TPTP Problem File: SWW476

TPTP Problem File: SWW476_3.p

%------------------------------------------------------------------------------
% File     : SWW476_3 : TPTP v8.2.0. Released v5.3.0.
% Domain   : Software Verification
% Problem  : Java type soundness line 197, 1000 axioms selected
% Version  : Especial.
% English  :

% Refs     : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
%          : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source   : [Bla11]
% Names    : jinja_1000_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    : 2604 ( 340 unt;1375 typ;   0 def)
%            Number of atoms       : 2860 (1287 equ)
%            Maximal formula atoms :   11 (   1 avg)
%            Number of connectives : 2073 ( 442   ~;  27   |; 121   &)
%                                         ( 178 <=>;1305  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   31 (   7 avg)
%            Maximal term depth    :   13 (   2 avg)
%            Number of types       :  557 ( 556 usr)
%            Number of type conns  : 1230 ( 700   >; 530   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  818 ( 818 usr; 119 con; 0-6 aty)
%            Number of variables   : 5600 (5501   !;  99   ?;5600   :)
% SPC      : TF0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2011-08-09 17:35:27
%------------------------------------------------------------------------------
%----Should-be-implicit typings (556)
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tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_254,type,
    fun_Pr1905081477_ty_ty: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_255,type,
    fun_Pr1693821262ty_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_256,type,
    fun_Pr967742621r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_257,type,
    fun_Pr31562774r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_258,type,
    fun_Pr718735977y_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_259,type,
    fun_Pr2080430770l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_260,type,
    fun_Pr1566767763har_ty: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_261,type,
    fun_Pr1149393094ar_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_262,type,
    fun_Pr176052370t_char: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_263,type,
    fun_Pr661739816l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_264,type,
    fun_Pr1439460619t_char: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_265,type,
    fun_Pr376272433ion_ty: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_266,type,
    fun_Pr1820304636val_ty: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_267,type,
    fun_Pr2009941573al_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_268,type,
    fun_Pr819181076r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_269,type,
    fun_Pr2102600973r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_270,type,
    fun_Pr489436466y_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_271,type,
    fun_Pr626733307l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_272,type,
    fun_Pr300893373ar_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_273,type,
    fun_Pr2023323325ar_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_274,type,
    fun_Pr1555044210ar_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_275,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__fun_Itc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_,type,
    fun_Pr643382121l_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__Expr,type,
    produc2048519645t_char: $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,
    produc91527719t_char: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_276,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__Lis,type,
    produc1200003175t_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__Type__Oty_J,type,
    produc917948472har_ty: $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__String__Ochar_J_Mtc__prod_Itc__List__Olist_,type,
    produc469582463har_ty: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__List__Olist_Itc__Type__Oty,type,
    produc1420746395ist_ty: $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__List__Olist_Itc__Value__Oval_J_Mtc__List__Olist_Itc__Value__,type,
    produc753553453st_val: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__,type,
    produc1497648875on_val: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__,type,
    produc143547239on_val: $tType ).

tff(ty_ty_tc__prod_Itc__String__Ochar_Mtc__String__Ochar_J,type,
    produc409241703r_char: $tType ).

tff(ty_ty_tc__prod_Itc__Type__Oty_Mtc__Type__Oty_J,type,
    product_prod_ty_ty: $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__277,type,
    produc349695911t_char: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_,type,
    produc245756905har_ty: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist__278,type,
    produc1147203250ar_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist__279,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 ).

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Li,type,
    produc1312961703ar_val: $tType ).

%----Explicit typings (819)
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_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__List__Olist_Itc__,type,
    cOMBB_383678192on_val: fun_fu114905943l_bool ).

tff(sy_c_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc_,type,
    cOMBB_1303934920on_val: fun_fu781882819l_bool ).

tff(sy_c_COMBB_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__fun_Itc__fun_Itc__prod,type,
    cOMBB_352765746t_char: fun_fu2088691401ion_ty ).

tff(sy_c_COMBB_000tc__Type__Oty_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List_,type,
    cOMBB_1888336841t_char: fun_fu1705731887ion_ty ).

tff(sy_c_COMBB_000tc__Value__Oval_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String,type,
    cOMBB_311099133val_ty: fun_fu124241277ar_val ).

tff(sy_c_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc_,type,
    cOMBB_1718333400on_val: fun_fu48585473l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__Value__Oval_Mtc__prod_Itc__prod_Itc__List__Olist_Itc_,type,
    cOMBB_388225803t_char: fun_fu945706003ar_val ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option,type,
    cOMBB_1518282696on_val: fun_fu938561337l_bool ).

tff(sy_c_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption,type,
    cOMBC_832625297y_bool: fun_fu2083094209l_bool ).

tff(sy_c_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__O,type,
    cOMBC_2027949654l_bool: fun_fu1680591819l_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_It,type,
    cOMBC_2111366340ar_val: fun_fu1227413499ar_val ).

tff(sy_c_COMBK_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__fun_Itc__prod_Itc__Lis,type,
    cOMBK_184479553on_val: fun_op1983271469ion_ty ).

tff(sy_c_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__List__Olist_Itc__Str,type,
    cOMBK_1097134891t_char: fun_op2076490582on_val ).

tff(sy_c_COMBK_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String__Ochar_,type,
    cOMBK_1944287343al_nat: fun_op637900998on_val ).

tff(sy_c_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__O,type,
    cOMBS_570216337l_bool: ( fun_fu1806184744l_bool * fun_fu100249073l_bool ) > fun_fu100249073l_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_fu1246919812l_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_fu2141444501y_bool ).

tff(sy_c_Decl_Ois__class_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__,type,
    is_cla570604648t_char: list_P1999446415t_char > fun_list_char_bool ).

tff(sy_c_Exceptions_OClassCast,type,
    classCast: list_char ).

tff(sy_c_Exceptions_ONullPointer,type,
    nullPointer: list_char ).

tff(sy_c_Exceptions_OOutOfMemory,type,
    outOfMemory: list_char ).

tff(sy_c_Exceptions_Oaddr__of__sys__xcpt,type,
    addr_of_sys_xcpt: fun_list_char_nat ).

tff(sy_c_Exceptions_Opreallocated,type,
    preallocated: fun_na939144002on_val > bool ).

tff(sy_c_Exceptions_Osys__xcpts,type,
    sys_xcpts: fun_list_char_bool ).

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

tff(sy_c_Expr_Obop_OAdd,type,
    add: bop ).

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_OCond_000tc__List__Olist_Itc__String__Ochar_J,type,
    cond_list_char: ( exp_list_char * exp_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_Onew_000tc__List__Olist_Itc__String__Ochar_J,type,
    new_list_char: 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_Expr_Ofv,type,
    fv: exp_list_char > fun_list_char_bool ).

tff(sy_c_Fun_Ocomp_000tc__List__Olist_Itc__List__Olist_Itc__prod_Itc__prod_Itc__List,type,
    comp_l347675690har_ty: ( fun_li801778361on_val * fun_li760419782ar_val ) > fun_li1714359792on_val ).

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__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Stri,type,
    comp_l424027617har_ty: ( fun_li889387821on_val * fun_li867521386ar_val ) > fun_li750181430on_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_280,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_Lattices_Osemilattice__sup__class_Osup_000tc__fun_Itc__List__Olist_Itc__Str,type,
    semila919158006r_bool: ( fun_list_char_bool * fun_list_char_bool ) > fun_list_char_bool ).

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_Oappend_000tc__List__Olist_Itc__String__Ochar_J,type,
    append_list_char: ( list_list_char * list_list_char ) > list_list_char ).

tff(sy_c_List_Oappend_000tc__Option__Ooption_Itc__Type__Oty_J,type,
    append_option_ty: ( list_option_ty * list_option_ty ) > list_option_ty ).

tff(sy_c_List_Oappend_000tc__Type__Oty,type,
    append_ty: ( list_ty * list_ty ) > list_ty ).

tff(sy_c_List_Oappend_000tc__Value__Oval,type,
    append_val: ( list_val * list_val ) > list_val ).

tff(sy_c_List_Oappend_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mt,type,
    append590652462har_ty: ( list_P2023964830har_ty * list_P2023964830har_ty ) > list_P2023964830har_ty ).

tff(sy_c_List_Oappend_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mt_281,type,
    append1049742455ar_val: ( list_P1697858023ar_val * list_P1697858023ar_val ) > list_P1697858023ar_val ).

tff(sy_c_List_Odistinct_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
    distin1416307044t_char: list_exp_list_char > bool ).

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

tff(sy_c_List_Odistinct_000tc__Nat__Onat,type,
    distinct_nat: list_nat > bool ).

tff(sy_c_List_Odistinct_000tc__Type__Oty,type,
    distinct_ty: list_ty > bool ).

tff(sy_c_List_Odistinct_000tc__Value__Oval,type,
    distinct_val: list_val > bool ).

tff(sy_c_List_Odistinct_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List_,type,
    distin1973552748t_char: list_P1916372464t_char > bool ).

tff(sy_c_List_Odistinct_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__,type,
    distin179070212on_val: list_P1439941640on_val > bool ).

tff(sy_c_List_Odistinct_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__,type,
    distin1349260956on_val: list_P507235360on_val > bool ).

tff(sy_c_List_Olex_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
    lex_exp_list_char: fun_Pr136267935r_bool > fun_Pr716652265r_bool ).

tff(sy_c_List_Olex_000tc__List__Olist_Itc__String__Ochar_J,type,
    lex_list_char: fun_Pr565113489r_bool > fun_Pr382120745r_bool ).

tff(sy_c_List_Olex_000tc__String__Ochar,type,
    lex_char: fun_Pr638203177r_bool > fun_Pr565113489r_bool ).

tff(sy_c_List_Olex_000tc__Type__Oty,type,
    lex_ty: fun_Pr2087862441y_bool > fun_Pr306783325y_bool ).

tff(sy_c_List_Olex_000tc__Value__Oval,type,
    lex_val: fun_Pr2081272681l_bool > fun_Pr1618624239l_bool ).

tff(sy_c_List_Olex_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J,type,
    lex_Pr979517357on_val: fun_Pr691271849l_bool > fun_Pr564925613l_bool ).

tff(sy_c_List_Olex_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
    lex_Pr830868420on_val: fun_Pr859510977l_bool > fun_Pr872262185l_bool ).

tff(sy_c_List_Olexn_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
    lexn_exp_list_char: ( fun_Pr136267935r_bool * nat ) > fun_Pr716652265r_bool ).

tff(sy_c_List_Olexn_000tc__List__Olist_Itc__String__Ochar_J,type,
    lexn_list_char: ( fun_Pr565113489r_bool * nat ) > fun_Pr382120745r_bool ).

tff(sy_c_List_Olexn_000tc__String__Ochar,type,
    lexn_char: ( fun_Pr638203177r_bool * nat ) > fun_Pr565113489r_bool ).

tff(sy_c_List_Olexn_000tc__Type__Oty,type,
    lexn_ty: ( fun_Pr2087862441y_bool * nat ) > fun_Pr306783325y_bool ).

tff(sy_c_List_Olexn_000tc__Value__Oval,type,
    lexn_val: ( fun_Pr2081272681l_bool * nat ) > fun_Pr1618624239l_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 > fun_li1279027773t_char ).

tff(sy_c_List_Olist_OCons_000tc__List__Olist_Itc__String__Ochar_J,type,
    cons_list_char: list_char > fun_li1898638973t_char ).

tff(sy_c_List_Olist_OCons_000tc__Nat__Onat,type,
    cons_nat: nat > fun_li1155097699st_nat ).

tff(sy_c_List_Olist_OCons_000tc__Option__Ooption_Itc__Type__Oty_J,type,
    cons_option_ty: option_ty > fun_li735972349ion_ty ).

tff(sy_c_List_Olist_OCons_000tc__String__Ochar,type,
    cons_char: char > fun_li1751394789t_char ).

tff(sy_c_List_Olist_OCons_000tc__Type__Oty,type,
    cons_ty: ty > fun_list_ty_list_ty ).

tff(sy_c_List_Olist_OCons_000tc__Value__Oval,type,
    cons_val: val > fun_li1707879747st_val ).

tff(sy_c_List_Olist_OCons_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__,type,
    cons_P1917484281on_val: produc124828825on_val > fun_li729885185on_val ).

tff(sy_c_List_Olist_OCons_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol,type,
    cons_P1190705016on_val: produc2061676504on_val > fun_li1486652797on_val ).

tff(sy_c_List_Olist_OCons_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis,type,
    cons_P2009561711t_char: produc1278157519t_char > fun_li1304494141t_char ).

tff(sy_c_List_Olist_OCons_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
    cons_P511631239on_val: produc1102272487on_val > fun_li1479469629on_val ).

tff(sy_c_List_Olist_OCons_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc,type,
    cons_P1546421407on_val: produc430140671on_val > fun_li1119704125on_val ).

tff(sy_c_List_Olist_OCons_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_,type,
    cons_P796333129har_ty: produc245756905har_ty > fun_li445813409har_ty ).

tff(sy_c_List_Olist_OCons_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar__282,type,
    cons_P2112347922ar_val: produc1147203250ar_val > fun_li1966627635ar_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 ) > fun_li652750717y_bool ).

tff(sy_c_List_Olist__all2_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J__283,type,
    list_a1552939645r_char: ( fun_ex2034987181r_bool * list_exp_list_char ) > fun_list_char_bool ).

tff(sy_c_List_Olist__all2_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J__284,type,
    list_a2080147979on_val: ( fun_ex1875415355l_bool * list_exp_list_char ) > fun_li89141392l_bool ).

tff(sy_c_List_Olist__all2_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J__285,type,
    list_a288514022on_val: ( fun_ex435221764l_bool * list_exp_list_char ) > fun_li1631375983l_bool ).

tff(sy_c_List_Olist__all2_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J__286,type,
    list_a623412059har_ty: ( fun_ex1280510859y_bool * list_exp_list_char ) > fun_li475498464y_bool ).

tff(sy_c_List_Olist__all2_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J__287,type,
    list_a1554965796ar_val: ( fun_ex1764228052l_bool * list_exp_list_char ) > fun_li94363049l_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 ) > fun_li652750717y_bool ).

tff(sy_c_List_Olist__all2_000tc__List__Olist_Itc__String__Ochar_J_000tc__String__Och,type,
    list_a1647123652r_char: ( fun_li752648358r_bool * list_list_char ) > fun_list_char_bool ).

tff(sy_c_List_Olist__all2_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__E,type,
    list_a1874290002on_val: ( fun_li923379764l_bool * list_list_char ) > fun_li89141392l_bool ).

tff(sy_c_List_Olist__all2_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__L,type,
    list_a809715167on_val: ( fun_li727108811l_bool * list_list_char ) > fun_li1631375983l_bool ).

tff(sy_c_List_Olist__all2_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__p,type,
    list_a1115291042har_ty: ( fun_li213500804y_bool * list_list_char ) > fun_li475498464y_bool ).

tff(sy_c_List_Olist__all2_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__p_288,type,
    list_a400141291ar_val: ( fun_li1849706317l_bool * list_list_char ) > fun_li94363049l_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 ) > fun_li639767902r_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 ) > fun_li161542487r_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 ) > fun_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 ) > fun_list_val_bool ).

tff(sy_c_List_Olist__all2_000tc__String__Ochar_000tc__Expr__Oexp_Itc__List__Olist_It,type,
    list_a196402809t_char: ( fun_ch691056635r_bool * list_char ) > fun_li639767902r_bool ).

tff(sy_c_List_Olist__all2_000tc__String__Ochar_000tc__List__Olist_Itc__String__Ochar,type,
    list_a1337954418t_char: ( fun_ch693599860r_bool * list_char ) > fun_li161542487r_bool ).

tff(sy_c_List_Olist__all2_000tc__String__Ochar_000tc__Type__Oty,type,
    list_all2_char_ty: ( fun_char_fun_ty_bool * list_char ) > fun_list_ty_bool ).

tff(sy_c_List_Olist__all2_000tc__String__Ochar_000tc__Value__Oval,type,
    list_all2_char_val: ( fun_ch496724692l_bool * list_char ) > fun_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 ) > fun_li652750717y_bool ).

tff(sy_c_List_Olist__all2_000tc__Type__Oty_000tc__String__Ochar,type,
    list_all2_ty_char: ( fun_ty_fun_char_bool * list_ty ) > fun_list_char_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 ) > fun_list_ty_bool ).

tff(sy_c_List_Olist__all2_000tc__Type__Oty_000tc__prod_Itc__Expr__Oexp_Itc__List__Ol,type,
    list_a216081281on_val: ( fun_ty1713482521l_bool * list_ty ) > fun_li89141392l_bool ).

tff(sy_c_List_Olist__all2_000tc__Type__Oty_000tc__prod_Itc__List__Olist_Itc__Expr__O,type,
    list_a392402672on_val: ( fun_ty1511004582l_bool * list_ty ) > fun_li1631375983l_bool ).

tff(sy_c_List_Olist__all2_000tc__Type__Oty_000tc__prod_Itc__prod_Itc__List__Olist_It,type,
    list_a860324561har_ty: ( fun_ty701313897y_bool * list_ty ) > fun_li475498464y_bool ).

tff(sy_c_List_Olist__all2_000tc__Type__Oty_000tc__prod_Itc__prod_Itc__List__Olist_It_289,type,
    list_a123308442ar_val: ( fun_ty1263539378l_bool * list_ty ) > fun_li94363049l_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 ) > fun_li652750717y_bool ).

tff(sy_c_List_Olist__all2_000tc__Value__Oval_000tc__String__Ochar,type,
    list_all2_val_char: ( fun_va1368839508r_bool * list_val ) > fun_list_char_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 ) > fun_list_ty_bool ).

tff(sy_c_List_Olist__all2_000tc__Value__Oval_000tc__prod_Itc__Expr__Oexp_Itc__List__,type,
    list_a1839848952on_val: ( fun_va267341538l_bool * list_val ) > fun_li89141392l_bool ).

tff(sy_c_List_Olist__all2_000tc__Value__Oval_000tc__prod_Itc__List__Olist_Itc__Expr_,type,
    list_a88719801on_val: ( fun_va1011302557l_bool * list_val ) > fun_li1631375983l_bool ).

tff(sy_c_List_Olist__all2_000tc__Value__Oval_000tc__prod_Itc__prod_Itc__List__Olist_,type,
    list_a2075757640har_ty: ( fun_va922339378y_bool * list_val ) > fun_li475498464y_bool ).

tff(sy_c_List_Olist__all2_000tc__Value__Oval_000tc__prod_Itc__prod_Itc__List__Olist__290,type,
    list_a1609582481ar_val: ( fun_va1181537531l_bool * list_val ) > fun_li94363049l_bool ).

tff(sy_c_List_Olist__all2_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__,type,
    list_a789546247t_char: ( fun_Pr1145000429r_bool * list_P1663965006on_val ) > fun_li639767902r_bool ).

tff(sy_c_List_Olist__all2_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String___291,type,
    list_a292640256t_char: ( fun_Pr2007843174r_bool * list_P1663965006on_val ) > fun_li161542487r_bool ).

tff(sy_c_List_Olist__all2_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String___292,type,
    list_a2001304881val_ty: ( fun_Pr960551193y_bool * list_P1663965006on_val ) > fun_list_ty_bool ).

tff(sy_c_List_Olist__all2_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String___293,type,
    list_a594658042al_val: ( fun_Pr755913058l_bool * list_P1663965006on_val ) > fun_list_val_bool ).

tff(sy_c_List_Olist__all2_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol,type,
    list_a1478901862t_char: ( fun_Pr1480657058r_bool * list_P249777017on_val ) > fun_li639767902r_bool ).

tff(sy_c_List_Olist__all2_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol_294,type,
    list_a1169722591t_char: ( fun_Pr2103285403r_bool * list_P249777017on_val ) > fun_li161542487r_bool ).

tff(sy_c_List_Olist__all2_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol_295,type,
    list_a182912018val_ty: ( fun_Pr123818788y_bool * list_P249777017on_val ) > fun_list_ty_bool ).

tff(sy_c_List_Olist__all2_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol_296,type,
    list_a595061083al_val: ( fun_Pr66876909l_bool * list_P249777017on_val ) > fun_list_val_bool ).

tff(sy_c_List_Olist__all2_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_,type,
    list_a1822188631t_char: ( fun_Pr967742621r_bool * list_P2023964830har_ty ) > fun_li639767902r_bool ).

tff(sy_c_List_Olist__all2_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar__297,type,
    list_a1479679312t_char: ( fun_Pr31562774r_bool * list_P2023964830har_ty ) > fun_li161542487r_bool ).

tff(sy_c_List_Olist__all2_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar__298,type,
    list_a985311713_ty_ty: ( fun_Pr718735977y_bool * list_P2023964830har_ty ) > fun_list_ty_bool ).

tff(sy_c_List_Olist__all2_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar__299,type,
    list_a1068996522ty_val: ( fun_Pr2080430770l_bool * list_P2023964830har_ty ) > fun_list_val_bool ).

tff(sy_c_List_Olist__all2_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar__300,type,
    list_a422786208t_char: ( fun_Pr819181076r_bool * list_P1697858023ar_val ) > fun_li639767902r_bool ).

tff(sy_c_List_Olist__all2_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar__301,type,
    list_a24143385t_char: ( fun_Pr2102600973r_bool * list_P1697858023ar_val ) > fun_li161542487r_bool ).

tff(sy_c_List_Olist__all2_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar__302,type,
    list_a307207512val_ty: ( fun_Pr489436466y_bool * list_P1697858023ar_val ) > fun_list_ty_bool ).

tff(sy_c_List_Olist__all2_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar__303,type,
    list_a1889288097al_val: ( fun_Pr626733307l_bool * list_P1697858023ar_val ) > fun_list_val_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___304,type,
    map_ex178392974ar_val: fun_ex292271891ar_val > fun_li337688157ar_val ).

tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___305,type,
    map_ex1185884067ar_nat: fun_ex432391284ar_nat > fun_li1890191168st_nat ).

tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___306,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___307,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___308,type,
    map_ex1634568356r_char: fun_ex608259829r_char > fun_li79274049t_char ).

tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___309,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___310,type,
    map_ex1279484156on_val: fun_ex1362790221on_val > fun_li1562283673on_val ).

tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___311,type,
    map_ex1452011826on_val: fun_ex139963011on_val > fun_li1788539855on_val ).

tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___312,type,
    map_ex20783615on_val: fun_ex500270084on_val > fun_li867484494on_val ).

tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___313,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___314,type,
    map_ex2035595288har_ty: fun_ex1813935209har_ty > fun_li32322485har_ty ).

tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___315,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___316,type,
    map_ex2031894694on_val: fun_ex1957978155on_val > fun_li1135544693on_val ).

tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___317,type,
    map_ex1811769730har_ty: fun_ex1739657427har_ty > fun_li1512323871har_ty ).

tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___318,type,
    map_ex1319446475ar_val: fun_ex611469212ar_val > fun_li855547112ar_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__List__Olist_Itc__p,type,
    map_li401377927ar_val: fun_li1267938444ar_val > fun_li1791555364ar_val ).

tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__Nat__Onat,type,
    map_list_char_nat: fun_list_char_nat > fun_li1325798073st_nat ).

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_319,type,
    map_li50976719on_val: fun_li1432931796on_val > fun_li1580442732on_val ).

tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__String__Ochar,type,
    map_list_char_char: fun_list_char_char > fun_li1239651002t_char ).

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__fun_Itc__prod_Itc_,type,
    map_li1461022915on_val: fun_li905540756on_val > fun_li1668453138on_val ).

tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__Expr__Oe,type,
    map_li586533881on_val: fun_li744874698on_val > fun_li177368392on_val ).

tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__List__Ol,type,
    map_li1622452344on_val: fun_li563662077on_val > fun_li2071992469on_val ).

tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__List__Ol_320,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__List__Ol_321,type,
    map_li56668639har_ty: fun_li1248349104har_ty > fun_li1999687214har_ty ).

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_322,type,
    map_li1925379487on_val: fun_li328275876on_val > fun_li917540924on_val ).

tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__prod_Itc_323,type,
    map_li1980326729har_ty: fun_li1174071322har_ty > fun_li1332204952har_ty ).

tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__prod_Itc_324,type,
    map_li37924370ar_val: fun_li1882647395ar_val > fun_li1202359009ar_val ).

tff(sy_c_List_Omap_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Stri,type,
    map_li912744805ar_val: fun_li867521386ar_val > fun_li760419782ar_val ).

tff(sy_c_List_Omap_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Stri_325,type,
    map_li1065623653on_val: fun_li750181430on_val > fun_li1714359792on_val ).

tff(sy_c_List_Omap_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Stri_326,type,
    map_li596218076on_val: fun_li889387821on_val > fun_li801778361on_val ).

tff(sy_c_List_Omap_000tc__Nat__Onat_000tc__Nat__Onat,type,
    map_nat_nat: fun_nat_nat > fun_li1155097699st_nat ).

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__Type__Oty_J_000tc__prod_Itc__prod_Itc,type,
    map_op1852210284ar_val: fun_op1549449661ar_val > fun_li181851399ar_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__String__Ochar_000tc__Expr__Oexp_Itc__List__Olist_Itc__Stri,type,
    map_ch278031520t_char: fun_ch1888757611t_char > fun_li471109017t_char ).

tff(sy_c_List_Omap_000tc__String__Ochar_000tc__List__Olist_Itc__String__Ochar_J,type,
    map_char_list_char: fun_char_list_char > fun_li211407762t_char ).

tff(sy_c_List_Omap_000tc__String__Ochar_000tc__Option__Ooption_Itc__Type__Oty_J,type,
    map_char_option_ty: fun_char_option_ty > fun_li234662328ion_ty ).

tff(sy_c_List_Omap_000tc__String__Ochar_000tc__Type__Oty,type,
    map_char_ty: fun_char_ty > fun_li754043211ist_ty ).

tff(sy_c_List_Omap_000tc__String__Ochar_000tc__Value__Oval,type,
    map_char_val: fun_char_val > fun_li535708692st_val ).

tff(sy_c_List_Omap_000tc__String__Ochar_000tc__prod_Itc__prod_Itc__List__Olist_Itc__,type,
    map_ch1589830937ar_val: fun_ch2033169700ar_val > fun_li1267938444ar_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__List__Olist_Itc__prod_Itc__prod_Itc__List,type,
    map_ty217218598ar_val: fun_ty719916017ar_val > fun_li646409939ar_val ).

tff(sy_c_List_Omap_000tc__Type__Oty_000tc__Nat__Onat,type,
    map_ty_nat: fun_ty_nat > fun_list_ty_list_nat ).

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__String__Ochar,type,
    map_ty_char: fun_ty_char > fun_li162253899t_char ).

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__fun_Itc__prod_Itc__List__Olist_Itc__Strin,type,
    map_ty330392676on_val: fun_ty2061842671on_val > fun_li1332088483on_val ).

tff(sy_c_List_Omap_000tc__Type__Oty_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
    map_ty763542682on_val: fun_ty876164645on_val > fun_li1222710745on_val ).

tff(sy_c_List_Omap_000tc__Type__Oty_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc,type,
    map_ty268240023on_val: fun_ty1472322018on_val > fun_li501969092on_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__List__Olist_Itc__String__Ochar__327,type,
    map_ty1735732096har_ty: fun_ty1560310283har_ty > fun_li1092644799har_ty ).

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__Type__Oty_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Stri,type,
    map_ty1511906538har_ty: fun_ty1486032501har_ty > fun_li425162537har_ty ).

tff(sy_c_List_Omap_000tc__Type__Oty_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Stri_328,type,
    map_ty15886131ar_val: fun_ty434869310ar_val > fun_li423654386ar_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__List__Olist_Itc__prod_Itc__prod_Itc__Li,type,
    map_va45294063ar_val: fun_va1465032250ar_val > fun_li1597490890ar_val ).

tff(sy_c_List_Omap_000tc__Value__Oval_000tc__Nat__Onat,type,
    map_val_nat: fun_val_nat > fun_li101582227st_nat ).

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__String__Ochar,type,
    map_val_char: fun_val_char > fun_li1661102996t_char ).

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__fun_Itc__prod_Itc__List__Olist_Itc__Str,type,
    map_va1286924123on_val: fun_va347778406on_val > fun_li1337614316on_val ).

tff(sy_c_List_Omap_000tc__Value__Oval_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_I,type,
    map_va828275345on_val: fun_va1155687836on_val > fun_li207121442on_val ).

tff(sy_c_List_Omap_000tc__Value__Oval_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_I,type,
    map_va1077464032on_val: fun_va1082347435on_val > fun_li1112589627on_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__List__Olist_Itc__String__Ocha_329,type,
    map_va44677239har_ty: fun_va1221587074har_ty > fun_li1206728456har_ty ).

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__Value__Oval_000tc__prod_Itc__prod_Itc__List__Olist_Itc__St,type,
    map_va1968335329har_ty: fun_va1147309292har_ty > fun_li539246194har_ty ).

tff(sy_c_List_Omap_000tc__Value__Oval_000tc__prod_Itc__prod_Itc__List__Olist_Itc__St_330,type,
    map_va742516906ar_val: fun_va1416972085ar_val > fun_li470558395ar_val ).

tff(sy_c_List_Omap_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J,type,
    map_Pr161410094t_char: fun_Pr664085497t_char > fun_li203067531t_char ).

tff(sy_c_List_Omap_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_331,type,
    map_Pr1152367783t_char: fun_Pr213997554t_char > fun_li130774916t_char ).

tff(sy_c_List_Omap_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_332,type,
    map_Pr590903501ion_ty: fun_Pr1298293016ion_ty > fun_li154029482ion_ty ).

tff(sy_c_List_Omap_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_333,type,
    map_Pr401282634val_ty: fun_Pr685918677val_ty > fun_li614790617ist_ty ).

tff(sy_c_List_Omap_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_334,type,
    map_Pr1730568083al_val: fun_Pr1341722270al_val > fun_li1589119394st_val ).

tff(sy_c_List_Omap_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_335,type,
    map_Pr618945291ar_val: fun_Pr971959830ar_val > fun_li1563778074ar_val ).

tff(sy_c_List_Omap_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
    map_Pr1211171455t_char: fun_Pr645859204t_char > fun_li1574664172t_char ).

tff(sy_c_List_Omap_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc_336,type,
    map_Pr1982459768t_char: fun_Pr1262402813t_char > fun_li27018085t_char ).

tff(sy_c_List_Omap_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc_337,type,
    map_Pr1420995486ion_ty: fun_Pr199214627ion_ty > fun_li50272651ion_ty ).

tff(sy_c_List_Omap_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc_338,type,
    map_Pr58749369val_ty: fun_Pr722806154val_ty > fun_li372218936ist_ty ).

tff(sy_c_List_Omap_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc_339,type,
    map_Pr1583805314al_val: fun_Pr160391123al_val > fun_li404189313st_val ).

tff(sy_c_List_Omap_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc_340,type,
    map_Pr1591425018ar_val: fun_Pr276820555ar_val > fun_li347839481ar_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__List__Olist_Itc__String__Ochar_J_Mtc__Type__Oty_,type,
    map_Pr1471044963har_ty: fun_Pr107226222har_ty > fun_li1848428912har_ty ).

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_Omap_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__,type,
    map_Pr863062654t_char: fun_Pr580238665t_char > fun_li672142651t_char ).

tff(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___341,type,
    map_Pr197231351t_char: fun_Pr563796290t_char > fun_li974066740t_char ).

tff(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___342,type,
    map_Pr1783250717ion_ty: fun_Pr1648091752ion_ty > fun_li997321306ion_ty ).

tff(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___343,type,
    map_Pr1636893690_ty_ty: fun_Pr1905081477_ty_ty > fun_li368076073ist_ty ).

tff(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___344,type,
    map_Pr961574211ty_val: fun_Pr1693821262ty_val > fun_li715182322st_val ).

tff(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___345,type,
    map_Pr1267419400har_ty: fun_Pr1566767763har_ty > fun_li1113295671har_ty ).

tff(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___346,type,
    map_Pr1153581243ar_val: fun_Pr1149393094ar_val > fun_li867521386ar_val ).

tff(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___347,type,
    map_Pr187266887t_char: fun_Pr176052370t_char > fun_li645506098t_char ).

tff(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___348,type,
    map_Pr1809410112t_char: fun_Pr1439460619t_char > fun_li771345067t_char ).

tff(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___349,type,
    map_Pr1247945830ion_ty: fun_Pr376272433ion_ty > fun_li794599633ion_ty ).

tff(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___350,type,
    map_Pr199785201val_ty: fun_Pr1820304636val_ty > fun_li1202111090ist_ty ).

tff(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___351,type,
    map_Pr1022222522al_val: fun_Pr2009941573al_val > fun_li1357584827st_val ).

tff(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___352,type,
    map_Pr879013170ar_val: fun_Pr2023323325ar_val > fun_li1966627635ar_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__Nat__Onat,type,
    set_nat: list_nat > fun_nat_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_List_Oset_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__,type,
    set_Pr1831523898har_ty: list_P2023964830har_ty > fun_Pr2102567903y_bool ).

tff(sy_c_List_Oset_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___353,type,
    set_Pr309835907ar_val: list_P1697858023ar_val > fun_Pr661739816l_bool ).

tff(sy_c_Map_Odom_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
    dom_list_char_val: fun_li1432931796on_val > fun_list_char_bool ).

tff(sy_c_Map_Odom_000tc__Nat__Onat_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J,type,
    dom_na996029170on_val: fun_na939144002on_val > fun_nat_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__of_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__O,type,
    map_of1247784410ar_val: fun_li889387821on_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_Map_Orestrict__map_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Ov,type,
    restri761823004ar_val: ( fun_li1432931796on_val * fun_list_char_bool ) > fun_li1432931796on_val ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_,type,
    size_s1143674878t_char: fun_li1786110815ar_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__List__Olist_Itc__String__Och,type,
    size_s2113983095t_char: fun_li136542502ar_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__List__Olist_Itc__prod_Itc__p,type,
    size_s764697941har_ty: fun_li1802730952ty_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__List__Olist_Itc__prod_Itc__p_354,type,
    size_s655688734ar_val: fun_li74239807al_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Nat__Onat_J,type,
    size_size_list_nat: fun_list_nat_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Option__Ooption_Itc__Type__O,type,
    size_s1050794909ion_ty: fun_li359420288ty_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Option__Ooption_Itc__Value__,type,
    size_s1595297126on_val: fun_li1715509239al_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__String__Ochar_J,type,
    size_size_list_char: fun_list_char_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Type__Oty_J,type,
    size_size_list_ty: fun_list_ty_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Value__Oval_J,type,
    size_size_list_val: fun_list_val_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__fun_Itc__prod_Itc__List__Oli,type,
    size_s1457910402on_val: fun_li853190243al_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__prod_Itc__Expr__Oexp_Itc__Li,type,
    size_s60479160on_val: fun_li722721709al_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__E,type,
    size_s470606735on_val: fun_li33935886al_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__S,type,
    size_s1010401542t_char: fun_li208403543ar_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__S_355,type,
    size_s1760542935har_ty: fun_li1893346126ty_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__S_356,type,
    size_s1518787998har_ty: fun_li82217543ty_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__prod_Itc__prod_Itc__Expr__Oe,type,
    size_s1699857438on_val: fun_li1364025663al_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Ol,type,
    size_s2086378294on_val: fun_li1662826023al_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Ol_357,type,
    size_s1444510216har_ty: fun_li808562781ty_nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Ol_358,type,
    size_s760178257ar_val: fun_li621434964al_nat ).

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

tff(sy_c_Objects_Oinit__fields,type,
    init_fields: fun_li750181430on_val ).

tff(sy_c_Objects_Onew__Addr,type,
    new_Addr: fun_na939144002on_val > option_nat ).

tff(sy_c_Objects_Oobj__ty,type,
    obj_ty: produc639455274on_val > ty ).

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

tff(sy_c_Option_Ooption_ONone_000tc__Nat__Onat,type,
    none_nat: option_nat ).

tff(sy_c_Option_Ooption_ONone_000tc__Type__Oty,type,
    none_ty: option_ty ).

tff(sy_c_Option_Ooption_ONone_000tc__Value__Oval,type,
    none_val: option_val ).

tff(sy_c_Option_Ooption_ONone_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_,type,
    none_P179726773on_val: option1479284511on_val ).

tff(sy_c_Option_Ooption_OSome_000tc__Nat__Onat,type,
    some_nat: fun_nat_option_nat ).

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_Ooption_Ooption__case_000tc__Option__Ooption_Itc__Type__Oty_J_000tc_,type,
    option1388193227on_val: ( option_ty * fun_Pr876827561ion_ty * option1479284511on_val ) > option_ty ).

tff(sy_c_Option_Othe_000tc__Nat__Onat,type,
    the_nat: fun_option_nat_nat ).

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_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__List__Olist_Itc__String__Oc,type,
    ord_le2092826700r_bool: ( fun_list_char_bool * fun_list_char_bool ) > bool ).

tff(sy_c_Product__Type_OPair_000tc__Expr__Obop_000tc__prod_Itc__Value__Oval_Mtc__Val,type,
    produc621191550al_val: fun_bo1153317747al_val ).

tff(sy_c_Product__Type_OPair_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J,type,
    produc943465171t_char: fun_ex660466419t_char ).

tff(sy_c_Product__Type_OPair_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_359,type,
    produc1259058957on_val: fun_ex977868519on_val ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
    produc1237966615t_char: fun_li1918445737t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc_360,type,
    produc379668296on_val: fun_li856594443on_val ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_,type,
    produc1147572817t_char: fun_li1727207611t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar__361,type,
    produc2035944023t_char: fun_li399153499t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar__362,type,
    produc921874948t_char: fun_li455628155t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__List__Ol,type,
    produc5062597t_char: fun_li835958565t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__Type__Ot,type,
    produc251930284har_ty: fun_li885125749har_ty ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc_,type,
    produc823076510on_val: fun_li1436431093on_val ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc,type,
    produc1002914035har_ty: fun_li1324969141har_ty ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_,type,
    produc512429457ist_ty: fun_li475043185ist_ty ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Type__Oty_J_000tc__prod_Itc__Li,type,
    produc1909267824t_char: fun_li1548633647t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Value__Oval_J_000tc__Expr__Oexp,type,
    produc1916172923t_char: fun_li1751446259t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olis,type,
    produc2078839843st_val: fun_li1981758019st_val ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__prod_Itc__Expr__Oexp_Itc__List_,type,
    produc584381409on_val: fun_li1721496513on_val ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Expr,type,
    produc493060183on_val: fun_li475287435on_val ).

tff(sy_c_Product__Type_OPair_000tc__String__Ochar_000tc__String__Ochar,type,
    produc601902295r_char: fun_ch1000319279r_char ).

tff(sy_c_Product__Type_OPair_000tc__Type__Oty_000tc__Type__Oty,type,
    product_Pair_ty_ty: fun_ty595889787_ty_ty ).

tff(sy_c_Product__Type_OPair_000tc__Value__Oval_000tc__Value__Oval,type,
    product_Pair_val_val: fun_va959426509al_val ).

tff(sy_c_Product__Type_OPair_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pro,type,
    produc899768717on_val: fun_fu1639641777on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_,type,
    produc1924279125al_val: fun_Pr559170997al_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
    produc1441475159on_val: fun_Pr1391347915on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List_,type,
    produc1611380469on_val: fun_Pr1643560277on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri,type,
    produc1897818327t_char: fun_Pr1328683975t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri_363,type,
    produc24551831t_char: fun_Pr1477781613t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__,type,
    produc1265154397har_ty: fun_Pr201309399har_ty ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___364,type,
    produc2036181286ar_val: fun_Pr1702428311ar_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___365,type,
    produc2080520419t_char: fun_Pr130739971t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___366,type,
    produc499151895on_val: fun_Pr278209965on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod,type,
    produc57279289t_char: fun_Pr1541015321t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Ex,type,
    produc1299387215t_char: fun_Pr324048879t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__,type,
    produc1244920211al_val: fun_Pr1703971251al_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooptio,type,
    produc870913623on_val: fun_Pr1305575371on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_,type,
    produc1564932627on_val: fun_Pr449337907on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_,type,
    produc1951691075on_val: fun_Pr998206307on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Och,type,
    produc1317546007ar_val: fun_Pr300893373ar_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_367,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__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__String__Ochar_J_Mtc_,type,
    produc218426791l_bool: fun_Pr661739816l_bool > fun_Pr2055965540l_bool ).

tff(sy_c_Product__Type_Ofst_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__,type,
    produc1230355531on_val: fun_Pr1940015747t_char ).

tff(sy_c_Product__Type_Ofst_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod,type,
    produc1517998010on_val: fun_Pr820147700on_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000,type,
    produc907433735ion_ty: fun_li1301775111ion_ty > fun_Pr876827561ion_ty ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt,type,
    produc1958875245l_bool: fun_fu100249073l_bool > fun_Pr1696029455l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__String__O,type,
    produc1553344466ar_val: fun_Pr130335392ar_val > fun_Pr1149393094ar_val ).

tff(sy_c_Progress_OWTrt_H,type,
    wTrt_1: ( list_P1999446415t_char * fun_na939144002on_val * fun_li688206603ion_ty * exp_list_char * ty ) > bool ).

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

tff(sy_c_SmallStep_Oassigned,type,
    assigned: ( list_char * exp_list_char ) > 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: fun_Pr820147700on_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__368,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_369,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_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__List__Olist_Itc__St,type,
    transi1600669663ar_val: fun_Pr643382121l_bool > fun_Pr643382121l_bool ).

tff(sy_c_Transitive__Closure_Ortranclp_000tc__List__Olist_Itc__String__Ochar_J,type,
    transi1065307915t_char: fun_li860735411r_bool > fun_li860735411r_bool ).

tff(sy_c_TypeRel_OFields_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__,type,
    fields1147507508t_char: ( list_P1999446415t_char * list_char * list_P2023964830har_ty ) > 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_Ohas__field_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri,type,
    has_fi1183600461t_char: ( list_P1999446415t_char * list_char * list_char * ty ) > 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_Osubcls1p_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String,type,
    subcls744239332t_char: list_P1999446415t_char > fun_li860735411r_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__vvmnfelbag_Osconf,type,
    typeSa1917327191_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: fun_list_char_ty ).

tff(sy_c_Type_Oty_ONT,type,
    nt: ty ).

tff(sy_c_Type_Oty_OVoid,type,
    void: ty ).

tff(sy_c_Value_Odefault__val,type,
    default_val: fun_ty_val ).

tff(sy_c_Value_Othe__Addr,type,
    the_Addr: fun_val_nat ).

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_WWellForm_Owwf__J__mdecl,type,
    wwf_J_mdecl: fun_li318226104r_bool ).

tff(sy_c_WellForm_Owf__prog_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Strin,type,
    wf_pro755087577t_char: ( fun_li318226104r_bool * list_P1999446415t_char ) > bool ).

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_1: ( 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_fconj,type,
    fconj: fun_bo1549164019l_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__Obop_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Ov_370,type,
    hAPP_b1229254591al_val: ( fun_bo1153317747al_val * bop ) > fun_Pr1615326228al_val ).

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_e1376201919t_char: ( fun_ex660466419t_char * exp_list_char ) > fun_ex1695787785t_char ).

tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_I_371,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__fun_I_372,type,
    hAPP_e1659493427on_val: ( fun_ex977868519on_val * exp_list_char ) > fun_Pr231134077on_val ).

tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__prod_,type,
    hAPP_e817857447t_char: ( fun_ex1695787785t_char * exp_list_char ) > produc2048519645t_char ).

tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__prod__373,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__374,type,
    hAPP_e1752110927t_char: ( fun_ex588373425t_char * exp_list_char ) > produc662261637t_char ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,type,
    hAPP_bool_bool: ( fun_bool_bool * bool ) > bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
    hAPP_b589554111l_bool: ( fun_bo1549164019l_bool * bool ) > fun_bool_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar,type,
    hAPP_l1538097584r_bool: ( fun_li639767902r_bool * list_exp_list_char ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_375,type,
    hAPP_l2011456725t_char: ( fun_li1279027773t_char * list_exp_list_char ) > list_exp_list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_376,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_377,type,
    hAPP_l121373941ar_val: ( fun_li337688157ar_val * list_exp_list_char ) > list_l350949640ar_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_378,type,
    hAPP_l1496769042st_nat: ( fun_li1890191168st_nat * list_exp_list_char ) > list_nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_379,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_380,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_381,type,
    hAPP_l89656979t_char: ( fun_li79274049t_char * list_exp_list_char ) > list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_382,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_383,type,
    hAPP_l1463304939on_val: ( fun_li1562283673on_val * list_exp_list_char ) > list_f43234584on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_384,type,
    hAPP_l1429130273on_val: ( fun_li1788539855on_val * list_exp_list_char ) > list_P1663965006on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_385,type,
    hAPP_l897806566on_val: ( fun_li867484494on_val * list_exp_list_char ) > list_P249777017on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_386,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_387,type,
    hAPP_l602170375har_ty: ( fun_li32322485har_ty * list_exp_list_char ) > list_P2098242612har_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_388,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_389,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_390,type,
    hAPP_l527892593har_ty: ( fun_li1512323871har_ty * list_exp_list_char ) > list_P2023964830har_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_391,type,
    hAPP_l1207846970ar_val: ( fun_li855547112ar_val * list_exp_list_char ) > list_P1697858023ar_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_392,type,
    hAPP_l452123639ar_nat: ( fun_li1786110815ar_nat * list_exp_list_char ) > nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_393,type,
    hAPP_l1105836155t_char: ( fun_li1918445737t_char * list_exp_list_char ) > fun_li1726629416t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_394,type,
    hAPP_l146377954l_bool: ( fun_li1372729616l_bool * list_exp_list_char ) > fun_Pr1696029455l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_395,type,
    hAPP_l1275479261on_val: ( fun_li856594443on_val * list_exp_list_char ) > fun_Pr254484106on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_396,type,
    hAPP_l1648260346t_char: ( fun_li1726629416t_char * list_exp_list_char ) > produc91527719t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__HOL_,type,
    hAPP_l1948381865r_bool: ( fun_li161542487r_bool * list_list_char ) > 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_397,type,
    hAPP_l1975021756ar_val: ( fun_li1791555364ar_val * list_list_char ) > list_l350949640ar_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_398,type,
    hAPP_l1111097995st_nat: ( fun_li1325798073st_nat * list_list_char ) > list_nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_399,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_400,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_401,type,
    hAPP_l838080012t_char: ( fun_li1239651002t_char * list_list_char ) > list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_402,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_403,type,
    hAPP_l164125796on_val: ( fun_li1668453138on_val * list_list_char ) > list_f43234584on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_404,type,
    hAPP_l713251482on_val: ( fun_li177368392on_val * list_list_char ) > list_P1663965006on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_405,type,
    hAPP_l1956999469on_val: ( fun_li2071992469on_val * list_list_char ) > list_P249777017on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_406,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_407,type,
    hAPP_l1336021888har_ty: ( fun_li1999687214har_ty * list_list_char ) > list_P2098242612har_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_408,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_409,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__List_410,type,
    hAPP_l1261744106har_ty: ( fun_li1332204952har_ty * list_list_char ) > list_P2023964830har_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_411,type,
    hAPP_l1298778931ar_val: ( fun_li1202359009ar_val * list_list_char ) > list_P1697858023ar_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__Nat_,type,
    hAPP_l66428094ar_nat: ( fun_li136542502ar_nat * list_list_char ) > nat ).

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__412,type,
    hAPP_l796364813t_char: ( fun_li1727207611t_char * list_list_char ) > fun_ex303050433t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun__413,type,
    hAPP_l2019537453t_char: ( fun_li399153499t_char * list_list_char ) > fun_li892090081t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun__414,type,
    hAPP_l217977712r_bool: ( fun_li1024794712r_bool * list_list_char ) > fun_Pr46158268r_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun__415,type,
    hAPP_l1873467853t_char: ( fun_li455628155t_char * list_list_char ) > fun_Pr141094017t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__prod,type,
    hAPP_l1883348915t_char: ( fun_li892090081t_char * list_list_char ) > produc1200003175t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__prod_Itc__prod_Itc__List__Oli,type,
    hAPP_l823328606ar_val: ( fun_li760419782ar_val * list_l38846271har_ty ) > list_l350949640ar_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__prod_Itc__prod_Itc__List__Oli_416,type,
    hAPP_l721971010on_val: ( fun_li1714359792on_val * list_l38846271har_ty ) > list_f43234584on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__prod_Itc__prod_Itc__List__Oli_417,type,
    hAPP_l23466336ty_nat: ( fun_li1802730952ty_nat * list_l38846271har_ty ) > nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__prod_Itc__prod_Itc__List__Oli_418,type,
    hAPP_l1790629643on_val: ( fun_li801778361on_val * list_l350949640ar_val ) > list_f43234584on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__prod_Itc__prod_Itc__List__Oli_419,type,
    hAPP_l49336279al_nat: ( fun_li74239807al_nat * list_l350949640ar_val ) > nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Nat__Onat_J_000tc__List__Olist_Itc__Nat__Onat_,type,
    hAPP_l248265089st_nat: ( fun_li1155097699st_nat * list_nat ) > list_nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Nat__Onat_J_000tc__Nat__Onat,type,
    hAPP_list_nat_nat: ( fun_list_nat_nat * list_nat ) > nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Option__Ooption_Itc__Type__Oty_J_J_000tc__HOL_,type,
    hAPP_l292106447y_bool: ( fun_li652750717y_bool * list_option_ty ) > 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_420,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_421,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_422,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_423,type,
    hAPP_l336371937st_val: ( fun_li1333774223st_val * list_option_ty ) > list_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Option__Ooption_Itc__Type__Oty_J_J_000tc__List_424,type,
    hAPP_l278271321ar_val: ( fun_li181851399ar_val * list_option_ty ) > list_P1697858023ar_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Option__Ooption_Itc__Type__Oty_J_J_000tc__Nat_,type,
    hAPP_l289305880ty_nat: ( fun_li359420288ty_nat * list_option_ty ) > nat ).

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__Option__Ooption_Itc__Value__Oval_J_J_000tc__Na,type,
    hAPP_l870066319al_nat: ( fun_li1715509239al_nat * list_option_val ) > nat ).

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__Expr__,type,
    hAPP_l925187813t_char: ( fun_li471109017t_char * list_char ) > list_exp_list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__List__Olist_Itc__List__,type,
    hAPP_l1927076062t_char: ( fun_li211407762t_char * list_char ) > list_list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__List__Olist_Itc__Option,type,
    hAPP_l863887876ion_ty: ( fun_li234662328ion_ty * list_char ) > list_option_ty ).

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__List__Olist_Itc__Type__,type,
    hAPP_l1044806633ist_ty: ( fun_li754043211ist_ty * list_char ) > list_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__List__Olist_Itc__Value_,type,
    hAPP_l473790130st_val: ( fun_li535708692st_val * list_char ) > list_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__List__Olist_Itc__prod_I,type,
    hAPP_l606396970ar_val: ( fun_li1267938444ar_val * list_char ) > list_P1697858023ar_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__Nat__Onat,type,
    hAPP_list_char_nat: ( fun_list_char_nat * list_char ) > nat ).

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__Type__Oty,type,
    hAPP_list_char_ty: ( fun_list_char_ty * list_char ) > ty ).

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__List__Olist_It_425,type,
    hAPP_l208357873t_char: ( fun_li835958565t_char * list_char ) > fun_li1857149300t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__Type__Oty_Mtc_,type,
    hAPP_l1948972481har_ty: ( fun_li885125749har_ty * list_char ) > fun_ty397449156har_ty ).

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__fun_Itc__fun_Itc__prod__426,type,
    hAPP_l2000496933ion_ty: ( fun_li1301775111ion_ty * list_char ) > fun_fu357191650ion_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__fun_Itc__prod__427,type,
    hAPP_l1786340417on_val: ( fun_li1436431093on_val * list_char ) > fun_fu1718160452on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__List,type,
    hAPP_l848957697har_ty: ( fun_li1324969141har_ty * list_char ) > fun_Pr181504004har_ty ).

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__HOL__Obool,type,
    hAPP_list_ty_bool: ( fun_list_ty_bool * list_ty ) > bool ).

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__List__Olis_428,type,
    hAPP_l654786079ar_val: ( fun_li646409939ar_val * list_ty ) > list_l350949640ar_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__Nat__Onat_,type,
    hAPP_l277434984st_nat: ( fun_list_ty_list_nat * list_ty ) > list_nat ).

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_429,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__String__Oc,type,
    hAPP_l1705142505t_char: ( fun_li162253899t_char * list_ty ) > list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__Type__Oty_,type,
    hAPP_list_ty_list_ty: ( fun_list_ty_list_ty * list_ty ) > list_ty ).

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__fun_Itc__p,type,
    hAPP_l642124097on_val: ( fun_li1332088483on_val * list_ty ) > list_f43234584on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__prod_Itc__,type,
    hAPP_l664719479on_val: ( fun_li1222710745on_val * list_ty ) > list_P1663965006on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__prod_Itc___430,type,
    hAPP_l273343760on_val: ( fun_li501969092on_val * list_ty ) > list_P249777017on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__prod_Itc___431,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___432,type,
    hAPP_l573877853har_ty: ( fun_li1092644799har_ty * list_ty ) > list_P2098242612har_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__prod_Itc___433,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___434,type,
    hAPP_l2092195639on_val: ( fun_li2066832875on_val * list_ty ) > list_P507235360on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__prod_Itc___435,type,
    hAPP_l499600071har_ty: ( fun_li425162537har_ty * list_ty ) > list_P2023964830har_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__prod_Itc___436,type,
    hAPP_l958580624ar_val: ( fun_li423654386ar_val * list_ty ) > list_P1697858023ar_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__Nat__Onat,type,
    hAPP_list_ty_nat: ( fun_list_ty_nat * list_ty ) > nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__fun_Itc__List__Olist_Itc__T,type,
    hAPP_l1770520637ist_ty: ( fun_li475043185ist_ty * list_ty ) > fun_li452671142ist_ty ).

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__Type__Oty_J_000tc__fun_Itc__prod_Itc__List__Ol_437,type,
    hAPP_l14371579t_char: ( fun_li1548633647t_char * list_ty ) > fun_Pr1504659044t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__prod_Itc__List__Olist_Itc__,type,
    hAPP_l1319068228ist_ty: ( fun_li452671142ist_ty * list_ty ) > produc1420746395ist_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__HOL__Obool,type,
    hAPP_list_val_bool: ( fun_list_val_bool * list_val ) > 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__List__Ol_438,type,
    hAPP_l1426221334ar_val: ( fun_li1597490890ar_val * list_val ) > list_l350949640ar_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__Nat__Ona,type,
    hAPP_l324487089st_nat: ( fun_li101582227st_nat * list_val ) > list_nat ).

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___439,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__String__,type,
    hAPP_l281179442t_char: ( fun_li1661102996t_char * list_val ) > list_char ).

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__fun_Itc_,type,
    hAPP_l1725810570on_val: ( fun_li1337614316on_val * list_val ) > list_f43234584on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__prod_Itc,type,
    hAPP_l863146944on_val: ( fun_li207121442on_val * list_val ) > list_P1663965006on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__prod_Itc_440,type,
    hAPP_l1097436295on_val: ( fun_li1112589627on_val * list_val ) > list_P249777017on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__prod_Itc_441,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_442,type,
    hAPP_l294838950har_ty: ( fun_li1206728456har_ty * list_val ) > list_P2098242612har_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__prod_Itc_443,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_444,type,
    hAPP_l1134997550on_val: ( fun_li1897585634on_val * list_val ) > list_P507235360on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__prod_Itc_445,type,
    hAPP_l220561168har_ty: ( fun_li539246194har_ty * list_val ) > list_P2023964830har_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__prod_Itc_446,type,
    hAPP_l412706649ar_val: ( fun_li470558395ar_val * list_val ) > list_P1697858023ar_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__Nat__Onat,type,
    hAPP_list_val_nat: ( fun_list_val_nat * list_val ) > nat ).

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__Value__Oval_J_000tc__fun_Itc__Expr__Oexp_Itc___447,type,
    hAPP_l1859255743t_char: ( fun_li1751446259t_char * list_val ) > fun_ex588373425t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__fun_Itc__List__Olist_Itc_,type,
    hAPP_l103437071st_val: ( fun_li1981758019st_val * list_val ) > fun_li351020801st_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__prod_Itc__List__Olist_Itc,type,
    hAPP_l1249476511st_val: ( fun_li351020801st_val * list_val ) > produc753553453st_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Oc,type,
    hAPP_l1718801839al_nat: ( fun_li853190243al_nat * list_f43234584on_val ) > nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str,type,
    hAPP_l2060099886l_bool: ( fun_li89141392l_bool * list_P1663965006on_val ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_448,type,
    hAPP_l2043127767t_char: ( fun_li203067531t_char * list_P1663965006on_val ) > list_exp_list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_449,type,
    hAPP_l244703952t_char: ( fun_li130774916t_char * list_P1663965006on_val ) > list_list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_450,type,
    hAPP_l1328999414ion_ty: ( fun_li154029482ion_ty * list_P1663965006on_val ) > list_option_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_451,type,
    hAPP_l560448119ist_ty: ( fun_li614790617ist_ty * list_P1663965006on_val ) > list_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_452,type,
    hAPP_l1023956544st_val: ( fun_li1589119394st_val * list_P1663965006on_val ) > list_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_453,type,
    hAPP_l76241055on_val: ( fun_li729885185on_val * list_P1663965006on_val ) > list_P1663965006on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_454,type,
    hAPP_l2147361720ar_val: ( fun_li1563778074ar_val * list_P1663965006on_val ) > list_P1697858023ar_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_455,type,
    hAPP_l1746926841al_nat: ( fun_li722721709al_nat * list_P1663965006on_val ) > nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_456,type,
    hAPP_l1324137613on_val: ( fun_li1721496513on_val * list_P1663965006on_val ) > fun_li483948318on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_457,type,
    hAPP_l1485560508on_val: ( fun_li483948318on_val * list_P1663965006on_val ) > produc1497648875on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__Lis,type,
    hAPP_l1440102849l_bool: ( fun_li1631375983l_bool * list_P249777017on_val ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__Lis_458,type,
    hAPP_l1683732356t_char: ( fun_li1574664172t_char * list_P249777017on_val ) > list_exp_list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__Lis_459,type,
    hAPP_l1664314621t_char: ( fun_li27018085t_char * list_P249777017on_val ) > list_list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__Lis_460,type,
    hAPP_l601126435ion_ty: ( fun_li50272651ion_ty * list_P249777017on_val ) > list_option_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__Lis_461,type,
    hAPP_l674002314ist_ty: ( fun_li372218936ist_ty * list_P249777017on_val ) > list_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__Lis_462,type,
    hAPP_l1342091219st_val: ( fun_li404189313st_val * list_P249777017on_val ) > list_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__Lis_463,type,
    hAPP_l254081045on_val: ( fun_li1486652797on_val * list_P249777017on_val ) > list_P249777017on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__Lis_464,type,
    hAPP_l102711883ar_val: ( fun_li347839481ar_val * list_P249777017on_val ) > list_P1697858023ar_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__Lis_465,type,
    hAPP_l1766199206al_nat: ( fun_li33935886al_nat * list_P249777017on_val ) > nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__Lis_466,type,
    hAPP_l1588290397on_val: ( fun_li475287435on_val * list_P249777017on_val ) > fun_li1630075129on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__Lis_467,type,
    hAPP_l1701465547on_val: ( fun_li1630075129on_val * list_P249777017on_val ) > produc143547239on_val ).

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__List__Olist_Itc__String__Ochar_J_Mtc_468,type,
    hAPP_l365675759ar_nat: ( fun_li208403543ar_nat * list_P1916372464t_char ) > nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_469,type,
    hAPP_l162677262har_ty: ( fun_li1848428912har_ty * list_P1940453997har_ty ) > list_P2023964830har_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_470,type,
    hAPP_l1526684570ty_nat: ( fun_li1893346126ty_nat * list_P1940453997har_ty ) > nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_471,type,
    hAPP_l1961350547ty_nat: ( fun_li82217543ty_nat * list_P2098242612har_ty ) > nat ).

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__Expr__Oexp_Itc__List__Olis_472,type,
    hAPP_l1794950871al_nat: ( fun_li1364025663al_nat * list_P1439941640on_val ) > nat ).

