%------------------------------------------------------------------------------
% File     : SWW477_3 : TPTP v8.2.0. Released v5.3.0.
% Domain   : Software Verification
% Problem  : Java type soundness line 346, 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_l346 [Bla11]

% Status   : Theorem
% Rating   : 1.00 v5.5.0, 0.75 v5.4.0, 1.00 v5.3.0
% Syntax   : Number of formulae    : 2741 ( 451 unt;1453 typ;   0 def)
%            Number of atoms       : 2910 ( 941 equ)
%            Maximal formula atoms :   11 (   1 avg)
%            Number of connectives : 2253 ( 631   ~;  14   |;  58   &)
%                                         ( 295 <=>;1255  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   31 (   7 avg)
%            Maximal term depth    :   13 (   2 avg)
%            Number of types       :  560 ( 559 usr)
%            Number of type conns  : 1258 ( 637   >; 621   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  893 ( 893 usr; 257 con; 0-6 aty)
%            Number of variables   : 5776 (5652   !; 124   ?;5776   :)
% SPC      : TF0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2011-08-09 17:49:15
%------------------------------------------------------------------------------
%----Should-be-implicit typings (559)
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tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_335,type,
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tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_336,type,
    fun_Pr1972615991t_char: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_337,type,
    fun_Pr1637081264t_char: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_338,type,
    fun_Pr143388889al_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_339,type,
    fun_Pr1833267965on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_340,type,
    fun_Pr336360217on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_341,type,
    fun_Pr1058687409on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_342,type,
    fun_Pr582032790ar_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_343,type,
    fun_Pr84821017on_val: $tType ).

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

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

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String___344,type,
    fun_Pr220980979l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String___345,type,
    fun_Pr449337907on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String___346,type,
    fun_Pr1727285475on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String___347,type,
    fun_Pr609382377on_val: $tType ).

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

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol_348,type,
    fun_Pr1511900787l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol_349,type,
    fun_Pr998206307on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol_350,type,
    fun_Pr205535947on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol_351,type,
    fun_Pr807902897on_val: $tType ).

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

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__352,type,
    fun_Pr1895638121r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis,type,
    fun_Pr2102567903y_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_353,type,
    fun_Pr1566767763har_ty: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_354,type,
    fun_Pr1149393094ar_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_355,type,
    fun_Pr661739816l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_356,type,
    fun_Pr1858730867l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_357,type,
    fun_Pr300893373ar_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_358,type,
    fun_Pr327509002har_ty: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_359,type,
    fun_Pr1555044210ar_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_360,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__String__Ochar_J_Mtc__pro,type,
    fun_Pr981088873r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__pro_361,type,
    fun_Pr1538825897r_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__List__Olist_Itc__prod_Itc__List__Olist_It,type,
    fun_Pr286306793r_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__prod,type,
    produc124828825on_val: $tType ).

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

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

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

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

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__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__String__Ochar_J_Mtc__prod_Itc__List__Olist__362,type,
    produc1971331930t_char: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__Olist__363,type,
    produc1013743697t_char: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__Olist__364,type,
    produc952412819t_char: $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__Type__Oty_J_Mtc__prod_Itc__Type__Oty_Mtc__p,type,
    produc1025221954t_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__prod_Itc__List__Olist_Itc__String__Ochar_J_,type,
    produc2146869324t_char: $tType ).

tff(ty_ty_tc__prod_Itc__Type__Oty_Mtc__prod_Itc__List__Olist_Itc__List__Olist_Itc__S,type,
    produc1059328077t_char: $tType ).

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

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

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

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

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

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

tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J__365,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__366,type,
    produc1147203250ar_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist__367,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__String__Ochar_J_Mtc__prod_Itc__Li,type,
    produc84451751t_char: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__Li_368,type,
    produc740765671t_char: $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__List__Olist_Itc__prod_Itc__List__Olist_Itc__String,type,
    produc494726439t_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 (894)
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__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt,type,
    cOMBB_1124198201st_val: fun_fu1489862231r_bool ).

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__Type__Oty_Mtc__prod_Itc__List__Olist_Itc__String__Och,type,
    cOMBB_510504510t_char: fun_fu1075882367ar_val ).

tff(sy_c_COMBB_000tc__fun_Itc__Type__Oty_Mtc__prod_Itc__prod_Itc__List__Olist_Itc__S,type,
    cOMBB_491542469t_char: fun_fu1040051697ar_val ).

tff(sy_c_COMBB_000tc__fun_Itc__Type__Oty_Mtc__prod_Itc__prod_Itc__List__Olist_Itc__S_369,type,
    cOMBB_1905001812t_char: fun_fu1913157203ar_val ).

tff(sy_c_COMBB_000tc__fun_Itc__Type__Oty_Mtc__prod_Itc__prod_Itc__List__Olist_Itc__S_370,type,
    cOMBB_1380239526t_char: fun_fu1537186191y_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__Type__Oty_Mtc__prod_Itc__prod_Itc__List__Olist_Itc__S_371,type,
    cOMBB_424865560t_char: fun_fu70488741har_ty ).

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_1522540928on_val: fun_fu816125185l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_372,type,
    cOMBB_1518282696on_val: fun_fu938561337l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_373,type,
    cOMBB_1210977579on_val: fun_fu783298731l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_374,type,
    cOMBB_1466889536on_val: fun_fu626845499l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_375,type,
    cOMBB_157777659on_val: fun_fu922838283l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_376,type,
    cOMBB_225914878on_val: fun_fu422832955l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_377,type,
    cOMBB_1443356337on_val: fun_fu1344420091l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_378,type,
    cOMBB_2040779506on_val: fun_fu574939677l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_379,type,
    cOMBB_1511810527on_val: fun_fu1112258939l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_380,type,
    cOMBB_1962662865on_val: fun_fu1813077499l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_381,type,
    cOMBB_625124865on_val: fun_fu192001787l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_382,type,
    cOMBB_2122619962on_val: fun_fu1901042235l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_383,type,
    cOMBB_1472123293on_val: fun_fu364696775l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_384,type,
    cOMBB_335252392on_val: fun_fu850298545l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_385,type,
    cOMBB_955482355on_val: fun_fu2059521659l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_386,type,
    cOMBB_223841226on_val: fun_fu621800173l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_387,type,
    cOMBB_1153617344on_val: fun_fu698854459l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_388,type,
    cOMBB_1259202826on_val: fun_fu1755700589l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_389,type,
    cOMBB_1330725154on_val: fun_fu398975933l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_390,type,
    cOMBB_238112345on_val: fun_fu908807163l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M,type,
    cOMBB_864319000t_char: fun_fu182032103ion_ty ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc,type,
    cOMBB_635947099on_val: fun_fu1452544581l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis,type,
    cOMBB_607314500on_val: fun_fu598721017l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc_,type,
    cOMBB_889837233t_char: fun_fu2100278593r_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__O,type,
    cOMBB_1843549548ist_ty: fun_fu421554835r_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__prod_It,type,
    cOMBB_1150072860ol_bop: fun_fu775697111l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc,type,
    cOMBB_819439237t_char: fun_fu1104572687l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc_391,type,
    cOMBB_143000234t_char: fun_fu133802373l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__Ov,type,
    cOMBB_448128005on_val: fun_fu164521751l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_M,type,
    cOMBB_171276332on_val: fun_fu369322201l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__St,type,
    cOMBB_1466435125on_val: fun_fu1708954391l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_,type,
    cOMBB_1334418926on_val: fun_fu1791670741l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J__392,type,
    cOMBB_1837440507on_val: fun_fu2143035323l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_It,type,
    cOMBB_678146046on_val: fun_fu981148631l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Type__Oty_J_00,type,
    cOMBB_165135181on_val: fun_fu957923863l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_,type,
    cOMBB_1543649755on_val: fun_fu1354978043l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod__393,type,
    cOMBB_2041093409on_val: fun_fu549698637ion_ty ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List,type,
    cOMBB_351318850val_ty: fun_fu157779645ar_val ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List_394,type,
    cOMBB_247395499on_val: fun_fu1734514779l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List_395,type,
    cOMBB_914590898on_val: fun_fu817010765l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Ol,type,
    cOMBB_95569939on_val: fun_fu522605719l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__,type,
    cOMBB_1733006024on_val: fun_fu398537559l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__,type,
    cOMBB_1452070457on_val: fun_fu1385195071l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__HOL__Obool_000,type,
    cOMBB_558176806on_val: fun_fu353473623l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It,type,
    cOMBB_1539035119t_char: fun_fu1144956587r_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_396,type,
    cOMBB_1750801836on_val: fun_fu121169625l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_397,type,
    cOMBB_1083177073on_val: fun_fu1929656089l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_398,type,
    cOMBB_1173566976on_val: fun_fu1791999053l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_399,type,
    cOMBB_1980206754t_char: fun_fu1819396497r_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_400,type,
    cOMBB_1115744685t_char: fun_fu1962037031r_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_401,type,
    cOMBB_840638159al_val: fun_fu908828651l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_402,type,
    cOMBB_877741809on_val: fun_fu1802993177l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O,type,
    cOMBB_1292453606on_val: fun_fu169292119l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli,type,
    cOMBB_132741582on_val: fun_fu1512615383l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List,type,
    cOMBB_239784108val_ty: fun_fu298705725ar_val ).

tff(sy_c_COMBB_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List_403,type,
    cOMBB_1881684336ool_ty: fun_fu1303078475y_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List_404,type,
    cOMBB_844549459on_val: fun_fu1875970059l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List_405,type,
    cOMBB_1320677736_ty_ty: fun_fu1997004221har_ty ).

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_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: 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__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_406,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_JWellForm_Owf__J__mdecl,type,
    wf_J_mdecl: fun_li318226104r_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_Odistinct_000tc__List__Olist_Itc__String__Ochar_J,type,
    distinct_list_char: list_list_char > bool ).

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

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

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

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

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

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__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__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__Option__Ooption_Itc__Type__Oty_J,type,
    map_val_option_ty: fun_val_option_ty > fun_li1144067913ion_ty ).

tff(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__,type,
    map_Pr1153581243ar_val: fun_Pr1149393094ar_val > fun_li867521386ar_val ).

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__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__,type,
    set_Pr1494163115t_char: list_P1999446415t_char > fun_Pr1861226704r_bool ).

tff(sy_c_List_Oset_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc___407,type,
    set_Pr2033386304t_char: list_P341299826t_char > fun_Pr70170387r_bool ).

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: list_exp_list_char > nat ).

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

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

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

tff(sy_c_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__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,
    produc1259058957on_val: fun_ex977868519on_val ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc,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__408,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__String__Ochar_J_000tc__prod_Itc_409,type,
    produc822965838t_char: fun_li937397365t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc_410,type,
    produc1331140167t_char: fun_li1093980969t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc_411,type,
    produc1483578759t_char: fun_li2006863797t_char ).

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__Type__Oty_J_000tc__prod_Itc__Ty,type,
    produc2016959032t_char: fun_li997290943t_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__prod_Itc__List__Olist_Itc__Stri,type,
    produc1152259904t_char: fun_li1497997787t_char ).

tff(sy_c_Product__Type_OPair_000tc__Type__Oty_000tc__prod_Itc__List__Olist_Itc__List,type,
    produc1545444669t_char: fun_ty540739655t_char ).

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_412,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___413,type,
    produc2036181286ar_val: fun_Pr1702428311ar_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___414,type,
    produc2080520419t_char: fun_Pr130739971t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___415,type,
    produc499151895on_val: fun_Pr278209965on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___416,type,
    produc1641293463t_char: fun_Pr1812345101t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___417,type,
    produc1431439831t_char: fun_Pr1926185279t_char ).

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__List__Olist_Itc__prod_Itc__List__Olist,type,
    produc635935767t_char: fun_Pr505221745t_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_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_Ointernal__split_000tc__Expr__Obop_000tc__prod_Itc__Value__Ov,type,
    produc85367547l_bool: fun_fu1534370419l_bool ).

tff(sy_c_Product__Type_Ointernal__split_000tc__Expr__Oexp_Itc__List__Olist_Itc__Stri,type,
    produc399384568l_bool: fun_fu254083683l_bool ).

tff(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__Expr__Oexp_Itc__List,type,
    produc1631960005l_bool: fun_fu1386081147l_bool ).

tff(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__List__Olist_Itc__Str,type,
    produc181628604r_bool: fun_fu664489995r_bool ).

tff(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__List__Olist_Itc__Str_418,type,
    produc19303535r_bool: fun_fu362106225r_bool ).

tff(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__String__Ochar_J_000t,type,
    produc1779501634r_bool: fun_fu552814479r_bool ).

tff(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__String__Ochar_J_000t_419,type,
    produc1373896038har_ty: fun_fu1427310951har_ty ).

tff(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__String__Ochar_J_000t_420,type,
    produc2046300823y_bool: fun_fu1848662099y_bool ).

tff(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__String__Ochar_J_000t_421,type,
    produc1626136111har_ty: fun_fu2106606265har_ty ).

tff(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__String__Ochar_J_000t_422,type,
    produc1741654153l_bool: fun_fu1011371575l_bool ).

tff(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__String__Ochar_J_000t_423,type,
    produc1577326610ion_ty: fun_fu571290057ion_ty ).

tff(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__String__Ochar_J_000t_424,type,
    produc1186154681r_bool: fun_fu144904343r_bool ).

tff(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__String__Ochar_J_000t_425,type,
    produc181333746r_bool: fun_fu1763478281r_bool ).

tff(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__Type__Oty_J_000tc__p,type,
    produc1657965293r_bool: fun_fu963020827r_bool ).

tff(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__Value__Oval_J_000tc_,type,
    produc684674552r_bool: fun_fu361964333r_bool ).

tff(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__prod_Itc__List__Olis,type,
    produc538535851r_bool: fun_fu402575125r_bool ).

tff(sy_c_Product__Type_Ointernal__split_000tc__Value__Oval_000tc__Value__Oval_000tc_,type,
    produc1401528596l_bool: fun_fu228202007l_bool ).

tff(sy_c_Product__Type_Ointernal__split_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopti,type,
    produc2128769400l_bool: fun_fu947198233l_bool ).

tff(sy_c_Product__Type_Ointernal__split_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist,type,
    produc1988544340l_bool: fun_fu371764249l_bool ).

tff(sy_c_Product__Type_Ointernal__split_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp,type,
    produc2085082994l_bool: fun_fu2032275391l_bool ).

tff(sy_c_Product__Type_Ointernal__split_000tc__prod_Itc__List__Olist_Itc__String__Oc,type,
    produc448987860har_ty: fun_fu1260628695har_ty ).

tff(sy_c_Product__Type_Ointernal__split_000tc__prod_Itc__List__Olist_Itc__String__Oc_426,type,
    produc1713493127ar_val: fun_fu922016919ar_val ).

tff(sy_c_Product__Type_Ointernal__split_000tc__prod_Itc__List__Olist_Itc__String__Oc_427,type,
    produc1055753489l_bool: fun_fu1259695653l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Obop_000tc__prod_Itc__Value__O,type,
    produc1326056646l_bool: fun_fu1534370419l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Obop_000tc__prod_Itc__Value__O_428,type,
    produc996400752on_val: fun_fu370674997on_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Oexp_Itc__List__Olist_Itc__Str,type,
    produc1815960045l_bool: fun_fu254083683l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Oexp_Itc__List__Olist_Itc__Str_429,type,
    produc1174947465on_val: fun_fu1924376903on_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Expr__Oexp_Itc__Lis,type,
    produc1491230096l_bool: fun_fu1386081147l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Expr__Oexp_Itc__Lis_430,type,
    produc1450794278on_val: fun_fu1577740957on_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__List__Olist_Itc__St,type,
    produc1732333873r_bool: fun_fu664489995r_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__List__Olist_Itc__St_431,type,
    produc2027921764r_bool: fun_fu362106225r_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__List__Olist_Itc__St_432,type,
    produc726497362on_val: fun_fu368478899on_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000,type,
    produc1704639885r_bool: fun_fu552814479r_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_433,type,
    produc1096552923har_ty: fun_fu1427310951har_ty ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_434,type,
    produc1322037260y_bool: fun_fu1848662099y_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_435,type,
    produc2074304634har_ty: fun_fu2106606265har_ty ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_436,type,
    produc2026840771ar_val: fun_fu1034932985ar_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_437,type,
    produc392960766l_bool: fun_fu1011371575l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_438,type,
    produc907433735ion_ty: fun_fu571290057ion_ty ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_439,type,
    produc802464979y_bool: fun_fu141894497y_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_440,type,
    produc615345852ar_val: fun_fu124825145ar_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_441,type,
    produc723279022r_bool: fun_fu144904343r_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_442,type,
    produc65850127r_bool: fun_fu89151759r_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_443,type,
    produc1324280167r_bool: fun_fu1763478281r_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Type__Oty_J_000tc__,type,
    produc154616760r_bool: fun_fu963020827r_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Type__Oty_J_000tc___444,type,
    produc534648062on_val: fun_fu173853817on_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Value__Oval_J_000tc,type,
    produc21910851r_bool: fun_fu361964333r_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Value__Oval_J_000tc_445,type,
    produc2083294131on_val: fun_fu2003512885on_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__prod_Itc__List__Oli,type,
    produc1596557472r_bool: fun_fu402575125r_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__Value__Oval_000tc__Value__Oval_000tc,type,
    produc769963999l_bool: fun_fu228202007l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt,type,
    produc1958875245l_bool: fun_fu947198233l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_446,type,
    produc234747160al_val: fun_fu405972463al_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_447,type,
    produc901351817on_val: fun_fu192331261on_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_448,type,
    produc1202869992on_val: fun_fu901917071on_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_449,type,
    produc1034582855t_char: fun_fu2024363645t_char ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_450,type,
    produc1597824762t_char: fun_fu1262881469t_char ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_451,type,
    produc576623071t_char: fun_fu1409163261t_char ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_452,type,
    produc1250213160har_ty: fun_fu1469746877har_ty ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_453,type,
    produc928527642on_val: fun_fu21671997on_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_454,type,
    produc323997770t_char: fun_fu1575744957t_char ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_455,type,
    produc2036010883t_char: fun_fu652765565t_char ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_456,type,
    produc493500298t_char: fun_fu597866707t_char ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_457,type,
    produc1139048085t_char: fun_fu1899184489t_char ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_458,type,
    produc1842330940t_char: fun_fu1722633277t_char ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_459,type,
    produc1260869559al_val: fun_fu967282605al_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_460,type,
    produc1148763895on_val: fun_fu442091053on_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_461,type,
    produc1476705295on_val: fun_fu102462557on_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__fun_Itc__Nat__Onat_Mtc__Option__Oopt_462,type,
    produc305181602ar_val: fun_fu1334817853ar_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__,type,
    produc1296464157l_bool: fun_fu271564831l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Expr__Oexp_Itc__List__Olis,type,
    produc1911463199l_bool: fun_fu371764249l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Expr__Oexp_Itc__List__Olis_463,type,
    produc1003071703on_val: fun_fu1753546205on_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__Expr__Oex,type,
    produc70644925l_bool: fun_fu2032275391l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__Expr__Oex_464,type,
    produc653117369on_val: fun_fu1457149779on_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__List__Oli,type,
    produc1946648479r_bool: fun_fu12246301r_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__List__Oli_465,type,
    produc1294339167r_bool: fun_fu1475028087r_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__String__O,type,
    produc1851383869y_bool: fun_fu1313558547y_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__String__O_466,type,
    produc499452831har_ty: fun_fu1260628695har_ty ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__String__O_467,type,
    produc1553344466ar_val: fun_fu922016919ar_val ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__String__O_468,type,
    produc1873777030l_bool: fun_fu1259695653l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__String__O_469,type,
    produc1582135574har_ty: fun_fu1143492759har_ty ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__String__O_470,type,
    produc1131232171r_bool: fun_fu764902125r_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__String__O_471,type,
    produc870083295l_bool: fun_fu609296951l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__String__O_472,type,
    produc310626655r_bool: fun_fu1162000855r_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__String__O_473,type,
    produc1113940127r_bool: fun_fu1124492197r_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__Type__Oty,type,
    produc1470355201r_bool: fun_fu163040387r_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__Value__Ov,type,
    produc22827031r_bool: fun_fu1856194777r_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__List__Olist_Itc__prod_Itc_,type,
    produc1458513631r_bool: fun_fu1490758259r_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Value__Oval_Mtc__Value__Ov,type,
    produc506816603l_bool: fun_fu994348445l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Op,type,
    produc1193275679l_bool: fun_fu2060419353l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__,type,
    produc1229156571l_bool: fun_fu55871005l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__prod_Itc__List__Olist_Itc_,type,
    produc376173579l_bool: fun_fu709144397l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__prod_Itc__List__Olist_Itc__474,type,
    produc891186911l_bool: fun_fu1386151719l_bool ).

tff(sy_c_Progress_OWTrt_H,type,
    wTrt_1: ( list_P1999446415t_char * fun_na939144002on_val * fun_li688206603ion_ty * exp_list_char ) > fun_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_Set_OCollect_000tc__Type__Oty,type,
    collect_ty: fun_ty_bool > fun_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__475,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_476,type,
    transi61620055on_val: fun_Pr235369833l_bool > fun_Pr235369833l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__String__Ocha_477,type,
    transi1123801095t_char: fun_Pr981088873r_bool > fun_Pr981088873r_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__String__Ocha_478,type,
    transi2005320128t_char: fun_Pr1538825897r_bool > fun_Pr1538825897r_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__List__Olist_Itc__prod_Itc__Li,type,
    transi772168185t_char: fun_Pr286306793r_bool > fun_Pr286306793r_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: fun_ty_bool ).

tff(sy_c_Type_Othis,type,
    this: list_char ).

tff(sy_c_Type_Oty_OBoolean,type,
    boolean: ty ).

tff(sy_c_Type_Oty_OClass,type,
    class: fun_list_char_ty ).

tff(sy_c_Type_Oty_OInteger,type,
    integer: ty ).

tff(sy_c_Type_Oty_ONT,type,
    nt: ty ).

tff(sy_c_Type_Oty_OVoid,type,
    void: ty ).

tff(sy_c_Type_Oty_Oty__case_000tc__HOL__Obool,type,
    ty_case_bool: ( bool * bool * bool * bool * fun_list_char_bool ) > fun_ty_bool ).

tff(sy_c_Value_Odefault__val,type,
    default_val: fun_ty_val ).

tff(sy_c_Value_Othe__Addr,type,
    the_Addr: 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 ) > fun_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__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_479,type,
    hAPP_b1229254591al_val: ( fun_bo1153317747al_val * bop ) > fun_Pr1615326228al_val ).

tff(sy_c_hAPP_000tc__Expr__Obop_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Ov_480,type,
    hAPP_b420404024on_val: ( fun_bo180791194on_val * bop ) > fun_Pr1618910755on_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_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_481,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__fun_I_482,type,
    hAPP_e108155315on_val: ( fun_ex1005552999on_val * exp_list_char ) > fun_Pr1833267965on_val ).

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

tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__prod__483,type,
    hAPP_e1752110927t_char: ( fun_ex588373425t_char * exp_list_char ) > produc662261637t_char ).

tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__prod__484,type,
    hAPP_e1410803407on_val: ( fun_ex929394691on_val * exp_list_char ) > produc12694297on_val ).

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_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_485,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_486,type,
    hAPP_l1012006762on_val: ( fun_li414426834on_val * list_exp_list_char ) > fun_Pr1833267965on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List,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__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__487,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__488,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__489,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__fun__490,type,
    hAPP_l451552092on_val: ( fun_li175451530on_val * list_list_char ) > fun_Pr1289494032on_val ).

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

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__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__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_491,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_l1734756650y_bool: ( fun_li634443788y_bool * list_char ) > fun_ty_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__Type__Oty_Mtc__492,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__Type__Oty_Mtc__493,type,
    hAPP_l826728946har_ty: ( fun_li70432166har_ty * list_char ) > fun_ty1486032501har_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__Type__Oty_Mtc__494,type,
    hAPP_l1836284219ar_val: ( fun_li199902191ar_val * list_char ) > fun_ty434869310ar_val ).

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__495,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__496,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_l1665608433y_bool: ( fun_li800818899y_bool * list_char ) > fun_Pr1127025070y_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__List_497,type,
    hAPP_l848957697har_ty: ( fun_li1324969141har_ty * list_char ) > fun_Pr181504004har_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__List_498,type,
    hAPP_l2054741776r_bool: ( fun_li616154692r_bool * list_char ) > fun_Pr70170387r_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__List_499,type,
    hAPP_l2140727500r_bool: ( fun_li522008110r_bool * list_char ) > fun_Pr1898949769r_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__List_500,type,
    hAPP_l902950593t_char: ( fun_li937397365t_char * list_char ) > fun_Pr880942020t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__List_501,type,
    hAPP_l165010689r_bool: ( fun_li1960983605r_bool * list_char ) > fun_Pr571271812r_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__List_502,type,
    hAPP_l1388836853t_char: ( fun_li1093980969t_char * list_char ) > fun_Pr165123960t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__List_503,type,
    hAPP_l1342015621r_bool: ( fun_li485148903r_bool * list_char ) > fun_Pr1669461698r_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__List_504,type,
    hAPP_l309186817t_char: ( fun_li2006863797t_char * list_char ) > fun_Pr32647428t_char ).

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

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__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__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_505,type,
    hAPP_l14371579t_char: ( fun_li1548633647t_char * list_ty ) > fun_Pr1504659044t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__fun_Itc__prod_Itc__List__Ol_506,type,
    hAPP_l1004879342on_val: ( fun_li434706128on_val * list_ty ) > fun_Pr1632109509on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__fun_Itc__prod_Itc__Type__Ot,type,
    hAPP_l2048923787t_char: ( fun_li997290943t_char * list_ty ) > fun_Pr862403572t_char ).

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__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__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___507,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__Expr__Oexp_Itc___508,type,
    hAPP_l1870161525on_val: ( fun_li2113382231on_val * list_val ) > fun_ex929394691on_val ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc,type,
    hAPP_l24694616r_bool: ( fun_li1305328058r_bool * list_P1940453997har_ty ) > fun_li1070812648r_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_509,type,
    hAPP_l352172327t_char: ( fun_li1497997787t_char * list_P1940453997har_ty ) > fun_li618628759t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_510,type,
    hAPP_l2138409430r_bool: ( fun_li318226104r_bool * list_P1999446415t_char ) > fun_li616154692r_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_511,type,
    hAPP_l902158906r_bool: ( fun_li1070812648r_bool * list_P341299826t_char ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_512,type,
    hAPP_l277216047t_char: ( fun_li618628759t_char * list_P341299826t_char ) > produc2146869324t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__O,type,
    hAPP_l968768258on_val: ( fun_li750181430on_val * list_P2023964830har_ty ) > fun_Pr806764899on_val ).

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__Type__Oty_J_000tc__HOL__Obool,type,
    hAPP_option_ty_bool: ( fun_option_ty_bool * option_ty ) > bool ).

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_513,type,
    hAPP_o1977518472on_val: ( fun_op498348476on_val * option1479284511on_val ) > produc639455274on_val ).

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

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

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

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

tff(sy_c_hAPP_000tc__Type__Oty_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olis,type,
    hAPP_t1369077401t_char: ( fun_ty540739655t_char * ty ) > fun_Pr1151918909t_char ).

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__List__Olist_Itc__String__Ochar_J_Mtc_514,type,
    hAPP_t931865635har_ty: ( fun_ty1560310283har_ty * ty ) > produc469582463har_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_515,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__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__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__Expr__Obop_Mtc__fun_Itc__prod_Itc__Value__Oval_Mtc__Va,type,
    hAPP_f340876351l_bool: ( fun_fu1534370419l_bool * fun_bo1454185032l_bool ) > fun_Pr252072522l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Expr__Obop_Mtc__fun_Itc__prod_Itc__Value__Oval_Mtc__Va_516,type,
    hAPP_f1150574413l_bool: ( fun_fu298067067l_bool * fun_bo180791194on_val ) > fun_bo1454185032l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Expr__Obop_Mtc__fun_Itc__prod_Itc__Value__Oval_Mtc__Va_517,type,
    hAPP_f1090181127on_val: ( fun_fu370674997on_val * fun_bo180791194on_val ) > fun_Pr1439582210on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc,type,
    hAPP_f1930574389l_bool: ( fun_fu254083683l_bool * fun_ex1201926843l_bool ) > fun_Pr680585871l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc_518,type,
    hAPP_f653692369l_bool: ( fun_fu676595845l_bool * fun_ex1005552999on_val ) > fun_ex1201926843l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc_519,type,
    hAPP_f1520199827on_val: ( fun_fu1924376903on_val * fun_ex1005552999on_val ) > fun_Pr2087158653on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc_520,type,
    hAPP_f716957699r_bool: ( fun_fu2039807031r_bool * fun_ex929394691on_val ) > fun_ex736065929r_bool ).

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__Expr__Oexp_Itc__List__Olist_Itc__Stri,type,
    hAPP_f1634841927l_bool: ( fun_fu1386081147l_bool * fun_li1372729616l_bool ) > fun_Pr248118298l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Stri_521,type,
    hAPP_f896993613l_bool: ( fun_fu601150075l_bool * fun_li414426834on_val ) > fun_li1372729616l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Stri_522,type,
    hAPP_f797861231on_val: ( fun_fu1577740957on_val * fun_li414426834on_val ) > fun_Pr1142159922on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mt,type,
    hAPP_f1484794973r_bool: ( fun_fu664489995r_bool * fun_li221477r_bool ) > fun_Pr1336948301r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_523,type,
    hAPP_f1613448899r_bool: ( fun_fu362106225r_bool * fun_li1024794712r_bool ) > fun_Pr227936640r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_524,type,
    hAPP_f829041291r_bool: ( fun_fu838608831r_bool * fun_li175451530on_val ) > fun_li1024794712r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_525,type,
    hAPP_f2030092415on_val: ( fun_fu368478899on_val * fun_li175451530on_val ) > fun_Pr1381808460on_val ).

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__526,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__527,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__528,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__529,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__530,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__531,type,
    hAPP_f384373191al_val: ( fun_fu544554869al_val * fun_li1432931796on_val ) > produc1645268488al_val ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__532,type,
    hAPP_f1926378906on_val: ( fun_fu277794946on_val * fun_li1432931796on_val ) > produc124828825on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__533,type,
    hAPP_f637291415on_val: ( fun_fu432179525on_val * fun_li1432931796on_val ) > produc2061676504on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__534,type,
    hAPP_f1953285592t_char: ( fun_fu928390720t_char * fun_li1432931796on_val ) > produc809539159t_char ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__535,type,
    hAPP_f848628235t_char: ( fun_fu2058915699t_char * fun_li1432931796on_val ) > produc1285161482t_char ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__536,type,
    hAPP_f338074126t_char: ( fun_fu593680828t_char * fun_li1432931796on_val ) > produc1278157519t_char ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__537,type,
    hAPP_f1746527929har_ty: ( fun_fu1959448993har_ty * fun_li1432931796on_val ) > produc917948472har_ty ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__538,type,
    hAPP_f2106552235on_val: ( fun_fu194330259on_val * fun_li1432931796on_val ) > produc639455274on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__539,type,
    hAPP_f1032572507t_char: ( fun_fu240779971t_char * fun_li1432931796on_val ) > produc1971331930t_char ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__540,type,
    hAPP_f596349460t_char: ( fun_fu1872782460t_char * fun_li1432931796on_val ) > produc952412819t_char ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__541,type,
    hAPP_f1911830329t_char: ( fun_fu725512935t_char * fun_li1432931796on_val ) > produc220283002t_char ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__542,type,
    hAPP_f1555843780t_char: ( fun_fu1856635762t_char * fun_li1432931796on_val ) > produc662261637t_char ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__543,type,
    hAPP_f268764237t_char: ( fun_fu1855747253t_char * fun_li1432931796on_val ) > produc2146869324t_char ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__544,type,
    hAPP_f1181212006al_val: ( fun_fu1481433236al_val * fun_li1432931796on_val ) > product_prod_val_val ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__545,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__Option__Ooption__546,type,
    hAPP_f602593190on_val: ( fun_fu1622757844on_val * fun_li1432931796on_val ) > produc1102272487on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__547,type,
    hAPP_f1416324670on_val: ( fun_fu1921615852on_val * fun_li1432931796on_val ) > produc430140671on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__548,type,
    hAPP_f901144627ar_val: ( fun_fu1586296091ar_val * fun_li1432931796on_val ) > produc1147203250ar_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__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__List__O,type,
    hAPP_f2132060507r_bool: ( fun_fu552814479r_bool * fun_li860735411r_bool ) > fun_Pr565113489r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__List__O_549,type,
    hAPP_f1303264185har_ty: ( fun_fu1427310951har_ty * fun_li1185462113har_ty ) > fun_Pr868791661har_ty ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__Type__O,type,
    hAPP_f695389733y_bool: ( fun_fu1848662099y_bool * fun_li634443788y_bool ) > fun_Pr1127025070y_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__Type__O_550,type,
    hAPP_f1286352408ar_val: ( fun_fu759914106ar_val * fun_li70432166har_ty ) > fun_li199902191ar_val ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__Type__O_551,type,
    hAPP_f909647877har_ty: ( fun_fu2106606265har_ty * fun_li70432166har_ty ) > fun_Pr107226222har_ty ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__Type__O_552,type,
    hAPP_f528845893ar_val: ( fun_fu1034932985ar_val * fun_li199902191ar_val ) > fun_Pr1092566455ar_val ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__fun_Itc,type,
    hAPP_f1443410953l_bool: ( fun_fu1011371575l_bool * fun_li823162622l_bool ) > fun_Pr315804320l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__fun_Itc_553,type,
    hAPP_f46308763ion_ty: ( fun_fu571290057ion_ty * fun_li1301775111ion_ty ) > fun_Pr876827561ion_ty ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__fun_Itc_554,type,
    hAPP_f802560783ion_ty: ( fun_fu1747693763ion_ty * fun_li1436431093on_val ) > fun_li1301775111ion_ty ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_It,type,
    hAPP_f1134484787y_bool: ( fun_fu141894497y_bool * fun_li800818899y_bool ) > fun_Pr758558581y_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_It_555,type,
    hAPP_f65736581ar_val: ( fun_fu124825145ar_val * fun_li1266570728ar_val ) > fun_Pr839981232ar_val ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_It_556,type,
    hAPP_f952817385r_bool: ( fun_fu144904343r_bool * fun_li522008110r_bool ) > fun_Pr1861226704r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_It_557,type,
    hAPP_f433337307r_bool: ( fun_fu89151759r_bool * fun_li1960983605r_bool ) > fun_Pr70170387r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_It_558,type,
    hAPP_f252398939r_bool: ( fun_fu1763478281r_bool * fun_li485148903r_bool ) > fun_Pr1898949769r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Type__Oty_J_Mtc__fun_Itc__prod_Itc__L,type,
    hAPP_f102021095r_bool: ( fun_fu963020827r_bool * fun_li887890578r_bool ) > fun_Pr46158268r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Type__Oty_J_Mtc__fun_Itc__prod_Itc__L_559,type,
    hAPP_f1944156365r_bool: ( fun_fu449023483r_bool * fun_li434706128on_val ) > fun_li887890578r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Type__Oty_J_Mtc__fun_Itc__prod_Itc__L_560,type,
    hAPP_f505735499on_val: ( fun_fu173853817on_val * fun_li434706128on_val ) > fun_Pr1289494032on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Value__Oval_J_Mtc__fun_Itc__Expr__Oex,type,
    hAPP_f1697332217r_bool: ( fun_fu361964333r_bool * fun_li826105035r_bool ) > fun_Pr827765831r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Value__Oval_J_Mtc__fun_Itc__Expr__Oex_561,type,
    hAPP_f1339377933r_bool: ( fun_fu1651792187r_bool * fun_li2113382231on_val ) > fun_li826105035r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Value__Oval_J_Mtc__fun_Itc__Expr__Oex_562,type,
    hAPP_f1679543815on_val: ( fun_fu2003512885on_val * fun_li2113382231on_val ) > fun_Pr1632109509on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Oc,type,
    hAPP_f895126887r_bool: ( fun_fu402575125r_bool * fun_li1305328058r_bool ) > fun_Pr1669461698r_bool ).

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_563,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_564,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_565,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_566,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_567,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_568,type,
    hAPP_f1779904442al_val: ( fun_fu1978109084al_val * fun_na939144002on_val ) > fun_fu544554869al_val ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_569,type,
    hAPP_f1840640125on_val: ( fun_fu2073188913on_val * fun_na939144002on_val ) > fun_fu277794946on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_570,type,
    hAPP_f336970122on_val: ( fun_fu1035619948on_val * fun_na939144002on_val ) > fun_fu432179525on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_571,type,
    hAPP_f1445211579t_char: ( fun_fu612303599t_char * fun_na939144002on_val ) > fun_fu928390720t_char ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_572,type,
    hAPP_f78832750t_char: ( fun_fu798026914t_char * fun_na939144002on_val ) > fun_fu2058915699t_char ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_573,type,
    hAPP_f1628326017t_char: ( fun_fu1104134499t_char * fun_na939144002on_val ) > fun_fu593680828t_char ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_574,type,
    hAPP_f993605148har_ty: ( fun_fu63623632har_ty * fun_na939144002on_val ) > fun_fu1959448993har_ty ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_575,type,
    hAPP_f1614126606on_val: ( fun_fu540338626on_val * fun_na939144002on_val ) > fun_fu194330259on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_576,type,
    hAPP_f1486366910t_char: ( fun_fu1941783538t_char * fun_na939144002on_val ) > fun_fu240779971t_char ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_577,type,
    hAPP_f1363205111t_char: ( fun_fu868535083t_char * fun_na939144002on_val ) > fun_fu1872782460t_char ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_578,type,
    hAPP_f157410348t_char: ( fun_fu313651982t_char * fun_na939144002on_val ) > fun_fu725512935t_char ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_579,type,
    hAPP_f1297079863t_char: ( fun_fu1679523865t_char * fun_na939144002on_val ) > fun_fu1856635762t_char ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_580,type,
    hAPP_f371326384t_char: ( fun_fu511951076t_char * fun_na939144002on_val ) > fun_fu1855747253t_char ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_581,type,
    hAPP_f1695781849al_val: ( fun_fu2114777659al_val * fun_na939144002on_val ) > fun_fu1481433236al_val ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_582,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_583,type,
    hAPP_f600512025on_val: ( fun_fu1133203323on_val * fun_na939144002on_val ) > fun_fu1622757844on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_584,type,
    hAPP_f865889457on_val: ( fun_fu239230867on_val * fun_na939144002on_val ) > fun_fu1921615852on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_585,type,
    hAPP_f1925626518ar_val: ( fun_fu474293322ar_val * fun_na939144002on_val ) > fun_fu1586296091ar_val ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_586,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__Type__Oty_Mtc__prod_Itc__List__Olist_Itc__String__Ocha,type,
    hAPP_f500340936ar_val: ( fun_fu676796720ar_val * fun_ty1560310283har_ty ) > fun_ty434869310ar_val ).

tff(sy_c_hAPP_000tc__fun_Itc__Type__Oty_Mtc__prod_Itc__prod_Itc__List__Olist_Itc__St,type,
    hAPP_f151191262ar_val: ( fun_fu327647046ar_val * fun_ty1486032501har_ty ) > fun_ty434869310ar_val ).

tff(sy_c_hAPP_000tc__fun_Itc__Type__Oty_Mtc__prod_Itc__prod_Itc__List__Olist_Itc__St_587,type,
    hAPP_f457123984y_bool: ( fun_fu1517809086y_bool * fun_ty434869310ar_val ) > fun_ty_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Type__Oty_Mtc__prod_Itc__prod_Itc__List__Olist_Itc__St_588,type,
    hAPP_f1734435490har_ty: ( fun_fu1443638794har_ty * fun_ty434869310ar_val ) > fun_ty1560310283har_ty ).

tff(sy_c_hAPP_000tc__fun_Itc__Value__Oval_Mtc__fun_Itc__Value__Oval_Mtc__HOL__Obool_,type,
    hAPP_f1534412387l_bool: ( fun_fu228202007l_bool * fun_val_fun_val_bool ) > fun_Pr2081272681l_bool ).

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__Expr__Oexp_Itc__List__Olist_Itc__String__Ocha,type,
    hAPP_f1165187701r_bool: ( fun_fu1489862231r_bool * fun_fu2039807031r_bool ) > fun_fu1651792187r_bool ).

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__589,type,
    hAPP_f181262431l_bool: ( fun_fu2083094209l_bool * fun_fu1670877422y_bool ) > fun_fu2075294830l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__590,type,
    hAPP_f2061154754l_bool: ( fun_fu79989156l_bool * fun_fu544554869al_val ) > fun_fu1693644106l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__591,type,
    hAPP_f318082871l_bool: ( fun_fu1640122725l_bool * fun_fu277794946on_val ) > fun_fu1693644106l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__592,type,
    hAPP_f502623122l_bool: ( fun_fu578833268l_bool * fun_fu432179525on_val ) > fun_fu1693644106l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__593,type,
    hAPP_f1390791157l_bool: ( fun_fu1343863587l_bool * fun_fu928390720t_char ) > fun_fu1693644106l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__594,type,
    hAPP_f1212990632l_bool: ( fun_fu320829654l_bool * fun_fu2058915699t_char ) > fun_fu1693644106l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__595,type,
    hAPP_f1326058377l_bool: ( fun_fu1255792747l_bool * fun_fu593680828t_char ) > fun_fu1693644106l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__596,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__597,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__598,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__599,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__600,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__601,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__602,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__603,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__604,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__605,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__606,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__607,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__608,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__609,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__610,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__611,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__612,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__613,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__615,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__617,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__618,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__619,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__620,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__621,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__622,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__623,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__624,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__625,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__626,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__627,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__629,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__630,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__631,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__632,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__633,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__634,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__635,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__636,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__637,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__638,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__639,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__640,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__641,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__642,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__643,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__644,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__645,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__646,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__647,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Type__Oty_Mtc__prod_Itc__List__Olist_Itc__Str,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Type__Oty_Mtc__prod_Itc__prod_Itc__List__Olis,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Type__Oty_Mtc__prod_Itc__prod_Itc__List__Olis_648,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Type__Oty_Mtc__prod_Itc__prod_Itc__List__Olis_649,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Type__Oty_Mtc__prod_Itc__prod_Itc__List__Olis_650,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Value__Oval_Mtc__prod_Itc__prod_Itc__List__Ol,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc_651,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc_652,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc_653,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc_654,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc_655,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc_656,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc_657,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc_658,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc_662,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc_663,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_678,type,
    hAPP_f599509029on_val: ( fun_fu1457149779on_val * fun_Pr390299247on_val ) > fun_Pr205535947on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_679,type,
    hAPP_f1540354981l_bool: ( fun_fu976626649l_bool * fun_Pr1142159922on_val ) > fun_Pr248118298l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Oc,type,
    hAPP_f99607667l_bool: ( fun_fu1791670741l_bool * fun_Pr1336948301r_bool ) > fun_fu1343863587l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Oc_680,type,
    hAPP_f1728305001r_bool: ( fun_fu12246301r_bool * fun_Pr92408125r_bool ) > fun_Pr908866473r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Oc_681,type,
    hAPP_f764883801l_bool: ( fun_fu2143035323l_bool * fun_Pr227936640r_bool ) > fun_fu320829654l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Oc_682,type,
    hAPP_f655949763r_bool: ( fun_fu1475028087r_bool * fun_Pr1794669603r_bool ) > fun_Pr1895638121r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__,type,
    hAPP_f1804599279l_bool: ( fun_fu981148631l_bool * fun_Pr565113489r_bool ) > fun_fu1255792747l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___683,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___684,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___685,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___686,type,
    hAPP_f201105125y_bool: ( fun_fu1313558547y_bool * fun_Pr1633645595y_bool ) > fun_Pr2102567903y_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___687,type,
    hAPP_f1582750480ar_val: ( fun_fu181821042ar_val * fun_Pr868791661har_ty ) > fun_Pr130335392ar_val ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___688,type,
    hAPP_f513000995har_ty: ( fun_fu1260628695har_ty * fun_Pr868791661har_ty ) > fun_Pr1566767763har_ty ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___689,type,
    hAPP_f2096521338ar_val: ( fun_fu695591900ar_val * fun_Pr201309399har_ty ) > fun_Pr130335392ar_val ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___690,type,
    hAPP_f1796274104y_bool: ( fun_fu1077003884y_bool * fun_Pr130335392ar_val ) > fun_Pr1633645595y_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___691,type,
    hAPP_f1820012432har_ty: ( fun_fu971430642har_ty * fun_Pr130335392ar_val ) > fun_Pr868791661har_ty ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___692,type,
    hAPP_f1295640803ar_val: ( fun_fu922016919ar_val * fun_Pr130335392ar_val ) > fun_Pr1149393094ar_val ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___693,type,
    hAPP_f1663301111l_bool: ( fun_fu1259695653l_bool * fun_Pr2055965540l_bool ) > fun_Pr661739816l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___694,type,
    hAPP_f533118691har_ty: ( fun_fu1143492759har_ty * fun_Pr1941388516har_ty ) > fun_Pr327509002har_ty ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___695,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___696,type,
    hAPP_f59905689ar_val: ( fun_fu1227413499ar_val * fun_Pr593787031ar_val ) > fun_fu1907319807ar_val ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___697,type,
    hAPP_f39862969r_bool: ( fun_fu764902125r_bool * fun_Pr185059443r_bool ) > fun_Pr1336847023r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Type__,type,
    hAPP_f86617653l_bool: ( fun_fu957923863l_bool * fun_Pr1127025070y_bool ) > fun_fu893105924l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_It,type,
    hAPP_f2020099865l_bool: ( fun_fu1354978043l_bool * fun_Pr315804320l_bool ) > fun_fu1358756598l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_It_698,type,
    hAPP_f69964139ion_ty: ( fun_fu549698637ion_ty * fun_Pr876827561ion_ty ) > fun_fu564156607ion_ty ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_It_699,type,
    hAPP_f834198659l_bool: ( fun_fu609296951l_bool * fun_Pr788853347l_bool ) > fun_Pr235369833l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I,type,
    hAPP_f1675912277ar_val: ( fun_fu157779645ar_val * fun_Pr839981232ar_val ) > fun_fu676796720ar_val ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_700,type,
    hAPP_f1566130425l_bool: ( fun_fu1734514779l_bool * fun_Pr1861226704r_bool ) > fun_fu1268449830l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_701,type,
    hAPP_f72760099r_bool: ( fun_fu1162000855r_bool * fun_Pr1963999939r_bool ) > fun_Pr981088873r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_702,type,
    hAPP_f2114578667l_bool: ( fun_fu817010765l_bool * fun_Pr1898949769r_bool ) > fun_fu173213535l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_703,type,
    hAPP_f1774800369r_bool: ( fun_fu1124492197r_bool * fun_Pr1401771957r_bool ) > fun_Pr1538825897r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__,type,
    hAPP_f962366127l_bool: ( fun_fu522605719l_bool * fun_Pr46158268r_bool ) > fun_fu1169582102l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc___704,type,
    hAPP_f1377529935r_bool: ( fun_fu163040387r_bool * fun_Pr1074372915r_bool ) > fun_Pr1728267013r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc___705,type,
    hAPP_f1957179113r_bool: ( fun_fu309852445r_bool * fun_Pr1289494032on_val ) > fun_Pr46158268r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oe,type,
    hAPP_f737797743l_bool: ( fun_fu398537559l_bool * fun_Pr827765831r_bool ) > fun_fu1741592865l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oe_706,type,
    hAPP_f523402917r_bool: ( fun_fu1856194777r_bool * fun_Pr378536435r_bool ) > fun_Pr1890037787r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oe_707,type,
    hAPP_f1915623807r_bool: ( fun_fu306838195r_bool * fun_Pr1632109509on_val ) > fun_Pr827765831r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__,type,
    hAPP_f1809473245l_bool: ( fun_fu1385195071l_bool * fun_Pr1669461698r_bool ) > fun_fu1038842648l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc___708,type,
    hAPP_f1760165311r_bool: ( fun_fu1490758259r_bool * fun_Pr1881815719r_bool ) > fun_Pr286306793r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__HOL__Obo,type,
    hAPP_f1589017327l_bool: ( fun_fu353473623l_bool * fun_Pr2081272681l_bool ) > fun_fu680686147l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__fun_Itc_,type,
    hAPP_f1774252649l_bool: ( fun_fu994348445l_bool * fun_Pr324760563l_bool ) > fun_Pr832147423l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__prod_Itc,type,
    hAPP_f497008323l_bool: ( fun_fu436897911l_bool * fun_Pr1618910755on_val ) > fun_Pr2081272681l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc_,type,
    hAPP_f106757449r_bool: ( fun_fu1144956587r_bool * fun_Pr1696029455l_bool ) > fun_fu2039807031r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__709,type,
    hAPP_f2057883639l_bool: ( fun_fu121169625l_bool * fun_Pr1696029455l_bool ) > fun_fu1176066021l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__710,type,
    hAPP_f881985847l_bool: ( fun_fu1929656089l_bool * fun_Pr1696029455l_bool ) > fun_fu2085256997l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__711,type,
    hAPP_f2131288811l_bool: ( fun_fu1791999053l_bool * fun_Pr1696029455l_bool ) > fun_fu976626649l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__712,type,
    hAPP_f1096084527r_bool: ( fun_fu1819396497r_bool * fun_Pr1696029455l_bool ) > fun_fu309852445r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__713,type,
    hAPP_f1346522053r_bool: ( fun_fu1962037031r_bool * fun_Pr1696029455l_bool ) > fun_fu306838195r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__714,type,
    hAPP_f1936466825l_bool: ( fun_fu908828651l_bool * fun_Pr1696029455l_bool ) > fun_fu436897911l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__715,type,
    hAPP_f1825030711l_bool: ( fun_fu1802993177l_bool * fun_Pr1696029455l_bool ) > fun_fu225006629l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__716,type,
    hAPP_f662143077l_bool: ( fun_fu2060419353l_bool * fun_Pr598845249l_bool ) > fun_Pr693020585l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__717,type,
    hAPP_f1301559543l_bool: ( fun_fu225006629l_bool * fun_Pr1833267965on_val ) > fun_Pr1696029455l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__S,type,
    hAPP_f2052660463l_bool: ( fun_fu169292119l_bool * fun_Pr691271849l_bool ) > fun_fu964448643l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__S_718,type,
    hAPP_f1363805417l_bool: ( fun_fu55871005l_bool * fun_Pr220980979l_bool ) > fun_Pr903661919l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__L,type,
    hAPP_f28987375l_bool: ( fun_fu1512615383l_bool * fun_Pr859510977l_bool ) > fun_fu1610988187l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__L_719,type,
    hAPP_f1600283417l_bool: ( fun_fu709144397l_bool * fun_Pr1511900787l_bool ) > fun_Pr302334223l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M,type,
    hAPP_f1061710805ar_val: ( fun_fu298705725ar_val * fun_Pr1149393094ar_val ) > fun_fu327647046ar_val ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_720,type,
    hAPP_f1391360361y_bool: ( fun_fu1303078475y_bool * fun_Pr661739816l_bool ) > fun_fu1517809086y_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_721,type,
    hAPP_f975490601l_bool: ( fun_fu1875970059l_bool * fun_Pr661739816l_bool ) > fun_fu1910987134l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_722,type,
    hAPP_f1653906803l_bool: ( fun_fu1386151719l_bool * fun_Pr1858730867l_bool ) > fun_Pr643382121l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_723,type,
    hAPP_f393578581har_ty: ( fun_fu1997004221har_ty * fun_Pr327509002har_ty ) > fun_fu1443638794har_ty ).

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_724,type,
    hAPP_P323054207l_bool: ( fun_Pr1713170355l_bool * produc1645268488al_val ) > fun_Pr252072522l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__Ova_725,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_726,type,
    hAPP_P294971854on_val: ( fun_Pr1439582210on_val * produc1645268488al_val ) > produc12694297on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__Ova_727,type,
    hAPP_P2123720426al_val: ( fun_Pr1899415884al_val * produc1645268488al_val ) > produc630464863al_val ).

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

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_728,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_729,type,
    hAPP_P2083594489on_val: ( fun_Pr1719283041on_val * produc124828825on_val ) > fun_Pr2087158653on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_730,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_731,type,
    hAPP_P789556885on_val: ( fun_Pr2087158653on_val * produc124828825on_val ) > produc12694297on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_732,type,
    hAPP_P1886180715on_val: ( fun_Pr714818201on_val * produc124828825on_val ) > produc1102272487on_val ).

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

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_733,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_734,type,
    hAPP_P308812685on_val: ( fun_Pr390299247on_val * produc2061676504on_val ) > fun_Pr1142159922on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_735,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_736,type,
    hAPP_P1892658174on_val: ( fun_Pr1142159922on_val * produc2061676504on_val ) > produc12694297on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_737,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_738,type,
    hAPP_P1939418767r_bool: ( fun_Pr92408125r_bool * produc809539159t_char ) > fun_Pr1336948301r_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_739,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_740,type,
    hAPP_P1661798543t_char: ( fun_Pr1151918909t_char * produc809539159t_char ) > produc1059328077t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_741,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_742,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_743,type,
    hAPP_P1928969845r_bool: ( fun_Pr1794669603r_bool * produc1285161482t_char ) > fun_Pr227936640r_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_744,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_745,type,
    hAPP_P94592612on_val: ( fun_Pr1381808460on_val * produc1285161482t_char ) > produc12694297on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_746,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_747,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_748,type,
    hAPP_P1845004857y_bool: ( fun_Pr1633645595y_bool * produc1278157519t_char ) > fun_ty_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc_749,type,
    hAPP_P901867449har_ty: ( fun_Pr868791661har_ty * produc1278157519t_char ) > fun_ty1560310283har_ty ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc_750,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_751,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_752,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_753,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_754,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_755,type,
    hAPP_P663876415r_bool: ( fun_Pr185059443r_bool * produc1278157519t_char ) > fun_Pr565113489r_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc_756,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_757,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_758,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__Type__Oty_J_000_759,type,
    hAPP_P71962758har_ty: ( fun_Pr107226222har_ty * produc917948472har_ty ) > produc245756905har_ty ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Type__Oty_J_000_760,type,
    hAPP_P1057393871ar_val: ( fun_Pr1092566455ar_val * produc917948472har_ty ) > produc1147203250ar_val ).

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_761,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_762,type,
    hAPP_P1228500987ion_ty: ( fun_Pr876827561ion_ty * produc639455274on_val ) > option_ty ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I_763,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_764,type,
    hAPP_P416784693l_bool: ( fun_Pr788853347l_bool * produc639455274on_val ) > fun_Pr315804320l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I_765,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_766,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__String__Ochar_J_Mtc__prod_Itc__List__767,type,
    hAPP_P532450504ar_val: ( fun_Pr839981232ar_val * produc469582463har_ty ) > produc1147203250ar_val ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__768,type,
    hAPP_P1680401186r_bool: ( fun_Pr1861226704r_bool * produc1971331930t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__769,type,
    hAPP_P1117344277r_bool: ( fun_Pr1963999939r_bool * produc1971331930t_char ) > fun_Pr1861226704r_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__770,type,
    hAPP_P1958775007t_char: ( fun_Pr1812345101t_char * produc1971331930t_char ) > fun_Pr1993365530t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__771,type,
    hAPP_P991802092t_char: ( fun_Pr1993365530t_char * produc1971331930t_char ) > produc84451751t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__772,type,
    hAPP_P1384137393r_bool: ( fun_Pr70170387r_bool * produc1013743697t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__773,type,
    hAPP_P659547099r_bool: ( fun_Pr1898949769r_bool * produc952412819t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__774,type,
    hAPP_P194929415r_bool: ( fun_Pr1401771957r_bool * produc952412819t_char ) > fun_Pr1898949769r_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__775,type,
    hAPP_P777914897t_char: ( fun_Pr1926185279t_char * produc952412819t_char ) > fun_Pr5003411t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__776,type,
    hAPP_P1224499548t_char: ( fun_Pr880942020t_char * produc952412819t_char ) > produc1971331930t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__777,type,
    hAPP_P579374437t_char: ( fun_Pr5003411t_char * produc952412819t_char ) > produc740765671t_char ).

