205479on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__,type,
    hAPP_P378063101l_bool: ( fun_Pr903661919l_bool * produc231486621on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__,type,
    hAPP_P2028072621l_bool: ( fun_Pr302334223l_bool * produc1466422861on_val ) > bool ).

tff(sy_c_hBOOL,type,
    hBOOL: bool > $o ).

tff(sy_c_member_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
    member_exp_list_char: ( exp_list_char * fun_ex736065929r_bool ) > bool ).

tff(sy_c_member_000tc__List__Olist_Itc__String__Ochar_J,type,
    member_list_char: ( list_char * fun_list_char_bool ) > bool ).

tff(sy_c_member_000tc__Option__Ooption_Itc__Type__Oty_J,type,
    member_option_ty: ( option_ty * fun_option_ty_bool ) > bool ).

tff(sy_c_member_000tc__Type__Oty,type,
    member_ty: ( ty * fun_ty_bool ) > bool ).

tff(sy_c_member_000tc__Value__Oval,type,
    member_val: ( val * fun_val_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_I,type,
    member1251428284t_char: ( produc1278157519t_char * fun_Pr565113489r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J,type,
    member649088532al_val: ( product_prod_val_val * fun_Pr2081272681l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc,type,
    member1732271180al_val: ( produc630464863al_val * fun_Pr897334561l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__,type,
    member773094996on_val: ( produc1102272487on_val * fun_Pr691271849l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol,type,
    member875476972on_val: ( produc430140671on_val * fun_Pr859510977l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String_,type,
    member1999287380t_char: ( produc1534059751t_char * fun_Pr908866473r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__148,type,
    member1420286996t_char: ( produc349695911t_char * fun_Pr1895638121r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis,type,
    member794220506t_char: ( produc1350825965t_char * fun_Pr1336847023r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun,type,
    member1322055188on_val: ( produc87279271on_val * fun_Pr235369833l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_It,type,
    member125098544t_char: ( produc1406897475t_char * fun_Pr1728267013r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr_,type,
    member1161907014t_char: ( produc1826280281t_char * fun_Pr1890037787r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__prod_,type,
    member837208074al_val: ( produc800118557al_val * fun_Pr832147423l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_I,type,
    member563141460on_val: ( produc409205479on_val * fun_Pr693020585l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
    member808015754on_val: ( produc231486621on_val * fun_Pr903661919l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc,type,
    member88670778on_val: ( produc1466422861on_val * fun_Pr302334223l_bool ) > bool ).

tff(sy_v_E,type,
    e_1: fun_li688206603ion_ty ).

tff(sy_v_P,type,
    p: list_P1999446415t_char ).

tff(sy_v_T,type,
    t: ty ).

tff(sy_v_Ts,type,
    ts: list_ty ).

tff(sy_v_Vs,type,
    vs_1: list_list_char ).

tff(sy_v_e,type,
    e: exp_list_char ).

tff(sy_v_h,type,
    h: fun_na939144002on_val ).

tff(sy_v_vs,type,
    vs: list_val ).

%----Relevant facts (700)
tff(fact_0_widens__refl,axiom,
    ! [Pa: list_P1999446415t_char,Xs: list_ty] : hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Xs,Xs)) ).

tff(fact_1_widen__refl,axiom,
    ! [P_4: list_P1999446415t_char,T_6: ty] : hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_4),T_6),T_6)) ).

tff(fact_2_widens__trans,axiom,
    ! [Us: list_ty,Pa: list_P1999446415t_char,Ss: list_ty,Tsa: list_ty] :
      ( hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ss,Tsa))
     => ( hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Tsa,Us))
       => hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ss,Us)) ) ) ).

tff(fact_3_list__all2__lengthD,axiom,
    ! [Pa: fun_li1351943641y_bool,Xs: list_list_char,Ys: list_option_ty] :
      ( hBOOL(list_a1834344429ion_ty(Pa,Xs,Ys))
     => ( size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys) ) ) ).

tff(fact_4_list__all2__lengthD,axiom,
    ! [Pa: fun_ty1580608948y_bool,Xs: list_ty,Ys: list_option_ty] :
      ( hBOOL(list_a1880637950ion_ty(Pa,Xs,Ys))
     => ( size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys) ) ) ).

tff(fact_5_list__all2__lengthD,axiom,
    ! [Pa: fun_va642468779y_bool,Xs: list_val,Ys: list_option_ty] :
      ( hBOOL(list_a1462908359ion_ty(Pa,Xs,Ys))
     => ( size_size_list_val(Xs) = size_s1050794909ion_ty(Ys) ) ) ).

tff(fact_6_list__all2__lengthD,axiom,
    ! [Pa: fun_ex1708156690y_bool,Xs: list_exp_list_char,Ys: list_option_ty] :
      ( hBOOL(list_a52822260ion_ty(Pa,Xs,Ys))
     => ( size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys) ) ) ).

tff(fact_7_list__all2__lengthD,axiom,
    ! [Pa: fun_op668690445r_bool,Xs: list_option_ty,Ys: list_list_char] :
      ( hBOOL(list_a839443437t_char(Pa,Xs,Ys))
     => ( size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys) ) ) ).

tff(fact_8_list__all2__lengthD,axiom,
    ! [Pa: fun_op174240306y_bool,Xs: list_option_ty,Ys: list_ty] :
      ( hBOOL(list_a2039389316_ty_ty(Pa,Xs,Ys))
     => ( size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys) ) ) ).

tff(fact_9_list__all2__lengthD,axiom,
    ! [Pa: fun_op1696804347l_bool,Xs: list_option_ty,Ys: list_val] :
      ( hBOOL(list_a1073113293ty_val(Pa,Xs,Ys))
     => ( size_s1050794909ion_ty(Xs) = size_size_list_val(Ys) ) ) ).

tff(fact_10_list__all2__lengthD,axiom,
    ! [Pa: fun_op14579988r_bool,Xs: list_option_ty,Ys: list_exp_list_char] :
      ( hBOOL(list_a283687028t_char(Pa,Xs,Ys))
     => ( size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys) ) ) ).

tff(fact_11_list__all2__lengthD,axiom,
    ! [Pa: fun_ty_fun_ty_bool,Xs: list_ty,Ys: list_ty] :
      ( hBOOL(list_all2_ty_ty(Pa,Xs,Ys))
     => ( size_size_list_ty(Xs) = size_size_list_ty(Ys) ) ) ).

tff(fact_12_list__all2__lengthD,axiom,
    ! [Pa: fun_val_fun_ty_bool,Xs: list_val,Ys: list_ty] :
      ( hBOOL(list_all2_val_ty(Pa,Xs,Ys))
     => ( size_size_list_val(Xs) = size_size_list_ty(Ys) ) ) ).

tff(fact_13_length__map,axiom,
    ! [F_1: fun_Pr1380325635t_char,Xs: list_P1916372464t_char] : size_s1010401542t_char(hAPP_l250787541t_char(map_Pr361633150t_char(F_1),Xs)) = size_s1010401542t_char(Xs) ).

tff(fact_14_length__map,axiom,
    ! [F_1: fun_Pr1898553187on_val,Xs: list_P507235360on_val] : size_s2086378294on_val(hAPP_l1208602837on_val(map_Pr1729094110on_val(F_1),Xs)) = size_s2086378294on_val(Xs) ).

tff(fact_15_length__map,axiom,
    ! [F_1: fun_Pr12181427on_val,Xs: list_P1439941640on_val] : size_s1699857438on_val(hAPP_l1695428693on_val(map_Pr1655409582on_val(F_1),Xs)) = size_s1699857438on_val(Xs) ).

tff(fact_16_length__map,axiom,
    ! [F_1: fun_op195029515t_char,Xs: list_option_ty] : size_s2113983095t_char(hAPP_l1368737135t_char(map_op1924521862t_char(F_1),Xs)) = size_s1050794909ion_ty(Xs) ).

tff(fact_17_length__map,axiom,
    ! [F_1: fun_option_ty_ty,Xs: list_option_ty] : size_size_list_ty(hAPP_l1583451544ist_ty(map_option_ty_ty(F_1),Xs)) = size_s1050794909ion_ty(Xs) ).

tff(fact_18_length__map,axiom,
    ! [F_1: fun_option_val_val,Xs: list_option_val] : size_size_list_val(hAPP_l228474410st_val(map_option_val_val(F_1),Xs)) = size_s1595297126on_val(Xs) ).

tff(fact_19_length__map,axiom,
    ! [F_1: fun_option_ty_val,Xs: list_option_ty] : size_size_list_val(hAPP_l336371937st_val(map_option_ty_val(F_1),Xs)) = size_s1050794909ion_ty(Xs) ).

tff(fact_20_length__map,axiom,
    ! [F_1: fun_op1508857234t_char,Xs: list_option_ty] : size_s1143674878t_char(hAPP_l330149622t_char(map_op1779340173t_char(F_1),Xs)) = size_s1050794909ion_ty(Xs) ).

tff(fact_21_length__map,axiom,
    ! [F_1: fun_li1432931796on_val,Xs: list_list_char] : size_s1595297126on_val(hAPP_l297961988on_val(map_li50976719on_val(F_1),Xs)) = size_s2113983095t_char(Xs) ).

tff(fact_22_length__map,axiom,
    ! [F_1: fun_li1751394789t_char,Xs: list_list_char] : size_s2113983095t_char(hAPP_l407174677t_char(map_li1333403488t_char(F_1),Xs)) = size_s2113983095t_char(Xs) ).

tff(fact_23_length__map,axiom,
    ! [F_1: fun_li688206603ion_ty,Xs: list_list_char] : size_s1050794909ion_ty(hAPP_l1491470139ion_ty(map_li771939206ion_ty(F_1),Xs)) = size_s2113983095t_char(Xs) ).

tff(fact_24_length__map,axiom,
    ! [F_1: fun_ex12316946ion_ty,Xs: list_exp_list_char] : size_s1050794909ion_ty(hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F_1),Xs)) = size_s1143674878t_char(Xs) ).

tff(fact_25_length__map,axiom,
    ! [F_1: fun_val_option_ty,Xs: list_val] : size_s1050794909ion_ty(hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Xs)) = size_size_list_val(Xs) ).

tff(fact_26_length__map,axiom,
    ! [F_1: fun_ty_option_ty,Xs: list_ty] : size_s1050794909ion_ty(hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Xs)) = size_size_list_ty(Xs) ).

tff(fact_27_length__map,axiom,
    ! [F_1: fun_va223928858t_char,Xs: list_val] : size_s1143674878t_char(hAPP_l732421366t_char(map_va1934808527t_char(F_1),Xs)) = size_size_list_val(Xs) ).

tff(fact_28_length__map,axiom,
    ! [F_1: fun_list_char_val,Xs: list_list_char] : size_size_list_val(hAPP_l1892737211st_val(map_list_char_val(F_1),Xs)) = size_s2113983095t_char(Xs) ).

tff(fact_29_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li1857149300t_char,Xs: list_list_char,G: fun_Pr1380325635t_char,Ys: list_P1916372464t_char] :
      ( ( hAPP_l1416713636t_char(map_li239070063t_char(F_1),Xs) = hAPP_l250787541t_char(map_Pr361633150t_char(G),Ys) )
     => ( size_s2113983095t_char(Xs) = size_s1010401542t_char(Ys) ) ) ).

tff(fact_30_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li328275876on_val,Xs: list_list_char,G: fun_Pr1898553187on_val,Ys: list_P507235360on_val] :
      ( ( hAPP_l2122855380on_val(map_li1925379487on_val(F_1),Xs) = hAPP_l1208602837on_val(map_Pr1729094110on_val(G),Ys) )
     => ( size_s2113983095t_char(Xs) = size_s2086378294on_val(Ys) ) ) ).

tff(fact_31_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li2145367436on_val,Xs: list_list_char,G: fun_Pr12181427on_val,Ys: list_P1439941640on_val] :
      ( ( hAPP_l418486716on_val(map_li1100402823on_val(F_1),Xs) = hAPP_l1695428693on_val(map_Pr1655409582on_val(G),Ys) )
     => ( size_s2113983095t_char(Xs) = size_s1699857438on_val(Ys) ) ) ).

tff(fact_32_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ty_val,Xs: list_ty,G: fun_option_val_val,Ys: list_option_val] :
      ( ( hAPP_l1530663448st_val(map_ty_val(F_1),Xs) = hAPP_l228474410st_val(map_option_val_val(G),Ys) )
     => ( size_size_list_ty(Xs) = size_s1595297126on_val(Ys) ) ) ).

tff(fact_33_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ty_option_val,Xs: list_ty,G: fun_li1432931796on_val,Ys: list_list_char] :
      ( ( hAPP_l1014734695on_val(map_ty_option_val(F_1),Xs) = hAPP_l297961988on_val(map_li50976719on_val(G),Ys) )
     => ( size_size_list_ty(Xs) = size_s2113983095t_char(Ys) ) ) ).

tff(fact_34_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ty_list_char,Xs: list_ty,G: fun_li1751394789t_char,Ys: list_list_char] :
      ( ( hAPP_l402740472t_char(map_ty_list_char(F_1),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys) )
     => ( size_size_list_ty(Xs) = size_s2113983095t_char(Ys) ) ) ).

tff(fact_35_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ty2043669721t_char,Xs: list_ty,G: fun_Pr1380325635t_char,Ys: list_P1916372464t_char] :
      ( ( hAPP_l1218266887t_char(map_ty1751634702t_char(F_1),Xs) = hAPP_l250787541t_char(map_Pr361633150t_char(G),Ys) )
     => ( size_size_list_ty(Xs) = size_s1010401542t_char(Ys) ) ) ).

tff(fact_36_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ty1366122761on_val,Xs: list_ty,G: fun_Pr1898553187on_val,Ys: list_P507235360on_val] :
      ( ( hAPP_l2092195639on_val(map_ty1597677374on_val(F_1),Xs) = hAPP_l1208602837on_val(map_Pr1729094110on_val(G),Ys) )
     => ( size_size_list_ty(Xs) = size_s2086378294on_val(Ys) ) ) ).

tff(fact_37_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ty2028523121on_val,Xs: list_ty,G: fun_Pr12181427on_val,Ys: list_P1439941640on_val] :
      ( ( hAPP_l1634001311on_val(map_ty891785382on_val(F_1),Xs) = hAPP_l1695428693on_val(map_Pr1655409582on_val(G),Ys) )
     => ( size_size_list_ty(Xs) = size_s1699857438on_val(Ys) ) ) ).

tff(fact_38_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_val_val,Xs: list_val,G: fun_option_val_val,Ys: list_option_val] :
      ( ( hAPP_l273806049st_val(map_val_val(F_1),Xs) = hAPP_l228474410st_val(map_option_val_val(G),Ys) )
     => ( size_size_list_val(Xs) = size_s1595297126on_val(Ys) ) ) ).

tff(fact_39_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_val_option_val,Xs: list_val,G: fun_li1432931796on_val,Ys: list_list_char] :
      ( ( hAPP_l761459294on_val(map_val_option_val(F_1),Xs) = hAPP_l297961988on_val(map_li50976719on_val(G),Ys) )
     => ( size_size_list_val(Xs) = size_s2113983095t_char(Ys) ) ) ).

tff(fact_40_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_val_list_char,Xs: list_val,G: fun_li1751394789t_char,Ys: list_list_char] :
      ( ( hAPP_l922645359t_char(map_val_list_char(F_1),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys) )
     => ( size_size_list_val(Xs) = size_s2113983095t_char(Ys) ) ) ).

tff(fact_41_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_va318401314t_char,Xs: list_val,G: fun_Pr1380325635t_char,Ys: list_P1916372464t_char] :
      ( ( hAPP_l1687586302t_char(map_va234578647t_char(F_1),Xs) = hAPP_l250787541t_char(map_Pr361633150t_char(G),Ys) )
     => ( size_size_list_val(Xs) = size_s1010401542t_char(Ys) ) ) ).

tff(fact_42_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_va358894930on_val,Xs: list_val,G: fun_Pr1898553187on_val,Ys: list_P507235360on_val] :
      ( ( hAPP_l1134997550on_val(map_va787979527on_val(F_1),Xs) = hAPP_l1208602837on_val(map_Pr1729094110on_val(G),Ys) )
     => ( size_size_list_val(Xs) = size_s2086378294on_val(Ys) ) ) ).

tff(fact_43_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_va172965946on_val,Xs: list_val,G: fun_Pr12181427on_val,Ys: list_P1439941640on_val] :
      ( ( hAPP_l382831894on_val(map_va527586287on_val(F_1),Xs) = hAPP_l1695428693on_val(map_Pr1655409582on_val(G),Ys) )
     => ( size_size_list_val(Xs) = size_s1699857438on_val(Ys) ) ) ).

tff(fact_44_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ex793263652ar_val,Xs: list_exp_list_char,G: fun_option_val_val,Ys: list_option_val] :
      ( ( hAPP_l1539861698st_val(map_ex740158547ar_val(F_1),Xs) = hAPP_l228474410st_val(map_option_val_val(G),Ys) )
     => ( size_s1143674878t_char(Xs) = size_s1595297126on_val(Ys) ) ) ).

tff(fact_45_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ex1158871131on_val,Xs: list_exp_list_char,G: fun_li1432931796on_val,Ys: list_list_char] :
      ( ( hAPP_l1607890493on_val(map_ex1598883030on_val(F_1),Xs) = hAPP_l297961988on_val(map_li50976719on_val(G),Ys) )
     => ( size_s1143674878t_char(Xs) = size_s2113983095t_char(Ys) ) ) ).

tff(fact_46_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ex1075505132t_char,Xs: list_exp_list_char,G: fun_li1751394789t_char,Ys: list_list_char] :
      ( ( hAPP_l2065413838t_char(map_ex2109939687t_char(F_1),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys) )
     => ( size_s1143674878t_char(Xs) = size_s2113983095t_char(Ys) ) ) ).

tff(fact_47_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ex360394747t_char,Xs: list_exp_list_char,G: fun_Pr1380325635t_char,Ys: list_P1916372464t_char] :
      ( ( hAPP_l1379210717t_char(map_ex230966390t_char(F_1),Xs) = hAPP_l250787541t_char(map_Pr361633150t_char(G),Ys) )
     => ( size_s1143674878t_char(Xs) = size_s1010401542t_char(Ys) ) ) ).

tff(fact_48_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ex1957978155on_val,Xs: list_exp_list_char,G: fun_Pr1898553187on_val,Ys: list_P507235360on_val] :
      ( ( hAPP_l1585742349on_val(map_ex2031894694on_val(F_1),Xs) = hAPP_l1208602837on_val(map_Pr1729094110on_val(G),Ys) )
     => ( size_s1143674878t_char(Xs) = size_s2086378294on_val(Ys) ) ) ).

tff(fact_49_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ex1732915347on_val,Xs: list_exp_list_char,G: fun_Pr12181427on_val,Ys: list_P1439941640on_val] :
      ( ( hAPP_l1557845365on_val(map_ex840371726on_val(F_1),Xs) = hAPP_l1695428693on_val(map_Pr1655409582on_val(G),Ys) )
     => ( size_s1143674878t_char(Xs) = size_s1699857438on_val(Ys) ) ) ).

tff(fact_50_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li1432931796on_val,Xs: list_list_char,G: fun_li1432931796on_val,Ys: list_list_char] :
      ( ( hAPP_l297961988on_val(map_li50976719on_val(F_1),Xs) = hAPP_l297961988on_val(map_li50976719on_val(G),Ys) )
     => ( size_s2113983095t_char(Xs) = size_s2113983095t_char(Ys) ) ) ).

tff(fact_51_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li1751394789t_char,Xs: list_list_char,G: fun_li1751394789t_char,Ys: list_list_char] :
      ( ( hAPP_l407174677t_char(map_li1333403488t_char(F_1),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys) )
     => ( size_s2113983095t_char(Xs) = size_s2113983095t_char(Ys) ) ) ).

tff(fact_52_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1380325635t_char,Xs: list_P1916372464t_char,G: fun_li1857149300t_char,Ys: list_list_char] :
      ( ( hAPP_l250787541t_char(map_Pr361633150t_char(F_1),Xs) = hAPP_l1416713636t_char(map_li239070063t_char(G),Ys) )
     => ( size_s1010401542t_char(Xs) = size_s2113983095t_char(Ys) ) ) ).

tff(fact_53_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1898553187on_val,Xs: list_P507235360on_val,G: fun_li328275876on_val,Ys: list_list_char] :
      ( ( hAPP_l1208602837on_val(map_Pr1729094110on_val(F_1),Xs) = hAPP_l2122855380on_val(map_li1925379487on_val(G),Ys) )
     => ( size_s2086378294on_val(Xs) = size_s2113983095t_char(Ys) ) ) ).

tff(fact_54_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr12181427on_val,Xs: list_P1439941640on_val,G: fun_li2145367436on_val,Ys: list_list_char] :
      ( ( hAPP_l1695428693on_val(map_Pr1655409582on_val(F_1),Xs) = hAPP_l418486716on_val(map_li1100402823on_val(G),Ys) )
     => ( size_s1699857438on_val(Xs) = size_s2113983095t_char(Ys) ) ) ).

tff(fact_55_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_option_val_val,Xs: list_option_val,G: fun_ty_val,Ys: list_ty] :
      ( ( hAPP_l228474410st_val(map_option_val_val(F_1),Xs) = hAPP_l1530663448st_val(map_ty_val(G),Ys) )
     => ( size_s1595297126on_val(Xs) = size_size_list_ty(Ys) ) ) ).

tff(fact_56_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li1432931796on_val,Xs: list_list_char,G: fun_ty_option_val,Ys: list_ty] :
      ( ( hAPP_l297961988on_val(map_li50976719on_val(F_1),Xs) = hAPP_l1014734695on_val(map_ty_option_val(G),Ys) )
     => ( size_s2113983095t_char(Xs) = size_size_list_ty(Ys) ) ) ).

tff(fact_57_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li1751394789t_char,Xs: list_list_char,G: fun_ty_list_char,Ys: list_ty] :
      ( ( hAPP_l407174677t_char(map_li1333403488t_char(F_1),Xs) = hAPP_l402740472t_char(map_ty_list_char(G),Ys) )
     => ( size_s2113983095t_char(Xs) = size_size_list_ty(Ys) ) ) ).

tff(fact_58_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1380325635t_char,Xs: list_P1916372464t_char,G: fun_ty2043669721t_char,Ys: list_ty] :
      ( ( hAPP_l250787541t_char(map_Pr361633150t_char(F_1),Xs) = hAPP_l1218266887t_char(map_ty1751634702t_char(G),Ys) )
     => ( size_s1010401542t_char(Xs) = size_size_list_ty(Ys) ) ) ).

tff(fact_59_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1898553187on_val,Xs: list_P507235360on_val,G: fun_ty1366122761on_val,Ys: list_ty] :
      ( ( hAPP_l1208602837on_val(map_Pr1729094110on_val(F_1),Xs) = hAPP_l2092195639on_val(map_ty1597677374on_val(G),Ys) )
     => ( size_s2086378294on_val(Xs) = size_size_list_ty(Ys) ) ) ).

tff(fact_60_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr12181427on_val,Xs: list_P1439941640on_val,G: fun_ty2028523121on_val,Ys: list_ty] :
      ( ( hAPP_l1695428693on_val(map_Pr1655409582on_val(F_1),Xs) = hAPP_l1634001311on_val(map_ty891785382on_val(G),Ys) )
     => ( size_s1699857438on_val(Xs) = size_size_list_ty(Ys) ) ) ).

tff(fact_61_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_option_val_val,Xs: list_option_val,G: fun_val_val,Ys: list_val] :
      ( ( hAPP_l228474410st_val(map_option_val_val(F_1),Xs) = hAPP_l273806049st_val(map_val_val(G),Ys) )
     => ( size_s1595297126on_val(Xs) = size_size_list_val(Ys) ) ) ).

tff(fact_62_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li1432931796on_val,Xs: list_list_char,G: fun_val_option_val,Ys: list_val] :
      ( ( hAPP_l297961988on_val(map_li50976719on_val(F_1),Xs) = hAPP_l761459294on_val(map_val_option_val(G),Ys) )
     => ( size_s2113983095t_char(Xs) = size_size_list_val(Ys) ) ) ).

tff(fact_63_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li1751394789t_char,Xs: list_list_char,G: fun_val_list_char,Ys: list_val] :
      ( ( hAPP_l407174677t_char(map_li1333403488t_char(F_1),Xs) = hAPP_l922645359t_char(map_val_list_char(G),Ys) )
     => ( size_s2113983095t_char(Xs) = size_size_list_val(Ys) ) ) ).

tff(fact_64_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1380325635t_char,Xs: list_P1916372464t_char,G: fun_va318401314t_char,Ys: list_val] :
      ( ( hAPP_l250787541t_char(map_Pr361633150t_char(F_1),Xs) = hAPP_l1687586302t_char(map_va234578647t_char(G),Ys) )
     => ( size_s1010401542t_char(Xs) = size_size_list_val(Ys) ) ) ).

tff(fact_65_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1898553187on_val,Xs: list_P507235360on_val,G: fun_va358894930on_val,Ys: list_val] :
      ( ( hAPP_l1208602837on_val(map_Pr1729094110on_val(F_1),Xs) = hAPP_l1134997550on_val(map_va787979527on_val(G),Ys) )
     => ( size_s2086378294on_val(Xs) = size_size_list_val(Ys) ) ) ).

tff(fact_66_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr12181427on_val,Xs: list_P1439941640on_val,G: fun_va172965946on_val,Ys: list_val] :
      ( ( hAPP_l1695428693on_val(map_Pr1655409582on_val(F_1),Xs) = hAPP_l382831894on_val(map_va527586287on_val(G),Ys) )
     => ( size_s1699857438on_val(Xs) = size_size_list_val(Ys) ) ) ).

tff(fact_67_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_option_val_val,Xs: list_option_val,G: fun_ex793263652ar_val,Ys: list_exp_list_char] :
      ( ( hAPP_l228474410st_val(map_option_val_val(F_1),Xs) = hAPP_l1539861698st_val(map_ex740158547ar_val(G),Ys) )
     => ( size_s1595297126on_val(Xs) = size_s1143674878t_char(Ys) ) ) ).

tff(fact_68_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li1432931796on_val,Xs: list_list_char,G: fun_ex1158871131on_val,Ys: list_exp_list_char] :
      ( ( hAPP_l297961988on_val(map_li50976719on_val(F_1),Xs) = hAPP_l1607890493on_val(map_ex1598883030on_val(G),Ys) )
     => ( size_s2113983095t_char(Xs) = size_s1143674878t_char(Ys) ) ) ).

tff(fact_69_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li1751394789t_char,Xs: list_list_char,G: fun_ex1075505132t_char,Ys: list_exp_list_char] :
      ( ( hAPP_l407174677t_char(map_li1333403488t_char(F_1),Xs) = hAPP_l2065413838t_char(map_ex2109939687t_char(G),Ys) )
     => ( size_s2113983095t_char(Xs) = size_s1143674878t_char(Ys) ) ) ).

tff(fact_70_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1380325635t_char,Xs: list_P1916372464t_char,G: fun_ex360394747t_char,Ys: list_exp_list_char] :
      ( ( hAPP_l250787541t_char(map_Pr361633150t_char(F_1),Xs) = hAPP_l1379210717t_char(map_ex230966390t_char(G),Ys) )
     => ( size_s1010401542t_char(Xs) = size_s1143674878t_char(Ys) ) ) ).

tff(fact_71_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1898553187on_val,Xs: list_P507235360on_val,G: fun_ex1957978155on_val,Ys: list_exp_list_char] :
      ( ( hAPP_l1208602837on_val(map_Pr1729094110on_val(F_1),Xs) = hAPP_l1585742349on_val(map_ex2031894694on_val(G),Ys) )
     => ( size_s2086378294on_val(Xs) = size_s1143674878t_char(Ys) ) ) ).

tff(fact_72_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr12181427on_val,Xs: list_P1439941640on_val,G: fun_ex1732915347on_val,Ys: list_exp_list_char] :
      ( ( hAPP_l1695428693on_val(map_Pr1655409582on_val(F_1),Xs) = hAPP_l1557845365on_val(map_ex840371726on_val(G),Ys) )
     => ( size_s1699857438on_val(Xs) = size_s1143674878t_char(Ys) ) ) ).

tff(fact_73_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_val_option_ty,Xs: list_val,G: fun_op1279324977ion_ty,Ys: list_option_ty] :
      ( ( hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Xs) = hAPP_l305548949ion_ty(map_op1363057580ion_ty(G),Ys) )
     => ( size_size_list_val(Xs) = size_s1050794909ion_ty(Ys) ) ) ).

tff(fact_74_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ty_option_ty,Xs: list_ty,G: fun_op1279324977ion_ty,Ys: list_option_ty] :
      ( ( hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Xs) = hAPP_l305548949ion_ty(map_op1363057580ion_ty(G),Ys) )
     => ( size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys) ) ) ).

tff(fact_75_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_va223928858t_char,Xs: list_val,G: fun_op1508857234t_char,Ys: list_option_ty] :
      ( ( hAPP_l732421366t_char(map_va1934808527t_char(F_1),Xs) = hAPP_l330149622t_char(map_op1779340173t_char(G),Ys) )
     => ( size_size_list_val(Xs) = size_s1050794909ion_ty(Ys) ) ) ).

tff(fact_76_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_list_char_val,Xs: list_list_char,G: fun_option_val_val,Ys: list_option_val] :
      ( ( hAPP_l1892737211st_val(map_list_char_val(F_1),Xs) = hAPP_l228474410st_val(map_option_val_val(G),Ys) )
     => ( size_s2113983095t_char(Xs) = size_s1595297126on_val(Ys) ) ) ).

tff(fact_77_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_list_char_val,Xs: list_list_char,G: fun_option_ty_val,Ys: list_option_ty] :
      ( ( hAPP_l1892737211st_val(map_list_char_val(F_1),Xs) = hAPP_l336371937st_val(map_option_ty_val(G),Ys) )
     => ( size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys) ) ) ).

tff(fact_78_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_op1279324977ion_ty,Xs: list_option_ty,G: fun_val_option_ty,Ys: list_val] :
      ( ( hAPP_l305548949ion_ty(map_op1363057580ion_ty(F_1),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys) )
     => ( size_s1050794909ion_ty(Xs) = size_size_list_val(Ys) ) ) ).

tff(fact_79_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_op1279324977ion_ty,Xs: list_option_ty,G: fun_ty_option_ty,Ys: list_ty] :
      ( ( hAPP_l305548949ion_ty(map_op1363057580ion_ty(F_1),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys) )
     => ( size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys) ) ) ).

tff(fact_80_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_op1508857234t_char,Xs: list_option_ty,G: fun_va223928858t_char,Ys: list_val] :
      ( ( hAPP_l330149622t_char(map_op1779340173t_char(F_1),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Ys) )
     => ( size_s1050794909ion_ty(Xs) = size_size_list_val(Ys) ) ) ).

tff(fact_81_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_option_val_val,Xs: list_option_val,G: fun_list_char_val,Ys: list_list_char] :
      ( ( hAPP_l228474410st_val(map_option_val_val(F_1),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Ys) )
     => ( size_s1595297126on_val(Xs) = size_s2113983095t_char(Ys) ) ) ).

tff(fact_82_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_option_ty_val,Xs: list_option_ty,G: fun_list_char_val,Ys: list_list_char] :
      ( ( hAPP_l336371937st_val(map_option_ty_val(F_1),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Ys) )
     => ( size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys) ) ) ).

tff(fact_83_prod__induct5,axiom,
    ! [X_1: produc349695911t_char,Pa: fun_Pr1895638121r_bool] :
      ( ! [A_1: produc1285161482t_char,B_1: list_list_char,C_4: list_ty,D_1: list_val,E_4: exp_list_char] : hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(produc24551831t_char(A_1),hAPP_P767818445t_char(produc921874948t_char(B_1),hAPP_P1392904962t_char(produc1909267824t_char(C_4),hAPP_e1752110927t_char(produc1916172923t_char(D_1),E_4))))))
     => hBOOL(hAPP_P824029447r_bool(Pa,X_1)) ) ).

tff(fact_84_prod__induct5,axiom,
    ! [X_1: produc1466422861on_val,Pa: fun_Pr302334223l_bool] :
      ( ! [A_1: produc430140671on_val,B_1: produc2061676504on_val,C_4: list_exp_list_char,D_1: fun_na939144002on_val,E_4: fun_li1432931796on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(produc1951691075on_val(A_1),hAPP_P658340954on_val(produc1611380469on_val(B_1),hAPP_P1963616220on_val(produc379668296on_val(C_4),hAPP_f1727192346on_val(produc899768717on_val(D_1),E_4))))))
     => hBOOL(hAPP_P2028072621l_bool(Pa,X_1)) ) ).

tff(fact_85_prod__induct5,axiom,
    ! [X_1: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
      ( ! [A_1: produc1102272487on_val,B_1: produc124828825on_val,C_4: exp_list_char,D_1: fun_na939144002on_val,E_4: fun_li1432931796on_val] : hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(produc1564932627on_val(A_1),hAPP_P1886180715on_val(produc1441475159on_val(B_1),hAPP_P604205461on_val(produc1259058957on_val(C_4),hAPP_f1727192346on_val(produc899768717on_val(D_1),E_4))))))
     => hBOOL(hAPP_P378063101l_bool(Pa,X_1)) ) ).

tff(fact_86_prod__cases5,axiom,
    ! [Y_6: produc349695911t_char] :
      ~ ! [A_1: produc1285161482t_char,B_1: list_list_char,C_4: list_ty,D_1: list_val,E_4: exp_list_char] : Y_6 != hAPP_P1539798428t_char(produc24551831t_char(A_1),hAPP_P767818445t_char(produc921874948t_char(B_1),hAPP_P1392904962t_char(produc1909267824t_char(C_4),hAPP_e1752110927t_char(produc1916172923t_char(D_1),E_4)))) ).

tff(fact_87_prod__cases5,axiom,
    ! [Y_3: produc1466422861on_val] :
      ~ ! [A_1: produc430140671on_val,B_1: produc2061676504on_val,C_4: list_exp_list_char,D_1: fun_na939144002on_val,E_4: fun_li1432931796on_val] : Y_3 != hAPP_P1758592847on_val(produc1951691075on_val(A_1),hAPP_P658340954on_val(produc1611380469on_val(B_1),hAPP_P1963616220on_val(produc379668296on_val(C_4),hAPP_f1727192346on_val(produc899768717on_val(D_1),E_4)))) ).

tff(fact_88_prod__cases5,axiom,
    ! [Y_3: produc231486621on_val] :
      ~ ! [A_1: produc1102272487on_val,B_1: produc124828825on_val,C_4: exp_list_char,D_1: fun_na939144002on_val,E_4: fun_li1432931796on_val] : Y_3 != hAPP_P1486793863on_val(produc1564932627on_val(A_1),hAPP_P1886180715on_val(produc1441475159on_val(B_1),hAPP_P604205461on_val(produc1259058957on_val(C_4),hAPP_f1727192346on_val(produc899768717on_val(D_1),E_4)))) ).

tff(fact_89_prod__induct4,axiom,
    ! [X_1: produc1285161482t_char,Pa: fun_Pr227936640r_bool] :
      ( ! [A_1: list_list_char,B_1: list_ty,C_4: list_val,D_1: exp_list_char] : hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(produc921874948t_char(A_1),hAPP_P1392904962t_char(produc1909267824t_char(B_1),hAPP_e1752110927t_char(produc1916172923t_char(C_4),D_1)))))
     => hBOOL(hAPP_P92196306r_bool(Pa,X_1)) ) ).

