%------------------------------------------------------------------------------
% File     : SWW478_30 : TPTP v8.2.0. Released v8.2.0.
% Domain   : Software Verification
% Problem  : Java type soundness line 479, 1000 axioms selected
% Version  : SWW478_3 with the conjecture removed
% English  :

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

% Status   : Satisfiable
% Rating   : 1.00 v8.2.0
% Syntax   : Number of formulae    : 3144 ( 395 unt;1795 typ;   0 def)
%            Number of atoms       : 3162 (1063 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives : 2360 ( 547   ~;  41   |;  91   &)
%                                         ( 266 <=>;1415  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   31 (   7 avg)
%            Maximal term depth    :   13 (   2 avg)
%            Number of types       :  690 ( 689 usr)
%            Number of type conns  : 1571 ( 823   >; 748   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    : 1105 (1105 usr; 283 con; 0-6 aty)
%            Number of variables   : 5869 (5799   !;  70   ?;5869   :)
% SPC      : TF0_SAT_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2011-08-09 18:02:07
%------------------------------------------------------------------------------
%----Should-be-implicit typings (689)
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tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_403,type,
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tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_404,type,
    fun_Pr84821017on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_405,type,
    fun_Pr442654869l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_406,type,
    fun_Pr519703875l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J,type,
    fun_Pr369549609l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_407,type,
    fun_Pr1110793451l_bool: $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__Obop_Mtc__prod_Itc__Value__Oval_Mtc_408,type,
    fun_Pr358512219l_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___409,type,
    fun_Pr1041696489l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String___410,type,
    fun_Pr243362283l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String___411,type,
    fun_Pr449337907on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String___412,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_413,type,
    fun_Pr2072119505l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol_414,type,
    fun_Pr1441107355l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol_415,type,
    fun_Pr998206307on_val: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol_416,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__417,type,
    fun_Pr253198059l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__418,type,
    fun_Pr1895638121r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__419,type,
    fun_Pr2058021739l_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_420,type,
    fun_Pr1336847023r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_421,type,
    fun_Pr180031351l_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__fun_422,type,
    fun_Pr700359275l_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_423,type,
    fun_Pr81279339l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__pro_424,type,
    fun_Pr1538825897r_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__pro_425,type,
    fun_Pr740107499l_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__Type__Oty_J_Mtc__prod_It_426,type,
    fun_Pr949587491l_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__Value__Oval_J_Mtc__Expr__427,type,
    fun_Pr54558799l_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__List__Olist_Itc__prod_Itc__List__Olist_It_428,type,
    fun_Pr1377562219l_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__Value__Oval_Mtc__Value__Oval_J_Mtc__prod__429,type,
    fun_Pr2114942679l_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__fun_Itc__Nat__Onat_Mtc__Option__Ooption_I_430,type,
    fun_Pr736615915l_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__Expr__Oexp_Itc__List__Olist_Itc_431,type,
    fun_Pr1043842007l_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__Expr__Oexp_Itc_432,type,
    fun_Pr1519167543l_bool: $tType ).

tff(ty_ty_tc__prod_Itc__Expr__Obop_Mtc__Expr__Obop_J,type,
    product_prod_bop_bop: $tType ).

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

tff(ty_ty_tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__Expr,type,
    produc2048519645t_char: $tType ).

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

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc,type,
    produc91527719t_char: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_433,type,
    produc2061676504on_val: $tType ).

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

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__Lis,type,
    produc1200003175t_char: $tType ).

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

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

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Type__Oty_J,type,
    produc917948472har_ty: $tType ).

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

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__Olist_,type,
    produc1971331930t_char: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__Olist__434,type,
    produc1013743697t_char: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__Olist__435,type,
    produc952412819t_char: $tType ).

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

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

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__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__Value__Oval_J_Mtc__List__Olist_Itc__Value__,type,
    produc753553453st_val: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_,type,
    produc450000425har_ty: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J__436,type,
    produc2146869324t_char: $tType ).

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J__437,type,
    produc244676007t_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__List__Olist_Itc__String__Ochar_J_Mtc__Option__Oopti,type,
    produc1127210791on_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__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__438,type,
    produc644889299on_val: $tType ).

tff(ty_ty_tc__prod_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis,type,
    produc2104958055on_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__439,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__440,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_441,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 ).

%----Explicit typings (1106)
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__List__Olist_Itc__String__O,type,
    cOMBB_1091123364t_char: fun_fu2039604123r_bool ).

tff(sy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat,type,
    cOMBB_bool_bool_nat: fun_fu1509210819t_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_984708934t_char: fun_fu1811849795l_bool ).

tff(sy_c_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__442,type,
    cOMBB_1015721476ol_nat: fun_fu1849968923l_bool ).

tff(sy_c_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__443,type,
    cOMBB_1303934920on_val: fun_fu781882819l_bool ).

tff(sy_c_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__444,type,
    cOMBB_1643767893t_char: fun_fu1562611971l_bool ).

tff(sy_c_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__445,type,
    cOMBB_808210516t_char: fun_fu585405563l_bool ).

tff(sy_c_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__446,type,
    cOMBB_565990871t_char: fun_fu1347399555l_bool ).

tff(sy_c_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__447,type,
    cOMBB_705522285on_val: fun_fu14434691l_bool ).

tff(sy_c_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__448,type,
    cOMBB_1617503877on_val: fun_fu1266804483l_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__Option__Ooption_Itc__Value__Oval_J_000tc__fun_Itc__Option__Oop,type,
    cOMBB_1112666310t_char: fun_fu268320615l_bool ).

tff(sy_c_COMBB_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String__Ochar_,type,
    cOMBB_731867268ol_nat: fun_fu701816347l_bool ).

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__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt,type,
    cOMBB_2143526097t_char: fun_fu2114536561r_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_449,type,
    cOMBB_308691073st_val: fun_fu1287147451r_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_450,type,
    cOMBB_33167485t_char: fun_fu594565489l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_451,type,
    cOMBB_2078271971st_val: fun_fu168630475l_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__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__fun_It,type,
    cOMBB_1551681790t_char: fun_fu445571679r_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List_,type,
    cOMBB_526805108t_char: fun_fu130047471l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__O,type,
    cOMBB_657296617har_ty: fun_fu232818571r_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__O_452,type,
    cOMBB_859890145har_ty: fun_fu1260000795l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__Value__Oval_Mtc__fun_Itc__fun_Itc__prod_Itc__Value__O,type,
    cOMBB_1701031980ol_val: fun_fu308030371l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__Value__Oval_Mtc__prod_Itc__Value__Oval_Mtc__Value__Ov,type,
    cOMBB_815843940ol_val: fun_fu22126627l_bool ).

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_453,type,
    cOMBB_1518282696on_val: fun_fu938561337l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_454,type,
    cOMBB_2084052674on_val: fun_fu802010103l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_455,type,
    cOMBB_1153617344on_val: fun_fu698854459l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_456,type,
    cOMBB_588525814on_val: fun_fu724130311l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M,type,
    cOMBB_1200577438t_char: fun_fu54393727l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_457,type,
    cOMBB_864319000t_char: fun_fu182032103ion_ty ).

tff(sy_c_COMBB_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_458,type,
    cOMBB_109816436t_char: fun_fu1941383183l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc,type,
    cOMBB_1223415373on_val: fun_fu44119137l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_459,type,
    cOMBB_1977588741on_val: fun_fu280119905l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis,type,
    cOMBB_779086262on_val: fun_fu1451279551l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis_460,type,
    cOMBB_555068556on_val: fun_fu1063302223l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_,type,
    cOMBB_672864638t_char: fun_fu1167317887r_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod__461,type,
    cOMBB_741416308t_char: fun_fu1922972687l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc_,type,
    cOMBB_550632017t_char: fun_fu596555377r_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__462,type,
    cOMBB_2042763133t_char: fun_fu2060731249l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__463,type,
    cOMBB_1490692730t_char: fun_fu221466727r_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__464,type,
    cOMBB_1705938036t_char: fun_fu1930358519l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__O,type,
    cOMBB_338473166ist_ty: fun_fu1113701619r_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__O_465,type,
    cOMBB_68065882ist_ty: fun_fu579122691l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc_,type,
    cOMBB_847828016t_char: fun_fu2003654783r_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__466,type,
    cOMBB_1558246132t_char: fun_fu1080828303l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__fun_Itc,type,
    cOMBB_761748254ol_bop: fun_fu1818728571l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__prod_It,type,
    cOMBB_1458388806ol_bop: fun_fu1941566603l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc,type,
    cOMBB_673739729t_char: fun_fu168240291l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc_467,type,
    cOMBB_773375802t_char: fun_fu276262911l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc_468,type,
    cOMBB_507006011t_char: fun_fu56207283l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc_469,type,
    cOMBB_1270208498t_char: fun_fu312143231l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__Ov,type,
    cOMBB_2139740953al_val: fun_fu2027889989l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_M,type,
    cOMBB_985659173on_val: fun_fu1053658365l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__St,type,
    cOMBB_1078680455on_val: fun_fu353693025l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_,type,
    cOMBB_1033145403t_char: fun_fu932873447l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J__470,type,
    cOMBB_123628846t_char: fun_fu1773666471l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_It,type,
    cOMBB_1586673472t_char: fun_fu363313207l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_,type,
    cOMBB_2041093409on_val: fun_fu549698637ion_ty ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod__471,type,
    cOMBB_1153773871on_val: fun_fu124510717l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List,type,
    cOMBB_1520154591t_char: fun_fu1225586941l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List_472,type,
    cOMBB_1681501894t_char: fun_fu176695091l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List_473,type,
    cOMBB_773661144t_char: fun_fu136853693l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Ol,type,
    cOMBB_147773915t_char: fun_fu7682913l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__,type,
    cOMBB_961360819t_char: fun_fu1687349387l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__,type,
    cOMBB_1035649854t_char: fun_fu851447613l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_Itc__fun_I,type,
    cOMBB_2078984970ol_val: fun_fu1127606179l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It,type,
    cOMBB_1750801836on_val: fun_fu121169625l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_474,type,
    cOMBB_1293776864on_val: fun_fu2070930493l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O,type,
    cOMBB_565412073on_val: fun_fu2017766753l_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli,type,
    cOMBB_1034324152on_val: fun_fu917063127l_bool ).

tff(sy_c_COMBC_000tc__Expr__Obop_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc_,type,
    cOMBC_199425070l_bool: fun_fu1124575819l_bool ).

tff(sy_c_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_,type,
    cOMBC_562612496l_bool: fun_fu1848909487l_bool ).

tff(sy_c_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun__475,type,
    cOMBC_220519196l_bool: fun_fu1223433803r_bool ).

tff(sy_c_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun__476,type,
    cOMBC_818212448l_bool: fun_fu1888091987r_bool ).

tff(sy_c_COMBC_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ocha,type,
    cOMBC_622308798l_bool: fun_fu1999472363l_bool ).

tff(sy_c_COMBC_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun,type,
    cOMBC_790582442r_bool: fun_fu232735701r_bool ).

tff(sy_c_COMBC_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_477,type,
    cOMBC_1718404842r_bool: fun_fu1374106197r_bool ).

tff(sy_c_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooption_Itc__V,type,
    cOMBC_442485623l_bool: fun_fu1734620171r_bool ).

tff(sy_c_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__List__Olist_I,type,
    cOMBC_892477410l_bool: fun_fu683689373r_bool ).

tff(sy_c_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__Lis,type,
    cOMBC_1603044337l_bool: fun_fu1125427583r_bool ).

tff(sy_c_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__Lis_478,type,
    cOMBC_389248878r_bool: fun_fu1361373153r_bool ).

tff(sy_c_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__Lis_479,type,
    cOMBC_1535683812l_bool: fun_fu695096899l_bool ).

tff(sy_c_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__Lis_480,type,
    cOMBC_1784597444r_bool: fun_fu1188864163r_bool ).

tff(sy_c_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__Lis_481,type,
    cOMBC_654453230r_bool: fun_fu1931408741r_bool ).

tff(sy_c_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__Lis_482,type,
    cOMBC_1025440566r_bool: fun_fu1706763477r_bool ).

tff(sy_c_COMBC_000tc__List__Olist_Itc__Type__Oty_J_000tc__fun_Itc__prod_Itc__List__O,type,
    cOMBC_1127703214r_bool: fun_fu377199967r_bool ).

tff(sy_c_COMBC_000tc__List__Olist_Itc__Value__Oval_J_000tc__fun_Itc__prod_Itc__List_,type,
    cOMBC_1387630958r_bool: fun_fu1402349329r_bool ).

tff(sy_c_COMBC_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mt,type,
    cOMBC_886773442r_bool: fun_fu1721346721r_bool ).

tff(sy_c_COMBC_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mt_483,type,
    cOMBC_1407716098l_bool: fun_fu989111613r_bool ).

tff(sy_c_COMBC_000tc__Nat__Onat_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_It,type,
    cOMBC_229530231l_bool: fun_fu1620074797t_bool ).

tff(sy_c_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__H,type,
    cOMBC_226598744l_bool: fun_fu80187629t_bool ).

tff(sy_c_COMBC_000tc__Value__Oval_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__,type,
    cOMBC_331963401l_bool: fun_fu600031817l_bool ).

tff(sy_c_COMBC_000tc__Value__Oval_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value___484,type,
    cOMBC_1979963740l_bool: fun_fu1280349935l_bool ).

tff(sy_c_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption,type,
    cOMBC_832625297y_bool: fun_fu2083094209l_bool ).

tff(sy_c_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_485,type,
    cOMBC_1518234801l_bool: fun_fu735196737l_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__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__O_486,type,
    cOMBC_1317565126l_bool: fun_fu1686228965l_bool ).

tff(sy_c_COMBC_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List_,type,
    cOMBC_317789649l_bool: fun_fu49805983l_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_M,type,
    cOMBC_1608987946l_bool: fun_fu1666573063l_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_M_487,type,
    cOMBC_967917532l_bool: fun_fu1161062123l_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__St,type,
    cOMBC_1491642377l_bool: fun_fu1668998687l_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__St_488,type,
    cOMBC_766524526l_bool: fun_fu1389374689l_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_It,type,
    cOMBC_148995234l_bool: fun_fu1782878143r_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List,type,
    cOMBC_1297648632l_bool: fun_fu1097435533r_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List_489,type,
    cOMBC_36589090l_bool: fun_fu903908411r_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List_490,type,
    cOMBC_1338332465l_bool: fun_fu1928247679r_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Ol,type,
    cOMBC_407285762l_bool: fun_fu839442891r_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__Type__Ot,type,
    cOMBC_390659185l_bool: fun_fu1497625339r_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__,type,
    cOMBC_1365742487l_bool: fun_fu1034987497r_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__,type,
    cOMBC_516637475l_bool: fun_fu935579185r_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_Itc__prod_,type,
    cOMBC_813705475l_bool: fun_fu1248515149l_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It,type,
    cOMBC_1585774710l_bool: fun_fu1525621451l_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_491,type,
    cOMBC_2141828763l_bool: fun_fu76765545l_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O,type,
    cOMBC_1021753250l_bool: fun_fu105086607l_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli,type,
    cOMBC_475083938l_bool: fun_fu916360031l_bool ).

tff(sy_c_COMBK_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist_Itc__Strin,type,
    cOMBK_1294242658t_char: fun_op1371746710ion_ty ).

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__Value__Oval_J_000tc__prod_Itc__List__Olis,type,
    cOMBK_1867744698t_char: fun_op227821541on_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__List__Olist_Itc__String__Ochar_J_000tc__HOL__Obool_000tc__HOL_,type,
    cOMBS_1502238389l_bool: ( fun_li332530512l_bool * fun_list_char_bool ) > fun_list_char_bool ).

tff(sy_c_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool,type,
    cOMBS_nat_bool_bool: ( fun_na1469252690l_bool * fun_nat_bool ) > fun_nat_bool ).

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_COMBS_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_It,type,
    cOMBS_350755140l_bool: ( fun_Pr1475963649l_bool * fun_Pr565113489r_bool ) > fun_Pr565113489r_bool ).

tff(sy_c_COMBS_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List,type,
    cOMBS_635570165l_bool: ( fun_Pr1882154498l_bool * fun_Pr1861226704r_bool ) > fun_Pr1861226704r_bool ).

tff(sy_c_COMBS_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List_492,type,
    cOMBS_1743887558l_bool: ( fun_Pr1361196031l_bool * fun_Pr70170387r_bool ) > fun_Pr70170387r_bool ).

tff(sy_c_COMBS_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O,type,
    cOMBS_1319864284l_bool: ( fun_Pr1041696489l_bool * fun_Pr691271849l_bool ) > fun_Pr691271849l_bool ).

tff(sy_c_COMBS_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli,type,
    cOMBS_1218320756l_bool: ( fun_Pr2072119505l_bool * fun_Pr859510977l_bool ) > fun_Pr859510977l_bool ).

tff(sy_c_Conform_Oconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Oc,type,
    conf_P373316194t_char: ( list_P1999446415t_char * fun_na939144002on_val * val * ty ) > bool ).

tff(sy_c_Conform_Ohconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
    hconf_97414254t_char: list_P1999446415t_char > fun_fu1246919812l_bool ).

tff(sy_c_Conform_Olconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
    lconf_496643946t_char: list_P1999446415t_char > fun_fu2141444501y_bool ).

tff(sy_c_Conform_Ooconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
    oconf_1869808039t_char: ( list_P1999446415t_char * fun_na939144002on_val ) > fun_Pr315804320l_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_DefAss_O_092_060D_062_000tc__List__Olist_Itc__String__Ochar_J,type,
    d_list_char: ( exp_list_char * option466449911r_bool ) > 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_Expr_Ofvs,type,
    fvs: list_exp_list_char > fun_list_char_bool ).

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_493,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_Lattices_Osemilattice__sup__class_Osup_000tc__fun_Itc__List__Olist_Itc__Str,type,
    semila919158006r_bool: ( fun_list_char_bool * fun_list_char_bool ) > fun_list_char_bool ).

tff(sy_c_Lattices_Osemilattice__sup__class_Osup_000tc__fun_Itc__Nat__Onat_Mtc__HOL__,type,
    semila465093516t_bool: ( fun_nat_bool * fun_nat_bool ) > fun_nat_bool ).

tff(sy_c_Lattices_Osemilattice__sup__class_Osup_000tc__fun_Itc__prod_Itc__List__Olis,type,
    semila1168318597r_bool: ( fun_Pr565113489r_bool * fun_Pr565113489r_bool ) > fun_Pr565113489r_bool ).

tff(sy_c_Lattices_Osemilattice__sup__class_Osup_000tc__fun_Itc__prod_Itc__List__Olis_494,type,
    semila1346223580r_bool: ( fun_Pr1861226704r_bool * fun_Pr1861226704r_bool ) > fun_Pr1861226704r_bool ).

tff(sy_c_Lattices_Osemilattice__sup__class_Osup_000tc__fun_Itc__prod_Itc__List__Olis_495,type,
    semila1731249415r_bool: ( fun_Pr70170387r_bool * fun_Pr70170387r_bool ) > fun_Pr70170387r_bool ).

tff(sy_c_Lattices_Osemilattice__sup__class_Osup_000tc__fun_Itc__prod_Itc__prod_Itc__,type,
    semila751111325l_bool: ( fun_Pr691271849l_bool * fun_Pr691271849l_bool ) > fun_Pr691271849l_bool ).

tff(sy_c_Lattices_Osemilattice__sup__class_Osup_000tc__fun_Itc__prod_Itc__prod_Itc___496,type,
    semila449273525l_bool: ( fun_Pr859510977l_bool * fun_Pr859510977l_bool ) > fun_Pr859510977l_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 * list_list_char ) > list_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 * list_ty ) > list_option_ty ).

tff(sy_c_List_Omap_000tc__Value__Oval_000tc__Expr__Oexp_Itc__List__Olist_Itc__String,type,
    map_va1934808527t_char: ( fun_va223928858t_char * list_val ) > list_exp_list_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 * list_val ) > list_option_ty ).

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___497,type,
    set_Pr2033386304t_char: list_P341299826t_char > fun_Pr70170387r_bool ).

tff(sy_c_Map_Odom_000tc__List__Olist_Itc__String__Ochar_J_000tc__Type__Oty,type,
    dom_list_char_ty: fun_li688206603ion_ty > fun_list_char_bool ).

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

tff(sy_c_Map_Odom_000tc__Nat__Onat_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J,type,
    dom_na996029170on_val: fun_na939144002on_val > fun_nat_bool ).

tff(sy_c_Map_Odom_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist,type,
    dom_Pr695701035ar_val: fun_Pr806764899on_val > fun_Pr565113489r_bool ).

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

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

tff(sy_c_Map_Omap__add_000tc__Nat__Onat_000tc__prod_Itc__List__Olist_Itc__String__Oc,type,
    map_ad61982421on_val: ( fun_na939144002on_val * fun_na939144002on_val ) > fun_na939144002on_val ).

tff(sy_c_Map_Omap__add_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__,type,
    map_ad1185064968ar_val: ( fun_Pr806764899on_val * fun_Pr806764899on_val ) > fun_Pr806764899on_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: list_P2023964830har_ty > fun_Pr806764899on_val ).

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

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__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__,type,
    none_f478147469r_bool: option466449911r_bool ).

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__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__,type,
    some_f80346385r_bool: fun_fu450339090r_bool ).

tff(sy_c_Option_Ooption_OSome_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_,type,
    some_P948696889on_val: fun_Pr357631842on_val ).

tff(sy_c_Option_Ooption_Ooption__case_000tc__Option__Ooption_Itc__Type__Oty_J_000tc_,type,
    option1388193227on_val: ( option_ty * fun_Pr876827561ion_ty * option1479284511on_val ) > option_ty ).

tff(sy_c_Option_Othe_000tc__Nat__Onat,type,
    the_nat: fun_option_nat_nat ).

tff(sy_c_Option_Othe_000tc__Type__Oty,type,
    the_ty: fun_option_ty_ty ).

tff(sy_c_Option_Othe_000tc__Value__Oval,type,
    the_val: fun_option_val_val ).

tff(sy_c_Option_Othe_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__HOL__Oboo,type,
    the_fu297177755r_bool: fun_op1531141308r_bool ).

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__HOL__Obool,type,
    ord_less_eq_bool: bool > fun_bool_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__Expr__Obop_Mtc__fun_Itc__pr,type,
    ord_le1725884030l_bool: fun_bo1454185032l_bool > fun_fu570042250l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist,type,
    ord_le1080391173l_bool: fun_ex1201926843l_bool > fun_fu1520189105l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__List__Olist_Itc__Expr__Oexp,type,
    ord_le285175110l_bool: fun_li1372729616l_bool > fun_fu1939745362l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__List__Olist_Itc__List__Olis,type,
    ord_le176694639r_bool: fun_li221477r_bool > fun_fu317217051l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__List__Olist_Itc__List__Olis_498,type,
    ord_le817953186r_bool: fun_li1024794712r_bool > fun_fu1924808654l_bool ).

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_fu1364670840l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__List__Olist_Itc__String__Oc_499,type,
    ord_le1871967977r_bool: fun_li860735411r_bool > fun_fu1166999157l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__List__Olist_Itc__String__Oc_500,type,
    ord_le188521288l_bool: fun_li823162622l_bool > fun_fu1983549044l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__List__Olist_Itc__String__Oc_501,type,
    ord_le735260024r_bool: fun_li522008110r_bool > fun_fu1021591716l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__List__Olist_Itc__String__Oc_502,type,
    ord_le2008677227r_bool: fun_li1960983605r_bool > fun_fu1409702391l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__List__Olist_Itc__String__Oc_503,type,
    ord_le1151384881r_bool: fun_li485148903r_bool > fun_fu2048960477l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__List__Olist_Itc__Type__Oty_,type,
    ord_le1449176264r_bool: fun_li887890578r_bool > fun_fu1099362516l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__List__Olist_Itc__Value__Ova,type,
    ord_le989574145r_bool: fun_li826105035r_bool > fun_fu1965526925l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__List__Olist_Itc__prod_Itc__,type,
    ord_le458107652r_bool: fun_li1305328058r_bool > fun_fu142481456l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J,type,
    ord_le1568362934t_bool: fun_nat_bool > fun_fu425979586l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__Value__Oval_Mtc__fun_Itc__V,type,
    ord_le408082617l_bool: fun_val_fun_val_bool > fun_fu533549125l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Opt,type,
    ord_le125655867l_bool: fun_fu100249073l_bool > fun_fu299475175l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc__p,type,
    ord_le1467847572l_bool: fun_Pr252072522l_bool > fun_fu1654159552l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__L,type,
    ord_le1668954565l_bool: fun_Pr680585871l_bool > fun_fu1845830481l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__L_504,type,
    ord_le1050317687l_bool: fun_Pr633696065l_bool > fun_fu2042905603l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__List__Olist_Itc__,type,
    ord_le1461833060l_bool: fun_Pr248118298l_bool > fun_fu749996688l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__List__Olist_Itc___505,type,
    ord_le1270183657l_bool: fun_Pr597144499l_bool > fun_fu1375444597l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__List__Olist_Itc___506,type,
    ord_le715555971r_bool: fun_Pr1336948301r_bool > fun_fu1983565583l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__List__Olist_Itc___507,type,
    ord_le1579844278r_bool: fun_Pr227936640r_bool > fun_fu1984450498l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__List__Olist_Itc___508,type,
    ord_le640323803r_bool: fun_Pr565113489r_bool > fun_fu2033725063l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__List__Olist_Itc___509,type,
    ord_le1744419030l_bool: fun_Pr315804320l_bool > fun_fu962543074l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__List__Olist_Itc___510,type,
    ord_le117566470r_bool: fun_Pr1861226704r_bool > fun_fu754983186l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__List__Olist_Itc___511,type,
    ord_le1987888477r_bool: fun_Pr70170387r_bool > fun_fu1338423817l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__List__Olist_Itc___512,type,
    ord_le725666495r_bool: fun_Pr1898949769r_bool > fun_fu1008682827l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__List__Olist_Itc___513,type,
    ord_le1218729222r_bool: fun_Pr46158268r_bool > fun_fu184232242l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__List__Olist_Itc___514,type,
    ord_le1852058257r_bool: fun_Pr827765831r_bool > fun_fu1054881085l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__List__Olist_Itc___515,type,
    ord_le1734858744r_bool: fun_Pr1669461698r_bool > fun_fu1272536068l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__,type,
    ord_le310098611l_bool: fun_Pr2081272681l_bool > fun_fu1210184799l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Ona,type,
    ord_le1908998213l_bool: fun_Pr1696029455l_bool > fun_fu1493047761l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__prod_Itc__Expr__O,type,
    ord_le1776148979l_bool: fun_Pr691271849l_bool > fun_fu1001966495l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__prod_Itc__List__O,type,
    ord_le1438917387l_bool: fun_Pr859510977l_bool > fun_fu1544014007l_bool ).

tff(sy_c_Product__Type_OPair_000tc__Expr__Obop_000tc__Expr__Obop,type,
    product_Pair_bop_bop: fun_bo2022740553op_bop ).

tff(sy_c_Product__Type_OPair_000tc__Expr__Obop_000tc__prod_Itc__Value__Oval_Mtc__Val,type,
    produc621191550al_val: fun_bo1153317747al_val ).

tff(sy_c_Product__Type_OPair_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J,type,
    produc943465171t_char: fun_ex660466419t_char ).

tff(sy_c_Product__Type_OPair_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_516,type,
    produc1259058957on_val: fun_ex977868519on_val ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
    produc1237966615t_char: fun_li1918445737t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc_517,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__518,type,
    produc2035944023t_char: fun_li399153499t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar__519,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,
    produc822965838t_char: fun_li937397365t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc_520,type,
    produc1331140167t_char: fun_li1093980969t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc_521,type,
    produc1483578759t_char: fun_li2006863797t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_,type,
    produc512429457ist_ty: fun_li475043185ist_ty ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Type__Oty_J_000tc__prod_Itc__Li,type,
    produc1909267824t_char: fun_li1548633647t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__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__Value__Oval_J_000tc__List__Olis,type,
    produc2078839843st_val: fun_li1981758019st_val ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Stri,type,
    produc1860789535har_ty: fun_li1679860159har_ty ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Stri_522,type,
    produc1152259904t_char: fun_li1497997787t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Stri_523,type,
    produc436875159t_char: fun_li310247229t_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__List__Olist_Itc__String__Ochar_J_Mtc__O,type,
    produc1960514199on_val: fun_fu760919681on_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__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pro_524,type,
    produc1712663241on_val: fun_fu1932450473on_val ).

tff(sy_c_Product__Type_OPair_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ocha,type,
    produc1618304727on_val: fun_fu766397407on_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_525,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___526,type,
    produc2080520419t_char: fun_Pr130739971t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___527,type,
    produc499151895on_val: fun_Pr278209965on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___528,type,
    produc1641293463t_char: fun_Pr1812345101t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___529,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_Ocurry_000tc__Expr__Obop_000tc__prod_Itc__Value__Oval_Mtc__Va,type,
    produc1555310053l_bool: fun_Pr252072522l_bool > fun_bo1454185032l_bool ).

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

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

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

tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_530,type,
    produc1574020101r_bool: fun_Pr227936640r_bool > fun_li1024794712r_bool ).

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

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

tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc_531,type,
    produc1675615144ion_ty: fun_Pr876827561ion_ty > fun_li1301775111ion_ty ).

tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_It,type,
    produc1588781647r_bool: fun_Pr1861226704r_bool > fun_li522008110r_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_It_532,type,
    produc266042248r_bool: fun_Pr1898949769r_bool > fun_li485148903r_bool ).

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

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

tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Str,type,
    produc2116052801r_bool: fun_Pr1669461698r_bool > fun_li1305328058r_bool ).

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

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

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

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

tff(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__String__Ochar_J_000t,type,
    produc1577326610ion_ty: fun_fu571290057ion_ty ).

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_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__Oexp_Itc__List__Olist_Itc__Str,type,
    produc1815960045l_bool: fun_fu254083683l_bool ).

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__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_533,type,
    produc2027921764r_bool: fun_fu362106225r_bool ).

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_534,type,
    produc392960766l_bool: fun_fu1011371575l_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_535,type,
    produc907433735ion_ty: fun_fu571290057ion_ty ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_536,type,
    produc723279022r_bool: fun_fu144904343r_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_537,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__Value__Oval_J_000tc,type,
    produc21910851r_bool: fun_fu361964333r_bool ).

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__prod_Itc__Expr__Oexp_Itc__List__Olis,type,
    produc1911463199l_bool: fun_fu371764249l_bool ).

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

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

tff(sy_c_Set_OCollect_000tc__List__Olist_Itc__String__Ochar_J,type,
    collect_list_char: fun_list_char_bool > fun_list_char_bool ).

tff(sy_c_Set_OCollect_000tc__Nat__Onat,type,
    collect_nat: fun_nat_bool > fun_nat_bool ).

tff(sy_c_Set_OCollect_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__O,type,
    collec1797130234t_char: fun_Pr565113489r_bool > fun_Pr565113489r_bool ).

tff(sy_c_Set_OCollect_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_It,type,
    collec1583467887t_char: fun_Pr1861226704r_bool > fun_Pr1861226704r_bool ).

tff(sy_c_Set_OCollect_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_It_538,type,
    collec1387638140t_char: fun_Pr70170387r_bool > fun_Pr70170387r_bool ).

tff(sy_c_Set_OCollect_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__St,type,
    collec718040978on_val: fun_Pr691271849l_bool > fun_Pr691271849l_bool ).

tff(sy_c_Set_OCollect_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__Li,type,
    collec2087910442on_val: fun_Pr859510977l_bool > fun_Pr859510977l_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: produc12694297on_val > fun_na939144002on_val ).

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

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

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

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

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

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

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__List__Olist__539,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_540,type,
    transi61620055on_val: fun_Pr235369833l_bool > fun_Pr235369833l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__String__Ocha_541,type,
    transi1123801095t_char: fun_Pr981088873r_bool > fun_Pr981088873r_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__String__Ocha_542,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_Ortranclp_000tc__List__Olist_Itc__String__Ochar_J,type,
    transi1065307915t_char: fun_li860735411r_bool > fun_li860735411r_bool ).

tff(sy_c_TypeRel_OFields_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__,type,
    fields1147507508t_char: ( list_P1999446415t_char * list_char * list_P2023964830har_ty ) > bool ).

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

tff(sy_c_TypeRel_Ohas__field_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri,type,
    has_fi1183600461t_char: ( list_P1999446415t_char * list_char * list_char * ty ) > fun_list_char_bool ).

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

tff(sy_c_TypeRel_Osubcls1p_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String,type,
    subcls744239332t_char: list_P1999446415t_char > fun_li860735411r_bool ).

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

tff(sy_c_TypeSafe__Mirabelle__vvmnfelbag_Osconf,type,
    typeSa1917327191_sconf: ( list_P1999446415t_char * fun_li688206603ion_ty ) > fun_Pr1696029455l_bool ).

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

tff(sy_c_Type_Othis,type,
    this: list_char ).

tff(sy_c_Type_Oty_OClass,type,
    class: fun_list_char_ty ).

tff(sy_c_Type_Oty_ONT,type,
    nt: ty ).

tff(sy_c_Type_Oty_OVoid,type,
    void: ty ).

tff(sy_c_Value_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_1: ( list_P1999446415t_char * fun_na939144002on_val * fun_li688206603ion_ty * exp_list_char * ty ) > bool ).

tff(sy_c_WellTypeRT_OWTrts,type,
    wTrts_1: ( list_P1999446415t_char * fun_na939144002on_val * fun_li688206603ion_ty * list_exp_list_char * list_ty ) > bool ).

tff(sy_c_Wellfounded_Olex__prod_000tc__Expr__Obop_000tc__prod_Itc__Value__Oval_Mtc__,type,
    lex_pr1932514710al_val: ( fun_Pr851759157p_bool * fun_Pr832147423l_bool ) > fun_Pr897334561l_bool ).

tff(sy_c_Wellfounded_Olex__prod_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ocha,type,
    lex_pr69619957on_val: ( fun_Pr136267935r_bool * fun_Pr693020585l_bool ) > fun_Pr691271849l_bool ).

tff(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_,type,
    lex_pr1541028704on_val: ( fun_Pr716652265r_bool * fun_Pr693020585l_bool ) > fun_Pr859510977l_bool ).

tff(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__List__Olist_Itc__String__Och,type,
    lex_pr1787105337t_char: ( fun_Pr382120745r_bool * fun_Pr136267935r_bool ) > fun_Pr908866473r_bool ).

tff(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__List__Olist_Itc__String__Och_543,type,
    lex_pr1876288492t_char: ( fun_Pr382120745r_bool * fun_Pr1728267013r_bool ) > fun_Pr1895638121r_bool ).

tff(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__String__Ochar_J_000tc__List_,type,
    lex_pr280535005t_char: ( fun_Pr565113489r_bool * fun_Pr565113489r_bool ) > fun_Pr1336847023r_bool ).

tff(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_I,type,
    lex_pr1971266694on_val: ( fun_Pr565113489r_bool * fun_Pr369549609l_bool ) > fun_Pr235369833l_bool ).

tff(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_,type,
    lex_pr1668767798t_char: ( fun_Pr565113489r_bool * fun_Pr1538825897r_bool ) > fun_Pr981088873r_bool ).

tff(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod__544,type,
    lex_pr167435119t_char: ( fun_Pr565113489r_bool * fun_Pr286306793r_bool ) > fun_Pr1538825897r_bool ).

tff(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__Type__Oty_J_000tc__prod_Itc_,type,
    lex_pr1588300168t_char: ( fun_Pr306783325y_bool * fun_Pr1890037787r_bool ) > fun_Pr1728267013r_bool ).

tff(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__Value__Oval_J_000tc__Expr__O,type,
    lex_pr307591827t_char: ( fun_Pr1618624239l_bool * fun_Pr136267935r_bool ) > fun_Pr1890037787r_bool ).

tff(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__S,type,
    lex_pr213428520t_char: ( fun_Pr263169771y_bool * fun_Pr2024675945r_bool ) > fun_Pr286306793r_bool ).

tff(sy_c_Wellfounded_Olex__prod_000tc__Value__Oval_000tc__Value__Oval,type,
    lex_prod_val_val: ( fun_Pr2081272681l_bool * fun_Pr2081272681l_bool ) > fun_Pr832147423l_bool ).

tff(sy_c_Wellfounded_Olex__prod_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__,type,
    lex_pr731210613on_val: ( fun_Pr442654869l_bool * fun_Pr673659369l_bool ) > fun_Pr693020585l_bool ).

tff(sy_c_Wellfounded_Olex__prod_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__St,type,
    lex_pr1038007919on_val: ( fun_Pr691271849l_bool * fun_Pr691271849l_bool ) > fun_Pr903661919l_bool ).

tff(sy_c_Wellfounded_Olex__prod_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__Li,type,
    lex_pr2110711565on_val: ( fun_Pr859510977l_bool * fun_Pr859510977l_bool ) > fun_Pr302334223l_bool ).

tff(sy_c_fFalse,type,
    fFalse: bool ).

tff(sy_c_fNot,type,
    fNot: fun_bool_bool ).

tff(sy_c_fTrue,type,
    fTrue: bool ).

tff(sy_c_fconj,type,
    fconj: fun_bo1549164019l_bool ).

tff(sy_c_fdisj,type,
    fdisj: fun_bo1549164019l_bool ).

tff(sy_c_fequal_000tc__Option__Ooption_Itc__Value__Oval_J,type,
    fequal_option_val: fun_op860648563l_bool ).

tff(sy_c_fequal_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String__Ochar,type,
    fequal1937332960on_val: fun_op1529201523l_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__Expr__Obop_Mtc__prod_Itc__Expr__Obop,type,
    hAPP_b1058859669op_bop: ( fun_bo2022740553op_bop * bop ) > fun_bo218022378op_bop ).

tff(sy_c_hAPP_000tc__Expr__Obop_000tc__fun_Itc__fun_Itc__prod_Itc__Expr__Obop_Mtc__p,type,
    hAPP_b1257035143l_bool: ( fun_bo655815611l_bool * bop ) > fun_fu559253084l_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_545,type,
    hAPP_b406740087l_bool: ( fun_bo1312031403l_bool * bop ) > fun_Pr1856441676l_bool ).

tff(sy_c_hAPP_000tc__Expr__Obop_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Ov_546,type,
    hAPP_b1229254591al_val: ( fun_bo1153317747al_val * bop ) > fun_Pr1615326228al_val ).

tff(sy_c_hAPP_000tc__Expr__Obop_000tc__prod_Itc__Expr__Obop_Mtc__Expr__Obop_J,type,
    hAPP_b1909667208op_bop: ( fun_bo218022378op_bop * bop ) > product_prod_bop_bop ).

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

tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_I,type,
    hAPP_e1376201919t_char: ( fun_ex660466419t_char * exp_list_char ) > fun_ex1695787785t_char ).

tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_I_547,type,
    hAPP_e1705922617l_bool: ( fun_ex897949293l_bool * exp_list_char ) > fun_fu237977731l_bool ).

tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_I_548,type,
    hAPP_e1303556805l_bool: ( fun_ex535087353l_bool * exp_list_char ) > fun_fu1983565583l_bool ).

tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_I_549,type,
    hAPP_e53687815l_bool: ( fun_ex1789610473l_bool * exp_list_char ) > fun_fu1054881085l_bool ).

tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_I_550,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_551,type,
    hAPP_e286792811l_bool: ( fun_ex1231581599l_bool * exp_list_char ) > fun_Pr966331573l_bool ).

tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_I_552,type,
    hAPP_e1659493427on_val: ( fun_ex977868519on_val * exp_list_char ) > fun_Pr231134077on_val ).

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

tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__prod__553,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__554,type,
    hAPP_e1752110927t_char: ( fun_ex588373425t_char * exp_list_char ) > produc662261637t_char ).

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

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

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar,type,
    hAPP_l1105836155t_char: ( fun_li1918445737t_char * list_exp_list_char ) > fun_li1726629416t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_555,type,
    hAPP_l177734933l_bool: ( fun_li1961812931l_bool * list_exp_list_char ) > fun_fu173338434l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_556,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_557,type,
    hAPP_l232580245l_bool: ( fun_li616301379l_bool * list_exp_list_char ) > fun_Pr228183746l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_558,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_559,type,
    hAPP_l1648260346t_char: ( fun_li1726629416t_char * list_exp_list_char ) > produc91527719t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__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__560,type,
    hAPP_l551544901l_bool: ( fun_li99597427l_bool * list_list_char ) > fun_ex535087353l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun__561,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__562,type,
    hAPP_l2019537453t_char: ( fun_li399153499t_char * list_list_char ) > fun_li892090081t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun__563,type,
    hAPP_l753659065r_bool: ( fun_li2102970087r_bool * list_list_char ) > fun_fu737201517r_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun__564,type,
    hAPP_l1783480313r_bool: ( fun_li1077890343r_bool * list_list_char ) > fun_fu614077613r_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun__565,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__566,type,
    hAPP_l1571522437l_bool: ( fun_li404360883l_bool * list_list_char ) > fun_Pr402119737l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun__567,type,
    hAPP_l1873467853t_char: ( fun_li455628155t_char * list_list_char ) > fun_Pr141094017t_char ).

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

tff(sy_c_hAPP_000tc__List__Olist_Itc__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__HOL__Obool_Mtc,type,
    hAPP_l2010421276l_bool: ( fun_li332530512l_bool * list_char ) > fun_bool_bool ).

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_568,type,
    hAPP_l1425867561l_bool: ( fun_li515230429l_bool * list_char ) > fun_li758413868l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__List__Olist_It_569,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__Option__Ooptio,type,
    hAPP_l1646953198l_bool: ( fun_li511029026l_bool * list_char ) > fun_option_val_bool ).

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

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__fun_Itc__List_,type,
    hAPP_l1903254203l_bool: ( fun_li1362522525l_bool * list_char ) > fun_fu1364670840l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__fun_Itc__prod_,type,
    hAPP_l553007690l_bool: ( fun_li758413868l_bool * list_char ) > fun_fu2033725063l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__fun_Itc__prod__570,type,
    hAPP_l1335043179r_bool: ( fun_li248212255r_bool * list_char ) > fun_fu667589486r_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__fun_Itc__prod__571,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__572,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__573,type,
    hAPP_l2111308793l_bool: ( fun_li1000975661l_bool * list_char ) > fun_fu1361433468l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__fun_Itc__prod__574,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__fun_Itc__prod__575,type,
    hAPP_l1739862107l_bool: ( fun_li1383188623l_bool * list_char ) > fun_fu989986782l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__fun_Itc__prod__576,type,
    hAPP_l923073979r_bool: ( fun_li1555920111r_bool * list_char ) > fun_fu2134889022r_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__fun_Itc__prod__577,type,
    hAPP_l2053770731r_bool: ( fun_li977323167r_bool * list_char ) > fun_fu873633006r_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__fun_Itc__prod__578,type,
    hAPP_l1988620845r_bool: ( fun_li486265185r_bool * list_char ) > fun_fu52588976r_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__List,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_579,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_580,type,
    hAPP_l1591404153l_bool: ( fun_li95346349l_bool * list_char ) > fun_Pr655735548l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__List_581,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_582,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_583,type,
    hAPP_l1845912621l_bool: ( fun_li429005281l_bool * list_char ) > fun_Pr665774896l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__List_584,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_585,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_586,type,
    hAPP_l810309945l_bool: ( fun_li1927639661l_bool * list_char ) > fun_Pr1021761724l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__prod_Itc__List_587,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__fun_Itc__List__Olist_Itc__T,type,
    hAPP_l1770520637ist_ty: ( fun_li475043185ist_ty * list_ty ) > fun_li452671142ist_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__fun_Itc__fun_Itc__prod_Itc_,type,
    hAPP_l96108383r_bool: ( fun_li1851424531r_bool * list_ty ) > fun_fu848650568r_bool ).