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_778,type,
    hAPP_P1214880255r_bool: ( fun_Pr1074372915r_bool * produc220283002t_char ) > fun_Pr46158268r_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Oli_779,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_780,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_781,type,
    hAPP_P216502748on_val: ( fun_Pr1289494032on_val * produc220283002t_char ) > produc12694297on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Oli_782,type,
    hAPP_P1333668416t_char: ( fun_Pr612024994t_char * produc220283002t_char ) > produc1406897475t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__Type__Oty,type,
    hAPP_P1187139874r_bool: ( fun_Pr571271812r_bool * produc1025221954t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__Type__Oty_783,type,
    hAPP_P242904598t_char: ( fun_Pr165123960t_char * produc1025221954t_char ) > produc1013743697t_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_784,type,
    hAPP_P357098431r_bool: ( fun_Pr378536435r_bool * produc662261637t_char ) > fun_Pr827765831r_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__L_785,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_786,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_787,type,
    hAPP_P214139537on_val: ( fun_Pr1632109509on_val * produc662261637t_char ) > produc12694297on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__L_788,type,
    hAPP_P1220989409t_char: ( fun_Pr1620417347t_char * produc662261637t_char ) > produc1826280281t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__O,type,
    hAPP_P828904212r_bool: ( fun_Pr1669461698r_bool * produc2146869324t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__O_789,type,
    hAPP_P225001977r_bool: ( fun_Pr1881815719r_bool * produc2146869324t_char ) > fun_Pr1669461698r_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__O_790,type,
    hAPP_P1756548163t_char: ( fun_Pr505221745t_char * produc2146869324t_char ) > fun_Pr1795545228t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__O_791,type,
    hAPP_P1423780764t_char: ( fun_Pr32647428t_char * produc2146869324t_char ) > produc952412819t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__O_792,type,
    hAPP_P1247668062t_char: ( fun_Pr1795545228t_char * produc2146869324t_char ) > produc494726439t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__Type__Oty_Mtc__prod_Itc__List__Olist_Itc__List__Olist,type,
    hAPP_P976433298t_char: ( fun_Pr862403572t_char * produc1059328077t_char ) > produc1025221954t_char ).

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

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

tff(sy_c_hAPP_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_Itc__prod_I_793,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__fun_I,type,
    hAPP_P147338735on_val: ( fun_Pr1618910755on_val * product_prod_val_val ) > produc12694297on_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_794,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_795,type,
    hAPP_P1988153107l_bool: ( fun_Pr598845249l_bool * produc12694297on_val ) > fun_Pr1696029455l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_796,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_797,type,
    hAPP_P1067836940al_val: ( fun_Pr1009028282al_val * produc12694297on_val ) > produc1645268488al_val ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_798,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_799,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_800,type,
    hAPP_P1849356627t_char: ( fun_Pr646484155t_char * produc12694297on_val ) > produc809539159t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_801,type,
    hAPP_P1849522950t_char: ( fun_Pr1502660462t_char * produc12694297on_val ) > produc1285161482t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_802,type,
    hAPP_P193916115t_char: ( fun_Pr2135303553t_char * produc12694297on_val ) > produc1278157519t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_803,type,
    hAPP_P1571579700har_ty: ( fun_Pr747280668har_ty * produc12694297on_val ) > produc917948472har_ty ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_804,type,
    hAPP_P1936714534on_val: ( fun_Pr1684668686on_val * produc12694297on_val ) > produc639455274on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_805,type,
    hAPP_P894177366t_char: ( fun_Pr1560218558t_char * produc12694297on_val ) > produc1971331930t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_806,type,
    hAPP_P1548494223t_char: ( fun_Pr1791835895t_char * produc12694297on_val ) > produc952412819t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_807,type,
    hAPP_P616991870t_char: ( fun_Pr1730691372t_char * produc12694297on_val ) > produc220283002t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_808,type,
    hAPP_P1871645065t_char: ( fun_Pr1972615991t_char * produc12694297on_val ) > produc662261637t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_809,type,
    hAPP_P256420168t_char: ( fun_Pr1637081264t_char * produc12694297on_val ) > produc2146869324t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_810,type,
    hAPP_P2013623467al_val: ( fun_Pr143388889al_val * produc12694297on_val ) > product_prod_val_val ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_811,type,
    hAPP_P1776198677on_val: ( fun_Pr1833267965on_val * produc12694297on_val ) > produc12694297on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_812,type,
    hAPP_P2024243179on_val: ( fun_Pr336360217on_val * produc12694297on_val ) > produc1102272487on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_813,type,
    hAPP_P963849987on_val: ( fun_Pr1058687409on_val * produc12694297on_val ) > produc430140671on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_814,type,
    hAPP_P1143488942ar_val: ( fun_Pr582032790ar_val * produc12694297on_val ) > produc1147203250ar_val ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_815,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_816,type,
    hAPP_P2062527807l_bool: ( fun_Pr220980979l_bool * produc1102272487on_val ) > fun_Pr691271849l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_817,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_818,type,
    hAPP_P1760219823on_val: ( fun_Pr1727285475on_val * produc1102272487on_val ) > produc12694297on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_819,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_820,type,
    hAPP_P220718911l_bool: ( fun_Pr1511900787l_bool * produc430140671on_val ) > fun_Pr859510977l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis_821,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_822,type,
    hAPP_P931655063on_val: ( fun_Pr205535947on_val * produc430140671on_val ) > produc12694297on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis_823,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_824,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__825,type,
    hAPP_P385447595har_ty: ( fun_Pr1566767763har_ty * produc245756905har_ty ) > produc469582463har_ty ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__826,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__827,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__828,type,
    hAPP_P1236192325l_bool: ( fun_Pr1858730867l_bool * produc1147203250ar_val ) > fun_Pr661739816l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__829,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__830,type,
    hAPP_P1409535266har_ty: ( fun_Pr327509002har_ty * produc1147203250ar_val ) > produc469582463har_ty ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__831,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__832,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__String__Ochar_J_Mtc__prod_,type,
    hAPP_P975284999r_bool: ( fun_Pr981088873r_bool * produc84451751t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod__833,type,
    hAPP_P929449287r_bool: ( fun_Pr1538825897r_bool * produc740765671t_char ) > 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__List__Olist_Itc__prod_Itc__List__Olist_Itc_,type,
    hAPP_P801803911r_bool: ( fun_Pr286306793r_bool * produc494726439t_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__List__Olist_Itc__String__Ochar_J,type,
    member_list_char: ( list_char * fun_list_char_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__O,type,
    member1417904245al_val: ( produc1645268488al_val * fun_Pr252072522l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_,type,
    member840932460on_val: ( produc124828825on_val * fun_Pr680585871l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__S,type,
    member1972431429on_val: ( produc2061676504on_val * fun_Pr248118298l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J,type,
    member1840112042t_char: ( produc809539159t_char * fun_Pr1336948301r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_834,type,
    member133545693t_char: ( produc1285161482t_char * fun_Pr227936640r_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__String__Ochar_J_Mtc__Type__Oty_J,type,
    member503779467har_ty: ( produc917948472har_ty * fun_Pr1127025070y_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod,type,
    member1542417277on_val: ( produc639455274on_val * fun_Pr315804320l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__Lis,type,
    member2007117138har_ty: ( produc469582463har_ty * fun_Pr758558581y_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__Lis_835,type,
    member1467889965t_char: ( produc1971331930t_char * fun_Pr1861226704r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__Lis_836,type,
    member1601084734t_char: ( produc1013743697t_char * fun_Pr70170387r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__Lis_837,type,
    member1771544038t_char: ( produc952412819t_char * fun_Pr1898949769r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__O,type,
    member140606439t_char: ( produc220283002t_char * fun_Pr46158268r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc_,type,
    member699351154t_char: ( produc662261637t_char * fun_Pr827765831r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String_,type,
    member1379348767t_char: ( produc2146869324t_char * fun_Pr1669461698r_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__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I,type,
    member763590124on_val: ( produc12694297on_val * fun_Pr1696029455l_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__838,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_839,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_840,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__String__Ochar_J_Mtc__pro,type,
    member162552852t_char: ( produc84451751t_char * fun_Pr981088873r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__pro_841,type,
    member1607118676t_char: ( produc740765671t_char * fun_Pr1538825897r_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__List__Olist_Itc__prod_Itc__List__Olist_It,type,
    member1551446420t_char: ( produc494726439t_char * fun_Pr286306793r_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_D____,type,
    d: list_char ).

tff(sy_v_E____,type,
    e: fun_li688206603ion_ty ).

tff(sy_v_F____,type,
    f: list_char ).

tff(sy_v_P,type,
    p: list_P1999446415t_char ).

tff(sy_v_T____,type,
    t: ty ).

tff(sy_v_e_092_060_094isub_0622____,type,
    e_2: exp_list_char ).

tff(sy_v_e_Ha____,type,
    e_a: exp_list_char ).

tff(sy_v_ea____,type,
    ea: exp_list_char ).

tff(sy_v_h_Ha____,type,
    h_a: fun_na939144002on_val ).

tff(sy_v_ha____,type,
    ha: fun_na939144002on_val ).

tff(sy_v_l_Ha____,type,
    l_a: fun_li1432931796on_val ).

tff(sy_v_la____,type,
    la: fun_li1432931796on_val ).

%----Relevant facts (1200)
tff(fact_0__096P_ME_Mh_A_092_060turnstile_062_Ae_A_058_ANT_096,axiom,
    hBOOL(hAPP_ty_bool(wTrt(p,ha,e,ea),nt)) ).

tff(fact_1__096_B_BT_O_AP_ME_Mh_A_092_060turnstile_062_Ae_A_058_AT_A_061_061_062_AEX,axiom,
    ! [Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(p,ha,e,ea),Ta))
     => ? [U_2: ty] :
          ( hBOOL(hAPP_ty_bool(wTrt(p,h_a,e,e_a),U_2))
          & hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(p),U_2),Ta)) ) ) ).

tff(fact_2_assms,axiom,
    hBOOL(wf_pro755087577t_char(wf_J_mdecl,p)) ).

tff(fact_3_IH,axiom,
    ! [Ta: ty,Ea: fun_li688206603ion_ty] :
      ( hBOOL(hAPP_P159683425l_bool(typeSa1917327191_sconf(p,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),la)))
     => ( hBOOL(hAPP_ty_bool(wTrt(p,ha,Ea,ea),Ta))
       => ? [U_2: ty] :
            ( hBOOL(hAPP_ty_bool(wTrt(p,h_a,Ea,e_a),U_2))
            & hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(p),U_2),Ta)) ) ) ) ).

tff(fact_4_conf,axiom,
    hBOOL(hAPP_P159683425l_bool(typeSa1917327191_sconf(p,e),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),la))) ).

tff(fact_5_wt,axiom,
    hBOOL(hAPP_ty_bool(wTrt(p,ha,e,fAss_list_char(ea,f,d,e_2)),t)) ).

tff(fact_6_WTrtFAccNT,axiom,
    ! [Fa: list_char,Da: list_char,Ta: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),nt))
     => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,fAcc_list_char(Eb,Fa,Da)),Ta)) ) ).

tff(fact_7_FAssRed1_I2_J,axiom,
    ! [Ta: ty,Ea: fun_li688206603ion_ty] :
      ( hBOOL(hAPP_P159683425l_bool(typeSa1917327191_sconf(p,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),la)))
     => ( hBOOL(hAPP_ty_bool(wTrt(p,ha,Ea,ea),Ta))
       => ? [T_5: ty] :
            ( hBOOL(hAPP_ty_bool(wTrt(p,h_a,Ea,e_a),T_5))
            & hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(p),T_5),Ta)) ) ) ) ).

tff(fact_8_red,axiom,
    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),la))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,e_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,h_a),l_a))),red(p))) ).

tff(fact_9_ty_Osimps_I25_J,axiom,
    ! [F1: bool,F2: bool,F3: bool,F4: bool,F5: fun_list_char_bool] :
      ( hBOOL(hAPP_ty_bool(ty_case_bool(F1,F2,F3,F4,F5),nt))
    <=> hBOOL(F4) ) ).

tff(fact_10_FAssRed1_I4_J,axiom,
    hBOOL(hAPP_ty_bool(wTrt(p,ha,e,fAss_list_char(ea,f,d,e_2)),t)) ).

tff(fact_11_FAssRed1_I3_J,axiom,
    hBOOL(hAPP_P159683425l_bool(typeSa1917327191_sconf(p,e),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),la))) ).

tff(fact_12_ty_Osimps_I13_J,axiom,
    nt != boolean ).

tff(fact_13_ty_Osimps_I23_J,axiom,
    ! [F1: bool,F2: bool,F3: bool,F4: bool,F5: fun_list_char_bool] :
      ( hBOOL(hAPP_ty_bool(ty_case_bool(F1,F2,F3,F4,F5),boolean))
    <=> hBOOL(F2) ) ).

tff(fact_14_ty_Osimps_I12_J,axiom,
    boolean != nt ).

tff(fact_15_red__reds_OFAccRed,axiom,
    ! [Fa: list_char,Da: list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(Eb,Fa,Da)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(E_b,Fa,Da)),S_2)),red(Pa))) ) ).

tff(fact_16_red__reds_OFAssRed1,axiom,
    ! [Fa: list_char,Da: list_char,E_2: exp_list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(Eb,Fa,Da,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(E_b,Fa,Da,E_2)),S_2)),red(Pa))) ) ).

tff(fact_17_void,axiom,
    t = void ).

tff(fact_18_widen__refl,axiom,
    ! [P_4: list_P1999446415t_char,T_10: ty] : hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_4),T_10),T_10)) ).

tff(fact_19_red__preserves__hconf,axiom,
    ! [Ea: fun_li688206603ion_ty,Ta: ty,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: 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,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa)))
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),Ta))
       => ( hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),Hb))
         => hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),H_b)) ) ) ) ).

tff(fact_20_red__preserves__lconf,axiom,
    ! [Ea: fun_li688206603ion_ty,Ta: ty,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: 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,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa)))
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),Ta))
       => ( hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Hb),Lb),Ea))
         => hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),H_b),L_b),Ea)) ) ) ) ).

tff(fact_21_exp_Osimps_I154_J,axiom,
    ! [Exp_55: exp_list_char,List1_37: list_char,List2_37: list_char,Exp1_109: exp_list_char,List1_36: list_char,List2_36: list_char,Exp2_109: exp_list_char] : fAcc_list_char(Exp_55,List1_37,List2_37) != fAss_list_char(Exp1_109,List1_36,List2_36,Exp2_109) ).

tff(fact_22_exp_Osimps_I155_J,axiom,
    ! [Exp1_108: exp_list_char,List1_35: list_char,List2_35: list_char,Exp2_108: exp_list_char,Exp_54: exp_list_char,List1_34: list_char,List2_34: list_char] : fAss_list_char(Exp1_108,List1_35,List2_35,Exp2_108) != fAcc_list_char(Exp_54,List1_34,List2_34) ).

tff(fact_23_red__preserves__sconf,axiom,
    ! [Ea: fun_li688206603ion_ty,Ta: ty,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),red(Pa)))
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,hAPP_P703866694on_val(hp,S),Ea,Eb),Ta))
       => ( hBOOL(hAPP_P159683425l_bool(typeSa1917327191_sconf(Pa,Ea),S))
         => hBOOL(hAPP_P159683425l_bool(typeSa1917327191_sconf(Pa,Ea),S_2)) ) ) ) ).

tff(fact_24_prod__induct5,axiom,
    ! [X_2: produc1466422861on_val,Pa: fun_Pr302334223l_bool] :
      ( ! [A_1: produc430140671on_val,B_1: produc2061676504on_val,C_4: list_exp_list_char,D: fun_na939144002on_val,E_3: fun_li1432931796on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),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),E_3))))))
     => hBOOL(hAPP_P2028072621l_bool(Pa,X_2)) ) ).

tff(fact_25_prod__induct5,axiom,
    ! [X_2: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
      ( ! [A_1: produc1102272487on_val,B_1: produc124828825on_val,C_4: exp_list_char,D: fun_na939144002on_val,E_3: fun_li1432931796on_val] : hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),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),E_3))))))
     => hBOOL(hAPP_P378063101l_bool(Pa,X_2)) ) ).

tff(fact_26_prod__induct5,axiom,
    ! [X_2: produc349695911t_char,Pa: fun_Pr1895638121r_bool] :
      ( ! [A_1: produc1285161482t_char,B_1: list_list_char,C_4: list_ty,D: list_val,E_3: exp_list_char] : hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),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),E_3))))))
     => hBOOL(hAPP_P824029447r_bool(Pa,X_2)) ) ).

tff(fact_27_prod__induct5,axiom,
    ! [X_2: produc84451751t_char,Pa: fun_Pr981088873r_bool] :
      ( ! [A_1: produc1971331930t_char,B_1: list_char,C_4: list_char,D: list_P1940453997har_ty,E_3: list_P341299826t_char] : hBOOL(hAPP_P975284999r_bool(Pa,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,B_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,C_4),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,D),E_3))))))
     => hBOOL(hAPP_P975284999r_bool(Pa,X_2)) ) ).

tff(fact_28_prod__induct5,axiom,
    ! [X_2: produc1013743697t_char,Pa: fun_Pr70170387r_bool] :
      ( ! [A_1: list_char,B_1: list_ty,C_4: ty,D: list_list_char,E_3: exp_list_char] : hBOOL(hAPP_P1384137393r_bool(Pa,hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),hAPP_P976433298t_char(hAPP_l2048923787t_char(produc2016959032t_char,B_1),hAPP_P1661798543t_char(hAPP_t1369077401t_char(produc1545444669t_char,C_4),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,D),E_3))))))
     => hBOOL(hAPP_P1384137393r_bool(Pa,X_2)) ) ).

tff(fact_29_ty_Osimps_I7_J,axiom,
    nt != void ).

tff(fact_30_ty_Osimps_I6_J,axiom,
    void != nt ).

tff(fact_31_ty_Osimps_I3_J,axiom,
    boolean != void ).

tff(fact_32_ty_Osimps_I2_J,axiom,
    void != boolean ).

tff(fact_33_ty_Osimps_I22_J,axiom,
    ! [F1: bool,F2: bool,F3: bool,F4: bool,F5: fun_list_char_bool] :
      ( hBOOL(hAPP_ty_bool(ty_case_bool(F1,F2,F3,F4,F5),void))
    <=> hBOOL(F1) ) ).

tff(fact_34_Pair__inject,axiom,
    ! [A_24: list_char,B_4: produc917948472har_ty,A_23: list_char,B_3: produc917948472har_ty] :
      ( ( hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,A_24),B_4) = hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_35_Pair__inject,axiom,
    ! [A_24: list_char,B_4: ty,A_23: list_char,B_3: ty] :
      ( ( hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_24),B_4) = hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_36_Pair__inject,axiom,
    ! [A_24: produc1147203250ar_val,B_4: produc1147203250ar_val,A_23: produc1147203250ar_val,B_3: produc1147203250ar_val] :
      ( ( hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,A_24),B_4) = hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_37_Pair__inject,axiom,
    ! [A_24: produc809539159t_char,B_4: produc809539159t_char,A_23: produc809539159t_char,B_3: produc809539159t_char] :
      ( ( hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_24),B_4) = hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_38_Pair__inject,axiom,
    ! [A_24: produc2146869324t_char,B_4: produc2146869324t_char,A_23: produc2146869324t_char,B_3: produc2146869324t_char] :
      ( ( hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_24),B_4) = hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_39_Pair__inject,axiom,
    ! [A_24: produc952412819t_char,B_4: produc952412819t_char,A_23: produc952412819t_char,B_3: produc952412819t_char] :
      ( ( hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_24),B_4) = hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_40_Pair__inject,axiom,
    ! [A_24: produc1971331930t_char,B_4: produc1971331930t_char,A_23: produc1971331930t_char,B_3: produc1971331930t_char] :
      ( ( hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_24),B_4) = hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_41_Pair__inject,axiom,
    ! [A_24: produc1278157519t_char,B_4: produc1278157519t_char,A_23: produc1278157519t_char,B_3: produc1278157519t_char] :
      ( ( hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_24),B_4) = hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_42_Pair__inject,axiom,
    ! [A: produc639455274on_val,B: produc639455274on_val,A_15: produc639455274on_val,B_2: produc639455274on_val] :
      ( ( hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A),B) = hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_15),B_2) )
     => ~ ( ( A = A_15 )
         => ( B != B_2 ) ) ) ).

tff(fact_43_Pair__inject,axiom,
    ! [A_24: product_prod_val_val,B_4: product_prod_val_val,A_23: product_prod_val_val,B_3: product_prod_val_val] :
      ( ( hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_24),B_4) = hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_44_Pair__inject,axiom,
    ! [A_24: produc1645268488al_val,B_4: produc1645268488al_val,A_23: produc1645268488al_val,B_3: produc1645268488al_val] :
      ( ( hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_24),B_4) = hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_45_Pair__inject,axiom,
    ! [A_24: produc662261637t_char,B_4: produc662261637t_char,A_23: produc662261637t_char,B_3: produc662261637t_char] :
      ( ( hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_24),B_4) = hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_46_Pair__inject,axiom,
    ! [A_24: produc220283002t_char,B_4: produc220283002t_char,A_23: produc220283002t_char,B_3: produc220283002t_char] :
      ( ( hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_24),B_4) = hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_47_Pair__inject,axiom,
    ! [A_24: produc1285161482t_char,B_4: produc1285161482t_char,A_23: produc1285161482t_char,B_3: produc1285161482t_char] :
      ( ( hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_24),B_4) = hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_48_Pair__inject,axiom,
    ! [A: produc430140671on_val,B: produc430140671on_val,A_15: produc430140671on_val,B_2: produc430140671on_val] :
      ( ( hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A),B) = hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_15),B_2) )
     => ~ ( ( A = A_15 )
         => ( B != B_2 ) ) ) ).

tff(fact_49_Pair__inject,axiom,
    ! [A: produc1102272487on_val,B: produc1102272487on_val,A_15: produc1102272487on_val,B_2: produc1102272487on_val] :
      ( ( hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A),B) = hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_15),B_2) )
     => ~ ( ( A = A_15 )
         => ( B != B_2 ) ) ) ).

tff(fact_50_Pair__inject,axiom,
    ! [A: produc12694297on_val,B: produc12694297on_val,A_15: produc12694297on_val,B_2: produc12694297on_val] :
      ( ( hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A),B) = hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_15),B_2) )
     => ~ ( ( A = A_15 )
         => ( B != B_2 ) ) ) ).

tff(fact_51_Pair__inject,axiom,
    ! [A_24: produc1278157519t_char,B_4: ty,A_23: produc1278157519t_char,B_3: ty] :
      ( ( hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_24),B_4) = hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_52_Pair__inject,axiom,
    ! [A_24: list_char,B_4: produc1025221954t_char,A_23: list_char,B_3: produc1025221954t_char] :
      ( ( hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_24),B_4) = hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_53_Pair__inject,axiom,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,A_15: fun_na939144002on_val,B_2: fun_li1432931796on_val] :
      ( ( hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B) = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B_2) )
     => ~ ( ( A = A_15 )
         => ( B != B_2 ) ) ) ).

tff(fact_54_Pair__inject,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,A_15: produc124828825on_val,B_2: produc124828825on_val] :
      ( ( hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B) = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B_2) )
     => ~ ( ( A = A_15 )
         => ( B != B_2 ) ) ) ).

tff(fact_55_Pair__inject,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,A_15: exp_list_char,B_2: produc12694297on_val] :
      ( ( hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B) = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B_2) )
     => ~ ( ( A = A_15 )
         => ( B != B_2 ) ) ) ).

tff(fact_56_Pair__inject,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,A_15: produc2061676504on_val,B_2: produc2061676504on_val] :
      ( ( hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B) = hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_15),B_2) )
     => ~ ( ( A = A_15 )
         => ( B != B_2 ) ) ) ).

tff(fact_57_Pair__inject,axiom,
    ! [A: list_exp_list_char,B: produc12694297on_val,A_15: list_exp_list_char,B_2: produc12694297on_val] :
      ( ( hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B) = hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_15),B_2) )
     => ~ ( ( A = A_15 )
         => ( B != B_2 ) ) ) ).

tff(fact_58_Pair__inject,axiom,
    ! [A_24: list_list_char,B_4: produc220283002t_char,A_23: list_list_char,B_3: produc220283002t_char] :
      ( ( hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_24),B_4) = hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_59_Pair__inject,axiom,
    ! [A_24: list_ty,B_4: produc662261637t_char,A_23: list_ty,B_3: produc662261637t_char] :
      ( ( hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_24),B_4) = hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_60_Pair__inject,axiom,
    ! [A_24: list_val,B_4: exp_list_char,A_23: list_val,B_3: exp_list_char] :
      ( ( hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_24),B_4) = hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_61_Pair__inject,axiom,
    ! [A_24: bop,B_4: product_prod_val_val,A_23: bop,B_3: product_prod_val_val] :
      ( ( hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_24),B_4) = hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_62_Pair__inject,axiom,
    ! [A_24: val,B_4: val,A_23: val,B_3: val] :
      ( ( hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_24),B_4) = hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_63_Pair__inject,axiom,
    ! [A: list_char,B: fun_Pr806764899on_val,A_15: list_char,B_2: fun_Pr806764899on_val] :
      ( ( hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B) = hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_15),B_2) )
     => ~ ( ( A = A_15 )
         => ( B != B_2 ) ) ) ).

tff(fact_64_Pair__inject,axiom,
    ! [A_24: list_char,B_4: list_char,A_23: list_char,B_3: list_char] :
      ( ( hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_24),B_4) = hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_65_Pair__inject,axiom,
    ! [A_24: list_char,B_4: produc952412819t_char,A_23: list_char,B_3: produc952412819t_char] :
      ( ( hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_24),B_4) = hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_66_Pair__inject,axiom,
    ! [A_24: list_char,B_4: produc2146869324t_char,A_23: list_char,B_3: produc2146869324t_char] :
      ( ( hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_24),B_4) = hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_67_Pair__inject,axiom,
    ! [A_24: list_P1940453997har_ty,B_4: list_P341299826t_char,A_23: list_P1940453997har_ty,B_3: list_P341299826t_char] :
      ( ( hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_24),B_4) = hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_68_Pair__inject,axiom,
    ! [A_24: list_list_char,B_4: exp_list_char,A_23: list_list_char,B_3: exp_list_char] :
      ( ( hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_24),B_4) = hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_69_Pair__inject,axiom,
    ! [A_24: produc1278157519t_char,B_4: val,A_23: produc1278157519t_char,B_3: val] :
      ( ( hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_24),B_4) = hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_23),B_3) )
     => ~ ( ( A_24 = A_23 )
         => ( B_4 != B_3 ) ) ) ).

tff(fact_70_Pair__eq,axiom,
    ! [A: list_char,B: produc917948472har_ty,A_15: list_char,B_2: produc917948472har_ty] :
      ( ( hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,A),B) = hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_71_Pair__eq,axiom,
    ! [A: list_char,B: ty,A_15: list_char,B_2: ty] :
      ( ( hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A),B) = hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_72_Pair__eq,axiom,
    ! [A: produc1147203250ar_val,B: produc1147203250ar_val,A_15: produc1147203250ar_val,B_2: produc1147203250ar_val] :
      ( ( hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,A),B) = hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_73_Pair__eq,axiom,
    ! [A: produc809539159t_char,B: produc809539159t_char,A_15: produc809539159t_char,B_2: produc809539159t_char] :
      ( ( hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A),B) = hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_74_Pair__eq,axiom,
    ! [A: produc2146869324t_char,B: produc2146869324t_char,A_15: produc2146869324t_char,B_2: produc2146869324t_char] :
      ( ( hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A),B) = hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_75_Pair__eq,axiom,
    ! [A: produc952412819t_char,B: produc952412819t_char,A_15: produc952412819t_char,B_2: produc952412819t_char] :
      ( ( hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A),B) = hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_76_Pair__eq,axiom,
    ! [A: produc1971331930t_char,B: produc1971331930t_char,A_15: produc1971331930t_char,B_2: produc1971331930t_char] :
      ( ( hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A),B) = hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_77_Pair__eq,axiom,
    ! [A: produc1278157519t_char,B: produc1278157519t_char,A_15: produc1278157519t_char,B_2: produc1278157519t_char] :
      ( ( hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A),B) = hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_78_Pair__eq,axiom,
    ! [A: produc639455274on_val,B: produc639455274on_val,A_15: produc639455274on_val,B_2: produc639455274on_val] :
      ( ( hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A),B) = hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_79_Pair__eq,axiom,
    ! [A: product_prod_val_val,B: product_prod_val_val,A_15: product_prod_val_val,B_2: product_prod_val_val] :
      ( ( hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A),B) = hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_80_Pair__eq,axiom,
    ! [A: produc1645268488al_val,B: produc1645268488al_val,A_15: produc1645268488al_val,B_2: produc1645268488al_val] :
      ( ( hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A),B) = hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_81_Pair__eq,axiom,
    ! [A: produc662261637t_char,B: produc662261637t_char,A_15: produc662261637t_char,B_2: produc662261637t_char] :
      ( ( hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A),B) = hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_82_Pair__eq,axiom,
    ! [A: produc220283002t_char,B: produc220283002t_char,A_15: produc220283002t_char,B_2: produc220283002t_char] :
      ( ( hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A),B) = hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_83_Pair__eq,axiom,
    ! [A: produc1285161482t_char,B: produc1285161482t_char,A_15: produc1285161482t_char,B_2: produc1285161482t_char] :
      ( ( hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A),B) = hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_84_Pair__eq,axiom,
    ! [A: produc430140671on_val,B: produc430140671on_val,A_15: produc430140671on_val,B_2: produc430140671on_val] :
      ( ( hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A),B) = hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_85_Pair__eq,axiom,
    ! [A: produc1102272487on_val,B: produc1102272487on_val,A_15: produc1102272487on_val,B_2: produc1102272487on_val] :
      ( ( hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A),B) = hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_86_Pair__eq,axiom,
    ! [A: produc12694297on_val,B: produc12694297on_val,A_15: produc12694297on_val,B_2: produc12694297on_val] :
      ( ( hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A),B) = hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_87_Pair__eq,axiom,
    ! [A: produc1278157519t_char,B: ty,A_15: produc1278157519t_char,B_2: ty] :
      ( ( hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A),B) = hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_88_Pair__eq,axiom,
    ! [A: list_char,B: produc1025221954t_char,A_15: list_char,B_2: produc1025221954t_char] :
      ( ( hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A),B) = hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_89_Pair__eq,axiom,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,A_15: fun_na939144002on_val,B_2: fun_li1432931796on_val] :
      ( ( hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B) = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_90_Pair__eq,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,A_15: produc124828825on_val,B_2: produc124828825on_val] :
      ( ( hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B) = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_91_Pair__eq,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,A_15: exp_list_char,B_2: produc12694297on_val] :
      ( ( hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B) = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_92_Pair__eq,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,A_15: produc2061676504on_val,B_2: produc2061676504on_val] :
      ( ( hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B) = hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_93_Pair__eq,axiom,
    ! [A: list_exp_list_char,B: produc12694297on_val,A_15: list_exp_list_char,B_2: produc12694297on_val] :
      ( ( hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B) = hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_94_Pair__eq,axiom,
    ! [A: list_list_char,B: produc220283002t_char,A_15: list_list_char,B_2: produc220283002t_char] :
      ( ( hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B) = hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_95_Pair__eq,axiom,
    ! [A: list_ty,B: produc662261637t_char,A_15: list_ty,B_2: produc662261637t_char] :
      ( ( hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B) = hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_96_Pair__eq,axiom,
    ! [A: list_val,B: exp_list_char,A_15: list_val,B_2: exp_list_char] :
      ( ( hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B) = hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_97_Pair__eq,axiom,
    ! [A: bop,B: product_prod_val_val,A_15: bop,B_2: product_prod_val_val] :
      ( ( hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B) = hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_98_Pair__eq,axiom,
    ! [A: val,B: val,A_15: val,B_2: val] :
      ( ( hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B) = hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_99_Pair__eq,axiom,
    ! [A: list_char,B: fun_Pr806764899on_val,A_15: list_char,B_2: fun_Pr806764899on_val] :
      ( ( hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B) = hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_100_Pair__eq,axiom,
    ! [A: list_char,B: list_char,A_15: list_char,B_2: list_char] :
      ( ( hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B) = hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_101_Pair__eq,axiom,
    ! [A: list_char,B: produc952412819t_char,A_15: list_char,B_2: produc952412819t_char] :
      ( ( hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B) = hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_102_Pair__eq,axiom,
    ! [A: list_char,B: produc2146869324t_char,A_15: list_char,B_2: produc2146869324t_char] :
      ( ( hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B) = hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_103_Pair__eq,axiom,
    ! [A: list_P1940453997har_ty,B: list_P341299826t_char,A_15: list_P1940453997har_ty,B_2: list_P341299826t_char] :
      ( ( hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B) = hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_104_Pair__eq,axiom,
    ! [A: list_list_char,B: exp_list_char,A_15: list_list_char,B_2: exp_list_char] :
      ( ( hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B) = hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_105_Pair__eq,axiom,
    ! [A: produc1278157519t_char,B: val,A_15: produc1278157519t_char,B_2: val] :
      ( ( hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A),B) = hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_15),B_2) )
    <=> ( ( A = A_15 )
        & ( B = B_2 ) ) ) ).

tff(fact_106_split__paired__All,axiom,
    ! [Pa: fun_Pr758558581y_bool] :
      ( ! [X1: produc469582463har_ty] : hBOOL(hAPP_P831231943y_bool(Pa,X1))
    <=> ! [A_1: list_char,B_1: produc917948472har_ty] : hBOOL(hAPP_P831231943y_bool(Pa,hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,A_1),B_1))) ) ).

tff(fact_107_split__paired__All,axiom,
    ! [Pa: fun_Pr1127025070y_bool] :
      ( ! [X1: produc917948472har_ty] : hBOOL(hAPP_P748443392y_bool(Pa,X1))
    <=> ! [A_1: list_char,B_1: ty] : hBOOL(hAPP_P748443392y_bool(Pa,hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_1),B_1))) ) ).

tff(fact_108_split__paired__All,axiom,
    ! [Pa: fun_Pr643382121l_bool] :
      ( ! [X1: produc1312961703ar_val] : hBOOL(hAPP_P439015943l_bool(Pa,X1))
    <=> ! [A_1: produc1147203250ar_val,B_1: produc1147203250ar_val] : hBOOL(hAPP_P439015943l_bool(Pa,hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,A_1),B_1))) ) ).

tff(fact_109_split__paired__All,axiom,
    ! [Pa: fun_Pr908866473r_bool] :
      ( ! [X1: produc1534059751t_char] : hBOOL(hAPP_P1002912327r_bool(Pa,X1))
    <=> ! [A_1: produc809539159t_char,B_1: produc809539159t_char] : hBOOL(hAPP_P1002912327r_bool(Pa,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_1),B_1))) ) ).

tff(fact_110_split__paired__All,axiom,
    ! [Pa: fun_Pr286306793r_bool] :
      ( ! [X1: produc494726439t_char] : hBOOL(hAPP_P801803911r_bool(Pa,X1))
    <=> ! [A_1: produc2146869324t_char,B_1: produc2146869324t_char] : hBOOL(hAPP_P801803911r_bool(Pa,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_1),B_1))) ) ).

tff(fact_111_split__paired__All,axiom,
    ! [Pa: fun_Pr1538825897r_bool] :
      ( ! [X1: produc740765671t_char] : hBOOL(hAPP_P929449287r_bool(Pa,X1))
    <=> ! [A_1: produc952412819t_char,B_1: produc952412819t_char] : hBOOL(hAPP_P929449287r_bool(Pa,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_1),B_1))) ) ).

tff(fact_112_split__paired__All,axiom,
    ! [Pa: fun_Pr981088873r_bool] :
      ( ! [X1: produc84451751t_char] : hBOOL(hAPP_P975284999r_bool(Pa,X1))
    <=> ! [A_1: produc1971331930t_char,B_1: produc1971331930t_char] : hBOOL(hAPP_P975284999r_bool(Pa,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),B_1))) ) ).

tff(fact_113_split__paired__All,axiom,
    ! [Pa: fun_Pr1336847023r_bool] :
      ( ! [X1: produc1350825965t_char] : hBOOL(hAPP_P2010574925r_bool(Pa,X1))
    <=> ! [A_1: produc1278157519t_char,B_1: produc1278157519t_char] : hBOOL(hAPP_P2010574925r_bool(Pa,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_1),B_1))) ) ).

tff(fact_114_split__paired__All,axiom,
    ! [Pa: fun_Pr235369833l_bool] :
      ( ! [X1: produc87279271on_val] : hBOOL(hAPP_P124632071l_bool(Pa,X1))
    <=> ! [A_1: produc639455274on_val,B_1: produc639455274on_val] : hBOOL(hAPP_P124632071l_bool(Pa,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_1),B_1))) ) ).

tff(fact_115_split__paired__All,axiom,
    ! [Pa: fun_Pr832147423l_bool] :
      ( ! [X1: produc800118557al_val] : hBOOL(hAPP_P2123002749l_bool(Pa,X1))
    <=> ! [A_1: product_prod_val_val,B_1: product_prod_val_val] : hBOOL(hAPP_P2123002749l_bool(Pa,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_1),B_1))) ) ).

tff(fact_116_split__paired__All,axiom,
    ! [Pa: fun_Pr897334561l_bool] :
      ( ! [X1: produc630464863al_val] : hBOOL(hAPP_P738987199l_bool(Pa,X1))
    <=> ! [A_1: produc1645268488al_val,B_1: produc1645268488al_val] : hBOOL(hAPP_P738987199l_bool(Pa,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_1),B_1))) ) ).

tff(fact_117_split__paired__All,axiom,
    ! [Pa: fun_Pr1890037787r_bool] :
      ( ! [X1: produc1826280281t_char] : hBOOL(hAPP_P1183499705r_bool(Pa,X1))
    <=> ! [A_1: produc662261637t_char,B_1: produc662261637t_char] : hBOOL(hAPP_P1183499705r_bool(Pa,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_1),B_1))) ) ).

tff(fact_118_split__paired__All,axiom,
    ! [Pa: fun_Pr1728267013r_bool] :
      ( ! [X1: produc1406897475t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,X1))
    <=> ! [A_1: produc220283002t_char,B_1: produc220283002t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_1),B_1))) ) ).

tff(fact_119_split__paired__All,axiom,
    ! [Pa: fun_Pr1895638121r_bool] :
      ( ! [X1: produc349695911t_char] : hBOOL(hAPP_P824029447r_bool(Pa,X1))
    <=> ! [A_1: produc1285161482t_char,B_1: produc1285161482t_char] : hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),B_1))) ) ).

tff(fact_120_split__paired__All,axiom,
    ! [Pa: fun_Pr302334223l_bool] :
      ( ! [X1: produc1466422861on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,X1))
    <=> ! [A_1: produc430140671on_val,B_1: produc430140671on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),B_1))) ) ).

tff(fact_121_split__paired__All,axiom,
    ! [Pa: fun_Pr903661919l_bool] :
      ( ! [X1: produc231486621on_val] : hBOOL(hAPP_P378063101l_bool(Pa,X1))
    <=> ! [A_1: produc1102272487on_val,B_1: produc1102272487on_val] : hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),B_1))) ) ).

tff(fact_122_split__paired__All,axiom,
    ! [Pa: fun_Pr693020585l_bool] :
      ( ! [X1: produc409205479on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,X1))
    <=> ! [A_1: produc12694297on_val,B_1: produc12694297on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_1),B_1))) ) ).

tff(fact_123_split__paired__All,axiom,
    ! [Pa: fun_Pr2102567903y_bool] :
      ( ! [X1: produc245756905har_ty] : hBOOL(hAPP_P27757617y_bool(Pa,X1))
    <=> ! [A_1: produc1278157519t_char,B_1: ty] : hBOOL(hAPP_P27757617y_bool(Pa,hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_1),B_1))) ) ).

tff(fact_124_split__paired__All,axiom,
    ! [Pa: fun_Pr70170387r_bool] :
      ( ! [X1: produc1013743697t_char] : hBOOL(hAPP_P1384137393r_bool(Pa,X1))
    <=> ! [A_1: list_char,B_1: produc1025221954t_char] : hBOOL(hAPP_P1384137393r_bool(Pa,hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),B_1))) ) ).

tff(fact_125_split__paired__All,axiom,
    ! [Pa: fun_Pr1696029455l_bool] :
      ( ! [X1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
    <=> ! [A_1: fun_na939144002on_val,B_1: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(Pa,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_1))) ) ).

tff(fact_126_split__paired__All,axiom,
    ! [Pa: fun_Pr691271849l_bool] :
      ( ! [X1: produc1102272487on_val] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
    <=> ! [A_1: produc124828825on_val,B_1: produc124828825on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_1))) ) ).

tff(fact_127_split__paired__All,axiom,
    ! [Pa: fun_Pr680585871l_bool] :
      ( ! [X1: produc124828825on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
    <=> ! [A_1: exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_1))) ) ).

tff(fact_128_split__paired__All,axiom,
    ! [Pa: fun_Pr859510977l_bool] :
      ( ! [X1: produc430140671on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,X1))
    <=> ! [A_1: produc2061676504on_val,B_1: produc2061676504on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_1))) ) ).

tff(fact_129_split__paired__All,axiom,
    ! [Pa: fun_Pr248118298l_bool] :
      ( ! [X1: produc2061676504on_val] : hBOOL(hAPP_P71593144l_bool(Pa,X1))
    <=> ! [A_1: list_exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P71593144l_bool(Pa,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_1))) ) ).

tff(fact_130_split__paired__All,axiom,
    ! [Pa: fun_Pr227936640r_bool] :
      ( ! [X1: produc1285161482t_char] : hBOOL(hAPP_P92196306r_bool(Pa,X1))
    <=> ! [A_1: list_list_char,B_1: produc220283002t_char] : hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_1))) ) ).

tff(fact_131_split__paired__All,axiom,
    ! [Pa: fun_Pr46158268r_bool] :
      ( ! [X1: produc220283002t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,X1))
    <=> ! [A_1: list_ty,B_1: produc662261637t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_1))) ) ).

tff(fact_132_split__paired__All,axiom,
    ! [Pa: fun_Pr827765831r_bool] :
      ( ! [X1: produc662261637t_char] : hBOOL(hAPP_P2118621157r_bool(Pa,X1))
    <=> ! [A_1: list_val,B_1: exp_list_char] : hBOOL(hAPP_P2118621157r_bool(Pa,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_1))) ) ).

tff(fact_133_split__paired__All,axiom,
    ! [Pa: fun_Pr252072522l_bool] :
      ( ! [X1: produc1645268488al_val] : hBOOL(hAPP_P943837928l_bool(Pa,X1))
    <=> ! [A_1: bop,B_1: product_prod_val_val] : hBOOL(hAPP_P943837928l_bool(Pa,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_1))) ) ).

tff(fact_134_split__paired__All,axiom,
    ! [Pa: fun_Pr2081272681l_bool] :
      ( ! [X1: product_prod_val_val] : hBOOL(hAPP_P929938951l_bool(Pa,X1))
    <=> ! [A_1: val,B_1: val] : hBOOL(hAPP_P929938951l_bool(Pa,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_1))) ) ).

tff(fact_135_split__paired__All,axiom,
    ! [Pa: fun_Pr315804320l_bool] :
      ( ! [X1: produc639455274on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,X1))
    <=> ! [A_1: list_char,B_1: fun_Pr806764899on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_1))) ) ).

tff(fact_136_split__paired__All,axiom,
    ! [Pa: fun_Pr565113489r_bool] :
      ( ! [X1: produc1278157519t_char] : hBOOL(hAPP_P449474095r_bool(Pa,X1))
    <=> ! [A_1: list_char,B_1: list_char] : hBOOL(hAPP_P449474095r_bool(Pa,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_1))) ) ).

tff(fact_137_split__paired__All,axiom,
    ! [Pa: fun_Pr1861226704r_bool] :
      ( ! [X1: produc1971331930t_char] : hBOOL(hAPP_P1680401186r_bool(Pa,X1))
    <=> ! [A_1: list_char,B_1: produc952412819t_char] : hBOOL(hAPP_P1680401186r_bool(Pa,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_1))) ) ).

tff(fact_138_split__paired__All,axiom,
    ! [Pa: fun_Pr1898949769r_bool] :
      ( ! [X1: produc952412819t_char] : hBOOL(hAPP_P659547099r_bool(Pa,X1))
    <=> ! [A_1: list_char,B_1: produc2146869324t_char] : hBOOL(hAPP_P659547099r_bool(Pa,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_1))) ) ).

tff(fact_139_split__paired__All,axiom,
    ! [Pa: fun_Pr1669461698r_bool] :
      ( ! [X1: produc2146869324t_char] : hBOOL(hAPP_P828904212r_bool(Pa,X1))
    <=> ! [A_1: list_P1940453997har_ty,B_1: list_P341299826t_char] : hBOOL(hAPP_P828904212r_bool(Pa,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_1))) ) ).

tff(fact_140_split__paired__All,axiom,
    ! [Pa: fun_Pr1336948301r_bool] :
      ( ! [X1: produc809539159t_char] : hBOOL(hAPP_P2014166431r_bool(Pa,X1))
    <=> ! [A_1: list_list_char,B_1: exp_list_char] : hBOOL(hAPP_P2014166431r_bool(Pa,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_1))) ) ).

tff(fact_141_split__paired__All,axiom,
    ! [Pa: fun_Pr661739816l_bool] :
      ( ! [X1: produc1147203250ar_val] : hBOOL(hAPP_P1070896250l_bool(Pa,X1))
    <=> ! [A_1: produc1278157519t_char,B_1: val] : hBOOL(hAPP_P1070896250l_bool(Pa,hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_1),B_1))) ) ).

tff(fact_142_widen__trans,axiom,
    ! [T_9: ty,P_3: list_P1999446415t_char,S_5: ty,U_1: ty] :
      ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_3),S_5),U_1))
     => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_3),U_1),T_9))
       => hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_3),S_5),T_9)) ) ) ).

tff(fact_143_exp_Osimps_I8_J,axiom,
    ! [Exp1_61: exp_list_char,List1_33: list_char,List2_33: list_char,Exp2_61: exp_list_char,Exp1_60: exp_list_char,List1_32: list_char,List2_32: list_char,Exp2_60: exp_list_char] :
      ( ( fAss_list_char(Exp1_61,List1_33,List2_33,Exp2_61) = fAss_list_char(Exp1_60,List1_32,List2_32,Exp2_60) )
    <=> ( ( Exp1_61 = Exp1_60 )
        & ( List1_33 = List1_32 )
        & ( List2_33 = List2_32 )
        & ( Exp2_61 = Exp2_60 ) ) ) ).

tff(fact_144_exp_Osimps_I7_J,axiom,
    ! [Exp_29: exp_list_char,List1_33: list_char,List2_33: list_char,Exp_28: exp_list_char,List1_32: list_char,List2_32: list_char] :
      ( ( fAcc_list_char(Exp_29,List1_33,List2_33) = fAcc_list_char(Exp_28,List1_32,List2_32) )
    <=> ( ( Exp_29 = Exp_28 )
        & ( List1_33 = List1_32 )
        & ( List2_33 = List2_32 ) ) ) ).

tff(fact_145_WTrtFAssNT,axiom,
    ! [Fa: list_char,Da: list_char,E_2: exp_list_char,T_2: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_1),nt))
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_2),T_2))
       => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,fAss_list_char(E_1,Fa,Da,E_2)),void)) ) ) ).

tff(fact_146_prod__cases5,axiom,
    ! [Y_3: produc1466422861on_val] :
      ~ ! [A_1: produc430140671on_val,B_1: produc2061676504on_val,C_4: list_exp_list_char,D: fun_na939144002on_val,E_3: fun_li1432931796on_val] : Y_3 != hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),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),E_3)))) ).

tff(fact_147_prod__cases5,axiom,
    ! [Y_3: produc231486621on_val] :
      ~ ! [A_1: produc1102272487on_val,B_1: produc124828825on_val,C_4: exp_list_char,D: fun_na939144002on_val,E_3: fun_li1432931796on_val] : Y_3 != hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),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),E_3)))) ).

tff(fact_148_prod__cases5,axiom,
    ! [Y_6: produc349695911t_char] :
      ~ ! [A_1: produc1285161482t_char,B_1: list_list_char,C_4: list_ty,D: list_val,E_3: exp_list_char] : Y_6 != hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),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),E_3)))) ).

tff(fact_149_prod__cases5,axiom,
    ! [Y_6: produc84451751t_char] :
      ~ ! [A_1: produc1971331930t_char,B_1: list_char,C_4: list_char,D: list_P1940453997har_ty,E_3: list_P341299826t_char] : Y_6 != hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,B_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,C_4),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,D),E_3)))) ).

tff(fact_150_prod__cases5,axiom,
    ! [Y_6: produc1013743697t_char] :
      ~ ! [A_1: list_char,B_1: list_ty,C_4: ty,D: list_list_char,E_3: exp_list_char] : Y_6 != hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),hAPP_P976433298t_char(hAPP_l2048923787t_char(produc2016959032t_char,B_1),hAPP_P1661798543t_char(hAPP_t1369077401t_char(produc1545444669t_char,C_4),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,D),E_3)))) ).

tff(fact_151_prod__cases4,axiom,
    ! [Y_5: produc1013743697t_char] :
      ~ ! [A_1: list_char,B_1: list_ty,C_4: ty,D: produc809539159t_char] : Y_5 != hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),hAPP_P976433298t_char(hAPP_l2048923787t_char(produc2016959032t_char,B_1),hAPP_P1661798543t_char(hAPP_t1369077401t_char(produc1545444669t_char,C_4),D))) ).

tff(fact_152_prod__cases4,axiom,
    ! [Y_3: produc1102272487on_val] :
      ~ ! [A_1: produc124828825on_val,B_1: exp_list_char,C_4: fun_na939144002on_val,D: fun_li1432931796on_val] : Y_3 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_4),D))) ).

tff(fact_153_prod__cases4,axiom,
    ! [Y_3: produc430140671on_val] :
      ~ ! [A_1: produc2061676504on_val,B_1: list_exp_list_char,C_4: fun_na939144002on_val,D: fun_li1432931796on_val] : Y_3 != hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,B_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_4),D))) ).

tff(fact_154_prod__cases4,axiom,
    ! [Y_5: produc1285161482t_char] :
      ~ ! [A_1: list_list_char,B_1: list_ty,C_4: list_val,D: exp_list_char] : Y_5 != hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,C_4),D))) ).

tff(fact_155_prod__cases4,axiom,
    ! [Y_5: produc1971331930t_char] :
      ~ ! [A_1: list_char,B_1: list_char,C_4: list_P1940453997har_ty,D: list_P341299826t_char] : Y_5 != hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,C_4),D))) ).

tff(fact_156_prod__cases4,axiom,
    ! [Y_3: produc231486621on_val] :
      ~ ! [A_1: produc1102272487on_val,B_1: produc124828825on_val,C_4: exp_list_char,D: produc12694297on_val] : Y_3 != hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_4),D))) ).

tff(fact_157_prod__cases4,axiom,
    ! [Y_3: produc1466422861on_val] :
      ~ ! [A_1: produc430140671on_val,B_1: produc2061676504on_val,C_4: list_exp_list_char,D: produc12694297on_val] : Y_3 != hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,C_4),D))) ).

tff(fact_158_prod__cases4,axiom,
    ! [Y_5: produc349695911t_char] :
      ~ ! [A_1: produc1285161482t_char,B_1: list_list_char,C_4: list_ty,D: produc662261637t_char] : Y_5 != hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,C_4),D))) ).

tff(fact_159_prod__cases4,axiom,
    ! [Y_5: produc1406897475t_char] :
      ~ ! [A_1: produc220283002t_char,B_1: list_ty,C_4: list_val,D: exp_list_char] : Y_5 != hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,C_4),D))) ).

tff(fact_160_prod__cases4,axiom,
    ! [Y_5: produc630464863al_val] :
      ~ ! [A_1: produc1645268488al_val,B_1: bop,C_4: val,D: val] : Y_5 != hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_1),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,B_1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,C_4),D))) ).

tff(fact_161_prod__cases4,axiom,
    ! [Y_5: produc84451751t_char] :
      ~ ! [A_1: produc1971331930t_char,B_1: list_char,C_4: list_char,D: produc2146869324t_char] : Y_5 != hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,B_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,C_4),D))) ).

tff(fact_162_prod__cases4,axiom,
    ! [Y_5: produc740765671t_char] :
      ~ ! [A_1: produc952412819t_char,B_1: list_char,C_4: list_P1940453997har_ty,D: list_P341299826t_char] : Y_5 != hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,C_4),D))) ).

tff(fact_163_prod__induct4,axiom,
    ! [X_2: produc1013743697t_char,Pa: fun_Pr70170387r_bool] :
      ( ! [A_1: list_char,B_1: list_ty,C_4: ty,D: produc809539159t_char] : hBOOL(hAPP_P1384137393r_bool(Pa,hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),hAPP_P976433298t_char(hAPP_l2048923787t_char(produc2016959032t_char,B_1),hAPP_P1661798543t_char(hAPP_t1369077401t_char(produc1545444669t_char,C_4),D)))))
     => hBOOL(hAPP_P1384137393r_bool(Pa,X_2)) ) ).

tff(fact_164_prod__induct4,axiom,
    ! [X_2: produc1102272487on_val,Pa: fun_Pr691271849l_bool] :
      ( ! [A_1: produc124828825on_val,B_1: exp_list_char,C_4: fun_na939144002on_val,D: fun_li1432931796on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_4),D)))))
     => hBOOL(hAPP_P282169671l_bool(Pa,X_2)) ) ).

tff(fact_165_prod__induct4,axiom,
    ! [X_2: produc430140671on_val,Pa: fun_Pr859510977l_bool] :
      ( ! [A_1: produc2061676504on_val,B_1: list_exp_list_char,C_4: fun_na939144002on_val,D: fun_li1432931796on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,B_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_4),D)))))
     => hBOOL(hAPP_P1333315679l_bool(Pa,X_2)) ) ).

tff(fact_166_prod__induct4,axiom,
    ! [X_2: produc1285161482t_char,Pa: fun_Pr227936640r_bool] :
      ( ! [A_1: list_list_char,B_1: list_ty,C_4: list_val,D: exp_list_char] : hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,C_4),D)))))
     => hBOOL(hAPP_P92196306r_bool(Pa,X_2)) ) ).

tff(fact_167_prod__induct4,axiom,
    ! [X_2: produc1971331930t_char,Pa: fun_Pr1861226704r_bool] :
      ( ! [A_1: list_char,B_1: list_char,C_4: list_P1940453997har_ty,D: list_P341299826t_char] : hBOOL(hAPP_P1680401186r_bool(Pa,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,C_4),D)))))
     => hBOOL(hAPP_P1680401186r_bool(Pa,X_2)) ) ).

tff(fact_168_prod__induct4,axiom,
    ! [X_2: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
      ( ! [A_1: produc1102272487on_val,B_1: produc124828825on_val,C_4: exp_list_char,D: produc12694297on_val] : hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_4),D)))))
     => hBOOL(hAPP_P378063101l_bool(Pa,X_2)) ) ).

tff(fact_169_prod__induct4,axiom,
    ! [X_2: produc1466422861on_val,Pa: fun_Pr302334223l_bool] :
      ( ! [A_1: produc430140671on_val,B_1: produc2061676504on_val,C_4: list_exp_list_char,D: produc12694297on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,C_4),D)))))
     => hBOOL(hAPP_P2028072621l_bool(Pa,X_2)) ) ).

tff(fact_170_prod__induct4,axiom,
    ! [X_2: produc349695911t_char,Pa: fun_Pr1895638121r_bool] :
      ( ! [A_1: produc1285161482t_char,B_1: list_list_char,C_4: list_ty,D: produc662261637t_char] : hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,C_4),D)))))
     => hBOOL(hAPP_P824029447r_bool(Pa,X_2)) ) ).