tff(fact_90_prod__induct4,axiom,
    ! [X_1: produc1102272487on_val,Pa: fun_Pr691271849l_bool] :
      ( ! [A_1: produc124828825on_val,B_1: exp_list_char,C_4: fun_na939144002on_val,D_1: fun_li1432931796on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(produc1441475159on_val(A_1),hAPP_P604205461on_val(produc1259058957on_val(B_1),hAPP_f1727192346on_val(produc899768717on_val(C_4),D_1)))))
     => hBOOL(hAPP_P282169671l_bool(Pa,X_1)) ) ).

tff(fact_91_prod__induct4,axiom,
    ! [X_1: produc430140671on_val,Pa: fun_Pr859510977l_bool] :
      ( ! [A_1: produc2061676504on_val,B_1: list_exp_list_char,C_4: fun_na939144002on_val,D_1: fun_li1432931796on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(produc1611380469on_val(A_1),hAPP_P1963616220on_val(produc379668296on_val(B_1),hAPP_f1727192346on_val(produc899768717on_val(C_4),D_1)))))
     => hBOOL(hAPP_P1333315679l_bool(Pa,X_1)) ) ).

tff(fact_92_prod__induct4,axiom,
    ! [X_1: produc349695911t_char,Pa: fun_Pr1895638121r_bool] :
      ( ! [A_1: produc1285161482t_char,B_1: list_list_char,C_4: list_ty,D_1: produc662261637t_char] : hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(produc24551831t_char(A_1),hAPP_P767818445t_char(produc921874948t_char(B_1),hAPP_P1392904962t_char(produc1909267824t_char(C_4),D_1)))))
     => hBOOL(hAPP_P824029447r_bool(Pa,X_1)) ) ).

tff(fact_93_prod__induct4,axiom,
    ! [X_1: produc1406897475t_char,Pa: fun_Pr1728267013r_bool] :
      ( ! [A_1: produc220283002t_char,B_1: list_ty,C_4: list_val,D_1: exp_list_char] : hBOOL(hAPP_P1240100515r_bool(Pa,hAPP_P1333668416t_char(produc57279289t_char(A_1),hAPP_P1392904962t_char(produc1909267824t_char(B_1),hAPP_e1752110927t_char(produc1916172923t_char(C_4),D_1)))))
     => hBOOL(hAPP_P1240100515r_bool(Pa,X_1)) ) ).

tff(fact_94_prod__induct4,axiom,
    ! [X_1: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
      ( ! [A_1: produc1102272487on_val,B_1: produc124828825on_val,C_4: exp_list_char,D_1: produc12694297on_val] : hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(produc1564932627on_val(A_1),hAPP_P1886180715on_val(produc1441475159on_val(B_1),hAPP_P604205461on_val(produc1259058957on_val(C_4),D_1)))))
     => hBOOL(hAPP_P378063101l_bool(Pa,X_1)) ) ).

tff(fact_95_prod__induct4,axiom,
    ! [X_1: produc1466422861on_val,Pa: fun_Pr302334223l_bool] :
      ( ! [A_1: produc430140671on_val,B_1: produc2061676504on_val,C_4: list_exp_list_char,D_1: produc12694297on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(produc1951691075on_val(A_1),hAPP_P658340954on_val(produc1611380469on_val(B_1),hAPP_P1963616220on_val(produc379668296on_val(C_4),D_1)))))
     => hBOOL(hAPP_P2028072621l_bool(Pa,X_1)) ) ).

tff(fact_96_prod__induct4,axiom,
    ! [X_1: produc630464863al_val,Pa: fun_Pr897334561l_bool] :
      ( ! [A_1: produc1645268488al_val,B_1: bop,C_4: val,D_1: val] : hBOOL(hAPP_P738987199l_bool(Pa,hAPP_P2123720426al_val(produc1924279125al_val(A_1),hAPP_P929466802al_val(produc621191550al_val(B_1),hAPP_v852496844al_val(product_Pair_val_val(C_4),D_1)))))
     => hBOOL(hAPP_P738987199l_bool(Pa,X_1)) ) ).

tff(fact_97_prod__cases4,axiom,
    ! [Y_5: produc1285161482t_char] :
      ~ ! [A_1: list_list_char,B_1: list_ty,C_4: list_val,D_1: exp_list_char] : Y_5 != hAPP_P767818445t_char(produc921874948t_char(A_1),hAPP_P1392904962t_char(produc1909267824t_char(B_1),hAPP_e1752110927t_char(produc1916172923t_char(C_4),D_1))) ).

tff(fact_98_prod__cases4,axiom,
    ! [Y_3: produc1102272487on_val] :
      ~ ! [A_1: produc124828825on_val,B_1: exp_list_char,C_4: fun_na939144002on_val,D_1: fun_li1432931796on_val] : Y_3 != hAPP_P1886180715on_val(produc1441475159on_val(A_1),hAPP_P604205461on_val(produc1259058957on_val(B_1),hAPP_f1727192346on_val(produc899768717on_val(C_4),D_1))) ).

tff(fact_99_prod__cases4,axiom,
    ! [Y_3: produc430140671on_val] :
      ~ ! [A_1: produc2061676504on_val,B_1: list_exp_list_char,C_4: fun_na939144002on_val,D_1: fun_li1432931796on_val] : Y_3 != hAPP_P658340954on_val(produc1611380469on_val(A_1),hAPP_P1963616220on_val(produc379668296on_val(B_1),hAPP_f1727192346on_val(produc899768717on_val(C_4),D_1))) ).

tff(fact_100_prod__cases4,axiom,
    ! [Y_5: produc349695911t_char] :
      ~ ! [A_1: produc1285161482t_char,B_1: list_list_char,C_4: list_ty,D_1: produc662261637t_char] : Y_5 != hAPP_P1539798428t_char(produc24551831t_char(A_1),hAPP_P767818445t_char(produc921874948t_char(B_1),hAPP_P1392904962t_char(produc1909267824t_char(C_4),D_1))) ).

tff(fact_101_prod__cases4,axiom,
    ! [Y_5: produc1406897475t_char] :
      ~ ! [A_1: produc220283002t_char,B_1: list_ty,C_4: list_val,D_1: exp_list_char] : Y_5 != hAPP_P1333668416t_char(produc57279289t_char(A_1),hAPP_P1392904962t_char(produc1909267824t_char(B_1),hAPP_e1752110927t_char(produc1916172923t_char(C_4),D_1))) ).

tff(fact_102_prod__cases4,axiom,
    ! [Y_3: produc231486621on_val] :
      ~ ! [A_1: produc1102272487on_val,B_1: produc124828825on_val,C_4: exp_list_char,D_1: produc12694297on_val] : Y_3 != hAPP_P1486793863on_val(produc1564932627on_val(A_1),hAPP_P1886180715on_val(produc1441475159on_val(B_1),hAPP_P604205461on_val(produc1259058957on_val(C_4),D_1))) ).

tff(fact_103_prod__cases4,axiom,
    ! [Y_3: produc1466422861on_val] :
      ~ ! [A_1: produc430140671on_val,B_1: produc2061676504on_val,C_4: list_exp_list_char,D_1: produc12694297on_val] : Y_3 != hAPP_P1758592847on_val(produc1951691075on_val(A_1),hAPP_P658340954on_val(produc1611380469on_val(B_1),hAPP_P1963616220on_val(produc379668296on_val(C_4),D_1))) ).

tff(fact_104_prod__cases4,axiom,
    ! [Y_5: produc630464863al_val] :
      ~ ! [A_1: produc1645268488al_val,B_1: bop,C_4: val,D_1: val] : Y_5 != hAPP_P2123720426al_val(produc1924279125al_val(A_1),hAPP_P929466802al_val(produc621191550al_val(B_1),hAPP_v852496844al_val(product_Pair_val_val(C_4),D_1))) ).

tff(fact_105_Pair__inject,axiom,
    ! [A_5: produc809539159t_char,B_4: produc809539159t_char,A_4: produc809539159t_char,B_3: produc809539159t_char] :
      ( ( hAPP_P1342907945t_char(produc1897818327t_char(A_5),B_4) = hAPP_P1342907945t_char(produc1897818327t_char(A_4),B_3) )
     => ~ ( ( A_5 = A_4 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_106_Pair__inject,axiom,
    ! [A_5: produc1278157519t_char,B_4: produc1278157519t_char,A_4: produc1278157519t_char,B_3: produc1278157519t_char] :
      ( ( hAPP_P1657265855t_char(produc2080520419t_char(A_5),B_4) = hAPP_P1657265855t_char(produc2080520419t_char(A_4),B_3) )
     => ~ ( ( A_5 = A_4 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_107_Pair__inject,axiom,
    ! [A_5: product_prod_val_val,B_4: product_prod_val_val,A_4: product_prod_val_val,B_3: product_prod_val_val] :
      ( ( hAPP_P47773639al_val(produc1244920211al_val(A_5),B_4) = hAPP_P47773639al_val(produc1244920211al_val(A_4),B_3) )
     => ~ ( ( A_5 = A_4 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_108_Pair__inject,axiom,
    ! [A_5: produc1645268488al_val,B_4: produc1645268488al_val,A_4: produc1645268488al_val,B_3: produc1645268488al_val] :
      ( ( hAPP_P2123720426al_val(produc1924279125al_val(A_5),B_4) = hAPP_P2123720426al_val(produc1924279125al_val(A_4),B_3) )
     => ~ ( ( A_5 = A_4 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_109_Pair__inject,axiom,
    ! [A: produc430140671on_val,B: produc430140671on_val,A_3: produc430140671on_val,B_2: produc430140671on_val] :
      ( ( hAPP_P1758592847on_val(produc1951691075on_val(A),B) = hAPP_P1758592847on_val(produc1951691075on_val(A_3),B_2) )
     => ~ ( ( A = A_3 )
         => ( B != B_2 ) ) ) ).

tff(fact_110_Pair__inject,axiom,
    ! [A: produc639455274on_val,B: produc639455274on_val,A_3: produc639455274on_val,B_2: produc639455274on_val] :
      ( ( hAPP_P330218428on_val(produc499151895on_val(A),B) = hAPP_P330218428on_val(produc499151895on_val(A_3),B_2) )
     => ~ ( ( A = A_3 )
         => ( B != B_2 ) ) ) ).

tff(fact_111_Pair__inject,axiom,
    ! [A: produc1102272487on_val,B: produc1102272487on_val,A_3: produc1102272487on_val,B_2: produc1102272487on_val] :
      ( ( hAPP_P1486793863on_val(produc1564932627on_val(A),B) = hAPP_P1486793863on_val(produc1564932627on_val(A_3),B_2) )
     => ~ ( ( A = A_3 )
         => ( B != B_2 ) ) ) ).

tff(fact_112_Pair__inject,axiom,
    ! [A: produc12694297on_val,B: produc12694297on_val,A_3: produc12694297on_val,B_2: produc12694297on_val] :
      ( ( hAPP_P291613419on_val(produc870913623on_val(A),B) = hAPP_P291613419on_val(produc870913623on_val(A_3),B_2) )
     => ~ ( ( A = A_3 )
         => ( B != B_2 ) ) ) ).

tff(fact_113_Pair__inject,axiom,
    ! [A_5: produc662261637t_char,B_4: produc662261637t_char,A_4: produc662261637t_char,B_3: produc662261637t_char] :
      ( ( hAPP_P1220989409t_char(produc1299387215t_char(A_5),B_4) = hAPP_P1220989409t_char(produc1299387215t_char(A_4),B_3) )
     => ~ ( ( A_5 = A_4 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_114_Pair__inject,axiom,
    ! [A_5: produc220283002t_char,B_4: produc220283002t_char,A_4: produc220283002t_char,B_3: produc220283002t_char] :
      ( ( hAPP_P1333668416t_char(produc57279289t_char(A_5),B_4) = hAPP_P1333668416t_char(produc57279289t_char(A_4),B_3) )
     => ~ ( ( A_5 = A_4 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_115_Pair__inject,axiom,
    ! [A_5: produc1285161482t_char,B_4: produc1285161482t_char,A_4: produc1285161482t_char,B_3: produc1285161482t_char] :
      ( ( hAPP_P1539798428t_char(produc24551831t_char(A_5),B_4) = hAPP_P1539798428t_char(produc24551831t_char(A_4),B_3) )
     => ~ ( ( A_5 = A_4 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_116_Pair__inject,axiom,
    ! [A_5: list_list_char,B_4: produc220283002t_char,A_4: list_list_char,B_3: produc220283002t_char] :
      ( ( hAPP_P767818445t_char(produc921874948t_char(A_5),B_4) = hAPP_P767818445t_char(produc921874948t_char(A_4),B_3) )
     => ~ ( ( A_5 = A_4 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_117_Pair__inject,axiom,
    ! [A_5: list_ty,B_4: produc662261637t_char,A_4: list_ty,B_3: produc662261637t_char] :
      ( ( hAPP_P1392904962t_char(produc1909267824t_char(A_5),B_4) = hAPP_P1392904962t_char(produc1909267824t_char(A_4),B_3) )
     => ~ ( ( A_5 = A_4 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_118_Pair__inject,axiom,
    ! [A_5: list_val,B_4: exp_list_char,A_4: list_val,B_3: exp_list_char] :
      ( ( hAPP_e1752110927t_char(produc1916172923t_char(A_5),B_4) = hAPP_e1752110927t_char(produc1916172923t_char(A_4),B_3) )
     => ~ ( ( A_5 = A_4 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_119_Pair__inject,axiom,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,A_3: fun_na939144002on_val,B_2: fun_li1432931796on_val] :
      ( ( hAPP_f1727192346on_val(produc899768717on_val(A),B) = hAPP_f1727192346on_val(produc899768717on_val(A_3),B_2) )
     => ~ ( ( A = A_3 )
         => ( B != B_2 ) ) ) ).

tff(fact_120_Pair__inject,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,A_3: produc124828825on_val,B_2: produc124828825on_val] :
      ( ( hAPP_P1886180715on_val(produc1441475159on_val(A),B) = hAPP_P1886180715on_val(produc1441475159on_val(A_3),B_2) )
     => ~ ( ( A = A_3 )
         => ( B != B_2 ) ) ) ).

tff(fact_121_Pair__inject,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,A_3: exp_list_char,B_2: produc12694297on_val] :
      ( ( hAPP_P604205461on_val(produc1259058957on_val(A),B) = hAPP_P604205461on_val(produc1259058957on_val(A_3),B_2) )
     => ~ ( ( A = A_3 )
         => ( B != B_2 ) ) ) ).

tff(fact_122_Pair__inject,axiom,
    ! [A: list_char,B: fun_Pr806764899on_val,A_3: list_char,B_2: fun_Pr806764899on_val] :
      ( ( hAPP_f900686428on_val(produc823076510on_val(A),B) = hAPP_f900686428on_val(produc823076510on_val(A_3),B_2) )
     => ~ ( ( A = A_3 )
         => ( B != B_2 ) ) ) ).

tff(fact_123_Pair__inject,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,A_3: produc2061676504on_val,B_2: produc2061676504on_val] :
      ( ( hAPP_P658340954on_val(produc1611380469on_val(A),B) = hAPP_P658340954on_val(produc1611380469on_val(A_3),B_2) )
     => ~ ( ( A = A_3 )
         => ( B != B_2 ) ) ) ).

tff(fact_124_Pair__inject,axiom,
    ! [A: list_exp_list_char,B: produc12694297on_val,A_3: list_exp_list_char,B_2: produc12694297on_val] :
      ( ( hAPP_P1963616220on_val(produc379668296on_val(A),B) = hAPP_P1963616220on_val(produc379668296on_val(A_3),B_2) )
     => ~ ( ( A = A_3 )
         => ( B != B_2 ) ) ) ).

tff(fact_125_Pair__inject,axiom,
    ! [A_5: bop,B_4: product_prod_val_val,A_4: bop,B_3: product_prod_val_val] :
      ( ( hAPP_P929466802al_val(produc621191550al_val(A_5),B_4) = hAPP_P929466802al_val(produc621191550al_val(A_4),B_3) )
     => ~ ( ( A_5 = A_4 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_126_Pair__inject,axiom,
    ! [A_5: val,B_4: val,A_4: val,B_3: val] :
      ( ( hAPP_v852496844al_val(product_Pair_val_val(A_5),B_4) = hAPP_v852496844al_val(product_Pair_val_val(A_4),B_3) )
     => ~ ( ( A_5 = A_4 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_127_Pair__inject,axiom,
    ! [A_5: list_char,B_4: list_char,A_4: list_char,B_3: list_char] :
      ( ( hAPP_l2100324114t_char(produc5062597t_char(A_5),B_4) = hAPP_l2100324114t_char(produc5062597t_char(A_4),B_3) )
     => ~ ( ( A_5 = A_4 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_128_Pair__inject,axiom,
    ! [A_5: list_list_char,B_4: exp_list_char,A_4: list_list_char,B_3: exp_list_char] :
      ( ( hAPP_e952791821t_char(produc1147572817t_char(A_5),B_4) = hAPP_e952791821t_char(produc1147572817t_char(A_4),B_3) )
     => ~ ( ( A_5 = A_4 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_129_Pair__eq,axiom,
    ! [A: produc809539159t_char,B: produc809539159t_char,A_3: produc809539159t_char,B_2: produc809539159t_char] :
      ( ( hAPP_P1342907945t_char(produc1897818327t_char(A),B) = hAPP_P1342907945t_char(produc1897818327t_char(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_130_Pair__eq,axiom,
    ! [A: produc1278157519t_char,B: produc1278157519t_char,A_3: produc1278157519t_char,B_2: produc1278157519t_char] :
      ( ( hAPP_P1657265855t_char(produc2080520419t_char(A),B) = hAPP_P1657265855t_char(produc2080520419t_char(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_131_Pair__eq,axiom,
    ! [A: product_prod_val_val,B: product_prod_val_val,A_3: product_prod_val_val,B_2: product_prod_val_val] :
      ( ( hAPP_P47773639al_val(produc1244920211al_val(A),B) = hAPP_P47773639al_val(produc1244920211al_val(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_132_Pair__eq,axiom,
    ! [A: produc1645268488al_val,B: produc1645268488al_val,A_3: produc1645268488al_val,B_2: produc1645268488al_val] :
      ( ( hAPP_P2123720426al_val(produc1924279125al_val(A),B) = hAPP_P2123720426al_val(produc1924279125al_val(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_133_Pair__eq,axiom,
    ! [A: produc430140671on_val,B: produc430140671on_val,A_3: produc430140671on_val,B_2: produc430140671on_val] :
      ( ( hAPP_P1758592847on_val(produc1951691075on_val(A),B) = hAPP_P1758592847on_val(produc1951691075on_val(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_134_Pair__eq,axiom,
    ! [A: produc639455274on_val,B: produc639455274on_val,A_3: produc639455274on_val,B_2: produc639455274on_val] :
      ( ( hAPP_P330218428on_val(produc499151895on_val(A),B) = hAPP_P330218428on_val(produc499151895on_val(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_135_Pair__eq,axiom,
    ! [A: produc1102272487on_val,B: produc1102272487on_val,A_3: produc1102272487on_val,B_2: produc1102272487on_val] :
      ( ( hAPP_P1486793863on_val(produc1564932627on_val(A),B) = hAPP_P1486793863on_val(produc1564932627on_val(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_136_Pair__eq,axiom,
    ! [A: produc12694297on_val,B: produc12694297on_val,A_3: produc12694297on_val,B_2: produc12694297on_val] :
      ( ( hAPP_P291613419on_val(produc870913623on_val(A),B) = hAPP_P291613419on_val(produc870913623on_val(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_137_Pair__eq,axiom,
    ! [A: produc662261637t_char,B: produc662261637t_char,A_3: produc662261637t_char,B_2: produc662261637t_char] :
      ( ( hAPP_P1220989409t_char(produc1299387215t_char(A),B) = hAPP_P1220989409t_char(produc1299387215t_char(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_138_Pair__eq,axiom,
    ! [A: produc220283002t_char,B: produc220283002t_char,A_3: produc220283002t_char,B_2: produc220283002t_char] :
      ( ( hAPP_P1333668416t_char(produc57279289t_char(A),B) = hAPP_P1333668416t_char(produc57279289t_char(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_139_Pair__eq,axiom,
    ! [A: produc1285161482t_char,B: produc1285161482t_char,A_3: produc1285161482t_char,B_2: produc1285161482t_char] :
      ( ( hAPP_P1539798428t_char(produc24551831t_char(A),B) = hAPP_P1539798428t_char(produc24551831t_char(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_140_Pair__eq,axiom,
    ! [A: list_list_char,B: produc220283002t_char,A_3: list_list_char,B_2: produc220283002t_char] :
      ( ( hAPP_P767818445t_char(produc921874948t_char(A),B) = hAPP_P767818445t_char(produc921874948t_char(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_141_Pair__eq,axiom,
    ! [A: list_ty,B: produc662261637t_char,A_3: list_ty,B_2: produc662261637t_char] :
      ( ( hAPP_P1392904962t_char(produc1909267824t_char(A),B) = hAPP_P1392904962t_char(produc1909267824t_char(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_142_Pair__eq,axiom,
    ! [A: list_val,B: exp_list_char,A_3: list_val,B_2: exp_list_char] :
      ( ( hAPP_e1752110927t_char(produc1916172923t_char(A),B) = hAPP_e1752110927t_char(produc1916172923t_char(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_143_Pair__eq,axiom,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,A_3: fun_na939144002on_val,B_2: fun_li1432931796on_val] :
      ( ( hAPP_f1727192346on_val(produc899768717on_val(A),B) = hAPP_f1727192346on_val(produc899768717on_val(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_144_Pair__eq,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,A_3: produc124828825on_val,B_2: produc124828825on_val] :
      ( ( hAPP_P1886180715on_val(produc1441475159on_val(A),B) = hAPP_P1886180715on_val(produc1441475159on_val(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_145_Pair__eq,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,A_3: exp_list_char,B_2: produc12694297on_val] :
      ( ( hAPP_P604205461on_val(produc1259058957on_val(A),B) = hAPP_P604205461on_val(produc1259058957on_val(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_146_Pair__eq,axiom,
    ! [A: list_char,B: fun_Pr806764899on_val,A_3: list_char,B_2: fun_Pr806764899on_val] :
      ( ( hAPP_f900686428on_val(produc823076510on_val(A),B) = hAPP_f900686428on_val(produc823076510on_val(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_147_Pair__eq,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,A_3: produc2061676504on_val,B_2: produc2061676504on_val] :
      ( ( hAPP_P658340954on_val(produc1611380469on_val(A),B) = hAPP_P658340954on_val(produc1611380469on_val(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_148_Pair__eq,axiom,
    ! [A: list_exp_list_char,B: produc12694297on_val,A_3: list_exp_list_char,B_2: produc12694297on_val] :
      ( ( hAPP_P1963616220on_val(produc379668296on_val(A),B) = hAPP_P1963616220on_val(produc379668296on_val(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_149_Pair__eq,axiom,
    ! [A: bop,B: product_prod_val_val,A_3: bop,B_2: product_prod_val_val] :
      ( ( hAPP_P929466802al_val(produc621191550al_val(A),B) = hAPP_P929466802al_val(produc621191550al_val(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_150_Pair__eq,axiom,
    ! [A: val,B: val,A_3: val,B_2: val] :
      ( ( hAPP_v852496844al_val(product_Pair_val_val(A),B) = hAPP_v852496844al_val(product_Pair_val_val(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_151_Pair__eq,axiom,
    ! [A: list_char,B: list_char,A_3: list_char,B_2: list_char] :
      ( ( hAPP_l2100324114t_char(produc5062597t_char(A),B) = hAPP_l2100324114t_char(produc5062597t_char(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_152_Pair__eq,axiom,
    ! [A: list_list_char,B: exp_list_char,A_3: list_list_char,B_2: exp_list_char] :
      ( ( hAPP_e952791821t_char(produc1147572817t_char(A),B) = hAPP_e952791821t_char(produc1147572817t_char(A_3),B_2) )
    <=> ( ( A = A_3 )
        & ( B = B_2 ) ) ) ).

tff(fact_153_split__paired__All,axiom,
    ! [Pa: fun_Pr908866473r_bool] :
      ( ! [X1: produc1534059751t_char] : hBOOL(hAPP_P1002912327r_bool(Pa,X1))
    <=> ! [A_1: produc809539159t_char,B_1: produc809539159t_char] : hBOOL(hAPP_P1002912327r_bool(Pa,hAPP_P1342907945t_char(produc1897818327t_char(A_1),B_1))) ) ).

tff(fact_154_split__paired__All,axiom,
    ! [Pa: fun_Pr1336847023r_bool] :
      ( ! [X1: produc1350825965t_char] : hBOOL(hAPP_P2010574925r_bool(Pa,X1))
    <=> ! [A_1: produc1278157519t_char,B_1: produc1278157519t_char] : hBOOL(hAPP_P2010574925r_bool(Pa,hAPP_P1657265855t_char(produc2080520419t_char(A_1),B_1))) ) ).

tff(fact_155_split__paired__All,axiom,
    ! [Pa: fun_Pr832147423l_bool] :
      ( ! [X1: produc800118557al_val] : hBOOL(hAPP_P2123002749l_bool(Pa,X1))
    <=> ! [A_1: product_prod_val_val,B_1: product_prod_val_val] : hBOOL(hAPP_P2123002749l_bool(Pa,hAPP_P47773639al_val(produc1244920211al_val(A_1),B_1))) ) ).

tff(fact_156_split__paired__All,axiom,
    ! [Pa: fun_Pr897334561l_bool] :
      ( ! [X1: produc630464863al_val] : hBOOL(hAPP_P738987199l_bool(Pa,X1))
    <=> ! [A_1: produc1645268488al_val,B_1: produc1645268488al_val] : hBOOL(hAPP_P738987199l_bool(Pa,hAPP_P2123720426al_val(produc1924279125al_val(A_1),B_1))) ) ).

tff(fact_157_split__paired__All,axiom,
    ! [Pa: fun_Pr302334223l_bool] :
      ( ! [X1: produc1466422861on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,X1))
    <=> ! [A_1: produc430140671on_val,B_1: produc430140671on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(produc1951691075on_val(A_1),B_1))) ) ).

tff(fact_158_split__paired__All,axiom,
    ! [Pa: fun_Pr235369833l_bool] :
      ( ! [X1: produc87279271on_val] : hBOOL(hAPP_P124632071l_bool(Pa,X1))
    <=> ! [A_1: produc639455274on_val,B_1: produc639455274on_val] : hBOOL(hAPP_P124632071l_bool(Pa,hAPP_P330218428on_val(produc499151895on_val(A_1),B_1))) ) ).

tff(fact_159_split__paired__All,axiom,
    ! [Pa: fun_Pr903661919l_bool] :
      ( ! [X1: produc231486621on_val] : hBOOL(hAPP_P378063101l_bool(Pa,X1))
    <=> ! [A_1: produc1102272487on_val,B_1: produc1102272487on_val] : hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(produc1564932627on_val(A_1),B_1))) ) ).

tff(fact_160_split__paired__All,axiom,
    ! [Pa: fun_Pr693020585l_bool] :
      ( ! [X1: produc409205479on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,X1))
    <=> ! [A_1: produc12694297on_val,B_1: produc12694297on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,hAPP_P291613419on_val(produc870913623on_val(A_1),B_1))) ) ).

tff(fact_161_split__paired__All,axiom,
    ! [Pa: fun_Pr1890037787r_bool] :
      ( ! [X1: produc1826280281t_char] : hBOOL(hAPP_P1183499705r_bool(Pa,X1))
    <=> ! [A_1: produc662261637t_char,B_1: produc662261637t_char] : hBOOL(hAPP_P1183499705r_bool(Pa,hAPP_P1220989409t_char(produc1299387215t_char(A_1),B_1))) ) ).

tff(fact_162_split__paired__All,axiom,
    ! [Pa: fun_Pr1728267013r_bool] :
      ( ! [X1: produc1406897475t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,X1))
    <=> ! [A_1: produc220283002t_char,B_1: produc220283002t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,hAPP_P1333668416t_char(produc57279289t_char(A_1),B_1))) ) ).

tff(fact_163_split__paired__All,axiom,
    ! [Pa: fun_Pr1895638121r_bool] :
      ( ! [X1: produc349695911t_char] : hBOOL(hAPP_P824029447r_bool(Pa,X1))
    <=> ! [A_1: produc1285161482t_char,B_1: produc1285161482t_char] : hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(produc24551831t_char(A_1),B_1))) ) ).

tff(fact_164_split__paired__All,axiom,
    ! [Pa: fun_Pr227936640r_bool] :
      ( ! [X1: produc1285161482t_char] : hBOOL(hAPP_P92196306r_bool(Pa,X1))
    <=> ! [A_1: list_list_char,B_1: produc220283002t_char] : hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(produc921874948t_char(A_1),B_1))) ) ).

tff(fact_165_split__paired__All,axiom,
    ! [Pa: fun_Pr46158268r_bool] :
      ( ! [X1: produc220283002t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,X1))
    <=> ! [A_1: list_ty,B_1: produc662261637t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,hAPP_P1392904962t_char(produc1909267824t_char(A_1),B_1))) ) ).

tff(fact_166_split__paired__All,axiom,
    ! [Pa: fun_Pr827765831r_bool] :
      ( ! [X1: produc662261637t_char] : hBOOL(hAPP_P2118621157r_bool(Pa,X1))
    <=> ! [A_1: list_val,B_1: exp_list_char] : hBOOL(hAPP_P2118621157r_bool(Pa,hAPP_e1752110927t_char(produc1916172923t_char(A_1),B_1))) ) ).

tff(fact_167_split__paired__All,axiom,
    ! [Pa: fun_Pr1696029455l_bool] :
      ( ! [X1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
    <=> ! [A_1: fun_na939144002on_val,B_1: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(Pa,hAPP_f1727192346on_val(produc899768717on_val(A_1),B_1))) ) ).

tff(fact_168_split__paired__All,axiom,
    ! [Pa: fun_Pr691271849l_bool] :
      ( ! [X1: produc1102272487on_val] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
    <=> ! [A_1: produc124828825on_val,B_1: produc124828825on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(produc1441475159on_val(A_1),B_1))) ) ).

tff(fact_169_split__paired__All,axiom,
    ! [Pa: fun_Pr680585871l_bool] :
      ( ! [X1: produc124828825on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
    <=> ! [A_1: exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(produc1259058957on_val(A_1),B_1))) ) ).

tff(fact_170_split__paired__All,axiom,
    ! [Pa: fun_Pr315804320l_bool] :
      ( ! [X1: produc639455274on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,X1))
    <=> ! [A_1: list_char,B_1: fun_Pr806764899on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,hAPP_f900686428on_val(produc823076510on_val(A_1),B_1))) ) ).

tff(fact_171_split__paired__All,axiom,
    ! [Pa: fun_Pr859510977l_bool] :
      ( ! [X1: produc430140671on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,X1))
    <=> ! [A_1: produc2061676504on_val,B_1: produc2061676504on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(produc1611380469on_val(A_1),B_1))) ) ).

tff(fact_172_split__paired__All,axiom,
    ! [Pa: fun_Pr248118298l_bool] :
      ( ! [X1: produc2061676504on_val] : hBOOL(hAPP_P71593144l_bool(Pa,X1))
    <=> ! [A_1: list_exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P71593144l_bool(Pa,hAPP_P1963616220on_val(produc379668296on_val(A_1),B_1))) ) ).

tff(fact_173_split__paired__All,axiom,
    ! [Pa: fun_Pr252072522l_bool] :
      ( ! [X1: produc1645268488al_val] : hBOOL(hAPP_P943837928l_bool(Pa,X1))
    <=> ! [A_1: bop,B_1: product_prod_val_val] : hBOOL(hAPP_P943837928l_bool(Pa,hAPP_P929466802al_val(produc621191550al_val(A_1),B_1))) ) ).

tff(fact_174_split__paired__All,axiom,
    ! [Pa: fun_Pr2081272681l_bool] :
      ( ! [X1: product_prod_val_val] : hBOOL(hAPP_P929938951l_bool(Pa,X1))
    <=> ! [A_1: val,B_1: val] : hBOOL(hAPP_P929938951l_bool(Pa,hAPP_v852496844al_val(product_Pair_val_val(A_1),B_1))) ) ).

tff(fact_175_split__paired__All,axiom,
    ! [Pa: fun_Pr565113489r_bool] :
      ( ! [X1: produc1278157519t_char] : hBOOL(hAPP_P449474095r_bool(Pa,X1))
    <=> ! [A_1: list_char,B_1: list_char] : hBOOL(hAPP_P449474095r_bool(Pa,hAPP_l2100324114t_char(produc5062597t_char(A_1),B_1))) ) ).

tff(fact_176_split__paired__All,axiom,
    ! [Pa: fun_Pr1336948301r_bool] :
      ( ! [X1: produc809539159t_char] : hBOOL(hAPP_P2014166431r_bool(Pa,X1))
    <=> ! [A_1: list_list_char,B_1: exp_list_char] : hBOOL(hAPP_P2014166431r_bool(Pa,hAPP_e952791821t_char(produc1147572817t_char(A_1),B_1))) ) ).

tff(fact_177_neq__if__length__neq,axiom,
    ! [Xs_2: list_option_ty,Ys_2: list_option_ty] :
      ( ( size_s1050794909ion_ty(Xs_2) != size_s1050794909ion_ty(Ys_2) )
     => ( Xs_2 != Ys_2 ) ) ).

tff(fact_178_neq__if__length__neq,axiom,
    ! [Xs_2: list_list_char,Ys_2: list_list_char] :
      ( ( size_s2113983095t_char(Xs_2) != size_s2113983095t_char(Ys_2) )
     => ( Xs_2 != Ys_2 ) ) ).

tff(fact_179_neq__if__length__neq,axiom,
    ! [Xs_2: list_ty,Ys_2: list_ty] :
      ( ( size_size_list_ty(Xs_2) != size_size_list_ty(Ys_2) )
     => ( Xs_2 != Ys_2 ) ) ).

tff(fact_180_neq__if__length__neq,axiom,
    ! [Xs_2: list_val,Ys_2: list_val] :
      ( ( size_size_list_val(Xs_2) != size_size_list_val(Ys_2) )
     => ( Xs_2 != Ys_2 ) ) ).

tff(fact_181_neq__if__length__neq,axiom,
    ! [Xs_2: list_exp_list_char,Ys_2: list_exp_list_char] :
      ( ( size_s1143674878t_char(Xs_2) != size_s1143674878t_char(Ys_2) )
     => ( Xs_2 != Ys_2 ) ) ).

tff(fact_182_list__all2__eq,axiom,
    ! [Xs: list_ty,Ys: list_ty] :
      ( ( Xs = Ys )
    <=> hBOOL(list_all2_ty_ty(fequal_ty,Xs,Ys)) ) ).

tff(fact_183_widen__trans,axiom,
    ! [T_5: ty,P_3: list_P1999446415t_char,S_4: ty,U_1: ty] :
      ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_3),S_4),U_1))
     => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_3),U_1),T_5))
       => hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_3),S_4),T_5)) ) ) ).