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_588,type,
    hAPP_l1117138611l_bool: ( fun_li1135330407l_bool * list_ty ) > fun_Pr1869680796l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__fun_Itc__prod_Itc__List__Ol_589,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__Type__Ot,type,
    hAPP_l2048923787t_char: ( fun_li997290943t_char * list_ty ) > fun_Pr862403572t_char ).

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

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__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___590,type,
    hAPP_l1842007287l_bool: ( fun_li1225301163l_bool * list_val ) > fun_ex1789610473l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__fun_Itc__Expr__Oexp_Itc___591,type,
    hAPP_l1859255743t_char: ( fun_li1751446259t_char * list_val ) > fun_ex588373425t_char ).

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

tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__fun_Itc__fun_Itc__prod_It,type,
    hAPP_l296209613r_bool: ( fun_li968298881r_bool * list_val ) > fun_fu243812799r_bool ).

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

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc,type,
    hAPP_l1657578379har_ty: ( fun_li1679860159har_ty * list_P1940453997har_ty ) > fun_li846919931har_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_592,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_593,type,
    hAPP_l1536299231l_bool: ( fun_li1358910483l_bool * list_P1940453997har_ty ) > fun_li1548711503l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_594,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_595,type,
    hAPP_l1129005983r_bool: ( fun_li1774921427r_bool * list_P1940453997har_ty ) > fun_fu1141418255r_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_596,type,
    hAPP_l1294856089har_ty: ( fun_li846919931har_ty * list_P1940453997har_ty ) > produc450000425har_ty ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_597,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_598,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_599,type,
    hAPP_l1450984463t_char: ( fun_li310247229t_char * list_P341299826t_char ) > fun_li614370610t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_600,type,
    hAPP_l213519975l_bool: ( fun_li1548711503l_bool * list_P341299826t_char ) > fun_fu1272536068l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_601,type,
    hAPP_l277216047t_char: ( fun_li618628759t_char * list_P341299826t_char ) > produc2146869324t_char ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_602,type,
    hAPP_l1334098948t_char: ( fun_li614370610t_char * list_P341299826t_char ) > produc244676007t_char ).

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

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__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__Nat__Onat_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
    hAPP_n1006566506l_bool: ( fun_na1469252690l_bool * nat ) > fun_bool_bool ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Option__Ooption_Itc__prod_Itc__List__,type,
    hAPP_n95946796l_bool: ( fun_na712147476l_bool * nat ) > fun_op362161377l_bool ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_,type,
    hAPP_n215258509l_bool: ( fun_na1436237685l_bool * nat ) > fun_fu425979586l_bool ).

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__Nat__Onat_J_000tc__Nat__Onat,type,
    hAPP_option_nat_nat: ( fun_option_nat_nat * option_nat ) > nat ).

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__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__Type__Oty,type,
    hAPP_option_ty_ty: ( fun_option_ty_ty * option_ty ) > ty ).

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__fun_Itc__List__Olist_It,type,
    hAPP_o1240645474ion_ty: ( fun_op1371746710ion_ty * option_ty ) > fun_li688206603ion_ty ).

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__fun_Itc__fun_Itc__prod_,type,
    hAPP_o534509643ion_ty: ( fun_op1983271469ion_ty * option_ty ) > fun_fu357191650ion_ty ).

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__HOL__Obool,type,
    hAPP_option_val_bool: ( fun_option_val_bool * option_val ) > bool ).

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_o453398608r_bool: ( fun_op649618820r_bool * option_val ) > fun_list_char_bool ).

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__fun_Itc__List__Olist__603,type,
    hAPP_o538043682on_val: ( fun_op2076490582on_val * option_val ) > fun_li1432931796on_val ).

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__fun_Itc__Option__Oopt,type,
    hAPP_o586881855l_bool: ( fun_op860648563l_bool * option_val ) > fun_option_val_bool ).

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__fun_Itc__prod_Itc__Li,type,
    hAPP_o1269033393on_val: ( fun_op227821541on_val * option_val ) > fun_Pr806764899on_val ).

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_,type,
    hAPP_o285151112r_bool: ( fun_op1531141308r_bool * option466449911r_bool ) > fun_list_char_bool ).

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J,type,
    hAPP_o2007402111l_bool: ( fun_op362161377l_bool * option1479284511on_val ) > bool ).

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_604,type,
    hAPP_o1566711458t_bool: ( fun_op790144516t_bool * option1479284511on_val ) > fun_nat_bool ).

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_605,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_606,type,
    hAPP_o1968908095l_bool: ( fun_op1529201523l_bool * option1479284511on_val ) > fun_op362161377l_bool ).

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_607,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__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__prod_Itc__List__Olist_Itc__String__O,type,
    hAPP_t708040077har_ty: ( fun_ty1486032501har_ty * ty ) > produc245756905har_ty ).

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__fun_Itc__fun_Itc__,type,
    hAPP_v417179479l_bool: ( fun_va2018308997l_bool * val ) > fun_va633994418l_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__fun_Itc__fun_Itc__prod_Itc__Value__Oval_Mtc_,type,
    hAPP_v3604996l_bool: ( fun_va633994418l_bool * val ) > fun_fu1210184799l_bool ).

tff(sy_c_hAPP_000tc__Value__Oval_000tc__fun_Itc__fun_Itc__prod_Itc__Value__Oval_Mtc__608,type,
    hAPP_v1988122071l_bool: ( fun_va310403589l_bool * val ) > fun_fu57453362l_bool ).

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

tff(sy_c_hAPP_000tc__fun_Itc__Expr__Obop_Mtc__fun_Itc__fun_Itc__prod_Itc__Expr__Obop,type,
    hAPP_f1100052969l_bool: ( fun_fu1124575819l_bool * fun_bo655815611l_bool ) > fun_fu1239462955l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Expr__Obop_Mtc__fun_Itc__prod_Itc__Value__Oval_Mtc__Va,type,
    hAPP_f1776070952l_bool: ( fun_fu570042250l_bool * fun_bo1454185032l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Expr__Obop_Mtc__fun_Itc__prod_Itc__Value__Oval_Mtc__Va_609,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_610,type,
    hAPP_f2100207721l_bool: ( fun_fu274598091l_bool * fun_bo1312031403l_bool ) > fun_bo655815611l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Expr__Obop_Mtc__fun_Itc__prod_Itc__Value__Oval_Mtc__Va_611,type,
    hAPP_f866074145l_bool: ( fun_fu1489350019l_bool * fun_bo1153317747al_val ) > fun_bo1312031403l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc,type,
    hAPP_f40682957l_bool: ( fun_fu1848909487l_bool * fun_ex897949293l_bool ) > fun_fu582209117l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc_612,type,
    hAPP_f1766231913r_bool: ( fun_fu1223433803r_bool * fun_ex535087353l_bool ) > fun_fu737201517r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc_613,type,
    hAPP_f388097003r_bool: ( fun_fu1888091987r_bool * fun_ex1789610473l_bool ) > fun_fu243812799r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc_614,type,
    hAPP_f570766339l_bool: ( fun_fu1520189105l_bool * fun_ex1201926843l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc_615,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_616,type,
    hAPP_f1475571983l_bool: ( fun_fu1605616113l_bool * fun_ex1231581599l_bool ) > fun_ex897949293l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc_617,type,
    hAPP_f1614195593l_bool: ( fun_fu750322283l_bool * fun_ex977868519on_val ) > fun_ex1231581599l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc_618,type,
    hAPP_f901718717l_bool: ( fun_fu1302866591l_bool * fun_ex303050433t_char ) > fun_ex535087353l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc_619,type,
    hAPP_f361629773l_bool: ( fun_fu1082830261l_bool * fun_ex588373425t_char ) > fun_ex1789610473l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc__,type,
    hAPP_f1861125939r_bool: ( fun_fu2039604123r_bool * fun_bool_bool ) > fun_fu297867453r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc___620,type,
    hAPP_f894608603t_bool: ( fun_fu1509210819t_bool * fun_bool_bool ) > fun_fu821463397t_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc___621,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_f1157863905l_bool: ( fun_fu1811849795l_bool * fun_bo1549164019l_bool ) > fun_fu125051371l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J__622,type,
    hAPP_f1080886329l_bool: ( fun_fu1849968923l_bool * fun_bo1549164019l_bool ) > fun_fu2104074051l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J__623,type,
    hAPP_f1977633121l_bool: ( fun_fu781882819l_bool * fun_bo1549164019l_bool ) > fun_fu1457514859l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J__624,type,
    hAPP_f722872225l_bool: ( fun_fu1562611971l_bool * fun_bo1549164019l_bool ) > fun_fu164328875l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J__625,type,
    hAPP_f321462169l_bool: ( fun_fu585405563l_bool * fun_bo1549164019l_bool ) > fun_fu6617763l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J__626,type,
    hAPP_f1169733153l_bool: ( fun_fu1347399555l_bool * fun_bo1549164019l_bool ) > fun_fu2049369131l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J__627,type,
    hAPP_f606945057l_bool: ( fun_fu14434691l_bool * fun_bo1549164019l_bool ) > fun_fu1140187947l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J__628,type,
    hAPP_f1600936353l_bool: ( fun_fu1266804483l_bool * fun_bo1549164019l_bool ) > fun_fu1126530987l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Stri,type,
    hAPP_f348508809l_bool: ( fun_fu1999472363l_bool * fun_li1961812931l_bool ) > fun_fu17279171l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Stri_629,type,
    hAPP_f2041029616l_bool: ( fun_fu1939745362l_bool * fun_li1372729616l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Stri_630,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_631,type,
    hAPP_f1149562121l_bool: ( fun_fu822026603l_bool * fun_li616301379l_bool ) > fun_li1961812931l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Stri_632,type,
    hAPP_f1752856401l_bool: ( fun_fu338455219l_bool * fun_li856594443on_val ) > fun_li616301379l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mt,type,
    hAPP_f539072365l_bool: ( fun_fu317217051l_bool * fun_li221477r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_633,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_634,type,
    hAPP_f2059406941r_bool: ( fun_fu141557567r_bool * fun_li99597427l_bool ) > fun_li2102970087r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_635,type,
    hAPP_f165071409l_bool: ( fun_fu1934570515l_bool * fun_li1727207611t_char ) > fun_li99597427l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_636,type,
    hAPP_f1820115955r_bool: ( fun_fu232735701r_bool * fun_li2102970087r_bool ) > fun_fu1561705993r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_637,type,
    hAPP_f308875635r_bool: ( fun_fu1374106197r_bool * fun_li1077890343r_bool ) > fun_fu2033315657r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_638,type,
    hAPP_f998390560l_bool: ( fun_fu1924808654l_bool * fun_li1024794712r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_639,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_640,type,
    hAPP_f531187933r_bool: ( fun_fu1637505727r_bool * fun_li404360883l_bool ) > fun_li1077890343r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_641,type,
    hAPP_f1136362289l_bool: ( fun_fu2070744595l_bool * fun_li455628155t_char ) > fun_li404360883l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__HOL__Obool_J_000,type,
    hAPP_f986089162l_bool: ( fun_fu1364670840l_bool * fun_list_char_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__HOL__Obool_J_000_642,type,
    hAPP_f363827556r_bool: ( fun_fu450339090r_bool * fun_list_char_bool ) > option466449911r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__HOL__Obool_J_000_643,type,
    hAPP_f1371002581r_bool: ( fun_fu297867453r_bool * fun_list_char_bool ) > fun_list_char_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__HOL__Obool_J_000_644,type,
    hAPP_f1163760061l_bool: ( fun_fu125051371l_bool * fun_list_char_bool ) > fun_li332530512l_bool ).

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

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__645,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__646,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__647,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__648,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__649,type,
    hAPP_f396807521l_bool: ( fun_fu1819434639l_bool * fun_li1432931796on_val ) > fun_li511029026l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__650,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__651,type,
    hAPP_f864891091on_val: ( fun_fu760919681on_val * fun_li1432931796on_val ) > fun_fu620918548on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__652,type,
    hAPP_f720086610l_bool: ( fun_fu1796901562l_bool * fun_li1432931796on_val ) > fun_fu1493047761l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__653,type,
    hAPP_f1741070310on_val: ( fun_fu620918548on_val * fun_li1432931796on_val ) > produc1127210791on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption__654,type,
    hAPP_f1727192346on_val: ( fun_fu1690035458on_val * fun_li1432931796on_val ) > produc12694297on_val ).

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

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__List__O,type,
    hAPP_f1776419603l_bool: ( fun_fu1166999157l_bool * fun_li860735411r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__List__O_655,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_656,type,
    hAPP_f1032444159r_bool: ( fun_fu388839521r_bool * fun_li515230429l_bool ) > fun_li248212255r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__List__O_657,type,
    hAPP_f1764180741l_bool: ( fun_fu1196958311l_bool * fun_li835958565t_char ) > fun_li515230429l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__Option_,type,
    hAPP_f399018025r_bool: ( fun_fu1734620171r_bool * fun_li511029026l_bool ) > fun_op649618820r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__fun_Itc,type,
    hAPP_f522372661r_bool: ( fun_fu683689373r_bool * fun_li1362522525l_bool ) > fun_fu297867453r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__fun_Itc_658,type,
    hAPP_f1367982615r_bool: ( fun_fu1125427583r_bool * fun_li758413868l_bool ) > fun_fu667589486r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__fun_Itc_659,type,
    hAPP_f447563647r_bool: ( fun_fu1361373153r_bool * fun_li248212255r_bool ) > fun_fu1278980701r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__fun_Itc_660,type,
    hAPP_f678833350l_bool: ( fun_fu1983549044l_bool * fun_li823162622l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__fun_Itc_661,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_662,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_663,type,
    hAPP_f1094343359l_bool: ( fun_fu500553633l_bool * fun_li1000975661l_bool ) > fun_li1383188623l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__fun_Itc_664,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__fun_Itc_665,type,
    hAPP_f1370205989l_bool: ( fun_fu1537555463l_bool * fun_li1436431093on_val ) > fun_li1000975661l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__fun_Itc_666,type,
    hAPP_f350189921l_bool: ( fun_fu695096899l_bool * fun_li1383188623l_bool ) > fun_fu1554319823l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__fun_Itc_667,type,
    hAPP_f1500560577r_bool: ( fun_fu1188864163r_bool * fun_li1555920111r_bool ) > fun_fu1567715023r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__fun_Itc_668,type,
    hAPP_f521496323r_bool: ( fun_fu1931408741r_bool * fun_li977323167r_bool ) > fun_fu1396152417r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__fun_Itc_669,type,
    hAPP_f2133563379r_bool: ( fun_fu1706763477r_bool * fun_li486265185r_bool ) > fun_fu82046351r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_It,type,
    hAPP_f1795246582l_bool: ( fun_fu1021591716l_bool * fun_li522008110r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_It_670,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_671,type,
    hAPP_f29105311r_bool: ( fun_fu222752897r_bool * fun_li95346349l_bool ) > fun_li1555920111r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_It_672,type,
    hAPP_f333583909l_bool: ( fun_fu1785489927l_bool * fun_li937397365t_char ) > fun_li95346349l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_It_673,type,
    hAPP_f1931964053l_bool: ( fun_fu1409702391l_bool * fun_li1960983605r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_It_674,type,
    hAPP_f732843907r_bool: ( fun_fu1416208101r_bool * fun_li429005281l_bool ) > fun_li977323167r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_It_675,type,
    hAPP_f1868463117l_bool: ( fun_fu1411172719l_bool * fun_li1093980969t_char ) > fun_li429005281l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_It_676,type,
    hAPP_f1520735791l_bool: ( fun_fu2048960477l_bool * fun_li485148903r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_It_677,type,
    hAPP_f252398939r_bool: ( fun_fu1763478281r_bool * fun_li485148903r_bool ) > fun_Pr1898949769r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_It_678,type,
    hAPP_f1957374161r_bool: ( fun_fu1860299955r_bool * fun_li1927639661l_bool ) > fun_li486265185r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_It_679,type,
    hAPP_f1817350437l_bool: ( fun_fu30674439l_bool * fun_li2006863797t_char ) > fun_li1927639661l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__,type,
    hAPP_f558380429l_bool: ( fun_fu453549301l_bool * fun_li1857149300t_char ) > fun_li758413868l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Type__Oty_J_Mtc__fun_Itc__fun_Itc__pr,type,
    hAPP_f133320957r_bool: ( fun_fu377199967r_bool * fun_li1851424531r_bool ) > fun_fu1122234343r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Type__Oty_J_Mtc__fun_Itc__prod_Itc__L,type,
    hAPP_f1889282162l_bool: ( fun_fu1099362516l_bool * fun_li887890578r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Type__Oty_J_Mtc__fun_Itc__prod_Itc__L_680,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_681,type,
    hAPP_f1608277885r_bool: ( fun_fu330880479r_bool * fun_li1135330407l_bool ) > fun_li1851424531r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Type__Oty_J_Mtc__fun_Itc__prod_Itc__L_682,type,
    hAPP_f2047757465l_bool: ( fun_fu103864315l_bool * fun_li1548633647t_char ) > fun_li1135330407l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Value__Oval_J_Mtc__fun_Itc__Expr__Oex,type,
    hAPP_f1118567467l_bool: ( fun_fu1965526925l_bool * fun_li826105035r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Value__Oval_J_Mtc__fun_Itc__Expr__Oex_683,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_684,type,
    hAPP_f1449341487r_bool: ( fun_fu1488582801r_bool * fun_li1225301163l_bool ) > fun_li968298881r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Value__Oval_J_Mtc__fun_Itc__Expr__Oex_685,type,
    hAPP_f2118054305l_bool: ( fun_fu226247171l_bool * fun_li1751446259t_char ) > fun_li1225301163l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Value__Oval_J_Mtc__fun_Itc__fun_Itc__,type,
    hAPP_f987862447r_bool: ( fun_fu1402349329r_bool * fun_li968298881r_bool ) > fun_fu923263787r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Oc,type,
    hAPP_f1409772418l_bool: ( fun_fu142481456l_bool * fun_li1305328058r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Oc_686,type,
    hAPP_f895126887r_bool: ( fun_fu402575125r_bool * fun_li1305328058r_bool ) > fun_Pr1669461698r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Oc_687,type,
    hAPP_f1749915625r_bool: ( fun_fu146328523r_bool * fun_li1358910483l_bool ) > fun_li1774921427r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Oc_688,type,
    hAPP_f935003377l_bool: ( fun_fu1158944723l_bool * fun_li1497997787t_char ) > fun_li1358910483l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Oc_689,type,
    hAPP_f197435839r_bool: ( fun_fu1721346721r_bool * fun_li1774921427r_bool ) > fun_fu34004457r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Oc_690,type,
    hAPP_f841257045r_bool: ( fun_fu989111613r_bool * fun_li1548711503l_bool ) > fun_fu1141418255r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Oc_691,type,
    hAPP_f156692813l_bool: ( fun_fu2068145461l_bool * fun_li618628759t_char ) > fun_li1548711503l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool,type,
    hAPP_f54304608l_bool: ( fun_fu425979586l_bool * fun_nat_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Nat__Onat_,type,
    hAPP_f800510211t_bool: ( fun_fu821463397t_bool * fun_nat_bool ) > fun_nat_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Nat__Onat__692,type,
    hAPP_f1146629647l_bool: ( fun_fu2104074051l_bool * fun_nat_bool ) > fun_na1469252690l_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_693,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_694,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_695,type,
    hAPP_f1677329295l_bool: ( fun_fu1092588739l_bool * fun_na939144002on_val ) > fun_na712147476l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_696,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_697,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_698,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_699,type,
    hAPP_f613075253l_bool: ( fun_fu1165575785l_bool * fun_na939144002on_val ) > fun_fu1796901562l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_700,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_701,type,
    hAPP_f1805337205on_val: ( fun_fu1932450473on_val * fun_na939144002on_val ) > fun_fu708489978on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_702,type,
    hAPP_f1492320500l_bool: ( fun_fu1806184744l_bool * fun_na939144002on_val ) > fun_fu1590192889l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_703,type,
    hAPP_f893576377l_bool: ( fun_fu114548717l_bool * fun_na939144002on_val ) > fun_fu2077402686l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_704,type,
    hAPP_f368284312on_val: ( fun_fu708489978on_val * fun_na939144002on_val ) > produc644889299on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__fun_Itc__Option__Ooption_Itc__prod_Itc_,type,
    hAPP_f489569861t_bool: ( fun_fu1620074797t_bool * fun_na712147476l_bool ) > fun_op790144516t_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__O,type,
    hAPP_f1722879237t_bool: ( fun_fu80187629t_bool * fun_na1436237685l_bool ) > fun_fu821463397t_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__Option__Ooption_Itc__Value__Oval_J_Mtc__fun_Itc__Optio,type,
    hAPP_f926979333l_bool: ( fun_fu268320615l_bool * fun_op860648563l_bool ) > fun_fu1819434639l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String,type,
    hAPP_f1611569977l_bool: ( fun_fu701816347l_bool * fun_op1529201523l_bool ) > fun_fu1092588739l_bool ).

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__Value__Oval_Mtc__fun_Itc__Value__Oval_Mtc__HOL__Obool_,type,
    hAPP_f2071159779l_bool: ( fun_fu533549125l_bool * fun_val_fun_val_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Value__Oval_Mtc__fun_Itc__Value__Oval_Mtc__HOL__Obool__705,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__fun_Itc__Value__Oval_Mtc__fun_Itc__fu,type,
    hAPP_f1859053709l_bool: ( fun_fu1270086127l_bool * fun_va2018308997l_bool ) > fun_va310403589l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Value__Oval_Mtc__fun_Itc__Value__Oval_Mtc__prod_Itc__V,type,
    hAPP_f293485653l_bool: ( fun_fu436604087l_bool * fun_va959426509al_val ) > fun_va2018308997l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Value__Oval_Mtc__fun_Itc__fun_Itc__prod_Itc__Value__Ov,type,
    hAPP_f1764548711l_bool: ( fun_fu600031817l_bool * fun_va633994418l_bool ) > fun_fu57453362l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Value__Oval_Mtc__fun_Itc__fun_Itc__prod_Itc__Value__Ov_706,type,
    hAPP_f1880802701l_bool: ( fun_fu1280349935l_bool * fun_va310403589l_bool ) > fun_fu166563973l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Value__Oval_Mtc__prod_Itc__Value__Oval_Mtc__Value__Ova,type,
    hAPP_f1394668591l_bool: ( fun_fu1915524369l_bool * fun_va1923334394al_val ) > fun_va633994418l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ocha,type,
    hAPP_f108089737r_bool: ( fun_fu2114536561r_bool * fun_fu1223433803r_bool ) > fun_fu141557567r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ocha_707,type,
    hAPP_f1823921107r_bool: ( fun_fu1287147451r_bool * fun_fu1888091987r_bool ) > fun_fu1488582801r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ocha_708,type,
    hAPP_f1174637065l_bool: ( fun_fu594565489l_bool * fun_fu1302866591l_bool ) > fun_fu1934570515l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ocha_709,type,
    hAPP_f1687138147l_bool: ( fun_fu168630475l_bool * fun_fu1082830261l_bool ) > fun_fu226247171l_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__710,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__711,type,
    hAPP_f510152537l_bool: ( fun_fu735196737l_bool * fun_fu1796901562l_bool ) > fun_fu2077402686l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__712,type,
    hAPP_f1008932791l_bool: ( fun_fu1176066021l_bool * fun_fu1690035458on_val ) > fun_fu1693644106l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__713,type,
    hAPP_f292637069l_bool: ( fun_fu1608823157l_bool * fun_fu1690035458on_val ) > fun_fu1796901562l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc,type,
    hAPP_f254182519r_bool: ( fun_fu445571679r_bool * fun_fu1125427583r_bool ) > fun_fu388839521r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_It,type,
    hAPP_f247798919l_bool: ( fun_fu130047471l_bool * fun_fu453549301l_bool ) > fun_fu1196958311l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__S,type,
    hAPP_f842743203r_bool: ( fun_fu232818571r_bool * fun_fu989111613r_bool ) > fun_fu146328523r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__S_714,type,
    hAPP_f162154931l_bool: ( fun_fu1260000795l_bool * fun_fu2068145461l_bool ) > fun_fu1158944723l_bool ).

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

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__715,type,
    hAPP_f1523875321l_bool: ( fun_fu1989717467l_bool * fun_fu250820942l_bool ) > fun_fu1806184744l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__716,type,
    hAPP_f838396643l_bool: ( fun_fu1680591819l_bool * fun_fu570492181l_bool ) > fun_fu863769827l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__717,type,
    hAPP_f1450446905l_bool: ( fun_fu299475175l_bool * fun_fu100249073l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__718,type,
    hAPP_f555424277l_bool: ( fun_fu459093885l_bool * fun_fu100249073l_bool ) > fun_fu100249073l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__719,type,
    hAPP_f2121594859l_bool: ( fun_fu947198233l_bool * fun_fu100249073l_bool ) > fun_Pr1696029455l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__720,type,
    hAPP_f857351829l_bool: ( fun_fu712248957l_bool * fun_fu2141444501y_bool ) > fun_fu570492181l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__721,type,
    hAPP_f1250221913l_bool: ( fun_fu322466363l_bool * fun_fu1165575785l_bool ) > fun_fu114548717l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__722,type,
    hAPP_f1363667773l_bool: ( fun_fu1722968561l_bool * fun_fu1639641777on_val ) > fun_fu100249073l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__723,type,
    hAPP_f1670595613l_bool: ( fun_fu681302015l_bool * fun_fu1639641777on_val ) > fun_fu1165575785l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__724,type,
    hAPP_f77033475l_bool: ( fun_fu1686228965l_bool * fun_fu114548717l_bool ) > fun_fu1076543251l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Value__Oval_Mtc__fun_Itc__fun_Itc__prod_Itc__,type,
    hAPP_f400269243l_bool: ( fun_fu308030371l_bool * fun_fu600031817l_bool ) > fun_fu1270086127l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Value__Oval_Mtc__prod_Itc__Value__Oval_Mtc__V,type,
    hAPP_f565735867l_bool: ( fun_fu22126627l_bool * fun_fu1915524369l_bool ) > fun_fu436604087l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc,type,
    hAPP_f1734879897l_bool: ( fun_fu816125185l_bool * fun_fu1590192889l_bool ) > fun_fu459093885l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc_725,type,
    hAPP_f348318673l_bool: ( fun_fu938561337l_bool * fun_fu2083094209l_bool ) > fun_fu712248957l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc_726,type,
    hAPP_f1860331535l_bool: ( fun_fu802010103l_bool * fun_fu735196737l_bool ) > fun_fu322466363l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc_727,type,
    hAPP_f1050935001l_bool: ( fun_fu698854459l_bool * fun_fu1176066021l_bool ) > fun_fu1722968561l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc_728,type,
    hAPP_f1472899487l_bool: ( fun_fu724130311l_bool * fun_fu1608823157l_bool ) > fun_fu681302015l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__O,type,
    hAPP_f876671127l_bool: ( fun_fu54393727l_bool * fun_fu49805983l_bool ) > fun_fu500553633l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__O_729,type,
    hAPP_f7643013ion_ty: ( fun_fu182032103ion_ty * fun_fu564156607ion_ty ) > fun_fu1747693763ion_ty ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__O_730,type,
    hAPP_f1406462375l_bool: ( fun_fu1941383183l_bool * fun_fu1263594869l_bool ) > fun_fu1537555463l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__St,type,
    hAPP_f1135930489l_bool: ( fun_fu44119137l_bool * fun_fu1666573063l_bool ) > fun_fu532278763l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__St_731,type,
    hAPP_f2026692601l_bool: ( fun_fu280119905l_bool * fun_fu1839421007l_bool ) > fun_fu1636870067l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__Li,type,
    hAPP_f32926423l_bool: ( fun_fu1451279551l_bool * fun_fu1668998687l_bool ) > fun_fu1295272801l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__Li_732,type,
    hAPP_f869803751l_bool: ( fun_fu1063302223l_bool * fun_fu450552565l_bool ) > fun_fu1848982215l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mt,type,
    hAPP_f1166017719l_bool: ( fun_fu49805983l_bool * fun_fu1361433468l_bool ) > fun_fu989986782l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mt_733,type,
    hAPP_f2110071953ion_ty: ( fun_fu564156607ion_ty * fun_fu1718160452on_val ) > fun_fu357191650ion_ty ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mt_734,type,
    hAPP_f1099622285l_bool: ( fun_fu1263594869l_bool * fun_fu1718160452on_val ) > fun_fu1361433468l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mt_735,type,
    hAPP_f953097879r_bool: ( fun_fu1167317887r_bool * fun_fu1928247679r_bool ) > fun_fu222752897r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mt_736,type,
    hAPP_f1407048615l_bool: ( fun_fu1922972687l_bool * fun_fu696652149l_bool ) > fun_fu1785489927l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__p,type,
    hAPP_f179418505r_bool: ( fun_fu596555377r_bool * fun_fu839442891r_bool ) > fun_fu1637505727r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__p_737,type,
    hAPP_f1736484361l_bool: ( fun_fu2060731249l_bool * fun_fu821374111l_bool ) > fun_fu2070744595l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__p_738,type,
    hAPP_f1563448447r_bool: ( fun_fu221466727r_bool * fun_fu1497625339r_bool ) > fun_fu1416208101r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__p_739,type,
    hAPP_f1365840271l_bool: ( fun_fu1930358519l_bool * fun_fu748506869l_bool ) > fun_fu1411172719l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc_,type,
    hAPP_f1134248971r_bool: ( fun_fu1113701619r_bool * fun_fu1034987497r_bool ) > fun_fu330880479r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__740,type,
    hAPP_f466945179l_bool: ( fun_fu579122691l_bool * fun_fu1167149685l_bool ) > fun_fu103864315l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Ol,type,
    hAPP_f304993943r_bool: ( fun_fu2003654783r_bool * fun_fu935579185r_bool ) > fun_fu1860299955r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Ol_741,type,
    hAPP_f614662951l_bool: ( fun_fu1080828303l_bool * fun_fu1331594741l_bool ) > fun_fu30674439l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc_,type,
    hAPP_f1374595987l_bool: ( fun_fu1818728571l_bool * fun_fu1248515149l_bool ) > fun_fu274598091l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__742,type,
    hAPP_f877616419l_bool: ( fun_fu1941566603l_bool * fun_fu847194997l_bool ) > fun_fu1489350019l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Oop,type,
    hAPP_f1946480059l_bool: ( fun_fu168240291l_bool * fun_fu1525621451l_bool ) > fun_fu1605616113l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Oop_743,type,
    hAPP_f1850037271l_bool: ( fun_fu276262911l_bool * fun_fu76765545l_bool ) > fun_fu822026603l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Oop_744,type,
    hAPP_f705562443l_bool: ( fun_fu56207283l_bool * fun_fu1816861237l_bool ) > fun_fu750322283l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Oop_745,type,
    hAPP_f552300311l_bool: ( fun_fu312143231l_bool * fun_fu793340337l_bool ) > fun_fu338455219l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc__Expr__Obop_J_Mtc__HOL__Obool,type,
    hAPP_f1854361213l_bool: ( fun_fu318834731l_bool * fun_Pr851759157p_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__V,type,
    hAPP_f742333458l_bool: ( fun_fu1654159552l_bool * fun_Pr252072522l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__V_746,type,
    hAPP_f257113085l_bool: ( fun_fu1239462955l_bool * fun_Pr252072522l_bool ) > fun_bo1454185032l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__V_747,type,
    hAPP_f1335946228l_bool: ( fun_fu559253084l_bool * fun_Pr252072522l_bool ) > fun_Pr2081272681l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__V_748,type,
    hAPP_f62511709l_bool: ( fun_fu2027889989l_bool * fun_Pr285446189l_bool ) > fun_fu847194997l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och,type,
    hAPP_f588675559l_bool: ( fun_fu366820245l_bool * fun_Pr136267935r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och_749,type,
    hAPP_f91506671l_bool: ( fun_fu1845830481l_bool * fun_Pr680585871l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och_750,type,
    hAPP_f989077673l_bool: ( fun_fu582209117l_bool * fun_Pr680585871l_bool ) > fun_ex1201926843l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och_751,type,
    hAPP_f1175362209l_bool: ( fun_fu237977731l_bool * fun_Pr680585871l_bool ) > fun_Pr1696029455l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och_752,type,
    hAPP_f1639555093l_bool: ( fun_fu1053658365l_bool * fun_Pr1751899445l_bool ) > fun_fu1816861237l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och_753,type,
    hAPP_f961387813l_bool: ( fun_fu1666573063l_bool * fun_Pr973229009l_bool ) > fun_fu1055869009l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och_754,type,
    hAPP_f1089788553l_bool: ( fun_fu1161062123l_bool * fun_Pr519971843l_bool ) > fun_fu1965088899l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och_755,type,
    hAPP_f434955681l_bool: ( fun_fu2042905603l_bool * fun_Pr633696065l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och_756,type,
    hAPP_f635218277l_bool: ( fun_fu371764249l_bool * fun_Pr633696065l_bool ) > fun_Pr691271849l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och_757,type,
    hAPP_f2095325577l_bool: ( fun_fu532278763l_bool * fun_Pr2043111299l_bool ) > fun_Pr519971843l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och_758,type,
    hAPP_f1204100177l_bool: ( fun_fu1636870067l_bool * fun_Pr1391347915on_val ) > fun_Pr2043111299l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och_759,type,
    hAPP_f762728813l_bool: ( fun_fu1839421007l_bool * fun_Pr714818201on_val ) > fun_Pr973229009l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist,type,
    hAPP_f1734260017l_bool: ( fun_fu814665183l_bool * fun_Pr716652265r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_760,type,
    hAPP_f837795298l_bool: ( fun_fu749996688l_bool * fun_Pr248118298l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_761,type,
    hAPP_f844901525l_bool: ( fun_fu17279171l_bool * fun_Pr248118298l_bool ) > fun_li1372729616l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_762,type,
    hAPP_f1526206996l_bool: ( fun_fu173338434l_bool * fun_Pr248118298l_bool ) > fun_Pr1696029455l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_763,type,
    hAPP_f1564338425l_bool: ( fun_fu353693025l_bool * fun_Pr1964766157l_bool ) > fun_fu793340337l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_764,type,
    hAPP_f1734997943l_bool: ( fun_fu1668998687l_bool * fun_Pr730004340l_bool ) > fun_fu1422346070l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_765,type,
    hAPP_f2052909183l_bool: ( fun_fu1389374689l_bool * fun_Pr164273135l_bool ) > fun_fu1275216525l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_766,type,
    hAPP_f861853459l_bool: ( fun_fu1375444597l_bool * fun_Pr597144499l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_767,type,
    hAPP_f1525114763l_bool: ( fun_fu2032275391l_bool * fun_Pr597144499l_bool ) > fun_Pr859510977l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_768,type,
    hAPP_f1427871743l_bool: ( fun_fu1295272801l_bool * fun_Pr1689395469l_bool ) > fun_Pr164273135l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_769,type,
    hAPP_f1082373989l_bool: ( fun_fu1848982215l_bool * fun_Pr1643560277on_val ) > fun_Pr1689395469l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_770,type,
    hAPP_f1776493709l_bool: ( fun_fu450552565l_bool * fun_Pr2075414204on_val ) > fun_Pr730004340l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Oc,type,
    hAPP_f82569901l_bool: ( fun_fu1983565583l_bool * fun_Pr1336948301r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Oc_771,type,
    hAPP_f1466436665r_bool: ( fun_fu737201517r_bool * fun_Pr1336948301r_bool ) > fun_ex736065929r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Oc_772,type,
    hAPP_f2091926485r_bool: ( fun_fu1561705993r_bool * fun_Pr1336948301r_bool ) > fun_li221477r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Oc_773,type,
    hAPP_f380623487l_bool: ( fun_fu932873447l_bool * fun_Pr1777565493l_bool ) > fun_fu1302866591l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Oc_774,type,
    hAPP_f479632753l_bool: ( fun_fu1410993183l_bool * fun_Pr382120745r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Oc_775,type,
    hAPP_f1780084320l_bool: ( fun_fu1984450498l_bool * fun_Pr227936640r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Oc_776,type,
    hAPP_f1044627221r_bool: ( fun_fu2033315657r_bool * fun_Pr227936640r_bool ) > fun_li1024794712r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Oc_777,type,
    hAPP_f1874697593r_bool: ( fun_fu614077613r_bool * fun_Pr227936640r_bool ) > fun_Pr46158268r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Oc_778,type,
    hAPP_f1715733055l_bool: ( fun_fu1773666471l_bool * fun_Pr1982141813l_bool ) > fun_fu821374111l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__,type,
    hAPP_f2106398425l_bool: ( fun_fu2033725063l_bool * fun_Pr565113489r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___779,type,
    hAPP_f335969926r_bool: ( fun_fu667589486r_bool * fun_Pr565113489r_bool ) > fun_list_char_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___780,type,
    hAPP_f344506159r_bool: ( fun_fu1278980701r_bool * fun_Pr565113489r_bool ) > fun_li860735411r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___781,type,
    hAPP_f112056853r_bool: ( fun_fu941389053r_bool * fun_Pr565113489r_bool ) > fun_Pr565113489r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___782,type,
    hAPP_f644972157l_bool: ( fun_fu164328875l_bool * fun_Pr565113489r_bool ) > fun_Pr1475963649l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___783,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___784,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___785,type,
    hAPP_f1744304433on_val: ( fun_fu766397407on_val * fun_Pr806764899on_val ) > fun_fu1153772003on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___786,type,
    hAPP_f749178132l_bool: ( fun_fu1361433468l_bool * fun_Pr806764899on_val ) > fun_fu962543074l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___787,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___788,type,
    hAPP_f1146435765on_val: ( fun_fu1153772003on_val * fun_Pr806764899on_val ) > produc2104958055on_val ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___789,type,
    hAPP_f144783951l_bool: ( fun_fu363313207l_bool * fun_Pr534396731l_bool ) > fun_fu453549301l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___790,type,
    hAPP_f1876889431r_bool: ( fun_fu1782878143r_bool * fun_Pr534396731l_bool ) > fun_fu941389053r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_It,type,
    hAPP_f1134950784l_bool: ( fun_fu962543074l_bool * fun_Pr315804320l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_It_791,type,
    hAPP_f2080627739l_bool: ( fun_fu1554319823l_bool * fun_Pr315804320l_bool ) > fun_li823162622l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_It_792,type,
    hAPP_f1579743228l_bool: ( fun_fu989986782l_bool * fun_Pr315804320l_bool ) > fun_fu177229913l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_It_793,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_794,type,
    hAPP_f919000597l_bool: ( fun_fu124510717l_bool * fun_Pr1372407413l_bool ) > fun_fu1263594869l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I,type,
    hAPP_f515912112l_bool: ( fun_fu754983186l_bool * fun_Pr1861226704r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_795,type,
    hAPP_f2025561243r_bool: ( fun_fu1567715023r_bool * fun_Pr1861226704r_bool ) > fun_li522008110r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_796,type,
    hAPP_f1666729379r_bool: ( fun_fu1786144261r_bool * fun_Pr1861226704r_bool ) > fun_Pr1861226704r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_797,type,
    hAPP_f561246575l_bool: ( fun_fu6617763l_bool * fun_Pr1861226704r_bool ) > fun_Pr1882154498l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_798,type,
    hAPP_f658521820r_bool: ( fun_fu2134889022r_bool * fun_Pr1861226704r_bool ) > fun_Pr1898949769r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_799,type,
    hAPP_f1020753317r_bool: ( fun_fu1097435533r_bool * fun_Pr2054894453l_bool ) > fun_fu1786144261r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_800,type,
    hAPP_f937861397l_bool: ( fun_fu1225586941l_bool * fun_Pr2054894453l_bool ) > fun_fu696652149l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_801,type,
    hAPP_f483496539l_bool: ( fun_fu1338423817l_bool * fun_Pr70170387r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_802,type,
    hAPP_f1209019955r_bool: ( fun_fu1396152417r_bool * fun_Pr70170387r_bool ) > fun_li1960983605r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_803,type,
    hAPP_f1853572245r_bool: ( fun_fu1216816765r_bool * fun_Pr70170387r_bool ) > fun_Pr70170387r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_804,type,
    hAPP_f1985672189l_bool: ( fun_fu2049369131l_bool * fun_Pr70170387r_bool ) > fun_Pr1361196031l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_805,type,
    hAPP_f279818502r_bool: ( fun_fu873633006r_bool * fun_Pr70170387r_bool ) > fun_Pr571271812r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_806,type,
    hAPP_f1933376467r_bool: ( fun_fu903908411r_bool * fun_Pr1752471359l_bool ) > fun_fu1216816765r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_807,type,
    hAPP_f1937828171l_bool: ( fun_fu176695091l_bool * fun_Pr1752471359l_bool ) > fun_fu748506869l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_808,type,
    hAPP_f2050077417l_bool: ( fun_fu1008682827l_bool * fun_Pr1898949769r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_809,type,
    hAPP_f719350875r_bool: ( fun_fu82046351r_bool * fun_Pr1898949769r_bool ) > fun_li485148903r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_810,type,
    hAPP_f764724814r_bool: ( fun_fu52588976r_bool * fun_Pr1898949769r_bool ) > fun_Pr1669461698r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_811,type,
    hAPP_f454222487r_bool: ( fun_fu1928247679r_bool * fun_Pr655735548l_bool ) > fun_fu2134889022r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_812,type,
    hAPP_f251669717l_bool: ( fun_fu136853693l_bool * fun_Pr1572485173l_bool ) > fun_fu1331594741l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_I_813,type,
    hAPP_f1107475085l_bool: ( fun_fu696652149l_bool * fun_Pr880942020t_char ) > fun_Pr655735548l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__List__Olis,type,
    hAPP_f433445541l_bool: ( fun_fu880361043l_bool * fun_Pr306783325y_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__,type,
    hAPP_f1746574980l_bool: ( fun_fu184232242l_bool * fun_Pr46158268r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc___814,type,
    hAPP_f2071340985r_bool: ( fun_fu1122234343r_bool * fun_Pr46158268r_bool ) > fun_li887890578r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc___815,type,
    hAPP_f1298720864r_bool: ( fun_fu848650568r_bool * fun_Pr46158268r_bool ) > fun_Pr827765831r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc___816,type,
    hAPP_f1707979241r_bool: ( fun_fu839442891r_bool * fun_Pr402119737l_bool ) > fun_fu614077613r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc___817,type,
    hAPP_f693085049l_bool: ( fun_fu7682913l_bool * fun_Pr1758548753l_bool ) > fun_fu1167149685l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc___818,type,
    hAPP_f1233028029l_bool: ( fun_fu821374111l_bool * fun_Pr141094017t_char ) > fun_Pr402119737l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc___819,type,
    hAPP_f1419180947r_bool: ( fun_fu1497625339r_bool * fun_Pr665774896l_bool ) > fun_fu873633006r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc___820,type,
    hAPP_f1239832973l_bool: ( fun_fu748506869l_bool * fun_Pr165123960t_char ) > fun_Pr665774896l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oe,type,
    hAPP_f1314764175l_bool: ( fun_fu1054881085l_bool * fun_Pr827765831r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oe_821,type,
    hAPP_f1724656343r_bool: ( fun_fu243812799r_bool * fun_Pr827765831r_bool ) > fun_ex736065929r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oe_822,type,
    hAPP_f1051205629r_bool: ( fun_fu923263787r_bool * fun_Pr827765831r_bool ) > fun_li826105035r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oe_823,type,
    hAPP_f225832321r_bool: ( fun_fu1034987497r_bool * fun_Pr1869680796l_bool ) > fun_fu848650568r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oe_824,type,
    hAPP_f1612138403l_bool: ( fun_fu1687349387l_bool * fun_Pr1253690279l_bool ) > fun_fu1082830261l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oe_825,type,
    hAPP_f921434893l_bool: ( fun_fu1167149685l_bool * fun_Pr1504659044t_char ) > fun_Pr1869680796l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__List__Ol,type,
    hAPP_f348753975l_bool: ( fun_fu58576357l_bool * fun_Pr1618624239l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__,type,
    hAPP_f288221747l_bool: ( fun_fu654219233l_bool * fun_Pr263169771y_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc___826,type,
    hAPP_f1161798306l_bool: ( fun_fu1272536068l_bool * fun_Pr1669461698r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc___827,type,
    hAPP_f306469557r_bool: ( fun_fu34004457r_bool * fun_Pr1669461698r_bool ) > fun_li1305328058r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc___828,type,
    hAPP_f605643693r_bool: ( fun_fu1141418255r_bool * fun_Pr1669461698r_bool ) > fun_li1070812648r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc___829,type,
    hAPP_f1410576713r_bool: ( fun_fu935579185r_bool * fun_Pr1021761724l_bool ) > fun_fu52588976r_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc___830,type,
    hAPP_f1847120981l_bool: ( fun_fu851447613l_bool * fun_Pr1300573173l_bool ) > fun_fu2068145461l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc___831,type,
    hAPP_f2037329933l_bool: ( fun_fu1331594741l_bool * fun_Pr32647428t_char ) > fun_Pr1021761724l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc___832,type,
    hAPP_f1748390065l_bool: ( fun_fu951593311l_bool * fun_Pr2024675945r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__HOL__Obo,type,
    hAPP_f2028441009l_bool: ( fun_fu1210184799l_bool * fun_Pr2081272681l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__HOL__Obo_833,type,
    hAPP_f1728541444l_bool: ( fun_fu57453362l_bool * fun_Pr2081272681l_bool ) > fun_val_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__HOL__Obo_834,type,
    hAPP_f198821591l_bool: ( fun_fu166563973l_bool * fun_Pr2081272681l_bool ) > fun_val_fun_val_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__fun_Itc_,type,
    hAPP_f263393637l_bool: ( fun_fu1248515149l_bool * fun_Pr1856441676l_bool ) > fun_fu559253084l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__fun_Itc__835,type,
    hAPP_f183649339l_bool: ( fun_fu1127606179l_bool * fun_Pr1095905387l_bool ) > fun_fu1915524369l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__prod_Itc,type,
    hAPP_f1646911885l_bool: ( fun_fu847194997l_bool * fun_Pr1615326228al_val ) > fun_Pr1856441676l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mt,type,
    hAPP_f1661305905l_bool: ( fun_fu280400607l_bool * fun_Pr673659369l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc_,type,
    hAPP_f966411375l_bool: ( fun_fu1493047761l_bool * fun_Pr1696029455l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__836,type,
    hAPP_f33142364l_bool: ( fun_fu2077402686l_bool * fun_Pr1696029455l_bool ) > fun_fu1693644106l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__837,type,
    hAPP_f47713631l_bool: ( fun_fu1076543251l_bool * fun_Pr1696029455l_bool ) > fun_fu100249073l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__838,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__839,type,
    hAPP_f101237475l_bool: ( fun_fu1525621451l_bool * fun_Pr966331573l_bool ) > fun_fu237977731l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__840,type,
    hAPP_f1467537159l_bool: ( fun_fu76765545l_bool * fun_Pr228183746l_bool ) > fun_fu173338434l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__841,type,
    hAPP_f1168269397l_bool: ( fun_fu2070930493l_bool * fun_Pr2070293557l_bool ) > fun_fu1608823157l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__842,type,
    hAPP_f826324045l_bool: ( fun_fu1816861237l_bool * fun_Pr231134077on_val ) > fun_Pr966331573l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__843,type,
    hAPP_f375531599l_bool: ( fun_fu793340337l_bool * fun_Pr254484106on_val ) > fun_Pr228183746l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__844,type,
    hAPP_f1754555101l_bool: ( fun_fu633905803l_bool * fun_Pr442654869l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__,type,
    hAPP_f983152497l_bool: ( fun_fu417665055l_bool * fun_Pr369549609l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__O,type,
    hAPP_f126136681l_bool: ( fun_fu908926231l_bool * fun_Pr897334561l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__S,type,
    hAPP_f1453283057l_bool: ( fun_fu1001966495l_bool * fun_Pr691271849l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__S_845,type,
    hAPP_f973018659l_bool: ( fun_fu1055869009l_bool * fun_Pr691271849l_bool ) > fun_Pr680585871l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__S_846,type,
    hAPP_f1200025813l_bool: ( fun_fu1965088899l_bool * fun_Pr691271849l_bool ) > fun_Pr633696065l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__S_847,type,
    hAPP_f2036784149l_bool: ( fun_fu874440573l_bool * fun_Pr691271849l_bool ) > fun_Pr691271849l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__S_848,type,
    hAPP_f379976829l_bool: ( fun_fu1140187947l_bool * fun_Pr691271849l_bool ) > fun_Pr1041696489l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__S_849,type,
    hAPP_f1510763001l_bool: ( fun_fu2017766753l_bool * fun_Pr243362283l_bool ) > fun_fu1839421007l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__S_850,type,
    hAPP_f1720452391l_bool: ( fun_fu105086607l_bool * fun_Pr243362283l_bool ) > fun_fu874440573l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__L,type,
    hAPP_f458849545l_bool: ( fun_fu1544014007l_bool * fun_Pr859510977l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__L_851,type,
    hAPP_f1317381998l_bool: ( fun_fu1422346070l_bool * fun_Pr859510977l_bool ) > fun_Pr248118298l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__L_852,type,
    hAPP_f447422815l_bool: ( fun_fu1275216525l_bool * fun_Pr859510977l_bool ) > fun_Pr597144499l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__L_853,type,
    hAPP_f1856968213l_bool: ( fun_fu884927229l_bool * fun_Pr859510977l_bool ) > fun_Pr859510977l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__L_854,type,
    hAPP_f914702973l_bool: ( fun_fu1126530987l_bool * fun_Pr859510977l_bool ) > fun_Pr2072119505l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__L_855,type,
    hAPP_f810261999l_bool: ( fun_fu917063127l_bool * fun_Pr1441107355l_bool ) > fun_fu450552565l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__L_856,type,
    hAPP_f677078775l_bool: ( fun_fu916360031l_bool * fun_Pr1441107355l_bool ) > fun_fu884927229l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__,type,
    hAPP_f595031537l_bool: ( fun_fu1661458591l_bool * fun_Pr908866473r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc___857,type,
    hAPP_f528956081l_bool: ( fun_fu1710531423l_bool * fun_Pr1895638121r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M,type,
    hAPP_f851858423l_bool: ( fun_fu9090469l_bool * fun_Pr1336847023r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_858,type,
    hAPP_f665343921l_bool: ( fun_fu1259600479l_bool * fun_Pr235369833l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_859,type,
    hAPP_f538118321l_bool: ( fun_fu625235295l_bool * fun_Pr981088873r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_860,type,
    hAPP_f272179441l_bool: ( fun_fu1579426719l_bool * fun_Pr1538825897r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__,type,
    hAPP_f258424141l_bool: ( fun_fu1794770171l_bool * fun_Pr1728267013r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc,type,
    hAPP_f1145574243l_bool: ( fun_fu365643025l_bool * fun_Pr1890037787r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__O,type,
    hAPP_f126445617l_bool: ( fun_fu1018437855l_bool * fun_Pr286306793r_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc,type,
    hAPP_f2129782055l_bool: ( fun_fu1869898965l_bool * fun_Pr832147423l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Oo,type,
    hAPP_f1297673713l_bool: ( fun_fu1598647967l_bool * fun_Pr693020585l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Ol,type,
    hAPP_f1261741735l_bool: ( fun_fu850739797l_bool * fun_Pr903661919l_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__O,type,
    hAPP_f1980787287l_bool: ( fun_fu1380660229l_bool * fun_Pr302334223l_bool ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Obop_Mtc__Expr__Obop_J_000tc__HOL__Obool,type,
    hAPP_P1085566419p_bool: ( fun_Pr851759157p_bool * product_prod_bop_bop ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Obop_Mtc__Expr__Obop_J_000tc__fun_Itc__fun_Itc_,type,
    hAPP_P1034346913l_bool: ( fun_Pr583124355l_bool * product_prod_bop_bop ) > fun_fu318834731l_bool ).