tff(fact_171_prod__induct4,axiom,
    ! [X_2: produc1406897475t_char,Pa: fun_Pr1728267013r_bool] :
      ( ! [A_1: produc220283002t_char,B_1: list_ty,C_4: list_val,D: exp_list_char] : hBOOL(hAPP_P1240100515r_bool(Pa,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,C_4),D)))))
     => hBOOL(hAPP_P1240100515r_bool(Pa,X_2)) ) ).

tff(fact_172_prod__induct4,axiom,
    ! [X_2: produc630464863al_val,Pa: fun_Pr897334561l_bool] :
      ( ! [A_1: produc1645268488al_val,B_1: bop,C_4: val,D: val] : hBOOL(hAPP_P738987199l_bool(Pa,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_1),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,B_1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,C_4),D)))))
     => hBOOL(hAPP_P738987199l_bool(Pa,X_2)) ) ).

tff(fact_173_prod__induct4,axiom,
    ! [X_2: produc84451751t_char,Pa: fun_Pr981088873r_bool] :
      ( ! [A_1: produc1971331930t_char,B_1: list_char,C_4: list_char,D: produc2146869324t_char] : hBOOL(hAPP_P975284999r_bool(Pa,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,B_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,C_4),D)))))
     => hBOOL(hAPP_P975284999r_bool(Pa,X_2)) ) ).

tff(fact_174_prod__induct4,axiom,
    ! [X_2: produc740765671t_char,Pa: fun_Pr1538825897r_bool] :
      ( ! [A_1: produc952412819t_char,B_1: list_char,C_4: list_P1940453997har_ty,D: list_P341299826t_char] : hBOOL(hAPP_P929449287r_bool(Pa,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,C_4),D)))))
     => hBOOL(hAPP_P929449287r_bool(Pa,X_2)) ) ).

tff(fact_175_prod__cases3,axiom,
    ! [Y_4: produc469582463har_ty] :
      ~ ! [A_1: list_char,B_1: list_char,C_4: ty] : Y_4 != hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,A_1),hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,B_1),C_4)) ).

tff(fact_176_prod__cases3,axiom,
    ! [Y_4: produc1013743697t_char] :
      ~ ! [A_1: list_char,B_1: list_ty,C_4: produc1059328077t_char] : Y_4 != hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),hAPP_P976433298t_char(hAPP_l2048923787t_char(produc2016959032t_char,B_1),C_4)) ).

tff(fact_177_prod__cases3,axiom,
    ! [Y_3: produc1102272487on_val] :
      ~ ! [A_1: produc124828825on_val,B_1: exp_list_char,C_4: produc12694297on_val] : Y_3 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B_1),C_4)) ).

tff(fact_178_prod__cases3,axiom,
    ! [Y_3: produc124828825on_val] :
      ~ ! [A_1: exp_list_char,B_1: fun_na939144002on_val,C_4: fun_li1432931796on_val] : Y_3 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_1),C_4)) ).

tff(fact_179_prod__cases3,axiom,
    ! [Y_3: produc430140671on_val] :
      ~ ! [A_1: produc2061676504on_val,B_1: list_exp_list_char,C_4: produc12694297on_val] : Y_3 != hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,B_1),C_4)) ).

tff(fact_180_prod__cases3,axiom,
    ! [Y_3: produc2061676504on_val] :
      ~ ! [A_1: list_exp_list_char,B_1: fun_na939144002on_val,C_4: fun_li1432931796on_val] : Y_3 != hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_1),C_4)) ).

tff(fact_181_prod__cases3,axiom,
    ! [Y_4: produc1285161482t_char] :
      ~ ! [A_1: list_list_char,B_1: list_ty,C_4: produc662261637t_char] : Y_4 != hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_1),C_4)) ).

tff(fact_182_prod__cases3,axiom,
    ! [Y_4: produc220283002t_char] :
      ~ ! [A_1: list_ty,B_1: list_val,C_4: exp_list_char] : Y_4 != hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,B_1),C_4)) ).

tff(fact_183_prod__cases3,axiom,
    ! [Y_4: produc1645268488al_val] :
      ~ ! [A_1: bop,B_1: val,C_4: val] : Y_4 != hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B_1),C_4)) ).

tff(fact_184_prod__cases3,axiom,
    ! [Y_4: produc1971331930t_char] :
      ~ ! [A_1: list_char,B_1: list_char,C_4: produc2146869324t_char] : Y_4 != hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_1),C_4)) ).

tff(fact_185_prod__cases3,axiom,
    ! [Y_4: produc952412819t_char] :
      ~ ! [A_1: list_char,B_1: list_P1940453997har_ty,C_4: list_P341299826t_char] : Y_4 != hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,B_1),C_4)) ).

tff(fact_186_prod__cases3,axiom,
    ! [Y_3: produc409205479on_val] :
      ~ ! [A_1: produc12694297on_val,B_1: fun_na939144002on_val,C_4: fun_li1432931796on_val] : Y_3 != hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_1),C_4)) ).

tff(fact_187_prod__cases3,axiom,
    ! [Y_3: produc231486621on_val] :
      ~ ! [A_1: produc1102272487on_val,B_1: produc124828825on_val,C_4: produc124828825on_val] : Y_3 != hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_1),C_4)) ).

tff(fact_188_prod__cases3,axiom,
    ! [Y_3: produc1466422861on_val] :
      ~ ! [A_1: produc430140671on_val,B_1: produc2061676504on_val,C_4: produc2061676504on_val] : Y_3 != hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_1),C_4)) ).

tff(fact_189_prod__cases3,axiom,
    ! [Y_4: produc349695911t_char] :
      ~ ! [A_1: produc1285161482t_char,B_1: list_list_char,C_4: produc220283002t_char] : Y_4 != hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_1),C_4)) ).

tff(fact_190_prod__cases3,axiom,
    ! [Y_4: produc1406897475t_char] :
      ~ ! [A_1: produc220283002t_char,B_1: list_ty,C_4: produc662261637t_char] : Y_4 != hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_1),C_4)) ).

tff(fact_191_prod__cases3,axiom,
    ! [Y_4: produc1826280281t_char] :
      ~ ! [A_1: produc662261637t_char,B_1: list_val,C_4: exp_list_char] : Y_4 != hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,B_1),C_4)) ).

tff(fact_192_prod__cases3,axiom,
    ! [Y_4: produc630464863al_val] :
      ~ ! [A_1: produc1645268488al_val,B_1: bop,C_4: product_prod_val_val] : Y_4 != hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_1),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,B_1),C_4)) ).

tff(fact_193_prod__cases3,axiom,
    ! [Y_4: produc800118557al_val] :
      ~ ! [A_1: product_prod_val_val,B_1: val,C_4: val] : Y_4 != hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B_1),C_4)) ).

tff(fact_194_prod__cases3,axiom,
    ! [Y_3: produc87279271on_val] :
      ~ ! [A_1: produc639455274on_val,B_1: list_char,C_4: fun_Pr806764899on_val] : Y_3 != hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_1),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,B_1),C_4)) ).

tff(fact_195_prod__cases3,axiom,
    ! [Y_4: produc1350825965t_char] :
      ~ ! [A_1: produc1278157519t_char,B_1: list_char,C_4: list_char] : Y_4 != hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_1),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B_1),C_4)) ).

tff(fact_196_prod__cases3,axiom,
    ! [Y_4: produc84451751t_char] :
      ~ ! [A_1: produc1971331930t_char,B_1: list_char,C_4: produc952412819t_char] : Y_4 != hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,B_1),C_4)) ).

tff(fact_197_prod__cases3,axiom,
    ! [Y_4: produc740765671t_char] :
      ~ ! [A_1: produc952412819t_char,B_1: list_char,C_4: produc2146869324t_char] : Y_4 != hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_1),C_4)) ).

tff(fact_198_prod__cases3,axiom,
    ! [Y_4: produc494726439t_char] :
      ~ ! [A_1: produc2146869324t_char,B_1: list_P1940453997har_ty,C_4: list_P341299826t_char] : Y_4 != hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,B_1),C_4)) ).

tff(fact_199_prod__cases3,axiom,
    ! [Y_4: produc1534059751t_char] :
      ~ ! [A_1: produc809539159t_char,B_1: list_list_char,C_4: exp_list_char] : Y_4 != hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_1),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,B_1),C_4)) ).

tff(fact_200_prod__cases3,axiom,
    ! [Y_4: produc1312961703ar_val] :
      ~ ! [A_1: produc1147203250ar_val,B_1: produc1278157519t_char,C_4: val] : Y_4 != hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,A_1),hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,B_1),C_4)) ).

tff(fact_201_prod__induct3,axiom,
    ! [X_2: produc469582463har_ty,Pa: fun_Pr758558581y_bool] :
      ( ! [A_1: list_char,B_1: list_char,C_4: ty] : hBOOL(hAPP_P831231943y_bool(Pa,hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,A_1),hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,B_1),C_4))))
     => hBOOL(hAPP_P831231943y_bool(Pa,X_2)) ) ).

tff(fact_202_prod__induct3,axiom,
    ! [X_2: produc1013743697t_char,Pa: fun_Pr70170387r_bool] :
      ( ! [A_1: list_char,B_1: list_ty,C_4: produc1059328077t_char] : hBOOL(hAPP_P1384137393r_bool(Pa,hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),hAPP_P976433298t_char(hAPP_l2048923787t_char(produc2016959032t_char,B_1),C_4))))
     => hBOOL(hAPP_P1384137393r_bool(Pa,X_2)) ) ).

tff(fact_203_prod__induct3,axiom,
    ! [X_2: produc1102272487on_val,Pa: fun_Pr691271849l_bool] :
      ( ! [A_1: produc124828825on_val,B_1: exp_list_char,C_4: produc12694297on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B_1),C_4))))
     => hBOOL(hAPP_P282169671l_bool(Pa,X_2)) ) ).

tff(fact_204_prod__induct3,axiom,
    ! [X_2: produc124828825on_val,Pa: fun_Pr680585871l_bool] :
      ( ! [A_1: exp_list_char,B_1: fun_na939144002on_val,C_4: fun_li1432931796on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_1),C_4))))
     => hBOOL(hAPP_P1708370145l_bool(Pa,X_2)) ) ).

tff(fact_205_prod__induct3,axiom,
    ! [X_2: produc430140671on_val,Pa: fun_Pr859510977l_bool] :
      ( ! [A_1: produc2061676504on_val,B_1: list_exp_list_char,C_4: produc12694297on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,B_1),C_4))))
     => hBOOL(hAPP_P1333315679l_bool(Pa,X_2)) ) ).

tff(fact_206_prod__induct3,axiom,
    ! [X_2: produc2061676504on_val,Pa: fun_Pr248118298l_bool] :
      ( ! [A_1: list_exp_list_char,B_1: fun_na939144002on_val,C_4: fun_li1432931796on_val] : hBOOL(hAPP_P71593144l_bool(Pa,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_1),C_4))))
     => hBOOL(hAPP_P71593144l_bool(Pa,X_2)) ) ).

tff(fact_207_prod__induct3,axiom,
    ! [X_2: produc1285161482t_char,Pa: fun_Pr227936640r_bool] :
      ( ! [A_1: list_list_char,B_1: list_ty,C_4: produc662261637t_char] : hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_1),C_4))))
     => hBOOL(hAPP_P92196306r_bool(Pa,X_2)) ) ).

tff(fact_208_prod__induct3,axiom,
    ! [X_2: produc220283002t_char,Pa: fun_Pr46158268r_bool] :
      ( ! [A_1: list_ty,B_1: list_val,C_4: exp_list_char] : hBOOL(hAPP_P1907982426r_bool(Pa,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,B_1),C_4))))
     => hBOOL(hAPP_P1907982426r_bool(Pa,X_2)) ) ).

tff(fact_209_prod__induct3,axiom,
    ! [X_2: produc1645268488al_val,Pa: fun_Pr252072522l_bool] :
      ( ! [A_1: bop,B_1: val,C_4: val] : hBOOL(hAPP_P943837928l_bool(Pa,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B_1),C_4))))
     => hBOOL(hAPP_P943837928l_bool(Pa,X_2)) ) ).

tff(fact_210_prod__induct3,axiom,
    ! [X_2: produc1971331930t_char,Pa: fun_Pr1861226704r_bool] :
      ( ! [A_1: list_char,B_1: list_char,C_4: produc2146869324t_char] : hBOOL(hAPP_P1680401186r_bool(Pa,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_1),C_4))))
     => hBOOL(hAPP_P1680401186r_bool(Pa,X_2)) ) ).

tff(fact_211_prod__induct3,axiom,
    ! [X_2: produc952412819t_char,Pa: fun_Pr1898949769r_bool] :
      ( ! [A_1: list_char,B_1: list_P1940453997har_ty,C_4: list_P341299826t_char] : hBOOL(hAPP_P659547099r_bool(Pa,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,B_1),C_4))))
     => hBOOL(hAPP_P659547099r_bool(Pa,X_2)) ) ).

tff(fact_212_prod__induct3,axiom,
    ! [X_2: produc409205479on_val,Pa: fun_Pr693020585l_bool] :
      ( ! [A_1: produc12694297on_val,B_1: fun_na939144002on_val,C_4: fun_li1432931796on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_1),C_4))))
     => hBOOL(hAPP_P1221872711l_bool(Pa,X_2)) ) ).

tff(fact_213_prod__induct3,axiom,
    ! [X_2: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
      ( ! [A_1: produc1102272487on_val,B_1: produc124828825on_val,C_4: produc124828825on_val] : hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_1),C_4))))
     => hBOOL(hAPP_P378063101l_bool(Pa,X_2)) ) ).

tff(fact_214_prod__induct3,axiom,
    ! [X_2: produc1466422861on_val,Pa: fun_Pr302334223l_bool] :
      ( ! [A_1: produc430140671on_val,B_1: produc2061676504on_val,C_4: produc2061676504on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_1),C_4))))
     => hBOOL(hAPP_P2028072621l_bool(Pa,X_2)) ) ).

tff(fact_215_prod__induct3,axiom,
    ! [X_2: produc349695911t_char,Pa: fun_Pr1895638121r_bool] :
      ( ! [A_1: produc1285161482t_char,B_1: list_list_char,C_4: produc220283002t_char] : hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_1),C_4))))
     => hBOOL(hAPP_P824029447r_bool(Pa,X_2)) ) ).

tff(fact_216_prod__induct3,axiom,
    ! [X_2: produc1406897475t_char,Pa: fun_Pr1728267013r_bool] :
      ( ! [A_1: produc220283002t_char,B_1: list_ty,C_4: produc662261637t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_1),C_4))))
     => hBOOL(hAPP_P1240100515r_bool(Pa,X_2)) ) ).

tff(fact_217_prod__induct3,axiom,
    ! [X_2: produc1826280281t_char,Pa: fun_Pr1890037787r_bool] :
      ( ! [A_1: produc662261637t_char,B_1: list_val,C_4: exp_list_char] : hBOOL(hAPP_P1183499705r_bool(Pa,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,B_1),C_4))))
     => hBOOL(hAPP_P1183499705r_bool(Pa,X_2)) ) ).

tff(fact_218_prod__induct3,axiom,
    ! [X_2: produc630464863al_val,Pa: fun_Pr897334561l_bool] :
      ( ! [A_1: produc1645268488al_val,B_1: bop,C_4: product_prod_val_val] : hBOOL(hAPP_P738987199l_bool(Pa,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_1),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,B_1),C_4))))
     => hBOOL(hAPP_P738987199l_bool(Pa,X_2)) ) ).

tff(fact_219_prod__induct3,axiom,
    ! [X_2: produc800118557al_val,Pa: fun_Pr832147423l_bool] :
      ( ! [A_1: product_prod_val_val,B_1: val,C_4: val] : hBOOL(hAPP_P2123002749l_bool(Pa,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B_1),C_4))))
     => hBOOL(hAPP_P2123002749l_bool(Pa,X_2)) ) ).

tff(fact_220_prod__induct3,axiom,
    ! [X_2: produc87279271on_val,Pa: fun_Pr235369833l_bool] :
      ( ! [A_1: produc639455274on_val,B_1: list_char,C_4: fun_Pr806764899on_val] : hBOOL(hAPP_P124632071l_bool(Pa,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_1),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,B_1),C_4))))
     => hBOOL(hAPP_P124632071l_bool(Pa,X_2)) ) ).

tff(fact_221_prod__induct3,axiom,
    ! [X_2: produc1350825965t_char,Pa: fun_Pr1336847023r_bool] :
      ( ! [A_1: produc1278157519t_char,B_1: list_char,C_4: list_char] : hBOOL(hAPP_P2010574925r_bool(Pa,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_1),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B_1),C_4))))
     => hBOOL(hAPP_P2010574925r_bool(Pa,X_2)) ) ).

tff(fact_222_prod__induct3,axiom,
    ! [X_2: produc84451751t_char,Pa: fun_Pr981088873r_bool] :
      ( ! [A_1: produc1971331930t_char,B_1: list_char,C_4: produc952412819t_char] : hBOOL(hAPP_P975284999r_bool(Pa,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,B_1),C_4))))
     => hBOOL(hAPP_P975284999r_bool(Pa,X_2)) ) ).

tff(fact_223_prod__induct3,axiom,
    ! [X_2: produc740765671t_char,Pa: fun_Pr1538825897r_bool] :
      ( ! [A_1: produc952412819t_char,B_1: list_char,C_4: produc2146869324t_char] : hBOOL(hAPP_P929449287r_bool(Pa,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_1),C_4))))
     => hBOOL(hAPP_P929449287r_bool(Pa,X_2)) ) ).

tff(fact_224_prod__induct3,axiom,
    ! [X_2: produc494726439t_char,Pa: fun_Pr286306793r_bool] :
      ( ! [A_1: produc2146869324t_char,B_1: list_P1940453997har_ty,C_4: list_P341299826t_char] : hBOOL(hAPP_P801803911r_bool(Pa,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,B_1),C_4))))
     => hBOOL(hAPP_P801803911r_bool(Pa,X_2)) ) ).

tff(fact_225_prod__induct3,axiom,
    ! [X_2: produc1534059751t_char,Pa: fun_Pr908866473r_bool] :
      ( ! [A_1: produc809539159t_char,B_1: list_list_char,C_4: exp_list_char] : hBOOL(hAPP_P1002912327r_bool(Pa,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_1),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,B_1),C_4))))
     => hBOOL(hAPP_P1002912327r_bool(Pa,X_2)) ) ).

tff(fact_226_prod__induct3,axiom,
    ! [X_2: produc1312961703ar_val,Pa: fun_Pr643382121l_bool] :
      ( ! [A_1: produc1147203250ar_val,B_1: produc1278157519t_char,C_4: val] : hBOOL(hAPP_P439015943l_bool(Pa,hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,A_1),hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,B_1),C_4))))
     => hBOOL(hAPP_P439015943l_bool(Pa,X_2)) ) ).

tff(fact_227_red__hext__incr,axiom,
    ! [Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: 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,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa)))
     => hBOOL(hext(Hb,H_b)) ) ).

tff(fact_228_red__lcl__add,axiom,
    ! [L_0_1: fun_li1432931796on_val,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: 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,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),map_ad325961431ar_val(L_0_1,Lb)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),map_ad325961431ar_val(L_0_1,L_b)))),red(Pa))) ) ).

tff(fact_229_prod_Oexhaust,axiom,
    ! [Y_2: produc469582463har_ty] :
      ~ ! [A_1: list_char,B_1: produc917948472har_ty] : Y_2 != hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,A_1),B_1) ).

tff(fact_230_prod_Oexhaust,axiom,
    ! [Y_2: produc917948472har_ty] :
      ~ ! [A_1: list_char,B_1: ty] : Y_2 != hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_1),B_1) ).

tff(fact_231_prod_Oexhaust,axiom,
    ! [Y_2: produc1312961703ar_val] :
      ~ ! [A_1: produc1147203250ar_val,B_1: produc1147203250ar_val] : Y_2 != hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,A_1),B_1) ).

tff(fact_232_prod_Oexhaust,axiom,
    ! [Y_2: produc1534059751t_char] :
      ~ ! [A_1: produc809539159t_char,B_1: produc809539159t_char] : Y_2 != hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_1),B_1) ).

tff(fact_233_prod_Oexhaust,axiom,
    ! [Y_2: produc494726439t_char] :
      ~ ! [A_1: produc2146869324t_char,B_1: produc2146869324t_char] : Y_2 != hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_1),B_1) ).

tff(fact_234_prod_Oexhaust,axiom,
    ! [Y_2: produc740765671t_char] :
      ~ ! [A_1: produc952412819t_char,B_1: produc952412819t_char] : Y_2 != hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_1),B_1) ).

tff(fact_235_prod_Oexhaust,axiom,
    ! [Y_2: produc84451751t_char] :
      ~ ! [A_1: produc1971331930t_char,B_1: produc1971331930t_char] : Y_2 != hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),B_1) ).

tff(fact_236_prod_Oexhaust,axiom,
    ! [Y_2: produc1350825965t_char] :
      ~ ! [A_1: produc1278157519t_char,B_1: produc1278157519t_char] : Y_2 != hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_1),B_1) ).

tff(fact_237_prod_Oexhaust,axiom,
    ! [Y_3: produc87279271on_val] :
      ~ ! [A_1: produc639455274on_val,B_1: produc639455274on_val] : Y_3 != hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_1),B_1) ).

tff(fact_238_prod_Oexhaust,axiom,
    ! [Y_2: produc800118557al_val] :
      ~ ! [A_1: product_prod_val_val,B_1: product_prod_val_val] : Y_2 != hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_1),B_1) ).

tff(fact_239_prod_Oexhaust,axiom,
    ! [Y_2: produc630464863al_val] :
      ~ ! [A_1: produc1645268488al_val,B_1: produc1645268488al_val] : Y_2 != hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_1),B_1) ).

tff(fact_240_prod_Oexhaust,axiom,
    ! [Y_2: produc1826280281t_char] :
      ~ ! [A_1: produc662261637t_char,B_1: produc662261637t_char] : Y_2 != hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_1),B_1) ).

tff(fact_241_prod_Oexhaust,axiom,
    ! [Y_2: produc1406897475t_char] :
      ~ ! [A_1: produc220283002t_char,B_1: produc220283002t_char] : Y_2 != hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_1),B_1) ).

tff(fact_242_prod_Oexhaust,axiom,
    ! [Y_2: produc349695911t_char] :
      ~ ! [A_1: produc1285161482t_char,B_1: produc1285161482t_char] : Y_2 != hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),B_1) ).

tff(fact_243_prod_Oexhaust,axiom,
    ! [Y_3: produc1466422861on_val] :
      ~ ! [A_1: produc430140671on_val,B_1: produc430140671on_val] : Y_3 != hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),B_1) ).

tff(fact_244_prod_Oexhaust,axiom,
    ! [Y_3: produc231486621on_val] :
      ~ ! [A_1: produc1102272487on_val,B_1: produc1102272487on_val] : Y_3 != hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),B_1) ).

tff(fact_245_prod_Oexhaust,axiom,
    ! [Y_3: produc409205479on_val] :
      ~ ! [A_1: produc12694297on_val,B_1: produc12694297on_val] : Y_3 != hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_1),B_1) ).

tff(fact_246_prod_Oexhaust,axiom,
    ! [Y_2: produc245756905har_ty] :
      ~ ! [A_1: produc1278157519t_char,B_1: ty] : Y_2 != hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_1),B_1) ).

tff(fact_247_prod_Oexhaust,axiom,
    ! [Y_2: produc1013743697t_char] :
      ~ ! [A_1: list_char,B_1: produc1025221954t_char] : Y_2 != hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),B_1) ).

tff(fact_248_prod_Oexhaust,axiom,
    ! [Y_3: produc12694297on_val] :
      ~ ! [A_1: fun_na939144002on_val,B_1: fun_li1432931796on_val] : Y_3 != hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_1) ).

tff(fact_249_prod_Oexhaust,axiom,
    ! [Y_3: produc1102272487on_val] :
      ~ ! [A_1: produc124828825on_val,B_1: produc124828825on_val] : Y_3 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_1) ).

tff(fact_250_prod_Oexhaust,axiom,
    ! [Y_3: produc124828825on_val] :
      ~ ! [A_1: exp_list_char,B_1: produc12694297on_val] : Y_3 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_1) ).

tff(fact_251_prod_Oexhaust,axiom,
    ! [Y_3: produc430140671on_val] :
      ~ ! [A_1: produc2061676504on_val,B_1: produc2061676504on_val] : Y_3 != hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_1) ).

tff(fact_252_prod_Oexhaust,axiom,
    ! [Y_3: produc2061676504on_val] :
      ~ ! [A_1: list_exp_list_char,B_1: produc12694297on_val] : Y_3 != hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_1) ).

tff(fact_253_prod_Oexhaust,axiom,
    ! [Y_2: produc1285161482t_char] :
      ~ ! [A_1: list_list_char,B_1: produc220283002t_char] : Y_2 != hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_1) ).

tff(fact_254_prod_Oexhaust,axiom,
    ! [Y_2: produc220283002t_char] :
      ~ ! [A_1: list_ty,B_1: produc662261637t_char] : Y_2 != hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_1) ).

tff(fact_255_prod_Oexhaust,axiom,
    ! [Y_2: produc662261637t_char] :
      ~ ! [A_1: list_val,B_1: exp_list_char] : Y_2 != hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_1) ).

tff(fact_256_prod_Oexhaust,axiom,
    ! [Y_2: produc1645268488al_val] :
      ~ ! [A_1: bop,B_1: product_prod_val_val] : Y_2 != hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_1) ).

tff(fact_257_prod_Oexhaust,axiom,
    ! [Y_2: product_prod_val_val] :
      ~ ! [A_1: val,B_1: val] : Y_2 != hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_1) ).

tff(fact_258_prod_Oexhaust,axiom,
    ! [Y_3: produc639455274on_val] :
      ~ ! [A_1: list_char,B_1: fun_Pr806764899on_val] : Y_3 != hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_1) ).

tff(fact_259_prod_Oexhaust,axiom,
    ! [Y_2: produc1278157519t_char] :
      ~ ! [A_1: list_char,B_1: list_char] : Y_2 != hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_1) ).

tff(fact_260_prod_Oexhaust,axiom,
    ! [Y_2: produc1971331930t_char] :
      ~ ! [A_1: list_char,B_1: produc952412819t_char] : Y_2 != hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_1) ).

tff(fact_261_prod_Oexhaust,axiom,
    ! [Y_2: produc952412819t_char] :
      ~ ! [A_1: list_char,B_1: produc2146869324t_char] : Y_2 != hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_1) ).

tff(fact_262_prod_Oexhaust,axiom,
    ! [Y_2: produc2146869324t_char] :
      ~ ! [A_1: list_P1940453997har_ty,B_1: list_P341299826t_char] : Y_2 != hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_1) ).

tff(fact_263_prod_Oexhaust,axiom,
    ! [Y_2: produc809539159t_char] :
      ~ ! [A_1: list_list_char,B_1: exp_list_char] : Y_2 != hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_1) ).

tff(fact_264_prod_Oexhaust,axiom,
    ! [Y_2: produc1147203250ar_val] :
      ~ ! [A_1: produc1278157519t_char,B_1: val] : Y_2 != hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_1),B_1) ).

tff(fact_265_PairE,axiom,
    ! [P_2: produc469582463har_ty] :
      ~ ! [X_1: list_char,Y_1: produc917948472har_ty] : P_2 != hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,X_1),Y_1) ).

tff(fact_266_PairE,axiom,
    ! [P_2: produc917948472har_ty] :
      ~ ! [X_1: list_char,Y_1: ty] : P_2 != hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,X_1),Y_1) ).

tff(fact_267_PairE,axiom,
    ! [P_2: produc1312961703ar_val] :
      ~ ! [X_1: produc1147203250ar_val,Y_1: produc1147203250ar_val] : P_2 != hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,X_1),Y_1) ).

tff(fact_268_PairE,axiom,
    ! [P_2: produc1534059751t_char] :
      ~ ! [X_1: produc809539159t_char,Y_1: produc809539159t_char] : P_2 != hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,X_1),Y_1) ).

tff(fact_269_PairE,axiom,
    ! [P_2: produc494726439t_char] :
      ~ ! [X_1: produc2146869324t_char,Y_1: produc2146869324t_char] : P_2 != hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,X_1),Y_1) ).

tff(fact_270_PairE,axiom,
    ! [P_2: produc740765671t_char] :
      ~ ! [X_1: produc952412819t_char,Y_1: produc952412819t_char] : P_2 != hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,X_1),Y_1) ).

tff(fact_271_PairE,axiom,
    ! [P_2: produc84451751t_char] :
      ~ ! [X_1: produc1971331930t_char,Y_1: produc1971331930t_char] : P_2 != hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,X_1),Y_1) ).

tff(fact_272_PairE,axiom,
    ! [P_2: produc1350825965t_char] :
      ~ ! [X_1: produc1278157519t_char,Y_1: produc1278157519t_char] : P_2 != hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,X_1),Y_1) ).

tff(fact_273_PairE,axiom,
    ! [P_1: produc87279271on_val] :
      ~ ! [X_1: produc639455274on_val,Y_1: produc639455274on_val] : P_1 != hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,X_1),Y_1) ).

tff(fact_274_PairE,axiom,
    ! [P_2: produc800118557al_val] :
      ~ ! [X_1: product_prod_val_val,Y_1: product_prod_val_val] : P_2 != hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,X_1),Y_1) ).

tff(fact_275_PairE,axiom,
    ! [P_2: produc630464863al_val] :
      ~ ! [X_1: produc1645268488al_val,Y_1: produc1645268488al_val] : P_2 != hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,X_1),Y_1) ).

tff(fact_276_PairE,axiom,
    ! [P_2: produc1826280281t_char] :
      ~ ! [X_1: produc662261637t_char,Y_1: produc662261637t_char] : P_2 != hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,X_1),Y_1) ).

tff(fact_277_PairE,axiom,
    ! [P_2: produc1406897475t_char] :
      ~ ! [X_1: produc220283002t_char,Y_1: produc220283002t_char] : P_2 != hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,X_1),Y_1) ).

tff(fact_278_PairE,axiom,
    ! [P_2: produc349695911t_char] :
      ~ ! [X_1: produc1285161482t_char,Y_1: produc1285161482t_char] : P_2 != hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,X_1),Y_1) ).

tff(fact_279_PairE,axiom,
    ! [P_1: produc1466422861on_val] :
      ~ ! [X_1: produc430140671on_val,Y_1: produc430140671on_val] : P_1 != hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,X_1),Y_1) ).

tff(fact_280_PairE,axiom,
    ! [P_1: produc231486621on_val] :
      ~ ! [X_1: produc1102272487on_val,Y_1: produc1102272487on_val] : P_1 != hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,X_1),Y_1) ).

tff(fact_281_PairE,axiom,
    ! [P_1: produc409205479on_val] :
      ~ ! [X_1: produc12694297on_val,Y_1: produc12694297on_val] : P_1 != hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,X_1),Y_1) ).

tff(fact_282_PairE,axiom,
    ! [P_2: produc245756905har_ty] :
      ~ ! [X_1: produc1278157519t_char,Y_1: ty] : P_2 != hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,X_1),Y_1) ).

tff(fact_283_PairE,axiom,
    ! [P_2: produc1013743697t_char] :
      ~ ! [X_1: list_char,Y_1: produc1025221954t_char] : P_2 != hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,X_1),Y_1) ).

tff(fact_284_PairE,axiom,
    ! [P_1: produc12694297on_val] :
      ~ ! [X_1: fun_na939144002on_val,Y_1: fun_li1432931796on_val] : P_1 != hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X_1),Y_1) ).

tff(fact_285_PairE,axiom,
    ! [P_1: produc1102272487on_val] :
      ~ ! [X_1: produc124828825on_val,Y_1: produc124828825on_val] : P_1 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X_1),Y_1) ).

tff(fact_286_PairE,axiom,
    ! [P_1: produc124828825on_val] :
      ~ ! [X_1: exp_list_char,Y_1: produc12694297on_val] : P_1 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X_1),Y_1) ).

tff(fact_287_PairE,axiom,
    ! [P_1: produc430140671on_val] :
      ~ ! [X_1: produc2061676504on_val,Y_1: produc2061676504on_val] : P_1 != hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,X_1),Y_1) ).

tff(fact_288_PairE,axiom,
    ! [P_1: produc2061676504on_val] :
      ~ ! [X_1: list_exp_list_char,Y_1: produc12694297on_val] : P_1 != hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,X_1),Y_1) ).

tff(fact_289_PairE,axiom,
    ! [P_2: produc1285161482t_char] :
      ~ ! [X_1: list_list_char,Y_1: produc220283002t_char] : P_2 != hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,X_1),Y_1) ).

tff(fact_290_PairE,axiom,
    ! [P_2: produc220283002t_char] :
      ~ ! [X_1: list_ty,Y_1: produc662261637t_char] : P_2 != hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,X_1),Y_1) ).

tff(fact_291_PairE,axiom,
    ! [P_2: produc662261637t_char] :
      ~ ! [X_1: list_val,Y_1: exp_list_char] : P_2 != hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,X_1),Y_1) ).

tff(fact_292_PairE,axiom,
    ! [P_2: produc1645268488al_val] :
      ~ ! [X_1: bop,Y_1: product_prod_val_val] : P_2 != hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,X_1),Y_1) ).

tff(fact_293_PairE,axiom,
    ! [P_2: product_prod_val_val] :
      ~ ! [X_1: val,Y_1: val] : P_2 != hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_1),Y_1) ).

tff(fact_294_PairE,axiom,
    ! [P_1: produc639455274on_val] :
      ~ ! [X_1: list_char,Y_1: fun_Pr806764899on_val] : P_1 != hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,X_1),Y_1) ).

tff(fact_295_PairE,axiom,
    ! [P_2: produc1278157519t_char] :
      ~ ! [X_1: list_char,Y_1: list_char] : P_2 != hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_1),Y_1) ).

tff(fact_296_PairE,axiom,
    ! [P_2: produc1971331930t_char] :
      ~ ! [X_1: list_char,Y_1: produc952412819t_char] : P_2 != hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,X_1),Y_1) ).

tff(fact_297_PairE,axiom,
    ! [P_2: produc952412819t_char] :
      ~ ! [X_1: list_char,Y_1: produc2146869324t_char] : P_2 != hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,X_1),Y_1) ).

tff(fact_298_PairE,axiom,
    ! [P_2: produc2146869324t_char] :
      ~ ! [X_1: list_P1940453997har_ty,Y_1: list_P341299826t_char] : P_2 != hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,X_1),Y_1) ).

tff(fact_299_PairE,axiom,
    ! [P_2: produc809539159t_char] :
      ~ ! [X_1: list_list_char,Y_1: exp_list_char] : P_2 != hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,X_1),Y_1) ).

tff(fact_300_PairE,axiom,
    ! [P_2: produc1147203250ar_val] :
      ~ ! [X_1: produc1278157519t_char,Y_1: val] : P_2 != hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,X_1),Y_1) ).

tff(fact_301_split__paired__Ex,axiom,
    ! [Pa: fun_Pr758558581y_bool] :
      ( ? [X1: produc469582463har_ty] : hBOOL(hAPP_P831231943y_bool(Pa,X1))
    <=> ? [A_1: list_char,B_1: produc917948472har_ty] : hBOOL(hAPP_P831231943y_bool(Pa,hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,A_1),B_1))) ) ).

tff(fact_302_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1127025070y_bool] :
      ( ? [X1: produc917948472har_ty] : hBOOL(hAPP_P748443392y_bool(Pa,X1))
    <=> ? [A_1: list_char,B_1: ty] : hBOOL(hAPP_P748443392y_bool(Pa,hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_1),B_1))) ) ).

tff(fact_303_split__paired__Ex,axiom,
    ! [Pa: fun_Pr643382121l_bool] :
      ( ? [X1: produc1312961703ar_val] : hBOOL(hAPP_P439015943l_bool(Pa,X1))
    <=> ? [A_1: produc1147203250ar_val,B_1: produc1147203250ar_val] : hBOOL(hAPP_P439015943l_bool(Pa,hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,A_1),B_1))) ) ).

tff(fact_304_split__paired__Ex,axiom,
    ! [Pa: fun_Pr908866473r_bool] :
      ( ? [X1: produc1534059751t_char] : hBOOL(hAPP_P1002912327r_bool(Pa,X1))
    <=> ? [A_1: produc809539159t_char,B_1: produc809539159t_char] : hBOOL(hAPP_P1002912327r_bool(Pa,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_1),B_1))) ) ).

tff(fact_305_split__paired__Ex,axiom,
    ! [Pa: fun_Pr286306793r_bool] :
      ( ? [X1: produc494726439t_char] : hBOOL(hAPP_P801803911r_bool(Pa,X1))
    <=> ? [A_1: produc2146869324t_char,B_1: produc2146869324t_char] : hBOOL(hAPP_P801803911r_bool(Pa,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_1),B_1))) ) ).

tff(fact_306_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1538825897r_bool] :
      ( ? [X1: produc740765671t_char] : hBOOL(hAPP_P929449287r_bool(Pa,X1))
    <=> ? [A_1: produc952412819t_char,B_1: produc952412819t_char] : hBOOL(hAPP_P929449287r_bool(Pa,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_1),B_1))) ) ).

tff(fact_307_split__paired__Ex,axiom,
    ! [Pa: fun_Pr981088873r_bool] :
      ( ? [X1: produc84451751t_char] : hBOOL(hAPP_P975284999r_bool(Pa,X1))
    <=> ? [A_1: produc1971331930t_char,B_1: produc1971331930t_char] : hBOOL(hAPP_P975284999r_bool(Pa,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),B_1))) ) ).

tff(fact_308_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1336847023r_bool] :
      ( ? [X1: produc1350825965t_char] : hBOOL(hAPP_P2010574925r_bool(Pa,X1))
    <=> ? [A_1: produc1278157519t_char,B_1: produc1278157519t_char] : hBOOL(hAPP_P2010574925r_bool(Pa,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_1),B_1))) ) ).

tff(fact_309_split__paired__Ex,axiom,
    ! [Pa: fun_Pr235369833l_bool] :
      ( ? [X1: produc87279271on_val] : hBOOL(hAPP_P124632071l_bool(Pa,X1))
    <=> ? [A_1: produc639455274on_val,B_1: produc639455274on_val] : hBOOL(hAPP_P124632071l_bool(Pa,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_1),B_1))) ) ).

tff(fact_310_split__paired__Ex,axiom,
    ! [Pa: fun_Pr832147423l_bool] :
      ( ? [X1: produc800118557al_val] : hBOOL(hAPP_P2123002749l_bool(Pa,X1))
    <=> ? [A_1: product_prod_val_val,B_1: product_prod_val_val] : hBOOL(hAPP_P2123002749l_bool(Pa,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_1),B_1))) ) ).

tff(fact_311_split__paired__Ex,axiom,
    ! [Pa: fun_Pr897334561l_bool] :
      ( ? [X1: produc630464863al_val] : hBOOL(hAPP_P738987199l_bool(Pa,X1))
    <=> ? [A_1: produc1645268488al_val,B_1: produc1645268488al_val] : hBOOL(hAPP_P738987199l_bool(Pa,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_1),B_1))) ) ).

tff(fact_312_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1890037787r_bool] :
      ( ? [X1: produc1826280281t_char] : hBOOL(hAPP_P1183499705r_bool(Pa,X1))
    <=> ? [A_1: produc662261637t_char,B_1: produc662261637t_char] : hBOOL(hAPP_P1183499705r_bool(Pa,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_1),B_1))) ) ).

tff(fact_313_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1728267013r_bool] :
      ( ? [X1: produc1406897475t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,X1))
    <=> ? [A_1: produc220283002t_char,B_1: produc220283002t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_1),B_1))) ) ).

tff(fact_314_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1895638121r_bool] :
      ( ? [X1: produc349695911t_char] : hBOOL(hAPP_P824029447r_bool(Pa,X1))
    <=> ? [A_1: produc1285161482t_char,B_1: produc1285161482t_char] : hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),B_1))) ) ).

tff(fact_315_split__paired__Ex,axiom,
    ! [Pa: fun_Pr302334223l_bool] :
      ( ? [X1: produc1466422861on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,X1))
    <=> ? [A_1: produc430140671on_val,B_1: produc430140671on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),B_1))) ) ).

tff(fact_316_split__paired__Ex,axiom,
    ! [Pa: fun_Pr903661919l_bool] :
      ( ? [X1: produc231486621on_val] : hBOOL(hAPP_P378063101l_bool(Pa,X1))
    <=> ? [A_1: produc1102272487on_val,B_1: produc1102272487on_val] : hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),B_1))) ) ).

tff(fact_317_split__paired__Ex,axiom,
    ! [Pa: fun_Pr693020585l_bool] :
      ( ? [X1: produc409205479on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,X1))
    <=> ? [A_1: produc12694297on_val,B_1: produc12694297on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_1),B_1))) ) ).

tff(fact_318_split__paired__Ex,axiom,
    ! [Pa: fun_Pr2102567903y_bool] :
      ( ? [X1: produc245756905har_ty] : hBOOL(hAPP_P27757617y_bool(Pa,X1))
    <=> ? [A_1: produc1278157519t_char,B_1: ty] : hBOOL(hAPP_P27757617y_bool(Pa,hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_1),B_1))) ) ).

tff(fact_319_split__paired__Ex,axiom,
    ! [Pa: fun_Pr70170387r_bool] :
      ( ? [X1: produc1013743697t_char] : hBOOL(hAPP_P1384137393r_bool(Pa,X1))
    <=> ? [A_1: list_char,B_1: produc1025221954t_char] : hBOOL(hAPP_P1384137393r_bool(Pa,hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),B_1))) ) ).

tff(fact_320_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1696029455l_bool] :
      ( ? [X1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
    <=> ? [A_1: fun_na939144002on_val,B_1: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(Pa,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_1))) ) ).

tff(fact_321_split__paired__Ex,axiom,
    ! [Pa: fun_Pr691271849l_bool] :
      ( ? [X1: produc1102272487on_val] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
    <=> ? [A_1: produc124828825on_val,B_1: produc124828825on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_1))) ) ).

tff(fact_322_split__paired__Ex,axiom,
    ! [Pa: fun_Pr680585871l_bool] :
      ( ? [X1: produc124828825on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
    <=> ? [A_1: exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_1))) ) ).

tff(fact_323_split__paired__Ex,axiom,
    ! [Pa: fun_Pr859510977l_bool] :
      ( ? [X1: produc430140671on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,X1))
    <=> ? [A_1: produc2061676504on_val,B_1: produc2061676504on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_1))) ) ).

tff(fact_324_split__paired__Ex,axiom,
    ! [Pa: fun_Pr248118298l_bool] :
      ( ? [X1: produc2061676504on_val] : hBOOL(hAPP_P71593144l_bool(Pa,X1))
    <=> ? [A_1: list_exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P71593144l_bool(Pa,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_1))) ) ).

tff(fact_325_split__paired__Ex,axiom,
    ! [Pa: fun_Pr227936640r_bool] :
      ( ? [X1: produc1285161482t_char] : hBOOL(hAPP_P92196306r_bool(Pa,X1))
    <=> ? [A_1: list_list_char,B_1: produc220283002t_char] : hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_1))) ) ).

tff(fact_326_split__paired__Ex,axiom,
    ! [Pa: fun_Pr46158268r_bool] :
      ( ? [X1: produc220283002t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,X1))
    <=> ? [A_1: list_ty,B_1: produc662261637t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_1))) ) ).

tff(fact_327_split__paired__Ex,axiom,
    ! [Pa: fun_Pr827765831r_bool] :
      ( ? [X1: produc662261637t_char] : hBOOL(hAPP_P2118621157r_bool(Pa,X1))
    <=> ? [A_1: list_val,B_1: exp_list_char] : hBOOL(hAPP_P2118621157r_bool(Pa,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_1))) ) ).

tff(fact_328_split__paired__Ex,axiom,
    ! [Pa: fun_Pr252072522l_bool] :
      ( ? [X1: produc1645268488al_val] : hBOOL(hAPP_P943837928l_bool(Pa,X1))
    <=> ? [A_1: bop,B_1: product_prod_val_val] : hBOOL(hAPP_P943837928l_bool(Pa,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_1))) ) ).

tff(fact_329_split__paired__Ex,axiom,
    ! [Pa: fun_Pr2081272681l_bool] :
      ( ? [X1: product_prod_val_val] : hBOOL(hAPP_P929938951l_bool(Pa,X1))
    <=> ? [A_1: val,B_1: val] : hBOOL(hAPP_P929938951l_bool(Pa,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_1))) ) ).

tff(fact_330_split__paired__Ex,axiom,
    ! [Pa: fun_Pr315804320l_bool] :
      ( ? [X1: produc639455274on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,X1))
    <=> ? [A_1: list_char,B_1: fun_Pr806764899on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_1))) ) ).

tff(fact_331_split__paired__Ex,axiom,
    ! [Pa: fun_Pr565113489r_bool] :
      ( ? [X1: produc1278157519t_char] : hBOOL(hAPP_P449474095r_bool(Pa,X1))
    <=> ? [A_1: list_char,B_1: list_char] : hBOOL(hAPP_P449474095r_bool(Pa,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_1))) ) ).

tff(fact_332_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1861226704r_bool] :
      ( ? [X1: produc1971331930t_char] : hBOOL(hAPP_P1680401186r_bool(Pa,X1))
    <=> ? [A_1: list_char,B_1: produc952412819t_char] : hBOOL(hAPP_P1680401186r_bool(Pa,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_1))) ) ).

tff(fact_333_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1898949769r_bool] :
      ( ? [X1: produc952412819t_char] : hBOOL(hAPP_P659547099r_bool(Pa,X1))
    <=> ? [A_1: list_char,B_1: produc2146869324t_char] : hBOOL(hAPP_P659547099r_bool(Pa,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_1))) ) ).

tff(fact_334_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1669461698r_bool] :
      ( ? [X1: produc2146869324t_char] : hBOOL(hAPP_P828904212r_bool(Pa,X1))
    <=> ? [A_1: list_P1940453997har_ty,B_1: list_P341299826t_char] : hBOOL(hAPP_P828904212r_bool(Pa,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_1))) ) ).

tff(fact_335_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1336948301r_bool] :
      ( ? [X1: produc809539159t_char] : hBOOL(hAPP_P2014166431r_bool(Pa,X1))
    <=> ? [A_1: list_list_char,B_1: exp_list_char] : hBOOL(hAPP_P2014166431r_bool(Pa,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_1))) ) ).

tff(fact_336_split__paired__Ex,axiom,
    ! [Pa: fun_Pr661739816l_bool] :
      ( ? [X1: produc1147203250ar_val] : hBOOL(hAPP_P1070896250l_bool(Pa,X1))
    <=> ? [A_1: produc1278157519t_char,B_1: val] : hBOOL(hAPP_P1070896250l_bool(Pa,hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_1),B_1))) ) ).

tff(fact_337_WTrt__hext__mono,axiom,
    ! [H_b: fun_na939144002on_val,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),Ta))
     => ( hBOOL(hext(Hb,H_b))
       => hBOOL(hAPP_ty_bool(wTrt(Pa,H_b,Ea,Eb),Ta)) ) ) ).

tff(fact_338_hext__refl,axiom,
    ! [Hb: fun_na939144002on_val] : hBOOL(hext(Hb,Hb)) ).

tff(fact_339_lconf__hext,axiom,
    ! [H_b: fun_na939144002on_val,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Ea: fun_li688206603ion_ty] :
      ( hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Hb),Lb),Ea))
     => ( hBOOL(hext(Hb,H_b))
       => hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),H_b),Lb),Ea)) ) ) ).

tff(fact_340_Red__lcl__add,axiom,
    ! [L_0_1: fun_li1432931796on_val,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: 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,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),map_ad325961431ar_val(L_0_1,Lb)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),map_ad325961431ar_val(L_0_1,L_b)))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_341_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr2102567903y_bool,R_2: fun_Pr2102567903y_bool] :
      ( ! [X_1: produc1278157519t_char,Xa: ty] :
          ( hBOOL(member1783291580har_ty(hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,X_1),Xa),R_2))
        <=> hBOOL(member1783291580har_ty(hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_342_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr1127025070y_bool,R_2: fun_Pr1127025070y_bool] :
      ( ! [X_1: list_char,Xa: ty] :
          ( hBOOL(member503779467har_ty(hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,X_1),Xa),R_2))
        <=> hBOOL(member503779467har_ty(hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_343_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr643382121l_bool,R_2: fun_Pr643382121l_bool] :
      ( ! [X_1: produc1147203250ar_val,Xa: produc1147203250ar_val] :
          ( hBOOL(member619264020ar_val(hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,X_1),Xa),R_2))
        <=> hBOOL(member619264020ar_val(hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_344_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr908866473r_bool,R_2: fun_Pr908866473r_bool] :
      ( ! [X_1: produc809539159t_char,Xa: produc809539159t_char] :
          ( hBOOL(member1999287380t_char(hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,X_1),Xa),R_2))
        <=> hBOOL(member1999287380t_char(hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_345_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr286306793r_bool,R_2: fun_Pr286306793r_bool] :
      ( ! [X_1: produc2146869324t_char,Xa: produc2146869324t_char] :
          ( hBOOL(member1551446420t_char(hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,X_1),Xa),R_2))
        <=> hBOOL(member1551446420t_char(hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_346_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr1538825897r_bool,R_2: fun_Pr1538825897r_bool] :
      ( ! [X_1: produc952412819t_char,Xa: produc952412819t_char] :
          ( hBOOL(member1607118676t_char(hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,X_1),Xa),R_2))
        <=> hBOOL(member1607118676t_char(hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_347_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr981088873r_bool,R_2: fun_Pr981088873r_bool] :
      ( ! [X_1: produc1971331930t_char,Xa: produc1971331930t_char] :
          ( hBOOL(member162552852t_char(hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,X_1),Xa),R_2))
        <=> hBOOL(member162552852t_char(hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_348_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr1336847023r_bool,R_2: fun_Pr1336847023r_bool] :
      ( ! [X_1: produc1278157519t_char,Xa: produc1278157519t_char] :
          ( hBOOL(member794220506t_char(hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,X_1),Xa),R_2))
        <=> hBOOL(member794220506t_char(hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_349_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr235369833l_bool,R_2: fun_Pr235369833l_bool] :
      ( ! [X_1: produc639455274on_val,Xa: produc639455274on_val] :
          ( hBOOL(member1322055188on_val(hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,X_1),Xa),R_2))
        <=> hBOOL(member1322055188on_val(hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_350_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr832147423l_bool,R_2: fun_Pr832147423l_bool] :
      ( ! [X_1: product_prod_val_val,Xa: product_prod_val_val] :
          ( hBOOL(member837208074al_val(hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,X_1),Xa),R_2))
        <=> hBOOL(member837208074al_val(hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_351_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr897334561l_bool,R_2: fun_Pr897334561l_bool] :
      ( ! [X_1: produc1645268488al_val,Xa: produc1645268488al_val] :
          ( hBOOL(member1732271180al_val(hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,X_1),Xa),R_2))
        <=> hBOOL(member1732271180al_val(hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_352_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr1890037787r_bool,R_2: fun_Pr1890037787r_bool] :
      ( ! [X_1: produc662261637t_char,Xa: produc662261637t_char] :
          ( hBOOL(member1161907014t_char(hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,X_1),Xa),R_2))
        <=> hBOOL(member1161907014t_char(hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_353_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr1728267013r_bool,R_2: fun_Pr1728267013r_bool] :
      ( ! [X_1: produc220283002t_char,Xa: produc220283002t_char] :
          ( hBOOL(member125098544t_char(hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,X_1),Xa),R_2))
        <=> hBOOL(member125098544t_char(hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_354_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr1895638121r_bool,R_2: fun_Pr1895638121r_bool] :
      ( ! [X_1: produc1285161482t_char,Xa: produc1285161482t_char] :
          ( hBOOL(member1420286996t_char(hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,X_1),Xa),R_2))
        <=> hBOOL(member1420286996t_char(hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_355_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr302334223l_bool,R_2: fun_Pr302334223l_bool] :
      ( ! [X_1: produc430140671on_val,Xa: produc430140671on_val] :
          ( hBOOL(member88670778on_val(hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,X_1),Xa),R_2))
        <=> hBOOL(member88670778on_val(hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_356_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr903661919l_bool,R_2: fun_Pr903661919l_bool] :
      ( ! [X_1: produc1102272487on_val,Xa: produc1102272487on_val] :
          ( hBOOL(member808015754on_val(hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,X_1),Xa),R_2))
        <=> hBOOL(member808015754on_val(hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_357_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr693020585l_bool,R_2: fun_Pr693020585l_bool] :
      ( ! [X_1: produc12694297on_val,Xa: produc12694297on_val] :
          ( hBOOL(member563141460on_val(hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,X_1),Xa),R_2))
        <=> hBOOL(member563141460on_val(hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_358_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr758558581y_bool,R_2: fun_Pr758558581y_bool] :
      ( ! [X_1: list_char,Xa: produc917948472har_ty] :
          ( hBOOL(member2007117138har_ty(hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,X_1),Xa),R_2))
        <=> hBOOL(member2007117138har_ty(hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_359_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr1696029455l_bool,R_2: fun_Pr1696029455l_bool] :
      ( ! [X_1: fun_na939144002on_val,Xa: fun_li1432931796on_val] :
          ( hBOOL(member763590124on_val(hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X_1),Xa),R_2))
        <=> hBOOL(member763590124on_val(hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_360_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr680585871l_bool,R_2: fun_Pr680585871l_bool] :
      ( ! [X_1: exp_list_char,Xa: produc12694297on_val] :
          ( hBOOL(member840932460on_val(hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X_1),Xa),R_2))
        <=> hBOOL(member840932460on_val(hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_361_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr248118298l_bool,R_2: fun_Pr248118298l_bool] :
      ( ! [X_1: list_exp_list_char,Xa: produc12694297on_val] :
          ( hBOOL(member1972431429on_val(hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,X_1),Xa),R_2))
        <=> hBOOL(member1972431429on_val(hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_362_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr227936640r_bool,R_2: fun_Pr227936640r_bool] :
      ( ! [X_1: list_list_char,Xa: produc220283002t_char] :
          ( hBOOL(member133545693t_char(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,X_1),Xa),R_2))
        <=> hBOOL(member133545693t_char(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_363_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr46158268r_bool,R_2: fun_Pr46158268r_bool] :
      ( ! [X_1: list_ty,Xa: produc662261637t_char] :
          ( hBOOL(member140606439t_char(hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,X_1),Xa),R_2))
        <=> hBOOL(member140606439t_char(hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_364_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr827765831r_bool,R_2: fun_Pr827765831r_bool] :
      ( ! [X_1: list_val,Xa: exp_list_char] :
          ( hBOOL(member699351154t_char(hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,X_1),Xa),R_2))
        <=> hBOOL(member699351154t_char(hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_365_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr252072522l_bool,R_2: fun_Pr252072522l_bool] :
      ( ! [X_1: bop,Xa: product_prod_val_val] :
          ( hBOOL(member1417904245al_val(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,X_1),Xa),R_2))
        <=> hBOOL(member1417904245al_val(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_366_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr2081272681l_bool,R_2: fun_Pr2081272681l_bool] :
      ( ! [X_1: val,Xa: val] :
          ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_1),Xa),R_2))
        <=> hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_367_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr315804320l_bool,R_2: fun_Pr315804320l_bool] :
      ( ! [X_1: list_char,Xa: fun_Pr806764899on_val] :
          ( hBOOL(member1542417277on_val(hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,X_1),Xa),R_2))
        <=> hBOOL(member1542417277on_val(hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_368_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr1898949769r_bool,R_2: fun_Pr1898949769r_bool] :
      ( ! [X_1: list_char,Xa: produc2146869324t_char] :
          ( hBOOL(member1771544038t_char(hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,X_1),Xa),R_2))
        <=> hBOOL(member1771544038t_char(hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_369_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr1669461698r_bool,R_2: fun_Pr1669461698r_bool] :
      ( ! [X_1: list_P1940453997har_ty,Xa: list_P341299826t_char] :
          ( hBOOL(member1379348767t_char(hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,X_1),Xa),R_2))
        <=> hBOOL(member1379348767t_char(hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_370_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr1336948301r_bool,R_2: fun_Pr1336948301r_bool] :
      ( ! [X_1: list_list_char,Xa: exp_list_char] :
          ( hBOOL(member1840112042t_char(hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,X_1),Xa),R_2))
        <=> hBOOL(member1840112042t_char(hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_371_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr661739816l_bool,R_2: fun_Pr661739816l_bool] :
      ( ! [X_1: produc1278157519t_char,Xa: val] :
          ( hBOOL(member806854661ar_val(hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,X_1),Xa),R_2))
        <=> hBOOL(member806854661ar_val(hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_372_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr691271849l_bool,R_2: fun_Pr691271849l_bool] :
      ( ! [X_1: produc124828825on_val,Xa: produc124828825on_val] :
          ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X_1),Xa),R_2))
        <=> hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_373_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr859510977l_bool,R_2: fun_Pr859510977l_bool] :
      ( ! [X_1: produc2061676504on_val,Xa: produc2061676504on_val] :
          ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,X_1),Xa),R_2))
        <=> hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_374_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr565113489r_bool,R_2: fun_Pr565113489r_bool] :
      ( ! [X_1: list_char,Xa: list_char] :
          ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_1),Xa),R_2))
        <=> hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_375_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr1861226704r_bool,R_2: fun_Pr1861226704r_bool] :
      ( ! [X_1: list_char,Xa: produc952412819t_char] :
          ( hBOOL(member1467889965t_char(hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,X_1),Xa),R_2))
        <=> hBOOL(member1467889965t_char(hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_376_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr70170387r_bool,R_2: fun_Pr70170387r_bool] :
      ( ! [X_1: list_char,Xa: produc1025221954t_char] :
          ( hBOOL(member1601084734t_char(hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,X_1),Xa),R_2))
        <=> hBOOL(member1601084734t_char(hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,X_1),Xa),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_377_internal__split__conv,axiom,
    ! [C_1: fun_Pr130335392ar_val,A: produc1278157519t_char,B: ty] : hAPP_P841862366ar_val(hAPP_f1295640803ar_val(produc1713493127ar_val,C_1),hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A),B)) = hAPP_t97533526ar_val(hAPP_P221287148ar_val(C_1,A),B) ).