tff(fact_184_prod__cases3,axiom,
    ! [Y_4: produc1285161482t_char] :
      ~ ! [A_1: list_list_char,B_1: list_ty,C_4: produc662261637t_char] : Y_4 != hAPP_P767818445t_char(produc921874948t_char(A_1),hAPP_P1392904962t_char(produc1909267824t_char(B_1),C_4)) ).

tff(fact_185_prod__cases3,axiom,
    ! [Y_4: produc220283002t_char] :
      ~ ! [A_1: list_ty,B_1: list_val,C_4: exp_list_char] : Y_4 != hAPP_P1392904962t_char(produc1909267824t_char(A_1),hAPP_e1752110927t_char(produc1916172923t_char(B_1),C_4)) ).

tff(fact_186_prod__cases3,axiom,
    ! [Y_3: produc1102272487on_val] :
      ~ ! [A_1: produc124828825on_val,B_1: exp_list_char,C_4: produc12694297on_val] : Y_3 != hAPP_P1886180715on_val(produc1441475159on_val(A_1),hAPP_P604205461on_val(produc1259058957on_val(B_1),C_4)) ).

tff(fact_187_prod__cases3,axiom,
    ! [Y_3: produc124828825on_val] :
      ~ ! [A_1: exp_list_char,B_1: fun_na939144002on_val,C_4: fun_li1432931796on_val] : Y_3 != hAPP_P604205461on_val(produc1259058957on_val(A_1),hAPP_f1727192346on_val(produc899768717on_val(B_1),C_4)) ).

tff(fact_188_prod__cases3,axiom,
    ! [Y_3: produc430140671on_val] :
      ~ ! [A_1: produc2061676504on_val,B_1: list_exp_list_char,C_4: produc12694297on_val] : Y_3 != hAPP_P658340954on_val(produc1611380469on_val(A_1),hAPP_P1963616220on_val(produc379668296on_val(B_1),C_4)) ).

tff(fact_189_prod__cases3,axiom,
    ! [Y_3: produc2061676504on_val] :
      ~ ! [A_1: list_exp_list_char,B_1: fun_na939144002on_val,C_4: fun_li1432931796on_val] : Y_3 != hAPP_P1963616220on_val(produc379668296on_val(A_1),hAPP_f1727192346on_val(produc899768717on_val(B_1),C_4)) ).

tff(fact_190_prod__cases3,axiom,
    ! [Y_4: produc1645268488al_val] :
      ~ ! [A_1: bop,B_1: val,C_4: val] : Y_4 != hAPP_P929466802al_val(produc621191550al_val(A_1),hAPP_v852496844al_val(product_Pair_val_val(B_1),C_4)) ).

tff(fact_191_prod__cases3,axiom,
    ! [Y_4: produc349695911t_char] :
      ~ ! [A_1: produc1285161482t_char,B_1: list_list_char,C_4: produc220283002t_char] : Y_4 != hAPP_P1539798428t_char(produc24551831t_char(A_1),hAPP_P767818445t_char(produc921874948t_char(B_1),C_4)) ).

tff(fact_192_prod__cases3,axiom,
    ! [Y_4: produc1406897475t_char] :
      ~ ! [A_1: produc220283002t_char,B_1: list_ty,C_4: produc662261637t_char] : Y_4 != hAPP_P1333668416t_char(produc57279289t_char(A_1),hAPP_P1392904962t_char(produc1909267824t_char(B_1),C_4)) ).

tff(fact_193_prod__cases3,axiom,
    ! [Y_4: produc1826280281t_char] :
      ~ ! [A_1: produc662261637t_char,B_1: list_val,C_4: exp_list_char] : Y_4 != hAPP_P1220989409t_char(produc1299387215t_char(A_1),hAPP_e1752110927t_char(produc1916172923t_char(B_1),C_4)) ).

tff(fact_194_prod__cases3,axiom,
    ! [Y_3: produc409205479on_val] :
      ~ ! [A_1: produc12694297on_val,B_1: fun_na939144002on_val,C_4: fun_li1432931796on_val] : Y_3 != hAPP_P291613419on_val(produc870913623on_val(A_1),hAPP_f1727192346on_val(produc899768717on_val(B_1),C_4)) ).

tff(fact_195_prod__cases3,axiom,
    ! [Y_3: produc231486621on_val] :
      ~ ! [A_1: produc1102272487on_val,B_1: produc124828825on_val,C_4: produc124828825on_val] : Y_3 != hAPP_P1486793863on_val(produc1564932627on_val(A_1),hAPP_P1886180715on_val(produc1441475159on_val(B_1),C_4)) ).

tff(fact_196_prod__cases3,axiom,
    ! [Y_3: produc87279271on_val] :
      ~ ! [A_1: produc639455274on_val,B_1: list_char,C_4: fun_Pr806764899on_val] : Y_3 != hAPP_P330218428on_val(produc499151895on_val(A_1),hAPP_f900686428on_val(produc823076510on_val(B_1),C_4)) ).

tff(fact_197_prod__cases3,axiom,
    ! [Y_3: produc1466422861on_val] :
      ~ ! [A_1: produc430140671on_val,B_1: produc2061676504on_val,C_4: produc2061676504on_val] : Y_3 != hAPP_P1758592847on_val(produc1951691075on_val(A_1),hAPP_P658340954on_val(produc1611380469on_val(B_1),C_4)) ).

tff(fact_198_prod__cases3,axiom,
    ! [Y_4: produc630464863al_val] :
      ~ ! [A_1: produc1645268488al_val,B_1: bop,C_4: product_prod_val_val] : Y_4 != hAPP_P2123720426al_val(produc1924279125al_val(A_1),hAPP_P929466802al_val(produc621191550al_val(B_1),C_4)) ).

tff(fact_199_prod__cases3,axiom,
    ! [Y_4: produc800118557al_val] :
      ~ ! [A_1: product_prod_val_val,B_1: val,C_4: val] : Y_4 != hAPP_P47773639al_val(produc1244920211al_val(A_1),hAPP_v852496844al_val(product_Pair_val_val(B_1),C_4)) ).

tff(fact_200_prod__cases3,axiom,
    ! [Y_4: produc1350825965t_char] :
      ~ ! [A_1: produc1278157519t_char,B_1: list_char,C_4: list_char] : Y_4 != hAPP_P1657265855t_char(produc2080520419t_char(A_1),hAPP_l2100324114t_char(produc5062597t_char(B_1),C_4)) ).

tff(fact_201_prod__cases3,axiom,
    ! [Y_4: produc1534059751t_char] :
      ~ ! [A_1: produc809539159t_char,B_1: list_list_char,C_4: exp_list_char] : Y_4 != hAPP_P1342907945t_char(produc1897818327t_char(A_1),hAPP_e952791821t_char(produc1147572817t_char(B_1),C_4)) ).

tff(fact_202_prod__induct3,axiom,
    ! [X_1: produc1285161482t_char,Pa: fun_Pr227936640r_bool] :
      ( ! [A_1: list_list_char,B_1: list_ty,C_4: produc662261637t_char] : hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(produc921874948t_char(A_1),hAPP_P1392904962t_char(produc1909267824t_char(B_1),C_4))))
     => hBOOL(hAPP_P92196306r_bool(Pa,X_1)) ) ).

tff(fact_203_prod__induct3,axiom,
    ! [X_1: produc220283002t_char,Pa: fun_Pr46158268r_bool] :
      ( ! [A_1: list_ty,B_1: list_val,C_4: exp_list_char] : hBOOL(hAPP_P1907982426r_bool(Pa,hAPP_P1392904962t_char(produc1909267824t_char(A_1),hAPP_e1752110927t_char(produc1916172923t_char(B_1),C_4))))
     => hBOOL(hAPP_P1907982426r_bool(Pa,X_1)) ) ).

tff(fact_204_prod__induct3,axiom,
    ! [X_1: produc1102272487on_val,Pa: fun_Pr691271849l_bool] :
      ( ! [A_1: produc124828825on_val,B_1: exp_list_char,C_4: produc12694297on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(produc1441475159on_val(A_1),hAPP_P604205461on_val(produc1259058957on_val(B_1),C_4))))
     => hBOOL(hAPP_P282169671l_bool(Pa,X_1)) ) ).

tff(fact_205_prod__induct3,axiom,
    ! [X_1: produc124828825on_val,Pa: fun_Pr680585871l_bool] :
      ( ! [A_1: exp_list_char,B_1: fun_na939144002on_val,C_4: fun_li1432931796on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(produc1259058957on_val(A_1),hAPP_f1727192346on_val(produc899768717on_val(B_1),C_4))))
     => hBOOL(hAPP_P1708370145l_bool(Pa,X_1)) ) ).

tff(fact_206_prod__induct3,axiom,
    ! [X_1: produc430140671on_val,Pa: fun_Pr859510977l_bool] :
      ( ! [A_1: produc2061676504on_val,B_1: list_exp_list_char,C_4: produc12694297on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(produc1611380469on_val(A_1),hAPP_P1963616220on_val(produc379668296on_val(B_1),C_4))))
     => hBOOL(hAPP_P1333315679l_bool(Pa,X_1)) ) ).

tff(fact_207_prod__induct3,axiom,
    ! [X_1: produc2061676504on_val,Pa: fun_Pr248118298l_bool] :
      ( ! [A_1: list_exp_list_char,B_1: fun_na939144002on_val,C_4: fun_li1432931796on_val] : hBOOL(hAPP_P71593144l_bool(Pa,hAPP_P1963616220on_val(produc379668296on_val(A_1),hAPP_f1727192346on_val(produc899768717on_val(B_1),C_4))))
     => hBOOL(hAPP_P71593144l_bool(Pa,X_1)) ) ).

tff(fact_208_prod__induct3,axiom,
    ! [X_1: produc1645268488al_val,Pa: fun_Pr252072522l_bool] :
      ( ! [A_1: bop,B_1: val,C_4: val] : hBOOL(hAPP_P943837928l_bool(Pa,hAPP_P929466802al_val(produc621191550al_val(A_1),hAPP_v852496844al_val(product_Pair_val_val(B_1),C_4))))
     => hBOOL(hAPP_P943837928l_bool(Pa,X_1)) ) ).

tff(fact_209_prod__induct3,axiom,
    ! [X_1: produc349695911t_char,Pa: fun_Pr1895638121r_bool] :
      ( ! [A_1: produc1285161482t_char,B_1: list_list_char,C_4: produc220283002t_char] : hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(produc24551831t_char(A_1),hAPP_P767818445t_char(produc921874948t_char(B_1),C_4))))
     => hBOOL(hAPP_P824029447r_bool(Pa,X_1)) ) ).

tff(fact_210_prod__induct3,axiom,
    ! [X_1: produc1406897475t_char,Pa: fun_Pr1728267013r_bool] :
      ( ! [A_1: produc220283002t_char,B_1: list_ty,C_4: produc662261637t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,hAPP_P1333668416t_char(produc57279289t_char(A_1),hAPP_P1392904962t_char(produc1909267824t_char(B_1),C_4))))
     => hBOOL(hAPP_P1240100515r_bool(Pa,X_1)) ) ).

tff(fact_211_prod__induct3,axiom,
    ! [X_1: produc1826280281t_char,Pa: fun_Pr1890037787r_bool] :
      ( ! [A_1: produc662261637t_char,B_1: list_val,C_4: exp_list_char] : hBOOL(hAPP_P1183499705r_bool(Pa,hAPP_P1220989409t_char(produc1299387215t_char(A_1),hAPP_e1752110927t_char(produc1916172923t_char(B_1),C_4))))
     => hBOOL(hAPP_P1183499705r_bool(Pa,X_1)) ) ).

tff(fact_212_prod__induct3,axiom,
    ! [X_1: produc409205479on_val,Pa: fun_Pr693020585l_bool] :
      ( ! [A_1: produc12694297on_val,B_1: fun_na939144002on_val,C_4: fun_li1432931796on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,hAPP_P291613419on_val(produc870913623on_val(A_1),hAPP_f1727192346on_val(produc899768717on_val(B_1),C_4))))
     => hBOOL(hAPP_P1221872711l_bool(Pa,X_1)) ) ).

tff(fact_213_prod__induct3,axiom,
    ! [X_1: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
      ( ! [A_1: produc1102272487on_val,B_1: produc124828825on_val,C_4: produc124828825on_val] : hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(produc1564932627on_val(A_1),hAPP_P1886180715on_val(produc1441475159on_val(B_1),C_4))))
     => hBOOL(hAPP_P378063101l_bool(Pa,X_1)) ) ).

tff(fact_214_prod__induct3,axiom,
    ! [X_1: produc87279271on_val,Pa: fun_Pr235369833l_bool] :
      ( ! [A_1: produc639455274on_val,B_1: list_char,C_4: fun_Pr806764899on_val] : hBOOL(hAPP_P124632071l_bool(Pa,hAPP_P330218428on_val(produc499151895on_val(A_1),hAPP_f900686428on_val(produc823076510on_val(B_1),C_4))))
     => hBOOL(hAPP_P124632071l_bool(Pa,X_1)) ) ).

tff(fact_215_prod__induct3,axiom,
    ! [X_1: produc1466422861on_val,Pa: fun_Pr302334223l_bool] :
      ( ! [A_1: produc430140671on_val,B_1: produc2061676504on_val,C_4: produc2061676504on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(produc1951691075on_val(A_1),hAPP_P658340954on_val(produc1611380469on_val(B_1),C_4))))
     => hBOOL(hAPP_P2028072621l_bool(Pa,X_1)) ) ).

tff(fact_216_prod__induct3,axiom,
    ! [X_1: produc630464863al_val,Pa: fun_Pr897334561l_bool] :
      ( ! [A_1: produc1645268488al_val,B_1: bop,C_4: product_prod_val_val] : hBOOL(hAPP_P738987199l_bool(Pa,hAPP_P2123720426al_val(produc1924279125al_val(A_1),hAPP_P929466802al_val(produc621191550al_val(B_1),C_4))))
     => hBOOL(hAPP_P738987199l_bool(Pa,X_1)) ) ).

tff(fact_217_prod__induct3,axiom,
    ! [X_1: produc800118557al_val,Pa: fun_Pr832147423l_bool] :
      ( ! [A_1: product_prod_val_val,B_1: val,C_4: val] : hBOOL(hAPP_P2123002749l_bool(Pa,hAPP_P47773639al_val(produc1244920211al_val(A_1),hAPP_v852496844al_val(product_Pair_val_val(B_1),C_4))))
     => hBOOL(hAPP_P2123002749l_bool(Pa,X_1)) ) ).

tff(fact_218_prod__induct3,axiom,
    ! [X_1: produc1350825965t_char,Pa: fun_Pr1336847023r_bool] :
      ( ! [A_1: produc1278157519t_char,B_1: list_char,C_4: list_char] : hBOOL(hAPP_P2010574925r_bool(Pa,hAPP_P1657265855t_char(produc2080520419t_char(A_1),hAPP_l2100324114t_char(produc5062597t_char(B_1),C_4))))
     => hBOOL(hAPP_P2010574925r_bool(Pa,X_1)) ) ).

tff(fact_219_prod__induct3,axiom,
    ! [X_1: produc1534059751t_char,Pa: fun_Pr908866473r_bool] :
      ( ! [A_1: produc809539159t_char,B_1: list_list_char,C_4: exp_list_char] : hBOOL(hAPP_P1002912327r_bool(Pa,hAPP_P1342907945t_char(produc1897818327t_char(A_1),hAPP_e952791821t_char(produc1147572817t_char(B_1),C_4))))
     => hBOOL(hAPP_P1002912327r_bool(Pa,X_1)) ) ).

tff(fact_220_confs__conv__map,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,Vsa: list_val,Ts_1: list_ty] :
      ( hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa,Ts_1))
    <=> ? [Ts_2: list_ty] :
          ( ( hAPP_l2006940821ion_ty(map_val_option_ty(typeof_h(Ha)),Vsa) = hAPP_l1487035934ion_ty(map_ty_option_ty(some_ty),Ts_2) )
          & hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_2,Ts_1)) ) ) ).

tff(fact_221_list__all2__mono,axiom,
    ! [Q: fun_ty_fun_ty_bool,Pa: fun_ty_fun_ty_bool,Xs: list_ty,Ys: list_ty] :
      ( hBOOL(list_all2_ty_ty(Pa,Xs,Ys))
     => ( ! [Xs_1: ty,Ys_1: ty] :
            ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Pa,Xs_1),Ys_1))
           => hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Q,Xs_1),Ys_1)) )
       => hBOOL(list_all2_ty_ty(Q,Xs,Ys)) ) ) ).

tff(fact_222_list__all2__mono,axiom,
    ! [Q: fun_val_fun_ty_bool,Pa: fun_val_fun_ty_bool,Xs: list_val,Ys: list_ty] :
      ( hBOOL(list_all2_val_ty(Pa,Xs,Ys))
     => ( ! [Xs_1: val,Ys_1: ty] :
            ( hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(Pa,Xs_1),Ys_1))
           => hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(Q,Xs_1),Ys_1)) )
       => hBOOL(list_all2_val_ty(Q,Xs,Ys)) ) ) ).

tff(fact_223_list__all2__refl,axiom,
    ! [Xs: list_ty,Pa: fun_ty_fun_ty_bool] :
      ( ! [X_3: ty] : hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Pa,X_3),X_3))
     => hBOOL(list_all2_ty_ty(Pa,Xs,Xs)) ) ).

tff(fact_224_list__all2__antisym,axiom,
    ! [Xs: list_ty,Ys: list_ty,Q: fun_ty_fun_ty_bool,Pa: fun_ty_fun_ty_bool] :
      ( ! [X_3: ty,Y_1: ty] :
          ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Pa,X_3),Y_1))
         => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Q,Y_1),X_3))
           => ( X_3 = Y_1 ) ) )
     => ( hBOOL(list_all2_ty_ty(Pa,Xs,Ys))
       => ( hBOOL(list_all2_ty_ty(Q,Ys,Xs))
         => ( Xs = Ys ) ) ) ) ).

tff(fact_225_Ex__list__of__length,axiom,
    ! [N_1: nat] :
    ? [Xs_1: list_option_ty] : size_s1050794909ion_ty(Xs_1) = N_1 ).

tff(fact_226_Ex__list__of__length,axiom,
    ! [N_1: nat] :
    ? [Xs_1: list_list_char] : size_s2113983095t_char(Xs_1) = N_1 ).

tff(fact_227_Ex__list__of__length,axiom,
    ! [N_1: nat] :
    ? [Xs_1: list_ty] : size_size_list_ty(Xs_1) = N_1 ).

tff(fact_228_Ex__list__of__length,axiom,
    ! [N_1: nat] :
    ? [Xs_1: list_val] : size_size_list_val(Xs_1) = N_1 ).

tff(fact_229_Ex__list__of__length,axiom,
    ! [N_1: nat] :
    ? [Xs_1: list_exp_list_char] : size_s1143674878t_char(Xs_1) = N_1 ).

tff(fact_230_prod_Oexhaust,axiom,
    ! [Y_2: produc1534059751t_char] :
      ~ ! [A_1: produc809539159t_char,B_1: produc809539159t_char] : Y_2 != hAPP_P1342907945t_char(produc1897818327t_char(A_1),B_1) ).

tff(fact_231_prod_Oexhaust,axiom,
    ! [Y_2: produc1350825965t_char] :
      ~ ! [A_1: produc1278157519t_char,B_1: produc1278157519t_char] : Y_2 != hAPP_P1657265855t_char(produc2080520419t_char(A_1),B_1) ).

tff(fact_232_prod_Oexhaust,axiom,
    ! [Y_2: produc800118557al_val] :
      ~ ! [A_1: product_prod_val_val,B_1: product_prod_val_val] : Y_2 != hAPP_P47773639al_val(produc1244920211al_val(A_1),B_1) ).

tff(fact_233_prod_Oexhaust,axiom,
    ! [Y_2: produc630464863al_val] :
      ~ ! [A_1: produc1645268488al_val,B_1: produc1645268488al_val] : Y_2 != hAPP_P2123720426al_val(produc1924279125al_val(A_1),B_1) ).

tff(fact_234_prod_Oexhaust,axiom,
    ! [Y_3: produc1466422861on_val] :
      ~ ! [A_1: produc430140671on_val,B_1: produc430140671on_val] : Y_3 != hAPP_P1758592847on_val(produc1951691075on_val(A_1),B_1) ).

tff(fact_235_prod_Oexhaust,axiom,
    ! [Y_3: produc87279271on_val] :
      ~ ! [A_1: produc639455274on_val,B_1: produc639455274on_val] : Y_3 != hAPP_P330218428on_val(produc499151895on_val(A_1),B_1) ).

tff(fact_236_prod_Oexhaust,axiom,
    ! [Y_3: produc231486621on_val] :
      ~ ! [A_1: produc1102272487on_val,B_1: produc1102272487on_val] : Y_3 != hAPP_P1486793863on_val(produc1564932627on_val(A_1),B_1) ).

tff(fact_237_prod_Oexhaust,axiom,
    ! [Y_3: produc409205479on_val] :
      ~ ! [A_1: produc12694297on_val,B_1: produc12694297on_val] : Y_3 != hAPP_P291613419on_val(produc870913623on_val(A_1),B_1) ).

tff(fact_238_prod_Oexhaust,axiom,
    ! [Y_2: produc1826280281t_char] :
      ~ ! [A_1: produc662261637t_char,B_1: produc662261637t_char] : Y_2 != hAPP_P1220989409t_char(produc1299387215t_char(A_1),B_1) ).

tff(fact_239_prod_Oexhaust,axiom,
    ! [Y_2: produc1406897475t_char] :
      ~ ! [A_1: produc220283002t_char,B_1: produc220283002t_char] : Y_2 != hAPP_P1333668416t_char(produc57279289t_char(A_1),B_1) ).

tff(fact_240_prod_Oexhaust,axiom,
    ! [Y_2: produc349695911t_char] :
      ~ ! [A_1: produc1285161482t_char,B_1: produc1285161482t_char] : Y_2 != hAPP_P1539798428t_char(produc24551831t_char(A_1),B_1) ).

tff(fact_241_prod_Oexhaust,axiom,
    ! [Y_2: produc1285161482t_char] :
      ~ ! [A_1: list_list_char,B_1: produc220283002t_char] : Y_2 != hAPP_P767818445t_char(produc921874948t_char(A_1),B_1) ).

tff(fact_242_prod_Oexhaust,axiom,
    ! [Y_2: produc220283002t_char] :
      ~ ! [A_1: list_ty,B_1: produc662261637t_char] : Y_2 != hAPP_P1392904962t_char(produc1909267824t_char(A_1),B_1) ).

tff(fact_243_prod_Oexhaust,axiom,
    ! [Y_2: produc662261637t_char] :
      ~ ! [A_1: list_val,B_1: exp_list_char] : Y_2 != hAPP_e1752110927t_char(produc1916172923t_char(A_1),B_1) ).

tff(fact_244_prod_Oexhaust,axiom,
    ! [Y_3: produc12694297on_val] :
      ~ ! [A_1: fun_na939144002on_val,B_1: fun_li1432931796on_val] : Y_3 != hAPP_f1727192346on_val(produc899768717on_val(A_1),B_1) ).

tff(fact_245_prod_Oexhaust,axiom,
    ! [Y_3: produc1102272487on_val] :
      ~ ! [A_1: produc124828825on_val,B_1: produc124828825on_val] : Y_3 != hAPP_P1886180715on_val(produc1441475159on_val(A_1),B_1) ).

tff(fact_246_prod_Oexhaust,axiom,
    ! [Y_3: produc124828825on_val] :
      ~ ! [A_1: exp_list_char,B_1: produc12694297on_val] : Y_3 != hAPP_P604205461on_val(produc1259058957on_val(A_1),B_1) ).

tff(fact_247_prod_Oexhaust,axiom,
    ! [Y_3: produc639455274on_val] :
      ~ ! [A_1: list_char,B_1: fun_Pr806764899on_val] : Y_3 != hAPP_f900686428on_val(produc823076510on_val(A_1),B_1) ).

tff(fact_248_prod_Oexhaust,axiom,
    ! [Y_3: produc430140671on_val] :
      ~ ! [A_1: produc2061676504on_val,B_1: produc2061676504on_val] : Y_3 != hAPP_P658340954on_val(produc1611380469on_val(A_1),B_1) ).

tff(fact_249_prod_Oexhaust,axiom,
    ! [Y_3: produc2061676504on_val] :
      ~ ! [A_1: list_exp_list_char,B_1: produc12694297on_val] : Y_3 != hAPP_P1963616220on_val(produc379668296on_val(A_1),B_1) ).

tff(fact_250_prod_Oexhaust,axiom,
    ! [Y_2: produc1645268488al_val] :
      ~ ! [A_1: bop,B_1: product_prod_val_val] : Y_2 != hAPP_P929466802al_val(produc621191550al_val(A_1),B_1) ).

tff(fact_251_prod_Oexhaust,axiom,
    ! [Y_2: product_prod_val_val] :
      ~ ! [A_1: val,B_1: val] : Y_2 != hAPP_v852496844al_val(product_Pair_val_val(A_1),B_1) ).

tff(fact_252_prod_Oexhaust,axiom,
    ! [Y_2: produc1278157519t_char] :
      ~ ! [A_1: list_char,B_1: list_char] : Y_2 != hAPP_l2100324114t_char(produc5062597t_char(A_1),B_1) ).

tff(fact_253_prod_Oexhaust,axiom,
    ! [Y_2: produc809539159t_char] :
      ~ ! [A_1: list_list_char,B_1: exp_list_char] : Y_2 != hAPP_e952791821t_char(produc1147572817t_char(A_1),B_1) ).

tff(fact_254_PairE,axiom,
    ! [P_2: produc1534059751t_char] :
      ~ ! [X_3: produc809539159t_char,Y_1: produc809539159t_char] : P_2 != hAPP_P1342907945t_char(produc1897818327t_char(X_3),Y_1) ).

tff(fact_255_PairE,axiom,
    ! [P_2: produc1350825965t_char] :
      ~ ! [X_3: produc1278157519t_char,Y_1: produc1278157519t_char] : P_2 != hAPP_P1657265855t_char(produc2080520419t_char(X_3),Y_1) ).

tff(fact_256_PairE,axiom,
    ! [P_2: produc800118557al_val] :
      ~ ! [X_3: product_prod_val_val,Y_1: product_prod_val_val] : P_2 != hAPP_P47773639al_val(produc1244920211al_val(X_3),Y_1) ).

tff(fact_257_PairE,axiom,
    ! [P_2: produc630464863al_val] :
      ~ ! [X_3: produc1645268488al_val,Y_1: produc1645268488al_val] : P_2 != hAPP_P2123720426al_val(produc1924279125al_val(X_3),Y_1) ).

tff(fact_258_PairE,axiom,
    ! [P_1: produc1466422861on_val] :
      ~ ! [X_3: produc430140671on_val,Y_1: produc430140671on_val] : P_1 != hAPP_P1758592847on_val(produc1951691075on_val(X_3),Y_1) ).

tff(fact_259_PairE,axiom,
    ! [P_1: produc87279271on_val] :
      ~ ! [X_3: produc639455274on_val,Y_1: produc639455274on_val] : P_1 != hAPP_P330218428on_val(produc499151895on_val(X_3),Y_1) ).

tff(fact_260_PairE,axiom,
    ! [P_1: produc231486621on_val] :
      ~ ! [X_3: produc1102272487on_val,Y_1: produc1102272487on_val] : P_1 != hAPP_P1486793863on_val(produc1564932627on_val(X_3),Y_1) ).

tff(fact_261_PairE,axiom,
    ! [P_1: produc409205479on_val] :
      ~ ! [X_3: produc12694297on_val,Y_1: produc12694297on_val] : P_1 != hAPP_P291613419on_val(produc870913623on_val(X_3),Y_1) ).

tff(fact_262_PairE,axiom,
    ! [P_2: produc1826280281t_char] :
      ~ ! [X_3: produc662261637t_char,Y_1: produc662261637t_char] : P_2 != hAPP_P1220989409t_char(produc1299387215t_char(X_3),Y_1) ).

tff(fact_263_PairE,axiom,
    ! [P_2: produc1406897475t_char] :
      ~ ! [X_3: produc220283002t_char,Y_1: produc220283002t_char] : P_2 != hAPP_P1333668416t_char(produc57279289t_char(X_3),Y_1) ).

tff(fact_264_PairE,axiom,
    ! [P_2: produc349695911t_char] :
      ~ ! [X_3: produc1285161482t_char,Y_1: produc1285161482t_char] : P_2 != hAPP_P1539798428t_char(produc24551831t_char(X_3),Y_1) ).

tff(fact_265_PairE,axiom,
    ! [P_2: produc1285161482t_char] :
      ~ ! [X_3: list_list_char,Y_1: produc220283002t_char] : P_2 != hAPP_P767818445t_char(produc921874948t_char(X_3),Y_1) ).

tff(fact_266_PairE,axiom,
    ! [P_2: produc220283002t_char] :
      ~ ! [X_3: list_ty,Y_1: produc662261637t_char] : P_2 != hAPP_P1392904962t_char(produc1909267824t_char(X_3),Y_1) ).

tff(fact_267_PairE,axiom,
    ! [P_2: produc662261637t_char] :
      ~ ! [X_3: list_val,Y_1: exp_list_char] : P_2 != hAPP_e1752110927t_char(produc1916172923t_char(X_3),Y_1) ).

tff(fact_268_PairE,axiom,
    ! [P_1: produc12694297on_val] :
      ~ ! [X_3: fun_na939144002on_val,Y_1: fun_li1432931796on_val] : P_1 != hAPP_f1727192346on_val(produc899768717on_val(X_3),Y_1) ).

tff(fact_269_PairE,axiom,
    ! [P_1: produc1102272487on_val] :
      ~ ! [X_3: produc124828825on_val,Y_1: produc124828825on_val] : P_1 != hAPP_P1886180715on_val(produc1441475159on_val(X_3),Y_1) ).

tff(fact_270_PairE,axiom,
    ! [P_1: produc124828825on_val] :
      ~ ! [X_3: exp_list_char,Y_1: produc12694297on_val] : P_1 != hAPP_P604205461on_val(produc1259058957on_val(X_3),Y_1) ).

tff(fact_271_PairE,axiom,
    ! [P_1: produc639455274on_val] :
      ~ ! [X_3: list_char,Y_1: fun_Pr806764899on_val] : P_1 != hAPP_f900686428on_val(produc823076510on_val(X_3),Y_1) ).

tff(fact_272_PairE,axiom,
    ! [P_1: produc430140671on_val] :
      ~ ! [X_3: produc2061676504on_val,Y_1: produc2061676504on_val] : P_1 != hAPP_P658340954on_val(produc1611380469on_val(X_3),Y_1) ).

tff(fact_273_PairE,axiom,
    ! [P_1: produc2061676504on_val] :
      ~ ! [X_3: list_exp_list_char,Y_1: produc12694297on_val] : P_1 != hAPP_P1963616220on_val(produc379668296on_val(X_3),Y_1) ).

tff(fact_274_PairE,axiom,
    ! [P_2: produc1645268488al_val] :
      ~ ! [X_3: bop,Y_1: product_prod_val_val] : P_2 != hAPP_P929466802al_val(produc621191550al_val(X_3),Y_1) ).

tff(fact_275_PairE,axiom,
    ! [P_2: product_prod_val_val] :
      ~ ! [X_3: val,Y_1: val] : P_2 != hAPP_v852496844al_val(product_Pair_val_val(X_3),Y_1) ).

tff(fact_276_PairE,axiom,
    ! [P_2: produc1278157519t_char] :
      ~ ! [X_3: list_char,Y_1: list_char] : P_2 != hAPP_l2100324114t_char(produc5062597t_char(X_3),Y_1) ).

tff(fact_277_PairE,axiom,
    ! [P_2: produc809539159t_char] :
      ~ ! [X_3: list_list_char,Y_1: exp_list_char] : P_2 != hAPP_e952791821t_char(produc1147572817t_char(X_3),Y_1) ).

tff(fact_278_conf__widen,axiom,
    ! [T: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,V_2: val,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_2),Ta))
     => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),Ta),T))
       => hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_2),T)) ) ) ).

tff(fact_279_typeof__conf,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,V_2: val,Ta: ty] :
      ( ( hAPP_val_option_ty(typeof_h(Ha),V_2) = hAPP_ty_option_ty(some_ty,Ta) )
     => hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_2),Ta)) ) ).

tff(fact_280_confs__widens,axiom,
    ! [Ts_1: list_ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,Vsa: list_val,Tsa: list_ty] :
      ( hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa,Tsa))
     => ( hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Tsa,Ts_1))
       => hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa,Ts_1)) ) ) ).

tff(fact_281_conf__def,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,V_2: val,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_2),Ta))
    <=> ? [T_4: ty] :
          ( ( hAPP_val_option_ty(typeof_h(Ha),V_2) = hAPP_ty_option_ty(some_ty,T_4) )
          & hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_4),Ta)) ) ) ).

tff(fact_282_split__paired__Ex,axiom,
    ! [Pa: fun_Pr908866473r_bool] :
      ( ? [X1: produc1534059751t_char] : hBOOL(hAPP_P1002912327r_bool(Pa,X1))
    <=> ? [A_1: produc809539159t_char,B_1: produc809539159t_char] : hBOOL(hAPP_P1002912327r_bool(Pa,hAPP_P1342907945t_char(produc1897818327t_char(A_1),B_1))) ) ).

tff(fact_283_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1336847023r_bool] :
      ( ? [X1: produc1350825965t_char] : hBOOL(hAPP_P2010574925r_bool(Pa,X1))
    <=> ? [A_1: produc1278157519t_char,B_1: produc1278157519t_char] : hBOOL(hAPP_P2010574925r_bool(Pa,hAPP_P1657265855t_char(produc2080520419t_char(A_1),B_1))) ) ).

tff(fact_284_split__paired__Ex,axiom,
    ! [Pa: fun_Pr832147423l_bool] :
      ( ? [X1: produc800118557al_val] : hBOOL(hAPP_P2123002749l_bool(Pa,X1))
    <=> ? [A_1: product_prod_val_val,B_1: product_prod_val_val] : hBOOL(hAPP_P2123002749l_bool(Pa,hAPP_P47773639al_val(produc1244920211al_val(A_1),B_1))) ) ).

tff(fact_285_split__paired__Ex,axiom,
    ! [Pa: fun_Pr897334561l_bool] :
      ( ? [X1: produc630464863al_val] : hBOOL(hAPP_P738987199l_bool(Pa,X1))
    <=> ? [A_1: produc1645268488al_val,B_1: produc1645268488al_val] : hBOOL(hAPP_P738987199l_bool(Pa,hAPP_P2123720426al_val(produc1924279125al_val(A_1),B_1))) ) ).

tff(fact_286_split__paired__Ex,axiom,
    ! [Pa: fun_Pr302334223l_bool] :
      ( ? [X1: produc1466422861on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,X1))
    <=> ? [A_1: produc430140671on_val,B_1: produc430140671on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(produc1951691075on_val(A_1),B_1))) ) ).

tff(fact_287_split__paired__Ex,axiom,
    ! [Pa: fun_Pr235369833l_bool] :
      ( ? [X1: produc87279271on_val] : hBOOL(hAPP_P124632071l_bool(Pa,X1))
    <=> ? [A_1: produc639455274on_val,B_1: produc639455274on_val] : hBOOL(hAPP_P124632071l_bool(Pa,hAPP_P330218428on_val(produc499151895on_val(A_1),B_1))) ) ).