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__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oex_473,type,
    hAPP_l1593094847al_nat: ( fun_li1662826023al_nat * list_P507235360on_val ) > nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O,type,
    hAPP_l1176981118y_bool: ( fun_li475498464y_bool * list_P2023964830har_ty ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_474,type,
    hAPP_l2038191751t_char: ( fun_li672142651t_char * list_P2023964830har_ty ) > list_exp_list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_475,type,
    hAPP_l632662400t_char: ( fun_li974066740t_char * list_P2023964830har_ty ) > list_list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_476,type,
    hAPP_l1716957862ion_ty: ( fun_li997321306ion_ty * list_P2023964830har_ty ) > list_option_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_477,type,
    hAPP_l1097172935ist_ty: ( fun_li368076073ist_ty * list_P2023964830har_ty ) > list_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_478,type,
    hAPP_l1473803152st_val: ( fun_li715182322st_val * list_P2023964830har_ty ) > list_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_479,type,
    hAPP_l1910281173har_ty: ( fun_li1113295671har_ty * list_P2023964830har_ty ) > list_P2098242612har_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_480,type,
    hAPP_l1836003391har_ty: ( fun_li445813409har_ty * list_P2023964830har_ty ) > list_P2023964830har_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_481,type,
    hAPP_l608137480ar_val: ( fun_li867521386ar_val * list_P2023964830har_ty ) > list_P1697858023ar_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_482,type,
    hAPP_l540212137ty_nat: ( fun_li808562781ty_nat * list_P2023964830har_ty ) > nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_483,type,
    hAPP_l968768258on_val: ( fun_li750181430on_val * list_P2023964830har_ty ) > fun_Pr806764899on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_484,type,
    hAPP_l492540231l_bool: ( fun_li94363049l_bool * list_P1697858023ar_val ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_485,type,
    hAPP_l347191422t_char: ( fun_li645506098t_char * list_P1697858023ar_val ) > list_exp_list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_486,type,
    hAPP_l1890693879t_char: ( fun_li771345067t_char * list_P1697858023ar_val ) > list_list_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_487,type,
    hAPP_l827505693ion_ty: ( fun_li794599633ion_ty * list_P1697858023ar_val ) > list_option_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_488,type,
    hAPP_l1538085392ist_ty: ( fun_li1202111090ist_ty * list_P1697858023ar_val ) > list_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_489,type,
    hAPP_l1523427673st_val: ( fun_li1357584827st_val * list_P1697858023ar_val ) > list_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_490,type,
    hAPP_l1462265297ar_val: ( fun_li1966627635ar_val * list_P1697858023ar_val ) > list_P1697858023ar_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_491,type,
    hAPP_l1280603808al_nat: ( fun_li621434964al_nat * list_P1697858023ar_val ) > nat ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_492,type,
    hAPP_l1000746233on_val: ( fun_li889387821on_val * list_P1697858023ar_val ) > fun_Pr806764899on_val ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,type,
    hAPP_nat_bool: ( fun_nat_bool * nat ) > bool ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__Nat__Onat,type,
    hAPP_nat_nat: ( fun_nat_nat * nat ) > nat ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__Option__Ooption_Itc__Nat__Onat_J,type,
    hAPP_nat_option_nat: ( fun_nat_option_nat * nat ) > option_nat ).

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__Nat__Onat_J_000tc__Nat__Onat,type,
    hAPP_option_nat_nat: ( fun_option_nat_nat * option_nat ) > nat ).

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__Type__Oty_J_000tc__fun_Itc__fun_Itc__prod_,type,
    hAPP_o534509643ion_ty: ( fun_op1983271469ion_ty * option_ty ) > fun_fu357191650ion_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__Value__Oval_J_000tc__fun_Itc__List__Olist_,type,
    hAPP_o538043682on_val: ( fun_op2076490582on_val * option_val ) > fun_li1432931796on_val ).

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J,type,
    hAPP_o1576581476on_val: ( fun_op637900998on_val * option1479284511on_val ) > fun_na939144002on_val ).

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_493,type,
    hAPP_o1977518472on_val: ( fun_op498348476on_val * option1479284511on_val ) > produc639455274on_val ).

tff(sy_c_hAPP_000tc__String__Ochar_000tc__fun_Itc__String__Ochar_Mtc__prod_Itc__Stri,type,
    hAPP_c1242523777r_char: ( fun_ch1000319279r_char * char ) > fun_ch703860619r_char ).

tff(sy_c_hAPP_000tc__String__Ochar_000tc__prod_Itc__String__Ochar_Mtc__String__Ochar,type,
    hAPP_c802977373r_char: ( fun_ch703860619r_char * char ) > produc409241703r_char ).

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__Type__Oty_000tc__fun_Itc__Type__Oty_Mtc__prod_Itc__Type__Oty_Mt,type,
    hAPP_t1494094285_ty_ty: ( fun_ty595889787_ty_ty * ty ) > fun_ty1409104497_ty_ty ).

tff(sy_c_hAPP_000tc__Type__Oty_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc,type,
    hAPP_t1875766236har_ty: ( fun_ty397449156har_ty * ty ) > produc917948472har_ty ).

tff(sy_c_hAPP_000tc__Type__Oty_000tc__prod_Itc__Type__Oty_Mtc__Type__Oty_J,type,
    hAPP_t65172803_ty_ty: ( fun_ty1409104497_ty_ty * ty ) > product_prod_ty_ty ).

tff(sy_c_hAPP_000tc__Type__Oty_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__O,type,
    hAPP_t708040077har_ty: ( fun_ty1486032501har_ty * ty ) > produc245756905har_ty ).

tff(sy_c_hAPP_000tc__Type__Oty_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__O_494,type,
    hAPP_t97533526ar_val: ( fun_ty434869310ar_val * ty ) > produc1147203250ar_val ).

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__Nat__Onat,type,
    hAPP_val_nat: ( fun_val_nat * val ) > nat ).

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__fun_Itc__Value__Oval_Mtc__prod_Itc__Value__O,type,
    hAPP_v1519391al_val: ( fun_va959426509al_val * val ) > fun_va1923334394al_val ).

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__Value__Oval_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String_,type,
    hAPP_v48258637ar_val: ( fun_va1416972085ar_val * val ) > produc1147203250ar_val ).

tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc__,type,
    hAPP_f1863694447l_bool: ( fun_fu114905943l_bool * fun_bool_bool ) > fun_fu1590192889l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_,type,
    hAPP_f1977633121l_bool: ( fun_fu781882819l_bool * fun_bo1549164019l_bool ) > fun_fu1457514859l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_,type,
    hAPP_f1001225811y_bool: ( fun_fu964075521y_bool * fun_li688206603ion_ty ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__495,type,
    hAPP_f451501457ion_ty: ( fun_fu2078908153ion_ty * fun_li688206603ion_ty ) > fun_li1301775111ion_ty ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__496,type,
    hAPP_f603925568l_bool: ( fun_fu2075294830l_bool * fun_li688206603ion_ty ) > fun_fu1693644106l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__497,type,
    hAPP_f550652027l_bool: ( fun_fu863769827l_bool * fun_li688206603ion_ty ) > fun_fu100249073l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__498,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__499,type,
    hAPP_f2060496320y_bool: ( fun_fu1670877422y_bool * fun_li1432931796on_val ) > fun_fu964075521y_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__500,type,
    hAPP_f1727192346on_val: ( fun_fu1690035458on_val * fun_li1432931796on_val ) > produc12694297on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Type__Oty_J_000t,type,
    hAPP_f359949478ion_ty: ( fun_fu101523418ion_ty * fun_list_char_ty ) > fun_li688206603ion_ty ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol,type,
    hAPP_f61040418l_bool: ( fun_fu1246919812l_bool * fun_na939144002on_val ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_501,type,
    hAPP_f1145256474l_bool: ( fun_fu250820942l_bool * fun_na939144002on_val ) > fun_bool_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_502,type,
    hAPP_f388705405r_bool: ( fun_fu311765169r_bool * fun_na939144002on_val ) > fun_list_char_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_503,type,
    hAPP_f1617787571l_bool: ( fun_fu570492181l_bool * fun_na939144002on_val ) > fun_fu2075294830l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_504,type,
    hAPP_f1175813647l_bool: ( fun_fu100249073l_bool * fun_na939144002on_val ) > fun_fu1693644106l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_505,type,
    hAPP_f1213370163y_bool: ( fun_fu2141444501y_bool * fun_na939144002on_val ) > fun_fu1670877422y_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_506,type,
    hAPP_f1849790461on_val: ( fun_fu1639641777on_val * fun_na939144002on_val ) > fun_fu1690035458on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_507,type,
    hAPP_f1492320500l_bool: ( fun_fu1806184744l_bool * fun_na939144002on_val ) > fun_fu1590192889l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Option__Ooption_Itc__Type__Oty_J_Mtc__fun_Itc__fun_Itc,type,
    hAPP_f509342689ion_ty: ( fun_fu2088691401ion_ty * fun_op1983271469ion_ty ) > fun_fu2078908153ion_ty ).

tff(sy_c_hAPP_000tc__fun_Itc__Type__Oty_Mtc__Option__Ooption_Itc__Type__Oty_J_J_000t,type,
    hAPP_f1243585741ion_ty: ( fun_fu1705731887ion_ty * fun_ty_option_ty ) > fun_fu101523418ion_ty ).

tff(sy_c_hAPP_000tc__fun_Itc__Type__Oty_Mtc__Value__Oval_J_000tc__fun_Itc__Type__Oty,type,
    hAPP_f883560141ar_val: ( fun_fu1628826677ar_val * fun_ty_val ) > fun_ty434869310ar_val ).

tff(sy_c_hAPP_000tc__fun_Itc__Type__Oty_Mtc__Value__Oval_J_000tc__fun_Itc__prod_Itc_,type,
    hAPP_f1668074321ar_val: ( fun_fu1907319807ar_val * fun_ty_val ) > fun_Pr130335392ar_val ).

tff(sy_c_hAPP_000tc__fun_Itc__Value__Oval_Mtc__prod_Itc__prod_Itc__List__Olist_Itc__,type,
    hAPP_f1951920661ar_val: ( fun_fu124241277ar_val * fun_va1416972085ar_val ) > fun_fu1628826677ar_val ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_Mtc__fun_Itc__fu,type,
    hAPP_f592397849l_bool: ( fun_fu48585473l_bool * fun_fu114905943l_bool ) > fun_fu1989717467l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_,type,
    hAPP_f1074020887l_bool: ( fun_fu1590192889l_bool * fun_fu1693644106l_bool ) > fun_fu1693644106l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__508,type,
    hAPP_f181262431l_bool: ( fun_fu2083094209l_bool * fun_fu1670877422y_bool ) > fun_fu2075294830l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_,type,
    hAPP_f1452292669l_bool: ( fun_fu1457514859l_bool * fun_fu1246919812l_bool ) > fun_fu250820942l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__509,type,
    hAPP_f1523875321l_bool: ( fun_fu1989717467l_bool * fun_fu250820942l_bool ) > fun_fu1806184744l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__510,type,
    hAPP_f838396643l_bool: ( fun_fu1680591819l_bool * fun_fu570492181l_bool ) > fun_fu863769827l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__511,type,
    hAPP_f857351829l_bool: ( fun_fu712248957l_bool * fun_fu2141444501y_bool ) > fun_fu570492181l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Value__Oval_Mtc__prod_Itc__prod_Itc__List__Ol,type,
    hAPP_f332422699ar_val: ( fun_fu945706003ar_val * fun_fu124241277ar_val ) > fun_fu1290851475ar_val ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc,type,
    hAPP_f348318673l_bool: ( fun_fu938561337l_bool * fun_fu2083094209l_bool ) > fun_fu712248957l_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___512,type,
    hAPP_f652398900ion_ty: ( fun_fu357191650ion_ty * fun_Pr806764899on_val ) > option_ty ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___513,type,
    hAPP_f900686428on_val: ( fun_fu1718160452on_val * fun_Pr806764899on_val ) > produc639455274on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___514,type,
    hAPP_f1240485169ar_val: ( fun_fu1290851475ar_val * fun_Pr1702428311ar_val ) > fun_Pr593787031ar_val ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___515,type,
    hAPP_f59905689ar_val: ( fun_fu1227413499ar_val * fun_Pr593787031ar_val ) > fun_fu1907319807ar_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_516,type,
    hAPP_P1538518401al_val: ( fun_Pr559170997al_val * produc1645268488al_val ) > fun_Pr1899415884al_val ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__Ova_517,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_P1632759357r_bool: ( fun_Pr136267935r_bool * produc2048519645t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_518,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_519,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_520,type,
    hAPP_P1870962205on_val: ( fun_Pr1391347915on_val * produc124828825on_val ) > fun_Pr714818201on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_521,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_P499022727r_bool: ( fun_Pr716652265r_bool * produc91527719t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_522,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_523,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_524,type,
    hAPP_P1526035745on_val: ( fun_Pr1643560277on_val * produc2061676504on_val ) > fun_Pr2075414204on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_525,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_526,type,
    hAPP_P91410073t_char: ( fun_Pr1328683975t_char * produc809539159t_char ) > fun_Pr1453773143t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_527,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_528,type,
    hAPP_P476431815r_bool: ( fun_Pr382120745r_bool * produc1200003175t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_529,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_530,type,
    hAPP_P719127871t_char: ( fun_Pr1477781613t_char * produc1285161482t_char ) > fun_Pr743134922t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_531,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_532,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_533,type,
    hAPP_P827589667har_ty: ( fun_Pr201309399har_ty * produc1278157519t_char ) > fun_ty1486032501har_ty ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc_534,type,
    hAPP_P221287148ar_val: ( fun_Pr130335392ar_val * produc1278157519t_char ) > fun_ty434869310ar_val ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc_535,type,
    hAPP_P486515074l_bool: ( fun_Pr2055965540l_bool * produc1278157519t_char ) > fun_val_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc_536,type,
    hAPP_P1321848547ar_val: ( fun_Pr1702428311ar_val * produc1278157519t_char ) > fun_va1416972085ar_val ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc_537,type,
    hAPP_P289594851ar_val: ( fun_Pr593787031ar_val * produc1278157519t_char ) > fun_fu1628826677ar_val ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc_538,type,
    hAPP_P1071727823t_char: ( fun_Pr130739971t_char * produc1278157519t_char ) > fun_Pr1785445921t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc_539,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_540,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__Type__Oty_J_000,type,
    hAPP_P748443392y_bool: ( fun_Pr1127025070y_bool * produc917948472har_ty ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Type__Oty_J_000_541,type,
    hAPP_P295788316har_ty: ( fun_Pr181504004har_ty * produc917948472har_ty ) > produc469582463har_ty ).

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_542,type,
    hAPP_P1789965269t_char: ( fun_Pr1940015747t_char * produc639455274on_val ) > list_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I_543,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_544,type,
    hAPP_P1875010047on_val: ( fun_Pr278209965on_val * produc639455274on_val ) > fun_Pr1948698346on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I_545,type,
    hAPP_P330218428on_val: ( fun_Pr1948698346on_val * produc639455274on_val ) > produc87279271on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List_,type,
    hAPP_P831231943y_bool: ( fun_Pr758558581y_bool * produc469582463har_ty ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__List__Olist_Itc__Ty,type,
    hAPP_P1574824955y_bool: ( fun_Pr306783325y_bool * produc1420746395ist_ty ) > bool ).

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_546,type,
    hAPP_P1859316965t_char: ( fun_Pr1541015321t_char * produc220283002t_char ) > fun_Pr612024994t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Oli_547,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_548,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_549,type,
    hAPP_P1668407995t_char: ( fun_Pr324048879t_char * produc662261637t_char ) > fun_Pr1620417347t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__L_550,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_551,type,
    hAPP_P1220989409t_char: ( fun_Pr1620417347t_char * produc662261637t_char ) > produc1826280281t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__List__Olist_Itc__,type,
    hAPP_P2115985549l_bool: ( fun_Pr1618624239l_bool * produc753553453st_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__Expr__Oexp_Itc__List__Olis,type,
    hAPP_P1038730315l_bool: ( fun_Pr564925613l_bool * produc1497648875on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Expr__Oex,type,
    hAPP_P1821438151l_bool: ( fun_Pr872262185l_bool * produc143547239on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__String__Ochar_Mtc__String__Ochar_J_000tc__HOL__Obool,type,
    hAPP_P1700239815r_bool: ( fun_Pr638203177r_bool * produc409241703r_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Type__Oty_Mtc__Type__Oty_J_000tc__HOL__Obool,type,
    hAPP_P1716187463y_bool: ( fun_Pr2087862441y_bool * product_prod_ty_ty ) > bool ).

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_P1874979071al_val: ( fun_Pr1703971251al_val * product_prod_val_val ) > fun_Pr1637618473al_val ).

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_552,type,
    hAPP_P703866694on_val: ( fun_Pr820147700on_val * produc12694297on_val ) > fun_na939144002on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_553,type,
    hAPP_P265246237on_val: ( fun_Pr1305575371on_val * produc12694297on_val ) > fun_Pr84821017on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_554,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_555,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_556,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_557,type,
    hAPP_P2077211775on_val: ( fun_Pr449337907on_val * produc1102272487on_val ) > fun_Pr609382377on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_558,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_559,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_560,type,
    hAPP_P2015431471on_val: ( fun_Pr998206307on_val * produc430140671on_val ) > fun_Pr807902897on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis_561,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_562,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_563,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_P27757617y_bool: ( fun_Pr2102567903y_bool * produc245756905har_ty ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__564,type,
    hAPP_P841862366ar_val: ( fun_Pr1149393094ar_val * produc245756905har_ty ) > produc1147203250ar_val ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__565,type,
    hAPP_P1070896250l_bool: ( fun_Pr661739816l_bool * produc1147203250ar_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__566,type,
    hAPP_P800634639ar_val: ( fun_Pr300893373ar_val * produc1147203250ar_val ) > fun_Pr1555044210ar_val ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__567,type,
    hAPP_P976385092ar_val: ( fun_Pr1555044210ar_val * produc1147203250ar_val ) > produc1312961703ar_val ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__568,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_hAPP_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_,type,
    hAPP_P439015943l_bool: ( fun_Pr643382121l_bool * produc1312961703ar_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__Nat__Onat,type,
    member_nat: ( nat * fun_nat_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__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_,type,
    member1199939018t_char: ( produc2048519645t_char * fun_Pr136267935r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__S,type,
    member894971540t_char: ( produc91527719t_char * fun_Pr716652265r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J,type,
    member817832404t_char: ( produc1200003175t_char * fun_Pr382120745r_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__List__Olist_Itc__Type__Oty_J_Mtc__List__Olist_Itc__,type,
    member104734088ist_ty: ( produc1420746395ist_ty * fun_Pr306783325y_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__List__Olist_Itc,type,
    member273646106st_val: ( produc753553453st_val * fun_Pr1618624239l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__Expr__Oexp_Itc__List__Ol,type,
    member1942985176on_val: ( produc1497648875on_val * fun_Pr564925613l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Expr__O,type,
    member295766740on_val: ( produc143547239on_val * fun_Pr872262185l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__String__Ochar_Mtc__String__Ochar_J,type,
    member1725532372r_char: ( produc409241703r_char * fun_Pr638203177r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__Type__Oty_Mtc__Type__Oty_J,type,
    member1736614484_ty_ty: ( product_prod_ty_ty * fun_Pr2087862441y_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__569,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,
    member1783291580har_ty: ( produc245756905har_ty * fun_Pr2102567903y_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_570,type,
    member806854661ar_val: ( produc1147203250ar_val * fun_Pr661739816l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_571,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_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_,type,
    member619264020ar_val: ( produc1312961703ar_val * fun_Pr643382121l_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 (1200)
tff(fact_0_widens__refl,axiom,
    ! [Pa: list_P1999446415t_char,Xs: list_ty] : hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(widen_2090681816t_char(Pa),Xs),Xs)) ).

tff(fact_1_widen__refl,axiom,
    ! [P_4: list_P1999446415t_char,T_9: ty] : hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_4),T_9),T_9)) ).

tff(fact_2_widens__trans,axiom,
    ! [Us_3: list_ty,Pa: list_P1999446415t_char,Ss: list_ty,Tsa: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(widen_2090681816t_char(Pa),Ss),Tsa))
     => ( hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(widen_2090681816t_char(Pa),Tsa),Us_3))
       => hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(widen_2090681816t_char(Pa),Ss),Us_3)) ) ) ).

tff(fact_3_list__all2__lengthD,axiom,
    ! [Pa: fun_li727108811l_bool,Xs: list_list_char,Ys: list_P249777017on_val] :
      ( hBOOL(hAPP_l1440102849l_bool(list_a809715167on_val(Pa,Xs),Ys))
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l1766199206al_nat(size_s470606735on_val,Ys) ) ) ).

tff(fact_4_list__all2__lengthD,axiom,
    ! [Pa: fun_li923379764l_bool,Xs: list_list_char,Ys: list_P1663965006on_val] :
      ( hBOOL(hAPP_l2060099886l_bool(list_a1874290002on_val(Pa,Xs),Ys))
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l1746926841al_nat(size_s60479160on_val,Ys) ) ) ).

tff(fact_5_list__all2__lengthD,axiom,
    ! [Pa: fun_li752648358r_bool,Xs: list_list_char,Ys: list_char] :
      ( hBOOL(hAPP_list_char_bool(list_a1647123652r_char(Pa,Xs),Ys))
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_list_char_nat(size_size_list_char,Ys) ) ) ).

tff(fact_6_list__all2__lengthD,axiom,
    ! [Pa: fun_li213500804y_bool,Xs: list_list_char,Ys: list_P2023964830har_ty] :
      ( hBOOL(hAPP_l1176981118y_bool(list_a1115291042har_ty(Pa,Xs),Ys))
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys) ) ) ).

tff(fact_7_list__all2__lengthD,axiom,
    ! [Pa: fun_li1849706317l_bool,Xs: list_list_char,Ys: list_P1697858023ar_val] :
      ( hBOOL(hAPP_l492540231l_bool(list_a400141291ar_val(Pa,Xs),Ys))
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l1280603808al_nat(size_s760178257ar_val,Ys) ) ) ).

tff(fact_8_list__all2__lengthD,axiom,
    ! [Pa: fun_li1351943641y_bool,Xs: list_list_char,Ys: list_option_ty] :
      ( hBOOL(hAPP_l292106447y_bool(list_a1834344429ion_ty(Pa,Xs),Ys))
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l289305880ty_nat(size_s1050794909ion_ty,Ys) ) ) ).

tff(fact_9_list__all2__lengthD,axiom,
    ! [Pa: fun_ty1511004582l_bool,Xs: list_ty,Ys: list_P249777017on_val] :
      ( hBOOL(hAPP_l1440102849l_bool(list_a392402672on_val(Pa,Xs),Ys))
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l1766199206al_nat(size_s470606735on_val,Ys) ) ) ).

tff(fact_10_list__all2__lengthD,axiom,
    ! [Pa: fun_ty1713482521l_bool,Xs: list_ty,Ys: list_P1663965006on_val] :
      ( hBOOL(hAPP_l2060099886l_bool(list_a216081281on_val(Pa,Xs),Ys))
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l1746926841al_nat(size_s60479160on_val,Ys) ) ) ).

tff(fact_11_list__all2__lengthD,axiom,
    ! [Pa: fun_ty_fun_char_bool,Xs: list_ty,Ys: list_char] :
      ( hBOOL(hAPP_list_char_bool(list_all2_ty_char(Pa,Xs),Ys))
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_list_char_nat(size_size_list_char,Ys) ) ) ).

tff(fact_12_list__all2__lengthD,axiom,
    ! [Pa: fun_ty701313897y_bool,Xs: list_ty,Ys: list_P2023964830har_ty] :
      ( hBOOL(hAPP_l1176981118y_bool(list_a860324561har_ty(Pa,Xs),Ys))
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys) ) ) ).

tff(fact_13_list__all2__lengthD,axiom,
    ! [Pa: fun_ty1263539378l_bool,Xs: list_ty,Ys: list_P1697858023ar_val] :
      ( hBOOL(hAPP_l492540231l_bool(list_a123308442ar_val(Pa,Xs),Ys))
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l1280603808al_nat(size_s760178257ar_val,Ys) ) ) ).

tff(fact_14_list__all2__lengthD,axiom,
    ! [Pa: fun_ty1580608948y_bool,Xs: list_ty,Ys: list_option_ty] :
      ( hBOOL(hAPP_l292106447y_bool(list_a1880637950ion_ty(Pa,Xs),Ys))
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l289305880ty_nat(size_s1050794909ion_ty,Ys) ) ) ).

tff(fact_15_list__all2__lengthD,axiom,
    ! [Pa: fun_va1011302557l_bool,Xs: list_val,Ys: list_P249777017on_val] :
      ( hBOOL(hAPP_l1440102849l_bool(list_a88719801on_val(Pa,Xs),Ys))
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l1766199206al_nat(size_s470606735on_val,Ys) ) ) ).

tff(fact_16_list__all2__lengthD,axiom,
    ! [Pa: fun_va267341538l_bool,Xs: list_val,Ys: list_P1663965006on_val] :
      ( hBOOL(hAPP_l2060099886l_bool(list_a1839848952on_val(Pa,Xs),Ys))
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l1746926841al_nat(size_s60479160on_val,Ys) ) ) ).

tff(fact_17_list__all2__lengthD,axiom,
    ! [Pa: fun_va1368839508r_bool,Xs: list_val,Ys: list_char] :
      ( hBOOL(hAPP_list_char_bool(list_all2_val_char(Pa,Xs),Ys))
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_list_char_nat(size_size_list_char,Ys) ) ) ).

tff(fact_18_list__all2__lengthD,axiom,
    ! [Pa: fun_va922339378y_bool,Xs: list_val,Ys: list_P2023964830har_ty] :
      ( hBOOL(hAPP_l1176981118y_bool(list_a2075757640har_ty(Pa,Xs),Ys))
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys) ) ) ).

tff(fact_19_list__all2__lengthD,axiom,
    ! [Pa: fun_va1181537531l_bool,Xs: list_val,Ys: list_P1697858023ar_val] :
      ( hBOOL(hAPP_l492540231l_bool(list_a1609582481ar_val(Pa,Xs),Ys))
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l1280603808al_nat(size_s760178257ar_val,Ys) ) ) ).

tff(fact_20_list__all2__lengthD,axiom,
    ! [Pa: fun_va642468779y_bool,Xs: list_val,Ys: list_option_ty] :
      ( hBOOL(hAPP_l292106447y_bool(list_a1462908359ion_ty(Pa,Xs),Ys))
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l289305880ty_nat(size_s1050794909ion_ty,Ys) ) ) ).

tff(fact_21_list__all2__lengthD,axiom,
    ! [Pa: fun_ex435221764l_bool,Xs: list_exp_list_char,Ys: list_P249777017on_val] :
      ( hBOOL(hAPP_l1440102849l_bool(list_a288514022on_val(Pa,Xs),Ys))
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_l1766199206al_nat(size_s470606735on_val,Ys) ) ) ).

tff(fact_22_list__all2__lengthD,axiom,
    ! [Pa: fun_ex1875415355l_bool,Xs: list_exp_list_char,Ys: list_P1663965006on_val] :
      ( hBOOL(hAPP_l2060099886l_bool(list_a2080147979on_val(Pa,Xs),Ys))
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_l1746926841al_nat(size_s60479160on_val,Ys) ) ) ).

tff(fact_23_list__all2__lengthD,axiom,
    ! [Pa: fun_ex2034987181r_bool,Xs: list_exp_list_char,Ys: list_char] :
      ( hBOOL(hAPP_list_char_bool(list_a1552939645r_char(Pa,Xs),Ys))
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_list_char_nat(size_size_list_char,Ys) ) ) ).

tff(fact_24_list__all2__lengthD,axiom,
    ! [Pa: fun_ex1280510859y_bool,Xs: list_exp_list_char,Ys: list_P2023964830har_ty] :
      ( hBOOL(hAPP_l1176981118y_bool(list_a623412059har_ty(Pa,Xs),Ys))
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys) ) ) ).

tff(fact_25_list__all2__lengthD,axiom,
    ! [Pa: fun_ex1764228052l_bool,Xs: list_exp_list_char,Ys: list_P1697858023ar_val] :
      ( hBOOL(hAPP_l492540231l_bool(list_a1554965796ar_val(Pa,Xs),Ys))
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_l1280603808al_nat(size_s760178257ar_val,Ys) ) ) ).

tff(fact_26_list__all2__lengthD,axiom,
    ! [Pa: fun_ex1708156690y_bool,Xs: list_exp_list_char,Ys: list_option_ty] :
      ( hBOOL(hAPP_l292106447y_bool(list_a52822260ion_ty(Pa,Xs),Ys))
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_l289305880ty_nat(size_s1050794909ion_ty,Ys) ) ) ).

tff(fact_27_list__all2__lengthD,axiom,
    ! [Pa: fun_Pr2103285403r_bool,Xs: list_P249777017on_val,Ys: list_list_char] :
      ( hBOOL(hAPP_l1948381865r_bool(list_a1169722591t_char(Pa,Xs),Ys))
     => ( hAPP_l1766199206al_nat(size_s470606735on_val,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_28_list__all2__lengthD,axiom,
    ! [Pa: fun_Pr2007843174r_bool,Xs: list_P1663965006on_val,Ys: list_list_char] :
      ( hBOOL(hAPP_l1948381865r_bool(list_a292640256t_char(Pa,Xs),Ys))
     => ( hAPP_l1746926841al_nat(size_s60479160on_val,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_29_list__all2__lengthD,axiom,
    ! [Pa: fun_ch693599860r_bool,Xs: list_char,Ys: list_list_char] :
      ( hBOOL(hAPP_l1948381865r_bool(list_a1337954418t_char(Pa,Xs),Ys))
     => ( hAPP_list_char_nat(size_size_list_char,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_30_list__all2__lengthD,axiom,
    ! [Pa: fun_Pr31562774r_bool,Xs: list_P2023964830har_ty,Ys: list_list_char] :
      ( hBOOL(hAPP_l1948381865r_bool(list_a1479679312t_char(Pa,Xs),Ys))
     => ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_31_list__all2__lengthD,axiom,
    ! [Pa: fun_Pr2102600973r_bool,Xs: list_P1697858023ar_val,Ys: list_list_char] :
      ( hBOOL(hAPP_l1948381865r_bool(list_a24143385t_char(Pa,Xs),Ys))
     => ( hAPP_l1280603808al_nat(size_s760178257ar_val,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_32_list__all2__lengthD,axiom,
    ! [Pa: fun_op668690445r_bool,Xs: list_option_ty,Ys: list_list_char] :
      ( hBOOL(hAPP_l1948381865r_bool(list_a839443437t_char(Pa,Xs),Ys))
     => ( hAPP_l289305880ty_nat(size_s1050794909ion_ty,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_33_list__all2__lengthD,axiom,
    ! [Pa: fun_Pr123818788y_bool,Xs: list_P249777017on_val,Ys: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_a182912018val_ty(Pa,Xs),Ys))
     => ( hAPP_l1766199206al_nat(size_s470606735on_val,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_34_list__all2__lengthD,axiom,
    ! [Pa: fun_Pr960551193y_bool,Xs: list_P1663965006on_val,Ys: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_a2001304881val_ty(Pa,Xs),Ys))
     => ( hAPP_l1746926841al_nat(size_s60479160on_val,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_35_list__all2__lengthD,axiom,
    ! [Pa: fun_char_fun_ty_bool,Xs: list_char,Ys: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_all2_char_ty(Pa,Xs),Ys))
     => ( hAPP_list_char_nat(size_size_list_char,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_36_list__all2__lengthD,axiom,
    ! [Pa: fun_Pr718735977y_bool,Xs: list_P2023964830har_ty,Ys: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_a985311713_ty_ty(Pa,Xs),Ys))
     => ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_37_list__all2__lengthD,axiom,
    ! [Pa: fun_Pr489436466y_bool,Xs: list_P1697858023ar_val,Ys: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_a307207512val_ty(Pa,Xs),Ys))
     => ( hAPP_l1280603808al_nat(size_s760178257ar_val,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_38_list__all2__lengthD,axiom,
    ! [Pa: fun_op174240306y_bool,Xs: list_option_ty,Ys: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_a2039389316_ty_ty(Pa,Xs),Ys))
     => ( hAPP_l289305880ty_nat(size_s1050794909ion_ty,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_39_list__all2__lengthD,axiom,
    ! [Pa: fun_Pr66876909l_bool,Xs: list_P249777017on_val,Ys: list_val] :
      ( hBOOL(hAPP_list_val_bool(list_a595061083al_val(Pa,Xs),Ys))
     => ( hAPP_l1766199206al_nat(size_s470606735on_val,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_40_list__all2__lengthD,axiom,
    ! [Pa: fun_Pr755913058l_bool,Xs: list_P1663965006on_val,Ys: list_val] :
      ( hBOOL(hAPP_list_val_bool(list_a594658042al_val(Pa,Xs),Ys))
     => ( hAPP_l1746926841al_nat(size_s60479160on_val,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_41_list__all2__lengthD,axiom,
    ! [Pa: fun_ch496724692l_bool,Xs: list_char,Ys: list_val] :
      ( hBOOL(hAPP_list_val_bool(list_all2_char_val(Pa,Xs),Ys))
     => ( hAPP_list_char_nat(size_size_list_char,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_42_list__all2__lengthD,axiom,
    ! [Pa: fun_Pr2080430770l_bool,Xs: list_P2023964830har_ty,Ys: list_val] :
      ( hBOOL(hAPP_list_val_bool(list_a1068996522ty_val(Pa,Xs),Ys))
     => ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_43_list__all2__lengthD,axiom,
    ! [Pa: fun_Pr626733307l_bool,Xs: list_P1697858023ar_val,Ys: list_val] :
      ( hBOOL(hAPP_list_val_bool(list_a1889288097al_val(Pa,Xs),Ys))
     => ( hAPP_l1280603808al_nat(size_s760178257ar_val,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_44_list__all2__lengthD,axiom,
    ! [Pa: fun_op1696804347l_bool,Xs: list_option_ty,Ys: list_val] :
      ( hBOOL(hAPP_list_val_bool(list_a1073113293ty_val(Pa,Xs),Ys))
     => ( hAPP_l289305880ty_nat(size_s1050794909ion_ty,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_45_list__all2__lengthD,axiom,
    ! [Pa: fun_Pr1480657058r_bool,Xs: list_P249777017on_val,Ys: list_exp_list_char] :
      ( hBOOL(hAPP_l1538097584r_bool(list_a1478901862t_char(Pa,Xs),Ys))
     => ( hAPP_l1766199206al_nat(size_s470606735on_val,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) ) ).

tff(fact_46_list__all2__lengthD,axiom,
    ! [Pa: fun_Pr1145000429r_bool,Xs: list_P1663965006on_val,Ys: list_exp_list_char] :
      ( hBOOL(hAPP_l1538097584r_bool(list_a789546247t_char(Pa,Xs),Ys))
     => ( hAPP_l1746926841al_nat(size_s60479160on_val,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) ) ).

tff(fact_47_list__all2__lengthD,axiom,
    ! [Pa: fun_ch691056635r_bool,Xs: list_char,Ys: list_exp_list_char] :
      ( hBOOL(hAPP_l1538097584r_bool(list_a196402809t_char(Pa,Xs),Ys))
     => ( hAPP_list_char_nat(size_size_list_char,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) ) ).

tff(fact_48_list__all2__lengthD,axiom,
    ! [Pa: fun_Pr967742621r_bool,Xs: list_P2023964830har_ty,Ys: list_exp_list_char] :
      ( hBOOL(hAPP_l1538097584r_bool(list_a1822188631t_char(Pa,Xs),Ys))
     => ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) ) ).

tff(fact_49_list__all2__lengthD,axiom,
    ! [Pa: fun_Pr819181076r_bool,Xs: list_P1697858023ar_val,Ys: list_exp_list_char] :
      ( hBOOL(hAPP_l1538097584r_bool(list_a422786208t_char(Pa,Xs),Ys))
     => ( hAPP_l1280603808al_nat(size_s760178257ar_val,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) ) ).

tff(fact_50_list__all2__lengthD,axiom,
    ! [Pa: fun_op14579988r_bool,Xs: list_option_ty,Ys: list_exp_list_char] :
      ( hBOOL(hAPP_l1538097584r_bool(list_a283687028t_char(Pa,Xs),Ys))
     => ( hAPP_l289305880ty_nat(size_s1050794909ion_ty,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) ) ).

tff(fact_51_list__all2__lengthD,axiom,
    ! [Pa: fun_ty_fun_ty_bool,Xs: list_ty,Ys: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(Pa,Xs),Ys))
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_52_list__all2__lengthD,axiom,
    ! [Pa: fun_val_fun_ty_bool,Xs: list_val,Ys: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_all2_val_ty(Pa,Xs),Ys))
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_53_length__map,axiom,
    ! [F_1: fun_Pr1566767763har_ty,Xs: list_P2023964830har_ty] : hAPP_l1961350547ty_nat(size_s1518787998har_ty,hAPP_l1910281173har_ty(map_Pr1267419400har_ty(F_1),Xs)) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) ).

tff(fact_54_length__map,axiom,
    ! [F_1: fun_Pr107226222har_ty,Xs: list_P1940453997har_ty] : hAPP_l540212137ty_nat(size_s1444510216har_ty,hAPP_l162677262har_ty(map_Pr1471044963har_ty(F_1),Xs)) = hAPP_l1526684570ty_nat(size_s1760542935har_ty,Xs) ).

tff(fact_55_length__map,axiom,
    ! [F_1: fun_li889387821on_val,Xs: list_l350949640ar_val] : hAPP_l1718801839al_nat(size_s1457910402on_val,hAPP_l1790629643on_val(map_li596218076on_val(F_1),Xs)) = hAPP_l49336279al_nat(size_s655688734ar_val,Xs) ).

tff(fact_56_length__map,axiom,
    ! [F_1: fun_li867521386ar_val,Xs: list_l38846271har_ty] : hAPP_l49336279al_nat(size_s655688734ar_val,hAPP_l823328606ar_val(map_li912744805ar_val(F_1),Xs)) = hAPP_l23466336ty_nat(size_s764697941har_ty,Xs) ).

tff(fact_57_length__map,axiom,
    ! [F_1: fun_li750181430on_val,Xs: list_l38846271har_ty] : hAPP_l1718801839al_nat(size_s1457910402on_val,hAPP_l721971010on_val(map_li1065623653on_val(F_1),Xs)) = hAPP_l23466336ty_nat(size_s764697941har_ty,Xs) ).

tff(fact_58_length__map,axiom,
    ! [F_1: fun_nat_nat,Xs: list_nat] : hAPP_list_nat_nat(size_size_list_nat,hAPP_l248265089st_nat(map_nat_nat(F_1),Xs)) = hAPP_list_nat_nat(size_size_list_nat,Xs) ).

tff(fact_59_length__map,axiom,
    ! [F_1: fun_Pr1380325635t_char,Xs: list_P1916372464t_char] : hAPP_l365675759ar_nat(size_s1010401542t_char,hAPP_l250787541t_char(map_Pr361633150t_char(F_1),Xs)) = hAPP_l365675759ar_nat(size_s1010401542t_char,Xs) ).

tff(fact_60_length__map,axiom,
    ! [F_1: fun_Pr1898553187on_val,Xs: list_P507235360on_val] : hAPP_l1593094847al_nat(size_s2086378294on_val,hAPP_l1208602837on_val(map_Pr1729094110on_val(F_1),Xs)) = hAPP_l1593094847al_nat(size_s2086378294on_val,Xs) ).

tff(fact_61_length__map,axiom,
    ! [F_1: fun_Pr12181427on_val,Xs: list_P1439941640on_val] : hAPP_l1794950871al_nat(size_s1699857438on_val,hAPP_l1695428693on_val(map_Pr1655409582on_val(F_1),Xs)) = hAPP_l1794950871al_nat(size_s1699857438on_val,Xs) ).

tff(fact_62_length__map,axiom,
    ! [F_1: fun_Pr1262402813t_char,Xs: list_P249777017on_val] : hAPP_l66428094ar_nat(size_s2113983095t_char,hAPP_l1664314621t_char(map_Pr1982459768t_char(F_1),Xs)) = hAPP_l1766199206al_nat(size_s470606735on_val,Xs) ).

tff(fact_63_length__map,axiom,
    ! [F_1: fun_Pr213997554t_char,Xs: list_P1663965006on_val] : hAPP_l66428094ar_nat(size_s2113983095t_char,hAPP_l244703952t_char(map_Pr1152367783t_char(F_1),Xs)) = hAPP_l1746926841al_nat(size_s60479160on_val,Xs) ).

tff(fact_64_length__map,axiom,
    ! [F_1: fun_char_list_char,Xs: list_char] : hAPP_l66428094ar_nat(size_s2113983095t_char,hAPP_l1927076062t_char(map_char_list_char(F_1),Xs)) = hAPP_list_char_nat(size_size_list_char,Xs) ).

tff(fact_65_length__map,axiom,
    ! [F_1: fun_Pr563796290t_char,Xs: list_P2023964830har_ty] : hAPP_l66428094ar_nat(size_s2113983095t_char,hAPP_l632662400t_char(map_Pr197231351t_char(F_1),Xs)) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) ).

tff(fact_66_length__map,axiom,
    ! [F_1: fun_Pr1439460619t_char,Xs: list_P1697858023ar_val] : hAPP_l66428094ar_nat(size_s2113983095t_char,hAPP_l1890693879t_char(map_Pr1809410112t_char(F_1),Xs)) = hAPP_l1280603808al_nat(size_s760178257ar_val,Xs) ).

tff(fact_67_length__map,axiom,
    ! [F_1: fun_op195029515t_char,Xs: list_option_ty] : hAPP_l66428094ar_nat(size_s2113983095t_char,hAPP_l1368737135t_char(map_op1924521862t_char(F_1),Xs)) = hAPP_l289305880ty_nat(size_s1050794909ion_ty,Xs) ).

tff(fact_68_length__map,axiom,
    ! [F_1: fun_Pr722806154val_ty,Xs: list_P249777017on_val] : hAPP_list_ty_nat(size_size_list_ty,hAPP_l674002314ist_ty(map_Pr58749369val_ty(F_1),Xs)) = hAPP_l1766199206al_nat(size_s470606735on_val,Xs) ).

tff(fact_69_length__map,axiom,
    ! [F_1: fun_Pr685918677val_ty,Xs: list_P1663965006on_val] : hAPP_list_ty_nat(size_size_list_ty,hAPP_l560448119ist_ty(map_Pr401282634val_ty(F_1),Xs)) = hAPP_l1746926841al_nat(size_s60479160on_val,Xs) ).

tff(fact_70_length__map,axiom,
    ! [F_1: fun_char_ty,Xs: list_char] : hAPP_list_ty_nat(size_size_list_ty,hAPP_l1044806633ist_ty(map_char_ty(F_1),Xs)) = hAPP_list_char_nat(size_size_list_char,Xs) ).

tff(fact_71_length__map,axiom,
    ! [F_1: fun_Pr1905081477_ty_ty,Xs: list_P2023964830har_ty] : hAPP_list_ty_nat(size_size_list_ty,hAPP_l1097172935ist_ty(map_Pr1636893690_ty_ty(F_1),Xs)) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) ).

tff(fact_72_length__map,axiom,
    ! [F_1: fun_Pr1820304636val_ty,Xs: list_P1697858023ar_val] : hAPP_list_ty_nat(size_size_list_ty,hAPP_l1538085392ist_ty(map_Pr199785201val_ty(F_1),Xs)) = hAPP_l1280603808al_nat(size_s760178257ar_val,Xs) ).

tff(fact_73_length__map,axiom,
    ! [F_1: fun_option_ty_ty,Xs: list_option_ty] : hAPP_list_ty_nat(size_size_list_ty,hAPP_l1583451544ist_ty(map_option_ty_ty(F_1),Xs)) = hAPP_l289305880ty_nat(size_s1050794909ion_ty,Xs) ).

tff(fact_74_length__map,axiom,
    ! [F_1: fun_option_val_val,Xs: list_option_val] : hAPP_list_val_nat(size_size_list_val,hAPP_l228474410st_val(map_option_val_val(F_1),Xs)) = hAPP_l870066319al_nat(size_s1595297126on_val,Xs) ).

tff(fact_75_length__map,axiom,
    ! [F_1: fun_Pr160391123al_val,Xs: list_P249777017on_val] : hAPP_list_val_nat(size_size_list_val,hAPP_l1342091219st_val(map_Pr1583805314al_val(F_1),Xs)) = hAPP_l1766199206al_nat(size_s470606735on_val,Xs) ).

tff(fact_76_length__map,axiom,
    ! [F_1: fun_Pr1341722270al_val,Xs: list_P1663965006on_val] : hAPP_list_val_nat(size_size_list_val,hAPP_l1023956544st_val(map_Pr1730568083al_val(F_1),Xs)) = hAPP_l1746926841al_nat(size_s60479160on_val,Xs) ).

tff(fact_77_length__map,axiom,
    ! [F_1: fun_char_val,Xs: list_char] : hAPP_list_val_nat(size_size_list_val,hAPP_l473790130st_val(map_char_val(F_1),Xs)) = hAPP_list_char_nat(size_size_list_char,Xs) ).

tff(fact_78_length__map,axiom,
    ! [F_1: fun_Pr1693821262ty_val,Xs: list_P2023964830har_ty] : hAPP_list_val_nat(size_size_list_val,hAPP_l1473803152st_val(map_Pr961574211ty_val(F_1),Xs)) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) ).

tff(fact_79_length__map,axiom,
    ! [F_1: fun_Pr2009941573al_val,Xs: list_P1697858023ar_val] : hAPP_list_val_nat(size_size_list_val,hAPP_l1523427673st_val(map_Pr1022222522al_val(F_1),Xs)) = hAPP_l1280603808al_nat(size_s760178257ar_val,Xs) ).

tff(fact_80_length__map,axiom,
    ! [F_1: fun_option_ty_val,Xs: list_option_ty] : hAPP_list_val_nat(size_size_list_val,hAPP_l336371937st_val(map_option_ty_val(F_1),Xs)) = hAPP_l289305880ty_nat(size_s1050794909ion_ty,Xs) ).

tff(fact_81_length__map,axiom,
    ! [F_1: fun_Pr645859204t_char,Xs: list_P249777017on_val] : hAPP_l452123639ar_nat(size_s1143674878t_char,hAPP_l1683732356t_char(map_Pr1211171455t_char(F_1),Xs)) = hAPP_l1766199206al_nat(size_s470606735on_val,Xs) ).

tff(fact_82_length__map,axiom,
    ! [F_1: fun_Pr664085497t_char,Xs: list_P1663965006on_val] : hAPP_l452123639ar_nat(size_s1143674878t_char,hAPP_l2043127767t_char(map_Pr161410094t_char(F_1),Xs)) = hAPP_l1746926841al_nat(size_s60479160on_val,Xs) ).

tff(fact_83_length__map,axiom,
    ! [F_1: fun_ch1888757611t_char,Xs: list_char] : hAPP_l452123639ar_nat(size_s1143674878t_char,hAPP_l925187813t_char(map_ch278031520t_char(F_1),Xs)) = hAPP_list_char_nat(size_size_list_char,Xs) ).

tff(fact_84_length__map,axiom,
    ! [F_1: fun_Pr580238665t_char,Xs: list_P2023964830har_ty] : hAPP_l452123639ar_nat(size_s1143674878t_char,hAPP_l2038191751t_char(map_Pr863062654t_char(F_1),Xs)) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) ).

tff(fact_85_length__map,axiom,
    ! [F_1: fun_Pr176052370t_char,Xs: list_P1697858023ar_val] : hAPP_l452123639ar_nat(size_s1143674878t_char,hAPP_l347191422t_char(map_Pr187266887t_char(F_1),Xs)) = hAPP_l1280603808al_nat(size_s760178257ar_val,Xs) ).

tff(fact_86_length__map,axiom,
    ! [F_1: fun_op1508857234t_char,Xs: list_option_ty] : hAPP_l452123639ar_nat(size_s1143674878t_char,hAPP_l330149622t_char(map_op1779340173t_char(F_1),Xs)) = hAPP_l289305880ty_nat(size_s1050794909ion_ty,Xs) ).

tff(fact_87_length__map,axiom,
    ! [F_1: fun_li1432931796on_val,Xs: list_list_char] : hAPP_l870066319al_nat(size_s1595297126on_val,hAPP_l297961988on_val(map_li50976719on_val(F_1),Xs)) = hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) ).

tff(fact_88_length__map,axiom,
    ! [F_1: fun_li1751394789t_char,Xs: list_list_char] : hAPP_l66428094ar_nat(size_s2113983095t_char,hAPP_l407174677t_char(map_li1333403488t_char(F_1),Xs)) = hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) ).

tff(fact_89_length__map,axiom,
    ! [F_1: fun_li563662077on_val,Xs: list_list_char] : hAPP_l1766199206al_nat(size_s470606735on_val,hAPP_l1956999469on_val(map_li1622452344on_val(F_1),Xs)) = hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) ).

tff(fact_90_length__map,axiom,
    ! [F_1: fun_li744874698on_val,Xs: list_list_char] : hAPP_l1746926841al_nat(size_s60479160on_val,hAPP_l713251482on_val(map_li586533881on_val(F_1),Xs)) = hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) ).

tff(fact_91_length__map,axiom,
    ! [F_1: fun_list_char_char,Xs: list_list_char] : hAPP_list_char_nat(size_size_list_char,hAPP_l838080012t_char(map_list_char_char(F_1),Xs)) = hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) ).

tff(fact_92_length__map,axiom,
    ! [F_1: fun_li1174071322har_ty,Xs: list_list_char] : hAPP_l540212137ty_nat(size_s1444510216har_ty,hAPP_l1261744106har_ty(map_li1980326729har_ty(F_1),Xs)) = hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) ).

tff(fact_93_length__map,axiom,
    ! [F_1: fun_li1882647395ar_val,Xs: list_list_char] : hAPP_l1280603808al_nat(size_s760178257ar_val,hAPP_l1298778931ar_val(map_li37924370ar_val(F_1),Xs)) = hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) ).

tff(fact_94_length__map,axiom,
    ! [F_1: fun_li688206603ion_ty,Xs: list_list_char] : hAPP_l289305880ty_nat(size_s1050794909ion_ty,hAPP_l1491470139ion_ty(map_li771939206ion_ty(F_1),Xs)) = hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) ).

tff(fact_95_length__map,axiom,
    ! [F_1: fun_ty1472322018on_val,Xs: list_ty] : hAPP_l1766199206al_nat(size_s470606735on_val,hAPP_l273343760on_val(map_ty268240023on_val(F_1),Xs)) = hAPP_list_ty_nat(size_size_list_ty,Xs) ).

tff(fact_96_length__map,axiom,
    ! [F_1: fun_ty876164645on_val,Xs: list_ty] : hAPP_l1746926841al_nat(size_s60479160on_val,hAPP_l664719479on_val(map_ty763542682on_val(F_1),Xs)) = hAPP_list_ty_nat(size_size_list_ty,Xs) ).

tff(fact_97_length__map,axiom,
    ! [F_1: fun_ty_char,Xs: list_ty] : hAPP_list_char_nat(size_size_list_char,hAPP_l1705142505t_char(map_ty_char(F_1),Xs)) = hAPP_list_ty_nat(size_size_list_ty,Xs) ).

tff(fact_98_length__map,axiom,
    ! [F_1: fun_ty1486032501har_ty,Xs: list_ty] : hAPP_l540212137ty_nat(size_s1444510216har_ty,hAPP_l499600071har_ty(map_ty1511906538har_ty(F_1),Xs)) = hAPP_list_ty_nat(size_size_list_ty,Xs) ).

tff(fact_99_length__map,axiom,
    ! [F_1: fun_ty434869310ar_val,Xs: list_ty] : hAPP_l1280603808al_nat(size_s760178257ar_val,hAPP_l958580624ar_val(map_ty15886131ar_val(F_1),Xs)) = hAPP_list_ty_nat(size_size_list_ty,Xs) ).

tff(fact_100_length__map,axiom,
    ! [F_1: fun_va1082347435on_val,Xs: list_val] : hAPP_l1766199206al_nat(size_s470606735on_val,hAPP_l1097436295on_val(map_va1077464032on_val(F_1),Xs)) = hAPP_list_val_nat(size_size_list_val,Xs) ).

tff(fact_101_length__map,axiom,
    ! [F_1: fun_va1155687836on_val,Xs: list_val] : hAPP_l1746926841al_nat(size_s60479160on_val,hAPP_l863146944on_val(map_va828275345on_val(F_1),Xs)) = hAPP_list_val_nat(size_size_list_val,Xs) ).

tff(fact_102_length__map,axiom,
    ! [F_1: fun_val_char,Xs: list_val] : hAPP_list_char_nat(size_size_list_char,hAPP_l281179442t_char(map_val_char(F_1),Xs)) = hAPP_list_val_nat(size_size_list_val,Xs) ).

tff(fact_103_length__map,axiom,
    ! [F_1: fun_va1147309292har_ty,Xs: list_val] : hAPP_l540212137ty_nat(size_s1444510216har_ty,hAPP_l220561168har_ty(map_va1968335329har_ty(F_1),Xs)) = hAPP_list_val_nat(size_size_list_val,Xs) ).

tff(fact_104_length__map,axiom,
    ! [F_1: fun_va1416972085ar_val,Xs: list_val] : hAPP_l1280603808al_nat(size_s760178257ar_val,hAPP_l412706649ar_val(map_va742516906ar_val(F_1),Xs)) = hAPP_list_val_nat(size_size_list_val,Xs) ).

tff(fact_105_length__map,axiom,
    ! [F_1: fun_ex500270084on_val,Xs: list_exp_list_char] : hAPP_l1766199206al_nat(size_s470606735on_val,hAPP_l897806566on_val(map_ex20783615on_val(F_1),Xs)) = hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) ).

tff(fact_106_length__map,axiom,
    ! [F_1: fun_ex139963011on_val,Xs: list_exp_list_char] : hAPP_l1746926841al_nat(size_s60479160on_val,hAPP_l1429130273on_val(map_ex1452011826on_val(F_1),Xs)) = hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) ).

tff(fact_107_length__map,axiom,
    ! [F_1: fun_ex608259829r_char,Xs: list_exp_list_char] : hAPP_list_char_nat(size_size_list_char,hAPP_l89656979t_char(map_ex1634568356r_char(F_1),Xs)) = hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) ).

tff(fact_108_length__map,axiom,
    ! [F_1: fun_ex1739657427har_ty,Xs: list_exp_list_char] : hAPP_l540212137ty_nat(size_s1444510216har_ty,hAPP_l527892593har_ty(map_ex1811769730har_ty(F_1),Xs)) = hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) ).

tff(fact_109_length__map,axiom,
    ! [F_1: fun_ex611469212ar_val,Xs: list_exp_list_char] : hAPP_l1280603808al_nat(size_s760178257ar_val,hAPP_l1207846970ar_val(map_ex1319446475ar_val(F_1),Xs)) = hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) ).

tff(fact_110_length__map,axiom,
    ! [F_1: fun_ex12316946ion_ty,Xs: list_exp_list_char] : hAPP_l289305880ty_nat(size_s1050794909ion_ty,hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F_1),Xs)) = hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) ).

tff(fact_111_length__map,axiom,
    ! [F_1: fun_val_option_ty,Xs: list_val] : hAPP_l289305880ty_nat(size_s1050794909ion_ty,hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Xs)) = hAPP_list_val_nat(size_size_list_val,Xs) ).

tff(fact_112_length__map,axiom,
    ! [F_1: fun_ty_option_ty,Xs: list_ty] : hAPP_l289305880ty_nat(size_s1050794909ion_ty,hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Xs)) = hAPP_list_ty_nat(size_size_list_ty,Xs) ).

tff(fact_113_length__map,axiom,
    ! [F_1: fun_va223928858t_char,Xs: list_val] : hAPP_l452123639ar_nat(size_s1143674878t_char,hAPP_l732421366t_char(map_va1934808527t_char(F_1),Xs)) = hAPP_list_val_nat(size_size_list_val,Xs) ).

tff(fact_114_length__map,axiom,
    ! [F_1: fun_list_char_val,Xs: list_list_char] : hAPP_list_val_nat(size_size_list_val,hAPP_l1892737211st_val(map_list_char_val(F_1),Xs)) = hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) ).

tff(fact_115_length__map,axiom,
    ! [F_1: fun_Pr1149393094ar_val,Xs: list_P2023964830har_ty] : hAPP_l1280603808al_nat(size_s760178257ar_val,hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),Xs)) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) ).

tff(fact_116_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li1248349104har_ty,Xs: list_list_char,G: fun_Pr1566767763har_ty,Ys: list_P2023964830har_ty] :
      ( ( hAPP_l1336021888har_ty(map_li56668639har_ty(F_1),Xs) = hAPP_l1910281173har_ty(map_Pr1267419400har_ty(G),Ys) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys) ) ) ).

tff(fact_117_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li1174071322har_ty,Xs: list_list_char,G: fun_Pr107226222har_ty,Ys: list_P1940453997har_ty] :
      ( ( hAPP_l1261744106har_ty(map_li1980326729har_ty(F_1),Xs) = hAPP_l162677262har_ty(map_Pr1471044963har_ty(G),Ys) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l1526684570ty_nat(size_s1760542935har_ty,Ys) ) ) ).

tff(fact_118_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li905540756on_val,Xs: list_list_char,G: fun_li889387821on_val,Ys: list_l350949640ar_val] :
      ( ( hAPP_l164125796on_val(map_li1461022915on_val(F_1),Xs) = hAPP_l1790629643on_val(map_li596218076on_val(G),Ys) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l49336279al_nat(size_s655688734ar_val,Ys) ) ) ).

tff(fact_119_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li1267938444ar_val,Xs: list_list_char,G: fun_li867521386ar_val,Ys: list_l38846271har_ty] :
      ( ( hAPP_l1975021756ar_val(map_li401377927ar_val(F_1),Xs) = hAPP_l823328606ar_val(map_li912744805ar_val(G),Ys) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l23466336ty_nat(size_s764697941har_ty,Ys) ) ) ).

tff(fact_120_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li905540756on_val,Xs: list_list_char,G: fun_li750181430on_val,Ys: list_l38846271har_ty] :
      ( ( hAPP_l164125796on_val(map_li1461022915on_val(F_1),Xs) = hAPP_l721971010on_val(map_li1065623653on_val(G),Ys) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l23466336ty_nat(size_s764697941har_ty,Ys) ) ) ).

tff(fact_121_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_list_char_nat,Xs: list_list_char,G: fun_nat_nat,Ys: list_nat] :
      ( ( hAPP_l1111097995st_nat(map_list_char_nat(F_1),Xs) = hAPP_l248265089st_nat(map_nat_nat(G),Ys) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_list_nat_nat(size_size_list_nat,Ys) ) ) ).

tff(fact_122_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) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l365675759ar_nat(size_s1010401542t_char,Ys) ) ) ).

tff(fact_123_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) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l1593094847al_nat(size_s2086378294on_val,Ys) ) ) ).

tff(fact_124_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) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l1794950871al_nat(size_s1699857438on_val,Ys) ) ) ).

tff(fact_125_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ty1560310283har_ty,Xs: list_ty,G: fun_Pr1566767763har_ty,Ys: list_P2023964830har_ty] :
      ( ( hAPP_l573877853har_ty(map_ty1735732096har_ty(F_1),Xs) = hAPP_l1910281173har_ty(map_Pr1267419400har_ty(G),Ys) )
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys) ) ) ).

tff(fact_126_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ty1486032501har_ty,Xs: list_ty,G: fun_Pr107226222har_ty,Ys: list_P1940453997har_ty] :
      ( ( hAPP_l499600071har_ty(map_ty1511906538har_ty(F_1),Xs) = hAPP_l162677262har_ty(map_Pr1471044963har_ty(G),Ys) )
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l1526684570ty_nat(size_s1760542935har_ty,Ys) ) ) ).

tff(fact_127_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ty2061842671on_val,Xs: list_ty,G: fun_li889387821on_val,Ys: list_l350949640ar_val] :
      ( ( hAPP_l642124097on_val(map_ty330392676on_val(F_1),Xs) = hAPP_l1790629643on_val(map_li596218076on_val(G),Ys) )
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l49336279al_nat(size_s655688734ar_val,Ys) ) ) ).