tff(fact_378_internal__split__conv,axiom,
    ! [C_1: fun_fu100249073l_bool,A: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc2128769400l_bool,C_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B)))
    <=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(C_1,A),B)) ) ).

tff(fact_379_internal__split__conv,axiom,
    ! [C_1: fun_li1301775111ion_ty,A: list_char,B: fun_Pr806764899on_val] : hAPP_P1228500987ion_ty(hAPP_f46308763ion_ty(produc1577326610ion_ty,C_1),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B)) = hAPP_f652398900ion_ty(hAPP_l2000496933ion_ty(C_1,A),B) ).

tff(fact_380_WTrtWhile,axiom,
    ! [C_1: exp_list_char,Ta: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),boolean))
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,C_1),Ta))
       => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,while_list_char(Eb,C_1)),void)) ) ) ).

tff(fact_381_sconf__def,axiom,
    ! [Pa: list_P1999446415t_char,Ea: fun_li688206603ion_ty,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(typeSa1917327191_sconf(Pa,Ea),S))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_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))),Ea))),S)) ) ).

tff(fact_382_WTrtCond,axiom,
    ! [Ta: ty,E_2: exp_list_char,T_2: ty,E_1: exp_list_char,T_1: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),boolean))
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_1),T_1))
       => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_2),T_2))
         => ( ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1),T_2))
              | hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2),T_1)) )
           => ( ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1),T_2))
               => ( Ta = T_2 ) )
             => ( ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2),T_1))
                 => ( Ta = T_1 ) )
               => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,cond_list_char(Eb,E_1,E_2)),Ta)) ) ) ) ) ) ) ).

tff(fact_383_hext__trans,axiom,
    ! [H_4: fun_na939144002on_val,Hb: fun_na939144002on_val,H_b: fun_na939144002on_val] :
      ( hBOOL(hext(Hb,H_b))
     => ( hBOOL(hext(H_b,H_4))
       => hBOOL(hext(Hb,H_4)) ) ) ).

tff(fact_384_red__reds_OFAssRed2,axiom,
    ! [V_1: val,Fa: list_char,Da: list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),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_1),Fa,Da,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,V_1),Fa,Da,E_b)),S_2)),red(Pa))) ) ).

tff(fact_385_red__reds_OFAccThrow,axiom,
    ! [Eb: exp_list_char,Fa: list_char,Da: 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,fAcc_list_char(throw_list_char(Eb),Fa,Da)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S)),red(Pa))) ).

tff(fact_386_prod__caseI,axiom,
    ! [F1: fun_li800818899y_bool,A: list_char,B: produc917948472har_ty] :
      ( hBOOL(hAPP_P748443392y_bool(hAPP_l1665608433y_bool(F1,A),B))
     => hBOOL(hAPP_P831231943y_bool(hAPP_f1134484787y_bool(produc802464979y_bool,F1),hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,A),B))) ) ).

tff(fact_387_prod__caseI,axiom,
    ! [F1: fun_li634443788y_bool,A: list_char,B: ty] :
      ( hBOOL(hAPP_ty_bool(hAPP_l1734756650y_bool(F1,A),B))
     => hBOOL(hAPP_P748443392y_bool(hAPP_f695389733y_bool(produc1322037260y_bool,F1),hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A),B))) ) ).

tff(fact_388_prod__caseI,axiom,
    ! [F1: fun_Pr1858730867l_bool,A: produc1147203250ar_val,B: produc1147203250ar_val] :
      ( hBOOL(hAPP_P1070896250l_bool(hAPP_P1236192325l_bool(F1,A),B))
     => hBOOL(hAPP_P439015943l_bool(hAPP_f1653906803l_bool(produc891186911l_bool,F1),hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,A),B))) ) ).

tff(fact_389_prod__caseI,axiom,
    ! [F1: fun_Pr92408125r_bool,A: produc809539159t_char,B: produc809539159t_char] :
      ( hBOOL(hAPP_P2014166431r_bool(hAPP_P1939418767r_bool(F1,A),B))
     => hBOOL(hAPP_P1002912327r_bool(hAPP_f1728305001r_bool(produc1946648479r_bool,F1),hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A),B))) ) ).

tff(fact_390_prod__caseI,axiom,
    ! [F1: fun_Pr1881815719r_bool,A: produc2146869324t_char,B: produc2146869324t_char] :
      ( hBOOL(hAPP_P828904212r_bool(hAPP_P225001977r_bool(F1,A),B))
     => hBOOL(hAPP_P801803911r_bool(hAPP_f1760165311r_bool(produc1458513631r_bool,F1),hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A),B))) ) ).

tff(fact_391_prod__caseI,axiom,
    ! [F1: fun_Pr1401771957r_bool,A: produc952412819t_char,B: produc952412819t_char] :
      ( hBOOL(hAPP_P659547099r_bool(hAPP_P194929415r_bool(F1,A),B))
     => hBOOL(hAPP_P929449287r_bool(hAPP_f1774800369r_bool(produc1113940127r_bool,F1),hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A),B))) ) ).

tff(fact_392_prod__caseI,axiom,
    ! [F1: fun_Pr1963999939r_bool,A: produc1971331930t_char,B: produc1971331930t_char] :
      ( hBOOL(hAPP_P1680401186r_bool(hAPP_P1117344277r_bool(F1,A),B))
     => hBOOL(hAPP_P975284999r_bool(hAPP_f72760099r_bool(produc310626655r_bool,F1),hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A),B))) ) ).

tff(fact_393_prod__caseI,axiom,
    ! [F1: fun_Pr185059443r_bool,A: produc1278157519t_char,B: produc1278157519t_char] :
      ( hBOOL(hAPP_P449474095r_bool(hAPP_P663876415r_bool(F1,A),B))
     => hBOOL(hAPP_P2010574925r_bool(hAPP_f39862969r_bool(produc1131232171r_bool,F1),hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A),B))) ) ).

tff(fact_394_prod__caseI,axiom,
    ! [F1: fun_Pr788853347l_bool,A: produc639455274on_val,B: produc639455274on_val] :
      ( hBOOL(hAPP_P1235399154l_bool(hAPP_P416784693l_bool(F1,A),B))
     => hBOOL(hAPP_P124632071l_bool(hAPP_f834198659l_bool(produc870083295l_bool,F1),hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A),B))) ) ).

tff(fact_395_prod__caseI,axiom,
    ! [F1: fun_Pr324760563l_bool,A: product_prod_val_val,B: product_prod_val_val] :
      ( hBOOL(hAPP_P929938951l_bool(hAPP_P1815899455l_bool(F1,A),B))
     => hBOOL(hAPP_P2123002749l_bool(hAPP_f1774252649l_bool(produc506816603l_bool,F1),hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A),B))) ) ).

tff(fact_396_prod__caseI,axiom,
    ! [F1: fun_Pr1713170355l_bool,A: produc1645268488al_val,B: produc1645268488al_val] :
      ( hBOOL(hAPP_P943837928l_bool(hAPP_P323054207l_bool(F1,A),B))
     => hBOOL(hAPP_P738987199l_bool(hAPP_f463140843l_bool(produc1296464157l_bool,F1),hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A),B))) ) ).

tff(fact_397_prod__caseI,axiom,
    ! [F1: fun_Pr378536435r_bool,A: produc662261637t_char,B: produc662261637t_char] :
      ( hBOOL(hAPP_P2118621157r_bool(hAPP_P357098431r_bool(F1,A),B))
     => hBOOL(hAPP_P1183499705r_bool(hAPP_f523402917r_bool(produc22827031r_bool,F1),hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A),B))) ) ).

tff(fact_398_prod__caseI,axiom,
    ! [F1: fun_Pr1074372915r_bool,A: produc220283002t_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(hAPP_P1214880255r_bool(F1,A),B))
     => hBOOL(hAPP_P1240100515r_bool(hAPP_f1377529935r_bool(produc1470355201r_bool,F1),hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A),B))) ) ).

tff(fact_399_prod__caseI,axiom,
    ! [F1: fun_Pr1794669603r_bool,A: produc1285161482t_char,B: produc1285161482t_char] :
      ( hBOOL(hAPP_P92196306r_bool(hAPP_P1928969845r_bool(F1,A),B))
     => hBOOL(hAPP_P824029447r_bool(hAPP_f655949763r_bool(produc1294339167r_bool,F1),hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A),B))) ) ).

tff(fact_400_prod__caseI,axiom,
    ! [F1: fun_Pr1511900787l_bool,A: produc430140671on_val,B: produc430140671on_val] :
      ( hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(F1,A),B))
     => hBOOL(hAPP_P2028072621l_bool(hAPP_f1600283417l_bool(produc376173579l_bool,F1),hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A),B))) ) ).

tff(fact_401_prod__caseI,axiom,
    ! [F1: fun_Pr220980979l_bool,A: produc1102272487on_val,B: produc1102272487on_val] :
      ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(F1,A),B))
     => hBOOL(hAPP_P378063101l_bool(hAPP_f1363805417l_bool(produc1229156571l_bool,F1),hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A),B))) ) ).

tff(fact_402_prod__caseI,axiom,
    ! [F1: fun_Pr598845249l_bool,A: produc12694297on_val,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(F1,A),B))
     => hBOOL(hAPP_P1221872711l_bool(hAPP_f662143077l_bool(produc1193275679l_bool,F1),hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A),B))) ) ).

tff(fact_403_prod__caseI,axiom,
    ! [F1: fun_Pr1633645595y_bool,A: produc1278157519t_char,B: ty] :
      ( hBOOL(hAPP_ty_bool(hAPP_P1845004857y_bool(F1,A),B))
     => hBOOL(hAPP_P27757617y_bool(hAPP_f201105125y_bool(produc1851383869y_bool,F1),hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A),B))) ) ).

tff(fact_404_prod__caseI,axiom,
    ! [F1: fun_li1960983605r_bool,A: list_char,B: produc1025221954t_char] :
      ( hBOOL(hAPP_P1187139874r_bool(hAPP_l165010689r_bool(F1,A),B))
     => hBOOL(hAPP_P1384137393r_bool(hAPP_f433337307r_bool(produc65850127r_bool,F1),hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A),B))) ) ).

tff(fact_405_prod__caseI,axiom,
    ! [F1: fun_fu100249073l_bool,A: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F1,A),B))
     => hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B))) ) ).

tff(fact_406_prod__caseI,axiom,
    ! [F1: fun_Pr633696065l_bool,A: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F1,A),B))
     => hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B))) ) ).

tff(fact_407_prod__caseI,axiom,
    ! [F1: fun_ex1201926843l_bool,A: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F1,A),B))
     => hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B))) ) ).

tff(fact_408_prod__caseI,axiom,
    ! [F1: fun_Pr597144499l_bool,A: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(F1,A),B))
     => hBOOL(hAPP_P1333315679l_bool(hAPP_f1525114763l_bool(produc70644925l_bool,F1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B))) ) ).

tff(fact_409_prod__caseI,axiom,
    ! [F1: fun_li1372729616l_bool,A: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(F1,A),B))
     => hBOOL(hAPP_P71593144l_bool(hAPP_f1634841927l_bool(produc1491230096l_bool,F1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B))) ) ).

tff(fact_410_prod__caseI,axiom,
    ! [F1: fun_li1024794712r_bool,A: list_list_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(F1,A),B))
     => hBOOL(hAPP_P92196306r_bool(hAPP_f1613448899r_bool(produc2027921764r_bool,F1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B))) ) ).

tff(fact_411_prod__caseI,axiom,
    ! [F1: fun_li887890578r_bool,A: list_ty,B: produc662261637t_char] :
      ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(F1,A),B))
     => hBOOL(hAPP_P1907982426r_bool(hAPP_f102021095r_bool(produc154616760r_bool,F1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B))) ) ).

tff(fact_412_prod__caseI,axiom,
    ! [F1: fun_li826105035r_bool,A: list_val,B: exp_list_char] :
      ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(F1,A),B))
     => hBOOL(hAPP_P2118621157r_bool(hAPP_f1697332217r_bool(produc21910851r_bool,F1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B))) ) ).

tff(fact_413_prod__caseI,axiom,
    ! [F1: fun_bo1454185032l_bool,A: bop,B: product_prod_val_val] :
      ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(F1,A),B))
     => hBOOL(hAPP_P943837928l_bool(hAPP_f340876351l_bool(produc1326056646l_bool,F1),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B))) ) ).

tff(fact_414_prod__caseI,axiom,
    ! [F1: fun_val_fun_val_bool,A: val,B: val] :
      ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(F1,A),B))
     => hBOOL(hAPP_P929938951l_bool(hAPP_f1534412387l_bool(produc769963999l_bool,F1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B))) ) ).

tff(fact_415_prod__caseI,axiom,
    ! [F1: fun_li823162622l_bool,A: list_char,B: fun_Pr806764899on_val] :
      ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(F1,A),B))
     => hBOOL(hAPP_P1235399154l_bool(hAPP_f1443410953l_bool(produc392960766l_bool,F1),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B))) ) ).

tff(fact_416_prod__caseI,axiom,
    ! [F1: fun_li860735411r_bool,A: list_char,B: list_char] :
      ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(F1,A),B))
     => hBOOL(hAPP_P449474095r_bool(hAPP_f2132060507r_bool(produc1704639885r_bool,F1),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B))) ) ).

tff(fact_417_prod__caseI,axiom,
    ! [F1: fun_li522008110r_bool,A: list_char,B: produc952412819t_char] :
      ( hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(F1,A),B))
     => hBOOL(hAPP_P1680401186r_bool(hAPP_f952817385r_bool(produc723279022r_bool,F1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B))) ) ).

tff(fact_418_prod__caseI,axiom,
    ! [F1: fun_li485148903r_bool,A: list_char,B: produc2146869324t_char] :
      ( hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(F1,A),B))
     => hBOOL(hAPP_P659547099r_bool(hAPP_f252398939r_bool(produc1324280167r_bool,F1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B))) ) ).

tff(fact_419_prod__caseI,axiom,
    ! [F1: fun_li1305328058r_bool,A: list_P1940453997har_ty,B: list_P341299826t_char] :
      ( hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(F1,A),B))
     => hBOOL(hAPP_P828904212r_bool(hAPP_f895126887r_bool(produc1596557472r_bool,F1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B))) ) ).

tff(fact_420_prod__caseI,axiom,
    ! [F1: fun_li221477r_bool,A: list_list_char,B: exp_list_char] :
      ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(F1,A),B))
     => hBOOL(hAPP_P2014166431r_bool(hAPP_f1484794973r_bool(produc1732333873r_bool,F1),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B))) ) ).

tff(fact_421_prod__caseI,axiom,
    ! [F1: fun_Pr2055965540l_bool,A: produc1278157519t_char,B: val] :
      ( hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(F1,A),B))
     => hBOOL(hAPP_P1070896250l_bool(hAPP_f1663301111l_bool(produc1873777030l_bool,F1),hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A),B))) ) ).

tff(fact_422_splitI,axiom,
    ! [F: fun_li800818899y_bool,A: list_char,B: produc917948472har_ty] :
      ( hBOOL(hAPP_P748443392y_bool(hAPP_l1665608433y_bool(F,A),B))
     => hBOOL(hAPP_P831231943y_bool(hAPP_f1134484787y_bool(produc802464979y_bool,F),hAPP_P295788316har_ty(hAPP_l848957697har_ty(produc1002914035har_ty,A),B))) ) ).

tff(fact_423_splitI,axiom,
    ! [F: fun_li634443788y_bool,A: list_char,B: ty] :
      ( hBOOL(hAPP_ty_bool(hAPP_l1734756650y_bool(F,A),B))
     => hBOOL(hAPP_P748443392y_bool(hAPP_f695389733y_bool(produc1322037260y_bool,F),hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A),B))) ) ).

tff(fact_424_splitI,axiom,
    ! [F: fun_Pr1858730867l_bool,A: produc1147203250ar_val,B: produc1147203250ar_val] :
      ( hBOOL(hAPP_P1070896250l_bool(hAPP_P1236192325l_bool(F,A),B))
     => hBOOL(hAPP_P439015943l_bool(hAPP_f1653906803l_bool(produc891186911l_bool,F),hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,A),B))) ) ).

tff(fact_425_splitI,axiom,
    ! [F: fun_Pr92408125r_bool,A: produc809539159t_char,B: produc809539159t_char] :
      ( hBOOL(hAPP_P2014166431r_bool(hAPP_P1939418767r_bool(F,A),B))
     => hBOOL(hAPP_P1002912327r_bool(hAPP_f1728305001r_bool(produc1946648479r_bool,F),hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A),B))) ) ).

tff(fact_426_splitI,axiom,
    ! [F: fun_Pr1881815719r_bool,A: produc2146869324t_char,B: produc2146869324t_char] :
      ( hBOOL(hAPP_P828904212r_bool(hAPP_P225001977r_bool(F,A),B))
     => hBOOL(hAPP_P801803911r_bool(hAPP_f1760165311r_bool(produc1458513631r_bool,F),hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A),B))) ) ).

tff(fact_427_splitI,axiom,
    ! [F: fun_Pr1401771957r_bool,A: produc952412819t_char,B: produc952412819t_char] :
      ( hBOOL(hAPP_P659547099r_bool(hAPP_P194929415r_bool(F,A),B))
     => hBOOL(hAPP_P929449287r_bool(hAPP_f1774800369r_bool(produc1113940127r_bool,F),hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A),B))) ) ).

tff(fact_428_splitI,axiom,
    ! [F: fun_Pr1963999939r_bool,A: produc1971331930t_char,B: produc1971331930t_char] :
      ( hBOOL(hAPP_P1680401186r_bool(hAPP_P1117344277r_bool(F,A),B))
     => hBOOL(hAPP_P975284999r_bool(hAPP_f72760099r_bool(produc310626655r_bool,F),hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A),B))) ) ).

tff(fact_429_splitI,axiom,
    ! [F: fun_Pr185059443r_bool,A: produc1278157519t_char,B: produc1278157519t_char] :
      ( hBOOL(hAPP_P449474095r_bool(hAPP_P663876415r_bool(F,A),B))
     => hBOOL(hAPP_P2010574925r_bool(hAPP_f39862969r_bool(produc1131232171r_bool,F),hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A),B))) ) ).

tff(fact_430_splitI,axiom,
    ! [F: fun_Pr788853347l_bool,A: produc639455274on_val,B: produc639455274on_val] :
      ( hBOOL(hAPP_P1235399154l_bool(hAPP_P416784693l_bool(F,A),B))
     => hBOOL(hAPP_P124632071l_bool(hAPP_f834198659l_bool(produc870083295l_bool,F),hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A),B))) ) ).

tff(fact_431_splitI,axiom,
    ! [F: fun_Pr324760563l_bool,A: product_prod_val_val,B: product_prod_val_val] :
      ( hBOOL(hAPP_P929938951l_bool(hAPP_P1815899455l_bool(F,A),B))
     => hBOOL(hAPP_P2123002749l_bool(hAPP_f1774252649l_bool(produc506816603l_bool,F),hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A),B))) ) ).

tff(fact_432_splitI,axiom,
    ! [F: fun_Pr1713170355l_bool,A: produc1645268488al_val,B: produc1645268488al_val] :
      ( hBOOL(hAPP_P943837928l_bool(hAPP_P323054207l_bool(F,A),B))
     => hBOOL(hAPP_P738987199l_bool(hAPP_f463140843l_bool(produc1296464157l_bool,F),hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A),B))) ) ).

tff(fact_433_splitI,axiom,
    ! [F: fun_Pr378536435r_bool,A: produc662261637t_char,B: produc662261637t_char] :
      ( hBOOL(hAPP_P2118621157r_bool(hAPP_P357098431r_bool(F,A),B))
     => hBOOL(hAPP_P1183499705r_bool(hAPP_f523402917r_bool(produc22827031r_bool,F),hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A),B))) ) ).

tff(fact_434_splitI,axiom,
    ! [F: fun_Pr1074372915r_bool,A: produc220283002t_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(hAPP_P1214880255r_bool(F,A),B))
     => hBOOL(hAPP_P1240100515r_bool(hAPP_f1377529935r_bool(produc1470355201r_bool,F),hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A),B))) ) ).

tff(fact_435_splitI,axiom,
    ! [F: fun_Pr1794669603r_bool,A: produc1285161482t_char,B: produc1285161482t_char] :
      ( hBOOL(hAPP_P92196306r_bool(hAPP_P1928969845r_bool(F,A),B))
     => hBOOL(hAPP_P824029447r_bool(hAPP_f655949763r_bool(produc1294339167r_bool,F),hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A),B))) ) ).

tff(fact_436_splitI,axiom,
    ! [F: fun_Pr1511900787l_bool,A: produc430140671on_val,B: produc430140671on_val] :
      ( hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(F,A),B))
     => hBOOL(hAPP_P2028072621l_bool(hAPP_f1600283417l_bool(produc376173579l_bool,F),hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A),B))) ) ).

tff(fact_437_splitI,axiom,
    ! [F: fun_Pr220980979l_bool,A: produc1102272487on_val,B: produc1102272487on_val] :
      ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(F,A),B))
     => hBOOL(hAPP_P378063101l_bool(hAPP_f1363805417l_bool(produc1229156571l_bool,F),hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A),B))) ) ).

tff(fact_438_splitI,axiom,
    ! [F: fun_Pr598845249l_bool,A: produc12694297on_val,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(F,A),B))
     => hBOOL(hAPP_P1221872711l_bool(hAPP_f662143077l_bool(produc1193275679l_bool,F),hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A),B))) ) ).

tff(fact_439_splitI,axiom,
    ! [F: fun_Pr1633645595y_bool,A: produc1278157519t_char,B: ty] :
      ( hBOOL(hAPP_ty_bool(hAPP_P1845004857y_bool(F,A),B))
     => hBOOL(hAPP_P27757617y_bool(hAPP_f201105125y_bool(produc1851383869y_bool,F),hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A),B))) ) ).

tff(fact_440_splitI,axiom,
    ! [F: fun_li1960983605r_bool,A: list_char,B: produc1025221954t_char] :
      ( hBOOL(hAPP_P1187139874r_bool(hAPP_l165010689r_bool(F,A),B))
     => hBOOL(hAPP_P1384137393r_bool(hAPP_f433337307r_bool(produc65850127r_bool,F),hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A),B))) ) ).

tff(fact_441_splitI,axiom,
    ! [F: fun_fu100249073l_bool,A: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F,A),B))
     => hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B))) ) ).

tff(fact_442_splitI,axiom,
    ! [F: fun_Pr633696065l_bool,A: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F,A),B))
     => hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B))) ) ).

tff(fact_443_splitI,axiom,
    ! [F: fun_ex1201926843l_bool,A: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F,A),B))
     => hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B))) ) ).

tff(fact_444_splitI,axiom,
    ! [F: fun_Pr597144499l_bool,A: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(F,A),B))
     => hBOOL(hAPP_P1333315679l_bool(hAPP_f1525114763l_bool(produc70644925l_bool,F),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B))) ) ).

tff(fact_445_splitI,axiom,
    ! [F: fun_li1372729616l_bool,A: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(F,A),B))
     => hBOOL(hAPP_P71593144l_bool(hAPP_f1634841927l_bool(produc1491230096l_bool,F),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B))) ) ).

tff(fact_446_splitI,axiom,
    ! [F: fun_li1024794712r_bool,A: list_list_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(F,A),B))
     => hBOOL(hAPP_P92196306r_bool(hAPP_f1613448899r_bool(produc2027921764r_bool,F),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B))) ) ).

tff(fact_447_splitI,axiom,
    ! [F: fun_li887890578r_bool,A: list_ty,B: produc662261637t_char] :
      ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(F,A),B))
     => hBOOL(hAPP_P1907982426r_bool(hAPP_f102021095r_bool(produc154616760r_bool,F),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B))) ) ).

tff(fact_448_splitI,axiom,
    ! [F: fun_li826105035r_bool,A: list_val,B: exp_list_char] :
      ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(F,A),B))
     => hBOOL(hAPP_P2118621157r_bool(hAPP_f1697332217r_bool(produc21910851r_bool,F),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B))) ) ).

tff(fact_449_splitI,axiom,
    ! [F: fun_bo1454185032l_bool,A: bop,B: product_prod_val_val] :
      ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(F,A),B))
     => hBOOL(hAPP_P943837928l_bool(hAPP_f340876351l_bool(produc1326056646l_bool,F),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B))) ) ).

tff(fact_450_splitI,axiom,
    ! [F: fun_val_fun_val_bool,A: val,B: val] :
      ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(F,A),B))
     => hBOOL(hAPP_P929938951l_bool(hAPP_f1534412387l_bool(produc769963999l_bool,F),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B))) ) ).

tff(fact_451_splitI,axiom,
    ! [F: fun_li823162622l_bool,A: list_char,B: fun_Pr806764899on_val] :
      ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(F,A),B))
     => hBOOL(hAPP_P1235399154l_bool(hAPP_f1443410953l_bool(produc392960766l_bool,F),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B))) ) ).

tff(fact_452_splitI,axiom,
    ! [F: fun_li860735411r_bool,A: list_char,B: list_char] :
      ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(F,A),B))
     => hBOOL(hAPP_P449474095r_bool(hAPP_f2132060507r_bool(produc1704639885r_bool,F),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B))) ) ).

tff(fact_453_splitI,axiom,
    ! [F: fun_li522008110r_bool,A: list_char,B: produc952412819t_char] :
      ( hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(F,A),B))
     => hBOOL(hAPP_P1680401186r_bool(hAPP_f952817385r_bool(produc723279022r_bool,F),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B))) ) ).

tff(fact_454_splitI,axiom,
    ! [F: fun_li485148903r_bool,A: list_char,B: produc2146869324t_char] :
      ( hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(F,A),B))
     => hBOOL(hAPP_P659547099r_bool(hAPP_f252398939r_bool(produc1324280167r_bool,F),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B))) ) ).

tff(fact_455_splitI,axiom,
    ! [F: fun_li1305328058r_bool,A: list_P1940453997har_ty,B: list_P341299826t_char] :
      ( hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(F,A),B))
     => hBOOL(hAPP_P828904212r_bool(hAPP_f895126887r_bool(produc1596557472r_bool,F),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B))) ) ).

tff(fact_456_splitI,axiom,
    ! [F: fun_li221477r_bool,A: list_list_char,B: exp_list_char] :
      ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(F,A),B))
     => hBOOL(hAPP_P2014166431r_bool(hAPP_f1484794973r_bool(produc1732333873r_bool,F),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B))) ) ).

tff(fact_457_splitI,axiom,
    ! [F: fun_Pr2055965540l_bool,A: produc1278157519t_char,B: val] :
      ( hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(F,A),B))
     => hBOOL(hAPP_P1070896250l_bool(hAPP_f1663301111l_bool(produc1873777030l_bool,F),hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A),B))) ) ).

tff(fact_458_exp_Osimps_I90_J,axiom,
    ! [Val_19: val,Exp_53: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_19) != throw_list_char(Exp_53) ).

tff(fact_459_exp_Osimps_I91_J,axiom,
    ! [Exp_52: exp_list_char,Val_18: val] : throw_list_char(Exp_52) != hAPP_v834067052t_char(val_list_char,Val_18) ).

tff(fact_460_exp_Osimps_I88_J,axiom,
    ! [Val_17: val,Exp1_107: exp_list_char,Exp2_107: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_17) != while_list_char(Exp1_107,Exp2_107) ).

tff(fact_461_exp_Osimps_I221_J,axiom,
    ! [Exp_51: exp_list_char,Exp1_106: exp_list_char,Exp2_106: exp_list_char] : throw_list_char(Exp_51) != while_list_char(Exp1_106,Exp2_106) ).

tff(fact_462_exp_Osimps_I86_J,axiom,
    ! [Val_16: val,Exp1_105: exp_list_char,Exp2_105: exp_list_char,Exp3_19: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_16) != cond_list_char(Exp1_105,Exp2_105,Exp3_19) ).

tff(fact_463_exp_Osimps_I217_J,axiom,
    ! [Exp_50: exp_list_char,Exp1_104: exp_list_char,Exp2_104: exp_list_char,Exp3_18: exp_list_char] : throw_list_char(Exp_50) != cond_list_char(Exp1_104,Exp2_104,Exp3_18) ).

tff(fact_464_exp_Osimps_I220_J,axiom,
    ! [Exp1_103: exp_list_char,Exp2_103: exp_list_char,Exp_49: exp_list_char] : while_list_char(Exp1_103,Exp2_103) != throw_list_char(Exp_49) ).

tff(fact_465_exp_Osimps_I89_J,axiom,
    ! [Exp1_102: exp_list_char,Exp2_102: exp_list_char,Val_15: val] : while_list_char(Exp1_102,Exp2_102) != hAPP_v834067052t_char(val_list_char,Val_15) ).

tff(fact_466_mem__def,axiom,
    ! [X_2: produc245756905har_ty,A_22: fun_Pr2102567903y_bool] :
      ( hBOOL(member1783291580har_ty(X_2,A_22))
    <=> hBOOL(hAPP_P27757617y_bool(A_22,X_2)) ) ).

tff(fact_467_mem__def,axiom,
    ! [X_2: produc917948472har_ty,A_22: fun_Pr1127025070y_bool] :
      ( hBOOL(member503779467har_ty(X_2,A_22))
    <=> hBOOL(hAPP_P748443392y_bool(A_22,X_2)) ) ).

tff(fact_468_mem__def,axiom,
    ! [X_2: product_prod_val_val,A_22: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(X_2,A_22))
    <=> hBOOL(hAPP_P929938951l_bool(A_22,X_2)) ) ).

tff(fact_469_mem__def,axiom,
    ! [X_2: produc1312961703ar_val,A_22: fun_Pr643382121l_bool] :
      ( hBOOL(member619264020ar_val(X_2,A_22))
    <=> hBOOL(hAPP_P439015943l_bool(A_22,X_2)) ) ).

tff(fact_470_mem__def,axiom,
    ! [X_2: produc1534059751t_char,A_22: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(X_2,A_22))
    <=> hBOOL(hAPP_P1002912327r_bool(A_22,X_2)) ) ).

tff(fact_471_mem__def,axiom,
    ! [X_2: produc494726439t_char,A_22: fun_Pr286306793r_bool] :
      ( hBOOL(member1551446420t_char(X_2,A_22))
    <=> hBOOL(hAPP_P801803911r_bool(A_22,X_2)) ) ).

tff(fact_472_mem__def,axiom,
    ! [X_2: produc740765671t_char,A_22: fun_Pr1538825897r_bool] :
      ( hBOOL(member1607118676t_char(X_2,A_22))
    <=> hBOOL(hAPP_P929449287r_bool(A_22,X_2)) ) ).

tff(fact_473_mem__def,axiom,
    ! [X_2: produc84451751t_char,A_22: fun_Pr981088873r_bool] :
      ( hBOOL(member162552852t_char(X_2,A_22))
    <=> hBOOL(hAPP_P975284999r_bool(A_22,X_2)) ) ).

tff(fact_474_mem__def,axiom,
    ! [X_2: produc1350825965t_char,A_22: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(X_2,A_22))
    <=> hBOOL(hAPP_P2010574925r_bool(A_22,X_2)) ) ).

tff(fact_475_mem__def,axiom,
    ! [X_2: produc87279271on_val,A_22: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(X_2,A_22))
    <=> hBOOL(hAPP_P124632071l_bool(A_22,X_2)) ) ).

tff(fact_476_mem__def,axiom,
    ! [X_2: produc800118557al_val,A_22: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(X_2,A_22))
    <=> hBOOL(hAPP_P2123002749l_bool(A_22,X_2)) ) ).

tff(fact_477_mem__def,axiom,
    ! [X_2: produc630464863al_val,A_22: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(X_2,A_22))
    <=> hBOOL(hAPP_P738987199l_bool(A_22,X_2)) ) ).

tff(fact_478_mem__def,axiom,
    ! [X_2: produc1826280281t_char,A_22: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(X_2,A_22))
    <=> hBOOL(hAPP_P1183499705r_bool(A_22,X_2)) ) ).

tff(fact_479_mem__def,axiom,
    ! [X_2: produc1406897475t_char,A_22: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(X_2,A_22))
    <=> hBOOL(hAPP_P1240100515r_bool(A_22,X_2)) ) ).

tff(fact_480_mem__def,axiom,
    ! [X_2: produc349695911t_char,A_22: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(X_2,A_22))
    <=> hBOOL(hAPP_P824029447r_bool(A_22,X_2)) ) ).

tff(fact_481_mem__def,axiom,
    ! [X_2: produc1466422861on_val,A_22: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(X_2,A_22))
    <=> hBOOL(hAPP_P2028072621l_bool(A_22,X_2)) ) ).

tff(fact_482_mem__def,axiom,
    ! [X_2: produc231486621on_val,A_22: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(X_2,A_22))
    <=> hBOOL(hAPP_P378063101l_bool(A_22,X_2)) ) ).

tff(fact_483_mem__def,axiom,
    ! [X_2: produc409205479on_val,A_22: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(X_2,A_22))
    <=> hBOOL(hAPP_P1221872711l_bool(A_22,X_2)) ) ).

tff(fact_484_mem__def,axiom,
    ! [X_2: produc1147203250ar_val,A_22: fun_Pr661739816l_bool] :
      ( hBOOL(member806854661ar_val(X_2,A_22))
    <=> hBOOL(hAPP_P1070896250l_bool(A_22,X_2)) ) ).

tff(fact_485_mem__def,axiom,
    ! [X_2: produc809539159t_char,A_22: fun_Pr1336948301r_bool] :
      ( hBOOL(member1840112042t_char(X_2,A_22))
    <=> hBOOL(hAPP_P2014166431r_bool(A_22,X_2)) ) ).

tff(fact_486_mem__def,axiom,
    ! [X_2: produc2146869324t_char,A_22: fun_Pr1669461698r_bool] :
      ( hBOOL(member1379348767t_char(X_2,A_22))
    <=> hBOOL(hAPP_P828904212r_bool(A_22,X_2)) ) ).

tff(fact_487_mem__def,axiom,
    ! [X_2: produc952412819t_char,A_22: fun_Pr1898949769r_bool] :
      ( hBOOL(member1771544038t_char(X_2,A_22))
    <=> hBOOL(hAPP_P659547099r_bool(A_22,X_2)) ) ).

tff(fact_488_mem__def,axiom,
    ! [X_2: produc639455274on_val,A_22: fun_Pr315804320l_bool] :
      ( hBOOL(member1542417277on_val(X_2,A_22))
    <=> hBOOL(hAPP_P1235399154l_bool(A_22,X_2)) ) ).

tff(fact_489_mem__def,axiom,
    ! [X_2: produc1645268488al_val,A_22: fun_Pr252072522l_bool] :
      ( hBOOL(member1417904245al_val(X_2,A_22))
    <=> hBOOL(hAPP_P943837928l_bool(A_22,X_2)) ) ).

tff(fact_490_mem__def,axiom,
    ! [X_2: produc662261637t_char,A_22: fun_Pr827765831r_bool] :
      ( hBOOL(member699351154t_char(X_2,A_22))
    <=> hBOOL(hAPP_P2118621157r_bool(A_22,X_2)) ) ).

tff(fact_491_mem__def,axiom,
    ! [X_2: produc220283002t_char,A_22: fun_Pr46158268r_bool] :
      ( hBOOL(member140606439t_char(X_2,A_22))
    <=> hBOOL(hAPP_P1907982426r_bool(A_22,X_2)) ) ).

tff(fact_492_mem__def,axiom,
    ! [X_2: produc1285161482t_char,A_22: fun_Pr227936640r_bool] :
      ( hBOOL(member133545693t_char(X_2,A_22))
    <=> hBOOL(hAPP_P92196306r_bool(A_22,X_2)) ) ).

tff(fact_493_mem__def,axiom,
    ! [X_2: produc2061676504on_val,A_22: fun_Pr248118298l_bool] :
      ( hBOOL(member1972431429on_val(X_2,A_22))
    <=> hBOOL(hAPP_P71593144l_bool(A_22,X_2)) ) ).

tff(fact_494_mem__def,axiom,
    ! [X_2: produc124828825on_val,A_22: fun_Pr680585871l_bool] :
      ( hBOOL(member840932460on_val(X_2,A_22))
    <=> hBOOL(hAPP_P1708370145l_bool(A_22,X_2)) ) ).

tff(fact_495_mem__def,axiom,
    ! [X_2: produc12694297on_val,A_22: fun_Pr1696029455l_bool] :
      ( hBOOL(member763590124on_val(X_2,A_22))
    <=> hBOOL(hAPP_P159683425l_bool(A_22,X_2)) ) ).

tff(fact_496_mem__def,axiom,
    ! [X_2: produc1102272487on_val,A_22: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(X_2,A_22))
    <=> hBOOL(hAPP_P282169671l_bool(A_22,X_2)) ) ).

tff(fact_497_mem__def,axiom,
    ! [X_2: produc430140671on_val,A_22: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(X_2,A_22))
    <=> hBOOL(hAPP_P1333315679l_bool(A_22,X_2)) ) ).

tff(fact_498_mem__def,axiom,
    ! [X_2: produc1278157519t_char,A_22: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(X_2,A_22))
    <=> hBOOL(hAPP_P449474095r_bool(A_22,X_2)) ) ).

tff(fact_499_mem__def,axiom,
    ! [X_2: list_char,A_22: fun_list_char_bool] :
      ( hBOOL(member_list_char(X_2,A_22))
    <=> hBOOL(hAPP_list_char_bool(A_22,X_2)) ) ).

tff(fact_500_mem__def,axiom,
    ! [X_2: produc1971331930t_char,A_22: fun_Pr1861226704r_bool] :
      ( hBOOL(member1467889965t_char(X_2,A_22))
    <=> hBOOL(hAPP_P1680401186r_bool(A_22,X_2)) ) ).

tff(fact_501_mem__def,axiom,
    ! [X_2: produc1013743697t_char,A_22: fun_Pr70170387r_bool] :
      ( hBOOL(member1601084734t_char(X_2,A_22))
    <=> hBOOL(hAPP_P1384137393r_bool(A_22,X_2)) ) ).

tff(fact_502_Collect__def,axiom,
    ! [Pa: fun_ty_bool] : collect_ty(Pa) = Pa ).

tff(fact_503_exp_Osimps_I215_J,axiom,
    ! [Exp1_101: exp_list_char,Exp2_101: exp_list_char,Exp1_100: exp_list_char,Exp2_100: exp_list_char,Exp3_17: exp_list_char] : while_list_char(Exp1_101,Exp2_101) != cond_list_char(Exp1_100,Exp2_100,Exp3_17) ).

tff(fact_504_exp_Osimps_I216_J,axiom,
    ! [Exp1_99: exp_list_char,Exp2_99: exp_list_char,Exp3_16: exp_list_char,Exp_48: exp_list_char] : cond_list_char(Exp1_99,Exp2_99,Exp3_16) != throw_list_char(Exp_48) ).

tff(fact_505_exp_Osimps_I87_J,axiom,
    ! [Exp1_98: exp_list_char,Exp2_98: exp_list_char,Exp3_15: exp_list_char,Val_14: val] : cond_list_char(Exp1_98,Exp2_98,Exp3_15) != hAPP_v834067052t_char(val_list_char,Val_14) ).

tff(fact_506_exp_Osimps_I214_J,axiom,
    ! [Exp1_97: exp_list_char,Exp2_97: exp_list_char,Exp3_14: exp_list_char,Exp1_96: exp_list_char,Exp2_96: exp_list_char] : cond_list_char(Exp1_97,Exp2_97,Exp3_14) != while_list_char(Exp1_96,Exp2_96) ).

tff(fact_507_exp_Osimps_I3_J,axiom,
    ! [Val_13: val,Val_12: val] :
      ( ( hAPP_v834067052t_char(val_list_char,Val_13) = hAPP_v834067052t_char(val_list_char,Val_12) )
    <=> ( Val_13 = Val_12 ) ) ).

tff(fact_508_exp_Osimps_I14_J,axiom,
    ! [Exp_29: exp_list_char,Exp_28: exp_list_char] :
      ( ( throw_list_char(Exp_29) = throw_list_char(Exp_28) )
    <=> ( Exp_29 = Exp_28 ) ) ).

tff(fact_509_exp_Osimps_I13_J,axiom,
    ! [Exp1_61: exp_list_char,Exp2_61: exp_list_char,Exp1_60: exp_list_char,Exp2_60: exp_list_char] :
      ( ( while_list_char(Exp1_61,Exp2_61) = while_list_char(Exp1_60,Exp2_60) )
    <=> ( ( Exp1_61 = Exp1_60 )
        & ( Exp2_61 = Exp2_60 ) ) ) ).

tff(fact_510_exp_Osimps_I12_J,axiom,
    ! [Exp1_61: exp_list_char,Exp2_61: exp_list_char,Exp3_13: exp_list_char,Exp1_60: exp_list_char,Exp2_60: exp_list_char,Exp3_12: exp_list_char] :
      ( ( cond_list_char(Exp1_61,Exp2_61,Exp3_13) = cond_list_char(Exp1_60,Exp2_60,Exp3_12) )
    <=> ( ( Exp1_61 = Exp1_60 )
        & ( Exp2_61 = Exp2_60 )
        & ( Exp3_13 = Exp3_12 ) ) ) ).

tff(fact_511_internal__split__def,axiom,
    produc1373896038har_ty = produc1096552923har_ty ).

tff(fact_512_internal__split__def,axiom,
    produc448987860har_ty = produc499452831har_ty ).

tff(fact_513_internal__split__def,axiom,
    produc1626136111har_ty = produc2074304634har_ty ).

tff(fact_514_internal__split__def,axiom,
    produc2046300823y_bool = produc1322037260y_bool ).

tff(fact_515_internal__split__def,axiom,
    produc1055753489l_bool = produc1873777030l_bool ).

tff(fact_516_internal__split__def,axiom,
    produc181628604r_bool = produc1732333873r_bool ).

tff(fact_517_internal__split__def,axiom,
    produc538535851r_bool = produc1596557472r_bool ).

tff(fact_518_internal__split__def,axiom,
    produc181333746r_bool = produc1324280167r_bool ).

tff(fact_519_internal__split__def,axiom,
    produc1186154681r_bool = produc723279022r_bool ).

tff(fact_520_internal__split__def,axiom,
    produc1779501634r_bool = produc1704639885r_bool ).

tff(fact_521_internal__split__def,axiom,
    produc1741654153l_bool = produc392960766l_bool ).

tff(fact_522_internal__split__def,axiom,
    produc1401528596l_bool = produc769963999l_bool ).

tff(fact_523_internal__split__def,axiom,
    produc85367547l_bool = produc1326056646l_bool ).

tff(fact_524_internal__split__def,axiom,
    produc684674552r_bool = produc21910851r_bool ).

tff(fact_525_internal__split__def,axiom,
    produc1657965293r_bool = produc154616760r_bool ).

tff(fact_526_internal__split__def,axiom,
    produc19303535r_bool = produc2027921764r_bool ).

tff(fact_527_internal__split__def,axiom,
    produc1631960005l_bool = produc1491230096l_bool ).

tff(fact_528_internal__split__def,axiom,
    produc2085082994l_bool = produc70644925l_bool ).

tff(fact_529_internal__split__def,axiom,
    produc399384568l_bool = produc1815960045l_bool ).

tff(fact_530_internal__split__def,axiom,
    produc1988544340l_bool = produc1911463199l_bool ).

tff(fact_531_internal__split__def,axiom,
    produc2128769400l_bool = produc1958875245l_bool ).

tff(fact_532_internal__split__def,axiom,
    produc1577326610ion_ty = produc907433735ion_ty ).

tff(fact_533_internal__split__def,axiom,
    produc1713493127ar_val = produc1553344466ar_val ).

tff(fact_534_split__weak__cong,axiom,
    ! [C_1: fun_li1185462113har_ty,P_1: produc1278157519t_char,Q_2: produc1278157519t_char] :
      ( ( P_1 = Q_2 )
     => ( hAPP_P901867449har_ty(hAPP_f1303264185har_ty(produc1096552923har_ty,C_1),P_1) = hAPP_P901867449har_ty(hAPP_f1303264185har_ty(produc1096552923har_ty,C_1),Q_2) ) ) ).

tff(fact_535_split__weak__cong,axiom,
    ! [C_1: fun_Pr868791661har_ty,P_1: produc245756905har_ty,Q_2: produc245756905har_ty] :
      ( ( P_1 = Q_2 )
     => ( hAPP_P385447595har_ty(hAPP_f513000995har_ty(produc499452831har_ty,C_1),P_1) = hAPP_P385447595har_ty(hAPP_f513000995har_ty(produc499452831har_ty,C_1),Q_2) ) ) ).

tff(fact_536_split__weak__cong,axiom,
    ! [C_1: fun_li70432166har_ty,P_1: produc917948472har_ty,Q_2: produc917948472har_ty] :
      ( ( P_1 = Q_2 )
     => ( hAPP_P71962758har_ty(hAPP_f909647877har_ty(produc2074304634har_ty,C_1),P_1) = hAPP_P71962758har_ty(hAPP_f909647877har_ty(produc2074304634har_ty,C_1),Q_2) ) ) ).

tff(fact_537_split__weak__cong,axiom,
    ! [C_1: fun_li634443788y_bool,P_1: produc917948472har_ty,Q_2: produc917948472har_ty] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P748443392y_bool(hAPP_f695389733y_bool(produc1322037260y_bool,C_1),P_1))
      <=> hBOOL(hAPP_P748443392y_bool(hAPP_f695389733y_bool(produc1322037260y_bool,C_1),Q_2)) ) ) ).

tff(fact_538_split__weak__cong,axiom,
    ! [C_1: fun_Pr2055965540l_bool,P_1: produc1147203250ar_val,Q_2: produc1147203250ar_val] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P1070896250l_bool(hAPP_f1663301111l_bool(produc1873777030l_bool,C_1),P_1))
      <=> hBOOL(hAPP_P1070896250l_bool(hAPP_f1663301111l_bool(produc1873777030l_bool,C_1),Q_2)) ) ) ).

tff(fact_539_split__weak__cong,axiom,
    ! [C_1: fun_li221477r_bool,P_1: produc809539159t_char,Q_2: produc809539159t_char] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P2014166431r_bool(hAPP_f1484794973r_bool(produc1732333873r_bool,C_1),P_1))
      <=> hBOOL(hAPP_P2014166431r_bool(hAPP_f1484794973r_bool(produc1732333873r_bool,C_1),Q_2)) ) ) ).

tff(fact_540_split__weak__cong,axiom,
    ! [C_1: fun_li1305328058r_bool,P_1: produc2146869324t_char,Q_2: produc2146869324t_char] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P828904212r_bool(hAPP_f895126887r_bool(produc1596557472r_bool,C_1),P_1))
      <=> hBOOL(hAPP_P828904212r_bool(hAPP_f895126887r_bool(produc1596557472r_bool,C_1),Q_2)) ) ) ).

tff(fact_541_split__weak__cong,axiom,
    ! [C_1: fun_li485148903r_bool,P_1: produc952412819t_char,Q_2: produc952412819t_char] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P659547099r_bool(hAPP_f252398939r_bool(produc1324280167r_bool,C_1),P_1))
      <=> hBOOL(hAPP_P659547099r_bool(hAPP_f252398939r_bool(produc1324280167r_bool,C_1),Q_2)) ) ) ).

tff(fact_542_split__weak__cong,axiom,
    ! [C_1: fun_li522008110r_bool,P_1: produc1971331930t_char,Q_2: produc1971331930t_char] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P1680401186r_bool(hAPP_f952817385r_bool(produc723279022r_bool,C_1),P_1))
      <=> hBOOL(hAPP_P1680401186r_bool(hAPP_f952817385r_bool(produc723279022r_bool,C_1),Q_2)) ) ) ).

tff(fact_543_split__weak__cong,axiom,
    ! [C_1: fun_li860735411r_bool,P_1: produc1278157519t_char,Q_2: produc1278157519t_char] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P449474095r_bool(hAPP_f2132060507r_bool(produc1704639885r_bool,C_1),P_1))
      <=> hBOOL(hAPP_P449474095r_bool(hAPP_f2132060507r_bool(produc1704639885r_bool,C_1),Q_2)) ) ) ).

tff(fact_544_split__weak__cong,axiom,
    ! [C_1: fun_li823162622l_bool,P_1: produc639455274on_val,Q_2: produc639455274on_val] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P1235399154l_bool(hAPP_f1443410953l_bool(produc392960766l_bool,C_1),P_1))
      <=> hBOOL(hAPP_P1235399154l_bool(hAPP_f1443410953l_bool(produc392960766l_bool,C_1),Q_2)) ) ) ).

tff(fact_545_split__weak__cong,axiom,
    ! [C_1: fun_val_fun_val_bool,P_1: product_prod_val_val,Q_2: product_prod_val_val] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P929938951l_bool(hAPP_f1534412387l_bool(produc769963999l_bool,C_1),P_1))
      <=> hBOOL(hAPP_P929938951l_bool(hAPP_f1534412387l_bool(produc769963999l_bool,C_1),Q_2)) ) ) ).

tff(fact_546_split__weak__cong,axiom,
    ! [C_1: fun_bo1454185032l_bool,P_1: produc1645268488al_val,Q_2: produc1645268488al_val] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P943837928l_bool(hAPP_f340876351l_bool(produc1326056646l_bool,C_1),P_1))
      <=> hBOOL(hAPP_P943837928l_bool(hAPP_f340876351l_bool(produc1326056646l_bool,C_1),Q_2)) ) ) ).

tff(fact_547_split__weak__cong,axiom,
    ! [C_1: fun_li826105035r_bool,P_1: produc662261637t_char,Q_2: produc662261637t_char] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P2118621157r_bool(hAPP_f1697332217r_bool(produc21910851r_bool,C_1),P_1))
      <=> hBOOL(hAPP_P2118621157r_bool(hAPP_f1697332217r_bool(produc21910851r_bool,C_1),Q_2)) ) ) ).

tff(fact_548_split__weak__cong,axiom,
    ! [C_1: fun_li887890578r_bool,P_1: produc220283002t_char,Q_2: produc220283002t_char] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P1907982426r_bool(hAPP_f102021095r_bool(produc154616760r_bool,C_1),P_1))
      <=> hBOOL(hAPP_P1907982426r_bool(hAPP_f102021095r_bool(produc154616760r_bool,C_1),Q_2)) ) ) ).

tff(fact_549_split__weak__cong,axiom,
    ! [C_1: fun_li1024794712r_bool,P_1: produc1285161482t_char,Q_2: produc1285161482t_char] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P92196306r_bool(hAPP_f1613448899r_bool(produc2027921764r_bool,C_1),P_1))
      <=> hBOOL(hAPP_P92196306r_bool(hAPP_f1613448899r_bool(produc2027921764r_bool,C_1),Q_2)) ) ) ).

tff(fact_550_split__weak__cong,axiom,
    ! [C_1: fun_li1372729616l_bool,P_1: produc2061676504on_val,Q_2: produc2061676504on_val] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P71593144l_bool(hAPP_f1634841927l_bool(produc1491230096l_bool,C_1),P_1))
      <=> hBOOL(hAPP_P71593144l_bool(hAPP_f1634841927l_bool(produc1491230096l_bool,C_1),Q_2)) ) ) ).

tff(fact_551_split__weak__cong,axiom,
    ! [C_1: fun_Pr597144499l_bool,P_1: produc430140671on_val,Q_2: produc430140671on_val] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P1333315679l_bool(hAPP_f1525114763l_bool(produc70644925l_bool,C_1),P_1))
      <=> hBOOL(hAPP_P1333315679l_bool(hAPP_f1525114763l_bool(produc70644925l_bool,C_1),Q_2)) ) ) ).

tff(fact_552_split__weak__cong,axiom,
    ! [C_1: fun_ex1201926843l_bool,P_1: produc124828825on_val,Q_2: produc124828825on_val] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C_1),P_1))
      <=> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C_1),Q_2)) ) ) ).

tff(fact_553_split__weak__cong,axiom,
    ! [C_1: fun_Pr633696065l_bool,P_1: produc1102272487on_val,Q_2: produc1102272487on_val] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C_1),P_1))
      <=> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C_1),Q_2)) ) ) ).

tff(fact_554_split__weak__cong,axiom,
    ! [C_1: fun_fu100249073l_bool,P_1: produc12694297on_val,Q_2: produc12694297on_val] :
      ( ( P_1 = Q_2 )
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C_1),P_1))
      <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C_1),Q_2)) ) ) ).

tff(fact_555_split__weak__cong,axiom,
    ! [C_1: fun_li1301775111ion_ty,P_1: produc639455274on_val,Q_2: produc639455274on_val] :
      ( ( P_1 = Q_2 )
     => ( hAPP_P1228500987ion_ty(hAPP_f46308763ion_ty(produc907433735ion_ty,C_1),P_1) = hAPP_P1228500987ion_ty(hAPP_f46308763ion_ty(produc907433735ion_ty,C_1),Q_2) ) ) ).

tff(fact_556_split__weak__cong,axiom,
    ! [C_1: fun_Pr130335392ar_val,P_1: produc245756905har_ty,Q_2: produc245756905har_ty] :
      ( ( P_1 = Q_2 )
     => ( hAPP_P841862366ar_val(hAPP_f1295640803ar_val(produc1553344466ar_val,C_1),P_1) = hAPP_P841862366ar_val(hAPP_f1295640803ar_val(produc1553344466ar_val,C_1),Q_2) ) ) ).