tff(fact_288_split__paired__Ex,axiom,
    ! [Pa: fun_Pr903661919l_bool] :
      ( ? [X1: produc231486621on_val] : hBOOL(hAPP_P378063101l_bool(Pa,X1))
    <=> ? [A_1: produc1102272487on_val,B_1: produc1102272487on_val] : hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(produc1564932627on_val(A_1),B_1))) ) ).

tff(fact_289_split__paired__Ex,axiom,
    ! [Pa: fun_Pr693020585l_bool] :
      ( ? [X1: produc409205479on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,X1))
    <=> ? [A_1: produc12694297on_val,B_1: produc12694297on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,hAPP_P291613419on_val(produc870913623on_val(A_1),B_1))) ) ).

tff(fact_290_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1890037787r_bool] :
      ( ? [X1: produc1826280281t_char] : hBOOL(hAPP_P1183499705r_bool(Pa,X1))
    <=> ? [A_1: produc662261637t_char,B_1: produc662261637t_char] : hBOOL(hAPP_P1183499705r_bool(Pa,hAPP_P1220989409t_char(produc1299387215t_char(A_1),B_1))) ) ).

tff(fact_291_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1728267013r_bool] :
      ( ? [X1: produc1406897475t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,X1))
    <=> ? [A_1: produc220283002t_char,B_1: produc220283002t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,hAPP_P1333668416t_char(produc57279289t_char(A_1),B_1))) ) ).

tff(fact_292_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1895638121r_bool] :
      ( ? [X1: produc349695911t_char] : hBOOL(hAPP_P824029447r_bool(Pa,X1))
    <=> ? [A_1: produc1285161482t_char,B_1: produc1285161482t_char] : hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(produc24551831t_char(A_1),B_1))) ) ).

tff(fact_293_split__paired__Ex,axiom,
    ! [Pa: fun_Pr227936640r_bool] :
      ( ? [X1: produc1285161482t_char] : hBOOL(hAPP_P92196306r_bool(Pa,X1))
    <=> ? [A_1: list_list_char,B_1: produc220283002t_char] : hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(produc921874948t_char(A_1),B_1))) ) ).

tff(fact_294_split__paired__Ex,axiom,
    ! [Pa: fun_Pr46158268r_bool] :
      ( ? [X1: produc220283002t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,X1))
    <=> ? [A_1: list_ty,B_1: produc662261637t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,hAPP_P1392904962t_char(produc1909267824t_char(A_1),B_1))) ) ).

tff(fact_295_split__paired__Ex,axiom,
    ! [Pa: fun_Pr827765831r_bool] :
      ( ? [X1: produc662261637t_char] : hBOOL(hAPP_P2118621157r_bool(Pa,X1))
    <=> ? [A_1: list_val,B_1: exp_list_char] : hBOOL(hAPP_P2118621157r_bool(Pa,hAPP_e1752110927t_char(produc1916172923t_char(A_1),B_1))) ) ).

tff(fact_296_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1696029455l_bool] :
      ( ? [X1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
    <=> ? [A_1: fun_na939144002on_val,B_1: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(Pa,hAPP_f1727192346on_val(produc899768717on_val(A_1),B_1))) ) ).

tff(fact_297_split__paired__Ex,axiom,
    ! [Pa: fun_Pr691271849l_bool] :
      ( ? [X1: produc1102272487on_val] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
    <=> ? [A_1: produc124828825on_val,B_1: produc124828825on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(produc1441475159on_val(A_1),B_1))) ) ).

tff(fact_298_split__paired__Ex,axiom,
    ! [Pa: fun_Pr680585871l_bool] :
      ( ? [X1: produc124828825on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
    <=> ? [A_1: exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(produc1259058957on_val(A_1),B_1))) ) ).

tff(fact_299_split__paired__Ex,axiom,
    ! [Pa: fun_Pr315804320l_bool] :
      ( ? [X1: produc639455274on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,X1))
    <=> ? [A_1: list_char,B_1: fun_Pr806764899on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,hAPP_f900686428on_val(produc823076510on_val(A_1),B_1))) ) ).

tff(fact_300_split__paired__Ex,axiom,
    ! [Pa: fun_Pr859510977l_bool] :
      ( ? [X1: produc430140671on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,X1))
    <=> ? [A_1: produc2061676504on_val,B_1: produc2061676504on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(produc1611380469on_val(A_1),B_1))) ) ).

tff(fact_301_split__paired__Ex,axiom,
    ! [Pa: fun_Pr248118298l_bool] :
      ( ? [X1: produc2061676504on_val] : hBOOL(hAPP_P71593144l_bool(Pa,X1))
    <=> ? [A_1: list_exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P71593144l_bool(Pa,hAPP_P1963616220on_val(produc379668296on_val(A_1),B_1))) ) ).

tff(fact_302_split__paired__Ex,axiom,
    ! [Pa: fun_Pr252072522l_bool] :
      ( ? [X1: produc1645268488al_val] : hBOOL(hAPP_P943837928l_bool(Pa,X1))
    <=> ? [A_1: bop,B_1: product_prod_val_val] : hBOOL(hAPP_P943837928l_bool(Pa,hAPP_P929466802al_val(produc621191550al_val(A_1),B_1))) ) ).

tff(fact_303_split__paired__Ex,axiom,
    ! [Pa: fun_Pr2081272681l_bool] :
      ( ? [X1: product_prod_val_val] : hBOOL(hAPP_P929938951l_bool(Pa,X1))
    <=> ? [A_1: val,B_1: val] : hBOOL(hAPP_P929938951l_bool(Pa,hAPP_v852496844al_val(product_Pair_val_val(A_1),B_1))) ) ).

tff(fact_304_split__paired__Ex,axiom,
    ! [Pa: fun_Pr565113489r_bool] :
      ( ? [X1: produc1278157519t_char] : hBOOL(hAPP_P449474095r_bool(Pa,X1))
    <=> ? [A_1: list_char,B_1: list_char] : hBOOL(hAPP_P449474095r_bool(Pa,hAPP_l2100324114t_char(produc5062597t_char(A_1),B_1))) ) ).

tff(fact_305_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1336948301r_bool] :
      ( ? [X1: produc809539159t_char] : hBOOL(hAPP_P2014166431r_bool(Pa,X1))
    <=> ? [A_1: list_list_char,B_1: exp_list_char] : hBOOL(hAPP_P2014166431r_bool(Pa,hAPP_e952791821t_char(produc1147572817t_char(A_1),B_1))) ) ).

tff(fact_306_confs__hext,axiom,
    ! [H_1: fun_na939144002on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,Vsa: list_val,Tsa: list_ty] :
      ( hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa,Tsa))
     => ( hBOOL(hext(Ha,H_1))
       => hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,H_1),Vsa,Tsa)) ) ) ).

tff(fact_307_blocksEval,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E_1: exp_list_char,H_1: fun_na939144002on_val,L_2: fun_li1432931796on_val,Vsa: list_val,Ps: list_list_char,Tsa: list_ty] :
      ( ( size_s2113983095t_char(Ps) = size_size_list_ty(Tsa) )
     => ( ( size_s2113983095t_char(Ps) = size_size_list_val(Vsa) )
       => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,blocks(hAPP_P767818445t_char(produc921874948t_char(Ps),hAPP_P1392904962t_char(produc1909267824t_char(Tsa),hAPP_e1752110927t_char(produc1916172923t_char(Vsa),Ea)))),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1)),E_1),hAPP_f1727192346on_val(produc899768717on_val(H_1),L_2)))
         => ? [L_4: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,hAPP_f1727192346on_val(produc899768717on_val(Ha),map_up1085636310ar_val(L_1,Ps,Vsa))),E_1),hAPP_f1727192346on_val(produc899768717on_val(H_1),L_4))) ) ) ) ).

tff(fact_308_option_Oinject,axiom,
    ! [A: ty,A_3: ty] :
      ( ( hAPP_ty_option_ty(some_ty,A) = hAPP_ty_option_ty(some_ty,A_3) )
    <=> ( A = A_3 ) ) ).

tff(fact_309_option_Oinject,axiom,
    ! [A: produc639455274on_val,A_3: produc639455274on_val] :
      ( ( hAPP_P1510515380on_val(some_P948696889on_val,A) = hAPP_P1510515380on_val(some_P948696889on_val,A_3) )
    <=> ( A = A_3 ) ) ).

tff(fact_310_option_Oinject,axiom,
    ! [A: val,A_3: val] :
      ( ( hAPP_val_option_val(some_val,A) = hAPP_val_option_val(some_val,A_3) )
    <=> ( A = A_3 ) ) ).

tff(fact_311_curryI,axiom,
    ! [F_1: fun_Pr908866473r_bool,A: produc809539159t_char,B: produc809539159t_char] :
      ( hBOOL(hAPP_P1002912327r_bool(F_1,hAPP_P1342907945t_char(produc1897818327t_char(A),B)))
     => hBOOL(hAPP_P2014166431r_bool(hAPP_P1939418767r_bool(produc1295142846r_bool(F_1),A),B)) ) ).

tff(fact_312_curryI,axiom,
    ! [F_1: fun_Pr1336847023r_bool,A: produc1278157519t_char,B: produc1278157519t_char] :
      ( hBOOL(hAPP_P2010574925r_bool(F_1,hAPP_P1657265855t_char(produc2080520419t_char(A),B)))
     => hBOOL(hAPP_P449474095r_bool(hAPP_P663876415r_bool(produc715708746r_bool(F_1),A),B)) ) ).

tff(fact_313_curryI,axiom,
    ! [F_1: fun_Pr832147423l_bool,A: product_prod_val_val,B: product_prod_val_val] :
      ( hBOOL(hAPP_P2123002749l_bool(F_1,hAPP_P47773639al_val(produc1244920211al_val(A),B)))
     => hBOOL(hAPP_P929938951l_bool(hAPP_P1815899455l_bool(produc1034940666l_bool(F_1),A),B)) ) ).

tff(fact_314_curryI,axiom,
    ! [F_1: fun_Pr897334561l_bool,A: produc1645268488al_val,B: produc1645268488al_val] :
      ( hBOOL(hAPP_P738987199l_bool(F_1,hAPP_P2123720426al_val(produc1924279125al_val(A),B)))
     => hBOOL(hAPP_P943837928l_bool(hAPP_P323054207l_bool(produc1969754044l_bool(F_1),A),B)) ) ).

tff(fact_315_curryI,axiom,
    ! [F_1: fun_Pr302334223l_bool,A: produc430140671on_val,B: produc430140671on_val] :
      ( hBOOL(hAPP_P2028072621l_bool(F_1,hAPP_P1758592847on_val(produc1951691075on_val(A),B)))
     => hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(produc971707818l_bool(F_1),A),B)) ) ).

tff(fact_316_curryI,axiom,
    ! [F_1: fun_Pr235369833l_bool,A: produc639455274on_val,B: produc639455274on_val] :
      ( hBOOL(hAPP_P124632071l_bool(F_1,hAPP_P330218428on_val(produc499151895on_val(A),B)))
     => hBOOL(hAPP_P1235399154l_bool(hAPP_P416784693l_bool(produc1996970750l_bool(F_1),A),B)) ) ).

tff(fact_317_curryI,axiom,
    ! [F_1: fun_Pr903661919l_bool,A: produc1102272487on_val,B: produc1102272487on_val] :
      ( hBOOL(hAPP_P378063101l_bool(F_1,hAPP_P1486793863on_val(produc1564932627on_val(A),B)))
     => hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(produc1497005946l_bool(F_1),A),B)) ) ).

tff(fact_318_curryI,axiom,
    ! [F_1: fun_Pr693020585l_bool,A: produc12694297on_val,B: produc12694297on_val] :
      ( hBOOL(hAPP_P1221872711l_bool(F_1,hAPP_P291613419on_val(produc870913623on_val(A),B)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(produc1073654846l_bool(F_1),A),B)) ) ).

tff(fact_319_curryI,axiom,
    ! [F_1: fun_Pr1890037787r_bool,A: produc662261637t_char,B: produc662261637t_char] :
      ( hBOOL(hAPP_P1183499705r_bool(F_1,hAPP_P1220989409t_char(produc1299387215t_char(A),B)))
     => hBOOL(hAPP_P2118621157r_bool(hAPP_P357098431r_bool(produc1535899062r_bool(F_1),A),B)) ) ).

tff(fact_320_curryI,axiom,
    ! [F_1: fun_Pr1728267013r_bool,A: produc220283002t_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P1240100515r_bool(F_1,hAPP_P1333668416t_char(produc57279289t_char(A),B)))
     => hBOOL(hAPP_P1907982426r_bool(hAPP_P1214880255r_bool(produc1268552608r_bool(F_1),A),B)) ) ).

tff(fact_321_curryI,axiom,
    ! [F_1: fun_Pr1895638121r_bool,A: produc1285161482t_char,B: produc1285161482t_char] :
      ( hBOOL(hAPP_P824029447r_bool(F_1,hAPP_P1539798428t_char(produc24551831t_char(A),B)))
     => hBOOL(hAPP_P92196306r_bool(hAPP_P1928969845r_bool(produc17861502r_bool(F_1),A),B)) ) ).

tff(fact_322_curryI,axiom,
    ! [F_1: fun_Pr227936640r_bool,A: list_list_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P92196306r_bool(F_1,hAPP_P767818445t_char(produc921874948t_char(A),B)))
     => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F_1),A),B)) ) ).

tff(fact_323_curryI,axiom,
    ! [F_1: fun_Pr46158268r_bool,A: list_ty,B: produc662261637t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(F_1,hAPP_P1392904962t_char(produc1909267824t_char(A),B)))
     => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F_1),A),B)) ) ).

tff(fact_324_curryI,axiom,
    ! [F_1: fun_Pr827765831r_bool,A: list_val,B: exp_list_char] :
      ( hBOOL(hAPP_P2118621157r_bool(F_1,hAPP_e1752110927t_char(produc1916172923t_char(A),B)))
     => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F_1),A),B)) ) ).

tff(fact_325_curryI,axiom,
    ! [F_1: fun_Pr1696029455l_bool,A: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(F_1,hAPP_f1727192346on_val(produc899768717on_val(A),B)))
     => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F_1),A),B)) ) ).

tff(fact_326_curryI,axiom,
    ! [F_1: fun_Pr691271849l_bool,A: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P282169671l_bool(F_1,hAPP_P1886180715on_val(produc1441475159on_val(A),B)))
     => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F_1),A),B)) ) ).

tff(fact_327_curryI,axiom,
    ! [F_1: fun_Pr680585871l_bool,A: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(F_1,hAPP_P604205461on_val(produc1259058957on_val(A),B)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F_1),A),B)) ) ).

tff(fact_328_curryI,axiom,
    ! [F_1: fun_Pr315804320l_bool,A: list_char,B: fun_Pr806764899on_val] :
      ( hBOOL(hAPP_P1235399154l_bool(F_1,hAPP_f900686428on_val(produc823076510on_val(A),B)))
     => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F_1),A),B)) ) ).

tff(fact_329_curryI,axiom,
    ! [F_1: fun_Pr859510977l_bool,A: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P1333315679l_bool(F_1,hAPP_P658340954on_val(produc1611380469on_val(A),B)))
     => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(produc2053127004l_bool(F_1),A),B)) ) ).

tff(fact_330_curryI,axiom,
    ! [F_1: fun_Pr248118298l_bool,A: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P71593144l_bool(F_1,hAPP_P1963616220on_val(produc379668296on_val(A),B)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(produc1838470831l_bool(F_1),A),B)) ) ).

tff(fact_331_curryI,axiom,
    ! [F_1: fun_Pr252072522l_bool,A: bop,B: product_prod_val_val] :
      ( hBOOL(hAPP_P943837928l_bool(F_1,hAPP_P929466802al_val(produc621191550al_val(A),B)))
     => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(produc1555310053l_bool(F_1),A),B)) ) ).

tff(fact_332_curryI,axiom,
    ! [F_1: fun_Pr2081272681l_bool,A: val,B: val] :
      ( hBOOL(hAPP_P929938951l_bool(F_1,hAPP_v852496844al_val(product_Pair_val_val(A),B)))
     => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(produc886919678l_bool(F_1),A),B)) ) ).

tff(fact_333_curryI,axiom,
    ! [F_1: fun_Pr565113489r_bool,A: list_char,B: list_char] :
      ( hBOOL(hAPP_P449474095r_bool(F_1,hAPP_l2100324114t_char(produc5062597t_char(A),B)))
     => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(produc95371820r_bool(F_1),A),B)) ) ).

tff(fact_334_curryI,axiom,
    ! [F_1: fun_Pr1336948301r_bool,A: list_list_char,B: exp_list_char] :
      ( hBOOL(hAPP_P2014166431r_bool(F_1,hAPP_e952791821t_char(produc1147572817t_char(A),B)))
     => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(produc288369490r_bool(F_1),A),B)) ) ).

tff(fact_335_WTrts__Val,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E: fun_li688206603ion_ty,Vsa: list_val,Tsa: list_ty] :
      ( hBOOL(wTrts(Pa,Ha,E,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa),Tsa))
    <=> ( hAPP_l2006940821ion_ty(map_val_option_ty(typeof_h(Ha)),Vsa) = hAPP_l1487035934ion_ty(map_ty_option_ty(some_ty),Tsa) ) ) ).

tff(fact_336_defval__conf,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,Ta: ty] : hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),hAPP_ty_val(default_val,Ta)),Ta)) ).

tff(fact_337_blocksFinal,axiom,
    ! [Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,Vsa: list_val,Vsa_1: list_list_char,Tsa: list_ty] :
      ( ( size_s2113983095t_char(Vsa_1) = size_size_list_ty(Tsa) )
     => ( ( size_size_list_val(Vsa) = size_size_list_ty(Tsa) )
       => ( hBOOL(final_list_char(Ea))
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(blocks(hAPP_P767818445t_char(produc921874948t_char(Vsa_1),hAPP_P1392904962t_char(produc1909267824t_char(Tsa),hAPP_e1752110927t_char(produc1916172923t_char(Vsa),Ea))))),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))),hAPP_P604205461on_val(produc1259058957on_val(Ea),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_338_WTrtVal,axiom,
    ! [Pa: list_P1999446415t_char,E: fun_li688206603ion_ty,Ha: fun_na939144002on_val,V_2: val,Ta: ty] :
      ( ( hAPP_val_option_ty(typeof_h(Ha),V_2) = hAPP_ty_option_ty(some_ty,Ta) )
     => hBOOL(wTrt(Pa,Ha,E,hAPP_v834067052t_char(val_list_char,V_2),Ta)) ) ).

tff(fact_339_WTrts__hext__mono,axiom,
    ! [H_1: fun_na939144002on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E: fun_li688206603ion_ty,Es: list_exp_list_char,Tsa: list_ty] :
      ( hBOOL(wTrts(Pa,Ha,E,Es,Tsa))
     => ( hBOOL(hext(Ha,H_1))
       => hBOOL(wTrts(Pa,H_1,E,Es,Tsa)) ) ) ).

tff(fact_340_WTrt__hext__mono,axiom,
    ! [H_1: fun_na939144002on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E: fun_li688206603ion_ty,Ea: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Ha,E,Ea,Ta))
     => ( hBOOL(hext(Ha,H_1))
       => hBOOL(wTrt(Pa,H_1,E,Ea,Ta)) ) ) ).

tff(fact_341_WTrts__same__length,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E: fun_li688206603ion_ty,Es: list_exp_list_char,Tsa: list_ty] :
      ( hBOOL(wTrts(Pa,Ha,E,Es,Tsa))
     => ( size_s1143674878t_char(Es) = size_size_list_ty(Tsa) ) ) ).

tff(fact_342_conf__hext,axiom,
    ! [Pa: list_P1999446415t_char,V_2: val,Ta: ty,Ha: fun_na939144002on_val,H_1: fun_na939144002on_val] :
      ( hBOOL(hext(Ha,H_1))
     => ( hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_2),Ta))
       => hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,H_1),V_2),Ta)) ) ) ).

tff(fact_343_curryE,axiom,
    ! [F_1: fun_Pr1336948301r_bool,A: list_list_char,B: exp_list_char] :
      ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(produc288369490r_bool(F_1),A),B))
     => hBOOL(hAPP_P2014166431r_bool(F_1,hAPP_e952791821t_char(produc1147572817t_char(A),B))) ) ).

tff(fact_344_curryE,axiom,
    ! [F_1: fun_Pr565113489r_bool,A: list_char,B: list_char] :
      ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(produc95371820r_bool(F_1),A),B))
     => hBOOL(hAPP_P449474095r_bool(F_1,hAPP_l2100324114t_char(produc5062597t_char(A),B))) ) ).

tff(fact_345_curryE,axiom,
    ! [F_1: fun_Pr2081272681l_bool,A: val,B: val] :
      ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(produc886919678l_bool(F_1),A),B))
     => hBOOL(hAPP_P929938951l_bool(F_1,hAPP_v852496844al_val(product_Pair_val_val(A),B))) ) ).

tff(fact_346_curryE,axiom,
    ! [F_1: fun_Pr252072522l_bool,A: bop,B: product_prod_val_val] :
      ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(produc1555310053l_bool(F_1),A),B))
     => hBOOL(hAPP_P943837928l_bool(F_1,hAPP_P929466802al_val(produc621191550al_val(A),B))) ) ).

tff(fact_347_curryE,axiom,
    ! [F_1: fun_Pr248118298l_bool,A: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(produc1838470831l_bool(F_1),A),B))
     => hBOOL(hAPP_P71593144l_bool(F_1,hAPP_P1963616220on_val(produc379668296on_val(A),B))) ) ).

tff(fact_348_curryE,axiom,
    ! [F_1: fun_Pr859510977l_bool,A: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(produc2053127004l_bool(F_1),A),B))
     => hBOOL(hAPP_P1333315679l_bool(F_1,hAPP_P658340954on_val(produc1611380469on_val(A),B))) ) ).

tff(fact_349_curryE,axiom,
    ! [F_1: fun_Pr315804320l_bool,A: list_char,B: fun_Pr806764899on_val] :
      ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F_1),A),B))
     => hBOOL(hAPP_P1235399154l_bool(F_1,hAPP_f900686428on_val(produc823076510on_val(A),B))) ) ).

tff(fact_350_curryE,axiom,
    ! [F_1: fun_Pr680585871l_bool,A: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F_1),A),B))
     => hBOOL(hAPP_P1708370145l_bool(F_1,hAPP_P604205461on_val(produc1259058957on_val(A),B))) ) ).

tff(fact_351_curryE,axiom,
    ! [F_1: fun_Pr691271849l_bool,A: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F_1),A),B))
     => hBOOL(hAPP_P282169671l_bool(F_1,hAPP_P1886180715on_val(produc1441475159on_val(A),B))) ) ).

tff(fact_352_curryE,axiom,
    ! [F_1: fun_Pr1696029455l_bool,A: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F_1),A),B))
     => hBOOL(hAPP_P159683425l_bool(F_1,hAPP_f1727192346on_val(produc899768717on_val(A),B))) ) ).

tff(fact_353_curryE,axiom,
    ! [F_1: fun_Pr827765831r_bool,A: list_val,B: exp_list_char] :
      ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F_1),A),B))
     => hBOOL(hAPP_P2118621157r_bool(F_1,hAPP_e1752110927t_char(produc1916172923t_char(A),B))) ) ).

tff(fact_354_curryE,axiom,
    ! [F_1: fun_Pr46158268r_bool,A: list_ty,B: produc662261637t_char] :
      ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F_1),A),B))
     => hBOOL(hAPP_P1907982426r_bool(F_1,hAPP_P1392904962t_char(produc1909267824t_char(A),B))) ) ).

tff(fact_355_curryE,axiom,
    ! [F_1: fun_Pr227936640r_bool,A: list_list_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F_1),A),B))
     => hBOOL(hAPP_P92196306r_bool(F_1,hAPP_P767818445t_char(produc921874948t_char(A),B))) ) ).

tff(fact_356_curryD,axiom,
    ! [F_1: fun_Pr1336948301r_bool,A: list_list_char,B: exp_list_char] :
      ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(produc288369490r_bool(F_1),A),B))
     => hBOOL(hAPP_P2014166431r_bool(F_1,hAPP_e952791821t_char(produc1147572817t_char(A),B))) ) ).

tff(fact_357_curryD,axiom,
    ! [F_1: fun_Pr565113489r_bool,A: list_char,B: list_char] :
      ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(produc95371820r_bool(F_1),A),B))
     => hBOOL(hAPP_P449474095r_bool(F_1,hAPP_l2100324114t_char(produc5062597t_char(A),B))) ) ).

tff(fact_358_curryD,axiom,
    ! [F_1: fun_Pr2081272681l_bool,A: val,B: val] :
      ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(produc886919678l_bool(F_1),A),B))
     => hBOOL(hAPP_P929938951l_bool(F_1,hAPP_v852496844al_val(product_Pair_val_val(A),B))) ) ).

tff(fact_359_curryD,axiom,
    ! [F_1: fun_Pr252072522l_bool,A: bop,B: product_prod_val_val] :
      ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(produc1555310053l_bool(F_1),A),B))
     => hBOOL(hAPP_P943837928l_bool(F_1,hAPP_P929466802al_val(produc621191550al_val(A),B))) ) ).

tff(fact_360_curryD,axiom,
    ! [F_1: fun_Pr248118298l_bool,A: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(produc1838470831l_bool(F_1),A),B))
     => hBOOL(hAPP_P71593144l_bool(F_1,hAPP_P1963616220on_val(produc379668296on_val(A),B))) ) ).

tff(fact_361_curryD,axiom,
    ! [F_1: fun_Pr859510977l_bool,A: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(produc2053127004l_bool(F_1),A),B))
     => hBOOL(hAPP_P1333315679l_bool(F_1,hAPP_P658340954on_val(produc1611380469on_val(A),B))) ) ).

tff(fact_362_curryD,axiom,
    ! [F_1: fun_Pr315804320l_bool,A: list_char,B: fun_Pr806764899on_val] :
      ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F_1),A),B))
     => hBOOL(hAPP_P1235399154l_bool(F_1,hAPP_f900686428on_val(produc823076510on_val(A),B))) ) ).

tff(fact_363_curryD,axiom,
    ! [F_1: fun_Pr680585871l_bool,A: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F_1),A),B))
     => hBOOL(hAPP_P1708370145l_bool(F_1,hAPP_P604205461on_val(produc1259058957on_val(A),B))) ) ).

tff(fact_364_curryD,axiom,
    ! [F_1: fun_Pr691271849l_bool,A: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F_1),A),B))
     => hBOOL(hAPP_P282169671l_bool(F_1,hAPP_P1886180715on_val(produc1441475159on_val(A),B))) ) ).

tff(fact_365_curryD,axiom,
    ! [F_1: fun_Pr1696029455l_bool,A: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F_1),A),B))
     => hBOOL(hAPP_P159683425l_bool(F_1,hAPP_f1727192346on_val(produc899768717on_val(A),B))) ) ).

tff(fact_366_curryD,axiom,
    ! [F_1: fun_Pr827765831r_bool,A: list_val,B: exp_list_char] :
      ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F_1),A),B))
     => hBOOL(hAPP_P2118621157r_bool(F_1,hAPP_e1752110927t_char(produc1916172923t_char(A),B))) ) ).

tff(fact_367_curryD,axiom,
    ! [F_1: fun_Pr46158268r_bool,A: list_ty,B: produc662261637t_char] :
      ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F_1),A),B))
     => hBOOL(hAPP_P1907982426r_bool(F_1,hAPP_P1392904962t_char(produc1909267824t_char(A),B))) ) ).

tff(fact_368_curryD,axiom,
    ! [F_1: fun_Pr227936640r_bool,A: list_list_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F_1),A),B))
     => hBOOL(hAPP_P92196306r_bool(F_1,hAPP_P767818445t_char(produc921874948t_char(A),B))) ) ).

tff(fact_369_red__hext__incr,axiom,
    ! [Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E_1: exp_list_char,H_1: fun_na939144002on_val,L_2: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))),hAPP_P604205461on_val(produc1259058957on_val(E_1),hAPP_f1727192346on_val(produc899768717on_val(H_1),L_2))),red(Pa)))
     => hBOOL(hext(Ha,H_1)) ) ).

tff(fact_370_rtrancl_Ortrancl__refl,axiom,
    ! [A: list_char,R: fun_Pr565113489r_bool] : hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(A),A),transi1395422419t_char(R))) ).

tff(fact_371_rtrancl_Ortrancl__refl,axiom,
    ! [A: produc2061676504on_val,R: fun_Pr859510977l_bool] : hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(A),A),transi374442731on_val(R))) ).

tff(fact_372_rtrancl_Ortrancl__refl,axiom,
    ! [A: produc124828825on_val,R: fun_Pr691271849l_bool] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(A),A),transi2024712006on_val(R))) ).

tff(fact_373_rtrancl_Ortrancl__refl,axiom,
    ! [A: val,R: fun_Pr2081272681l_bool] : hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(A),A),transi935034983cl_val(R))) ).

tff(fact_374_hext__typeof__mono,axiom,
    ! [V_2: val,Ta: ty,Ha: fun_na939144002on_val,H_1: fun_na939144002on_val] :
      ( hBOOL(hext(Ha,H_1))
     => ( ( hAPP_val_option_ty(typeof_h(Ha),V_2) = hAPP_ty_option_ty(some_ty,Ta) )
       => ( hAPP_val_option_ty(typeof_h(H_1),V_2) = hAPP_ty_option_ty(some_ty,Ta) ) ) ) ).

tff(fact_375_eval__hext,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E_1: exp_list_char,H_1: fun_na939144002on_val,L_2: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1)),E_1),hAPP_f1727192346on_val(produc899768717on_val(H_1),L_2)))
     => hBOOL(hext(Ha,H_1)) ) ).

tff(fact_376_hext__refl,axiom,
    ! [Ha: fun_na939144002on_val] : hBOOL(hext(Ha,Ha)) ).

tff(fact_377_r__into__rtrancl,axiom,
    ! [P_1: produc1278157519t_char,R: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(P_1,R))
     => hBOOL(member1251428284t_char(P_1,transi1395422419t_char(R))) ) ).

tff(fact_378_r__into__rtrancl,axiom,
    ! [P_1: produc430140671on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(P_1,R))
     => hBOOL(member875476972on_val(P_1,transi374442731on_val(R))) ) ).

tff(fact_379_r__into__rtrancl,axiom,
    ! [P_1: produc1102272487on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(P_1,R))
     => hBOOL(member773094996on_val(P_1,transi2024712006on_val(R))) ) ).

tff(fact_380_red__preserves__hconf,axiom,
    ! [E: fun_li688206603ion_ty,Ta: ty,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E_1: exp_list_char,H_1: fun_na939144002on_val,L_2: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))),hAPP_P604205461on_val(produc1259058957on_val(E_1),hAPP_f1727192346on_val(produc899768717on_val(H_1),L_2))),red(Pa)))
     => ( hBOOL(wTrt(Pa,Ha,E,Ea,Ta))
       => ( hBOOL(hconf_97414254t_char(Pa,Ha))
         => hBOOL(hconf_97414254t_char(Pa,H_1)) ) ) ) ).

tff(fact_381_eval__finalId,axiom,
    ! [Pa: list_P1999446415t_char,S: produc12694297on_val,Ea: exp_list_char] :
      ( hBOOL(final_list_char(Ea))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S),Ea),S)) ) ).

tff(fact_382_eval__final,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S),E_1),S_1))
     => hBOOL(final_list_char(E_1)) ) ).

tff(fact_383_red__preserves__lconf,axiom,
    ! [E: fun_li688206603ion_ty,Ta: ty,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E_1: exp_list_char,H_1: fun_na939144002on_val,L_2: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))),hAPP_P604205461on_val(produc1259058957on_val(E_1),hAPP_f1727192346on_val(produc899768717on_val(H_1),L_2))),red(Pa)))
     => ( hBOOL(wTrt(Pa,Ha,E,Ea,Ta))
       => ( hBOOL(lconf_496643946t_char(Pa,Ha,L_1,E))
         => hBOOL(lconf_496643946t_char(Pa,H_1,L_2,E)) ) ) ) ).

tff(fact_384_lconf__hext,axiom,
    ! [H_1: fun_na939144002on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: fun_li688206603ion_ty] :
      ( hBOOL(lconf_496643946t_char(Pa,Ha,L_1,E))
     => ( hBOOL(hext(Ha,H_1))
       => hBOOL(lconf_496643946t_char(Pa,H_1,L_1,E)) ) ) ).

tff(fact_385_rtrancl__idemp,axiom,
    ! [R: fun_Pr565113489r_bool] : transi1395422419t_char(transi1395422419t_char(R)) = transi1395422419t_char(R) ).

tff(fact_386_rtrancl__idemp,axiom,
    ! [R: fun_Pr859510977l_bool] : transi374442731on_val(transi374442731on_val(R)) = transi374442731on_val(R) ).

tff(fact_387_rtrancl__idemp,axiom,
    ! [R: fun_Pr691271849l_bool] : transi2024712006on_val(transi2024712006on_val(R)) = transi2024712006on_val(R) ).

tff(fact_388_hext__trans,axiom,
    ! [H_3: fun_na939144002on_val,Ha: fun_na939144002on_val,H_1: fun_na939144002on_val] :
      ( hBOOL(hext(Ha,H_1))
     => ( hBOOL(hext(H_1,H_3))
       => hBOOL(hext(Ha,H_3)) ) ) ).

tff(fact_389_converse__rtrancl__into__rtrancl,axiom,
    ! [C_3: list_char,A: list_char,B: list_char,R: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(A),B),R))
     => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(B),C_3),transi1395422419t_char(R)))
       => hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(A),C_3),transi1395422419t_char(R))) ) ) ).

tff(fact_390_converse__rtrancl__into__rtrancl,axiom,
    ! [C_3: produc2061676504on_val,A: produc2061676504on_val,B: produc2061676504on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(A),B),R))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(B),C_3),transi374442731on_val(R)))
       => hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(A),C_3),transi374442731on_val(R))) ) ) ).

tff(fact_391_converse__rtrancl__into__rtrancl,axiom,
    ! [C_3: produc124828825on_val,A: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(A),B),R))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(B),C_3),transi2024712006on_val(R)))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(A),C_3),transi2024712006on_val(R))) ) ) ).

tff(fact_392_converse__rtrancl__into__rtrancl,axiom,
    ! [C_3: val,A: val,B: val,R: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(A),B),R))
     => ( hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(B),C_3),transi935034983cl_val(R)))
       => hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(A),C_3),transi935034983cl_val(R))) ) ) ).

tff(fact_393_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_3: list_char,A: list_char,B: list_char,R: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(A),B),transi1395422419t_char(R)))
     => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(B),C_3),R))
       => hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(A),C_3),transi1395422419t_char(R))) ) ) ).

tff(fact_394_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_3: produc2061676504on_val,A: produc2061676504on_val,B: produc2061676504on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(A),B),transi374442731on_val(R)))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(B),C_3),R))
       => hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(A),C_3),transi374442731on_val(R))) ) ) ).

tff(fact_395_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_3: produc124828825on_val,A: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(A),B),transi2024712006on_val(R)))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(B),C_3),R))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(A),C_3),transi2024712006on_val(R))) ) ) ).

tff(fact_396_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_3: val,A: val,B: val,R: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(A),B),transi935034983cl_val(R)))
     => ( hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(B),C_3),R))
       => hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(A),C_3),transi935034983cl_val(R))) ) ) ).