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_861,type,
    hAPP_P1653675595l_bool: ( fun_Pr285446189l_bool * produc1645268488al_val ) > fun_fu1654159552l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__Ova_862,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_863,type,
    hAPP_P2123720426al_val: ( fun_Pr1899415884al_val * produc1645268488al_val ) > produc630464863al_val ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt,type,
    hAPP_P1632759357r_bool: ( fun_Pr136267935r_bool * produc2048519645t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_864,type,
    hAPP_P1860450421l_bool: ( fun_Pr430256983l_bool * produc2048519645t_char ) > fun_fu366820245l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_865,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_866,type,
    hAPP_P2015860941l_bool: ( fun_Pr1751899445l_bool * produc124828825on_val ) > fun_fu1845830481l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_867,type,
    hAPP_P638161699l_bool: ( fun_Pr973229009l_bool * produc124828825on_val ) > fun_fu1001966495l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_868,type,
    hAPP_P609938901l_bool: ( fun_Pr519971843l_bool * produc124828825on_val ) > fun_fu1055869009l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_869,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_870,type,
    hAPP_P527298901l_bool: ( fun_Pr2043111299l_bool * produc124828825on_val ) > fun_Pr973229009l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_871,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_872,type,
    hAPP_P1886180715on_val: ( fun_Pr714818201on_val * produc124828825on_val ) > produc1102272487on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str,type,
    hAPP_P499022727r_bool: ( fun_Pr716652265r_bool * produc91527719t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_873,type,
    hAPP_P53416969l_bool: ( fun_Pr15022187l_bool * produc91527719t_char ) > fun_fu814665183l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_874,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_875,type,
    hAPP_P483670507l_bool: ( fun_Pr1964766157l_bool * produc2061676504on_val ) > fun_fu749996688l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_876,type,
    hAPP_P88824722l_bool: ( fun_Pr730004340l_bool * produc2061676504on_val ) > fun_fu1544014007l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_877,type,
    hAPP_P768428603l_bool: ( fun_Pr164273135l_bool * produc2061676504on_val ) > fun_fu1422346070l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_878,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_879,type,
    hAPP_P76086873l_bool: ( fun_Pr1689395469l_bool * produc2061676504on_val ) > fun_Pr730004340l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_880,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_881,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_882,type,
    hAPP_P1293136973l_bool: ( fun_Pr1777565493l_bool * produc809539159t_char ) > fun_fu1983565583l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_883,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_884,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_885,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_886,type,
    hAPP_P476431815r_bool: ( fun_Pr382120745r_bool * produc1200003175t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_887,type,
    hAPP_P153687689l_bool: ( fun_Pr1499304939l_bool * produc1200003175t_char ) > fun_fu1410993183l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_888,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_889,type,
    hAPP_P1472618637l_bool: ( fun_Pr1982141813l_bool * produc1285161482t_char ) > fun_fu1984450498l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_890,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_891,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_892,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_893,type,
    hAPP_P1457625805l_bool: ( fun_Pr1475963649l_bool * produc1278157519t_char ) > fun_bool_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc_894,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_895,type,
    hAPP_P1180869721l_bool: ( fun_Pr534396731l_bool * produc1278157519t_char ) > fun_fu2033725063l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc_896,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_897,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__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_898,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_899,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_900,type,
    hAPP_P1217996045l_bool: ( fun_Pr1372407413l_bool * produc639455274on_val ) > fun_fu962543074l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I_901,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_902,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_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__903,type,
    hAPP_P1552072218l_bool: ( fun_Pr1882154498l_bool * produc1971331930t_char ) > fun_bool_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__904,type,
    hAPP_P205570445l_bool: ( fun_Pr2054894453l_bool * produc1971331930t_char ) > fun_fu754983186l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__905,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__906,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__907,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__908,type,
    hAPP_P415257547l_bool: ( fun_Pr1361196031l_bool * produc1013743697t_char ) > fun_bool_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__909,type,
    hAPP_P7095645l_bool: ( fun_Pr1752471359l_bool * produc1013743697t_char ) > fun_fu1338423817l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__910,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__911,type,
    hAPP_P780018708l_bool: ( fun_Pr655735548l_bool * produc952412819t_char ) > fun_fu754983186l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__912,type,
    hAPP_P1517699917l_bool: ( fun_Pr1572485173l_bool * produc952412819t_char ) > fun_fu1008682827l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__913,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__914,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__915,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__List__Olist_Itc__Ty,type,
    hAPP_P1574824955y_bool: ( fun_Pr306783325y_bool * produc1420746395ist_ty ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__List__Olist_Itc__Ty_916,type,
    hAPP_P1019319281l_bool: ( fun_Pr1983900371l_bool * produc1420746395ist_ty ) > fun_fu880361043l_bool ).

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

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Oli_917,type,
    hAPP_P1562529797l_bool: ( fun_Pr402119737l_bool * produc220283002t_char ) > fun_fu1984450498l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Oli_918,type,
    hAPP_P1198052655l_bool: ( fun_Pr1758548753l_bool * produc220283002t_char ) > fun_fu184232242l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Oli_919,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_920,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_921,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_922,type,
    hAPP_P1383068750l_bool: ( fun_Pr665774896l_bool * produc1025221954t_char ) > fun_fu1338423817l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__Type__Oty_923,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_924,type,
    hAPP_P2028292026l_bool: ( fun_Pr1869680796l_bool * produc662261637t_char ) > fun_fu184232242l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__L_925,type,
    hAPP_P845017029l_bool: ( fun_Pr1253690279l_bool * produc662261637t_char ) > fun_fu1054881085l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__L_926,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_927,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_928,type,
    hAPP_P1220989409t_char: ( fun_Pr1620417347t_char * produc662261637t_char ) > produc1826280281t_char ).

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

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__List__Olist_Itc___929,type,
    hAPP_P1033205013l_bool: ( fun_Pr1642705399l_bool * produc753553453st_val ) > fun_fu58576357l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__O,type,
    hAPP_P2053453961y_bool: ( fun_Pr263169771y_bool * produc450000425har_ty ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__O_930,type,
    hAPP_P569585933l_bool: ( fun_Pr1345558511l_bool * produc450000425har_ty ) > fun_fu654219233l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__O_931,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_932,type,
    hAPP_P1418247892l_bool: ( fun_Pr1021761724l_bool * produc2146869324t_char ) > fun_fu1008682827l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__O_933,type,
    hAPP_P1327510541l_bool: ( fun_Pr1300573173l_bool * produc2146869324t_char ) > fun_fu1272536068l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__O_934,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_935,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_936,type,
    hAPP_P1247668062t_char: ( fun_Pr1795545228t_char * produc2146869324t_char ) > produc494726439t_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__O_937,type,
    hAPP_P1926698759r_bool: ( fun_Pr2024675945r_bool * produc244676007t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__O_938,type,
    hAPP_P1503283977l_bool: ( fun_Pr269504363l_bool * produc244676007t_char ) > fun_fu951593311l_bool ).

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__fun_It,type,
    hAPP_P1614880106l_bool: ( fun_Pr1856441676l_bool * product_prod_val_val ) > fun_fu1654159552l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_Itc__fun_It_939,type,
    hAPP_P530382601l_bool: ( fun_Pr1095905387l_bool * product_prod_val_val ) > fun_fu1210184799l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_Itc__prod_I,type,
    hAPP_P1874979071al_val: ( fun_Pr1703971251al_val * product_prod_val_val ) > fun_Pr1637618473al_val ).

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

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

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option,type,
    hAPP_P468446343l_bool: ( fun_Pr673659369l_bool * produc1127210791on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option_940,type,
    hAPP_P1878549513l_bool: ( fun_Pr1364095339l_bool * produc1127210791on_val ) > fun_fu280400607l_bool ).

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_941,type,
    hAPP_P1609485901l_bool: ( fun_Pr966331573l_bool * produc12694297on_val ) > fun_fu1845830481l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_942,type,
    hAPP_P594889876l_bool: ( fun_Pr228183746l_bool * produc12694297on_val ) > fun_fu749996688l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_943,type,
    hAPP_P998768845l_bool: ( fun_Pr2070293557l_bool * produc12694297on_val ) > fun_fu1493047761l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_944,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_945,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_946,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_947,type,
    hAPP_P291613419on_val: ( fun_Pr84821017on_val * produc12694297on_val ) > produc409205479on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_948,type,
    hAPP_P2077557811l_bool: ( fun_Pr442654869l_bool * produc644889299on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_949,type,
    hAPP_P1679186017l_bool: ( fun_Pr519703875l_bool * produc644889299on_val ) > fun_fu633905803l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M,type,
    hAPP_P504978887l_bool: ( fun_Pr369549609l_bool * produc2104958055on_val ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_950,type,
    hAPP_P1953134729l_bool: ( fun_Pr1110793451l_bool * produc2104958055on_val ) > fun_fu417665055l_bool ).

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__Obop_Mtc__prod_Itc__Value__Oval_Mtc___951,type,
    hAPP_P982127993l_bool: ( fun_Pr358512219l_bool * produc630464863al_val ) > fun_fu908926231l_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_952,type,
    hAPP_P1402001845l_bool: ( fun_Pr1041696489l_bool * produc1102272487on_val ) > fun_bool_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_953,type,
    hAPP_P1303341961l_bool: ( fun_Pr243362283l_bool * produc1102272487on_val ) > fun_fu1001966495l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_954,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_955,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_956,type,
    hAPP_P895943837l_bool: ( fun_Pr2072119505l_bool * produc430140671on_val ) > fun_bool_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis_957,type,
    hAPP_P126004409l_bool: ( fun_Pr1441107355l_bool * produc430140671on_val ) > fun_fu1544014007l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis_958,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_959,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_960,type,
    hAPP_P1862681481l_bool: ( fun_Pr253198059l_bool * produc1534059751t_char ) > fun_fu1661458591l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O_961,type,
    hAPP_P824029447r_bool: ( fun_Pr1895638121r_bool * produc349695911t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O_962,type,
    hAPP_P325013257l_bool: ( fun_Pr2058021739l_bool * produc349695911t_char ) > fun_fu1710531423l_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__963,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__List__964,type,
    hAPP_P786771093l_bool: ( fun_Pr180031351l_bool * produc1350825965t_char ) > fun_fu9090469l_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__fun_I_965,type,
    hAPP_P502294281l_bool: ( fun_Pr700359275l_bool * produc87279271on_val ) > fun_fu1259600479l_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__966,type,
    hAPP_P1390376713l_bool: ( fun_Pr81279339l_bool * produc84451751t_char ) > fun_fu625235295l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod__967,type,
    hAPP_P929449287r_bool: ( fun_Pr1538825897r_bool * produc740765671t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod__968,type,
    hAPP_P396425609l_bool: ( fun_Pr740107499l_bool * produc740765671t_char ) > fun_fu1579426719l_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__Type__Oty_J_Mtc__prod_Itc__969,type,
    hAPP_P409642305l_bool: ( fun_Pr949587491l_bool * produc1406897475t_char ) > fun_fu1794770171l_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__Value__Oval_J_Mtc__Expr__O_970,type,
    hAPP_P2139822957l_bool: ( fun_Pr54558799l_bool * produc1826280281t_char ) > fun_fu365643025l_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__List__Olist_Itc__prod_Itc__List__Olist_Itc__971,type,
    hAPP_P1313790473l_bool: ( fun_Pr1377562219l_bool * produc494726439t_char ) > fun_fu1018437855l_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__Value__Oval_Mtc__Value__Oval_J_Mtc__prod_It_972,type,
    hAPP_P124661l_bool: ( fun_Pr2114942679l_bool * produc800118557al_val ) > fun_fu1869898965l_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__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc_973,type,
    hAPP_P240409993l_bool: ( fun_Pr736615915l_bool * produc409205479on_val ) > fun_fu1598647967l_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__Expr__Oexp_Itc__List__Olist_Itc___974,type,
    hAPP_P1362631157l_bool: ( fun_Pr1043842007l_bool * produc231486621on_val ) > fun_fu850739797l_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__Expr__Oexp_Itc___975,type,
    hAPP_P274544981l_bool: ( fun_Pr1519167543l_bool * produc1466422861on_val ) > fun_fu1380660229l_bool ).

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

tff(sy_c_member_000tc__List__Olist_Itc__String__Ochar_J,type,
    member_list_char: fun_li1362522525l_bool ).

tff(sy_c_member_000tc__Nat__Onat,type,
    member_nat: fun_na1436237685l_bool ).

tff(sy_c_member_000tc__prod_Itc__Expr__Obop_Mtc__Expr__Obop_J,type,
    member978285664op_bop: fun_Pr583124355l_bool ).

tff(sy_c_member_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__O,type,
    member1417904245al_val: fun_Pr285446189l_bool ).

tff(sy_c_member_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_,type,
    member1199939018t_char: fun_Pr430256983l_bool ).

tff(sy_c_member_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J__976,type,
    member840932460on_val: fun_Pr1751899445l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__S,type,
    member894971540t_char: fun_Pr15022187l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__S_977,type,
    member1972431429on_val: fun_Pr1964766157l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J,type,
    member1840112042t_char: fun_Pr1777565493l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_978,type,
    member817832404t_char: fun_Pr1499304939l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_979,type,
    member133545693t_char: fun_Pr1982141813l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_I,type,
    member1251428284t_char: fun_Pr534396731l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod,type,
    member1542417277on_val: fun_Pr1372407413l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__Lis,type,
    member1467889965t_char: fun_Pr2054894453l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__Lis_980,type,
    member1601084734t_char: fun_Pr1752471359l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__Lis_981,type,
    member1771544038t_char: fun_Pr1572485173l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__List__Olist_Itc__,type,
    member104734088ist_ty: fun_Pr1983900371l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__O,type,
    member140606439t_char: fun_Pr1758548753l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc_,type,
    member699351154t_char: fun_Pr1253690279l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__List__Olist_Itc,type,
    member273646106st_val: fun_Pr1642705399l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String_,type,
    member520253462har_ty: fun_Pr1345558511l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__982,type,
    member1379348767t_char: fun_Pr1300573173l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__983,type,
    member1580476948t_char: fun_Pr269504363l_bool ).

tff(sy_c_member_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J,type,
    member649088532al_val: fun_Pr1095905387l_bool ).

tff(sy_c_member_000tc__prod_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Opti,type,
    member490182804on_val: fun_Pr1364095339l_bool ).

tff(sy_c_member_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I,type,
    member763590124on_val: fun_Pr2070293557l_bool ).

tff(sy_c_member_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_984,type,
    member1337019328on_val: fun_Pr519703875l_bool ).

tff(sy_c_member_000tc__prod_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J,type,
    member781783252on_val: fun_Pr1110793451l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc,type,
    member1732271180al_val: fun_Pr358512219l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__,type,
    member773094996on_val: fun_Pr243362283l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol,type,
    member875476972on_val: fun_Pr1441107355l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String_,type,
    member1999287380t_char: fun_Pr253198059l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__985,type,
    member1420286996t_char: fun_Pr2058021739l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis,type,
    member794220506t_char: fun_Pr180031351l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun,type,
    member1322055188on_val: fun_Pr700359275l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__pro,type,
    member162552852t_char: fun_Pr81279339l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__pro_986,type,
    member1607118676t_char: fun_Pr740107499l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_It,type,
    member125098544t_char: fun_Pr949587491l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr_,type,
    member1161907014t_char: fun_Pr54558799l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_It,type,
    member1551446420t_char: fun_Pr1377562219l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__prod_,type,
    member837208074al_val: fun_Pr2114942679l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_I,type,
    member563141460on_val: fun_Pr736615915l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
    member808015754on_val: fun_Pr1043842007l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc,type,
    member88670778on_val: fun_Pr1519167543l_bool ).

tff(sy_v_E____,type,
    e: fun_li688206603ion_ty ).

tff(sy_v_P,type,
    p: list_P1999446415t_char ).

tff(sy_v_T_H____,type,
    t: ty ).

tff(sy_v_T____,type,
    t_1: ty ).

tff(sy_v_V____,type,
    v_1: 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 ).

tff(sy_v_v_H____,type,
    v_2: val ).

tff(sy_v_v____,type,
    v: val ).

%----Relevant facts (1200)
tff(fact_0_InitBlockRed_I3_J,axiom,
    hAPP_l207779698on_val(l_a,v_1) = hAPP_val_option_val(some_val,v_2) ).

tff(fact_1_InitBlockRed_I1_J,axiom,
    hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),fun_up1149430426on_val(la,v_1,hAPP_val_option_val(some_val,v))))),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_2_fun__upd__triv,axiom,
    ! [F_1: fun_li1432931796on_val,X_2: list_char] : fun_up1149430426on_val(F_1,X_2,hAPP_l207779698on_val(F_1,X_2)) = F_1 ).

tff(fact_3_fun__upd__triv,axiom,
    ! [F_1: fun_li688206603ion_ty,X_2: list_char] : fun_up424764369ion_ty(F_1,X_2,hAPP_l512744617ion_ty(F_1,X_2)) = F_1 ).

tff(fact_4_fun__upd__triv,axiom,
    ! [F_1: fun_na939144002on_val,X_2: nat] : fun_up2041264236on_val(F_1,X_2,hAPP_n546249108on_val(F_1,X_2)) = F_1 ).

tff(fact_5_fun__upd__triv,axiom,
    ! [F_1: fun_Pr806764899on_val,X_2: produc1278157519t_char] : fun_up204312361on_val(F_1,X_2,hAPP_P2094403585on_val(F_1,X_2)) = F_1 ).

tff(fact_6_assms,axiom,
    hBOOL(wf_pro755087577t_char(wf_J_mdecl,p)) ).

tff(fact_7_map__upd__Some__unfold,axiom,
    ! [M_1: fun_li1432931796on_val,A: list_char,B: val,X_2: list_char,Y_2: val] :
      ( ( hAPP_l207779698on_val(fun_up1149430426on_val(M_1,A,hAPP_val_option_val(some_val,B)),X_2) = hAPP_val_option_val(some_val,Y_2) )
    <=> ( ( ( X_2 = A )
          & ( B = Y_2 ) )
        | ( ( X_2 != A )
          & ( hAPP_l207779698on_val(M_1,X_2) = hAPP_val_option_val(some_val,Y_2) ) ) ) ) ).

tff(fact_8_map__upd__Some__unfold,axiom,
    ! [M_1: fun_li688206603ion_ty,A: list_char,B: ty,X_2: list_char,Y_2: ty] :
      ( ( hAPP_l512744617ion_ty(fun_up424764369ion_ty(M_1,A,hAPP_ty_option_ty(some_ty,B)),X_2) = hAPP_ty_option_ty(some_ty,Y_2) )
    <=> ( ( ( X_2 = A )
          & ( B = Y_2 ) )
        | ( ( X_2 != A )
          & ( hAPP_l512744617ion_ty(M_1,X_2) = hAPP_ty_option_ty(some_ty,Y_2) ) ) ) ) ).

tff(fact_9_map__upd__Some__unfold,axiom,
    ! [M_1: fun_na939144002on_val,A: nat,B: produc639455274on_val,X_2: nat,Y_2: produc639455274on_val] :
      ( ( hAPP_n546249108on_val(fun_up2041264236on_val(M_1,A,hAPP_P1510515380on_val(some_P948696889on_val,B)),X_2) = hAPP_P1510515380on_val(some_P948696889on_val,Y_2) )
    <=> ( ( ( X_2 = A )
          & ( B = Y_2 ) )
        | ( ( X_2 != A )
          & ( hAPP_n546249108on_val(M_1,X_2) = hAPP_P1510515380on_val(some_P948696889on_val,Y_2) ) ) ) ) ).

tff(fact_10_map__upd__Some__unfold,axiom,
    ! [M_1: fun_Pr806764899on_val,A: produc1278157519t_char,B: val,X_2: produc1278157519t_char,Y_2: val] :
      ( ( hAPP_P2094403585on_val(fun_up204312361on_val(M_1,A,hAPP_val_option_val(some_val,B)),X_2) = hAPP_val_option_val(some_val,Y_2) )
    <=> ( ( ( X_2 = A )
          & ( B = Y_2 ) )
        | ( ( X_2 != A )
          & ( hAPP_P2094403585on_val(M_1,X_2) = hAPP_val_option_val(some_val,Y_2) ) ) ) ) ).

tff(fact_11_map__upd__triv,axiom,
    ! [T_2: fun_li1432931796on_val,K: list_char,X_2: val] :
      ( ( hAPP_l207779698on_val(T_2,K) = hAPP_val_option_val(some_val,X_2) )
     => ( fun_up1149430426on_val(T_2,K,hAPP_val_option_val(some_val,X_2)) = T_2 ) ) ).

tff(fact_12_map__upd__triv,axiom,
    ! [T_2: fun_li688206603ion_ty,K: list_char,X_2: ty] :
      ( ( hAPP_l512744617ion_ty(T_2,K) = hAPP_ty_option_ty(some_ty,X_2) )
     => ( fun_up424764369ion_ty(T_2,K,hAPP_ty_option_ty(some_ty,X_2)) = T_2 ) ) ).

tff(fact_13_map__upd__triv,axiom,
    ! [T_2: fun_na939144002on_val,K: nat,X_2: produc639455274on_val] :
      ( ( hAPP_n546249108on_val(T_2,K) = hAPP_P1510515380on_val(some_P948696889on_val,X_2) )
     => ( fun_up2041264236on_val(T_2,K,hAPP_P1510515380on_val(some_P948696889on_val,X_2)) = T_2 ) ) ).

tff(fact_14_map__upd__triv,axiom,
    ! [T_2: fun_Pr806764899on_val,K: produc1278157519t_char,X_2: val] :
      ( ( hAPP_P2094403585on_val(T_2,K) = hAPP_val_option_val(some_val,X_2) )
     => ( fun_up204312361on_val(T_2,K,hAPP_val_option_val(some_val,X_2)) = T_2 ) ) ).

tff(fact_15_map__upd__eqD1,axiom,
    ! [M_1: fun_li1432931796on_val,A: list_char,X_2: val,N: fun_li1432931796on_val,Y_2: val] :
      ( ( fun_up1149430426on_val(M_1,A,hAPP_val_option_val(some_val,X_2)) = fun_up1149430426on_val(N,A,hAPP_val_option_val(some_val,Y_2)) )
     => ( X_2 = Y_2 ) ) ).

tff(fact_16_map__upd__eqD1,axiom,
    ! [M_1: fun_li688206603ion_ty,A: list_char,X_2: ty,N: fun_li688206603ion_ty,Y_2: ty] :
      ( ( fun_up424764369ion_ty(M_1,A,hAPP_ty_option_ty(some_ty,X_2)) = fun_up424764369ion_ty(N,A,hAPP_ty_option_ty(some_ty,Y_2)) )
     => ( X_2 = Y_2 ) ) ).

tff(fact_17_map__upd__eqD1,axiom,
    ! [M_1: fun_na939144002on_val,A: nat,X_2: produc639455274on_val,N: fun_na939144002on_val,Y_2: produc639455274on_val] :
      ( ( fun_up2041264236on_val(M_1,A,hAPP_P1510515380on_val(some_P948696889on_val,X_2)) = fun_up2041264236on_val(N,A,hAPP_P1510515380on_val(some_P948696889on_val,Y_2)) )
     => ( X_2 = Y_2 ) ) ).

tff(fact_18_map__upd__eqD1,axiom,
    ! [M_1: fun_Pr806764899on_val,A: produc1278157519t_char,X_2: val,N: fun_Pr806764899on_val,Y_2: val] :
      ( ( fun_up204312361on_val(M_1,A,hAPP_val_option_val(some_val,X_2)) = fun_up204312361on_val(N,A,hAPP_val_option_val(some_val,Y_2)) )
     => ( X_2 = Y_2 ) ) ).

tff(fact_19_InitBlockRed_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),fun_up1149430426on_val(la,v_1,hAPP_val_option_val(some_val,v)))))
     => ( hBOOL(wTrt_1(p,ha,Ea,ea,Ta))
       => ? [T_5: ty] :
            ( hBOOL(wTrt_1(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_20_prod__induct5,axiom,
    ! [X_2: produc1466422861on_val,Pa: fun_Pr302334223l_bool] :
      ( ! [A_1: produc430140671on_val,B_2: produc2061676504on_val,C_4: list_exp_list_char,D_2: fun_na939144002on_val,E_4: 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_2),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,C_4),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,D_2),E_4))))))
     => hBOOL(hAPP_P2028072621l_bool(Pa,X_2)) ) ).

tff(fact_21_prod__induct5,axiom,
    ! [X_2: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
      ( ! [A_1: produc1102272487on_val,B_2: produc124828825on_val,C_4: exp_list_char,D_2: fun_na939144002on_val,E_4: 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_2),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_4),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,D_2),E_4))))))
     => hBOOL(hAPP_P378063101l_bool(Pa,X_2)) ) ).

tff(fact_22_prod__induct5,axiom,
    ! [X_2: produc349695911t_char,Pa: fun_Pr1895638121r_bool] :
      ( ! [A_1: produc1285161482t_char,B_2: list_list_char,C_4: list_ty,D_2: list_val,E_4: 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_2),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,C_4),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,D_2),E_4))))))
     => hBOOL(hAPP_P824029447r_bool(Pa,X_2)) ) ).

tff(fact_23_prod__induct5,axiom,
    ! [X_2: produc84451751t_char,Pa: fun_Pr981088873r_bool] :
      ( ! [A_1: produc1971331930t_char,B_2: list_char,C_4: list_char,D_2: list_P1940453997har_ty,E_4: 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_2),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,C_4),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,D_2),E_4))))))
     => hBOOL(hAPP_P975284999r_bool(Pa,X_2)) ) ).

tff(fact_24_prod__induct5,axiom,
    ! [X_2: produc1013743697t_char,Pa: fun_Pr70170387r_bool] :
      ( ! [A_1: list_char,B_2: list_ty,C_4: ty,D_2: list_list_char,E_4: 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_2),hAPP_P1661798543t_char(hAPP_t1369077401t_char(produc1545444669t_char,C_4),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,D_2),E_4))))))
     => hBOOL(hAPP_P1384137393r_bool(Pa,X_2)) ) ).

tff(fact_25_prod__cases5,axiom,
    ! [Y_2: produc1466422861on_val] :
      ~ ! [A_1: produc430140671on_val,B_2: produc2061676504on_val,C_4: list_exp_list_char,D_2: fun_na939144002on_val,E_4: fun_li1432931796on_val] : Y_2 != hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_2),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,C_4),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,D_2),E_4)))) ).

tff(fact_26_prod__cases5,axiom,
    ! [Y_2: produc231486621on_val] :
      ~ ! [A_1: produc1102272487on_val,B_2: produc124828825on_val,C_4: exp_list_char,D_2: fun_na939144002on_val,E_4: fun_li1432931796on_val] : Y_2 != hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_2),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_4),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,D_2),E_4)))) ).

tff(fact_27_prod__cases5,axiom,
    ! [Y_7: produc349695911t_char] :
      ~ ! [A_1: produc1285161482t_char,B_2: list_list_char,C_4: list_ty,D_2: list_val,E_4: exp_list_char] : Y_7 != hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_2),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,C_4),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,D_2),E_4)))) ).

tff(fact_28_prod__cases5,axiom,
    ! [Y_7: produc84451751t_char] :
      ~ ! [A_1: produc1971331930t_char,B_2: list_char,C_4: list_char,D_2: list_P1940453997har_ty,E_4: list_P341299826t_char] : Y_7 != hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,B_2),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,C_4),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,D_2),E_4)))) ).

tff(fact_29_prod__cases5,axiom,
    ! [Y_7: produc1013743697t_char] :
      ~ ! [A_1: list_char,B_2: list_ty,C_4: ty,D_2: list_list_char,E_4: exp_list_char] : Y_7 != hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),hAPP_P976433298t_char(hAPP_l2048923787t_char(produc2016959032t_char,B_2),hAPP_P1661798543t_char(hAPP_t1369077401t_char(produc1545444669t_char,C_4),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,D_2),E_4)))) ).

tff(fact_30_prod__induct4,axiom,
    ! [X_2: produc1013743697t_char,Pa: fun_Pr70170387r_bool] :
      ( ! [A_1: list_char,B_2: list_ty,C_4: ty,D_2: 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_2),hAPP_P1661798543t_char(hAPP_t1369077401t_char(produc1545444669t_char,C_4),D_2)))))
     => hBOOL(hAPP_P1384137393r_bool(Pa,X_2)) ) ).

tff(fact_31_prod__induct4,axiom,
    ! [X_2: produc1102272487on_val,Pa: fun_Pr691271849l_bool] :
      ( ! [A_1: produc124828825on_val,B_2: exp_list_char,C_4: fun_na939144002on_val,D_2: fun_li1432931796on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_4),D_2)))))
     => hBOOL(hAPP_P282169671l_bool(Pa,X_2)) ) ).

tff(fact_32_prod__induct4,axiom,
    ! [X_2: produc430140671on_val,Pa: fun_Pr859510977l_bool] :
      ( ! [A_1: produc2061676504on_val,B_2: list_exp_list_char,C_4: fun_na939144002on_val,D_2: fun_li1432931796on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,B_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_4),D_2)))))
     => hBOOL(hAPP_P1333315679l_bool(Pa,X_2)) ) ).

tff(fact_33_prod__induct4,axiom,
    ! [X_2: produc1285161482t_char,Pa: fun_Pr227936640r_bool] :
      ( ! [A_1: list_list_char,B_2: list_ty,C_4: list_val,D_2: exp_list_char] : hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_2),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,C_4),D_2)))))
     => hBOOL(hAPP_P92196306r_bool(Pa,X_2)) ) ).

tff(fact_34_prod__induct4,axiom,
    ! [X_2: produc1971331930t_char,Pa: fun_Pr1861226704r_bool] :
      ( ! [A_1: list_char,B_2: list_char,C_4: list_P1940453997har_ty,D_2: 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_2),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,C_4),D_2)))))
     => hBOOL(hAPP_P1680401186r_bool(Pa,X_2)) ) ).

tff(fact_35_prod__induct4,axiom,
    ! [X_2: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
      ( ! [A_1: produc1102272487on_val,B_2: produc124828825on_val,C_4: exp_list_char,D_2: produc12694297on_val] : hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_2),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_4),D_2)))))
     => hBOOL(hAPP_P378063101l_bool(Pa,X_2)) ) ).

tff(fact_36_prod__induct4,axiom,
    ! [X_2: produc630464863al_val,Pa: fun_Pr897334561l_bool] :
      ( ! [A_1: produc1645268488al_val,B_2: bop,C_4: val,D_2: 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_2),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,C_4),D_2)))))
     => hBOOL(hAPP_P738987199l_bool(Pa,X_2)) ) ).

tff(fact_37_prod__induct4,axiom,
    ! [X_2: produc1466422861on_val,Pa: fun_Pr302334223l_bool] :
      ( ! [A_1: produc430140671on_val,B_2: produc2061676504on_val,C_4: list_exp_list_char,D_2: produc12694297on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_2),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,C_4),D_2)))))
     => hBOOL(hAPP_P2028072621l_bool(Pa,X_2)) ) ).

tff(fact_38_prod__induct4,axiom,
    ! [X_2: produc349695911t_char,Pa: fun_Pr1895638121r_bool] :
      ( ! [A_1: produc1285161482t_char,B_2: list_list_char,C_4: list_ty,D_2: produc662261637t_char] : hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_2),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,C_4),D_2)))))
     => hBOOL(hAPP_P824029447r_bool(Pa,X_2)) ) ).

tff(fact_39_prod__induct4,axiom,
    ! [X_2: produc1406897475t_char,Pa: fun_Pr1728267013r_bool] :
      ( ! [A_1: produc220283002t_char,B_2: list_ty,C_4: list_val,D_2: exp_list_char] : hBOOL(hAPP_P1240100515r_bool(Pa,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_2),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,C_4),D_2)))))
     => hBOOL(hAPP_P1240100515r_bool(Pa,X_2)) ) ).

tff(fact_40_prod__induct4,axiom,
    ! [X_2: produc84451751t_char,Pa: fun_Pr981088873r_bool] :
      ( ! [A_1: produc1971331930t_char,B_2: list_char,C_4: list_char,D_2: 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_2),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,C_4),D_2)))))
     => hBOOL(hAPP_P975284999r_bool(Pa,X_2)) ) ).

tff(fact_41_prod__induct4,axiom,
    ! [X_2: produc740765671t_char,Pa: fun_Pr1538825897r_bool] :
      ( ! [A_1: produc952412819t_char,B_2: list_char,C_4: list_P1940453997har_ty,D_2: 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_2),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,C_4),D_2)))))
     => hBOOL(hAPP_P929449287r_bool(Pa,X_2)) ) ).

tff(fact_42_prod__cases4,axiom,
    ! [Y_6: produc1013743697t_char] :
      ~ ! [A_1: list_char,B_2: list_ty,C_4: ty,D_2: produc809539159t_char] : Y_6 != hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),hAPP_P976433298t_char(hAPP_l2048923787t_char(produc2016959032t_char,B_2),hAPP_P1661798543t_char(hAPP_t1369077401t_char(produc1545444669t_char,C_4),D_2))) ).