tff(fact_557_split__twice,axiom,
    ! [F: fun_fu100249073l_bool,G: fun_bo180791194on_val,P_1: produc1645268488al_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_P294971854on_val(hAPP_f1090181127on_val(produc996400752on_val,G),P_1)))
    <=> hBOOL(hAPP_P943837928l_bool(hAPP_f340876351l_bool(produc1326056646l_bool,hAPP_f1150574413l_bool(hAPP_f295212021l_bool(cOMBB_1150072860ol_bop,hAPP_f1936466825l_bool(cOMBB_840638159al_val,hAPP_f2121594859l_bool(produc1958875245l_bool,F))),G)),P_1)) ) ).

tff(fact_558_split__twice,axiom,
    ! [F: fun_fu100249073l_bool,G: fun_li2113382231on_val,P_1: produc662261637t_char] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_P214139537on_val(hAPP_f1679543815on_val(produc2083294131on_val,G),P_1)))
    <=> hBOOL(hAPP_P2118621157r_bool(hAPP_f1697332217r_bool(produc21910851r_bool,hAPP_f1339377933r_bool(hAPP_f1165187701r_bool(cOMBB_1124198201st_val,hAPP_f106757449r_bool(cOMBB_1539035119t_char,hAPP_f2121594859l_bool(produc1958875245l_bool,F))),G)),P_1)) ) ).

tff(fact_559_split__twice,axiom,
    ! [F: fun_fu100249073l_bool,G: fun_li434706128on_val,P_1: produc220283002t_char] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_P216502748on_val(hAPP_f505735499on_val(produc534648062on_val,G),P_1)))
    <=> hBOOL(hAPP_P1907982426r_bool(hAPP_f102021095r_bool(produc154616760r_bool,hAPP_f1944156365r_bool(hAPP_f918235057r_bool(cOMBB_1843549548ist_ty,hAPP_f1346522053r_bool(cOMBB_1115744685t_char,hAPP_f2121594859l_bool(produc1958875245l_bool,F))),G)),P_1)) ) ).

tff(fact_560_split__twice,axiom,
    ! [F: fun_fu100249073l_bool,G: fun_li175451530on_val,P_1: produc1285161482t_char] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_P94592612on_val(hAPP_f2030092415on_val(produc726497362on_val,G),P_1)))
    <=> hBOOL(hAPP_P92196306r_bool(hAPP_f1613448899r_bool(produc2027921764r_bool,hAPP_f829041291r_bool(hAPP_f1691034591r_bool(cOMBB_889837233t_char,hAPP_f1096084527r_bool(cOMBB_1980206754t_char,hAPP_f2121594859l_bool(produc1958875245l_bool,F))),G)),P_1)) ) ).

tff(fact_561_split__twice,axiom,
    ! [F: fun_fu100249073l_bool,G: fun_li414426834on_val,P_1: produc2061676504on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_P1892658174on_val(hAPP_f797861231on_val(produc1450794278on_val,G),P_1)))
    <=> hBOOL(hAPP_P71593144l_bool(hAPP_f1634841927l_bool(produc1491230096l_bool,hAPP_f896993613l_bool(hAPP_f219814819l_bool(cOMBB_143000234t_char,hAPP_f1825030711l_bool(cOMBB_877741809on_val,hAPP_f2121594859l_bool(produc1958875245l_bool,F))),G)),P_1)) ) ).

tff(fact_562_split__twice,axiom,
    ! [F: fun_fu100249073l_bool,G: fun_Pr390299247on_val,P_1: produc430140671on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_P931655063on_val(hAPP_f599509029on_val(produc653117369on_val,G),P_1)))
    <=> hBOOL(hAPP_P1333315679l_bool(hAPP_f1525114763l_bool(produc70644925l_bool,hAPP_f1909521165l_bool(hAPP_f1779944471l_bool(cOMBB_607314500on_val,hAPP_f2131288811l_bool(cOMBB_1173566976on_val,hAPP_f2121594859l_bool(produc1958875245l_bool,F))),G)),P_1)) ) ).

tff(fact_563_split__twice,axiom,
    ! [F: fun_fu100249073l_bool,G: fun_ex1005552999on_val,P_1: produc124828825on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_P789556885on_val(hAPP_f1520199827on_val(produc1174947465on_val,G),P_1)))
    <=> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,hAPP_f653692369l_bool(hAPP_f516738477l_bool(cOMBB_819439237t_char,hAPP_f1825030711l_bool(cOMBB_877741809on_val,hAPP_f2121594859l_bool(produc1958875245l_bool,F))),G)),P_1)) ) ).

tff(fact_564_split__twice,axiom,
    ! [F: fun_fu100249073l_bool,G: fun_Pr1719283041on_val,P_1: produc1102272487on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_P1760219823on_val(hAPP_f394183983on_val(produc1003071703on_val,G),P_1)))
    <=> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,hAPP_f1241216909l_bool(hAPP_f1438732387l_bool(cOMBB_635947099on_val,hAPP_f881985847l_bool(cOMBB_1083177073on_val,hAPP_f2121594859l_bool(produc1958875245l_bool,F))),G)),P_1)) ) ).

tff(fact_565_split__twice,axiom,
    ! [F: fun_Pr130335392ar_val,G: fun_li70432166har_ty,P_1: produc917948472har_ty] : hAPP_P841862366ar_val(hAPP_f1295640803ar_val(produc1553344466ar_val,F),hAPP_P71962758har_ty(hAPP_f909647877har_ty(produc2074304634har_ty,G),P_1)) = hAPP_P1057393871ar_val(hAPP_f528845893ar_val(produc2026840771ar_val,hAPP_f1286352408ar_val(hAPP_f922986761ar_val(cOMBB_491542469t_char,hAPP_f1061710805ar_val(cOMBB_239784108val_ty,hAPP_f1295640803ar_val(produc1553344466ar_val,F))),G)),P_1) ).

tff(fact_566_split__twice,axiom,
    ! [F: fun_Pr1941388516har_ty,G: fun_Pr130335392ar_val,P_1: produc245756905har_ty] : hAPP_P1409535266har_ty(hAPP_f533118691har_ty(produc1582135574har_ty,F),hAPP_P841862366ar_val(hAPP_f1295640803ar_val(produc1553344466ar_val,G),P_1)) = hAPP_P385447595har_ty(hAPP_f513000995har_ty(produc499452831har_ty,hAPP_f1820012432har_ty(hAPP_f1720458941har_ty(cOMBB_424865560t_char,hAPP_f393578581har_ty(cOMBB_1320677736_ty_ty,hAPP_f533118691har_ty(produc1582135574har_ty,F))),G)),P_1) ).

tff(fact_567_split__twice,axiom,
    ! [F: fun_Pr2055965540l_bool,G: fun_Pr130335392ar_val,P_1: produc245756905har_ty] :
      ( hBOOL(hAPP_P1070896250l_bool(hAPP_f1663301111l_bool(produc1873777030l_bool,F),hAPP_P841862366ar_val(hAPP_f1295640803ar_val(produc1553344466ar_val,G),P_1)))
    <=> hBOOL(hAPP_P27757617y_bool(hAPP_f201105125y_bool(produc1851383869y_bool,hAPP_f1796274104y_bool(hAPP_f1589954605y_bool(cOMBB_1380239526t_char,hAPP_f1391360361y_bool(cOMBB_1881684336ool_ty,hAPP_f1663301111l_bool(produc1873777030l_bool,F))),G)),P_1)) ) ).

tff(fact_568_split__twice,axiom,
    ! [F: fun_li634443788y_bool,G: fun_fu63623632har_ty,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P748443392y_bool(hAPP_f695389733y_bool(produc1322037260y_bool,F),hAPP_P1571579700har_ty(hAPP_f1301228297har_ty(produc1250213160har_ty,G),P_1)))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f1617838686l_bool(hAPP_f1740025881l_bool(cOMBB_1511810527on_val,hAPP_f86617653l_bool(cOMBB_165135181on_val,hAPP_f695389733y_bool(produc1322037260y_bool,F))),G)),P_1)) ) ).

tff(fact_569_split__twice,axiom,
    ! [F: fun_Pr2055965540l_bool,G: fun_fu474293322ar_val,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P1070896250l_bool(hAPP_f1663301111l_bool(produc1873777030l_bool,F),hAPP_P1143488942ar_val(hAPP_f1942188169ar_val(produc305181602ar_val,G),P_1)))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f1812276580l_bool(hAPP_f1292837529l_bool(cOMBB_238112345on_val,hAPP_f975490601l_bool(cOMBB_844549459on_val,hAPP_f1663301111l_bool(produc1873777030l_bool,F))),G)),P_1)) ) ).

tff(fact_570_split__twice,axiom,
    ! [F: fun_li221477r_bool,G: fun_fu612303599t_char,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P2014166431r_bool(hAPP_f1484794973r_bool(produc1732333873r_bool,F),hAPP_P1849356627t_char(hAPP_f1865872201t_char(produc1034582855t_char,G),P_1)))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f1351102847l_bool(hAPP_f1342439769l_bool(cOMBB_225914878on_val,hAPP_f99607667l_bool(cOMBB_1334418926on_val,hAPP_f1484794973r_bool(produc1732333873r_bool,F))),G)),P_1)) ) ).

tff(fact_571_split__twice,axiom,
    ! [F: fun_li1305328058r_bool,G: fun_fu511951076t_char,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P828904212r_bool(hAPP_f895126887r_bool(produc1596557472r_bool,F),hAPP_P256420168t_char(hAPP_f2107248649t_char(produc1842330940t_char,G),P_1)))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f337607754l_bool(hAPP_f1546157465l_bool(cOMBB_955482355on_val,hAPP_f1809473245l_bool(cOMBB_1452070457on_val,hAPP_f895126887r_bool(produc1596557472r_bool,F))),G)),P_1)) ) ).

tff(fact_572_split__twice,axiom,
    ! [F: fun_li485148903r_bool,G: fun_fu868535083t_char,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P659547099r_bool(hAPP_f252398939r_bool(produc1324280167r_bool,F),hAPP_P1548494223t_char(hAPP_f681548873t_char(produc2036010883t_char,G),P_1)))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f1525647939l_bool(hAPP_f1338219097l_bool(cOMBB_2122619962on_val,hAPP_f2114578667l_bool(cOMBB_914590898on_val,hAPP_f252398939r_bool(produc1324280167r_bool,F))),G)),P_1)) ) ).

tff(fact_573_split__twice,axiom,
    ! [F: fun_li522008110r_bool,G: fun_fu1941783538t_char,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P1680401186r_bool(hAPP_f952817385r_bool(produc723279022r_bool,F),hAPP_P894177366t_char(hAPP_f1644828553t_char(produc323997770t_char,G),P_1)))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f1158121916l_bool(hAPP_f527861785l_bool(cOMBB_625124865on_val,hAPP_f1566130425l_bool(cOMBB_247395499on_val,hAPP_f952817385r_bool(produc723279022r_bool,F))),G)),P_1)) ) ).

tff(fact_574_split__twice,axiom,
    ! [F: fun_li860735411r_bool,G: fun_fu1104134499t_char,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P449474095r_bool(hAPP_f2132060507r_bool(produc1704639885r_bool,F),hAPP_P193916115t_char(hAPP_f15579599t_char(produc576623071t_char,G),P_1)))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f1996106275l_bool(hAPP_f1550515381l_bool(cOMBB_2040779506on_val,hAPP_f1804599279l_bool(cOMBB_678146046on_val,hAPP_f2132060507r_bool(produc1704639885r_bool,F))),G)),P_1)) ) ).

tff(fact_575_split__twice,axiom,
    ! [F: fun_li823162622l_bool,G: fun_fu540338626on_val,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P1235399154l_bool(hAPP_f1443410953l_bool(produc392960766l_bool,F),hAPP_P1936714534on_val(hAPP_f1271281289on_val(produc928527642on_val,G),P_1)))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f1145600492l_bool(hAPP_f630712985l_bool(cOMBB_1962662865on_val,hAPP_f2020099865l_bool(cOMBB_1543649755on_val,hAPP_f1443410953l_bool(produc392960766l_bool,F))),G)),P_1)) ) ).

tff(fact_576_split__twice,axiom,
    ! [F: fun_val_fun_val_bool,G: fun_fu2114777659al_val,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P929938951l_bool(hAPP_f1534412387l_bool(produc769963999l_bool,F),hAPP_P2013623467al_val(hAPP_f902010623al_val(produc1260869559al_val,G),P_1)))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f1153851723l_bool(hAPP_f151189509l_bool(cOMBB_223841226on_val,hAPP_f1589017327l_bool(cOMBB_558176806on_val,hAPP_f1534412387l_bool(produc769963999l_bool,F))),G)),P_1)) ) ).

tff(fact_577_split__twice,axiom,
    ! [F: fun_bo1454185032l_bool,G: fun_fu1978109084al_val,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P943837928l_bool(hAPP_f340876351l_bool(produc1326056646l_bool,F),hAPP_P1067836940al_val(hAPP_f928795841al_val(produc234747160al_val,G),P_1)))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f828778154l_bool(hAPP_f1572306499l_bool(cOMBB_1210977579on_val,hAPP_f1777594159l_bool(cOMBB_448128005on_val,hAPP_f340876351l_bool(produc1326056646l_bool,F))),G)),P_1)) ) ).

tff(fact_578_split__twice,axiom,
    ! [F: fun_li826105035r_bool,G: fun_fu1679523865t_char,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P2118621157r_bool(hAPP_f1697332217r_bool(produc21910851r_bool,F),hAPP_P1871645065t_char(hAPP_f2116844091t_char(produc1139048085t_char,G),P_1)))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f1576637933l_bool(hAPP_f154583625l_bool(cOMBB_335252392on_val,hAPP_f737797743l_bool(cOMBB_1733006024on_val,hAPP_f1697332217r_bool(produc21910851r_bool,F))),G)),P_1)) ) ).

tff(fact_579_split__twice,axiom,
    ! [F: fun_li887890578r_bool,G: fun_fu313651982t_char,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P1907982426r_bool(hAPP_f102021095r_bool(produc154616760r_bool,F),hAPP_P616991870t_char(hAPP_f1401070501t_char(produc493500298t_char,G),P_1)))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f1121261496l_bool(hAPP_f1331093087l_bool(cOMBB_1472123293on_val,hAPP_f962366127l_bool(cOMBB_95569939on_val,hAPP_f102021095r_bool(produc154616760r_bool,F))),G)),P_1)) ) ).

tff(fact_580_split__twice,axiom,
    ! [F: fun_li1024794712r_bool,G: fun_fu798026914t_char,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P92196306r_bool(hAPP_f1613448899r_bool(produc2027921764r_bool,F),hAPP_P1849522950t_char(hAPP_f314126729t_char(produc1597824762t_char,G),P_1)))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f1089411340l_bool(hAPP_f2012169497l_bool(cOMBB_1443356337on_val,hAPP_f764883801l_bool(cOMBB_1837440507on_val,hAPP_f1613448899r_bool(produc2027921764r_bool,F))),G)),P_1)) ) ).

tff(fact_581_split__twice,axiom,
    ! [F: fun_li1372729616l_bool,G: fun_fu1035619948on_val,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P71593144l_bool(hAPP_f1634841927l_bool(produc1491230096l_bool,F),hAPP_P1963616220on_val(hAPP_f1027788897on_val(produc1202869992on_val,G),P_1)))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f556306650l_bool(hAPP_f1538372259l_bool(cOMBB_157777659on_val,hAPP_f1000925999l_bool(cOMBB_1466435125on_val,hAPP_f1634841927l_bool(produc1491230096l_bool,F))),G)),P_1)) ) ).

tff(fact_582_split__twice,axiom,
    ! [F: fun_Pr597144499l_bool,G: fun_fu239230867on_val,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P1333315679l_bool(hAPP_f1525114763l_bool(produc70644925l_bool,F),hAPP_P963849987on_val(hAPP_f1239545903on_val(produc1476705295on_val,G),P_1)))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f1505175539l_bool(hAPP_f924423253l_bool(cOMBB_1330725154on_val,hAPP_f28987375l_bool(cOMBB_132741582on_val,hAPP_f1525114763l_bool(produc70644925l_bool,F))),G)),P_1)) ) ).

tff(fact_583_split__twice,axiom,
    ! [F: fun_ex1201926843l_bool,G: fun_fu2073188913on_val,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F),hAPP_P604205461on_val(hAPP_f1309113673on_val(produc901351817on_val,G),P_1)))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f850751421l_bool(hAPP_f399538905l_bool(cOMBB_1466889536on_val,hAPP_f1233687287l_bool(cOMBB_171276332on_val,hAPP_f1930574389l_bool(produc1815960045l_bool,F))),G)),P_1)) ) ).

tff(fact_584_split__twice,axiom,
    ! [F: fun_Pr633696065l_bool,G: fun_fu1133203323on_val,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F),hAPP_P2024243179on_val(hAPP_f204556415on_val(produc1148763895on_val,G),P_1)))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f927043595l_bool(hAPP_f1043869573l_bool(cOMBB_1259202826on_val,hAPP_f2052660463l_bool(cOMBB_1292453606on_val,hAPP_f635218277l_bool(produc1911463199l_bool,F))),G)),P_1)) ) ).

tff(fact_585_split__twice,axiom,
    ! [F: fun_li1266570728ar_val,G: fun_Pr868791661har_ty,P_1: produc245756905har_ty] : hAPP_P532450504ar_val(hAPP_f65736581ar_val(produc615345852ar_val,F),hAPP_P385447595har_ty(hAPP_f513000995har_ty(produc499452831har_ty,G),P_1)) = hAPP_P841862366ar_val(hAPP_f1295640803ar_val(produc1553344466ar_val,hAPP_f1582750480ar_val(hAPP_f1761801623ar_val(cOMBB_510504510t_char,hAPP_f1675912277ar_val(cOMBB_351318850val_ty,hAPP_f65736581ar_val(produc615345852ar_val,F))),G)),P_1) ).

tff(fact_586_split__part,axiom,
    ! [Pa: bool,Q_1: fun_fu100249073l_bool,X_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f555424277l_bool(hAPP_f1734879897l_bool(cOMBB_1522540928on_val,hAPP_f1863694447l_bool(cOMBB_383678192on_val,hAPP_b589554111l_bool(fconj,Pa))),Q_1)),X_1))
    <=> ( hBOOL(Pa)
        & hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,Q_1),X_1)) ) ) ).

tff(fact_587_splitD,axiom,
    ! [F: fun_Pr2055965540l_bool,A: produc1278157519t_char,B: val] :
      ( hBOOL(hAPP_P1070896250l_bool(hAPP_f1663301111l_bool(produc1873777030l_bool,F),hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A),B)))
     => hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(F,A),B)) ) ).

tff(fact_588_splitD,axiom,
    ! [F: fun_li221477r_bool,A: list_list_char,B: exp_list_char] :
      ( hBOOL(hAPP_P2014166431r_bool(hAPP_f1484794973r_bool(produc1732333873r_bool,F),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B)))
     => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(F,A),B)) ) ).

tff(fact_589_splitD,axiom,
    ! [F: fun_li1305328058r_bool,A: list_P1940453997har_ty,B: list_P341299826t_char] :
      ( hBOOL(hAPP_P828904212r_bool(hAPP_f895126887r_bool(produc1596557472r_bool,F),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B)))
     => hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(F,A),B)) ) ).

tff(fact_590_splitD,axiom,
    ! [F: fun_li485148903r_bool,A: list_char,B: produc2146869324t_char] :
      ( hBOOL(hAPP_P659547099r_bool(hAPP_f252398939r_bool(produc1324280167r_bool,F),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B)))
     => hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(F,A),B)) ) ).

tff(fact_591_splitD,axiom,
    ! [F: fun_li522008110r_bool,A: list_char,B: produc952412819t_char] :
      ( hBOOL(hAPP_P1680401186r_bool(hAPP_f952817385r_bool(produc723279022r_bool,F),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B)))
     => hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(F,A),B)) ) ).

tff(fact_592_splitD,axiom,
    ! [F: fun_li860735411r_bool,A: list_char,B: list_char] :
      ( hBOOL(hAPP_P449474095r_bool(hAPP_f2132060507r_bool(produc1704639885r_bool,F),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B)))
     => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(F,A),B)) ) ).

tff(fact_593_splitD,axiom,
    ! [F: fun_li823162622l_bool,A: list_char,B: fun_Pr806764899on_val] :
      ( hBOOL(hAPP_P1235399154l_bool(hAPP_f1443410953l_bool(produc392960766l_bool,F),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B)))
     => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(F,A),B)) ) ).

tff(fact_594_splitD,axiom,
    ! [F: fun_val_fun_val_bool,A: val,B: val] :
      ( hBOOL(hAPP_P929938951l_bool(hAPP_f1534412387l_bool(produc769963999l_bool,F),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B)))
     => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(F,A),B)) ) ).

tff(fact_595_splitD,axiom,
    ! [F: fun_bo1454185032l_bool,A: bop,B: product_prod_val_val] :
      ( hBOOL(hAPP_P943837928l_bool(hAPP_f340876351l_bool(produc1326056646l_bool,F),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B)))
     => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(F,A),B)) ) ).

tff(fact_596_splitD,axiom,
    ! [F: fun_li826105035r_bool,A: list_val,B: exp_list_char] :
      ( hBOOL(hAPP_P2118621157r_bool(hAPP_f1697332217r_bool(produc21910851r_bool,F),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B)))
     => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(F,A),B)) ) ).

tff(fact_597_splitD,axiom,
    ! [F: fun_li887890578r_bool,A: list_ty,B: produc662261637t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(hAPP_f102021095r_bool(produc154616760r_bool,F),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B)))
     => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(F,A),B)) ) ).

tff(fact_598_splitD,axiom,
    ! [F: fun_li1024794712r_bool,A: list_list_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P92196306r_bool(hAPP_f1613448899r_bool(produc2027921764r_bool,F),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B)))
     => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(F,A),B)) ) ).

tff(fact_599_splitD,axiom,
    ! [F: fun_li1372729616l_bool,A: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P71593144l_bool(hAPP_f1634841927l_bool(produc1491230096l_bool,F),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(F,A),B)) ) ).

tff(fact_600_splitD,axiom,
    ! [F: fun_Pr597144499l_bool,A: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P1333315679l_bool(hAPP_f1525114763l_bool(produc70644925l_bool,F),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B)))
     => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(F,A),B)) ) ).

tff(fact_601_splitD,axiom,
    ! [F: fun_ex1201926843l_bool,A: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F,A),B)) ) ).

tff(fact_602_splitD,axiom,
    ! [F: fun_Pr633696065l_bool,A: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B)))
     => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F,A),B)) ) ).

tff(fact_603_splitD,axiom,
    ! [F: fun_fu100249073l_bool,A: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B)))
     => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F,A),B)) ) ).

tff(fact_604_prod_Osimps_I2_J,axiom,
    ! [F1: fun_Pr130335392ar_val,A: produc1278157519t_char,B: ty] : hAPP_P841862366ar_val(hAPP_f1295640803ar_val(produc1553344466ar_val,F1),hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A),B)) = hAPP_t97533526ar_val(hAPP_P221287148ar_val(F1,A),B) ).

tff(fact_605_prod_Osimps_I2_J,axiom,
    ! [F1: fun_li1301775111ion_ty,A: list_char,B: fun_Pr806764899on_val] : hAPP_P1228500987ion_ty(hAPP_f46308763ion_ty(produc907433735ion_ty,F1),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B)) = hAPP_f652398900ion_ty(hAPP_l2000496933ion_ty(F1,A),B) ).

tff(fact_606_prod_Osimps_I2_J,axiom,
    ! [F1: fun_fu100249073l_bool,A: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B)))
    <=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F1,A),B)) ) ).

tff(fact_607_split__conv,axiom,
    ! [F: fun_Pr130335392ar_val,A: produc1278157519t_char,B: ty] : hAPP_P841862366ar_val(hAPP_f1295640803ar_val(produc1553344466ar_val,F),hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A),B)) = hAPP_t97533526ar_val(hAPP_P221287148ar_val(F,A),B) ).

tff(fact_608_split__conv,axiom,
    ! [F: fun_li1301775111ion_ty,A: list_char,B: fun_Pr806764899on_val] : hAPP_P1228500987ion_ty(hAPP_f46308763ion_ty(produc907433735ion_ty,F),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B)) = hAPP_f652398900ion_ty(hAPP_l2000496933ion_ty(F,A),B) ).

tff(fact_609_split__conv,axiom,
    ! [F: fun_fu100249073l_bool,A: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B)))
    <=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F,A),B)) ) ).

tff(fact_610_exp_Osimps_I79_J,axiom,
    ! [Exp1_95: exp_list_char,List1_31: list_char,List2_31: list_char,Exp2_95: exp_list_char,Val_11: val] : fAss_list_char(Exp1_95,List1_31,List2_31,Exp2_95) != hAPP_v834067052t_char(val_list_char,Val_11) ).

tff(fact_611_exp_Osimps_I78_J,axiom,
    ! [Val_10: val,Exp1_94: exp_list_char,List1_30: list_char,List2_30: list_char,Exp2_94: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_10) != fAss_list_char(Exp1_94,List1_30,List2_30,Exp2_94) ).

tff(fact_612_exp_Osimps_I77_J,axiom,
    ! [Exp_47: exp_list_char,List1_29: list_char,List2_29: list_char,Val_9: val] : fAcc_list_char(Exp_47,List1_29,List2_29) != hAPP_v834067052t_char(val_list_char,Val_9) ).

tff(fact_613_exp_Osimps_I76_J,axiom,
    ! [Val_8: val,Exp_46: exp_list_char,List1_28: list_char,List2_28: list_char] : hAPP_v834067052t_char(val_list_char,Val_8) != fAcc_list_char(Exp_46,List1_28,List2_28) ).

tff(fact_614_exp_Osimps_I180_J,axiom,
    ! [Exp1_93: exp_list_char,List1_27: list_char,List2_27: list_char,Exp2_93: exp_list_char,Exp_45: exp_list_char] : fAss_list_char(Exp1_93,List1_27,List2_27,Exp2_93) != throw_list_char(Exp_45) ).

tff(fact_615_exp_Osimps_I181_J,axiom,
    ! [Exp_44: exp_list_char,Exp1_92: exp_list_char,List1_26: list_char,List2_26: list_char,Exp2_92: exp_list_char] : throw_list_char(Exp_44) != fAss_list_char(Exp1_92,List1_26,List2_26,Exp2_92) ).

tff(fact_616_red__reds_OCondThrow,axiom,
    ! [Eb: exp_list_char,E_1: exp_list_char,E_2: 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,cond_list_char(throw_list_char(Eb),E_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S)),red(Pa))) ).

tff(fact_617_exp_Osimps_I166_J,axiom,
    ! [Exp_43: exp_list_char,List1_25: list_char,List2_25: list_char,Exp_42: exp_list_char] : fAcc_list_char(Exp_43,List1_25,List2_25) != throw_list_char(Exp_42) ).

tff(fact_618_exp_Osimps_I167_J,axiom,
    ! [Exp_41: exp_list_char,Exp_40: exp_list_char,List1_24: list_char,List2_24: list_char] : throw_list_char(Exp_41) != fAcc_list_char(Exp_40,List1_24,List2_24) ).

tff(fact_619_exp_Osimps_I176_J,axiom,
    ! [Exp1_91: exp_list_char,List1_23: list_char,List2_23: list_char,Exp2_91: exp_list_char,Exp1_90: exp_list_char,Exp2_90: exp_list_char,Exp3_11: exp_list_char] : fAss_list_char(Exp1_91,List1_23,List2_23,Exp2_91) != cond_list_char(Exp1_90,Exp2_90,Exp3_11) ).

tff(fact_620_exp_Osimps_I178_J,axiom,
    ! [Exp1_89: exp_list_char,List1_22: list_char,List2_22: list_char,Exp2_89: exp_list_char,Exp1_88: exp_list_char,Exp2_88: exp_list_char] : fAss_list_char(Exp1_89,List1_22,List2_22,Exp2_89) != while_list_char(Exp1_88,Exp2_88) ).

tff(fact_621_exp_Osimps_I177_J,axiom,
    ! [Exp1_87: exp_list_char,Exp2_87: exp_list_char,Exp3_10: exp_list_char,Exp1_86: exp_list_char,List1_21: list_char,List2_21: list_char,Exp2_86: exp_list_char] : cond_list_char(Exp1_87,Exp2_87,Exp3_10) != fAss_list_char(Exp1_86,List1_21,List2_21,Exp2_86) ).

tff(fact_622_exp_Osimps_I179_J,axiom,
    ! [Exp1_85: exp_list_char,Exp2_85: exp_list_char,Exp1_84: exp_list_char,List1_20: list_char,List2_20: list_char,Exp2_84: exp_list_char] : while_list_char(Exp1_85,Exp2_85) != fAss_list_char(Exp1_84,List1_20,List2_20,Exp2_84) ).

tff(fact_623_exp_Osimps_I162_J,axiom,
    ! [Exp_39: exp_list_char,List1_19: list_char,List2_19: list_char,Exp1_83: exp_list_char,Exp2_83: exp_list_char,Exp3_9: exp_list_char] : fAcc_list_char(Exp_39,List1_19,List2_19) != cond_list_char(Exp1_83,Exp2_83,Exp3_9) ).

tff(fact_624_exp_Osimps_I163_J,axiom,
    ! [Exp1_82: exp_list_char,Exp2_82: exp_list_char,Exp3_8: exp_list_char,Exp_38: exp_list_char,List1_18: list_char,List2_18: list_char] : cond_list_char(Exp1_82,Exp2_82,Exp3_8) != fAcc_list_char(Exp_38,List1_18,List2_18) ).

tff(fact_625_exp_Osimps_I164_J,axiom,
    ! [Exp_37: exp_list_char,List1_17: list_char,List2_17: list_char,Exp1_81: exp_list_char,Exp2_81: exp_list_char] : fAcc_list_char(Exp_37,List1_17,List2_17) != while_list_char(Exp1_81,Exp2_81) ).

tff(fact_626_exp_Osimps_I165_J,axiom,
    ! [Exp1_80: exp_list_char,Exp2_80: exp_list_char,Exp_36: exp_list_char,List1_16: list_char,List2_16: list_char] : while_list_char(Exp1_80,Exp2_80) != fAcc_list_char(Exp_36,List1_16,List2_16) ).

tff(fact_627_split__eta,axiom,
    ! [F: fun_Pr1149393094ar_val] : hAPP_f1295640803ar_val(produc1553344466ar_val,hAPP_f2096521338ar_val(hAPP_f1210767211ar_val(cOMBB_1905001812t_char,hAPP_f1061710805ar_val(cOMBB_239784108val_ty,F)),produc1265154397har_ty)) = F ).

tff(fact_628_split__eta,axiom,
    ! [F: fun_Pr876827561ion_ty] : hAPP_f46308763ion_ty(produc907433735ion_ty,hAPP_f802560783ion_ty(hAPP_f7643013ion_ty(cOMBB_864319000t_char,hAPP_f69964139ion_ty(cOMBB_2041093409on_val,F)),produc823076510on_val)) = F ).

tff(fact_629_split__eta,axiom,
    ! [F: fun_Pr1696029455l_bool] : hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f1363667773l_bool(hAPP_f1050935001l_bool(cOMBB_1153617344on_val,hAPP_f2057883639l_bool(cOMBB_1750801836on_val,F)),produc899768717on_val)) = F ).

tff(fact_630_red__reds_OFAssThrow2,axiom,
    ! [V_1: val,Fa: list_char,Da: list_char,Eb: 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,fAss_list_char(hAPP_v834067052t_char(val_list_char,V_1),Fa,Da,throw_list_char(Eb))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S)),red(Pa))) ).

tff(fact_631_red__reds_OThrowRed,axiom,
    ! [Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E_b)),S_2)),red(Pa))) ) ).

tff(fact_632_red__reds_OThrowThrow,axiom,
    ! [Eb: 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,throw_list_char(throw_list_char(Eb))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S)),red(Pa))) ).

tff(fact_633_red__reds_OCondRed,axiom,
    ! [E_1: exp_list_char,E_2: exp_list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(Eb,E_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(E_b,E_1,E_2)),S_2)),red(Pa))) ) ).

tff(fact_634_red__reds_OFAssThrow1,axiom,
    ! [Eb: exp_list_char,Fa: list_char,Da: list_char,E_2: 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,fAss_list_char(throw_list_char(Eb),Fa,Da,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S)),red(Pa))) ).

tff(fact_635_WTrt__elim__cases_I3_J,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,C_1: exp_list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,while_list_char(Eb,C_1)),Ta))
     => ~ ( ( Ta = void )
         => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),boolean))
           => ! [T_3: ty] : ~ hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,C_1),T_3)) ) ) ) ).

tff(fact_636_WTrt__elim__cases_I2_J,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,E_1: exp_list_char,E_2: exp_list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,cond_list_char(Eb,E_1,E_2)),Ta))
     => ~ ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),boolean))
         => ! [T_1_1: ty] :
              ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_1),T_1_1))
             => ! [T_2_1: ty] :
                  ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,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(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_1),T_1_1)) )
                   => ( ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_1),T_2_1))
                       => ( Ta = T_2_1 ) )
                     => ~ ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_1),T_1_1))
                         => ( Ta = T_1_1 ) ) ) ) ) ) ) ) ).

tff(fact_637_FAssRedsThrow2,axiom,
    ! [Fa: list_char,Da: list_char,E_2: exp_list_char,Eb: exp_list_char,S_2_1: produc12694297on_val,E_1: exp_list_char,S_0: produc12694297on_val,V_1: 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,E_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1)),S_1)),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)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),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,Fa,Da,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_638_WhileRedsThrow,axiom,
    ! [C_1: exp_list_char,B: exp_list_char,S: produc12694297on_val,Eb: exp_list_char,S_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)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S_2)),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_1)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_639_FAccRedsThrow,axiom,
    ! [Fa: list_char,Da: list_char,Eb: exp_list_char,S: produc12694297on_val,A: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2)),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(Eb,Fa,Da)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_640_CondRedsThrow,axiom,
    ! [E_1: exp_list_char,E_2: exp_list_char,Eb: exp_list_char,S: produc12694297on_val,A: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2)),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(Eb,E_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_641_FAssRedsThrow1,axiom,
    ! [Fa: list_char,Da: list_char,E_2: exp_list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E_b)),S_2)),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(Eb,Fa,Da,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E_b)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_642_FAssReds2,axiom,
    ! [V_1: val,Fa: list_char,Da: list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),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_1),Fa,Da,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,V_1),Fa,Da,E_b)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_643_splitE,axiom,
    ! [C_1: fun_Pr2055965540l_bool,P_1: produc1147203250ar_val] :
      ( hBOOL(hAPP_P1070896250l_bool(hAPP_f1663301111l_bool(produc1873777030l_bool,C_1),P_1))
     => ~ ! [X_1: produc1278157519t_char,Y_1: val] :
            ( ( P_1 = hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,X_1),Y_1) )
           => ~ hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(C_1,X_1),Y_1)) ) ) ).

tff(fact_644_splitE,axiom,
    ! [C_1: fun_li221477r_bool,P_1: produc809539159t_char] :
      ( hBOOL(hAPP_P2014166431r_bool(hAPP_f1484794973r_bool(produc1732333873r_bool,C_1),P_1))
     => ~ ! [X_1: list_list_char,Y_1: exp_list_char] :
            ( ( P_1 = hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,X_1),Y_1) )
           => ~ hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(C_1,X_1),Y_1)) ) ) ).

tff(fact_645_splitE,axiom,
    ! [C_1: fun_li1305328058r_bool,P_1: produc2146869324t_char] :
      ( hBOOL(hAPP_P828904212r_bool(hAPP_f895126887r_bool(produc1596557472r_bool,C_1),P_1))
     => ~ ! [X_1: list_P1940453997har_ty,Y_1: list_P341299826t_char] :
            ( ( P_1 = hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,X_1),Y_1) )
           => ~ hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(C_1,X_1),Y_1)) ) ) ).

tff(fact_646_splitE,axiom,
    ! [C_1: fun_li485148903r_bool,P_1: produc952412819t_char] :
      ( hBOOL(hAPP_P659547099r_bool(hAPP_f252398939r_bool(produc1324280167r_bool,C_1),P_1))
     => ~ ! [X_1: list_char,Y_1: produc2146869324t_char] :
            ( ( P_1 = hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,X_1),Y_1) )
           => ~ hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(C_1,X_1),Y_1)) ) ) ).

tff(fact_647_splitE,axiom,
    ! [C_1: fun_li522008110r_bool,P_1: produc1971331930t_char] :
      ( hBOOL(hAPP_P1680401186r_bool(hAPP_f952817385r_bool(produc723279022r_bool,C_1),P_1))
     => ~ ! [X_1: list_char,Y_1: produc952412819t_char] :
            ( ( P_1 = hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,X_1),Y_1) )
           => ~ hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(C_1,X_1),Y_1)) ) ) ).

tff(fact_648_splitE,axiom,
    ! [C_1: fun_li860735411r_bool,P_1: produc1278157519t_char] :
      ( hBOOL(hAPP_P449474095r_bool(hAPP_f2132060507r_bool(produc1704639885r_bool,C_1),P_1))
     => ~ ! [X_1: list_char,Y_1: list_char] :
            ( ( P_1 = hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_1),Y_1) )
           => ~ hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(C_1,X_1),Y_1)) ) ) ).

tff(fact_649_splitE,axiom,
    ! [C_1: fun_li823162622l_bool,P_1: produc639455274on_val] :
      ( hBOOL(hAPP_P1235399154l_bool(hAPP_f1443410953l_bool(produc392960766l_bool,C_1),P_1))
     => ~ ! [X_1: list_char,Y_1: fun_Pr806764899on_val] :
            ( ( P_1 = hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,X_1),Y_1) )
           => ~ hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(C_1,X_1),Y_1)) ) ) ).

tff(fact_650_splitE,axiom,
    ! [C_1: fun_val_fun_val_bool,P_1: product_prod_val_val] :
      ( hBOOL(hAPP_P929938951l_bool(hAPP_f1534412387l_bool(produc769963999l_bool,C_1),P_1))
     => ~ ! [X_1: val,Y_1: val] :
            ( ( P_1 = hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_1),Y_1) )
           => ~ hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(C_1,X_1),Y_1)) ) ) ).

tff(fact_651_splitE,axiom,
    ! [C_1: fun_bo1454185032l_bool,P_1: produc1645268488al_val] :
      ( hBOOL(hAPP_P943837928l_bool(hAPP_f340876351l_bool(produc1326056646l_bool,C_1),P_1))
     => ~ ! [X_1: bop,Y_1: product_prod_val_val] :
            ( ( P_1 = hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,X_1),Y_1) )
           => ~ hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(C_1,X_1),Y_1)) ) ) ).

tff(fact_652_splitE,axiom,
    ! [C_1: fun_li826105035r_bool,P_1: produc662261637t_char] :
      ( hBOOL(hAPP_P2118621157r_bool(hAPP_f1697332217r_bool(produc21910851r_bool,C_1),P_1))
     => ~ ! [X_1: list_val,Y_1: exp_list_char] :
            ( ( P_1 = hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,X_1),Y_1) )
           => ~ hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(C_1,X_1),Y_1)) ) ) ).

tff(fact_653_splitE,axiom,
    ! [C_1: fun_li887890578r_bool,P_1: produc220283002t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(hAPP_f102021095r_bool(produc154616760r_bool,C_1),P_1))
     => ~ ! [X_1: list_ty,Y_1: produc662261637t_char] :
            ( ( P_1 = hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,X_1),Y_1) )
           => ~ hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(C_1,X_1),Y_1)) ) ) ).

tff(fact_654_splitE,axiom,
    ! [C_1: fun_li1024794712r_bool,P_1: produc1285161482t_char] :
      ( hBOOL(hAPP_P92196306r_bool(hAPP_f1613448899r_bool(produc2027921764r_bool,C_1),P_1))
     => ~ ! [X_1: list_list_char,Y_1: produc220283002t_char] :
            ( ( P_1 = hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,X_1),Y_1) )
           => ~ hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(C_1,X_1),Y_1)) ) ) ).

tff(fact_655_splitE,axiom,
    ! [C_1: fun_li1372729616l_bool,P_1: produc2061676504on_val] :
      ( hBOOL(hAPP_P71593144l_bool(hAPP_f1634841927l_bool(produc1491230096l_bool,C_1),P_1))
     => ~ ! [X_1: list_exp_list_char,Y_1: produc12694297on_val] :
            ( ( P_1 = hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,X_1),Y_1) )
           => ~ hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(C_1,X_1),Y_1)) ) ) ).

tff(fact_656_splitE,axiom,
    ! [C_1: fun_Pr597144499l_bool,P_1: produc430140671on_val] :
      ( hBOOL(hAPP_P1333315679l_bool(hAPP_f1525114763l_bool(produc70644925l_bool,C_1),P_1))
     => ~ ! [X_1: produc2061676504on_val,Y_1: produc2061676504on_val] :
            ( ( P_1 = hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,X_1),Y_1) )
           => ~ hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(C_1,X_1),Y_1)) ) ) ).

tff(fact_657_splitE,axiom,
    ! [C_1: fun_ex1201926843l_bool,P_1: produc124828825on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C_1),P_1))
     => ~ ! [X_1: exp_list_char,Y_1: produc12694297on_val] :
            ( ( P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X_1),Y_1) )
           => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(C_1,X_1),Y_1)) ) ) ).

tff(fact_658_splitE,axiom,
    ! [C_1: fun_Pr633696065l_bool,P_1: produc1102272487on_val] :
      ( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C_1),P_1))
     => ~ ! [X_1: produc124828825on_val,Y_1: produc124828825on_val] :
            ( ( P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X_1),Y_1) )
           => ~ hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(C_1,X_1),Y_1)) ) ) ).

tff(fact_659_splitE,axiom,
    ! [C_1: fun_fu100249073l_bool,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C_1),P_1))
     => ~ ! [X_1: fun_na939144002on_val,Y_1: fun_li1432931796on_val] :
            ( ( P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X_1),Y_1) )
           => ~ hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(C_1,X_1),Y_1)) ) ) ).

tff(fact_660_splitI2,axiom,
    ! [C_1: fun_Pr2055965540l_bool,P_1: produc1147203250ar_val] :
      ( ! [A_1: produc1278157519t_char,B_1: val] :
          ( ( P_1 = hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_1),B_1) )
         => hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(C_1,A_1),B_1)) )
     => hBOOL(hAPP_P1070896250l_bool(hAPP_f1663301111l_bool(produc1873777030l_bool,C_1),P_1)) ) ).

tff(fact_661_splitI2,axiom,
    ! [C_1: fun_li221477r_bool,P_1: produc809539159t_char] :
      ( ! [A_1: list_list_char,B_1: exp_list_char] :
          ( ( P_1 = hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_1) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(C_1,A_1),B_1)) )
     => hBOOL(hAPP_P2014166431r_bool(hAPP_f1484794973r_bool(produc1732333873r_bool,C_1),P_1)) ) ).

tff(fact_662_splitI2,axiom,
    ! [C_1: fun_li1305328058r_bool,P_1: produc2146869324t_char] :
      ( ! [A_1: list_P1940453997har_ty,B_1: list_P341299826t_char] :
          ( ( P_1 = hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_1) )
         => hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(C_1,A_1),B_1)) )
     => hBOOL(hAPP_P828904212r_bool(hAPP_f895126887r_bool(produc1596557472r_bool,C_1),P_1)) ) ).

tff(fact_663_splitI2,axiom,
    ! [C_1: fun_li485148903r_bool,P_1: produc952412819t_char] :
      ( ! [A_1: list_char,B_1: produc2146869324t_char] :
          ( ( P_1 = hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_1) )
         => hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(C_1,A_1),B_1)) )
     => hBOOL(hAPP_P659547099r_bool(hAPP_f252398939r_bool(produc1324280167r_bool,C_1),P_1)) ) ).

tff(fact_664_splitI2,axiom,
    ! [C_1: fun_li522008110r_bool,P_1: produc1971331930t_char] :
      ( ! [A_1: list_char,B_1: produc952412819t_char] :
          ( ( P_1 = hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_1) )
         => hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(C_1,A_1),B_1)) )
     => hBOOL(hAPP_P1680401186r_bool(hAPP_f952817385r_bool(produc723279022r_bool,C_1),P_1)) ) ).

tff(fact_665_splitI2,axiom,
    ! [C_1: fun_li860735411r_bool,P_1: produc1278157519t_char] :
      ( ! [A_1: list_char,B_1: list_char] :
          ( ( P_1 = hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_1) )
         => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(C_1,A_1),B_1)) )
     => hBOOL(hAPP_P449474095r_bool(hAPP_f2132060507r_bool(produc1704639885r_bool,C_1),P_1)) ) ).

tff(fact_666_splitI2,axiom,
    ! [C_1: fun_li823162622l_bool,P_1: produc639455274on_val] :
      ( ! [A_1: list_char,B_1: fun_Pr806764899on_val] :
          ( ( P_1 = hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_1) )
         => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(C_1,A_1),B_1)) )
     => hBOOL(hAPP_P1235399154l_bool(hAPP_f1443410953l_bool(produc392960766l_bool,C_1),P_1)) ) ).

tff(fact_667_splitI2,axiom,
    ! [C_1: fun_val_fun_val_bool,P_1: product_prod_val_val] :
      ( ! [A_1: val,B_1: val] :
          ( ( P_1 = hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_1) )
         => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(C_1,A_1),B_1)) )
     => hBOOL(hAPP_P929938951l_bool(hAPP_f1534412387l_bool(produc769963999l_bool,C_1),P_1)) ) ).

tff(fact_668_splitI2,axiom,
    ! [C_1: fun_bo1454185032l_bool,P_1: produc1645268488al_val] :
      ( ! [A_1: bop,B_1: product_prod_val_val] :
          ( ( P_1 = hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_1) )
         => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(C_1,A_1),B_1)) )
     => hBOOL(hAPP_P943837928l_bool(hAPP_f340876351l_bool(produc1326056646l_bool,C_1),P_1)) ) ).

tff(fact_669_splitI2,axiom,
    ! [C_1: fun_li826105035r_bool,P_1: produc662261637t_char] :
      ( ! [A_1: list_val,B_1: exp_list_char] :
          ( ( P_1 = hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_1) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(C_1,A_1),B_1)) )
     => hBOOL(hAPP_P2118621157r_bool(hAPP_f1697332217r_bool(produc21910851r_bool,C_1),P_1)) ) ).

tff(fact_670_splitI2,axiom,
    ! [C_1: fun_li887890578r_bool,P_1: produc220283002t_char] :
      ( ! [A_1: list_ty,B_1: produc662261637t_char] :
          ( ( P_1 = hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_1) )
         => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(C_1,A_1),B_1)) )
     => hBOOL(hAPP_P1907982426r_bool(hAPP_f102021095r_bool(produc154616760r_bool,C_1),P_1)) ) ).

tff(fact_671_splitI2,axiom,
    ! [C_1: fun_li1024794712r_bool,P_1: produc1285161482t_char] :
      ( ! [A_1: list_list_char,B_1: produc220283002t_char] :
          ( ( P_1 = hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_1) )
         => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(C_1,A_1),B_1)) )
     => hBOOL(hAPP_P92196306r_bool(hAPP_f1613448899r_bool(produc2027921764r_bool,C_1),P_1)) ) ).

tff(fact_672_splitI2,axiom,
    ! [C_1: fun_li1372729616l_bool,P_1: produc2061676504on_val] :
      ( ! [A_1: list_exp_list_char,B_1: produc12694297on_val] :
          ( ( P_1 = hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_1) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(C_1,A_1),B_1)) )
     => hBOOL(hAPP_P71593144l_bool(hAPP_f1634841927l_bool(produc1491230096l_bool,C_1),P_1)) ) ).

tff(fact_673_splitI2,axiom,
    ! [C_1: fun_Pr597144499l_bool,P_1: produc430140671on_val] :
      ( ! [A_1: produc2061676504on_val,B_1: produc2061676504on_val] :
          ( ( P_1 = hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_1) )
         => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(C_1,A_1),B_1)) )
     => hBOOL(hAPP_P1333315679l_bool(hAPP_f1525114763l_bool(produc70644925l_bool,C_1),P_1)) ) ).

tff(fact_674_splitI2,axiom,
    ! [C_1: fun_ex1201926843l_bool,P_1: produc124828825on_val] :
      ( ! [A_1: exp_list_char,B_1: produc12694297on_val] :
          ( ( P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_1) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(C_1,A_1),B_1)) )
     => hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C_1),P_1)) ) ).

tff(fact_675_splitI2,axiom,
    ! [C_1: fun_Pr633696065l_bool,P_1: produc1102272487on_val] :
      ( ! [A_1: produc124828825on_val,B_1: produc124828825on_val] :
          ( ( P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_1) )
         => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(C_1,A_1),B_1)) )
     => hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C_1),P_1)) ) ).

tff(fact_676_splitI2,axiom,
    ! [C_1: fun_fu100249073l_bool,P_1: produc12694297on_val] :
      ( ! [A_1: fun_na939144002on_val,B_1: fun_li1432931796on_val] :
          ( ( P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_1) )
         => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(C_1,A_1),B_1)) )
     => hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C_1),P_1)) ) ).

tff(fact_677_ThrowReds,axiom,
    ! [Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),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(Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E_b)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_678_ThrowRedsThrow,axiom,
    ! [Eb: exp_list_char,S: produc12694297on_val,A: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2)),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(Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_679_FAssReds1,axiom,
    ! [Fa: list_char,Da: list_char,E_2: exp_list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),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(Eb,Fa,Da,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(E_b,Fa,Da,E_2)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_680_CondReds,axiom,
    ! [E_1: exp_list_char,E_2: exp_list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),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(Eb,E_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(E_b,E_1,E_2)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_681_FAccReds,axiom,
    ! [Fa: list_char,Da: list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),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(Eb,Fa,Da)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(E_b,Fa,Da)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_682_rtrancl_Ortrancl__refl,axiom,
    ! [A: list_char,R_1: fun_Pr565113489r_bool] : hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),A),transi1395422419t_char(R_1))) ).

tff(fact_683_rtrancl_Ortrancl__refl,axiom,
    ! [A: produc2061676504on_val,R_1: fun_Pr859510977l_bool] : hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),A),transi374442731on_val(R_1))) ).

tff(fact_684_rtrancl_Ortrancl__refl,axiom,
    ! [A: produc124828825on_val,R_1: fun_Pr691271849l_bool] : hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),A),transi2024712006on_val(R_1))) ).

tff(fact_685_rtrancl_Ortrancl__refl,axiom,
    ! [A: val,R_1: fun_Pr2081272681l_bool] : hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),A),transi935034983cl_val(R_1))) ).

tff(fact_686_cond__split__eta,axiom,
    ! [F: fun_Pr130335392ar_val,G: fun_Pr1149393094ar_val] :
      ( ! [X_1: produc1278157519t_char,Y_1: ty] : hAPP_t97533526ar_val(hAPP_P221287148ar_val(F,X_1),Y_1) = hAPP_P841862366ar_val(G,hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,X_1),Y_1))
     => ( hAPP_f1295640803ar_val(produc1553344466ar_val,F) = G ) ) ).

tff(fact_687_cond__split__eta,axiom,
    ! [F: fun_li1301775111ion_ty,G: fun_Pr876827561ion_ty] :
      ( ! [X_1: list_char,Y_1: fun_Pr806764899on_val] : hAPP_f652398900ion_ty(hAPP_l2000496933ion_ty(F,X_1),Y_1) = hAPP_P1228500987ion_ty(G,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,X_1),Y_1))
     => ( hAPP_f46308763ion_ty(produc907433735ion_ty,F) = G ) ) ).

tff(fact_688_cond__split__eta,axiom,
    ! [G: fun_Pr1696029455l_bool,F: fun_fu100249073l_bool] :
      ( ! [X_1: fun_na939144002on_val,Y_1: fun_li1432931796on_val] :
          ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F,X_1),Y_1))
        <=> hBOOL(hAPP_P159683425l_bool(G,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X_1),Y_1))) )
     => ( hAPP_f2121594859l_bool(produc1958875245l_bool,F) = G ) ) ).

tff(fact_689_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_690_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_691_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_692_WhileTRedsThrow,axiom,
    ! [C_1: exp_list_char,Eb: exp_list_char,S_2_1: produc12694297on_val,B: exp_list_char,S_0: produc12694297on_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,B),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_1),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),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_1)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_693_splitE2,axiom,
    ! [Q_1: fun_Pr661739816l_bool,Pa: fun_Pr130335392ar_val,Z_1: produc245756905har_ty] :
      ( hBOOL(hAPP_P1070896250l_bool(Q_1,hAPP_P841862366ar_val(hAPP_f1295640803ar_val(produc1553344466ar_val,Pa),Z_1)))
     => ~ ! [X_1: produc1278157519t_char,Y_1: ty] :
            ( ( Z_1 = hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,X_1),Y_1) )
           => ~ hBOOL(hAPP_P1070896250l_bool(Q_1,hAPP_t97533526ar_val(hAPP_P221287148ar_val(Pa,X_1),Y_1))) ) ) ).

tff(fact_694_splitE2,axiom,
    ! [Q_1: fun_option_ty_bool,Pa: fun_li1301775111ion_ty,Z_1: produc639455274on_val] :
      ( hBOOL(hAPP_option_ty_bool(Q_1,hAPP_P1228500987ion_ty(hAPP_f46308763ion_ty(produc907433735ion_ty,Pa),Z_1)))
     => ~ ! [X_1: list_char,Y_1: fun_Pr806764899on_val] :
            ( ( Z_1 = hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,X_1),Y_1) )
           => ~ hBOOL(hAPP_option_ty_bool(Q_1,hAPP_f652398900ion_ty(hAPP_l2000496933ion_ty(Pa,X_1),Y_1))) ) ) ).

tff(fact_695_splitE2,axiom,
    ! [Q_1: fun_bool_bool,Pa: fun_fu100249073l_bool,Z_1: produc12694297on_val] :
      ( hBOOL(hAPP_bool_bool(Q_1,hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,Pa),Z_1)))
     => ~ ! [X_1: fun_na939144002on_val,Y_1: fun_li1432931796on_val] :
            ( ( Z_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X_1),Y_1) )
           => ~ hBOOL(hAPP_bool_bool(Q_1,hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,X_1),Y_1))) ) ) ).

tff(fact_696_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr565113489r_bool] : transi1395422419t_char(transi1395422419t_char(R_1)) = transi1395422419t_char(R_1) ).

tff(fact_697_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr859510977l_bool] : transi374442731on_val(transi374442731on_val(R_1)) = transi374442731on_val(R_1) ).

tff(fact_698_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr691271849l_bool] : transi2024712006on_val(transi2024712006on_val(R_1)) = transi2024712006on_val(R_1) ).

tff(fact_699_red__reds_ORedCondF,axiom,
    ! [E_1: exp_list_char,E_2: 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,cond_list_char(hAPP_v834067052t_char(val_list_char,bool_1(fFalse)),E_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S)),red(Pa))) ).

tff(fact_700_red__reds_ORedCondT,axiom,
    ! [E_1: exp_list_char,E_2: 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,cond_list_char(hAPP_v834067052t_char(val_list_char,bool_1(fTrue)),E_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1),S)),red(Pa))) ).

tff(fact_701_rtrancl__trans,axiom,
    ! [C_1: list_char,A: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B),transi1395422419t_char(R_1)))
     => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B),C_1),transi1395422419t_char(R_1)))
       => hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),C_1),transi1395422419t_char(R_1))) ) ) ).

tff(fact_702_rtrancl__trans,axiom,
    ! [C_1: produc2061676504on_val,A: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B),transi374442731on_val(R_1)))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B),C_1),transi374442731on_val(R_1)))
       => hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),C_1),transi374442731on_val(R_1))) ) ) ).

tff(fact_703_rtrancl__trans,axiom,
    ! [C_1: produc124828825on_val,A: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B),transi2024712006on_val(R_1)))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B),C_1),transi2024712006on_val(R_1)))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),C_1),transi2024712006on_val(R_1))) ) ) ).

tff(fact_704_rtrancl__trans,axiom,
    ! [C_1: val,A: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B),transi935034983cl_val(R_1)))
     => ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B),C_1),transi935034983cl_val(R_1)))
       => hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),C_1),transi935034983cl_val(R_1))) ) ) ).