tff(fact_397_rtrancl__trans,axiom,
    ! [C_3: list_char,A: list_char,B: list_char,R: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(A),B),transi1395422419t_char(R)))
     => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(B),C_3),transi1395422419t_char(R)))
       => hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(A),C_3),transi1395422419t_char(R))) ) ) ).

tff(fact_398_rtrancl__trans,axiom,
    ! [C_3: produc2061676504on_val,A: produc2061676504on_val,B: produc2061676504on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(A),B),transi374442731on_val(R)))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(B),C_3),transi374442731on_val(R)))
       => hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(A),C_3),transi374442731on_val(R))) ) ) ).

tff(fact_399_rtrancl__trans,axiom,
    ! [C_3: produc124828825on_val,A: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(A),B),transi2024712006on_val(R)))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(B),C_3),transi2024712006on_val(R)))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(A),C_3),transi2024712006on_val(R))) ) ) ).

tff(fact_400_rtrancl__trans,axiom,
    ! [C_3: val,A: val,B: val,R: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(A),B),transi935034983cl_val(R)))
     => ( hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(B),C_3),transi935034983cl_val(R)))
       => hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(A),C_3),transi935034983cl_val(R))) ) ) ).

tff(fact_401_eval__cases_I2_J,axiom,
    ! [Pa: list_P1999446415t_char,V_2: val,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,hAPP_v834067052t_char(val_list_char,V_2),S),E_1),S_1))
     => ~ ( ( E_1 = hAPP_v834067052t_char(val_list_char,V_2) )
         => ( S_1 != S ) ) ) ).

tff(fact_402_Val,axiom,
    ! [Pa: list_P1999446415t_char,V_2: val,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,hAPP_v834067052t_char(val_list_char,V_2),S),hAPP_v834067052t_char(val_list_char,V_2)),S)) ).

tff(fact_403_lconf__def,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: fun_li688206603ion_ty] :
      ( hBOOL(lconf_496643946t_char(Pa,Ha,L_1,E))
    <=> ! [V_3: list_char,V_1: val] :
          ( ( hAPP_l207779698on_val(L_1,V_3) = hAPP_val_option_val(some_val,V_1) )
         => ? [T_3: ty] :
              ( ( hAPP_l512744617ion_ty(E,V_3) = hAPP_ty_option_ty(some_ty,T_3) )
              & hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_1),T_3)) ) ) ) ).

tff(fact_404_converse__rtranclE2,axiom,
    ! [Xa_1: list_exp_list_char,Xb: produc12694297on_val,Za: list_exp_list_char,Zb: produc12694297on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(Xa_1),Xb)),hAPP_P1963616220on_val(produc379668296on_val(Za),Zb)),transi374442731on_val(R)))
     => ( ( hAPP_P1963616220on_val(produc379668296on_val(Xa_1),Xb) != hAPP_P1963616220on_val(produc379668296on_val(Za),Zb) )
       => ~ ! [A_1: list_exp_list_char,B_1: produc12694297on_val] :
              ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(Xa_1),Xb)),hAPP_P1963616220on_val(produc379668296on_val(A_1),B_1)),R))
             => ~ hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(A_1),B_1)),hAPP_P1963616220on_val(produc379668296on_val(Za),Zb)),transi374442731on_val(R))) ) ) ) ).

tff(fact_405_converse__rtranclE2,axiom,
    ! [Xa_1: exp_list_char,Xb: produc12694297on_val,Za: exp_list_char,Zb: produc12694297on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Xa_1),Xb)),hAPP_P604205461on_val(produc1259058957on_val(Za),Zb)),transi2024712006on_val(R)))
     => ( ( hAPP_P604205461on_val(produc1259058957on_val(Xa_1),Xb) != hAPP_P604205461on_val(produc1259058957on_val(Za),Zb) )
       => ~ ! [A_1: exp_list_char,B_1: produc12694297on_val] :
              ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Xa_1),Xb)),hAPP_P604205461on_val(produc1259058957on_val(A_1),B_1)),R))
             => ~ hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(A_1),B_1)),hAPP_P604205461on_val(produc1259058957on_val(Za),Zb)),transi2024712006on_val(R))) ) ) ) ).

tff(fact_406_converse__rtranclE2,axiom,
    ! [Xa_1: list_list_char,Xb: exp_list_char,Za: list_list_char,Zb: exp_list_char,R: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(hAPP_P1342907945t_char(produc1897818327t_char(hAPP_e952791821t_char(produc1147572817t_char(Xa_1),Xb)),hAPP_e952791821t_char(produc1147572817t_char(Za),Zb)),transi198989188t_char(R)))
     => ( ( hAPP_e952791821t_char(produc1147572817t_char(Xa_1),Xb) != hAPP_e952791821t_char(produc1147572817t_char(Za),Zb) )
       => ~ ! [A_1: list_list_char,B_1: exp_list_char] :
              ( hBOOL(member1999287380t_char(hAPP_P1342907945t_char(produc1897818327t_char(hAPP_e952791821t_char(produc1147572817t_char(Xa_1),Xb)),hAPP_e952791821t_char(produc1147572817t_char(A_1),B_1)),R))
             => ~ hBOOL(member1999287380t_char(hAPP_P1342907945t_char(produc1897818327t_char(hAPP_e952791821t_char(produc1147572817t_char(A_1),B_1)),hAPP_e952791821t_char(produc1147572817t_char(Za),Zb)),transi198989188t_char(R))) ) ) ) ).

tff(fact_407_converse__rtranclE2,axiom,
    ! [Xa_1: list_char,Xb: list_char,Za: list_char,Zb: list_char,R: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(hAPP_P1657265855t_char(produc2080520419t_char(hAPP_l2100324114t_char(produc5062597t_char(Xa_1),Xb)),hAPP_l2100324114t_char(produc5062597t_char(Za),Zb)),transi1095029602t_char(R)))
     => ( ( hAPP_l2100324114t_char(produc5062597t_char(Xa_1),Xb) != hAPP_l2100324114t_char(produc5062597t_char(Za),Zb) )
       => ~ ! [A_1: list_char,B_1: list_char] :
              ( hBOOL(member794220506t_char(hAPP_P1657265855t_char(produc2080520419t_char(hAPP_l2100324114t_char(produc5062597t_char(Xa_1),Xb)),hAPP_l2100324114t_char(produc5062597t_char(A_1),B_1)),R))
             => ~ hBOOL(member794220506t_char(hAPP_P1657265855t_char(produc2080520419t_char(hAPP_l2100324114t_char(produc5062597t_char(A_1),B_1)),hAPP_l2100324114t_char(produc5062597t_char(Za),Zb)),transi1095029602t_char(R))) ) ) ) ).

tff(fact_408_converse__rtranclE2,axiom,
    ! [Xa_1: val,Xb: val,Za: val,Zb: val,R: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(hAPP_P47773639al_val(produc1244920211al_val(hAPP_v852496844al_val(product_Pair_val_val(Xa_1),Xb)),hAPP_v852496844al_val(product_Pair_val_val(Za),Zb)),transi1423755450al_val(R)))
     => ( ( hAPP_v852496844al_val(product_Pair_val_val(Xa_1),Xb) != hAPP_v852496844al_val(product_Pair_val_val(Za),Zb) )
       => ~ ! [A_1: val,B_1: val] :
              ( hBOOL(member837208074al_val(hAPP_P47773639al_val(produc1244920211al_val(hAPP_v852496844al_val(product_Pair_val_val(Xa_1),Xb)),hAPP_v852496844al_val(product_Pair_val_val(A_1),B_1)),R))
             => ~ hBOOL(member837208074al_val(hAPP_P47773639al_val(produc1244920211al_val(hAPP_v852496844al_val(product_Pair_val_val(A_1),B_1)),hAPP_v852496844al_val(product_Pair_val_val(Za),Zb)),transi1423755450al_val(R))) ) ) ) ).

tff(fact_409_converse__rtranclE2,axiom,
    ! [Xa_1: bop,Xb: product_prod_val_val,Za: bop,Zb: product_prod_val_val,R: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(hAPP_P2123720426al_val(produc1924279125al_val(hAPP_P929466802al_val(produc621191550al_val(Xa_1),Xb)),hAPP_P929466802al_val(produc621191550al_val(Za),Zb)),transi1906258203al_val(R)))
     => ( ( hAPP_P929466802al_val(produc621191550al_val(Xa_1),Xb) != hAPP_P929466802al_val(produc621191550al_val(Za),Zb) )
       => ~ ! [A_1: bop,B_1: product_prod_val_val] :
              ( hBOOL(member1732271180al_val(hAPP_P2123720426al_val(produc1924279125al_val(hAPP_P929466802al_val(produc621191550al_val(Xa_1),Xb)),hAPP_P929466802al_val(produc621191550al_val(A_1),B_1)),R))
             => ~ hBOOL(member1732271180al_val(hAPP_P2123720426al_val(produc1924279125al_val(hAPP_P929466802al_val(produc621191550al_val(A_1),B_1)),hAPP_P929466802al_val(produc621191550al_val(Za),Zb)),transi1906258203al_val(R))) ) ) ) ).

tff(fact_410_converse__rtranclE2,axiom,
    ! [Xa_1: produc2061676504on_val,Xb: produc2061676504on_val,Za: produc2061676504on_val,Zb: produc2061676504on_val,R: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(hAPP_P1758592847on_val(produc1951691075on_val(hAPP_P658340954on_val(produc1611380469on_val(Xa_1),Xb)),hAPP_P658340954on_val(produc1611380469on_val(Za),Zb)),transi208336786on_val(R)))
     => ( ( hAPP_P658340954on_val(produc1611380469on_val(Xa_1),Xb) != hAPP_P658340954on_val(produc1611380469on_val(Za),Zb) )
       => ~ ! [A_1: produc2061676504on_val,B_1: produc2061676504on_val] :
              ( hBOOL(member88670778on_val(hAPP_P1758592847on_val(produc1951691075on_val(hAPP_P658340954on_val(produc1611380469on_val(Xa_1),Xb)),hAPP_P658340954on_val(produc1611380469on_val(A_1),B_1)),R))
             => ~ hBOOL(member88670778on_val(hAPP_P1758592847on_val(produc1951691075on_val(hAPP_P658340954on_val(produc1611380469on_val(A_1),B_1)),hAPP_P658340954on_val(produc1611380469on_val(Za),Zb)),transi208336786on_val(R))) ) ) ) ).

tff(fact_411_converse__rtranclE2,axiom,
    ! [Xa_1: list_char,Xb: fun_Pr806764899on_val,Za: list_char,Zb: fun_Pr806764899on_val,R: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(hAPP_P330218428on_val(produc499151895on_val(hAPP_f900686428on_val(produc823076510on_val(Xa_1),Xb)),hAPP_f900686428on_val(produc823076510on_val(Za),Zb)),transi61620055on_val(R)))
     => ( ( hAPP_f900686428on_val(produc823076510on_val(Xa_1),Xb) != hAPP_f900686428on_val(produc823076510on_val(Za),Zb) )
       => ~ ! [A_1: list_char,B_1: fun_Pr806764899on_val] :
              ( hBOOL(member1322055188on_val(hAPP_P330218428on_val(produc499151895on_val(hAPP_f900686428on_val(produc823076510on_val(Xa_1),Xb)),hAPP_f900686428on_val(produc823076510on_val(A_1),B_1)),R))
             => ~ hBOOL(member1322055188on_val(hAPP_P330218428on_val(produc499151895on_val(hAPP_f900686428on_val(produc823076510on_val(A_1),B_1)),hAPP_f900686428on_val(produc823076510on_val(Za),Zb)),transi61620055on_val(R))) ) ) ) ).

tff(fact_412_converse__rtranclE2,axiom,
    ! [Xa_1: produc124828825on_val,Xb: produc124828825on_val,Za: produc124828825on_val,Zb: produc124828825on_val,R: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(hAPP_P1486793863on_val(produc1564932627on_val(hAPP_P1886180715on_val(produc1441475159on_val(Xa_1),Xb)),hAPP_P1886180715on_val(produc1441475159on_val(Za),Zb)),transi910771962on_val(R)))
     => ( ( hAPP_P1886180715on_val(produc1441475159on_val(Xa_1),Xb) != hAPP_P1886180715on_val(produc1441475159on_val(Za),Zb) )
       => ~ ! [A_1: produc124828825on_val,B_1: produc124828825on_val] :
              ( hBOOL(member808015754on_val(hAPP_P1486793863on_val(produc1564932627on_val(hAPP_P1886180715on_val(produc1441475159on_val(Xa_1),Xb)),hAPP_P1886180715on_val(produc1441475159on_val(A_1),B_1)),R))
             => ~ hBOOL(member808015754on_val(hAPP_P1486793863on_val(produc1564932627on_val(hAPP_P1886180715on_val(produc1441475159on_val(A_1),B_1)),hAPP_P1886180715on_val(produc1441475159on_val(Za),Zb)),transi910771962on_val(R))) ) ) ) ).

tff(fact_413_converse__rtranclE2,axiom,
    ! [Xa_1: fun_na939144002on_val,Xb: fun_li1432931796on_val,Za: fun_na939144002on_val,Zb: fun_li1432931796on_val,R: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(hAPP_P291613419on_val(produc870913623on_val(hAPP_f1727192346on_val(produc899768717on_val(Xa_1),Xb)),hAPP_f1727192346on_val(produc899768717on_val(Za),Zb)),transi921647814on_val(R)))
     => ( ( hAPP_f1727192346on_val(produc899768717on_val(Xa_1),Xb) != hAPP_f1727192346on_val(produc899768717on_val(Za),Zb) )
       => ~ ! [A_1: fun_na939144002on_val,B_1: fun_li1432931796on_val] :
              ( hBOOL(member563141460on_val(hAPP_P291613419on_val(produc870913623on_val(hAPP_f1727192346on_val(produc899768717on_val(Xa_1),Xb)),hAPP_f1727192346on_val(produc899768717on_val(A_1),B_1)),R))
             => ~ hBOOL(member563141460on_val(hAPP_P291613419on_val(produc870913623on_val(hAPP_f1727192346on_val(produc899768717on_val(A_1),B_1)),hAPP_f1727192346on_val(produc899768717on_val(Za),Zb)),transi921647814on_val(R))) ) ) ) ).

tff(fact_414_converse__rtranclE2,axiom,
    ! [Xa_1: list_val,Xb: exp_list_char,Za: list_val,Zb: exp_list_char,R: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(hAPP_P1220989409t_char(produc1299387215t_char(hAPP_e1752110927t_char(produc1916172923t_char(Xa_1),Xb)),hAPP_e1752110927t_char(produc1916172923t_char(Za),Zb)),transi1789604888t_char(R)))
     => ( ( hAPP_e1752110927t_char(produc1916172923t_char(Xa_1),Xb) != hAPP_e1752110927t_char(produc1916172923t_char(Za),Zb) )
       => ~ ! [A_1: list_val,B_1: exp_list_char] :
              ( hBOOL(member1161907014t_char(hAPP_P1220989409t_char(produc1299387215t_char(hAPP_e1752110927t_char(produc1916172923t_char(Xa_1),Xb)),hAPP_e1752110927t_char(produc1916172923t_char(A_1),B_1)),R))
             => ~ hBOOL(member1161907014t_char(hAPP_P1220989409t_char(produc1299387215t_char(hAPP_e1752110927t_char(produc1916172923t_char(A_1),B_1)),hAPP_e1752110927t_char(produc1916172923t_char(Za),Zb)),transi1789604888t_char(R))) ) ) ) ).

tff(fact_415_converse__rtranclE2,axiom,
    ! [Xa_1: list_ty,Xb: produc662261637t_char,Za: list_ty,Zb: produc662261637t_char,R: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(hAPP_P1333668416t_char(produc57279289t_char(hAPP_P1392904962t_char(produc1909267824t_char(Xa_1),Xb)),hAPP_P1392904962t_char(produc1909267824t_char(Za),Zb)),transi1257872013t_char(R)))
     => ( ( hAPP_P1392904962t_char(produc1909267824t_char(Xa_1),Xb) != hAPP_P1392904962t_char(produc1909267824t_char(Za),Zb) )
       => ~ ! [A_1: list_ty,B_1: produc662261637t_char] :
              ( hBOOL(member125098544t_char(hAPP_P1333668416t_char(produc57279289t_char(hAPP_P1392904962t_char(produc1909267824t_char(Xa_1),Xb)),hAPP_P1392904962t_char(produc1909267824t_char(A_1),B_1)),R))
             => ~ hBOOL(member125098544t_char(hAPP_P1333668416t_char(produc57279289t_char(hAPP_P1392904962t_char(produc1909267824t_char(A_1),B_1)),hAPP_P1392904962t_char(produc1909267824t_char(Za),Zb)),transi1257872013t_char(R))) ) ) ) ).

tff(fact_416_converse__rtranclE2,axiom,
    ! [Xa_1: list_list_char,Xb: produc220283002t_char,Za: list_list_char,Zb: produc220283002t_char,R: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(hAPP_P1539798428t_char(produc24551831t_char(hAPP_P767818445t_char(produc921874948t_char(Xa_1),Xb)),hAPP_P767818445t_char(produc921874948t_char(Za),Zb)),transi122195895t_char(R)))
     => ( ( hAPP_P767818445t_char(produc921874948t_char(Xa_1),Xb) != hAPP_P767818445t_char(produc921874948t_char(Za),Zb) )
       => ~ ! [A_1: list_list_char,B_1: produc220283002t_char] :
              ( hBOOL(member1420286996t_char(hAPP_P1539798428t_char(produc24551831t_char(hAPP_P767818445t_char(produc921874948t_char(Xa_1),Xb)),hAPP_P767818445t_char(produc921874948t_char(A_1),B_1)),R))
             => ~ hBOOL(member1420286996t_char(hAPP_P1539798428t_char(produc24551831t_char(hAPP_P767818445t_char(produc921874948t_char(A_1),B_1)),hAPP_P767818445t_char(produc921874948t_char(Za),Zb)),transi122195895t_char(R))) ) ) ) ).

tff(fact_417_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li1372729616l_bool,Ax: list_exp_list_char,Ay: produc12694297on_val,Bx: list_exp_list_char,By: produc12694297on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(Ax),Ay)),hAPP_P1963616220on_val(produc379668296on_val(Bx),By)),transi374442731on_val(R)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Bx),By))
       => ( ! [A_1: list_exp_list_char,B_1: produc12694297on_val,Aa: list_exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(A_1),B_1)),hAPP_P1963616220on_val(produc379668296on_val(Aa),Ba)),R))
             => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(Aa),Ba)),hAPP_P1963616220on_val(produc379668296on_val(Bx),By)),transi374442731on_val(R)))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_418_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_ex1201926843l_bool,Ax: exp_list_char,Ay: produc12694297on_val,Bx: exp_list_char,By: produc12694297on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ax),Ay)),hAPP_P604205461on_val(produc1259058957on_val(Bx),By)),transi2024712006on_val(R)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By))
       => ( ! [A_1: exp_list_char,B_1: produc12694297on_val,Aa: exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(A_1),B_1)),hAPP_P604205461on_val(produc1259058957on_val(Aa),Ba)),R))
             => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Aa),Ba)),hAPP_P604205461on_val(produc1259058957on_val(Bx),By)),transi2024712006on_val(R)))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_419_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li221477r_bool,Ax: list_list_char,Ay: exp_list_char,Bx: list_list_char,By: exp_list_char,R: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(hAPP_P1342907945t_char(produc1897818327t_char(hAPP_e952791821t_char(produc1147572817t_char(Ax),Ay)),hAPP_e952791821t_char(produc1147572817t_char(Bx),By)),transi198989188t_char(R)))
     => ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Bx),By))
       => ( ! [A_1: list_list_char,B_1: exp_list_char,Aa: list_list_char,Ba: exp_list_char] :
              ( hBOOL(member1999287380t_char(hAPP_P1342907945t_char(produc1897818327t_char(hAPP_e952791821t_char(produc1147572817t_char(A_1),B_1)),hAPP_e952791821t_char(produc1147572817t_char(Aa),Ba)),R))
             => ( hBOOL(member1999287380t_char(hAPP_P1342907945t_char(produc1897818327t_char(hAPP_e952791821t_char(produc1147572817t_char(Aa),Ba)),hAPP_e952791821t_char(produc1147572817t_char(Bx),By)),transi198989188t_char(R)))
               => ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_420_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li860735411r_bool,Ax: list_char,Ay: list_char,Bx: list_char,By: list_char,R: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(hAPP_P1657265855t_char(produc2080520419t_char(hAPP_l2100324114t_char(produc5062597t_char(Ax),Ay)),hAPP_l2100324114t_char(produc5062597t_char(Bx),By)),transi1095029602t_char(R)))
     => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Bx),By))
       => ( ! [A_1: list_char,B_1: list_char,Aa: list_char,Ba: list_char] :
              ( hBOOL(member794220506t_char(hAPP_P1657265855t_char(produc2080520419t_char(hAPP_l2100324114t_char(produc5062597t_char(A_1),B_1)),hAPP_l2100324114t_char(produc5062597t_char(Aa),Ba)),R))
             => ( hBOOL(member794220506t_char(hAPP_P1657265855t_char(produc2080520419t_char(hAPP_l2100324114t_char(produc5062597t_char(Aa),Ba)),hAPP_l2100324114t_char(produc5062597t_char(Bx),By)),transi1095029602t_char(R)))
               => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_421_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_val_fun_val_bool,Ax: val,Ay: val,Bx: val,By: val,R: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(hAPP_P47773639al_val(produc1244920211al_val(hAPP_v852496844al_val(product_Pair_val_val(Ax),Ay)),hAPP_v852496844al_val(product_Pair_val_val(Bx),By)),transi1423755450al_val(R)))
     => ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Bx),By))
       => ( ! [A_1: val,B_1: val,Aa: val,Ba: val] :
              ( hBOOL(member837208074al_val(hAPP_P47773639al_val(produc1244920211al_val(hAPP_v852496844al_val(product_Pair_val_val(A_1),B_1)),hAPP_v852496844al_val(product_Pair_val_val(Aa),Ba)),R))
             => ( hBOOL(member837208074al_val(hAPP_P47773639al_val(produc1244920211al_val(hAPP_v852496844al_val(product_Pair_val_val(Aa),Ba)),hAPP_v852496844al_val(product_Pair_val_val(Bx),By)),transi1423755450al_val(R)))
               => ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_422_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_bo1454185032l_bool,Ax: bop,Ay: product_prod_val_val,Bx: bop,By: product_prod_val_val,R: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(hAPP_P2123720426al_val(produc1924279125al_val(hAPP_P929466802al_val(produc621191550al_val(Ax),Ay)),hAPP_P929466802al_val(produc621191550al_val(Bx),By)),transi1906258203al_val(R)))
     => ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Bx),By))
       => ( ! [A_1: bop,B_1: product_prod_val_val,Aa: bop,Ba: product_prod_val_val] :
              ( hBOOL(member1732271180al_val(hAPP_P2123720426al_val(produc1924279125al_val(hAPP_P929466802al_val(produc621191550al_val(A_1),B_1)),hAPP_P929466802al_val(produc621191550al_val(Aa),Ba)),R))
             => ( hBOOL(member1732271180al_val(hAPP_P2123720426al_val(produc1924279125al_val(hAPP_P929466802al_val(produc621191550al_val(Aa),Ba)),hAPP_P929466802al_val(produc621191550al_val(Bx),By)),transi1906258203al_val(R)))
               => ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_423_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr597144499l_bool,Ax: produc2061676504on_val,Ay: produc2061676504on_val,Bx: produc2061676504on_val,By: produc2061676504on_val,R: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(hAPP_P1758592847on_val(produc1951691075on_val(hAPP_P658340954on_val(produc1611380469on_val(Ax),Ay)),hAPP_P658340954on_val(produc1611380469on_val(Bx),By)),transi208336786on_val(R)))
     => ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Bx),By))
       => ( ! [A_1: produc2061676504on_val,B_1: produc2061676504on_val,Aa: produc2061676504on_val,Ba: produc2061676504on_val] :
              ( hBOOL(member88670778on_val(hAPP_P1758592847on_val(produc1951691075on_val(hAPP_P658340954on_val(produc1611380469on_val(A_1),B_1)),hAPP_P658340954on_val(produc1611380469on_val(Aa),Ba)),R))
             => ( hBOOL(member88670778on_val(hAPP_P1758592847on_val(produc1951691075on_val(hAPP_P658340954on_val(produc1611380469on_val(Aa),Ba)),hAPP_P658340954on_val(produc1611380469on_val(Bx),By)),transi208336786on_val(R)))
               => ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_424_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li823162622l_bool,Ax: list_char,Ay: fun_Pr806764899on_val,Bx: list_char,By: fun_Pr806764899on_val,R: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(hAPP_P330218428on_val(produc499151895on_val(hAPP_f900686428on_val(produc823076510on_val(Ax),Ay)),hAPP_f900686428on_val(produc823076510on_val(Bx),By)),transi61620055on_val(R)))
     => ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Bx),By))
       => ( ! [A_1: list_char,B_1: fun_Pr806764899on_val,Aa: list_char,Ba: fun_Pr806764899on_val] :
              ( hBOOL(member1322055188on_val(hAPP_P330218428on_val(produc499151895on_val(hAPP_f900686428on_val(produc823076510on_val(A_1),B_1)),hAPP_f900686428on_val(produc823076510on_val(Aa),Ba)),R))
             => ( hBOOL(member1322055188on_val(hAPP_P330218428on_val(produc499151895on_val(hAPP_f900686428on_val(produc823076510on_val(Aa),Ba)),hAPP_f900686428on_val(produc823076510on_val(Bx),By)),transi61620055on_val(R)))
               => ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_425_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr633696065l_bool,Ax: produc124828825on_val,Ay: produc124828825on_val,Bx: produc124828825on_val,By: produc124828825on_val,R: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(hAPP_P1486793863on_val(produc1564932627on_val(hAPP_P1886180715on_val(produc1441475159on_val(Ax),Ay)),hAPP_P1886180715on_val(produc1441475159on_val(Bx),By)),transi910771962on_val(R)))
     => ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By))
       => ( ! [A_1: produc124828825on_val,B_1: produc124828825on_val,Aa: produc124828825on_val,Ba: produc124828825on_val] :
              ( hBOOL(member808015754on_val(hAPP_P1486793863on_val(produc1564932627on_val(hAPP_P1886180715on_val(produc1441475159on_val(A_1),B_1)),hAPP_P1886180715on_val(produc1441475159on_val(Aa),Ba)),R))
             => ( hBOOL(member808015754on_val(hAPP_P1486793863on_val(produc1564932627on_val(hAPP_P1886180715on_val(produc1441475159on_val(Aa),Ba)),hAPP_P1886180715on_val(produc1441475159on_val(Bx),By)),transi910771962on_val(R)))
               => ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_426_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_fu100249073l_bool,Ax: fun_na939144002on_val,Ay: fun_li1432931796on_val,Bx: fun_na939144002on_val,By: fun_li1432931796on_val,R: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(hAPP_P291613419on_val(produc870913623on_val(hAPP_f1727192346on_val(produc899768717on_val(Ax),Ay)),hAPP_f1727192346on_val(produc899768717on_val(Bx),By)),transi921647814on_val(R)))
     => ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By))
       => ( ! [A_1: fun_na939144002on_val,B_1: fun_li1432931796on_val,Aa: fun_na939144002on_val,Ba: fun_li1432931796on_val] :
              ( hBOOL(member563141460on_val(hAPP_P291613419on_val(produc870913623on_val(hAPP_f1727192346on_val(produc899768717on_val(A_1),B_1)),hAPP_f1727192346on_val(produc899768717on_val(Aa),Ba)),R))
             => ( hBOOL(member563141460on_val(hAPP_P291613419on_val(produc870913623on_val(hAPP_f1727192346on_val(produc899768717on_val(Aa),Ba)),hAPP_f1727192346on_val(produc899768717on_val(Bx),By)),transi921647814on_val(R)))
               => ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_427_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li826105035r_bool,Ax: list_val,Ay: exp_list_char,Bx: list_val,By: exp_list_char,R: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(hAPP_P1220989409t_char(produc1299387215t_char(hAPP_e1752110927t_char(produc1916172923t_char(Ax),Ay)),hAPP_e1752110927t_char(produc1916172923t_char(Bx),By)),transi1789604888t_char(R)))
     => ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Bx),By))
       => ( ! [A_1: list_val,B_1: exp_list_char,Aa: list_val,Ba: exp_list_char] :
              ( hBOOL(member1161907014t_char(hAPP_P1220989409t_char(produc1299387215t_char(hAPP_e1752110927t_char(produc1916172923t_char(A_1),B_1)),hAPP_e1752110927t_char(produc1916172923t_char(Aa),Ba)),R))
             => ( hBOOL(member1161907014t_char(hAPP_P1220989409t_char(produc1299387215t_char(hAPP_e1752110927t_char(produc1916172923t_char(Aa),Ba)),hAPP_e1752110927t_char(produc1916172923t_char(Bx),By)),transi1789604888t_char(R)))
               => ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_428_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li887890578r_bool,Ax: list_ty,Ay: produc662261637t_char,Bx: list_ty,By: produc662261637t_char,R: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(hAPP_P1333668416t_char(produc57279289t_char(hAPP_P1392904962t_char(produc1909267824t_char(Ax),Ay)),hAPP_P1392904962t_char(produc1909267824t_char(Bx),By)),transi1257872013t_char(R)))
     => ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Bx),By))
       => ( ! [A_1: list_ty,B_1: produc662261637t_char,Aa: list_ty,Ba: produc662261637t_char] :
              ( hBOOL(member125098544t_char(hAPP_P1333668416t_char(produc57279289t_char(hAPP_P1392904962t_char(produc1909267824t_char(A_1),B_1)),hAPP_P1392904962t_char(produc1909267824t_char(Aa),Ba)),R))
             => ( hBOOL(member125098544t_char(hAPP_P1333668416t_char(produc57279289t_char(hAPP_P1392904962t_char(produc1909267824t_char(Aa),Ba)),hAPP_P1392904962t_char(produc1909267824t_char(Bx),By)),transi1257872013t_char(R)))
               => ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_429_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li1024794712r_bool,Ax: list_list_char,Ay: produc220283002t_char,Bx: list_list_char,By: produc220283002t_char,R: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(hAPP_P1539798428t_char(produc24551831t_char(hAPP_P767818445t_char(produc921874948t_char(Ax),Ay)),hAPP_P767818445t_char(produc921874948t_char(Bx),By)),transi122195895t_char(R)))
     => ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Bx),By))
       => ( ! [A_1: list_list_char,B_1: produc220283002t_char,Aa: list_list_char,Ba: produc220283002t_char] :
              ( hBOOL(member1420286996t_char(hAPP_P1539798428t_char(produc24551831t_char(hAPP_P767818445t_char(produc921874948t_char(A_1),B_1)),hAPP_P767818445t_char(produc921874948t_char(Aa),Ba)),R))
             => ( hBOOL(member1420286996t_char(hAPP_P1539798428t_char(produc24551831t_char(hAPP_P767818445t_char(produc921874948t_char(Aa),Ba)),hAPP_P767818445t_char(produc921874948t_char(Bx),By)),transi122195895t_char(R)))
               => ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_430_rtrancl__induct2,axiom,
    ! [Pa: fun_li1372729616l_bool,Ax: list_exp_list_char,Ay: produc12694297on_val,Bx: list_exp_list_char,By: produc12694297on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(Ax),Ay)),hAPP_P1963616220on_val(produc379668296on_val(Bx),By)),transi374442731on_val(R)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_exp_list_char,B_1: produc12694297on_val,Aa: list_exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(Ax),Ay)),hAPP_P1963616220on_val(produc379668296on_val(A_1),B_1)),transi374442731on_val(R)))
             => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(A_1),B_1)),hAPP_P1963616220on_val(produc379668296on_val(Aa),Ba)),R))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_431_rtrancl__induct2,axiom,
    ! [Pa: fun_ex1201926843l_bool,Ax: exp_list_char,Ay: produc12694297on_val,Bx: exp_list_char,By: produc12694297on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ax),Ay)),hAPP_P604205461on_val(produc1259058957on_val(Bx),By)),transi2024712006on_val(R)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay))
       => ( ! [A_1: exp_list_char,B_1: produc12694297on_val,Aa: exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ax),Ay)),hAPP_P604205461on_val(produc1259058957on_val(A_1),B_1)),transi2024712006on_val(R)))
             => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(A_1),B_1)),hAPP_P604205461on_val(produc1259058957on_val(Aa),Ba)),R))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_432_rtrancl__induct2,axiom,
    ! [Pa: fun_li221477r_bool,Ax: list_list_char,Ay: exp_list_char,Bx: list_list_char,By: exp_list_char,R: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(hAPP_P1342907945t_char(produc1897818327t_char(hAPP_e952791821t_char(produc1147572817t_char(Ax),Ay)),hAPP_e952791821t_char(produc1147572817t_char(Bx),By)),transi198989188t_char(R)))
     => ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_list_char,B_1: exp_list_char,Aa: list_list_char,Ba: exp_list_char] :
              ( hBOOL(member1999287380t_char(hAPP_P1342907945t_char(produc1897818327t_char(hAPP_e952791821t_char(produc1147572817t_char(Ax),Ay)),hAPP_e952791821t_char(produc1147572817t_char(A_1),B_1)),transi198989188t_char(R)))
             => ( hBOOL(member1999287380t_char(hAPP_P1342907945t_char(produc1897818327t_char(hAPP_e952791821t_char(produc1147572817t_char(A_1),B_1)),hAPP_e952791821t_char(produc1147572817t_char(Aa),Ba)),R))
               => ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_433_rtrancl__induct2,axiom,
    ! [Pa: fun_li860735411r_bool,Ax: list_char,Ay: list_char,Bx: list_char,By: list_char,R: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(hAPP_P1657265855t_char(produc2080520419t_char(hAPP_l2100324114t_char(produc5062597t_char(Ax),Ay)),hAPP_l2100324114t_char(produc5062597t_char(Bx),By)),transi1095029602t_char(R)))
     => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_char,B_1: list_char,Aa: list_char,Ba: list_char] :
              ( hBOOL(member794220506t_char(hAPP_P1657265855t_char(produc2080520419t_char(hAPP_l2100324114t_char(produc5062597t_char(Ax),Ay)),hAPP_l2100324114t_char(produc5062597t_char(A_1),B_1)),transi1095029602t_char(R)))
             => ( hBOOL(member794220506t_char(hAPP_P1657265855t_char(produc2080520419t_char(hAPP_l2100324114t_char(produc5062597t_char(A_1),B_1)),hAPP_l2100324114t_char(produc5062597t_char(Aa),Ba)),R))
               => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_434_rtrancl__induct2,axiom,
    ! [Pa: fun_val_fun_val_bool,Ax: val,Ay: val,Bx: val,By: val,R: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(hAPP_P47773639al_val(produc1244920211al_val(hAPP_v852496844al_val(product_Pair_val_val(Ax),Ay)),hAPP_v852496844al_val(product_Pair_val_val(Bx),By)),transi1423755450al_val(R)))
     => ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Ax),Ay))
       => ( ! [A_1: val,B_1: val,Aa: val,Ba: val] :
              ( hBOOL(member837208074al_val(hAPP_P47773639al_val(produc1244920211al_val(hAPP_v852496844al_val(product_Pair_val_val(Ax),Ay)),hAPP_v852496844al_val(product_Pair_val_val(A_1),B_1)),transi1423755450al_val(R)))
             => ( hBOOL(member837208074al_val(hAPP_P47773639al_val(produc1244920211al_val(hAPP_v852496844al_val(product_Pair_val_val(A_1),B_1)),hAPP_v852496844al_val(product_Pair_val_val(Aa),Ba)),R))
               => ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_435_rtrancl__induct2,axiom,
    ! [Pa: fun_bo1454185032l_bool,Ax: bop,Ay: product_prod_val_val,Bx: bop,By: product_prod_val_val,R: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(hAPP_P2123720426al_val(produc1924279125al_val(hAPP_P929466802al_val(produc621191550al_val(Ax),Ay)),hAPP_P929466802al_val(produc621191550al_val(Bx),By)),transi1906258203al_val(R)))
     => ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Ax),Ay))
       => ( ! [A_1: bop,B_1: product_prod_val_val,Aa: bop,Ba: product_prod_val_val] :
              ( hBOOL(member1732271180al_val(hAPP_P2123720426al_val(produc1924279125al_val(hAPP_P929466802al_val(produc621191550al_val(Ax),Ay)),hAPP_P929466802al_val(produc621191550al_val(A_1),B_1)),transi1906258203al_val(R)))
             => ( hBOOL(member1732271180al_val(hAPP_P2123720426al_val(produc1924279125al_val(hAPP_P929466802al_val(produc621191550al_val(A_1),B_1)),hAPP_P929466802al_val(produc621191550al_val(Aa),Ba)),R))
               => ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_436_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr597144499l_bool,Ax: produc2061676504on_val,Ay: produc2061676504on_val,Bx: produc2061676504on_val,By: produc2061676504on_val,R: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(hAPP_P1758592847on_val(produc1951691075on_val(hAPP_P658340954on_val(produc1611380469on_val(Ax),Ay)),hAPP_P658340954on_val(produc1611380469on_val(Bx),By)),transi208336786on_val(R)))
     => ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Ax),Ay))
       => ( ! [A_1: produc2061676504on_val,B_1: produc2061676504on_val,Aa: produc2061676504on_val,Ba: produc2061676504on_val] :
              ( hBOOL(member88670778on_val(hAPP_P1758592847on_val(produc1951691075on_val(hAPP_P658340954on_val(produc1611380469on_val(Ax),Ay)),hAPP_P658340954on_val(produc1611380469on_val(A_1),B_1)),transi208336786on_val(R)))
             => ( hBOOL(member88670778on_val(hAPP_P1758592847on_val(produc1951691075on_val(hAPP_P658340954on_val(produc1611380469on_val(A_1),B_1)),hAPP_P658340954on_val(produc1611380469on_val(Aa),Ba)),R))
               => ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_437_rtrancl__induct2,axiom,
    ! [Pa: fun_li823162622l_bool,Ax: list_char,Ay: fun_Pr806764899on_val,Bx: list_char,By: fun_Pr806764899on_val,R: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(hAPP_P330218428on_val(produc499151895on_val(hAPP_f900686428on_val(produc823076510on_val(Ax),Ay)),hAPP_f900686428on_val(produc823076510on_val(Bx),By)),transi61620055on_val(R)))
     => ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_char,B_1: fun_Pr806764899on_val,Aa: list_char,Ba: fun_Pr806764899on_val] :
              ( hBOOL(member1322055188on_val(hAPP_P330218428on_val(produc499151895on_val(hAPP_f900686428on_val(produc823076510on_val(Ax),Ay)),hAPP_f900686428on_val(produc823076510on_val(A_1),B_1)),transi61620055on_val(R)))
             => ( hBOOL(member1322055188on_val(hAPP_P330218428on_val(produc499151895on_val(hAPP_f900686428on_val(produc823076510on_val(A_1),B_1)),hAPP_f900686428on_val(produc823076510on_val(Aa),Ba)),R))
               => ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_438_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr633696065l_bool,Ax: produc124828825on_val,Ay: produc124828825on_val,Bx: produc124828825on_val,By: produc124828825on_val,R: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(hAPP_P1486793863on_val(produc1564932627on_val(hAPP_P1886180715on_val(produc1441475159on_val(Ax),Ay)),hAPP_P1886180715on_val(produc1441475159on_val(Bx),By)),transi910771962on_val(R)))
     => ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay))
       => ( ! [A_1: produc124828825on_val,B_1: produc124828825on_val,Aa: produc124828825on_val,Ba: produc124828825on_val] :
              ( hBOOL(member808015754on_val(hAPP_P1486793863on_val(produc1564932627on_val(hAPP_P1886180715on_val(produc1441475159on_val(Ax),Ay)),hAPP_P1886180715on_val(produc1441475159on_val(A_1),B_1)),transi910771962on_val(R)))
             => ( hBOOL(member808015754on_val(hAPP_P1486793863on_val(produc1564932627on_val(hAPP_P1886180715on_val(produc1441475159on_val(A_1),B_1)),hAPP_P1886180715on_val(produc1441475159on_val(Aa),Ba)),R))
               => ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_439_rtrancl__induct2,axiom,
    ! [Pa: fun_fu100249073l_bool,Ax: fun_na939144002on_val,Ay: fun_li1432931796on_val,Bx: fun_na939144002on_val,By: fun_li1432931796on_val,R: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(hAPP_P291613419on_val(produc870913623on_val(hAPP_f1727192346on_val(produc899768717on_val(Ax),Ay)),hAPP_f1727192346on_val(produc899768717on_val(Bx),By)),transi921647814on_val(R)))
     => ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay))
       => ( ! [A_1: fun_na939144002on_val,B_1: fun_li1432931796on_val,Aa: fun_na939144002on_val,Ba: fun_li1432931796on_val] :
              ( hBOOL(member563141460on_val(hAPP_P291613419on_val(produc870913623on_val(hAPP_f1727192346on_val(produc899768717on_val(Ax),Ay)),hAPP_f1727192346on_val(produc899768717on_val(A_1),B_1)),transi921647814on_val(R)))
             => ( hBOOL(member563141460on_val(hAPP_P291613419on_val(produc870913623on_val(hAPP_f1727192346on_val(produc899768717on_val(A_1),B_1)),hAPP_f1727192346on_val(produc899768717on_val(Aa),Ba)),R))
               => ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_440_rtrancl__induct2,axiom,
    ! [Pa: fun_li826105035r_bool,Ax: list_val,Ay: exp_list_char,Bx: list_val,By: exp_list_char,R: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(hAPP_P1220989409t_char(produc1299387215t_char(hAPP_e1752110927t_char(produc1916172923t_char(Ax),Ay)),hAPP_e1752110927t_char(produc1916172923t_char(Bx),By)),transi1789604888t_char(R)))
     => ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_val,B_1: exp_list_char,Aa: list_val,Ba: exp_list_char] :
              ( hBOOL(member1161907014t_char(hAPP_P1220989409t_char(produc1299387215t_char(hAPP_e1752110927t_char(produc1916172923t_char(Ax),Ay)),hAPP_e1752110927t_char(produc1916172923t_char(A_1),B_1)),transi1789604888t_char(R)))
             => ( hBOOL(member1161907014t_char(hAPP_P1220989409t_char(produc1299387215t_char(hAPP_e1752110927t_char(produc1916172923t_char(A_1),B_1)),hAPP_e1752110927t_char(produc1916172923t_char(Aa),Ba)),R))
               => ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_441_rtrancl__induct2,axiom,
    ! [Pa: fun_li887890578r_bool,Ax: list_ty,Ay: produc662261637t_char,Bx: list_ty,By: produc662261637t_char,R: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(hAPP_P1333668416t_char(produc57279289t_char(hAPP_P1392904962t_char(produc1909267824t_char(Ax),Ay)),hAPP_P1392904962t_char(produc1909267824t_char(Bx),By)),transi1257872013t_char(R)))
     => ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_ty,B_1: produc662261637t_char,Aa: list_ty,Ba: produc662261637t_char] :
              ( hBOOL(member125098544t_char(hAPP_P1333668416t_char(produc57279289t_char(hAPP_P1392904962t_char(produc1909267824t_char(Ax),Ay)),hAPP_P1392904962t_char(produc1909267824t_char(A_1),B_1)),transi1257872013t_char(R)))
             => ( hBOOL(member125098544t_char(hAPP_P1333668416t_char(produc57279289t_char(hAPP_P1392904962t_char(produc1909267824t_char(A_1),B_1)),hAPP_P1392904962t_char(produc1909267824t_char(Aa),Ba)),R))
               => ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_442_rtrancl__induct2,axiom,
    ! [Pa: fun_li1024794712r_bool,Ax: list_list_char,Ay: produc220283002t_char,Bx: list_list_char,By: produc220283002t_char,R: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(hAPP_P1539798428t_char(produc24551831t_char(hAPP_P767818445t_char(produc921874948t_char(Ax),Ay)),hAPP_P767818445t_char(produc921874948t_char(Bx),By)),transi122195895t_char(R)))
     => ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_list_char,B_1: produc220283002t_char,Aa: list_list_char,Ba: produc220283002t_char] :
              ( hBOOL(member1420286996t_char(hAPP_P1539798428t_char(produc24551831t_char(hAPP_P767818445t_char(produc921874948t_char(Ax),Ay)),hAPP_P767818445t_char(produc921874948t_char(A_1),B_1)),transi122195895t_char(R)))
             => ( hBOOL(member1420286996t_char(hAPP_P1539798428t_char(produc24551831t_char(hAPP_P767818445t_char(produc921874948t_char(A_1),B_1)),hAPP_P767818445t_char(produc921874948t_char(Aa),Ba)),R))
               => ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_443_rtranclE,axiom,
    ! [A: list_char,B: list_char,R: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(A),B),transi1395422419t_char(R)))
     => ( ( A != B )
       => ~ ! [Y_1: list_char] :
              ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(A),Y_1),transi1395422419t_char(R)))
             => ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(Y_1),B),R)) ) ) ) ).