tff(fact_43_prod__cases4,axiom,
    ! [Y_2: produc1102272487on_val] :
      ~ ! [A_1: produc124828825on_val,B_2: exp_list_char,C_4: fun_na939144002on_val,D_2: fun_li1432931796on_val] : Y_2 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_4),D_2))) ).

tff(fact_44_prod__cases4,axiom,
    ! [Y_2: produc430140671on_val] :
      ~ ! [A_1: produc2061676504on_val,B_2: list_exp_list_char,C_4: fun_na939144002on_val,D_2: fun_li1432931796on_val] : Y_2 != hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,B_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_4),D_2))) ).

tff(fact_45_prod__cases4,axiom,
    ! [Y_6: produc1285161482t_char] :
      ~ ! [A_1: list_list_char,B_2: list_ty,C_4: list_val,D_2: exp_list_char] : Y_6 != hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_2),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,C_4),D_2))) ).

tff(fact_46_prod__cases4,axiom,
    ! [Y_6: produc1971331930t_char] :
      ~ ! [A_1: list_char,B_2: list_char,C_4: list_P1940453997har_ty,D_2: list_P341299826t_char] : Y_6 != hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_2),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,C_4),D_2))) ).

tff(fact_47_prod__cases4,axiom,
    ! [Y_2: produc231486621on_val] :
      ~ ! [A_1: produc1102272487on_val,B_2: produc124828825on_val,C_4: exp_list_char,D_2: produc12694297on_val] : Y_2 != hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_2),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_4),D_2))) ).

tff(fact_48_prod__cases4,axiom,
    ! [Y_6: produc630464863al_val] :
      ~ ! [A_1: produc1645268488al_val,B_2: bop,C_4: val,D_2: val] : Y_6 != hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_1),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,B_2),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,C_4),D_2))) ).

tff(fact_49_prod__cases4,axiom,
    ! [Y_2: produc1466422861on_val] :
      ~ ! [A_1: produc430140671on_val,B_2: produc2061676504on_val,C_4: list_exp_list_char,D_2: produc12694297on_val] : Y_2 != hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_2),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,C_4),D_2))) ).

tff(fact_50_prod__cases4,axiom,
    ! [Y_6: produc349695911t_char] :
      ~ ! [A_1: produc1285161482t_char,B_2: list_list_char,C_4: list_ty,D_2: produc662261637t_char] : Y_6 != hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_2),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,C_4),D_2))) ).

tff(fact_51_prod__cases4,axiom,
    ! [Y_6: produc1406897475t_char] :
      ~ ! [A_1: produc220283002t_char,B_2: list_ty,C_4: list_val,D_2: exp_list_char] : Y_6 != hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_2),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,C_4),D_2))) ).

tff(fact_52_prod__cases4,axiom,
    ! [Y_6: produc84451751t_char] :
      ~ ! [A_1: produc1971331930t_char,B_2: list_char,C_4: list_char,D_2: produc2146869324t_char] : Y_6 != hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,B_2),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,C_4),D_2))) ).

tff(fact_53_prod__cases4,axiom,
    ! [Y_6: produc740765671t_char] :
      ~ ! [A_1: produc952412819t_char,B_2: list_char,C_4: list_P1940453997har_ty,D_2: list_P341299826t_char] : Y_6 != hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_2),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,C_4),D_2))) ).

tff(fact_54_InitBlockRed_I4_J,axiom,
    hBOOL(hAPP_P159683425l_bool(typeSa1917327191_sconf(p,e),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),la))) ).

tff(fact_55_Pair__inject,axiom,
    ! [A_19: list_char,B_5: ty,A_18: list_char,B_4: ty] :
      ( ( hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_19),B_5) = hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_56_Pair__inject,axiom,
    ! [A_19: produc1278157519t_char,B_5: ty,A_18: produc1278157519t_char,B_4: ty] :
      ( ( hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_19),B_5) = hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_57_Pair__inject,axiom,
    ! [A_19: list_char,B_5: produc1025221954t_char,A_18: list_char,B_4: produc1025221954t_char] :
      ( ( hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_19),B_5) = hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_58_Pair__inject,axiom,
    ! [A_19: produc809539159t_char,B_5: produc809539159t_char,A_18: produc809539159t_char,B_4: produc809539159t_char] :
      ( ( hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_19),B_5) = hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_59_Pair__inject,axiom,
    ! [A_19: produc2146869324t_char,B_5: produc2146869324t_char,A_18: produc2146869324t_char,B_4: produc2146869324t_char] :
      ( ( hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_19),B_5) = hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_60_Pair__inject,axiom,
    ! [A_19: produc952412819t_char,B_5: produc952412819t_char,A_18: produc952412819t_char,B_4: produc952412819t_char] :
      ( ( hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_19),B_5) = hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_61_Pair__inject,axiom,
    ! [A_19: produc1971331930t_char,B_5: produc1971331930t_char,A_18: produc1971331930t_char,B_4: produc1971331930t_char] :
      ( ( hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_19),B_5) = hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_62_Pair__inject,axiom,
    ! [A_19: produc662261637t_char,B_5: produc662261637t_char,A_18: produc662261637t_char,B_4: produc662261637t_char] :
      ( ( hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_19),B_5) = hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_63_Pair__inject,axiom,
    ! [A_19: produc220283002t_char,B_5: produc220283002t_char,A_18: produc220283002t_char,B_4: produc220283002t_char] :
      ( ( hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_19),B_5) = hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_64_Pair__inject,axiom,
    ! [A_19: produc1285161482t_char,B_5: produc1285161482t_char,A_18: produc1285161482t_char,B_4: produc1285161482t_char] :
      ( ( hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_19),B_5) = hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_65_Pair__inject,axiom,
    ! [A: produc430140671on_val,B: produc430140671on_val,A_3: produc430140671on_val,B_3: produc430140671on_val] :
      ( ( hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A),B) = hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_3),B_3) )
     => ~ ( ( A = A_3 )
         => ( B != B_3 ) ) ) ).

tff(fact_66_Pair__inject,axiom,
    ! [A_19: product_prod_val_val,B_5: product_prod_val_val,A_18: product_prod_val_val,B_4: product_prod_val_val] :
      ( ( hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_19),B_5) = hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_67_Pair__inject,axiom,
    ! [A_19: produc1645268488al_val,B_5: produc1645268488al_val,A_18: produc1645268488al_val,B_4: produc1645268488al_val] :
      ( ( hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_19),B_5) = hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_68_Pair__inject,axiom,
    ! [A_19: produc1278157519t_char,B_5: produc1278157519t_char,A_18: produc1278157519t_char,B_4: produc1278157519t_char] :
      ( ( hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_19),B_5) = hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_69_Pair__inject,axiom,
    ! [A: produc639455274on_val,B: produc639455274on_val,A_3: produc639455274on_val,B_3: produc639455274on_val] :
      ( ( hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A),B) = hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_3),B_3) )
     => ~ ( ( A = A_3 )
         => ( B != B_3 ) ) ) ).

tff(fact_70_Pair__inject,axiom,
    ! [A: produc12694297on_val,B: produc12694297on_val,A_3: produc12694297on_val,B_3: produc12694297on_val] :
      ( ( hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A),B) = hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_3),B_3) )
     => ~ ( ( A = A_3 )
         => ( B != B_3 ) ) ) ).

tff(fact_71_Pair__inject,axiom,
    ! [A: produc1102272487on_val,B: produc1102272487on_val,A_3: produc1102272487on_val,B_3: produc1102272487on_val] :
      ( ( hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A),B) = hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_3),B_3) )
     => ~ ( ( A = A_3 )
         => ( B != B_3 ) ) ) ).

tff(fact_72_Pair__inject,axiom,
    ! [A_19: list_exp_list_char,B_5: list_exp_list_char,A_18: list_exp_list_char,B_4: list_exp_list_char] :
      ( ( hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,A_19),B_5) = hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_73_Pair__inject,axiom,
    ! [A_19: exp_list_char,B_5: exp_list_char,A_18: exp_list_char,B_4: exp_list_char] :
      ( ( hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,A_19),B_5) = hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_74_Pair__inject,axiom,
    ! [A_19: list_list_char,B_5: list_list_char,A_18: list_list_char,B_4: list_list_char] :
      ( ( hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A_19),B_5) = hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_75_Pair__inject,axiom,
    ! [A_19: list_P1940453997har_ty,B_5: list_P1940453997har_ty,A_18: list_P1940453997har_ty,B_4: list_P1940453997har_ty] :
      ( ( hAPP_l1294856089har_ty(hAPP_l1657578379har_ty(produc1860789535har_ty,A_19),B_5) = hAPP_l1294856089har_ty(hAPP_l1657578379har_ty(produc1860789535har_ty,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_76_Pair__inject,axiom,
    ! [A_19: list_P341299826t_char,B_5: list_P341299826t_char,A_18: list_P341299826t_char,B_4: list_P341299826t_char] :
      ( ( hAPP_l1334098948t_char(hAPP_l1450984463t_char(produc436875159t_char,A_19),B_5) = hAPP_l1334098948t_char(hAPP_l1450984463t_char(produc436875159t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_77_Pair__inject,axiom,
    ! [A_19: list_val,B_5: list_val,A_18: list_val,B_4: list_val] :
      ( ( hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,A_19),B_5) = hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_78_Pair__inject,axiom,
    ! [A_19: list_ty,B_5: list_ty,A_18: list_ty,B_4: list_ty] :
      ( ( hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,A_19),B_5) = hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_79_Pair__inject,axiom,
    ! [A_19: bop,B_5: bop,A_18: bop,B_4: bop] :
      ( ( hAPP_b1909667208op_bop(hAPP_b1058859669op_bop(product_Pair_bop_bop,A_19),B_5) = hAPP_b1909667208op_bop(hAPP_b1058859669op_bop(product_Pair_bop_bop,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_80_Pair__inject,axiom,
    ! [A: fun_Pr806764899on_val,B: fun_Pr806764899on_val,A_3: fun_Pr806764899on_val,B_3: fun_Pr806764899on_val] :
      ( ( hAPP_f1146435765on_val(hAPP_f1744304433on_val(produc1618304727on_val,A),B) = hAPP_f1146435765on_val(hAPP_f1744304433on_val(produc1618304727on_val,A_3),B_3) )
     => ~ ( ( A = A_3 )
         => ( B != B_3 ) ) ) ).

tff(fact_81_Pair__inject,axiom,
    ! [A: fun_na939144002on_val,B: fun_na939144002on_val,A_3: fun_na939144002on_val,B_3: fun_na939144002on_val] :
      ( ( hAPP_f368284312on_val(hAPP_f1805337205on_val(produc1712663241on_val,A),B) = hAPP_f368284312on_val(hAPP_f1805337205on_val(produc1712663241on_val,A_3),B_3) )
     => ~ ( ( A = A_3 )
         => ( B != B_3 ) ) ) ).

tff(fact_82_Pair__inject,axiom,
    ! [A: fun_li1432931796on_val,B: fun_li1432931796on_val,A_3: fun_li1432931796on_val,B_3: fun_li1432931796on_val] :
      ( ( hAPP_f1741070310on_val(hAPP_f864891091on_val(produc1960514199on_val,A),B) = hAPP_f1741070310on_val(hAPP_f864891091on_val(produc1960514199on_val,A_3),B_3) )
     => ~ ( ( A = A_3 )
         => ( B != B_3 ) ) ) ).

tff(fact_83_Pair__inject,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,A_3: produc124828825on_val,B_3: produc124828825on_val] :
      ( ( hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B) = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_3),B_3) )
     => ~ ( ( A = A_3 )
         => ( B != B_3 ) ) ) ).

tff(fact_84_Pair__inject,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,A_3: exp_list_char,B_3: produc12694297on_val] :
      ( ( hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B) = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_3),B_3) )
     => ~ ( ( A = A_3 )
         => ( B != B_3 ) ) ) ).

tff(fact_85_Pair__inject,axiom,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,A_3: fun_na939144002on_val,B_3: fun_li1432931796on_val] :
      ( ( hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B) = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_3),B_3) )
     => ~ ( ( A = A_3 )
         => ( B != B_3 ) ) ) ).

tff(fact_86_Pair__inject,axiom,
    ! [A: list_char,B: fun_Pr806764899on_val,A_3: list_char,B_3: fun_Pr806764899on_val] :
      ( ( hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B) = hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_3),B_3) )
     => ~ ( ( A = A_3 )
         => ( B != B_3 ) ) ) ).

tff(fact_87_Pair__inject,axiom,
    ! [A_19: list_char,B_5: list_char,A_18: list_char,B_4: list_char] :
      ( ( hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_19),B_5) = hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_88_Pair__inject,axiom,
    ! [A_19: bop,B_5: product_prod_val_val,A_18: bop,B_4: product_prod_val_val] :
      ( ( hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_19),B_5) = hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_89_Pair__inject,axiom,
    ! [A_19: val,B_5: val,A_18: val,B_4: val] :
      ( ( hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_19),B_5) = hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_90_Pair__inject,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,A_3: produc2061676504on_val,B_3: produc2061676504on_val] :
      ( ( hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B) = hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_3),B_3) )
     => ~ ( ( A = A_3 )
         => ( B != B_3 ) ) ) ).

tff(fact_91_Pair__inject,axiom,
    ! [A: list_exp_list_char,B: produc12694297on_val,A_3: list_exp_list_char,B_3: produc12694297on_val] :
      ( ( hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B) = hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_3),B_3) )
     => ~ ( ( A = A_3 )
         => ( B != B_3 ) ) ) ).

tff(fact_92_Pair__inject,axiom,
    ! [A_19: list_list_char,B_5: produc220283002t_char,A_18: list_list_char,B_4: produc220283002t_char] :
      ( ( hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_19),B_5) = hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_93_Pair__inject,axiom,
    ! [A_19: list_ty,B_5: produc662261637t_char,A_18: list_ty,B_4: produc662261637t_char] :
      ( ( hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_19),B_5) = hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_94_Pair__inject,axiom,
    ! [A_19: list_val,B_5: exp_list_char,A_18: list_val,B_4: exp_list_char] :
      ( ( hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_19),B_5) = hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_95_Pair__inject,axiom,
    ! [A_19: list_char,B_5: produc952412819t_char,A_18: list_char,B_4: produc952412819t_char] :
      ( ( hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_19),B_5) = hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_96_Pair__inject,axiom,
    ! [A_19: list_char,B_5: produc2146869324t_char,A_18: list_char,B_4: produc2146869324t_char] :
      ( ( hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_19),B_5) = hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_97_Pair__inject,axiom,
    ! [A_19: list_P1940453997har_ty,B_5: list_P341299826t_char,A_18: list_P1940453997har_ty,B_4: list_P341299826t_char] :
      ( ( hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_19),B_5) = hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_98_Pair__inject,axiom,
    ! [A_19: list_list_char,B_5: exp_list_char,A_18: list_list_char,B_4: exp_list_char] :
      ( ( hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_19),B_5) = hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_18),B_4) )
     => ~ ( ( A_19 = A_18 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_99_Pair__eq,axiom,
    ! [A: list_char,B: ty,A_3: list_char,B_3: ty] :
      ( ( hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A),B) = hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_100_Pair__eq,axiom,
    ! [A: produc1278157519t_char,B: ty,A_3: produc1278157519t_char,B_3: ty] :
      ( ( hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A),B) = hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_101_Pair__eq,axiom,
    ! [A: list_char,B: produc1025221954t_char,A_3: list_char,B_3: produc1025221954t_char] :
      ( ( hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A),B) = hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_102_Pair__eq,axiom,
    ! [A: produc809539159t_char,B: produc809539159t_char,A_3: produc809539159t_char,B_3: produc809539159t_char] :
      ( ( hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A),B) = hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_103_Pair__eq,axiom,
    ! [A: produc2146869324t_char,B: produc2146869324t_char,A_3: produc2146869324t_char,B_3: produc2146869324t_char] :
      ( ( hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A),B) = hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_104_Pair__eq,axiom,
    ! [A: produc952412819t_char,B: produc952412819t_char,A_3: produc952412819t_char,B_3: produc952412819t_char] :
      ( ( hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A),B) = hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_105_Pair__eq,axiom,
    ! [A: produc1971331930t_char,B: produc1971331930t_char,A_3: produc1971331930t_char,B_3: produc1971331930t_char] :
      ( ( hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A),B) = hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_106_Pair__eq,axiom,
    ! [A: produc662261637t_char,B: produc662261637t_char,A_3: produc662261637t_char,B_3: produc662261637t_char] :
      ( ( hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A),B) = hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_107_Pair__eq,axiom,
    ! [A: produc220283002t_char,B: produc220283002t_char,A_3: produc220283002t_char,B_3: produc220283002t_char] :
      ( ( hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A),B) = hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_108_Pair__eq,axiom,
    ! [A: produc1285161482t_char,B: produc1285161482t_char,A_3: produc1285161482t_char,B_3: produc1285161482t_char] :
      ( ( hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A),B) = hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_109_Pair__eq,axiom,
    ! [A: produc430140671on_val,B: produc430140671on_val,A_3: produc430140671on_val,B_3: produc430140671on_val] :
      ( ( hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A),B) = hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_110_Pair__eq,axiom,
    ! [A: product_prod_val_val,B: product_prod_val_val,A_3: product_prod_val_val,B_3: product_prod_val_val] :
      ( ( hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A),B) = hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_111_Pair__eq,axiom,
    ! [A: produc1645268488al_val,B: produc1645268488al_val,A_3: produc1645268488al_val,B_3: produc1645268488al_val] :
      ( ( hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A),B) = hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_112_Pair__eq,axiom,
    ! [A: produc1278157519t_char,B: produc1278157519t_char,A_3: produc1278157519t_char,B_3: produc1278157519t_char] :
      ( ( hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A),B) = hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_113_Pair__eq,axiom,
    ! [A: produc639455274on_val,B: produc639455274on_val,A_3: produc639455274on_val,B_3: produc639455274on_val] :
      ( ( hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A),B) = hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_114_Pair__eq,axiom,
    ! [A: produc12694297on_val,B: produc12694297on_val,A_3: produc12694297on_val,B_3: produc12694297on_val] :
      ( ( hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A),B) = hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_115_Pair__eq,axiom,
    ! [A: produc1102272487on_val,B: produc1102272487on_val,A_3: produc1102272487on_val,B_3: produc1102272487on_val] :
      ( ( hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A),B) = hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_116_Pair__eq,axiom,
    ! [A: list_exp_list_char,B: list_exp_list_char,A_3: list_exp_list_char,B_3: list_exp_list_char] :
      ( ( hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,A),B) = hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_117_Pair__eq,axiom,
    ! [A: exp_list_char,B: exp_list_char,A_3: exp_list_char,B_3: exp_list_char] :
      ( ( hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,A),B) = hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_118_Pair__eq,axiom,
    ! [A: list_list_char,B: list_list_char,A_3: list_list_char,B_3: list_list_char] :
      ( ( hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A),B) = hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_119_Pair__eq,axiom,
    ! [A: list_P1940453997har_ty,B: list_P1940453997har_ty,A_3: list_P1940453997har_ty,B_3: list_P1940453997har_ty] :
      ( ( hAPP_l1294856089har_ty(hAPP_l1657578379har_ty(produc1860789535har_ty,A),B) = hAPP_l1294856089har_ty(hAPP_l1657578379har_ty(produc1860789535har_ty,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_120_Pair__eq,axiom,
    ! [A: list_P341299826t_char,B: list_P341299826t_char,A_3: list_P341299826t_char,B_3: list_P341299826t_char] :
      ( ( hAPP_l1334098948t_char(hAPP_l1450984463t_char(produc436875159t_char,A),B) = hAPP_l1334098948t_char(hAPP_l1450984463t_char(produc436875159t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_121_Pair__eq,axiom,
    ! [A: list_val,B: list_val,A_3: list_val,B_3: list_val] :
      ( ( hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,A),B) = hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_122_Pair__eq,axiom,
    ! [A: list_ty,B: list_ty,A_3: list_ty,B_3: list_ty] :
      ( ( hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,A),B) = hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_123_Pair__eq,axiom,
    ! [A: bop,B: bop,A_3: bop,B_3: bop] :
      ( ( hAPP_b1909667208op_bop(hAPP_b1058859669op_bop(product_Pair_bop_bop,A),B) = hAPP_b1909667208op_bop(hAPP_b1058859669op_bop(product_Pair_bop_bop,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_124_Pair__eq,axiom,
    ! [A: fun_Pr806764899on_val,B: fun_Pr806764899on_val,A_3: fun_Pr806764899on_val,B_3: fun_Pr806764899on_val] :
      ( ( hAPP_f1146435765on_val(hAPP_f1744304433on_val(produc1618304727on_val,A),B) = hAPP_f1146435765on_val(hAPP_f1744304433on_val(produc1618304727on_val,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_125_Pair__eq,axiom,
    ! [A: fun_na939144002on_val,B: fun_na939144002on_val,A_3: fun_na939144002on_val,B_3: fun_na939144002on_val] :
      ( ( hAPP_f368284312on_val(hAPP_f1805337205on_val(produc1712663241on_val,A),B) = hAPP_f368284312on_val(hAPP_f1805337205on_val(produc1712663241on_val,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_126_Pair__eq,axiom,
    ! [A: fun_li1432931796on_val,B: fun_li1432931796on_val,A_3: fun_li1432931796on_val,B_3: fun_li1432931796on_val] :
      ( ( hAPP_f1741070310on_val(hAPP_f864891091on_val(produc1960514199on_val,A),B) = hAPP_f1741070310on_val(hAPP_f864891091on_val(produc1960514199on_val,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_127_Pair__eq,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,A_3: produc124828825on_val,B_3: produc124828825on_val] :
      ( ( hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B) = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_128_Pair__eq,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,A_3: exp_list_char,B_3: produc12694297on_val] :
      ( ( hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B) = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_129_Pair__eq,axiom,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,A_3: fun_na939144002on_val,B_3: fun_li1432931796on_val] :
      ( ( hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B) = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_130_Pair__eq,axiom,
    ! [A: list_char,B: fun_Pr806764899on_val,A_3: list_char,B_3: fun_Pr806764899on_val] :
      ( ( hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B) = hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_131_Pair__eq,axiom,
    ! [A: list_char,B: list_char,A_3: list_char,B_3: list_char] :
      ( ( hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B) = hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_132_Pair__eq,axiom,
    ! [A: bop,B: product_prod_val_val,A_3: bop,B_3: product_prod_val_val] :
      ( ( hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B) = hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_133_Pair__eq,axiom,
    ! [A: val,B: val,A_3: val,B_3: val] :
      ( ( hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B) = hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_134_Pair__eq,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,A_3: produc2061676504on_val,B_3: produc2061676504on_val] :
      ( ( hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B) = hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_135_Pair__eq,axiom,
    ! [A: list_exp_list_char,B: produc12694297on_val,A_3: list_exp_list_char,B_3: produc12694297on_val] :
      ( ( hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B) = hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_136_Pair__eq,axiom,
    ! [A: list_list_char,B: produc220283002t_char,A_3: list_list_char,B_3: produc220283002t_char] :
      ( ( hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B) = hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_137_Pair__eq,axiom,
    ! [A: list_ty,B: produc662261637t_char,A_3: list_ty,B_3: produc662261637t_char] :
      ( ( hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B) = hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_138_Pair__eq,axiom,
    ! [A: list_val,B: exp_list_char,A_3: list_val,B_3: exp_list_char] :
      ( ( hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B) = hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_139_Pair__eq,axiom,
    ! [A: list_char,B: produc952412819t_char,A_3: list_char,B_3: produc952412819t_char] :
      ( ( hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B) = hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_140_Pair__eq,axiom,
    ! [A: list_char,B: produc2146869324t_char,A_3: list_char,B_3: produc2146869324t_char] :
      ( ( hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B) = hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_141_Pair__eq,axiom,
    ! [A: list_P1940453997har_ty,B: list_P341299826t_char,A_3: list_P1940453997har_ty,B_3: list_P341299826t_char] :
      ( ( hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B) = hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_142_Pair__eq,axiom,
    ! [A: list_list_char,B: exp_list_char,A_3: list_list_char,B_3: exp_list_char] :
      ( ( hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B) = hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_3),B_3) )
    <=> ( ( A = A_3 )
        & ( B = B_3 ) ) ) ).

tff(fact_143_split__paired__All,axiom,
    ! [Pa: fun_Pr1127025070y_bool] :
      ( ! [X1: produc917948472har_ty] : hBOOL(hAPP_P748443392y_bool(Pa,X1))
    <=> ! [A_1: list_char,B_2: ty] : hBOOL(hAPP_P748443392y_bool(Pa,hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_1),B_2))) ) ).

tff(fact_144_split__paired__All,axiom,
    ! [Pa: fun_Pr2102567903y_bool] :
      ( ! [X1: produc245756905har_ty] : hBOOL(hAPP_P27757617y_bool(Pa,X1))
    <=> ! [A_1: produc1278157519t_char,B_2: ty] : hBOOL(hAPP_P27757617y_bool(Pa,hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_1),B_2))) ) ).

tff(fact_145_split__paired__All,axiom,
    ! [Pa: fun_Pr70170387r_bool] :
      ( ! [X1: produc1013743697t_char] : hBOOL(hAPP_P1384137393r_bool(Pa,X1))
    <=> ! [A_1: list_char,B_2: produc1025221954t_char] : hBOOL(hAPP_P1384137393r_bool(Pa,hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),B_2))) ) ).

tff(fact_146_split__paired__All,axiom,
    ! [Pa: fun_Pr908866473r_bool] :
      ( ! [X1: produc1534059751t_char] : hBOOL(hAPP_P1002912327r_bool(Pa,X1))
    <=> ! [A_1: produc809539159t_char,B_2: produc809539159t_char] : hBOOL(hAPP_P1002912327r_bool(Pa,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_1),B_2))) ) ).

tff(fact_147_split__paired__All,axiom,
    ! [Pa: fun_Pr286306793r_bool] :
      ( ! [X1: produc494726439t_char] : hBOOL(hAPP_P801803911r_bool(Pa,X1))
    <=> ! [A_1: produc2146869324t_char,B_2: produc2146869324t_char] : hBOOL(hAPP_P801803911r_bool(Pa,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_1),B_2))) ) ).

tff(fact_148_split__paired__All,axiom,
    ! [Pa: fun_Pr1538825897r_bool] :
      ( ! [X1: produc740765671t_char] : hBOOL(hAPP_P929449287r_bool(Pa,X1))
    <=> ! [A_1: produc952412819t_char,B_2: produc952412819t_char] : hBOOL(hAPP_P929449287r_bool(Pa,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_1),B_2))) ) ).

tff(fact_149_split__paired__All,axiom,
    ! [Pa: fun_Pr981088873r_bool] :
      ( ! [X1: produc84451751t_char] : hBOOL(hAPP_P975284999r_bool(Pa,X1))
    <=> ! [A_1: produc1971331930t_char,B_2: produc1971331930t_char] : hBOOL(hAPP_P975284999r_bool(Pa,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),B_2))) ) ).

tff(fact_150_split__paired__All,axiom,
    ! [Pa: fun_Pr1890037787r_bool] :
      ( ! [X1: produc1826280281t_char] : hBOOL(hAPP_P1183499705r_bool(Pa,X1))
    <=> ! [A_1: produc662261637t_char,B_2: produc662261637t_char] : hBOOL(hAPP_P1183499705r_bool(Pa,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_1),B_2))) ) ).

tff(fact_151_split__paired__All,axiom,
    ! [Pa: fun_Pr1728267013r_bool] :
      ( ! [X1: produc1406897475t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,X1))
    <=> ! [A_1: produc220283002t_char,B_2: produc220283002t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_1),B_2))) ) ).

tff(fact_152_split__paired__All,axiom,
    ! [Pa: fun_Pr1895638121r_bool] :
      ( ! [X1: produc349695911t_char] : hBOOL(hAPP_P824029447r_bool(Pa,X1))
    <=> ! [A_1: produc1285161482t_char,B_2: produc1285161482t_char] : hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),B_2))) ) ).

tff(fact_153_split__paired__All,axiom,
    ! [Pa: fun_Pr302334223l_bool] :
      ( ! [X1: produc1466422861on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,X1))
    <=> ! [A_1: produc430140671on_val,B_2: produc430140671on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),B_2))) ) ).

tff(fact_154_split__paired__All,axiom,
    ! [Pa: fun_Pr832147423l_bool] :
      ( ! [X1: produc800118557al_val] : hBOOL(hAPP_P2123002749l_bool(Pa,X1))
    <=> ! [A_1: product_prod_val_val,B_2: product_prod_val_val] : hBOOL(hAPP_P2123002749l_bool(Pa,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_1),B_2))) ) ).

tff(fact_155_split__paired__All,axiom,
    ! [Pa: fun_Pr897334561l_bool] :
      ( ! [X1: produc630464863al_val] : hBOOL(hAPP_P738987199l_bool(Pa,X1))
    <=> ! [A_1: produc1645268488al_val,B_2: produc1645268488al_val] : hBOOL(hAPP_P738987199l_bool(Pa,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_1),B_2))) ) ).

tff(fact_156_split__paired__All,axiom,
    ! [Pa: fun_Pr1336847023r_bool] :
      ( ! [X1: produc1350825965t_char] : hBOOL(hAPP_P2010574925r_bool(Pa,X1))
    <=> ! [A_1: produc1278157519t_char,B_2: produc1278157519t_char] : hBOOL(hAPP_P2010574925r_bool(Pa,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_1),B_2))) ) ).

tff(fact_157_split__paired__All,axiom,
    ! [Pa: fun_Pr235369833l_bool] :
      ( ! [X1: produc87279271on_val] : hBOOL(hAPP_P124632071l_bool(Pa,X1))
    <=> ! [A_1: produc639455274on_val,B_2: produc639455274on_val] : hBOOL(hAPP_P124632071l_bool(Pa,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_1),B_2))) ) ).

tff(fact_158_split__paired__All,axiom,
    ! [Pa: fun_Pr693020585l_bool] :
      ( ! [X1: produc409205479on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,X1))
    <=> ! [A_1: produc12694297on_val,B_2: produc12694297on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_1),B_2))) ) ).

tff(fact_159_split__paired__All,axiom,
    ! [Pa: fun_Pr903661919l_bool] :
      ( ! [X1: produc231486621on_val] : hBOOL(hAPP_P378063101l_bool(Pa,X1))
    <=> ! [A_1: produc1102272487on_val,B_2: produc1102272487on_val] : hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),B_2))) ) ).

tff(fact_160_split__paired__All,axiom,
    ! [Pa: fun_Pr716652265r_bool] :
      ( ! [X1: produc91527719t_char] : hBOOL(hAPP_P499022727r_bool(Pa,X1))
    <=> ! [A_1: list_exp_list_char,B_2: list_exp_list_char] : hBOOL(hAPP_P499022727r_bool(Pa,hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,A_1),B_2))) ) ).

tff(fact_161_split__paired__All,axiom,
    ! [Pa: fun_Pr136267935r_bool] :
      ( ! [X1: produc2048519645t_char] : hBOOL(hAPP_P1632759357r_bool(Pa,X1))
    <=> ! [A_1: exp_list_char,B_2: exp_list_char] : hBOOL(hAPP_P1632759357r_bool(Pa,hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,A_1),B_2))) ) ).

tff(fact_162_split__paired__All,axiom,
    ! [Pa: fun_Pr382120745r_bool] :
      ( ! [X1: produc1200003175t_char] : hBOOL(hAPP_P476431815r_bool(Pa,X1))
    <=> ! [A_1: list_list_char,B_2: list_list_char] : hBOOL(hAPP_P476431815r_bool(Pa,hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A_1),B_2))) ) ).

tff(fact_163_split__paired__All,axiom,
    ! [Pa: fun_Pr263169771y_bool] :
      ( ! [X1: produc450000425har_ty] : hBOOL(hAPP_P2053453961y_bool(Pa,X1))
    <=> ! [A_1: list_P1940453997har_ty,B_2: list_P1940453997har_ty] : hBOOL(hAPP_P2053453961y_bool(Pa,hAPP_l1294856089har_ty(hAPP_l1657578379har_ty(produc1860789535har_ty,A_1),B_2))) ) ).

tff(fact_164_split__paired__All,axiom,
    ! [Pa: fun_Pr2024675945r_bool] :
      ( ! [X1: produc244676007t_char] : hBOOL(hAPP_P1926698759r_bool(Pa,X1))
    <=> ! [A_1: list_P341299826t_char,B_2: list_P341299826t_char] : hBOOL(hAPP_P1926698759r_bool(Pa,hAPP_l1334098948t_char(hAPP_l1450984463t_char(produc436875159t_char,A_1),B_2))) ) ).

tff(fact_165_split__paired__All,axiom,
    ! [Pa: fun_Pr1618624239l_bool] :
      ( ! [X1: produc753553453st_val] : hBOOL(hAPP_P2115985549l_bool(Pa,X1))
    <=> ! [A_1: list_val,B_2: list_val] : hBOOL(hAPP_P2115985549l_bool(Pa,hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,A_1),B_2))) ) ).

tff(fact_166_split__paired__All,axiom,
    ! [Pa: fun_Pr306783325y_bool] :
      ( ! [X1: produc1420746395ist_ty] : hBOOL(hAPP_P1574824955y_bool(Pa,X1))
    <=> ! [A_1: list_ty,B_2: list_ty] : hBOOL(hAPP_P1574824955y_bool(Pa,hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,A_1),B_2))) ) ).

tff(fact_167_split__paired__All,axiom,
    ! [Pa: fun_Pr851759157p_bool] :
      ( ! [X1: product_prod_bop_bop] : hBOOL(hAPP_P1085566419p_bool(Pa,X1))
    <=> ! [A_1: bop,B_2: bop] : hBOOL(hAPP_P1085566419p_bool(Pa,hAPP_b1909667208op_bop(hAPP_b1058859669op_bop(product_Pair_bop_bop,A_1),B_2))) ) ).

tff(fact_168_split__paired__All,axiom,
    ! [Pa: fun_Pr369549609l_bool] :
      ( ! [X1: produc2104958055on_val] : hBOOL(hAPP_P504978887l_bool(Pa,X1))
    <=> ! [A_1: fun_Pr806764899on_val,B_2: fun_Pr806764899on_val] : hBOOL(hAPP_P504978887l_bool(Pa,hAPP_f1146435765on_val(hAPP_f1744304433on_val(produc1618304727on_val,A_1),B_2))) ) ).

tff(fact_169_split__paired__All,axiom,
    ! [Pa: fun_Pr442654869l_bool] :
      ( ! [X1: produc644889299on_val] : hBOOL(hAPP_P2077557811l_bool(Pa,X1))
    <=> ! [A_1: fun_na939144002on_val,B_2: fun_na939144002on_val] : hBOOL(hAPP_P2077557811l_bool(Pa,hAPP_f368284312on_val(hAPP_f1805337205on_val(produc1712663241on_val,A_1),B_2))) ) ).

tff(fact_170_split__paired__All,axiom,
    ! [Pa: fun_Pr673659369l_bool] :
      ( ! [X1: produc1127210791on_val] : hBOOL(hAPP_P468446343l_bool(Pa,X1))
    <=> ! [A_1: fun_li1432931796on_val,B_2: fun_li1432931796on_val] : hBOOL(hAPP_P468446343l_bool(Pa,hAPP_f1741070310on_val(hAPP_f864891091on_val(produc1960514199on_val,A_1),B_2))) ) ).

tff(fact_171_split__paired__All,axiom,
    ! [Pa: fun_Pr691271849l_bool] :
      ( ! [X1: produc1102272487on_val] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
    <=> ! [A_1: produc124828825on_val,B_2: produc124828825on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_2))) ) ).

tff(fact_172_split__paired__All,axiom,
    ! [Pa: fun_Pr680585871l_bool] :
      ( ! [X1: produc124828825on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
    <=> ! [A_1: exp_list_char,B_2: produc12694297on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_2))) ) ).

tff(fact_173_split__paired__All,axiom,
    ! [Pa: fun_Pr1696029455l_bool] :
      ( ! [X1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
    <=> ! [A_1: fun_na939144002on_val,B_2: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(Pa,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_2))) ) ).

tff(fact_174_split__paired__All,axiom,
    ! [Pa: fun_Pr315804320l_bool] :
      ( ! [X1: produc639455274on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,X1))
    <=> ! [A_1: list_char,B_2: fun_Pr806764899on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_2))) ) ).

tff(fact_175_split__paired__All,axiom,
    ! [Pa: fun_Pr565113489r_bool] :
      ( ! [X1: produc1278157519t_char] : hBOOL(hAPP_P449474095r_bool(Pa,X1))
    <=> ! [A_1: list_char,B_2: list_char] : hBOOL(hAPP_P449474095r_bool(Pa,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_2))) ) ).

tff(fact_176_split__paired__All,axiom,
    ! [Pa: fun_Pr252072522l_bool] :
      ( ! [X1: produc1645268488al_val] : hBOOL(hAPP_P943837928l_bool(Pa,X1))
    <=> ! [A_1: bop,B_2: product_prod_val_val] : hBOOL(hAPP_P943837928l_bool(Pa,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_2))) ) ).

tff(fact_177_split__paired__All,axiom,
    ! [Pa: fun_Pr2081272681l_bool] :
      ( ! [X1: product_prod_val_val] : hBOOL(hAPP_P929938951l_bool(Pa,X1))
    <=> ! [A_1: val,B_2: val] : hBOOL(hAPP_P929938951l_bool(Pa,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_2))) ) ).

tff(fact_178_split__paired__All,axiom,
    ! [Pa: fun_Pr859510977l_bool] :
      ( ! [X1: produc430140671on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,X1))
    <=> ! [A_1: produc2061676504on_val,B_2: produc2061676504on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_2))) ) ).

tff(fact_179_split__paired__All,axiom,
    ! [Pa: fun_Pr248118298l_bool] :
      ( ! [X1: produc2061676504on_val] : hBOOL(hAPP_P71593144l_bool(Pa,X1))
    <=> ! [A_1: list_exp_list_char,B_2: produc12694297on_val] : hBOOL(hAPP_P71593144l_bool(Pa,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_2))) ) ).

tff(fact_180_split__paired__All,axiom,
    ! [Pa: fun_Pr227936640r_bool] :
      ( ! [X1: produc1285161482t_char] : hBOOL(hAPP_P92196306r_bool(Pa,X1))
    <=> ! [A_1: list_list_char,B_2: produc220283002t_char] : hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_2))) ) ).

tff(fact_181_split__paired__All,axiom,
    ! [Pa: fun_Pr46158268r_bool] :
      ( ! [X1: produc220283002t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,X1))
    <=> ! [A_1: list_ty,B_2: produc662261637t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_2))) ) ).

tff(fact_182_split__paired__All,axiom,
    ! [Pa: fun_Pr827765831r_bool] :
      ( ! [X1: produc662261637t_char] : hBOOL(hAPP_P2118621157r_bool(Pa,X1))
    <=> ! [A_1: list_val,B_2: exp_list_char] : hBOOL(hAPP_P2118621157r_bool(Pa,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_2))) ) ).

tff(fact_183_split__paired__All,axiom,
    ! [Pa: fun_Pr1861226704r_bool] :
      ( ! [X1: produc1971331930t_char] : hBOOL(hAPP_P1680401186r_bool(Pa,X1))
    <=> ! [A_1: list_char,B_2: produc952412819t_char] : hBOOL(hAPP_P1680401186r_bool(Pa,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_2))) ) ).

tff(fact_184_split__paired__All,axiom,
    ! [Pa: fun_Pr1898949769r_bool] :
      ( ! [X1: produc952412819t_char] : hBOOL(hAPP_P659547099r_bool(Pa,X1))
    <=> ! [A_1: list_char,B_2: produc2146869324t_char] : hBOOL(hAPP_P659547099r_bool(Pa,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_2))) ) ).

tff(fact_185_split__paired__All,axiom,
    ! [Pa: fun_Pr1669461698r_bool] :
      ( ! [X1: produc2146869324t_char] : hBOOL(hAPP_P828904212r_bool(Pa,X1))
    <=> ! [A_1: list_P1940453997har_ty,B_2: list_P341299826t_char] : hBOOL(hAPP_P828904212r_bool(Pa,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_2))) ) ).

tff(fact_186_split__paired__All,axiom,
    ! [Pa: fun_Pr1336948301r_bool] :
      ( ! [X1: produc809539159t_char] : hBOOL(hAPP_P2014166431r_bool(Pa,X1))
    <=> ! [A_1: list_list_char,B_2: exp_list_char] : hBOOL(hAPP_P2014166431r_bool(Pa,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_2))) ) ).

tff(fact_187_fun__upd__def,axiom,
    ! [F_1: fun_li1432931796on_val,B: option_val,A: list_char,X_1: list_char] :
      ( ( ( X_1 = A )
       => ( hAPP_l207779698on_val(fun_up1149430426on_val(F_1,A,B),X_1) = B ) )
      & ( ( X_1 != A )
       => ( hAPP_l207779698on_val(fun_up1149430426on_val(F_1,A,B),X_1) = hAPP_l207779698on_val(F_1,X_1) ) ) ) ).

tff(fact_188_fun__upd__def,axiom,
    ! [F_1: fun_li688206603ion_ty,B: option_ty,A: list_char,X_1: list_char] :
      ( ( ( X_1 = A )
       => ( hAPP_l512744617ion_ty(fun_up424764369ion_ty(F_1,A,B),X_1) = B ) )
      & ( ( X_1 != A )
       => ( hAPP_l512744617ion_ty(fun_up424764369ion_ty(F_1,A,B),X_1) = hAPP_l512744617ion_ty(F_1,X_1) ) ) ) ).

tff(fact_189_fun__upd__def,axiom,
    ! [F_1: fun_na939144002on_val,B: option1479284511on_val,A: nat,X_1: nat] :
      ( ( ( X_1 = A )
       => ( hAPP_n546249108on_val(fun_up2041264236on_val(F_1,A,B),X_1) = B ) )
      & ( ( X_1 != A )
       => ( hAPP_n546249108on_val(fun_up2041264236on_val(F_1,A,B),X_1) = hAPP_n546249108on_val(F_1,X_1) ) ) ) ).

tff(fact_190_fun__upd__def,axiom,
    ! [F_1: fun_Pr806764899on_val,B: option_val,A: produc1278157519t_char,X_1: produc1278157519t_char] :
      ( ( ( X_1 = A )
       => ( hAPP_P2094403585on_val(fun_up204312361on_val(F_1,A,B),X_1) = B ) )
      & ( ( X_1 != A )
       => ( hAPP_P2094403585on_val(fun_up204312361on_val(F_1,A,B),X_1) = hAPP_P2094403585on_val(F_1,X_1) ) ) ) ).

tff(fact_191_fun__upd__idem,axiom,
    ! [F_1: fun_li1432931796on_val,X_2: list_char,Y_2: option_val] :
      ( ( hAPP_l207779698on_val(F_1,X_2) = Y_2 )
     => ( fun_up1149430426on_val(F_1,X_2,Y_2) = F_1 ) ) ).