tff(fact_705_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: list_char,A: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B),transi1395422419t_char(R_1)))
     => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B),C_1),R_1))
       => hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),C_1),transi1395422419t_char(R_1))) ) ) ).

tff(fact_706_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc2061676504on_val,A: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B),transi374442731on_val(R_1)))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B),C_1),R_1))
       => hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),C_1),transi374442731on_val(R_1))) ) ) ).

tff(fact_707_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc124828825on_val,A: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B),transi2024712006on_val(R_1)))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B),C_1),R_1))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),C_1),transi2024712006on_val(R_1))) ) ) ).

tff(fact_708_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: val,A: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B),transi935034983cl_val(R_1)))
     => ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B),C_1),R_1))
       => hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),C_1),transi935034983cl_val(R_1))) ) ) ).

tff(fact_709_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: list_char,A: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B),R_1))
     => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B),C_1),transi1395422419t_char(R_1)))
       => hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),C_1),transi1395422419t_char(R_1))) ) ) ).

tff(fact_710_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc2061676504on_val,A: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B),R_1))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B),C_1),transi374442731on_val(R_1)))
       => hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),C_1),transi374442731on_val(R_1))) ) ) ).

tff(fact_711_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc124828825on_val,A: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B),R_1))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B),C_1),transi2024712006on_val(R_1)))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),C_1),transi2024712006on_val(R_1))) ) ) ).

tff(fact_712_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: val,A: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B),R_1))
     => ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B),C_1),transi935034983cl_val(R_1)))
       => hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),C_1),transi935034983cl_val(R_1))) ) ) ).

tff(fact_713_CondReds2F,axiom,
    ! [E_1: exp_list_char,E_2: exp_list_char,E_b: exp_list_char,S_2_1: produc12694297on_val,Eb: exp_list_char,S_0: produc12694297on_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,Eb),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,bool_1(fFalse))),S_1)),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)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),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(Eb,E_1,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_714_CondReds2T,axiom,
    ! [E_2: exp_list_char,E_1: exp_list_char,E_b: exp_list_char,S_2_1: produc12694297on_val,Eb: exp_list_char,S_0: produc12694297on_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,Eb),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1)),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)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),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(Eb,E_1,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_715_WhileTReds,axiom,
    ! [Eb: exp_list_char,S_3_1: produc12694297on_val,C_1: exp_list_char,V_1_2: val,S_2_1: produc12694297on_val,B: exp_list_char,S_0: produc12694297on_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,B),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_1),S_1)),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_1)),S_2_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),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_1)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S_3_1)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_716_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_1: 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_1),B_1)),R_1))
             => ~ hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Za),Zb)),transi374442731on_val(R_1))) ) ) ) ).

tff(fact_717_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_1: 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_1),B_1)),R_1))
             => ~ hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Za),Zb)),transi2024712006on_val(R_1))) ) ) ) ).

tff(fact_718_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_1: 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_1),B_1)),R_1))
             => ~ hBOOL(member619264020ar_val(hAPP_P976385092ar_val(hAPP_P800634639ar_val(produc1317546007ar_val,hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,A_1),B_1)),hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,Za),Zb)),transi1600669663ar_val(R_1))) ) ) ) ).

tff(fact_719_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_1: 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_1),B_1)),R_1))
             => ~ hBOOL(member1999287380t_char(hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_1)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Za),Zb)),transi198989188t_char(R_1))) ) ) ) ).

tff(fact_720_converse__rtranclE2,axiom,
    ! [Xa_1: list_P1940453997har_ty,Xb_1: list_P341299826t_char,Za: list_P1940453997har_ty,Zb: list_P341299826t_char,R_1: fun_Pr286306793r_bool] :
      ( hBOOL(member1551446420t_char(hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Xa_1),Xb_1)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Za),Zb)),transi772168185t_char(R_1)))
     => ( ( hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Xa_1),Xb_1) != hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Za),Zb) )
       => ~ ! [A_1: list_P1940453997har_ty,B_1: list_P341299826t_char] :
              ( hBOOL(member1551446420t_char(hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Xa_1),Xb_1)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_1)),R_1))
             => ~ hBOOL(member1551446420t_char(hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_1)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Za),Zb)),transi772168185t_char(R_1))) ) ) ) ).

tff(fact_721_converse__rtranclE2,axiom,
    ! [Xa_1: list_char,Xb_1: produc2146869324t_char,Za: list_char,Zb: produc2146869324t_char,R_1: fun_Pr1538825897r_bool] :
      ( hBOOL(member1607118676t_char(hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Xa_1),Xb_1)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Za),Zb)),transi2005320128t_char(R_1)))
     => ( ( hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Xa_1),Xb_1) != hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Za),Zb) )
       => ~ ! [A_1: list_char,B_1: produc2146869324t_char] :
              ( hBOOL(member1607118676t_char(hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Xa_1),Xb_1)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_1)),R_1))
             => ~ hBOOL(member1607118676t_char(hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_1)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Za),Zb)),transi2005320128t_char(R_1))) ) ) ) ).

tff(fact_722_converse__rtranclE2,axiom,
    ! [Xa_1: list_char,Xb_1: produc952412819t_char,Za: list_char,Zb: produc952412819t_char,R_1: fun_Pr981088873r_bool] :
      ( hBOOL(member162552852t_char(hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Xa_1),Xb_1)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Za),Zb)),transi1123801095t_char(R_1)))
     => ( ( hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Xa_1),Xb_1) != hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Za),Zb) )
       => ~ ! [A_1: list_char,B_1: produc952412819t_char] :
              ( hBOOL(member162552852t_char(hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Xa_1),Xb_1)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_1)),R_1))
             => ~ hBOOL(member162552852t_char(hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_1)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Za),Zb)),transi1123801095t_char(R_1))) ) ) ) ).

tff(fact_723_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_1: 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_1),B_1)),R_1))
             => ~ hBOOL(member794220506t_char(hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_1)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Za),Zb)),transi1095029602t_char(R_1))) ) ) ) ).

tff(fact_724_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_1: 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_1),B_1)),R_1))
             => ~ hBOOL(member1322055188on_val(hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_1)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Za),Zb)),transi61620055on_val(R_1))) ) ) ) ).

tff(fact_725_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_1: 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_1),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_1),B_1)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Za),Zb)),transi1423755450al_val(R_1))) ) ) ) ).

tff(fact_726_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_1: 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_1),B_1)),R_1))
             => ~ hBOOL(member1732271180al_val(hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_1)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Za),Zb)),transi1906258203al_val(R_1))) ) ) ) ).

tff(fact_727_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_1: 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_1),B_1)),R_1))
             => ~ hBOOL(member1161907014t_char(hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_1)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Za),Zb)),transi1789604888t_char(R_1))) ) ) ) ).

tff(fact_728_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_1: 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_1),B_1)),R_1))
             => ~ hBOOL(member125098544t_char(hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_1)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Za),Zb)),transi1257872013t_char(R_1))) ) ) ) ).

tff(fact_729_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_1: 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_1),B_1)),R_1))
             => ~ hBOOL(member1420286996t_char(hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_1)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Za),Zb)),transi122195895t_char(R_1))) ) ) ) ).

tff(fact_730_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_1: 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_1),B_1)),R_1))
             => ~ hBOOL(member88670778on_val(hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_1)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Za),Zb)),transi208336786on_val(R_1))) ) ) ) ).

tff(fact_731_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_1: 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_1),B_1)),R_1))
             => ~ hBOOL(member808015754on_val(hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_1)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Za),Zb)),transi910771962on_val(R_1))) ) ) ) ).

tff(fact_732_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_1: 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_1),B_1)),R_1))
             => ~ hBOOL(member563141460on_val(hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Za),Zb)),transi921647814on_val(R_1))) ) ) ) ).

tff(fact_733_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_1: 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_1),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_1),B_1)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_734_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_1: 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_1),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_1),B_1)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_735_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_1: 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_1),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_1),B_1)) ) ) )
         => hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_736_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_1: 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_1),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_1),B_1)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_737_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li1305328058r_bool,Ax: list_P1940453997har_ty,Ay: list_P341299826t_char,Bx: list_P1940453997har_ty,By: list_P341299826t_char,R_1: fun_Pr286306793r_bool] :
      ( hBOOL(member1551446420t_char(hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Ax),Ay)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Bx),By)),transi772168185t_char(R_1)))
     => ( hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,Bx),By))
       => ( ! [A_1: list_P1940453997har_ty,B_1: list_P341299826t_char,Aa: list_P1940453997har_ty,Ba: list_P341299826t_char] :
              ( hBOOL(member1551446420t_char(hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_1)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Aa),Ba)),R_1))
             => ( hBOOL(member1551446420t_char(hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Aa),Ba)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Bx),By)),transi772168185t_char(R_1)))
               => ( hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_738_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li485148903r_bool,Ax: list_char,Ay: produc2146869324t_char,Bx: list_char,By: produc2146869324t_char,R_1: fun_Pr1538825897r_bool] :
      ( hBOOL(member1607118676t_char(hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Ax),Ay)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Bx),By)),transi2005320128t_char(R_1)))
     => ( hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,Bx),By))
       => ( ! [A_1: list_char,B_1: produc2146869324t_char,Aa: list_char,Ba: produc2146869324t_char] :
              ( hBOOL(member1607118676t_char(hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_1)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Aa),Ba)),R_1))
             => ( hBOOL(member1607118676t_char(hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Aa),Ba)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Bx),By)),transi2005320128t_char(R_1)))
               => ( hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_739_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li522008110r_bool,Ax: list_char,Ay: produc952412819t_char,Bx: list_char,By: produc952412819t_char,R_1: fun_Pr981088873r_bool] :
      ( hBOOL(member162552852t_char(hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Ax),Ay)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Bx),By)),transi1123801095t_char(R_1)))
     => ( hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,Bx),By))
       => ( ! [A_1: list_char,B_1: produc952412819t_char,Aa: list_char,Ba: produc952412819t_char] :
              ( hBOOL(member162552852t_char(hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_1)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Aa),Ba)),R_1))
             => ( hBOOL(member162552852t_char(hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Aa),Ba)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Bx),By)),transi1123801095t_char(R_1)))
               => ( hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_740_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_1: 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_1),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_1),B_1)) ) ) )
         => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_741_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_1: 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_1),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_1),B_1)) ) ) )
         => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_742_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_1: 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_1),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_1),B_1)) ) ) )
         => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_743_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_1: 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_1),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_1),B_1)) ) ) )
         => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_744_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_1: 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_1),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_1),B_1)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_745_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_1: 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_1),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_1),B_1)) ) ) )
         => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_746_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_1: 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_1),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_1),B_1)) ) ) )
         => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_747_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_1: 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_1),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_1),B_1)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_748_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_1: 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_1),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_1),B_1)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_749_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_1: 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_1),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_1),B_1)) ) ) )
         => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_750_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_1: 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_1),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_1),B_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_751_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_1: 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_1),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_1),B_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_752_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_1: 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_1),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_1),B_1)),hAPP_v48258637ar_val(hAPP_P1321848547ar_val(produc2036181286ar_val,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_val_bool(hAPP_P486515074l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_753_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_1: 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_1),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_1),B_1)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_754_rtrancl__induct2,axiom,
    ! [Pa: fun_li1305328058r_bool,Ax: list_P1940453997har_ty,Ay: list_P341299826t_char,Bx: list_P1940453997har_ty,By: list_P341299826t_char,R_1: fun_Pr286306793r_bool] :
      ( hBOOL(member1551446420t_char(hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Ax),Ay)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Bx),By)),transi772168185t_char(R_1)))
     => ( hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_P1940453997har_ty,B_1: list_P341299826t_char,Aa: list_P1940453997har_ty,Ba: list_P341299826t_char] :
              ( hBOOL(member1551446420t_char(hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Ax),Ay)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_1)),transi772168185t_char(R_1)))
             => ( hBOOL(member1551446420t_char(hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_1)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_755_rtrancl__induct2,axiom,
    ! [Pa: fun_li485148903r_bool,Ax: list_char,Ay: produc2146869324t_char,Bx: list_char,By: produc2146869324t_char,R_1: fun_Pr1538825897r_bool] :
      ( hBOOL(member1607118676t_char(hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Ax),Ay)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Bx),By)),transi2005320128t_char(R_1)))
     => ( hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_char,B_1: produc2146869324t_char,Aa: list_char,Ba: produc2146869324t_char] :
              ( hBOOL(member1607118676t_char(hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Ax),Ay)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_1)),transi2005320128t_char(R_1)))
             => ( hBOOL(member1607118676t_char(hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_1)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_756_rtrancl__induct2,axiom,
    ! [Pa: fun_li522008110r_bool,Ax: list_char,Ay: produc952412819t_char,Bx: list_char,By: produc952412819t_char,R_1: fun_Pr981088873r_bool] :
      ( hBOOL(member162552852t_char(hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Ax),Ay)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Bx),By)),transi1123801095t_char(R_1)))
     => ( hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_char,B_1: produc952412819t_char,Aa: list_char,Ba: produc952412819t_char] :
              ( hBOOL(member162552852t_char(hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Ax),Ay)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_1)),transi1123801095t_char(R_1)))
             => ( hBOOL(member162552852t_char(hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_1)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_757_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_1: 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_1),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_1),B_1)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_758_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_1: 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_1),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_1),B_1)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_759_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_1: 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_1),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_1),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_1),B_1))
                 => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_760_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_1: 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_1),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_1),B_1)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_761_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_1: 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_1),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_1),B_1)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_762_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_1: 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_1),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_1),B_1)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_763_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_1: 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_1),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_1),B_1)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_764_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_1: 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_1),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_1),B_1)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_765_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_1: 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_1),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_1),B_1)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_766_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_1: 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_1),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_1),B_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Aa),Ba)),R_1))
               => ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_767_WhileFReds,axiom,
    ! [C_1: exp_list_char,B: exp_list_char,S: produc12694297on_val,S_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)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,bool_1(fFalse))),S_2)),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_1)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,unit)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_768_rtranclE,axiom,
    ! [A: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B),transi1395422419t_char(R_1)))
     => ( ( A != B )
       => ~ ! [Y_1: list_char] :
              ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),Y_1),transi1395422419t_char(R_1)))
             => ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Y_1),B),R_1)) ) ) ) ).

tff(fact_769_rtranclE,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B),transi374442731on_val(R_1)))
     => ( ( A != B )
       => ~ ! [Y_1: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),Y_1),transi374442731on_val(R_1)))
             => ~ hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Y_1),B),R_1)) ) ) ) ).

tff(fact_770_rtranclE,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B),transi2024712006on_val(R_1)))
     => ( ( A != B )
       => ~ ! [Y_1: produc124828825on_val] :
              ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),Y_1),transi2024712006on_val(R_1)))
             => ~ hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Y_1),B),R_1)) ) ) ) ).

tff(fact_771_rtranclE,axiom,
    ! [A: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B),transi935034983cl_val(R_1)))
     => ( ( A != B )
       => ~ ! [Y_1: val] :
              ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),Y_1),transi935034983cl_val(R_1)))
             => ~ hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Y_1),B),R_1)) ) ) ) ).

tff(fact_772_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_1: list_char] :
              ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_2),Y_1),R_1))
             => ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Y_1),Z_1),transi1395422419t_char(R_1))) ) ) ) ).

tff(fact_773_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_1: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,X_2),Y_1),R_1))
             => ~ hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Y_1),Z_1),transi374442731on_val(R_1))) ) ) ) ).

tff(fact_774_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_1: produc124828825on_val] :
              ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X_2),Y_1),R_1))
             => ~ hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Y_1),Z_1),transi2024712006on_val(R_1))) ) ) ) ).

tff(fact_775_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_1: val] :
              ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_2),Y_1),R_1))
             => ~ hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Y_1),Z_1),transi935034983cl_val(R_1))) ) ) ) ).

tff(fact_776_converse__rtrancl__induct,axiom,
    ! [Pa: fun_list_char_bool,A: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B),transi1395422419t_char(R_1)))
     => ( hBOOL(hAPP_list_char_bool(Pa,B))
       => ( ! [Y_1: list_char,Z: list_char] :
              ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Y_1),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_1)) ) ) )
         => hBOOL(hAPP_list_char_bool(Pa,A)) ) ) ) ).

tff(fact_777_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr248118298l_bool,A: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B),transi374442731on_val(R_1)))
     => ( hBOOL(hAPP_P71593144l_bool(Pa,B))
       => ( ! [Y_1: produc2061676504on_val,Z: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Y_1),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_1)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(Pa,A)) ) ) ) ).

tff(fact_778_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr680585871l_bool,A: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B),transi2024712006on_val(R_1)))
     => ( hBOOL(hAPP_P1708370145l_bool(Pa,B))
       => ( ! [Y_1: produc124828825on_val,Z: produc124828825on_val] :
              ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Y_1),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_1)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(Pa,A)) ) ) ) ).

tff(fact_779_converse__rtrancl__induct,axiom,
    ! [Pa: fun_val_bool,A: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B),transi935034983cl_val(R_1)))
     => ( hBOOL(hAPP_val_bool(Pa,B))
       => ( ! [Y_1: val,Z: val] :
              ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Y_1),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_1)) ) ) )
         => hBOOL(hAPP_val_bool(Pa,A)) ) ) ) ).

tff(fact_780_rtrancl__induct,axiom,
    ! [Pa: fun_list_char_bool,A: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B),transi1395422419t_char(R_1)))
     => ( hBOOL(hAPP_list_char_bool(Pa,A))
       => ( ! [Y_1: list_char,Z: list_char] :
              ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),Y_1),transi1395422419t_char(R_1)))
             => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Y_1),Z),R_1))
               => ( hBOOL(hAPP_list_char_bool(Pa,Y_1))
                 => hBOOL(hAPP_list_char_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_list_char_bool(Pa,B)) ) ) ) ).

tff(fact_781_rtrancl__induct,axiom,
    ! [Pa: fun_Pr248118298l_bool,A: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B),transi374442731on_val(R_1)))
     => ( hBOOL(hAPP_P71593144l_bool(Pa,A))
       => ( ! [Y_1: produc2061676504on_val,Z: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),Y_1),transi374442731on_val(R_1)))
             => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Y_1),Z),R_1))
               => ( hBOOL(hAPP_P71593144l_bool(Pa,Y_1))
                 => hBOOL(hAPP_P71593144l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(Pa,B)) ) ) ) ).

tff(fact_782_rtrancl__induct,axiom,
    ! [Pa: fun_Pr680585871l_bool,A: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B),transi2024712006on_val(R_1)))
     => ( hBOOL(hAPP_P1708370145l_bool(Pa,A))
       => ( ! [Y_1: produc124828825on_val,Z: produc124828825on_val] :
              ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),Y_1),transi2024712006on_val(R_1)))
             => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Y_1),Z),R_1))
               => ( hBOOL(hAPP_P1708370145l_bool(Pa,Y_1))
                 => hBOOL(hAPP_P1708370145l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(Pa,B)) ) ) ) ).

tff(fact_783_rtrancl__induct,axiom,
    ! [Pa: fun_val_bool,A: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B),transi935034983cl_val(R_1)))
     => ( hBOOL(hAPP_val_bool(Pa,A))
       => ( ! [Y_1: val,Z: val] :
              ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),Y_1),transi935034983cl_val(R_1)))
             => ( hBOOL(member649088532al_val(hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Y_1),Z),R_1))
               => ( hBOOL(hAPP_val_bool(Pa,Y_1))
                 => hBOOL(hAPP_val_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_val_bool(Pa,B)) ) ) ) ).

tff(fact_784_WTrtThrow,axiom,
    ! [Ta: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,T_r: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),T_r))
     => ( hBOOL(hAPP_ty_bool(is_refT,T_r))
       => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,throw_list_char(Eb)),Ta)) ) ) ).

tff(fact_785_WTrt__elim__cases_I4_J,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,throw_list_char(Eb)),Ta))
     => ~ ! [T_r_1: ty] :
            ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),T_r_1))
           => ~ hBOOL(hAPP_ty_bool(is_refT,T_r_1)) ) ) ).

tff(fact_786_val_Osimps_I6_J,axiom,
    ! [Bool_1: bool] : unit != bool_1(Bool_1) ).

tff(fact_787_val_Osimps_I7_J,axiom,
    ! [Bool_1: bool] : bool_1(Bool_1) != unit ).

tff(fact_788_red__reds_ORedWhile,axiom,
    ! [B: exp_list_char,C_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,while_list_char(B,C_1)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(B,seq_list_char(C_1,while_list_char(B,C_1)),hAPP_v834067052t_char(val_list_char,unit))),S)),red(Pa))) ).

tff(fact_789_BinOpRedsThrow2,axiom,
    ! [Bop: bop,E_2: exp_list_char,Eb: exp_list_char,S_2_1: produc12694297on_val,E_1: exp_list_char,S_0: produc12694297on_val,V_1_2: 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,E_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1_2)),S_1)),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)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),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(Eb)),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_790_TryRedsVal,axiom,
    ! [C: list_char,V: list_char,E_2: exp_list_char,Eb: exp_list_char,S: produc12694297on_val,V_1: val,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1)),S_2)),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(Eb,C,V,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_791_CastRedsThrow,axiom,
    ! [C: list_char,Eb: exp_list_char,S: produc12694297on_val,A: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2)),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,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_792_BinOpRedsThrow1,axiom,
    ! [Bop: bop,E_2: exp_list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E_b)),S_2)),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(Eb,Bop,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E_b)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_793_WTrtSeq,axiom,
    ! [E_2: exp_list_char,T_2: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1: exp_list_char,T_1: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_1),T_1))
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_2),T_2))
       => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,seq_list_char(E_1,E_2)),T_2)) ) ) ).

tff(fact_794_exp_Osimps_I61_J,axiom,
    ! [Exp1_79: exp_list_char,Exp2_79: exp_list_char,List_39: list_char,Exp_35: exp_list_char] : seq_list_char(Exp1_79,Exp2_79) != cast_list_char(List_39,Exp_35) ).

tff(fact_795_exp_Osimps_I60_J,axiom,
    ! [List_38: list_char,Exp_34: exp_list_char,Exp1_78: exp_list_char,Exp2_78: exp_list_char] : cast_list_char(List_38,Exp_34) != seq_list_char(Exp1_78,Exp2_78) ).

tff(fact_796_exp_Osimps_I107_J,axiom,
    ! [Exp1_77: exp_list_char,Exp2_77: exp_list_char,Exp1_76: exp_list_char,Bop_19: bop,Exp2_76: exp_list_char] : seq_list_char(Exp1_77,Exp2_77) != binOp_list_char(Exp1_76,Bop_19,Exp2_76) ).

tff(fact_797_exp_Osimps_I46_J,axiom,
    ! [List_37: list_char,Exp_33: exp_list_char,Exp1_75: exp_list_char,Bop_18: bop,Exp2_75: exp_list_char] : cast_list_char(List_37,Exp_33) != binOp_list_char(Exp1_75,Bop_18,Exp2_75) ).

tff(fact_798_exp_Osimps_I212_J,axiom,
    ! [Exp1_74: exp_list_char,Exp2_74: exp_list_char,Exp1_73: exp_list_char,List_36: list_char,A_21: list_char,Exp2_73: exp_list_char] : seq_list_char(Exp1_74,Exp2_74) != tryCatch_list_char(Exp1_73,List_36,A_21,Exp2_73) ).

tff(fact_799_exp_Osimps_I68_J,axiom,
    ! [List_35: list_char,Exp_32: exp_list_char,Exp1_72: exp_list_char,List_34: list_char,A_20: list_char,Exp2_72: exp_list_char] : cast_list_char(List_35,Exp_32) != tryCatch_list_char(Exp1_72,List_34,A_20,Exp2_72) ).

tff(fact_800_exp_Osimps_I106_J,axiom,
    ! [Exp1_71: exp_list_char,Bop_17: bop,Exp2_71: exp_list_char,Exp1_70: exp_list_char,Exp2_70: exp_list_char] : binOp_list_char(Exp1_71,Bop_17,Exp2_71) != seq_list_char(Exp1_70,Exp2_70) ).

tff(fact_801_exp_Osimps_I47_J,axiom,
    ! [Exp1_69: exp_list_char,Bop_16: bop,Exp2_69: exp_list_char,List_33: list_char,Exp_31: exp_list_char] : binOp_list_char(Exp1_69,Bop_16,Exp2_69) != cast_list_char(List_33,Exp_31) ).

tff(fact_802_exp_Osimps_I114_J,axiom,
    ! [Exp1_68: exp_list_char,Bop_15: bop,Exp2_68: exp_list_char,Exp1_67: exp_list_char,List_32: list_char,A_19: list_char,Exp2_67: exp_list_char] : binOp_list_char(Exp1_68,Bop_15,Exp2_68) != tryCatch_list_char(Exp1_67,List_32,A_19,Exp2_67) ).

tff(fact_803_exp_Osimps_I213_J,axiom,
    ! [Exp1_66: exp_list_char,List_31: list_char,A_18: list_char,Exp2_66: exp_list_char,Exp1_65: exp_list_char,Exp2_65: exp_list_char] : tryCatch_list_char(Exp1_66,List_31,A_18,Exp2_66) != seq_list_char(Exp1_65,Exp2_65) ).

tff(fact_804_exp_Osimps_I69_J,axiom,
    ! [Exp1_64: exp_list_char,List_30: list_char,A_17: list_char,Exp2_64: exp_list_char,List_29: list_char,Exp_30: exp_list_char] : tryCatch_list_char(Exp1_64,List_30,A_17,Exp2_64) != cast_list_char(List_29,Exp_30) ).

tff(fact_805_exp_Osimps_I115_J,axiom,
    ! [Exp1_63: exp_list_char,List_28: list_char,A_16: list_char,Exp2_63: exp_list_char,Exp1_62: exp_list_char,Bop_14: bop,Exp2_62: exp_list_char] : tryCatch_list_char(Exp1_63,List_28,A_16,Exp2_63) != binOp_list_char(Exp1_62,Bop_14,Exp2_62) ).

tff(fact_806_exp_Osimps_I11_J,axiom,
    ! [Exp1_61: exp_list_char,Exp2_61: exp_list_char,Exp1_60: exp_list_char,Exp2_60: exp_list_char] :
      ( ( seq_list_char(Exp1_61,Exp2_61) = seq_list_char(Exp1_60,Exp2_60) )
    <=> ( ( Exp1_61 = Exp1_60 )
        & ( Exp2_61 = Exp2_60 ) ) ) ).

tff(fact_807_exp_Osimps_I2_J,axiom,
    ! [List_3: list_char,Exp_29: exp_list_char,List_2: list_char,Exp_28: exp_list_char] :
      ( ( cast_list_char(List_3,Exp_29) = cast_list_char(List_2,Exp_28) )
    <=> ( ( List_3 = List_2 )
        & ( Exp_29 = Exp_28 ) ) ) ).

tff(fact_808_exp_Osimps_I4_J,axiom,
    ! [Exp1_61: exp_list_char,Bop: bop,Exp2_61: exp_list_char,Exp1_60: exp_list_char,Bop_13: bop,Exp2_60: exp_list_char] :
      ( ( binOp_list_char(Exp1_61,Bop,Exp2_61) = binOp_list_char(Exp1_60,Bop_13,Exp2_60) )
    <=> ( ( Exp1_61 = Exp1_60 )
        & ( Bop = Bop_13 )
        & ( Exp2_61 = Exp2_60 ) ) ) ).

tff(fact_809_exp_Osimps_I15_J,axiom,
    ! [Exp1_61: exp_list_char,List_3: list_char,A: list_char,Exp2_61: exp_list_char,Exp1_60: exp_list_char,List_2: list_char,A_15: list_char,Exp2_60: exp_list_char] :
      ( ( tryCatch_list_char(Exp1_61,List_3,A,Exp2_61) = tryCatch_list_char(Exp1_60,List_2,A_15,Exp2_60) )
    <=> ( ( Exp1_61 = Exp1_60 )
        & ( List_3 = List_2 )
        & ( A = A_15 )
        & ( Exp2_61 = Exp2_60 ) ) ) ).

tff(fact_810_exp_Osimps_I84_J,axiom,
    ! [Val_7: val,Exp1_59: exp_list_char,Exp2_59: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_7) != seq_list_char(Exp1_59,Exp2_59) ).

tff(fact_811_exp_Osimps_I45_J,axiom,
    ! [Val_6: val,List_27: list_char,Exp_27: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_6) != cast_list_char(List_27,Exp_27) ).

tff(fact_812_exp_Osimps_I70_J,axiom,
    ! [Val_5: val,Exp1_58: exp_list_char,Bop_12: bop,Exp2_58: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_5) != binOp_list_char(Exp1_58,Bop_12,Exp2_58) ).

tff(fact_813_exp_Osimps_I92_J,axiom,
    ! [Val_4: val,Exp1_57: exp_list_char,List_26: list_char,A_14: list_char,Exp2_57: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_4) != tryCatch_list_char(Exp1_57,List_26,A_14,Exp2_57) ).

tff(fact_814_exp_Osimps_I85_J,axiom,
    ! [Exp1_56: exp_list_char,Exp2_56: exp_list_char,Val_3: val] : seq_list_char(Exp1_56,Exp2_56) != hAPP_v834067052t_char(val_list_char,Val_3) ).

tff(fact_815_exp_Osimps_I44_J,axiom,
    ! [List_25: list_char,Exp_26: exp_list_char,Val_2: val] : cast_list_char(List_25,Exp_26) != hAPP_v834067052t_char(val_list_char,Val_2) ).

tff(fact_816_exp_Osimps_I71_J,axiom,
    ! [Exp1_55: exp_list_char,Bop_11: bop,Exp2_55: exp_list_char,Val_1: val] : binOp_list_char(Exp1_55,Bop_11,Exp2_55) != hAPP_v834067052t_char(val_list_char,Val_1) ).

tff(fact_817_exp_Osimps_I93_J,axiom,
    ! [Exp1_54: exp_list_char,List_24: list_char,A_13: list_char,Exp2_54: exp_list_char,Val: val] : tryCatch_list_char(Exp1_54,List_24,A_13,Exp2_54) != hAPP_v834067052t_char(val_list_char,Val) ).

tff(fact_818_exp_Osimps_I211_J,axiom,
    ! [Exp_25: exp_list_char,Exp1_53: exp_list_char,Exp2_53: exp_list_char] : throw_list_char(Exp_25) != seq_list_char(Exp1_53,Exp2_53) ).

tff(fact_819_exp_Osimps_I67_J,axiom,
    ! [Exp_24: exp_list_char,List_23: list_char,Exp_23: exp_list_char] : throw_list_char(Exp_24) != cast_list_char(List_23,Exp_23) ).

tff(fact_820_exp_Osimps_I113_J,axiom,
    ! [Exp_22: exp_list_char,Exp1_52: exp_list_char,Bop_10: bop,Exp2_52: exp_list_char] : throw_list_char(Exp_22) != binOp_list_char(Exp1_52,Bop_10,Exp2_52) ).

tff(fact_821_exp_Osimps_I224_J,axiom,
    ! [Exp_21: exp_list_char,Exp1_51: exp_list_char,List_22: list_char,A_12: list_char,Exp2_51: exp_list_char] : throw_list_char(Exp_21) != tryCatch_list_char(Exp1_51,List_22,A_12,Exp2_51) ).

tff(fact_822_exp_Osimps_I210_J,axiom,
    ! [Exp1_50: exp_list_char,Exp2_50: exp_list_char,Exp_20: exp_list_char] : seq_list_char(Exp1_50,Exp2_50) != throw_list_char(Exp_20) ).

tff(fact_823_exp_Osimps_I66_J,axiom,
    ! [List_21: list_char,Exp_19: exp_list_char,Exp_18: exp_list_char] : cast_list_char(List_21,Exp_19) != throw_list_char(Exp_18) ).

tff(fact_824_exp_Osimps_I112_J,axiom,
    ! [Exp1_49: exp_list_char,Bop_9: bop,Exp2_49: exp_list_char,Exp_17: exp_list_char] : binOp_list_char(Exp1_49,Bop_9,Exp2_49) != throw_list_char(Exp_17) ).

tff(fact_825_exp_Osimps_I225_J,axiom,
    ! [Exp1_48: exp_list_char,List_20: list_char,A_11: list_char,Exp2_48: exp_list_char,Exp_16: exp_list_char] : tryCatch_list_char(Exp1_48,List_20,A_11,Exp2_48) != throw_list_char(Exp_16) ).

tff(fact_826_exp_Osimps_I183_J,axiom,
    ! [Exp1_47: exp_list_char,List_19: list_char,A_10: list_char,Exp2_47: exp_list_char,Exp1_46: exp_list_char,List1_15: list_char,List2_15: list_char,Exp2_46: exp_list_char] : tryCatch_list_char(Exp1_47,List_19,A_10,Exp2_47) != fAss_list_char(Exp1_46,List1_15,List2_15,Exp2_46) ).

tff(fact_827_exp_Osimps_I182_J,axiom,
    ! [Exp1_45: exp_list_char,List1_14: list_char,List2_14: list_char,Exp2_45: exp_list_char,Exp1_44: exp_list_char,List_18: list_char,A_9: list_char,Exp2_44: exp_list_char] : fAss_list_char(Exp1_45,List1_14,List2_14,Exp2_45) != tryCatch_list_char(Exp1_44,List_18,A_9,Exp2_44) ).

tff(fact_828_exp_Osimps_I101_J,axiom,
    ! [Exp1_43: exp_list_char,List1_13: list_char,List2_13: list_char,Exp2_43: exp_list_char,Exp1_42: exp_list_char,Bop_8: bop,Exp2_42: exp_list_char] : fAss_list_char(Exp1_43,List1_13,List2_13,Exp2_43) != binOp_list_char(Exp1_42,Bop_8,Exp2_42) ).

tff(fact_829_exp_Osimps_I55_J,axiom,
    ! [Exp1_41: exp_list_char,List1_12: list_char,List2_12: list_char,Exp2_41: exp_list_char,List_17: list_char,Exp_15: exp_list_char] : fAss_list_char(Exp1_41,List1_12,List2_12,Exp2_41) != cast_list_char(List_17,Exp_15) ).

tff(fact_830_exp_Osimps_I174_J,axiom,
    ! [Exp1_40: exp_list_char,List1_11: list_char,List2_11: list_char,Exp2_40: exp_list_char,Exp1_39: exp_list_char,Exp2_39: exp_list_char] : fAss_list_char(Exp1_40,List1_11,List2_11,Exp2_40) != seq_list_char(Exp1_39,Exp2_39) ).

tff(fact_831_exp_Osimps_I100_J,axiom,
    ! [Exp1_38: exp_list_char,Bop_7: bop,Exp2_38: exp_list_char,Exp1_37: exp_list_char,List1_10: list_char,List2_10: list_char,Exp2_37: exp_list_char] : binOp_list_char(Exp1_38,Bop_7,Exp2_38) != fAss_list_char(Exp1_37,List1_10,List2_10,Exp2_37) ).

tff(fact_832_exp_Osimps_I54_J,axiom,
    ! [List_16: list_char,Exp_14: exp_list_char,Exp1_36: exp_list_char,List1_9: list_char,List2_9: list_char,Exp2_36: exp_list_char] : cast_list_char(List_16,Exp_14) != fAss_list_char(Exp1_36,List1_9,List2_9,Exp2_36) ).

tff(fact_833_exp_Osimps_I175_J,axiom,
    ! [Exp1_35: exp_list_char,Exp2_35: exp_list_char,Exp1_34: exp_list_char,List1_8: list_char,List2_8: list_char,Exp2_34: exp_list_char] : seq_list_char(Exp1_35,Exp2_35) != fAss_list_char(Exp1_34,List1_8,List2_8,Exp2_34) ).

tff(fact_834_exp_Osimps_I206_J,axiom,
    ! [Exp1_33: exp_list_char,Exp2_33: exp_list_char,Exp1_32: exp_list_char,Exp2_32: exp_list_char,Exp3_7: exp_list_char] : seq_list_char(Exp1_33,Exp2_33) != cond_list_char(Exp1_32,Exp2_32,Exp3_7) ).

tff(fact_835_exp_Osimps_I62_J,axiom,
    ! [List_15: list_char,Exp_13: exp_list_char,Exp1_31: exp_list_char,Exp2_31: exp_list_char,Exp3_6: exp_list_char] : cast_list_char(List_15,Exp_13) != cond_list_char(Exp1_31,Exp2_31,Exp3_6) ).

tff(fact_836_exp_Osimps_I207_J,axiom,
    ! [Exp1_30: exp_list_char,Exp2_30: exp_list_char,Exp3_5: exp_list_char,Exp1_29: exp_list_char,Exp2_29: exp_list_char] : cond_list_char(Exp1_30,Exp2_30,Exp3_5) != seq_list_char(Exp1_29,Exp2_29) ).

tff(fact_837_exp_Osimps_I63_J,axiom,
    ! [Exp1_28: exp_list_char,Exp2_28: exp_list_char,Exp3_4: exp_list_char,List_14: list_char,Exp_12: exp_list_char] : cond_list_char(Exp1_28,Exp2_28,Exp3_4) != cast_list_char(List_14,Exp_12) ).

tff(fact_838_exp_Osimps_I109_J,axiom,
    ! [Exp1_27: exp_list_char,Exp2_27: exp_list_char,Exp3_3: exp_list_char,Exp1_26: exp_list_char,Bop_6: bop,Exp2_26: exp_list_char] : cond_list_char(Exp1_27,Exp2_27,Exp3_3) != binOp_list_char(Exp1_26,Bop_6,Exp2_26) ).

tff(fact_839_exp_Osimps_I108_J,axiom,
    ! [Exp1_25: exp_list_char,Bop_5: bop,Exp2_25: exp_list_char,Exp1_24: exp_list_char,Exp2_24: exp_list_char,Exp3_2: exp_list_char] : binOp_list_char(Exp1_25,Bop_5,Exp2_25) != cond_list_char(Exp1_24,Exp2_24,Exp3_2) ).

tff(fact_840_exp_Osimps_I218_J,axiom,
    ! [Exp1_23: exp_list_char,Exp2_23: exp_list_char,Exp3_1: exp_list_char,Exp1_22: exp_list_char,List_13: list_char,A_8: list_char,Exp2_22: exp_list_char] : cond_list_char(Exp1_23,Exp2_23,Exp3_1) != tryCatch_list_char(Exp1_22,List_13,A_8,Exp2_22) ).

tff(fact_841_exp_Osimps_I219_J,axiom,
    ! [Exp1_21: exp_list_char,List_12: list_char,A_7: list_char,Exp2_21: exp_list_char,Exp1_20: exp_list_char,Exp2_20: exp_list_char,Exp3: exp_list_char] : tryCatch_list_char(Exp1_21,List_12,A_7,Exp2_21) != cond_list_char(Exp1_20,Exp2_20,Exp3) ).

tff(fact_842_exp_Osimps_I169_J,axiom,
    ! [Exp1_19: exp_list_char,List_11: list_char,A_6: list_char,Exp2_19: exp_list_char,Exp_11: exp_list_char,List1_7: list_char,List2_7: list_char] : tryCatch_list_char(Exp1_19,List_11,A_6,Exp2_19) != fAcc_list_char(Exp_11,List1_7,List2_7) ).

tff(fact_843_exp_Osimps_I168_J,axiom,
    ! [Exp_10: exp_list_char,List1_6: list_char,List2_6: list_char,Exp1_18: exp_list_char,List_10: list_char,A_5: list_char,Exp2_18: exp_list_char] : fAcc_list_char(Exp_10,List1_6,List2_6) != tryCatch_list_char(Exp1_18,List_10,A_5,Exp2_18) ).

tff(fact_844_exp_Osimps_I98_J,axiom,
    ! [Exp1_17: exp_list_char,Bop_4: bop,Exp2_17: exp_list_char,Exp_9: exp_list_char,List1_5: list_char,List2_5: list_char] : binOp_list_char(Exp1_17,Bop_4,Exp2_17) != fAcc_list_char(Exp_9,List1_5,List2_5) ).

tff(fact_845_exp_Osimps_I99_J,axiom,
    ! [Exp_8: exp_list_char,List1_4: list_char,List2_4: list_char,Exp1_16: exp_list_char,Bop_3: bop,Exp2_16: exp_list_char] : fAcc_list_char(Exp_8,List1_4,List2_4) != binOp_list_char(Exp1_16,Bop_3,Exp2_16) ).

tff(fact_846_exp_Osimps_I53_J,axiom,
    ! [Exp_7: exp_list_char,List1_3: list_char,List2_3: list_char,List_9: list_char,Exp_6: exp_list_char] : fAcc_list_char(Exp_7,List1_3,List2_3) != cast_list_char(List_9,Exp_6) ).

tff(fact_847_exp_Osimps_I160_J,axiom,
    ! [Exp_5: exp_list_char,List1_2: list_char,List2_2: list_char,Exp1_15: exp_list_char,Exp2_15: exp_list_char] : fAcc_list_char(Exp_5,List1_2,List2_2) != seq_list_char(Exp1_15,Exp2_15) ).

tff(fact_848_exp_Osimps_I52_J,axiom,
    ! [List_8: list_char,Exp_4: exp_list_char,Exp_3: exp_list_char,List1_1: list_char,List2_1: list_char] : cast_list_char(List_8,Exp_4) != fAcc_list_char(Exp_3,List1_1,List2_1) ).

tff(fact_849_exp_Osimps_I161_J,axiom,
    ! [Exp1_14: exp_list_char,Exp2_14: exp_list_char,Exp_2: exp_list_char,List1: list_char,List2: list_char] : seq_list_char(Exp1_14,Exp2_14) != fAcc_list_char(Exp_2,List1,List2) ).

tff(fact_850_exp_Osimps_I208_J,axiom,
    ! [Exp1_13: exp_list_char,Exp2_13: exp_list_char,Exp1_12: exp_list_char,Exp2_12: exp_list_char] : seq_list_char(Exp1_13,Exp2_13) != while_list_char(Exp1_12,Exp2_12) ).

tff(fact_851_exp_Osimps_I64_J,axiom,
    ! [List_7: list_char,Exp_1: exp_list_char,Exp1_11: exp_list_char,Exp2_11: exp_list_char] : cast_list_char(List_7,Exp_1) != while_list_char(Exp1_11,Exp2_11) ).

tff(fact_852_exp_Osimps_I209_J,axiom,
    ! [Exp1_10: exp_list_char,Exp2_10: exp_list_char,Exp1_9: exp_list_char,Exp2_9: exp_list_char] : while_list_char(Exp1_10,Exp2_10) != seq_list_char(Exp1_9,Exp2_9) ).

tff(fact_853_exp_Osimps_I65_J,axiom,
    ! [Exp1_8: exp_list_char,Exp2_8: exp_list_char,List_6: list_char,Exp: exp_list_char] : while_list_char(Exp1_8,Exp2_8) != cast_list_char(List_6,Exp) ).

tff(fact_854_exp_Osimps_I111_J,axiom,
    ! [Exp1_7: exp_list_char,Exp2_7: exp_list_char,Exp1_6: exp_list_char,Bop_2: bop,Exp2_6: exp_list_char] : while_list_char(Exp1_7,Exp2_7) != binOp_list_char(Exp1_6,Bop_2,Exp2_6) ).

tff(fact_855_exp_Osimps_I222_J,axiom,
    ! [Exp1_5: exp_list_char,Exp2_5: exp_list_char,Exp1_4: exp_list_char,List_5: list_char,A_4: list_char,Exp2_4: exp_list_char] : while_list_char(Exp1_5,Exp2_5) != tryCatch_list_char(Exp1_4,List_5,A_4,Exp2_4) ).

tff(fact_856_exp_Osimps_I110_J,axiom,
    ! [Exp1_3: exp_list_char,Bop_1: bop,Exp2_3: exp_list_char,Exp1_2: exp_list_char,Exp2_2: exp_list_char] : binOp_list_char(Exp1_3,Bop_1,Exp2_3) != while_list_char(Exp1_2,Exp2_2) ).

tff(fact_857_exp_Osimps_I223_J,axiom,
    ! [Exp1_1: exp_list_char,List_4: list_char,A_3: list_char,Exp2_1: exp_list_char,Exp1: exp_list_char,Exp2: exp_list_char] : tryCatch_list_char(Exp1_1,List_4,A_3,Exp2_1) != while_list_char(Exp1,Exp2) ).

tff(fact_858_red__reds_OSeqRed,axiom,
    ! [E_2: exp_list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(Eb,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(E_b,E_2)),S_2)),red(Pa))) ) ).

tff(fact_859_red__reds_OBinOpRed1,axiom,
    ! [Bop: bop,E_2: exp_list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(Eb,Bop,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(E_b,Bop,E_2)),S_2)),red(Pa))) ) ).

tff(fact_860_red__reds_OCastRed,axiom,
    ! [C: list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),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,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,E_b)),S_2)),red(Pa))) ) ).

tff(fact_861_red__reds_OTryRed,axiom,
    ! [C: list_char,V: list_char,E_2: exp_list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(Eb,C,V,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(E_b,C,V,E_2)),S_2)),red(Pa))) ) ).

tff(fact_862_val_Osimps_I1_J,axiom,
    ! [Bool: bool,Bool_1: bool] :
      ( ( bool_1(Bool) = bool_1(Bool_1) )
    <=> ( hBOOL(Bool)
      <=> hBOOL(Bool_1) ) ) ).

tff(fact_863_red__reds_ORedSeq,axiom,
    ! [V_1: val,E_2: 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,seq_list_char(hAPP_v834067052t_char(val_list_char,V_1),E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S)),red(Pa))) ).

tff(fact_864_red__reds_OSeqThrow,axiom,
    ! [Eb: exp_list_char,E_2: 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,seq_list_char(throw_list_char(Eb),E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S)),red(Pa))) ).

tff(fact_865_SeqReds,axiom,
    ! [E_2: exp_list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),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(Eb,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(E_b,E_2)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_866_red__reds_OBinOpRed2,axiom,
    ! [V_1_2: val,Bop: bop,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),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,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,E_b)),S_2)),red(Pa))) ) ).

tff(fact_867_red__reds_OBinOpThrow1,axiom,
    ! [Eb: exp_list_char,Bop: bop,E_2: 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,binOp_list_char(throw_list_char(Eb),Bop,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S)),red(Pa))) ).

tff(fact_868_BinOp1Reds,axiom,
    ! [Bop: bop,E_2: exp_list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),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(Eb,Bop,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(E_b,Bop,E_2)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_869_red__reds_OCastThrow,axiom,
    ! [C: list_char,Eb: 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,cast_list_char(C,throw_list_char(Eb))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S)),red(Pa))) ).

tff(fact_870_CastReds,axiom,
    ! [C: list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),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,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,E_b)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_871_red__reds_ORedTry,axiom,
    ! [V_1: val,C: list_char,V: list_char,E_2: 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,tryCatch_list_char(hAPP_v834067052t_char(val_list_char,V_1),C,V,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1)),S)),red(Pa))) ).

tff(fact_872_TryReds,axiom,
    ! [C: list_char,V: list_char,E_2: exp_list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),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(Eb,C,V,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(E_b,C,V,E_2)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_873_SeqReds2,axiom,
    ! [E_2: exp_list_char,E_2_a: exp_list_char,S_2_1: produc12694297on_val,E_1: exp_list_char,S_0: produc12694297on_val,V_1_2: 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,E_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1_2)),S_1)),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)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2_a),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_a),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_874_SeqRedsThrow,axiom,
    ! [E_2: exp_list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E_b)),S_2)),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(Eb,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E_b)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_875_red__reds_OBinOpThrow2,axiom,
    ! [V_1_2: val,Bop: bop,Eb: 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,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,throw_list_char(Eb))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S)),red(Pa))) ).

tff(fact_876_BinOp2Reds,axiom,
    ! [V_1: val,Bop: bop,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),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_1),Bop,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Bop,E_b)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_877_WTrtBinOpEq,axiom,
    ! [E_2: exp_list_char,T_2: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1: exp_list_char,T_1: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_1),T_1))
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_2),T_2))
       => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,binOp_list_char(E_1,c_Expr_Obop_OEq,E_2)),boolean)) ) ) ).

tff(fact_878_CastRedsNull,axiom,
    ! [C: list_char,Eb: exp_list_char,S: produc12694297on_val,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S_2)),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,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_879_red__reds_ORedCastNull,axiom,
    ! [C: 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,cast_list_char(C,hAPP_v834067052t_char(val_list_char,null))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S)),red(Pa))) ).

tff(fact_880_redp__redsp_ORedWhile,axiom,
    ! [Pa: list_P1999446415t_char,B: exp_list_char,C_1: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,while_list_char(B,C_1),S),cond_list_char(B,seq_list_char(C_1,while_list_char(B,C_1)),hAPP_v834067052t_char(val_list_char,unit))),S)) ).

tff(fact_881_default__val_Osimps_I2_J,axiom,
    hAPP_ty_val(default_val,boolean) = bool_1(fFalse) ).

tff(fact_882_default__val_Osimps_I1_J,axiom,
    hAPP_ty_val(default_val,void) = unit ).

tff(fact_883_unfold__while,axiom,
    ! [Pa: list_P1999446415t_char,B: exp_list_char,C_1: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(B,C_1),S),E_b),S_2))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(B,seq_list_char(C_1,while_list_char(B,C_1)),hAPP_v834067052t_char(val_list_char,unit)),S),E_b),S_2)) ) ).

tff(fact_884_CallRedsThrowObj,axiom,
    ! [M: list_char,Esa: list_exp_list_char,Eb: exp_list_char,S0: produc12694297on_val,A: 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,Eb),S0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_1)),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(Eb,M,Esa)),S0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_885_redp__redsp_OCallObj,axiom,
    ! [M: list_char,Esa: list_exp_list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(Eb,M,Esa),S),call_list_char(E_b,M,Esa)),S_2)) ) ).

tff(fact_886_redp__redsp_OCallThrowObj,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,M: list_char,Esa: list_exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(throw_list_char(Eb),M,Esa),S),throw_list_char(Eb)),S)) ).

tff(fact_887_default__val_Osimps_I4_J,axiom,
    hAPP_ty_val(default_val,nt) = null ).

tff(fact_888_redp__redsp_OThrowRed,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,throw_list_char(Eb),S),throw_list_char(E_b)),S_2)) ) ).

tff(fact_889_redp__redsp_OThrowThrow,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,throw_list_char(throw_list_char(Eb)),S),throw_list_char(Eb)),S)) ).

tff(fact_890_redp__redsp_ORedCastNull,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,hAPP_v834067052t_char(val_list_char,null)),S),hAPP_v834067052t_char(val_list_char,null)),S)) ).

tff(fact_891_redp__redsp_OSeqRed,axiom,
    ! [E_2: exp_list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(Eb,E_2),S),seq_list_char(E_b,E_2)),S_2)) ) ).

tff(fact_892_redp__redsp_OFAssRed1,axiom,
    ! [Fa: list_char,Da: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(Eb,Fa,Da,E_2),S),fAss_list_char(E_b,Fa,Da,E_2)),S_2)) ) ).

tff(fact_893_redp__redsp_OBinOpRed1,axiom,
    ! [Bop: bop,E_2: exp_list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(Eb,Bop,E_2),S),binOp_list_char(E_b,Bop,E_2)),S_2)) ) ).

tff(fact_894_redp__redsp_OCondRed,axiom,
    ! [E_1: exp_list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cond_list_char(Eb,E_1,E_2),S),cond_list_char(E_b,E_1,E_2)),S_2)) ) ).

tff(fact_895_redp__redsp_OCastRed,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,Eb),S),cast_list_char(C,E_b)),S_2)) ) ).

tff(fact_896_redp__redsp_OFAccRed,axiom,
    ! [Fa: list_char,Da: list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(Eb,Fa,Da),S),fAcc_list_char(E_b,Fa,Da)),S_2)) ) ).

tff(fact_897_redp__redsp_OTryRed,axiom,
    ! [C: list_char,V: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,tryCatch_list_char(Eb,C,V,E_2),S),tryCatch_list_char(E_b,C,V,E_2)),S_2)) ) ).

tff(fact_898_val_Osimps_I12_J,axiom,
    ! [Bool_1: bool] : null != bool_1(Bool_1) ).

tff(fact_899_val_Osimps_I13_J,axiom,
    ! [Bool_1: bool] : bool_1(Bool_1) != null ).

tff(fact_900_val_Osimps_I5_J,axiom,
    null != unit ).

tff(fact_901_val_Osimps_I4_J,axiom,
    unit != null ).

tff(fact_902_redp__redsp_ORedSeq,axiom,
    ! [Pa: list_P1999446415t_char,V_1: val,E_2: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(hAPP_v834067052t_char(val_list_char,V_1),E_2),S),E_2),S)) ).

tff(fact_903_redp__redsp_OFAssRed2,axiom,
    ! [V_1: val,Fa: list_char,Da: list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,V_1),Fa,Da,Eb),S),fAss_list_char(hAPP_v834067052t_char(val_list_char,V_1),Fa,Da,E_b)),S_2)) ) ).

tff(fact_904_redp__redsp_OBinOpRed2,axiom,
    ! [V_1_2: val,Bop: bop,Pa: list_P1999446415t_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,Eb),S),binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,E_b)),S_2)) ) ).

tff(fact_905_redp__redsp_OSeqThrow,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,E_2: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(throw_list_char(Eb),E_2),S),throw_list_char(Eb)),S)) ).

tff(fact_906_redp__redsp_OFAssThrow1,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,Fa: list_char,Da: list_char,E_2: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(throw_list_char(Eb),Fa,Da,E_2),S),throw_list_char(Eb)),S)) ).

tff(fact_907_redp__redsp_OBinOpThrow1,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,Bop: bop,E_2: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(throw_list_char(Eb),Bop,E_2),S),throw_list_char(Eb)),S)) ).

tff(fact_908_redp__redsp_OCondThrow,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,E_1: exp_list_char,E_2: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cond_list_char(throw_list_char(Eb),E_1,E_2),S),throw_list_char(Eb)),S)) ).

tff(fact_909_redp__redsp_OCastThrow,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,Eb: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,throw_list_char(Eb)),S),throw_list_char(Eb)),S)) ).

tff(fact_910_redp__redsp_ORedTry,axiom,
    ! [Pa: list_P1999446415t_char,V_1: val,C: list_char,V: list_char,E_2: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,tryCatch_list_char(hAPP_v834067052t_char(val_list_char,V_1),C,V,E_2),S),hAPP_v834067052t_char(val_list_char,V_1)),S)) ).

tff(fact_911_redp__redsp_OFAccThrow,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,Fa: list_char,Da: list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(throw_list_char(Eb),Fa,Da),S),throw_list_char(Eb)),S)) ).

tff(fact_912_redp__redsp_OFAssThrow2,axiom,
    ! [Pa: list_P1999446415t_char,V_1: val,Fa: list_char,Da: list_char,Eb: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,V_1),Fa,Da,throw_list_char(Eb)),S),throw_list_char(Eb)),S)) ).

tff(fact_913_redp__redsp_OBinOpThrow2,axiom,
    ! [Pa: list_P1999446415t_char,V_1_2: val,Bop: bop,Eb: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,throw_list_char(Eb)),S),throw_list_char(Eb)),S)) ).

tff(fact_914_red__reds_OCallObj,axiom,
    ! [M: list_char,Esa: list_exp_list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),red(Pa)))
     => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(Eb,M,Esa)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(E_b,M,Esa)),S_2)),red(Pa))) ) ).

tff(fact_915_redp__redsp_ORedCondF,axiom,
    ! [Pa: list_P1999446415t_char,E_1: exp_list_char,E_2: exp_list_char,S: 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),E_2),S)) ).

tff(fact_916_redp__redsp_ORedCondT,axiom,
    ! [Pa: list_P1999446415t_char,E_1: exp_list_char,E_2: exp_list_char,S: 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),E_1),S)) ).

tff(fact_917_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_918_red__reds_OCallThrowObj,axiom,
    ! [Eb: exp_list_char,M: list_char,Esa: list_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,call_list_char(throw_list_char(Eb),M,Esa)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S)),red(Pa))) ).