tff(fact_444_rtranclE,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(A),B),transi374442731on_val(R)))
     => ( ( A != B )
       => ~ ! [Y_1: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(A),Y_1),transi374442731on_val(R)))
             => ~ hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(Y_1),B),R)) ) ) ) ).

tff(fact_445_rtranclE,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(A),B),transi2024712006on_val(R)))
     => ( ( A != B )
       => ~ ! [Y_1: produc124828825on_val] :
              ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(A),Y_1),transi2024712006on_val(R)))
             => ~ hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(Y_1),B),R)) ) ) ) ).

tff(fact_446_rtranclE,axiom,
    ! [A: val,B: val,R: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(A),B),transi935034983cl_val(R)))
     => ( ( A != B )
       => ~ ! [Y_1: val] :
              ( hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(A),Y_1),transi935034983cl_val(R)))
             => ~ hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(Y_1),B),R)) ) ) ) ).

tff(fact_447_converse__rtranclE,axiom,
    ! [X_1: list_char,Z_1: list_char,R: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(X_1),Z_1),transi1395422419t_char(R)))
     => ( ( X_1 != Z_1 )
       => ~ ! [Y_1: list_char] :
              ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(X_1),Y_1),R))
             => ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(Y_1),Z_1),transi1395422419t_char(R))) ) ) ) ).

tff(fact_448_converse__rtranclE,axiom,
    ! [X_1: produc2061676504on_val,Z_1: produc2061676504on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(X_1),Z_1),transi374442731on_val(R)))
     => ( ( X_1 != Z_1 )
       => ~ ! [Y_1: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(X_1),Y_1),R))
             => ~ hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(Y_1),Z_1),transi374442731on_val(R))) ) ) ) ).

tff(fact_449_converse__rtranclE,axiom,
    ! [X_1: produc124828825on_val,Z_1: produc124828825on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(X_1),Z_1),transi2024712006on_val(R)))
     => ( ( X_1 != Z_1 )
       => ~ ! [Y_1: produc124828825on_val] :
              ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(X_1),Y_1),R))
             => ~ hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(Y_1),Z_1),transi2024712006on_val(R))) ) ) ) ).

tff(fact_450_converse__rtranclE,axiom,
    ! [X_1: val,Z_1: val,R: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(X_1),Z_1),transi935034983cl_val(R)))
     => ( ( X_1 != Z_1 )
       => ~ ! [Y_1: val] :
              ( hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(X_1),Y_1),R))
             => ~ hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(Y_1),Z_1),transi935034983cl_val(R))) ) ) ) ).

tff(fact_451_converse__rtrancl__induct,axiom,
    ! [Pa: fun_list_char_bool,A: list_char,B: list_char,R: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(A),B),transi1395422419t_char(R)))
     => ( hBOOL(hAPP_list_char_bool(Pa,B))
       => ( ! [Y_1: list_char,Z: list_char] :
              ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(Y_1),Z),R))
             => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(Z),B),transi1395422419t_char(R)))
               => ( hBOOL(hAPP_list_char_bool(Pa,Z))
                 => hBOOL(hAPP_list_char_bool(Pa,Y_1)) ) ) )
         => hBOOL(hAPP_list_char_bool(Pa,A)) ) ) ) ).

tff(fact_452_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr248118298l_bool,A: produc2061676504on_val,B: produc2061676504on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(A),B),transi374442731on_val(R)))
     => ( hBOOL(hAPP_P71593144l_bool(Pa,B))
       => ( ! [Y_1: produc2061676504on_val,Z: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(Y_1),Z),R))
             => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(Z),B),transi374442731on_val(R)))
               => ( hBOOL(hAPP_P71593144l_bool(Pa,Z))
                 => hBOOL(hAPP_P71593144l_bool(Pa,Y_1)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(Pa,A)) ) ) ) ).

tff(fact_453_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr680585871l_bool,A: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(A),B),transi2024712006on_val(R)))
     => ( hBOOL(hAPP_P1708370145l_bool(Pa,B))
       => ( ! [Y_1: produc124828825on_val,Z: produc124828825on_val] :
              ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(Y_1),Z),R))
             => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(Z),B),transi2024712006on_val(R)))
               => ( hBOOL(hAPP_P1708370145l_bool(Pa,Z))
                 => hBOOL(hAPP_P1708370145l_bool(Pa,Y_1)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(Pa,A)) ) ) ) ).

tff(fact_454_converse__rtrancl__induct,axiom,
    ! [Pa: fun_val_bool,A: val,B: val,R: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(A),B),transi935034983cl_val(R)))
     => ( hBOOL(hAPP_val_bool(Pa,B))
       => ( ! [Y_1: val,Z: val] :
              ( hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(Y_1),Z),R))
             => ( hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(Z),B),transi935034983cl_val(R)))
               => ( hBOOL(hAPP_val_bool(Pa,Z))
                 => hBOOL(hAPP_val_bool(Pa,Y_1)) ) ) )
         => hBOOL(hAPP_val_bool(Pa,A)) ) ) ) ).

tff(fact_455_mem__def,axiom,
    ! [X_1: produc1278157519t_char,A_2: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(X_1,A_2))
    <=> hBOOL(hAPP_P449474095r_bool(A_2,X_1)) ) ).

tff(fact_456_mem__def,axiom,
    ! [X_1: produc430140671on_val,A_2: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(X_1,A_2))
    <=> hBOOL(hAPP_P1333315679l_bool(A_2,X_1)) ) ).

tff(fact_457_mem__def,axiom,
    ! [X_1: produc1102272487on_val,A_2: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(X_1,A_2))
    <=> hBOOL(hAPP_P282169671l_bool(A_2,X_1)) ) ).

tff(fact_458_rtrancl__induct,axiom,
    ! [Pa: fun_list_char_bool,A: list_char,B: list_char,R: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(A),B),transi1395422419t_char(R)))
     => ( hBOOL(hAPP_list_char_bool(Pa,A))
       => ( ! [Y_1: list_char,Z: list_char] :
              ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(A),Y_1),transi1395422419t_char(R)))
             => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(Y_1),Z),R))
               => ( hBOOL(hAPP_list_char_bool(Pa,Y_1))
                 => hBOOL(hAPP_list_char_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_list_char_bool(Pa,B)) ) ) ) ).

tff(fact_459_rtrancl__induct,axiom,
    ! [Pa: fun_Pr248118298l_bool,A: produc2061676504on_val,B: produc2061676504on_val,R: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(A),B),transi374442731on_val(R)))
     => ( hBOOL(hAPP_P71593144l_bool(Pa,A))
       => ( ! [Y_1: produc2061676504on_val,Z: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(A),Y_1),transi374442731on_val(R)))
             => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(Y_1),Z),R))
               => ( hBOOL(hAPP_P71593144l_bool(Pa,Y_1))
                 => hBOOL(hAPP_P71593144l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(Pa,B)) ) ) ) ).

tff(fact_460_rtrancl__induct,axiom,
    ! [Pa: fun_Pr680585871l_bool,A: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(A),B),transi2024712006on_val(R)))
     => ( hBOOL(hAPP_P1708370145l_bool(Pa,A))
       => ( ! [Y_1: produc124828825on_val,Z: produc124828825on_val] :
              ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(A),Y_1),transi2024712006on_val(R)))
             => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(Y_1),Z),R))
               => ( hBOOL(hAPP_P1708370145l_bool(Pa,Y_1))
                 => hBOOL(hAPP_P1708370145l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(Pa,B)) ) ) ) ).

tff(fact_461_rtrancl__induct,axiom,
    ! [Pa: fun_val_bool,A: val,B: val,R: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(A),B),transi935034983cl_val(R)))
     => ( hBOOL(hAPP_val_bool(Pa,A))
       => ( ! [Y_1: val,Z: val] :
              ( hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(A),Y_1),transi935034983cl_val(R)))
             => ( hBOOL(member649088532al_val(hAPP_v852496844al_val(product_Pair_val_val(Y_1),Z),R))
               => ( hBOOL(hAPP_val_bool(Pa,Y_1))
                 => hBOOL(hAPP_val_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_val_bool(Pa,B)) ) ) ) ).

tff(fact_462_blocksRedsFinal,axiom,
    ! [L_3: fun_li1432931796on_val,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E_1: exp_list_char,H_1: fun_na939144002on_val,L_2: fun_li1432931796on_val,Pa: list_P1999446415t_char,Vsa: list_val,Vsa_1: list_list_char,Tsa: list_ty] :
      ( ( size_s2113983095t_char(Vsa_1) = size_size_list_ty(Tsa) )
     => ( ( size_size_list_val(Vsa) = size_size_list_ty(Tsa) )
       => ( hBOOL(distinct_list_char(Vsa_1))
         => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),hAPP_f1727192346on_val(produc899768717on_val(Ha),map_up1085636310ar_val(L_1,Vsa_1,Vsa)))),hAPP_P604205461on_val(produc1259058957on_val(E_1),hAPP_f1727192346on_val(produc899768717on_val(H_1),L_2))),transi2024712006on_val(red(Pa))))
           => ( hBOOL(final_list_char(E_1))
             => ( ( L_3 = overri2012515291on_val(L_2,L_1,set_list_char(Vsa_1)) )
               => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(blocks(hAPP_P767818445t_char(produc921874948t_char(Vsa_1),hAPP_P1392904962t_char(produc1909267824t_char(Tsa),hAPP_e1752110927t_char(produc1916172923t_char(Vsa),Ea))))),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))),hAPP_P604205461on_val(produc1259058957on_val(E_1),hAPP_f1727192346on_val(produc899768717on_val(H_1),L_3))),transi2024712006on_val(red(Pa)))) ) ) ) ) ) ) ).

tff(fact_463_map__eq__conv,axiom,
    ! [F_1: fun_list_char_val,Xs: list_list_char,G: fun_list_char_val] :
      ( ( hAPP_l1892737211st_val(map_list_char_val(F_1),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Xs) )
    <=> ! [X_3: list_char] :
          ( hBOOL(member_list_char(X_3,set_list_char(Xs)))
         => ( hAPP_list_char_val(F_1,X_3) = hAPP_list_char_val(G,X_3) ) ) ) ).

tff(fact_464_map__eq__conv,axiom,
    ! [F_1: fun_va223928858t_char,Xs: list_val,G: fun_va223928858t_char] :
      ( ( hAPP_l732421366t_char(map_va1934808527t_char(F_1),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Xs) )
    <=> ! [X_3: val] :
          ( hBOOL(member_val(X_3,set_val(Xs)))
         => ( hAPP_v834067052t_char(F_1,X_3) = hAPP_v834067052t_char(G,X_3) ) ) ) ).

tff(fact_465_map__eq__conv,axiom,
    ! [F_1: fun_ty_option_ty,Xs: list_ty,G: fun_ty_option_ty] :
      ( ( hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Xs) )
    <=> ! [X_3: ty] :
          ( hBOOL(member_ty(X_3,set_ty(Xs)))
         => ( hAPP_ty_option_ty(F_1,X_3) = hAPP_ty_option_ty(G,X_3) ) ) ) ).

tff(fact_466_map__eq__conv,axiom,
    ! [F_1: fun_val_option_ty,Xs: list_val,G: fun_val_option_ty] :
      ( ( hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Xs) )
    <=> ! [X_3: val] :
          ( hBOOL(member_val(X_3,set_val(Xs)))
         => ( hAPP_val_option_ty(F_1,X_3) = hAPP_val_option_ty(G,X_3) ) ) ) ).

tff(fact_467_blocksReds,axiom,
    ! [Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E_1: exp_list_char,H_1: fun_na939144002on_val,L_2: fun_li1432931796on_val,Pa: list_P1999446415t_char,Vsa: list_val,Vsa_1: list_list_char,Tsa: list_ty] :
      ( ( size_s2113983095t_char(Vsa_1) = size_size_list_ty(Tsa) )
     => ( ( size_size_list_val(Vsa) = size_size_list_ty(Tsa) )
       => ( hBOOL(distinct_list_char(Vsa_1))
         => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),hAPP_f1727192346on_val(produc899768717on_val(Ha),map_up1085636310ar_val(L_1,Vsa_1,Vsa)))),hAPP_P604205461on_val(produc1259058957on_val(E_1),hAPP_f1727192346on_val(produc899768717on_val(H_1),L_2))),transi2024712006on_val(red(Pa))))
           => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(blocks(hAPP_P767818445t_char(produc921874948t_char(Vsa_1),hAPP_P1392904962t_char(produc1909267824t_char(Tsa),hAPP_e1752110927t_char(produc1916172923t_char(Vsa),Ea))))),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))),hAPP_P604205461on_val(produc1259058957on_val(blocks(hAPP_P767818445t_char(produc921874948t_char(Vsa_1),hAPP_P1392904962t_char(produc1909267824t_char(Tsa),hAPP_e1752110927t_char(produc1916172923t_char(hAPP_l1892737211st_val(map_list_char_val(comp_o1129292306t_char(the_val,L_2)),Vsa_1)),E_1))))),hAPP_f1727192346on_val(produc899768717on_val(H_1),overri2012515291on_val(L_2,L_1,set_list_char(Vsa_1))))),transi2024712006on_val(red(Pa)))) ) ) ) ) ).

tff(fact_468_map__cong,axiom,
    ! [F_1: fun_list_char_val,G: fun_list_char_val,Xs: list_list_char,Ys: list_list_char] :
      ( ( Xs = Ys )
     => ( ! [X_3: list_char] :
            ( hBOOL(member_list_char(X_3,set_list_char(Ys)))
           => ( hAPP_list_char_val(F_1,X_3) = hAPP_list_char_val(G,X_3) ) )
       => ( hAPP_l1892737211st_val(map_list_char_val(F_1),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Ys) ) ) ) ).

tff(fact_469_map__cong,axiom,
    ! [F_1: fun_va223928858t_char,G: fun_va223928858t_char,Xs: list_val,Ys: list_val] :
      ( ( Xs = Ys )
     => ( ! [X_3: val] :
            ( hBOOL(member_val(X_3,set_val(Ys)))
           => ( hAPP_v834067052t_char(F_1,X_3) = hAPP_v834067052t_char(G,X_3) ) )
       => ( hAPP_l732421366t_char(map_va1934808527t_char(F_1),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Ys) ) ) ) ).

tff(fact_470_map__cong,axiom,
    ! [F_1: fun_ty_option_ty,G: fun_ty_option_ty,Xs: list_ty,Ys: list_ty] :
      ( ( Xs = Ys )
     => ( ! [X_3: ty] :
            ( hBOOL(member_ty(X_3,set_ty(Ys)))
           => ( hAPP_ty_option_ty(F_1,X_3) = hAPP_ty_option_ty(G,X_3) ) )
       => ( hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys) ) ) ) ).

tff(fact_471_map__cong,axiom,
    ! [F_1: fun_val_option_ty,G: fun_val_option_ty,Xs: list_val,Ys: list_val] :
      ( ( Xs = Ys )
     => ( ! [X_3: val] :
            ( hBOOL(member_val(X_3,set_val(Ys)))
           => ( hAPP_val_option_ty(F_1,X_3) = hAPP_val_option_ty(G,X_3) ) )
       => ( hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys) ) ) ) ).

tff(fact_472_map__idI,axiom,
    ! [F_1: fun_li1751394789t_char,Xs: list_list_char] :
      ( ! [X_3: list_char] :
          ( hBOOL(member_list_char(X_3,set_list_char(Xs)))
         => ( hAPP_l1074208899t_char(F_1,X_3) = X_3 ) )
     => ( hAPP_l407174677t_char(map_li1333403488t_char(F_1),Xs) = Xs ) ) ).

tff(fact_473_map__idI,axiom,
    ! [F_1: fun_Pr1380325635t_char,Xs: list_P1916372464t_char] :
      ( ! [X_3: produc1278157519t_char] :
          ( hBOOL(member1251428284t_char(X_3,set_Pr550895038t_char(Xs)))
         => ( hAPP_P760138657t_char(F_1,X_3) = X_3 ) )
     => ( hAPP_l250787541t_char(map_Pr361633150t_char(F_1),Xs) = Xs ) ) ).

tff(fact_474_map__idI,axiom,
    ! [F_1: fun_Pr1898553187on_val,Xs: list_P507235360on_val] :
      ( ! [X_3: produc430140671on_val] :
          ( hBOOL(member875476972on_val(X_3,set_Pr771975662on_val(Xs)))
         => ( hAPP_P1439304705on_val(F_1,X_3) = X_3 ) )
     => ( hAPP_l1208602837on_val(map_Pr1729094110on_val(F_1),Xs) = Xs ) ) ).

tff(fact_475_map__idI,axiom,
    ! [F_1: fun_Pr12181427on_val,Xs: list_P1439941640on_val] :
      ( ! [X_3: produc1102272487on_val] :
          ( hBOOL(member773094996on_val(X_3,set_Pr1921835862on_val(Xs)))
         => ( hAPP_P918220497on_val(F_1,X_3) = X_3 ) )
     => ( hAPP_l1695428693on_val(map_Pr1655409582on_val(F_1),Xs) = Xs ) ) ).

tff(fact_476_map__ext,axiom,
    ! [F_1: fun_list_char_val,G: fun_list_char_val,Xs: list_list_char] :
      ( ! [X_3: list_char] :
          ( hBOOL(member_list_char(X_3,set_list_char(Xs)))
         => ( hAPP_list_char_val(F_1,X_3) = hAPP_list_char_val(G,X_3) ) )
     => ( hAPP_l1892737211st_val(map_list_char_val(F_1),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Xs) ) ) ).

tff(fact_477_map__ext,axiom,
    ! [F_1: fun_va223928858t_char,G: fun_va223928858t_char,Xs: list_val] :
      ( ! [X_3: val] :
          ( hBOOL(member_val(X_3,set_val(Xs)))
         => ( hAPP_v834067052t_char(F_1,X_3) = hAPP_v834067052t_char(G,X_3) ) )
     => ( hAPP_l732421366t_char(map_va1934808527t_char(F_1),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Xs) ) ) ).

tff(fact_478_map__ext,axiom,
    ! [F_1: fun_ty_option_ty,G: fun_ty_option_ty,Xs: list_ty] :
      ( ! [X_3: ty] :
          ( hBOOL(member_ty(X_3,set_ty(Xs)))
         => ( hAPP_ty_option_ty(F_1,X_3) = hAPP_ty_option_ty(G,X_3) ) )
     => ( hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Xs) ) ) ).

tff(fact_479_map__ext,axiom,
    ! [F_1: fun_val_option_ty,G: fun_val_option_ty,Xs: list_val] :
      ( ! [X_3: val] :
          ( hBOOL(member_val(X_3,set_val(Xs)))
         => ( hAPP_val_option_ty(F_1,X_3) = hAPP_val_option_ty(G,X_3) ) )
     => ( hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Xs) ) ) ).

tff(fact_480_ex__map__conv,axiom,
    ! [Ys: list_val,F_1: fun_list_char_val] :
      ( ? [Xs_1: list_list_char] : Ys = hAPP_l1892737211st_val(map_list_char_val(F_1),Xs_1)
    <=> ! [X_3: val] :
          ( hBOOL(member_val(X_3,set_val(Ys)))
         => ? [Xa: list_char] : X_3 = hAPP_list_char_val(F_1,Xa) ) ) ).

tff(fact_481_ex__map__conv,axiom,
    ! [Ys: list_exp_list_char,F_1: fun_va223928858t_char] :
      ( ? [Xs_1: list_val] : Ys = hAPP_l732421366t_char(map_va1934808527t_char(F_1),Xs_1)
    <=> ! [X_3: exp_list_char] :
          ( hBOOL(member_exp_list_char(X_3,set_exp_list_char(Ys)))
         => ? [Xa: val] : X_3 = hAPP_v834067052t_char(F_1,Xa) ) ) ).

tff(fact_482_ex__map__conv,axiom,
    ! [Ys: list_option_ty,F_1: fun_ty_option_ty] :
      ( ? [Xs_1: list_ty] : Ys = hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Xs_1)
    <=> ! [X_3: option_ty] :
          ( hBOOL(member_option_ty(X_3,set_option_ty(Ys)))
         => ? [Xa: ty] : X_3 = hAPP_ty_option_ty(F_1,Xa) ) ) ).

tff(fact_483_ex__map__conv,axiom,
    ! [Ys: list_option_ty,F_1: fun_val_option_ty] :
      ( ? [Xs_1: list_val] : Ys = hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Xs_1)
    <=> ! [X_3: option_ty] :
          ( hBOOL(member_option_ty(X_3,set_option_ty(Ys)))
         => ? [Xa: val] : X_3 = hAPP_val_option_ty(F_1,Xa) ) ) ).

tff(fact_484_map__upds__apply__nontin,axiom,
    ! [F_1: fun_li1432931796on_val,Ys: list_val,X_1: list_char,Xs: list_list_char] :
      ( ~ hBOOL(member_list_char(X_1,set_list_char(Xs)))
     => ( hAPP_l207779698on_val(map_up1085636310ar_val(F_1,Xs,Ys),X_1) = hAPP_l207779698on_val(F_1,X_1) ) ) ).

tff(fact_485_map__upds__apply__nontin,axiom,
    ! [F_1: fun_li688206603ion_ty,Ys: list_ty,X_1: list_char,Xs: list_list_char] :
      ( ~ hBOOL(member_list_char(X_1,set_list_char(Xs)))
     => ( hAPP_l512744617ion_ty(map_up891053837har_ty(F_1,Xs,Ys),X_1) = hAPP_l512744617ion_ty(F_1,X_1) ) ) ).

tff(fact_486_Red__lcl__add,axiom,
    ! [L_0: fun_li1432931796on_val,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E_1: exp_list_char,H_1: fun_na939144002on_val,L_2: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))),hAPP_P604205461on_val(produc1259058957on_val(E_1),hAPP_f1727192346on_val(produc899768717on_val(H_1),L_2))),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),hAPP_f1727192346on_val(produc899768717on_val(Ha),map_ad325961431ar_val(L_0,L_1)))),hAPP_P604205461on_val(produc1259058957on_val(E_1),hAPP_f1727192346on_val(produc899768717on_val(H_1),map_ad325961431ar_val(L_0,L_2)))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_487_hext__def,axiom,
    ! [Ha: fun_na939144002on_val,H_1: fun_na939144002on_val] :
      ( hBOOL(hext(Ha,H_1))
    <=> ! [A_1: nat,C_1: list_char,Fs_2: fun_Pr806764899on_val] :
          ( ( hAPP_n546249108on_val(Ha,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C_1),Fs_2)) )
         => ? [Fs_3: fun_Pr806764899on_val] : hAPP_n546249108on_val(H_1,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C_1),Fs_3)) ) ) ).

tff(fact_488_List_Omap_Ocomp,axiom,
    ! [F_1: fun_option_val_val,G: fun_li1432931796on_val] : comp_l1825390573t_char(map_option_val_val(F_1),map_li50976719on_val(G)) = map_list_char_val(comp_o1129292306t_char(F_1,G)) ).

tff(fact_489_map__comp__map,axiom,
    ! [F_1: fun_option_val_val,G: fun_li1432931796on_val] : comp_l1825390573t_char(map_option_val_val(F_1),map_li50976719on_val(G)) = map_list_char_val(comp_o1129292306t_char(F_1,G)) ).

tff(fact_490_map__add__assoc,axiom,
    ! [M1: fun_li1432931796on_val,M2: fun_li1432931796on_val,M3: fun_li1432931796on_val] : map_ad325961431ar_val(M1,map_ad325961431ar_val(M2,M3)) = map_ad325961431ar_val(map_ad325961431ar_val(M1,M2),M3) ).

tff(fact_491_map__add__find__right,axiom,
    ! [M_1: fun_li1432931796on_val,N: fun_li1432931796on_val,K: list_char,Xx: val] :
      ( ( hAPP_l207779698on_val(N,K) = hAPP_val_option_val(some_val,Xx) )
     => ( hAPP_l207779698on_val(map_ad325961431ar_val(M_1,N),K) = hAPP_val_option_val(some_val,Xx) ) ) ).

tff(fact_492_map__add__upds,axiom,
    ! [M1: fun_li1432931796on_val,M2: fun_li1432931796on_val,Xs: list_list_char,Ys: list_val] : map_ad325961431ar_val(M1,map_up1085636310ar_val(M2,Xs,Ys)) = map_up1085636310ar_val(map_ad325961431ar_val(M1,M2),Xs,Ys) ).

tff(fact_493_map__add__upds,axiom,
    ! [M1: fun_li688206603ion_ty,M2: fun_li688206603ion_ty,Xs: list_list_char,Ys: list_ty] : map_add_list_char_ty(M1,map_up891053837har_ty(M2,Xs,Ys)) = map_up891053837har_ty(map_add_list_char_ty(M1,M2),Xs,Ys) ).

tff(fact_494_map__map,axiom,
    ! [F_1: fun_option_val_val,G: fun_li1432931796on_val,Xs: list_list_char] : hAPP_l228474410st_val(map_option_val_val(F_1),hAPP_l297961988on_val(map_li50976719on_val(G),Xs)) = hAPP_l1892737211st_val(map_list_char_val(comp_o1129292306t_char(F_1,G)),Xs) ).

tff(fact_495_List_Omap_Ocompositionality,axiom,
    ! [F_1: fun_option_val_val,G: fun_li1432931796on_val,List: list_list_char] : hAPP_l228474410st_val(map_option_val_val(F_1),hAPP_l297961988on_val(map_li50976719on_val(G),List)) = hAPP_l1892737211st_val(map_list_char_val(comp_o1129292306t_char(F_1,G)),List) ).

tff(fact_496_the_Osimps,axiom,
    ! [X_2: val] : hAPP_option_val_val(the_val,hAPP_val_option_val(some_val,X_2)) = X_2 ).