tff(fact_192_fun__upd__idem,axiom,
    ! [F_1: fun_li688206603ion_ty,X_2: list_char,Y_2: option_ty] :
      ( ( hAPP_l512744617ion_ty(F_1,X_2) = Y_2 )
     => ( fun_up424764369ion_ty(F_1,X_2,Y_2) = F_1 ) ) ).

tff(fact_193_fun__upd__idem,axiom,
    ! [F_1: fun_na939144002on_val,X_2: nat,Y_2: option1479284511on_val] :
      ( ( hAPP_n546249108on_val(F_1,X_2) = Y_2 )
     => ( fun_up2041264236on_val(F_1,X_2,Y_2) = F_1 ) ) ).

tff(fact_194_fun__upd__idem,axiom,
    ! [F_1: fun_Pr806764899on_val,X_2: produc1278157519t_char,Y_2: option_val] :
      ( ( hAPP_P2094403585on_val(F_1,X_2) = Y_2 )
     => ( fun_up204312361on_val(F_1,X_2,Y_2) = F_1 ) ) ).

tff(fact_195_fun__upd__other,axiom,
    ! [F_1: fun_li1432931796on_val,Y_2: option_val,Z_1: list_char,X_2: list_char] :
      ( ( Z_1 != X_2 )
     => ( hAPP_l207779698on_val(fun_up1149430426on_val(F_1,X_2,Y_2),Z_1) = hAPP_l207779698on_val(F_1,Z_1) ) ) ).

tff(fact_196_fun__upd__other,axiom,
    ! [F_1: fun_li688206603ion_ty,Y_2: option_ty,Z_1: list_char,X_2: list_char] :
      ( ( Z_1 != X_2 )
     => ( hAPP_l512744617ion_ty(fun_up424764369ion_ty(F_1,X_2,Y_2),Z_1) = hAPP_l512744617ion_ty(F_1,Z_1) ) ) ).

tff(fact_197_fun__upd__other,axiom,
    ! [F_1: fun_na939144002on_val,Y_2: option1479284511on_val,Z_1: nat,X_2: nat] :
      ( ( Z_1 != X_2 )
     => ( hAPP_n546249108on_val(fun_up2041264236on_val(F_1,X_2,Y_2),Z_1) = hAPP_n546249108on_val(F_1,Z_1) ) ) ).

tff(fact_198_fun__upd__other,axiom,
    ! [F_1: fun_Pr806764899on_val,Y_2: option_val,Z_1: produc1278157519t_char,X_2: produc1278157519t_char] :
      ( ( Z_1 != X_2 )
     => ( hAPP_P2094403585on_val(fun_up204312361on_val(F_1,X_2,Y_2),Z_1) = hAPP_P2094403585on_val(F_1,Z_1) ) ) ).

tff(fact_199_fun__upd__twist,axiom,
    ! [M_1: fun_li1432931796on_val,B: option_val,D_1: option_val,A: list_char,C_2: list_char] :
      ( ( A != C_2 )
     => ( fun_up1149430426on_val(fun_up1149430426on_val(M_1,A,B),C_2,D_1) = fun_up1149430426on_val(fun_up1149430426on_val(M_1,C_2,D_1),A,B) ) ) ).

tff(fact_200_fun__upd__twist,axiom,
    ! [M_1: fun_li688206603ion_ty,B: option_ty,D_1: option_ty,A: list_char,C_2: list_char] :
      ( ( A != C_2 )
     => ( fun_up424764369ion_ty(fun_up424764369ion_ty(M_1,A,B),C_2,D_1) = fun_up424764369ion_ty(fun_up424764369ion_ty(M_1,C_2,D_1),A,B) ) ) ).

tff(fact_201_fun__upd__twist,axiom,
    ! [M_1: fun_na939144002on_val,B: option1479284511on_val,D_1: option1479284511on_val,A: nat,C_2: nat] :
      ( ( A != C_2 )
     => ( fun_up2041264236on_val(fun_up2041264236on_val(M_1,A,B),C_2,D_1) = fun_up2041264236on_val(fun_up2041264236on_val(M_1,C_2,D_1),A,B) ) ) ).

tff(fact_202_fun__upd__twist,axiom,
    ! [M_1: fun_Pr806764899on_val,B: option_val,D_1: option_val,A: produc1278157519t_char,C_2: produc1278157519t_char] :
      ( ( A != C_2 )
     => ( fun_up204312361on_val(fun_up204312361on_val(M_1,A,B),C_2,D_1) = fun_up204312361on_val(fun_up204312361on_val(M_1,C_2,D_1),A,B) ) ) ).

tff(fact_203_fun__upd__apply,axiom,
    ! [F_1: fun_li1432931796on_val,Y_2: option_val,Z_1: list_char,X_2: list_char] :
      ( ( ( Z_1 = X_2 )
       => ( hAPP_l207779698on_val(fun_up1149430426on_val(F_1,X_2,Y_2),Z_1) = Y_2 ) )
      & ( ( Z_1 != X_2 )
       => ( hAPP_l207779698on_val(fun_up1149430426on_val(F_1,X_2,Y_2),Z_1) = hAPP_l207779698on_val(F_1,Z_1) ) ) ) ).

tff(fact_204_fun__upd__apply,axiom,
    ! [F_1: fun_li688206603ion_ty,Y_2: option_ty,Z_1: list_char,X_2: list_char] :
      ( ( ( Z_1 = X_2 )
       => ( hAPP_l512744617ion_ty(fun_up424764369ion_ty(F_1,X_2,Y_2),Z_1) = Y_2 ) )
      & ( ( Z_1 != X_2 )
       => ( hAPP_l512744617ion_ty(fun_up424764369ion_ty(F_1,X_2,Y_2),Z_1) = hAPP_l512744617ion_ty(F_1,Z_1) ) ) ) ).

tff(fact_205_fun__upd__apply,axiom,
    ! [F_1: fun_na939144002on_val,Y_2: option1479284511on_val,Z_1: nat,X_2: nat] :
      ( ( ( Z_1 = X_2 )
       => ( hAPP_n546249108on_val(fun_up2041264236on_val(F_1,X_2,Y_2),Z_1) = Y_2 ) )
      & ( ( Z_1 != X_2 )
       => ( hAPP_n546249108on_val(fun_up2041264236on_val(F_1,X_2,Y_2),Z_1) = hAPP_n546249108on_val(F_1,Z_1) ) ) ) ).

tff(fact_206_fun__upd__apply,axiom,
    ! [F_1: fun_Pr806764899on_val,Y_2: option_val,Z_1: produc1278157519t_char,X_2: produc1278157519t_char] :
      ( ( ( Z_1 = X_2 )
       => ( hAPP_P2094403585on_val(fun_up204312361on_val(F_1,X_2,Y_2),Z_1) = Y_2 ) )
      & ( ( Z_1 != X_2 )
       => ( hAPP_P2094403585on_val(fun_up204312361on_val(F_1,X_2,Y_2),Z_1) = hAPP_P2094403585on_val(F_1,Z_1) ) ) ) ).

tff(fact_207_fun__upd__same,axiom,
    ! [F_1: fun_li1432931796on_val,X_2: list_char,Y_2: option_val] : hAPP_l207779698on_val(fun_up1149430426on_val(F_1,X_2,Y_2),X_2) = Y_2 ).

tff(fact_208_fun__upd__same,axiom,
    ! [F_1: fun_li688206603ion_ty,X_2: list_char,Y_2: option_ty] : hAPP_l512744617ion_ty(fun_up424764369ion_ty(F_1,X_2,Y_2),X_2) = Y_2 ).

tff(fact_209_fun__upd__same,axiom,
    ! [F_1: fun_na939144002on_val,X_2: nat,Y_2: option1479284511on_val] : hAPP_n546249108on_val(fun_up2041264236on_val(F_1,X_2,Y_2),X_2) = Y_2 ).

tff(fact_210_fun__upd__same,axiom,
    ! [F_1: fun_Pr806764899on_val,X_2: produc1278157519t_char,Y_2: option_val] : hAPP_P2094403585on_val(fun_up204312361on_val(F_1,X_2,Y_2),X_2) = Y_2 ).

tff(fact_211_fun__upd__upd,axiom,
    ! [F_1: fun_li1432931796on_val,X_2: list_char,Y_2: option_val,Z_1: option_val] : fun_up1149430426on_val(fun_up1149430426on_val(F_1,X_2,Y_2),X_2,Z_1) = fun_up1149430426on_val(F_1,X_2,Z_1) ).

tff(fact_212_fun__upd__upd,axiom,
    ! [F_1: fun_li688206603ion_ty,X_2: list_char,Y_2: option_ty,Z_1: option_ty] : fun_up424764369ion_ty(fun_up424764369ion_ty(F_1,X_2,Y_2),X_2,Z_1) = fun_up424764369ion_ty(F_1,X_2,Z_1) ).

tff(fact_213_fun__upd__upd,axiom,
    ! [F_1: fun_na939144002on_val,X_2: nat,Y_2: option1479284511on_val,Z_1: option1479284511on_val] : fun_up2041264236on_val(fun_up2041264236on_val(F_1,X_2,Y_2),X_2,Z_1) = fun_up2041264236on_val(F_1,X_2,Z_1) ).

tff(fact_214_fun__upd__upd,axiom,
    ! [F_1: fun_Pr806764899on_val,X_2: produc1278157519t_char,Y_2: option_val,Z_1: option_val] : fun_up204312361on_val(fun_up204312361on_val(F_1,X_2,Y_2),X_2,Z_1) = fun_up204312361on_val(F_1,X_2,Z_1) ).

tff(fact_215_fun__upd__idem__iff,axiom,
    ! [F_1: fun_li1432931796on_val,X_2: list_char,Y_2: option_val] :
      ( ( fun_up1149430426on_val(F_1,X_2,Y_2) = F_1 )
    <=> ( hAPP_l207779698on_val(F_1,X_2) = Y_2 ) ) ).

tff(fact_216_fun__upd__idem__iff,axiom,
    ! [F_1: fun_li688206603ion_ty,X_2: list_char,Y_2: option_ty] :
      ( ( fun_up424764369ion_ty(F_1,X_2,Y_2) = F_1 )
    <=> ( hAPP_l512744617ion_ty(F_1,X_2) = Y_2 ) ) ).

tff(fact_217_fun__upd__idem__iff,axiom,
    ! [F_1: fun_na939144002on_val,X_2: nat,Y_2: option1479284511on_val] :
      ( ( fun_up2041264236on_val(F_1,X_2,Y_2) = F_1 )
    <=> ( hAPP_n546249108on_val(F_1,X_2) = Y_2 ) ) ).

tff(fact_218_fun__upd__idem__iff,axiom,
    ! [F_1: fun_Pr806764899on_val,X_2: produc1278157519t_char,Y_2: option_val] :
      ( ( fun_up204312361on_val(F_1,X_2,Y_2) = F_1 )
    <=> ( hAPP_P2094403585on_val(F_1,X_2) = Y_2 ) ) ).

tff(fact_219_widen__refl,axiom,
    ! [P_4: list_P1999446415t_char,T_7: ty] : hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_4),T_7),T_7)) ).

tff(fact_220_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(wTrt_1(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_221_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(wTrt_1(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_222_prod__cases3,axiom,
    ! [Y_5: produc1013743697t_char] :
      ~ ! [A_1: list_char,B_2: list_ty,C_4: produc1059328077t_char] : Y_5 != hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),hAPP_P976433298t_char(hAPP_l2048923787t_char(produc2016959032t_char,B_2),C_4)) ).

tff(fact_223_prod__cases3,axiom,
    ! [Y_2: produc1102272487on_val] :
      ~ ! [A_1: produc124828825on_val,B_2: exp_list_char,C_4: produc12694297on_val] : Y_2 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B_2),C_4)) ).

tff(fact_224_prod__cases3,axiom,
    ! [Y_2: produc124828825on_val] :
      ~ ! [A_1: exp_list_char,B_2: fun_na939144002on_val,C_4: fun_li1432931796on_val] : Y_2 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_2),C_4)) ).

tff(fact_225_prod__cases3,axiom,
    ! [Y_5: produc1645268488al_val] :
      ~ ! [A_1: bop,B_2: val,C_4: val] : Y_5 != hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B_2),C_4)) ).

tff(fact_226_prod__cases3,axiom,
    ! [Y_2: produc430140671on_val] :
      ~ ! [A_1: produc2061676504on_val,B_2: list_exp_list_char,C_4: produc12694297on_val] : Y_2 != hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,B_2),C_4)) ).

tff(fact_227_prod__cases3,axiom,
    ! [Y_2: produc2061676504on_val] :
      ~ ! [A_1: list_exp_list_char,B_2: fun_na939144002on_val,C_4: fun_li1432931796on_val] : Y_2 != hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_2),C_4)) ).

tff(fact_228_prod__cases3,axiom,
    ! [Y_5: produc1285161482t_char] :
      ~ ! [A_1: list_list_char,B_2: list_ty,C_4: produc662261637t_char] : Y_5 != hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_2),C_4)) ).

tff(fact_229_prod__cases3,axiom,
    ! [Y_5: produc220283002t_char] :
      ~ ! [A_1: list_ty,B_2: list_val,C_4: exp_list_char] : Y_5 != hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,B_2),C_4)) ).

tff(fact_230_prod__cases3,axiom,
    ! [Y_5: produc1971331930t_char] :
      ~ ! [A_1: list_char,B_2: list_char,C_4: produc2146869324t_char] : Y_5 != hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_2),C_4)) ).

tff(fact_231_prod__cases3,axiom,
    ! [Y_5: produc952412819t_char] :
      ~ ! [A_1: list_char,B_2: list_P1940453997har_ty,C_4: list_P341299826t_char] : Y_5 != hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,B_2),C_4)) ).

tff(fact_232_prod__cases3,axiom,
    ! [Y_2: produc231486621on_val] :
      ~ ! [A_1: produc1102272487on_val,B_2: produc124828825on_val,C_4: produc124828825on_val] : Y_2 != hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_2),C_4)) ).

tff(fact_233_prod__cases3,axiom,
    ! [Y_2: produc409205479on_val] :
      ~ ! [A_1: produc12694297on_val,B_2: fun_na939144002on_val,C_4: fun_li1432931796on_val] : Y_2 != hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_2),C_4)) ).

tff(fact_234_prod__cases3,axiom,
    ! [Y_2: produc87279271on_val] :
      ~ ! [A_1: produc639455274on_val,B_2: list_char,C_4: fun_Pr806764899on_val] : Y_2 != hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_1),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,B_2),C_4)) ).

tff(fact_235_prod__cases3,axiom,
    ! [Y_5: produc1350825965t_char] :
      ~ ! [A_1: produc1278157519t_char,B_2: list_char,C_4: list_char] : Y_5 != hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_1),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B_2),C_4)) ).

tff(fact_236_prod__cases3,axiom,
    ! [Y_5: produc630464863al_val] :
      ~ ! [A_1: produc1645268488al_val,B_2: bop,C_4: product_prod_val_val] : Y_5 != hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_1),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,B_2),C_4)) ).

tff(fact_237_prod__cases3,axiom,
    ! [Y_5: produc800118557al_val] :
      ~ ! [A_1: product_prod_val_val,B_2: val,C_4: val] : Y_5 != hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B_2),C_4)) ).

tff(fact_238_prod__cases3,axiom,
    ! [Y_2: produc1466422861on_val] :
      ~ ! [A_1: produc430140671on_val,B_2: produc2061676504on_val,C_4: produc2061676504on_val] : Y_2 != hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_2),C_4)) ).

tff(fact_239_prod__cases3,axiom,
    ! [Y_5: produc349695911t_char] :
      ~ ! [A_1: produc1285161482t_char,B_2: list_list_char,C_4: produc220283002t_char] : Y_5 != hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_2),C_4)) ).

tff(fact_240_prod__cases3,axiom,
    ! [Y_5: produc1406897475t_char] :
      ~ ! [A_1: produc220283002t_char,B_2: list_ty,C_4: produc662261637t_char] : Y_5 != hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_2),C_4)) ).

tff(fact_241_prod__cases3,axiom,
    ! [Y_5: produc1826280281t_char] :
      ~ ! [A_1: produc662261637t_char,B_2: list_val,C_4: exp_list_char] : Y_5 != hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,B_2),C_4)) ).

tff(fact_242_prod__cases3,axiom,
    ! [Y_5: produc84451751t_char] :
      ~ ! [A_1: produc1971331930t_char,B_2: list_char,C_4: produc952412819t_char] : Y_5 != hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,B_2),C_4)) ).

tff(fact_243_prod__cases3,axiom,
    ! [Y_5: produc740765671t_char] :
      ~ ! [A_1: produc952412819t_char,B_2: list_char,C_4: produc2146869324t_char] : Y_5 != hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_2),C_4)) ).

tff(fact_244_prod__cases3,axiom,
    ! [Y_5: produc494726439t_char] :
      ~ ! [A_1: produc2146869324t_char,B_2: list_P1940453997har_ty,C_4: list_P341299826t_char] : Y_5 != hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,B_2),C_4)) ).

tff(fact_245_prod__cases3,axiom,
    ! [Y_5: produc1534059751t_char] :
      ~ ! [A_1: produc809539159t_char,B_2: list_list_char,C_4: exp_list_char] : Y_5 != hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_1),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,B_2),C_4)) ).

tff(fact_246_prod__induct3,axiom,
    ! [X_2: produc1013743697t_char,Pa: fun_Pr70170387r_bool] :
      ( ! [A_1: list_char,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P1384137393r_bool(Pa,X_2)) ) ).

tff(fact_247_prod__induct3,axiom,
    ! [X_2: produc1102272487on_val,Pa: fun_Pr691271849l_bool] :
      ( ! [A_1: produc124828825on_val,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P282169671l_bool(Pa,X_2)) ) ).

tff(fact_248_prod__induct3,axiom,
    ! [X_2: produc124828825on_val,Pa: fun_Pr680585871l_bool] :
      ( ! [A_1: exp_list_char,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P1708370145l_bool(Pa,X_2)) ) ).

tff(fact_249_prod__induct3,axiom,
    ! [X_2: produc1645268488al_val,Pa: fun_Pr252072522l_bool] :
      ( ! [A_1: bop,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P943837928l_bool(Pa,X_2)) ) ).

tff(fact_250_prod__induct3,axiom,
    ! [X_2: produc430140671on_val,Pa: fun_Pr859510977l_bool] :
      ( ! [A_1: produc2061676504on_val,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P1333315679l_bool(Pa,X_2)) ) ).

tff(fact_251_prod__induct3,axiom,
    ! [X_2: produc2061676504on_val,Pa: fun_Pr248118298l_bool] :
      ( ! [A_1: list_exp_list_char,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P71593144l_bool(Pa,X_2)) ) ).

tff(fact_252_prod__induct3,axiom,
    ! [X_2: produc1285161482t_char,Pa: fun_Pr227936640r_bool] :
      ( ! [A_1: list_list_char,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P92196306r_bool(Pa,X_2)) ) ).

tff(fact_253_prod__induct3,axiom,
    ! [X_2: produc220283002t_char,Pa: fun_Pr46158268r_bool] :
      ( ! [A_1: list_ty,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P1907982426r_bool(Pa,X_2)) ) ).

tff(fact_254_prod__induct3,axiom,
    ! [X_2: produc1971331930t_char,Pa: fun_Pr1861226704r_bool] :
      ( ! [A_1: list_char,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P1680401186r_bool(Pa,X_2)) ) ).

tff(fact_255_prod__induct3,axiom,
    ! [X_2: produc952412819t_char,Pa: fun_Pr1898949769r_bool] :
      ( ! [A_1: list_char,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P659547099r_bool(Pa,X_2)) ) ).

tff(fact_256_prod__induct3,axiom,
    ! [X_2: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
      ( ! [A_1: produc1102272487on_val,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P378063101l_bool(Pa,X_2)) ) ).

tff(fact_257_prod__induct3,axiom,
    ! [X_2: produc409205479on_val,Pa: fun_Pr693020585l_bool] :
      ( ! [A_1: produc12694297on_val,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P1221872711l_bool(Pa,X_2)) ) ).

tff(fact_258_prod__induct3,axiom,
    ! [X_2: produc87279271on_val,Pa: fun_Pr235369833l_bool] :
      ( ! [A_1: produc639455274on_val,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P124632071l_bool(Pa,X_2)) ) ).

tff(fact_259_prod__induct3,axiom,
    ! [X_2: produc1350825965t_char,Pa: fun_Pr1336847023r_bool] :
      ( ! [A_1: produc1278157519t_char,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P2010574925r_bool(Pa,X_2)) ) ).

tff(fact_260_prod__induct3,axiom,
    ! [X_2: produc630464863al_val,Pa: fun_Pr897334561l_bool] :
      ( ! [A_1: produc1645268488al_val,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P738987199l_bool(Pa,X_2)) ) ).

tff(fact_261_prod__induct3,axiom,
    ! [X_2: produc800118557al_val,Pa: fun_Pr832147423l_bool] :
      ( ! [A_1: product_prod_val_val,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P2123002749l_bool(Pa,X_2)) ) ).

tff(fact_262_prod__induct3,axiom,
    ! [X_2: produc1466422861on_val,Pa: fun_Pr302334223l_bool] :
      ( ! [A_1: produc430140671on_val,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P2028072621l_bool(Pa,X_2)) ) ).

tff(fact_263_prod__induct3,axiom,
    ! [X_2: produc349695911t_char,Pa: fun_Pr1895638121r_bool] :
      ( ! [A_1: produc1285161482t_char,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P824029447r_bool(Pa,X_2)) ) ).

tff(fact_264_prod__induct3,axiom,
    ! [X_2: produc1406897475t_char,Pa: fun_Pr1728267013r_bool] :
      ( ! [A_1: produc220283002t_char,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P1240100515r_bool(Pa,X_2)) ) ).

tff(fact_265_prod__induct3,axiom,
    ! [X_2: produc1826280281t_char,Pa: fun_Pr1890037787r_bool] :
      ( ! [A_1: produc662261637t_char,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P1183499705r_bool(Pa,X_2)) ) ).

tff(fact_266_prod__induct3,axiom,
    ! [X_2: produc84451751t_char,Pa: fun_Pr981088873r_bool] :
      ( ! [A_1: produc1971331930t_char,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P975284999r_bool(Pa,X_2)) ) ).

tff(fact_267_prod__induct3,axiom,
    ! [X_2: produc740765671t_char,Pa: fun_Pr1538825897r_bool] :
      ( ! [A_1: produc952412819t_char,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P929449287r_bool(Pa,X_2)) ) ).

tff(fact_268_prod__induct3,axiom,
    ! [X_2: produc494726439t_char,Pa: fun_Pr286306793r_bool] :
      ( ! [A_1: produc2146869324t_char,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P801803911r_bool(Pa,X_2)) ) ).

tff(fact_269_prod__induct3,axiom,
    ! [X_2: produc1534059751t_char,Pa: fun_Pr908866473r_bool] :
      ( ! [A_1: produc809539159t_char,B_2: 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_2),C_4))))
     => hBOOL(hAPP_P1002912327r_bool(Pa,X_2)) ) ).

tff(fact_270_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(wTrt_1(Pa,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_271_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr716652265r_bool,R_2: fun_Pr716652265r_bool] :
      ( ! [X_1: list_exp_list_char,Xa: list_exp_list_char] :
          ( hBOOL(hAPP_f1734260017l_bool(hAPP_P53416969l_bool(member894971540t_char,hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f1734260017l_bool(hAPP_P53416969l_bool(member894971540t_char,hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_272_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr136267935r_bool,R_2: fun_Pr136267935r_bool] :
      ( ! [X_1: exp_list_char,Xa: exp_list_char] :
          ( hBOOL(hAPP_f588675559l_bool(hAPP_P1860450421l_bool(member1199939018t_char,hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f588675559l_bool(hAPP_P1860450421l_bool(member1199939018t_char,hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_273_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr382120745r_bool,R_2: fun_Pr382120745r_bool] :
      ( ! [X_1: list_list_char,Xa: list_list_char] :
          ( hBOOL(hAPP_f479632753l_bool(hAPP_P153687689l_bool(member817832404t_char,hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f479632753l_bool(hAPP_P153687689l_bool(member817832404t_char,hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_274_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr263169771y_bool,R_2: fun_Pr263169771y_bool] :
      ( ! [X_1: list_P1940453997har_ty,Xa: list_P1940453997har_ty] :
          ( hBOOL(hAPP_f288221747l_bool(hAPP_P569585933l_bool(member520253462har_ty,hAPP_l1294856089har_ty(hAPP_l1657578379har_ty(produc1860789535har_ty,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f288221747l_bool(hAPP_P569585933l_bool(member520253462har_ty,hAPP_l1294856089har_ty(hAPP_l1657578379har_ty(produc1860789535har_ty,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_275_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr2024675945r_bool,R_2: fun_Pr2024675945r_bool] :
      ( ! [X_1: list_P341299826t_char,Xa: list_P341299826t_char] :
          ( hBOOL(hAPP_f1748390065l_bool(hAPP_P1503283977l_bool(member1580476948t_char,hAPP_l1334098948t_char(hAPP_l1450984463t_char(produc436875159t_char,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f1748390065l_bool(hAPP_P1503283977l_bool(member1580476948t_char,hAPP_l1334098948t_char(hAPP_l1450984463t_char(produc436875159t_char,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_276_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr1618624239l_bool,R_2: fun_Pr1618624239l_bool] :
      ( ! [X_1: list_val,Xa: list_val] :
          ( hBOOL(hAPP_f348753975l_bool(hAPP_P1033205013l_bool(member273646106st_val,hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f348753975l_bool(hAPP_P1033205013l_bool(member273646106st_val,hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_277_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr306783325y_bool,R_2: fun_Pr306783325y_bool] :
      ( ! [X_1: list_ty,Xa: list_ty] :
          ( hBOOL(hAPP_f433445541l_bool(hAPP_P1019319281l_bool(member104734088ist_ty,hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f433445541l_bool(hAPP_P1019319281l_bool(member104734088ist_ty,hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_278_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr851759157p_bool,R_2: fun_Pr851759157p_bool] :
      ( ! [X_1: bop,Xa: bop] :
          ( hBOOL(hAPP_f1854361213l_bool(hAPP_P1034346913l_bool(member978285664op_bop,hAPP_b1909667208op_bop(hAPP_b1058859669op_bop(product_Pair_bop_bop,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f1854361213l_bool(hAPP_P1034346913l_bool(member978285664op_bop,hAPP_b1909667208op_bop(hAPP_b1058859669op_bop(product_Pair_bop_bop,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_279_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr369549609l_bool,R_2: fun_Pr369549609l_bool] :
      ( ! [X_1: fun_Pr806764899on_val,Xa: fun_Pr806764899on_val] :
          ( hBOOL(hAPP_f983152497l_bool(hAPP_P1953134729l_bool(member781783252on_val,hAPP_f1146435765on_val(hAPP_f1744304433on_val(produc1618304727on_val,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f983152497l_bool(hAPP_P1953134729l_bool(member781783252on_val,hAPP_f1146435765on_val(hAPP_f1744304433on_val(produc1618304727on_val,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_280_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr442654869l_bool,R_2: fun_Pr442654869l_bool] :
      ( ! [X_1: fun_na939144002on_val,Xa: fun_na939144002on_val] :
          ( hBOOL(hAPP_f1754555101l_bool(hAPP_P1679186017l_bool(member1337019328on_val,hAPP_f368284312on_val(hAPP_f1805337205on_val(produc1712663241on_val,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f1754555101l_bool(hAPP_P1679186017l_bool(member1337019328on_val,hAPP_f368284312on_val(hAPP_f1805337205on_val(produc1712663241on_val,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_281_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr673659369l_bool,R_2: fun_Pr673659369l_bool] :
      ( ! [X_1: fun_li1432931796on_val,Xa: fun_li1432931796on_val] :
          ( hBOOL(hAPP_f1661305905l_bool(hAPP_P1878549513l_bool(member490182804on_val,hAPP_f1741070310on_val(hAPP_f864891091on_val(produc1960514199on_val,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f1661305905l_bool(hAPP_P1878549513l_bool(member490182804on_val,hAPP_f1741070310on_val(hAPP_f864891091on_val(produc1960514199on_val,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_282_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr680585871l_bool,R_2: fun_Pr680585871l_bool] :
      ( ! [X_1: exp_list_char,Xa: produc12694297on_val] :
          ( hBOOL(hAPP_f91506671l_bool(hAPP_P2015860941l_bool(member840932460on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f91506671l_bool(hAPP_P2015860941l_bool(member840932460on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_283_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr1696029455l_bool,R_2: fun_Pr1696029455l_bool] :
      ( ! [X_1: fun_na939144002on_val,Xa: fun_li1432931796on_val] :
          ( hBOOL(hAPP_f966411375l_bool(hAPP_P998768845l_bool(member763590124on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f966411375l_bool(hAPP_P998768845l_bool(member763590124on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_284_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr315804320l_bool,R_2: fun_Pr315804320l_bool] :
      ( ! [X_1: list_char,Xa: fun_Pr806764899on_val] :
          ( hBOOL(hAPP_f1134950784l_bool(hAPP_P1217996045l_bool(member1542417277on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f1134950784l_bool(hAPP_P1217996045l_bool(member1542417277on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_285_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr252072522l_bool,R_2: fun_Pr252072522l_bool] :
      ( ! [X_1: bop,Xa: product_prod_val_val] :
          ( hBOOL(hAPP_f742333458l_bool(hAPP_P1653675595l_bool(member1417904245al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f742333458l_bool(hAPP_P1653675595l_bool(member1417904245al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_286_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr2081272681l_bool,R_2: fun_Pr2081272681l_bool] :
      ( ! [X_1: val,Xa: val] :
          ( hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_287_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr248118298l_bool,R_2: fun_Pr248118298l_bool] :
      ( ! [X_1: list_exp_list_char,Xa: produc12694297on_val] :
          ( hBOOL(hAPP_f837795298l_bool(hAPP_P483670507l_bool(member1972431429on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f837795298l_bool(hAPP_P483670507l_bool(member1972431429on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_288_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr227936640r_bool,R_2: fun_Pr227936640r_bool] :
      ( ! [X_1: list_list_char,Xa: produc220283002t_char] :
          ( hBOOL(hAPP_f1780084320l_bool(hAPP_P1472618637l_bool(member133545693t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f1780084320l_bool(hAPP_P1472618637l_bool(member133545693t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_289_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr46158268r_bool,R_2: fun_Pr46158268r_bool] :
      ( ! [X_1: list_ty,Xa: produc662261637t_char] :
          ( hBOOL(hAPP_f1746574980l_bool(hAPP_P1198052655l_bool(member140606439t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f1746574980l_bool(hAPP_P1198052655l_bool(member140606439t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_290_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr827765831r_bool,R_2: fun_Pr827765831r_bool] :
      ( ! [X_1: list_val,Xa: exp_list_char] :
          ( hBOOL(hAPP_f1314764175l_bool(hAPP_P845017029l_bool(member699351154t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f1314764175l_bool(hAPP_P845017029l_bool(member699351154t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_291_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr1898949769r_bool,R_2: fun_Pr1898949769r_bool] :
      ( ! [X_1: list_char,Xa: produc2146869324t_char] :
          ( hBOOL(hAPP_f2050077417l_bool(hAPP_P1517699917l_bool(member1771544038t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f2050077417l_bool(hAPP_P1517699917l_bool(member1771544038t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_292_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr1669461698r_bool,R_2: fun_Pr1669461698r_bool] :
      ( ! [X_1: list_P1940453997har_ty,Xa: list_P341299826t_char] :
          ( hBOOL(hAPP_f1161798306l_bool(hAPP_P1327510541l_bool(member1379348767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f1161798306l_bool(hAPP_P1327510541l_bool(member1379348767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_293_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr1336948301r_bool,R_2: fun_Pr1336948301r_bool] :
      ( ! [X_1: list_list_char,Xa: exp_list_char] :
          ( hBOOL(hAPP_f82569901l_bool(hAPP_P1293136973l_bool(member1840112042t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f82569901l_bool(hAPP_P1293136973l_bool(member1840112042t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_294_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr691271849l_bool,R_2: fun_Pr691271849l_bool] :
      ( ! [X_1: produc124828825on_val,Xa: produc124828825on_val] :
          ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_295_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr565113489r_bool,R_2: fun_Pr565113489r_bool] :
      ( ! [X_1: list_char,Xa: list_char] :
          ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_296_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr859510977l_bool,R_2: fun_Pr859510977l_bool] :
      ( ! [X_1: produc2061676504on_val,Xa: produc2061676504on_val] :
          ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_297_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr1861226704r_bool,R_2: fun_Pr1861226704r_bool] :
      ( ! [X_1: list_char,Xa: produc952412819t_char] :
          ( hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_298_pred__equals__eq2,axiom,
    ! [S_4: fun_Pr70170387r_bool,R_2: fun_Pr70170387r_bool] :
      ( ! [X_1: list_char,Xa: produc1025221954t_char] :
          ( hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,X_1),Xa)),R_2))
        <=> hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,X_1),Xa)),S_4)) )
    <=> ( R_2 = S_4 ) ) ).

tff(fact_299_prod_Oexhaust,axiom,
    ! [Y_4: produc809539159t_char] :
      ~ ! [A_1: list_list_char,B_2: exp_list_char] : Y_4 != hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_2) ).

tff(fact_300_prod_Oexhaust,axiom,
    ! [Y_4: produc2146869324t_char] :
      ~ ! [A_1: list_P1940453997har_ty,B_2: list_P341299826t_char] : Y_4 != hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_2) ).

tff(fact_301_prod_Oexhaust,axiom,
    ! [Y_4: produc952412819t_char] :
      ~ ! [A_1: list_char,B_2: produc2146869324t_char] : Y_4 != hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_2) ).

tff(fact_302_prod_Oexhaust,axiom,
    ! [Y_4: produc1971331930t_char] :
      ~ ! [A_1: list_char,B_2: produc952412819t_char] : Y_4 != hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_2) ).

tff(fact_303_prod_Oexhaust,axiom,
    ! [Y_4: produc662261637t_char] :
      ~ ! [A_1: list_val,B_2: exp_list_char] : Y_4 != hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_2) ).

tff(fact_304_prod_Oexhaust,axiom,
    ! [Y_4: produc220283002t_char] :
      ~ ! [A_1: list_ty,B_2: produc662261637t_char] : Y_4 != hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_2) ).

tff(fact_305_prod_Oexhaust,axiom,
    ! [Y_4: produc1285161482t_char] :
      ~ ! [A_1: list_list_char,B_2: produc220283002t_char] : Y_4 != hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_2) ).

tff(fact_306_prod_Oexhaust,axiom,
    ! [Y_2: produc2061676504on_val] :
      ~ ! [A_1: list_exp_list_char,B_2: produc12694297on_val] : Y_2 != hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_2) ).

tff(fact_307_prod_Oexhaust,axiom,
    ! [Y_2: produc430140671on_val] :
      ~ ! [A_1: produc2061676504on_val,B_2: produc2061676504on_val] : Y_2 != hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_2) ).

tff(fact_308_prod_Oexhaust,axiom,
    ! [Y_4: product_prod_val_val] :
      ~ ! [A_1: val,B_2: val] : Y_4 != hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_2) ).

tff(fact_309_prod_Oexhaust,axiom,
    ! [Y_4: produc1645268488al_val] :
      ~ ! [A_1: bop,B_2: product_prod_val_val] : Y_4 != hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_2) ).

tff(fact_310_prod_Oexhaust,axiom,
    ! [Y_4: produc1278157519t_char] :
      ~ ! [A_1: list_char,B_2: list_char] : Y_4 != hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_2) ).

tff(fact_311_prod_Oexhaust,axiom,
    ! [Y_2: produc639455274on_val] :
      ~ ! [A_1: list_char,B_2: fun_Pr806764899on_val] : Y_2 != hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_2) ).

tff(fact_312_prod_Oexhaust,axiom,
    ! [Y_2: produc12694297on_val] :
      ~ ! [A_1: fun_na939144002on_val,B_2: fun_li1432931796on_val] : Y_2 != hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_2) ).

tff(fact_313_prod_Oexhaust,axiom,
    ! [Y_2: produc124828825on_val] :
      ~ ! [A_1: exp_list_char,B_2: produc12694297on_val] : Y_2 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_2) ).

tff(fact_314_prod_Oexhaust,axiom,
    ! [Y_2: produc1102272487on_val] :
      ~ ! [A_1: produc124828825on_val,B_2: produc124828825on_val] : Y_2 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_2) ).

tff(fact_315_PairE,axiom,
    ! [P_3: produc809539159t_char] :
      ~ ! [X_1: list_list_char,Y_1: exp_list_char] : P_3 != hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,X_1),Y_1) ).

tff(fact_316_PairE,axiom,
    ! [P_3: produc2146869324t_char] :
      ~ ! [X_1: list_P1940453997har_ty,Y_1: list_P341299826t_char] : P_3 != hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,X_1),Y_1) ).

tff(fact_317_PairE,axiom,
    ! [P_3: produc952412819t_char] :
      ~ ! [X_1: list_char,Y_1: produc2146869324t_char] : P_3 != hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,X_1),Y_1) ).

tff(fact_318_PairE,axiom,
    ! [P_3: produc1971331930t_char] :
      ~ ! [X_1: list_char,Y_1: produc952412819t_char] : P_3 != hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,X_1),Y_1) ).

tff(fact_319_PairE,axiom,
    ! [P_3: produc662261637t_char] :
      ~ ! [X_1: list_val,Y_1: exp_list_char] : P_3 != hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,X_1),Y_1) ).

tff(fact_320_PairE,axiom,
    ! [P_3: produc220283002t_char] :
      ~ ! [X_1: list_ty,Y_1: produc662261637t_char] : P_3 != hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,X_1),Y_1) ).

tff(fact_321_PairE,axiom,
    ! [P_3: produc1285161482t_char] :
      ~ ! [X_1: list_list_char,Y_1: produc220283002t_char] : P_3 != hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,X_1),Y_1) ).

tff(fact_322_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_323_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_324_PairE,axiom,
    ! [P_3: product_prod_val_val] :
      ~ ! [X_1: val,Y_1: val] : P_3 != hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_1),Y_1) ).

tff(fact_325_PairE,axiom,
    ! [P_3: produc1645268488al_val] :
      ~ ! [X_1: bop,Y_1: product_prod_val_val] : P_3 != hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,X_1),Y_1) ).

tff(fact_326_PairE,axiom,
    ! [P_3: produc1278157519t_char] :
      ~ ! [X_1: list_char,Y_1: list_char] : P_3 != hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_1),Y_1) ).

tff(fact_327_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_328_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_329_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_330_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_331_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1336948301r_bool] :
      ( ? [X1: produc809539159t_char] : hBOOL(hAPP_P2014166431r_bool(Pa,X1))
    <=> ? [A_1: list_list_char,B_2: exp_list_char] : hBOOL(hAPP_P2014166431r_bool(Pa,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_2))) ) ).

tff(fact_332_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1669461698r_bool] :
      ( ? [X1: produc2146869324t_char] : hBOOL(hAPP_P828904212r_bool(Pa,X1))
    <=> ? [A_1: list_P1940453997har_ty,B_2: list_P341299826t_char] : hBOOL(hAPP_P828904212r_bool(Pa,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_2))) ) ).