tff(fact_919_CallRedsObj,axiom,
    ! [M: list_char,Esa: list_exp_list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_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(Eb,M,Esa)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(E_b,M,Esa)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_920_WhileF,axiom,
    ! [C_1: exp_list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,bool_1(fFalse))),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Eb,C_1),S_0),hAPP_v834067052t_char(val_list_char,unit)),S_1)) ) ).

tff(fact_921_WhileBodyThrow,axiom,
    ! [C_1: exp_list_char,E_b: exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_1,S_1),throw_list_char(E_b)),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Eb,C_1),S_0),throw_list_char(E_b)),S_2_1)) ) ) ).

tff(fact_922_WhileT,axiom,
    ! [E_3_1: exp_list_char,S_3_1: produc12694297on_val,C_1: exp_list_char,V_1_2: val,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_1,S_1),hAPP_v834067052t_char(val_list_char,V_1_2)),S_2_1))
       => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Eb,C_1),S_2_1),E_3_1),S_3_1))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Eb,C_1),S_0),E_3_1),S_3_1)) ) ) ) ).

tff(fact_923_CondT,axiom,
    ! [E_2: exp_list_char,E_1: exp_list_char,E_b: exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_1),E_b),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(Eb,E_1,E_2),S_0),E_b),S_2_1)) ) ) ).

tff(fact_924_CondF,axiom,
    ! [E_1: exp_list_char,E_2: exp_list_char,E_b: exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,bool_1(fFalse))),S_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1),E_b),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(Eb,E_1,E_2),S_0),E_b),S_2_1)) ) ) ).

tff(fact_925_CastNull,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,Eb),S_0),hAPP_v834067052t_char(val_list_char,null)),S_1)) ) ).

tff(fact_926_eval__evals_OBinOpThrow2,axiom,
    ! [Bop: bop,E_2: exp_list_char,Eb: 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: 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))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1),throw_list_char(Eb)),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(Eb)),S_2_1)) ) ) ).

tff(fact_927_Val,axiom,
    ! [Pa: list_P1999446415t_char,V_1: val,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,hAPP_v834067052t_char(val_list_char,V_1),S),hAPP_v834067052t_char(val_list_char,V_1)),S)) ).

tff(fact_928_eval__cases_I2_J,axiom,
    ! [Pa: list_P1999446415t_char,V_1: val,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,hAPP_v834067052t_char(val_list_char,V_1),S),E_b),S_2))
     => ~ ( ( E_b = hAPP_v834067052t_char(val_list_char,V_1) )
         => ( S_2 != S ) ) ) ).

tff(fact_929_eval__evals_OThrowThrow,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,E_b: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),throw_list_char(E_b)),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(Eb),S_0),throw_list_char(E_b)),S_1)) ) ).

tff(fact_930_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_1: val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_0,S_0),hAPP_v834067052t_char(val_list_char,V_1)),S_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_1),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_931_eval__evals_OSeqThrow,axiom,
    ! [E_1: exp_list_char,Pa: list_P1999446415t_char,E_0: exp_list_char,S_0: produc12694297on_val,Eb: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_0,S_0),throw_list_char(Eb)),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,seq_list_char(E_0,E_1),S_0),throw_list_char(Eb)),S_1)) ) ).

tff(fact_932_eval__evals_OFAssThrow1,axiom,
    ! [Fa: list_char,Da: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,E_1: exp_list_char,S_0: produc12694297on_val,E_b: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_0),throw_list_char(E_b)),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAss_list_char(E_1,Fa,Da,E_2),S_0),throw_list_char(E_b)),S_1)) ) ).

tff(fact_933_CallObjThrow,axiom,
    ! [M: list_char,Ps: list_exp_list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,E_b: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),throw_list_char(E_b)),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,call_list_char(Eb,M,Ps),S_0),throw_list_char(E_b)),S_1)) ) ).

tff(fact_934_eval__evals_OBinOpThrow1,axiom,
    ! [Bop: bop,E_2: exp_list_char,Pa: list_P1999446415t_char,E_1: exp_list_char,S_0: produc12694297on_val,Eb: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_0),throw_list_char(Eb)),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,binOp_list_char(E_1,Bop,E_2),S_0),throw_list_char(Eb)),S_1)) ) ).

tff(fact_935_eval__evals_OCastThrow,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,E_b: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),throw_list_char(E_b)),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,Eb),S_0),throw_list_char(E_b)),S_1)) ) ).

tff(fact_936_eval__evals_OCondThrow,axiom,
    ! [E_1: exp_list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,E_b: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),throw_list_char(E_b)),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(Eb,E_1,E_2),S_0),throw_list_char(E_b)),S_1)) ) ).

tff(fact_937_Try,axiom,
    ! [C: list_char,V: 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: 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))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,tryCatch_list_char(E_1,C,V,E_2),S_0),hAPP_v834067052t_char(val_list_char,V_1_2)),S_1)) ) ).

tff(fact_938_eval__evals_OFAccThrow,axiom,
    ! [Fa: list_char,Da: list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,E_b: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),throw_list_char(E_b)),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAcc_list_char(Eb,Fa,Da),S_0),throw_list_char(E_b)),S_1)) ) ).

tff(fact_939_WhileCondThrow,axiom,
    ! [C_1: exp_list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,E_b: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),throw_list_char(E_b)),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Eb,C_1),S_0),throw_list_char(E_b)),S_1)) ) ).

tff(fact_940_eval__hext,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))
     => hBOOL(hext(Hb,H_b)) ) ).

tff(fact_941_eval__evals_OFAssThrow2,axiom,
    ! [Fa: list_char,Da: list_char,E_2: exp_list_char,E_b: exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,E_1: exp_list_char,S_0: produc12694297on_val,V_1: val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_0),hAPP_v834067052t_char(val_list_char,V_1)),S_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1),throw_list_char(E_b)),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAss_list_char(E_1,Fa,Da,E_2),S_0),throw_list_char(E_b)),S_2_1)) ) ) ).

tff(fact_942_big__by__small,axiom,
    ! [Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),E_b),S_2))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_943_extend__eval,axiom,
    ! [E_b: exp_list_char,S_2: produc12694297on_val,Eb: exp_list_char,S: 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,Eb),S)),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_b),S_2))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),E_b),S_2)) ) ) ) ).

tff(fact_944_CallRedsParams,axiom,
    ! [V_1: val,M: list_char,Esa: list_exp_list_char,S: produc12694297on_val,Es_a: list_exp_list_char,S_2: 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,Esa),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),S_2)),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_1),M,Esa)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(hAPP_v834067052t_char(val_list_char,V_1),M,Es_a)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_945_eval__cases_I11_J,axiom,
    ! [Pa: list_P1999446415t_char,B: exp_list_char,C_1: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(B,C_1),S),E_b),S_2))
     => ( ( ( E_b = hAPP_v834067052t_char(val_list_char,unit) )
         => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,B,S),hAPP_v834067052t_char(val_list_char,bool_1(fFalse))),S_2)) )
       => ( ! [S_1_1: produc12694297on_val] :
              ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,B,S),hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1_1))
             => ! [V_1_3: val,S_2_2: produc12694297on_val] :
                  ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_1,S_1_1),hAPP_v834067052t_char(val_list_char,V_1_3)),S_2_2))
                 => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(B,C_1),S_2_2),E_b),S_2)) ) )
         => ( ! [E: exp_list_char] :
                ( ( E_b = throw_list_char(E) )
               => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,B,S),throw_list_char(E)),S_2)) )
           => ~ ! [S_1_1: produc12694297on_val,E: exp_list_char] :
                  ( ( E_b = throw_list_char(E) )
                 => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,B,S),hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1_1))
                   => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_1,S_1_1),throw_list_char(E)),S_2)) ) ) ) ) ) ) ).

tff(fact_946_extend__1__eval,axiom,
    ! [E_b: exp_list_char,S_2: produc12694297on_val,Eb: exp_list_char,S: 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,Eb),S)),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_b),S_2))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),E_b),S_2)) ) ) ) ).

tff(fact_947_eval__cases_I9_J,axiom,
    ! [Pa: list_P1999446415t_char,E_1: exp_list_char,E_2: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,seq_list_char(E_1,E_2),S),E_b),S_2))
     => ( ! [V_2: val,S_1_1: produc12694297on_val] :
            ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S),hAPP_v834067052t_char(val_list_char,V_2)),S_1_1))
           => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_1),E_b),S_2)) )
       => ~ ! [E_3: exp_list_char] :
              ( ( E_b = throw_list_char(E_3) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S),throw_list_char(E_3)),S_2)) ) ) ) ).

tff(fact_948_reds__hext__incr,axiom,
    ! [Esa: list_exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Es_a: list_exp_list_char,H_b: fun_na939144002on_val,L_b: 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,Esa),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),reds(Pa)))
     => hBOOL(hext(Hb,H_b)) ) ).

tff(fact_949_red__reds_OCallParams,axiom,
    ! [V_1: val,M: list_char,Esa: list_exp_list_char,S: produc12694297on_val,Es_a: list_exp_list_char,S_2: 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,Esa),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),S_2)),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_1),M,Esa)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(hAPP_v834067052t_char(val_list_char,V_1),M,Es_a)),S_2)),red(Pa))) ) ).

tff(fact_950_wf__prog__wwf__prog,axiom,
    ! [Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wf_J_mdecl,Pa))
     => hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa)) ) ).

tff(fact_951_big__iff__small,axiom,
    ! [Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),E_b),S_2))
      <=> ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),transi2024712006on_val(red(Pa))))
          & hBOOL(final_list_char(E_b)) ) ) ) ).

tff(fact_952_small__by__big,axiom,
    ! [Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),transi2024712006on_val(red(Pa))))
       => ( hBOOL(final_list_char(E_b))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),E_b),S_2)) ) ) ) ).

tff(fact_953_ListRedsVal,axiom,
    ! [Esa: list_exp_list_char,Es_a: list_exp_list_char,S_2_1: produc12694297on_val,Eb: exp_list_char,S_0: produc12694297on_val,V_1: 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,Eb),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1)),S_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),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,cons_exp_list_char(Eb,Esa)),S_0)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Es_a)),S_2_1)),transi374442731on_val(reds(Pa)))) ) ) ).

tff(fact_954_extend__evals,axiom,
    ! [Es_a: list_exp_list_char,S_2: produc12694297on_val,Esa: list_exp_list_char,S: produc12694297on_val,Es_1: 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,Esa),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),S_3)),transi374442731on_val(reds(Pa))))
       => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es_1,S_3),Es_a),S_2))
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S),Es_a),S_2)) ) ) ) ).

tff(fact_955_bigs__by__smalls,axiom,
    ! [Esa: list_exp_list_char,S: produc12694297on_val,Es_a: list_exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S),Es_a),S_2))
       => hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),S_2)),transi374442731on_val(reds(Pa)))) ) ) ).

tff(fact_956_eval__evals_OCons,axiom,
    ! [Esa: list_exp_list_char,Es_a: list_exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,V_1: val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,V_1)),S_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S_1),Es_a),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,cons_exp_list_char(Eb,Esa),S_0),cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Es_a)),S_2_1)) ) ) ).

tff(fact_957_ConsThrow,axiom,
    ! [Esa: list_exp_list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,E_b: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),throw_list_char(E_b)),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,cons_exp_list_char(Eb,Esa),S_0),cons_exp_list_char(throw_list_char(E_b),Esa)),S_1)) ) ).

tff(fact_958_eval__final,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),E_b),S_2))
     => hBOOL(final_list_char(E_b)) ) ).

tff(fact_959_eval__finalId,axiom,
    ! [Pa: list_P1999446415t_char,S: produc12694297on_val,Eb: exp_list_char] :
      ( hBOOL(final_list_char(Eb))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),Eb),S)) ) ).

tff(fact_960_evals__hext,axiom,
    ! [Pa: list_P1999446415t_char,Esa: list_exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Es_a: list_exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),Es_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))
     => hBOOL(hext(Hb,H_b)) ) ).

tff(fact_961_red__reds_OListRed2,axiom,
    ! [V_1: val,Esa: list_exp_list_char,S: produc12694297on_val,Es_a: list_exp_list_char,S_2: 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,Esa),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),S_2)),reds(Pa)))
     => hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Esa)),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Es_a)),S_2)),reds(Pa))) ) ).

tff(fact_962_ListReds2,axiom,
    ! [V_1: val,Esa: list_exp_list_char,S: produc12694297on_val,Es_a: list_exp_list_char,S_2: 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,Esa),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),S_2)),transi374442731on_val(reds(Pa))))
     => hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Esa)),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Es_a)),S_2)),transi374442731on_val(reds(Pa)))) ) ).

tff(fact_963_red__reds_OListRed1,axiom,
    ! [Esa: list_exp_list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),red(Pa)))
     => hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(Eb,Esa)),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(E_b,Esa)),S_2)),reds(Pa))) ) ).

tff(fact_964_extend__1__evals,axiom,
    ! [Es_a: list_exp_list_char,T_8: produc12694297on_val,Esa: list_exp_list_char,T_7: produc12694297on_val,Es_1: list_exp_list_char,T_6: 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,Esa),T_7)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),T_6)),reds(Pa)))
       => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es_1,T_6),Es_a),T_8))
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,T_7),Es_a),T_8)) ) ) ) ).

tff(fact_965_ListReds1,axiom,
    ! [Esa: list_exp_list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),transi2024712006on_val(red(Pa))))
     => hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(Eb,Esa)),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(E_b,Esa)),S_2)),transi374442731on_val(reds(Pa)))) ) ).

tff(fact_966_wf__mdecl__wwf__mdecl,axiom,
    ! [P: list_P1999446415t_char,C_3: list_char,Md: produc1013743697t_char] :
      ( hBOOL(hAPP_P1384137393r_bool(hAPP_l2054741776r_bool(hAPP_l2138409430r_bool(wf_J_mdecl,P),C_3),Md))
     => hBOOL(hAPP_P1384137393r_bool(hAPP_l2054741776r_bool(hAPP_l2138409430r_bool(wwf_J_mdecl,P),C_3),Md)) ) ).

tff(fact_967_evals__cases_I2_J,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,Esa: list_exp_list_char,S: produc12694297on_val,E_b: list_exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,cons_exp_list_char(Eb,Esa),S),E_b),S_2))
     => ( ! [V_2: val,S_1_1: produc12694297on_val,Es: list_exp_list_char] :
            ( ( E_b = cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_2),Es) )
           => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),hAPP_v834067052t_char(val_list_char,V_2)),S_1_1))
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S_1_1),Es),S_2)) ) )
       => ~ ! [E: exp_list_char] :
              ( ( E_b = cons_exp_list_char(throw_list_char(E),Esa) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),throw_list_char(E)),S_2)) ) ) ) ).

tff(fact_968_reds__preserves__sconf,axiom,
    ! [Ea: fun_li688206603ion_ty,Ts: list_ty,Esa: list_exp_list_char,S: produc12694297on_val,Es_a: list_exp_list_char,S_2: 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,Esa),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),S_2)),reds(Pa)))
     => ( hBOOL(wTrts_1(Pa,hAPP_P703866694on_val(hp,S),Ea,Esa,Ts))
       => ( hBOOL(hAPP_P159683425l_bool(typeSa1917327191_sconf(Pa,Ea),S))
         => hBOOL(hAPP_P159683425l_bool(typeSa1917327191_sconf(Pa,Ea),S_2)) ) ) ) ).

tff(fact_969_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_970_reds__preserves__lconf,axiom,
    ! [Ea: fun_li688206603ion_ty,Ts: list_ty,Esa: list_exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Es_a: list_exp_list_char,H_b: fun_na939144002on_val,L_b: 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,Esa),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),reds(Pa)))
     => ( hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts))
       => ( hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Hb),Lb),Ea))
         => hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),H_b),L_b),Ea)) ) ) ) ).

tff(fact_971_reds__preserves__hconf,axiom,
    ! [Ea: fun_li688206603ion_ty,Ts: list_ty,Esa: list_exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Es_a: list_exp_list_char,H_b: fun_na939144002on_val,L_b: 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,Esa),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),reds(Pa)))
     => ( hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts))
       => ( hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),Hb))
         => hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),H_b)) ) ) ) ).

tff(fact_972_WTrts__hext__mono,axiom,
    ! [H_b: fun_na939144002on_val,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Esa: list_exp_list_char,Ts: list_ty] :
      ( hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts))
     => ( hBOOL(hext(Hb,H_b))
       => hBOOL(wTrts_1(Pa,H_b,Ea,Esa,Ts)) ) ) ).

tff(fact_973_redp__redsp_OListRed2,axiom,
    ! [V_1: val,Pa: list_P1999446415t_char,Esa: list_exp_list_char,S: produc12694297on_val,Es_a: list_exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,Esa,S),Es_a),S_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Esa),S),cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Es_a)),S_2)) ) ).

tff(fact_974_redp__redsp_OListRed1,axiom,
    ! [Esa: list_exp_list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,cons_exp_list_char(Eb,Esa),S),cons_exp_list_char(E_b,Esa)),S_2)) ) ).

tff(fact_975_WTrtCallNT,axiom,
    ! [M: list_char,Ta: ty,Esa: list_exp_list_char,Ts: list_ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),nt))
     => ( hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts))
       => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,call_list_char(Eb,M,Esa)),Ta)) ) ) ).

tff(fact_976_redp__redsp_OCallParams,axiom,
    ! [V_1: val,M: list_char,Pa: list_P1999446415t_char,Esa: list_exp_list_char,S: produc12694297on_val,Es_a: list_exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,Esa,S),Es_a),S_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(hAPP_v834067052t_char(val_list_char,V_1),M,Esa),S),call_list_char(hAPP_v834067052t_char(val_list_char,V_1),M,Es_a)),S_2)) ) ).

tff(fact_977_eval__cases_I10_J,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,E_1: exp_list_char,E_2: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(Eb,E_1,E_2),S),E_b),S_2))
     => ( ! [S_1_1: produc12694297on_val] :
            ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),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_b),S_2)) )
       => ( ! [S_1_1: produc12694297on_val] :
              ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),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_b),S_2)) )
         => ~ ! [E: exp_list_char] :
                ( ( E_b = throw_list_char(E) )
               => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),throw_list_char(E)),S_2)) ) ) ) ) ).

tff(fact_978_CallRedsThrowParams,axiom,
    ! [M: list_char,Esa: list_exp_list_char,Vs_1_1: list_val,A: exp_list_char,Es_2: list_exp_list_char,S_2_1: produc12694297on_val,Eb: exp_list_char,S0: produc12694297on_val,V_1: 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,Eb),S0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1)),S_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vs_1_1),cons_exp_list_char(throw_list_char(A),Es_2))),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(Eb,M,Esa)),S0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_979_redp__redsp_OCallThrowParams,axiom,
    ! [Pa: list_P1999446415t_char,V_1: val,M: list_char,S: produc12694297on_val,Esa: list_exp_list_char,Vs_1: list_val,Eb: exp_list_char,Es_a: list_exp_list_char] :
      ( ( Esa = append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vs_1),cons_exp_list_char(throw_list_char(Eb),Es_a)) )
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(hAPP_v834067052t_char(val_list_char,V_1),M,Esa),S),throw_list_char(Eb)),S)) ) ).

tff(fact_980_list__eval__Throw,axiom,
    ! [Vs_1: list_val,Es_a: list_exp_list_char,Pa: list_P1999446415t_char,X_2: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(X_2),S),E_b),S_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vs_1),cons_exp_list_char(throw_list_char(X_2),Es_a)),S),append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vs_1),cons_exp_list_char(E_b,Es_a))),S_2)) ) ).

tff(fact_981_CallParamsThrow,axiom,
    ! [M: list_char,Esa: list_exp_list_char,Vs_1: list_val,Ex: exp_list_char,Es_a: list_exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,V_1: val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,V_1)),S_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S_1),append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vs_1),cons_exp_list_char(throw_list_char(Ex),Es_a))),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,call_list_char(Eb,M,Esa),S_0),throw_list_char(Ex)),S_2_1)) ) ) ).

tff(fact_982_red__reds_OCallThrowParams,axiom,
    ! [V_1: val,M: list_char,S: produc12694297on_val,Pa: list_P1999446415t_char,Esa: list_exp_list_char,Vs_1: list_val,Eb: exp_list_char,Es_a: list_exp_list_char] :
      ( ( Esa = append_exp_list_char(hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vs_1),cons_exp_list_char(throw_list_char(Eb),Es_a)) )
     => 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_1),M,Esa)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S)),red(Pa))) ) ).

tff(fact_983_eval__finalsId,axiom,
    ! [Pa: list_P1999446415t_char,S: produc12694297on_val,Esa: list_exp_list_char] :
      ( hBOOL(finals_list_char(Esa))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S),Esa),S)) ) ).

tff(fact_984_evals__final,axiom,
    ! [Pa: list_P1999446415t_char,Esa: list_exp_list_char,S: produc12694297on_val,Es_a: list_exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S),Es_a),S_2))
     => hBOOL(finals_list_char(Es_a)) ) ).

tff(fact_985_CallRedsNull,axiom,
    ! [M: list_char,Esa: list_exp_list_char,Vs_1: list_val,S_2_1: produc12694297on_val,Eb: exp_list_char,S_0: produc12694297on_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,Eb),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vs_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(Eb,M,Esa)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_986_WTrtCons,axiom,
    ! [Esa: list_exp_list_char,Ts: list_ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),Ta))
     => ( hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts))
       => hBOOL(wTrts_1(Pa,Hb,Ea,cons_exp_list_char(Eb,Esa),cons_ty(Ta,Ts))) ) ) ).

tff(fact_987_val_Osimps_I3_J,axiom,
    ! [Nat_2: nat,Nat_1: nat] :
      ( ( addr(Nat_2) = addr(Nat_1) )
    <=> ( Nat_2 = Nat_1 ) ) ).

tff(fact_988_val_Osimps_I17_J,axiom,
    ! [Nat: nat] : addr(Nat) != null ).

tff(fact_989_val_Osimps_I16_J,axiom,
    ! [Nat: nat] : null != addr(Nat) ).

tff(fact_990_val_Osimps_I21_J,axiom,
    ! [Nat_1: nat,Bool: bool] : addr(Nat_1) != bool_1(Bool) ).

tff(fact_991_val_Osimps_I20_J,axiom,
    ! [Bool: bool,Nat_1: nat] : bool_1(Bool) != addr(Nat_1) ).

tff(fact_992_val_Osimps_I10_J,axiom,
    ! [Nat: nat] : unit != addr(Nat) ).

tff(fact_993_val_Osimps_I11_J,axiom,
    ! [Nat: nat] : addr(Nat) != unit ).

tff(fact_994_ThrowNull,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(Eb),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_1)) ) ).

tff(fact_995_redp__redsp_ORedThrowNull,axiom,
    ! [Pa: list_P1999446415t_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,throw_list_char(hAPP_v834067052t_char(val_list_char,null)),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S)) ).

tff(fact_996_FAssNull,axiom,
    ! [Fa: list_char,Da: list_char,E_2: exp_list_char,V_1: val,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,E_1: exp_list_char,S_0: produc12694297on_val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1),hAPP_v834067052t_char(val_list_char,V_1)),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAss_list_char(E_1,Fa,Da,E_2),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2_1)) ) ) ).

tff(fact_997_FAccNull,axiom,
    ! [Fa: list_char,Da: list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAcc_list_char(Eb,Fa,Da),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_1)) ) ).

tff(fact_998_redp__redsp_ORedFAssNull,axiom,
    ! [Pa: list_P1999446415t_char,Fa: list_char,Da: list_char,V_1: val,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,null),Fa,Da,hAPP_v834067052t_char(val_list_char,V_1)),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S)) ).

tff(fact_999_redp__redsp_ORedFAccNull,axiom,
    ! [Pa: list_P1999446415t_char,Fa: list_char,Da: list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(hAPP_v834067052t_char(val_list_char,null),Fa,Da),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S)) ).

tff(fact_1000_red__reds_ORedThrowNull,axiom,
    ! [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,throw_list_char(hAPP_v834067052t_char(val_list_char,null))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S)),red(Pa))) ).

tff(fact_1001_redp__redsp_ORedCallNull,axiom,
    ! [Pa: list_P1999446415t_char,M: list_char,Vs_1: list_val,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(hAPP_v834067052t_char(val_list_char,null),M,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vs_1)),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S)) ).

tff(fact_1002_ThrowRedsNull,axiom,
    ! [Eb: exp_list_char,S: produc12694297on_val,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S_2)),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(Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1003_red__reds_ORedFAssNull,axiom,
    ! [Fa: list_char,Da: list_char,V_1: 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,fAss_list_char(hAPP_v834067052t_char(val_list_char,null),Fa,Da,hAPP_v834067052t_char(val_list_char,V_1))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S)),red(Pa))) ).

tff(fact_1004_red__reds_ORedFAccNull,axiom,
    ! [Fa: list_char,Da: 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,fAcc_list_char(hAPP_v834067052t_char(val_list_char,null),Fa,Da)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S)),red(Pa))) ).

tff(fact_1005_CallNull,axiom,
    ! [M: list_char,Ps: list_exp_list_char,Vs_1: list_val,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Ps,S_1),hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vs_1)),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,call_list_char(Eb,M,Ps),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2_1)) ) ) ).

tff(fact_1006_Throw,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,A: nat,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(Eb),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S_1)) ) ).

tff(fact_1007_FAssRedsNull,axiom,
    ! [Fa: list_char,Da: list_char,E_2: exp_list_char,V_1: val,S_2_1: produc12694297on_val,E_1: exp_list_char,S_0: produc12694297on_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,E_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S_1)),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)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_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,fAss_list_char(E_1,Fa,Da,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_1008_FAccRedsNull,axiom,
    ! [Fa: list_char,Da: list_char,Eb: exp_list_char,S: produc12694297on_val,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S_2)),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(Eb,Fa,Da)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1009_red__reds_ORedCallNull,axiom,
    ! [M: list_char,Vs_1: list_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,call_list_char(hAPP_v834067052t_char(val_list_char,null),M,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vs_1))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S)),red(Pa))) ).

tff(fact_1010_eval__cases_I12_J,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(Eb),S),E_b),S_2))
     => ( ! [A_1: nat] :
            ( ( E_b = throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))) )
           => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),hAPP_v834067052t_char(val_list_char,addr(A_1))),S_2)) )
       => ( ( ( E_b = throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer)))) )
           => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),hAPP_v834067052t_char(val_list_char,null)),S_2)) )
         => ~ ! [E: exp_list_char] :
                ( ( E_b = throw_list_char(E) )
               => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),throw_list_char(E)),S_2)) ) ) ) ) ).

tff(fact_1011_red__reds_OBlockThrow,axiom,
    ! [V: list_char,Ta: ty,A: 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,block_list_char(V,Ta,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S)),red(Pa))) ).

tff(fact_1012_the__Addr_Osimps,axiom,
    ! [A_2: nat] : the_Addr(addr(A_2)) = A_2 ).

tff(fact_1013_LAssRedsThrow,axiom,
    ! [V: list_char,Eb: exp_list_char,S: produc12694297on_val,A: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2)),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,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1014_not__refTE,axiom,
    ! [T_4: ty] :
      ( ~ hBOOL(hAPP_ty_bool(is_refT,T_4))
     => ( ( T_4 = void )
        | ( T_4 = boolean )
        | ( T_4 = integer ) ) ) ).

tff(fact_1015_redp__redsp_OLAssRed,axiom,
    ! [V: list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(V,Eb),S),lAss_list_char(V,E_b)),S_2)) ) ).

tff(fact_1016_redp__redsp_ORedInitBlock,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,Ta: ty,V_1: val,U: val,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V,Ta,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),hAPP_v834067052t_char(val_list_char,U))),S),hAPP_v834067052t_char(val_list_char,U)),S)) ).

tff(fact_1017_ty_Osimps_I5_J,axiom,
    integer != void ).

tff(fact_1018_ty_Osimps_I4_J,axiom,
    void != integer ).

tff(fact_1019_ty_Osimps_I16_J,axiom,
    integer != nt ).

tff(fact_1020_ty_Osimps_I17_J,axiom,
    nt != integer ).

tff(fact_1021_ty_Osimps_I10_J,axiom,
    boolean != integer ).

tff(fact_1022_ty_Osimps_I11_J,axiom,
    integer != boolean ).

tff(fact_1023_eval__evals_OLAssThrow,axiom,
    ! [V: list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,E_b: exp_list_char,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),throw_list_char(E_b)),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,lAss_list_char(V,Eb),S_0),throw_list_char(E_b)),S_1)) ) ).

tff(fact_1024_redp__redsp_OLAssThrow,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,Eb: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(V,throw_list_char(Eb)),S),throw_list_char(Eb)),S)) ).

tff(fact_1025_redp__redsp_ORedBlock,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,Ta: ty,U: val,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V,Ta,hAPP_v834067052t_char(val_list_char,U)),S),hAPP_v834067052t_char(val_list_char,U)),S)) ).

tff(fact_1026_red__reds_ORedInitBlock,axiom,
    ! [V: list_char,Ta: ty,V_1: val,U: 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,block_list_char(V,Ta,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),hAPP_v834067052t_char(val_list_char,U)))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,U)),S)),red(Pa))) ).

tff(fact_1027_redp__redsp_OInitBlockThrow,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,Ta: ty,V_1: val,A: nat,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V,Ta,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))))),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S)) ).

tff(fact_1028_red__reds_OLAssRed,axiom,
    ! [V: list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),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,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(V,E_b)),S_2)),red(Pa))) ) ).

tff(fact_1029_red__reds_OInitBlockThrow,axiom,
    ! [V: list_char,Ta: ty,V_1: val,A: 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,block_list_char(V,Ta,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S)),red(Pa))) ).

tff(fact_1030_red__reds_OLAssThrow,axiom,
    ! [V: list_char,Eb: 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,lAss_list_char(V,throw_list_char(Eb))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S)),red(Pa))) ).

tff(fact_1031_LAssReds,axiom,
    ! [V: list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2)),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,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(V,E_b)),S_2)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1032_red__reds_ORedBlock,axiom,
    ! [V: list_char,Ta: ty,U: 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,block_list_char(V,Ta,hAPP_v834067052t_char(val_list_char,U))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,U)),S)),red(Pa))) ).

tff(fact_1033_redp__redsp_OBlockThrow,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,Ta: ty,A: nat,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V,Ta,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S)) ).

tff(fact_1034_blocks_Osimps_I1_J,axiom,
    ! [V_5: list_char,Vs_3: list_list_char,T_4: ty,Ts_3: list_ty,V_3: val,Vs_2: list_val,E_4: exp_list_char] : blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,cons_list_char(V_5,Vs_3)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,cons_ty(T_4,Ts_3)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,cons_val(V_3,Vs_2)),E_4)))) = block_list_char(V_5,T_4,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_3),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ts_3),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Vs_2),E_4)))))) ).

tff(fact_1035_WTrt__elim__cases_I9_J,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1: exp_list_char,Bop: bop,E_2: exp_list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,binOp_list_char(E_1,Bop,E_2)),Ta))
     => ( ( ( Ta = boolean )
         => ( ? [T_1_1: ty] : hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_1),T_1_1))
           => ( ? [X1: ty] : hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_2),X1))
             => ( Bop != c_Expr_Obop_OEq ) ) ) )
       => ~ ( ( Ta = integer )
           => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_1),integer))
             => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_2),integer))
               => ( Bop != add ) ) ) ) ) ) ).

tff(fact_1036_WTrtBinOpAdd,axiom,
    ! [E_2: exp_list_char,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_1),integer))
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_2),integer))
       => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,binOp_list_char(E_1,add,E_2)),integer)) ) ) ).

tff(fact_1037_WTrtLAss,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Eb: exp_list_char,T: ty,Ea: fun_li688206603ion_ty,V: list_char,Ta: ty] :
      ( ( hAPP_l512744617ion_ty(Ea,V) = hAPP_ty_option_ty(some_ty,Ta) )
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),T))
       => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T),Ta))
         => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,lAss_list_char(V,Eb)),void)) ) ) ) ).

tff(fact_1038_InitBlockRedsFinal,axiom,
    ! [Ta: ty,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,V: list_char,V_1: val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: 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,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,V,hAPP_val_option_val(some_val,V_1))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),transi2024712006on_val(red(Pa))))
     => ( hBOOL(final_list_char(E_b))
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V,Ta,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),Eb))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,V,hAPP_l207779698on_val(Lb,V))))),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_1039_bop_Osimps_I1_J,axiom,
    c_Expr_Obop_OEq != add ).

tff(fact_1040_bop_Osimps_I2_J,axiom,
    add != c_Expr_Obop_OEq ).

tff(fact_1041_bop_Oexhaust,axiom,
    ! [Y: bop] :
      ( ( Y != c_Expr_Obop_OEq )
     => ( Y = add ) ) ).

tff(fact_1042_LAss,axiom,
    ! [L_b: fun_li1432931796on_val,V: list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,V_1: val,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,V_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)))
     => ( ( L_b = fun_up1149430426on_val(Lb,V,hAPP_val_option_val(some_val,V_1)) )
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,lAss_list_char(V,Eb),S_0),hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),L_b))) ) ) ).

tff(fact_1043_redp__redsp_ORedLAss,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,V_1: val,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,V,hAPP_val_option_val(some_val,V_1))))) ).

tff(fact_1044_redp__redsp_OInitBlockRed,axiom,
    ! [Ta: ty,V_4: val,Pa: list_P1999446415t_char,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,V: list_char,V_1: val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,V,hAPP_val_option_val(some_val,V_1)))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))
     => ( ( hAPP_l207779698on_val(L_b,V) = hAPP_val_option_val(some_val,V_4) )
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V,Ta,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),Eb)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),block_list_char(V,Ta,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_4)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,V,hAPP_l207779698on_val(Lb,V))))) ) ) ).

tff(fact_1045_red__reds_ORedLAss,axiom,
    ! [V: list_char,V_1: val,Hb: fun_na939144002on_val,Lb: 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,hAPP_v834067052t_char(val_list_char,V_1))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,V,hAPP_val_option_val(some_val,V_1))))),red(Pa))) ).

tff(fact_1046_LAssRedsVal,axiom,
    ! [V: list_char,Eb: exp_list_char,S: produc12694297on_val,V_1: val,H_b: fun_na939144002on_val,L_b: 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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),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,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,V,hAPP_val_option_val(some_val,V_1))))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1047_red__reds_OInitBlockRed,axiom,
    ! [Ta: ty,V_4: val,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,V: list_char,V_1: val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: 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,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,V,hAPP_val_option_val(some_val,V_1))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa)))
     => ( ( hAPP_l207779698on_val(L_b,V) = hAPP_val_option_val(some_val,V_4) )
       => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V,Ta,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),Eb))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V,Ta,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_4)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,V,hAPP_l207779698on_val(Lb,V))))),red(Pa))) ) ) ).

tff(fact_1048_WTrt__elim__cases_I1_J,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,V_1: list_char,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,lAss_list_char(V_1,Eb)),Ta))
     => ~ ( ( Ta = void )
         => ! [T_3: ty] :
              ( ( hAPP_l512744617ion_ty(Ea,V_1) = hAPP_ty_option_ty(some_ty,T_3) )
             => ! [T_5: ty] :
                  ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),T_5))
                 => ~ hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_5),T_3)) ) ) ) ) ).

tff(fact_1049_InitBlockReds,axiom,
    ! [Ta: ty,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,V: list_char,V_1: val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: 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,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,V,hAPP_val_option_val(some_val,V_1))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),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,Ta,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),Eb))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V,Ta,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,hAPP_option_val_val(the_val,hAPP_l207779698on_val(L_b,V)))),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,V,hAPP_l207779698on_val(Lb,V))))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1050_eval__cases_I4_J,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,lAss_list_char(V,Eb),S),E_b),S_2))
     => ( ( ( E_b = hAPP_v834067052t_char(val_list_char,unit) )
         => ! [V_2: val,H: fun_na939144002on_val,L_4: fun_li1432931796on_val] :
              ( ( S_2 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),fun_up1149430426on_val(L_4,V,hAPP_val_option_val(some_val,V_2))) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),hAPP_v834067052t_char(val_list_char,V_2)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L_4))) ) )
       => ~ ! [E: exp_list_char] :
              ( ( E_b = throw_list_char(E) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),throw_list_char(E)),S_2)) ) ) ) ).

tff(fact_1051_BinOpRedsVal,axiom,
    ! [Bop: bop,V_1: val,E_2: exp_list_char,V_2_2: val,S_2_1: produc12694297on_val,E_1: exp_list_char,S_0: produc12694297on_val,V_1_2: 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,E_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1_2)),S_1)),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)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_2_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_2))) = hAPP_val_option_val(some_val,V_1) )
         => 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_1)),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1052_binop_Osimps_I1_J,axiom,
    ! [V_1_2: val,V_2_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_2))) = hAPP_val_option_val(some_val,bool_1(hAPP_val_bool(hAPP_v1392248405l_bool(fequal_val,V_1_2),V_2_2))) ).

tff(fact_1053_BinOp,axiom,
    ! [Bop: bop,V_1: val,E_2: exp_list_char,V_2_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: 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))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1),hAPP_v834067052t_char(val_list_char,V_2_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_2))) = hAPP_val_option_val(some_val,V_1) )
         => 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_1)),S_2_1)) ) ) ) ).

tff(fact_1054_redp__redsp_ORedBinOp,axiom,
    ! [Pa: list_P1999446415t_char,S: produc12694297on_val,Bop: bop,V_1_2: val,V_2_2: val,V_1: 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_2))) = hAPP_val_option_val(some_val,V_1) )
     => 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_2)),S),hAPP_v834067052t_char(val_list_char,V_1)),S)) ) ).

tff(fact_1055_red__reds_ORedBinOp,axiom,
    ! [S: produc12694297on_val,Pa: list_P1999446415t_char,Bop: bop,V_1_2: val,V_2_2: val,V_1: 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_2))) = hAPP_val_option_val(some_val,V_1) )
     => 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_2))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1)),S)),red(Pa))) ) ).

tff(fact_1056_eval__cases_I3_J,axiom,
    ! [Pa: list_P1999446415t_char,E_1: exp_list_char,Bop: bop,E_2: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,binOp_list_char(E_1,Bop,E_2),S),E_b),S_2))
     => ( ! [V_1_3: val,S_1_1: produc12694297on_val,V_2_3: val,V_2: val] :
            ( ( E_b = hAPP_v834067052t_char(val_list_char,V_2) )
           => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S),hAPP_v834067052t_char(val_list_char,V_1_3)),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_3)),S_2))
               => ( binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Bop),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_3),V_2_3))) != hAPP_val_option_val(some_val,V_2) ) ) ) )
       => ( ! [E_3: exp_list_char] :
              ( ( E_b = throw_list_char(E_3) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S),throw_list_char(E_3)),S_2)) )
         => ~ ! [V_1_3: val,S_1_1: produc12694297on_val,E_3: exp_list_char] :
                ( ( E_b = throw_list_char(E_3) )
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S),hAPP_v834067052t_char(val_list_char,V_1_3)),S_1_1))
                 => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_1),throw_list_char(E_3)),S_2)) ) ) ) ) ) ).

tff(fact_1057_FAccRedsVal,axiom,
    ! [Fa: list_char,Da: list_char,V_1: val,C: list_char,Fs: fun_Pr806764899on_val,Eb: exp_list_char,S: produc12694297on_val,A: nat,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A))),S_2)),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_2),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) )
       => ( ( hAPP_P2094403585on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Fa),Da)) = hAPP_val_option_val(some_val,V_1) )
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(Eb,Fa,Da)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1)),S_2)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1058_WTrtBlock,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,V: list_char,Ta: ty,Eb: exp_list_char,T: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,fun_up424764369ion_ty(Ea,V,hAPP_ty_option_ty(some_ty,Ta)),Eb),T))
     => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,block_list_char(V,Ta,Eb)),T)) ) ).

tff(fact_1059_hext__upd__obj,axiom,
    ! [Fs_2: fun_Pr806764899on_val,Hb: fun_na939144002on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) )
     => hBOOL(hext(Hb,fun_up2041264236on_val(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_2))))) ) ).

tff(fact_1060_FAss,axiom,
    ! [H_2_1: fun_na939144002on_val,Fs_2: fun_Pr806764899on_val,Fa: list_char,Da: list_char,C: list_char,Fs: fun_Pr806764899on_val,E_2: exp_list_char,V_1: 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: nat,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),S_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1),hAPP_v834067052t_char(val_list_char,V_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2)))
       => ( ( hAPP_n546249108on_val(H_2,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) )
         => ( ( Fs_2 = fun_up204312361on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Fa),Da),hAPP_val_option_val(some_val,V_1)) )
           => ( ( H_2_1 = fun_up2041264236on_val(H_2,A,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,Fa,Da,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_1061_redp__redsp_ORedFAss,axiom,
    ! [Pa: list_P1999446415t_char,Fa: list_char,Da: list_char,V_1: val,Lb: fun_li1432931796on_val,Hb: fun_na939144002on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) )
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),Fa,Da,hAPP_v834067052t_char(val_list_char,V_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,fun_up2041264236on_val(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),fun_up204312361on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Fa),Da),hAPP_val_option_val(some_val,V_1)))))),Lb))) ) ).

tff(fact_1062_red__reds_ORedFAss,axiom,
    ! [Fa: list_char,Da: list_char,V_1: val,Lb: fun_li1432931796on_val,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) )
     => 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)),Fa,Da,hAPP_v834067052t_char(val_list_char,V_1))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),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(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),fun_up204312361on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Fa),Da),hAPP_val_option_val(some_val,V_1)))))),Lb))),red(Pa))) ) ).

tff(fact_1063_FAssRedsVal,axiom,
    ! [Fa: list_char,Da: list_char,C: list_char,Fs: fun_Pr806764899on_val,E_2: exp_list_char,V_1: val,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,E_1: exp_list_char,S_0: produc12694297on_val,A: 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,E_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A))),S_1)),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)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1)),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)) = hAPP_n546249108on_val(H_2,A) )
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(E_1,Fa,Da,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,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),fun_up204312361on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Fa),Da),hAPP_val_option_val(some_val,V_1)))))),L_2))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1064_FAcc,axiom,
    ! [Fa: list_char,Da: list_char,V_1: val,C: list_char,Fs: fun_Pr806764899on_val,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,A: nat,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)))
     => ( ( hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) )
       => ( ( hAPP_P2094403585on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Fa),Da)) = hAPP_val_option_val(some_val,V_1) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAcc_list_char(Eb,Fa,Da),S_0),hAPP_v834067052t_char(val_list_char,V_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))) ) ) ) ).

tff(fact_1065_redp__redsp_ORedFAcc,axiom,
    ! [Pa: list_P1999446415t_char,Fa: list_char,Da: list_char,V_1: val,S: produc12694297on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) )
     => ( ( hAPP_P2094403585on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Fa),Da)) = hAPP_val_option_val(some_val,V_1) )
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),Fa,Da),S),hAPP_v834067052t_char(val_list_char,V_1)),S)) ) ) ).

tff(fact_1066_red__reds_ORedFAcc,axiom,
    ! [Pa: list_P1999446415t_char,Fa: list_char,Da: list_char,V_1: val,S: produc12694297on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) )
     => ( ( hAPP_P2094403585on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Fa),Da)) = hAPP_val_option_val(some_val,V_1) )
       => 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)),Fa,Da)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1)),S)),red(Pa))) ) ) ).

tff(fact_1067_TryCatchRedsFinal,axiom,
    ! [E_2: exp_list_char,V: list_char,E_2_a: exp_list_char,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,C: list_char,Da: list_char,Fs: fun_Pr806764899on_val,E_1: exp_list_char,S_0: produc12694297on_val,A: nat,H_1_1: fun_na939144002on_val,L_1_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_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1_1),L_1_2))),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(H_1_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Da),Fs)) )
       => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Da),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_1),fun_up1149430426on_val(L_1_2,V,hAPP_val_option_val(some_val,addr(A)))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2))),transi2024712006on_val(red(Pa))))
           => ( hBOOL(final_list_char(E_2_a))
             => 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,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),fun_up1149430426on_val(L_2,V,hAPP_l207779698on_val(L_1_2,V))))),transi2024712006on_val(red(Pa)))) ) ) ) ) ) ).

tff(fact_1068_hext__def,axiom,
    ! [Hb: fun_na939144002on_val,H_b: fun_na939144002on_val] :
      ( hBOOL(hext(Hb,H_b))
    <=> ! [A_1: nat,C_2: list_char,Fs_1: fun_Pr806764899on_val] :
          ( ( hAPP_n546249108on_val(Hb,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C_2),Fs_1)) )
         => ? [Fs_3: fun_Pr806764899on_val] : hAPP_n546249108on_val(H_b,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C_2),Fs_3)) ) ) ).

tff(fact_1069_hext__objD,axiom,
    ! [A: nat,C: list_char,Fs: fun_Pr806764899on_val,Hb: fun_na939144002on_val,H_b: fun_na939144002on_val] :
      ( hBOOL(hext(Hb,H_b))
     => ( ( hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) )
       => ? [Fs_3: fun_Pr806764899on_val] : hAPP_n546249108on_val(H_b,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_3)) ) ) ).

tff(fact_1070_TryRedsFail,axiom,
    ! [V: list_char,E_2: exp_list_char,C: list_char,Da: list_char,Fs: fun_Pr806764899on_val,E_1: exp_list_char,S: produc12694297on_val,A: nat,Hb: fun_na939144002on_val,Lb: 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)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Da),Fs)) )
       => ( ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Da),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,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1071_Cast,axiom,
    ! [C: list_char,Da: list_char,Fs: fun_Pr806764899on_val,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,A: nat,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)))
     => ( ( hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Da),Fs)) )
       => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Da),C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,Eb),S_0),hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))) ) ) ) ).

tff(fact_1072_TryThrow,axiom,
    ! [V: list_char,E_2: exp_list_char,C: list_char,Da: list_char,Fs: fun_Pr806764899on_val,Pa: list_P1999446415t_char,E_1: exp_list_char,S_0: produc12694297on_val,A: nat,H_1_1: fun_na939144002on_val,L_1_2: 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)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1_1),L_1_2)))
     => ( ( hAPP_n546249108on_val(H_1_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Da),Fs)) )
       => ( ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Da),C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,tryCatch_list_char(E_1,C,V,E_2),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1_1),L_1_2))) ) ) ) ).

tff(fact_1073_red__reds_ORedCast,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,S: produc12694297on_val,A: nat,Da: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Da),Fs)) )
     => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Da),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)))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A))),S)),red(Pa))) ) ) ).

tff(fact_1074_red__reds_ORedTryFail,axiom,
    ! [V: list_char,E_2: exp_list_char,C: list_char,Pa: list_P1999446415t_char,S: produc12694297on_val,A: nat,Da: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Da),Fs)) )
     => ( ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Da),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))),C,V,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S)),red(Pa))) ) ) ).

tff(fact_1075_CastRedsAddr,axiom,
    ! [C: list_char,Da: list_char,Fs: fun_Pr806764899on_val,Eb: exp_list_char,S: produc12694297on_val,A: nat,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A))),S_2)),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_2),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Da),Fs)) )
       => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Da),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,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A))),S_2)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1076_TryCatch,axiom,
    ! [E_2: exp_list_char,V: list_char,E_2_a: exp_list_char,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,C: list_char,Da: list_char,Fs: fun_Pr806764899on_val,Pa: list_P1999446415t_char,E_1: exp_list_char,S_0: produc12694297on_val,A: nat,H_1_1: fun_na939144002on_val,L_1_2: 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)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1_1),L_1_2)))
     => ( ( hAPP_n546249108on_val(H_1_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Da),Fs)) )
       => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Da),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_1),fun_up1149430426on_val(L_1_2,V,hAPP_val_option_val(some_val,addr(A))))),E_2_a),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,E_2),S_0),E_2_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),fun_up1149430426on_val(L_2,V,hAPP_l207779698on_val(L_1_2,V))))) ) ) ) ) ).

tff(fact_1077_CastRedsFail,axiom,
    ! [C: list_char,Da: list_char,Fs: fun_Pr806764899on_val,Eb: exp_list_char,S: produc12694297on_val,A: nat,S_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,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A))),S_2)),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_2),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Da),Fs)) )
       => ( ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Da),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,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(classCast))))),S_2)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1078_red__reds_ORedCastFail,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,S: produc12694297on_val,A: nat,Da: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Da),Fs)) )
     => ( ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Da),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)))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(classCast))))),S)),red(Pa))) ) ) ).

tff(fact_1079_CastFail,axiom,
    ! [C: list_char,Da: list_char,Fs: fun_Pr806764899on_val,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,A: nat,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)))
     => ( ( hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Da),Fs)) )
       => ( ~ hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Da),C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,Eb),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(classCast))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))) ) ) ) ).

tff(fact_1080_red__reds_ORedTryCatch,axiom,
    ! [V: list_char,E_2: exp_list_char,C: list_char,Pa: list_P1999446415t_char,S: produc12694297on_val,A: nat,Da: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Da),Fs)) )
     => ( hBOOL(member1251428284t_char(hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Da),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))),C,V,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V,hAPP_list_char_ty(class,C),seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,addr(A))),E_2))),S)),red(Pa))) ) ) ).

tff(fact_1081_BlockRedsFinal,axiom,
    ! [Ta: ty,H_0_1: fun_na939144002on_val,L_0_1: fun_li1432931796on_val,V: 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_1),fun_up1149430426on_val(L_0_1,V,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,Ta,E_0)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0_1),L_0_1))),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,hAPP_l207779698on_val(L_0_1,V))))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1082_WTrtTry,axiom,
    ! [V: list_char,C: list_char,E_2: exp_list_char,T_2: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1: exp_list_char,T_1: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_1),T_1))
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,fun_up424764369ion_ty(Ea,V,hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,C))),E_2),T_2))
       => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1),T_2))
         => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,tryCatch_list_char(E_1,C,V,E_2)),T_2)) ) ) ) ).

tff(fact_1083_ty_Osimps_I8_J,axiom,
    ! [List_1: list_char] : void != hAPP_list_char_ty(class,List_1) ).

tff(fact_1084_ty_Osimps_I9_J,axiom,
    ! [List_1: list_char] : hAPP_list_char_ty(class,List_1) != void ).

tff(fact_1085_ty_Oinject,axiom,
    ! [List_3: list_char,List_2: list_char] :
      ( ( hAPP_list_char_ty(class,List_3) = hAPP_list_char_ty(class,List_2) )
    <=> ( List_3 = List_2 ) ) ).

tff(fact_1086_ty_Osimps_I15_J,axiom,
    ! [List_1: list_char] : hAPP_list_char_ty(class,List_1) != boolean ).

tff(fact_1087_ty_Osimps_I14_J,axiom,
    ! [List_1: list_char] : boolean != hAPP_list_char_ty(class,List_1) ).

tff(fact_1088_ty_Osimps_I20_J,axiom,
    ! [List_1: list_char] : nt != hAPP_list_char_ty(class,List_1) ).

tff(fact_1089_ty_Osimps_I21_J,axiom,
    ! [List_1: list_char] : hAPP_list_char_ty(class,List_1) != nt ).

tff(fact_1090_ty_Osimps_I18_J,axiom,
    ! [List_1: list_char] : integer != hAPP_list_char_ty(class,List_1) ).

tff(fact_1091_ty_Osimps_I19_J,axiom,
    ! [List_1: list_char] : hAPP_list_char_ty(class,List_1) != integer ).

tff(fact_1092_is__refT__def,axiom,
    ! [Ta: ty] :
      ( hBOOL(hAPP_ty_bool(is_refT,Ta))
    <=> ( ( Ta = nt )
        | ? [C_2: list_char] : Ta = hAPP_list_char_ty(class,C_2) ) ) ).

tff(fact_1093_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_1094_Block,axiom,
    ! [Ta: ty,Pa: list_P1999446415t_char,E_0: exp_list_char,H_0_1: fun_na939144002on_val,L_0_1: fun_li1432931796on_val,V: list_char,E_1: exp_list_char,H_1_1: fun_na939144002on_val,L_1_2: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_0,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0_1),fun_up1149430426on_val(L_0_1,V,none_val))),E_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1_1),L_1_2)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,block_list_char(V,Ta,E_0),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0_1),L_0_1)),E_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1_1),fun_up1149430426on_val(L_1_2,V,hAPP_l207779698on_val(L_0_1,V))))) ) ).

tff(fact_1095_binop_Osimps_I10_J,axiom,
    ! [V_1_1: 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_1),addr(V_3)))) = none_val ).

tff(fact_1096_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_1097_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_1098_binop_Osimps_I8_J,axiom,
    ! [V_1_1: val] : binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_1),null))) = none_val ).

tff(fact_1099_binop_Osimps_I9_J,axiom,
    ! [V_1_2: val,V_1: 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_1)))) = none_val ).

tff(fact_1100_binop_Osimps_I5_J,axiom,
    ! [V_1: bool,V_2_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_1)),V_2_2))) = none_val ).

tff(fact_1101_binop_Osimps_I7_J,axiom,
    ! [V_1_1: val] : binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_1),unit))) = none_val ).

tff(fact_1102_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_1103_WTrt__elim__cases_I5_J,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1: exp_list_char,C: list_char,V: list_char,E_2: exp_list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,tryCatch_list_char(E_1,C,V,E_2)),Ta))
     => ~ ! [T_1_1: ty] :
            ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_1),T_1_1))
           => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,fun_up424764369ion_ty(Ea,V,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_1),Ta)) ) ) ) ).

tff(fact_1104_red__reds_OBlockRedSome,axiom,
    ! [Ta: ty,V_1: val,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,V: list_char,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: 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,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,V,none_val)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa)))
     => ( ( hAPP_l207779698on_val(L_b,V) = hAPP_val_option_val(some_val,V_1) )
       => ( ~ hBOOL(assigned(V,Eb))
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V,Ta,Eb)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V,Ta,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,V,hAPP_l207779698on_val(Lb,V))))),red(Pa))) ) ) ) ).

tff(fact_1105_hext__new,axiom,
    ! [X_2: produc639455274on_val,Hb: fun_na939144002on_val,A: nat] :
      ( ( hAPP_n546249108on_val(Hb,A) = none_P179726773on_val )
     => hBOOL(hext(Hb,fun_up2041264236on_val(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,X_2)))) ) ).

tff(fact_1106_redp__redsp_OBlockRedNone,axiom,
    ! [Ta: ty,Pa: list_P1999446415t_char,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,V: list_char,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,V,none_val))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))
     => ( ( hAPP_l207779698on_val(L_b,V) = none_val )
       => ( ~ hBOOL(assigned(V,Eb))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V,Ta,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),block_list_char(V,Ta,E_b)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,V,hAPP_l207779698on_val(Lb,V))))) ) ) ) ).

tff(fact_1107_red__reds_OBlockRedNone,axiom,
    ! [Ta: ty,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,V: list_char,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: 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,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,V,none_val)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa)))
     => ( ( hAPP_l207779698on_val(L_b,V) = none_val )
       => ( ~ hBOOL(assigned(V,Eb))
         => hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V,Ta,Eb)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(V,Ta,E_b)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,V,hAPP_l207779698on_val(Lb,V))))),red(Pa))) ) ) ) ).

tff(fact_1108_redp__redsp_OBlockRedSome,axiom,
    ! [Ta: ty,V_1: val,Pa: list_P1999446415t_char,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,V: list_char,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,V,none_val))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))
     => ( ( hAPP_l207779698on_val(L_b,V) = hAPP_val_option_val(some_val,V_1) )
       => ( ~ hBOOL(assigned(V,Eb))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V,Ta,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),block_list_char(V,Ta,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,V,hAPP_l207779698on_val(Lb,V))))) ) ) ) ).

tff(fact_1109_ty_Oexhaust,axiom,
    ! [Y: ty] :
      ( ( Y != void )
     => ( ( Y != boolean )
       => ( ( Y != integer )
         => ( ( Y != nt )
           => ~ ! [List: list_char] : Y != hAPP_list_char_ty(class,List) ) ) ) ) ).