tff(fact_497_the_Osimps,axiom,
    ! [X_1: produc639455274on_val] : hAPP_o1977518472on_val(the_Pr431167171on_val,hAPP_P1510515380on_val(some_P948696889on_val,X_1)) = X_1 ).

tff(fact_498_the_Osimps,axiom,
    ! [X_2: ty] : hAPP_option_ty_ty(the_ty,hAPP_ty_option_ty(some_ty,X_2)) = X_2 ).

tff(fact_499_red__lcl__add,axiom,
    ! [L_0: fun_li1432931796on_val,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E_1: exp_list_char,H_1: fun_na939144002on_val,L_2: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))),hAPP_P604205461on_val(produc1259058957on_val(E_1),hAPP_f1727192346on_val(produc899768717on_val(H_1),L_2))),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),hAPP_f1727192346on_val(produc899768717on_val(Ha),map_ad325961431ar_val(L_0,L_1)))),hAPP_P604205461on_val(produc1259058957on_val(E_1),hAPP_f1727192346on_val(produc899768717on_val(H_1),map_ad325961431ar_val(L_0,L_2)))),red(Pa))) ) ).

tff(fact_500_hext__objD,axiom,
    ! [A: nat,C: list_char,Fs: fun_Pr806764899on_val,Ha: fun_na939144002on_val,H_1: fun_na939144002on_val] :
      ( hBOOL(hext(Ha,H_1))
     => ( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C),Fs)) )
       => ? [Fs_3: fun_Pr806764899on_val] : hAPP_n546249108on_val(H_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C),Fs_3)) ) ) ).

tff(fact_501_hextI,axiom,
    ! [H_1: fun_na939144002on_val,Ha: fun_na939144002on_val] :
      ( ! [A_1: nat,C_1: list_char,Fs_2: fun_Pr806764899on_val] :
          ( ( hAPP_n546249108on_val(Ha,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C_1),Fs_2)) )
         => ? [Fs_3: fun_Pr806764899on_val] : hAPP_n546249108on_val(H_1,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C_1),Fs_3)) )
     => hBOOL(hext(Ha,H_1)) ) ).

tff(fact_502_TryRedsVal,axiom,
    ! [C: list_char,V: list_char,E_2_1: exp_list_char,Ea: exp_list_char,S: produc12694297on_val,V_2: val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_2)),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(tryCatch_list_char(Ea,C,V,E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_2)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_503_reds__preserves__lconf,axiom,
    ! [E: fun_li688206603ion_ty,Tsa: list_ty,Es: list_exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,Es_1: list_exp_list_char,H_1: fun_na939144002on_val,L_2: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(Es),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))),hAPP_P1963616220on_val(produc379668296on_val(Es_1),hAPP_f1727192346on_val(produc899768717on_val(H_1),L_2))),reds(Pa)))
     => ( hBOOL(wTrts(Pa,Ha,E,Es,Tsa))
       => ( hBOOL(lconf_496643946t_char(Pa,Ha,L_1,E))
         => hBOOL(lconf_496643946t_char(Pa,H_1,L_2,E)) ) ) ) ).

tff(fact_504_reds__preserves__hconf,axiom,
    ! [E: fun_li688206603ion_ty,Tsa: list_ty,Es: list_exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,Es_1: list_exp_list_char,H_1: fun_na939144002on_val,L_2: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(Es),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))),hAPP_P1963616220on_val(produc379668296on_val(Es_1),hAPP_f1727192346on_val(produc899768717on_val(H_1),L_2))),reds(Pa)))
     => ( hBOOL(wTrts(Pa,Ha,E,Es,Tsa))
       => ( hBOOL(hconf_97414254t_char(Pa,Ha))
         => hBOOL(hconf_97414254t_char(Pa,H_1)) ) ) ) ).

tff(fact_505_BinOp2Reds,axiom,
    ! [V_2: val,Bop: bop,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(binOp_list_char(hAPP_v834067052t_char(val_list_char,V_2),Bop,Ea)),S)),hAPP_P604205461on_val(produc1259058957on_val(binOp_list_char(hAPP_v834067052t_char(val_list_char,V_2),Bop,E_1)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_506_FAssReds2,axiom,
    ! [V_2: val,F: list_char,D: list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAss_list_char(hAPP_v834067052t_char(val_list_char,V_2),F,D,Ea)),S)),hAPP_P604205461on_val(produc1259058957on_val(fAss_list_char(hAPP_v834067052t_char(val_list_char,V_2),F,D,E_1)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_507_SeqReds2,axiom,
    ! [E_2_1: exp_list_char,E_2_2: exp_list_char,S_2: produc12694297on_val,E_1_1: exp_list_char,S_0: produc12694297on_val,V_1_1: val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(E_1_1),S_0)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1_1)),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(E_2_1),S_1_1)),hAPP_P604205461on_val(produc1259058957on_val(E_2_2),S_2)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(seq_list_char(E_1_1,E_2_1)),S_0)),hAPP_P604205461on_val(produc1259058957on_val(E_2_2),S_2)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_508_WTrtSeq,axiom,
    ! [E_2_1: exp_list_char,T_2: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E: fun_li688206603ion_ty,E_1_1: exp_list_char,T_1_1: ty] :
      ( hBOOL(wTrt(Pa,Ha,E,E_1_1,T_1_1))
     => ( hBOOL(wTrt(Pa,Ha,E,E_2_1,T_2))
       => hBOOL(wTrt(Pa,Ha,E,seq_list_char(E_1_1,E_2_1),T_2)) ) ) ).

tff(fact_509_Seq,axiom,
    ! [E_1_1: exp_list_char,E_2_1: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char,E_0: exp_list_char,S_0: produc12694297on_val,V_2: val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_0,S_0),hAPP_v834067052t_char(val_list_char,V_2)),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_1_1),E_2_1),S_2))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,seq_list_char(E_0,E_1_1),S_0),E_2_1),S_2)) ) ) ).

tff(fact_510_Try,axiom,
    ! [C: list_char,V: list_char,E_2_1: exp_list_char,Pa: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc12694297on_val,V_1_1: val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,V_1_1)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,tryCatch_list_char(E_1_1,C,V,E_2_1),S_0),hAPP_v834067052t_char(val_list_char,V_1_1)),S_1_1)) ) ).

tff(fact_511_red__reds_OSeqRed,axiom,
    ! [E_2_1: exp_list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(seq_list_char(Ea,E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(seq_list_char(E_1,E_2_1)),S_1)),red(Pa))) ) ).

tff(fact_512_red__reds_OFAssRed1,axiom,
    ! [F: list_char,D: list_char,E_2_1: exp_list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAss_list_char(Ea,F,D,E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(fAss_list_char(E_1,F,D,E_2_1)),S_1)),red(Pa))) ) ).

tff(fact_513_red__reds_OBinOpRed1,axiom,
    ! [Bop: bop,E_2_1: exp_list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(binOp_list_char(Ea,Bop,E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(binOp_list_char(E_1,Bop,E_2_1)),S_1)),red(Pa))) ) ).

tff(fact_514_reds__hext__incr,axiom,
    ! [Es: list_exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,Es_1: list_exp_list_char,H_1: fun_na939144002on_val,L_2: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(Es),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))),hAPP_P1963616220on_val(produc379668296on_val(Es_1),hAPP_f1727192346on_val(produc899768717on_val(H_1),L_2))),reds(Pa)))
     => hBOOL(hext(Ha,H_1)) ) ).

tff(fact_515_red__reds_OTryRed,axiom,
    ! [C: list_char,V: list_char,E_2_1: exp_list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(tryCatch_list_char(Ea,C,V,E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(tryCatch_list_char(E_1,C,V,E_2_1)),S_1)),red(Pa))) ) ).

tff(fact_516_red__reds_ORedSeq,axiom,
    ! [V_2: val,E_2_1: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(seq_list_char(hAPP_v834067052t_char(val_list_char,V_2),E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(E_2_1),S)),red(Pa))) ).

tff(fact_517_SeqReds,axiom,
    ! [E_2_1: exp_list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(seq_list_char(Ea,E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(seq_list_char(E_1,E_2_1)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_518_red__reds_OFAssRed2,axiom,
    ! [V_2: val,F: list_char,D: list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAss_list_char(hAPP_v834067052t_char(val_list_char,V_2),F,D,Ea)),S)),hAPP_P604205461on_val(produc1259058957on_val(fAss_list_char(hAPP_v834067052t_char(val_list_char,V_2),F,D,E_1)),S_1)),red(Pa))) ) ).

tff(fact_519_red__reds_OBinOpRed2,axiom,
    ! [V_1_1: val,Bop: bop,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_1),Bop,Ea)),S)),hAPP_P604205461on_val(produc1259058957on_val(binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_1),Bop,E_1)),S_1)),red(Pa))) ) ).

tff(fact_520_FAssReds1,axiom,
    ! [F: list_char,D: list_char,E_2_1: exp_list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAss_list_char(Ea,F,D,E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(fAss_list_char(E_1,F,D,E_2_1)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_521_BinOp1Reds,axiom,
    ! [Bop: bop,E_2_1: exp_list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(binOp_list_char(Ea,Bop,E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(binOp_list_char(E_1,Bop,E_2_1)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_522_red__reds_ORedTry,axiom,
    ! [V_2: val,C: list_char,V: list_char,E_2_1: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(tryCatch_list_char(hAPP_v834067052t_char(val_list_char,V_2),C,V,E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_2)),S)),red(Pa))) ).

tff(fact_523_TryReds,axiom,
    ! [C: list_char,V: list_char,E_2_1: exp_list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(tryCatch_list_char(Ea,C,V,E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(tryCatch_list_char(E_1,C,V,E_2_1)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_524_BinOpRedsVal,axiom,
    ! [Bop: bop,V_2: val,E_2_1: exp_list_char,V_2_1: val,S_2: produc12694297on_val,E_1_1: exp_list_char,S_0: produc12694297on_val,V_1_1: val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(E_1_1),S_0)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1_1)),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(E_2_1),S_1_1)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_2_1)),S_2)),transi2024712006on_val(red(Pa))))
       => ( ( binop(hAPP_P929466802al_val(produc621191550al_val(Bop),hAPP_v852496844al_val(product_Pair_val_val(V_1_1),V_2_1))) = hAPP_val_option_val(some_val,V_2) )
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(binOp_list_char(E_1_1,Bop,E_2_1)),S_0)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_2)),S_2)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_525_red__reds_ORedBinOp,axiom,
    ! [S: produc12694297on_val,Pa: list_P1999446415t_char,Bop: bop,V_1_1: val,V_2_1: val,V_2: val] :
      ( ( binop(hAPP_P929466802al_val(produc621191550al_val(Bop),hAPP_v852496844al_val(product_Pair_val_val(V_1_1),V_2_1))) = hAPP_val_option_val(some_val,V_2) )
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_1),Bop,hAPP_v834067052t_char(val_list_char,V_2_1))),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_2)),S)),red(Pa))) ) ).

tff(fact_526_CallRedsParams,axiom,
    ! [V_2: val,M: list_char,Es: list_exp_list_char,S: produc12694297on_val,Es_1: list_exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(Es),S)),hAPP_P1963616220on_val(produc379668296on_val(Es_1),S_1)),transi374442731on_val(reds(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(call_list_char(hAPP_v834067052t_char(val_list_char,V_2),M,Es)),S)),hAPP_P604205461on_val(produc1259058957on_val(call_list_char(hAPP_v834067052t_char(val_list_char,V_2),M,Es_1)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_527_ListRedsVal,axiom,
    ! [Es: list_exp_list_char,Es_1: list_exp_list_char,S_2: produc12694297on_val,Ea: exp_list_char,S_0: produc12694297on_val,V_2: val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S_0)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_2)),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(Es),S_1_1)),hAPP_P1963616220on_val(produc379668296on_val(Es_1),S_2)),transi374442731on_val(reds(Pa))))
       => hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(cons_exp_list_char(Ea,Es)),S_0)),hAPP_P1963616220on_val(produc379668296on_val(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_2),Es_1)),S_2)),transi374442731on_val(reds(Pa)))) ) ) ).

tff(fact_528_red__reds_OCallObj,axiom,
    ! [M: list_char,Es: list_exp_list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(call_list_char(Ea,M,Es)),S)),hAPP_P604205461on_val(produc1259058957on_val(call_list_char(E_1,M,Es)),S_1)),red(Pa))) ) ).

tff(fact_529_CallRedsObj,axiom,
    ! [M: list_char,Es: list_exp_list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(call_list_char(Ea,M,Es)),S)),hAPP_P604205461on_val(produc1259058957on_val(call_list_char(E_1,M,Es)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_530_ListReds2,axiom,
    ! [V_2: val,Es: list_exp_list_char,S: produc12694297on_val,Es_1: list_exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(Es),S)),hAPP_P1963616220on_val(produc379668296on_val(Es_1),S_1)),transi374442731on_val(reds(Pa))))
     => hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_2),Es)),S)),hAPP_P1963616220on_val(produc379668296on_val(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_2),Es_1)),S_1)),transi374442731on_val(reds(Pa)))) ) ).

tff(fact_531_red__reds_OListRed2,axiom,
    ! [V_2: val,Es: list_exp_list_char,S: produc12694297on_val,Es_1: list_exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(Es),S)),hAPP_P1963616220on_val(produc379668296on_val(Es_1),S_1)),reds(Pa)))
     => hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_2),Es)),S)),hAPP_P1963616220on_val(produc379668296on_val(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_2),Es_1)),S_1)),reds(Pa))) ) ).

tff(fact_532_red__reds_OListRed1,axiom,
    ! [Es: list_exp_list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),red(Pa)))
     => hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(cons_exp_list_char(Ea,Es)),S)),hAPP_P1963616220on_val(produc379668296on_val(cons_exp_list_char(E_1,Es)),S_1)),reds(Pa))) ) ).

tff(fact_533_BinOp,axiom,
    ! [Bop: bop,V_2: val,E_2_1: exp_list_char,V_2_1: val,S_2: produc12694297on_val,Pa: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc12694297on_val,V_1_1: val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,V_1_1)),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2_1,S_1_1),hAPP_v834067052t_char(val_list_char,V_2_1)),S_2))
       => ( ( binop(hAPP_P929466802al_val(produc621191550al_val(Bop),hAPP_v852496844al_val(product_Pair_val_val(V_1_1),V_2_1))) = hAPP_val_option_val(some_val,V_2) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,binOp_list_char(E_1_1,Bop,E_2_1),S_0),hAPP_v834067052t_char(val_list_char,V_2)),S_2)) ) ) ) ).

tff(fact_534_red__reds_OCallParams,axiom,
    ! [V_2: val,M: list_char,Es: list_exp_list_char,S: produc12694297on_val,Es_1: list_exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(Es),S)),hAPP_P1963616220on_val(produc379668296on_val(Es_1),S_1)),reds(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(call_list_char(hAPP_v834067052t_char(val_list_char,V_2),M,Es)),S)),hAPP_P604205461on_val(produc1259058957on_val(call_list_char(hAPP_v834067052t_char(val_list_char,V_2),M,Es_1)),S_1)),red(Pa))) ) ).

tff(fact_535_ListReds1,axiom,
    ! [Es: list_exp_list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(cons_exp_list_char(Ea,Es)),S)),hAPP_P1963616220on_val(produc379668296on_val(cons_exp_list_char(E_1,Es)),S_1)),transi374442731on_val(reds(Pa)))) ) ).

tff(fact_536_redp__redsp_ORedBinOp,axiom,
    ! [Pa: list_P1999446415t_char,S: produc12694297on_val,Bop: bop,V_1_1: val,V_2_1: val,V_2: val] :
      ( ( binop(hAPP_P929466802al_val(produc621191550al_val(Bop),hAPP_v852496844al_val(product_Pair_val_val(V_1_1),V_2_1))) = hAPP_val_option_val(some_val,V_2) )
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_1),Bop,hAPP_v834067052t_char(val_list_char,V_2_1)),S),hAPP_v834067052t_char(val_list_char,V_2)),S)) ) ).

tff(fact_537_CallRedsThrowParams,axiom,
    ! [M: list_char,Es: list_exp_list_char,Vs_1: list_val,A: exp_list_char,Es_2_1: list_exp_list_char,S_2: produc12694297on_val,Ea: exp_list_char,S0: produc12694297on_val,V_2: val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S0)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_2)),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(Es),S_1_1)),hAPP_P1963616220on_val(produc379668296on_val(append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vs_1),cons_exp_list_char(throw_list_char(A),Es_2_1))),S_2)),transi374442731on_val(reds(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(call_list_char(Ea,M,Es)),S0)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(A)),S_2)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_538_WTrtCons,axiom,
    ! [Es: list_exp_list_char,Tsa: list_ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E: fun_li688206603ion_ty,Ea: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Ha,E,Ea,Ta))
     => ( hBOOL(wTrts(Pa,Ha,E,Es,Tsa))
       => hBOOL(wTrts(Pa,Ha,E,cons_exp_list_char(Ea,Es),cons_ty(Ta,Tsa))) ) ) ).

tff(fact_539_redp__redsp_OFAssThrow1,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,F: list_char,D: list_char,E_2_1: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(throw_list_char(Ea),F,D,E_2_1),S),throw_list_char(Ea)),S)) ).

tff(fact_540_redp__redsp_OBinOpThrow1,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,Bop: bop,E_2_1: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(throw_list_char(Ea),Bop,E_2_1),S),throw_list_char(Ea)),S)) ).

tff(fact_541_redp__redsp_OCallThrowObj,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,M: list_char,Es: list_exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(throw_list_char(Ea),M,Es),S),throw_list_char(Ea)),S)) ).

tff(fact_542_redp__redsp_OThrowRed,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S),E_1),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,throw_list_char(Ea),S),throw_list_char(E_1)),S_1)) ) ).

tff(fact_543_redp__redsp_OThrowThrow,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,throw_list_char(throw_list_char(Ea)),S),throw_list_char(Ea)),S)) ).

tff(fact_544_redp__redsp_OSeqThrow,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,E_2_1: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(throw_list_char(Ea),E_2_1),S),throw_list_char(Ea)),S)) ).

tff(fact_545_redp__redsp_OFAssThrow2,axiom,
    ! [Pa: list_P1999446415t_char,V_2: val,F: list_char,D: list_char,Ea: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,V_2),F,D,throw_list_char(Ea)),S),throw_list_char(Ea)),S)) ).

tff(fact_546_redp__redsp_OBinOpThrow2,axiom,
    ! [Pa: list_P1999446415t_char,V_1_1: val,Bop: bop,Ea: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_1),Bop,throw_list_char(Ea)),S),throw_list_char(Ea)),S)) ).

tff(fact_547_eval__evals_OThrowThrow,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E_1: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E_1)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(Ea),S_0),throw_list_char(E_1)),S_1_1)) ) ).

tff(fact_548_redp__redsp_OSeqRed,axiom,
    ! [E_2_1: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S),E_1),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(Ea,E_2_1),S),seq_list_char(E_1,E_2_1)),S_1)) ) ).

tff(fact_549_redp__redsp_OFAssRed1,axiom,
    ! [F: list_char,D: list_char,E_2_1: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S),E_1),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(Ea,F,D,E_2_1),S),fAss_list_char(E_1,F,D,E_2_1)),S_1)) ) ).

tff(fact_550_redp__redsp_OCallObj,axiom,
    ! [M: list_char,Es: list_exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S),E_1),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(Ea,M,Es),S),call_list_char(E_1,M,Es)),S_1)) ) ).

tff(fact_551_redp__redsp_OBinOpRed1,axiom,
    ! [Bop: bop,E_2_1: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S),E_1),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(Ea,Bop,E_2_1),S),binOp_list_char(E_1,Bop,E_2_1)),S_1)) ) ).

tff(fact_552_redp__redsp_OTryRed,axiom,
    ! [C: list_char,V: list_char,E_2_1: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S),E_1),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,tryCatch_list_char(Ea,C,V,E_2_1),S),tryCatch_list_char(E_1,C,V,E_2_1)),S_1)) ) ).

tff(fact_553_redp__redsp_OCallThrowParams,axiom,
    ! [Pa: list_P1999446415t_char,V_2: val,M: list_char,S: produc12694297on_val,Es: list_exp_list_char,Vsa: list_val,Ea: exp_list_char,Es_1: list_exp_list_char] :
      ( ( Es = append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa),cons_exp_list_char(throw_list_char(Ea),Es_1)) )
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(hAPP_v834067052t_char(val_list_char,V_2),M,Es),S),throw_list_char(Ea)),S)) ) ).

tff(fact_554_redp__redsp_ORedSeq,axiom,
    ! [Pa: list_P1999446415t_char,V_2: val,E_2_1: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(hAPP_v834067052t_char(val_list_char,V_2),E_2_1),S),E_2_1),S)) ).

tff(fact_555_redp__redsp_OFAssRed2,axiom,
    ! [V_2: val,F: list_char,D: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S),E_1),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,V_2),F,D,Ea),S),fAss_list_char(hAPP_v834067052t_char(val_list_char,V_2),F,D,E_1)),S_1)) ) ).

tff(fact_556_redp__redsp_OBinOpRed2,axiom,
    ! [V_1_1: val,Bop: bop,Pa: list_P1999446415t_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S),E_1),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_1),Bop,Ea),S),binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_1),Bop,E_1)),S_1)) ) ).

tff(fact_557_redp__redsp_ORedTry,axiom,
    ! [Pa: list_P1999446415t_char,V_2: val,C: list_char,V: list_char,E_2_1: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,tryCatch_list_char(hAPP_v834067052t_char(val_list_char,V_2),C,V,E_2_1),S),hAPP_v834067052t_char(val_list_char,V_2)),S)) ).

tff(fact_558_eval__evals_OSeqThrow,axiom,
    ! [E_1_1: exp_list_char,Pa: list_P1999446415t_char,E_0: exp_list_char,S_0: produc12694297on_val,Ea: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_0,S_0),throw_list_char(Ea)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,seq_list_char(E_0,E_1_1),S_0),throw_list_char(Ea)),S_1_1)) ) ).

tff(fact_559_eval__evals_OFAssThrow1,axiom,
    ! [F: list_char,D: list_char,E_2_1: exp_list_char,Pa: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc12694297on_val,E_1: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),throw_list_char(E_1)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAss_list_char(E_1_1,F,D,E_2_1),S_0),throw_list_char(E_1)),S_1_1)) ) ).

tff(fact_560_CallObjThrow,axiom,
    ! [M: list_char,Ps: list_exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E_1: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E_1)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,call_list_char(Ea,M,Ps),S_0),throw_list_char(E_1)),S_1_1)) ) ).

tff(fact_561_eval__evals_OBinOpThrow1,axiom,
    ! [Bop: bop,E_2_1: exp_list_char,Pa: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc12694297on_val,Ea: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),throw_list_char(Ea)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,binOp_list_char(E_1_1,Bop,E_2_1),S_0),throw_list_char(Ea)),S_1_1)) ) ).

tff(fact_562_red__reds_OThrowRed,axiom,
    ! [Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(E_1)),S_1)),red(Pa))) ) ).

tff(fact_563_red__reds_OThrowThrow,axiom,
    ! [Ea: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(throw_list_char(Ea))),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S)),red(Pa))) ).

tff(fact_564_eval__evals_OFAssThrow2,axiom,
    ! [F: list_char,D: list_char,E_2_1: exp_list_char,E_1: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc12694297on_val,V_2: val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,V_2)),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2_1,S_1_1),throw_list_char(E_1)),S_2))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAss_list_char(E_1_1,F,D,E_2_1),S_0),throw_list_char(E_1)),S_2)) ) ) ).

tff(fact_565_eval__evals_OBinOpThrow2,axiom,
    ! [Bop: bop,E_2_1: exp_list_char,Ea: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc12694297on_val,V_1_1: val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,V_1_1)),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2_1,S_1_1),throw_list_char(Ea)),S_2))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,binOp_list_char(E_1_1,Bop,E_2_1),S_0),throw_list_char(Ea)),S_2)) ) ) ).

tff(fact_566_red__reds_OCallThrowParams,axiom,
    ! [V_2: val,M: list_char,S: produc12694297on_val,Pa: list_P1999446415t_char,Es: list_exp_list_char,Vsa: list_val,Ea: exp_list_char,Es_1: list_exp_list_char] :
      ( ( Es = append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa),cons_exp_list_char(throw_list_char(Ea),Es_1)) )
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(call_list_char(hAPP_v834067052t_char(val_list_char,V_2),M,Es)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S)),red(Pa))) ) ).

tff(fact_567_ThrowRedsThrow,axiom,
    ! [Ea: exp_list_char,S: produc12694297on_val,A: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(A)),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(A)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_568_ThrowReds,axiom,
    ! [Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(E_1)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_569_red__reds_OSeqThrow,axiom,
    ! [Ea: exp_list_char,E_2_1: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(seq_list_char(throw_list_char(Ea),E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S)),red(Pa))) ).

tff(fact_570_red__reds_OFAssThrow1,axiom,
    ! [Ea: exp_list_char,F: list_char,D: list_char,E_2_1: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAss_list_char(throw_list_char(Ea),F,D,E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S)),red(Pa))) ).

tff(fact_571_red__reds_OCallThrowObj,axiom,
    ! [Ea: exp_list_char,M: list_char,Es: list_exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(call_list_char(throw_list_char(Ea),M,Es)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S)),red(Pa))) ).

tff(fact_572_red__reds_OBinOpThrow1,axiom,
    ! [Ea: exp_list_char,Bop: bop,E_2_1: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(binOp_list_char(throw_list_char(Ea),Bop,E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S)),red(Pa))) ).

tff(fact_573_red__reds_OFAssThrow2,axiom,
    ! [V_2: val,F: list_char,D: list_char,Ea: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAss_list_char(hAPP_v834067052t_char(val_list_char,V_2),F,D,throw_list_char(Ea))),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S)),red(Pa))) ).

tff(fact_574_red__reds_OBinOpThrow2,axiom,
    ! [V_1_1: val,Bop: bop,Ea: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_1),Bop,throw_list_char(Ea))),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S)),red(Pa))) ).

tff(fact_575_SeqRedsThrow,axiom,
    ! [E_2_1: exp_list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(E_1)),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(seq_list_char(Ea,E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(E_1)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_576_FAssRedsThrow1,axiom,
    ! [F: list_char,D: list_char,E_2_1: exp_list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(E_1)),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAss_list_char(Ea,F,D,E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(E_1)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_577_CallRedsThrowObj,axiom,
    ! [M: list_char,Es: list_exp_list_char,Ea: exp_list_char,S0: produc12694297on_val,A: exp_list_char,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S0)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(A)),S_1_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(call_list_char(Ea,M,Es)),S0)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(A)),S_1_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_578_BinOpRedsThrow1,axiom,
    ! [Bop: bop,E_2_1: exp_list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(E_1)),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(binOp_list_char(Ea,Bop,E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(E_1)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_579_FAssRedsThrow2,axiom,
    ! [F: list_char,D: list_char,E_2_1: exp_list_char,Ea: exp_list_char,S_2: produc12694297on_val,E_1_1: exp_list_char,S_0: produc12694297on_val,V_2: val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(E_1_1),S_0)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_2)),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(E_2_1),S_1_1)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S_2)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAss_list_char(E_1_1,F,D,E_2_1)),S_0)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S_2)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_580_BinOpRedsThrow2,axiom,
    ! [Bop: bop,E_2_1: exp_list_char,Ea: exp_list_char,S_2: produc12694297on_val,E_1_1: exp_list_char,S_0: produc12694297on_val,V_1_1: val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(E_1_1),S_0)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1_1)),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(E_2_1),S_1_1)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S_2)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(binOp_list_char(E_1_1,Bop,E_2_1)),S_0)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S_2)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_581_eval__cases_I3_J,axiom,
    ! [Pa: list_P1999446415t_char,E_1_1: exp_list_char,Bop: bop,E_2_1: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,binOp_list_char(E_1_1,Bop,E_2_1),S),E_1),S_1))
     => ( ! [V_1_2: val,S_1_2: produc12694297on_val,V_2_2: val,V_1: val] :
            ( ( E_1 = hAPP_v834067052t_char(val_list_char,V_1) )
           => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S),hAPP_v834067052t_char(val_list_char,V_1_2)),S_1_2))
             => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2_1,S_1_2),hAPP_v834067052t_char(val_list_char,V_2_2)),S_1))
               => ( binop(hAPP_P929466802al_val(produc621191550al_val(Bop),hAPP_v852496844al_val(product_Pair_val_val(V_1_2),V_2_2))) != hAPP_val_option_val(some_val,V_1) ) ) ) )
       => ( ! [E_4: exp_list_char] :
              ( ( E_1 = throw_list_char(E_4) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S),throw_list_char(E_4)),S_1)) )
         => ~ ! [V_1_2: val,S_1_2: produc12694297on_val,E_4: exp_list_char] :
                ( ( E_1 = throw_list_char(E_4) )
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S),hAPP_v834067052t_char(val_list_char,V_1_2)),S_1_2))
                 => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2_1,S_1_2),throw_list_char(E_4)),S_1)) ) ) ) ) ) ).

tff(fact_582_CallParamsThrow,axiom,
    ! [M: list_char,Es: list_exp_list_char,Vsa: list_val,Ex: exp_list_char,Es_1: list_exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,V_2: val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,V_2)),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es,S_1_1),append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa),cons_exp_list_char(throw_list_char(Ex),Es_1))),S_2))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,call_list_char(Ea,M,Es),S_0),throw_list_char(Ex)),S_2)) ) ) ).

tff(fact_583_list__eval__Throw,axiom,
    ! [Vsa: list_val,Es_1: list_exp_list_char,Pa: list_P1999446415t_char,X_1: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(X_1),S),E_1),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa),cons_exp_list_char(throw_list_char(X_1),Es_1)),S),append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa),cons_exp_list_char(E_1,Es_1))),S_1)) ) ).

tff(fact_584_eval__cases_I9_J,axiom,
    ! [Pa: list_P1999446415t_char,E_1_1: exp_list_char,E_2_1: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,seq_list_char(E_1_1,E_2_1),S),E_1),S_1))
     => ( ! [V_1: val,S_1_2: produc12694297on_val] :
            ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S),hAPP_v834067052t_char(val_list_char,V_1)),S_1_2))
           => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2_1,S_1_2),E_1),S_1)) )
       => ~ ! [E_4: exp_list_char] :
              ( ( E_1 = throw_list_char(E_4) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S),throw_list_char(E_4)),S_1)) ) ) ) ).

tff(fact_585_redp__redsp_OCallParams,axiom,
    ! [V_2: val,M: list_char,Pa: list_P1999446415t_char,Es: list_exp_list_char,S: produc12694297on_val,Es_1: list_exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,Es,S),Es_1),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(hAPP_v834067052t_char(val_list_char,V_2),M,Es),S),call_list_char(hAPP_v834067052t_char(val_list_char,V_2),M,Es_1)),S_1)) ) ).

tff(fact_586_evals__final,axiom,
    ! [Pa: list_P1999446415t_char,Es: list_exp_list_char,S: produc12694297on_val,Es_1: list_exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es,S),Es_1),S_1))
     => hBOOL(finals_list_char(Es_1)) ) ).

tff(fact_587_eval__finalsId,axiom,
    ! [Pa: list_P1999446415t_char,S: produc12694297on_val,Es: list_exp_list_char] :
      ( hBOOL(finals_list_char(Es))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es,S),Es),S)) ) ).

tff(fact_588_evals__hext,axiom,
    ! [Pa: list_P1999446415t_char,Es: list_exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,Es_1: list_exp_list_char,H_1: fun_na939144002on_val,L_2: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es,hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1)),Es_1),hAPP_f1727192346on_val(produc899768717on_val(H_1),L_2)))
     => hBOOL(hext(Ha,H_1)) ) ).

tff(fact_589_redp__redsp_OListRed2,axiom,
    ! [V_2: val,Pa: list_P1999446415t_char,Es: list_exp_list_char,S: produc12694297on_val,Es_1: list_exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,Es,S),Es_1),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_2),Es),S),cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_2),Es_1)),S_1)) ) ).

tff(fact_590_eval__evals_OCons,axiom,
    ! [Es: list_exp_list_char,Es_1: list_exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,V_2: val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,V_2)),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es,S_1_1),Es_1),S_2))
       => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,cons_exp_list_char(Ea,Es),S_0),cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_2),Es_1)),S_2)) ) ) ).

tff(fact_591_ConsThrow,axiom,
    ! [Es: list_exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E_1: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E_1)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,cons_exp_list_char(Ea,Es),S_0),cons_exp_list_char(throw_list_char(E_1),Es)),S_1_1)) ) ).

tff(fact_592_redp__redsp_OListRed1,axiom,
    ! [Es: list_exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S),E_1),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,cons_exp_list_char(Ea,Es),S),cons_exp_list_char(E_1,Es)),S_1)) ) ).

tff(fact_593_evals__cases_I2_J,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,Es: list_exp_list_char,S: produc12694297on_val,E_1: list_exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,cons_exp_list_char(Ea,Es),S),E_1),S_1))
     => ( ! [V_1: val,S_1_2: produc12694297on_val,Es_2: list_exp_list_char] :
            ( ( E_1 = cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Es_2) )
           => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S),hAPP_v834067052t_char(val_list_char,V_1)),S_1_2))
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es,S_1_2),Es_2),S_1)) ) )
       => ~ ! [E_2: exp_list_char] :
              ( ( E_1 = cons_exp_list_char(throw_list_char(E_2),Es) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S),throw_list_char(E_2)),S_1)) ) ) ) ).

tff(fact_594_WTrtThrow,axiom,
    ! [Ta: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E: fun_li688206603ion_ty,Ea: exp_list_char,T_r_1: ty] :
      ( hBOOL(wTrt(Pa,Ha,E,Ea,T_r_1))
     => ( hBOOL(is_refT(T_r_1))
       => hBOOL(wTrt(Pa,Ha,E,throw_list_char(Ea),Ta)) ) ) ).

tff(fact_595_WTrt__elim__cases_I4_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E: fun_li688206603ion_ty,Ea: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Ha,E,throw_list_char(Ea),Ta))
     => ~ ! [T_r: ty] :
            ( hBOOL(wTrt(Pa,Ha,E,Ea,T_r))
           => ~ hBOOL(is_refT(T_r)) ) ) ).

tff(fact_596_WhileRedsThrow,axiom,
    ! [C_3: exp_list_char,B: exp_list_char,S: produc12694297on_val,Ea: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(B),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(while_list_char(B,C_3)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_597_FAccRedsThrow,axiom,
    ! [F: list_char,D: list_char,Ea: exp_list_char,S: produc12694297on_val,A: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(A)),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAcc_list_char(Ea,F,D)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(A)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_598_redp__redsp_OFAccRed,axiom,
    ! [F: list_char,D: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S),E_1),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(Ea,F,D),S),fAcc_list_char(E_1,F,D)),S_1)) ) ).

tff(fact_599_eval__evals_OFAccThrow,axiom,
    ! [F: list_char,D: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E_1: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E_1)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAcc_list_char(Ea,F,D),S_0),throw_list_char(E_1)),S_1_1)) ) ).

tff(fact_600_WhileCondThrow,axiom,
    ! [C_3: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E_1: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E_1)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Ea,C_3),S_0),throw_list_char(E_1)),S_1_1)) ) ).

tff(fact_601_redp__redsp_OFAccThrow,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,F: list_char,D: list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(throw_list_char(Ea),F,D),S),throw_list_char(Ea)),S)) ).