tff(fact_128_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ty719916017ar_val,Xs: list_ty,G: fun_li867521386ar_val,Ys: list_l38846271har_ty] :
      ( ( hAPP_l654786079ar_val(map_ty217218598ar_val(F_1),Xs) = hAPP_l823328606ar_val(map_li912744805ar_val(G),Ys) )
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l23466336ty_nat(size_s764697941har_ty,Ys) ) ) ).

tff(fact_129_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ty2061842671on_val,Xs: list_ty,G: fun_li750181430on_val,Ys: list_l38846271har_ty] :
      ( ( hAPP_l642124097on_val(map_ty330392676on_val(F_1),Xs) = hAPP_l721971010on_val(map_li1065623653on_val(G),Ys) )
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l23466336ty_nat(size_s764697941har_ty,Ys) ) ) ).

tff(fact_130_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) )
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l870066319al_nat(size_s1595297126on_val,Ys) ) ) ).

tff(fact_131_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) )
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_132_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) )
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_133_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ty_nat,Xs: list_ty,G: fun_nat_nat,Ys: list_nat] :
      ( ( hAPP_l277434984st_nat(map_ty_nat(F_1),Xs) = hAPP_l248265089st_nat(map_nat_nat(G),Ys) )
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_list_nat_nat(size_size_list_nat,Ys) ) ) ).

tff(fact_134_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) )
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l365675759ar_nat(size_s1010401542t_char,Ys) ) ) ).

tff(fact_135_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) )
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l1593094847al_nat(size_s2086378294on_val,Ys) ) ) ).

tff(fact_136_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) )
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l1794950871al_nat(size_s1699857438on_val,Ys) ) ) ).

tff(fact_137_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_va1221587074har_ty,Xs: list_val,G: fun_Pr1566767763har_ty,Ys: list_P2023964830har_ty] :
      ( ( hAPP_l294838950har_ty(map_va44677239har_ty(F_1),Xs) = hAPP_l1910281173har_ty(map_Pr1267419400har_ty(G),Ys) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys) ) ) ).

tff(fact_138_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_va1147309292har_ty,Xs: list_val,G: fun_Pr107226222har_ty,Ys: list_P1940453997har_ty] :
      ( ( hAPP_l220561168har_ty(map_va1968335329har_ty(F_1),Xs) = hAPP_l162677262har_ty(map_Pr1471044963har_ty(G),Ys) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l1526684570ty_nat(size_s1760542935har_ty,Ys) ) ) ).

tff(fact_139_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_va347778406on_val,Xs: list_val,G: fun_li889387821on_val,Ys: list_l350949640ar_val] :
      ( ( hAPP_l1725810570on_val(map_va1286924123on_val(F_1),Xs) = hAPP_l1790629643on_val(map_li596218076on_val(G),Ys) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l49336279al_nat(size_s655688734ar_val,Ys) ) ) ).

tff(fact_140_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_va1465032250ar_val,Xs: list_val,G: fun_li867521386ar_val,Ys: list_l38846271har_ty] :
      ( ( hAPP_l1426221334ar_val(map_va45294063ar_val(F_1),Xs) = hAPP_l823328606ar_val(map_li912744805ar_val(G),Ys) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l23466336ty_nat(size_s764697941har_ty,Ys) ) ) ).

tff(fact_141_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_va347778406on_val,Xs: list_val,G: fun_li750181430on_val,Ys: list_l38846271har_ty] :
      ( ( hAPP_l1725810570on_val(map_va1286924123on_val(F_1),Xs) = hAPP_l721971010on_val(map_li1065623653on_val(G),Ys) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l23466336ty_nat(size_s764697941har_ty,Ys) ) ) ).

tff(fact_142_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) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l870066319al_nat(size_s1595297126on_val,Ys) ) ) ).

tff(fact_143_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) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_144_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) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_145_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_val_nat,Xs: list_val,G: fun_nat_nat,Ys: list_nat] :
      ( ( hAPP_l324487089st_nat(map_val_nat(F_1),Xs) = hAPP_l248265089st_nat(map_nat_nat(G),Ys) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_list_nat_nat(size_size_list_nat,Ys) ) ) ).

tff(fact_146_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) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l365675759ar_nat(size_s1010401542t_char,Ys) ) ) ).

tff(fact_147_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) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l1593094847al_nat(size_s2086378294on_val,Ys) ) ) ).

tff(fact_148_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) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l1794950871al_nat(size_s1699857438on_val,Ys) ) ) ).

tff(fact_149_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ex1813935209har_ty,Xs: list_exp_list_char,G: fun_Pr1566767763har_ty,Ys: list_P2023964830har_ty] :
      ( ( hAPP_l602170375har_ty(map_ex2035595288har_ty(F_1),Xs) = hAPP_l1910281173har_ty(map_Pr1267419400har_ty(G),Ys) )
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys) ) ) ).

tff(fact_150_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ex1739657427har_ty,Xs: list_exp_list_char,G: fun_Pr107226222har_ty,Ys: list_P1940453997har_ty] :
      ( ( hAPP_l527892593har_ty(map_ex1811769730har_ty(F_1),Xs) = hAPP_l162677262har_ty(map_Pr1471044963har_ty(G),Ys) )
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_l1526684570ty_nat(size_s1760542935har_ty,Ys) ) ) ).

tff(fact_151_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ex1362790221on_val,Xs: list_exp_list_char,G: fun_li889387821on_val,Ys: list_l350949640ar_val] :
      ( ( hAPP_l1463304939on_val(map_ex1279484156on_val(F_1),Xs) = hAPP_l1790629643on_val(map_li596218076on_val(G),Ys) )
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_l49336279al_nat(size_s655688734ar_val,Ys) ) ) ).

tff(fact_152_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ex292271891ar_val,Xs: list_exp_list_char,G: fun_li867521386ar_val,Ys: list_l38846271har_ty] :
      ( ( hAPP_l121373941ar_val(map_ex178392974ar_val(F_1),Xs) = hAPP_l823328606ar_val(map_li912744805ar_val(G),Ys) )
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_l23466336ty_nat(size_s764697941har_ty,Ys) ) ) ).

tff(fact_153_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ex1362790221on_val,Xs: list_exp_list_char,G: fun_li750181430on_val,Ys: list_l38846271har_ty] :
      ( ( hAPP_l1463304939on_val(map_ex1279484156on_val(F_1),Xs) = hAPP_l721971010on_val(map_li1065623653on_val(G),Ys) )
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_l23466336ty_nat(size_s764697941har_ty,Ys) ) ) ).

tff(fact_154_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) )
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_l870066319al_nat(size_s1595297126on_val,Ys) ) ) ).

tff(fact_155_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) )
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_156_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) )
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_157_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ex432391284ar_nat,Xs: list_exp_list_char,G: fun_nat_nat,Ys: list_nat] :
      ( ( hAPP_l1496769042st_nat(map_ex1185884067ar_nat(F_1),Xs) = hAPP_l248265089st_nat(map_nat_nat(G),Ys) )
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_list_nat_nat(size_size_list_nat,Ys) ) ) ).

tff(fact_158_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) )
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_l365675759ar_nat(size_s1010401542t_char,Ys) ) ) ).

tff(fact_159_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) )
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_l1593094847al_nat(size_s2086378294on_val,Ys) ) ) ).

tff(fact_160_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) )
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_l1794950871al_nat(size_s1699857438on_val,Ys) ) ) ).

tff(fact_161_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1566767763har_ty,Xs: list_P2023964830har_ty,G: fun_li1248349104har_ty,Ys: list_list_char] :
      ( ( hAPP_l1910281173har_ty(map_Pr1267419400har_ty(F_1),Xs) = hAPP_l1336021888har_ty(map_li56668639har_ty(G),Ys) )
     => ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_162_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr107226222har_ty,Xs: list_P1940453997har_ty,G: fun_li1174071322har_ty,Ys: list_list_char] :
      ( ( hAPP_l162677262har_ty(map_Pr1471044963har_ty(F_1),Xs) = hAPP_l1261744106har_ty(map_li1980326729har_ty(G),Ys) )
     => ( hAPP_l1526684570ty_nat(size_s1760542935har_ty,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_163_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li889387821on_val,Xs: list_l350949640ar_val,G: fun_li905540756on_val,Ys: list_list_char] :
      ( ( hAPP_l1790629643on_val(map_li596218076on_val(F_1),Xs) = hAPP_l164125796on_val(map_li1461022915on_val(G),Ys) )
     => ( hAPP_l49336279al_nat(size_s655688734ar_val,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_164_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li867521386ar_val,Xs: list_l38846271har_ty,G: fun_li1267938444ar_val,Ys: list_list_char] :
      ( ( hAPP_l823328606ar_val(map_li912744805ar_val(F_1),Xs) = hAPP_l1975021756ar_val(map_li401377927ar_val(G),Ys) )
     => ( hAPP_l23466336ty_nat(size_s764697941har_ty,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_165_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li750181430on_val,Xs: list_l38846271har_ty,G: fun_li905540756on_val,Ys: list_list_char] :
      ( ( hAPP_l721971010on_val(map_li1065623653on_val(F_1),Xs) = hAPP_l164125796on_val(map_li1461022915on_val(G),Ys) )
     => ( hAPP_l23466336ty_nat(size_s764697941har_ty,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_166_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) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_167_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) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_168_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_nat_nat,Xs: list_nat,G: fun_list_char_nat,Ys: list_list_char] :
      ( ( hAPP_l248265089st_nat(map_nat_nat(F_1),Xs) = hAPP_l1111097995st_nat(map_list_char_nat(G),Ys) )
     => ( hAPP_list_nat_nat(size_size_list_nat,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_169_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) )
     => ( hAPP_l365675759ar_nat(size_s1010401542t_char,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_170_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) )
     => ( hAPP_l1593094847al_nat(size_s2086378294on_val,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_171_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) )
     => ( hAPP_l1794950871al_nat(size_s1699857438on_val,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_172_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1566767763har_ty,Xs: list_P2023964830har_ty,G: fun_ty1560310283har_ty,Ys: list_ty] :
      ( ( hAPP_l1910281173har_ty(map_Pr1267419400har_ty(F_1),Xs) = hAPP_l573877853har_ty(map_ty1735732096har_ty(G),Ys) )
     => ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_173_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr107226222har_ty,Xs: list_P1940453997har_ty,G: fun_ty1486032501har_ty,Ys: list_ty] :
      ( ( hAPP_l162677262har_ty(map_Pr1471044963har_ty(F_1),Xs) = hAPP_l499600071har_ty(map_ty1511906538har_ty(G),Ys) )
     => ( hAPP_l1526684570ty_nat(size_s1760542935har_ty,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_174_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li889387821on_val,Xs: list_l350949640ar_val,G: fun_ty2061842671on_val,Ys: list_ty] :
      ( ( hAPP_l1790629643on_val(map_li596218076on_val(F_1),Xs) = hAPP_l642124097on_val(map_ty330392676on_val(G),Ys) )
     => ( hAPP_l49336279al_nat(size_s655688734ar_val,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_175_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li867521386ar_val,Xs: list_l38846271har_ty,G: fun_ty719916017ar_val,Ys: list_ty] :
      ( ( hAPP_l823328606ar_val(map_li912744805ar_val(F_1),Xs) = hAPP_l654786079ar_val(map_ty217218598ar_val(G),Ys) )
     => ( hAPP_l23466336ty_nat(size_s764697941har_ty,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_176_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li750181430on_val,Xs: list_l38846271har_ty,G: fun_ty2061842671on_val,Ys: list_ty] :
      ( ( hAPP_l721971010on_val(map_li1065623653on_val(F_1),Xs) = hAPP_l642124097on_val(map_ty330392676on_val(G),Ys) )
     => ( hAPP_l23466336ty_nat(size_s764697941har_ty,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_177_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) )
     => ( hAPP_l870066319al_nat(size_s1595297126on_val,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_178_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) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_179_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) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_180_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_nat_nat,Xs: list_nat,G: fun_ty_nat,Ys: list_ty] :
      ( ( hAPP_l248265089st_nat(map_nat_nat(F_1),Xs) = hAPP_l277434984st_nat(map_ty_nat(G),Ys) )
     => ( hAPP_list_nat_nat(size_size_list_nat,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_181_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) )
     => ( hAPP_l365675759ar_nat(size_s1010401542t_char,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_182_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) )
     => ( hAPP_l1593094847al_nat(size_s2086378294on_val,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_183_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) )
     => ( hAPP_l1794950871al_nat(size_s1699857438on_val,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_184_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1566767763har_ty,Xs: list_P2023964830har_ty,G: fun_va1221587074har_ty,Ys: list_val] :
      ( ( hAPP_l1910281173har_ty(map_Pr1267419400har_ty(F_1),Xs) = hAPP_l294838950har_ty(map_va44677239har_ty(G),Ys) )
     => ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_185_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr107226222har_ty,Xs: list_P1940453997har_ty,G: fun_va1147309292har_ty,Ys: list_val] :
      ( ( hAPP_l162677262har_ty(map_Pr1471044963har_ty(F_1),Xs) = hAPP_l220561168har_ty(map_va1968335329har_ty(G),Ys) )
     => ( hAPP_l1526684570ty_nat(size_s1760542935har_ty,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_186_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li889387821on_val,Xs: list_l350949640ar_val,G: fun_va347778406on_val,Ys: list_val] :
      ( ( hAPP_l1790629643on_val(map_li596218076on_val(F_1),Xs) = hAPP_l1725810570on_val(map_va1286924123on_val(G),Ys) )
     => ( hAPP_l49336279al_nat(size_s655688734ar_val,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_187_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li867521386ar_val,Xs: list_l38846271har_ty,G: fun_va1465032250ar_val,Ys: list_val] :
      ( ( hAPP_l823328606ar_val(map_li912744805ar_val(F_1),Xs) = hAPP_l1426221334ar_val(map_va45294063ar_val(G),Ys) )
     => ( hAPP_l23466336ty_nat(size_s764697941har_ty,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_188_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li750181430on_val,Xs: list_l38846271har_ty,G: fun_va347778406on_val,Ys: list_val] :
      ( ( hAPP_l721971010on_val(map_li1065623653on_val(F_1),Xs) = hAPP_l1725810570on_val(map_va1286924123on_val(G),Ys) )
     => ( hAPP_l23466336ty_nat(size_s764697941har_ty,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_189_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) )
     => ( hAPP_l870066319al_nat(size_s1595297126on_val,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_190_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) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_191_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) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_192_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_nat_nat,Xs: list_nat,G: fun_val_nat,Ys: list_val] :
      ( ( hAPP_l248265089st_nat(map_nat_nat(F_1),Xs) = hAPP_l324487089st_nat(map_val_nat(G),Ys) )
     => ( hAPP_list_nat_nat(size_size_list_nat,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_193_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) )
     => ( hAPP_l365675759ar_nat(size_s1010401542t_char,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_194_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) )
     => ( hAPP_l1593094847al_nat(size_s2086378294on_val,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_195_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) )
     => ( hAPP_l1794950871al_nat(size_s1699857438on_val,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_196_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1566767763har_ty,Xs: list_P2023964830har_ty,G: fun_ex1813935209har_ty,Ys: list_exp_list_char] :
      ( ( hAPP_l1910281173har_ty(map_Pr1267419400har_ty(F_1),Xs) = hAPP_l602170375har_ty(map_ex2035595288har_ty(G),Ys) )
     => ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) ) ).

tff(fact_197_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr107226222har_ty,Xs: list_P1940453997har_ty,G: fun_ex1739657427har_ty,Ys: list_exp_list_char] :
      ( ( hAPP_l162677262har_ty(map_Pr1471044963har_ty(F_1),Xs) = hAPP_l527892593har_ty(map_ex1811769730har_ty(G),Ys) )
     => ( hAPP_l1526684570ty_nat(size_s1760542935har_ty,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) ) ).

tff(fact_198_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li889387821on_val,Xs: list_l350949640ar_val,G: fun_ex1362790221on_val,Ys: list_exp_list_char] :
      ( ( hAPP_l1790629643on_val(map_li596218076on_val(F_1),Xs) = hAPP_l1463304939on_val(map_ex1279484156on_val(G),Ys) )
     => ( hAPP_l49336279al_nat(size_s655688734ar_val,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) ) ).

tff(fact_199_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li867521386ar_val,Xs: list_l38846271har_ty,G: fun_ex292271891ar_val,Ys: list_exp_list_char] :
      ( ( hAPP_l823328606ar_val(map_li912744805ar_val(F_1),Xs) = hAPP_l121373941ar_val(map_ex178392974ar_val(G),Ys) )
     => ( hAPP_l23466336ty_nat(size_s764697941har_ty,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) ) ).

tff(fact_200_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_li750181430on_val,Xs: list_l38846271har_ty,G: fun_ex1362790221on_val,Ys: list_exp_list_char] :
      ( ( hAPP_l721971010on_val(map_li1065623653on_val(F_1),Xs) = hAPP_l1463304939on_val(map_ex1279484156on_val(G),Ys) )
     => ( hAPP_l23466336ty_nat(size_s764697941har_ty,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) ) ).

tff(fact_201_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) )
     => ( hAPP_l870066319al_nat(size_s1595297126on_val,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) ) ).

tff(fact_202_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) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) ) ).

tff(fact_203_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) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) ) ).

tff(fact_204_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_nat_nat,Xs: list_nat,G: fun_ex432391284ar_nat,Ys: list_exp_list_char] :
      ( ( hAPP_l248265089st_nat(map_nat_nat(F_1),Xs) = hAPP_l1496769042st_nat(map_ex1185884067ar_nat(G),Ys) )
     => ( hAPP_list_nat_nat(size_size_list_nat,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) ) ).

tff(fact_205_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) )
     => ( hAPP_l365675759ar_nat(size_s1010401542t_char,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) ) ).

tff(fact_206_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) )
     => ( hAPP_l1593094847al_nat(size_s2086378294on_val,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) ) ).

tff(fact_207_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) )
     => ( hAPP_l1794950871al_nat(size_s1699857438on_val,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) ) ).

tff(fact_208_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_val_option_ty,Xs: list_val,G: fun_Pr199214627ion_ty,Ys: list_P249777017on_val] :
      ( ( hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Xs) = hAPP_l601126435ion_ty(map_Pr1420995486ion_ty(G),Ys) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l1766199206al_nat(size_s470606735on_val,Ys) ) ) ).

tff(fact_209_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_val_option_ty,Xs: list_val,G: fun_Pr1298293016ion_ty,Ys: list_P1663965006on_val] :
      ( ( hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Xs) = hAPP_l1328999414ion_ty(map_Pr590903501ion_ty(G),Ys) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l1746926841al_nat(size_s60479160on_val,Ys) ) ) ).

tff(fact_210_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_val_option_ty,Xs: list_val,G: fun_char_option_ty,Ys: list_char] :
      ( ( hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Xs) = hAPP_l863887876ion_ty(map_char_option_ty(G),Ys) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_list_char_nat(size_size_list_char,Ys) ) ) ).

tff(fact_211_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_val_option_ty,Xs: list_val,G: fun_Pr1648091752ion_ty,Ys: list_P2023964830har_ty] :
      ( ( hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Xs) = hAPP_l1716957862ion_ty(map_Pr1783250717ion_ty(G),Ys) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys) ) ) ).

tff(fact_212_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_val_option_ty,Xs: list_val,G: fun_Pr376272433ion_ty,Ys: list_P1697858023ar_val] :
      ( ( hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Xs) = hAPP_l827505693ion_ty(map_Pr1247945830ion_ty(G),Ys) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l1280603808al_nat(size_s760178257ar_val,Ys) ) ) ).

tff(fact_213_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) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l289305880ty_nat(size_s1050794909ion_ty,Ys) ) ) ).

tff(fact_214_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ty_option_ty,Xs: list_ty,G: fun_Pr199214627ion_ty,Ys: list_P249777017on_val] :
      ( ( hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Xs) = hAPP_l601126435ion_ty(map_Pr1420995486ion_ty(G),Ys) )
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l1766199206al_nat(size_s470606735on_val,Ys) ) ) ).

tff(fact_215_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ty_option_ty,Xs: list_ty,G: fun_Pr1298293016ion_ty,Ys: list_P1663965006on_val] :
      ( ( hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Xs) = hAPP_l1328999414ion_ty(map_Pr590903501ion_ty(G),Ys) )
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l1746926841al_nat(size_s60479160on_val,Ys) ) ) ).

tff(fact_216_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ty_option_ty,Xs: list_ty,G: fun_char_option_ty,Ys: list_char] :
      ( ( hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Xs) = hAPP_l863887876ion_ty(map_char_option_ty(G),Ys) )
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_list_char_nat(size_size_list_char,Ys) ) ) ).

tff(fact_217_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ty_option_ty,Xs: list_ty,G: fun_Pr1648091752ion_ty,Ys: list_P2023964830har_ty] :
      ( ( hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Xs) = hAPP_l1716957862ion_ty(map_Pr1783250717ion_ty(G),Ys) )
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys) ) ) ).

tff(fact_218_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ty_option_ty,Xs: list_ty,G: fun_Pr376272433ion_ty,Ys: list_P1697858023ar_val] :
      ( ( hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Xs) = hAPP_l827505693ion_ty(map_Pr1247945830ion_ty(G),Ys) )
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l1280603808al_nat(size_s760178257ar_val,Ys) ) ) ).

tff(fact_219_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) )
     => ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_l289305880ty_nat(size_s1050794909ion_ty,Ys) ) ) ).

tff(fact_220_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_va223928858t_char,Xs: list_val,G: fun_Pr645859204t_char,Ys: list_P249777017on_val] :
      ( ( hAPP_l732421366t_char(map_va1934808527t_char(F_1),Xs) = hAPP_l1683732356t_char(map_Pr1211171455t_char(G),Ys) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l1766199206al_nat(size_s470606735on_val,Ys) ) ) ).

tff(fact_221_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_va223928858t_char,Xs: list_val,G: fun_Pr664085497t_char,Ys: list_P1663965006on_val] :
      ( ( hAPP_l732421366t_char(map_va1934808527t_char(F_1),Xs) = hAPP_l2043127767t_char(map_Pr161410094t_char(G),Ys) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l1746926841al_nat(size_s60479160on_val,Ys) ) ) ).

tff(fact_222_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_va223928858t_char,Xs: list_val,G: fun_ch1888757611t_char,Ys: list_char] :
      ( ( hAPP_l732421366t_char(map_va1934808527t_char(F_1),Xs) = hAPP_l925187813t_char(map_ch278031520t_char(G),Ys) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_list_char_nat(size_size_list_char,Ys) ) ) ).

tff(fact_223_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_va223928858t_char,Xs: list_val,G: fun_Pr580238665t_char,Ys: list_P2023964830har_ty] :
      ( ( hAPP_l732421366t_char(map_va1934808527t_char(F_1),Xs) = hAPP_l2038191751t_char(map_Pr863062654t_char(G),Ys) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys) ) ) ).

tff(fact_224_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_va223928858t_char,Xs: list_val,G: fun_Pr176052370t_char,Ys: list_P1697858023ar_val] :
      ( ( hAPP_l732421366t_char(map_va1934808527t_char(F_1),Xs) = hAPP_l347191422t_char(map_Pr187266887t_char(G),Ys) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l1280603808al_nat(size_s760178257ar_val,Ys) ) ) ).

tff(fact_225_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) )
     => ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_l289305880ty_nat(size_s1050794909ion_ty,Ys) ) ) ).

tff(fact_226_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) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l870066319al_nat(size_s1595297126on_val,Ys) ) ) ).

tff(fact_227_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_list_char_val,Xs: list_list_char,G: fun_Pr160391123al_val,Ys: list_P249777017on_val] :
      ( ( hAPP_l1892737211st_val(map_list_char_val(F_1),Xs) = hAPP_l1342091219st_val(map_Pr1583805314al_val(G),Ys) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l1766199206al_nat(size_s470606735on_val,Ys) ) ) ).

tff(fact_228_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_list_char_val,Xs: list_list_char,G: fun_Pr1341722270al_val,Ys: list_P1663965006on_val] :
      ( ( hAPP_l1892737211st_val(map_list_char_val(F_1),Xs) = hAPP_l1023956544st_val(map_Pr1730568083al_val(G),Ys) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l1746926841al_nat(size_s60479160on_val,Ys) ) ) ).

tff(fact_229_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_list_char_val,Xs: list_list_char,G: fun_char_val,Ys: list_char] :
      ( ( hAPP_l1892737211st_val(map_list_char_val(F_1),Xs) = hAPP_l473790130st_val(map_char_val(G),Ys) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_list_char_nat(size_size_list_char,Ys) ) ) ).

tff(fact_230_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_list_char_val,Xs: list_list_char,G: fun_Pr1693821262ty_val,Ys: list_P2023964830har_ty] :
      ( ( hAPP_l1892737211st_val(map_list_char_val(F_1),Xs) = hAPP_l1473803152st_val(map_Pr961574211ty_val(G),Ys) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys) ) ) ).

tff(fact_231_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_list_char_val,Xs: list_list_char,G: fun_Pr2009941573al_val,Ys: list_P1697858023ar_val] :
      ( ( hAPP_l1892737211st_val(map_list_char_val(F_1),Xs) = hAPP_l1523427673st_val(map_Pr1022222522al_val(G),Ys) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l1280603808al_nat(size_s760178257ar_val,Ys) ) ) ).

tff(fact_232_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) )
     => ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l289305880ty_nat(size_s1050794909ion_ty,Ys) ) ) ).

tff(fact_233_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1149393094ar_val,Xs: list_P2023964830har_ty,G: fun_Pr276820555ar_val,Ys: list_P249777017on_val] :
      ( ( hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),Xs) = hAPP_l102711883ar_val(map_Pr1591425018ar_val(G),Ys) )
     => ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) = hAPP_l1766199206al_nat(size_s470606735on_val,Ys) ) ) ).

tff(fact_234_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1149393094ar_val,Xs: list_P2023964830har_ty,G: fun_Pr971959830ar_val,Ys: list_P1663965006on_val] :
      ( ( hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),Xs) = hAPP_l2147361720ar_val(map_Pr618945291ar_val(G),Ys) )
     => ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) = hAPP_l1746926841al_nat(size_s60479160on_val,Ys) ) ) ).

tff(fact_235_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1149393094ar_val,Xs: list_P2023964830har_ty,G: fun_ch2033169700ar_val,Ys: list_char] :
      ( ( hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),Xs) = hAPP_l606396970ar_val(map_ch1589830937ar_val(G),Ys) )
     => ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) = hAPP_list_char_nat(size_size_list_char,Ys) ) ) ).

tff(fact_236_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1149393094ar_val,Xs: list_P2023964830har_ty,G: fun_Pr2023323325ar_val,Ys: list_P1697858023ar_val] :
      ( ( hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),Xs) = hAPP_l1462265297ar_val(map_Pr879013170ar_val(G),Ys) )
     => ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) = hAPP_l1280603808al_nat(size_s760178257ar_val,Ys) ) ) ).

tff(fact_237_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1149393094ar_val,Xs: list_P2023964830har_ty,G: fun_op1549449661ar_val,Ys: list_option_ty] :
      ( ( hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),Xs) = hAPP_l278271321ar_val(map_op1852210284ar_val(G),Ys) )
     => ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) = hAPP_l289305880ty_nat(size_s1050794909ion_ty,Ys) ) ) ).

tff(fact_238_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr199214627ion_ty,Xs: list_P249777017on_val,G: fun_val_option_ty,Ys: list_val] :
      ( ( hAPP_l601126435ion_ty(map_Pr1420995486ion_ty(F_1),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys) )
     => ( hAPP_l1766199206al_nat(size_s470606735on_val,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_239_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1298293016ion_ty,Xs: list_P1663965006on_val,G: fun_val_option_ty,Ys: list_val] :
      ( ( hAPP_l1328999414ion_ty(map_Pr590903501ion_ty(F_1),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys) )
     => ( hAPP_l1746926841al_nat(size_s60479160on_val,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_240_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_char_option_ty,Xs: list_char,G: fun_val_option_ty,Ys: list_val] :
      ( ( hAPP_l863887876ion_ty(map_char_option_ty(F_1),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys) )
     => ( hAPP_list_char_nat(size_size_list_char,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_241_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1648091752ion_ty,Xs: list_P2023964830har_ty,G: fun_val_option_ty,Ys: list_val] :
      ( ( hAPP_l1716957862ion_ty(map_Pr1783250717ion_ty(F_1),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys) )
     => ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_242_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr376272433ion_ty,Xs: list_P1697858023ar_val,G: fun_val_option_ty,Ys: list_val] :
      ( ( hAPP_l827505693ion_ty(map_Pr1247945830ion_ty(F_1),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys) )
     => ( hAPP_l1280603808al_nat(size_s760178257ar_val,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_243_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) )
     => ( hAPP_l289305880ty_nat(size_s1050794909ion_ty,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_244_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr199214627ion_ty,Xs: list_P249777017on_val,G: fun_ty_option_ty,Ys: list_ty] :
      ( ( hAPP_l601126435ion_ty(map_Pr1420995486ion_ty(F_1),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys) )
     => ( hAPP_l1766199206al_nat(size_s470606735on_val,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_245_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1298293016ion_ty,Xs: list_P1663965006on_val,G: fun_ty_option_ty,Ys: list_ty] :
      ( ( hAPP_l1328999414ion_ty(map_Pr590903501ion_ty(F_1),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys) )
     => ( hAPP_l1746926841al_nat(size_s60479160on_val,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_246_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_char_option_ty,Xs: list_char,G: fun_ty_option_ty,Ys: list_ty] :
      ( ( hAPP_l863887876ion_ty(map_char_option_ty(F_1),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys) )
     => ( hAPP_list_char_nat(size_size_list_char,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_247_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1648091752ion_ty,Xs: list_P2023964830har_ty,G: fun_ty_option_ty,Ys: list_ty] :
      ( ( hAPP_l1716957862ion_ty(map_Pr1783250717ion_ty(F_1),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys) )
     => ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_248_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr376272433ion_ty,Xs: list_P1697858023ar_val,G: fun_ty_option_ty,Ys: list_ty] :
      ( ( hAPP_l827505693ion_ty(map_Pr1247945830ion_ty(F_1),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys) )
     => ( hAPP_l1280603808al_nat(size_s760178257ar_val,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_249_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) )
     => ( hAPP_l289305880ty_nat(size_s1050794909ion_ty,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) ) ).

tff(fact_250_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr645859204t_char,Xs: list_P249777017on_val,G: fun_va223928858t_char,Ys: list_val] :
      ( ( hAPP_l1683732356t_char(map_Pr1211171455t_char(F_1),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Ys) )
     => ( hAPP_l1766199206al_nat(size_s470606735on_val,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_251_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr664085497t_char,Xs: list_P1663965006on_val,G: fun_va223928858t_char,Ys: list_val] :
      ( ( hAPP_l2043127767t_char(map_Pr161410094t_char(F_1),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Ys) )
     => ( hAPP_l1746926841al_nat(size_s60479160on_val,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_252_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ch1888757611t_char,Xs: list_char,G: fun_va223928858t_char,Ys: list_val] :
      ( ( hAPP_l925187813t_char(map_ch278031520t_char(F_1),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Ys) )
     => ( hAPP_list_char_nat(size_size_list_char,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_253_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr580238665t_char,Xs: list_P2023964830har_ty,G: fun_va223928858t_char,Ys: list_val] :
      ( ( hAPP_l2038191751t_char(map_Pr863062654t_char(F_1),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Ys) )
     => ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_254_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr176052370t_char,Xs: list_P1697858023ar_val,G: fun_va223928858t_char,Ys: list_val] :
      ( ( hAPP_l347191422t_char(map_Pr187266887t_char(F_1),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Ys) )
     => ( hAPP_l1280603808al_nat(size_s760178257ar_val,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_255_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) )
     => ( hAPP_l289305880ty_nat(size_s1050794909ion_ty,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) ) ).

tff(fact_256_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) )
     => ( hAPP_l870066319al_nat(size_s1595297126on_val,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_257_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr160391123al_val,Xs: list_P249777017on_val,G: fun_list_char_val,Ys: list_list_char] :
      ( ( hAPP_l1342091219st_val(map_Pr1583805314al_val(F_1),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Ys) )
     => ( hAPP_l1766199206al_nat(size_s470606735on_val,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_258_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1341722270al_val,Xs: list_P1663965006on_val,G: fun_list_char_val,Ys: list_list_char] :
      ( ( hAPP_l1023956544st_val(map_Pr1730568083al_val(F_1),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Ys) )
     => ( hAPP_l1746926841al_nat(size_s60479160on_val,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_259_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_char_val,Xs: list_char,G: fun_list_char_val,Ys: list_list_char] :
      ( ( hAPP_l473790130st_val(map_char_val(F_1),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Ys) )
     => ( hAPP_list_char_nat(size_size_list_char,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_260_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1693821262ty_val,Xs: list_P2023964830har_ty,G: fun_list_char_val,Ys: list_list_char] :
      ( ( hAPP_l1473803152st_val(map_Pr961574211ty_val(F_1),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Ys) )
     => ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_261_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr2009941573al_val,Xs: list_P1697858023ar_val,G: fun_list_char_val,Ys: list_list_char] :
      ( ( hAPP_l1523427673st_val(map_Pr1022222522al_val(F_1),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Ys) )
     => ( hAPP_l1280603808al_nat(size_s760178257ar_val,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_262_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) )
     => ( hAPP_l289305880ty_nat(size_s1050794909ion_ty,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) ) ).

tff(fact_263_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr276820555ar_val,Xs: list_P249777017on_val,G: fun_Pr1149393094ar_val,Ys: list_P2023964830har_ty] :
      ( ( hAPP_l102711883ar_val(map_Pr1591425018ar_val(F_1),Xs) = hAPP_l608137480ar_val(map_Pr1153581243ar_val(G),Ys) )
     => ( hAPP_l1766199206al_nat(size_s470606735on_val,Xs) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys) ) ) ).

tff(fact_264_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr971959830ar_val,Xs: list_P1663965006on_val,G: fun_Pr1149393094ar_val,Ys: list_P2023964830har_ty] :
      ( ( hAPP_l2147361720ar_val(map_Pr618945291ar_val(F_1),Xs) = hAPP_l608137480ar_val(map_Pr1153581243ar_val(G),Ys) )
     => ( hAPP_l1746926841al_nat(size_s60479160on_val,Xs) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys) ) ) ).

tff(fact_265_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_ch2033169700ar_val,Xs: list_char,G: fun_Pr1149393094ar_val,Ys: list_P2023964830har_ty] :
      ( ( hAPP_l606396970ar_val(map_ch1589830937ar_val(F_1),Xs) = hAPP_l608137480ar_val(map_Pr1153581243ar_val(G),Ys) )
     => ( hAPP_list_char_nat(size_size_list_char,Xs) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys) ) ) ).

tff(fact_266_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr1149393094ar_val,Xs: list_P2023964830har_ty,G: fun_Pr1149393094ar_val,Ys: list_P2023964830har_ty] :
      ( ( hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),Xs) = hAPP_l608137480ar_val(map_Pr1153581243ar_val(G),Ys) )
     => ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys) ) ) ).

tff(fact_267_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_Pr2023323325ar_val,Xs: list_P1697858023ar_val,G: fun_Pr1149393094ar_val,Ys: list_P2023964830har_ty] :
      ( ( hAPP_l1462265297ar_val(map_Pr879013170ar_val(F_1),Xs) = hAPP_l608137480ar_val(map_Pr1153581243ar_val(G),Ys) )
     => ( hAPP_l1280603808al_nat(size_s760178257ar_val,Xs) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys) ) ) ).

tff(fact_268_map__eq__imp__length__eq,axiom,
    ! [F_1: fun_op1549449661ar_val,Xs: list_option_ty,G: fun_Pr1149393094ar_val,Ys: list_P2023964830har_ty] :
      ( ( hAPP_l278271321ar_val(map_op1852210284ar_val(F_1),Xs) = hAPP_l608137480ar_val(map_Pr1153581243ar_val(G),Ys) )
     => ( hAPP_l289305880ty_nat(size_s1050794909ion_ty,Xs) = hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys) ) ) ).

tff(fact_269_prod__induct5,axiom,
    ! [X_2: produc349695911t_char,Pa: fun_Pr1895638121r_bool] :
      ( ! [A_2: produc1285161482t_char,B_1: list_list_char,C_4: list_ty,D_2: list_val,E_7: exp_list_char] : hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_2),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,C_4),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,D_2),E_7))))))
     => hBOOL(hAPP_P824029447r_bool(Pa,X_2)) ) ).

tff(fact_270_prod__induct5,axiom,
    ! [X_2: produc1466422861on_val,Pa: fun_Pr302334223l_bool] :
      ( ! [A_2: produc430140671on_val,B_1: produc2061676504on_val,C_4: list_exp_list_char,D_2: fun_na939144002on_val,E_7: fun_li1432931796on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_2),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,C_4),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,D_2),E_7))))))
     => hBOOL(hAPP_P2028072621l_bool(Pa,X_2)) ) ).

tff(fact_271_prod__induct5,axiom,
    ! [X_2: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
      ( ! [A_2: produc1102272487on_val,B_1: produc124828825on_val,C_4: exp_list_char,D_2: fun_na939144002on_val,E_7: fun_li1432931796on_val] : hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_2),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_4),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,D_2),E_7))))))
     => hBOOL(hAPP_P378063101l_bool(Pa,X_2)) ) ).

tff(fact_272_prod__cases5,axiom,
    ! [Y_6: produc349695911t_char] :
      ~ ! [A_2: produc1285161482t_char,B_1: list_list_char,C_4: list_ty,D_2: list_val,E_7: exp_list_char] : Y_6 != hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_2),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,C_4),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,D_2),E_7)))) ).

tff(fact_273_prod__cases5,axiom,
    ! [Y_1: produc1466422861on_val] :
      ~ ! [A_2: produc430140671on_val,B_1: produc2061676504on_val,C_4: list_exp_list_char,D_2: fun_na939144002on_val,E_7: fun_li1432931796on_val] : Y_1 != hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_2),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,C_4),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,D_2),E_7)))) ).

tff(fact_274_prod__cases5,axiom,
    ! [Y_1: produc231486621on_val] :
      ~ ! [A_2: produc1102272487on_val,B_1: produc124828825on_val,C_4: exp_list_char,D_2: fun_na939144002on_val,E_7: fun_li1432931796on_val] : Y_1 != hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_2),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_4),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,D_2),E_7)))) ).

tff(fact_275_prod__induct4,axiom,
    ! [X_2: produc1285161482t_char,Pa: fun_Pr227936640r_bool] :
      ( ! [A_2: list_list_char,B_1: list_ty,C_4: list_val,D_2: exp_list_char] : hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_2),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,C_4),D_2)))))
     => hBOOL(hAPP_P92196306r_bool(Pa,X_2)) ) ).

tff(fact_276_prod__induct4,axiom,
    ! [X_2: produc1102272487on_val,Pa: fun_Pr691271849l_bool] :
      ( ! [A_2: produc124828825on_val,B_1: exp_list_char,C_4: fun_na939144002on_val,D_2: fun_li1432931796on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_2),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_4),D_2)))))
     => hBOOL(hAPP_P282169671l_bool(Pa,X_2)) ) ).

tff(fact_277_prod__induct4,axiom,
    ! [X_2: produc430140671on_val,Pa: fun_Pr859510977l_bool] :
      ( ! [A_2: produc2061676504on_val,B_1: list_exp_list_char,C_4: fun_na939144002on_val,D_2: fun_li1432931796on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_2),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,B_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_4),D_2)))))
     => hBOOL(hAPP_P1333315679l_bool(Pa,X_2)) ) ).

tff(fact_278_prod__induct4,axiom,
    ! [X_2: produc349695911t_char,Pa: fun_Pr1895638121r_bool] :
      ( ! [A_2: produc1285161482t_char,B_1: list_list_char,C_4: list_ty,D_2: produc662261637t_char] : hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_2),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,C_4),D_2)))))
     => hBOOL(hAPP_P824029447r_bool(Pa,X_2)) ) ).

tff(fact_279_prod__induct4,axiom,
    ! [X_2: produc1406897475t_char,Pa: fun_Pr1728267013r_bool] :
      ( ! [A_2: produc220283002t_char,B_1: list_ty,C_4: list_val,D_2: exp_list_char] : hBOOL(hAPP_P1240100515r_bool(Pa,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_2),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,C_4),D_2)))))
     => hBOOL(hAPP_P1240100515r_bool(Pa,X_2)) ) ).

tff(fact_280_prod__induct4,axiom,
    ! [X_2: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
      ( ! [A_2: produc1102272487on_val,B_1: produc124828825on_val,C_4: exp_list_char,D_2: produc12694297on_val] : hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_2),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_4),D_2)))))
     => hBOOL(hAPP_P378063101l_bool(Pa,X_2)) ) ).

tff(fact_281_prod__induct4,axiom,
    ! [X_2: produc1466422861on_val,Pa: fun_Pr302334223l_bool] :
      ( ! [A_2: produc430140671on_val,B_1: produc2061676504on_val,C_4: list_exp_list_char,D_2: produc12694297on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_2),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,C_4),D_2)))))
     => hBOOL(hAPP_P2028072621l_bool(Pa,X_2)) ) ).

tff(fact_282_prod__induct4,axiom,
    ! [X_2: produc630464863al_val,Pa: fun_Pr897334561l_bool] :
      ( ! [A_2: produc1645268488al_val,B_1: bop,C_4: val,D_2: val] : hBOOL(hAPP_P738987199l_bool(Pa,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_2),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,B_1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,C_4),D_2)))))
     => hBOOL(hAPP_P738987199l_bool(Pa,X_2)) ) ).

tff(fact_283_prod__cases4,axiom,
    ! [Y_5: produc1285161482t_char] :
      ~ ! [A_2: list_list_char,B_1: list_ty,C_4: list_val,D_2: exp_list_char] : Y_5 != hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_2),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,C_4),D_2))) ).

tff(fact_284_prod__cases4,axiom,
    ! [Y_1: produc1102272487on_val] :
      ~ ! [A_2: produc124828825on_val,B_1: exp_list_char,C_4: fun_na939144002on_val,D_2: fun_li1432931796on_val] : Y_1 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_2),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_4),D_2))) ).

tff(fact_285_prod__cases4,axiom,
    ! [Y_1: produc430140671on_val] :
      ~ ! [A_2: produc2061676504on_val,B_1: list_exp_list_char,C_4: fun_na939144002on_val,D_2: fun_li1432931796on_val] : Y_1 != hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_2),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,B_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_4),D_2))) ).

tff(fact_286_prod__cases4,axiom,
    ! [Y_5: produc349695911t_char] :
      ~ ! [A_2: produc1285161482t_char,B_1: list_list_char,C_4: list_ty,D_2: produc662261637t_char] : Y_5 != hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_2),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,C_4),D_2))) ).

tff(fact_287_prod__cases4,axiom,
    ! [Y_5: produc1406897475t_char] :
      ~ ! [A_2: produc220283002t_char,B_1: list_ty,C_4: list_val,D_2: exp_list_char] : Y_5 != hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_2),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,C_4),D_2))) ).

tff(fact_288_prod__cases4,axiom,
    ! [Y_1: produc231486621on_val] :
      ~ ! [A_2: produc1102272487on_val,B_1: produc124828825on_val,C_4: exp_list_char,D_2: produc12694297on_val] : Y_1 != hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_2),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_4),D_2))) ).

tff(fact_289_prod__cases4,axiom,
    ! [Y_1: produc1466422861on_val] :
      ~ ! [A_2: produc430140671on_val,B_1: produc2061676504on_val,C_4: list_exp_list_char,D_2: produc12694297on_val] : Y_1 != hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_2),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,C_4),D_2))) ).

tff(fact_290_prod__cases4,axiom,
    ! [Y_5: produc630464863al_val] :
      ~ ! [A_2: produc1645268488al_val,B_1: bop,C_4: val,D_2: val] : Y_5 != hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_2),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,B_1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,C_4),D_2))) ).

tff(fact_291_Pair__inject,axiom,
    ! [A_18: list_char,B_4: produc917948472har_ty,A_17: list_char,B_3: produc917948472har_ty] :
      ( ( hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,A_18),B_4) = hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_292_Pair__inject,axiom,
    ! [A_18: produc1278157519t_char,B_4: ty,A_17: produc1278157519t_char,B_3: ty] :
      ( ( hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_18),B_4) = hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_293_Pair__inject,axiom,
    ! [A_18: list_char,B_4: ty,A_17: list_char,B_3: ty] :
      ( ( hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_18),B_4) = hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_294_Pair__inject,axiom,
    ! [A_18: list_list_char,B_4: list_list_char,A_17: list_list_char,B_3: list_list_char] :
      ( ( hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A_18),B_4) = hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_295_Pair__inject,axiom,
    ! [A_1: list_P249777017on_val,B: list_P249777017on_val,A_8: list_P249777017on_val,B_2: list_P249777017on_val] :
      ( ( hAPP_l1701465547on_val(hAPP_l1588290397on_val(produc493060183on_val,A_1),B) = hAPP_l1701465547on_val(hAPP_l1588290397on_val(produc493060183on_val,A_8),B_2) )
     => ~ ( ( A_1 = A_8 )
         => ( B != B_2 ) ) ) ).

tff(fact_296_Pair__inject,axiom,
    ! [A_1: list_P1663965006on_val,B: list_P1663965006on_val,A_8: list_P1663965006on_val,B_2: list_P1663965006on_val] :
      ( ( hAPP_l1485560508on_val(hAPP_l1324137613on_val(produc584381409on_val,A_1),B) = hAPP_l1485560508on_val(hAPP_l1324137613on_val(produc584381409on_val,A_8),B_2) )
     => ~ ( ( A_1 = A_8 )
         => ( B != B_2 ) ) ) ).

tff(fact_297_Pair__inject,axiom,
    ! [A_18: char,B_4: char,A_17: char,B_3: char] :
      ( ( hAPP_c802977373r_char(hAPP_c1242523777r_char(produc601902295r_char,A_18),B_4) = hAPP_c802977373r_char(hAPP_c1242523777r_char(produc601902295r_char,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_298_Pair__inject,axiom,
    ! [A_18: list_val,B_4: list_val,A_17: list_val,B_3: list_val] :
      ( ( hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,A_18),B_4) = hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_299_Pair__inject,axiom,
    ! [A_18: list_ty,B_4: list_ty,A_17: list_ty,B_3: list_ty] :
      ( ( hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,A_18),B_4) = hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_300_Pair__inject,axiom,
    ! [A_18: ty,B_4: ty,A_17: ty,B_3: ty] :
      ( ( hAPP_t65172803_ty_ty(hAPP_t1494094285_ty_ty(product_Pair_ty_ty,A_18),B_4) = hAPP_t65172803_ty_ty(hAPP_t1494094285_ty_ty(product_Pair_ty_ty,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_301_Pair__inject,axiom,
    ! [A_18: list_exp_list_char,B_4: list_exp_list_char,A_17: list_exp_list_char,B_3: list_exp_list_char] :
      ( ( hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,A_18),B_4) = hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_302_Pair__inject,axiom,
    ! [A_18: exp_list_char,B_4: exp_list_char,A_17: exp_list_char,B_3: exp_list_char] :
      ( ( hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,A_18),B_4) = hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_303_Pair__inject,axiom,
    ! [A_18: produc1147203250ar_val,B_4: produc1147203250ar_val,A_17: produc1147203250ar_val,B_3: produc1147203250ar_val] :
      ( ( hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,A_18),B_4) = hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_304_Pair__inject,axiom,
    ! [A_18: produc809539159t_char,B_4: produc809539159t_char,A_17: produc809539159t_char,B_3: produc809539159t_char] :
      ( ( hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_18),B_4) = hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_305_Pair__inject,axiom,
    ! [A_18: produc1278157519t_char,B_4: produc1278157519t_char,A_17: produc1278157519t_char,B_3: produc1278157519t_char] :
      ( ( hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_18),B_4) = hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_306_Pair__inject,axiom,
    ! [A_18: product_prod_val_val,B_4: product_prod_val_val,A_17: product_prod_val_val,B_3: product_prod_val_val] :
      ( ( hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_18),B_4) = hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_307_Pair__inject,axiom,
    ! [A_18: produc1645268488al_val,B_4: produc1645268488al_val,A_17: produc1645268488al_val,B_3: produc1645268488al_val] :
      ( ( hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_18),B_4) = hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_308_Pair__inject,axiom,
    ! [A_1: produc430140671on_val,B: produc430140671on_val,A_8: produc430140671on_val,B_2: produc430140671on_val] :
      ( ( hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),B) = hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_8),B_2) )
     => ~ ( ( A_1 = A_8 )
         => ( B != B_2 ) ) ) ).

tff(fact_309_Pair__inject,axiom,
    ! [A_1: produc639455274on_val,B: produc639455274on_val,A_8: produc639455274on_val,B_2: produc639455274on_val] :
      ( ( hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_1),B) = hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_8),B_2) )
     => ~ ( ( A_1 = A_8 )
         => ( B != B_2 ) ) ) ).

tff(fact_310_Pair__inject,axiom,
    ! [A_1: produc1102272487on_val,B: produc1102272487on_val,A_8: produc1102272487on_val,B_2: produc1102272487on_val] :
      ( ( hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),B) = hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_8),B_2) )
     => ~ ( ( A_1 = A_8 )
         => ( B != B_2 ) ) ) ).

tff(fact_311_Pair__inject,axiom,
    ! [A_1: produc12694297on_val,B: produc12694297on_val,A_8: produc12694297on_val,B_2: produc12694297on_val] :
      ( ( hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_1),B) = hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_8),B_2) )
     => ~ ( ( A_1 = A_8 )
         => ( B != B_2 ) ) ) ).

tff(fact_312_Pair__inject,axiom,
    ! [A_18: produc662261637t_char,B_4: produc662261637t_char,A_17: produc662261637t_char,B_3: produc662261637t_char] :
      ( ( hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_18),B_4) = hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_313_Pair__inject,axiom,
    ! [A_18: produc220283002t_char,B_4: produc220283002t_char,A_17: produc220283002t_char,B_3: produc220283002t_char] :
      ( ( hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_18),B_4) = hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_314_Pair__inject,axiom,
    ! [A_18: produc1285161482t_char,B_4: produc1285161482t_char,A_17: produc1285161482t_char,B_3: produc1285161482t_char] :
      ( ( hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_18),B_4) = hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_315_Pair__inject,axiom,
    ! [A_18: list_list_char,B_4: produc220283002t_char,A_17: list_list_char,B_3: produc220283002t_char] :
      ( ( hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_18),B_4) = hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_316_Pair__inject,axiom,
    ! [A_18: list_ty,B_4: produc662261637t_char,A_17: list_ty,B_3: produc662261637t_char] :
      ( ( hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_18),B_4) = hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_317_Pair__inject,axiom,
    ! [A_18: list_val,B_4: exp_list_char,A_17: list_val,B_3: exp_list_char] :
      ( ( hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_18),B_4) = hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_318_Pair__inject,axiom,
    ! [A_1: fun_na939144002on_val,B: fun_li1432931796on_val,A_8: fun_na939144002on_val,B_2: fun_li1432931796on_val] :
      ( ( hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B) = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_8),B_2) )
     => ~ ( ( A_1 = A_8 )
         => ( B != B_2 ) ) ) ).

tff(fact_319_Pair__inject,axiom,
    ! [A_1: produc124828825on_val,B: produc124828825on_val,A_8: produc124828825on_val,B_2: produc124828825on_val] :
      ( ( hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B) = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_8),B_2) )
     => ~ ( ( A_1 = A_8 )
         => ( B != B_2 ) ) ) ).

tff(fact_320_Pair__inject,axiom,
    ! [A_1: exp_list_char,B: produc12694297on_val,A_8: exp_list_char,B_2: produc12694297on_val] :
      ( ( hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B) = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_8),B_2) )
     => ~ ( ( A_1 = A_8 )
         => ( B != B_2 ) ) ) ).

tff(fact_321_Pair__inject,axiom,
    ! [A_1: list_char,B: fun_Pr806764899on_val,A_8: list_char,B_2: fun_Pr806764899on_val] :
      ( ( hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B) = hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_8),B_2) )
     => ~ ( ( A_1 = A_8 )
         => ( B != B_2 ) ) ) ).

tff(fact_322_Pair__inject,axiom,
    ! [A_1: produc2061676504on_val,B: produc2061676504on_val,A_8: produc2061676504on_val,B_2: produc2061676504on_val] :
      ( ( hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B) = hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_8),B_2) )
     => ~ ( ( A_1 = A_8 )
         => ( B != B_2 ) ) ) ).

tff(fact_323_Pair__inject,axiom,
    ! [A_1: list_exp_list_char,B: produc12694297on_val,A_8: list_exp_list_char,B_2: produc12694297on_val] :
      ( ( hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B) = hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_8),B_2) )
     => ~ ( ( A_1 = A_8 )
         => ( B != B_2 ) ) ) ).

tff(fact_324_Pair__inject,axiom,
    ! [A_18: bop,B_4: product_prod_val_val,A_17: bop,B_3: product_prod_val_val] :
      ( ( hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_18),B_4) = hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_325_Pair__inject,axiom,
    ! [A_18: val,B_4: val,A_17: val,B_3: val] :
      ( ( hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_18),B_4) = hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_326_Pair__inject,axiom,
    ! [A_18: list_char,B_4: list_char,A_17: list_char,B_3: list_char] :
      ( ( hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_18),B_4) = hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_327_Pair__inject,axiom,
    ! [A_18: list_list_char,B_4: exp_list_char,A_17: list_list_char,B_3: exp_list_char] :
      ( ( hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_18),B_4) = hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_328_Pair__inject,axiom,
    ! [A_18: produc1278157519t_char,B_4: val,A_17: produc1278157519t_char,B_3: val] :
      ( ( hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_18),B_4) = hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_17),B_3) )
     => ~ ( ( A_18 = A_17 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_329_Pair__eq,axiom,
    ! [A_1: list_char,B: produc917948472har_ty,A_8: list_char,B_2: produc917948472har_ty] :
      ( ( hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,A_1),B) = hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_330_Pair__eq,axiom,
    ! [A_1: produc1278157519t_char,B: ty,A_8: produc1278157519t_char,B_2: ty] :
      ( ( hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_1),B) = hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_331_Pair__eq,axiom,
    ! [A_1: list_char,B: ty,A_8: list_char,B_2: ty] :
      ( ( hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_1),B) = hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_332_Pair__eq,axiom,
    ! [A_1: list_list_char,B: list_list_char,A_8: list_list_char,B_2: list_list_char] :
      ( ( hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A_1),B) = hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_333_Pair__eq,axiom,
    ! [A_1: list_P249777017on_val,B: list_P249777017on_val,A_8: list_P249777017on_val,B_2: list_P249777017on_val] :
      ( ( hAPP_l1701465547on_val(hAPP_l1588290397on_val(produc493060183on_val,A_1),B) = hAPP_l1701465547on_val(hAPP_l1588290397on_val(produc493060183on_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_334_Pair__eq,axiom,
    ! [A_1: list_P1663965006on_val,B: list_P1663965006on_val,A_8: list_P1663965006on_val,B_2: list_P1663965006on_val] :
      ( ( hAPP_l1485560508on_val(hAPP_l1324137613on_val(produc584381409on_val,A_1),B) = hAPP_l1485560508on_val(hAPP_l1324137613on_val(produc584381409on_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_335_Pair__eq,axiom,
    ! [A_1: char,B: char,A_8: char,B_2: char] :
      ( ( hAPP_c802977373r_char(hAPP_c1242523777r_char(produc601902295r_char,A_1),B) = hAPP_c802977373r_char(hAPP_c1242523777r_char(produc601902295r_char,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_336_Pair__eq,axiom,
    ! [A_1: list_val,B: list_val,A_8: list_val,B_2: list_val] :
      ( ( hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,A_1),B) = hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_337_Pair__eq,axiom,
    ! [A_1: list_ty,B: list_ty,A_8: list_ty,B_2: list_ty] :
      ( ( hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,A_1),B) = hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_338_Pair__eq,axiom,
    ! [A_1: ty,B: ty,A_8: ty,B_2: ty] :
      ( ( hAPP_t65172803_ty_ty(hAPP_t1494094285_ty_ty(product_Pair_ty_ty,A_1),B) = hAPP_t65172803_ty_ty(hAPP_t1494094285_ty_ty(product_Pair_ty_ty,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_339_Pair__eq,axiom,
    ! [A_1: list_exp_list_char,B: list_exp_list_char,A_8: list_exp_list_char,B_2: list_exp_list_char] :
      ( ( hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,A_1),B) = hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_340_Pair__eq,axiom,
    ! [A_1: exp_list_char,B: exp_list_char,A_8: exp_list_char,B_2: exp_list_char] :
      ( ( hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,A_1),B) = hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_341_Pair__eq,axiom,
    ! [A_1: produc1147203250ar_val,B: produc1147203250ar_val,A_8: produc1147203250ar_val,B_2: produc1147203250ar_val] :
      ( ( hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,A_1),B) = hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_342_Pair__eq,axiom,
    ! [A_1: produc809539159t_char,B: produc809539159t_char,A_8: produc809539159t_char,B_2: produc809539159t_char] :
      ( ( hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_1),B) = hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_343_Pair__eq,axiom,
    ! [A_1: produc1278157519t_char,B: produc1278157519t_char,A_8: produc1278157519t_char,B_2: produc1278157519t_char] :
      ( ( hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_1),B) = hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_344_Pair__eq,axiom,
    ! [A_1: product_prod_val_val,B: product_prod_val_val,A_8: product_prod_val_val,B_2: product_prod_val_val] :
      ( ( hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_1),B) = hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_345_Pair__eq,axiom,
    ! [A_1: produc1645268488al_val,B: produc1645268488al_val,A_8: produc1645268488al_val,B_2: produc1645268488al_val] :
      ( ( hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_1),B) = hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_346_Pair__eq,axiom,
    ! [A_1: produc430140671on_val,B: produc430140671on_val,A_8: produc430140671on_val,B_2: produc430140671on_val] :
      ( ( hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),B) = hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_347_Pair__eq,axiom,
    ! [A_1: produc639455274on_val,B: produc639455274on_val,A_8: produc639455274on_val,B_2: produc639455274on_val] :
      ( ( hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_1),B) = hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_348_Pair__eq,axiom,
    ! [A_1: produc1102272487on_val,B: produc1102272487on_val,A_8: produc1102272487on_val,B_2: produc1102272487on_val] :
      ( ( hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),B) = hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_349_Pair__eq,axiom,
    ! [A_1: produc12694297on_val,B: produc12694297on_val,A_8: produc12694297on_val,B_2: produc12694297on_val] :
      ( ( hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_1),B) = hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_350_Pair__eq,axiom,
    ! [A_1: produc662261637t_char,B: produc662261637t_char,A_8: produc662261637t_char,B_2: produc662261637t_char] :
      ( ( hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_1),B) = hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_351_Pair__eq,axiom,
    ! [A_1: produc220283002t_char,B: produc220283002t_char,A_8: produc220283002t_char,B_2: produc220283002t_char] :
      ( ( hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_1),B) = hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_352_Pair__eq,axiom,
    ! [A_1: produc1285161482t_char,B: produc1285161482t_char,A_8: produc1285161482t_char,B_2: produc1285161482t_char] :
      ( ( hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),B) = hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_353_Pair__eq,axiom,
    ! [A_1: list_list_char,B: produc220283002t_char,A_8: list_list_char,B_2: produc220283002t_char] :
      ( ( hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B) = hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_354_Pair__eq,axiom,
    ! [A_1: list_ty,B: produc662261637t_char,A_8: list_ty,B_2: produc662261637t_char] :
      ( ( hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B) = hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_355_Pair__eq,axiom,
    ! [A_1: list_val,B: exp_list_char,A_8: list_val,B_2: exp_list_char] :
      ( ( hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B) = hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_356_Pair__eq,axiom,
    ! [A_1: fun_na939144002on_val,B: fun_li1432931796on_val,A_8: fun_na939144002on_val,B_2: fun_li1432931796on_val] :
      ( ( hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B) = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_357_Pair__eq,axiom,
    ! [A_1: produc124828825on_val,B: produc124828825on_val,A_8: produc124828825on_val,B_2: produc124828825on_val] :
      ( ( hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B) = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_358_Pair__eq,axiom,
    ! [A_1: exp_list_char,B: produc12694297on_val,A_8: exp_list_char,B_2: produc12694297on_val] :
      ( ( hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B) = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_359_Pair__eq,axiom,
    ! [A_1: list_char,B: fun_Pr806764899on_val,A_8: list_char,B_2: fun_Pr806764899on_val] :
      ( ( hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B) = hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_360_Pair__eq,axiom,
    ! [A_1: produc2061676504on_val,B: produc2061676504on_val,A_8: produc2061676504on_val,B_2: produc2061676504on_val] :
      ( ( hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B) = hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_361_Pair__eq,axiom,
    ! [A_1: list_exp_list_char,B: produc12694297on_val,A_8: list_exp_list_char,B_2: produc12694297on_val] :
      ( ( hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B) = hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_362_Pair__eq,axiom,
    ! [A_1: bop,B: product_prod_val_val,A_8: bop,B_2: product_prod_val_val] :
      ( ( hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B) = hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_363_Pair__eq,axiom,
    ! [A_1: val,B: val,A_8: val,B_2: val] :
      ( ( hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B) = hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_364_Pair__eq,axiom,
    ! [A_1: list_char,B: list_char,A_8: list_char,B_2: list_char] :
      ( ( hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B) = hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_365_Pair__eq,axiom,
    ! [A_1: list_list_char,B: exp_list_char,A_8: list_list_char,B_2: exp_list_char] :
      ( ( hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B) = hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_366_Pair__eq,axiom,
    ! [A_1: produc1278157519t_char,B: val,A_8: produc1278157519t_char,B_2: val] :
      ( ( hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_1),B) = hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_8),B_2) )
    <=> ( ( A_1 = A_8 )
        & ( B = B_2 ) ) ) ).