tff(fact_1110_eval__cases_I8_J,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,Ta: ty,E_1: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,block_list_char(V,Ta,E_1),S),E_b),S_2))
     => ~ ! [H_0: fun_na939144002on_val,L_0: fun_li1432931796on_val] :
            ( ( S = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),L_0) )
           => ! [H_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val] :
                ( ( S_2 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),fun_up1149430426on_val(L_1_1,V,hAPP_l207779698on_val(L_0,V))) )
               => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),fun_up1149430426on_val(L_0,V,none_val))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1))) ) ) ) ).

tff(fact_1111_assigned__def,axiom,
    ! [V: list_char,Eb: exp_list_char] :
      ( hBOOL(assigned(V,Eb))
    <=> ? [V_2: val,E: exp_list_char] : Eb = seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_2)),E) ) ).

tff(fact_1112_refTE,axiom,
    ! [T_4: ty] :
      ( hBOOL(hAPP_ty_bool(is_refT,T_4))
     => ( ( T_4 != nt )
       => ~ ! [C_2: list_char] : T_4 != hAPP_list_char_ty(class,C_2) ) ) ).

tff(fact_1113_redp__redsp_ORedTryCatch,axiom,
    ! [V: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,C: list_char,S: produc12694297on_val,A: nat,Da: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Da),Fs)) )
     => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(transi1065307915t_char(subcls744239332t_char(Pa)),Da),C))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,tryCatch_list_char(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))),C,V,E_2),S),block_list_char(V,hAPP_list_char_ty(class,C),seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,addr(A))),E_2))),S)) ) ) ).

tff(fact_1114_redp__redsp_ORedCastFail,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,S: produc12694297on_val,A: nat,Da: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Da),Fs)) )
     => ( ~ hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(transi1065307915t_char(subcls744239332t_char(Pa)),Da),C))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,hAPP_v834067052t_char(val_list_char,addr(A))),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(classCast))))),S)) ) ) ).

tff(fact_1115_redp__redsp_ORedCast,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,S: produc12694297on_val,A: nat,Da: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Da),Fs)) )
     => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(transi1065307915t_char(subcls744239332t_char(Pa)),Da),C))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,hAPP_v834067052t_char(val_list_char,addr(A))),S),hAPP_v834067052t_char(val_list_char,addr(A))),S)) ) ) ).

tff(fact_1116_redp__redsp_ORedTryFail,axiom,
    ! [V: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,C: list_char,S: produc12694297on_val,A: nat,Da: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Da),Fs)) )
     => ( ~ hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(transi1065307915t_char(subcls744239332t_char(Pa)),Da),C))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,tryCatch_list_char(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))),C,V,E_2),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S)) ) ) ).

tff(fact_1117_finalRefE,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),Ta))
     => ( hBOOL(hAPP_ty_bool(is_refT,Ta))
       => ( hBOOL(final_list_char(Eb))
         => ( ( Eb != hAPP_v834067052t_char(val_list_char,null) )
           => ( ( ? [A_1: nat] : Eb = hAPP_v834067052t_char(val_list_char,addr(A_1))
               => ! [C_2: list_char] : Ta != hAPP_list_char_ty(class,C_2) )
             => ~ ! [A_1: nat] : Eb != throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))) ) ) ) ) ) ).

tff(fact_1118_WTrtFAss,axiom,
    ! [E_2: exp_list_char,T_2: ty,Fa: list_char,Ta: ty,Da: list_char,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1: exp_list_char,C: list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_1),hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,Fa,Ta),Da))
       => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,E_2),T_2))
         => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2),Ta))
           => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,fAss_list_char(E_1,Fa,Da,E_2)),void)) ) ) ) ) ).

tff(fact_1119_WTrtFAcc,axiom,
    ! [Fa: list_char,Ta: ty,Da: list_char,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,C: list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,Fa,Ta),Da))
       => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,fAcc_list_char(Eb,Fa,Da)),Ta)) ) ) ).

tff(fact_1120_WTrt__elim__cases_I7_J,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Fa: list_char,Da: list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,fAcc_list_char(Eb,Fa,Da)),Ta))
     => ( ! [C_2: list_char] :
            ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),hAPP_list_char_ty(class,C_2)))
           => ~ hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C_2,Fa,Ta),Da)) )
       => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),nt)) ) ) ).

tff(fact_1121_WTrt__elim__cases_I8_J,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Fa: list_char,Da: list_char,V_1: exp_list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,fAss_list_char(Eb,Fa,Da,V_1)),Ta))
     => ( ( ( Ta = void )
         => ! [C_2: list_char] :
              ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),hAPP_list_char_ty(class,C_2)))
             => ! [T_3: ty] :
                  ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C_2,Fa,T_3),Da))
                 => ! [T_2_1: ty] :
                      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,V_1),T_2_1))
                     => ~ hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_1),T_3)) ) ) ) )
       => ~ ( ( Ta = void )
           => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),nt))
             => ! [T_2_1: ty] : ~ hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,V_1),T_2_1)) ) ) ) ) ).

tff(fact_1122_final__addrE,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,C: list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),hAPP_list_char_ty(class,C)))
     => ( hBOOL(final_list_char(Eb))
       => ( ! [A_1: nat] : Eb != hAPP_v834067052t_char(val_list_char,addr(A_1))
         => ~ ! [A_1: nat] : Eb != throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))) ) ) ) ).

tff(fact_1123_WTrtCast,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),Ta))
     => ( hBOOL(hAPP_ty_bool(is_refT,Ta))
       => ( hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C))
         => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,cast_list_char(C,Eb)),hAPP_list_char_ty(class,C))) ) ) ) ).

tff(fact_1124_WTrt__elim__cases_I6_J,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Da: list_char,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,cast_list_char(Da,Eb)),Ta))
     => ~ ( ( Ta = hAPP_list_char_ty(class,Da) )
         => ! [T_3: ty] :
              ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),T_3))
             => ( hBOOL(hAPP_ty_bool(is_refT,T_3))
               => ~ hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),Da)) ) ) ) ) ).

tff(fact_1125_hextI,axiom,
    ! [H_b: fun_na939144002on_val,Hb: fun_na939144002on_val] :
      ( ! [A_1: nat,C_2: list_char,Fs_1: fun_Pr806764899on_val] :
          ( ( hAPP_n546249108on_val(Hb,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C_2),Fs_1)) )
         => ? [Fs_3: fun_Pr806764899on_val] : hAPP_n546249108on_val(H_b,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C_2),Fs_3)) )
     => hBOOL(hext(Hb,H_b)) ) ).

tff(fact_1126_WTrts__Val,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Vs_1: list_val,Ts: list_ty] :
      ( hBOOL(wTrts_1(Pa,Hb,Ea,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vs_1),Ts))
    <=> ( hAPP_l2006940821ion_ty(map_val_option_ty(typeof_h(Hb)),Vs_1) = hAPP_l1487035934ion_ty(map_ty_option_ty(some_ty),Ts) ) ) ).

tff(fact_1127_WTrtVal,axiom,
    ! [Pa: list_P1999446415t_char,Ea: fun_li688206603ion_ty,Hb: fun_na939144002on_val,V_1: val,Ta: ty] :
      ( ( hAPP_val_option_ty(typeof_h(Hb),V_1) = hAPP_ty_option_ty(some_ty,Ta) )
     => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,hAPP_v834067052t_char(val_list_char,V_1)),Ta)) ) ).

tff(fact_1128_hext__typeof__mono,axiom,
    ! [V_1: val,Ta: ty,Hb: fun_na939144002on_val,H_b: fun_na939144002on_val] :
      ( hBOOL(hext(Hb,H_b))
     => ( ( hAPP_val_option_ty(typeof_h(Hb),V_1) = hAPP_ty_option_ty(some_ty,Ta) )
       => ( hAPP_val_option_ty(typeof_h(H_b),V_1) = hAPP_ty_option_ty(some_ty,Ta) ) ) ) ).

tff(fact_1129_typeof__lit__typeof,axiom,
    ! [Hb: fun_na939144002on_val,V_1: val,Ta: ty] :
      ( ( hAPP_val_option_ty(typeof_h(hAPP_o1576581476on_val(cOMBK_1944287343al_nat,none_P179726773on_val)),V_1) = hAPP_ty_option_ty(some_ty,Ta) )
     => ( hAPP_val_option_ty(typeof_h(Hb),V_1) = hAPP_ty_option_ty(some_ty,Ta) ) ) ).

tff(fact_1130_typeof__h_Osimps_I2_J,axiom,
    ! [Hb: fun_na939144002on_val] : hAPP_val_option_ty(typeof_h(Hb),null) = hAPP_ty_option_ty(some_ty,nt) ).

tff(fact_1131_typeof__h_Osimps_I3_J,axiom,
    ! [Hb: fun_na939144002on_val,B: bool] : hAPP_val_option_ty(typeof_h(Hb),bool_1(B)) = hAPP_ty_option_ty(some_ty,boolean) ).

tff(fact_1132_typeof__h_Osimps_I1_J,axiom,
    ! [Hb: fun_na939144002on_val] : hAPP_val_option_ty(typeof_h(Hb),unit) = hAPP_ty_option_ty(some_ty,void) ).

tff(fact_1133_typeof__h_Osimps_I5_J,axiom,
    ! [Hb: fun_na939144002on_val,A: nat] : hAPP_val_option_ty(typeof_h(Hb),addr(A)) = option1388193227on_val(none_ty,hAPP_f46308763ion_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(Hb,A)) ).

tff(fact_1134_WTrt_H__WTrts_H_Ointros_I16_J,axiom,
    ! [Ea: fun_li688206603ion_ty,V: list_char,E_2: exp_list_char,T_2: ty,Pa: list_P1999446415t_char,Ta: ty,Hb: fun_na939144002on_val,V_1: val,T_1: ty] :
      ( ( hAPP_val_option_ty(typeof_h(Hb),V_1) = hAPP_ty_option_ty(some_ty,T_1) )
     => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1),Ta))
       => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,fun_up424764369ion_ty(Ea,V,hAPP_ty_option_ty(some_ty,Ta)),E_2),T_2))
         => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,block_list_char(V,Ta,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),E_2))),T_2)) ) ) ) ).

tff(fact_1135_WTrt_H__WTrts_H_Ointros_I3_J,axiom,
    ! [Pa: list_P1999446415t_char,Ea: fun_li688206603ion_ty,Hb: fun_na939144002on_val,V_1: val,Ta: ty] :
      ( ( hAPP_val_option_ty(typeof_h(Hb),V_1) = hAPP_ty_option_ty(some_ty,Ta) )
     => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,hAPP_v834067052t_char(val_list_char,V_1)),Ta)) ) ).

tff(fact_1136_wt_H__iff__wt,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,Eb),Ta))
    <=> hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),Ta)) ) ).

tff(fact_1137_wt_H__wt,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,Eb),Ta))
     => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),Ta)) ) ).

tff(fact_1138_wt__wt_H,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),Ta))
     => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,Eb),Ta)) ) ).

tff(fact_1139_WTrt_H__WTrts_H_Ointros_I18_J,axiom,
    ! [E_2: exp_list_char,T_2: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1: exp_list_char,T_1: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,E_1),T_1))
     => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,E_2),T_2))
       => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,seq_list_char(E_1,E_2)),T_2)) ) ) ).

tff(fact_1140_WTrt_H__WTrts_H_Ointros_I9_J,axiom,
    ! [Fa: list_char,Da: list_char,Ta: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,Eb),nt))
     => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,fAcc_list_char(Eb,Fa,Da)),Ta)) ) ).

tff(fact_1141_WTrt_H__WTrts_H_Ointros_I21_J,axiom,
    ! [Ta: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,T_r: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,Eb),T_r))
     => ( hBOOL(hAPP_ty_bool(is_refT,T_r))
       => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,throw_list_char(Eb)),Ta)) ) ) ).

tff(fact_1142_WTrt_H__WTrts_H_Ointros_I11_J,axiom,
    ! [Fa: list_char,Da: list_char,E_2: exp_list_char,T_2: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,E_1),nt))
     => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,E_2),T_2))
       => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,fAss_list_char(E_1,Fa,Da,E_2)),void)) ) ) ).

tff(fact_1143_WTrt_H__WTrts_H_Ointros_I19_J,axiom,
    ! [Ta: ty,E_2: exp_list_char,T_2: ty,E_1: exp_list_char,T_1: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,Eb),boolean))
     => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,E_1),T_1))
       => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,E_2),T_2))
         => ( ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1),T_2))
              | hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2),T_1)) )
           => ( ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1),T_2))
               => ( Ta = T_2 ) )
             => ( ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2),T_1))
                 => ( Ta = T_1 ) )
               => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,cond_list_char(Eb,E_1,E_2)),Ta)) ) ) ) ) ) ) ).

tff(fact_1144_WTrt_H__WTrts_H_Ointros_I20_J,axiom,
    ! [C_1: exp_list_char,Ta: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,Eb),boolean))
     => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,C_1),Ta))
       => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,while_list_char(Eb,C_1)),void)) ) ) ).

tff(fact_1145_WTrt_H__WTrts_H_Ointros_I6_J,axiom,
    ! [E_2: exp_list_char,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,E_1),integer))
     => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,E_2),integer))
       => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,binOp_list_char(E_1,add,E_2)),integer)) ) ) ).

tff(fact_1146_WTrt_H__WTrts_H_Ointros_I5_J,axiom,
    ! [E_2: exp_list_char,T_2: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1: exp_list_char,T_1: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,E_1),T_1))
     => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,E_2),T_2))
       => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,binOp_list_char(E_1,c_Expr_Obop_OEq,E_2)),boolean)) ) ) ).

tff(fact_1147_WTrt_H__WTrts_H_Ointros_I8_J,axiom,
    ! [Fa: list_char,Ta: ty,Da: list_char,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,C: list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,Eb),hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,Fa,Ta),Da))
       => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,fAcc_list_char(Eb,Fa,Da)),Ta)) ) ) ).

tff(fact_1148_WTrt_H__WTrts_H_Ointros_I2_J,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,Eb),Ta))
     => ( hBOOL(hAPP_ty_bool(is_refT,Ta))
       => ( hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C))
         => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,cast_list_char(C,Eb)),hAPP_list_char_ty(class,C))) ) ) ) ).

tff(fact_1149_WTrt_H__WTrts_H_Ointros_I17_J,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,V: list_char,Ta: ty,Eb: exp_list_char,T: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,fun_up424764369ion_ty(Ea,V,hAPP_ty_option_ty(some_ty,Ta)),Eb),T))
     => ( ~ hBOOL(assigned(V,Eb))
       => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,block_list_char(V,Ta,Eb)),T)) ) ) ).

tff(fact_1150_WTrt_H__WTrts_H_Ointros_I22_J,axiom,
    ! [V: list_char,C: list_char,E_2: exp_list_char,T_2: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1: exp_list_char,T_1: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,E_1),T_1))
     => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,fun_up424764369ion_ty(Ea,V,hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,C))),E_2),T_2))
       => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1),T_2))
         => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,tryCatch_list_char(E_1,C,V,E_2)),T_2)) ) ) ) ).

tff(fact_1151_WTrt_H__WTrts_H_Ointros_I10_J,axiom,
    ! [E_2: exp_list_char,T_2: ty,Fa: list_char,Ta: ty,Da: list_char,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1: exp_list_char,C: list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,E_1),hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,Fa,Ta),Da))
       => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,E_2),T_2))
         => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2),Ta))
           => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,fAss_list_char(E_1,Fa,Da,E_2)),void)) ) ) ) ) ).

tff(fact_1152_typeof__ClassCast,axiom,
    ! [Hb: fun_na939144002on_val] :
      ( hBOOL(preallocated(Hb))
     => ( hAPP_val_option_ty(typeof_h(Hb),addr(addr_of_sys_xcpt(classCast))) = hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,classCast)) ) ) ).

tff(fact_1153_preallocated__hext,axiom,
    ! [H_b: fun_na939144002on_val,Hb: fun_na939144002on_val] :
      ( hBOOL(preallocated(Hb))
     => ( hBOOL(hext(Hb,H_b))
       => hBOOL(preallocated(H_b)) ) ) ).

tff(fact_1154_preallocated__upd__obj,axiom,
    ! [Fs_2: fun_Pr806764899on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val,Hb: fun_na939144002on_val] :
      ( hBOOL(preallocated(Hb))
     => ( ( hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) )
       => hBOOL(preallocated(fun_up2041264236on_val(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_2))))) ) ) ).

tff(fact_1155_preallocated__new,axiom,
    ! [X_2: produc639455274on_val,A: nat,Hb: fun_na939144002on_val] :
      ( hBOOL(preallocated(Hb))
     => ( ( hAPP_n546249108on_val(Hb,A) = none_P179726773on_val )
       => hBOOL(preallocated(fun_up2041264236on_val(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,X_2)))) ) ) ).

tff(fact_1156_typeof__NullPointer,axiom,
    ! [Hb: fun_na939144002on_val] :
      ( hBOOL(preallocated(Hb))
     => ( hAPP_val_option_ty(typeof_h(Hb),addr(addr_of_sys_xcpt(nullPointer))) = hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,nullPointer)) ) ) ).

tff(fact_1157_typeof__OutOfMemory,axiom,
    ! [Hb: fun_na939144002on_val] :
      ( hBOOL(preallocated(Hb))
     => ( hAPP_val_option_ty(typeof_h(Hb),addr(addr_of_sys_xcpt(outOfMemory))) = hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,outOfMemory)) ) ) ).

tff(fact_1158_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_1159_preallocatedE,axiom,
    ! [Pa: fun_fu311765169r_bool,C: list_char,Hb: fun_na939144002on_val] :
      ( hBOOL(preallocated(Hb))
     => ( hBOOL(member_list_char(C,sys_xcpts))
       => ( ! [Fs_1: fun_Pr806764899on_val] :
              ( ( hAPP_n546249108on_val(Hb,addr_of_sys_xcpt(C)) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)) )
             => hBOOL(hAPP_list_char_bool(hAPP_f388705405r_bool(Pa,Hb),C)) )
         => hBOOL(hAPP_list_char_bool(hAPP_f388705405r_bool(Pa,Hb),C)) ) ) ) ).

tff(fact_1160_preallocatedD,axiom,
    ! [C: list_char,Hb: fun_na939144002on_val] :
      ( hBOOL(preallocated(Hb))
     => ( hBOOL(member_list_char(C,sys_xcpts))
       => ? [Fs_1: fun_Pr806764899on_val] : hAPP_n546249108on_val(Hb,addr_of_sys_xcpt(C)) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)) ) ) ).

tff(fact_1161_preallocated__def,axiom,
    ! [Hb: fun_na939144002on_val] :
      ( hBOOL(preallocated(Hb))
    <=> ! [X_1: list_char] :
          ( hBOOL(member_list_char(X_1,sys_xcpts))
         => ? [Fs_1: fun_Pr806764899on_val] : hAPP_n546249108on_val(Hb,addr_of_sys_xcpt(X_1)) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,X_1),Fs_1)) ) ) ).

tff(fact_1162_red__reds_ORedNewFail,axiom,
    ! [C: list_char,Lb: fun_li1432931796on_val,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val] :
      ( ( new_Addr(Hb) = 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,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(outOfMemory))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),red(Pa))) ) ).

tff(fact_1163_WTrtNew,axiom,
    ! [Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Pa: list_P1999446415t_char,C: list_char] :
      ( hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C))
     => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,new_list_char(C)),hAPP_list_char_ty(class,C))) ) ).

tff(fact_1164_WTrt__elim__cases_I10_J,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,C: list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,new_list_char(C)),Ta))
     => ~ ( ( Ta = hAPP_list_char_ty(class,C) )
         => ~ hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C)) ) ) ).

tff(fact_1165_new__Addr__SomeD,axiom,
    ! [Hb: fun_na939144002on_val,A: nat] :
      ( ( new_Addr(Hb) = hAPP_nat_option_nat(some_nat,A) )
     => ( hAPP_n546249108on_val(Hb,A) = none_P179726773on_val ) ) ).

tff(fact_1166_New,axiom,
    ! [Lb: fun_li1432931796on_val,H_b: fun_na939144002on_val,Pa: list_P1999446415t_char,C: list_char,FDTs: list_P2023964830har_ty,Hb: fun_na939144002on_val,A: nat] :
      ( ( new_Addr(Hb) = hAPP_nat_option_nat(some_nat,A) )
     => ( hBOOL(fields1147507508t_char(Pa,C,FDTs))
       => ( ( H_b = fun_up2041264236on_val(Hb,A,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,Hb),Lb)),hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),Lb))) ) ) ) ).

tff(fact_1167_redp__redsp_ORedNew,axiom,
    ! [Lb: fun_li1432931796on_val,H_b: fun_na939144002on_val,Pa: list_P1999446415t_char,C: list_char,FDTs: list_P2023964830har_ty,Hb: fun_na939144002on_val,A: nat] :
      ( ( new_Addr(Hb) = hAPP_nat_option_nat(some_nat,A) )
     => ( hBOOL(fields1147507508t_char(Pa,C,FDTs))
       => ( ( H_b = fun_up2041264236on_val(Hb,A,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,Hb),Lb)),hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),Lb))) ) ) ) ).

tff(fact_1168_WTrt_H__WTrts_H_Ointros_I1_J,axiom,
    ! [Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Pa: list_P1999446415t_char,C: list_char] :
      ( hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C))
     => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,new_list_char(C)),hAPP_list_char_ty(class,C))) ) ).

tff(fact_1169_red__reds_ORedNew,axiom,
    ! [Lb: fun_li1432931796on_val,H_b: fun_na939144002on_val,Pa: list_P1999446415t_char,C: list_char,FDTs: list_P2023964830har_ty,Hb: fun_na939144002on_val,A: nat] :
      ( ( new_Addr(Hb) = hAPP_nat_option_nat(some_nat,A) )
     => ( hBOOL(fields1147507508t_char(Pa,C,FDTs))
       => ( ( H_b = fun_up2041264236on_val(Hb,A,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,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),Lb))),red(Pa))) ) ) ) ).

tff(fact_1170_NewFail,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,Lb: fun_li1432931796on_val,Hb: fun_na939144002on_val] :
      ( ( new_Addr(Hb) = none_nat )
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,new_list_char(C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(outOfMemory))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))) ) ).

tff(fact_1171_redp__redsp_ORedNewFail,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,Lb: fun_li1432931796on_val,Hb: fun_na939144002on_val] :
      ( ( new_Addr(Hb) = none_nat )
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,new_list_char(C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(outOfMemory))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))) ) ).

tff(fact_1172_wf__J__prog__wf__J__mdecl,axiom,
    ! [Jmdcl: produc1013743697t_char,C: list_char,Da: list_char,Fds: list_P1940453997har_ty,Mths: list_P341299826t_char,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wf_J_mdecl,Pa))
     => ( hBOOL(member1467889965t_char(hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,C),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Da),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Fds),Mths))),set_Pr1494163115t_char(Pa)))
       => ( hBOOL(member1601084734t_char(Jmdcl,set_Pr2033386304t_char(Mths)))
         => hBOOL(hAPP_P1384137393r_bool(hAPP_l2054741776r_bool(hAPP_l2138409430r_bool(wf_J_mdecl,Pa),C),Jmdcl)) ) ) ) ).

tff(fact_1173_Red__fv,axiom,
    ! [Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: 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,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),red(Pa)))
       => hBOOL(ord_le2092826700r_bool(fv(E_b),fv(Eb))) ) ) ).

tff(fact_1174_fv__fvs_Osimps_I14_J,axiom,
    ! [Eb: exp_list_char] : fv(throw_list_char(Eb)) = fv(Eb) ).

tff(fact_1175_fv__fvs_Osimps_I7_J,axiom,
    ! [Eb: exp_list_char,Fa: list_char,Da: list_char] : fv(fAcc_list_char(Eb,Fa,Da)) = fv(Eb) ).

tff(fact_1176_fv__fvs_Osimps_I2_J,axiom,
    ! [C: list_char,Eb: exp_list_char] : fv(cast_list_char(C,Eb)) = fv(Eb) ).

tff(fact_1177_eval__notfree__unchanged,axiom,
    ! [V: list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))
     => ( ~ hBOOL(member_list_char(V,fv(Eb)))
       => ( hAPP_l207779698on_val(L_b,V) = hAPP_l207779698on_val(Lb,V) ) ) ) ).

tff(fact_1178_eval__restrict__lcl,axiom,
    ! [W: fun_list_char_bool,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))
       => ( hBOOL(ord_le2092826700r_bool(fv(Eb),W))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),restri761823004ar_val(Lb,W))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),restri761823004ar_val(L_b,W)))) ) ) ) ).

tff(fact_1179_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,Ts: list_ty,Ta: ty,Pns: list_list_char,Body: exp_list_char,Da: list_char,C: list_char,Fs: fun_Pr806764899on_val,Esa: list_exp_list_char,Vs_1: list_val,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,Eb: exp_list_char,S_0: produc12694297on_val,A: nat,S_1: 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,Eb),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A))),S_1)),transi2024712006on_val(red(Pa))))
       => ( hBOOL(member875476972on_val(hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vs_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2))),transi374442731on_val(reds(Pa))))
         => ( ( hAPP_n546249108on_val(H_2,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) )
           => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Ts,Ta,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Pns),Body)),Da))
             => ( ( size_size_list_val(Vs_1) = 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))),Pns,Vs_1) )
                 => ( 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(Eb,M,Esa)),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_1180_Call,axiom,
    ! [E_b: exp_list_char,H_3: fun_na939144002on_val,L_3: fun_li1432931796on_val,L_2_1: fun_li1432931796on_val,M: list_char,Ts: list_ty,Ta: ty,Pns: list_list_char,Body: exp_list_char,Da: list_char,C: list_char,Fs: fun_Pr806764899on_val,Ps: list_exp_list_char,Vs_1: list_val,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,A: nat,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),S_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Ps,S_1),hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vs_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2)))
       => ( ( hAPP_n546249108on_val(H_2,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) )
         => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Ts,Ta,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Pns),Body)),Da))
           => ( ( size_size_list_val(Vs_1) = 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))),Pns,Vs_1) )
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Body,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2_1)),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_3),L_3)))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,call_list_char(Eb,M,Ps),S_0),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_3),L_2))) ) ) ) ) ) ) ) ).

tff(fact_1181_red__reds_ORedCall,axiom,
    ! [Vs_1: list_val,Pa: list_P1999446415t_char,M: list_char,Ts: list_ty,Ta: ty,Pns: list_list_char,Body: exp_list_char,Da: list_char,S: produc12694297on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) )
     => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Ts,Ta,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Pns),Body)),Da))
       => ( ( size_size_list_val(Vs_1) = size_s2113983095t_char(Pns) )
         => ( ( size_size_list_ty(Ts) = 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)),M,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vs_1))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,cons_list_char(this,Pns)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,cons_ty(hAPP_list_char_ty(class,Da),Ts)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,cons_val(addr(A),Vs_1)),Body))))),S)),red(Pa))) ) ) ) ) ).

tff(fact_1182_redp__redsp_ORedCall,axiom,
    ! [Vs_1: list_val,Pa: list_P1999446415t_char,M: list_char,Ts: list_ty,Ta: ty,Pns: list_list_char,Body: exp_list_char,Da: list_char,S: produc12694297on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) )
     => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Ts,Ta,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Pns),Body)),Da))
       => ( ( size_size_list_val(Vs_1) = size_s2113983095t_char(Pns) )
         => ( ( size_size_list_ty(Ts) = size_s2113983095t_char(Pns) )
           => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),M,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vs_1)),S),blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,cons_list_char(this,Pns)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,cons_ty(hAPP_list_char_ty(class,Da),Ts)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,cons_val(addr(A),Vs_1)),Body))))),S)) ) ) ) ) ).

tff(fact_1183_WTrts__same__length,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Esa: list_exp_list_char,Ts: list_ty] :
      ( hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts))
     => ( size_s1143674878t_char(Esa) = size_size_list_ty(Ts) ) ) ).

tff(fact_1184_blocksFinal,axiom,
    ! [Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Pa: list_P1999446415t_char,Eb: exp_list_char,Vs_1: list_val,Vs: list_list_char,Ts: list_ty] :
      ( ( size_s2113983095t_char(Vs) = size_size_list_ty(Ts) )
     => ( ( size_size_list_val(Vs_1) = size_size_list_ty(Ts) )
       => ( hBOOL(final_list_char(Eb))
         => 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,Vs),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ts),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Vs_1),Eb))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1185_blocksEval,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val,Vs_1: list_val,Ps: list_list_char,Ts: list_ty] :
      ( ( size_s2113983095t_char(Ps) = size_size_list_ty(Ts) )
     => ( ( size_s2113983095t_char(Ps) = size_size_list_val(Vs_1) )
       => ( 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,Ts),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Vs_1),Eb)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))
         => ? [L_1: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),map_up1085636310ar_val(Lb,Ps,Vs_1))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_1))) ) ) ) ).

tff(fact_1186_wt__blocks,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Ta: ty,Vs_1: list_val,Vs: list_list_char,Ts: list_ty] :
      ( ( size_s2113983095t_char(Vs) = size_size_list_ty(Ts) )
     => ( ( size_size_list_val(Vs_1) = size_size_list_ty(Ts) )
       => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Vs),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ts),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Vs_1),Eb))))),Ta))
        <=> ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,map_up891053837har_ty(Ea,Vs,Ts),Eb),Ta))
            & ? [Ts_2: list_ty] :
                ( ( hAPP_l2006940821ion_ty(map_val_option_ty(typeof_h(Hb)),Vs_1) = hAPP_l1487035934ion_ty(map_ty_option_ty(some_ty),Ts_2) )
                & hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_2,Ts)) ) ) ) ) ) ).

tff(fact_1187_WTrtCall,axiom,
    ! [Esa: list_exp_list_char,Ts_1: list_ty,M: list_char,Ts: list_ty,Ta: ty,Pns: list_list_char,Body: exp_list_char,Da: list_char,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,C: list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,Eb),hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Ts,Ta,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Pns),Body)),Da))
       => ( hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts_1))
         => ( hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_1,Ts))
           => hBOOL(hAPP_ty_bool(wTrt(Pa,Hb,Ea,call_list_char(Eb,M,Esa)),Ta)) ) ) ) ) ).

tff(fact_1188_WTrt_H__WTrts_H_Ointros_I12_J,axiom,
    ! [Esa: list_exp_list_char,Ts_1: list_ty,M: list_char,Ts: list_ty,Ta: ty,Pns: list_list_char,Body: exp_list_char,Da: list_char,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,C: list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,Eb),hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Ts,Ta,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Pns),Body)),Da))
       => ( hBOOL(wTrts(Pa,Hb,Ea,Esa,Ts_1))
         => ( hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_1,Ts))
           => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,call_list_char(Eb,M,Esa)),Ta)) ) ) ) ) ).

tff(fact_1189_wts_H__iff__wts,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Esa: list_exp_list_char,Ts: list_ty] :
      ( hBOOL(wTrts(Pa,Hb,Ea,Esa,Ts))
    <=> hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts)) ) ).

tff(fact_1190_wts_H__wts,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Esa: list_exp_list_char,Ts: list_ty] :
      ( hBOOL(wTrts(Pa,Hb,Ea,Esa,Ts))
     => hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts)) ) ).

tff(fact_1191_wts__wts_H,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Esa: list_exp_list_char,Ts: list_ty] :
      ( hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts))
     => hBOOL(wTrts(Pa,Hb,Ea,Esa,Ts)) ) ).

tff(fact_1192_WTrt_H__WTrts_H_Ointros_I13_J,axiom,
    ! [M: list_char,Ta: ty,Esa: list_exp_list_char,Ts: list_ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,Eb),nt))
     => ( hBOOL(wTrts(Pa,Hb,Ea,Esa,Ts))
       => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,call_list_char(Eb,M,Esa)),Ta)) ) ) ).

tff(fact_1193_WTrt_H__WTrts_H_Ointros_I15_J,axiom,
    ! [Esa: list_exp_list_char,Ts: list_ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Hb,Ea,Eb),Ta))
     => ( hBOOL(wTrts(Pa,Hb,Ea,Esa,Ts))
       => hBOOL(wTrts(Pa,Hb,Ea,cons_exp_list_char(Eb,Esa),cons_ty(Ta,Ts))) ) ) ).

tff(fact_1194_blocksRedsFinal,axiom,
    ! [L: fun_li1432931796on_val,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val,Pa: list_P1999446415t_char,Vs_1: list_val,Vs: list_list_char,Ts: list_ty] :
      ( ( size_s2113983095t_char(Vs) = size_size_list_ty(Ts) )
     => ( ( size_size_list_val(Vs_1) = size_size_list_ty(Ts) )
       => ( hBOOL(distinct_list_char(Vs))
         => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),map_up1085636310ar_val(Lb,Vs,Vs_1)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),transi2024712006on_val(red(Pa))))
           => ( hBOOL(final_list_char(E_b))
             => ( ( L = overri2012515291on_val(L_b,Lb,set_list_char(Vs)) )
               => 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,Vs),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ts),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Vs_1),Eb))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L))),transi2024712006on_val(red(Pa)))) ) ) ) ) ) ) ).

tff(fact_1195_blocksReds,axiom,
    ! [Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val,Pa: list_P1999446415t_char,Vs_1: list_val,Vs: list_list_char,Ts: list_ty] :
      ( ( size_s2113983095t_char(Vs) = size_size_list_ty(Ts) )
     => ( ( size_size_list_val(Vs_1) = size_size_list_ty(Ts) )
       => ( hBOOL(distinct_list_char(Vs))
         => ( hBOOL(member773094996on_val(hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),map_up1085636310ar_val(Lb,Vs,Vs_1)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))),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,Vs),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ts),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Vs_1),Eb))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Vs),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ts),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,hAPP_l1892737211st_val(map_list_char_val(comp_o1129292306t_char(the_val,L_b)),Vs)),E_b))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),overri2012515291on_val(L_b,Lb,set_list_char(Vs))))),transi2024712006on_val(red(Pa)))) ) ) ) ) ).

tff(fact_1196_init__fields__def,axiom,
    init_fields = comp_l424027617har_ty(map_of1247784410ar_val,map_Pr1153581243ar_val(hAPP_f1295640803ar_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_1197_obj__ty__def,axiom,
    ! [Obj: produc639455274on_val] : obj_ty(Obj) = hAPP_list_char_ty(class,hAPP_P1789965269t_char(produc1230355531on_val,Obj)) ).

tff(fact_1198_cname__of__xcp,axiom,
    ! [C: list_char,Hb: fun_na939144002on_val] :
      ( hBOOL(preallocated(Hb))
     => ( hBOOL(member_list_char(C,sys_xcpts))
       => ( hAPP_P1789965269t_char(produc1230355531on_val,hAPP_o1977518472on_val(the_Pr431167171on_val,hAPP_n546249108on_val(Hb,addr_of_sys_xcpt(C)))) = C ) ) ) ).

tff(fact_1199_hp__def,axiom,
    hp = produc1517998010on_val ).

%----Helper facts (87)
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__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__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J,axiom,
    ! [P: fun_Pr661739816l_bool,Q: fun_ty434869310ar_val,R: ty] : hAPP_ty_bool(hAPP_f457123984y_bool(hAPP_f1391360361y_bool(cOMBB_1881684336ool_ty,P),Q),R) = hAPP_P1070896250l_bool(P,hAPP_t97533526ar_val(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_COMBB_1_1_COMBB_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__HOL_,axiom,
    ! [P: fun_Pr2081272681l_bool,Q: fun_fu1481433236al_val,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f1935223905l_bool(hAPP_f1589017327l_bool(cOMBB_558176806on_val,P),Q),R) = hAPP_P929938951l_bool(P,hAPP_f1181212006al_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Type,axiom,
    ! [P: fun_Pr1127025070y_bool,Q: fun_fu1959448993har_ty,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f1189972950l_bool(hAPP_f86617653l_bool(cOMBB_165135181on_val,P),Q),R) = hAPP_P748443392y_bool(P,hAPP_f1746527929har_ty(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_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc_,axiom,
    ! [P: fun_Pr252072522l_bool,Q: fun_fu544554869al_val,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f2061154754l_bool(hAPP_f1777594159l_bool(cOMBB_448128005on_val,P),Q),R) = hAPP_P943837928l_bool(P,hAPP_f384373191al_val(Q,R)) ).

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_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List,axiom,
    ! [P: fun_Pr565113489r_bool,Q: fun_fu593680828t_char,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f1326058377l_bool(hAPP_f1804599279l_bool(cOMBB_678146046on_val,P),Q),R) = hAPP_P449474095r_bool(P,hAPP_f338074126t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__,axiom,
    ! [P: fun_Pr827765831r_bool,Q: fun_fu1856635762t_char,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f1468279871l_bool(hAPP_f737797743l_bool(cOMBB_1733006024on_val,P),Q),R) = hAPP_P2118621157r_bool(P,hAPP_f1555843780t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_842,axiom,
    ! [P: fun_Pr661739816l_bool,Q: fun_fu1586296091ar_val,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f1787894864l_bool(hAPP_f975490601l_bool(cOMBB_844549459on_val,P),Q),R) = hAPP_P1070896250l_bool(P,hAPP_f901144627ar_val(Q,R)) ).

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__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__,axiom,
    ! [P: fun_Pr1336948301r_bool,Q: fun_fu928390720t_char,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f1390791157l_bool(hAPP_f99607667l_bool(cOMBB_1334418926on_val,P),Q),R) = hAPP_P2014166431r_bool(P,hAPP_f1953285592t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod,axiom,
    ! [P: fun_Pr839981232ar_val,Q: fun_ty1560310283har_ty,R: ty] : hAPP_t97533526ar_val(hAPP_f500340936ar_val(hAPP_f1675912277ar_val(cOMBB_351318850val_ty,P),Q),R) = hAPP_P532450504ar_val(P,hAPP_t931865635har_ty(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_843,axiom,
    ! [P: fun_Pr1149393094ar_val,Q: fun_ty1486032501har_ty,R: ty] : hAPP_t97533526ar_val(hAPP_f151191262ar_val(hAPP_f1061710805ar_val(cOMBB_239784108val_ty,P),Q),R) = hAPP_P841862366ar_val(P,hAPP_t708040077har_ty(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_844,axiom,
    ! [P: fun_Pr327509002har_ty,Q: fun_ty434869310ar_val,R: ty] : hAPP_t931865635har_ty(hAPP_f1734435490har_ty(hAPP_f393578581har_ty(cOMBB_1320677736_ty_ty,P),Q),R) = hAPP_P1409535266har_ty(P,hAPP_t97533526ar_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc,axiom,
    ! [P: fun_Pr46158268r_bool,Q: fun_fu725512935t_char,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f1645102644l_bool(hAPP_f962366127l_bool(cOMBB_95569939on_val,P),Q),R) = hAPP_P1907982426r_bool(P,hAPP_f1911830329t_char(Q,R)) ).

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_COMBB_1_1_COMBB_000tc__fun_Itc__Type__Oty_Mtc__prod_Itc__prod_Itc__List__Ol,axiom,
    ! [P: fun_fu1517809086y_bool,Q: fun_Pr130335392ar_val,R: produc1278157519t_char] : hAPP_P1845004857y_bool(hAPP_f1796274104y_bool(hAPP_f1589954605y_bool(cOMBB_1380239526t_char,P),Q),R) = hAPP_f457123984y_bool(P,hAPP_P221287148ar_val(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__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_,axiom,
    ! [P: fun_Pr315804320l_bool,Q: fun_fu194330259on_val,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f1937467848l_bool(hAPP_f2020099865l_bool(cOMBB_1543649755on_val,P),Q),R) = hAPP_P1235399154l_bool(P,hAPP_f2106552235on_val(Q,R)) ).

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__Type__Oty_Mtc__prod_Itc__prod_Itc__List__Ol_845,axiom,
    ! [P: fun_fu327647046ar_val,Q: fun_li70432166har_ty,R: list_char] : hAPP_l1836284219ar_val(hAPP_f1286352408ar_val(hAPP_f922986761ar_val(cOMBB_491542469t_char,P),Q),R) = hAPP_f151191262ar_val(P,hAPP_l826728946har_ty(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String___846,axiom,
    ! [P: fun_Pr227936640r_bool,Q: fun_fu2058915699t_char,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f1212990632l_bool(hAPP_f764883801l_bool(cOMBB_1837440507on_val,P),Q),R) = hAPP_P92196306r_bool(P,hAPP_f848628235t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun__847,axiom,
    ! [P: fun_Pr876827561ion_ty,Q: fun_fu1718160452on_val,R: fun_Pr806764899on_val] : hAPP_f652398900ion_ty(hAPP_f2110071953ion_ty(hAPP_f69964139ion_ty(cOMBB_2041093409on_val,P),Q),R) = hAPP_P1228500987ion_ty(P,hAPP_f900686428on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Type__Oty_Mtc__prod_Itc__List__Olist_Itc__S,axiom,
    ! [P: fun_fu676796720ar_val,Q: fun_Pr868791661har_ty,R: produc1278157519t_char] : hAPP_P221287148ar_val(hAPP_f1582750480ar_val(hAPP_f1761801623ar_val(cOMBB_510504510t_char,P),Q),R) = hAPP_f500340936ar_val(P,hAPP_P901867449har_ty(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Type__Oty_Mtc__prod_Itc__prod_Itc__List__Ol_848,axiom,
    ! [P: fun_fu327647046ar_val,Q: fun_Pr201309399har_ty,R: produc1278157519t_char] : hAPP_P221287148ar_val(hAPP_f2096521338ar_val(hAPP_f1210767211ar_val(cOMBB_1905001812t_char,P),Q),R) = hAPP_f151191262ar_val(P,hAPP_P827589667har_ty(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Type__Oty_Mtc__prod_Itc__prod_Itc__List__Ol_849,axiom,
    ! [P: fun_fu1443638794har_ty,Q: fun_Pr130335392ar_val,R: produc1278157519t_char] : hAPP_P901867449har_ty(hAPP_f1820012432har_ty(hAPP_f1720458941har_ty(cOMBB_424865560t_char,P),Q),R) = hAPP_f1734435490har_ty(P,hAPP_P221287148ar_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It,axiom,
    ! [P: fun_Pr1696029455l_bool,Q: fun_Pr1618910755on_val,R: product_prod_val_val] : hAPP_P929938951l_bool(hAPP_f497008323l_bool(hAPP_f1936466825l_bool(cOMBB_840638159al_val,P),Q),R) = hAPP_P159683425l_bool(P,hAPP_P147338735on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_850,axiom,
    ! [P: fun_Pr1696029455l_bool,Q: fun_ex929394691on_val,R: exp_list_char] : hAPP_e544220455r_bool(hAPP_f716957699r_bool(hAPP_f106757449r_bool(cOMBB_1539035119t_char,P),Q),R) = hAPP_P159683425l_bool(P,hAPP_e1410803407on_val(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_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_851,axiom,
    ! [P: fun_Pr1696029455l_bool,Q: fun_fu1690035458on_val,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f1008932791l_bool(hAPP_f2057883639l_bool(cOMBB_1750801836on_val,P),Q),R) = hAPP_P159683425l_bool(P,hAPP_f1727192346on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_852,axiom,
    ! [P: fun_Pr1696029455l_bool,Q: fun_Pr1632109509on_val,R: produc662261637t_char] : hAPP_P2118621157r_bool(hAPP_f1915623807r_bool(hAPP_f1346522053r_bool(cOMBB_1115744685t_char,P),Q),R) = hAPP_P159683425l_bool(P,hAPP_P214139537on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc,axiom,
    ! [P: fun_Pr1669461698r_bool,Q: fun_fu1855747253t_char,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f1474698986l_bool(hAPP_f1809473245l_bool(cOMBB_1452070457on_val,P),Q),R) = hAPP_P828904212r_bool(P,hAPP_f268764237t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M,axiom,
    ! [P: fun_fu1590192889l_bool,Q: fun_fu100249073l_bool,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f555424277l_bool(hAPP_f1734879897l_bool(cOMBB_1522540928on_val,P),Q),R) = hAPP_f1074020887l_bool(P,hAPP_f1175813647l_bool(Q,R)) ).

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__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mt,axiom,
    ! [P: fun_fu436897911l_bool,Q: fun_bo180791194on_val,R: bop] : hAPP_b97269396l_bool(hAPP_f1150574413l_bool(hAPP_f295212021l_bool(cOMBB_1150072860ol_bop,P),Q),R) = hAPP_f497008323l_bool(P,hAPP_b420404024on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_853,axiom,
    ! [P: fun_fu680686147l_bool,Q: fun_fu2114777659al_val,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f1153851723l_bool(hAPP_f151189509l_bool(cOMBB_223841226on_val,P),Q),R) = hAPP_f1935223905l_bool(P,hAPP_f1695781849al_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_854,axiom,
    ! [P: fun_Pr1696029455l_bool,Q: fun_Pr1289494032on_val,R: produc220283002t_char] : hAPP_P1907982426r_bool(hAPP_f1957179113r_bool(hAPP_f1096084527r_bool(cOMBB_1980206754t_char,P),Q),R) = hAPP_P159683425l_bool(P,hAPP_P216502748on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O,axiom,
    ! [P: fun_Pr680585871l_bool,Q: fun_fu277794946on_val,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f318082871l_bool(hAPP_f1233687287l_bool(cOMBB_171276332on_val,P),Q),R) = hAPP_P1708370145l_bool(P,hAPP_f1926378906on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_855,axiom,
    ! [P: fun_Pr1898949769r_bool,Q: fun_fu1872782460t_char,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f679593521l_bool(hAPP_f2114578667l_bool(cOMBB_914590898on_val,P),Q),R) = hAPP_P659547099r_bool(P,hAPP_f596349460t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_856,axiom,
    ! [P: fun_fu893105924l_bool,Q: fun_fu63623632har_ty,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f1617838686l_bool(hAPP_f1740025881l_bool(cOMBB_1511810527on_val,P),Q),R) = hAPP_f1189972950l_bool(P,hAPP_f993605148har_ty(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__Expr__Oexp_Itc__List__Olist_Itc__String__Oc,axiom,
    ! [P: fun_fu2039807031r_bool,Q: fun_li2113382231on_val,R: list_val] : hAPP_l1062423959r_bool(hAPP_f1339377933r_bool(hAPP_f1165187701r_bool(cOMBB_1124198201st_val,P),Q),R) = hAPP_f716957699r_bool(P,hAPP_l1870161525on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_857,axiom,
    ! [P: fun_fu79989156l_bool,Q: fun_fu1978109084al_val,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f828778154l_bool(hAPP_f1572306499l_bool(cOMBB_1210977579on_val,P),Q),R) = hAPP_f2061154754l_bool(P,hAPP_f1779904442al_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli,axiom,
    ! [P: fun_Pr248118298l_bool,Q: fun_fu432179525on_val,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f502623122l_bool(hAPP_f1000925999l_bool(cOMBB_1466435125on_val,P),Q),R) = hAPP_P71593144l_bool(P,hAPP_f637291415on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_858,axiom,
    ! [P: fun_fu1255792747l_bool,Q: fun_fu1104134499t_char,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f1996106275l_bool(hAPP_f1550515381l_bool(cOMBB_2040779506on_val,P),Q),R) = hAPP_f1326058377l_bool(P,hAPP_f1628326017t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_859,axiom,
    ! [P: fun_fu1741592865l_bool,Q: fun_fu1679523865t_char,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f1576637933l_bool(hAPP_f154583625l_bool(cOMBB_335252392on_val,P),Q),R) = hAPP_f1468279871l_bool(P,hAPP_f1297079863t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String_,axiom,
    ! [P: fun_fu564156607ion_ty,Q: fun_li1436431093on_val,R: list_char] : hAPP_l2000496933ion_ty(hAPP_f802560783ion_ty(hAPP_f7643013ion_ty(cOMBB_864319000t_char,P),Q),R) = hAPP_f2110071953ion_ty(P,hAPP_l1786340417on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_860,axiom,
    ! [P: fun_Pr1861226704r_bool,Q: fun_fu240779971t_char,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f802970616l_bool(hAPP_f1566130425l_bool(cOMBB_247395499on_val,P),Q),R) = hAPP_P1680401186r_bool(P,hAPP_f1032572507t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_861,axiom,
    ! [P: fun_fu1910987134l_bool,Q: fun_fu474293322ar_val,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f1812276580l_bool(hAPP_f1292837529l_bool(cOMBB_238112345on_val,P),Q),R) = hAPP_f1787894864l_bool(P,hAPP_f1925626518ar_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_862,axiom,
    ! [P: fun_fu1343863587l_bool,Q: fun_fu612303599t_char,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f1351102847l_bool(hAPP_f1342439769l_bool(cOMBB_225914878on_val,P),Q),R) = hAPP_f1390791157l_bool(P,hAPP_f1445211579t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_863,axiom,
    ! [P: fun_fu1169582102l_bool,Q: fun_fu313651982t_char,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f1121261496l_bool(hAPP_f1331093087l_bool(cOMBB_1472123293on_val,P),Q),R) = hAPP_f1645102644l_bool(P,hAPP_f157410348t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mt,axiom,
    ! [P: fun_fu306838195r_bool,Q: fun_li434706128on_val,R: list_ty] : hAPP_l1987619678r_bool(hAPP_f1944156365r_bool(hAPP_f918235057r_bool(cOMBB_1843549548ist_ty,P),Q),R) = hAPP_f1915623807r_bool(P,hAPP_l1004879342on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_864,axiom,
    ! [P: fun_fu1358756598l_bool,Q: fun_fu540338626on_val,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f1145600492l_bool(hAPP_f630712985l_bool(cOMBB_1962662865on_val,P),Q),R) = hAPP_f1937467848l_bool(P,hAPP_f1614126606on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_865,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)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_866,axiom,
    ! [P: fun_fu320829654l_bool,Q: fun_fu798026914t_char,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f1089411340l_bool(hAPP_f2012169497l_bool(cOMBB_1443356337on_val,P),Q),R) = hAPP_f1212990632l_bool(P,hAPP_f78832750t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_867,axiom,
    ! [P: fun_Pr1696029455l_bool,Q: fun_Pr1833267965on_val,R: produc12694297on_val] : hAPP_P159683425l_bool(hAPP_f1301559543l_bool(hAPP_f1825030711l_bool(cOMBB_877741809on_val,P),Q),R) = hAPP_P159683425l_bool(P,hAPP_P1776198677on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc_,axiom,
    ! [P: fun_fu309852445r_bool,Q: fun_li175451530on_val,R: list_list_char] : hAPP_l217977712r_bool(hAPP_f829041291r_bool(hAPP_f1691034591r_bool(cOMBB_889837233t_char,P),Q),R) = hAPP_f1957179113r_bool(P,hAPP_l451552092on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_868,axiom,
    ! [P: fun_Pr1696029455l_bool,Q: fun_Pr2087158653on_val,R: produc124828825on_val] : hAPP_P1708370145l_bool(hAPP_f1712766199l_bool(hAPP_f881985847l_bool(cOMBB_1083177073on_val,P),Q),R) = hAPP_P159683425l_bool(P,hAPP_P789556885on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_869,axiom,
    ! [P: fun_Pr1696029455l_bool,Q: fun_Pr1142159922on_val,R: produc2061676504on_val] : hAPP_P71593144l_bool(hAPP_f1540354981l_bool(hAPP_f2131288811l_bool(cOMBB_1173566976on_val,P),Q),R) = hAPP_P159683425l_bool(P,hAPP_P1892658174on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_870,axiom,
    ! [P: fun_fu1176066021l_bool,Q: fun_fu1639641777on_val,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f1363667773l_bool(hAPP_f1050935001l_bool(cOMBB_1153617344on_val,P),Q),R) = hAPP_f1008932791l_bool(P,hAPP_f1849790461on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_871,axiom,
    ! [P: fun_fu1038842648l_bool,Q: fun_fu511951076t_char,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f337607754l_bool(hAPP_f1546157465l_bool(cOMBB_955482355on_val,P),Q),R) = hAPP_f1474698986l_bool(P,hAPP_f371326384t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_872,axiom,
    ! [P: fun_fu1640122725l_bool,Q: fun_fu2073188913on_val,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f850751421l_bool(hAPP_f399538905l_bool(cOMBB_1466889536on_val,P),Q),R) = hAPP_f318082871l_bool(P,hAPP_f1840640125on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_873,axiom,
    ! [P: fun_fu173213535l_bool,Q: fun_fu868535083t_char,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f1525647939l_bool(hAPP_f1338219097l_bool(cOMBB_2122619962on_val,P),Q),R) = hAPP_f679593521l_bool(P,hAPP_f1363205111t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_874,axiom,
    ! [P: fun_fu578833268l_bool,Q: fun_fu1035619948on_val,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f556306650l_bool(hAPP_f1538372259l_bool(cOMBB_157777659on_val,P),Q),R) = hAPP_f502623122l_bool(P,hAPP_f336970122on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_875,axiom,
    ! [P: fun_fu1268449830l_bool,Q: fun_fu1941783538t_char,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f1158121916l_bool(hAPP_f527861785l_bool(cOMBB_625124865on_val,P),Q),R) = hAPP_f802970616l_bool(P,hAPP_f1486366910t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_,axiom,
    ! [P: fun_Pr691271849l_bool,Q: fun_fu1622757844on_val,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f524589473l_bool(hAPP_f2052660463l_bool(cOMBB_1292453606on_val,P),Q),R) = hAPP_P282169671l_bool(P,hAPP_f602593190on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc_,axiom,
    ! [P: fun_Pr859510977l_bool,Q: fun_fu1921615852on_val,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f1546656185l_bool(hAPP_f28987375l_bool(cOMBB_132741582on_val,P),Q),R) = hAPP_P1333315679l_bool(P,hAPP_f1416324670on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O,axiom,
    ! [P: fun_fu225006629l_bool,Q: fun_ex1005552999on_val,R: exp_list_char] : hAPP_e1833980889l_bool(hAPP_f653692369l_bool(hAPP_f516738477l_bool(cOMBB_819439237t_char,P),Q),R) = hAPP_f1301559543l_bool(P,hAPP_e108155315on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_876,axiom,
    ! [P: fun_fu225006629l_bool,Q: fun_li414426834on_val,R: list_exp_list_char] : hAPP_l146377954l_bool(hAPP_f896993613l_bool(hAPP_f219814819l_bool(cOMBB_143000234t_char,P),Q),R) = hAPP_f1301559543l_bool(P,hAPP_l1012006762on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_877,axiom,
    ! [P: fun_fu964448643l_bool,Q: fun_fu1133203323on_val,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f927043595l_bool(hAPP_f1043869573l_bool(cOMBB_1259202826on_val,P),Q),R) = hAPP_f524589473l_bool(P,hAPP_f600512025on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_878,axiom,
    ! [P: fun_fu1610988187l_bool,Q: fun_fu239230867on_val,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f1505175539l_bool(hAPP_f924423253l_bool(cOMBB_1330725154on_val,P),Q),R) = hAPP_f1546656185l_bool(P,hAPP_f865889457on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__,axiom,
    ! [P: fun_fu2085256997l_bool,Q: fun_Pr1719283041on_val,R: produc124828825on_val] : hAPP_P1116729363l_bool(hAPP_f1241216909l_bool(hAPP_f1438732387l_bool(cOMBB_635947099on_val,P),Q),R) = hAPP_f1712766199l_bool(P,hAPP_P2083594489on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__,axiom,
    ! [P: fun_fu976626649l_bool,Q: fun_Pr390299247on_val,R: produc2061676504on_val] : hAPP_P1183008383l_bool(hAPP_f1909521165l_bool(hAPP_f1779944471l_bool(cOMBB_607314500on_val,P),Q),R) = hAPP_f1540354981l_bool(P,hAPP_P308812685on_val(Q,R)) ).

%----Conjectures (1)
tff(conj_0,conjecture,
    hBOOL(hAPP_ty_bool(wTrt(p,h_a,e,e_a),nt)) ).

%------------------------------------------------------------------------------