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_2: produc2146869324t_char] : hBOOL(hAPP_P659547099r_bool(Pa,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_2))) ) ).

tff(fact_334_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1861226704r_bool] :
      ( ? [X1: produc1971331930t_char] : hBOOL(hAPP_P1680401186r_bool(Pa,X1))
    <=> ? [A_1: list_char,B_2: produc952412819t_char] : hBOOL(hAPP_P1680401186r_bool(Pa,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_2))) ) ).

tff(fact_335_split__paired__Ex,axiom,
    ! [Pa: fun_Pr827765831r_bool] :
      ( ? [X1: produc662261637t_char] : hBOOL(hAPP_P2118621157r_bool(Pa,X1))
    <=> ? [A_1: list_val,B_2: exp_list_char] : hBOOL(hAPP_P2118621157r_bool(Pa,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_2))) ) ).

tff(fact_336_split__paired__Ex,axiom,
    ! [Pa: fun_Pr46158268r_bool] :
      ( ? [X1: produc220283002t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,X1))
    <=> ? [A_1: list_ty,B_2: produc662261637t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_2))) ) ).

tff(fact_337_split__paired__Ex,axiom,
    ! [Pa: fun_Pr227936640r_bool] :
      ( ? [X1: produc1285161482t_char] : hBOOL(hAPP_P92196306r_bool(Pa,X1))
    <=> ? [A_1: list_list_char,B_2: produc220283002t_char] : hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_2))) ) ).

tff(fact_338_split__paired__Ex,axiom,
    ! [Pa: fun_Pr248118298l_bool] :
      ( ? [X1: produc2061676504on_val] : hBOOL(hAPP_P71593144l_bool(Pa,X1))
    <=> ? [A_1: list_exp_list_char,B_2: produc12694297on_val] : hBOOL(hAPP_P71593144l_bool(Pa,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_2))) ) ).

tff(fact_339_split__paired__Ex,axiom,
    ! [Pa: fun_Pr859510977l_bool] :
      ( ? [X1: produc430140671on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,X1))
    <=> ? [A_1: produc2061676504on_val,B_2: produc2061676504on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_2))) ) ).

tff(fact_340_split__paired__Ex,axiom,
    ! [Pa: fun_Pr2081272681l_bool] :
      ( ? [X1: product_prod_val_val] : hBOOL(hAPP_P929938951l_bool(Pa,X1))
    <=> ? [A_1: val,B_2: val] : hBOOL(hAPP_P929938951l_bool(Pa,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_2))) ) ).

tff(fact_341_split__paired__Ex,axiom,
    ! [Pa: fun_Pr252072522l_bool] :
      ( ? [X1: produc1645268488al_val] : hBOOL(hAPP_P943837928l_bool(Pa,X1))
    <=> ? [A_1: bop,B_2: product_prod_val_val] : hBOOL(hAPP_P943837928l_bool(Pa,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_2))) ) ).

tff(fact_342_split__paired__Ex,axiom,
    ! [Pa: fun_Pr565113489r_bool] :
      ( ? [X1: produc1278157519t_char] : hBOOL(hAPP_P449474095r_bool(Pa,X1))
    <=> ? [A_1: list_char,B_2: list_char] : hBOOL(hAPP_P449474095r_bool(Pa,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_2))) ) ).

tff(fact_343_split__paired__Ex,axiom,
    ! [Pa: fun_Pr315804320l_bool] :
      ( ? [X1: produc639455274on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,X1))
    <=> ? [A_1: list_char,B_2: fun_Pr806764899on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_2))) ) ).

tff(fact_344_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1696029455l_bool] :
      ( ? [X1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
    <=> ? [A_1: fun_na939144002on_val,B_2: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(Pa,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_2))) ) ).

tff(fact_345_split__paired__Ex,axiom,
    ! [Pa: fun_Pr680585871l_bool] :
      ( ? [X1: produc124828825on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
    <=> ? [A_1: exp_list_char,B_2: produc12694297on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_2))) ) ).

tff(fact_346_split__paired__Ex,axiom,
    ! [Pa: fun_Pr691271849l_bool] :
      ( ? [X1: produc1102272487on_val] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
    <=> ? [A_1: produc124828825on_val,B_2: produc124828825on_val] : hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_2))) ) ).

tff(fact_347_widen__trans,axiom,
    ! [T_6: ty,P_2: list_P1999446415t_char,S_6: ty,U_1: ty] :
      ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_2),S_6),U_1))
     => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_2),U_1),T_6))
       => hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_2),S_6),T_6)) ) ) ).

tff(fact_348_InitBlockRed_I5_J,axiom,
    hBOOL(wTrt_1(p,ha,e,block_list_char(v_1,t_1,seq_list_char(lAss_list_char(v_1,hAPP_v834067052t_char(val_list_char,v)),ea)),t)) ).

tff(fact_349_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_350_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_351_red__preserves__defass,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(wf_J_mdecl,Pa))
     => ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(d_list_char(Eb,hAPP_f363827556r_bool(some_f80346385r_bool,dom_list_char_val(Lb))))
         => hBOOL(d_list_char(E_b,hAPP_f363827556r_bool(some_f80346385r_bool,dom_list_char_val(L_b)))) ) ) ) ).

tff(fact_352_option_Oinject,axiom,
    ! [A: nat,A_3: nat] :
      ( ( hAPP_nat_option_nat(some_nat,A) = hAPP_nat_option_nat(some_nat,A_3) )
    <=> ( A = A_3 ) ) ).

tff(fact_353_option_Oinject,axiom,
    ! [A: produc639455274on_val,A_3: produc639455274on_val] :
      ( ( hAPP_P1510515380on_val(some_P948696889on_val,A) = hAPP_P1510515380on_val(some_P948696889on_val,A_3) )
    <=> ( A = A_3 ) ) ).

tff(fact_354_option_Oinject,axiom,
    ! [A: ty,A_3: ty] :
      ( ( hAPP_ty_option_ty(some_ty,A) = hAPP_ty_option_ty(some_ty,A_3) )
    <=> ( A = A_3 ) ) ).

tff(fact_355_option_Oinject,axiom,
    ! [A: fun_list_char_bool,A_3: fun_list_char_bool] :
      ( ( hAPP_f363827556r_bool(some_f80346385r_bool,A) = hAPP_f363827556r_bool(some_f80346385r_bool,A_3) )
    <=> ( A = A_3 ) ) ).

tff(fact_356_option_Oinject,axiom,
    ! [A: val,A_3: val] :
      ( ( hAPP_val_option_val(some_val,A) = hAPP_val_option_val(some_val,A_3) )
    <=> ( A = A_3 ) ) ).

tff(fact_357_curryI,axiom,
    ! [F_1: fun_Pr1336948301r_bool,A: list_list_char,B: exp_list_char] :
      ( hBOOL(hAPP_P2014166431r_bool(F_1,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B)))
     => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(produc288369490r_bool(F_1),A),B)) ) ).

tff(fact_358_curryI,axiom,
    ! [F_1: fun_Pr1669461698r_bool,A: list_P1940453997har_ty,B: list_P341299826t_char] :
      ( hBOOL(hAPP_P828904212r_bool(F_1,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B)))
     => hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(produc2116052801r_bool(F_1),A),B)) ) ).

tff(fact_359_curryI,axiom,
    ! [F_1: fun_Pr1898949769r_bool,A: list_char,B: produc2146869324t_char] :
      ( hBOOL(hAPP_P659547099r_bool(F_1,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B)))
     => hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(produc266042248r_bool(F_1),A),B)) ) ).

tff(fact_360_curryI,axiom,
    ! [F_1: fun_Pr1861226704r_bool,A: list_char,B: produc952412819t_char] :
      ( hBOOL(hAPP_P1680401186r_bool(F_1,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B)))
     => hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(produc1588781647r_bool(F_1),A),B)) ) ).

tff(fact_361_curryI,axiom,
    ! [F_1: fun_Pr827765831r_bool,A: list_val,B: exp_list_char] :
      ( hBOOL(hAPP_P2118621157r_bool(F_1,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B)))
     => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F_1),A),B)) ) ).

tff(fact_362_curryI,axiom,
    ! [F_1: fun_Pr46158268r_bool,A: list_ty,B: produc662261637t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(F_1,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B)))
     => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F_1),A),B)) ) ).

tff(fact_363_curryI,axiom,
    ! [F_1: fun_Pr227936640r_bool,A: list_list_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P92196306r_bool(F_1,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B)))
     => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F_1),A),B)) ) ).

tff(fact_364_curryI,axiom,
    ! [F_1: fun_Pr248118298l_bool,A: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P71593144l_bool(F_1,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(produc1838470831l_bool(F_1),A),B)) ) ).

tff(fact_365_curryI,axiom,
    ! [F_1: fun_Pr859510977l_bool,A: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P1333315679l_bool(F_1,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B)))
     => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(produc2053127004l_bool(F_1),A),B)) ) ).

tff(fact_366_curryI,axiom,
    ! [F_1: fun_Pr2081272681l_bool,A: val,B: val] :
      ( hBOOL(hAPP_P929938951l_bool(F_1,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B)))
     => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(produc886919678l_bool(F_1),A),B)) ) ).

tff(fact_367_curryI,axiom,
    ! [F_1: fun_Pr252072522l_bool,A: bop,B: product_prod_val_val] :
      ( hBOOL(hAPP_P943837928l_bool(F_1,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B)))
     => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(produc1555310053l_bool(F_1),A),B)) ) ).

tff(fact_368_curryI,axiom,
    ! [F_1: fun_Pr565113489r_bool,A: list_char,B: list_char] :
      ( hBOOL(hAPP_P449474095r_bool(F_1,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B)))
     => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(produc95371820r_bool(F_1),A),B)) ) ).

tff(fact_369_curryI,axiom,
    ! [F_1: fun_Pr315804320l_bool,A: list_char,B: fun_Pr806764899on_val] :
      ( hBOOL(hAPP_P1235399154l_bool(F_1,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B)))
     => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F_1),A),B)) ) ).

tff(fact_370_curryI,axiom,
    ! [F_1: fun_Pr1696029455l_bool,A: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(F_1,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B)))
     => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F_1),A),B)) ) ).

tff(fact_371_curryI,axiom,
    ! [F_1: fun_Pr680585871l_bool,A: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(F_1,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F_1),A),B)) ) ).

tff(fact_372_curryI,axiom,
    ! [F_1: fun_Pr691271849l_bool,A: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P282169671l_bool(F_1,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B)))
     => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F_1),A),B)) ) ).

tff(fact_373_red__lcl__add,axiom,
    ! [L_0: 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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_f1453283057l_bool(hAPP_P1303341961l_bool(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,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,L_b))))),red(Pa))) ) ).

tff(fact_374_lconf__upd,axiom,
    ! [Va_1: list_char,Va: val,Ta: ty,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(conf_P373316194t_char(Pa,Hb,Va,Ta))
       => ( ( hAPP_l512744617ion_ty(Ea,Va_1) = hAPP_ty_option_ty(some_ty,Ta) )
         => hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Hb),fun_up1149430426on_val(Lb,Va_1,hAPP_val_option_val(some_val,Va))),Ea)) ) ) ) ).

tff(fact_375_lconf__upd2,axiom,
    ! [Va_1: list_char,Va: val,Ta: ty,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(conf_P373316194t_char(Pa,Hb,Va,Ta))
       => hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Hb),fun_up1149430426on_val(Lb,Va_1,hAPP_val_option_val(some_val,Va))),fun_up424764369ion_ty(Ea,Va_1,hAPP_ty_option_ty(some_ty,Ta)))) ) ) ).

tff(fact_376_in__lex__prod,axiom,
    ! [A: list_exp_list_char,B: produc12694297on_val,A_3: list_exp_list_char,B_3: produc12694297on_val,R_1: fun_Pr716652265r_bool,S: fun_Pr693020585l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_3),B_3))),lex_pr1541028704on_val(R_1,S)))
    <=> ( hBOOL(hAPP_f1734260017l_bool(hAPP_P53416969l_bool(member894971540t_char,hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,A),A_3)),R_1))
        | ( ( A = A_3 )
          & hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(member563141460on_val,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,B),B_3)),S)) ) ) ) ).

tff(fact_377_in__lex__prod,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,A_3: exp_list_char,B_3: produc12694297on_val,R_1: fun_Pr136267935r_bool,S: fun_Pr693020585l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_3),B_3))),lex_pr69619957on_val(R_1,S)))
    <=> ( hBOOL(hAPP_f588675559l_bool(hAPP_P1860450421l_bool(member1199939018t_char,hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,A),A_3)),R_1))
        | ( ( A = A_3 )
          & hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(member563141460on_val,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,B),B_3)),S)) ) ) ) ).

tff(fact_378_in__lex__prod,axiom,
    ! [A: list_list_char,B: exp_list_char,A_3: list_list_char,B_3: exp_list_char,R_1: fun_Pr382120745r_bool,S: fun_Pr136267935r_bool] :
      ( hBOOL(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(member1999287380t_char,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_3),B_3))),lex_pr1787105337t_char(R_1,S)))
    <=> ( hBOOL(hAPP_f479632753l_bool(hAPP_P153687689l_bool(member817832404t_char,hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A),A_3)),R_1))
        | ( ( A = A_3 )
          & hBOOL(hAPP_f588675559l_bool(hAPP_P1860450421l_bool(member1199939018t_char,hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,B),B_3)),S)) ) ) ) ).

tff(fact_379_in__lex__prod,axiom,
    ! [A: list_P1940453997har_ty,B: list_P341299826t_char,A_3: list_P1940453997har_ty,B_3: list_P341299826t_char,R_1: fun_Pr263169771y_bool,S: fun_Pr2024675945r_bool] :
      ( hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(member1551446420t_char,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_3),B_3))),lex_pr213428520t_char(R_1,S)))
    <=> ( hBOOL(hAPP_f288221747l_bool(hAPP_P569585933l_bool(member520253462har_ty,hAPP_l1294856089har_ty(hAPP_l1657578379har_ty(produc1860789535har_ty,A),A_3)),R_1))
        | ( ( A = A_3 )
          & hBOOL(hAPP_f1748390065l_bool(hAPP_P1503283977l_bool(member1580476948t_char,hAPP_l1334098948t_char(hAPP_l1450984463t_char(produc436875159t_char,B),B_3)),S)) ) ) ) ).

tff(fact_380_in__lex__prod,axiom,
    ! [A: list_char,B: produc2146869324t_char,A_3: list_char,B_3: produc2146869324t_char,R_1: fun_Pr565113489r_bool,S: fun_Pr286306793r_bool] :
      ( hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(member1607118676t_char,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_3),B_3))),lex_pr167435119t_char(R_1,S)))
    <=> ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),A_3)),R_1))
        | ( ( A = A_3 )
          & hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(member1551446420t_char,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,B),B_3)),S)) ) ) ) ).

tff(fact_381_in__lex__prod,axiom,
    ! [A: list_char,B: produc952412819t_char,A_3: list_char,B_3: produc952412819t_char,R_1: fun_Pr565113489r_bool,S: fun_Pr1538825897r_bool] :
      ( hBOOL(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(member162552852t_char,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_3),B_3))),lex_pr1668767798t_char(R_1,S)))
    <=> ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),A_3)),R_1))
        | ( ( A = A_3 )
          & hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(member1607118676t_char,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,B),B_3)),S)) ) ) ) ).

tff(fact_382_in__lex__prod,axiom,
    ! [A: list_val,B: exp_list_char,A_3: list_val,B_3: exp_list_char,R_1: fun_Pr1618624239l_bool,S: fun_Pr136267935r_bool] :
      ( hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(member1161907014t_char,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_3),B_3))),lex_pr307591827t_char(R_1,S)))
    <=> ( hBOOL(hAPP_f348753975l_bool(hAPP_P1033205013l_bool(member273646106st_val,hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,A),A_3)),R_1))
        | ( ( A = A_3 )
          & hBOOL(hAPP_f588675559l_bool(hAPP_P1860450421l_bool(member1199939018t_char,hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,B),B_3)),S)) ) ) ) ).

tff(fact_383_in__lex__prod,axiom,
    ! [A: list_ty,B: produc662261637t_char,A_3: list_ty,B_3: produc662261637t_char,R_1: fun_Pr306783325y_bool,S: fun_Pr1890037787r_bool] :
      ( hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(member125098544t_char,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_3),B_3))),lex_pr1588300168t_char(R_1,S)))
    <=> ( hBOOL(hAPP_f433445541l_bool(hAPP_P1019319281l_bool(member104734088ist_ty,hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,A),A_3)),R_1))
        | ( ( A = A_3 )
          & hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(member1161907014t_char,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,B),B_3)),S)) ) ) ) ).

tff(fact_384_in__lex__prod,axiom,
    ! [A: list_list_char,B: produc220283002t_char,A_3: list_list_char,B_3: produc220283002t_char,R_1: fun_Pr382120745r_bool,S: fun_Pr1728267013r_bool] :
      ( hBOOL(hAPP_f528956081l_bool(hAPP_P325013257l_bool(member1420286996t_char,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_3),B_3))),lex_pr1876288492t_char(R_1,S)))
    <=> ( hBOOL(hAPP_f479632753l_bool(hAPP_P153687689l_bool(member817832404t_char,hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A),A_3)),R_1))
        | ( ( A = A_3 )
          & hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(member125098544t_char,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,B),B_3)),S)) ) ) ) ).

tff(fact_385_in__lex__prod,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,A_3: produc2061676504on_val,B_3: produc2061676504on_val,R_1: fun_Pr859510977l_bool,S: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(member88670778on_val,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_3),B_3))),lex_pr2110711565on_val(R_1,S)))
    <=> ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),A_3)),R_1))
        | ( ( A = A_3 )
          & hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B),B_3)),S)) ) ) ) ).

tff(fact_386_in__lex__prod,axiom,
    ! [A: val,B: val,A_3: val,B_3: val,R_1: fun_Pr2081272681l_bool,S: fun_Pr2081272681l_bool] :
      ( hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(member837208074al_val,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_3),B_3))),lex_prod_val_val(R_1,S)))
    <=> ( hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),A_3)),R_1))
        | ( ( A = A_3 )
          & hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B),B_3)),S)) ) ) ) ).

tff(fact_387_in__lex__prod,axiom,
    ! [A: bop,B: product_prod_val_val,A_3: bop,B_3: product_prod_val_val,R_1: fun_Pr851759157p_bool,S: fun_Pr832147423l_bool] :
      ( hBOOL(hAPP_f126136681l_bool(hAPP_P982127993l_bool(member1732271180al_val,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_3),B_3))),lex_pr1932514710al_val(R_1,S)))
    <=> ( hBOOL(hAPP_f1854361213l_bool(hAPP_P1034346913l_bool(member978285664op_bop,hAPP_b1909667208op_bop(hAPP_b1058859669op_bop(product_Pair_bop_bop,A),A_3)),R_1))
        | ( ( A = A_3 )
          & hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(member837208074al_val,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,B),B_3)),S)) ) ) ) ).

tff(fact_388_in__lex__prod,axiom,
    ! [A: list_char,B: list_char,A_3: list_char,B_3: list_char,R_1: fun_Pr565113489r_bool,S: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f851858423l_bool(hAPP_P786771093l_bool(member794220506t_char,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_3),B_3))),lex_pr280535005t_char(R_1,S)))
    <=> ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),A_3)),R_1))
        | ( ( A = A_3 )
          & hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B),B_3)),S)) ) ) ) ).

tff(fact_389_in__lex__prod,axiom,
    ! [A: list_char,B: fun_Pr806764899on_val,A_3: list_char,B_3: fun_Pr806764899on_val,R_1: fun_Pr565113489r_bool,S: fun_Pr369549609l_bool] :
      ( hBOOL(hAPP_f665343921l_bool(hAPP_P502294281l_bool(member1322055188on_val,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_3),B_3))),lex_pr1971266694on_val(R_1,S)))
    <=> ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),A_3)),R_1))
        | ( ( A = A_3 )
          & hBOOL(hAPP_f983152497l_bool(hAPP_P1953134729l_bool(member781783252on_val,hAPP_f1146435765on_val(hAPP_f1744304433on_val(produc1618304727on_val,B),B_3)),S)) ) ) ) ).

tff(fact_390_in__lex__prod,axiom,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,A_3: fun_na939144002on_val,B_3: fun_li1432931796on_val,R_1: fun_Pr442654869l_bool,S: fun_Pr673659369l_bool] :
      ( hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(member563141460on_val,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_3),B_3))),lex_pr731210613on_val(R_1,S)))
    <=> ( hBOOL(hAPP_f1754555101l_bool(hAPP_P1679186017l_bool(member1337019328on_val,hAPP_f368284312on_val(hAPP_f1805337205on_val(produc1712663241on_val,A),A_3)),R_1))
        | ( ( A = A_3 )
          & hBOOL(hAPP_f1661305905l_bool(hAPP_P1878549513l_bool(member490182804on_val,hAPP_f1741070310on_val(hAPP_f864891091on_val(produc1960514199on_val,B),B_3)),S)) ) ) ) ).

tff(fact_391_in__lex__prod,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,A_3: produc124828825on_val,B_3: produc124828825on_val,R_1: fun_Pr691271849l_bool,S: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(member808015754on_val,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_3),B_3))),lex_pr1038007919on_val(R_1,S)))
    <=> ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),A_3)),R_1))
        | ( ( A = A_3 )
          & hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B),B_3)),S)) ) ) ) ).

tff(fact_392_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_393_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_394_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_395_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_396_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_397_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_398_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_399_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_400_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_401_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_402_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_403_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_404_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_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_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_407_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_408_splitI,axiom,
    ! [F_1: fun_li221477r_bool,A: list_list_char,B: exp_list_char] :
      ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(F_1,A),B))
     => hBOOL(hAPP_P2014166431r_bool(hAPP_f1484794973r_bool(produc1732333873r_bool,F_1),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B))) ) ).

tff(fact_409_splitI,axiom,
    ! [F_1: fun_li1305328058r_bool,A: list_P1940453997har_ty,B: list_P341299826t_char] :
      ( hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(F_1,A),B))
     => hBOOL(hAPP_P828904212r_bool(hAPP_f895126887r_bool(produc1596557472r_bool,F_1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B))) ) ).

tff(fact_410_splitI,axiom,
    ! [F_1: fun_li485148903r_bool,A: list_char,B: produc2146869324t_char] :
      ( hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(F_1,A),B))
     => hBOOL(hAPP_P659547099r_bool(hAPP_f252398939r_bool(produc1324280167r_bool,F_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B))) ) ).

tff(fact_411_splitI,axiom,
    ! [F_1: fun_li522008110r_bool,A: list_char,B: produc952412819t_char] :
      ( hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(F_1,A),B))
     => hBOOL(hAPP_P1680401186r_bool(hAPP_f952817385r_bool(produc723279022r_bool,F_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B))) ) ).

tff(fact_412_splitI,axiom,
    ! [F_1: fun_li826105035r_bool,A: list_val,B: exp_list_char] :
      ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(F_1,A),B))
     => hBOOL(hAPP_P2118621157r_bool(hAPP_f1697332217r_bool(produc21910851r_bool,F_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B))) ) ).

tff(fact_413_splitI,axiom,
    ! [F_1: fun_li887890578r_bool,A: list_ty,B: produc662261637t_char] :
      ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(F_1,A),B))
     => hBOOL(hAPP_P1907982426r_bool(hAPP_f102021095r_bool(produc154616760r_bool,F_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B))) ) ).

tff(fact_414_splitI,axiom,
    ! [F_1: fun_li1024794712r_bool,A: list_list_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(F_1,A),B))
     => hBOOL(hAPP_P92196306r_bool(hAPP_f1613448899r_bool(produc2027921764r_bool,F_1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B))) ) ).

tff(fact_415_splitI,axiom,
    ! [F_1: fun_li1372729616l_bool,A: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(F_1,A),B))
     => hBOOL(hAPP_P71593144l_bool(hAPP_f1634841927l_bool(produc1491230096l_bool,F_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B))) ) ).

tff(fact_416_splitI,axiom,
    ! [F_1: fun_Pr597144499l_bool,A: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(F_1,A),B))
     => hBOOL(hAPP_P1333315679l_bool(hAPP_f1525114763l_bool(produc70644925l_bool,F_1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B))) ) ).

tff(fact_417_splitI,axiom,
    ! [F_1: fun_val_fun_val_bool,A: val,B: val] :
      ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(F_1,A),B))
     => hBOOL(hAPP_P929938951l_bool(hAPP_f1534412387l_bool(produc769963999l_bool,F_1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B))) ) ).

tff(fact_418_splitI,axiom,
    ! [F_1: fun_bo1454185032l_bool,A: bop,B: product_prod_val_val] :
      ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(F_1,A),B))
     => hBOOL(hAPP_P943837928l_bool(hAPP_f340876351l_bool(produc1326056646l_bool,F_1),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B))) ) ).

tff(fact_419_splitI,axiom,
    ! [F_1: fun_li860735411r_bool,A: list_char,B: list_char] :
      ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(F_1,A),B))
     => hBOOL(hAPP_P449474095r_bool(hAPP_f2132060507r_bool(produc1704639885r_bool,F_1),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B))) ) ).

tff(fact_420_splitI,axiom,
    ! [F_1: fun_li823162622l_bool,A: list_char,B: fun_Pr806764899on_val] :
      ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(F_1,A),B))
     => hBOOL(hAPP_P1235399154l_bool(hAPP_f1443410953l_bool(produc392960766l_bool,F_1),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B))) ) ).

tff(fact_421_splitI,axiom,
    ! [F_1: fun_fu100249073l_bool,A: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F_1,A),B))
     => hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B))) ) ).

tff(fact_422_splitI,axiom,
    ! [F_1: fun_ex1201926843l_bool,A: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F_1,A),B))
     => hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B))) ) ).

tff(fact_423_splitI,axiom,
    ! [F_1: fun_Pr633696065l_bool,A: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F_1,A),B))
     => hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F_1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B))) ) ).

tff(fact_424_map__add__dom__app__simps_I1_J,axiom,
    ! [L1: fun_na939144002on_val,M_1: nat,L2: fun_na939144002on_val] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,M_1),dom_na996029170on_val(L2)))
     => ( hAPP_n546249108on_val(map_ad61982421on_val(L1,L2),M_1) = hAPP_n546249108on_val(L2,M_1) ) ) ).

tff(fact_425_map__add__dom__app__simps_I1_J,axiom,
    ! [L1: fun_li1432931796on_val,M_1: list_char,L2: fun_li1432931796on_val] :
      ( hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,M_1),dom_list_char_val(L2)))
     => ( hAPP_l207779698on_val(map_ad325961431ar_val(L1,L2),M_1) = hAPP_l207779698on_val(L2,M_1) ) ) ).

tff(fact_426_split__weak__cong,axiom,
    ! [C_2: fun_li1301775111ion_ty,P_1: produc639455274on_val,Q_2: produc639455274on_val] :
      ( ( P_1 = Q_2 )
     => ( hAPP_P1228500987ion_ty(hAPP_f46308763ion_ty(produc907433735ion_ty,C_2),P_1) = hAPP_P1228500987ion_ty(hAPP_f46308763ion_ty(produc907433735ion_ty,C_2),Q_2) ) ) ).

tff(fact_427_split__weak__cong,axiom,
    ! [C_2: 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_2),P_1))
      <=> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C_2),Q_2)) ) ) ).

tff(fact_428_map__add__dom__app__simps_I3_J,axiom,
    ! [L1: fun_na939144002on_val,M_1: nat,L2: fun_na939144002on_val] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,M_1),dom_na996029170on_val(L2)))
     => ( hAPP_n546249108on_val(map_ad61982421on_val(L1,L2),M_1) = hAPP_n546249108on_val(L1,M_1) ) ) ).

tff(fact_429_map__add__dom__app__simps_I3_J,axiom,
    ! [L1: fun_li1432931796on_val,M_1: list_char,L2: fun_li1432931796on_val] :
      ( ~ hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,M_1),dom_list_char_val(L2)))
     => ( hAPP_l207779698on_val(map_ad325961431ar_val(L1,L2),M_1) = hAPP_l207779698on_val(L1,M_1) ) ) ).

tff(fact_430_map__add__dom__app__simps_I2_J,axiom,
    ! [L2: fun_na939144002on_val,M_1: nat,L1: fun_na939144002on_val] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,M_1),dom_na996029170on_val(L1)))
     => ( hAPP_n546249108on_val(map_ad61982421on_val(L1,L2),M_1) = hAPP_n546249108on_val(L2,M_1) ) ) ).

tff(fact_431_map__add__dom__app__simps_I2_J,axiom,
    ! [L2: fun_li1432931796on_val,M_1: list_char,L1: fun_li1432931796on_val] :
      ( ~ hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,M_1),dom_list_char_val(L1)))
     => ( hAPP_l207779698on_val(map_ad325961431ar_val(L1,L2),M_1) = hAPP_l207779698on_val(L2,M_1) ) ) ).

tff(fact_432_map__add__assoc,axiom,
    ! [M1: fun_li1432931796on_val,M2: fun_li1432931796on_val,M3: fun_li1432931796on_val] : map_ad325961431ar_val(M1,map_ad325961431ar_val(M2,M3)) = map_ad325961431ar_val(map_ad325961431ar_val(M1,M2),M3) ).

tff(fact_433_split__curry,axiom,
    ! [F_1: fun_Pr876827561ion_ty] : hAPP_f46308763ion_ty(produc907433735ion_ty,produc1675615144ion_ty(F_1)) = F_1 ).

tff(fact_434_split__curry,axiom,
    ! [F_1: fun_Pr1696029455l_bool] : hAPP_f2121594859l_bool(produc1958875245l_bool,produc2062775566l_bool(F_1)) = F_1 ).

tff(fact_435_curry__split,axiom,
    ! [F_1: fun_li1301775111ion_ty] : produc1675615144ion_ty(hAPP_f46308763ion_ty(produc907433735ion_ty,F_1)) = F_1 ).

tff(fact_436_curry__split,axiom,
    ! [F_1: fun_fu100249073l_bool] : produc2062775566l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F_1)) = F_1 ).

tff(fact_437_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_438_red__reds_ORedInitBlock,axiom,
    ! [Va_1: list_char,Ta: ty,Va: val,U: val,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),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_439_conf__widen,axiom,
    ! [T_a: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Va: val,Ta: ty] :
      ( hBOOL(conf_P373316194t_char(Pa,Hb,Va,Ta))
     => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),Ta),T_a))
       => hBOOL(conf_P373316194t_char(Pa,Hb,Va,T_a)) ) ) ).

tff(fact_440_splitD,axiom,
    ! [F_1: fun_li221477r_bool,A: list_list_char,B: exp_list_char] :
      ( hBOOL(hAPP_P2014166431r_bool(hAPP_f1484794973r_bool(produc1732333873r_bool,F_1),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B)))
     => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(F_1,A),B)) ) ).

tff(fact_441_splitD,axiom,
    ! [F_1: fun_li1305328058r_bool,A: list_P1940453997har_ty,B: list_P341299826t_char] :
      ( hBOOL(hAPP_P828904212r_bool(hAPP_f895126887r_bool(produc1596557472r_bool,F_1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B)))
     => hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(F_1,A),B)) ) ).

tff(fact_442_splitD,axiom,
    ! [F_1: fun_li485148903r_bool,A: list_char,B: produc2146869324t_char] :
      ( hBOOL(hAPP_P659547099r_bool(hAPP_f252398939r_bool(produc1324280167r_bool,F_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B)))
     => hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(F_1,A),B)) ) ).

tff(fact_443_splitD,axiom,
    ! [F_1: fun_li522008110r_bool,A: list_char,B: produc952412819t_char] :
      ( hBOOL(hAPP_P1680401186r_bool(hAPP_f952817385r_bool(produc723279022r_bool,F_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B)))
     => hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(F_1,A),B)) ) ).

tff(fact_444_splitD,axiom,
    ! [F_1: fun_li826105035r_bool,A: list_val,B: exp_list_char] :
      ( hBOOL(hAPP_P2118621157r_bool(hAPP_f1697332217r_bool(produc21910851r_bool,F_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B)))
     => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(F_1,A),B)) ) ).

tff(fact_445_splitD,axiom,
    ! [F_1: fun_li887890578r_bool,A: list_ty,B: produc662261637t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(hAPP_f102021095r_bool(produc154616760r_bool,F_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B)))
     => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(F_1,A),B)) ) ).

tff(fact_446_splitD,axiom,
    ! [F_1: fun_li1024794712r_bool,A: list_list_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P92196306r_bool(hAPP_f1613448899r_bool(produc2027921764r_bool,F_1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B)))
     => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(F_1,A),B)) ) ).

tff(fact_447_splitD,axiom,
    ! [F_1: fun_li1372729616l_bool,A: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P71593144l_bool(hAPP_f1634841927l_bool(produc1491230096l_bool,F_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(F_1,A),B)) ) ).

tff(fact_448_splitD,axiom,
    ! [F_1: fun_Pr597144499l_bool,A: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P1333315679l_bool(hAPP_f1525114763l_bool(produc70644925l_bool,F_1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B)))
     => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(F_1,A),B)) ) ).

tff(fact_449_splitD,axiom,
    ! [F_1: fun_val_fun_val_bool,A: val,B: val] :
      ( hBOOL(hAPP_P929938951l_bool(hAPP_f1534412387l_bool(produc769963999l_bool,F_1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B)))
     => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(F_1,A),B)) ) ).

tff(fact_450_splitD,axiom,
    ! [F_1: fun_bo1454185032l_bool,A: bop,B: product_prod_val_val] :
      ( hBOOL(hAPP_P943837928l_bool(hAPP_f340876351l_bool(produc1326056646l_bool,F_1),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B)))
     => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(F_1,A),B)) ) ).

tff(fact_451_splitD,axiom,
    ! [F_1: fun_li860735411r_bool,A: list_char,B: list_char] :
      ( hBOOL(hAPP_P449474095r_bool(hAPP_f2132060507r_bool(produc1704639885r_bool,F_1),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B)))
     => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(F_1,A),B)) ) ).

tff(fact_452_splitD,axiom,
    ! [F_1: fun_li823162622l_bool,A: list_char,B: fun_Pr806764899on_val] :
      ( hBOOL(hAPP_P1235399154l_bool(hAPP_f1443410953l_bool(produc392960766l_bool,F_1),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B)))
     => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(F_1,A),B)) ) ).

tff(fact_453_splitD,axiom,
    ! [F_1: fun_fu100249073l_bool,A: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B)))
     => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F_1,A),B)) ) ).

tff(fact_454_splitD,axiom,
    ! [F_1: fun_ex1201926843l_bool,A: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F_1,A),B)) ) ).

tff(fact_455_splitD,axiom,
    ! [F_1: fun_Pr633696065l_bool,A: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F_1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B)))
     => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F_1,A),B)) ) ).

tff(fact_456_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_457_red__reds_ORedSeq,axiom,
    ! [Va: val,E_2: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va),E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S))),red(Pa))) ).

tff(fact_458_map__add__upd__left,axiom,
    ! [E1: fun_na939144002on_val,U1: produc639455274on_val,M_1: nat,E2: fun_na939144002on_val] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,M_1),dom_na996029170on_val(E2)))
     => ( map_ad61982421on_val(fun_up2041264236on_val(E1,M_1,hAPP_P1510515380on_val(some_P948696889on_val,U1)),E2) = fun_up2041264236on_val(map_ad61982421on_val(E1,E2),M_1,hAPP_P1510515380on_val(some_P948696889on_val,U1)) ) ) ).

tff(fact_459_map__add__upd__left,axiom,
    ! [E1: fun_li1432931796on_val,U1: val,M_1: list_char,E2: fun_li1432931796on_val] :
      ( ~ hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,M_1),dom_list_char_val(E2)))
     => ( map_ad325961431ar_val(fun_up1149430426on_val(E1,M_1,hAPP_val_option_val(some_val,U1)),E2) = fun_up1149430426on_val(map_ad325961431ar_val(E1,E2),M_1,hAPP_val_option_val(some_val,U1)) ) ) ).

tff(fact_460_map__add__upd__left,axiom,
    ! [E1: fun_Pr806764899on_val,U1: val,M_1: produc1278157519t_char,E2: fun_Pr806764899on_val] :
      ( ~ hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,M_1),dom_Pr695701035ar_val(E2)))
     => ( map_ad1185064968ar_val(fun_up204312361on_val(E1,M_1,hAPP_val_option_val(some_val,U1)),E2) = fun_up204312361on_val(map_ad1185064968ar_val(E1,E2),M_1,hAPP_val_option_val(some_val,U1)) ) ) ).

tff(fact_461_map__add__upd__left,axiom,
    ! [E1: fun_li688206603ion_ty,U1: ty,M_1: list_char,E2: fun_li688206603ion_ty] :
      ( ~ hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,M_1),dom_list_char_ty(E2)))
     => ( map_add_list_char_ty(fun_up424764369ion_ty(E1,M_1,hAPP_ty_option_ty(some_ty,U1)),E2) = fun_up424764369ion_ty(map_add_list_char_ty(E1,E2),M_1,hAPP_ty_option_ty(some_ty,U1)) ) ) ).

tff(fact_462_red__reds_ORedBlock,axiom,
    ! [Va_1: list_char,Ta: ty,U: val,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,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_463_domI,axiom,
    ! [M_1: fun_na939144002on_val,A: nat,B: produc639455274on_val] :
      ( ( hAPP_n546249108on_val(M_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,B) )
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A),dom_na996029170on_val(M_1))) ) ).

tff(fact_464_domI,axiom,
    ! [M_1: fun_li1432931796on_val,A: list_char,B: val] :
      ( ( hAPP_l207779698on_val(M_1,A) = hAPP_val_option_val(some_val,B) )
     => hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,A),dom_list_char_val(M_1))) ) ).

tff(fact_465_red__reds_OInitBlockRed,axiom,
    ! [Ta: ty,V_a: val,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Va_1: list_char,Va: val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va_1,hAPP_val_option_val(some_val,Va))))),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,Va_1) = hAPP_val_option_val(some_val,V_a) )
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),Eb))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,V_a)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1)))))),red(Pa))) ) ) ).

tff(fact_466_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_467_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_468_split__conv,axiom,
    ! [F_1: fun_li1301775111ion_ty,A: list_char,B: fun_Pr806764899on_val] : hAPP_P1228500987ion_ty(hAPP_f46308763ion_ty(produc907433735ion_ty,F_1),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B)) = hAPP_f652398900ion_ty(hAPP_l2000496933ion_ty(F_1,A),B) ).

tff(fact_469_split__conv,axiom,
    ! [F_1: fun_fu100249073l_bool,A: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B)))
    <=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F_1,A),B)) ) ).

tff(fact_470_map__add__find__right,axiom,
    ! [M_1: fun_li1432931796on_val,N: fun_li1432931796on_val,K: list_char,Xx: val] :
      ( ( hAPP_l207779698on_val(N,K) = hAPP_val_option_val(some_val,Xx) )
     => ( hAPP_l207779698on_val(map_ad325961431ar_val(M_1,N),K) = hAPP_val_option_val(some_val,Xx) ) ) ).

tff(fact_471_mem__def,axiom,
    ! [X_2: produc1013743697t_char,A_2: fun_Pr70170387r_bool] :
      ( hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,X_2),A_2))
    <=> hBOOL(hAPP_P1384137393r_bool(A_2,X_2)) ) ).

tff(fact_472_mem__def,axiom,
    ! [X_2: produc1971331930t_char,A_2: fun_Pr1861226704r_bool] :
      ( hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,X_2),A_2))
    <=> hBOOL(hAPP_P1680401186r_bool(A_2,X_2)) ) ).

tff(fact_473_mem__def,axiom,
    ! [X_2: produc430140671on_val,A_2: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,X_2),A_2))
    <=> hBOOL(hAPP_P1333315679l_bool(A_2,X_2)) ) ).

tff(fact_474_mem__def,axiom,
    ! [X_2: nat,A_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_2))
    <=> hBOOL(hAPP_nat_bool(A_2,X_2)) ) ).

tff(fact_475_mem__def,axiom,
    ! [X_2: produc1278157519t_char,A_2: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,X_2),A_2))
    <=> hBOOL(hAPP_P449474095r_bool(A_2,X_2)) ) ).

tff(fact_476_mem__def,axiom,
    ! [X_2: list_char,A_2: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_2),A_2))
    <=> hBOOL(hAPP_list_char_bool(A_2,X_2)) ) ).

tff(fact_477_mem__def,axiom,
    ! [X_2: produc1102272487on_val,A_2: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,X_2),A_2))
    <=> hBOOL(hAPP_P282169671l_bool(A_2,X_2)) ) ).

tff(fact_478_split__eta,axiom,
    ! [F_1: fun_Pr876827561ion_ty] : hAPP_f46308763ion_ty(produc907433735ion_ty,hAPP_f802560783ion_ty(hAPP_f7643013ion_ty(cOMBB_864319000t_char,hAPP_f69964139ion_ty(cOMBB_2041093409on_val,F_1)),produc823076510on_val)) = F_1 ).

tff(fact_479_split__eta,axiom,
    ! [F_1: fun_Pr1696029455l_bool] : hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f1363667773l_bool(hAPP_f1050935001l_bool(cOMBB_1153617344on_val,hAPP_f2057883639l_bool(cOMBB_1750801836on_val,F_1)),produc899768717on_val)) = F_1 ).

tff(fact_480_red__reds_OLAssRed,axiom,
    ! [Va_1: list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,E_b)),S_2))),red(Pa))) ) ).

tff(fact_481_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_f1453283057l_bool(hAPP_P1303341961l_bool(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_482_curryE,axiom,
    ! [F_1: fun_Pr1336948301r_bool,A: list_list_char,B: exp_list_char] :
      ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(produc288369490r_bool(F_1),A),B))
     => hBOOL(hAPP_P2014166431r_bool(F_1,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B))) ) ).

tff(fact_483_curryE,axiom,
    ! [F_1: fun_Pr1669461698r_bool,A: list_P1940453997har_ty,B: list_P341299826t_char] :
      ( hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(produc2116052801r_bool(F_1),A),B))
     => hBOOL(hAPP_P828904212r_bool(F_1,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B))) ) ).

tff(fact_484_curryE,axiom,
    ! [F_1: fun_Pr1898949769r_bool,A: list_char,B: produc2146869324t_char] :
      ( hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(produc266042248r_bool(F_1),A),B))
     => hBOOL(hAPP_P659547099r_bool(F_1,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B))) ) ).

tff(fact_485_curryE,axiom,
    ! [F_1: fun_Pr1861226704r_bool,A: list_char,B: produc952412819t_char] :
      ( hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(produc1588781647r_bool(F_1),A),B))
     => hBOOL(hAPP_P1680401186r_bool(F_1,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B))) ) ).

tff(fact_486_curryE,axiom,
    ! [F_1: fun_Pr827765831r_bool,A: list_val,B: exp_list_char] :
      ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F_1),A),B))
     => hBOOL(hAPP_P2118621157r_bool(F_1,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B))) ) ).

tff(fact_487_curryE,axiom,
    ! [F_1: fun_Pr46158268r_bool,A: list_ty,B: produc662261637t_char] :
      ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F_1),A),B))
     => hBOOL(hAPP_P1907982426r_bool(F_1,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B))) ) ).

tff(fact_488_curryE,axiom,
    ! [F_1: fun_Pr227936640r_bool,A: list_list_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F_1),A),B))
     => hBOOL(hAPP_P92196306r_bool(F_1,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B))) ) ).

tff(fact_489_curryE,axiom,
    ! [F_1: fun_Pr248118298l_bool,A: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(produc1838470831l_bool(F_1),A),B))
     => hBOOL(hAPP_P71593144l_bool(F_1,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B))) ) ).

tff(fact_490_curryE,axiom,
    ! [F_1: fun_Pr859510977l_bool,A: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(produc2053127004l_bool(F_1),A),B))
     => hBOOL(hAPP_P1333315679l_bool(F_1,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B))) ) ).

tff(fact_491_curryE,axiom,
    ! [F_1: fun_Pr2081272681l_bool,A: val,B: val] :
      ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(produc886919678l_bool(F_1),A),B))
     => hBOOL(hAPP_P929938951l_bool(F_1,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B))) ) ).

tff(fact_492_curryE,axiom,
    ! [F_1: fun_Pr252072522l_bool,A: bop,B: product_prod_val_val] :
      ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(produc1555310053l_bool(F_1),A),B))
     => hBOOL(hAPP_P943837928l_bool(F_1,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B))) ) ).

tff(fact_493_curryE,axiom,
    ! [F_1: fun_Pr565113489r_bool,A: list_char,B: list_char] :
      ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(produc95371820r_bool(F_1),A),B))
     => hBOOL(hAPP_P449474095r_bool(F_1,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B))) ) ).

tff(fact_494_curryE,axiom,
    ! [F_1: fun_Pr315804320l_bool,A: list_char,B: fun_Pr806764899on_val] :
      ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F_1),A),B))
     => hBOOL(hAPP_P1235399154l_bool(F_1,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B))) ) ).

tff(fact_495_curryE,axiom,
    ! [F_1: fun_Pr1696029455l_bool,A: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F_1),A),B))
     => hBOOL(hAPP_P159683425l_bool(F_1,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B))) ) ).

tff(fact_496_curryE,axiom,
    ! [F_1: fun_Pr680585871l_bool,A: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F_1),A),B))
     => hBOOL(hAPP_P1708370145l_bool(F_1,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B))) ) ).

tff(fact_497_curryE,axiom,
    ! [F_1: fun_Pr691271849l_bool,A: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F_1),A),B))
     => hBOOL(hAPP_P282169671l_bool(F_1,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B))) ) ).

tff(fact_498_curryD,axiom,
    ! [F_1: fun_Pr1336948301r_bool,A: list_list_char,B: exp_list_char] :
      ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(produc288369490r_bool(F_1),A),B))
     => hBOOL(hAPP_P2014166431r_bool(F_1,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B))) ) ).

tff(fact_499_curryD,axiom,
    ! [F_1: fun_Pr1669461698r_bool,A: list_P1940453997har_ty,B: list_P341299826t_char] :
      ( hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(produc2116052801r_bool(F_1),A),B))
     => hBOOL(hAPP_P828904212r_bool(F_1,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B))) ) ).

tff(fact_500_curryD,axiom,
    ! [F_1: fun_Pr1898949769r_bool,A: list_char,B: produc2146869324t_char] :
      ( hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(produc266042248r_bool(F_1),A),B))
     => hBOOL(hAPP_P659547099r_bool(F_1,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B))) ) ).

tff(fact_501_curryD,axiom,
    ! [F_1: fun_Pr1861226704r_bool,A: list_char,B: produc952412819t_char] :
      ( hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(produc1588781647r_bool(F_1),A),B))
     => hBOOL(hAPP_P1680401186r_bool(F_1,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B))) ) ).