tff(fact_367_split__paired__All,axiom,
    ! [Pa: fun_Pr758558581y_bool] :
      ( ! [X1: produc469582463har_ty] : hBOOL(hAPP_P831231943y_bool(Pa,X1))
    <=> ! [A_2: list_char,B_1: produc917948472har_ty] : hBOOL(hAPP_P831231943y_bool(Pa,hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,A_2),B_1))) ) ).

tff(fact_368_split__paired__All,axiom,
    ! [Pa: fun_Pr2102567903y_bool] :
      ( ! [X1: produc245756905har_ty] : hBOOL(hAPP_P27757617y_bool(Pa,X1))
    <=> ! [A_2: produc1278157519t_char,B_1: ty] : hBOOL(hAPP_P27757617y_bool(Pa,hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_2),B_1))) ) ).

tff(fact_369_split__paired__All,axiom,
    ! [Pa: fun_Pr1127025070y_bool] :
      ( ! [X1: produc917948472har_ty] : hBOOL(hAPP_P748443392y_bool(Pa,X1))
    <=> ! [A_2: list_char,B_1: ty] : hBOOL(hAPP_P748443392y_bool(Pa,hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_2),B_1))) ) ).

tff(fact_370_split__paired__All,axiom,
    ! [Pa: fun_Pr382120745r_bool] :
      ( ! [X1: produc1200003175t_char] : hBOOL(hAPP_P476431815r_bool(Pa,X1))
    <=> ! [A_2: list_list_char,B_1: list_list_char] : hBOOL(hAPP_P476431815r_bool(Pa,hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A_2),B_1))) ) ).

tff(fact_371_split__paired__All,axiom,
    ! [Pa: fun_Pr872262185l_bool] :
      ( ! [X1: produc143547239on_val] : hBOOL(hAPP_P1821438151l_bool(Pa,X1))
    <=> ! [A_2: list_P249777017on_val,B_1: list_P249777017on_val] : hBOOL(hAPP_P1821438151l_bool(Pa,hAPP_l1701465547on_val(hAPP_l1588290397on_val(produc493060183on_val,A_2),B_1))) ) ).

tff(fact_372_split__paired__All,axiom,
    ! [Pa: fun_Pr564925613l_bool] :
      ( ! [X1: produc1497648875on_val] : hBOOL(hAPP_P1038730315l_bool(Pa,X1))
    <=> ! [A_2: list_P1663965006on_val,B_1: list_P1663965006on_val] : hBOOL(hAPP_P1038730315l_bool(Pa,hAPP_l1485560508on_val(hAPP_l1324137613on_val(produc584381409on_val,A_2),B_1))) ) ).

tff(fact_373_split__paired__All,axiom,
    ! [Pa: fun_Pr638203177r_bool] :
      ( ! [X1: produc409241703r_char] : hBOOL(hAPP_P1700239815r_bool(Pa,X1))
    <=> ! [A_2: char,B_1: char] : hBOOL(hAPP_P1700239815r_bool(Pa,hAPP_c802977373r_char(hAPP_c1242523777r_char(produc601902295r_char,A_2),B_1))) ) ).

tff(fact_374_split__paired__All,axiom,
    ! [Pa: fun_Pr1618624239l_bool] :
      ( ! [X1: produc753553453st_val] : hBOOL(hAPP_P2115985549l_bool(Pa,X1))
    <=> ! [A_2: list_val,B_1: list_val] : hBOOL(hAPP_P2115985549l_bool(Pa,hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,A_2),B_1))) ) ).

tff(fact_375_split__paired__All,axiom,
    ! [Pa: fun_Pr306783325y_bool] :
      ( ! [X1: produc1420746395ist_ty] : hBOOL(hAPP_P1574824955y_bool(Pa,X1))
    <=> ! [A_2: list_ty,B_1: list_ty] : hBOOL(hAPP_P1574824955y_bool(Pa,hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,A_2),B_1))) ) ).

tff(fact_376_split__paired__All,axiom,
    ! [Pa: fun_Pr2087862441y_bool] :
      ( ! [X1: product_prod_ty_ty] : hBOOL(hAPP_P1716187463y_bool(Pa,X1))
    <=> ! [A_2: ty,B_1: ty] : hBOOL(hAPP_P1716187463y_bool(Pa,hAPP_t65172803_ty_ty(hAPP_t1494094285_ty_ty(product_Pair_ty_ty,A_2),B_1))) ) ).

tff(fact_377_split__paired__All,axiom,
    ! [Pa: fun_Pr716652265r_bool] :
      ( ! [X1: produc91527719t_char] : hBOOL(hAPP_P499022727r_bool(Pa,X1))
    <=> ! [A_2: list_exp_list_char,B_1: list_exp_list_char] : hBOOL(hAPP_P499022727r_bool(Pa,hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,A_2),B_1))) ) ).

tff(fact_378_split__paired__All,axiom,
    ! [Pa: fun_Pr136267935r_bool] :
      ( ! [X1: produc2048519645t_char] : hBOOL(hAPP_P1632759357r_bool(Pa,X1))
    <=> ! [A_2: exp_list_char,B_1: exp_list_char] : hBOOL(hAPP_P1632759357r_bool(Pa,hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,A_2),B_1))) ) ).

tff(fact_379_split__paired__All,axiom,
    ! [Pa: fun_Pr643382121l_bool] :
      ( ! [X1: produc1312961703ar_val] : hBOOL(hAPP_P439015943l_bool(Pa,X1))
    <=> ! [A_2: produc1147203250ar_val,B_1: produc1147203250ar_val] : hBOOL(hAPP_P439015943l_bool(Pa,hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,A_2),B_1))) ) ).

tff(fact_380_split__paired__All,axiom,
    ! [Pa: fun_Pr908866473r_bool] :
      ( ! [X1: produc1534059751t_char] : hBOOL(hAPP_P1002912327r_bool(Pa,X1))
    <=> ! [A_2: produc809539159t_char,B_1: produc809539159t_char] : hBOOL(hAPP_P1002912327r_bool(Pa,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_2),B_1))) ) ).

tff(fact_381_split__paired__All,axiom,
    ! [Pa: fun_Pr1336847023r_bool] :
      ( ! [X1: produc1350825965t_char] : hBOOL(hAPP_P2010574925r_bool(Pa,X1))
    <=> ! [A_2: produc1278157519t_char,B_1: produc1278157519t_char] : hBOOL(hAPP_P2010574925r_bool(Pa,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_2),B_1))) ) ).

tff(fact_382_split__paired__All,axiom,
    ! [Pa: fun_Pr832147423l_bool] :
      ( ! [X1: produc800118557al_val] : hBOOL(hAPP_P2123002749l_bool(Pa,X1))
    <=> ! [A_2: product_prod_val_val,B_1: product_prod_val_val] : hBOOL(hAPP_P2123002749l_bool(Pa,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_2),B_1))) ) ).

tff(fact_383_split__paired__All,axiom,
    ! [Pa: fun_Pr897334561l_bool] :
      ( ! [X1: produc630464863al_val] : hBOOL(hAPP_P738987199l_bool(Pa,X1))
    <=> ! [A_2: produc1645268488al_val,B_1: produc1645268488al_val] : hBOOL(hAPP_P738987199l_bool(Pa,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_2),B_1))) ) ).

tff(fact_384_split__paired__All,axiom,
    ! [Pa: fun_Pr302334223l_bool] :
      ( ! [X1: produc1466422861on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,X1))
    <=> ! [A_2: produc430140671on_val,B_1: produc430140671on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_2),B_1))) ) ).

tff(fact_385_split__paired__All,axiom,
    ! [Pa: fun_Pr235369833l_bool] :
      ( ! [X1: produc87279271on_val] : hBOOL(hAPP_P124632071l_bool(Pa,X1))
    <=> ! [A_2: produc639455274on_val,B_1: produc639455274on_val] : hBOOL(hAPP_P124632071l_bool(Pa,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_2),B_1))) ) ).

tff(fact_386_split__paired__All,axiom,
    ! [Pa: fun_Pr903661919l_bool] :
      ( ! [X1: produc231486621on_val] : hBOOL(hAPP_P378063101l_bool(Pa,X1))
    <=> ! [A_2: produc1102272487on_val,B_1: produc1102272487on_val] : hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_2),B_1))) ) ).

tff(fact_387_split__paired__All,axiom,
    ! [Pa: fun_Pr693020585l_bool] :
      ( ! [X1: produc409205479on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,X1))
    <=> ! [A_2: produc12694297on_val,B_1: produc12694297on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_2),B_1))) ) ).

tff(fact_388_split__paired__All,axiom,
    ! [Pa: fun_Pr1890037787r_bool] :
      ( ! [X1: produc1826280281t_char] : hBOOL(hAPP_P1183499705r_bool(Pa,X1))
    <=> ! [A_2: produc662261637t_char,B_1: produc662261637t_char] : hBOOL(hAPP_P1183499705r_bool(Pa,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_2),B_1))) ) ).

tff(fact_389_split__paired__All,axiom,
    ! [Pa: fun_Pr1728267013r_bool] :
      ( ! [X1: produc1406897475t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,X1))
    <=> ! [A_2: produc220283002t_char,B_1: produc220283002t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_2),B_1))) ) ).

tff(fact_390_split__paired__All,axiom,
    ! [Pa: fun_Pr1895638121r_bool] :
      ( ! [X1: produc349695911t_char] : hBOOL(hAPP_P824029447r_bool(Pa,X1))
    <=> ! [A_2: produc1285161482t_char,B_1: produc1285161482t_char] : hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_2),B_1))) ) ).

tff(fact_391_split__paired__All,axiom,
    ! [Pa: fun_Pr227936640r_bool] :
      ( ! [X1: produc1285161482t_char] : hBOOL(hAPP_P92196306r_bool(Pa,X1))
    <=> ! [A_2: list_list_char,B_1: produc220283002t_char] : hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_2),B_1))) ) ).

tff(fact_392_split__paired__All,axiom,
    ! [Pa: fun_Pr46158268r_bool] :
      ( ! [X1: produc220283002t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,X1))
    <=> ! [A_2: list_ty,B_1: produc662261637t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_2),B_1))) ) ).

tff(fact_393_split__paired__All,axiom,
    ! [Pa: fun_Pr827765831r_bool] :
      ( ! [X1: produc662261637t_char] : hBOOL(hAPP_P2118621157r_bool(Pa,X1))
    <=> ! [A_2: list_val,B_1: exp_list_char] : hBOOL(hAPP_P2118621157r_bool(Pa,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_2),B_1))) ) ).

tff(fact_394_split__paired__All,axiom,
    ! [Pa: fun_Pr1696029455l_bool] :
      ( ! [X1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
    <=> ! [A_2: fun_na939144002on_val,B_1: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(Pa,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_2),B_1))) ) ).

tff(fact_395_split__paired__All,axiom,
    ! [Pa: fun_Pr691271849l_bool] :
      ( ! [X1: produc1102272487on_val] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
    <=> ! [A_2: produc124828825on_val,B_1: produc124828825on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_2),B_1))) ) ).

tff(fact_396_split__paired__All,axiom,
    ! [Pa: fun_Pr680585871l_bool] :
      ( ! [X1: produc124828825on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
    <=> ! [A_2: exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_2),B_1))) ) ).

tff(fact_397_split__paired__All,axiom,
    ! [Pa: fun_Pr315804320l_bool] :
      ( ! [X1: produc639455274on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,X1))
    <=> ! [A_2: list_char,B_1: fun_Pr806764899on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_2),B_1))) ) ).

tff(fact_398_split__paired__All,axiom,
    ! [Pa: fun_Pr859510977l_bool] :
      ( ! [X1: produc430140671on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,X1))
    <=> ! [A_2: produc2061676504on_val,B_1: produc2061676504on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_2),B_1))) ) ).

tff(fact_399_split__paired__All,axiom,
    ! [Pa: fun_Pr248118298l_bool] :
      ( ! [X1: produc2061676504on_val] : hBOOL(hAPP_P71593144l_bool(Pa,X1))
    <=> ! [A_2: list_exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P71593144l_bool(Pa,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_2),B_1))) ) ).

tff(fact_400_split__paired__All,axiom,
    ! [Pa: fun_Pr252072522l_bool] :
      ( ! [X1: produc1645268488al_val] : hBOOL(hAPP_P943837928l_bool(Pa,X1))
    <=> ! [A_2: bop,B_1: product_prod_val_val] : hBOOL(hAPP_P943837928l_bool(Pa,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_2),B_1))) ) ).

tff(fact_401_split__paired__All,axiom,
    ! [Pa: fun_Pr2081272681l_bool] :
      ( ! [X1: product_prod_val_val] : hBOOL(hAPP_P929938951l_bool(Pa,X1))
    <=> ! [A_2: val,B_1: val] : hBOOL(hAPP_P929938951l_bool(Pa,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_2),B_1))) ) ).

tff(fact_402_split__paired__All,axiom,
    ! [Pa: fun_Pr565113489r_bool] :
      ( ! [X1: produc1278157519t_char] : hBOOL(hAPP_P449474095r_bool(Pa,X1))
    <=> ! [A_2: list_char,B_1: list_char] : hBOOL(hAPP_P449474095r_bool(Pa,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_2),B_1))) ) ).

tff(fact_403_split__paired__All,axiom,
    ! [Pa: fun_Pr1336948301r_bool] :
      ( ! [X1: produc809539159t_char] : hBOOL(hAPP_P2014166431r_bool(Pa,X1))
    <=> ! [A_2: list_list_char,B_1: exp_list_char] : hBOOL(hAPP_P2014166431r_bool(Pa,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_2),B_1))) ) ).

tff(fact_404_split__paired__All,axiom,
    ! [Pa: fun_Pr661739816l_bool] :
      ( ! [X1: produc1147203250ar_val] : hBOOL(hAPP_P1070896250l_bool(Pa,X1))
    <=> ! [A_2: produc1278157519t_char,B_1: val] : hBOOL(hAPP_P1070896250l_bool(Pa,hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_2),B_1))) ) ).

tff(fact_405_neq__if__length__neq,axiom,
    ! [Xs: list_P249777017on_val,Ys: list_P249777017on_val] :
      ( ( hAPP_l1766199206al_nat(size_s470606735on_val,Xs) != hAPP_l1766199206al_nat(size_s470606735on_val,Ys) )
     => ( Xs != Ys ) ) ).

tff(fact_406_neq__if__length__neq,axiom,
    ! [Xs: list_P1663965006on_val,Ys: list_P1663965006on_val] :
      ( ( hAPP_l1746926841al_nat(size_s60479160on_val,Xs) != hAPP_l1746926841al_nat(size_s60479160on_val,Ys) )
     => ( Xs != Ys ) ) ).

tff(fact_407_neq__if__length__neq,axiom,
    ! [Xs_8: list_char,Ys_6: list_char] :
      ( ( hAPP_list_char_nat(size_size_list_char,Xs_8) != hAPP_list_char_nat(size_size_list_char,Ys_6) )
     => ( Xs_8 != Ys_6 ) ) ).

tff(fact_408_neq__if__length__neq,axiom,
    ! [Xs_8: list_P2023964830har_ty,Ys_6: list_P2023964830har_ty] :
      ( ( hAPP_l540212137ty_nat(size_s1444510216har_ty,Xs_8) != hAPP_l540212137ty_nat(size_s1444510216har_ty,Ys_6) )
     => ( Xs_8 != Ys_6 ) ) ).

tff(fact_409_neq__if__length__neq,axiom,
    ! [Xs_8: list_P1697858023ar_val,Ys_6: list_P1697858023ar_val] :
      ( ( hAPP_l1280603808al_nat(size_s760178257ar_val,Xs_8) != hAPP_l1280603808al_nat(size_s760178257ar_val,Ys_6) )
     => ( Xs_8 != Ys_6 ) ) ).

tff(fact_410_neq__if__length__neq,axiom,
    ! [Xs_8: list_option_ty,Ys_6: list_option_ty] :
      ( ( hAPP_l289305880ty_nat(size_s1050794909ion_ty,Xs_8) != hAPP_l289305880ty_nat(size_s1050794909ion_ty,Ys_6) )
     => ( Xs_8 != Ys_6 ) ) ).

tff(fact_411_neq__if__length__neq,axiom,
    ! [Xs_8: list_list_char,Ys_6: list_list_char] :
      ( ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs_8) != hAPP_l66428094ar_nat(size_s2113983095t_char,Ys_6) )
     => ( Xs_8 != Ys_6 ) ) ).

tff(fact_412_neq__if__length__neq,axiom,
    ! [Xs_8: list_ty,Ys_6: list_ty] :
      ( ( hAPP_list_ty_nat(size_size_list_ty,Xs_8) != hAPP_list_ty_nat(size_size_list_ty,Ys_6) )
     => ( Xs_8 != Ys_6 ) ) ).

tff(fact_413_neq__if__length__neq,axiom,
    ! [Xs_8: list_val,Ys_6: list_val] :
      ( ( hAPP_list_val_nat(size_size_list_val,Xs_8) != hAPP_list_val_nat(size_size_list_val,Ys_6) )
     => ( Xs_8 != Ys_6 ) ) ).

tff(fact_414_neq__if__length__neq,axiom,
    ! [Xs_8: list_exp_list_char,Ys_6: list_exp_list_char] :
      ( ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs_8) != hAPP_l452123639ar_nat(size_s1143674878t_char,Ys_6) )
     => ( Xs_8 != Ys_6 ) ) ).

tff(fact_415_list__all2__eq,axiom,
    ! [Xs: list_ty,Ys: list_ty] :
      ( ( Xs = Ys )
    <=> hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(fequal_ty,Xs),Ys)) ) ).

tff(fact_416_widen__trans,axiom,
    ! [T_8: 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_8))
       => hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_3),S_4),T_8)) ) ) ).

tff(fact_417_prod__cases3,axiom,
    ! [Y_4: produc469582463har_ty] :
      ~ ! [A_2: list_char,B_1: list_char,C_4: ty] : Y_4 != hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,A_2),hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,B_1),C_4)) ).

tff(fact_418_prod__cases3,axiom,
    ! [Y_4: produc1285161482t_char] :
      ~ ! [A_2: list_list_char,B_1: list_ty,C_4: produc662261637t_char] : Y_4 != hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_2),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_1),C_4)) ).

tff(fact_419_prod__cases3,axiom,
    ! [Y_4: produc220283002t_char] :
      ~ ! [A_2: list_ty,B_1: list_val,C_4: exp_list_char] : Y_4 != hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_2),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,B_1),C_4)) ).

tff(fact_420_prod__cases3,axiom,
    ! [Y_1: produc1102272487on_val] :
      ~ ! [A_2: produc124828825on_val,B_1: exp_list_char,C_4: produc12694297on_val] : Y_1 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_2),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B_1),C_4)) ).

tff(fact_421_prod__cases3,axiom,
    ! [Y_1: produc124828825on_val] :
      ~ ! [A_2: exp_list_char,B_1: fun_na939144002on_val,C_4: fun_li1432931796on_val] : Y_1 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_1),C_4)) ).

tff(fact_422_prod__cases3,axiom,
    ! [Y_1: produc430140671on_val] :
      ~ ! [A_2: produc2061676504on_val,B_1: list_exp_list_char,C_4: produc12694297on_val] : Y_1 != hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_2),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,B_1),C_4)) ).

tff(fact_423_prod__cases3,axiom,
    ! [Y_1: produc2061676504on_val] :
      ~ ! [A_2: list_exp_list_char,B_1: fun_na939144002on_val,C_4: fun_li1432931796on_val] : Y_1 != hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_1),C_4)) ).

tff(fact_424_prod__cases3,axiom,
    ! [Y_4: produc1645268488al_val] :
      ~ ! [A_2: bop,B_1: val,C_4: val] : Y_4 != hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_2),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B_1),C_4)) ).

tff(fact_425_prod__cases3,axiom,
    ! [Y_4: produc349695911t_char] :
      ~ ! [A_2: produc1285161482t_char,B_1: list_list_char,C_4: produc220283002t_char] : Y_4 != hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_2),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_1),C_4)) ).

tff(fact_426_prod__cases3,axiom,
    ! [Y_4: produc1406897475t_char] :
      ~ ! [A_2: produc220283002t_char,B_1: list_ty,C_4: produc662261637t_char] : Y_4 != hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_2),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_1),C_4)) ).

tff(fact_427_prod__cases3,axiom,
    ! [Y_4: produc1826280281t_char] :
      ~ ! [A_2: produc662261637t_char,B_1: list_val,C_4: exp_list_char] : Y_4 != hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_2),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,B_1),C_4)) ).

tff(fact_428_prod__cases3,axiom,
    ! [Y_1: produc409205479on_val] :
      ~ ! [A_2: produc12694297on_val,B_1: fun_na939144002on_val,C_4: fun_li1432931796on_val] : Y_1 != hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_1),C_4)) ).

tff(fact_429_prod__cases3,axiom,
    ! [Y_1: produc231486621on_val] :
      ~ ! [A_2: produc1102272487on_val,B_1: produc124828825on_val,C_4: produc124828825on_val] : Y_1 != hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_2),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_1),C_4)) ).

tff(fact_430_prod__cases3,axiom,
    ! [Y_1: produc87279271on_val] :
      ~ ! [A_2: produc639455274on_val,B_1: list_char,C_4: fun_Pr806764899on_val] : Y_1 != hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_2),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,B_1),C_4)) ).

tff(fact_431_prod__cases3,axiom,
    ! [Y_1: produc1466422861on_val] :
      ~ ! [A_2: produc430140671on_val,B_1: produc2061676504on_val,C_4: produc2061676504on_val] : Y_1 != hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_2),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_1),C_4)) ).

tff(fact_432_prod__cases3,axiom,
    ! [Y_4: produc630464863al_val] :
      ~ ! [A_2: produc1645268488al_val,B_1: bop,C_4: product_prod_val_val] : Y_4 != hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_2),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,B_1),C_4)) ).

tff(fact_433_prod__cases3,axiom,
    ! [Y_4: produc800118557al_val] :
      ~ ! [A_2: product_prod_val_val,B_1: val,C_4: val] : Y_4 != hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_2),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B_1),C_4)) ).

tff(fact_434_prod__cases3,axiom,
    ! [Y_4: produc1350825965t_char] :
      ~ ! [A_2: produc1278157519t_char,B_1: list_char,C_4: list_char] : Y_4 != hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_2),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B_1),C_4)) ).

tff(fact_435_prod__cases3,axiom,
    ! [Y_4: produc1534059751t_char] :
      ~ ! [A_2: produc809539159t_char,B_1: list_list_char,C_4: exp_list_char] : Y_4 != hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_2),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,B_1),C_4)) ).

tff(fact_436_prod__cases3,axiom,
    ! [Y_4: produc1312961703ar_val] :
      ~ ! [A_2: produc1147203250ar_val,B_1: produc1278157519t_char,C_4: val] : Y_4 != hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,A_2),hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,B_1),C_4)) ).

tff(fact_437_prod__induct3,axiom,
    ! [X_2: produc1645268488al_val,Pa: fun_Pr252072522l_bool] :
      ( ! [A_2: bop,B_1: val,C_4: val] : hBOOL(hAPP_P943837928l_bool(Pa,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_2),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B_1),C_4))))
     => hBOOL(hAPP_P943837928l_bool(Pa,X_2)) ) ).

tff(fact_438_prod__induct3,axiom,
    ! [X_2: produc2061676504on_val,Pa: fun_Pr248118298l_bool] :
      ( ! [A_2: list_exp_list_char,B_1: fun_na939144002on_val,C_4: fun_li1432931796on_val] : hBOOL(hAPP_P71593144l_bool(Pa,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_1),C_4))))
     => hBOOL(hAPP_P71593144l_bool(Pa,X_2)) ) ).

tff(fact_439_prod__induct3,axiom,
    ! [X_2: produc430140671on_val,Pa: fun_Pr859510977l_bool] :
      ( ! [A_2: produc2061676504on_val,B_1: list_exp_list_char,C_4: produc12694297on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_2),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,B_1),C_4))))
     => hBOOL(hAPP_P1333315679l_bool(Pa,X_2)) ) ).

tff(fact_440_prod__induct3,axiom,
    ! [X_2: produc124828825on_val,Pa: fun_Pr680585871l_bool] :
      ( ! [A_2: exp_list_char,B_1: fun_na939144002on_val,C_4: fun_li1432931796on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_1),C_4))))
     => hBOOL(hAPP_P1708370145l_bool(Pa,X_2)) ) ).

tff(fact_441_prod__induct3,axiom,
    ! [X_2: produc1102272487on_val,Pa: fun_Pr691271849l_bool] :
      ( ! [A_2: produc124828825on_val,B_1: exp_list_char,C_4: produc12694297on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_2),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B_1),C_4))))
     => hBOOL(hAPP_P282169671l_bool(Pa,X_2)) ) ).

tff(fact_442_prod__induct3,axiom,
    ! [X_2: produc220283002t_char,Pa: fun_Pr46158268r_bool] :
      ( ! [A_2: list_ty,B_1: list_val,C_4: exp_list_char] : hBOOL(hAPP_P1907982426r_bool(Pa,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_2),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,B_1),C_4))))
     => hBOOL(hAPP_P1907982426r_bool(Pa,X_2)) ) ).

tff(fact_443_prod__induct3,axiom,
    ! [X_2: produc1285161482t_char,Pa: fun_Pr227936640r_bool] :
      ( ! [A_2: list_list_char,B_1: list_ty,C_4: produc662261637t_char] : hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_2),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_1),C_4))))
     => hBOOL(hAPP_P92196306r_bool(Pa,X_2)) ) ).

tff(fact_444_prod__induct3,axiom,
    ! [X_2: produc1534059751t_char,Pa: fun_Pr908866473r_bool] :
      ( ! [A_2: produc809539159t_char,B_1: list_list_char,C_4: exp_list_char] : hBOOL(hAPP_P1002912327r_bool(Pa,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_2),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,B_1),C_4))))
     => hBOOL(hAPP_P1002912327r_bool(Pa,X_2)) ) ).

tff(fact_445_prod__induct3,axiom,
    ! [X_2: produc1312961703ar_val,Pa: fun_Pr643382121l_bool] :
      ( ! [A_2: produc1147203250ar_val,B_1: produc1278157519t_char,C_4: val] : hBOOL(hAPP_P439015943l_bool(Pa,hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,A_2),hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,B_1),C_4))))
     => hBOOL(hAPP_P439015943l_bool(Pa,X_2)) ) ).

tff(fact_446_confs__conv__map,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,Vsa: list_val,Ts_1: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa),Ts_1))
    <=> ? [Ts_4: list_ty] :
          ( ( hAPP_l2006940821ion_ty(map_val_option_ty(typeof_h(Ha)),Vsa) = hAPP_l1487035934ion_ty(map_ty_option_ty(some_ty),Ts_4) )
          & hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_4),Ts_1)) ) ) ).

tff(fact_447_list__all2__mono,axiom,
    ! [Q_1: fun_val_fun_ty_bool,Pa: fun_val_fun_ty_bool,Xs: list_val,Ys: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_all2_val_ty(Pa,Xs),Ys))
     => ( ! [Xs_7: val,Ys_5: ty] :
            ( hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(Pa,Xs_7),Ys_5))
           => hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(Q_1,Xs_7),Ys_5)) )
       => hBOOL(hAPP_list_ty_bool(list_all2_val_ty(Q_1,Xs),Ys)) ) ) ).

tff(fact_448_list__all2__mono,axiom,
    ! [Q_1: fun_ty_fun_ty_bool,Pa: fun_ty_fun_ty_bool,Xs: list_ty,Ys: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(Pa,Xs),Ys))
     => ( ! [Xs_7: ty,Ys_5: ty] :
            ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Pa,Xs_7),Ys_5))
           => hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Q_1,Xs_7),Ys_5)) )
       => hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(Q_1,Xs),Ys)) ) ) ).

tff(fact_449_list__all2__refl,axiom,
    ! [Xs: list_ty,Pa: fun_ty_fun_ty_bool] :
      ( ! [X_1: ty] : hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Pa,X_1),X_1))
     => hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(Pa,Xs),Xs)) ) ).

tff(fact_450_list__all2__antisym,axiom,
    ! [Xs: list_ty,Ys: list_ty,Q_1: fun_ty_fun_ty_bool,Pa: fun_ty_fun_ty_bool] :
      ( ! [X_1: ty,Y_2: ty] :
          ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Pa,X_1),Y_2))
         => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Q_1,Y_2),X_1))
           => ( X_1 = Y_2 ) ) )
     => ( hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(Pa,Xs),Ys))
       => ( hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(Q_1,Ys),Xs))
         => ( Xs = Ys ) ) ) ) ).

tff(fact_451_Ex__list__of__length,axiom,
    ! [N_1: nat] :
    ? [Xs_7: list_exp_list_char] : hAPP_l452123639ar_nat(size_s1143674878t_char,Xs_7) = N_1 ).

tff(fact_452_Ex__list__of__length,axiom,
    ! [N_1: nat] :
    ? [Xs_7: list_val] : hAPP_list_val_nat(size_size_list_val,Xs_7) = N_1 ).

tff(fact_453_Ex__list__of__length,axiom,
    ! [N_1: nat] :
    ? [Xs_7: list_ty] : hAPP_list_ty_nat(size_size_list_ty,Xs_7) = N_1 ).

tff(fact_454_Ex__list__of__length,axiom,
    ! [N_1: nat] :
    ? [Xs_7: list_list_char] : hAPP_l66428094ar_nat(size_s2113983095t_char,Xs_7) = N_1 ).

tff(fact_455_prod_Oexhaust,axiom,
    ! [Y_3: produc1147203250ar_val] :
      ~ ! [A_2: produc1278157519t_char,B_1: val] : Y_3 != hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_2),B_1) ).

tff(fact_456_prod_Oexhaust,axiom,
    ! [Y_3: produc809539159t_char] :
      ~ ! [A_2: list_list_char,B_1: exp_list_char] : Y_3 != hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_2),B_1) ).

tff(fact_457_prod_Oexhaust,axiom,
    ! [Y_3: produc1278157519t_char] :
      ~ ! [A_2: list_char,B_1: list_char] : Y_3 != hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_2),B_1) ).

tff(fact_458_prod_Oexhaust,axiom,
    ! [Y_3: product_prod_val_val] :
      ~ ! [A_2: val,B_1: val] : Y_3 != hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_2),B_1) ).

tff(fact_459_prod_Oexhaust,axiom,
    ! [Y_3: produc1645268488al_val] :
      ~ ! [A_2: bop,B_1: product_prod_val_val] : Y_3 != hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_2),B_1) ).

tff(fact_460_prod_Oexhaust,axiom,
    ! [Y_1: produc2061676504on_val] :
      ~ ! [A_2: list_exp_list_char,B_1: produc12694297on_val] : Y_1 != hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_2),B_1) ).

tff(fact_461_prod_Oexhaust,axiom,
    ! [Y_1: produc430140671on_val] :
      ~ ! [A_2: produc2061676504on_val,B_1: produc2061676504on_val] : Y_1 != hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_2),B_1) ).

tff(fact_462_prod_Oexhaust,axiom,
    ! [Y_1: produc639455274on_val] :
      ~ ! [A_2: list_char,B_1: fun_Pr806764899on_val] : Y_1 != hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_2),B_1) ).

tff(fact_463_prod_Oexhaust,axiom,
    ! [Y_1: produc124828825on_val] :
      ~ ! [A_2: exp_list_char,B_1: produc12694297on_val] : Y_1 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_2),B_1) ).

tff(fact_464_prod_Oexhaust,axiom,
    ! [Y_1: produc1102272487on_val] :
      ~ ! [A_2: produc124828825on_val,B_1: produc124828825on_val] : Y_1 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_2),B_1) ).

tff(fact_465_prod_Oexhaust,axiom,
    ! [Y_1: produc12694297on_val] :
      ~ ! [A_2: fun_na939144002on_val,B_1: fun_li1432931796on_val] : Y_1 != hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_2),B_1) ).

tff(fact_466_prod_Oexhaust,axiom,
    ! [Y_3: produc662261637t_char] :
      ~ ! [A_2: list_val,B_1: exp_list_char] : Y_3 != hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_2),B_1) ).

tff(fact_467_prod_Oexhaust,axiom,
    ! [Y_3: produc220283002t_char] :
      ~ ! [A_2: list_ty,B_1: produc662261637t_char] : Y_3 != hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_2),B_1) ).

tff(fact_468_prod_Oexhaust,axiom,
    ! [Y_3: produc1285161482t_char] :
      ~ ! [A_2: list_list_char,B_1: produc220283002t_char] : Y_3 != hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_2),B_1) ).

tff(fact_469_PairE,axiom,
    ! [P_2: produc1147203250ar_val] :
      ~ ! [X_1: produc1278157519t_char,Y_2: val] : P_2 != hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,X_1),Y_2) ).

tff(fact_470_PairE,axiom,
    ! [P_2: produc809539159t_char] :
      ~ ! [X_1: list_list_char,Y_2: exp_list_char] : P_2 != hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,X_1),Y_2) ).

tff(fact_471_PairE,axiom,
    ! [P_2: produc1278157519t_char] :
      ~ ! [X_1: list_char,Y_2: list_char] : P_2 != hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_1),Y_2) ).

tff(fact_472_PairE,axiom,
    ! [P_2: product_prod_val_val] :
      ~ ! [X_1: val,Y_2: val] : P_2 != hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_1),Y_2) ).

tff(fact_473_PairE,axiom,
    ! [P_2: produc1645268488al_val] :
      ~ ! [X_1: bop,Y_2: product_prod_val_val] : P_2 != hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,X_1),Y_2) ).

tff(fact_474_PairE,axiom,
    ! [P_1: produc2061676504on_val] :
      ~ ! [X_1: list_exp_list_char,Y_2: produc12694297on_val] : P_1 != hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,X_1),Y_2) ).

tff(fact_475_PairE,axiom,
    ! [P_1: produc430140671on_val] :
      ~ ! [X_1: produc2061676504on_val,Y_2: produc2061676504on_val] : P_1 != hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,X_1),Y_2) ).

tff(fact_476_PairE,axiom,
    ! [P_1: produc639455274on_val] :
      ~ ! [X_1: list_char,Y_2: fun_Pr806764899on_val] : P_1 != hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,X_1),Y_2) ).

tff(fact_477_PairE,axiom,
    ! [P_1: produc124828825on_val] :
      ~ ! [X_1: exp_list_char,Y_2: produc12694297on_val] : P_1 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X_1),Y_2) ).

tff(fact_478_PairE,axiom,
    ! [P_1: produc1102272487on_val] :
      ~ ! [X_1: produc124828825on_val,Y_2: produc124828825on_val] : P_1 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X_1),Y_2) ).

tff(fact_479_PairE,axiom,
    ! [P_1: produc12694297on_val] :
      ~ ! [X_1: fun_na939144002on_val,Y_2: fun_li1432931796on_val] : P_1 != hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X_1),Y_2) ).

tff(fact_480_PairE,axiom,
    ! [P_2: produc662261637t_char] :
      ~ ! [X_1: list_val,Y_2: exp_list_char] : P_2 != hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,X_1),Y_2) ).

tff(fact_481_PairE,axiom,
    ! [P_2: produc220283002t_char] :
      ~ ! [X_1: list_ty,Y_2: produc662261637t_char] : P_2 != hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,X_1),Y_2) ).

tff(fact_482_PairE,axiom,
    ! [P_2: produc1285161482t_char] :
      ~ ! [X_1: list_list_char,Y_2: produc220283002t_char] : P_2 != hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,X_1),Y_2) ).

tff(fact_483_split__paired__Ex,axiom,
    ! [Pa: fun_Pr661739816l_bool] :
      ( ? [X1: produc1147203250ar_val] : hBOOL(hAPP_P1070896250l_bool(Pa,X1))
    <=> ? [A_2: produc1278157519t_char,B_1: val] : hBOOL(hAPP_P1070896250l_bool(Pa,hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_2),B_1))) ) ).

tff(fact_484_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1336948301r_bool] :
      ( ? [X1: produc809539159t_char] : hBOOL(hAPP_P2014166431r_bool(Pa,X1))
    <=> ? [A_2: list_list_char,B_1: exp_list_char] : hBOOL(hAPP_P2014166431r_bool(Pa,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_2),B_1))) ) ).

tff(fact_485_split__paired__Ex,axiom,
    ! [Pa: fun_Pr565113489r_bool] :
      ( ? [X1: produc1278157519t_char] : hBOOL(hAPP_P449474095r_bool(Pa,X1))
    <=> ? [A_2: list_char,B_1: list_char] : hBOOL(hAPP_P449474095r_bool(Pa,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_2),B_1))) ) ).

tff(fact_486_split__paired__Ex,axiom,
    ! [Pa: fun_Pr2081272681l_bool] :
      ( ? [X1: product_prod_val_val] : hBOOL(hAPP_P929938951l_bool(Pa,X1))
    <=> ? [A_2: val,B_1: val] : hBOOL(hAPP_P929938951l_bool(Pa,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_2),B_1))) ) ).

tff(fact_487_split__paired__Ex,axiom,
    ! [Pa: fun_Pr252072522l_bool] :
      ( ? [X1: produc1645268488al_val] : hBOOL(hAPP_P943837928l_bool(Pa,X1))
    <=> ? [A_2: bop,B_1: product_prod_val_val] : hBOOL(hAPP_P943837928l_bool(Pa,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_2),B_1))) ) ).

tff(fact_488_split__paired__Ex,axiom,
    ! [Pa: fun_Pr248118298l_bool] :
      ( ? [X1: produc2061676504on_val] : hBOOL(hAPP_P71593144l_bool(Pa,X1))
    <=> ? [A_2: list_exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P71593144l_bool(Pa,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_2),B_1))) ) ).

tff(fact_489_split__paired__Ex,axiom,
    ! [Pa: fun_Pr859510977l_bool] :
      ( ? [X1: produc430140671on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,X1))
    <=> ? [A_2: produc2061676504on_val,B_1: produc2061676504on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_2),B_1))) ) ).

tff(fact_490_split__paired__Ex,axiom,
    ! [Pa: fun_Pr315804320l_bool] :
      ( ? [X1: produc639455274on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,X1))
    <=> ? [A_2: list_char,B_1: fun_Pr806764899on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_2),B_1))) ) ).

tff(fact_491_split__paired__Ex,axiom,
    ! [Pa: fun_Pr680585871l_bool] :
      ( ? [X1: produc124828825on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
    <=> ? [A_2: exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_2),B_1))) ) ).

tff(fact_492_split__paired__Ex,axiom,
    ! [Pa: fun_Pr691271849l_bool] :
      ( ? [X1: produc1102272487on_val] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
    <=> ? [A_2: produc124828825on_val,B_1: produc124828825on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_2),B_1))) ) ).

tff(fact_493_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1696029455l_bool] :
      ( ? [X1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
    <=> ? [A_2: fun_na939144002on_val,B_1: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(Pa,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_2),B_1))) ) ).

tff(fact_494_split__paired__Ex,axiom,
    ! [Pa: fun_Pr827765831r_bool] :
      ( ? [X1: produc662261637t_char] : hBOOL(hAPP_P2118621157r_bool(Pa,X1))
    <=> ? [A_2: list_val,B_1: exp_list_char] : hBOOL(hAPP_P2118621157r_bool(Pa,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_2),B_1))) ) ).

tff(fact_495_split__paired__Ex,axiom,
    ! [Pa: fun_Pr46158268r_bool] :
      ( ? [X1: produc220283002t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,X1))
    <=> ? [A_2: list_ty,B_1: produc662261637t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_2),B_1))) ) ).

tff(fact_496_split__paired__Ex,axiom,
    ! [Pa: fun_Pr227936640r_bool] :
      ( ? [X1: produc1285161482t_char] : hBOOL(hAPP_P92196306r_bool(Pa,X1))
    <=> ? [A_2: list_list_char,B_1: produc220283002t_char] : hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_2),B_1))) ) ).

tff(fact_497_conf__widen,axiom,
    ! [T_4: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,V: val,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V),Ta))
     => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),Ta),T_4))
       => hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V),T_4)) ) ) ).

tff(fact_498_confs__widens,axiom,
    ! [Ts_1: list_ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,Vsa: list_val,Tsa: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa),Tsa))
     => ( hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(widen_2090681816t_char(Pa),Tsa),Ts_1))
       => hBOOL(hAPP_list_ty_bool(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa),Ts_1)) ) ) ).

tff(fact_499_conf__def,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,V: val,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V),Ta))
    <=> ? [T_3: ty] :
          ( ( hAPP_val_option_ty(typeof_h(Ha),V) = hAPP_ty_option_ty(some_ty,T_3) )
          & hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_3),Ta)) ) ) ).

tff(fact_500_blocksEval,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Vsa: list_val,Ps: list_list_char,Tsa: list_ty] :
      ( ( hAPP_l66428094ar_nat(size_s2113983095t_char,Ps) = hAPP_list_ty_nat(size_size_list_ty,Tsa) )
     => ( ( hAPP_l66428094ar_nat(size_s2113983095t_char,Ps) = hAPP_list_val_nat(size_size_list_val,Vsa) )
       => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Ps),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Tsa),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Vsa),Ea)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1)),E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L)))
         => ? [L_6: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),map_up1085636310ar_val(L_1,Ps,Vsa))),E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L_6))) ) ) ) ).

tff(fact_501_option_Oinject,axiom,
    ! [A_1: nat,A_8: nat] :
      ( ( hAPP_nat_option_nat(some_nat,A_1) = hAPP_nat_option_nat(some_nat,A_8) )
    <=> ( A_1 = A_8 ) ) ).

tff(fact_502_option_Oinject,axiom,
    ! [A_1: val,A_8: val] :
      ( ( hAPP_val_option_val(some_val,A_1) = hAPP_val_option_val(some_val,A_8) )
    <=> ( A_1 = A_8 ) ) ).

tff(fact_503_option_Oinject,axiom,
    ! [A_1: produc639455274on_val,A_8: produc639455274on_val] :
      ( ( hAPP_P1510515380on_val(some_P948696889on_val,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,A_8) )
    <=> ( A_1 = A_8 ) ) ).

tff(fact_504_option_Oinject,axiom,
    ! [A_1: ty,A_8: ty] :
      ( ( hAPP_ty_option_ty(some_ty,A_1) = hAPP_ty_option_ty(some_ty,A_8) )
    <=> ( A_1 = A_8 ) ) ).

tff(fact_505_curryI,axiom,
    ! [F_1: fun_Pr661739816l_bool,A_1: produc1278157519t_char,B: val] :
      ( hBOOL(hAPP_P1070896250l_bool(F_1,hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_1),B)))
     => hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(produc218426791l_bool(F_1),A_1),B)) ) ).

tff(fact_506_curryI,axiom,
    ! [F_1: fun_Pr1336948301r_bool,A_1: list_list_char,B: exp_list_char] :
      ( hBOOL(hAPP_P2014166431r_bool(F_1,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B)))
     => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(produc288369490r_bool(F_1),A_1),B)) ) ).

tff(fact_507_curryI,axiom,
    ! [F_1: fun_Pr565113489r_bool,A_1: list_char,B: list_char] :
      ( hBOOL(hAPP_P449474095r_bool(F_1,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B)))
     => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(produc95371820r_bool(F_1),A_1),B)) ) ).

tff(fact_508_curryI,axiom,
    ! [F_1: fun_Pr2081272681l_bool,A_1: val,B: val] :
      ( hBOOL(hAPP_P929938951l_bool(F_1,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B)))
     => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(produc886919678l_bool(F_1),A_1),B)) ) ).

tff(fact_509_curryI,axiom,
    ! [F_1: fun_Pr252072522l_bool,A_1: bop,B: product_prod_val_val] :
      ( hBOOL(hAPP_P943837928l_bool(F_1,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B)))
     => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(produc1555310053l_bool(F_1),A_1),B)) ) ).

tff(fact_510_curryI,axiom,
    ! [F_1: fun_Pr248118298l_bool,A_1: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P71593144l_bool(F_1,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(produc1838470831l_bool(F_1),A_1),B)) ) ).

tff(fact_511_curryI,axiom,
    ! [F_1: fun_Pr859510977l_bool,A_1: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P1333315679l_bool(F_1,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B)))
     => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(produc2053127004l_bool(F_1),A_1),B)) ) ).

tff(fact_512_curryI,axiom,
    ! [F_1: fun_Pr315804320l_bool,A_1: list_char,B: fun_Pr806764899on_val] :
      ( hBOOL(hAPP_P1235399154l_bool(F_1,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B)))
     => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F_1),A_1),B)) ) ).

tff(fact_513_curryI,axiom,
    ! [F_1: fun_Pr680585871l_bool,A_1: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(F_1,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F_1),A_1),B)) ) ).

tff(fact_514_curryI,axiom,
    ! [F_1: fun_Pr691271849l_bool,A_1: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P282169671l_bool(F_1,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B)))
     => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F_1),A_1),B)) ) ).

tff(fact_515_curryI,axiom,
    ! [F_1: fun_Pr1696029455l_bool,A_1: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(F_1,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B)))
     => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F_1),A_1),B)) ) ).

tff(fact_516_curryI,axiom,
    ! [F_1: fun_Pr827765831r_bool,A_1: list_val,B: exp_list_char] :
      ( hBOOL(hAPP_P2118621157r_bool(F_1,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B)))
     => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F_1),A_1),B)) ) ).

tff(fact_517_curryI,axiom,
    ! [F_1: fun_Pr46158268r_bool,A_1: list_ty,B: produc662261637t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(F_1,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B)))
     => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F_1),A_1),B)) ) ).

tff(fact_518_curryI,axiom,
    ! [F_1: fun_Pr227936640r_bool,A_1: list_list_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P92196306r_bool(F_1,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B)))
     => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F_1),A_1),B)) ) ).

tff(fact_519_WTrts__Val,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Vsa: list_val,Tsa: list_ty] :
      ( hBOOL(wTrts_1(Pa,Ha,E_4,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_520_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] :
      ( ( hAPP_l66428094ar_nat(size_s2113983095t_char,Vsa_1) = hAPP_list_ty_nat(size_size_list_ty,Tsa) )
     => ( ( hAPP_list_val_nat(size_size_list_val,Vsa) = hAPP_list_ty_nat(size_size_list_ty,Tsa) )
       => ( hBOOL(final_list_char(Ea))
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Vsa_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Tsa),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Vsa),Ea))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_521_WTrtVal,axiom,
    ! [Pa: list_P1999446415t_char,E_4: fun_li688206603ion_ty,Ha: fun_na939144002on_val,V: val,Ta: ty] :
      ( ( hAPP_val_option_ty(typeof_h(Ha),V) = hAPP_ty_option_ty(some_ty,Ta) )
     => hBOOL(wTrt(Pa,Ha,E_4,hAPP_v834067052t_char(val_list_char,V),Ta)) ) ).

tff(fact_522_lexn__length,axiom,
    ! [Xs: list_char,Ys: list_char,R_1: fun_Pr638203177r_bool,N: nat] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Xs),Ys),lexn_char(R_1,N)))
     => ( ( hAPP_list_char_nat(size_size_list_char,Xs) = N )
        & ( hAPP_list_char_nat(size_size_list_char,Ys) = N ) ) ) ).

tff(fact_523_lexn__length,axiom,
    ! [Xs: list_exp_list_char,Ys: list_exp_list_char,R_1: fun_Pr136267935r_bool,N: nat] :
      ( hBOOL(member894971540t_char(hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,Xs),Ys),lexn_exp_list_char(R_1,N)))
     => ( ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = N )
        & ( hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) = N ) ) ) ).

tff(fact_524_lexn__length,axiom,
    ! [Xs: list_val,Ys: list_val,R_1: fun_Pr2081272681l_bool,N: nat] :
      ( hBOOL(member273646106st_val(hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,Xs),Ys),lexn_val(R_1,N)))
     => ( ( hAPP_list_val_nat(size_size_list_val,Xs) = N )
        & ( hAPP_list_val_nat(size_size_list_val,Ys) = N ) ) ) ).

tff(fact_525_lexn__length,axiom,
    ! [Xs: list_ty,Ys: list_ty,R_1: fun_Pr2087862441y_bool,N: nat] :
      ( hBOOL(member104734088ist_ty(hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,Xs),Ys),lexn_ty(R_1,N)))
     => ( ( hAPP_list_ty_nat(size_size_list_ty,Xs) = N )
        & ( hAPP_list_ty_nat(size_size_list_ty,Ys) = N ) ) ) ).

tff(fact_526_lexn__length,axiom,
    ! [Xs: list_list_char,Ys: list_list_char,R_1: fun_Pr565113489r_bool,N: nat] :
      ( hBOOL(member817832404t_char(hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,Xs),Ys),lexn_list_char(R_1,N)))
     => ( ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = N )
        & ( hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) = N ) ) ) ).

tff(fact_527_WTrts__hext__mono,axiom,
    ! [H: fun_na939144002on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Es_1: list_exp_list_char,Tsa: list_ty] :
      ( hBOOL(wTrts_1(Pa,Ha,E_4,Es_1,Tsa))
     => ( hBOOL(hext(Ha,H))
       => hBOOL(wTrts_1(Pa,H,E_4,Es_1,Tsa)) ) ) ).

tff(fact_528_WTrt__hext__mono,axiom,
    ! [H: fun_na939144002on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Ha,E_4,Ea,Ta))
     => ( hBOOL(hext(Ha,H))
       => hBOOL(wTrt(Pa,H,E_4,Ea,Ta)) ) ) ).

tff(fact_529_WTrts__same__length,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Es_1: list_exp_list_char,Tsa: list_ty] :
      ( hBOOL(wTrts_1(Pa,Ha,E_4,Es_1,Tsa))
     => ( hAPP_l452123639ar_nat(size_s1143674878t_char,Es_1) = hAPP_list_ty_nat(size_size_list_ty,Tsa) ) ) ).

tff(fact_530_curryE,axiom,
    ! [F_1: fun_Pr661739816l_bool,A_1: produc1278157519t_char,B: val] :
      ( hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(produc218426791l_bool(F_1),A_1),B))
     => hBOOL(hAPP_P1070896250l_bool(F_1,hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_1),B))) ) ).

tff(fact_531_curryE,axiom,
    ! [F_1: fun_Pr1336948301r_bool,A_1: list_list_char,B: exp_list_char] :
      ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(produc288369490r_bool(F_1),A_1),B))
     => hBOOL(hAPP_P2014166431r_bool(F_1,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B))) ) ).

tff(fact_532_curryE,axiom,
    ! [F_1: fun_Pr565113489r_bool,A_1: list_char,B: list_char] :
      ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(produc95371820r_bool(F_1),A_1),B))
     => hBOOL(hAPP_P449474095r_bool(F_1,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B))) ) ).

tff(fact_533_curryE,axiom,
    ! [F_1: fun_Pr2081272681l_bool,A_1: val,B: val] :
      ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(produc886919678l_bool(F_1),A_1),B))
     => hBOOL(hAPP_P929938951l_bool(F_1,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B))) ) ).

tff(fact_534_curryE,axiom,
    ! [F_1: fun_Pr252072522l_bool,A_1: bop,B: product_prod_val_val] :
      ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(produc1555310053l_bool(F_1),A_1),B))
     => hBOOL(hAPP_P943837928l_bool(F_1,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B))) ) ).

tff(fact_535_curryE,axiom,
    ! [F_1: fun_Pr248118298l_bool,A_1: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(produc1838470831l_bool(F_1),A_1),B))
     => hBOOL(hAPP_P71593144l_bool(F_1,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B))) ) ).

tff(fact_536_curryE,axiom,
    ! [F_1: fun_Pr859510977l_bool,A_1: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(produc2053127004l_bool(F_1),A_1),B))
     => hBOOL(hAPP_P1333315679l_bool(F_1,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B))) ) ).

tff(fact_537_curryE,axiom,
    ! [F_1: fun_Pr315804320l_bool,A_1: list_char,B: fun_Pr806764899on_val] :
      ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F_1),A_1),B))
     => hBOOL(hAPP_P1235399154l_bool(F_1,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B))) ) ).

tff(fact_538_curryE,axiom,
    ! [F_1: fun_Pr680585871l_bool,A_1: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F_1),A_1),B))
     => hBOOL(hAPP_P1708370145l_bool(F_1,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B))) ) ).

tff(fact_539_curryE,axiom,
    ! [F_1: fun_Pr691271849l_bool,A_1: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F_1),A_1),B))
     => hBOOL(hAPP_P282169671l_bool(F_1,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B))) ) ).

tff(fact_540_curryE,axiom,
    ! [F_1: fun_Pr1696029455l_bool,A_1: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F_1),A_1),B))
     => hBOOL(hAPP_P159683425l_bool(F_1,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B))) ) ).

tff(fact_541_curryE,axiom,
    ! [F_1: fun_Pr827765831r_bool,A_1: list_val,B: exp_list_char] :
      ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F_1),A_1),B))
     => hBOOL(hAPP_P2118621157r_bool(F_1,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B))) ) ).

tff(fact_542_curryE,axiom,
    ! [F_1: fun_Pr46158268r_bool,A_1: list_ty,B: produc662261637t_char] :
      ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F_1),A_1),B))
     => hBOOL(hAPP_P1907982426r_bool(F_1,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B))) ) ).

tff(fact_543_curryE,axiom,
    ! [F_1: fun_Pr227936640r_bool,A_1: list_list_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F_1),A_1),B))
     => hBOOL(hAPP_P92196306r_bool(F_1,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B))) ) ).

tff(fact_544_curryD,axiom,
    ! [F_1: fun_Pr661739816l_bool,A_1: produc1278157519t_char,B: val] :
      ( hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(produc218426791l_bool(F_1),A_1),B))
     => hBOOL(hAPP_P1070896250l_bool(F_1,hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_1),B))) ) ).

tff(fact_545_curryD,axiom,
    ! [F_1: fun_Pr1336948301r_bool,A_1: list_list_char,B: exp_list_char] :
      ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(produc288369490r_bool(F_1),A_1),B))
     => hBOOL(hAPP_P2014166431r_bool(F_1,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B))) ) ).

tff(fact_546_curryD,axiom,
    ! [F_1: fun_Pr565113489r_bool,A_1: list_char,B: list_char] :
      ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(produc95371820r_bool(F_1),A_1),B))
     => hBOOL(hAPP_P449474095r_bool(F_1,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B))) ) ).

tff(fact_547_curryD,axiom,
    ! [F_1: fun_Pr2081272681l_bool,A_1: val,B: val] :
      ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(produc886919678l_bool(F_1),A_1),B))
     => hBOOL(hAPP_P929938951l_bool(F_1,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B))) ) ).

tff(fact_548_curryD,axiom,
    ! [F_1: fun_Pr252072522l_bool,A_1: bop,B: product_prod_val_val] :
      ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(produc1555310053l_bool(F_1),A_1),B))
     => hBOOL(hAPP_P943837928l_bool(F_1,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B))) ) ).

tff(fact_549_curryD,axiom,
    ! [F_1: fun_Pr248118298l_bool,A_1: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(produc1838470831l_bool(F_1),A_1),B))
     => hBOOL(hAPP_P71593144l_bool(F_1,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B))) ) ).

tff(fact_550_curryD,axiom,
    ! [F_1: fun_Pr859510977l_bool,A_1: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(produc2053127004l_bool(F_1),A_1),B))
     => hBOOL(hAPP_P1333315679l_bool(F_1,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B))) ) ).

tff(fact_551_curryD,axiom,
    ! [F_1: fun_Pr315804320l_bool,A_1: list_char,B: fun_Pr806764899on_val] :
      ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F_1),A_1),B))
     => hBOOL(hAPP_P1235399154l_bool(F_1,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B))) ) ).

tff(fact_552_curryD,axiom,
    ! [F_1: fun_Pr680585871l_bool,A_1: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F_1),A_1),B))
     => hBOOL(hAPP_P1708370145l_bool(F_1,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B))) ) ).

tff(fact_553_curryD,axiom,
    ! [F_1: fun_Pr691271849l_bool,A_1: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F_1),A_1),B))
     => hBOOL(hAPP_P282169671l_bool(F_1,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B))) ) ).

tff(fact_554_curryD,axiom,
    ! [F_1: fun_Pr1696029455l_bool,A_1: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F_1),A_1),B))
     => hBOOL(hAPP_P159683425l_bool(F_1,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B))) ) ).

tff(fact_555_curryD,axiom,
    ! [F_1: fun_Pr827765831r_bool,A_1: list_val,B: exp_list_char] :
      ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F_1),A_1),B))
     => hBOOL(hAPP_P2118621157r_bool(F_1,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B))) ) ).

tff(fact_556_curryD,axiom,
    ! [F_1: fun_Pr46158268r_bool,A_1: list_ty,B: produc662261637t_char] :
      ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F_1),A_1),B))
     => hBOOL(hAPP_P1907982426r_bool(F_1,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B))) ) ).

tff(fact_557_curryD,axiom,
    ! [F_1: fun_Pr227936640r_bool,A_1: list_list_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F_1),A_1),B))
     => hBOOL(hAPP_P92196306r_bool(F_1,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B))) ) ).

tff(fact_558_red__hext__incr,axiom,
    ! [Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L))),red(Pa)))
     => hBOOL(hext(Ha,H)) ) ).

tff(fact_559_rtrancl_Ortrancl__refl,axiom,
    ! [A_1: list_char,R_1: fun_Pr565113489r_bool] : hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),A_1),transi1395422419t_char(R_1))) ).

tff(fact_560_rtrancl_Ortrancl__refl,axiom,
    ! [A_1: produc2061676504on_val,R_1: fun_Pr859510977l_bool] : hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),A_1),transi374442731on_val(R_1))) ).

tff(fact_561_rtrancl_Ortrancl__refl,axiom,
    ! [A_1: produc124828825on_val,R_1: fun_Pr691271849l_bool] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),A_1),transi2024712006on_val(R_1))) ).

tff(fact_562_rtrancl_Ortrancl__refl,axiom,
    ! [A_1: val,R_1: fun_Pr2081272681l_bool] : hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),A_1),transi935034983cl_val(R_1))) ).

tff(fact_563_hext__typeof__mono,axiom,
    ! [V: val,Ta: ty,Ha: fun_na939144002on_val,H: fun_na939144002on_val] :
      ( hBOOL(hext(Ha,H))
     => ( ( hAPP_val_option_ty(typeof_h(Ha),V) = hAPP_ty_option_ty(some_ty,Ta) )
       => ( hAPP_val_option_ty(typeof_h(H),V) = hAPP_ty_option_ty(some_ty,Ta) ) ) ) ).