tff(fact_602_red__reds_OFAccRed,axiom,
    ! [F: list_char,D: list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAcc_list_char(Ea,F,D)),S)),hAPP_P604205461on_val(produc1259058957on_val(fAcc_list_char(E_1,F,D)),S_1)),red(Pa))) ) ).

tff(fact_603_red__reds_OFAccThrow,axiom,
    ! [Ea: exp_list_char,F: list_char,D: list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAcc_list_char(throw_list_char(Ea),F,D)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S)),red(Pa))) ).

tff(fact_604_FAccReds,axiom,
    ! [F: list_char,D: list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAcc_list_char(Ea,F,D)),S)),hAPP_P604205461on_val(produc1259058957on_val(fAcc_list_char(E_1,F,D)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_605_WhileTRedsThrow,axiom,
    ! [C_3: exp_list_char,Ea: exp_list_char,S_2: produc12694297on_val,B: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(B),S_0)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(C_3),S_1_1)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S_2)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(while_list_char(B,C_3)),S_0)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S_2)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_606_WhileT,axiom,
    ! [E_3: exp_list_char,S_3: produc12694297on_val,C_3: exp_list_char,V_1_1: val,S_2: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_3,S_1_1),hAPP_v834067052t_char(val_list_char,V_1_1)),S_2))
       => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Ea,C_3),S_2),E_3),S_3))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Ea,C_3),S_0),E_3),S_3)) ) ) ) ).

tff(fact_607_WhileBodyThrow,axiom,
    ! [C_3: exp_list_char,E_1: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_3,S_1_1),throw_list_char(E_1)),S_2))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Ea,C_3),S_0),throw_list_char(E_1)),S_2)) ) ) ).

tff(fact_608_WhileTReds,axiom,
    ! [Ea: exp_list_char,S_3: produc12694297on_val,C_3: exp_list_char,V_1_1: val,S_2: produc12694297on_val,B: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(B),S_0)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(C_3),S_1_1)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1_1)),S_2)),transi2024712006on_val(red(Pa))))
       => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(while_list_char(B,C_3)),S_2)),hAPP_P604205461on_val(produc1259058957on_val(Ea),S_3)),transi2024712006on_val(red(Pa))))
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(while_list_char(B,C_3)),S_0)),hAPP_P604205461on_val(produc1259058957on_val(Ea),S_3)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_609_binop_Osimps_I1_J,axiom,
    ! [V_1_1: val,V_2_1: val] : binop(hAPP_P929466802al_val(produc621191550al_val(c_Expr_Obop_OEq),hAPP_v852496844al_val(product_Pair_val_val(V_1_1),V_2_1))) = hAPP_val_option_val(some_val,bool_1(hAPP_val_bool(hAPP_v1392248405l_bool(fequal_val,V_1_1),V_2_1))) ).

tff(fact_610_WhileFReds,axiom,
    ! [C_3: exp_list_char,B: exp_list_char,S: produc12694297on_val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(B),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,bool_1(fFalse))),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(while_list_char(B,C_3)),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,unit)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_611_FAcc,axiom,
    ! [F: list_char,D: list_char,V_2: val,C: list_char,Fs: fun_Pr806764899on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,A: nat,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1)))
     => ( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C),Fs)) )
       => ( ( hAPP_P2094403585on_val(Fs,hAPP_l2100324114t_char(produc5062597t_char(F),D)) = hAPP_val_option_val(some_val,V_2) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAcc_list_char(Ea,F,D),S_0),hAPP_v834067052t_char(val_list_char,V_2)),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))) ) ) ) ).

tff(fact_612_Throw,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,A: nat,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(Ea),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S_1_1)) ) ).

tff(fact_613_WhileF,axiom,
    ! [C_3: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,bool_1(fFalse))),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Ea,C_3),S_0),hAPP_v834067052t_char(val_list_char,unit)),S_1_1)) ) ).

tff(fact_614_FAccRedsVal,axiom,
    ! [F: list_char,D: list_char,V_2: val,C: list_char,Fs: fun_Pr806764899on_val,Ea: exp_list_char,S: produc12694297on_val,A: nat,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,addr(A))),S_1)),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(hp(S_1),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C),Fs)) )
       => ( ( hAPP_P2094403585on_val(Fs,hAPP_l2100324114t_char(produc5062597t_char(F),D)) = hAPP_val_option_val(some_val,V_2) )
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAcc_list_char(Ea,F,D)),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_2)),S_1)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_615_red__reds_ORedFAcc,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,V_2: val,S: produc12694297on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C),Fs)) )
     => ( ( hAPP_P2094403585on_val(Fs,hAPP_l2100324114t_char(produc5062597t_char(F),D)) = hAPP_val_option_val(some_val,V_2) )
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAcc_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),F,D)),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_2)),S)),red(Pa))) ) ) ).

tff(fact_616_redp__redsp_ORedFAcc,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,V_2: val,S: produc12694297on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C),Fs)) )
     => ( ( hAPP_P2094403585on_val(Fs,hAPP_l2100324114t_char(produc5062597t_char(F),D)) = hAPP_val_option_val(some_val,V_2) )
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),F,D),S),hAPP_v834067052t_char(val_list_char,V_2)),S)) ) ) ).

tff(fact_617_reds__preserves__sconf,axiom,
    ! [E: fun_li688206603ion_ty,Tsa: list_ty,Es: list_exp_list_char,S: produc12694297on_val,Es_1: list_exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(Es),S)),hAPP_P1963616220on_val(produc379668296on_val(Es_1),S_1)),reds(Pa)))
     => ( hBOOL(wTrts(Pa,hp(S),E,Es,Tsa))
       => ( hBOOL(hAPP_P159683425l_bool(typeSa525116494_sconf(Pa,E),S))
         => hBOOL(hAPP_P159683425l_bool(typeSa525116494_sconf(Pa,E),S_1)) ) ) ) ).

tff(fact_618_TryRedsFail,axiom,
    ! [V: list_char,E_2_1: exp_list_char,C: list_char,D: list_char,Fs: fun_Pr806764899on_val,E_1_1: exp_list_char,S: produc12694297on_val,A: nat,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(E_1_1),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(D),Fs)) )
       => ( ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(tryCatch_list_char(E_1_1,C,V,E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_619_red__reds_ORedTryFail,axiom,
    ! [V: list_char,E_2_1: exp_list_char,C: list_char,Pa: list_P1999446415t_char,S: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(D),Fs)) )
     => ( ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(tryCatch_list_char(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))),C,V,E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S)),red(Pa))) ) ) ).

tff(fact_620_TryThrow,axiom,
    ! [V: list_char,E_2_1: exp_list_char,C: list_char,D: list_char,Fs: fun_Pr806764899on_val,Pa: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc12694297on_val,A: nat,H_1_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),hAPP_f1727192346on_val(produc899768717on_val(H_1_1),L_1_1)))
     => ( ( hAPP_n546249108on_val(H_1_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(D),Fs)) )
       => ( ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,tryCatch_list_char(E_1_1,C,V,E_2_1),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),hAPP_f1727192346on_val(produc899768717on_val(H_1_1),L_1_1))) ) ) ) ).

tff(fact_621_red__preserves__sconf,axiom,
    ! [E: fun_li688206603ion_ty,Ta: ty,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),red(Pa)))
     => ( hBOOL(wTrt(Pa,hp(S),E,Ea,Ta))
       => ( hBOOL(hAPP_P159683425l_bool(typeSa525116494_sconf(Pa,E),S))
         => hBOOL(hAPP_P159683425l_bool(typeSa525116494_sconf(Pa,E),S_1)) ) ) ) ).

tff(fact_622_TryCatchRedsFinal,axiom,
    ! [E_2_1: exp_list_char,V: list_char,E_2_2: exp_list_char,H_2: fun_na939144002on_val,L_2_1: fun_li1432931796on_val,C: list_char,D: list_char,Fs: fun_Pr806764899on_val,E_1_1: exp_list_char,S_0: produc12694297on_val,A: nat,H_1_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(E_1_1),S_0)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),hAPP_f1727192346on_val(produc899768717on_val(H_1_1),L_1_1))),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(H_1_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(D),Fs)) )
       => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(E_2_1),hAPP_f1727192346on_val(produc899768717on_val(H_1_1),fun_up1149430426on_val(L_1_1,V,hAPP_val_option_val(some_val,addr(A)))))),hAPP_P604205461on_val(produc1259058957on_val(E_2_2),hAPP_f1727192346on_val(produc899768717on_val(H_2),L_2_1))),transi2024712006on_val(red(Pa))))
           => ( hBOOL(final_list_char(E_2_2))
             => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(tryCatch_list_char(E_1_1,C,V,E_2_1)),S_0)),hAPP_P604205461on_val(produc1259058957on_val(E_2_2),hAPP_f1727192346on_val(produc899768717on_val(H_2),fun_up1149430426on_val(L_2_1,V,hAPP_l207779698on_val(L_1_1,V))))),transi2024712006on_val(red(Pa)))) ) ) ) ) ) ).

tff(fact_623_CastRedsAddr,axiom,
    ! [C: list_char,D: list_char,Fs: fun_Pr806764899on_val,Ea: exp_list_char,S: produc12694297on_val,A: nat,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,addr(A))),S_1)),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(hp(S_1),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(D),Fs)) )
       => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(cast_list_char(C,Ea)),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,addr(A))),S_1)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_624_red__reds_ORedCast,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,S: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(D),Fs)) )
     => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(cast_list_char(C,hAPP_v834067052t_char(val_list_char,addr(A)))),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,addr(A))),S)),red(Pa))) ) ) ).

tff(fact_625_redp__redsp_OCastRed,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S),E_1),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,Ea),S),cast_list_char(C,E_1)),S_1)) ) ).

tff(fact_626_eval__evals_OCastThrow,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E_1: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E_1)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,Ea),S_0),throw_list_char(E_1)),S_1_1)) ) ).

tff(fact_627_redp__redsp_OCastThrow,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,Ea: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,throw_list_char(Ea)),S),throw_list_char(Ea)),S)) ).

tff(fact_628_red__reds_OCastRed,axiom,
    ! [C: list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(cast_list_char(C,Ea)),S)),hAPP_P604205461on_val(produc1259058957on_val(cast_list_char(C,E_1)),S_1)),red(Pa))) ) ).

tff(fact_629_red__reds_OCastThrow,axiom,
    ! [C: list_char,Ea: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(cast_list_char(C,throw_list_char(Ea))),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S)),red(Pa))) ).

tff(fact_630_CastReds,axiom,
    ! [C: list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(cast_list_char(C,Ea)),S)),hAPP_P604205461on_val(produc1259058957on_val(cast_list_char(C,E_1)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_631_CastRedsThrow,axiom,
    ! [C: list_char,Ea: exp_list_char,S: produc12694297on_val,A: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(A)),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(cast_list_char(C,Ea)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(A)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_632_Cast,axiom,
    ! [C: list_char,D: list_char,Fs: fun_Pr806764899on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,A: nat,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1)))
     => ( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(D),Fs)) )
       => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,Ea),S_0),hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))) ) ) ) ).

tff(fact_633_TryCatch,axiom,
    ! [E_2_1: exp_list_char,V: list_char,E_2_2: exp_list_char,H_2: fun_na939144002on_val,L_2_1: fun_li1432931796on_val,C: list_char,D: list_char,Fs: fun_Pr806764899on_val,Pa: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc12694297on_val,A: nat,H_1_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),hAPP_f1727192346on_val(produc899768717on_val(H_1_1),L_1_1)))
     => ( ( hAPP_n546249108on_val(H_1_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(D),Fs)) )
       => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2_1,hAPP_f1727192346on_val(produc899768717on_val(H_1_1),fun_up1149430426on_val(L_1_1,V,hAPP_val_option_val(some_val,addr(A))))),E_2_2),hAPP_f1727192346on_val(produc899768717on_val(H_2),L_2_1)))
           => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,tryCatch_list_char(E_1_1,C,V,E_2_1),S_0),E_2_2),hAPP_f1727192346on_val(produc899768717on_val(H_2),fun_up1149430426on_val(L_2_1,V,hAPP_l207779698on_val(L_1_1,V))))) ) ) ) ) ).

tff(fact_634_CastRedsFail,axiom,
    ! [C: list_char,D: list_char,Fs: fun_Pr806764899on_val,Ea: exp_list_char,S: produc12694297on_val,A: nat,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,addr(A))),S_1)),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(hp(S_1),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(D),Fs)) )
       => ( ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(cast_list_char(C,Ea)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(classCast))))),S_1)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_635_red__reds_ORedCastFail,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,S: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(D),Fs)) )
     => ( ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(cast_list_char(C,hAPP_v834067052t_char(val_list_char,addr(A)))),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(classCast))))),S)),red(Pa))) ) ) ).

tff(fact_636_red__reds_ORedCall,axiom,
    ! [Vsa: list_val,Pa: list_P1999446415t_char,M: list_char,Tsa: list_ty,Ta: ty,Pns: list_list_char,Body: exp_list_char,D: list_char,S: produc12694297on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C),Fs)) )
     => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Tsa,Ta,hAPP_e952791821t_char(produc1147572817t_char(Pns),Body)),D))
       => ( ( size_size_list_val(Vsa) = size_s2113983095t_char(Pns) )
         => ( ( size_size_list_ty(Tsa) = size_s2113983095t_char(Pns) )
           => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(call_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),M,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa))),S)),hAPP_P604205461on_val(produc1259058957on_val(blocks(hAPP_P767818445t_char(produc921874948t_char(cons_list_char(this,Pns)),hAPP_P1392904962t_char(produc1909267824t_char(cons_ty(class(D),Tsa)),hAPP_e1752110927t_char(produc1916172923t_char(cons_val(addr(A),Vsa)),Body))))),S)),red(Pa))) ) ) ) ) ).

tff(fact_637_WTrtTry,axiom,
    ! [V: list_char,C: list_char,E_2_1: exp_list_char,T_2: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E: fun_li688206603ion_ty,E_1_1: exp_list_char,T_1_1: ty] :
      ( hBOOL(wTrt(Pa,Ha,E,E_1_1,T_1_1))
     => ( hBOOL(wTrt(Pa,Ha,fun_up424764369ion_ty(E,V,hAPP_ty_option_ty(some_ty,class(C))),E_2_1,T_2))
       => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_1),T_2))
         => hBOOL(wTrt(Pa,Ha,E,tryCatch_list_char(E_1_1,C,V,E_2_1),T_2)) ) ) ) ).

tff(fact_638_WTrtCall,axiom,
    ! [Es: list_exp_list_char,Ts_1: list_ty,M: list_char,Tsa: list_ty,Ta: ty,Pns: list_list_char,Body: exp_list_char,D: list_char,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E: fun_li688206603ion_ty,Ea: exp_list_char,C: list_char] :
      ( hBOOL(wTrt(Pa,Ha,E,Ea,class(C)))
     => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Tsa,Ta,hAPP_e952791821t_char(produc1147572817t_char(Pns),Body)),D))
       => ( hBOOL(wTrts(Pa,Ha,E,Es,Ts_1))
         => ( hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_1,Tsa))
           => hBOOL(wTrt(Pa,Ha,E,call_list_char(Ea,M,Es),Ta)) ) ) ) ) ).

tff(fact_639_hext__upd__obj,axiom,
    ! [Fs_1: fun_Pr806764899on_val,Ha: fun_na939144002on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C),Fs)) )
     => hBOOL(hext(Ha,fun_up2041264236on_val(Ha,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C),Fs_1))))) ) ).

tff(fact_640_FAss,axiom,
    ! [H_2_1: fun_na939144002on_val,Fs_1: fun_Pr806764899on_val,F: list_char,D: list_char,C: list_char,Fs: fun_Pr806764899on_val,E_2_1: exp_list_char,V_2: val,H_2: fun_na939144002on_val,L_2_1: fun_li1432931796on_val,Pa: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc12694297on_val,A: nat,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2_1,S_1_1),hAPP_v834067052t_char(val_list_char,V_2)),hAPP_f1727192346on_val(produc899768717on_val(H_2),L_2_1)))
       => ( ( hAPP_n546249108on_val(H_2,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C),Fs)) )
         => ( ( Fs_1 = fun_up204312361on_val(Fs,hAPP_l2100324114t_char(produc5062597t_char(F),D),hAPP_val_option_val(some_val,V_2)) )
           => ( ( H_2_1 = fun_up2041264236on_val(H_2,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C),Fs_1))) )
             => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAss_list_char(E_1_1,F,D,E_2_1),S_0),hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(produc899768717on_val(H_2_1),L_2_1))) ) ) ) ) ) ).

tff(fact_641_redp__redsp_ORedFAss,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,V_2: val,L_1: fun_li1432931796on_val,Ha: fun_na939144002on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C),Fs)) )
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),F,D,hAPP_v834067052t_char(val_list_char,V_2)),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1)),hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(produc899768717on_val(fun_up2041264236on_val(Ha,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C),fun_up204312361on_val(Fs,hAPP_l2100324114t_char(produc5062597t_char(F),D),hAPP_val_option_val(some_val,V_2)))))),L_1))) ) ).

tff(fact_642_red__reds_ORedFAss,axiom,
    ! [F: list_char,D: list_char,V_2: val,L_1: fun_li1432931796on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C),Fs)) )
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAss_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),F,D,hAPP_v834067052t_char(val_list_char,V_2))),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(produc899768717on_val(fun_up2041264236on_val(Ha,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C),fun_up204312361on_val(Fs,hAPP_l2100324114t_char(produc5062597t_char(F),D),hAPP_val_option_val(some_val,V_2)))))),L_1))),red(Pa))) ) ).

tff(fact_643_FAssRedsVal,axiom,
    ! [F: list_char,D: list_char,C: list_char,Fs: fun_Pr806764899on_val,E_2_1: exp_list_char,V_2: val,H_2: fun_na939144002on_val,L_2_1: fun_li1432931796on_val,E_1_1: exp_list_char,S_0: produc12694297on_val,A: nat,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(E_1_1),S_0)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,addr(A))),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(E_2_1),S_1_1)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_2)),hAPP_f1727192346on_val(produc899768717on_val(H_2),L_2_1))),transi2024712006on_val(red(Pa))))
       => ( ( hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C),Fs)) = hAPP_n546249108on_val(H_2,A) )
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAss_list_char(E_1_1,F,D,E_2_1)),S_0)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(produc899768717on_val(fun_up2041264236on_val(H_2,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C),fun_up204312361on_val(Fs,hAPP_l2100324114t_char(produc5062597t_char(F),D),hAPP_val_option_val(some_val,V_2)))))),L_2_1))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_644_CastFail,axiom,
    ! [C: list_char,D: list_char,Fs: fun_Pr806764899on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,A: nat,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1)))
     => ( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(D),Fs)) )
       => ( ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,Ea),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(classCast))))),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))) ) ) ) ).

tff(fact_645_redp__redsp_ORedCall,axiom,
    ! [Vsa: list_val,Pa: list_P1999446415t_char,M: list_char,Tsa: list_ty,Ta: ty,Pns: list_list_char,Body: exp_list_char,D: list_char,S: produc12694297on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(C),Fs)) )
     => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Tsa,Ta,hAPP_e952791821t_char(produc1147572817t_char(Pns),Body)),D))
       => ( ( size_size_list_val(Vsa) = size_s2113983095t_char(Pns) )
         => ( ( size_size_list_ty(Tsa) = size_s2113983095t_char(Pns) )
           => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),M,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa)),S),blocks(hAPP_P767818445t_char(produc921874948t_char(cons_list_char(this,Pns)),hAPP_P1392904962t_char(produc1909267824t_char(cons_ty(class(D),Tsa)),hAPP_e1752110927t_char(produc1916172923t_char(cons_val(addr(A),Vsa)),Body))))),S)) ) ) ) ) ).

tff(fact_646_WTrt__elim__cases_I5_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E: fun_li688206603ion_ty,E_1_1: exp_list_char,C: list_char,V: list_char,E_2_1: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Ha,E,tryCatch_list_char(E_1_1,C,V,E_2_1),Ta))
     => ~ ! [T_1: ty] :
            ( hBOOL(wTrt(Pa,Ha,E,E_1_1,T_1))
           => ( hBOOL(wTrt(Pa,Ha,fun_up424764369ion_ty(E,V,hAPP_ty_option_ty(some_ty,class(C))),E_2_1,Ta))
             => ~ hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1),Ta)) ) ) ) ).

tff(fact_647_CallRedsNull,axiom,
    ! [M: list_char,Es: list_exp_list_char,Vsa: list_val,S_2: produc12694297on_val,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S_0)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,null)),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(produc1611380469on_val(hAPP_P1963616220on_val(produc379668296on_val(Es),S_1_1)),hAPP_P1963616220on_val(produc379668296on_val(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa)),S_2)),transi374442731on_val(reds(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(call_list_char(Ea,M,Es)),S_0)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_648_ThrowNull,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(Ea),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_1_1)) ) ).

tff(fact_649_redp__redsp_ORedThrowNull,axiom,
    ! [Pa: list_P1999446415t_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,throw_list_char(hAPP_v834067052t_char(val_list_char,null)),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S)) ).

tff(fact_650_CastNull,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,Ea),S_0),hAPP_v834067052t_char(val_list_char,null)),S_1_1)) ) ).

tff(fact_651_redp__redsp_ORedCastNull,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,hAPP_v834067052t_char(val_list_char,null)),S),hAPP_v834067052t_char(val_list_char,null)),S)) ).

tff(fact_652_FAssNull,axiom,
    ! [F: list_char,D: list_char,E_2_1: exp_list_char,V_2: val,S_2: produc12694297on_val,Pa: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2_1,S_1_1),hAPP_v834067052t_char(val_list_char,V_2)),S_2))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAss_list_char(E_1_1,F,D,E_2_1),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2)) ) ) ).

tff(fact_653_FAccNull,axiom,
    ! [F: list_char,D: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAcc_list_char(Ea,F,D),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_1_1)) ) ).

tff(fact_654_redp__redsp_ORedFAssNull,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,V_2: val,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,null),F,D,hAPP_v834067052t_char(val_list_char,V_2)),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S)) ).

tff(fact_655_redp__redsp_ORedFAccNull,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(hAPP_v834067052t_char(val_list_char,null),F,D),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S)) ).

tff(fact_656_red__reds_ORedThrowNull,axiom,
    ! [S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,null))),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S)),red(Pa))) ).

tff(fact_657_redp__redsp_ORedCallNull,axiom,
    ! [Pa: list_P1999446415t_char,M: list_char,Vsa: list_val,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(hAPP_v834067052t_char(val_list_char,null),M,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa)),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S)) ).

tff(fact_658_ThrowRedsNull,axiom,
    ! [Ea: exp_list_char,S: produc12694297on_val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,null)),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_659_red__reds_ORedFAssNull,axiom,
    ! [F: list_char,D: list_char,V_2: val,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAss_list_char(hAPP_v834067052t_char(val_list_char,null),F,D,hAPP_v834067052t_char(val_list_char,V_2))),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S)),red(Pa))) ).

tff(fact_660_red__reds_ORedFAccNull,axiom,
    ! [F: list_char,D: list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAcc_list_char(hAPP_v834067052t_char(val_list_char,null),F,D)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S)),red(Pa))) ).

tff(fact_661_CallNull,axiom,
    ! [M: list_char,Ps: list_exp_list_char,Vsa: list_val,S_2: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Ps,S_1_1),hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa)),S_2))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,call_list_char(Ea,M,Ps),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2)) ) ) ).

tff(fact_662_FAssRedsNull,axiom,
    ! [F: list_char,D: list_char,E_2_1: exp_list_char,V_2: val,S_2: produc12694297on_val,E_1_1: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(E_1_1),S_0)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,null)),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(E_2_1),S_1_1)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_2)),S_2)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAss_list_char(E_1_1,F,D,E_2_1)),S_0)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_663_FAccRedsNull,axiom,
    ! [F: list_char,D: list_char,Ea: exp_list_char,S: produc12694297on_val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,null)),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(fAcc_list_char(Ea,F,D)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_664_red__reds_ORedCallNull,axiom,
    ! [M: list_char,Vsa: list_val,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(call_list_char(hAPP_v834067052t_char(val_list_char,null),M,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa))),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S)),red(Pa))) ).

tff(fact_665_red__reds_ORedCastNull,axiom,
    ! [C: list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(cast_list_char(C,hAPP_v834067052t_char(val_list_char,null))),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,null)),S)),red(Pa))) ).

tff(fact_666_CastRedsNull,axiom,
    ! [C: list_char,Ea: exp_list_char,S: produc12694297on_val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,null)),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(cast_list_char(C,Ea)),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,null)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_667_eval__cases_I12_J,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(Ea),S),E_1),S_1))
     => ( ! [A_1: nat] :
            ( ( E_1 = throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))) )
           => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S),hAPP_v834067052t_char(val_list_char,addr(A_1))),S_1)) )
       => ( ( ( E_1 = throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer)))) )
           => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S),hAPP_v834067052t_char(val_list_char,null)),S_1)) )
         => ~ ! [E_2: exp_list_char] :
                ( ( E_1 = throw_list_char(E_2) )
               => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S),throw_list_char(E_2)),S_1)) ) ) ) ) ).

tff(fact_668_default__val_Osimps_I5_J,axiom,
    ! [C_2: list_char] : hAPP_ty_val(default_val,class(C_2)) = null ).

tff(fact_669_val_Osimps_I3_J,axiom,
    ! [Nat_2: nat,Nat_1: nat] :
      ( ( addr(Nat_2) = addr(Nat_1) )
    <=> ( Nat_2 = Nat_1 ) ) ).

tff(fact_670_val_Osimps_I1_J,axiom,
    ! [Bool_1: bool,Bool: bool] :
      ( ( bool_1(Bool_1) = bool_1(Bool) )
    <=> ( hBOOL(Bool_1)
      <=> hBOOL(Bool) ) ) ).

tff(fact_671_val_Osimps_I17_J,axiom,
    ! [Nat: nat] : addr(Nat) != null ).

tff(fact_672_val_Osimps_I16_J,axiom,
    ! [Nat: nat] : null != addr(Nat) ).

tff(fact_673_val_Osimps_I20_J,axiom,
    ! [Bool_1: bool,Nat_1: nat] : bool_1(Bool_1) != addr(Nat_1) ).

tff(fact_674_val_Osimps_I21_J,axiom,
    ! [Nat_1: nat,Bool_1: bool] : addr(Nat_1) != bool_1(Bool_1) ).

tff(fact_675_val_Osimps_I10_J,axiom,
    ! [Nat: nat] : unit != addr(Nat) ).

tff(fact_676_val_Osimps_I11_J,axiom,
    ! [Nat: nat] : addr(Nat) != unit ).

tff(fact_677_val_Osimps_I13_J,axiom,
    ! [Bool: bool] : bool_1(Bool) != null ).

tff(fact_678_val_Osimps_I12_J,axiom,
    ! [Bool: bool] : null != bool_1(Bool) ).

tff(fact_679_val_Osimps_I4_J,axiom,
    unit != null ).

tff(fact_680_val_Osimps_I5_J,axiom,
    null != unit ).

tff(fact_681_val_Osimps_I7_J,axiom,
    ! [Bool: bool] : bool_1(Bool) != unit ).

tff(fact_682_val_Osimps_I6_J,axiom,
    ! [Bool: bool] : unit != bool_1(Bool) ).

tff(fact_683_finalRefE,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E: fun_li688206603ion_ty,Ea: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Ha,E,Ea,Ta))
     => ( hBOOL(is_refT(Ta))
       => ( hBOOL(final_list_char(Ea))
         => ( ( Ea != hAPP_v834067052t_char(val_list_char,null) )
           => ( ( ? [A_1: nat] : Ea = hAPP_v834067052t_char(val_list_char,addr(A_1))
               => ! [C_1: list_char] : Ta != class(C_1) )
             => ~ ! [A_1: nat] : Ea != throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))) ) ) ) ) ) ).

tff(fact_684_final__addrE,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E: fun_li688206603ion_ty,Ea: exp_list_char,C: list_char] :
      ( hBOOL(wTrt(Pa,Ha,E,Ea,class(C)))
     => ( hBOOL(final_list_char(Ea))
       => ( ! [A_1: nat] : Ea != hAPP_v834067052t_char(val_list_char,addr(A_1))
         => ~ ! [A_1: nat] : Ea != throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))) ) ) ) ).

tff(fact_685_LAssRedsVal,axiom,
    ! [V: list_char,Ea: exp_list_char,S: produc12694297on_val,V_2: val,H_1: fun_na939144002on_val,L_2: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_2)),hAPP_f1727192346on_val(produc899768717on_val(H_1),L_2))),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(lAss_list_char(V,Ea)),S)),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(produc899768717on_val(H_1),fun_up1149430426on_val(L_2,V,hAPP_val_option_val(some_val,V_2))))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_686_redp__redsp_OLAssRed,axiom,
    ! [V: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S),E_1),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(V,Ea),S),lAss_list_char(V,E_1)),S_1)) ) ).

tff(fact_687_eval__evals_OLAssThrow,axiom,
    ! [V: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E_1: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E_1)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,lAss_list_char(V,Ea),S_0),throw_list_char(E_1)),S_1_1)) ) ).

tff(fact_688_redp__redsp_OLAssThrow,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,Ea: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(V,throw_list_char(Ea)),S),throw_list_char(Ea)),S)) ).

tff(fact_689_red__reds_OLAssRed,axiom,
    ! [V: list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(lAss_list_char(V,Ea)),S)),hAPP_P604205461on_val(produc1259058957on_val(lAss_list_char(V,E_1)),S_1)),red(Pa))) ) ).

tff(fact_690_red__reds_OLAssThrow,axiom,
    ! [V: list_char,Ea: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(lAss_list_char(V,throw_list_char(Ea))),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(Ea)),S)),red(Pa))) ).

tff(fact_691_LAssReds,axiom,
    ! [V: list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(E_1),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(lAss_list_char(V,Ea)),S)),hAPP_P604205461on_val(produc1259058957on_val(lAss_list_char(V,E_1)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_692_LAssRedsThrow,axiom,
    ! [V: list_char,Ea: exp_list_char,S: produc12694297on_val,A: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(Ea),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(A)),S_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(lAss_list_char(V,Ea)),S)),hAPP_P604205461on_val(produc1259058957on_val(throw_list_char(A)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_693_LAss,axiom,
    ! [L_2: fun_li1432931796on_val,V: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,V_2: val,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,V_2)),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1)))
     => ( ( L_2 = fun_up1149430426on_val(L_1,V,hAPP_val_option_val(some_val,V_2)) )
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,lAss_list_char(V,Ea),S_0),hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_2))) ) ) ).

tff(fact_694_redp__redsp_ORedLAss,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,V_2: val,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_2)),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1)),hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(produc899768717on_val(Ha),fun_up1149430426on_val(L_1,V,hAPP_val_option_val(some_val,V_2))))) ).

tff(fact_695_red__reds_ORedLAss,axiom,
    ! [V: list_char,V_2: val,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_2))),hAPP_f1727192346on_val(produc899768717on_val(Ha),L_1))),hAPP_P604205461on_val(produc1259058957on_val(hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(produc899768717on_val(Ha),fun_up1149430426on_val(L_1,V,hAPP_val_option_val(some_val,V_2))))),red(Pa))) ).

tff(fact_696_red__reds_ORedTryCatch,axiom,
    ! [V: list_char,E_2_1: exp_list_char,C: list_char,Pa: list_P1999446415t_char,S: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(produc823076510on_val(D),Fs)) )
     => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(produc5062597t_char(D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(produc1441475159on_val(hAPP_P604205461on_val(produc1259058957on_val(tryCatch_list_char(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))),C,V,E_2_1)),S)),hAPP_P604205461on_val(produc1259058957on_val(block_list_char(V,class(C),seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,addr(A))),E_2_1))),S)),red(Pa))) ) ) ).

tff(fact_697_eval__cases_I4_J,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,Ea: exp_list_char,S: produc12694297on_val,E_1: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,lAss_list_char(V,Ea),S),E_1),S_1))
     => ( ( ( E_1 = hAPP_v834067052t_char(val_list_char,unit) )
         => ! [V_1: val,H: fun_na939144002on_val,L: fun_li1432931796on_val] :
              ( ( S_1 = hAPP_f1727192346on_val(produc899768717on_val(H),fun_up1149430426on_val(L,V,hAPP_val_option_val(some_val,V_1))) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S),hAPP_v834067052t_char(val_list_char,V_1)),hAPP_f1727192346on_val(produc899768717on_val(H),L))) ) )
       => ~ ! [E_2: exp_list_char] :
              ( ( E_1 = throw_list_char(E_2) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S),throw_list_char(E_2)),S_1)) ) ) ) ).

tff(fact_698_WTrtBlock,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E: fun_li688206603ion_ty,V: list_char,Ta: ty,Ea: exp_list_char,T: ty] :
      ( hBOOL(wTrt(Pa,Ha,fun_up424764369ion_ty(E,V,hAPP_ty_option_ty(some_ty,Ta)),Ea,T))
     => hBOOL(wTrt(Pa,Ha,E,block_list_char(V,Ta,Ea),T)) ) ).

tff(fact_699_redp__redsp_ORedBlock,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,Ta: ty,U: val,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V,Ta,hAPP_v834067052t_char(val_list_char,U)),S),hAPP_v834067052t_char(val_list_char,U)),S)) ).

%----Helper facts (8)
tff(help_fTrue_1_1_U,axiom,
    hBOOL(fTrue) ).

tff(help_fTrue_1_1_T,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_fFalse_1_1_U,axiom,
    ~ hBOOL(fFalse) ).

tff(help_fFalse_1_1_T,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_fequal_1_1_fequal_000tc__Type__Oty_T,axiom,
    ! [X: ty,Y: ty] :
      ( ~ hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(fequal_ty,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__Type__Oty_T,axiom,
    ! [X: ty,Y: ty] :
      ( ( X != Y )
      | hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(fequal_ty,X),Y)) ) ).

tff(help_fequal_1_1_fequal_000tc__Value__Oval_T,axiom,
    ! [X: val,Y: val] :
      ( ~ hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(fequal_val,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__Value__Oval_T,axiom,
    ! [X: val,Y: val] :
      ( ( X != Y )
      | hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(fequal_val,X),Y)) ) ).

%----Conjectures (3)
tff(conj_0,hypothesis,
    size_s2113983095t_char(vs_1) = size_size_list_ty(ts) ).

tff(conj_1,hypothesis,
    size_size_list_val(vs) = size_size_list_ty(ts) ).

tff(conj_2,conjecture,
    ( hBOOL(wTrt(p,h,e_1,blocks(hAPP_P767818445t_char(produc921874948t_char(vs_1),hAPP_P1392904962t_char(produc1909267824t_char(ts),hAPP_e1752110927t_char(produc1916172923t_char(vs),e)))),t))
  <=> ( hBOOL(wTrt(p,h,map_up891053837har_ty(e_1,vs_1,ts),e,t))
      & ? [Ts: list_ty] :
          ( ( hAPP_l2006940821ion_ty(map_val_option_ty(typeof_h(h)),vs) = hAPP_l1487035934ion_ty(map_ty_option_ty(some_ty),Ts) )
          & hBOOL(list_all2_ty_ty(widen_2090681816t_char(p),Ts,ts)) ) ) ) ).

%------------------------------------------------------------------------------