tff(fact_502_curryD,axiom,
    ! [F_1: fun_Pr827765831r_bool,A: list_val,B: exp_list_char] :
      ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F_1),A),B))
     => hBOOL(hAPP_P2118621157r_bool(F_1,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B))) ) ).

tff(fact_503_curryD,axiom,
    ! [F_1: fun_Pr46158268r_bool,A: list_ty,B: produc662261637t_char] :
      ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F_1),A),B))
     => hBOOL(hAPP_P1907982426r_bool(F_1,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B))) ) ).

tff(fact_504_curryD,axiom,
    ! [F_1: fun_Pr227936640r_bool,A: list_list_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F_1),A),B))
     => hBOOL(hAPP_P92196306r_bool(F_1,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B))) ) ).

tff(fact_505_curryD,axiom,
    ! [F_1: fun_Pr248118298l_bool,A: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(produc1838470831l_bool(F_1),A),B))
     => hBOOL(hAPP_P71593144l_bool(F_1,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B))) ) ).

tff(fact_506_curryD,axiom,
    ! [F_1: fun_Pr859510977l_bool,A: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(produc2053127004l_bool(F_1),A),B))
     => hBOOL(hAPP_P1333315679l_bool(F_1,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B))) ) ).

tff(fact_507_curryD,axiom,
    ! [F_1: fun_Pr2081272681l_bool,A: val,B: val] :
      ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(produc886919678l_bool(F_1),A),B))
     => hBOOL(hAPP_P929938951l_bool(F_1,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B))) ) ).

tff(fact_508_curryD,axiom,
    ! [F_1: fun_Pr252072522l_bool,A: bop,B: product_prod_val_val] :
      ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(produc1555310053l_bool(F_1),A),B))
     => hBOOL(hAPP_P943837928l_bool(F_1,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B))) ) ).

tff(fact_509_curryD,axiom,
    ! [F_1: fun_Pr565113489r_bool,A: list_char,B: list_char] :
      ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(produc95371820r_bool(F_1),A),B))
     => hBOOL(hAPP_P449474095r_bool(F_1,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B))) ) ).

tff(fact_510_curryD,axiom,
    ! [F_1: fun_Pr315804320l_bool,A: list_char,B: fun_Pr806764899on_val] :
      ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F_1),A),B))
     => hBOOL(hAPP_P1235399154l_bool(F_1,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B))) ) ).

tff(fact_511_curryD,axiom,
    ! [F_1: fun_Pr1696029455l_bool,A: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F_1),A),B))
     => hBOOL(hAPP_P159683425l_bool(F_1,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B))) ) ).

tff(fact_512_curryD,axiom,
    ! [F_1: fun_Pr680585871l_bool,A: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F_1),A),B))
     => hBOOL(hAPP_P1708370145l_bool(F_1,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B))) ) ).

tff(fact_513_curryD,axiom,
    ! [F_1: fun_Pr691271849l_bool,A: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F_1),A),B))
     => hBOOL(hAPP_P282169671l_bool(F_1,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B))) ) ).

tff(fact_514_map__add__upd,axiom,
    ! [F_1: fun_Pr806764899on_val,G: fun_Pr806764899on_val,X_2: produc1278157519t_char,Y_2: val] : map_ad1185064968ar_val(F_1,fun_up204312361on_val(G,X_2,hAPP_val_option_val(some_val,Y_2))) = fun_up204312361on_val(map_ad1185064968ar_val(F_1,G),X_2,hAPP_val_option_val(some_val,Y_2)) ).

tff(fact_515_map__add__upd,axiom,
    ! [F_1: fun_na939144002on_val,G: fun_na939144002on_val,X_2: nat,Y_2: produc639455274on_val] : map_ad61982421on_val(F_1,fun_up2041264236on_val(G,X_2,hAPP_P1510515380on_val(some_P948696889on_val,Y_2))) = fun_up2041264236on_val(map_ad61982421on_val(F_1,G),X_2,hAPP_P1510515380on_val(some_P948696889on_val,Y_2)) ).

tff(fact_516_map__add__upd,axiom,
    ! [F_1: fun_li688206603ion_ty,G: fun_li688206603ion_ty,X_2: list_char,Y_2: ty] : map_add_list_char_ty(F_1,fun_up424764369ion_ty(G,X_2,hAPP_ty_option_ty(some_ty,Y_2))) = fun_up424764369ion_ty(map_add_list_char_ty(F_1,G),X_2,hAPP_ty_option_ty(some_ty,Y_2)) ).

tff(fact_517_map__add__upd,axiom,
    ! [F_1: fun_li1432931796on_val,G: fun_li1432931796on_val,X_2: list_char,Y_2: val] : map_ad325961431ar_val(F_1,fun_up1149430426on_val(G,X_2,hAPP_val_option_val(some_val,Y_2))) = fun_up1149430426on_val(map_ad325961431ar_val(F_1,G),X_2,hAPP_val_option_val(some_val,Y_2)) ).

tff(fact_518_internal__split__def,axiom,
    produc1577326610ion_ty = produc907433735ion_ty ).

tff(fact_519_internal__split__def,axiom,
    produc2128769400l_bool = produc1958875245l_bool ).

tff(fact_520_WTrtBlock,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Va_1: list_char,Ta: ty,Eb: exp_list_char,T_a: ty] :
      ( hBOOL(wTrt_1(Pa,Hb,fun_up424764369ion_ty(Ea,Va_1,hAPP_ty_option_ty(some_ty,Ta)),Eb,T_a))
     => hBOOL(wTrt_1(Pa,Hb,Ea,block_list_char(Va_1,Ta,Eb),T_a)) ) ).

tff(fact_521_splitE,axiom,
    ! [C_2: fun_li221477r_bool,P_1: produc809539159t_char] :
      ( hBOOL(hAPP_P2014166431r_bool(hAPP_f1484794973r_bool(produc1732333873r_bool,C_2),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_2,X_1),Y_1)) ) ) ).

tff(fact_522_splitE,axiom,
    ! [C_2: fun_li1305328058r_bool,P_1: produc2146869324t_char] :
      ( hBOOL(hAPP_P828904212r_bool(hAPP_f895126887r_bool(produc1596557472r_bool,C_2),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_2,X_1),Y_1)) ) ) ).

tff(fact_523_splitE,axiom,
    ! [C_2: fun_li485148903r_bool,P_1: produc952412819t_char] :
      ( hBOOL(hAPP_P659547099r_bool(hAPP_f252398939r_bool(produc1324280167r_bool,C_2),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_2,X_1),Y_1)) ) ) ).

tff(fact_524_splitE,axiom,
    ! [C_2: fun_li522008110r_bool,P_1: produc1971331930t_char] :
      ( hBOOL(hAPP_P1680401186r_bool(hAPP_f952817385r_bool(produc723279022r_bool,C_2),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_2,X_1),Y_1)) ) ) ).

tff(fact_525_splitE,axiom,
    ! [C_2: fun_li826105035r_bool,P_1: produc662261637t_char] :
      ( hBOOL(hAPP_P2118621157r_bool(hAPP_f1697332217r_bool(produc21910851r_bool,C_2),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_2,X_1),Y_1)) ) ) ).

tff(fact_526_splitE,axiom,
    ! [C_2: fun_li887890578r_bool,P_1: produc220283002t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(hAPP_f102021095r_bool(produc154616760r_bool,C_2),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_2,X_1),Y_1)) ) ) ).

tff(fact_527_splitE,axiom,
    ! [C_2: fun_li1024794712r_bool,P_1: produc1285161482t_char] :
      ( hBOOL(hAPP_P92196306r_bool(hAPP_f1613448899r_bool(produc2027921764r_bool,C_2),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_2,X_1),Y_1)) ) ) ).

tff(fact_528_splitE,axiom,
    ! [C_2: fun_li1372729616l_bool,P_1: produc2061676504on_val] :
      ( hBOOL(hAPP_P71593144l_bool(hAPP_f1634841927l_bool(produc1491230096l_bool,C_2),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_2,X_1),Y_1)) ) ) ).

tff(fact_529_splitE,axiom,
    ! [C_2: fun_Pr597144499l_bool,P_1: produc430140671on_val] :
      ( hBOOL(hAPP_P1333315679l_bool(hAPP_f1525114763l_bool(produc70644925l_bool,C_2),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_2,X_1),Y_1)) ) ) ).

tff(fact_530_splitE,axiom,
    ! [C_2: fun_val_fun_val_bool,P_1: product_prod_val_val] :
      ( hBOOL(hAPP_P929938951l_bool(hAPP_f1534412387l_bool(produc769963999l_bool,C_2),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_2,X_1),Y_1)) ) ) ).

tff(fact_531_splitE,axiom,
    ! [C_2: fun_bo1454185032l_bool,P_1: produc1645268488al_val] :
      ( hBOOL(hAPP_P943837928l_bool(hAPP_f340876351l_bool(produc1326056646l_bool,C_2),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_2,X_1),Y_1)) ) ) ).

tff(fact_532_splitE,axiom,
    ! [C_2: fun_li860735411r_bool,P_1: produc1278157519t_char] :
      ( hBOOL(hAPP_P449474095r_bool(hAPP_f2132060507r_bool(produc1704639885r_bool,C_2),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_2,X_1),Y_1)) ) ) ).

tff(fact_533_splitE,axiom,
    ! [C_2: fun_li823162622l_bool,P_1: produc639455274on_val] :
      ( hBOOL(hAPP_P1235399154l_bool(hAPP_f1443410953l_bool(produc392960766l_bool,C_2),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_2,X_1),Y_1)) ) ) ).

tff(fact_534_splitE,axiom,
    ! [C_2: fun_fu100249073l_bool,P_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C_2),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_2,X_1),Y_1)) ) ) ).

tff(fact_535_splitE,axiom,
    ! [C_2: fun_ex1201926843l_bool,P_1: produc124828825on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C_2),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_2,X_1),Y_1)) ) ) ).

tff(fact_536_splitE,axiom,
    ! [C_2: fun_Pr633696065l_bool,P_1: produc1102272487on_val] :
      ( hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C_2),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_2,X_1),Y_1)) ) ) ).

tff(fact_537_splitI2,axiom,
    ! [C_2: fun_li221477r_bool,P_1: produc809539159t_char] :
      ( ! [A_1: list_list_char,B_2: exp_list_char] :
          ( ( P_1 = hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_2) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(C_2,A_1),B_2)) )
     => hBOOL(hAPP_P2014166431r_bool(hAPP_f1484794973r_bool(produc1732333873r_bool,C_2),P_1)) ) ).

tff(fact_538_splitI2,axiom,
    ! [C_2: fun_li1305328058r_bool,P_1: produc2146869324t_char] :
      ( ! [A_1: list_P1940453997har_ty,B_2: list_P341299826t_char] :
          ( ( P_1 = hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_2) )
         => hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(C_2,A_1),B_2)) )
     => hBOOL(hAPP_P828904212r_bool(hAPP_f895126887r_bool(produc1596557472r_bool,C_2),P_1)) ) ).

tff(fact_539_splitI2,axiom,
    ! [C_2: fun_li485148903r_bool,P_1: produc952412819t_char] :
      ( ! [A_1: list_char,B_2: produc2146869324t_char] :
          ( ( P_1 = hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_2) )
         => hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(C_2,A_1),B_2)) )
     => hBOOL(hAPP_P659547099r_bool(hAPP_f252398939r_bool(produc1324280167r_bool,C_2),P_1)) ) ).

tff(fact_540_splitI2,axiom,
    ! [C_2: fun_li522008110r_bool,P_1: produc1971331930t_char] :
      ( ! [A_1: list_char,B_2: produc952412819t_char] :
          ( ( P_1 = hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_2) )
         => hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(C_2,A_1),B_2)) )
     => hBOOL(hAPP_P1680401186r_bool(hAPP_f952817385r_bool(produc723279022r_bool,C_2),P_1)) ) ).

tff(fact_541_splitI2,axiom,
    ! [C_2: fun_li826105035r_bool,P_1: produc662261637t_char] :
      ( ! [A_1: list_val,B_2: exp_list_char] :
          ( ( P_1 = hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_2) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(C_2,A_1),B_2)) )
     => hBOOL(hAPP_P2118621157r_bool(hAPP_f1697332217r_bool(produc21910851r_bool,C_2),P_1)) ) ).

tff(fact_542_splitI2,axiom,
    ! [C_2: fun_li887890578r_bool,P_1: produc220283002t_char] :
      ( ! [A_1: list_ty,B_2: produc662261637t_char] :
          ( ( P_1 = hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_2) )
         => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(C_2,A_1),B_2)) )
     => hBOOL(hAPP_P1907982426r_bool(hAPP_f102021095r_bool(produc154616760r_bool,C_2),P_1)) ) ).

tff(fact_543_splitI2,axiom,
    ! [C_2: fun_li1024794712r_bool,P_1: produc1285161482t_char] :
      ( ! [A_1: list_list_char,B_2: produc220283002t_char] :
          ( ( P_1 = hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_2) )
         => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(C_2,A_1),B_2)) )
     => hBOOL(hAPP_P92196306r_bool(hAPP_f1613448899r_bool(produc2027921764r_bool,C_2),P_1)) ) ).

tff(fact_544_splitI2,axiom,
    ! [C_2: fun_li1372729616l_bool,P_1: produc2061676504on_val] :
      ( ! [A_1: list_exp_list_char,B_2: produc12694297on_val] :
          ( ( P_1 = hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_2) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(C_2,A_1),B_2)) )
     => hBOOL(hAPP_P71593144l_bool(hAPP_f1634841927l_bool(produc1491230096l_bool,C_2),P_1)) ) ).

tff(fact_545_splitI2,axiom,
    ! [C_2: fun_Pr597144499l_bool,P_1: produc430140671on_val] :
      ( ! [A_1: produc2061676504on_val,B_2: produc2061676504on_val] :
          ( ( P_1 = hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_2) )
         => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(C_2,A_1),B_2)) )
     => hBOOL(hAPP_P1333315679l_bool(hAPP_f1525114763l_bool(produc70644925l_bool,C_2),P_1)) ) ).

tff(fact_546_splitI2,axiom,
    ! [C_2: fun_val_fun_val_bool,P_1: product_prod_val_val] :
      ( ! [A_1: val,B_2: val] :
          ( ( P_1 = hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_2) )
         => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(C_2,A_1),B_2)) )
     => hBOOL(hAPP_P929938951l_bool(hAPP_f1534412387l_bool(produc769963999l_bool,C_2),P_1)) ) ).

tff(fact_547_splitI2,axiom,
    ! [C_2: fun_bo1454185032l_bool,P_1: produc1645268488al_val] :
      ( ! [A_1: bop,B_2: product_prod_val_val] :
          ( ( P_1 = hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_2) )
         => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(C_2,A_1),B_2)) )
     => hBOOL(hAPP_P943837928l_bool(hAPP_f340876351l_bool(produc1326056646l_bool,C_2),P_1)) ) ).

tff(fact_548_splitI2,axiom,
    ! [C_2: fun_li860735411r_bool,P_1: produc1278157519t_char] :
      ( ! [A_1: list_char,B_2: list_char] :
          ( ( P_1 = hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_2) )
         => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(C_2,A_1),B_2)) )
     => hBOOL(hAPP_P449474095r_bool(hAPP_f2132060507r_bool(produc1704639885r_bool,C_2),P_1)) ) ).

tff(fact_549_splitI2,axiom,
    ! [C_2: fun_li823162622l_bool,P_1: produc639455274on_val] :
      ( ! [A_1: list_char,B_2: fun_Pr806764899on_val] :
          ( ( P_1 = hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_2) )
         => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(C_2,A_1),B_2)) )
     => hBOOL(hAPP_P1235399154l_bool(hAPP_f1443410953l_bool(produc392960766l_bool,C_2),P_1)) ) ).

tff(fact_550_splitI2,axiom,
    ! [C_2: fun_fu100249073l_bool,P_1: produc12694297on_val] :
      ( ! [A_1: fun_na939144002on_val,B_2: fun_li1432931796on_val] :
          ( ( P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_2) )
         => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(C_2,A_1),B_2)) )
     => hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C_2),P_1)) ) ).

tff(fact_551_splitI2,axiom,
    ! [C_2: fun_ex1201926843l_bool,P_1: produc124828825on_val] :
      ( ! [A_1: exp_list_char,B_2: produc12694297on_val] :
          ( ( P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_2) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(C_2,A_1),B_2)) )
     => hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C_2),P_1)) ) ).

tff(fact_552_splitI2,axiom,
    ! [C_2: fun_Pr633696065l_bool,P_1: produc1102272487on_val] :
      ( ! [A_1: produc124828825on_val,B_2: produc124828825on_val] :
          ( ( P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_2) )
         => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(C_2,A_1),B_2)) )
     => hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C_2),P_1)) ) ).

tff(fact_553_WTrtSeq,axiom,
    ! [E_2: exp_list_char,T_2_2: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1_1: exp_list_char,T_1_1: ty] :
      ( hBOOL(wTrt_1(Pa,Hb,Ea,E_1_1,T_1_1))
     => ( hBOOL(wTrt_1(Pa,Hb,Ea,E_2,T_2_2))
       => hBOOL(wTrt_1(Pa,Hb,Ea,seq_list_char(E_1_1,E_2),T_2_2)) ) ) ).

tff(fact_554_lconf__def,axiom,
    ! [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))
    <=> ! [V_3: list_char,V_2: val] :
          ( ( hAPP_l207779698on_val(Lb,V_3) = hAPP_val_option_val(some_val,V_2) )
         => ? [T_4: ty] :
              ( ( hAPP_l512744617ion_ty(Ea,V_3) = hAPP_ty_option_ty(some_ty,T_4) )
              & hBOOL(conf_P373316194t_char(Pa,Hb,V_2,T_4)) ) ) ) ).

tff(fact_555_red__reds_ORedLAss,axiom,
    ! [Va_1: list_char,Va: val,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va))),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,Va_1,hAPP_val_option_val(some_val,Va)))))),red(Pa))) ).

tff(fact_556_hext__refl,axiom,
    ! [Hb: fun_na939144002on_val] : hBOOL(hext(Hb,Hb)) ).

tff(fact_557_cond__split__eta,axiom,
    ! [F_1: fun_li1301775111ion_ty,G: fun_Pr876827561ion_ty] :
      ( ! [X_1: list_char,Y_1: fun_Pr806764899on_val] : hAPP_f652398900ion_ty(hAPP_l2000496933ion_ty(F_1,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_1) = G ) ) ).

tff(fact_558_cond__split__eta,axiom,
    ! [G: fun_Pr1696029455l_bool,F_1: fun_fu100249073l_bool] :
      ( ! [X_1: fun_na939144002on_val,Y_1: fun_li1432931796on_val] :
          ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F_1,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_1) = G ) ) ).

tff(fact_559_domD,axiom,
    ! [A: nat,M_1: fun_na939144002on_val] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A),dom_na996029170on_val(M_1)))
     => ? [B_2: produc639455274on_val] : hAPP_n546249108on_val(M_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,B_2) ) ).

tff(fact_560_domD,axiom,
    ! [A: list_char,M_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,A),dom_list_char_val(M_1)))
     => ? [B_2: val] : hAPP_l207779698on_val(M_1,A) = hAPP_val_option_val(some_val,B_2) ) ).

tff(fact_561_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_562_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_563_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(wTrt_1(Pa,Hb,Ea,Eb,Ta))
     => ( hBOOL(hext(Hb,H_b))
       => hBOOL(wTrt_1(Pa,H_b,Ea,Eb,Ta)) ) ) ).

tff(fact_564_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_565_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_566_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_567_hext__def,axiom,
    ! [Hb: fun_na939144002on_val,H_b: fun_na939144002on_val] :
      ( hBOOL(hext(Hb,H_b))
    <=> ! [A_1: nat,C_1: 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_1),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_1),Fs_3)) ) ) ).

tff(fact_568__092_060D_062___092_060D_062s_Osimps_I6_J,axiom,
    ! [Va_1: list_char,Eb: exp_list_char,A_2: option466449911r_bool] :
      ( hBOOL(d_list_char(lAss_list_char(Va_1,Eb),A_2))
    <=> hBOOL(d_list_char(Eb,A_2)) ) ).

tff(fact_569_exp_Osimps_I143_J,axiom,
    ! [A_17: list_char,Ty_7: ty,Exp_13: exp_list_char,A_16: list_char,Exp_12: exp_list_char] : block_list_char(A_17,Ty_7,Exp_13) != lAss_list_char(A_16,Exp_12) ).

tff(fact_570_exp_Osimps_I196_J,axiom,
    ! [A_15: list_char,Ty_6: ty,Exp_11: exp_list_char,Exp1_7: exp_list_char,Exp2_7: exp_list_char] : block_list_char(A_15,Ty_6,Exp_11) != seq_list_char(Exp1_7,Exp2_7) ).

tff(fact_571_exp_Osimps_I142_J,axiom,
    ! [A_14: list_char,Exp_10: exp_list_char,A_13: list_char,Ty_5: ty,Exp_9: exp_list_char] : lAss_list_char(A_14,Exp_10) != block_list_char(A_13,Ty_5,Exp_9) ).

tff(fact_572_exp_Osimps_I3_J,axiom,
    ! [Val_7: val,Val_6: val] :
      ( ( hAPP_v834067052t_char(val_list_char,Val_7) = hAPP_v834067052t_char(val_list_char,Val_6) )
    <=> ( Val_7 = Val_6 ) ) ).

tff(fact_573_exp_Osimps_I11_J,axiom,
    ! [Exp1_6: exp_list_char,Exp2_6: exp_list_char,Exp1_5: exp_list_char,Exp2_5: exp_list_char] :
      ( ( seq_list_char(Exp1_6,Exp2_6) = seq_list_char(Exp1_5,Exp2_5) )
    <=> ( ( Exp1_6 = Exp1_5 )
        & ( Exp2_6 = Exp2_5 ) ) ) ).

tff(fact_574_exp_Osimps_I6_J,axiom,
    ! [A: list_char,Exp_8: exp_list_char,A_3: list_char,Exp_7: exp_list_char] :
      ( ( lAss_list_char(A,Exp_8) = lAss_list_char(A_3,Exp_7) )
    <=> ( ( A = A_3 )
        & ( Exp_8 = Exp_7 ) ) ) ).

tff(fact_575_exp_Osimps_I10_J,axiom,
    ! [A: list_char,Ty_4: ty,Exp_8: exp_list_char,A_3: list_char,Ty_3: ty,Exp_7: exp_list_char] :
      ( ( block_list_char(A,Ty_4,Exp_8) = block_list_char(A_3,Ty_3,Exp_7) )
    <=> ( ( A = A_3 )
        & ( Ty_4 = Ty_3 )
        & ( Exp_8 = Exp_7 ) ) ) ).

tff(fact_576_exp_Osimps_I84_J,axiom,
    ! [Val_5: val,Exp1_4: exp_list_char,Exp2_4: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_5) != seq_list_char(Exp1_4,Exp2_4) ).

tff(fact_577_exp_Osimps_I74_J,axiom,
    ! [Val_4: val,A_12: list_char,Exp_6: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_4) != lAss_list_char(A_12,Exp_6) ).

tff(fact_578_exp_Osimps_I85_J,axiom,
    ! [Exp1_3: exp_list_char,Exp2_3: exp_list_char,Val_3: val] : seq_list_char(Exp1_3,Exp2_3) != hAPP_v834067052t_char(val_list_char,Val_3) ).

tff(fact_579_exp_Osimps_I75_J,axiom,
    ! [A_11: list_char,Exp_5: exp_list_char,Val_2: val] : lAss_list_char(A_11,Exp_5) != hAPP_v834067052t_char(val_list_char,Val_2) ).

tff(fact_580_exp_Osimps_I82_J,axiom,
    ! [Val_1: val,A_10: list_char,Ty_2: ty,Exp_4: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_1) != block_list_char(A_10,Ty_2,Exp_4) ).

tff(fact_581_exp_Osimps_I83_J,axiom,
    ! [A_9: list_char,Ty_1: ty,Exp_3: exp_list_char,Val: val] : block_list_char(A_9,Ty_1,Exp_3) != hAPP_v834067052t_char(val_list_char,Val) ).

tff(fact_582__092_060D_062___092_060D_062s_Osimps_I3_J,axiom,
    ! [Va: val,A_2: option466449911r_bool] : hBOOL(d_list_char(hAPP_v834067052t_char(val_list_char,Va),A_2)) ).

tff(fact_583_exp_Osimps_I145_J,axiom,
    ! [Exp1_2: exp_list_char,Exp2_2: exp_list_char,A_8: list_char,Exp_2: exp_list_char] : seq_list_char(Exp1_2,Exp2_2) != lAss_list_char(A_8,Exp_2) ).

tff(fact_584_exp_Osimps_I144_J,axiom,
    ! [A_7: list_char,Exp_1: exp_list_char,Exp1_1: exp_list_char,Exp2_1: exp_list_char] : lAss_list_char(A_7,Exp_1) != seq_list_char(Exp1_1,Exp2_1) ).

tff(fact_585_exp_Osimps_I197_J,axiom,
    ! [Exp1: exp_list_char,Exp2: exp_list_char,A_6: list_char,Ty: ty,Exp: exp_list_char] : seq_list_char(Exp1,Exp2) != block_list_char(A_6,Ty,Exp) ).

tff(fact_586_hconf__upd__obj,axiom,
    ! [Fs_2: fun_Pr806764899on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val] :
      ( hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),Hb))
     => ( ( hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) )
       => ( hBOOL(hAPP_P1235399154l_bool(oconf_1869808039t_char(Pa,Hb),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_2)))
         => hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),fun_up2041264236on_val(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_2))))) ) ) ) ).

tff(fact_587_redp__redsp_OInitBlockRed,axiom,
    ! [Ta: ty,V_a: val,Pa: list_P1999446415t_char,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Va_1: list_char,Va: 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,Va_1,hAPP_val_option_val(some_val,Va)))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))
     => ( ( hAPP_l207779698on_val(L_b,Va_1) = hAPP_val_option_val(some_val,V_a) )
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),Eb)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,V_a)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))) ) ) ).

tff(fact_588_red__reds_OBlockRedSome,axiom,
    ! [Ta: ty,Va: val,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Va_1: list_char,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va_1,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,Va_1) = hAPP_val_option_val(some_val,Va) )
       => ( ~ hBOOL(assigned(Va_1,Eb))
         => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,Eb)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1)))))),red(Pa))) ) ) ) ).

tff(fact_589_WTrtLAss,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Eb: exp_list_char,T_a: ty,Ea: fun_li688206603ion_ty,Va_1: list_char,Ta: ty] :
      ( ( hAPP_l512744617ion_ty(Ea,Va_1) = hAPP_ty_option_ty(some_ty,Ta) )
     => ( hBOOL(wTrt_1(Pa,Hb,Ea,Eb,T_a))
       => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_a),Ta))
         => hBOOL(wTrt_1(Pa,Hb,Ea,lAss_list_char(Va_1,Eb),void)) ) ) ) ).

tff(fact_590_LAssRedsVal,axiom,
    ! [Va_1: list_char,Eb: exp_list_char,S: produc12694297on_val,Va: val,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),transi2024712006on_val(red(Pa))))
     => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,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,Va_1,hAPP_val_option_val(some_val,Va)))))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_591_hextI,axiom,
    ! [H_b: fun_na939144002on_val,Hb: fun_na939144002on_val] :
      ( ! [A_1: nat,C_1: 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_1),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_1),Fs_3)) )
     => hBOOL(hext(Hb,H_b)) ) ).

tff(fact_592_redp__redsp_ORedLAss,axiom,
    ! [Pa: list_P1999446415t_char,Va_1: list_char,Va: val,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),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,Va_1,hAPP_val_option_val(some_val,Va))))) ).

tff(fact_593_red__lcl__incr,axiom,
    ! [Eb: exp_list_char,H_0: fun_na939144002on_val,L_0: fun_li1432931796on_val,E_b: exp_list_char,H_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,H_0),L_0))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1)))),red(Pa)))
     => hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(dom_list_char_val(L_0)),dom_list_char_val(L_1_1))) ) ).

tff(fact_594_lconf__empty,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty] : hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Hb),hAPP_o538043682on_val(cOMBK_1097134891t_char,none_val)),Ea)) ).

tff(fact_595_rev__predicate1D,axiom,
    ! [Q_1: fun_list_char_bool,Pa: fun_list_char_bool,X_2: list_char] :
      ( hBOOL(hAPP_list_char_bool(Pa,X_2))
     => ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Pa),Q_1))
       => hBOOL(hAPP_list_char_bool(Q_1,X_2)) ) ) ).

tff(fact_596_predicate1D,axiom,
    ! [X_2: list_char,Pa: fun_list_char_bool,Q_1: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Pa),Q_1))
     => ( hBOOL(hAPP_list_char_bool(Pa,X_2))
       => hBOOL(hAPP_list_char_bool(Q_1,X_2)) ) ) ).

tff(fact_597_pred__subset__eq,axiom,
    ! [R_2: fun_Pr70170387r_bool,S_4: fun_Pr70170387r_bool] :
      ( hBOOL(hAPP_f483496539l_bool(ord_le1987888477r_bool(hAPP_f1853572245r_bool(hAPP_f1933376467r_bool(cOMBC_36589090l_bool,member1601084734t_char),R_2)),hAPP_f1853572245r_bool(hAPP_f1933376467r_bool(cOMBC_36589090l_bool,member1601084734t_char),S_4)))
    <=> hBOOL(hAPP_f483496539l_bool(ord_le1987888477r_bool(R_2),S_4)) ) ).

tff(fact_598_pred__subset__eq,axiom,
    ! [R_2: fun_Pr1861226704r_bool,S_4: fun_Pr1861226704r_bool] :
      ( hBOOL(hAPP_f515912112l_bool(ord_le117566470r_bool(hAPP_f1666729379r_bool(hAPP_f1020753317r_bool(cOMBC_1297648632l_bool,member1467889965t_char),R_2)),hAPP_f1666729379r_bool(hAPP_f1020753317r_bool(cOMBC_1297648632l_bool,member1467889965t_char),S_4)))
    <=> hBOOL(hAPP_f515912112l_bool(ord_le117566470r_bool(R_2),S_4)) ) ).

tff(fact_599_pred__subset__eq,axiom,
    ! [R_2: fun_Pr859510977l_bool,S_4: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(hAPP_f1856968213l_bool(hAPP_f677078775l_bool(cOMBC_475083938l_bool,member875476972on_val),R_2)),hAPP_f1856968213l_bool(hAPP_f677078775l_bool(cOMBC_475083938l_bool,member875476972on_val),S_4)))
    <=> hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(R_2),S_4)) ) ).

tff(fact_600_pred__subset__eq,axiom,
    ! [R_2: fun_nat_bool,S_4: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(ord_le1568362934t_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_2)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_4)))
    <=> hBOOL(hAPP_f54304608l_bool(ord_le1568362934t_bool(R_2),S_4)) ) ).

tff(fact_601_pred__subset__eq,axiom,
    ! [R_2: fun_Pr565113489r_bool,S_4: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(hAPP_f112056853r_bool(hAPP_f1876889431r_bool(cOMBC_148995234l_bool,member1251428284t_char),R_2)),hAPP_f112056853r_bool(hAPP_f1876889431r_bool(cOMBC_148995234l_bool,member1251428284t_char),S_4)))
    <=> hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(R_2),S_4)) ) ).

tff(fact_602_pred__subset__eq,axiom,
    ! [R_2: fun_list_char_bool,S_4: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(hAPP_f1371002581r_bool(hAPP_f522372661r_bool(cOMBC_892477410l_bool,member_list_char),R_2)),hAPP_f1371002581r_bool(hAPP_f522372661r_bool(cOMBC_892477410l_bool,member_list_char),S_4)))
    <=> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(R_2),S_4)) ) ).

tff(fact_603_pred__subset__eq,axiom,
    ! [R_2: fun_Pr691271849l_bool,S_4: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(hAPP_f2036784149l_bool(hAPP_f1720452391l_bool(cOMBC_1021753250l_bool,member773094996on_val),R_2)),hAPP_f2036784149l_bool(hAPP_f1720452391l_bool(cOMBC_1021753250l_bool,member773094996on_val),S_4)))
    <=> hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(R_2),S_4)) ) ).

tff(fact_604_option_Osimps_I2_J,axiom,
    ! [A_5: nat] : none_nat != hAPP_nat_option_nat(some_nat,A_5) ).

tff(fact_605_option_Osimps_I2_J,axiom,
    ! [A_5: ty] : none_ty != hAPP_ty_option_ty(some_ty,A_5) ).

tff(fact_606_option_Osimps_I2_J,axiom,
    ! [A_3: produc639455274on_val] : none_P179726773on_val != hAPP_P1510515380on_val(some_P948696889on_val,A_3) ).

tff(fact_607_option_Osimps_I2_J,axiom,
    ! [A_5: val] : none_val != hAPP_val_option_val(some_val,A_5) ).

tff(fact_608_option_Osimps_I2_J,axiom,
    ! [A_3: fun_list_char_bool] : none_f478147469r_bool != hAPP_f363827556r_bool(some_f80346385r_bool,A_3) ).

tff(fact_609_option_Osimps_I3_J,axiom,
    ! [A_4: nat] : hAPP_nat_option_nat(some_nat,A_4) != none_nat ).

tff(fact_610_option_Osimps_I3_J,axiom,
    ! [A_4: ty] : hAPP_ty_option_ty(some_ty,A_4) != none_ty ).

tff(fact_611_option_Osimps_I3_J,axiom,
    ! [A_3: produc639455274on_val] : hAPP_P1510515380on_val(some_P948696889on_val,A_3) != none_P179726773on_val ).

tff(fact_612_option_Osimps_I3_J,axiom,
    ! [A_4: val] : hAPP_val_option_val(some_val,A_4) != none_val ).

tff(fact_613_option_Osimps_I3_J,axiom,
    ! [A_3: fun_list_char_bool] : hAPP_f363827556r_bool(some_f80346385r_bool,A_3) != none_f478147469r_bool ).

tff(fact_614_not__Some__eq,axiom,
    ! [X_2: option_nat] :
      ( ! [Y_1: nat] : X_2 != hAPP_nat_option_nat(some_nat,Y_1)
    <=> ( X_2 = none_nat ) ) ).

tff(fact_615_not__Some__eq,axiom,
    ! [X_2: option_ty] :
      ( ! [Y_1: ty] : X_2 != hAPP_ty_option_ty(some_ty,Y_1)
    <=> ( X_2 = none_ty ) ) ).

tff(fact_616_not__Some__eq,axiom,
    ! [X_2: option1479284511on_val] :
      ( ! [Y_1: produc639455274on_val] : X_2 != hAPP_P1510515380on_val(some_P948696889on_val,Y_1)
    <=> ( X_2 = none_P179726773on_val ) ) ).

tff(fact_617_not__Some__eq,axiom,
    ! [X_2: option_val] :
      ( ! [Y_1: val] : X_2 != hAPP_val_option_val(some_val,Y_1)
    <=> ( X_2 = none_val ) ) ).

tff(fact_618_not__Some__eq,axiom,
    ! [X_2: option466449911r_bool] :
      ( ! [Y_1: fun_list_char_bool] : X_2 != hAPP_f363827556r_bool(some_f80346385r_bool,Y_1)
    <=> ( X_2 = none_f478147469r_bool ) ) ).

tff(fact_619_not__None__eq,axiom,
    ! [X_2: option_nat] :
      ( ( X_2 != none_nat )
    <=> ? [Y_1: nat] : X_2 = hAPP_nat_option_nat(some_nat,Y_1) ) ).

tff(fact_620_not__None__eq,axiom,
    ! [X_2: option_ty] :
      ( ( X_2 != none_ty )
    <=> ? [Y_1: ty] : X_2 = hAPP_ty_option_ty(some_ty,Y_1) ) ).

tff(fact_621_not__None__eq,axiom,
    ! [X_2: option1479284511on_val] :
      ( ( X_2 != none_P179726773on_val )
    <=> ? [Y_1: produc639455274on_val] : X_2 = hAPP_P1510515380on_val(some_P948696889on_val,Y_1) ) ).

tff(fact_622_not__None__eq,axiom,
    ! [X_2: option_val] :
      ( ( X_2 != none_val )
    <=> ? [Y_1: val] : X_2 = hAPP_val_option_val(some_val,Y_1) ) ).

tff(fact_623_not__None__eq,axiom,
    ! [X_2: option466449911r_bool] :
      ( ( X_2 != none_f478147469r_bool )
    <=> ? [Y_1: fun_list_char_bool] : X_2 = hAPP_f363827556r_bool(some_f80346385r_bool,Y_1) ) ).

tff(fact_624_redp__redsp_OLAssRed,axiom,
    ! [Va_1: 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(Va_1,Eb),S),lAss_list_char(Va_1,E_b)),S_2)) ) ).

tff(fact_625_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_626_dom__def,axiom,
    ! [M_1: fun_na939144002on_val] : dom_na996029170on_val(M_1) = collect_nat(hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,fNot),hAPP_o1566711458t_bool(hAPP_f489569861t_bool(cOMBC_229530231l_bool,hAPP_f1677329295l_bool(hAPP_f1611569977l_bool(cOMBB_731867268ol_nat,fequal1937332960on_val),M_1)),none_P179726773on_val))) ).

tff(fact_627_dom__def,axiom,
    ! [M_1: fun_li1432931796on_val] : dom_list_char_val(M_1) = collect_list_char(hAPP_f1371002581r_bool(hAPP_f1861125939r_bool(cOMBB_1091123364t_char,fNot),hAPP_o453398608r_bool(hAPP_f399018025r_bool(cOMBC_442485623l_bool,hAPP_f396807521l_bool(hAPP_f926979333l_bool(cOMBB_1112666310t_char,fequal_option_val),M_1)),none_val))) ).

tff(fact_628_domIff,axiom,
    ! [A: nat,M_1: fun_na939144002on_val] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A),dom_na996029170on_val(M_1)))
    <=> ( hAPP_n546249108on_val(M_1,A) != none_P179726773on_val ) ) ).

tff(fact_629_domIff,axiom,
    ! [A: list_char,M_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,A),dom_list_char_val(M_1)))
    <=> ( hAPP_l207779698on_val(M_1,A) != none_val ) ) ).

tff(fact_630_redp__redsp_OBlockRedNone,axiom,
    ! [Ta: ty,Pa: list_P1999446415t_char,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Va_1: 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,Va_1,none_val))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))
     => ( ( hAPP_l207779698on_val(L_b,Va_1) = none_val )
       => ( ~ hBOOL(assigned(Va_1,Eb))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),block_list_char(Va_1,Ta,E_b)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))) ) ) ) ).

tff(fact_631_map__add__None,axiom,
    ! [M_1: fun_li1432931796on_val,N: fun_li1432931796on_val,K: list_char] :
      ( ( hAPP_l207779698on_val(map_ad325961431ar_val(M_1,N),K) = none_val )
    <=> ( ( hAPP_l207779698on_val(N,K) = none_val )
        & ( hAPP_l207779698on_val(M_1,K) = none_val ) ) ) ).

tff(fact_632_empty__upd__none,axiom,
    ! [X_2: produc1278157519t_char,X_1: produc1278157519t_char] : hAPP_P2094403585on_val(fun_up204312361on_val(hAPP_o1269033393on_val(cOMBK_1867744698t_char,none_val),X_2,none_val),X_1) = none_val ).

tff(fact_633_empty__upd__none,axiom,
    ! [X_2: nat,X_1: nat] : hAPP_n546249108on_val(fun_up2041264236on_val(hAPP_o1576581476on_val(cOMBK_1944287343al_nat,none_P179726773on_val),X_2,none_P179726773on_val),X_1) = none_P179726773on_val ).

tff(fact_634_empty__upd__none,axiom,
    ! [X_2: list_char,X_1: list_char] : hAPP_l512744617ion_ty(fun_up424764369ion_ty(hAPP_o1240645474ion_ty(cOMBK_1294242658t_char,none_ty),X_2,none_ty),X_1) = none_ty ).

tff(fact_635_empty__upd__none,axiom,
    ! [X_2: list_char,X_1: list_char] : hAPP_l207779698on_val(fun_up1149430426on_val(hAPP_o538043682on_val(cOMBK_1097134891t_char,none_val),X_2,none_val),X_1) = none_val ).

tff(fact_636_map__add__empty,axiom,
    ! [M_1: fun_li1432931796on_val] : map_ad325961431ar_val(M_1,hAPP_o538043682on_val(cOMBK_1097134891t_char,none_val)) = M_1 ).

tff(fact_637_empty__map__add,axiom,
    ! [M_1: fun_li1432931796on_val] : map_ad325961431ar_val(hAPP_o538043682on_val(cOMBK_1097134891t_char,none_val),M_1) = M_1 ).

tff(fact_638_redp__redsp_ORedSeq,axiom,
    ! [Pa: list_P1999446415t_char,Va: 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,Va),E_2),S),E_2),S)) ).

tff(fact_639_map__upd__nonempty,axiom,
    ! [T_2: fun_Pr806764899on_val,K: produc1278157519t_char,X_2: val] :
      ~ ! [X_1: produc1278157519t_char] : hAPP_P2094403585on_val(fun_up204312361on_val(T_2,K,hAPP_val_option_val(some_val,X_2)),X_1) = none_val ).

tff(fact_640_map__upd__nonempty,axiom,
    ! [T_2: fun_na939144002on_val,K: nat,X_2: produc639455274on_val] :
      ~ ! [X_1: nat] : hAPP_n546249108on_val(fun_up2041264236on_val(T_2,K,hAPP_P1510515380on_val(some_P948696889on_val,X_2)),X_1) = none_P179726773on_val ).

tff(fact_641_map__upd__nonempty,axiom,
    ! [T_2: fun_li688206603ion_ty,K: list_char,X_2: ty] :
      ~ ! [X_1: list_char] : hAPP_l512744617ion_ty(fun_up424764369ion_ty(T_2,K,hAPP_ty_option_ty(some_ty,X_2)),X_1) = none_ty ).

tff(fact_642_map__upd__nonempty,axiom,
    ! [T_2: fun_li1432931796on_val,K: list_char,X_2: val] :
      ~ ! [X_1: list_char] : hAPP_l207779698on_val(fun_up1149430426on_val(T_2,K,hAPP_val_option_val(some_val,X_2)),X_1) = none_val ).

tff(fact_643_redp__redsp_ORedBlock,axiom,
    ! [Pa: list_P1999446415t_char,Va_1: list_char,Ta: ty,U: val,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,hAPP_v834067052t_char(val_list_char,U)),S),hAPP_v834067052t_char(val_list_char,U)),S)) ).

tff(fact_644_map__add__SomeD,axiom,
    ! [M_1: fun_li1432931796on_val,N: fun_li1432931796on_val,K: list_char,X_2: val] :
      ( ( hAPP_l207779698on_val(map_ad325961431ar_val(M_1,N),K) = hAPP_val_option_val(some_val,X_2) )
     => ( ( hAPP_l207779698on_val(N,K) = hAPP_val_option_val(some_val,X_2) )
        | ( ( hAPP_l207779698on_val(N,K) = none_val )
          & ( hAPP_l207779698on_val(M_1,K) = hAPP_val_option_val(some_val,X_2) ) ) ) ) ).