tff(fact_564_eval__hext,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1)),E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L)))
     => hBOOL(hext(Ha,H)) ) ).

tff(fact_565_hext__refl,axiom,
    ! [Ha: fun_na939144002on_val] : hBOOL(hext(Ha,Ha)) ).

tff(fact_566_r__into__rtrancl,axiom,
    ! [P_1: produc1278157519t_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(P_1,R_1))
     => hBOOL(member1251428284t_char(P_1,transi1395422419t_char(R_1))) ) ).

tff(fact_567_r__into__rtrancl,axiom,
    ! [P_1: produc430140671on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(P_1,R_1))
     => hBOOL(member875476972on_val(P_1,transi374442731on_val(R_1))) ) ).

tff(fact_568_r__into__rtrancl,axiom,
    ! [P_1: produc1102272487on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(P_1,R_1))
     => hBOOL(member773094996on_val(P_1,transi2024712006on_val(R_1))) ) ).

tff(fact_569_red__preserves__hconf,axiom,
    ! [E_4: fun_li688206603ion_ty,Ta: ty,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L))),red(Pa)))
     => ( hBOOL(wTrt(Pa,Ha,E_4,Ea,Ta))
       => ( hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),Ha))
         => hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),H)) ) ) ) ).

tff(fact_570_eval__finalId,axiom,
    ! [Pa: list_P1999446415t_char,S_1: produc12694297on_val,Ea: exp_list_char] :
      ( hBOOL(final_list_char(Ea))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),Ea),S_1)) ) ).

tff(fact_571_eval__final,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),E),S))
     => hBOOL(final_list_char(E)) ) ).

tff(fact_572_red__preserves__lconf,axiom,
    ! [E_4: fun_li688206603ion_ty,Ta: ty,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L))),red(Pa)))
     => ( hBOOL(wTrt(Pa,Ha,E_4,Ea,Ta))
       => ( hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Ha),L_1),E_4))
         => hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),H),L),E_4)) ) ) ) ).

tff(fact_573_Val,axiom,
    ! [Pa: list_P1999446415t_char,V: val,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,hAPP_v834067052t_char(val_list_char,V),S_1),hAPP_v834067052t_char(val_list_char,V)),S_1)) ).

tff(fact_574_lconf__hext,axiom,
    ! [H: fun_na939144002on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E_4: fun_li688206603ion_ty] :
      ( hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Ha),L_1),E_4))
     => ( hBOOL(hext(Ha,H))
       => hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),H),L_1),E_4)) ) ) ).

tff(fact_575_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr565113489r_bool] : transi1395422419t_char(transi1395422419t_char(R_1)) = transi1395422419t_char(R_1) ).

tff(fact_576_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr859510977l_bool] : transi374442731on_val(transi374442731on_val(R_1)) = transi374442731on_val(R_1) ).

tff(fact_577_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr691271849l_bool] : transi2024712006on_val(transi2024712006on_val(R_1)) = transi2024712006on_val(R_1) ).

tff(fact_578_hext__trans,axiom,
    ! [H_5: fun_na939144002on_val,Ha: fun_na939144002on_val,H: fun_na939144002on_val] :
      ( hBOOL(hext(Ha,H))
     => ( hBOOL(hext(H,H_5))
       => hBOOL(hext(Ha,H_5)) ) ) ).

tff(fact_579_converse__rtrancl__into__rtrancl,axiom,
    ! [C_2: list_char,A_1: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B),R_1))
     => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B),C_2),transi1395422419t_char(R_1)))
       => hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),C_2),transi1395422419t_char(R_1))) ) ) ).

tff(fact_580_converse__rtrancl__into__rtrancl,axiom,
    ! [C_2: produc2061676504on_val,A_1: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B),R_1))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B),C_2),transi374442731on_val(R_1)))
       => hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),C_2),transi374442731on_val(R_1))) ) ) ).

tff(fact_581_converse__rtrancl__into__rtrancl,axiom,
    ! [C_2: produc124828825on_val,A_1: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B),R_1))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B),C_2),transi2024712006on_val(R_1)))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),C_2),transi2024712006on_val(R_1))) ) ) ).

tff(fact_582_converse__rtrancl__into__rtrancl,axiom,
    ! [C_2: val,A_1: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B),R_1))
     => ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B),C_2),transi935034983cl_val(R_1)))
       => hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),C_2),transi935034983cl_val(R_1))) ) ) ).

tff(fact_583_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_2: list_char,A_1: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B),transi1395422419t_char(R_1)))
     => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B),C_2),R_1))
       => hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),C_2),transi1395422419t_char(R_1))) ) ) ).

tff(fact_584_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_2: produc2061676504on_val,A_1: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B),transi374442731on_val(R_1)))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B),C_2),R_1))
       => hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),C_2),transi374442731on_val(R_1))) ) ) ).

tff(fact_585_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_2: produc124828825on_val,A_1: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B),transi2024712006on_val(R_1)))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B),C_2),R_1))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),C_2),transi2024712006on_val(R_1))) ) ) ).

tff(fact_586_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_2: val,A_1: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B),transi935034983cl_val(R_1)))
     => ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B),C_2),R_1))
       => hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),C_2),transi935034983cl_val(R_1))) ) ) ).

tff(fact_587_rtrancl__trans,axiom,
    ! [C_2: list_char,A_1: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B),transi1395422419t_char(R_1)))
     => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B),C_2),transi1395422419t_char(R_1)))
       => hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),C_2),transi1395422419t_char(R_1))) ) ) ).

tff(fact_588_rtrancl__trans,axiom,
    ! [C_2: produc2061676504on_val,A_1: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B),transi374442731on_val(R_1)))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B),C_2),transi374442731on_val(R_1)))
       => hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),C_2),transi374442731on_val(R_1))) ) ) ).

tff(fact_589_rtrancl__trans,axiom,
    ! [C_2: produc124828825on_val,A_1: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B),transi2024712006on_val(R_1)))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B),C_2),transi2024712006on_val(R_1)))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),C_2),transi2024712006on_val(R_1))) ) ) ).

tff(fact_590_rtrancl__trans,axiom,
    ! [C_2: val,A_1: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B),transi935034983cl_val(R_1)))
     => ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B),C_2),transi935034983cl_val(R_1)))
       => hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),C_2),transi935034983cl_val(R_1))) ) ) ).

tff(fact_591_eval__cases_I2_J,axiom,
    ! [Pa: list_P1999446415t_char,V: val,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,hAPP_v834067052t_char(val_list_char,V),S_1),E),S))
     => ~ ( ( E = hAPP_v834067052t_char(val_list_char,V) )
         => ( S != S_1 ) ) ) ).

tff(fact_592_lconf__def,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E_4: fun_li688206603ion_ty] :
      ( hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Ha),L_1),E_4))
    <=> ! [V_7: list_char,V_4: val] :
          ( ( hAPP_l207779698on_val(L_1,V_7) = hAPP_val_option_val(some_val,V_4) )
         => ? [T_1: ty] :
              ( ( hAPP_l512744617ion_ty(E_4,V_7) = hAPP_ty_option_ty(some_ty,T_1) )
              & hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_4),T_1)) ) ) ) ).

tff(fact_593_converse__rtranclE2,axiom,
    ! [Xa_1: list_exp_list_char,Xb_1: produc12694297on_val,Za: list_exp_list_char,Zb: produc12694297on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Xa_1),Xb_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Za),Zb)),transi374442731on_val(R_1)))
     => ( ( hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Xa_1),Xb_1) != hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Za),Zb) )
       => ~ ! [A_2: list_exp_list_char,B_1: produc12694297on_val] :
              ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Xa_1),Xb_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_2),B_1)),R_1))
             => ~ hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_2),B_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Za),Zb)),transi374442731on_val(R_1))) ) ) ) ).

tff(fact_594_converse__rtranclE2,axiom,
    ! [Xa_1: exp_list_char,Xb_1: produc12694297on_val,Za: exp_list_char,Zb: produc12694297on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Xa_1),Xb_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Za),Zb)),transi2024712006on_val(R_1)))
     => ( ( hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Xa_1),Xb_1) != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Za),Zb) )
       => ~ ! [A_2: exp_list_char,B_1: produc12694297on_val] :
              ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Xa_1),Xb_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_2),B_1)),R_1))
             => ~ hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_2),B_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Za),Zb)),transi2024712006on_val(R_1))) ) ) ) ).

tff(fact_595_converse__rtranclE2,axiom,
    ! [Xa_1: produc1278157519t_char,Xb_1: val,Za: produc1278157519t_char,Zb: val,R_1: fun_Pr643382121l_bool] :
      ( hBOOL(member619264020ar_val(hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,Xa_1),Xb_1)),hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,Za),Zb)),transi1600669663ar_val(R_1)))
     => ( ( hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,Xa_1),Xb_1) != hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,Za),Zb) )
       => ~ ! [A_2: produc1278157519t_char,B_1: val] :
              ( hBOOL(member619264020ar_val(hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,Xa_1),Xb_1)),hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_2),B_1)),R_1))
             => ~ hBOOL(member619264020ar_val(hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_2),B_1)),hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,Za),Zb)),transi1600669663ar_val(R_1))) ) ) ) ).

tff(fact_596_converse__rtranclE2,axiom,
    ! [Xa_1: list_list_char,Xb_1: exp_list_char,Za: list_list_char,Zb: exp_list_char,R_1: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Xa_1),Xb_1)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Za),Zb)),transi198989188t_char(R_1)))
     => ( ( hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Xa_1),Xb_1) != hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Za),Zb) )
       => ~ ! [A_2: list_list_char,B_1: exp_list_char] :
              ( hBOOL(member1999287380t_char(hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Xa_1),Xb_1)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_2),B_1)),R_1))
             => ~ hBOOL(member1999287380t_char(hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_2),B_1)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Za),Zb)),transi198989188t_char(R_1))) ) ) ) ).

tff(fact_597_converse__rtranclE2,axiom,
    ! [Xa_1: list_char,Xb_1: list_char,Za: list_char,Zb: list_char,R_1: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Xa_1),Xb_1)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Za),Zb)),transi1095029602t_char(R_1)))
     => ( ( hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Xa_1),Xb_1) != hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Za),Zb) )
       => ~ ! [A_2: list_char,B_1: list_char] :
              ( hBOOL(member794220506t_char(hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Xa_1),Xb_1)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_2),B_1)),R_1))
             => ~ hBOOL(member794220506t_char(hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_2),B_1)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Za),Zb)),transi1095029602t_char(R_1))) ) ) ) ).

tff(fact_598_converse__rtranclE2,axiom,
    ! [Xa_1: val,Xb_1: val,Za: val,Zb: val,R_1: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Xa_1),Xb_1)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Za),Zb)),transi1423755450al_val(R_1)))
     => ( ( hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Xa_1),Xb_1) != hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Za),Zb) )
       => ~ ! [A_2: val,B_1: val] :
              ( hBOOL(member837208074al_val(hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Xa_1),Xb_1)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_2),B_1)),R_1))
             => ~ hBOOL(member837208074al_val(hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_2),B_1)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Za),Zb)),transi1423755450al_val(R_1))) ) ) ) ).

tff(fact_599_converse__rtranclE2,axiom,
    ! [Xa_1: bop,Xb_1: product_prod_val_val,Za: bop,Zb: product_prod_val_val,R_1: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Xa_1),Xb_1)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Za),Zb)),transi1906258203al_val(R_1)))
     => ( ( hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Xa_1),Xb_1) != hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Za),Zb) )
       => ~ ! [A_2: bop,B_1: product_prod_val_val] :
              ( hBOOL(member1732271180al_val(hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Xa_1),Xb_1)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_2),B_1)),R_1))
             => ~ hBOOL(member1732271180al_val(hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_2),B_1)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Za),Zb)),transi1906258203al_val(R_1))) ) ) ) ).

tff(fact_600_converse__rtranclE2,axiom,
    ! [Xa_1: produc2061676504on_val,Xb_1: produc2061676504on_val,Za: produc2061676504on_val,Zb: produc2061676504on_val,R_1: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Xa_1),Xb_1)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Za),Zb)),transi208336786on_val(R_1)))
     => ( ( hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Xa_1),Xb_1) != hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Za),Zb) )
       => ~ ! [A_2: produc2061676504on_val,B_1: produc2061676504on_val] :
              ( hBOOL(member88670778on_val(hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Xa_1),Xb_1)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_2),B_1)),R_1))
             => ~ hBOOL(member88670778on_val(hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_2),B_1)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Za),Zb)),transi208336786on_val(R_1))) ) ) ) ).

tff(fact_601_converse__rtranclE2,axiom,
    ! [Xa_1: list_char,Xb_1: fun_Pr806764899on_val,Za: list_char,Zb: fun_Pr806764899on_val,R_1: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Xa_1),Xb_1)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Za),Zb)),transi61620055on_val(R_1)))
     => ( ( hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Xa_1),Xb_1) != hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Za),Zb) )
       => ~ ! [A_2: list_char,B_1: fun_Pr806764899on_val] :
              ( hBOOL(member1322055188on_val(hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Xa_1),Xb_1)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_2),B_1)),R_1))
             => ~ hBOOL(member1322055188on_val(hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_2),B_1)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Za),Zb)),transi61620055on_val(R_1))) ) ) ) ).

tff(fact_602_converse__rtranclE2,axiom,
    ! [Xa_1: produc124828825on_val,Xb_1: produc124828825on_val,Za: produc124828825on_val,Zb: produc124828825on_val,R_1: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Xa_1),Xb_1)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Za),Zb)),transi910771962on_val(R_1)))
     => ( ( hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Xa_1),Xb_1) != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Za),Zb) )
       => ~ ! [A_2: produc124828825on_val,B_1: produc124828825on_val] :
              ( hBOOL(member808015754on_val(hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Xa_1),Xb_1)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_2),B_1)),R_1))
             => ~ hBOOL(member808015754on_val(hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_2),B_1)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Za),Zb)),transi910771962on_val(R_1))) ) ) ) ).

tff(fact_603_converse__rtranclE2,axiom,
    ! [Xa_1: fun_na939144002on_val,Xb_1: fun_li1432931796on_val,Za: fun_na939144002on_val,Zb: fun_li1432931796on_val,R_1: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Xa_1),Xb_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Za),Zb)),transi921647814on_val(R_1)))
     => ( ( hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Xa_1),Xb_1) != hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Za),Zb) )
       => ~ ! [A_2: fun_na939144002on_val,B_1: fun_li1432931796on_val] :
              ( hBOOL(member563141460on_val(hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Xa_1),Xb_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_2),B_1)),R_1))
             => ~ hBOOL(member563141460on_val(hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_2),B_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Za),Zb)),transi921647814on_val(R_1))) ) ) ) ).

tff(fact_604_converse__rtranclE2,axiom,
    ! [Xa_1: list_val,Xb_1: exp_list_char,Za: list_val,Zb: exp_list_char,R_1: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Xa_1),Xb_1)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Za),Zb)),transi1789604888t_char(R_1)))
     => ( ( hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Xa_1),Xb_1) != hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Za),Zb) )
       => ~ ! [A_2: list_val,B_1: exp_list_char] :
              ( hBOOL(member1161907014t_char(hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Xa_1),Xb_1)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_2),B_1)),R_1))
             => ~ hBOOL(member1161907014t_char(hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_2),B_1)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Za),Zb)),transi1789604888t_char(R_1))) ) ) ) ).

tff(fact_605_converse__rtranclE2,axiom,
    ! [Xa_1: list_ty,Xb_1: produc662261637t_char,Za: list_ty,Zb: produc662261637t_char,R_1: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Xa_1),Xb_1)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Za),Zb)),transi1257872013t_char(R_1)))
     => ( ( hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Xa_1),Xb_1) != hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Za),Zb) )
       => ~ ! [A_2: list_ty,B_1: produc662261637t_char] :
              ( hBOOL(member125098544t_char(hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Xa_1),Xb_1)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_2),B_1)),R_1))
             => ~ hBOOL(member125098544t_char(hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_2),B_1)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Za),Zb)),transi1257872013t_char(R_1))) ) ) ) ).

tff(fact_606_converse__rtranclE2,axiom,
    ! [Xa_1: list_list_char,Xb_1: produc220283002t_char,Za: list_list_char,Zb: produc220283002t_char,R_1: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Xa_1),Xb_1)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Za),Zb)),transi122195895t_char(R_1)))
     => ( ( hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Xa_1),Xb_1) != hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Za),Zb) )
       => ~ ! [A_2: list_list_char,B_1: produc220283002t_char] :
              ( hBOOL(member1420286996t_char(hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Xa_1),Xb_1)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_2),B_1)),R_1))
             => ~ hBOOL(member1420286996t_char(hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_2),B_1)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Za),Zb)),transi122195895t_char(R_1))) ) ) ) ).

tff(fact_607_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_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Ax),Ay)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Bx),By)),transi374442731on_val(R_1)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Bx),By))
       => ( ! [A_2: list_exp_list_char,B_1: produc12694297on_val,Aa: list_exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_2),B_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Aa),Ba)),R_1))
             => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Aa),Ba)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Bx),By)),transi374442731on_val(R_1)))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,A_2),B_1)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_608_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_ex1201926843l_bool,Ax: exp_list_char,Ay: produc12694297on_val,Bx: exp_list_char,By: produc12694297on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ax),Ay)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Bx),By)),transi2024712006on_val(R_1)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By))
       => ( ! [A_2: exp_list_char,B_1: produc12694297on_val,Aa: exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_2),B_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Aa),Ba)),R_1))
             => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Aa),Ba)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Bx),By)),transi2024712006on_val(R_1)))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A_2),B_1)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_609_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr2055965540l_bool,Ax: produc1278157519t_char,Ay: val,Bx: produc1278157519t_char,By: val,R_1: fun_Pr643382121l_bool] :
      ( hBOOL(member619264020ar_val(hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,Ax),Ay)),hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,Bx),By)),transi1600669663ar_val(R_1)))
     => ( hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(Pa,Bx),By))
       => ( ! [A_2: produc1278157519t_char,B_1: val,Aa: produc1278157519t_char,Ba: val] :
              ( hBOOL(member619264020ar_val(hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_2),B_1)),hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,Aa),Ba)),R_1))
             => ( hBOOL(member619264020ar_val(hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,Aa),Ba)),hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,Bx),By)),transi1600669663ar_val(R_1)))
               => ( hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(Pa,A_2),B_1)) ) ) )
         => hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_610_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_1: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Ax),Ay)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Bx),By)),transi198989188t_char(R_1)))
     => ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Bx),By))
       => ( ! [A_2: list_list_char,B_1: exp_list_char,Aa: list_list_char,Ba: exp_list_char] :
              ( hBOOL(member1999287380t_char(hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_2),B_1)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Aa),Ba)),R_1))
             => ( hBOOL(member1999287380t_char(hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Aa),Ba)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Bx),By)),transi198989188t_char(R_1)))
               => ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,A_2),B_1)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_611_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li860735411r_bool,Ax: list_char,Ay: list_char,Bx: list_char,By: list_char,R_1: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Ax),Ay)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Bx),By)),transi1095029602t_char(R_1)))
     => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Bx),By))
       => ( ! [A_2: list_char,B_1: list_char,Aa: list_char,Ba: list_char] :
              ( hBOOL(member794220506t_char(hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_2),B_1)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Aa),Ba)),R_1))
             => ( hBOOL(member794220506t_char(hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Aa),Ba)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Bx),By)),transi1095029602t_char(R_1)))
               => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,A_2),B_1)) ) ) )
         => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_612_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_val_fun_val_bool,Ax: val,Ay: val,Bx: val,By: val,R_1: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Ax),Ay)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Bx),By)),transi1423755450al_val(R_1)))
     => ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Bx),By))
       => ( ! [A_2: val,B_1: val,Aa: val,Ba: val] :
              ( hBOOL(member837208074al_val(hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_2),B_1)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Aa),Ba)),R_1))
             => ( hBOOL(member837208074al_val(hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Aa),Ba)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Bx),By)),transi1423755450al_val(R_1)))
               => ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,A_2),B_1)) ) ) )
         => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_613_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_bo1454185032l_bool,Ax: bop,Ay: product_prod_val_val,Bx: bop,By: product_prod_val_val,R_1: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Ax),Ay)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Bx),By)),transi1906258203al_val(R_1)))
     => ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Bx),By))
       => ( ! [A_2: bop,B_1: product_prod_val_val,Aa: bop,Ba: product_prod_val_val] :
              ( hBOOL(member1732271180al_val(hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_2),B_1)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Aa),Ba)),R_1))
             => ( hBOOL(member1732271180al_val(hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Aa),Ba)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Bx),By)),transi1906258203al_val(R_1)))
               => ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,A_2),B_1)) ) ) )
         => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_614_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr597144499l_bool,Ax: produc2061676504on_val,Ay: produc2061676504on_val,Bx: produc2061676504on_val,By: produc2061676504on_val,R_1: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Ax),Ay)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Bx),By)),transi208336786on_val(R_1)))
     => ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Bx),By))
       => ( ! [A_2: produc2061676504on_val,B_1: produc2061676504on_val,Aa: produc2061676504on_val,Ba: produc2061676504on_val] :
              ( hBOOL(member88670778on_val(hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_2),B_1)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Aa),Ba)),R_1))
             => ( hBOOL(member88670778on_val(hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Aa),Ba)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Bx),By)),transi208336786on_val(R_1)))
               => ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,A_2),B_1)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_615_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li823162622l_bool,Ax: list_char,Ay: fun_Pr806764899on_val,Bx: list_char,By: fun_Pr806764899on_val,R_1: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Ax),Ay)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Bx),By)),transi61620055on_val(R_1)))
     => ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Bx),By))
       => ( ! [A_2: list_char,B_1: fun_Pr806764899on_val,Aa: list_char,Ba: fun_Pr806764899on_val] :
              ( hBOOL(member1322055188on_val(hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_2),B_1)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Aa),Ba)),R_1))
             => ( hBOOL(member1322055188on_val(hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Aa),Ba)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Bx),By)),transi61620055on_val(R_1)))
               => ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,A_2),B_1)) ) ) )
         => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_616_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr633696065l_bool,Ax: produc124828825on_val,Ay: produc124828825on_val,Bx: produc124828825on_val,By: produc124828825on_val,R_1: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Ax),Ay)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Bx),By)),transi910771962on_val(R_1)))
     => ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By))
       => ( ! [A_2: produc124828825on_val,B_1: produc124828825on_val,Aa: produc124828825on_val,Ba: produc124828825on_val] :
              ( hBOOL(member808015754on_val(hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_2),B_1)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Aa),Ba)),R_1))
             => ( hBOOL(member808015754on_val(hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Aa),Ba)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Bx),By)),transi910771962on_val(R_1)))
               => ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A_2),B_1)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_617_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_1: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ax),Ay)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Bx),By)),transi921647814on_val(R_1)))
     => ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By))
       => ( ! [A_2: fun_na939144002on_val,B_1: fun_li1432931796on_val,Aa: fun_na939144002on_val,Ba: fun_li1432931796on_val] :
              ( hBOOL(member563141460on_val(hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_2),B_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Aa),Ba)),R_1))
             => ( hBOOL(member563141460on_val(hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Aa),Ba)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Bx),By)),transi921647814on_val(R_1)))
               => ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A_2),B_1)) ) ) )
         => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_618_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li826105035r_bool,Ax: list_val,Ay: exp_list_char,Bx: list_val,By: exp_list_char,R_1: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Ax),Ay)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Bx),By)),transi1789604888t_char(R_1)))
     => ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Bx),By))
       => ( ! [A_2: list_val,B_1: exp_list_char,Aa: list_val,Ba: exp_list_char] :
              ( hBOOL(member1161907014t_char(hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_2),B_1)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Aa),Ba)),R_1))
             => ( hBOOL(member1161907014t_char(hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Aa),Ba)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Bx),By)),transi1789604888t_char(R_1)))
               => ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,A_2),B_1)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_619_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li887890578r_bool,Ax: list_ty,Ay: produc662261637t_char,Bx: list_ty,By: produc662261637t_char,R_1: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ax),Ay)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Bx),By)),transi1257872013t_char(R_1)))
     => ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Bx),By))
       => ( ! [A_2: list_ty,B_1: produc662261637t_char,Aa: list_ty,Ba: produc662261637t_char] :
              ( hBOOL(member125098544t_char(hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_2),B_1)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Aa),Ba)),R_1))
             => ( hBOOL(member125098544t_char(hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Aa),Ba)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Bx),By)),transi1257872013t_char(R_1)))
               => ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,A_2),B_1)) ) ) )
         => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_620_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li1024794712r_bool,Ax: list_list_char,Ay: produc220283002t_char,Bx: list_list_char,By: produc220283002t_char,R_1: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Ax),Ay)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Bx),By)),transi122195895t_char(R_1)))
     => ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Bx),By))
       => ( ! [A_2: list_list_char,B_1: produc220283002t_char,Aa: list_list_char,Ba: produc220283002t_char] :
              ( hBOOL(member1420286996t_char(hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_2),B_1)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Aa),Ba)),R_1))
             => ( hBOOL(member1420286996t_char(hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Aa),Ba)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Bx),By)),transi122195895t_char(R_1)))
               => ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,A_2),B_1)) ) ) )
         => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_621_rtrancl__induct2,axiom,
    ! [Pa: fun_li1372729616l_bool,Ax: list_exp_list_char,Ay: produc12694297on_val,Bx: list_exp_list_char,By: produc12694297on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Ax),Ay)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Bx),By)),transi374442731on_val(R_1)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Ax),Ay))
       => ( ! [A_2: list_exp_list_char,B_1: produc12694297on_val,Aa: list_exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Ax),Ay)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_2),B_1)),transi374442731on_val(R_1)))
             => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_2),B_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,A_2),B_1))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_622_rtrancl__induct2,axiom,
    ! [Pa: fun_ex1201926843l_bool,Ax: exp_list_char,Ay: produc12694297on_val,Bx: exp_list_char,By: produc12694297on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ax),Ay)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Bx),By)),transi2024712006on_val(R_1)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay))
       => ( ! [A_2: exp_list_char,B_1: produc12694297on_val,Aa: exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ax),Ay)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_2),B_1)),transi2024712006on_val(R_1)))
             => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_2),B_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A_2),B_1))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_623_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr2055965540l_bool,Ax: produc1278157519t_char,Ay: val,Bx: produc1278157519t_char,By: val,R_1: fun_Pr643382121l_bool] :
      ( hBOOL(member619264020ar_val(hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,Ax),Ay)),hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,Bx),By)),transi1600669663ar_val(R_1)))
     => ( hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(Pa,Ax),Ay))
       => ( ! [A_2: produc1278157519t_char,B_1: val,Aa: produc1278157519t_char,Ba: val] :
              ( hBOOL(member619264020ar_val(hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,Ax),Ay)),hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_2),B_1)),transi1600669663ar_val(R_1)))
             => ( hBOOL(member619264020ar_val(hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_2),B_1)),hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(Pa,A_2),B_1))
                 => hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_624_rtrancl__induct2,axiom,
    ! [Pa: fun_li221477r_bool,Ax: list_list_char,Ay: exp_list_char,Bx: list_list_char,By: exp_list_char,R_1: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Ax),Ay)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Bx),By)),transi198989188t_char(R_1)))
     => ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Ax),Ay))
       => ( ! [A_2: list_list_char,B_1: exp_list_char,Aa: list_list_char,Ba: exp_list_char] :
              ( hBOOL(member1999287380t_char(hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Ax),Ay)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_2),B_1)),transi198989188t_char(R_1)))
             => ( hBOOL(member1999287380t_char(hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_2),B_1)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,A_2),B_1))
                 => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_625_rtrancl__induct2,axiom,
    ! [Pa: fun_li860735411r_bool,Ax: list_char,Ay: list_char,Bx: list_char,By: list_char,R_1: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Ax),Ay)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Bx),By)),transi1095029602t_char(R_1)))
     => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Ax),Ay))
       => ( ! [A_2: list_char,B_1: list_char,Aa: list_char,Ba: list_char] :
              ( hBOOL(member794220506t_char(hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Ax),Ay)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_2),B_1)),transi1095029602t_char(R_1)))
             => ( hBOOL(member794220506t_char(hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_2),B_1)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,A_2),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_626_rtrancl__induct2,axiom,
    ! [Pa: fun_val_fun_val_bool,Ax: val,Ay: val,Bx: val,By: val,R_1: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Ax),Ay)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Bx),By)),transi1423755450al_val(R_1)))
     => ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Ax),Ay))
       => ( ! [A_2: val,B_1: val,Aa: val,Ba: val] :
              ( hBOOL(member837208074al_val(hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Ax),Ay)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_2),B_1)),transi1423755450al_val(R_1)))
             => ( hBOOL(member837208074al_val(hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_2),B_1)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,A_2),B_1))
                 => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_627_rtrancl__induct2,axiom,
    ! [Pa: fun_bo1454185032l_bool,Ax: bop,Ay: product_prod_val_val,Bx: bop,By: product_prod_val_val,R_1: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Ax),Ay)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Bx),By)),transi1906258203al_val(R_1)))
     => ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Ax),Ay))
       => ( ! [A_2: bop,B_1: product_prod_val_val,Aa: bop,Ba: product_prod_val_val] :
              ( hBOOL(member1732271180al_val(hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Ax),Ay)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_2),B_1)),transi1906258203al_val(R_1)))
             => ( hBOOL(member1732271180al_val(hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_2),B_1)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,A_2),B_1))
                 => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_628_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr597144499l_bool,Ax: produc2061676504on_val,Ay: produc2061676504on_val,Bx: produc2061676504on_val,By: produc2061676504on_val,R_1: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Ax),Ay)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Bx),By)),transi208336786on_val(R_1)))
     => ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Ax),Ay))
       => ( ! [A_2: produc2061676504on_val,B_1: produc2061676504on_val,Aa: produc2061676504on_val,Ba: produc2061676504on_val] :
              ( hBOOL(member88670778on_val(hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Ax),Ay)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_2),B_1)),transi208336786on_val(R_1)))
             => ( hBOOL(member88670778on_val(hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_2),B_1)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,A_2),B_1))
                 => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_629_rtrancl__induct2,axiom,
    ! [Pa: fun_li823162622l_bool,Ax: list_char,Ay: fun_Pr806764899on_val,Bx: list_char,By: fun_Pr806764899on_val,R_1: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Ax),Ay)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Bx),By)),transi61620055on_val(R_1)))
     => ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Ax),Ay))
       => ( ! [A_2: list_char,B_1: fun_Pr806764899on_val,Aa: list_char,Ba: fun_Pr806764899on_val] :
              ( hBOOL(member1322055188on_val(hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Ax),Ay)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_2),B_1)),transi61620055on_val(R_1)))
             => ( hBOOL(member1322055188on_val(hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_2),B_1)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,A_2),B_1))
                 => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_630_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr633696065l_bool,Ax: produc124828825on_val,Ay: produc124828825on_val,Bx: produc124828825on_val,By: produc124828825on_val,R_1: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Ax),Ay)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Bx),By)),transi910771962on_val(R_1)))
     => ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay))
       => ( ! [A_2: produc124828825on_val,B_1: produc124828825on_val,Aa: produc124828825on_val,Ba: produc124828825on_val] :
              ( hBOOL(member808015754on_val(hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Ax),Ay)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_2),B_1)),transi910771962on_val(R_1)))
             => ( hBOOL(member808015754on_val(hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_2),B_1)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A_2),B_1))
                 => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_631_rtrancl__induct2,axiom,
    ! [Pa: fun_fu100249073l_bool,Ax: fun_na939144002on_val,Ay: fun_li1432931796on_val,Bx: fun_na939144002on_val,By: fun_li1432931796on_val,R_1: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ax),Ay)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Bx),By)),transi921647814on_val(R_1)))
     => ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay))
       => ( ! [A_2: fun_na939144002on_val,B_1: fun_li1432931796on_val,Aa: fun_na939144002on_val,Ba: fun_li1432931796on_val] :
              ( hBOOL(member563141460on_val(hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ax),Ay)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_2),B_1)),transi921647814on_val(R_1)))
             => ( hBOOL(member563141460on_val(hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_2),B_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A_2),B_1))
                 => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_632_rtrancl__induct2,axiom,
    ! [Pa: fun_li826105035r_bool,Ax: list_val,Ay: exp_list_char,Bx: list_val,By: exp_list_char,R_1: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Ax),Ay)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Bx),By)),transi1789604888t_char(R_1)))
     => ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Ax),Ay))
       => ( ! [A_2: list_val,B_1: exp_list_char,Aa: list_val,Ba: exp_list_char] :
              ( hBOOL(member1161907014t_char(hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Ax),Ay)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_2),B_1)),transi1789604888t_char(R_1)))
             => ( hBOOL(member1161907014t_char(hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_2),B_1)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,A_2),B_1))
                 => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_633_rtrancl__induct2,axiom,
    ! [Pa: fun_li887890578r_bool,Ax: list_ty,Ay: produc662261637t_char,Bx: list_ty,By: produc662261637t_char,R_1: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ax),Ay)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Bx),By)),transi1257872013t_char(R_1)))
     => ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Ax),Ay))
       => ( ! [A_2: list_ty,B_1: produc662261637t_char,Aa: list_ty,Ba: produc662261637t_char] :
              ( hBOOL(member125098544t_char(hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ax),Ay)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_2),B_1)),transi1257872013t_char(R_1)))
             => ( hBOOL(member125098544t_char(hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_2),B_1)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,A_2),B_1))
                 => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_634_rtrancl__induct2,axiom,
    ! [Pa: fun_li1024794712r_bool,Ax: list_list_char,Ay: produc220283002t_char,Bx: list_list_char,By: produc220283002t_char,R_1: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Ax),Ay)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Bx),By)),transi122195895t_char(R_1)))
     => ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Ax),Ay))
       => ( ! [A_2: list_list_char,B_1: produc220283002t_char,Aa: list_list_char,Ba: produc220283002t_char] :
              ( hBOOL(member1420286996t_char(hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Ax),Ay)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_2),B_1)),transi122195895t_char(R_1)))
             => ( hBOOL(member1420286996t_char(hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_2),B_1)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,A_2),B_1))
                 => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_635_rtranclE,axiom,
    ! [A_1: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B),transi1395422419t_char(R_1)))
     => ( ( A_1 != B )
       => ~ ! [Y_2: list_char] :
              ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),Y_2),transi1395422419t_char(R_1)))
             => ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Y_2),B),R_1)) ) ) ) ).

tff(fact_636_rtranclE,axiom,
    ! [A_1: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B),transi374442731on_val(R_1)))
     => ( ( A_1 != B )
       => ~ ! [Y_2: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),Y_2),transi374442731on_val(R_1)))
             => ~ hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Y_2),B),R_1)) ) ) ) ).

tff(fact_637_rtranclE,axiom,
    ! [A_1: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B),transi2024712006on_val(R_1)))
     => ( ( A_1 != B )
       => ~ ! [Y_2: produc124828825on_val] :
              ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),Y_2),transi2024712006on_val(R_1)))
             => ~ hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Y_2),B),R_1)) ) ) ) ).

tff(fact_638_rtranclE,axiom,
    ! [A_1: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B),transi935034983cl_val(R_1)))
     => ( ( A_1 != B )
       => ~ ! [Y_2: val] :
              ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),Y_2),transi935034983cl_val(R_1)))
             => ~ hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Y_2),B),R_1)) ) ) ) ).

tff(fact_639_converse__rtranclE,axiom,
    ! [X_2: list_char,Z_1: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_2),Z_1),transi1395422419t_char(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: list_char] :
              ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_2),Y_2),R_1))
             => ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Y_2),Z_1),transi1395422419t_char(R_1))) ) ) ) ).

tff(fact_640_converse__rtranclE,axiom,
    ! [X_2: produc2061676504on_val,Z_1: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,X_2),Z_1),transi374442731on_val(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,X_2),Y_2),R_1))
             => ~ hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Y_2),Z_1),transi374442731on_val(R_1))) ) ) ) ).

tff(fact_641_converse__rtranclE,axiom,
    ! [X_2: produc124828825on_val,Z_1: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X_2),Z_1),transi2024712006on_val(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: produc124828825on_val] :
              ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X_2),Y_2),R_1))
             => ~ hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Y_2),Z_1),transi2024712006on_val(R_1))) ) ) ) ).

tff(fact_642_converse__rtranclE,axiom,
    ! [X_2: val,Z_1: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_2),Z_1),transi935034983cl_val(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: val] :
              ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_2),Y_2),R_1))
             => ~ hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Y_2),Z_1),transi935034983cl_val(R_1))) ) ) ) ).

tff(fact_643_mem__def,axiom,
    ! [X_2: nat,A_16: fun_nat_bool] :
      ( hBOOL(member_nat(X_2,A_16))
    <=> hBOOL(hAPP_nat_bool(A_16,X_2)) ) ).

tff(fact_644_mem__def,axiom,
    ! [X_2: list_char,A_16: fun_list_char_bool] :
      ( hBOOL(member_list_char(X_2,A_16))
    <=> hBOOL(hAPP_list_char_bool(A_16,X_2)) ) ).

tff(fact_645_mem__def,axiom,
    ! [X_2: produc1278157519t_char,A_16: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(X_2,A_16))
    <=> hBOOL(hAPP_P449474095r_bool(A_16,X_2)) ) ).

tff(fact_646_mem__def,axiom,
    ! [X_2: produc430140671on_val,A_16: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(X_2,A_16))
    <=> hBOOL(hAPP_P1333315679l_bool(A_16,X_2)) ) ).

tff(fact_647_mem__def,axiom,
    ! [X_2: produc1102272487on_val,A_16: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(X_2,A_16))
    <=> hBOOL(hAPP_P282169671l_bool(A_16,X_2)) ) ).

tff(fact_648_converse__rtrancl__induct,axiom,
    ! [Pa: fun_list_char_bool,A_1: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B),transi1395422419t_char(R_1)))
     => ( hBOOL(hAPP_list_char_bool(Pa,B))
       => ( ! [Y_2: list_char,Z: list_char] :
              ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Y_2),Z),R_1))
             => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Z),B),transi1395422419t_char(R_1)))
               => ( hBOOL(hAPP_list_char_bool(Pa,Z))
                 => hBOOL(hAPP_list_char_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_list_char_bool(Pa,A_1)) ) ) ) ).

tff(fact_649_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr248118298l_bool,A_1: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B),transi374442731on_val(R_1)))
     => ( hBOOL(hAPP_P71593144l_bool(Pa,B))
       => ( ! [Y_2: produc2061676504on_val,Z: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Y_2),Z),R_1))
             => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Z),B),transi374442731on_val(R_1)))
               => ( hBOOL(hAPP_P71593144l_bool(Pa,Z))
                 => hBOOL(hAPP_P71593144l_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(Pa,A_1)) ) ) ) ).

tff(fact_650_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr680585871l_bool,A_1: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B),transi2024712006on_val(R_1)))
     => ( hBOOL(hAPP_P1708370145l_bool(Pa,B))
       => ( ! [Y_2: produc124828825on_val,Z: produc124828825on_val] :
              ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Y_2),Z),R_1))
             => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Z),B),transi2024712006on_val(R_1)))
               => ( hBOOL(hAPP_P1708370145l_bool(Pa,Z))
                 => hBOOL(hAPP_P1708370145l_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(Pa,A_1)) ) ) ) ).

tff(fact_651_converse__rtrancl__induct,axiom,
    ! [Pa: fun_val_bool,A_1: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B),transi935034983cl_val(R_1)))
     => ( hBOOL(hAPP_val_bool(Pa,B))
       => ( ! [Y_2: val,Z: val] :
              ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Y_2),Z),R_1))
             => ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Z),B),transi935034983cl_val(R_1)))
               => ( hBOOL(hAPP_val_bool(Pa,Z))
                 => hBOOL(hAPP_val_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_val_bool(Pa,A_1)) ) ) ) ).

tff(fact_652_rtrancl__induct,axiom,
    ! [Pa: fun_list_char_bool,A_1: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B),transi1395422419t_char(R_1)))
     => ( hBOOL(hAPP_list_char_bool(Pa,A_1))
       => ( ! [Y_2: list_char,Z: list_char] :
              ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),Y_2),transi1395422419t_char(R_1)))
             => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Y_2),Z),R_1))
               => ( hBOOL(hAPP_list_char_bool(Pa,Y_2))
                 => hBOOL(hAPP_list_char_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_list_char_bool(Pa,B)) ) ) ) ).

tff(fact_653_rtrancl__induct,axiom,
    ! [Pa: fun_Pr248118298l_bool,A_1: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B),transi374442731on_val(R_1)))
     => ( hBOOL(hAPP_P71593144l_bool(Pa,A_1))
       => ( ! [Y_2: produc2061676504on_val,Z: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),Y_2),transi374442731on_val(R_1)))
             => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Y_2),Z),R_1))
               => ( hBOOL(hAPP_P71593144l_bool(Pa,Y_2))
                 => hBOOL(hAPP_P71593144l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(Pa,B)) ) ) ) ).

tff(fact_654_rtrancl__induct,axiom,
    ! [Pa: fun_Pr680585871l_bool,A_1: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B),transi2024712006on_val(R_1)))
     => ( hBOOL(hAPP_P1708370145l_bool(Pa,A_1))
       => ( ! [Y_2: produc124828825on_val,Z: produc124828825on_val] :
              ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),Y_2),transi2024712006on_val(R_1)))
             => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Y_2),Z),R_1))
               => ( hBOOL(hAPP_P1708370145l_bool(Pa,Y_2))
                 => hBOOL(hAPP_P1708370145l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(Pa,B)) ) ) ) ).

tff(fact_655_rtrancl__induct,axiom,
    ! [Pa: fun_val_bool,A_1: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B),transi935034983cl_val(R_1)))
     => ( hBOOL(hAPP_val_bool(Pa,A_1))
       => ( ! [Y_2: val,Z: val] :
              ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),Y_2),transi935034983cl_val(R_1)))
             => ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Y_2),Z),R_1))
               => ( hBOOL(hAPP_val_bool(Pa,Y_2))
                 => hBOOL(hAPP_val_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_val_bool(Pa,B)) ) ) ) ).

tff(fact_656_blocksRedsFinal,axiom,
    ! [L_5: fun_li1432931796on_val,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char,Vsa: list_val,Vsa_1: list_list_char,Tsa: list_ty] :
      ( ( hAPP_l66428094ar_nat(size_s2113983095t_char,Vsa_1) = hAPP_list_ty_nat(size_size_list_ty,Tsa) )
     => ( ( hAPP_list_val_nat(size_size_list_val,Vsa) = hAPP_list_ty_nat(size_size_list_ty,Tsa) )
       => ( hBOOL(distinct_list_char(Vsa_1))
         => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),map_up1085636310ar_val(L_1,Vsa_1,Vsa)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L))),transi2024712006on_val(red(Pa))))
           => ( hBOOL(final_list_char(E))
             => ( ( L_5 = overri2012515291on_val(L,L_1,set_list_char(Vsa_1)) )
               => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Vsa_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Tsa),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Vsa),Ea))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L_5))),transi2024712006on_val(red(Pa)))) ) ) ) ) ) ) ).

tff(fact_657_Red__lcl__add,axiom,
    ! [L_0: fun_li1432931796on_val,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L))),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),map_ad325961431ar_val(L_0,L_1)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),map_ad325961431ar_val(L_0,L)))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_658_map__eq__conv,axiom,
    ! [F_1: fun_Pr1149393094ar_val,Xs: list_P2023964830har_ty,G: fun_Pr1149393094ar_val] :
      ( ( hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),Xs) = hAPP_l608137480ar_val(map_Pr1153581243ar_val(G),Xs) )
    <=> ! [X_1: produc245756905har_ty] :
          ( hBOOL(member1783291580har_ty(X_1,set_Pr1831523898har_ty(Xs)))
         => ( hAPP_P841862366ar_val(F_1,X_1) = hAPP_P841862366ar_val(G,X_1) ) ) ) ).

tff(fact_659_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_1: list_char] :
          ( hBOOL(member_list_char(X_1,set_list_char(Xs)))
         => ( hAPP_list_char_val(F_1,X_1) = hAPP_list_char_val(G,X_1) ) ) ) ).

tff(fact_660_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_1: val] :
          ( hBOOL(member_val(X_1,set_val(Xs)))
         => ( hAPP_v834067052t_char(F_1,X_1) = hAPP_v834067052t_char(G,X_1) ) ) ) ).

tff(fact_661_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_1: ty] :
          ( hBOOL(member_ty(X_1,set_ty(Xs)))
         => ( hAPP_ty_option_ty(F_1,X_1) = hAPP_ty_option_ty(G,X_1) ) ) ) ).

tff(fact_662_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_1: val] :
          ( hBOOL(member_val(X_1,set_val(Xs)))
         => ( hAPP_val_option_ty(F_1,X_1) = hAPP_val_option_ty(G,X_1) ) ) ) ).

tff(fact_663_red__lcl__add,axiom,
    ! [L_0: fun_li1432931796on_val,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L))),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),map_ad325961431ar_val(L_0,L_1)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),map_ad325961431ar_val(L_0,L)))),red(Pa))) ) ).

tff(fact_664_blocksReds,axiom,
    ! [Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char,Vsa: list_val,Vsa_1: list_list_char,Tsa: list_ty] :
      ( ( hAPP_l66428094ar_nat(size_s2113983095t_char,Vsa_1) = hAPP_list_ty_nat(size_size_list_ty,Tsa) )
     => ( ( hAPP_list_val_nat(size_size_list_val,Vsa) = hAPP_list_ty_nat(size_size_list_ty,Tsa) )
       => ( hBOOL(distinct_list_char(Vsa_1))
         => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),map_up1085636310ar_val(L_1,Vsa_1,Vsa)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L))),transi2024712006on_val(red(Pa))))
           => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Vsa_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Tsa),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Vsa),Ea))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Vsa_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Tsa),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,hAPP_l1892737211st_val(map_list_char_val(comp_o1129292306t_char(the_val,L)),Vsa_1)),E))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),overri2012515291on_val(L,L_1,set_list_char(Vsa_1))))),transi2024712006on_val(red(Pa)))) ) ) ) ) ).

tff(fact_665_map__cong,axiom,
    ! [F_1: fun_Pr1149393094ar_val,G: fun_Pr1149393094ar_val,Xs: list_P2023964830har_ty,Ys: list_P2023964830har_ty] :
      ( ( Xs = Ys )
     => ( ! [X_1: produc245756905har_ty] :
            ( hBOOL(member1783291580har_ty(X_1,set_Pr1831523898har_ty(Ys)))
           => ( hAPP_P841862366ar_val(F_1,X_1) = hAPP_P841862366ar_val(G,X_1) ) )
       => ( hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),Xs) = hAPP_l608137480ar_val(map_Pr1153581243ar_val(G),Ys) ) ) ) ).

tff(fact_666_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_1: list_char] :
            ( hBOOL(member_list_char(X_1,set_list_char(Ys)))
           => ( hAPP_list_char_val(F_1,X_1) = hAPP_list_char_val(G,X_1) ) )
       => ( hAPP_l1892737211st_val(map_list_char_val(F_1),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Ys) ) ) ) ).

tff(fact_667_map__cong,axiom,
    ! [F_1: fun_va223928858t_char,G: fun_va223928858t_char,Xs: list_val,Ys: list_val] :
      ( ( Xs = Ys )
     => ( ! [X_1: val] :
            ( hBOOL(member_val(X_1,set_val(Ys)))
           => ( hAPP_v834067052t_char(F_1,X_1) = hAPP_v834067052t_char(G,X_1) ) )
       => ( hAPP_l732421366t_char(map_va1934808527t_char(F_1),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Ys) ) ) ) ).

tff(fact_668_map__cong,axiom,
    ! [F_1: fun_ty_option_ty,G: fun_ty_option_ty,Xs: list_ty,Ys: list_ty] :
      ( ( Xs = Ys )
     => ( ! [X_1: ty] :
            ( hBOOL(member_ty(X_1,set_ty(Ys)))
           => ( hAPP_ty_option_ty(F_1,X_1) = hAPP_ty_option_ty(G,X_1) ) )
       => ( hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys) ) ) ) ).

tff(fact_669_map__cong,axiom,
    ! [F_1: fun_val_option_ty,G: fun_val_option_ty,Xs: list_val,Ys: list_val] :
      ( ( Xs = Ys )
     => ( ! [X_1: val] :
            ( hBOOL(member_val(X_1,set_val(Ys)))
           => ( hAPP_val_option_ty(F_1,X_1) = hAPP_val_option_ty(G,X_1) ) )
       => ( hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys) ) ) ) ).

tff(fact_670_map__idI,axiom,
    ! [F_1: fun_li1751394789t_char,Xs: list_list_char] :
      ( ! [X_1: list_char] :
          ( hBOOL(member_list_char(X_1,set_list_char(Xs)))
         => ( hAPP_l1074208899t_char(F_1,X_1) = X_1 ) )
     => ( hAPP_l407174677t_char(map_li1333403488t_char(F_1),Xs) = Xs ) ) ).

tff(fact_671_map__idI,axiom,
    ! [F_1: fun_nat_nat,Xs: list_nat] :
      ( ! [X_1: nat] :
          ( hBOOL(member_nat(X_1,set_nat(Xs)))
         => ( hAPP_nat_nat(F_1,X_1) = X_1 ) )
     => ( hAPP_l248265089st_nat(map_nat_nat(F_1),Xs) = Xs ) ) ).

tff(fact_672_map__idI,axiom,
    ! [F_1: fun_Pr1380325635t_char,Xs: list_P1916372464t_char] :
      ( ! [X_1: produc1278157519t_char] :
          ( hBOOL(member1251428284t_char(X_1,set_Pr550895038t_char(Xs)))
         => ( hAPP_P760138657t_char(F_1,X_1) = X_1 ) )
     => ( hAPP_l250787541t_char(map_Pr361633150t_char(F_1),Xs) = Xs ) ) ).

tff(fact_673_map__idI,axiom,
    ! [F_1: fun_Pr1898553187on_val,Xs: list_P507235360on_val] :
      ( ! [X_1: produc430140671on_val] :
          ( hBOOL(member875476972on_val(X_1,set_Pr771975662on_val(Xs)))
         => ( hAPP_P1439304705on_val(F_1,X_1) = X_1 ) )
     => ( hAPP_l1208602837on_val(map_Pr1729094110on_val(F_1),Xs) = Xs ) ) ).

tff(fact_674_map__idI,axiom,
    ! [F_1: fun_Pr12181427on_val,Xs: list_P1439941640on_val] :
      ( ! [X_1: produc1102272487on_val] :
          ( hBOOL(member773094996on_val(X_1,set_Pr1921835862on_val(Xs)))
         => ( hAPP_P918220497on_val(F_1,X_1) = X_1 ) )
     => ( hAPP_l1695428693on_val(map_Pr1655409582on_val(F_1),Xs) = Xs ) ) ).

tff(fact_675_map__ext,axiom,
    ! [F_1: fun_Pr1149393094ar_val,G: fun_Pr1149393094ar_val,Xs: list_P2023964830har_ty] :
      ( ! [X_1: produc245756905har_ty] :
          ( hBOOL(member1783291580har_ty(X_1,set_Pr1831523898har_ty(Xs)))
         => ( hAPP_P841862366ar_val(F_1,X_1) = hAPP_P841862366ar_val(G,X_1) ) )
     => ( hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),Xs) = hAPP_l608137480ar_val(map_Pr1153581243ar_val(G),Xs) ) ) ).

tff(fact_676_map__ext,axiom,
    ! [F_1: fun_list_char_val,G: fun_list_char_val,Xs: list_list_char] :
      ( ! [X_1: list_char] :
          ( hBOOL(member_list_char(X_1,set_list_char(Xs)))
         => ( hAPP_list_char_val(F_1,X_1) = hAPP_list_char_val(G,X_1) ) )
     => ( hAPP_l1892737211st_val(map_list_char_val(F_1),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Xs) ) ) ).

tff(fact_677_map__ext,axiom,
    ! [F_1: fun_va223928858t_char,G: fun_va223928858t_char,Xs: list_val] :
      ( ! [X_1: val] :
          ( hBOOL(member_val(X_1,set_val(Xs)))
         => ( hAPP_v834067052t_char(F_1,X_1) = hAPP_v834067052t_char(G,X_1) ) )
     => ( hAPP_l732421366t_char(map_va1934808527t_char(F_1),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Xs) ) ) ).

tff(fact_678_map__ext,axiom,
    ! [F_1: fun_ty_option_ty,G: fun_ty_option_ty,Xs: list_ty] :
      ( ! [X_1: ty] :
          ( hBOOL(member_ty(X_1,set_ty(Xs)))
         => ( hAPP_ty_option_ty(F_1,X_1) = hAPP_ty_option_ty(G,X_1) ) )
     => ( hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Xs) ) ) ).

tff(fact_679_map__ext,axiom,
    ! [F_1: fun_val_option_ty,G: fun_val_option_ty,Xs: list_val] :
      ( ! [X_1: val] :
          ( hBOOL(member_val(X_1,set_val(Xs)))
         => ( hAPP_val_option_ty(F_1,X_1) = hAPP_val_option_ty(G,X_1) ) )
     => ( hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Xs) ) ) ).

tff(fact_680_ex__map__conv,axiom,
    ! [Ys: list_P1697858023ar_val,F_1: fun_Pr1149393094ar_val] :
      ( ? [Xs_7: list_P2023964830har_ty] : Ys = hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),Xs_7)
    <=> ! [X_1: produc1147203250ar_val] :
          ( hBOOL(member806854661ar_val(X_1,set_Pr309835907ar_val(Ys)))
         => ? [Xa: produc245756905har_ty] : X_1 = hAPP_P841862366ar_val(F_1,Xa) ) ) ).

tff(fact_681_ex__map__conv,axiom,
    ! [Ys: list_val,F_1: fun_list_char_val] :
      ( ? [Xs_7: list_list_char] : Ys = hAPP_l1892737211st_val(map_list_char_val(F_1),Xs_7)
    <=> ! [X_1: val] :
          ( hBOOL(member_val(X_1,set_val(Ys)))
         => ? [Xa: list_char] : X_1 = hAPP_list_char_val(F_1,Xa) ) ) ).

tff(fact_682_ex__map__conv,axiom,
    ! [Ys: list_exp_list_char,F_1: fun_va223928858t_char] :
      ( ? [Xs_7: list_val] : Ys = hAPP_l732421366t_char(map_va1934808527t_char(F_1),Xs_7)
    <=> ! [X_1: exp_list_char] :
          ( hBOOL(member_exp_list_char(X_1,set_exp_list_char(Ys)))
         => ? [Xa: val] : X_1 = hAPP_v834067052t_char(F_1,Xa) ) ) ).

tff(fact_683_ex__map__conv,axiom,
    ! [Ys: list_option_ty,F_1: fun_ty_option_ty] :
      ( ? [Xs_7: list_ty] : Ys = hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Xs_7)
    <=> ! [X_1: option_ty] :
          ( hBOOL(member_option_ty(X_1,set_option_ty(Ys)))
         => ? [Xa: ty] : X_1 = hAPP_ty_option_ty(F_1,Xa) ) ) ).

tff(fact_684_ex__map__conv,axiom,
    ! [Ys: list_option_ty,F_1: fun_val_option_ty] :
      ( ? [Xs_7: list_val] : Ys = hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Xs_7)
    <=> ! [X_1: option_ty] :
          ( hBOOL(member_option_ty(X_1,set_option_ty(Ys)))
         => ? [Xa: val] : X_1 = hAPP_val_option_ty(F_1,Xa) ) ) ).

tff(fact_685_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_686_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_687_map__upds__apply__nontin,axiom,
    ! [F_1: fun_li1432931796on_val,Ys: list_val,X_2: list_char,Xs: list_list_char] :
      ( ~ hBOOL(member_list_char(X_2,set_list_char(Xs)))
     => ( hAPP_l207779698on_val(map_up1085636310ar_val(F_1,Xs,Ys),X_2) = hAPP_l207779698on_val(F_1,X_2) ) ) ).

tff(fact_688_map__upds__apply__nontin,axiom,
    ! [F_1: fun_li688206603ion_ty,Ys: list_ty,X_2: list_char,Xs: list_list_char] :
      ( ~ hBOOL(member_list_char(X_2,set_list_char(Xs)))
     => ( hAPP_l512744617ion_ty(map_up891053837har_ty(F_1,Xs,Ys),X_2) = hAPP_l512744617ion_ty(F_1,X_2) ) ) ).

tff(fact_689_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_690_hext__def,axiom,
    ! [Ha: fun_na939144002on_val,H: fun_na939144002on_val] :
      ( hBOOL(hext(Ha,H))
    <=> ! [A_2: nat,C_1: list_char,Fs: fun_Pr806764899on_val] :
          ( ( hAPP_n546249108on_val(Ha,A_2) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C_1),Fs)) )
         => ? [Fs_3: fun_Pr806764899on_val] : hAPP_n546249108on_val(H,A_2) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C_1),Fs_3)) ) ) ).

tff(fact_691_hext__objD,axiom,
    ! [A_1: nat,C: list_char,Fs_1: fun_Pr806764899on_val,Ha: fun_na939144002on_val,H: fun_na939144002on_val] :
      ( hBOOL(hext(Ha,H))
     => ( ( hAPP_n546249108on_val(Ha,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)) )
       => ? [Fs_3: fun_Pr806764899on_val] : hAPP_n546249108on_val(H,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_3)) ) ) ).

tff(fact_692_map__comp__map,axiom,
    ! [F_1: fun_li889387821on_val,G: fun_li867521386ar_val] : comp_l347675690har_ty(map_li596218076on_val(F_1),map_li912744805ar_val(G)) = map_li1065623653on_val(comp_l424027617har_ty(F_1,G)) ).

tff(fact_693_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_694_List_Omap_Ocomp,axiom,
    ! [F_1: fun_li889387821on_val,G: fun_li867521386ar_val] : comp_l347675690har_ty(map_li596218076on_val(F_1),map_li912744805ar_val(G)) = map_li1065623653on_val(comp_l424027617har_ty(F_1,G)) ).

tff(fact_695_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_696_map__map,axiom,
    ! [F_1: fun_li889387821on_val,G: fun_li867521386ar_val,Xs: list_l38846271har_ty] : hAPP_l1790629643on_val(map_li596218076on_val(F_1),hAPP_l823328606ar_val(map_li912744805ar_val(G),Xs)) = hAPP_l721971010on_val(map_li1065623653on_val(comp_l424027617har_ty(F_1,G)),Xs) ).

tff(fact_697_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_698_List_Omap_Ocompositionality,axiom,
    ! [F_1: fun_li889387821on_val,G: fun_li867521386ar_val,List_2: list_l38846271har_ty] : hAPP_l1790629643on_val(map_li596218076on_val(F_1),hAPP_l823328606ar_val(map_li912744805ar_val(G),List_2)) = hAPP_l721971010on_val(map_li1065623653on_val(comp_l424027617har_ty(F_1,G)),List_2) ).

tff(fact_699_List_Omap_Ocompositionality,axiom,
    ! [F_1: fun_option_val_val,G: fun_li1432931796on_val,List_2: list_list_char] : hAPP_l228474410st_val(map_option_val_val(F_1),hAPP_l297961988on_val(map_li50976719on_val(G),List_2)) = hAPP_l1892737211st_val(map_list_char_val(comp_o1129292306t_char(F_1,G)),List_2) ).

tff(fact_700_the_Osimps,axiom,
    ! [X_2: produc639455274on_val] : hAPP_o1977518472on_val(the_Pr431167171on_val,hAPP_P1510515380on_val(some_P948696889on_val,X_2)) = X_2 ).

tff(fact_701_the_Osimps,axiom,
    ! [X_7: val] : hAPP_option_val_val(the_val,hAPP_val_option_val(some_val,X_7)) = X_7 ).

tff(fact_702_the_Osimps,axiom,
    ! [X_7: nat] : hAPP_option_nat_nat(the_nat,hAPP_nat_option_nat(some_nat,X_7)) = X_7 ).

tff(fact_703_the_Osimps,axiom,
    ! [X_7: ty] : hAPP_option_ty_ty(the_ty,hAPP_ty_option_ty(some_ty,X_7)) = X_7 ).

tff(fact_704_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_705_hextI,axiom,
    ! [H: fun_na939144002on_val,Ha: fun_na939144002on_val] :
      ( ! [A_2: nat,C_1: list_char,Fs: fun_Pr806764899on_val] :
          ( ( hAPP_n546249108on_val(Ha,A_2) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C_1),Fs)) )
         => ? [Fs_3: fun_Pr806764899on_val] : hAPP_n546249108on_val(H,A_2) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C_1),Fs_3)) )
     => hBOOL(hext(Ha,H)) ) ).

tff(fact_706_TryRedsVal,axiom,
    ! [C: list_char,V_1: list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,V: val,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V)),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(Ea,C,V_1,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_707_reds__preserves__lconf,axiom,
    ! [E_4: fun_li688206603ion_ty,Tsa: list_ty,Es_1: list_exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,Es: list_exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L))),reds(Pa)))
     => ( hBOOL(wTrts_1(Pa,Ha,E_4,Es_1,Tsa))
       => ( hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Ha),L_1),E_4))
         => hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),H),L),E_4)) ) ) ) ).

tff(fact_708_reds__preserves__hconf,axiom,
    ! [E_4: fun_li688206603ion_ty,Tsa: list_ty,Es_1: list_exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,Es: list_exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L))),reds(Pa)))
     => ( hBOOL(wTrts_1(Pa,Ha,E_4,Es_1,Tsa))
       => ( hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),Ha))
         => hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),H)) ) ) ) ).

tff(fact_709_BinOp2Reds,axiom,
    ! [V: val,Bop: bop,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(hAPP_v834067052t_char(val_list_char,V),Bop,Ea)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(hAPP_v834067052t_char(val_list_char,V),Bop,E)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_710_FAssReds2,axiom,
    ! [V: val,F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,V),F,D,Ea)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,V),F,D,E)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_711_SeqReds2,axiom,
    ! [E_2: exp_list_char,E_2_1: exp_list_char,S_2_1: produc12694297on_val,E_1: exp_list_char,S_0: produc12694297on_val,V_1_2: val,S_1_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1_2)),S_1_2)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S_1_2)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2_1),S_2_1)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(E_1,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2_1),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_712_override__on__apply__in,axiom,
    ! [F_1: fun_li1432931796on_val,G: fun_li1432931796on_val,A_1: list_char,A_16: fun_list_char_bool] :
      ( hBOOL(member_list_char(A_1,A_16))
     => ( hAPP_l207779698on_val(overri2012515291on_val(F_1,G,A_16),A_1) = hAPP_l207779698on_val(G,A_1) ) ) ).

tff(fact_713_override__on__apply__notin,axiom,
    ! [F_1: fun_li1432931796on_val,G: fun_li1432931796on_val,A_1: list_char,A_16: fun_list_char_bool] :
      ( ~ hBOOL(member_list_char(A_1,A_16))
     => ( hAPP_l207779698on_val(overri2012515291on_val(F_1,G,A_16),A_1) = hAPP_l207779698on_val(F_1,A_1) ) ) ).

tff(fact_714_override__on__def,axiom,
    ! [F_1: fun_li1432931796on_val,G: fun_li1432931796on_val,A_16: fun_list_char_bool,X_1: list_char] :
      ( ( hBOOL(member_list_char(X_1,A_16))
       => ( hAPP_l207779698on_val(overri2012515291on_val(F_1,G,A_16),X_1) = hAPP_l207779698on_val(G,X_1) ) )
      & ( ~ hBOOL(member_list_char(X_1,A_16))
       => ( hAPP_l207779698on_val(overri2012515291on_val(F_1,G,A_16),X_1) = hAPP_l207779698on_val(F_1,X_1) ) ) ) ).

tff(fact_715_WTrtSeq,axiom,
    ! [E_2: exp_list_char,T_2_1: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,E_1: exp_list_char,T_1_1: ty] :
      ( hBOOL(wTrt(Pa,Ha,E_4,E_1,T_1_1))
     => ( hBOOL(wTrt(Pa,Ha,E_4,E_2,T_2_1))
       => hBOOL(wTrt(Pa,Ha,E_4,seq_list_char(E_1,E_2),T_2_1)) ) ) ).

tff(fact_716_Seq,axiom,
    ! [E_1: exp_list_char,E_2: exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,E_0: exp_list_char,S_0: produc12694297on_val,V: val,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_0,S_0),hAPP_v834067052t_char(val_list_char,V)),S_1_2))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_1_2),E_2),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,seq_list_char(E_0,E_1),S_0),E_2),S_2_1)) ) ) ).

tff(fact_717_Try,axiom,
    ! [C: list_char,V_1: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,E_1: exp_list_char,S_0: produc12694297on_val,V_1_2: val,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_0),hAPP_v834067052t_char(val_list_char,V_1_2)),S_1_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,tryCatch_list_char(E_1,C,V_1,E_2),S_0),hAPP_v834067052t_char(val_list_char,V_1_2)),S_1_2)) ) ).

tff(fact_718_red__reds_OSeqRed,axiom,
    ! [E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(Ea,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(E,E_2)),S)),red(Pa))) ) ).

tff(fact_719_red__reds_OFAssRed1,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(Ea,F,D,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(E,F,D,E_2)),S)),red(Pa))) ) ).

tff(fact_720_red__reds_OBinOpRed1,axiom,
    ! [Bop: bop,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(Ea,Bop,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(E,Bop,E_2)),S)),red(Pa))) ) ).

tff(fact_721_reds__hext__incr,axiom,
    ! [Es_1: list_exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,Es: list_exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L))),reds(Pa)))
     => hBOOL(hext(Ha,H)) ) ).

tff(fact_722_red__reds_OTryRed,axiom,
    ! [C: list_char,V_1: list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(Ea,C,V_1,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(E,C,V_1,E_2)),S)),red(Pa))) ) ).

tff(fact_723_o__def,axiom,
    ! [F_1: fun_li889387821on_val,G: fun_li867521386ar_val,X_1: list_P2023964830har_ty] : hAPP_l968768258on_val(comp_l424027617har_ty(F_1,G),X_1) = hAPP_l1000746233on_val(F_1,hAPP_l608137480ar_val(G,X_1)) ).

tff(fact_724_o__def,axiom,
    ! [F_1: fun_option_val_val,G: fun_li1432931796on_val,X_1: list_char] : hAPP_list_char_val(comp_o1129292306t_char(F_1,G),X_1) = hAPP_option_val_val(F_1,hAPP_l207779698on_val(G,X_1)) ).

tff(fact_725_o__apply,axiom,
    ! [F_1: fun_li889387821on_val,G: fun_li867521386ar_val,X_2: list_P2023964830har_ty] : hAPP_l968768258on_val(comp_l424027617har_ty(F_1,G),X_2) = hAPP_l1000746233on_val(F_1,hAPP_l608137480ar_val(G,X_2)) ).

tff(fact_726_o__apply,axiom,
    ! [F_1: fun_option_val_val,G: fun_li1432931796on_val,X_2: list_char] : hAPP_list_char_val(comp_o1129292306t_char(F_1,G),X_2) = hAPP_option_val_val(F_1,hAPP_l207779698on_val(G,X_2)) ).

tff(fact_727_red__reds_ORedSeq,axiom,
    ! [V: val,E_2: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(hAPP_v834067052t_char(val_list_char,V),E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S_1)),red(Pa))) ).

tff(fact_728_SeqReds,axiom,
    ! [E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(Ea,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(E,E_2)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_729_red__reds_OFAssRed2,axiom,
    ! [V: val,F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,V),F,D,Ea)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,V),F,D,E)),S)),red(Pa))) ) ).

tff(fact_730_red__reds_OBinOpRed2,axiom,
    ! [V_1_2: val,Bop: bop,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,Ea)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,E)),S)),red(Pa))) ) ).

tff(fact_731_FAssReds1,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(Ea,F,D,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(E,F,D,E_2)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_732_BinOp1Reds,axiom,
    ! [Bop: bop,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(Ea,Bop,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(E,Bop,E_2)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_733_red__reds_ORedTry,axiom,
    ! [V: val,C: list_char,V_1: list_char,E_2: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(hAPP_v834067052t_char(val_list_char,V),C,V_1,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V)),S_1)),red(Pa))) ).

tff(fact_734_TryReds,axiom,
    ! [C: list_char,V_1: list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(Ea,C,V_1,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(E,C,V_1,E_2)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_735_BinOpRedsVal,axiom,
    ! [Bop: bop,V: val,E_2: exp_list_char,V_2: val,S_2_1: produc12694297on_val,E_1: exp_list_char,S_0: produc12694297on_val,V_1_2: val,S_1_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1_2)),S_1_2)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S_1_2)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_2)),S_2_1)),transi2024712006on_val(red(Pa))))
       => ( ( binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Bop),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_2),V_2))) = hAPP_val_option_val(some_val,V) )
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(E_1,Bop,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V)),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_736_red__reds_ORedBinOp,axiom,
    ! [S_1: produc12694297on_val,Pa: list_P1999446415t_char,Bop: bop,V_1_2: val,V_2: val,V: val] :
      ( ( binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Bop),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_2),V_2))) = hAPP_val_option_val(some_val,V) )
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,hAPP_v834067052t_char(val_list_char,V_2))),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V)),S_1)),red(Pa))) ) ).

tff(fact_737_CallRedsParams,axiom,
    ! [V: val,M: list_char,Es_1: list_exp_list_char,S_1: produc12694297on_val,Es: list_exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es),S)),transi374442731on_val(reds(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(hAPP_v834067052t_char(val_list_char,V),M,Es_1)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(hAPP_v834067052t_char(val_list_char,V),M,Es)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_738_ListRedsVal,axiom,
    ! [Es_1: list_exp_list_char,Es: list_exp_list_char,S_2_1: produc12694297on_val,Ea: exp_list_char,S_0: produc12694297on_val,V: val,S_1_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V)),S_1_2)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),S_1_2)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es),S_2_1)),transi374442731on_val(reds(Pa))))
       => hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,hAPP_l2011456725t_char(cons_exp_list_char(Ea),Es_1)),S_0)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,hAPP_l2011456725t_char(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V)),Es)),S_2_1)),transi374442731on_val(reds(Pa)))) ) ) ).

tff(fact_739_exp_Osimps_I114_J,axiom,
    ! [Exp1_49: exp_list_char,Bop_13: bop,Exp2_49: exp_list_char,Exp1_48: exp_list_char,List_14: list_char,A_15: list_char,Exp2_48: exp_list_char] : binOp_list_char(Exp1_49,Bop_13,Exp2_49) != tryCatch_list_char(Exp1_48,List_14,A_15,Exp2_48) ).

tff(fact_740_exp_Osimps_I115_J,axiom,
    ! [Exp1_47: exp_list_char,List_13: list_char,A_14: list_char,Exp2_47: exp_list_char,Exp1_46: exp_list_char,Bop_12: bop,Exp2_46: exp_list_char] : tryCatch_list_char(Exp1_47,List_13,A_14,Exp2_47) != binOp_list_char(Exp1_46,Bop_12,Exp2_46) ).

tff(fact_741_exp_Osimps_I182_J,axiom,
    ! [Exp1_45: exp_list_char,List1_25: list_char,List2_25: list_char,Exp2_45: exp_list_char,Exp1_44: exp_list_char,List_12: list_char,A_13: list_char,Exp2_44: exp_list_char] : fAss_list_char(Exp1_45,List1_25,List2_25,Exp2_45) != tryCatch_list_char(Exp1_44,List_12,A_13,Exp2_44) ).

tff(fact_742_exp_Osimps_I183_J,axiom,
    ! [Exp1_43: exp_list_char,List_11: list_char,A_12: list_char,Exp2_43: exp_list_char,Exp1_42: exp_list_char,List1_24: list_char,List2_24: list_char,Exp2_42: exp_list_char] : tryCatch_list_char(Exp1_43,List_11,A_12,Exp2_43) != fAss_list_char(Exp1_42,List1_24,List2_24,Exp2_42) ).

tff(fact_743_exp_Osimps_I212_J,axiom,
    ! [Exp1_41: exp_list_char,Exp2_41: exp_list_char,Exp1_40: exp_list_char,List_10: list_char,A_11: list_char,Exp2_40: exp_list_char] : seq_list_char(Exp1_41,Exp2_41) != tryCatch_list_char(Exp1_40,List_10,A_11,Exp2_40) ).

tff(fact_744_not__Cons__self,axiom,
    ! [Xs_6: list_val,X_6: val] : Xs_6 != hAPP_l273806049st_val(cons_val(X_6),Xs_6) ).

tff(fact_745_not__Cons__self,axiom,
    ! [Xs_6: list_list_char,X_6: list_char] : Xs_6 != hAPP_l407174677t_char(cons_list_char(X_6),Xs_6) ).

tff(fact_746_not__Cons__self,axiom,
    ! [Xs_6: list_ty,X_6: ty] : Xs_6 != hAPP_list_ty_list_ty(cons_ty(X_6),Xs_6) ).

tff(fact_747_not__Cons__self,axiom,
    ! [Xs_6: list_exp_list_char,X_6: exp_list_char] : Xs_6 != hAPP_l2011456725t_char(cons_exp_list_char(X_6),Xs_6) ).

tff(fact_748_not__Cons__self2,axiom,
    ! [X_5: val,Xs_5: list_val] : hAPP_l273806049st_val(cons_val(X_5),Xs_5) != Xs_5 ).

tff(fact_749_not__Cons__self2,axiom,
    ! [X_5: list_char,Xs_5: list_list_char] : hAPP_l407174677t_char(cons_list_char(X_5),Xs_5) != Xs_5 ).

tff(fact_750_not__Cons__self2,axiom,
    ! [X_5: ty,Xs_5: list_ty] : hAPP_list_ty_list_ty(cons_ty(X_5),Xs_5) != Xs_5 ).

tff(fact_751_not__Cons__self2,axiom,
    ! [X_5: exp_list_char,Xs_5: list_exp_list_char] : hAPP_l2011456725t_char(cons_exp_list_char(X_5),Xs_5) != Xs_5 ).

tff(fact_752_list_Oinject,axiom,
    ! [A_1: val,List_2: list_val,A_8: val,List_1: list_val] :
      ( ( hAPP_l273806049st_val(cons_val(A_1),List_2) = hAPP_l273806049st_val(cons_val(A_8),List_1) )
    <=> ( ( A_1 = A_8 )
        & ( List_2 = List_1 ) ) ) ).

tff(fact_753_list_Oinject,axiom,
    ! [A_1: list_char,List_2: list_list_char,A_8: list_char,List_1: list_list_char] :
      ( ( hAPP_l407174677t_char(cons_list_char(A_1),List_2) = hAPP_l407174677t_char(cons_list_char(A_8),List_1) )
    <=> ( ( A_1 = A_8 )
        & ( List_2 = List_1 ) ) ) ).

tff(fact_754_list_Oinject,axiom,
    ! [A_1: ty,List_2: list_ty,A_8: ty,List_1: list_ty] :
      ( ( hAPP_list_ty_list_ty(cons_ty(A_1),List_2) = hAPP_list_ty_list_ty(cons_ty(A_8),List_1) )
    <=> ( ( A_1 = A_8 )
        & ( List_2 = List_1 ) ) ) ).

tff(fact_755_list_Oinject,axiom,
    ! [A_1: exp_list_char,List_2: list_exp_list_char,A_8: exp_list_char,List_1: list_exp_list_char] :
      ( ( hAPP_l2011456725t_char(cons_exp_list_char(A_1),List_2) = hAPP_l2011456725t_char(cons_exp_list_char(A_8),List_1) )
    <=> ( ( A_1 = A_8 )
        & ( List_2 = List_1 ) ) ) ).

tff(fact_756_exp_Osimps_I9_J,axiom,
    ! [Exp_15: exp_list_char,List1_11: list_char,List2_11: list_exp_list_char,Exp_14: exp_list_char,List1_10: list_char,List2_10: list_exp_list_char] :
      ( ( call_list_char(Exp_15,List1_11,List2_11) = call_list_char(Exp_14,List1_10,List2_10) )
    <=> ( ( Exp_15 = Exp_14 )
        & ( List1_11 = List1_10 )
        & ( List2_11 = List2_10 ) ) ) ).

tff(fact_757_exp_Osimps_I81_J,axiom,
    ! [Exp_25: exp_list_char,List1_23: list_char,List2_23: list_exp_list_char,Val_13: val] : call_list_char(Exp_25,List1_23,List2_23) != hAPP_v834067052t_char(val_list_char,Val_13) ).

tff(fact_758_exp_Osimps_I80_J,axiom,
    ! [Val_12: val,Exp_24: exp_list_char,List1_22: list_char,List2_22: list_exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_12) != call_list_char(Exp_24,List1_22,List2_22) ).

tff(fact_759_exp_Osimps_I186_J,axiom,
    ! [Exp_23: exp_list_char,List1_21: list_char,List2_21: list_exp_list_char,Exp1_39: exp_list_char,Exp2_39: exp_list_char] : call_list_char(Exp_23,List1_21,List2_21) != seq_list_char(Exp1_39,Exp2_39) ).

tff(fact_760_exp_Osimps_I187_J,axiom,
    ! [Exp1_38: exp_list_char,Exp2_38: exp_list_char,Exp_22: exp_list_char,List1_20: list_char,List2_20: list_exp_list_char] : seq_list_char(Exp1_38,Exp2_38) != call_list_char(Exp_22,List1_20,List2_20) ).

tff(fact_761_exp_Osimps_I170_J,axiom,
    ! [Exp1_37: exp_list_char,List1_19: list_char,List2_19: list_char,Exp2_37: exp_list_char,Exp_21: exp_list_char,List1_18: list_char,List2_18: list_exp_list_char] : fAss_list_char(Exp1_37,List1_19,List2_19,Exp2_37) != call_list_char(Exp_21,List1_18,List2_18) ).

tff(fact_762_exp_Osimps_I171_J,axiom,
    ! [Exp_20: exp_list_char,List1_17: list_char,List2_17: list_exp_list_char,Exp1_36: exp_list_char,List1_16: list_char,List2_16: list_char,Exp2_36: exp_list_char] : call_list_char(Exp_20,List1_17,List2_17) != fAss_list_char(Exp1_36,List1_16,List2_16,Exp2_36) ).

tff(fact_763_exp_Osimps_I102_J,axiom,
    ! [Exp1_35: exp_list_char,Bop_11: bop,Exp2_35: exp_list_char,Exp_19: exp_list_char,List1_15: list_char,List2_15: list_exp_list_char] : binOp_list_char(Exp1_35,Bop_11,Exp2_35) != call_list_char(Exp_19,List1_15,List2_15) ).

tff(fact_764_exp_Osimps_I103_J,axiom,
    ! [Exp_18: exp_list_char,List1_14: list_char,List2_14: list_exp_list_char,Exp1_34: exp_list_char,Bop_10: bop,Exp2_34: exp_list_char] : call_list_char(Exp_18,List1_14,List2_14) != binOp_list_char(Exp1_34,Bop_10,Exp2_34) ).

tff(fact_765_exp_Osimps_I195_J,axiom,
    ! [Exp1_33: exp_list_char,List_9: list_char,A_10: list_char,Exp2_33: exp_list_char,Exp_17: exp_list_char,List1_13: list_char,List2_13: list_exp_list_char] : tryCatch_list_char(Exp1_33,List_9,A_10,Exp2_33) != call_list_char(Exp_17,List1_13,List2_13) ).

tff(fact_766_exp_Osimps_I194_J,axiom,
    ! [Exp_16: exp_list_char,List1_12: list_char,List2_12: list_exp_list_char,Exp1_32: exp_list_char,List_8: list_char,A_9: list_char,Exp2_32: exp_list_char] : call_list_char(Exp_16,List1_12,List2_12) != tryCatch_list_char(Exp1_32,List_8,A_9,Exp2_32) ).

tff(fact_767_set__ConsD,axiom,
    ! [Y_1: list_char,X_2: list_char,Xs: list_list_char] :
      ( hBOOL(member_list_char(Y_1,set_list_char(hAPP_l407174677t_char(cons_list_char(X_2),Xs))))
     => ( ( Y_1 = X_2 )
        | hBOOL(member_list_char(Y_1,set_list_char(Xs))) ) ) ).

tff(fact_768_set__ConsD,axiom,
    ! [Y_1: nat,X_2: nat,Xs: list_nat] :
      ( hBOOL(member_nat(Y_1,set_nat(hAPP_l248265089st_nat(cons_nat(X_2),Xs))))
     => ( ( Y_1 = X_2 )
        | hBOOL(member_nat(Y_1,set_nat(Xs))) ) ) ).

tff(fact_769_set__ConsD,axiom,
    ! [Y_1: produc1278157519t_char,X_2: produc1278157519t_char,Xs: list_P1916372464t_char] :
      ( hBOOL(member1251428284t_char(Y_1,set_Pr550895038t_char(hAPP_l250787541t_char(cons_P2009561711t_char(X_2),Xs))))
     => ( ( Y_1 = X_2 )
        | hBOOL(member1251428284t_char(Y_1,set_Pr550895038t_char(Xs))) ) ) ).

tff(fact_770_set__ConsD,axiom,
    ! [Y_1: produc430140671on_val,X_2: produc430140671on_val,Xs: list_P507235360on_val] :
      ( hBOOL(member875476972on_val(Y_1,set_Pr771975662on_val(hAPP_l1208602837on_val(cons_P1546421407on_val(X_2),Xs))))
     => ( ( Y_1 = X_2 )
        | hBOOL(member875476972on_val(Y_1,set_Pr771975662on_val(Xs))) ) ) ).

tff(fact_771_set__ConsD,axiom,
    ! [Y_1: produc1102272487on_val,X_2: produc1102272487on_val,Xs: list_P1439941640on_val] :
      ( hBOOL(member773094996on_val(Y_1,set_Pr1921835862on_val(hAPP_l1695428693on_val(cons_P511631239on_val(X_2),Xs))))
     => ( ( Y_1 = X_2 )
        | hBOOL(member773094996on_val(Y_1,set_Pr1921835862on_val(Xs))) ) ) ).

tff(fact_772_set__ConsD,axiom,
    ! [Y_1: val,X_2: val,Xs: list_val] :
      ( hBOOL(member_val(Y_1,set_val(hAPP_l273806049st_val(cons_val(X_2),Xs))))
     => ( ( Y_1 = X_2 )
        | hBOOL(member_val(Y_1,set_val(Xs))) ) ) ).

tff(fact_773_set__ConsD,axiom,
    ! [Y_1: ty,X_2: ty,Xs: list_ty] :
      ( hBOOL(member_ty(Y_1,set_ty(hAPP_list_ty_list_ty(cons_ty(X_2),Xs))))
     => ( ( Y_1 = X_2 )
        | hBOOL(member_ty(Y_1,set_ty(Xs))) ) ) ).

tff(fact_774_set__ConsD,axiom,
    ! [Y_1: exp_list_char,X_2: exp_list_char,Xs: list_exp_list_char] :
      ( hBOOL(member_exp_list_char(Y_1,set_exp_list_char(hAPP_l2011456725t_char(cons_exp_list_char(X_2),Xs))))
     => ( ( Y_1 = X_2 )
        | hBOOL(member_exp_list_char(Y_1,set_exp_list_char(Xs))) ) ) ).

tff(fact_775_map_Osimps_I2_J,axiom,
    ! [F_1: fun_Pr1149393094ar_val,X_2: produc245756905har_ty,Xs: list_P2023964830har_ty] : hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),hAPP_l1836003391har_ty(cons_P796333129har_ty(X_2),Xs)) = hAPP_l1462265297ar_val(cons_P2112347922ar_val(hAPP_P841862366ar_val(F_1,X_2)),hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),Xs)) ).

tff(fact_776_map_Osimps_I2_J,axiom,
    ! [F_1: fun_list_char_val,X_2: list_char,Xs: list_list_char] : hAPP_l1892737211st_val(map_list_char_val(F_1),hAPP_l407174677t_char(cons_list_char(X_2),Xs)) = hAPP_l273806049st_val(cons_val(hAPP_list_char_val(F_1,X_2)),hAPP_l1892737211st_val(map_list_char_val(F_1),Xs)) ).

tff(fact_777_map_Osimps_I2_J,axiom,
    ! [F_1: fun_va223928858t_char,X_2: val,Xs: list_val] : hAPP_l732421366t_char(map_va1934808527t_char(F_1),hAPP_l273806049st_val(cons_val(X_2),Xs)) = hAPP_l2011456725t_char(cons_exp_list_char(hAPP_v834067052t_char(F_1,X_2)),hAPP_l732421366t_char(map_va1934808527t_char(F_1),Xs)) ).

tff(fact_778_map_Osimps_I2_J,axiom,
    ! [F_1: fun_ty_option_ty,X_2: ty,Xs: list_ty] : hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),hAPP_list_ty_list_ty(cons_ty(X_2),Xs)) = hAPP_l305548949ion_ty(cons_option_ty(hAPP_ty_option_ty(F_1,X_2)),hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Xs)) ).

tff(fact_779_map_Osimps_I2_J,axiom,
    ! [F_1: fun_val_option_ty,X_2: val,Xs: list_val] : hAPP_l2006940821ion_ty(map_val_option_ty(F_1),hAPP_l273806049st_val(cons_val(X_2),Xs)) = hAPP_l305548949ion_ty(cons_option_ty(hAPP_val_option_ty(F_1,X_2)),hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Xs)) ).

tff(fact_780_list__all2__Cons,axiom,
    ! [Pa: fun_val_fun_ty_bool,X_2: val,Xs: list_val,Y_1: ty,Ys: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_all2_val_ty(Pa,hAPP_l273806049st_val(cons_val(X_2),Xs)),hAPP_list_ty_list_ty(cons_ty(Y_1),Ys)))
    <=> ( hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(Pa,X_2),Y_1))
        & hBOOL(hAPP_list_ty_bool(list_all2_val_ty(Pa,Xs),Ys)) ) ) ).

tff(fact_781_list__all2__Cons,axiom,
    ! [Pa: fun_ty_fun_ty_bool,X_2: ty,Xs: list_ty,Y_1: ty,Ys: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(Pa,hAPP_list_ty_list_ty(cons_ty(X_2),Xs)),hAPP_list_ty_list_ty(cons_ty(Y_1),Ys)))
    <=> ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Pa,X_2),Y_1))
        & hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(Pa,Xs),Ys)) ) ) ).

tff(fact_782_distinct_Osimps_I2_J,axiom,
    ! [X_2: list_char,Xs: list_list_char] :
      ( hBOOL(distinct_list_char(hAPP_l407174677t_char(cons_list_char(X_2),Xs)))
    <=> ( ~ hBOOL(member_list_char(X_2,set_list_char(Xs)))
        & hBOOL(distinct_list_char(Xs)) ) ) ).

tff(fact_783_distinct_Osimps_I2_J,axiom,
    ! [X_2: nat,Xs: list_nat] :
      ( hBOOL(distinct_nat(hAPP_l248265089st_nat(cons_nat(X_2),Xs)))
    <=> ( ~ hBOOL(member_nat(X_2,set_nat(Xs)))
        & hBOOL(distinct_nat(Xs)) ) ) ).

tff(fact_784_distinct_Osimps_I2_J,axiom,
    ! [X_2: produc1278157519t_char,Xs: list_P1916372464t_char] :
      ( hBOOL(distin1973552748t_char(hAPP_l250787541t_char(cons_P2009561711t_char(X_2),Xs)))
    <=> ( ~ hBOOL(member1251428284t_char(X_2,set_Pr550895038t_char(Xs)))
        & hBOOL(distin1973552748t_char(Xs)) ) ) ).

tff(fact_785_distinct_Osimps_I2_J,axiom,
    ! [X_2: produc430140671on_val,Xs: list_P507235360on_val] :
      ( hBOOL(distin1349260956on_val(hAPP_l1208602837on_val(cons_P1546421407on_val(X_2),Xs)))
    <=> ( ~ hBOOL(member875476972on_val(X_2,set_Pr771975662on_val(Xs)))
        & hBOOL(distin1349260956on_val(Xs)) ) ) ).

tff(fact_786_distinct_Osimps_I2_J,axiom,
    ! [X_2: produc1102272487on_val,Xs: list_P1439941640on_val] :
      ( hBOOL(distin179070212on_val(hAPP_l1695428693on_val(cons_P511631239on_val(X_2),Xs)))
    <=> ( ~ hBOOL(member773094996on_val(X_2,set_Pr1921835862on_val(Xs)))
        & hBOOL(distin179070212on_val(Xs)) ) ) ).

tff(fact_787_distinct_Osimps_I2_J,axiom,
    ! [X_2: val,Xs: list_val] :
      ( hBOOL(distinct_val(hAPP_l273806049st_val(cons_val(X_2),Xs)))
    <=> ( ~ hBOOL(member_val(X_2,set_val(Xs)))
        & hBOOL(distinct_val(Xs)) ) ) ).

tff(fact_788_distinct_Osimps_I2_J,axiom,
    ! [X_2: ty,Xs: list_ty] :
      ( hBOOL(distinct_ty(hAPP_list_ty_list_ty(cons_ty(X_2),Xs)))
    <=> ( ~ hBOOL(member_ty(X_2,set_ty(Xs)))
        & hBOOL(distinct_ty(Xs)) ) ) ).

tff(fact_789_distinct_Osimps_I2_J,axiom,
    ! [X_2: exp_list_char,Xs: list_exp_list_char] :
      ( hBOOL(distin1416307044t_char(hAPP_l2011456725t_char(cons_exp_list_char(X_2),Xs)))
    <=> ( ~ hBOOL(member_exp_list_char(X_2,set_exp_list_char(Xs)))
        & hBOOL(distin1416307044t_char(Xs)) ) ) ).

tff(fact_790_red__reds_OCallObj,axiom,
    ! [M: list_char,Es_1: list_exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(Ea,M,Es_1)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(E,M,Es_1)),S)),red(Pa))) ) ).

tff(fact_791_exp_Osimps_I3_J,axiom,
    ! [Val_11: val,Val_10: val] :
      ( ( hAPP_v834067052t_char(val_list_char,Val_11) = hAPP_v834067052t_char(val_list_char,Val_10) )
    <=> ( Val_11 = Val_10 ) ) ).

tff(fact_792_exp_Osimps_I11_J,axiom,
    ! [Exp1_31: exp_list_char,Exp2_31: exp_list_char,Exp1_30: exp_list_char,Exp2_30: exp_list_char] :
      ( ( seq_list_char(Exp1_31,Exp2_31) = seq_list_char(Exp1_30,Exp2_30) )
    <=> ( ( Exp1_31 = Exp1_30 )
        & ( Exp2_31 = Exp2_30 ) ) ) ).

tff(fact_793_exp_Osimps_I8_J,axiom,
    ! [Exp1_31: exp_list_char,List1_11: list_char,List2_11: list_char,Exp2_31: exp_list_char,Exp1_30: exp_list_char,List1_10: list_char,List2_10: list_char,Exp2_30: exp_list_char] :
      ( ( fAss_list_char(Exp1_31,List1_11,List2_11,Exp2_31) = fAss_list_char(Exp1_30,List1_10,List2_10,Exp2_30) )
    <=> ( ( Exp1_31 = Exp1_30 )
        & ( List1_11 = List1_10 )
        & ( List2_11 = List2_10 )
        & ( Exp2_31 = Exp2_30 ) ) ) ).

tff(fact_794_exp_Osimps_I4_J,axiom,
    ! [Exp1_31: exp_list_char,Bop: bop,Exp2_31: exp_list_char,Exp1_30: exp_list_char,Bop_9: bop,Exp2_30: exp_list_char] :
      ( ( binOp_list_char(Exp1_31,Bop,Exp2_31) = binOp_list_char(Exp1_30,Bop_9,Exp2_30) )
    <=> ( ( Exp1_31 = Exp1_30 )
        & ( Bop = Bop_9 )
        & ( Exp2_31 = Exp2_30 ) ) ) ).

tff(fact_795_exp_Osimps_I15_J,axiom,
    ! [Exp1_31: exp_list_char,List_2: list_char,A_1: list_char,Exp2_31: exp_list_char,Exp1_30: exp_list_char,List_1: list_char,A_8: list_char,Exp2_30: exp_list_char] :
      ( ( tryCatch_list_char(Exp1_31,List_2,A_1,Exp2_31) = tryCatch_list_char(Exp1_30,List_1,A_8,Exp2_30) )
    <=> ( ( Exp1_31 = Exp1_30 )
        & ( List_2 = List_1 )
        & ( A_1 = A_8 )
        & ( Exp2_31 = Exp2_30 ) ) ) ).

tff(fact_796_CallRedsObj,axiom,
    ! [M: list_char,Es_1: list_exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(Ea,M,Es_1)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(E,M,Es_1)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_797_ListReds2,axiom,
    ! [V: val,Es_1: list_exp_list_char,S_1: produc12694297on_val,Es: list_exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es),S)),transi374442731on_val(reds(Pa))))
     => hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,hAPP_l2011456725t_char(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V)),Es_1)),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,hAPP_l2011456725t_char(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V)),Es)),S)),transi374442731on_val(reds(Pa)))) ) ).

tff(fact_798_red__reds_OListRed2,axiom,
    ! [V: val,Es_1: list_exp_list_char,S_1: produc12694297on_val,Es: list_exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es),S)),reds(Pa)))
     => hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,hAPP_l2011456725t_char(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V)),Es_1)),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,hAPP_l2011456725t_char(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V)),Es)),S)),reds(Pa))) ) ).

tff(fact_799_red__reds_OListRed1,axiom,
    ! [Es_1: list_exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),red(Pa)))
     => hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,hAPP_l2011456725t_char(cons_exp_list_char(Ea),Es_1)),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,hAPP_l2011456725t_char(cons_exp_list_char(E),Es_1)),S)),reds(Pa))) ) ).

tff(fact_800_BinOp,axiom,
    ! [Bop: bop,V: val,E_2: exp_list_char,V_2: val,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,E_1: exp_list_char,S_0: produc12694297on_val,V_1_2: val,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_0),hAPP_v834067052t_char(val_list_char,V_1_2)),S_1_2))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_2),hAPP_v834067052t_char(val_list_char,V_2)),S_2_1))
       => ( ( binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Bop),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_2),V_2))) = hAPP_val_option_val(some_val,V) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,binOp_list_char(E_1,Bop,E_2),S_0),hAPP_v834067052t_char(val_list_char,V)),S_2_1)) ) ) ) ).

tff(fact_801_exp_Osimps_I85_J,axiom,
    ! [Exp1_29: exp_list_char,Exp2_29: exp_list_char,Val_9: val] : seq_list_char(Exp1_29,Exp2_29) != hAPP_v834067052t_char(val_list_char,Val_9) ).

tff(fact_802_exp_Osimps_I84_J,axiom,
    ! [Val_8: val,Exp1_28: exp_list_char,Exp2_28: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_8) != seq_list_char(Exp1_28,Exp2_28) ).

tff(fact_803_exp_Osimps_I79_J,axiom,
    ! [Exp1_27: exp_list_char,List1_9: list_char,List2_9: list_char,Exp2_27: exp_list_char,Val_7: val] : fAss_list_char(Exp1_27,List1_9,List2_9,Exp2_27) != hAPP_v834067052t_char(val_list_char,Val_7) ).

tff(fact_804_exp_Osimps_I78_J,axiom,
    ! [Val_6: val,Exp1_26: exp_list_char,List1_8: list_char,List2_8: list_char,Exp2_26: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_6) != fAss_list_char(Exp1_26,List1_8,List2_8,Exp2_26) ).

tff(fact_805_exp_Osimps_I71_J,axiom,
    ! [Exp1_25: exp_list_char,Bop_8: bop,Exp2_25: exp_list_char,Val_5: val] : binOp_list_char(Exp1_25,Bop_8,Exp2_25) != hAPP_v834067052t_char(val_list_char,Val_5) ).

tff(fact_806_exp_Osimps_I70_J,axiom,
    ! [Val_4: val,Exp1_24: exp_list_char,Bop_7: bop,Exp2_24: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_4) != binOp_list_char(Exp1_24,Bop_7,Exp2_24) ).

tff(fact_807_exp_Osimps_I93_J,axiom,
    ! [Exp1_23: exp_list_char,List_7: list_char,A_7: list_char,Exp2_23: exp_list_char,Val_3: val] : tryCatch_list_char(Exp1_23,List_7,A_7,Exp2_23) != hAPP_v834067052t_char(val_list_char,Val_3) ).

tff(fact_808_exp_Osimps_I92_J,axiom,
    ! [Val_2: val,Exp1_22: exp_list_char,List_6: list_char,A_6: list_char,Exp2_22: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_2) != tryCatch_list_char(Exp1_22,List_6,A_6,Exp2_22) ).

tff(fact_809_red__reds_OCallParams,axiom,
    ! [V: val,M: list_char,Es_1: list_exp_list_char,S_1: produc12694297on_val,Es: list_exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es),S)),reds(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(hAPP_v834067052t_char(val_list_char,V),M,Es_1)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(hAPP_v834067052t_char(val_list_char,V),M,Es)),S)),red(Pa))) ) ).

tff(fact_810_ListReds1,axiom,
    ! [Es_1: list_exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,hAPP_l2011456725t_char(cons_exp_list_char(Ea),Es_1)),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,hAPP_l2011456725t_char(cons_exp_list_char(E),Es_1)),S)),transi374442731on_val(reds(Pa)))) ) ).

tff(fact_811_exp_Osimps_I174_J,axiom,
    ! [Exp1_21: exp_list_char,List1_7: list_char,List2_7: list_char,Exp2_21: exp_list_char,Exp1_20: exp_list_char,Exp2_20: exp_list_char] : fAss_list_char(Exp1_21,List1_7,List2_7,Exp2_21) != seq_list_char(Exp1_20,Exp2_20) ).

tff(fact_812_exp_Osimps_I175_J,axiom,
    ! [Exp1_19: exp_list_char,Exp2_19: exp_list_char,Exp1_18: exp_list_char,List1_6: list_char,List2_6: list_char,Exp2_18: exp_list_char] : seq_list_char(Exp1_19,Exp2_19) != fAss_list_char(Exp1_18,List1_6,List2_6,Exp2_18) ).

tff(fact_813_exp_Osimps_I106_J,axiom,
    ! [Exp1_17: exp_list_char,Bop_6: bop,Exp2_17: exp_list_char,Exp1_16: exp_list_char,Exp2_16: exp_list_char] : binOp_list_char(Exp1_17,Bop_6,Exp2_17) != seq_list_char(Exp1_16,Exp2_16) ).

tff(fact_814_exp_Osimps_I107_J,axiom,
    ! [Exp1_15: exp_list_char,Exp2_15: exp_list_char,Exp1_14: exp_list_char,Bop_5: bop,Exp2_14: exp_list_char] : seq_list_char(Exp1_15,Exp2_15) != binOp_list_char(Exp1_14,Bop_5,Exp2_14) ).

tff(fact_815_exp_Osimps_I101_J,axiom,
    ! [Exp1_13: exp_list_char,List1_5: list_char,List2_5: list_char,Exp2_13: exp_list_char,Exp1_12: exp_list_char,Bop_4: bop,Exp2_12: exp_list_char] : fAss_list_char(Exp1_13,List1_5,List2_5,Exp2_13) != binOp_list_char(Exp1_12,Bop_4,Exp2_12) ).

tff(fact_816_exp_Osimps_I100_J,axiom,
    ! [Exp1_11: exp_list_char,Bop_3: bop,Exp2_11: exp_list_char,Exp1_10: exp_list_char,List1_4: list_char,List2_4: list_char,Exp2_10: exp_list_char] : binOp_list_char(Exp1_11,Bop_3,Exp2_11) != fAss_list_char(Exp1_10,List1_4,List2_4,Exp2_10) ).

tff(fact_817_exp_Osimps_I213_J,axiom,
    ! [Exp1_9: exp_list_char,List_5: list_char,A_5: list_char,Exp2_9: exp_list_char,Exp1_8: exp_list_char,Exp2_8: exp_list_char] : tryCatch_list_char(Exp1_9,List_5,A_5,Exp2_9) != seq_list_char(Exp1_8,Exp2_8) ).

tff(fact_818_list__all2__Cons2,axiom,
    ! [Pa: fun_val_fun_ty_bool,Xs: list_val,Y_1: ty,Ys: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_all2_val_ty(Pa,Xs),hAPP_list_ty_list_ty(cons_ty(Y_1),Ys)))
    <=> ? [Z: val,Zs_4: list_val] :
          ( ( Xs = hAPP_l273806049st_val(cons_val(Z),Zs_4) )
          & hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(Pa,Z),Y_1))
          & hBOOL(hAPP_list_ty_bool(list_all2_val_ty(Pa,Zs_4),Ys)) ) ) ).

tff(fact_819_list__all2__Cons2,axiom,
    ! [Pa: fun_ty_fun_ty_bool,Xs: list_ty,Y_1: ty,Ys: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(Pa,Xs),hAPP_list_ty_list_ty(cons_ty(Y_1),Ys)))
    <=> ? [Z: ty,Zs_4: list_ty] :
          ( ( Xs = hAPP_list_ty_list_ty(cons_ty(Z),Zs_4) )
          & hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Pa,Z),Y_1))
          & hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(Pa,Zs_4),Ys)) ) ) ).

tff(fact_820_list__all2__Cons1,axiom,
    ! [Pa: fun_val_fun_ty_bool,X_2: val,Xs: list_val,Ys: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_all2_val_ty(Pa,hAPP_l273806049st_val(cons_val(X_2),Xs)),Ys))
    <=> ? [Z: ty,Zs_4: list_ty] :
          ( ( Ys = hAPP_list_ty_list_ty(cons_ty(Z),Zs_4) )
          & hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(Pa,X_2),Z))
          & hBOOL(hAPP_list_ty_bool(list_all2_val_ty(Pa,Xs),Zs_4)) ) ) ).

tff(fact_821_list__all2__Cons1,axiom,
    ! [Pa: fun_ty_fun_ty_bool,X_2: ty,Xs: list_ty,Ys: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(Pa,hAPP_list_ty_list_ty(cons_ty(X_2),Xs)),Ys))
    <=> ? [Z: ty,Zs_4: list_ty] :
          ( ( Ys = hAPP_list_ty_list_ty(cons_ty(Z),Zs_4) )
          & hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Pa,X_2),Z))
          & hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(Pa,Xs),Zs_4)) ) ) ).

tff(fact_822_Cons__eq__map__conv,axiom,
    ! [X_2: produc1147203250ar_val,Xs: list_P1697858023ar_val,F_1: fun_Pr1149393094ar_val,Ys: list_P2023964830har_ty] :
      ( ( hAPP_l1462265297ar_val(cons_P2112347922ar_val(X_2),Xs) = hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),Ys) )
    <=> ? [Z: produc245756905har_ty,Zs_4: list_P2023964830har_ty] :
          ( ( Ys = hAPP_l1836003391har_ty(cons_P796333129har_ty(Z),Zs_4) )
          & ( X_2 = hAPP_P841862366ar_val(F_1,Z) )
          & ( Xs = hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),Zs_4) ) ) ) ).

tff(fact_823_Cons__eq__map__conv,axiom,
    ! [X_2: val,Xs: list_val,F_1: fun_list_char_val,Ys: list_list_char] :
      ( ( hAPP_l273806049st_val(cons_val(X_2),Xs) = hAPP_l1892737211st_val(map_list_char_val(F_1),Ys) )
    <=> ? [Z: list_char,Zs_4: list_list_char] :
          ( ( Ys = hAPP_l407174677t_char(cons_list_char(Z),Zs_4) )
          & ( X_2 = hAPP_list_char_val(F_1,Z) )
          & ( Xs = hAPP_l1892737211st_val(map_list_char_val(F_1),Zs_4) ) ) ) ).

tff(fact_824_Cons__eq__map__conv,axiom,
    ! [X_2: exp_list_char,Xs: list_exp_list_char,F_1: fun_va223928858t_char,Ys: list_val] :
      ( ( hAPP_l2011456725t_char(cons_exp_list_char(X_2),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(F_1),Ys) )
    <=> ? [Z: val,Zs_4: list_val] :
          ( ( Ys = hAPP_l273806049st_val(cons_val(Z),Zs_4) )
          & ( X_2 = hAPP_v834067052t_char(F_1,Z) )
          & ( Xs = hAPP_l732421366t_char(map_va1934808527t_char(F_1),Zs_4) ) ) ) ).

tff(fact_825_Cons__eq__map__conv,axiom,
    ! [X_2: option_ty,Xs: list_option_ty,F_1: fun_ty_option_ty,Ys: list_ty] :
      ( ( hAPP_l305548949ion_ty(cons_option_ty(X_2),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Ys) )
    <=> ? [Z: ty,Zs_4: list_ty] :
          ( ( Ys = hAPP_list_ty_list_ty(cons_ty(Z),Zs_4) )
          & ( X_2 = hAPP_ty_option_ty(F_1,Z) )
          & ( Xs = hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Zs_4) ) ) ) ).

tff(fact_826_Cons__eq__map__conv,axiom,
    ! [X_2: option_ty,Xs: list_option_ty,F_1: fun_val_option_ty,Ys: list_val] :
      ( ( hAPP_l305548949ion_ty(cons_option_ty(X_2),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Ys) )
    <=> ? [Z: val,Zs_4: list_val] :
          ( ( Ys = hAPP_l273806049st_val(cons_val(Z),Zs_4) )
          & ( X_2 = hAPP_val_option_ty(F_1,Z) )
          & ( Xs = hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Zs_4) ) ) ) ).

tff(fact_827_map__eq__Cons__conv,axiom,
    ! [F_1: fun_Pr1149393094ar_val,Xs: list_P2023964830har_ty,Y_1: produc1147203250ar_val,Ys: list_P1697858023ar_val] :
      ( ( hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),Xs) = hAPP_l1462265297ar_val(cons_P2112347922ar_val(Y_1),Ys) )
    <=> ? [Z: produc245756905har_ty,Zs_4: list_P2023964830har_ty] :
          ( ( Xs = hAPP_l1836003391har_ty(cons_P796333129har_ty(Z),Zs_4) )
          & ( hAPP_P841862366ar_val(F_1,Z) = Y_1 )
          & ( hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),Zs_4) = Ys ) ) ) ).

tff(fact_828_map__eq__Cons__conv,axiom,
    ! [F_1: fun_list_char_val,Xs: list_list_char,Y_1: val,Ys: list_val] :
      ( ( hAPP_l1892737211st_val(map_list_char_val(F_1),Xs) = hAPP_l273806049st_val(cons_val(Y_1),Ys) )
    <=> ? [Z: list_char,Zs_4: list_list_char] :
          ( ( Xs = hAPP_l407174677t_char(cons_list_char(Z),Zs_4) )
          & ( hAPP_list_char_val(F_1,Z) = Y_1 )
          & ( hAPP_l1892737211st_val(map_list_char_val(F_1),Zs_4) = Ys ) ) ) ).

tff(fact_829_map__eq__Cons__conv,axiom,
    ! [F_1: fun_va223928858t_char,Xs: list_val,Y_1: exp_list_char,Ys: list_exp_list_char] :
      ( ( hAPP_l732421366t_char(map_va1934808527t_char(F_1),Xs) = hAPP_l2011456725t_char(cons_exp_list_char(Y_1),Ys) )
    <=> ? [Z: val,Zs_4: list_val] :
          ( ( Xs = hAPP_l273806049st_val(cons_val(Z),Zs_4) )
          & ( hAPP_v834067052t_char(F_1,Z) = Y_1 )
          & ( hAPP_l732421366t_char(map_va1934808527t_char(F_1),Zs_4) = Ys ) ) ) ).

tff(fact_830_map__eq__Cons__conv,axiom,
    ! [F_1: fun_ty_option_ty,Xs: list_ty,Y_1: option_ty,Ys: list_option_ty] :
      ( ( hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Xs) = hAPP_l305548949ion_ty(cons_option_ty(Y_1),Ys) )
    <=> ? [Z: ty,Zs_4: list_ty] :
          ( ( Xs = hAPP_list_ty_list_ty(cons_ty(Z),Zs_4) )
          & ( hAPP_ty_option_ty(F_1,Z) = Y_1 )
          & ( hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Zs_4) = Ys ) ) ) ).

tff(fact_831_map__eq__Cons__conv,axiom,
    ! [F_1: fun_val_option_ty,Xs: list_val,Y_1: option_ty,Ys: list_option_ty] :
      ( ( hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Xs) = hAPP_l305548949ion_ty(cons_option_ty(Y_1),Ys) )
    <=> ? [Z: val,Zs_4: list_val] :
          ( ( Xs = hAPP_l273806049st_val(cons_val(Z),Zs_4) )
          & ( hAPP_val_option_ty(F_1,Z) = Y_1 )
          & ( hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Zs_4) = Ys ) ) ) ).

tff(fact_832_Cons__in__lex,axiom,
    ! [X_2: list_char,Xs: list_list_char,Y_1: list_char,Ys: list_list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member817832404t_char(hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,hAPP_l407174677t_char(cons_list_char(X_2),Xs)),hAPP_l407174677t_char(cons_list_char(Y_1),Ys)),lex_list_char(R_1)))
    <=> ( ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_2),Y_1),R_1))
          & ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_l66428094ar_nat(size_s2113983095t_char,Ys) ) )
        | ( ( X_2 = Y_1 )
          & hBOOL(member817832404t_char(hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,Xs),Ys),lex_list_char(R_1))) ) ) ) ).

tff(fact_833_Cons__in__lex,axiom,
    ! [X_2: produc2061676504on_val,Xs: list_P249777017on_val,Y_1: produc2061676504on_val,Ys: list_P249777017on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member295766740on_val(hAPP_l1701465547on_val(hAPP_l1588290397on_val(produc493060183on_val,hAPP_l254081045on_val(cons_P1190705016on_val(X_2),Xs)),hAPP_l254081045on_val(cons_P1190705016on_val(Y_1),Ys)),lex_Pr830868420on_val(R_1)))
    <=> ( ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,X_2),Y_1),R_1))
          & ( hAPP_l1766199206al_nat(size_s470606735on_val,Xs) = hAPP_l1766199206al_nat(size_s470606735on_val,Ys) ) )
        | ( ( X_2 = Y_1 )
          & hBOOL(member295766740on_val(hAPP_l1701465547on_val(hAPP_l1588290397on_val(produc493060183on_val,Xs),Ys),lex_Pr830868420on_val(R_1))) ) ) ) ).

tff(fact_834_Cons__in__lex,axiom,
    ! [X_2: produc124828825on_val,Xs: list_P1663965006on_val,Y_1: produc124828825on_val,Ys: list_P1663965006on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member1942985176on_val(hAPP_l1485560508on_val(hAPP_l1324137613on_val(produc584381409on_val,hAPP_l76241055on_val(cons_P1917484281on_val(X_2),Xs)),hAPP_l76241055on_val(cons_P1917484281on_val(Y_1),Ys)),lex_Pr979517357on_val(R_1)))
    <=> ( ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X_2),Y_1),R_1))
          & ( hAPP_l1746926841al_nat(size_s60479160on_val,Xs) = hAPP_l1746926841al_nat(size_s60479160on_val,Ys) ) )
        | ( ( X_2 = Y_1 )
          & hBOOL(member1942985176on_val(hAPP_l1485560508on_val(hAPP_l1324137613on_val(produc584381409on_val,Xs),Ys),lex_Pr979517357on_val(R_1))) ) ) ) ).

tff(fact_835_Cons__in__lex,axiom,
    ! [X_2: char,Xs: list_char,Y_1: char,Ys: list_char,R_1: fun_Pr638203177r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,hAPP_l1074208899t_char(cons_char(X_2),Xs)),hAPP_l1074208899t_char(cons_char(Y_1),Ys)),lex_char(R_1)))
    <=> ( ( hBOOL(member1725532372r_char(hAPP_c802977373r_char(hAPP_c1242523777r_char(produc601902295r_char,X_2),Y_1),R_1))
          & ( hAPP_list_char_nat(size_size_list_char,Xs) = hAPP_list_char_nat(size_size_list_char,Ys) ) )
        | ( ( X_2 = Y_1 )
          & hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Xs),Ys),lex_char(R_1))) ) ) ) ).

tff(fact_836_Cons__in__lex,axiom,
    ! [X_2: val,Xs: list_val,Y_1: val,Ys: list_val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member273646106st_val(hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,hAPP_l273806049st_val(cons_val(X_2),Xs)),hAPP_l273806049st_val(cons_val(Y_1),Ys)),lex_val(R_1)))
    <=> ( ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_2),Y_1),R_1))
          & ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) ) )
        | ( ( X_2 = Y_1 )
          & hBOOL(member273646106st_val(hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,Xs),Ys),lex_val(R_1))) ) ) ) ).

tff(fact_837_Cons__in__lex,axiom,
    ! [X_2: ty,Xs: list_ty,Y_1: ty,Ys: list_ty,R_1: fun_Pr2087862441y_bool] :
      ( hBOOL(member104734088ist_ty(hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,hAPP_list_ty_list_ty(cons_ty(X_2),Xs)),hAPP_list_ty_list_ty(cons_ty(Y_1),Ys)),lex_ty(R_1)))
    <=> ( ( hBOOL(member1736614484_ty_ty(hAPP_t65172803_ty_ty(hAPP_t1494094285_ty_ty(product_Pair_ty_ty,X_2),Y_1),R_1))
          & ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) ) )
        | ( ( X_2 = Y_1 )
          & hBOOL(member104734088ist_ty(hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,Xs),Ys),lex_ty(R_1))) ) ) ) ).

tff(fact_838_Cons__in__lex,axiom,
    ! [X_2: exp_list_char,Xs: list_exp_list_char,Y_1: exp_list_char,Ys: list_exp_list_char,R_1: fun_Pr136267935r_bool] :
      ( hBOOL(member894971540t_char(hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,hAPP_l2011456725t_char(cons_exp_list_char(X_2),Xs)),hAPP_l2011456725t_char(cons_exp_list_char(Y_1),Ys)),lex_exp_list_char(R_1)))
    <=> ( ( hBOOL(member1199939018t_char(hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,X_2),Y_1),R_1))
          & ( hAPP_l452123639ar_nat(size_s1143674878t_char,Xs) = hAPP_l452123639ar_nat(size_s1143674878t_char,Ys) ) )
        | ( ( X_2 = Y_1 )
          & hBOOL(member894971540t_char(hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,Xs),Ys),lex_exp_list_char(R_1))) ) ) ) ).

tff(fact_839_not__finals__ConsI,axiom,
    ! [Es_4: list_exp_list_char,E_8: exp_list_char] :
      ( ~ hBOOL(final_list_char(E_8))
     => ~ hBOOL(finals_list_char(hAPP_l2011456725t_char(cons_exp_list_char(E_8),Es_4))) ) ).

tff(fact_840_redp__redsp_ORedBinOp,axiom,
    ! [Pa: list_P1999446415t_char,S_1: produc12694297on_val,Bop: bop,V_1_2: val,V_2: val,V: val] :
      ( ( binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Bop),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_2),V_2))) = hAPP_val_option_val(some_val,V) )
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,hAPP_v834067052t_char(val_list_char,V_2)),S_1),hAPP_v834067052t_char(val_list_char,V)),S_1)) ) ).

tff(fact_841_CallRedsThrowParams,axiom,
    ! [M: list_char,Es_1: list_exp_list_char,Vs_1_1: list_val,A_1: exp_list_char,Es_2_1: list_exp_list_char,S_2_1: produc12694297on_val,Ea: exp_list_char,S0: produc12694297on_val,V: val,S_1_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V)),S_1_2)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),S_1_2)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vs_1_1),hAPP_l2011456725t_char(cons_exp_list_char(throw_list_char(A_1)),Es_2_1))),S_2_1)),transi374442731on_val(reds(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(Ea,M,Es_1)),S0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A_1)),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_842_BinOpRedsThrow2,axiom,
    ! [Bop: bop,E_2: exp_list_char,Ea: exp_list_char,S_2_1: produc12694297on_val,E_1: exp_list_char,S_0: produc12694297on_val,V_1_2: val,S_1_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1_2)),S_1_2)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S_1_2)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_2_1)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(E_1,Bop,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_843_WTrtCons,axiom,
    ! [Es_1: list_exp_list_char,Tsa: list_ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Ha,E_4,Ea,Ta))
     => ( hBOOL(wTrts_1(Pa,Ha,E_4,Es_1,Tsa))
       => hBOOL(wTrts_1(Pa,Ha,E_4,hAPP_l2011456725t_char(cons_exp_list_char(Ea),Es_1),hAPP_list_ty_list_ty(cons_ty(Ta),Tsa))) ) ) ).

tff(fact_844_redp__redsp_OFAssThrow1,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,F: list_char,D: list_char,E_2: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(throw_list_char(Ea),F,D,E_2),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_845_redp__redsp_OBinOpThrow1,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,Bop: bop,E_2: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(throw_list_char(Ea),Bop,E_2),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_846_redp__redsp_OSeqThrow,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(throw_list_char(Ea),E_2),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_847_exp_Osimps_I14_J,axiom,
    ! [Exp_15: exp_list_char,Exp_14: exp_list_char] :
      ( ( throw_list_char(Exp_15) = throw_list_char(Exp_14) )
    <=> ( Exp_15 = Exp_14 ) ) ).

tff(fact_848_redp__redsp_OCallThrowObj,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,M: list_char,Es_1: list_exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(throw_list_char(Ea),M,Es_1),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_849_redp__redsp_OThrowRed,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,throw_list_char(Ea),S_1),throw_list_char(E)),S)) ) ).

tff(fact_850_redp__redsp_OThrowThrow,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,throw_list_char(throw_list_char(Ea)),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_851_append__eq__appendI,axiom,
    ! [Ys_4: list_exp_list_char,Us_2: list_exp_list_char,Xs_4: list_exp_list_char,Xs1_1: list_exp_list_char,Zs_3: list_exp_list_char] :
      ( ( append_exp_list_char(Xs_4,Xs1_1) = Zs_3 )
     => ( ( Ys_4 = append_exp_list_char(Xs1_1,Us_2) )
       => ( append_exp_list_char(Xs_4,Ys_4) = append_exp_list_char(Zs_3,Us_2) ) ) ) ).

tff(fact_852_append__same__eq,axiom,
    ! [Ys: list_exp_list_char,Xs: list_exp_list_char,Zs: list_exp_list_char] :
      ( ( append_exp_list_char(Ys,Xs) = append_exp_list_char(Zs,Xs) )
    <=> ( Ys = Zs ) ) ).

tff(fact_853_same__append__eq,axiom,
    ! [Xs: list_exp_list_char,Ys: list_exp_list_char,Zs: list_exp_list_char] :
      ( ( append_exp_list_char(Xs,Ys) = append_exp_list_char(Xs,Zs) )
    <=> ( Ys = Zs ) ) ).

tff(fact_854_append__eq__append__conv2,axiom,
    ! [Xs: list_exp_list_char,Ys: list_exp_list_char,Zs: list_exp_list_char,Ts_3: list_exp_list_char] :
      ( ( append_exp_list_char(Xs,Ys) = append_exp_list_char(Zs,Ts_3) )
    <=> ? [Us_1: list_exp_list_char] :
          ( ( ( Xs = append_exp_list_char(Zs,Us_1) )
            & ( append_exp_list_char(Us_1,Ys) = Ts_3 ) )
          | ( ( append_exp_list_char(Xs,Us_1) = Zs )
            & ( Ys = append_exp_list_char(Us_1,Ts_3) ) ) ) ) ).

tff(fact_855_append__assoc,axiom,
    ! [Xs_3: list_exp_list_char,Ys_3: list_exp_list_char,Zs_2: list_exp_list_char] : append_exp_list_char(append_exp_list_char(Xs_3,Ys_3),Zs_2) = append_exp_list_char(Xs_3,append_exp_list_char(Ys_3,Zs_2)) ).

tff(fact_856_redp__redsp_OFAssThrow2,axiom,
    ! [Pa: list_P1999446415t_char,V: val,F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,V),F,D,throw_list_char(Ea)),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_857_redp__redsp_OBinOpThrow2,axiom,
    ! [Pa: list_P1999446415t_char,V_1_2: val,Bop: bop,Ea: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,throw_list_char(Ea)),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_858_Cons__eq__appendI,axiom,
    ! [Xs_2: list_exp_list_char,Zs_1: list_exp_list_char,X_4: exp_list_char,Xs1: list_exp_list_char,Ys_2: list_exp_list_char] :
      ( ( hAPP_l2011456725t_char(cons_exp_list_char(X_4),Xs1) = Ys_2 )
     => ( ( Xs_2 = append_exp_list_char(Xs1,Zs_1) )
       => ( hAPP_l2011456725t_char(cons_exp_list_char(X_4),Xs_2) = append_exp_list_char(Ys_2,Zs_1) ) ) ) ).

tff(fact_859_Cons__eq__appendI,axiom,
    ! [Xs_2: list_val,Zs_1: list_val,X_4: val,Xs1: list_val,Ys_2: list_val] :
      ( ( hAPP_l273806049st_val(cons_val(X_4),Xs1) = Ys_2 )
     => ( ( Xs_2 = append_val(Xs1,Zs_1) )
       => ( hAPP_l273806049st_val(cons_val(X_4),Xs_2) = append_val(Ys_2,Zs_1) ) ) ) ).

tff(fact_860_Cons__eq__appendI,axiom,
    ! [Xs_2: list_list_char,Zs_1: list_list_char,X_4: list_char,Xs1: list_list_char,Ys_2: list_list_char] :
      ( ( hAPP_l407174677t_char(cons_list_char(X_4),Xs1) = Ys_2 )
     => ( ( Xs_2 = append_list_char(Xs1,Zs_1) )
       => ( hAPP_l407174677t_char(cons_list_char(X_4),Xs_2) = append_list_char(Ys_2,Zs_1) ) ) ) ).

tff(fact_861_Cons__eq__appendI,axiom,
    ! [Xs_2: list_ty,Zs_1: list_ty,X_4: ty,Xs1: list_ty,Ys_2: list_ty] :
      ( ( hAPP_list_ty_list_ty(cons_ty(X_4),Xs1) = Ys_2 )
     => ( ( Xs_2 = append_ty(Xs1,Zs_1) )
       => ( hAPP_list_ty_list_ty(cons_ty(X_4),Xs_2) = append_ty(Ys_2,Zs_1) ) ) ) ).

tff(fact_862_append__Cons,axiom,
    ! [X_3: exp_list_char,Xs_1: list_exp_list_char,Ys_1: list_exp_list_char] : append_exp_list_char(hAPP_l2011456725t_char(cons_exp_list_char(X_3),Xs_1),Ys_1) = hAPP_l2011456725t_char(cons_exp_list_char(X_3),append_exp_list_char(Xs_1,Ys_1)) ).

tff(fact_863_append__Cons,axiom,
    ! [X_3: val,Xs_1: list_val,Ys_1: list_val] : append_val(hAPP_l273806049st_val(cons_val(X_3),Xs_1),Ys_1) = hAPP_l273806049st_val(cons_val(X_3),append_val(Xs_1,Ys_1)) ).

tff(fact_864_append__Cons,axiom,
    ! [X_3: list_char,Xs_1: list_list_char,Ys_1: list_list_char] : append_list_char(hAPP_l407174677t_char(cons_list_char(X_3),Xs_1),Ys_1) = hAPP_l407174677t_char(cons_list_char(X_3),append_list_char(Xs_1,Ys_1)) ).

tff(fact_865_append__Cons,axiom,
    ! [X_3: ty,Xs_1: list_ty,Ys_1: list_ty] : append_ty(hAPP_list_ty_list_ty(cons_ty(X_3),Xs_1),Ys_1) = hAPP_list_ty_list_ty(cons_ty(X_3),append_ty(Xs_1,Ys_1)) ).

tff(fact_866_map__append,axiom,
    ! [F_1: fun_Pr1149393094ar_val,Xs: list_P2023964830har_ty,Ys: list_P2023964830har_ty] : hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),append590652462har_ty(Xs,Ys)) = append1049742455ar_val(hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),Xs),hAPP_l608137480ar_val(map_Pr1153581243ar_val(F_1),Ys)) ).

tff(fact_867_map__append,axiom,
    ! [F_1: fun_list_char_val,Xs: list_list_char,Ys: list_list_char] : hAPP_l1892737211st_val(map_list_char_val(F_1),append_list_char(Xs,Ys)) = append_val(hAPP_l1892737211st_val(map_list_char_val(F_1),Xs),hAPP_l1892737211st_val(map_list_char_val(F_1),Ys)) ).

tff(fact_868_map__append,axiom,
    ! [F_1: fun_va223928858t_char,Xs: list_val,Ys: list_val] : hAPP_l732421366t_char(map_va1934808527t_char(F_1),append_val(Xs,Ys)) = append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(F_1),Xs),hAPP_l732421366t_char(map_va1934808527t_char(F_1),Ys)) ).

tff(fact_869_map__append,axiom,
    ! [F_1: fun_ty_option_ty,Xs: list_ty,Ys: list_ty] : hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),append_ty(Xs,Ys)) = append_option_ty(hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Xs),hAPP_l1487035934ion_ty(map_ty_option_ty(F_1),Ys)) ).

tff(fact_870_map__append,axiom,
    ! [F_1: fun_val_option_ty,Xs: list_val,Ys: list_val] : hAPP_l2006940821ion_ty(map_val_option_ty(F_1),append_val(Xs,Ys)) = append_option_ty(hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Xs),hAPP_l2006940821ion_ty(map_val_option_ty(F_1),Ys)) ).

tff(fact_871_eval__evals_OThrowThrow,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E: exp_list_char,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E)),S_1_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(Ea),S_0),throw_list_char(E)),S_1_2)) ) ).

tff(fact_872_list__all2__appendI,axiom,
    ! [C_2: list_val,D_1: list_ty,Pa: fun_val_fun_ty_bool,A_1: list_val,B: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_all2_val_ty(Pa,A_1),B))
     => ( hBOOL(hAPP_list_ty_bool(list_all2_val_ty(Pa,C_2),D_1))
       => hBOOL(hAPP_list_ty_bool(list_all2_val_ty(Pa,append_val(A_1,C_2)),append_ty(B,D_1))) ) ) ).

tff(fact_873_list__all2__appendI,axiom,
    ! [C_2: list_ty,D_1: list_ty,Pa: fun_ty_fun_ty_bool,A_1: list_ty,B: list_ty] :
      ( hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(Pa,A_1),B))
     => ( hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(Pa,C_2),D_1))
       => hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(Pa,append_ty(A_1,C_2)),append_ty(B,D_1))) ) ) ).

tff(fact_874_redp__redsp_OSeqRed,axiom,
    ! [E_2: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(Ea,E_2),S_1),seq_list_char(E,E_2)),S)) ) ).

tff(fact_875_redp__redsp_OFAssRed1,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(Ea,F,D,E_2),S_1),fAss_list_char(E,F,D,E_2)),S)) ) ).

tff(fact_876_redp__redsp_OCallObj,axiom,
    ! [M: list_char,Es_1: list_exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(Ea,M,Es_1),S_1),call_list_char(E,M,Es_1)),S)) ) ).

tff(fact_877_redp__redsp_OBinOpRed1,axiom,
    ! [Bop: bop,E_2: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(Ea,Bop,E_2),S_1),binOp_list_char(E,Bop,E_2)),S)) ) ).

tff(fact_878_redp__redsp_OTryRed,axiom,
    ! [C: list_char,V_1: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,tryCatch_list_char(Ea,C,V_1,E_2),S_1),tryCatch_list_char(E,C,V_1,E_2)),S)) ) ).

tff(fact_879_redp__redsp_OCallThrowParams,axiom,
    ! [Pa: list_P1999446415t_char,V: val,M: list_char,S_1: produc12694297on_val,Es_1: list_exp_list_char,Vsa: list_val,Ea: exp_list_char,Es: list_exp_list_char] :
      ( ( Es_1 = append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa),hAPP_l2011456725t_char(cons_exp_list_char(throw_list_char(Ea)),Es)) )
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(hAPP_v834067052t_char(val_list_char,V),M,Es_1),S_1),throw_list_char(Ea)),S_1)) ) ).

tff(fact_880_exp_Osimps_I90_J,axiom,
    ! [Val_1: val,Exp_13: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_1) != throw_list_char(Exp_13) ).

tff(fact_881_exp_Osimps_I91_J,axiom,
    ! [Exp_12: exp_list_char,Val: val] : throw_list_char(Exp_12) != hAPP_v834067052t_char(val_list_char,Val) ).

tff(fact_882_exp_Osimps_I211_J,axiom,
    ! [Exp_11: exp_list_char,Exp1_7: exp_list_char,Exp2_7: exp_list_char] : throw_list_char(Exp_11) != seq_list_char(Exp1_7,Exp2_7) ).

tff(fact_883_exp_Osimps_I210_J,axiom,
    ! [Exp1_6: exp_list_char,Exp2_6: exp_list_char,Exp_10: exp_list_char] : seq_list_char(Exp1_6,Exp2_6) != throw_list_char(Exp_10) ).

tff(fact_884_exp_Osimps_I181_J,axiom,
    ! [Exp_9: exp_list_char,Exp1_5: exp_list_char,List1_3: list_char,List2_3: list_char,Exp2_5: exp_list_char] : throw_list_char(Exp_9) != fAss_list_char(Exp1_5,List1_3,List2_3,Exp2_5) ).

tff(fact_885_exp_Osimps_I180_J,axiom,
    ! [Exp1_4: exp_list_char,List1_2: list_char,List2_2: list_char,Exp2_4: exp_list_char,Exp_8: exp_list_char] : fAss_list_char(Exp1_4,List1_2,List2_2,Exp2_4) != throw_list_char(Exp_8) ).

tff(fact_886_exp_Osimps_I193_J,axiom,
    ! [Exp_7: exp_list_char,Exp_6: exp_list_char,List1_1: list_char,List2_1: list_exp_list_char] : throw_list_char(Exp_7) != call_list_char(Exp_6,List1_1,List2_1) ).

tff(fact_887_exp_Osimps_I192_J,axiom,
    ! [Exp_5: exp_list_char,List1: list_char,List2: list_exp_list_char,Exp_4: exp_list_char] : call_list_char(Exp_5,List1,List2) != throw_list_char(Exp_4) ).

tff(fact_888_exp_Osimps_I113_J,axiom,
    ! [Exp_3: exp_list_char,Exp1_3: exp_list_char,Bop_2: bop,Exp2_3: exp_list_char] : throw_list_char(Exp_3) != binOp_list_char(Exp1_3,Bop_2,Exp2_3) ).

tff(fact_889_exp_Osimps_I112_J,axiom,
    ! [Exp1_2: exp_list_char,Bop_1: bop,Exp2_2: exp_list_char,Exp_2: exp_list_char] : binOp_list_char(Exp1_2,Bop_1,Exp2_2) != throw_list_char(Exp_2) ).

tff(fact_890_exp_Osimps_I224_J,axiom,
    ! [Exp_1: exp_list_char,Exp1_1: exp_list_char,List_4: list_char,A_4: list_char,Exp2_1: exp_list_char] : throw_list_char(Exp_1) != tryCatch_list_char(Exp1_1,List_4,A_4,Exp2_1) ).

tff(fact_891_exp_Osimps_I225_J,axiom,
    ! [Exp1: exp_list_char,List_3: list_char,A_3: list_char,Exp2: exp_list_char,Exp: exp_list_char] : tryCatch_list_char(Exp1,List_3,A_3,Exp2) != throw_list_char(Exp) ).

tff(fact_892_finals__app__map,axiom,
    ! [Vsa: list_val,Es_1: list_exp_list_char] :
      ( hBOOL(finals_list_char(append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa),Es_1)))
    <=> hBOOL(finals_list_char(Es_1)) ) ).

tff(fact_893_list__all2__append,axiom,
    ! [Pa: fun_val_fun_ty_bool,Us: list_val,Vsa: list_ty,Xs: list_val,Ys: list_ty] :
      ( ( hAPP_list_val_nat(size_size_list_val,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) )
     => ( hBOOL(hAPP_list_ty_bool(list_all2_val_ty(Pa,append_val(Xs,Us)),append_ty(Ys,Vsa)))
      <=> ( hBOOL(hAPP_list_ty_bool(list_all2_val_ty(Pa,Xs),Ys))
          & hBOOL(hAPP_list_ty_bool(list_all2_val_ty(Pa,Us),Vsa)) ) ) ) ).

tff(fact_894_list__all2__append,axiom,
    ! [Pa: fun_ty_fun_ty_bool,Us: list_ty,Vsa: list_ty,Xs: list_ty,Ys: list_ty] :
      ( ( hAPP_list_ty_nat(size_size_list_ty,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) )
     => ( hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(Pa,append_ty(Xs,Us)),append_ty(Ys,Vsa)))
      <=> ( hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(Pa,Xs),Ys))
          & hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(Pa,Us),Vsa)) ) ) ) ).

tff(fact_895_redp__redsp_ORedSeq,axiom,
    ! [Pa: list_P1999446415t_char,V: val,E_2: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(hAPP_v834067052t_char(val_list_char,V),E_2),S_1),E_2),S_1)) ).

tff(fact_896_redp__redsp_OFAssRed2,axiom,
    ! [V: val,F: list_char,D: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,V),F,D,Ea),S_1),fAss_list_char(hAPP_v834067052t_char(val_list_char,V),F,D,E)),S)) ) ).

tff(fact_897_redp__redsp_OBinOpRed2,axiom,
    ! [V_1_2: val,Bop: bop,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,Ea),S_1),binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,E)),S)) ) ).

tff(fact_898_fun__upds__append__drop,axiom,
    ! [M_1: fun_li1432931796on_val,Zs: list_list_char,Xs: list_list_char,Ys: list_val] :
      ( ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) )
     => ( map_up1085636310ar_val(M_1,append_list_char(Xs,Zs),Ys) = map_up1085636310ar_val(M_1,Xs,Ys) ) ) ).

tff(fact_899_fun__upds__append__drop,axiom,
    ! [M_1: fun_li688206603ion_ty,Zs: list_list_char,Xs: list_list_char,Ys: list_ty] :
      ( ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) )
     => ( map_up891053837har_ty(M_1,append_list_char(Xs,Zs),Ys) = map_up891053837har_ty(M_1,Xs,Ys) ) ) ).

tff(fact_900_fun__upds__append2__drop,axiom,
    ! [M_1: fun_li1432931796on_val,Zs: list_val,Xs: list_list_char,Ys: list_val] :
      ( ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_list_val_nat(size_size_list_val,Ys) )
     => ( map_up1085636310ar_val(M_1,Xs,append_val(Ys,Zs)) = map_up1085636310ar_val(M_1,Xs,Ys) ) ) ).

tff(fact_901_fun__upds__append2__drop,axiom,
    ! [M_1: fun_li688206603ion_ty,Zs: list_ty,Xs: list_list_char,Ys: list_ty] :
      ( ( hAPP_l66428094ar_nat(size_s2113983095t_char,Xs) = hAPP_list_ty_nat(size_size_list_ty,Ys) )
     => ( map_up891053837har_ty(M_1,Xs,append_ty(Ys,Zs)) = map_up891053837har_ty(M_1,Xs,Ys) ) ) ).

tff(fact_902_redp__redsp_ORedTry,axiom,
    ! [Pa: list_P1999446415t_char,V: val,C: list_char,V_1: list_char,E_2: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,tryCatch_list_char(hAPP_v834067052t_char(val_list_char,V),C,V_1,E_2),S_1),hAPP_v834067052t_char(val_list_char,V)),S_1)) ).

tff(fact_903_eval__evals_OSeqThrow,axiom,
    ! [E_1: exp_list_char,Pa: list_P1999446415t_char,E_0: exp_list_char,S_0: produc12694297on_val,Ea: exp_list_char,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_0,S_0),throw_list_char(Ea)),S_1_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,seq_list_char(E_0,E_1),S_0),throw_list_char(Ea)),S_1_2)) ) ).

tff(fact_904_eval__evals_OFAssThrow1,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,E_1: exp_list_char,S_0: produc12694297on_val,E: exp_list_char,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_0),throw_list_char(E)),S_1_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAss_list_char(E_1,F,D,E_2),S_0),throw_list_char(E)),S_1_2)) ) ).

tff(fact_905_CallObjThrow,axiom,
    ! [M: list_char,Ps: list_exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E: exp_list_char,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E)),S_1_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,call_list_char(Ea,M,Ps),S_0),throw_list_char(E)),S_1_2)) ) ).

tff(fact_906_eval__evals_OBinOpThrow1,axiom,
    ! [Bop: bop,E_2: exp_list_char,Pa: list_P1999446415t_char,E_1: exp_list_char,S_0: produc12694297on_val,Ea: exp_list_char,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_0),throw_list_char(Ea)),S_1_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,binOp_list_char(E_1,Bop,E_2),S_0),throw_list_char(Ea)),S_1_2)) ) ).

tff(fact_907_red__reds_OThrowRed,axiom,
    ! [Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E)),S)),red(Pa))) ) ).

tff(fact_908_red__reds_OThrowThrow,axiom,
    ! [Ea: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(throw_list_char(Ea))),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_1)),red(Pa))) ).

tff(fact_909_eval__evals_OFAssThrow2,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,E: exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,E_1: exp_list_char,S_0: produc12694297on_val,V: val,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_0),hAPP_v834067052t_char(val_list_char,V)),S_1_2))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_2),throw_list_char(E)),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAss_list_char(E_1,F,D,E_2),S_0),throw_list_char(E)),S_2_1)) ) ) ).

tff(fact_910_eval__evals_OBinOpThrow2,axiom,
    ! [Bop: bop,E_2: exp_list_char,Ea: exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,E_1: exp_list_char,S_0: produc12694297on_val,V_1_2: val,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_0),hAPP_v834067052t_char(val_list_char,V_1_2)),S_1_2))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_2),throw_list_char(Ea)),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,binOp_list_char(E_1,Bop,E_2),S_0),throw_list_char(Ea)),S_2_1)) ) ) ).

tff(fact_911_red__reds_OCallThrowParams,axiom,
    ! [V: val,M: list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char,Es_1: list_exp_list_char,Vsa: list_val,Ea: exp_list_char,Es: list_exp_list_char] :
      ( ( Es_1 = append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa),hAPP_l2011456725t_char(cons_exp_list_char(throw_list_char(Ea)),Es)) )
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(hAPP_v834067052t_char(val_list_char,V),M,Es_1)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_1)),red(Pa))) ) ).

tff(fact_912_ThrowRedsThrow,axiom,
    ! [Ea: exp_list_char,S_1: produc12694297on_val,A_1: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A_1)),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A_1)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_913_ThrowReds,axiom,
    ! [Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_914_red__reds_OSeqThrow,axiom,
    ! [Ea: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(throw_list_char(Ea),E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_1)),red(Pa))) ).

tff(fact_915_red__reds_OFAssThrow1,axiom,
    ! [Ea: exp_list_char,F: list_char,D: list_char,E_2: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(throw_list_char(Ea),F,D,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_1)),red(Pa))) ).

tff(fact_916_red__reds_OCallThrowObj,axiom,
    ! [Ea: exp_list_char,M: list_char,Es_1: list_exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(throw_list_char(Ea),M,Es_1)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_1)),red(Pa))) ).

tff(fact_917_red__reds_OBinOpThrow1,axiom,
    ! [Ea: exp_list_char,Bop: bop,E_2: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(throw_list_char(Ea),Bop,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_1)),red(Pa))) ).

tff(fact_918_red__reds_OFAssThrow2,axiom,
    ! [V: val,F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,V),F,D,throw_list_char(Ea))),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_1)),red(Pa))) ).

tff(fact_919_red__reds_OBinOpThrow2,axiom,
    ! [V_1_2: val,Bop: bop,Ea: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,throw_list_char(Ea))),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_1)),red(Pa))) ).

tff(fact_920_SeqRedsThrow,axiom,
    ! [E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E)),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(Ea,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_921_FAssRedsThrow1,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E)),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(Ea,F,D,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_922_CallRedsThrowObj,axiom,
    ! [M: list_char,Es_1: list_exp_list_char,Ea: exp_list_char,S0: produc12694297on_val,A_1: exp_list_char,S_1_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A_1)),S_1_2)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(Ea,M,Es_1)),S0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A_1)),S_1_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_923_BinOpRedsThrow1,axiom,
    ! [Bop: bop,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E)),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(Ea,Bop,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_924_FAssRedsThrow2,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,Ea: exp_list_char,S_2_1: produc12694297on_val,E_1: exp_list_char,S_0: produc12694297on_val,V: val,S_1_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V)),S_1_2)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S_1_2)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_2_1)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(E_1,F,D,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_925_eval__cases_I3_J,axiom,
    ! [Pa: list_P1999446415t_char,E_1: exp_list_char,Bop: bop,E_2: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,binOp_list_char(E_1,Bop,E_2),S_1),E),S))
     => ( ! [V_1_1: val,S_1_1: produc12694297on_val,V_2_2: val,V_4: val] :
            ( ( E = hAPP_v834067052t_char(val_list_char,V_4) )
           => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_1),hAPP_v834067052t_char(val_list_char,V_1_1)),S_1_1))
             => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_1),hAPP_v834067052t_char(val_list_char,V_2_2)),S))
               => ( binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Bop),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_1),V_2_2))) != hAPP_val_option_val(some_val,V_4) ) ) ) )
       => ( ! [E_7: exp_list_char] :
              ( ( E = throw_list_char(E_7) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_1),throw_list_char(E_7)),S)) )
         => ~ ! [V_1_1: val,S_1_1: produc12694297on_val,E_7: exp_list_char] :
                ( ( E = throw_list_char(E_7) )
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_1),hAPP_v834067052t_char(val_list_char,V_1_1)),S_1_1))
                 => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_1),throw_list_char(E_7)),S)) ) ) ) ) ) ).

tff(fact_926_CallParamsThrow,axiom,
    ! [M: list_char,Es_1: list_exp_list_char,Vsa: list_val,Ex: exp_list_char,Es: list_exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,V: val,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,V)),S_1_2))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es_1,S_1_2),append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa),hAPP_l2011456725t_char(cons_exp_list_char(throw_list_char(Ex)),Es))),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,call_list_char(Ea,M,Es_1),S_0),throw_list_char(Ex)),S_2_1)) ) ) ).

tff(fact_927_evals__final,axiom,
    ! [Pa: list_P1999446415t_char,Es_1: list_exp_list_char,S_1: produc12694297on_val,Es: list_exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es_1,S_1),Es),S))
     => hBOOL(finals_list_char(Es)) ) ).

tff(fact_928_eval__finalsId,axiom,
    ! [Pa: list_P1999446415t_char,S_1: produc12694297on_val,Es_1: list_exp_list_char] :
      ( hBOOL(finals_list_char(Es_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es_1,S_1),Es_1),S_1)) ) ).

tff(fact_929_evals__hext,axiom,
    ! [Pa: list_P1999446415t_char,Es_1: list_exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,Es: list_exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es_1,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1)),Es),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L)))
     => hBOOL(hext(Ha,H)) ) ).

tff(fact_930_eval__evals_OCons,axiom,
    ! [Es_1: list_exp_list_char,Es: list_exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,V: val,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,V)),S_1_2))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es_1,S_1_2),Es),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,hAPP_l2011456725t_char(cons_exp_list_char(Ea),Es_1),S_0),hAPP_l2011456725t_char(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V)),Es)),S_2_1)) ) ) ).

tff(fact_931_ConsThrow,axiom,
    ! [Es_1: list_exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E: exp_list_char,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E)),S_1_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,hAPP_l2011456725t_char(cons_exp_list_char(Ea),Es_1),S_0),hAPP_l2011456725t_char(cons_exp_list_char(throw_list_char(E)),Es_1)),S_1_2)) ) ).

tff(fact_932_list__eval__Throw,axiom,
    ! [Vsa: list_val,Es: list_exp_list_char,Pa: list_P1999446415t_char,X_2: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(X_2),S_1),E),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa),hAPP_l2011456725t_char(cons_exp_list_char(throw_list_char(X_2)),Es)),S_1),append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa),hAPP_l2011456725t_char(cons_exp_list_char(E),Es))),S)) ) ).

tff(fact_933_evals__cases_I2_J,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,Es_1: list_exp_list_char,S_1: produc12694297on_val,E: list_exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,hAPP_l2011456725t_char(cons_exp_list_char(Ea),Es_1),S_1),E),S))
     => ( ! [V_4: val,S_1_1: produc12694297on_val,Es_3: list_exp_list_char] :
            ( ( E = hAPP_l2011456725t_char(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_4)),Es_3) )
           => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),hAPP_v834067052t_char(val_list_char,V_4)),S_1_1))
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es_1,S_1_1),Es_3),S)) ) )
       => ~ ! [E_3: exp_list_char] :
              ( ( E = hAPP_l2011456725t_char(cons_exp_list_char(throw_list_char(E_3)),Es_1) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),throw_list_char(E_3)),S)) ) ) ) ).

tff(fact_934_eval__cases_I9_J,axiom,
    ! [Pa: list_P1999446415t_char,E_1: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,seq_list_char(E_1,E_2),S_1),E),S))
     => ( ! [V_4: val,S_1_1: produc12694297on_val] :
            ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_1),hAPP_v834067052t_char(val_list_char,V_4)),S_1_1))
           => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_1),E),S)) )
       => ~ ! [E_7: exp_list_char] :
              ( ( E = throw_list_char(E_7) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_1),throw_list_char(E_7)),S)) ) ) ) ).

tff(fact_935_redp__redsp_OCallParams,axiom,
    ! [V: val,M: list_char,Pa: list_P1999446415t_char,Es_1: list_exp_list_char,S_1: produc12694297on_val,Es: list_exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,Es_1,S_1),Es),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(hAPP_v834067052t_char(val_list_char,V),M,Es_1),S_1),call_list_char(hAPP_v834067052t_char(val_list_char,V),M,Es)),S)) ) ).

tff(fact_936_WTrtThrow,axiom,
    ! [Ta: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char,T_r: ty] :
      ( hBOOL(wTrt(Pa,Ha,E_4,Ea,T_r))
     => ( hBOOL(is_refT(T_r))
       => hBOOL(wTrt(Pa,Ha,E_4,throw_list_char(Ea),Ta)) ) ) ).

tff(fact_937_redp__redsp_OListRed2,axiom,
    ! [V: val,Pa: list_P1999446415t_char,Es_1: list_exp_list_char,S_1: produc12694297on_val,Es: list_exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,Es_1,S_1),Es),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,hAPP_l2011456725t_char(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V)),Es_1),S_1),hAPP_l2011456725t_char(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V)),Es)),S)) ) ).

tff(fact_938_redp__redsp_OListRed1,axiom,
    ! [Es_1: list_exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,hAPP_l2011456725t_char(cons_exp_list_char(Ea),Es_1),S_1),hAPP_l2011456725t_char(cons_exp_list_char(E),Es_1)),S)) ) ).

tff(fact_939_WTrt__elim__cases_I4_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Ha,E_4,throw_list_char(Ea),Ta))
     => ~ ! [T_r_1: ty] :
            ( hBOOL(wTrt(Pa,Ha,E_4,Ea,T_r_1))
           => ~ hBOOL(is_refT(T_r_1)) ) ) ).

tff(fact_940_WhileRedsThrow,axiom,
    ! [C_2: exp_list_char,B: exp_list_char,S_1: produc12694297on_val,Ea: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,while_list_char(B,C_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_941_FAccRedsThrow,axiom,
    ! [F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val,A_1: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A_1)),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(Ea,F,D)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A_1)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_942_CastRedsThrow,axiom,
    ! [C: list_char,Ea: exp_list_char,S_1: produc12694297on_val,A_1: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A_1)),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,Ea)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A_1)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_943_redp__redsp_OCastRed,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,Ea),S_1),cast_list_char(C,E)),S)) ) ).

tff(fact_944_redp__redsp_OFAccRed,axiom,
    ! [F: list_char,D: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(Ea,F,D),S_1),fAcc_list_char(E,F,D)),S)) ) ).

tff(fact_945_eval__evals_OCastThrow,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E: exp_list_char,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E)),S_1_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,Ea),S_0),throw_list_char(E)),S_1_2)) ) ).

tff(fact_946_eval__evals_OFAccThrow,axiom,
    ! [F: list_char,D: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E: exp_list_char,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E)),S_1_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAcc_list_char(Ea,F,D),S_0),throw_list_char(E)),S_1_2)) ) ).

tff(fact_947_WhileCondThrow,axiom,
    ! [C_2: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E: exp_list_char,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E)),S_1_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Ea,C_2),S_0),throw_list_char(E)),S_1_2)) ) ).

tff(fact_948_redp__redsp_OCastThrow,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,Ea: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,throw_list_char(Ea)),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_949_redp__redsp_OFAccThrow,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,F: list_char,D: list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(throw_list_char(Ea),F,D),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_950_red__reds_OCastRed,axiom,
    ! [C: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,Ea)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,E)),S)),red(Pa))) ) ).

tff(fact_951_red__reds_OFAccRed,axiom,
    ! [F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(Ea,F,D)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(E,F,D)),S)),red(Pa))) ) ).

tff(fact_952_red__reds_OCastThrow,axiom,
    ! [C: list_char,Ea: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,throw_list_char(Ea))),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_1)),red(Pa))) ).

tff(fact_953_CastReds,axiom,
    ! [C: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,Ea)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,E)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_954_red__reds_OFAccThrow,axiom,
    ! [Ea: exp_list_char,F: list_char,D: list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(throw_list_char(Ea),F,D)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_1)),red(Pa))) ).

tff(fact_955_FAccReds,axiom,
    ! [F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(Ea,F,D)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(E,F,D)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_956_WhileTRedsThrow,axiom,
    ! [C_2: exp_list_char,Ea: exp_list_char,S_2_1: produc12694297on_val,B: exp_list_char,S_0: produc12694297on_val,S_1_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1_2)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_2),S_1_2)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_2_1)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,while_list_char(B,C_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_957_WhileT,axiom,
    ! [E_3_1: exp_list_char,S_3_1: produc12694297on_val,C_2: exp_list_char,V_1_2: val,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_2: 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_2))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_2,S_1_2),hAPP_v834067052t_char(val_list_char,V_1_2)),S_2_1))
       => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Ea,C_2),S_2_1),E_3_1),S_3_1))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Ea,C_2),S_0),E_3_1),S_3_1)) ) ) ) ).

tff(fact_958_WhileBodyThrow,axiom,
    ! [C_2: exp_list_char,E: exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_2: 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_2))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_2,S_1_2),throw_list_char(E)),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Ea,C_2),S_0),throw_list_char(E)),S_2_1)) ) ) ).

tff(fact_959_WhileTReds,axiom,
    ! [Ea: exp_list_char,S_3_1: produc12694297on_val,C_2: exp_list_char,V_1_2: val,S_2_1: produc12694297on_val,B: exp_list_char,S_0: produc12694297on_val,S_1_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1_2)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_2),S_1_2)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1_2)),S_2_1)),transi2024712006on_val(red(Pa))))
       => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,while_list_char(B,C_2)),S_2_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_3_1)),transi2024712006on_val(red(Pa))))
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,while_list_char(B,C_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_3_1)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_960_binop_Osimps_I1_J,axiom,
    ! [V_1_2: val,V_2: val] : binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,c_Expr_Obop_OEq),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_2),V_2))) = hAPP_val_option_val(some_val,bool_1(hAPP_val_bool(hAPP_v1392248405l_bool(fequal_val,V_1_2),V_2))) ).

tff(fact_961_WhileFReds,axiom,
    ! [C_2: exp_list_char,B: exp_list_char,S_1: produc12694297on_val,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,bool_1(fFalse))),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,while_list_char(B,C_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,unit)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_962_CastRedsNull,axiom,
    ! [C: list_char,Ea: exp_list_char,S_1: produc12694297on_val,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,Ea)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_963_FAcc,axiom,
    ! [F: list_char,D: list_char,V: val,C: list_char,Fs_1: fun_Pr806764899on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,A_1: 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_1))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1)))
     => ( ( hAPP_n546249108on_val(Ha,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)) )
       => ( ( hAPP_P2094403585on_val(Fs_1,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D)) = hAPP_val_option_val(some_val,V) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAcc_list_char(Ea,F,D),S_0),hAPP_v834067052t_char(val_list_char,V)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))) ) ) ) ).

tff(fact_964_CondReds2T,axiom,
    ! [E_2: exp_list_char,E_1: exp_list_char,E: exp_list_char,S_2_1: produc12694297on_val,Ea: exp_list_char,S_0: produc12694297on_val,S_1_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1_2)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1),S_1_2)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S_2_1)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(Ea,E_1,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_965_redp__redsp_OCondRed,axiom,
    ! [E_1: exp_list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cond_list_char(Ea,E_1,E_2),S_1),cond_list_char(E,E_1,E_2)),S)) ) ).

tff(fact_966_eval__evals_OCondThrow,axiom,
    ! [E_1: exp_list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E: exp_list_char,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E)),S_1_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(Ea,E_1,E_2),S_0),throw_list_char(E)),S_1_2)) ) ).

tff(fact_967_redp__redsp_OCondThrow,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,E_1: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cond_list_char(throw_list_char(Ea),E_1,E_2),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_968_unfold__while,axiom,
    ! [Pa: list_P1999446415t_char,B: exp_list_char,C_2: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(B,C_2),S_1),E),S))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(B,seq_list_char(C_2,while_list_char(B,C_2)),hAPP_v834067052t_char(val_list_char,unit)),S_1),E),S)) ) ).

tff(fact_969_redp__redsp_ORedWhile,axiom,
    ! [Pa: list_P1999446415t_char,B: exp_list_char,C_2: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,while_list_char(B,C_2),S_1),cond_list_char(B,seq_list_char(C_2,while_list_char(B,C_2)),hAPP_v834067052t_char(val_list_char,unit))),S_1)) ).

tff(fact_970_Throw,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,A_1: nat,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,addr(A_1))),S_1_2))
     => 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_1)))),S_1_2)) ) ).

tff(fact_971_red__reds_OCondRed,axiom,
    ! [E_1: exp_list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(Ea,E_1,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(E,E_1,E_2)),S)),red(Pa))) ) ).

tff(fact_972_CondT,axiom,
    ! [E_2: exp_list_char,E_1: exp_list_char,E: exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_2: 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_2))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_1_2),E),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(Ea,E_1,E_2),S_0),E),S_2_1)) ) ) ).

tff(fact_973_CondF,axiom,
    ! [E_1: exp_list_char,E_2: exp_list_char,E: exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_2: 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_2))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_2),E),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(Ea,E_1,E_2),S_0),E),S_2_1)) ) ) ).

tff(fact_974_redp__redsp_ORedCondT,axiom,
    ! [Pa: list_P1999446415t_char,E_1: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cond_list_char(hAPP_v834067052t_char(val_list_char,bool_1(fTrue)),E_1,E_2),S_1),E_1),S_1)) ).

tff(fact_975_redp__redsp_ORedCondF,axiom,
    ! [Pa: list_P1999446415t_char,E_1: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cond_list_char(hAPP_v834067052t_char(val_list_char,bool_1(fFalse)),E_1,E_2),S_1),E_2),S_1)) ).

tff(fact_976_red__reds_ORedWhile,axiom,
    ! [B: exp_list_char,C_2: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,while_list_char(B,C_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(B,seq_list_char(C_2,while_list_char(B,C_2)),hAPP_v834067052t_char(val_list_char,unit))),S_1)),red(Pa))) ).

tff(fact_977_CastNull,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1_2))
     => 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_2)) ) ).

tff(fact_978_redp__redsp_ORedCastNull,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,hAPP_v834067052t_char(val_list_char,null)),S_1),hAPP_v834067052t_char(val_list_char,null)),S_1)) ).

tff(fact_979_red__reds_OCondThrow,axiom,
    ! [Ea: exp_list_char,E_1: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(throw_list_char(Ea),E_1,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_1)),red(Pa))) ).

tff(fact_980_CondReds,axiom,
    ! [E_1: exp_list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(Ea,E_1,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(E,E_1,E_2)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_981_CondRedsThrow,axiom,
    ! [E_1: exp_list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,A_1: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A_1)),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(Ea,E_1,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A_1)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_982_red__reds_ORedCondF,axiom,
    ! [E_1: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(hAPP_v834067052t_char(val_list_char,bool_1(fFalse)),E_1,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S_1)),red(Pa))) ).

tff(fact_983_red__reds_ORedCondT,axiom,
    ! [E_1: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(hAPP_v834067052t_char(val_list_char,bool_1(fTrue)),E_1,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1),S_1)),red(Pa))) ).

tff(fact_984_WhileF,axiom,
    ! [C_2: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_2: 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_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Ea,C_2),S_0),hAPP_v834067052t_char(val_list_char,unit)),S_1_2)) ) ).

tff(fact_985_red__reds_ORedCastNull,axiom,
    ! [C: list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,hAPP_v834067052t_char(val_list_char,null))),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S_1)),red(Pa))) ).

tff(fact_986_CondReds2F,axiom,
    ! [E_1: exp_list_char,E_2: exp_list_char,E: exp_list_char,S_2_1: produc12694297on_val,Ea: exp_list_char,S_0: produc12694297on_val,S_1_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,bool_1(fFalse))),S_1_2)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S_1_2)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S_2_1)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(Ea,E_1,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_987_FAccRedsVal,axiom,
    ! [F: list_char,D: list_char,V: val,C: list_char,Fs_1: fun_Pr806764899on_val,Ea: exp_list_char,S_1: produc12694297on_val,A_1: nat,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A_1))),S)),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S),A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)) )
       => ( ( hAPP_P2094403585on_val(Fs_1,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D)) = hAPP_val_option_val(some_val,V) )
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(Ea,F,D)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V)),S)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_988_red__reds_ORedFAcc,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,V: val,S_1: produc12694297on_val,A_1: nat,C: list_char,Fs_1: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)) )
     => ( ( hAPP_P2094403585on_val(Fs_1,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D)) = hAPP_val_option_val(some_val,V) )
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)),F,D)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V)),S_1)),red(Pa))) ) ) ).

tff(fact_989_TryRedsFail,axiom,
    ! [V_1: list_char,E_2: exp_list_char,C: list_char,D: list_char,Fs_1: fun_Pr806764899on_val,E_1: exp_list_char,S_1: produc12694297on_val,A_1: nat,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(Ha,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs_1)) )
       => ( ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(E_1,C,V_1,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_990_redp__redsp_ORedFAcc,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,V: val,S_1: produc12694297on_val,A_1: nat,C: list_char,Fs_1: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)) )
     => ( ( hAPP_P2094403585on_val(Fs_1,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D)) = hAPP_val_option_val(some_val,V) )
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)),F,D),S_1),hAPP_v834067052t_char(val_list_char,V)),S_1)) ) ) ).

tff(fact_991_red__reds_ORedCast,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,S_1: produc12694297on_val,A_1: nat,D: list_char,Fs_1: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs_1)) )
     => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,hAPP_v834067052t_char(val_list_char,addr(A_1)))),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A_1))),S_1)),red(Pa))) ) ) ).

tff(fact_992_red__reds_ORedTryFail,axiom,
    ! [V_1: list_char,E_2: exp_list_char,C: list_char,Pa: list_P1999446415t_char,S_1: produc12694297on_val,A_1: nat,D: list_char,Fs_1: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs_1)) )
     => ( ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))),C,V_1,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)))),S_1)),red(Pa))) ) ) ).

tff(fact_993_CastRedsAddr,axiom,
    ! [C: list_char,D: list_char,Fs_1: fun_Pr806764899on_val,Ea: exp_list_char,S_1: produc12694297on_val,A_1: nat,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A_1))),S)),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S),A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs_1)) )
       => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,Ea)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A_1))),S)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_994_Cast,axiom,
    ! [C: list_char,D: list_char,Fs_1: fun_Pr806764899on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,A_1: 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_1))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1)))
     => ( ( hAPP_n546249108on_val(Ha,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs_1)) )
       => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_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_1))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))) ) ) ) ).

tff(fact_995_TryThrow,axiom,
    ! [V_1: list_char,E_2: exp_list_char,C: list_char,D: list_char,Fs_1: fun_Pr806764899on_val,Pa: list_P1999446415t_char,E_1: exp_list_char,S_0: produc12694297on_val,A_1: nat,H_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1)))
     => ( ( hAPP_n546249108on_val(H_1,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs_1)) )
       => ( ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,tryCatch_list_char(E_1,C,V_1,E_2),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1))) ) ) ) ).

tff(fact_996_TryCatchRedsFinal,axiom,
    ! [E_2: exp_list_char,V_1: list_char,E_2_1: exp_list_char,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,C: list_char,D: list_char,Fs_1: fun_Pr806764899on_val,E_1: exp_list_char,S_0: produc12694297on_val,A_1: nat,H_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1))),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(H_1,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs_1)) )
       => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),fun_up1149430426on_val(L_1_1,V_1,hAPP_val_option_val(some_val,addr(A_1)))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2))),transi2024712006on_val(red(Pa))))
           => ( hBOOL(final_list_char(E_2_1))
             => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(E_1,C,V_1,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),fun_up1149430426on_val(L_2,V_1,hAPP_l207779698on_val(L_1_1,V_1))))),transi2024712006on_val(red(Pa)))) ) ) ) ) ) ).

tff(fact_997_reds__preserves__sconf,axiom,
    ! [E_4: fun_li688206603ion_ty,Tsa: list_ty,Es_1: list_exp_list_char,S_1: produc12694297on_val,Es: list_exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es),S)),reds(Pa)))
     => ( hBOOL(wTrts_1(Pa,hAPP_P703866694on_val(hp,S_1),E_4,Es_1,Tsa))
       => ( hBOOL(hAPP_P159683425l_bool(typeSa1917327191_sconf(Pa,E_4),S_1))
         => hBOOL(hAPP_P159683425l_bool(typeSa1917327191_sconf(Pa,E_4),S)) ) ) ) ).

tff(fact_998_red__preserves__sconf,axiom,
    ! [E_4: fun_li688206603ion_ty,Ta: ty,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),red(Pa)))
     => ( hBOOL(wTrt(Pa,hAPP_P703866694on_val(hp,S_1),E_4,Ea,Ta))
       => ( hBOOL(hAPP_P159683425l_bool(typeSa1917327191_sconf(Pa,E_4),S_1))
         => hBOOL(hAPP_P159683425l_bool(typeSa1917327191_sconf(Pa,E_4),S)) ) ) ) ).

tff(fact_999_TryCatch,axiom,
    ! [E_2: exp_list_char,V_1: list_char,E_2_1: exp_list_char,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,C: list_char,D: list_char,Fs_1: fun_Pr806764899on_val,Pa: list_P1999446415t_char,E_1: exp_list_char,S_0: produc12694297on_val,A_1: nat,H_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1)))
     => ( ( hAPP_n546249108on_val(H_1,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs_1)) )
       => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),fun_up1149430426on_val(L_1_1,V_1,hAPP_val_option_val(some_val,addr(A_1))))),E_2_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2)))
           => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,tryCatch_list_char(E_1,C,V_1,E_2),S_0),E_2_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),fun_up1149430426on_val(L_2,V_1,hAPP_l207779698on_val(L_1_1,V_1))))) ) ) ) ) ).

tff(fact_1000_CastRedsFail,axiom,
    ! [C: list_char,D: list_char,Fs_1: fun_Pr806764899on_val,Ea: exp_list_char,S_1: produc12694297on_val,A_1: nat,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A_1))),S)),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S),A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs_1)) )
       => ( ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,Ea)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,classCast))))),S)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1001_CastFail,axiom,
    ! [C: list_char,D: list_char,Fs_1: fun_Pr806764899on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,A_1: 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_1))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1)))
     => ( ( hAPP_n546249108on_val(Ha,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs_1)) )
       => ( ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_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(hAPP_list_char_nat(addr_of_sys_xcpt,classCast))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))) ) ) ) ).

tff(fact_1002_red__reds_ORedCastFail,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,S_1: produc12694297on_val,A_1: nat,D: list_char,Fs_1: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs_1)) )
     => ( ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,hAPP_v834067052t_char(val_list_char,addr(A_1)))),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,classCast))))),S_1)),red(Pa))) ) ) ).

tff(fact_1003_CallRedsNull,axiom,
    ! [M: list_char,Es_1: list_exp_list_char,Vsa: list_val,S_2_1: produc12694297on_val,Ea: exp_list_char,S_0: produc12694297on_val,S_1_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S_1_2)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),S_1_2)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa)),S_2_1)),transi374442731on_val(reds(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(Ea,M,Es_1)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,nullPointer))))),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_1004_red__reds_ORedCallNull,axiom,
    ! [M: list_char,Vsa: list_val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_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_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,nullPointer))))),S_1)),red(Pa))) ).

tff(fact_1005_FAccRedsNull,axiom,
    ! [F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(Ea,F,D)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,nullPointer))))),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1006_FAssRedsNull,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,V: val,S_2_1: produc12694297on_val,E_1: exp_list_char,S_0: produc12694297on_val,S_1_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S_1_2)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S_1_2)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V)),S_2_1)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(E_1,F,D,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,nullPointer))))),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_1007_hext__upd__obj,axiom,
    ! [Fs_2: fun_Pr806764899on_val,Ha: fun_na939144002on_val,A_1: nat,C: list_char,Fs_1: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(Ha,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)) )
     => hBOOL(hext(Ha,fun_up2041264236on_val(Ha,A_1,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_2))))) ) ).

tff(fact_1008_FAss,axiom,
    ! [H_2_1: fun_na939144002on_val,Fs_2: fun_Pr806764899on_val,F: list_char,D: list_char,C: list_char,Fs_1: fun_Pr806764899on_val,E_2: exp_list_char,V: val,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,Pa: list_P1999446415t_char,E_1: exp_list_char,S_0: produc12694297on_val,A_1: nat,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_0),hAPP_v834067052t_char(val_list_char,addr(A_1))),S_1_2))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_2),hAPP_v834067052t_char(val_list_char,V)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2)))
       => ( ( hAPP_n546249108on_val(H_2,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)) )
         => ( ( Fs_2 = fun_up204312361on_val(Fs_1,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D),hAPP_val_option_val(some_val,V)) )
           => ( ( H_2_1 = fun_up2041264236on_val(H_2,A_1,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_2))) )
             => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAss_list_char(E_1,F,D,E_2),S_0),hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2_1),L_2))) ) ) ) ) ) ).

tff(fact_1009_redp__redsp_ORedFAss,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,V: val,L_1: fun_li1432931796on_val,Ha: fun_na939144002on_val,A_1: nat,C: list_char,Fs_1: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(Ha,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)) )
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)),F,D,hAPP_v834067052t_char(val_list_char,V)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1)),hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,fun_up2041264236on_val(Ha,A_1,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),fun_up204312361on_val(Fs_1,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D),hAPP_val_option_val(some_val,V)))))),L_1))) ) ).

tff(fact_1010_red__reds_ORedFAss,axiom,
    ! [F: list_char,D: list_char,V: val,L_1: fun_li1432931796on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,A_1: nat,C: list_char,Fs_1: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(Ha,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)) )
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)),F,D,hAPP_v834067052t_char(val_list_char,V))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,fun_up2041264236on_val(Ha,A_1,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),fun_up204312361on_val(Fs_1,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D),hAPP_val_option_val(some_val,V)))))),L_1))),red(Pa))) ) ).

tff(fact_1011_FAssRedsVal,axiom,
    ! [F: list_char,D: list_char,C: list_char,Fs_1: fun_Pr806764899on_val,E_2: exp_list_char,V: val,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,E_1: exp_list_char,S_0: produc12694297on_val,A_1: nat,S_1_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A_1))),S_1_2)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S_1_2)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2))),transi2024712006on_val(red(Pa))))
       => ( ( hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)) = hAPP_n546249108on_val(H_2,A_1) )
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(E_1,F,D,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,fun_up2041264236on_val(H_2,A_1,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),fun_up204312361on_val(Fs_1,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D),hAPP_val_option_val(some_val,V)))))),L_2))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1012_ThrowNull,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1_2))
     => 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(hAPP_list_char_nat(addr_of_sys_xcpt,nullPointer))))),S_1_2)) ) ).

tff(fact_1013_redp__redsp_ORedThrowNull,axiom,
    ! [Pa: list_P1999446415t_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,throw_list_char(hAPP_v834067052t_char(val_list_char,null)),S_1),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,nullPointer))))),S_1)) ).

tff(fact_1014_FAssNull,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,V: val,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,E_1: exp_list_char,S_0: produc12694297on_val,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1_2))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_2),hAPP_v834067052t_char(val_list_char,V)),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAss_list_char(E_1,F,D,E_2),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,nullPointer))))),S_2_1)) ) ) ).

tff(fact_1015_FAccNull,axiom,
    ! [F: list_char,D: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1_2))
     => 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(hAPP_list_char_nat(addr_of_sys_xcpt,nullPointer))))),S_1_2)) ) ).

tff(fact_1016_redp__redsp_ORedFAssNull,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,V: val,S_1: 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)),S_1),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,nullPointer))))),S_1)) ).

tff(fact_1017_redp__redsp_ORedFAccNull,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(hAPP_v834067052t_char(val_list_char,null),F,D),S_1),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,nullPointer))))),S_1)) ).

tff(fact_1018_red__reds_ORedThrowNull,axiom,
    ! [S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,null))),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,nullPointer))))),S_1)),red(Pa))) ).

tff(fact_1019_redp__redsp_ORedCallNull,axiom,
    ! [Pa: list_P1999446415t_char,M: list_char,Vsa: list_val,S_1: 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_1),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,nullPointer))))),S_1)) ).

tff(fact_1020_ThrowRedsNull,axiom,
    ! [Ea: exp_list_char,S_1: produc12694297on_val,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,nullPointer))))),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1021_red__reds_ORedFAssNull,axiom,
    ! [F: list_char,D: list_char,V: val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,null),F,D,hAPP_v834067052t_char(val_list_char,V))),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,nullPointer))))),S_1)),red(Pa))) ).

tff(fact_1022_red__reds_ORedFAccNull,axiom,
    ! [F: list_char,D: list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(hAPP_v834067052t_char(val_list_char,null),F,D)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,nullPointer))))),S_1)),red(Pa))) ).

tff(fact_1023_CallNull,axiom,
    ! [M: list_char,Ps: list_exp_list_char,Vsa: list_val,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1_2))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Ps,S_1_2),hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa)),S_2_1))
       => 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(hAPP_list_char_nat(addr_of_sys_xcpt,nullPointer))))),S_2_1)) ) ) ).

tff(fact_1024_eval__cases_I12_J,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(Ea),S_1),E),S))
     => ( ! [A_2: nat] :
            ( ( E = throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_2))) )
           => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),hAPP_v834067052t_char(val_list_char,addr(A_2))),S)) )
       => ( ( ( E = throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,nullPointer)))) )
           => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),hAPP_v834067052t_char(val_list_char,null)),S)) )
         => ~ ! [E_3: exp_list_char] :
                ( ( E = throw_list_char(E_3) )
               => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),throw_list_char(E_3)),S)) ) ) ) ) ).

tff(fact_1025_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_1: produc12694297on_val,A_1: nat,C: list_char,Fs_1: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)) )
     => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Tsa,Ta,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Pns),Body)),D))
       => ( ( hAPP_list_val_nat(size_size_list_val,Vsa) = hAPP_l66428094ar_nat(size_s2113983095t_char,Pns) )
         => ( ( hAPP_list_ty_nat(size_size_list_ty,Tsa) = hAPP_l66428094ar_nat(size_s2113983095t_char,Pns) )
           => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)),M,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa))),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,hAPP_l407174677t_char(cons_list_char(this),Pns)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,hAPP_list_ty_list_ty(cons_ty(hAPP_list_char_ty(class,D)),Tsa)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,hAPP_l273806049st_val(cons_val(addr(A_1)),Vsa)),Body))))),S_1)),red(Pa))) ) ) ) ) ).

tff(fact_1026_LAssRedsVal,axiom,
    ! [V_1: list_char,Ea: exp_list_char,S_1: produc12694297on_val,V: val,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L))),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(V_1,Ea)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),fun_up1149430426on_val(L,V_1,hAPP_val_option_val(some_val,V))))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1027_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_1: produc12694297on_val,A_1: nat,C: list_char,Fs_1: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)) )
     => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Tsa,Ta,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Pns),Body)),D))
       => ( ( hAPP_list_val_nat(size_size_list_val,Vsa) = hAPP_l66428094ar_nat(size_s2113983095t_char,Pns) )
         => ( ( hAPP_list_ty_nat(size_size_list_ty,Tsa) = hAPP_l66428094ar_nat(size_s2113983095t_char,Pns) )
           => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)),M,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa)),S_1),blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,hAPP_l407174677t_char(cons_list_char(this),Pns)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,hAPP_list_ty_list_ty(cons_ty(hAPP_list_char_ty(class,D)),Tsa)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,hAPP_l273806049st_val(cons_val(addr(A_1)),Vsa)),Body))))),S_1)) ) ) ) ) ).

tff(fact_1028_WTrtTry,axiom,
    ! [V_1: list_char,C: list_char,E_2: exp_list_char,T_2_1: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,E_1: exp_list_char,T_1_1: ty] :
      ( hBOOL(wTrt(Pa,Ha,E_4,E_1,T_1_1))
     => ( hBOOL(wTrt(Pa,Ha,fun_up424764369ion_ty(E_4,V_1,hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,C))),E_2,T_2_1))
       => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_1),T_2_1))
         => hBOOL(wTrt(Pa,Ha,E_4,tryCatch_list_char(E_1,C,V_1,E_2),T_2_1)) ) ) ) ).

tff(fact_1029_redp__redsp_OLAssRed,axiom,
    ! [V_1: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(V_1,Ea),S_1),lAss_list_char(V_1,E)),S)) ) ).

tff(fact_1030_eval__evals_OLAssThrow,axiom,
    ! [V_1: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E: exp_list_char,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E)),S_1_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,lAss_list_char(V_1,Ea),S_0),throw_list_char(E)),S_1_2)) ) ).

tff(fact_1031_redp__redsp_OLAssThrow,axiom,
    ! [Pa: list_P1999446415t_char,V_1: list_char,Ea: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(V_1,throw_list_char(Ea)),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_1032_red__reds_OLAssRed,axiom,
    ! [V_1: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(V_1,Ea)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(V_1,E)),S)),red(Pa))) ) ).

tff(fact_1033_WTrtCall,axiom,
    ! [Es_1: 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_4: fun_li688206603ion_ty,Ea: exp_list_char,C: list_char] :
      ( hBOOL(wTrt(Pa,Ha,E_4,Ea,hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Tsa,Ta,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Pns),Body)),D))
       => ( hBOOL(wTrts_1(Pa,Ha,E_4,Es_1,Ts_1))
         => ( hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_1),Tsa))
           => hBOOL(wTrt(Pa,Ha,E_4,call_list_char(Ea,M,Es_1),Ta)) ) ) ) ) ).

tff(fact_1034_red__reds_OLAssThrow,axiom,
    ! [V_1: list_char,Ea: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(V_1,throw_list_char(Ea))),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Ea)),S_1)),red(Pa))) ).

tff(fact_1035_LAssReds,axiom,
    ! [V_1: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(V_1,Ea)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(V_1,E)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1036_LAssRedsThrow,axiom,
    ! [V_1: list_char,Ea: exp_list_char,S_1: produc12694297on_val,A_1: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A_1)),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(V_1,Ea)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A_1)),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1037_LAss,axiom,
    ! [L: fun_li1432931796on_val,V_1: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,V: 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)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1)))
     => ( ( L = fun_up1149430426on_val(L_1,V_1,hAPP_val_option_val(some_val,V)) )
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,lAss_list_char(V_1,Ea),S_0),hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L))) ) ) ).

tff(fact_1038_redp__redsp_ORedLAss,axiom,
    ! [Pa: list_P1999446415t_char,V_1: list_char,V: val,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,V)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1)),hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),fun_up1149430426on_val(L_1,V_1,hAPP_val_option_val(some_val,V))))) ).

tff(fact_1039_red__reds_ORedLAss,axiom,
    ! [V_1: list_char,V: val,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,V))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),fun_up1149430426on_val(L_1,V_1,hAPP_val_option_val(some_val,V))))),red(Pa))) ).

tff(fact_1040_WTrt__elim__cases_I5_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,E_1: exp_list_char,C: list_char,V_1: list_char,E_2: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Ha,E_4,tryCatch_list_char(E_1,C,V_1,E_2),Ta))
     => ~ ! [T_1_2: ty] :
            ( hBOOL(wTrt(Pa,Ha,E_4,E_1,T_1_2))
           => ( hBOOL(wTrt(Pa,Ha,fun_up424764369ion_ty(E_4,V_1,hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,C))),E_2,Ta))
             => ~ hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_2),Ta)) ) ) ) ).

tff(fact_1041_red__reds_ORedTryCatch,axiom,
    ! [V_1: list_char,E_2: exp_list_char,C: list_char,Pa: list_P1999446415t_char,S_1: produc12694297on_val,A_1: nat,D: list_char,Fs_1: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs_1)) )
     => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C),transi1395422419t_char(subcls851966956t_char(Pa))))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))),C,V_1,E_2)),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V_1,hAPP_list_char_ty(class,C),seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,addr(A_1))),E_2))),S_1)),red(Pa))) ) ) ).

tff(fact_1042_eval__cases_I4_J,axiom,
    ! [Pa: list_P1999446415t_char,V_1: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,lAss_list_char(V_1,Ea),S_1),E),S))
     => ( ( ( E = hAPP_v834067052t_char(val_list_char,unit) )
         => ! [V_4: val,H_4: fun_na939144002on_val,L_4: fun_li1432931796on_val] :
              ( ( S = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_4),fun_up1149430426on_val(L_4,V_1,hAPP_val_option_val(some_val,V_4))) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),hAPP_v834067052t_char(val_list_char,V_4)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_4),L_4))) ) )
       => ~ ! [E_3: exp_list_char] :
              ( ( E = throw_list_char(E_3) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),throw_list_char(E_3)),S)) ) ) ) ).

tff(fact_1043_default__val_Osimps_I5_J,axiom,
    ! [C_3: list_char] : hAPP_ty_val(default_val,hAPP_list_char_ty(class,C_3)) = null ).

tff(fact_1044_WTrtBlock,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,V_1: list_char,Ta: ty,Ea: exp_list_char,T_4: ty] :
      ( hBOOL(wTrt(Pa,Ha,fun_up424764369ion_ty(E_4,V_1,hAPP_ty_option_ty(some_ty,Ta)),Ea,T_4))
     => hBOOL(wTrt(Pa,Ha,E_4,block_list_char(V_1,Ta,Ea),T_4)) ) ).

tff(fact_1045_redp__redsp_ORedBlock,axiom,
    ! [Pa: list_P1999446415t_char,V_1: list_char,Ta: ty,U: val,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V_1,Ta,hAPP_v834067052t_char(val_list_char,U)),S_1),hAPP_v834067052t_char(val_list_char,U)),S_1)) ).

tff(fact_1046_val_Osimps_I3_J,axiom,
    ! [Nat_2: nat,Nat_1: nat] :
      ( ( addr(Nat_2) = addr(Nat_1) )
    <=> ( Nat_2 = Nat_1 ) ) ).

tff(fact_1047_val_Osimps_I1_J,axiom,
    ! [Bool_1: bool,Bool: bool] :
      ( ( bool_1(Bool_1) = bool_1(Bool) )
    <=> ( hBOOL(Bool_1)
      <=> hBOOL(Bool) ) ) ).

tff(fact_1048_red__reds_ORedBlock,axiom,
    ! [V_1: list_char,Ta: ty,U: val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V_1,Ta,hAPP_v834067052t_char(val_list_char,U))),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,U)),S_1)),red(Pa))) ).

tff(fact_1049_redp__redsp_OBlockThrow,axiom,
    ! [Pa: list_P1999446415t_char,V_1: list_char,Ta: ty,A_1: nat,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V_1,Ta,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)))),S_1),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)))),S_1)) ).

tff(fact_1050_redp__redsp_ORedInitBlock,axiom,
    ! [Pa: list_P1999446415t_char,V_1: list_char,Ta: ty,V: val,U: val,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V_1,Ta,seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,V)),hAPP_v834067052t_char(val_list_char,U))),S_1),hAPP_v834067052t_char(val_list_char,U)),S_1)) ).

tff(fact_1051_red__reds_OBlockThrow,axiom,
    ! [V_1: list_char,Ta: ty,A_1: nat,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V_1,Ta,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))))),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)))),S_1)),red(Pa))) ).

tff(fact_1052_red__reds_ORedInitBlock,axiom,
    ! [V_1: list_char,Ta: ty,V: val,U: val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V_1,Ta,seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,V)),hAPP_v834067052t_char(val_list_char,U)))),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,U)),S_1)),red(Pa))) ).

tff(fact_1053_redp__redsp_OInitBlockThrow,axiom,
    ! [Pa: list_P1999446415t_char,V_1: list_char,Ta: ty,V: val,A_1: nat,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V_1,Ta,seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,V)),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))))),S_1),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)))),S_1)) ).

tff(fact_1054_val_Osimps_I17_J,axiom,
    ! [Nat: nat] : addr(Nat) != null ).

tff(fact_1055_val_Osimps_I16_J,axiom,
    ! [Nat: nat] : null != addr(Nat) ).

tff(fact_1056_redp__redsp_OInitBlockRed,axiom,
    ! [Ta: ty,V_6: val,Pa: list_P1999446415t_char,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,V_1: list_char,V: val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),fun_up1149430426on_val(L_1,V_1,hAPP_val_option_val(some_val,V)))),E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L)))
     => ( ( hAPP_l207779698on_val(L,V_1) = hAPP_val_option_val(some_val,V_6) )
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V_1,Ta,seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,V)),Ea)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1)),block_list_char(V_1,Ta,seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,V_6)),E))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),fun_up1149430426on_val(L,V_1,hAPP_l207779698on_val(L_1,V_1))))) ) ) ).

tff(fact_1057_val_Osimps_I21_J,axiom,
    ! [Nat_1: nat,Bool_1: bool] : addr(Nat_1) != bool_1(Bool_1) ).

tff(fact_1058_val_Osimps_I20_J,axiom,
    ! [Bool_1: bool,Nat_1: nat] : bool_1(Bool_1) != addr(Nat_1) ).

tff(fact_1059_val_Osimps_I11_J,axiom,
    ! [Nat: nat] : addr(Nat) != unit ).

tff(fact_1060_val_Osimps_I10_J,axiom,
    ! [Nat: nat] : unit != addr(Nat) ).

tff(fact_1061_val_Osimps_I12_J,axiom,
    ! [Bool: bool] : null != bool_1(Bool) ).

tff(fact_1062_val_Osimps_I13_J,axiom,
    ! [Bool: bool] : bool_1(Bool) != null ).

tff(fact_1063_val_Osimps_I4_J,axiom,
    unit != null ).

tff(fact_1064_val_Osimps_I5_J,axiom,
    null != unit ).

tff(fact_1065_val_Osimps_I6_J,axiom,
    ! [Bool: bool] : unit != bool_1(Bool) ).

tff(fact_1066_val_Osimps_I7_J,axiom,
    ! [Bool: bool] : bool_1(Bool) != unit ).

tff(fact_1067_red__reds_OInitBlockThrow,axiom,
    ! [V_1: list_char,Ta: ty,V: val,A_1: nat,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V_1,Ta,seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,V)),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)))))),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)))),S_1)),red(Pa))) ).

tff(fact_1068_red__reds_OInitBlockRed,axiom,
    ! [Ta: ty,V_6: val,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,V_1: list_char,V: val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),fun_up1149430426on_val(L_1,V_1,hAPP_val_option_val(some_val,V))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L))),red(Pa)))
     => ( ( hAPP_l207779698on_val(L,V_1) = hAPP_val_option_val(some_val,V_6) )
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V_1,Ta,seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,V)),Ea))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V_1,Ta,seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,V_6)),E))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),fun_up1149430426on_val(L,V_1,hAPP_l207779698on_val(L_1,V_1))))),red(Pa))) ) ) ).

tff(fact_1069_InitBlockRedsFinal,axiom,
    ! [Ta: ty,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,V_1: list_char,V: val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),fun_up1149430426on_val(L_1,V_1,hAPP_val_option_val(some_val,V))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L))),transi2024712006on_val(red(Pa))))
     => ( hBOOL(final_list_char(E))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V_1,Ta,seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,V)),Ea))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),fun_up1149430426on_val(L,V_1,hAPP_l207779698on_val(L_1,V_1))))),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_1070_InitBlockReds,axiom,
    ! [Ta: ty,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,V_1: list_char,V: val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),fun_up1149430426on_val(L_1,V_1,hAPP_val_option_val(some_val,V))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L))),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V_1,Ta,seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,V)),Ea))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V_1,Ta,seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,hAPP_option_val_val(the_val,hAPP_l207779698on_val(L,V_1)))),E))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),fun_up1149430426on_val(L,V_1,hAPP_l207779698on_val(L_1,V_1))))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1071_blocks_Osimps_I1_J,axiom,
    ! [V_5: list_char,Vs_1: list_list_char,T: ty,Ts_2: list_ty,V_3: val,Vs: list_val,E_6: exp_list_char] : blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,hAPP_l407174677t_char(cons_list_char(V_5),Vs_1)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,hAPP_list_ty_list_ty(cons_ty(T),Ts_2)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,hAPP_l273806049st_val(cons_val(V_3),Vs)),E_6)))) = block_list_char(V_5,T,seq_list_char(lAss_list_char(V_5,hAPP_v834067052t_char(val_list_char,V_3)),blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Vs_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ts_2),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Vs),E_6)))))) ).

tff(fact_1072_finalRefE,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Ha,E_4,Ea,Ta))
     => ( hBOOL(is_refT(Ta))
       => ( hBOOL(final_list_char(Ea))
         => ( ( Ea != hAPP_v834067052t_char(val_list_char,null) )
           => ( ( ? [A_2: nat] : Ea = hAPP_v834067052t_char(val_list_char,addr(A_2))
               => ! [C_1: list_char] : Ta != hAPP_list_char_ty(class,C_1) )
             => ~ ! [A_2: nat] : Ea != throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_2))) ) ) ) ) ) ).

tff(fact_1073_final__addrE,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char,C: list_char] :
      ( hBOOL(wTrt(Pa,Ha,E_4,Ea,hAPP_list_char_ty(class,C)))
     => ( hBOOL(final_list_char(Ea))
       => ( ! [A_2: nat] : Ea != hAPP_v834067052t_char(val_list_char,addr(A_2))
         => ~ ! [A_2: nat] : Ea != throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_2))) ) ) ) ).

tff(fact_1074_WTrt_H__WTrts_H_Ointros_I16_J,axiom,
    ! [E_4: fun_li688206603ion_ty,V_1: list_char,E_2: exp_list_char,T_2_1: ty,Pa: list_P1999446415t_char,Ta: ty,Ha: fun_na939144002on_val,V: val,T_1_1: ty] :
      ( ( hAPP_val_option_ty(typeof_h(Ha),V) = hAPP_ty_option_ty(some_ty,T_1_1) )
     => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_1),Ta))
       => ( hBOOL(wTrt_1(Pa,Ha,fun_up424764369ion_ty(E_4,V_1,hAPP_ty_option_ty(some_ty,Ta)),E_2,T_2_1))
         => hBOOL(wTrt_1(Pa,Ha,E_4,block_list_char(V_1,Ta,seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,V)),E_2)),T_2_1)) ) ) ) ).

tff(fact_1075_redp__redsp_ORedTryCatch,axiom,
    ! [V_1: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,C: list_char,S_1: produc12694297on_val,A_1: nat,D: list_char,Fs_1: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs_1)) )
     => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(transi1065307915t_char(subcls744239332t_char(Pa)),D),C))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,tryCatch_list_char(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))),C,V_1,E_2),S_1),block_list_char(V_1,hAPP_list_char_ty(class,C),seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,addr(A_1))),E_2))),S_1)) ) ) ).

tff(fact_1076_WTrt_H__WTrts_H_Ointros_I3_J,axiom,
    ! [Pa: list_P1999446415t_char,E_4: fun_li688206603ion_ty,Ha: fun_na939144002on_val,V: val,Ta: ty] :
      ( ( hAPP_val_option_ty(typeof_h(Ha),V) = hAPP_ty_option_ty(some_ty,Ta) )
     => hBOOL(wTrt_1(Pa,Ha,E_4,hAPP_v834067052t_char(val_list_char,V),Ta)) ) ).

tff(fact_1077_WTrt_H__WTrts_H_Ointros_I18_J,axiom,
    ! [E_2: exp_list_char,T_2_1: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,E_1: exp_list_char,T_1_1: ty] :
      ( hBOOL(wTrt_1(Pa,Ha,E_4,E_1,T_1_1))
     => ( hBOOL(wTrt_1(Pa,Ha,E_4,E_2,T_2_1))
       => hBOOL(wTrt_1(Pa,Ha,E_4,seq_list_char(E_1,E_2),T_2_1)) ) ) ).

tff(fact_1078_wt_H__iff__wt,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt_1(Pa,Ha,E_4,Ea,Ta))
    <=> hBOOL(wTrt(Pa,Ha,E_4,Ea,Ta)) ) ).

tff(fact_1079_wt_H__wt,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt_1(Pa,Ha,E_4,Ea,Ta))
     => hBOOL(wTrt(Pa,Ha,E_4,Ea,Ta)) ) ).

tff(fact_1080_wt__wt_H,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Ha,E_4,Ea,Ta))
     => hBOOL(wTrt_1(Pa,Ha,E_4,Ea,Ta)) ) ).

tff(fact_1081_WTrt_H__WTrts_H_Ointros_I21_J,axiom,
    ! [Ta: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char,T_r: ty] :
      ( hBOOL(wTrt_1(Pa,Ha,E_4,Ea,T_r))
     => ( hBOOL(is_refT(T_r))
       => hBOOL(wTrt_1(Pa,Ha,E_4,throw_list_char(Ea),Ta)) ) ) ).

tff(fact_1082_redp__redsp_ORedCast,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,S_1: produc12694297on_val,A_1: nat,D: list_char,Fs_1: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs_1)) )
     => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(transi1065307915t_char(subcls744239332t_char(Pa)),D),C))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,hAPP_v834067052t_char(val_list_char,addr(A_1))),S_1),hAPP_v834067052t_char(val_list_char,addr(A_1))),S_1)) ) ) ).

tff(fact_1083_redp__redsp_ORedTryFail,axiom,
    ! [V_1: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,C: list_char,S_1: produc12694297on_val,A_1: nat,D: list_char,Fs_1: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs_1)) )
     => ( ~ hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(transi1065307915t_char(subcls744239332t_char(Pa)),D),C))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,tryCatch_list_char(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))),C,V_1,E_2),S_1),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)))),S_1)) ) ) ).

tff(fact_1084_WTrt_H__WTrts_H_Ointros_I22_J,axiom,
    ! [V_1: list_char,C: list_char,E_2: exp_list_char,T_2_1: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,E_1: exp_list_char,T_1_1: ty] :
      ( hBOOL(wTrt_1(Pa,Ha,E_4,E_1,T_1_1))
     => ( hBOOL(wTrt_1(Pa,Ha,fun_up424764369ion_ty(E_4,V_1,hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,C))),E_2,T_2_1))
       => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_1),T_2_1))
         => hBOOL(wTrt_1(Pa,Ha,E_4,tryCatch_list_char(E_1,C,V_1,E_2),T_2_1)) ) ) ) ).

tff(fact_1085_redp__redsp_ORedCastFail,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,S_1: produc12694297on_val,A_1: nat,D: list_char,Fs_1: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs_1)) )
     => ( ~ hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(transi1065307915t_char(subcls744239332t_char(Pa)),D),C))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,hAPP_v834067052t_char(val_list_char,addr(A_1))),S_1),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,classCast))))),S_1)) ) ) ).

tff(fact_1086_WTrt_H__WTrts_H_Ointros_I12_J,axiom,
    ! [Es_1: 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_4: fun_li688206603ion_ty,Ea: exp_list_char,C: list_char] :
      ( hBOOL(wTrt_1(Pa,Ha,E_4,Ea,hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Tsa,Ta,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Pns),Body)),D))
       => ( hBOOL(wTrts(Pa,Ha,E_4,Es_1,Ts_1))
         => ( hBOOL(hAPP_list_ty_bool(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_1),Tsa))
           => hBOOL(wTrt_1(Pa,Ha,E_4,call_list_char(Ea,M,Es_1),Ta)) ) ) ) ) ).

tff(fact_1087_WTrt_H__WTrts_H_Ointros_I17_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,V_1: list_char,Ta: ty,Ea: exp_list_char,T_4: ty] :
      ( hBOOL(wTrt_1(Pa,Ha,fun_up424764369ion_ty(E_4,V_1,hAPP_ty_option_ty(some_ty,Ta)),Ea,T_4))
     => ( ~ hBOOL(assigned(V_1,Ea))
       => hBOOL(wTrt_1(Pa,Ha,E_4,block_list_char(V_1,Ta,Ea),T_4)) ) ) ).

tff(fact_1088_BlockRedsFinal,axiom,
    ! [Ta: ty,H_0: fun_na939144002on_val,L_0: fun_li1432931796on_val,V_1: list_char,E_0: exp_list_char,S_0: produc12694297on_val,E_2: exp_list_char,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_0),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2))),transi2024712006on_val(red(Pa))))
     => ( hBOOL(final_list_char(E_2))
       => ( ( S_0 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),fun_up1149430426on_val(L_0,V_1,none_val)) )
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V_1,Ta,E_0)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),L_0))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),fun_up1149430426on_val(L_2,V_1,hAPP_l207779698on_val(L_0,V_1))))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1089_wts__wts_H,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Es_1: list_exp_list_char,Tsa: list_ty] :
      ( hBOOL(wTrts_1(Pa,Ha,E_4,Es_1,Tsa))
     => hBOOL(wTrts(Pa,Ha,E_4,Es_1,Tsa)) ) ).

tff(fact_1090_wts_H__wts,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Es_1: list_exp_list_char,Tsa: list_ty] :
      ( hBOOL(wTrts(Pa,Ha,E_4,Es_1,Tsa))
     => hBOOL(wTrts_1(Pa,Ha,E_4,Es_1,Tsa)) ) ).

tff(fact_1091_wts_H__iff__wts,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Es_1: list_exp_list_char,Tsa: list_ty] :
      ( hBOOL(wTrts(Pa,Ha,E_4,Es_1,Tsa))
    <=> hBOOL(wTrts_1(Pa,Ha,E_4,Es_1,Tsa)) ) ).

tff(fact_1092_redp__redsp_OBlockRedNone,axiom,
    ! [Ta: ty,Pa: list_P1999446415t_char,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,V_1: list_char,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),fun_up1149430426on_val(L_1,V_1,none_val))),E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L)))
     => ( ( hAPP_l207779698on_val(L,V_1) = none_val )
       => ( ~ hBOOL(assigned(V_1,Ea))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V_1,Ta,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1)),block_list_char(V_1,Ta,E)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),fun_up1149430426on_val(L,V_1,hAPP_l207779698on_val(L_1,V_1))))) ) ) ) ).

tff(fact_1093_red__reds_OBlockRedNone,axiom,
    ! [Ta: ty,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,V_1: list_char,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),fun_up1149430426on_val(L_1,V_1,none_val)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L))),red(Pa)))
     => ( ( hAPP_l207779698on_val(L,V_1) = none_val )
       => ( ~ hBOOL(assigned(V_1,Ea))
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V_1,Ta,Ea)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V_1,Ta,E)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),fun_up1149430426on_val(L,V_1,hAPP_l207779698on_val(L_1,V_1))))),red(Pa))) ) ) ) ).

tff(fact_1094_Block,axiom,
    ! [Ta: ty,Pa: list_P1999446415t_char,E_0: exp_list_char,H_0: fun_na939144002on_val,L_0: fun_li1432931796on_val,V_1: list_char,E_1: exp_list_char,H_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_0,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),fun_up1149430426on_val(L_0,V_1,none_val))),E_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,block_list_char(V_1,Ta,E_0),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),L_0)),E_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),fun_up1149430426on_val(L_1_1,V_1,hAPP_l207779698on_val(L_0,V_1))))) ) ).

tff(fact_1095_redp__redsp_OBlockRedSome,axiom,
    ! [Ta: ty,V: val,Pa: list_P1999446415t_char,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,V_1: list_char,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),fun_up1149430426on_val(L_1,V_1,none_val))),E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L)))
     => ( ( hAPP_l207779698on_val(L,V_1) = hAPP_val_option_val(some_val,V) )
       => ( ~ hBOOL(assigned(V_1,Ea))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V_1,Ta,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1)),block_list_char(V_1,Ta,seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,V)),E))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),fun_up1149430426on_val(L,V_1,hAPP_l207779698on_val(L_1,V_1))))) ) ) ) ).

tff(fact_1096_WTrt_H__WTrts_H_Ointros_I15_J,axiom,
    ! [Es_1: list_exp_list_char,Tsa: list_ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt_1(Pa,Ha,E_4,Ea,Ta))
     => ( hBOOL(wTrts(Pa,Ha,E_4,Es_1,Tsa))
       => hBOOL(wTrts(Pa,Ha,E_4,hAPP_l2011456725t_char(cons_exp_list_char(Ea),Es_1),hAPP_list_ty_list_ty(cons_ty(Ta),Tsa))) ) ) ).

tff(fact_1097_red__reds_OBlockRedSome,axiom,
    ! [Ta: ty,V: val,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,V_1: list_char,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),fun_up1149430426on_val(L_1,V_1,none_val)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L))),red(Pa)))
     => ( ( hAPP_l207779698on_val(L,V_1) = hAPP_val_option_val(some_val,V) )
       => ( ~ hBOOL(assigned(V_1,Ea))
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V_1,Ta,Ea)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V_1,Ta,seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,V)),E))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),fun_up1149430426on_val(L,V_1,hAPP_l207779698on_val(L_1,V_1))))),red(Pa))) ) ) ) ).

tff(fact_1098_eval__cases_I8_J,axiom,
    ! [Pa: list_P1999446415t_char,V_1: list_char,Ta: ty,E_1: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,block_list_char(V_1,Ta,E_1),S_1),E),S))
     => ~ ! [H_0_1: fun_na939144002on_val,L_0_1: fun_li1432931796on_val] :
            ( ( S_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0_1),L_0_1) )
           => ! [H_1_1: fun_na939144002on_val,L_1_2: fun_li1432931796on_val] :
                ( ( S = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1_1),fun_up1149430426on_val(L_1_2,V_1,hAPP_l207779698on_val(L_0_1,V_1))) )
               => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0_1),fun_up1149430426on_val(L_0_1,V_1,none_val))),E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1_1),L_1_2))) ) ) ) ).

tff(fact_1099_assigned__def,axiom,
    ! [V_1: list_char,Ea: exp_list_char] :
      ( hBOOL(assigned(V_1,Ea))
    <=> ? [V_4: val,E_3: exp_list_char] : Ea = seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,V_4)),E_3) ) ).

tff(fact_1100_Call,axiom,
    ! [E: exp_list_char,H_3: fun_na939144002on_val,L_3: fun_li1432931796on_val,L_2_1: fun_li1432931796on_val,M: list_char,Tsa: list_ty,Ta: ty,Pns: list_list_char,Body: exp_list_char,D: list_char,C: list_char,Fs_1: fun_Pr806764899on_val,Ps: list_exp_list_char,Vsa: list_val,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,A_1: nat,S_1_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,addr(A_1))),S_1_2))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Ps,S_1_2),hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2)))
       => ( ( hAPP_n546249108on_val(H_2,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)) )
         => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Tsa,Ta,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Pns),Body)),D))
           => ( ( hAPP_list_val_nat(size_size_list_val,Vsa) = hAPP_l66428094ar_nat(size_s2113983095t_char,Pns) )
             => ( ( L_2_1 = map_up1085636310ar_val(fun_up1149430426on_val(hAPP_o538043682on_val(cOMBK_1097134891t_char,none_val),this,hAPP_val_option_val(some_val,addr(A_1))),Pns,Vsa) )
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Body,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2_1)),E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_3),L_3)))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,call_list_char(Ea,M,Ps),S_0),E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_3),L_2))) ) ) ) ) ) ) ) ).

tff(fact_1101_typeof__lit__typeof,axiom,
    ! [Ha: fun_na939144002on_val,V: val,Ta: ty] :
      ( ( hAPP_val_option_ty(typeof_h(hAPP_o1576581476on_val(cOMBK_1944287343al_nat,none_P179726773on_val)),V) = hAPP_ty_option_ty(some_ty,Ta) )
     => ( hAPP_val_option_ty(typeof_h(Ha),V) = hAPP_ty_option_ty(some_ty,Ta) ) ) ).

tff(fact_1102_redsp__reds__eq,axiom,
    ! [Pa: list_P1999446415t_char,X_1: list_exp_list_char,Xa: produc12694297on_val,Xb: list_exp_list_char,Xc: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,X_1,Xa),Xb),Xc))
    <=> hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,X_1),Xa)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Xb),Xc)),reds(Pa))) ) ).

tff(fact_1103_redp__red__eq,axiom,
    ! [Pa: list_P1999446415t_char,X_1: exp_list_char,Xa: produc12694297on_val,Xb: exp_list_char,Xc: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,X_1,Xa),Xb),Xc))
    <=> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X_1),Xa)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Xb),Xc)),red(Pa))) ) ).

tff(fact_1104_hext__new,axiom,
    ! [X_2: produc639455274on_val,Ha: fun_na939144002on_val,A_1: nat] :
      ( ( hAPP_n546249108on_val(Ha,A_1) = none_P179726773on_val )
     => hBOOL(hext(Ha,fun_up2041264236on_val(Ha,A_1,hAPP_P1510515380on_val(some_P948696889on_val,X_2)))) ) ).

tff(fact_1105_CallRedsFinal,axiom,
    ! [Ef: exp_list_char,H_3: fun_na939144002on_val,L_3: fun_li1432931796on_val,L_2_1: fun_li1432931796on_val,M: list_char,Tsa: list_ty,Ta: ty,Pns: list_list_char,Body: exp_list_char,D: list_char,C: list_char,Fs_1: fun_Pr806764899on_val,Es_1: list_exp_list_char,Vsa: list_val,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,Ea: exp_list_char,S_0: produc12694297on_val,A_1: nat,S_1_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A_1))),S_1_2)),transi2024712006on_val(red(Pa))))
       => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),S_1_2)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2))),transi374442731on_val(reds(Pa))))
         => ( ( hAPP_n546249108on_val(H_2,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)) )
           => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Tsa,Ta,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Pns),Body)),D))
             => ( ( hAPP_list_val_nat(size_size_list_val,Vsa) = hAPP_l66428094ar_nat(size_s2113983095t_char,Pns) )
               => ( ( L_2_1 = map_up1085636310ar_val(fun_up1149430426on_val(hAPP_o538043682on_val(cOMBK_1097134891t_char,none_val),this,hAPP_val_option_val(some_val,addr(A_1))),Pns,Vsa) )
                 => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Body),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ef),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_3),L_3))),transi2024712006on_val(red(Pa))))
                   => ( hBOOL(final_list_char(Ef))
                     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(Ea,M,Es_1)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ef),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_3),L_2))),transi2024712006on_val(red(Pa)))) ) ) ) ) ) ) ) ) ) ).

tff(fact_1106_binop_Osimps_I3_J,axiom,
    ! [V_2_1: val] : binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,unit),V_2_1))) = none_val ).

tff(fact_1107_binop_Osimps_I7_J,axiom,
    ! [V_1_3: val] : binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_3),unit))) = none_val ).

tff(fact_1108_bop_Oexhaust,axiom,
    ! [Y: bop] :
      ( ( Y != c_Expr_Obop_OEq )
     => ( Y = add ) ) ).

tff(fact_1109_bop_Osimps_I2_J,axiom,
    add != c_Expr_Obop_OEq ).

tff(fact_1110_bop_Osimps_I1_J,axiom,
    c_Expr_Obop_OEq != add ).

tff(fact_1111_extend__1__eval,axiom,
    ! [E: exp_list_char,S: produc12694297on_val,Ea: exp_list_char,S_1: produc12694297on_val,E_5: exp_list_char,S_3: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_5),S_3)),red(Pa)))
       => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_5,S_3),E),S))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),E),S)) ) ) ) ).

tff(fact_1112_extend__1__evals,axiom,
    ! [Es: list_exp_list_char,T_7: produc12694297on_val,Es_1: list_exp_list_char,T_6: produc12694297on_val,Es_2: list_exp_list_char,T_5: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),T_6)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_2),T_5)),reds(Pa)))
       => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es_2,T_5),Es),T_7))
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es_1,T_6),Es),T_7)) ) ) ) ).

tff(fact_1113_big__by__small,axiom,
    ! [Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),E),S))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_1114_extend__eval,axiom,
    ! [E: exp_list_char,S: produc12694297on_val,Ea: exp_list_char,S_1: produc12694297on_val,E_5: exp_list_char,S_3: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_5),S_3)),transi2024712006on_val(red(Pa))))
       => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_5,S_3),E),S))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),E),S)) ) ) ) ).

tff(fact_1115_bigs__by__smalls,axiom,
    ! [Es_1: list_exp_list_char,S_1: produc12694297on_val,Es: list_exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es_1,S_1),Es),S))
       => hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es),S)),transi374442731on_val(reds(Pa)))) ) ) ).

tff(fact_1116_extend__evals,axiom,
    ! [Es: list_exp_list_char,S: produc12694297on_val,Es_1: list_exp_list_char,S_1: produc12694297on_val,Es_2: list_exp_list_char,S_3: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_2),S_3)),transi374442731on_val(reds(Pa))))
       => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es_2,S_3),Es),S))
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es_1,S_1),Es),S)) ) ) ) ).

tff(fact_1117_small__by__big,axiom,
    ! [Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),transi2024712006on_val(red(Pa))))
       => ( hBOOL(final_list_char(E))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),E),S)) ) ) ) ).

tff(fact_1118_big__iff__small,axiom,
    ! [Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),E),S))
      <=> ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),S)),transi2024712006on_val(red(Pa))))
          & hBOOL(final_list_char(E)) ) ) ) ).

tff(fact_1119_binop_Osimps_I6_J,axiom,
    ! [V_3: nat,V_2_1: val] : binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,addr(V_3)),V_2_1))) = none_val ).

tff(fact_1120_binop_Osimps_I10_J,axiom,
    ! [V_1_3: val,V_3: nat] : binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_3),addr(V_3)))) = none_val ).

tff(fact_1121_binop_Osimps_I8_J,axiom,
    ! [V_1_3: val] : binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_3),null))) = none_val ).

tff(fact_1122_binop_Osimps_I4_J,axiom,
    ! [V_2_1: val] : binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,null),V_2_1))) = none_val ).

tff(fact_1123_binop_Osimps_I5_J,axiom,
    ! [V: bool,V_2: val] : binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,bool_1(V)),V_2))) = none_val ).

tff(fact_1124_binop_Osimps_I9_J,axiom,
    ! [V_1_2: val,V: bool] : binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_2),bool_1(V)))) = none_val ).

tff(fact_1125_WTrtFAcc,axiom,
    ! [F: list_char,Ta: ty,D: list_char,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char,C: list_char] :
      ( hBOOL(wTrt(Pa,Ha,E_4,Ea,hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,F,Ta),D))
       => hBOOL(wTrt(Pa,Ha,E_4,fAcc_list_char(Ea,F,D),Ta)) ) ) ).

tff(fact_1126_WTrt_H__WTrts_H_Ointros_I8_J,axiom,
    ! [F: list_char,Ta: ty,D: list_char,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char,C: list_char] :
      ( hBOOL(wTrt_1(Pa,Ha,E_4,Ea,hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,F,Ta),D))
       => hBOOL(wTrt_1(Pa,Ha,E_4,fAcc_list_char(Ea,F,D),Ta)) ) ) ).

tff(fact_1127_eval__cases_I11_J,axiom,
    ! [Pa: list_P1999446415t_char,B: exp_list_char,C_2: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(B,C_2),S_1),E),S))
     => ( ( ( E = hAPP_v834067052t_char(val_list_char,unit) )
         => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,B,S_1),hAPP_v834067052t_char(val_list_char,bool_1(fFalse))),S)) )
       => ( ! [S_1_1: produc12694297on_val] :
              ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,B,S_1),hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1_1))
             => ! [V_1_1: val,S_2: produc12694297on_val] :
                  ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_2,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(B,C_2),S_2),E),S)) ) )
         => ( ! [E_3: exp_list_char] :
                ( ( E = throw_list_char(E_3) )
               => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,B,S_1),throw_list_char(E_3)),S)) )
           => ~ ! [S_1_1: produc12694297on_val,E_3: exp_list_char] :
                  ( ( E = throw_list_char(E_3) )
                 => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,B,S_1),hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1_1))
                   => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_2,S_1_1),throw_list_char(E_3)),S)) ) ) ) ) ) ) ).

tff(fact_1128_WTrtCast,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Ha,E_4,Ea,Ta))
     => ( hBOOL(is_refT(Ta))
       => ( hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C))
         => hBOOL(wTrt(Pa,Ha,E_4,cast_list_char(C,Ea),hAPP_list_char_ty(class,C))) ) ) ) ).

tff(fact_1129_WTrt_H__WTrts_H_Ointros_I2_J,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt_1(Pa,Ha,E_4,Ea,Ta))
     => ( hBOOL(is_refT(Ta))
       => ( hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C))
         => hBOOL(wTrt_1(Pa,Ha,E_4,cast_list_char(C,Ea),hAPP_list_char_ty(class,C))) ) ) ) ).

tff(fact_1130_WTrt__elim__cases_I6_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,D: list_char,Ea: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Ha,E_4,cast_list_char(D,Ea),Ta))
     => ~ ( ( Ta = hAPP_list_char_ty(class,D) )
         => ! [T_1: ty] :
              ( hBOOL(wTrt(Pa,Ha,E_4,Ea,T_1))
             => ( hBOOL(is_refT(T_1))
               => ~ hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),D)) ) ) ) ) ).

tff(fact_1131_WTrt_H__WTrts_H_Ointros_I10_J,axiom,
    ! [E_2: exp_list_char,T_2_1: ty,F: list_char,Ta: ty,D: list_char,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,E_1: exp_list_char,C: list_char] :
      ( hBOOL(wTrt_1(Pa,Ha,E_4,E_1,hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,F,Ta),D))
       => ( hBOOL(wTrt_1(Pa,Ha,E_4,E_2,T_2_1))
         => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_1),Ta))
           => hBOOL(wTrt_1(Pa,Ha,E_4,fAss_list_char(E_1,F,D,E_2),void)) ) ) ) ) ).

tff(fact_1132_Red__fv,axiom,
    ! [Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L))),red(Pa)))
       => hBOOL(ord_le2092826700r_bool(fv(E),fv(Ea))) ) ) ).

tff(fact_1133_WTrtLAss,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,Ea: exp_list_char,T_4: ty,E_4: fun_li688206603ion_ty,V_1: list_char,Ta: ty] :
      ( ( hAPP_l512744617ion_ty(E_4,V_1) = hAPP_ty_option_ty(some_ty,Ta) )
     => ( hBOOL(wTrt(Pa,Ha,E_4,Ea,T_4))
       => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_4),Ta))
         => hBOOL(wTrt(Pa,Ha,E_4,lAss_list_char(V_1,Ea),void)) ) ) ) ).

tff(fact_1134_fv__fvs_Osimps_I14_J,axiom,
    ! [Ea: exp_list_char] : fv(throw_list_char(Ea)) = fv(Ea) ).

tff(fact_1135_fv__fvs_Osimps_I7_J,axiom,
    ! [Ea: exp_list_char,F: list_char,D: list_char] : fv(fAcc_list_char(Ea,F,D)) = fv(Ea) ).

tff(fact_1136_fv__fvs_Osimps_I2_J,axiom,
    ! [C: list_char,Ea: exp_list_char] : fv(cast_list_char(C,Ea)) = fv(Ea) ).

tff(fact_1137_eval__notfree__unchanged,axiom,
    ! [V_1: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1)),E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L)))
     => ( ~ hBOOL(member_list_char(V_1,fv(Ea)))
       => ( hAPP_l207779698on_val(L,V_1) = hAPP_l207779698on_val(L_1,V_1) ) ) ) ).

tff(fact_1138_default__val_Osimps_I1_J,axiom,
    hAPP_ty_val(default_val,void) = unit ).

tff(fact_1139_typeof__h_Osimps_I1_J,axiom,
    ! [Ha: fun_na939144002on_val] : hAPP_val_option_ty(typeof_h(Ha),unit) = hAPP_ty_option_ty(some_ty,void) ).

tff(fact_1140_WTrtFAss,axiom,
    ! [E_2: exp_list_char,T_2_1: ty,F: list_char,Ta: ty,D: list_char,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,E_1: exp_list_char,C: list_char] :
      ( hBOOL(wTrt(Pa,Ha,E_4,E_1,hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,F,Ta),D))
       => ( hBOOL(wTrt(Pa,Ha,E_4,E_2,T_2_1))
         => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_1),Ta))
           => hBOOL(wTrt(Pa,Ha,E_4,fAss_list_char(E_1,F,D,E_2),void)) ) ) ) ) ).

tff(fact_1141_WTrt__elim__cases_I1_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,V: list_char,Ea: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Ha,E_4,lAss_list_char(V,Ea),Ta))
     => ~ ( ( Ta = void )
         => ! [T_1: ty] :
              ( ( hAPP_l512744617ion_ty(E_4,V) = hAPP_ty_option_ty(some_ty,T_1) )
             => ! [T_3: ty] :
                  ( hBOOL(wTrt(Pa,Ha,E_4,Ea,T_3))
                 => ~ hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_3),T_1)) ) ) ) ) ).

tff(fact_1142_eval__restrict__lcl,axiom,
    ! [W: fun_list_char_bool,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1)),E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L)))
       => ( hBOOL(ord_le2092826700r_bool(fv(Ea),W))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),restri761823004ar_val(L_1,W))),E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),restri761823004ar_val(L,W)))) ) ) ) ).

tff(fact_1143_ty_Osimps_I9_J,axiom,
    ! [List: list_char] : hAPP_list_char_ty(class,List) != void ).

tff(fact_1144_ty_Osimps_I8_J,axiom,
    ! [List: list_char] : void != hAPP_list_char_ty(class,List) ).

tff(fact_1145_ty_Oinject,axiom,
    ! [List_2: list_char,List_1: list_char] :
      ( ( hAPP_list_char_ty(class,List_2) = hAPP_list_char_ty(class,List_1) )
    <=> ( List_2 = List_1 ) ) ).

tff(fact_1146_typeof__ClassCast,axiom,
    ! [Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( hAPP_val_option_ty(typeof_h(Ha),addr(hAPP_list_char_nat(addr_of_sys_xcpt,classCast))) = hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,classCast)) ) ) ).

tff(fact_1147_ty_Osimps_I20_J,axiom,
    ! [List: list_char] : nt != hAPP_list_char_ty(class,List) ).

tff(fact_1148_ty_Osimps_I21_J,axiom,
    ! [List: list_char] : hAPP_list_char_ty(class,List) != nt ).

tff(fact_1149_ty_Osimps_I7_J,axiom,
    nt != void ).

tff(fact_1150_ty_Osimps_I6_J,axiom,
    void != nt ).

tff(fact_1151_preallocated__hext,axiom,
    ! [H: fun_na939144002on_val,Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( hBOOL(hext(Ha,H))
       => hBOOL(preallocated(H)) ) ) ).

tff(fact_1152_WTrtFAccNT,axiom,
    ! [F: list_char,D: list_char,Ta: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char] :
      ( hBOOL(wTrt(Pa,Ha,E_4,Ea,nt))
     => hBOOL(wTrt(Pa,Ha,E_4,fAcc_list_char(Ea,F,D),Ta)) ) ).

tff(fact_1153_WTrt_H__WTrts_H_Ointros_I9_J,axiom,
    ! [F: list_char,D: list_char,Ta: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char] :
      ( hBOOL(wTrt_1(Pa,Ha,E_4,Ea,nt))
     => hBOOL(wTrt_1(Pa,Ha,E_4,fAcc_list_char(Ea,F,D),Ta)) ) ).

tff(fact_1154_is__refT__def,axiom,
    ! [Ta: ty] :
      ( hBOOL(is_refT(Ta))
    <=> ( ( Ta = nt )
        | ? [C_1: list_char] : Ta = hAPP_list_char_ty(class,C_1) ) ) ).

tff(fact_1155_preallocated__upd__obj,axiom,
    ! [Fs_2: fun_Pr806764899on_val,A_1: nat,C: list_char,Fs_1: fun_Pr806764899on_val,Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( ( hAPP_n546249108on_val(Ha,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)) )
       => hBOOL(preallocated(fun_up2041264236on_val(Ha,A_1,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_2))))) ) ) ).

tff(fact_1156_default__val_Osimps_I4_J,axiom,
    hAPP_ty_val(default_val,nt) = null ).

tff(fact_1157_preallocated__new,axiom,
    ! [X_2: produc639455274on_val,A_1: nat,Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( ( hAPP_n546249108on_val(Ha,A_1) = none_P179726773on_val )
       => hBOOL(preallocated(fun_up2041264236on_val(Ha,A_1,hAPP_P1510515380on_val(some_P948696889on_val,X_2)))) ) ) ).

tff(fact_1158_WTrtFAssNT,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,T_2_1: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,E_1: exp_list_char] :
      ( hBOOL(wTrt(Pa,Ha,E_4,E_1,nt))
     => ( hBOOL(wTrt(Pa,Ha,E_4,E_2,T_2_1))
       => hBOOL(wTrt(Pa,Ha,E_4,fAss_list_char(E_1,F,D,E_2),void)) ) ) ).

tff(fact_1159_WTrt_H__WTrts_H_Ointros_I11_J,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,T_2_1: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,E_1: exp_list_char] :
      ( hBOOL(wTrt_1(Pa,Ha,E_4,E_1,nt))
     => ( hBOOL(wTrt_1(Pa,Ha,E_4,E_2,T_2_1))
       => hBOOL(wTrt_1(Pa,Ha,E_4,fAss_list_char(E_1,F,D,E_2),void)) ) ) ).

tff(fact_1160_WTrtCallNT,axiom,
    ! [M: list_char,Ta: ty,Es_1: list_exp_list_char,Tsa: list_ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char] :
      ( hBOOL(wTrt(Pa,Ha,E_4,Ea,nt))
     => ( hBOOL(wTrts_1(Pa,Ha,E_4,Es_1,Tsa))
       => hBOOL(wTrt(Pa,Ha,E_4,call_list_char(Ea,M,Es_1),Ta)) ) ) ).

tff(fact_1161_typeof__h_Osimps_I2_J,axiom,
    ! [Ha: fun_na939144002on_val] : hAPP_val_option_ty(typeof_h(Ha),null) = hAPP_ty_option_ty(some_ty,nt) ).

tff(fact_1162_WTrt_H__WTrts_H_Ointros_I13_J,axiom,
    ! [M: list_char,Ta: ty,Es_1: list_exp_list_char,Tsa: list_ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char] :
      ( hBOOL(wTrt_1(Pa,Ha,E_4,Ea,nt))
     => ( hBOOL(wTrts(Pa,Ha,E_4,Es_1,Tsa))
       => hBOOL(wTrt_1(Pa,Ha,E_4,call_list_char(Ea,M,Es_1),Ta)) ) ) ).

tff(fact_1163_typeof__NullPointer,axiom,
    ! [Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( hAPP_val_option_ty(typeof_h(Ha),addr(hAPP_list_char_nat(addr_of_sys_xcpt,nullPointer))) = hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,nullPointer)) ) ) ).

tff(fact_1164_WTrt__elim__cases_I7_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char,F: list_char,D: list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Ha,E_4,fAcc_list_char(Ea,F,D),Ta))
     => ( ! [C_1: list_char] :
            ( hBOOL(wTrt(Pa,Ha,E_4,Ea,hAPP_list_char_ty(class,C_1)))
           => ~ hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C_1,F,Ta),D)) )
       => hBOOL(wTrt(Pa,Ha,E_4,Ea,nt)) ) ) ).

tff(fact_1165_WTrt__elim__cases_I8_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Ea: exp_list_char,F: list_char,D: list_char,V: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Ha,E_4,fAss_list_char(Ea,F,D,V),Ta))
     => ( ( ( Ta = void )
         => ! [C_1: list_char] :
              ( hBOOL(wTrt(Pa,Ha,E_4,Ea,hAPP_list_char_ty(class,C_1)))
             => ! [T_1: ty] :
                  ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C_1,F,T_1),D))
                 => ! [T_2: ty] :
                      ( hBOOL(wTrt(Pa,Ha,E_4,V,T_2))
                     => ~ hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2),T_1)) ) ) ) )
       => ~ ( ( Ta = void )
           => ( hBOOL(wTrt(Pa,Ha,E_4,Ea,nt))
             => ! [T_2: ty] : ~ hBOOL(wTrt(Pa,Ha,E_4,V,T_2)) ) ) ) ) ).

tff(fact_1166_refTE,axiom,
    ! [T: ty] :
      ( hBOOL(is_refT(T))
     => ( ( T != nt )
       => ~ ! [C_1: list_char] : T != hAPP_list_char_ty(class,C_1) ) ) ).

tff(fact_1167_typeof__OutOfMemory,axiom,
    ! [Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( hAPP_val_option_ty(typeof_h(Ha),addr(hAPP_list_char_nat(addr_of_sys_xcpt,outOfMemory))) = hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,outOfMemory)) ) ) ).

tff(fact_1168_sconf__def,axiom,
    ! [Pa: list_P1999446415t_char,E_4: fun_li688206603ion_ty,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(typeSa1917327191_sconf(Pa,E_4),S_1))
    <=> hBOOL(hAPP_P159683425l_bool(produc1958875245l_bool(cOMBS_570216337l_bool(hAPP_f1523875321l_bool(hAPP_f592397849l_bool(cOMBB_1718333400on_val,cOMBB_383678192on_val),hAPP_f1452292669l_bool(hAPP_f1977633121l_bool(cOMBB_1303934920on_val,fconj),hconf_97414254t_char(Pa))),hAPP_f550652027l_bool(hAPP_f838396643l_bool(cOMBC_2027949654l_bool,hAPP_f857351829l_bool(hAPP_f348318673l_bool(cOMBB_1518282696on_val,cOMBC_832625297y_bool),lconf_496643946t_char(Pa))),E_4))),S_1)) ) ).

tff(fact_1169_typeof__h_Osimps_I5_J,axiom,
    ! [Ha: fun_na939144002on_val,A_1: nat] : hAPP_val_option_ty(typeof_h(Ha),addr(A_1)) = option1388193227on_val(none_ty,produc907433735ion_ty(hAPP_f451501457ion_ty(hAPP_f509342689ion_ty(cOMBB_352765746t_char,cOMBK_184479553on_val),hAPP_f359949478ion_ty(hAPP_f1243585741ion_ty(cOMBB_1888336841t_char,some_ty),class))),hAPP_n546249108on_val(Ha,A_1)) ).

tff(fact_1170_sys__xcpts__cases,axiom,
    ! [Pa: fun_list_char_bool,C: list_char] :
      ( hBOOL(member_list_char(C,sys_xcpts))
     => ( hBOOL(hAPP_list_char_bool(Pa,nullPointer))
       => ( hBOOL(hAPP_list_char_bool(Pa,outOfMemory))
         => ( hBOOL(hAPP_list_char_bool(Pa,classCast))
           => hBOOL(hAPP_list_char_bool(Pa,C)) ) ) ) ) ).

tff(fact_1171_preallocated__def,axiom,
    ! [Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
    <=> ! [X_1: list_char] :
          ( hBOOL(member_list_char(X_1,sys_xcpts))
         => ? [Fs: fun_Pr806764899on_val] : hAPP_n546249108on_val(Ha,hAPP_list_char_nat(addr_of_sys_xcpt,X_1)) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,X_1),Fs)) ) ) ).

tff(fact_1172_preallocatedD,axiom,
    ! [C: list_char,Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( hBOOL(member_list_char(C,sys_xcpts))
       => ? [Fs: fun_Pr806764899on_val] : hAPP_n546249108on_val(Ha,hAPP_list_char_nat(addr_of_sys_xcpt,C)) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) ) ) ).

tff(fact_1173_preallocatedE,axiom,
    ! [Pa: fun_fu311765169r_bool,C: list_char,Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( hBOOL(member_list_char(C,sys_xcpts))
       => ( ! [Fs: fun_Pr806764899on_val] :
              ( ( hAPP_n546249108on_val(Ha,hAPP_list_char_nat(addr_of_sys_xcpt,C)) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) )
             => hBOOL(hAPP_list_char_bool(hAPP_f388705405r_bool(Pa,Ha),C)) )
         => hBOOL(hAPP_list_char_bool(hAPP_f388705405r_bool(Pa,Ha),C)) ) ) ) ).

tff(fact_1174_red__reds_ORedNew,axiom,
    ! [L_1: fun_li1432931796on_val,H: fun_na939144002on_val,Pa: list_P1999446415t_char,C: list_char,FDTs: list_P2023964830har_ty,Ha: fun_na939144002on_val,A_1: nat] :
      ( ( new_Addr(Ha) = hAPP_nat_option_nat(some_nat,A_1) )
     => ( hBOOL(fields1147507508t_char(Pa,C,FDTs))
       => ( ( H = fun_up2041264236on_val(Ha,A_1,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),hAPP_l968768258on_val(init_fields,FDTs)))) )
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,new_list_char(C)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A_1))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L_1))),red(Pa))) ) ) ) ).

tff(fact_1175_WTrt__elim__cases_I10_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,C: list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Ha,E_4,new_list_char(C),Ta))
     => ~ ( ( Ta = hAPP_list_char_ty(class,C) )
         => ~ hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C)) ) ) ).

tff(fact_1176_WTrtNew,axiom,
    ! [Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Pa: list_P1999446415t_char,C: list_char] :
      ( hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C))
     => hBOOL(wTrt(Pa,Ha,E_4,new_list_char(C),hAPP_list_char_ty(class,C))) ) ).

tff(fact_1177_new__Addr__SomeD,axiom,
    ! [Ha: fun_na939144002on_val,A_1: nat] :
      ( ( new_Addr(Ha) = hAPP_nat_option_nat(some_nat,A_1) )
     => ( hAPP_n546249108on_val(Ha,A_1) = none_P179726773on_val ) ) ).

tff(fact_1178_WTrt_H__WTrts_H_Ointros_I1_J,axiom,
    ! [Ha: fun_na939144002on_val,E_4: fun_li688206603ion_ty,Pa: list_P1999446415t_char,C: list_char] :
      ( hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C))
     => hBOOL(wTrt_1(Pa,Ha,E_4,new_list_char(C),hAPP_list_char_ty(class,C))) ) ).

tff(fact_1179_NewFail,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,L_1: fun_li1432931796on_val,Ha: fun_na939144002on_val] :
      ( ( new_Addr(Ha) = none_nat )
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,new_list_char(C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1)),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,outOfMemory))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))) ) ).

tff(fact_1180_redp__redsp_ORedNewFail,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,L_1: fun_li1432931796on_val,Ha: fun_na939144002on_val] :
      ( ( new_Addr(Ha) = none_nat )
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,new_list_char(C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1)),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,outOfMemory))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))) ) ).

tff(fact_1181_New,axiom,
    ! [L_1: fun_li1432931796on_val,H: fun_na939144002on_val,Pa: list_P1999446415t_char,C: list_char,FDTs: list_P2023964830har_ty,Ha: fun_na939144002on_val,A_1: nat] :
      ( ( new_Addr(Ha) = hAPP_nat_option_nat(some_nat,A_1) )
     => ( hBOOL(fields1147507508t_char(Pa,C,FDTs))
       => ( ( H = fun_up2041264236on_val(Ha,A_1,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),hAPP_l968768258on_val(init_fields,FDTs)))) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,new_list_char(C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1)),hAPP_v834067052t_char(val_list_char,addr(A_1))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L_1))) ) ) ) ).

tff(fact_1182_redp__redsp_ORedNew,axiom,
    ! [L_1: fun_li1432931796on_val,H: fun_na939144002on_val,Pa: list_P1999446415t_char,C: list_char,FDTs: list_P2023964830har_ty,Ha: fun_na939144002on_val,A_1: nat] :
      ( ( new_Addr(Ha) = hAPP_nat_option_nat(some_nat,A_1) )
     => ( hBOOL(fields1147507508t_char(Pa,C,FDTs))
       => ( ( H = fun_up2041264236on_val(Ha,A_1,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),hAPP_l968768258on_val(init_fields,FDTs)))) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,new_list_char(C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1)),hAPP_v834067052t_char(val_list_char,addr(A_1))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L_1))) ) ) ) ).

tff(fact_1183_red__reds_ORedNewFail,axiom,
    ! [C: list_char,L_1: fun_li1432931796on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val] :
      ( ( new_Addr(Ha) = none_nat )
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,new_list_char(C)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(hAPP_list_char_nat(addr_of_sys_xcpt,outOfMemory))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),red(Pa))) ) ).

tff(fact_1184_eval__cases_I10_J,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,E_1: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(Ea,E_1,E_2),S_1),E),S))
     => ( ! [S_1_1: produc12694297on_val] :
            ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1_1))
           => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_1_1),E),S)) )
       => ( ! [S_1_1: produc12694297on_val] :
              ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),hAPP_v834067052t_char(val_list_char,bool_1(fFalse))),S_1_1))
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_1),E),S)) )
         => ~ ! [E_3: exp_list_char] :
                ( ( E = throw_list_char(E_3) )
               => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),throw_list_char(E_3)),S)) ) ) ) ) ).

tff(fact_1185_init__fields__def,axiom,
    init_fields = comp_l424027617har_ty(map_of1247784410ar_val,map_Pr1153581243ar_val(produc1553344466ar_val(hAPP_f1668074321ar_val(hAPP_f59905689ar_val(cOMBC_2111366340ar_val,hAPP_f1240485169ar_val(hAPP_f332422699ar_val(cOMBB_388225803t_char,cOMBB_311099133val_ty),produc2036181286ar_val)),default_val)))) ).

tff(fact_1186_cname__of__xcp,axiom,
    ! [C: list_char,Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( hBOOL(member_list_char(C,sys_xcpts))
       => ( hAPP_P1789965269t_char(produc1230355531on_val,hAPP_o1977518472on_val(the_Pr431167171on_val,hAPP_n546249108on_val(Ha,hAPP_list_char_nat(addr_of_sys_xcpt,C)))) = C ) ) ) ).

tff(fact_1187_hp__def,axiom,
    hp = produc1517998010on_val ).

tff(fact_1188_obj__ty__def,axiom,
    ! [Obj: produc639455274on_val] : obj_ty(Obj) = hAPP_list_char_ty(class,hAPP_P1789965269t_char(produc1230355531on_val,Obj)) ).

tff(fact_1189_the__Addr_Osimps,axiom,
    ! [A: nat] : hAPP_val_nat(the_Addr,addr(A)) = A ).

tff(fact_1190_eval__lcl__incr,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,H_0: fun_na939144002on_val,L_0: fun_li1432931796on_val,E: exp_list_char,H_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),L_0)),E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1)))
     => hBOOL(ord_le2092826700r_bool(dom_list_char_val(L_0),dom_list_char_val(L_1_1))) ) ).

tff(fact_1191_evals__lcl__incr,axiom,
    ! [Pa: list_P1999446415t_char,Es_1: list_exp_list_char,H_0: fun_na939144002on_val,L_0: fun_li1432931796on_val,Es: list_exp_list_char,H_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es_1,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),L_0)),Es),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1)))
     => hBOOL(ord_le2092826700r_bool(dom_list_char_val(L_0),dom_list_char_val(L_1_1))) ) ).

tff(fact_1192_preallocated__dom,axiom,
    ! [C: list_char,Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( hBOOL(member_list_char(C,sys_xcpts))
       => hBOOL(member_nat(hAPP_list_char_nat(addr_of_sys_xcpt,C),dom_na996029170on_val(Ha))) ) ) ).

tff(fact_1193_red__lcl__incr,axiom,
    ! [Ea: exp_list_char,H_0: fun_na939144002on_val,L_0: fun_li1432931796on_val,E: exp_list_char,H_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),L_0))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1))),red(Pa)))
     => hBOOL(ord_le2092826700r_bool(dom_list_char_val(L_0),dom_list_char_val(L_1_1))) ) ).

tff(fact_1194_Reds__dom__lcl,axiom,
    ! [Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ha),L_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L))),transi2024712006on_val(red(Pa))))
       => hBOOL(ord_le2092826700r_bool(dom_list_char_val(L),semila919158006r_bool(dom_list_char_val(L_1),fv(Ea)))) ) ) ).

tff(fact_1195_fv__fvs_Osimps_I11_J,axiom,
    ! [E_1: exp_list_char,E_2: exp_list_char] : fv(seq_list_char(E_1,E_2)) = semila919158006r_bool(fv(E_1),fv(E_2)) ).

tff(fact_1196_fv__fvs_Osimps_I8_J,axiom,
    ! [E_1: exp_list_char,F: list_char,D: list_char,E_2: exp_list_char] : fv(fAss_list_char(E_1,F,D,E_2)) = semila919158006r_bool(fv(E_1),fv(E_2)) ).

tff(fact_1197_fv__fvs_Osimps_I4_J,axiom,
    ! [E_1: exp_list_char,Bop: bop,E_2: exp_list_char] : fv(binOp_list_char(E_1,Bop,E_2)) = semila919158006r_bool(fv(E_1),fv(E_2)) ).

tff(fact_1198_fv__fvs_Osimps_I12_J,axiom,
    ! [B: exp_list_char,E_1: exp_list_char,E_2: exp_list_char] : fv(cond_list_char(B,E_1,E_2)) = semila919158006r_bool(semila919158006r_bool(fv(B),fv(E_1)),fv(E_2)) ).

tff(fact_1199_fv__fvs_Osimps_I13_J,axiom,
    ! [B: exp_list_char,Ea: exp_list_char] : fv(while_list_char(B,Ea)) = semila919158006r_bool(fv(B),fv(Ea)) ).

%----Helper facts (26)
tff(help_fTrue_1_1_U,axiom,
    hBOOL(fTrue) ).

tff(help_fTrue_1_1_T,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_fconj_1_1_U,axiom,
    ! [Q: bool,P: bool] :
      ( ~ hBOOL(P)
      | ~ hBOOL(Q)
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ) ).

tff(help_fconj_2_1_U,axiom,
    ! [P: bool,Q: bool] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
      | hBOOL(P) ) ).

tff(help_fconj_3_1_U,axiom,
    ! [P: bool,Q: bool] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
      | hBOOL(Q) ) ).

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)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__List__Olis,axiom,
    ! [P: option_val,Q: list_char] : hAPP_l207779698on_val(hAPP_o538043682on_val(cOMBK_1097134891t_char,P),Q) = P ).

tff(help_COMBB_1_1_COMBB_000tc__Type__Oty_000tc__Option__Ooption_Itc__Type__Oty_J_00,axiom,
    ! [P: fun_ty_option_ty,Q: fun_list_char_ty,R: list_char] : hAPP_l512744617ion_ty(hAPP_f359949478ion_ty(hAPP_f1243585741ion_ty(cOMBB_1888336841t_char,P),Q),R) = hAPP_ty_option_ty(P,hAPP_list_char_ty(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__List__O,axiom,
    ! [P: fun_bool_bool,Q: fun_fu1693644106l_bool,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f1074020887l_bool(hAPP_f1863694447l_bool(cOMBB_383678192on_val,P),Q),R) = hAPP_bool_bool(P,hAPP_f1033709212l_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__Value__Oval_000tc__prod_Itc__prod_Itc__List__Olist_I,axiom,
    ! [P: fun_va1416972085ar_val,Q: fun_ty_val,R: ty] : hAPP_t97533526ar_val(hAPP_f883560141ar_val(hAPP_f1951920661ar_val(cOMBB_311099133val_ty,P),Q),R) = hAPP_v48258637ar_val(P,hAPP_ty_val(Q,R)) ).

tff(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__fun_Itc__pro,axiom,
    ! [P: option_ty,Q: fun_Pr806764899on_val] : hAPP_f652398900ion_ty(hAPP_o534509643ion_ty(cOMBK_184479553on_val,P),Q) = P ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio,axiom,
    ! [P: fun_fu1670877422y_bool,Q: fun_li688206603ion_ty,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f603925568l_bool(hAPP_f181262431l_bool(cOMBC_832625297y_bool,P),Q),R) = hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(P,R),Q) ).

tff(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__Stri,axiom,
    ! [P: option1479284511on_val,Q: nat] : hAPP_n546249108on_val(hAPP_o1576581476on_val(cOMBK_1944287343al_nat,P),Q) = P ).

tff(help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__fun_Itc__fun,axiom,
    ! [P: fun_op1983271469ion_ty,Q: fun_li688206603ion_ty,R: list_char] : hAPP_l2000496933ion_ty(hAPP_f451501457ion_ty(hAPP_f509342689ion_ty(cOMBB_352765746t_char,P),Q),R) = hAPP_o534509643ion_ty(P,hAPP_l512744617ion_ty(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List,axiom,
    ! [P: fun_Pr593787031ar_val,Q: fun_ty_val,R: produc1278157519t_char] : hAPP_P221287148ar_val(hAPP_f1668074321ar_val(hAPP_f59905689ar_val(cOMBC_2111366340ar_val,P),Q),R) = hAPP_f883560141ar_val(hAPP_P289594851ar_val(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
    ! [P: fun_bo1549164019l_bool,Q: fun_fu1246919812l_bool,R: fun_na939144002on_val] : hAPP_f1145256474l_bool(hAPP_f1452292669l_bool(hAPP_f1977633121l_bool(cOMBB_1303934920on_val,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_f61040418l_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Value__Oval_Mtc__prod_Itc__prod_Itc__List__,axiom,
    ! [P: fun_fu124241277ar_val,Q: fun_Pr1702428311ar_val,R: produc1278157519t_char] : hAPP_P289594851ar_val(hAPP_f1240485169ar_val(hAPP_f332422699ar_val(cOMBB_388225803t_char,P),Q),R) = hAPP_f1951920661ar_val(P,hAPP_P1321848547ar_val(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It,axiom,
    ! [P: fun_fu570492181l_bool,Q: fun_li688206603ion_ty,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f550652027l_bool(hAPP_f838396643l_bool(cOMBC_2027949654l_bool,P),Q),R) = hAPP_f603925568l_bool(hAPP_f1617787571l_bool(P,R),Q) ).

tff(help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It,axiom,
    ! [P: fun_fu1806184744l_bool,Q: fun_fu100249073l_bool,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(cOMBS_570216337l_bool(P,Q),R) = hAPP_f1074020887l_bool(hAPP_f1492320500l_bool(P,R),hAPP_f1175813647l_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc,axiom,
    ! [P: fun_fu114905943l_bool,Q: fun_fu250820942l_bool,R: fun_na939144002on_val] : hAPP_f1492320500l_bool(hAPP_f1523875321l_bool(hAPP_f592397849l_bool(cOMBB_1718333400on_val,P),Q),R) = hAPP_f1863694447l_bool(P,hAPP_f1145256474l_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M,axiom,
    ! [P: fun_fu2083094209l_bool,Q: fun_fu2141444501y_bool,R: fun_na939144002on_val] : hAPP_f1617787571l_bool(hAPP_f857351829l_bool(hAPP_f348318673l_bool(cOMBB_1518282696on_val,P),Q),R) = hAPP_f181262431l_bool(P,hAPP_f1213370163y_bool(Q,R)) ).

%----Conjectures (3)
tff(conj_0,hypothesis,
    hAPP_l66428094ar_nat(size_s2113983095t_char,vs_1) = hAPP_list_ty_nat(size_size_list_ty,ts) ).

tff(conj_1,hypothesis,
    hAPP_list_val_nat(size_size_list_val,vs) = hAPP_list_ty_nat(size_size_list_ty,ts) ).

tff(conj_2,conjecture,
    ( hBOOL(wTrt(p,h,e_1,blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,vs_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,ts),hAPP_e1752110927t_char(hAPP_l1859255743t_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(hAPP_list_ty_bool(list_all2_ty_ty(widen_2090681816t_char(p),Ts),ts)) ) ) ) ).

%------------------------------------------------------------------------------