tff(fact_645_map__add__Some__iff,axiom,
    ! [M_1: fun_li1432931796on_val,N: fun_li1432931796on_val,K: list_char,X_2: val] :
      ( ( hAPP_l207779698on_val(map_ad325961431ar_val(M_1,N),K) = hAPP_val_option_val(some_val,X_2) )
    <=> ( ( hAPP_l207779698on_val(N,K) = hAPP_val_option_val(some_val,X_2) )
        | ( ( hAPP_l207779698on_val(N,K) = none_val )
          & ( hAPP_l207779698on_val(M_1,K) = hAPP_val_option_val(some_val,X_2) ) ) ) ) ).

tff(fact_646_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_647_LAssReds,axiom,
    ! [Va_1: list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,E_b)),S_2))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_648_redp__redsp_OBlockRedSome,axiom,
    ! [Ta: ty,Va: val,Pa: list_P1999446415t_char,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Va_1: 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,Va_1,none_val))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))
     => ( ( hAPP_l207779698on_val(L_b,Va_1) = hAPP_val_option_val(some_val,Va) )
       => ( ~ hBOOL(assigned(Va_1,Eb))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))) ) ) ) ).

tff(fact_649_SeqReds2,axiom,
    ! [E_2: exp_list_char,E_2_1: exp_list_char,S_2_1: produc12694297on_val,E_1_1: exp_list_char,S_0: produc12694297on_val,V_1_2: val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1),S_2_1))),transi2024712006on_val(red(Pa))))
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(E_1_1,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2_1),S_2_1))),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_650_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_651_hconfD,axiom,
    ! [A: nat,Obj: produc639455274on_val,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val] :
      ( hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),Hb))
     => ( ( hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,Obj) )
       => hBOOL(hAPP_P1235399154l_bool(oconf_1869808039t_char(Pa,Hb),Obj)) ) ) ).

tff(fact_652_redp__redsp_ORedInitBlock,axiom,
    ! [Pa: list_P1999446415t_char,Va_1: list_char,Ta: ty,Va: val,U: val,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),hAPP_v834067052t_char(val_list_char,U))),S),hAPP_v834067052t_char(val_list_char,U)),S)) ).

tff(fact_653_red__reds_OBlockRedNone,axiom,
    ! [Ta: ty,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Va_1: list_char,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va_1,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,Va_1) = none_val )
       => ( ~ hBOOL(assigned(Va_1,Eb))
         => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,Eb)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,E_b)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1)))))),red(Pa))) ) ) ) ).

tff(fact_654_Red__lcl__add,axiom,
    ! [L_0: 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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,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,L_b))))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_655_WTrt__elim__cases_I1_J,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Va: list_char,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt_1(Pa,Hb,Ea,lAss_list_char(Va,Eb),Ta))
     => ~ ( ( Ta = void )
         => ! [T_4: ty] :
              ( ( hAPP_l512744617ion_ty(Ea,Va) = hAPP_ty_option_ty(some_ty,T_4) )
             => ! [T_5: ty] :
                  ( hBOOL(wTrt_1(Pa,Hb,Ea,Eb,T_5))
                 => ~ hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_5),T_4)) ) ) ) ) ).

tff(fact_656_InitBlockReds,axiom,
    ! [Ta: ty,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Va_1: list_char,Va: val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va_1,hAPP_val_option_val(some_val,Va))))),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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),Eb))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,hAPP_option_val_val(the_val,hAPP_l207779698on_val(L_b,Va_1)))),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1)))))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_657_InitBlockRedsFinal,axiom,
    ! [Ta: ty,Eb: exp_list_char,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Va_1: list_char,Va: val,E_b: exp_list_char,H_b: fun_na939144002on_val,L_b: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va_1,hAPP_val_option_val(some_val,Va))))),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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),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,Va_1,hAPP_l207779698on_val(Lb,Va_1)))))),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_658_assigned__def,axiom,
    ! [Va_1: list_char,Eb: exp_list_char] :
      ( hBOOL(assigned(Va_1,Eb))
    <=> ? [V_2: val,E_1: exp_list_char] : Eb = seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,V_2)),E_1) ) ).

tff(fact_659_rtrancl_Ortrancl__refl,axiom,
    ! [A: produc2061676504on_val,R_1: fun_Pr859510977l_bool] : hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),A)),transi374442731on_val(R_1))) ).

tff(fact_660_rtrancl_Ortrancl__refl,axiom,
    ! [A: list_char,R_1: fun_Pr565113489r_bool] : hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),A)),transi1395422419t_char(R_1))) ).

tff(fact_661_rtrancl_Ortrancl__refl,axiom,
    ! [A: produc124828825on_val,R_1: fun_Pr691271849l_bool] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),A)),transi2024712006on_val(R_1))) ).

tff(fact_662_rtrancl_Ortrancl__refl,axiom,
    ! [A: val,R_1: fun_Pr2081272681l_bool] : hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),A)),transi935034983cl_val(R_1))) ).

tff(fact_663_BlockRedsFinal,axiom,
    ! [Ta: ty,H_0: fun_na939144002on_val,L_0: fun_li1432931796on_val,Va_1: list_char,E_0: exp_list_char,S_0: produc12694297on_val,E_2: exp_list_char,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_0),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2)))),transi2024712006on_val(red(Pa))))
     => ( hBOOL(final_list_char(E_2))
       => ( ( S_0 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),fun_up1149430426on_val(L_0,Va_1,none_val)) )
         => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,E_0)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),L_0))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),fun_up1149430426on_val(L_2,Va_1,hAPP_l207779698on_val(L_0,Va_1)))))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_664_oconf__fupd,axiom,
    ! [Fs: fun_Pr806764899on_val,Hb: fun_na939144002on_val,Va: val,Pa: list_P1999446415t_char,C: list_char,F: list_char,Ta: ty,D: list_char] :
      ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,F,Ta),D))
     => ( hBOOL(conf_P373316194t_char(Pa,Hb,Va,Ta))
       => ( hBOOL(hAPP_P1235399154l_bool(oconf_1869808039t_char(Pa,Hb),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)))
         => hBOOL(hAPP_P1235399154l_bool(oconf_1869808039t_char(Pa,Hb),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),fun_up204312361on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D),hAPP_val_option_val(some_val,Va))))) ) ) ) ).

tff(fact_665_r__into__rtrancl,axiom,
    ! [P_1: produc430140671on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,P_1),R_1))
     => hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,P_1),transi374442731on_val(R_1))) ) ).

tff(fact_666_r__into__rtrancl,axiom,
    ! [P_1: produc1278157519t_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,P_1),R_1))
     => hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,P_1),transi1395422419t_char(R_1))) ) ).

tff(fact_667_r__into__rtrancl,axiom,
    ! [P_1: produc1102272487on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,P_1),R_1))
     => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,P_1),transi2024712006on_val(R_1))) ) ).

tff(fact_668_equalityI,axiom,
    ! [A_2: fun_list_char_bool,B_1: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1))
     => ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(B_1),A_2))
       => ( A_2 = B_1 ) ) ) ).

tff(fact_669_subsetD,axiom,
    ! [C_2: produc1013743697t_char,A_2: fun_Pr70170387r_bool,B_1: fun_Pr70170387r_bool] :
      ( hBOOL(hAPP_f483496539l_bool(ord_le1987888477r_bool(A_2),B_1))
     => ( hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,C_2),A_2))
       => hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,C_2),B_1)) ) ) ).

tff(fact_670_subsetD,axiom,
    ! [C_2: produc1971331930t_char,A_2: fun_Pr1861226704r_bool,B_1: fun_Pr1861226704r_bool] :
      ( hBOOL(hAPP_f515912112l_bool(ord_le117566470r_bool(A_2),B_1))
     => ( hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,C_2),A_2))
       => hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,C_2),B_1)) ) ) ).

tff(fact_671_subsetD,axiom,
    ! [C_2: produc430140671on_val,A_2: fun_Pr859510977l_bool,B_1: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(A_2),B_1))
     => ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,C_2),A_2))
       => hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,C_2),B_1)) ) ) ).

tff(fact_672_subsetD,axiom,
    ! [C_2: nat,A_2: fun_nat_bool,B_1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(ord_le1568362934t_bool(A_2),B_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_1)) ) ) ).

tff(fact_673_subsetD,axiom,
    ! [C_2: produc1278157519t_char,A_2: fun_Pr565113489r_bool,B_1: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(A_2),B_1))
     => ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,C_2),A_2))
       => hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,C_2),B_1)) ) ) ).

tff(fact_674_subsetD,axiom,
    ! [C_2: list_char,A_2: fun_list_char_bool,B_1: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1))
     => ( hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C_2),A_2))
       => hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C_2),B_1)) ) ) ).

tff(fact_675_subsetD,axiom,
    ! [C_2: produc1102272487on_val,A_2: fun_Pr691271849l_bool,B_1: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(A_2),B_1))
     => ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,C_2),A_2))
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,C_2),B_1)) ) ) ).

tff(fact_676_rtrancl__mono,axiom,
    ! [R_1: fun_Pr859510977l_bool,S: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(R_1),S))
     => hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(transi374442731on_val(R_1)),transi374442731on_val(S))) ) ).

tff(fact_677_rtrancl__mono,axiom,
    ! [R_1: fun_Pr565113489r_bool,S: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(R_1),S))
     => hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(transi1395422419t_char(R_1)),transi1395422419t_char(S))) ) ).

tff(fact_678_rtrancl__mono,axiom,
    ! [R_1: fun_Pr691271849l_bool,S: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(R_1),S))
     => hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(transi2024712006on_val(R_1)),transi2024712006on_val(S))) ) ).

tff(fact_679_rtrancl__subset,axiom,
    ! [R_2: fun_Pr859510977l_bool,S_4: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(R_2),S_4))
     => ( hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(S_4),transi374442731on_val(R_2)))
       => ( transi374442731on_val(S_4) = transi374442731on_val(R_2) ) ) ) ).

tff(fact_680_rtrancl__subset,axiom,
    ! [R_2: fun_Pr565113489r_bool,S_4: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(R_2),S_4))
     => ( hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(S_4),transi1395422419t_char(R_2)))
       => ( transi1395422419t_char(S_4) = transi1395422419t_char(R_2) ) ) ) ).

tff(fact_681_rtrancl__subset,axiom,
    ! [R_2: fun_Pr691271849l_bool,S_4: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(R_2),S_4))
     => ( hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(S_4),transi2024712006on_val(R_2)))
       => ( transi2024712006on_val(S_4) = transi2024712006on_val(R_2) ) ) ) ).

tff(fact_682_rtrancl__subset__rtrancl,axiom,
    ! [R_1: fun_Pr859510977l_bool,S: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(R_1),transi374442731on_val(S)))
     => hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(transi374442731on_val(R_1)),transi374442731on_val(S))) ) ).

tff(fact_683_rtrancl__subset__rtrancl,axiom,
    ! [R_1: fun_Pr565113489r_bool,S: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(R_1),transi1395422419t_char(S)))
     => hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(transi1395422419t_char(R_1)),transi1395422419t_char(S))) ) ).

tff(fact_684_rtrancl__subset__rtrancl,axiom,
    ! [R_1: fun_Pr691271849l_bool,S: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(R_1),transi2024712006on_val(S)))
     => hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(transi2024712006on_val(R_1)),transi2024712006on_val(S))) ) ).

tff(fact_685_the_Osimps,axiom,
    ! [X_3: val] : hAPP_option_val_val(the_val,hAPP_val_option_val(some_val,X_3)) = X_3 ).

tff(fact_686_the_Osimps,axiom,
    ! [X_3: nat] : hAPP_option_nat_nat(the_nat,hAPP_nat_option_nat(some_nat,X_3)) = X_3 ).

tff(fact_687_the_Osimps,axiom,
    ! [X_2: produc639455274on_val] : hAPP_o1977518472on_val(the_Pr431167171on_val,hAPP_P1510515380on_val(some_P948696889on_val,X_2)) = X_2 ).

tff(fact_688_the_Osimps,axiom,
    ! [X_3: ty] : hAPP_option_ty_ty(the_ty,hAPP_ty_option_ty(some_ty,X_3)) = X_3 ).

tff(fact_689_the_Osimps,axiom,
    ! [X_2: fun_list_char_bool] : hAPP_o285151112r_bool(the_fu297177755r_bool,hAPP_f363827556r_bool(some_f80346385r_bool,X_2)) = X_2 ).

tff(fact_690_subset__refl,axiom,
    ! [A_2: fun_list_char_bool] : hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),A_2)) ).

tff(fact_691_set__eq__subset,axiom,
    ! [A_2: fun_list_char_bool,B_1: fun_list_char_bool] :
      ( ( A_2 = B_1 )
    <=> ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1))
        & hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(B_1),A_2)) ) ) ).

tff(fact_692_equalityD1,axiom,
    ! [A_2: fun_list_char_bool,B_1: fun_list_char_bool] :
      ( ( A_2 = B_1 )
     => hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1)) ) ).

tff(fact_693_equalityD2,axiom,
    ! [A_2: fun_list_char_bool,B_1: fun_list_char_bool] :
      ( ( A_2 = B_1 )
     => hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(B_1),A_2)) ) ).

tff(fact_694_in__mono,axiom,
    ! [X_2: produc1013743697t_char,A_2: fun_Pr70170387r_bool,B_1: fun_Pr70170387r_bool] :
      ( hBOOL(hAPP_f483496539l_bool(ord_le1987888477r_bool(A_2),B_1))
     => ( hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,X_2),A_2))
       => hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,X_2),B_1)) ) ) ).

tff(fact_695_in__mono,axiom,
    ! [X_2: produc1971331930t_char,A_2: fun_Pr1861226704r_bool,B_1: fun_Pr1861226704r_bool] :
      ( hBOOL(hAPP_f515912112l_bool(ord_le117566470r_bool(A_2),B_1))
     => ( hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,X_2),A_2))
       => hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,X_2),B_1)) ) ) ).

tff(fact_696_in__mono,axiom,
    ! [X_2: produc430140671on_val,A_2: fun_Pr859510977l_bool,B_1: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(A_2),B_1))
     => ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,X_2),A_2))
       => hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,X_2),B_1)) ) ) ).

tff(fact_697_in__mono,axiom,
    ! [X_2: nat,A_2: fun_nat_bool,B_1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(ord_le1568362934t_bool(A_2),B_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_1)) ) ) ).

tff(fact_698_in__mono,axiom,
    ! [X_2: produc1278157519t_char,A_2: fun_Pr565113489r_bool,B_1: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(A_2),B_1))
     => ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,X_2),A_2))
       => hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,X_2),B_1)) ) ) ).

tff(fact_699_in__mono,axiom,
    ! [X_2: list_char,A_2: fun_list_char_bool,B_1: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1))
     => ( hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_2),A_2))
       => hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_2),B_1)) ) ) ).

tff(fact_700_in__mono,axiom,
    ! [X_2: produc1102272487on_val,A_2: fun_Pr691271849l_bool,B_1: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(A_2),B_1))
     => ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,X_2),A_2))
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,X_2),B_1)) ) ) ).

tff(fact_701_set__rev__mp,axiom,
    ! [B_1: fun_Pr70170387r_bool,X_2: produc1013743697t_char,A_2: fun_Pr70170387r_bool] :
      ( hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,X_2),A_2))
     => ( hBOOL(hAPP_f483496539l_bool(ord_le1987888477r_bool(A_2),B_1))
       => hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,X_2),B_1)) ) ) ).

tff(fact_702_set__rev__mp,axiom,
    ! [B_1: fun_Pr1861226704r_bool,X_2: produc1971331930t_char,A_2: fun_Pr1861226704r_bool] :
      ( hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,X_2),A_2))
     => ( hBOOL(hAPP_f515912112l_bool(ord_le117566470r_bool(A_2),B_1))
       => hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,X_2),B_1)) ) ) ).

tff(fact_703_set__rev__mp,axiom,
    ! [B_1: fun_Pr859510977l_bool,X_2: produc430140671on_val,A_2: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,X_2),A_2))
     => ( hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(A_2),B_1))
       => hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,X_2),B_1)) ) ) ).

tff(fact_704_set__rev__mp,axiom,
    ! [B_1: fun_nat_bool,X_2: nat,A_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_2))
     => ( hBOOL(hAPP_f54304608l_bool(ord_le1568362934t_bool(A_2),B_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_1)) ) ) ).

tff(fact_705_set__rev__mp,axiom,
    ! [B_1: fun_Pr565113489r_bool,X_2: produc1278157519t_char,A_2: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,X_2),A_2))
     => ( hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(A_2),B_1))
       => hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,X_2),B_1)) ) ) ).

tff(fact_706_set__rev__mp,axiom,
    ! [B_1: fun_list_char_bool,X_2: list_char,A_2: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_2),A_2))
     => ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1))
       => hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_2),B_1)) ) ) ).

tff(fact_707_set__rev__mp,axiom,
    ! [B_1: fun_Pr691271849l_bool,X_2: produc1102272487on_val,A_2: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,X_2),A_2))
     => ( hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(A_2),B_1))
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,X_2),B_1)) ) ) ).

tff(fact_708_set__mp,axiom,
    ! [X_2: produc1013743697t_char,A_2: fun_Pr70170387r_bool,B_1: fun_Pr70170387r_bool] :
      ( hBOOL(hAPP_f483496539l_bool(ord_le1987888477r_bool(A_2),B_1))
     => ( hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,X_2),A_2))
       => hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,X_2),B_1)) ) ) ).

tff(fact_709_set__mp,axiom,
    ! [X_2: produc1971331930t_char,A_2: fun_Pr1861226704r_bool,B_1: fun_Pr1861226704r_bool] :
      ( hBOOL(hAPP_f515912112l_bool(ord_le117566470r_bool(A_2),B_1))
     => ( hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,X_2),A_2))
       => hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,X_2),B_1)) ) ) ).

tff(fact_710_set__mp,axiom,
    ! [X_2: produc430140671on_val,A_2: fun_Pr859510977l_bool,B_1: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(A_2),B_1))
     => ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,X_2),A_2))
       => hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,X_2),B_1)) ) ) ).

tff(fact_711_set__mp,axiom,
    ! [X_2: nat,A_2: fun_nat_bool,B_1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(ord_le1568362934t_bool(A_2),B_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_1)) ) ) ).

tff(fact_712_set__mp,axiom,
    ! [X_2: produc1278157519t_char,A_2: fun_Pr565113489r_bool,B_1: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(A_2),B_1))
     => ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,X_2),A_2))
       => hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,X_2),B_1)) ) ) ).

tff(fact_713_set__mp,axiom,
    ! [X_2: list_char,A_2: fun_list_char_bool,B_1: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1))
     => ( hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_2),A_2))
       => hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_2),B_1)) ) ) ).

tff(fact_714_set__mp,axiom,
    ! [X_2: produc1102272487on_val,A_2: fun_Pr691271849l_bool,B_1: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(A_2),B_1))
     => ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,X_2),A_2))
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,X_2),B_1)) ) ) ).

tff(fact_715_subset__trans,axiom,
    ! [C: fun_list_char_bool,A_2: fun_list_char_bool,B_1: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1))
     => ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(B_1),C))
       => hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),C)) ) ) ).

tff(fact_716_equalityE,axiom,
    ! [A_2: fun_list_char_bool,B_1: fun_list_char_bool] :
      ( ( A_2 = B_1 )
     => ~ ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1))
         => ~ hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(B_1),A_2)) ) ) ).

tff(fact_717_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_718_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr859510977l_bool] : transi374442731on_val(transi374442731on_val(R_1)) = transi374442731on_val(R_1) ).

tff(fact_719_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr565113489r_bool] : transi1395422419t_char(transi1395422419t_char(R_1)) = transi1395422419t_char(R_1) ).

tff(fact_720_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr691271849l_bool] : transi2024712006on_val(transi2024712006on_val(R_1)) = transi2024712006on_val(R_1) ).

tff(fact_721_hconf__new,axiom,
    ! [Obj: produc639455274on_val,A: nat,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val] :
      ( hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),Hb))
     => ( ( hAPP_n546249108on_val(Hb,A) = none_P179726773on_val )
       => ( hBOOL(hAPP_P1235399154l_bool(oconf_1869808039t_char(Pa,Hb),Obj))
         => hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),fun_up2041264236on_val(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,Obj)))) ) ) ) ).

tff(fact_722_converse__rtrancl__into__rtrancl,axiom,
    ! [C_2: produc2061676504on_val,A: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B)),R_1))
     => ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B),C_2)),transi374442731on_val(R_1)))
       => hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),C_2)),transi374442731on_val(R_1))) ) ) ).

tff(fact_723_converse__rtrancl__into__rtrancl,axiom,
    ! [C_2: list_char,A: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B)),R_1))
     => ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B),C_2)),transi1395422419t_char(R_1)))
       => hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),C_2)),transi1395422419t_char(R_1))) ) ) ).

tff(fact_724_converse__rtrancl__into__rtrancl,axiom,
    ! [C_2: produc124828825on_val,A: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B)),R_1))
     => ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B),C_2)),transi2024712006on_val(R_1)))
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),C_2)),transi2024712006on_val(R_1))) ) ) ).

tff(fact_725_converse__rtrancl__into__rtrancl,axiom,
    ! [C_2: val,A: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B)),R_1))
     => ( hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B),C_2)),transi935034983cl_val(R_1)))
       => hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),C_2)),transi935034983cl_val(R_1))) ) ) ).

tff(fact_726_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_2: produc2061676504on_val,A: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B)),transi374442731on_val(R_1)))
     => ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B),C_2)),R_1))
       => hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),C_2)),transi374442731on_val(R_1))) ) ) ).

tff(fact_727_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_2: list_char,A: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B)),transi1395422419t_char(R_1)))
     => ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B),C_2)),R_1))
       => hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),C_2)),transi1395422419t_char(R_1))) ) ) ).

tff(fact_728_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_2: produc124828825on_val,A: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B)),transi2024712006on_val(R_1)))
     => ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B),C_2)),R_1))
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),C_2)),transi2024712006on_val(R_1))) ) ) ).

tff(fact_729_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_2: val,A: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B)),transi935034983cl_val(R_1)))
     => ( hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B),C_2)),R_1))
       => hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),C_2)),transi935034983cl_val(R_1))) ) ) ).

tff(fact_730_rtrancl__trans,axiom,
    ! [C_2: produc2061676504on_val,A: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B)),transi374442731on_val(R_1)))
     => ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B),C_2)),transi374442731on_val(R_1)))
       => hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),C_2)),transi374442731on_val(R_1))) ) ) ).

tff(fact_731_rtrancl__trans,axiom,
    ! [C_2: list_char,A: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B)),transi1395422419t_char(R_1)))
     => ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B),C_2)),transi1395422419t_char(R_1)))
       => hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),C_2)),transi1395422419t_char(R_1))) ) ) ).

tff(fact_732_rtrancl__trans,axiom,
    ! [C_2: produc124828825on_val,A: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B)),transi2024712006on_val(R_1)))
     => ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B),C_2)),transi2024712006on_val(R_1)))
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),C_2)),transi2024712006on_val(R_1))) ) ) ).

tff(fact_733_rtrancl__trans,axiom,
    ! [C_2: val,A: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B)),transi935034983cl_val(R_1)))
     => ( hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B),C_2)),transi935034983cl_val(R_1)))
       => hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),C_2)),transi935034983cl_val(R_1))) ) ) ).

tff(fact_734_subsetI,axiom,
    ! [B_1: fun_Pr70170387r_bool,A_2: fun_Pr70170387r_bool] :
      ( ! [X_1: produc1013743697t_char] :
          ( hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,X_1),A_2))
         => hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,X_1),B_1)) )
     => hBOOL(hAPP_f483496539l_bool(ord_le1987888477r_bool(A_2),B_1)) ) ).

tff(fact_735_subsetI,axiom,
    ! [B_1: fun_Pr1861226704r_bool,A_2: fun_Pr1861226704r_bool] :
      ( ! [X_1: produc1971331930t_char] :
          ( hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,X_1),A_2))
         => hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,X_1),B_1)) )
     => hBOOL(hAPP_f515912112l_bool(ord_le117566470r_bool(A_2),B_1)) ) ).

tff(fact_736_subsetI,axiom,
    ! [B_1: fun_Pr859510977l_bool,A_2: fun_Pr859510977l_bool] :
      ( ! [X_1: produc430140671on_val] :
          ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,X_1),A_2))
         => hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,X_1),B_1)) )
     => hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(A_2),B_1)) ) ).

tff(fact_737_subsetI,axiom,
    ! [B_1: fun_nat_bool,A_2: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_1)) )
     => hBOOL(hAPP_f54304608l_bool(ord_le1568362934t_bool(A_2),B_1)) ) ).

tff(fact_738_subsetI,axiom,
    ! [B_1: fun_Pr565113489r_bool,A_2: fun_Pr565113489r_bool] :
      ( ! [X_1: produc1278157519t_char] :
          ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,X_1),A_2))
         => hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,X_1),B_1)) )
     => hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(A_2),B_1)) ) ).

tff(fact_739_subsetI,axiom,
    ! [B_1: fun_list_char_bool,A_2: fun_list_char_bool] :
      ( ! [X_1: list_char] :
          ( hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_1),A_2))
         => hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_1),B_1)) )
     => hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1)) ) ).

tff(fact_740_subsetI,axiom,
    ! [B_1: fun_Pr691271849l_bool,A_2: fun_Pr691271849l_bool] :
      ( ! [X_1: produc1102272487on_val] :
          ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,X_1),A_2))
         => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,X_1),B_1)) )
     => hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(A_2),B_1)) ) ).

tff(fact_741_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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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_2: produc12694297on_val] :
              ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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_2))),R_1))
             => ~ hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_2)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Za),Zb))),transi374442731on_val(R_1))) ) ) ) ).

tff(fact_742_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_2: produc12694297on_val] :
              ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_2))),R_1))
             => ~ hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_2)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Za),Zb))),transi2024712006on_val(R_1))) ) ) ) ).

tff(fact_743_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(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(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_2: exp_list_char] :
              ( hBOOL(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(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_2))),R_1))
             => ~ hBOOL(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(member1999287380t_char,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_2)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Za),Zb))),transi198989188t_char(R_1))) ) ) ) ).

tff(fact_744_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(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(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_2: list_P341299826t_char] :
              ( hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(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_2))),R_1))
             => ~ hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(member1551446420t_char,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_2)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Za),Zb))),transi772168185t_char(R_1))) ) ) ) ).

tff(fact_745_converse__rtranclE2,axiom,
    ! [Xa_1: list_char,Xb_1: produc2146869324t_char,Za: list_char,Zb: produc2146869324t_char,R_1: fun_Pr1538825897r_bool] :
      ( hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(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_2: produc2146869324t_char] :
              ( hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(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_2))),R_1))
             => ~ hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(member1607118676t_char,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_2)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Za),Zb))),transi2005320128t_char(R_1))) ) ) ) ).

tff(fact_746_converse__rtranclE2,axiom,
    ! [Xa_1: list_char,Xb_1: produc952412819t_char,Za: list_char,Zb: produc952412819t_char,R_1: fun_Pr981088873r_bool] :
      ( hBOOL(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(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_2: produc952412819t_char] :
              ( hBOOL(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(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_2))),R_1))
             => ~ hBOOL(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(member162552852t_char,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_2)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Za),Zb))),transi1123801095t_char(R_1))) ) ) ) ).

tff(fact_747_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(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(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_2: exp_list_char] :
              ( hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(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_2))),R_1))
             => ~ hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(member1161907014t_char,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_2)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Za),Zb))),transi1789604888t_char(R_1))) ) ) ) ).

tff(fact_748_converse__rtranclE2,axiom,
    ! [Xa_1: list_ty,Xb_1: produc662261637t_char,Za: list_ty,Zb: produc662261637t_char,R_1: fun_Pr1728267013r_bool] :
      ( hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(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_2: produc662261637t_char] :
              ( hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(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_2))),R_1))
             => ~ hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(member125098544t_char,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_2)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Za),Zb))),transi1257872013t_char(R_1))) ) ) ) ).

tff(fact_749_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(hAPP_f528956081l_bool(hAPP_P325013257l_bool(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_2: produc220283002t_char] :
              ( hBOOL(hAPP_f528956081l_bool(hAPP_P325013257l_bool(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_2))),R_1))
             => ~ hBOOL(hAPP_f528956081l_bool(hAPP_P325013257l_bool(member1420286996t_char,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_2)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Za),Zb))),transi122195895t_char(R_1))) ) ) ) ).

tff(fact_750_converse__rtranclE2,axiom,
    ! [Xa_1: produc2061676504on_val,Xb_1: produc2061676504on_val,Za: produc2061676504on_val,Zb: produc2061676504on_val,R_1: fun_Pr302334223l_bool] :
      ( hBOOL(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(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_2: produc2061676504on_val] :
              ( hBOOL(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(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_2))),R_1))
             => ~ hBOOL(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(member88670778on_val,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_2)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Za),Zb))),transi208336786on_val(R_1))) ) ) ) ).

tff(fact_751_converse__rtranclE2,axiom,
    ! [Xa_1: val,Xb_1: val,Za: val,Zb: val,R_1: fun_Pr832147423l_bool] :
      ( hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(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_2: val] :
              ( hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(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_2))),R_1))
             => ~ hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(member837208074al_val,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_2)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Za),Zb))),transi1423755450al_val(R_1))) ) ) ) ).

tff(fact_752_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(hAPP_f126136681l_bool(hAPP_P982127993l_bool(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_2: product_prod_val_val] :
              ( hBOOL(hAPP_f126136681l_bool(hAPP_P982127993l_bool(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_2))),R_1))
             => ~ hBOOL(hAPP_f126136681l_bool(hAPP_P982127993l_bool(member1732271180al_val,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_2)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Za),Zb))),transi1906258203al_val(R_1))) ) ) ) ).

tff(fact_753_converse__rtranclE2,axiom,
    ! [Xa_1: list_char,Xb_1: list_char,Za: list_char,Zb: list_char,R_1: fun_Pr1336847023r_bool] :
      ( hBOOL(hAPP_f851858423l_bool(hAPP_P786771093l_bool(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_2: list_char] :
              ( hBOOL(hAPP_f851858423l_bool(hAPP_P786771093l_bool(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_2))),R_1))
             => ~ hBOOL(hAPP_f851858423l_bool(hAPP_P786771093l_bool(member794220506t_char,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_2)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Za),Zb))),transi1095029602t_char(R_1))) ) ) ) ).

tff(fact_754_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(hAPP_f665343921l_bool(hAPP_P502294281l_bool(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_2: fun_Pr806764899on_val] :
              ( hBOOL(hAPP_f665343921l_bool(hAPP_P502294281l_bool(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_2))),R_1))
             => ~ hBOOL(hAPP_f665343921l_bool(hAPP_P502294281l_bool(member1322055188on_val,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_2)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Za),Zb))),transi61620055on_val(R_1))) ) ) ) ).

tff(fact_755_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(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(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_2: fun_li1432931796on_val] :
              ( hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(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_2))),R_1))
             => ~ hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(member563141460on_val,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_2)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Za),Zb))),transi921647814on_val(R_1))) ) ) ) ).

tff(fact_756_converse__rtranclE2,axiom,
    ! [Xa_1: produc124828825on_val,Xb_1: produc124828825on_val,Za: produc124828825on_val,Zb: produc124828825on_val,R_1: fun_Pr903661919l_bool] :
      ( hBOOL(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(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_2: produc124828825on_val] :
              ( hBOOL(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(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_2))),R_1))
             => ~ hBOOL(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(member808015754on_val,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_2)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Za),Zb))),transi910771962on_val(R_1))) ) ) ) ).

tff(fact_757_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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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_2: produc12694297on_val,Aa: list_exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_2)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Aa),Ba))),R_1))
             => ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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_2)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_758_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_2: produc12694297on_val,Aa: exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_2)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Aa),Ba))),R_1))
             => ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_2)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_759_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(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(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_2: exp_list_char,Aa: list_list_char,Ba: exp_list_char] :
              ( hBOOL(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(member1999287380t_char,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_2)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Aa),Ba))),R_1))
             => ( hBOOL(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(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_2)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_760_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(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(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_2: list_P341299826t_char,Aa: list_P1940453997har_ty,Ba: list_P341299826t_char] :
              ( hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(member1551446420t_char,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_2)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Aa),Ba))),R_1))
             => ( hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(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_2)) ) ) )
         => hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_761_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(hAPP_f272179441l_bool(hAPP_P396425609l_bool(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_2: produc2146869324t_char,Aa: list_char,Ba: produc2146869324t_char] :
              ( hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(member1607118676t_char,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_2)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Aa),Ba))),R_1))
             => ( hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(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_2)) ) ) )
         => hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_762_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(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(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_2: produc952412819t_char,Aa: list_char,Ba: produc952412819t_char] :
              ( hBOOL(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(member162552852t_char,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_2)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Aa),Ba))),R_1))
             => ( hBOOL(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(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_2)) ) ) )
         => hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_763_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(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(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_2: exp_list_char,Aa: list_val,Ba: exp_list_char] :
              ( hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(member1161907014t_char,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_2)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Aa),Ba))),R_1))
             => ( hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(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_2)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_764_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(hAPP_f258424141l_bool(hAPP_P409642305l_bool(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_2: produc662261637t_char,Aa: list_ty,Ba: produc662261637t_char] :
              ( hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(member125098544t_char,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_2)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Aa),Ba))),R_1))
             => ( hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(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_2)) ) ) )
         => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_765_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(hAPP_f528956081l_bool(hAPP_P325013257l_bool(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_2: produc220283002t_char,Aa: list_list_char,Ba: produc220283002t_char] :
              ( hBOOL(hAPP_f528956081l_bool(hAPP_P325013257l_bool(member1420286996t_char,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_2)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Aa),Ba))),R_1))
             => ( hBOOL(hAPP_f528956081l_bool(hAPP_P325013257l_bool(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_2)) ) ) )
         => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_766_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(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(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_2: produc2061676504on_val,Aa: produc2061676504on_val,Ba: produc2061676504on_val] :
              ( hBOOL(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(member88670778on_val,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_2)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Aa),Ba))),R_1))
             => ( hBOOL(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(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_2)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_767_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_val_fun_val_bool,Ax: val,Ay: val,Bx: val,By: val,R_1: fun_Pr832147423l_bool] :
      ( hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(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_2: val,Aa: val,Ba: val] :
              ( hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(member837208074al_val,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_2)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Aa),Ba))),R_1))
             => ( hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(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_2)) ) ) )
         => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_768_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(hAPP_f126136681l_bool(hAPP_P982127993l_bool(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_2: product_prod_val_val,Aa: bop,Ba: product_prod_val_val] :
              ( hBOOL(hAPP_f126136681l_bool(hAPP_P982127993l_bool(member1732271180al_val,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_2)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Aa),Ba))),R_1))
             => ( hBOOL(hAPP_f126136681l_bool(hAPP_P982127993l_bool(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_2)) ) ) )
         => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_769_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(hAPP_f851858423l_bool(hAPP_P786771093l_bool(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_2: list_char,Aa: list_char,Ba: list_char] :
              ( hBOOL(hAPP_f851858423l_bool(hAPP_P786771093l_bool(member794220506t_char,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_2)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Aa),Ba))),R_1))
             => ( hBOOL(hAPP_f851858423l_bool(hAPP_P786771093l_bool(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_2)) ) ) )
         => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_770_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(hAPP_f665343921l_bool(hAPP_P502294281l_bool(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_2: fun_Pr806764899on_val,Aa: list_char,Ba: fun_Pr806764899on_val] :
              ( hBOOL(hAPP_f665343921l_bool(hAPP_P502294281l_bool(member1322055188on_val,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_2)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Aa),Ba))),R_1))
             => ( hBOOL(hAPP_f665343921l_bool(hAPP_P502294281l_bool(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_2)) ) ) )
         => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_771_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(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(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_2: fun_li1432931796on_val,Aa: fun_na939144002on_val,Ba: fun_li1432931796on_val] :
              ( hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(member563141460on_val,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_2)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Aa),Ba))),R_1))
             => ( hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(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_2)) ) ) )
         => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_772_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(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(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_2: produc124828825on_val,Aa: produc124828825on_val,Ba: produc124828825on_val] :
              ( hBOOL(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(member808015754on_val,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_2)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Aa),Ba))),R_1))
             => ( hBOOL(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(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_2)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_773_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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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_2: produc12694297on_val,Aa: list_exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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_2))),transi374442731on_val(R_1)))
             => ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_2)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Aa),Ba))),R_1))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,A_1),B_2))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_774_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_2: produc12694297on_val,Aa: exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_2))),transi2024712006on_val(R_1)))
             => ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_2)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Aa),Ba))),R_1))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A_1),B_2))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_775_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(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(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_2: exp_list_char,Aa: list_list_char,Ba: exp_list_char] :
              ( hBOOL(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(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_2))),transi198989188t_char(R_1)))
             => ( hBOOL(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(member1999287380t_char,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_2)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Aa),Ba))),R_1))
               => ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,A_1),B_2))
                 => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_776_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(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(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_2: list_P341299826t_char,Aa: list_P1940453997har_ty,Ba: list_P341299826t_char] :
              ( hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(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_2))),transi772168185t_char(R_1)))
             => ( hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(member1551446420t_char,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_2)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Aa),Ba))),R_1))
               => ( hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,A_1),B_2))
                 => hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_777_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(hAPP_f272179441l_bool(hAPP_P396425609l_bool(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_2: produc2146869324t_char,Aa: list_char,Ba: produc2146869324t_char] :
              ( hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(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_2))),transi2005320128t_char(R_1)))
             => ( hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(member1607118676t_char,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_2)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Aa),Ba))),R_1))
               => ( hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,A_1),B_2))
                 => hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_778_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(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(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_2: produc952412819t_char,Aa: list_char,Ba: produc952412819t_char] :
              ( hBOOL(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(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_2))),transi1123801095t_char(R_1)))
             => ( hBOOL(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(member162552852t_char,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_2)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Aa),Ba))),R_1))
               => ( hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,A_1),B_2))
                 => hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_779_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(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(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_2: exp_list_char,Aa: list_val,Ba: exp_list_char] :
              ( hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(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_2))),transi1789604888t_char(R_1)))
             => ( hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(member1161907014t_char,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_2)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Aa),Ba))),R_1))
               => ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,A_1),B_2))
                 => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_780_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(hAPP_f258424141l_bool(hAPP_P409642305l_bool(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_2: produc662261637t_char,Aa: list_ty,Ba: produc662261637t_char] :
              ( hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(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_2))),transi1257872013t_char(R_1)))
             => ( hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(member125098544t_char,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_2)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Aa),Ba))),R_1))
               => ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,A_1),B_2))
                 => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_781_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(hAPP_f528956081l_bool(hAPP_P325013257l_bool(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_2: produc220283002t_char,Aa: list_list_char,Ba: produc220283002t_char] :
              ( hBOOL(hAPP_f528956081l_bool(hAPP_P325013257l_bool(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_2))),transi122195895t_char(R_1)))
             => ( hBOOL(hAPP_f528956081l_bool(hAPP_P325013257l_bool(member1420286996t_char,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_2)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Aa),Ba))),R_1))
               => ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,A_1),B_2))
                 => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_782_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(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(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_2: produc2061676504on_val,Aa: produc2061676504on_val,Ba: produc2061676504on_val] :
              ( hBOOL(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(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_2))),transi208336786on_val(R_1)))
             => ( hBOOL(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(member88670778on_val,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_2)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Aa),Ba))),R_1))
               => ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,A_1),B_2))
                 => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_783_rtrancl__induct2,axiom,
    ! [Pa: fun_val_fun_val_bool,Ax: val,Ay: val,Bx: val,By: val,R_1: fun_Pr832147423l_bool] :
      ( hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(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_2: val,Aa: val,Ba: val] :
              ( hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(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_2))),transi1423755450al_val(R_1)))
             => ( hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(member837208074al_val,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_2)),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_2))
                 => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_784_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(hAPP_f126136681l_bool(hAPP_P982127993l_bool(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_2: product_prod_val_val,Aa: bop,Ba: product_prod_val_val] :
              ( hBOOL(hAPP_f126136681l_bool(hAPP_P982127993l_bool(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_2))),transi1906258203al_val(R_1)))
             => ( hBOOL(hAPP_f126136681l_bool(hAPP_P982127993l_bool(member1732271180al_val,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_2)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Aa),Ba))),R_1))
               => ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,A_1),B_2))
                 => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_785_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(hAPP_f851858423l_bool(hAPP_P786771093l_bool(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_2: list_char,Aa: list_char,Ba: list_char] :
              ( hBOOL(hAPP_f851858423l_bool(hAPP_P786771093l_bool(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_2))),transi1095029602t_char(R_1)))
             => ( hBOOL(hAPP_f851858423l_bool(hAPP_P786771093l_bool(member794220506t_char,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_2)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Aa),Ba))),R_1))
               => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,A_1),B_2))
                 => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_786_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(hAPP_f665343921l_bool(hAPP_P502294281l_bool(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_2: fun_Pr806764899on_val,Aa: list_char,Ba: fun_Pr806764899on_val] :
              ( hBOOL(hAPP_f665343921l_bool(hAPP_P502294281l_bool(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_2))),transi61620055on_val(R_1)))
             => ( hBOOL(hAPP_f665343921l_bool(hAPP_P502294281l_bool(member1322055188on_val,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_2)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Aa),Ba))),R_1))
               => ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,A_1),B_2))
                 => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_787_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(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(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_2: fun_li1432931796on_val,Aa: fun_na939144002on_val,Ba: fun_li1432931796on_val] :
              ( hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(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_2))),transi921647814on_val(R_1)))
             => ( hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(member563141460on_val,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_2)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Aa),Ba))),R_1))
               => ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A_1),B_2))
                 => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_788_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(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(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_2: produc124828825on_val,Aa: produc124828825on_val,Ba: produc124828825on_val] :
              ( hBOOL(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(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_2))),transi910771962on_val(R_1)))
             => ( hBOOL(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(member808015754on_val,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_2)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Aa),Ba))),R_1))
               => ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A_1),B_2))
                 => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_789_progress,axiom,
    ! [Lb: fun_li1432931796on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Ta: ty,Hb: fun_na939144002on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),Hb))
       => ( hBOOL(wTrt_1(Pa,Hb,Ea,Eb,Ta))
         => ( hBOOL(d_list_char(Eb,hAPP_f363827556r_bool(some_f80346385r_bool,dom_list_char_val(Lb))))
           => ( ~ hBOOL(final_list_char(Eb))
             => ? [E_1: exp_list_char,S_5: produc12694297on_val] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1),S_5))),red(Pa))) ) ) ) ) ) ).

tff(fact_790_option_Oexhaust,axiom,
    ! [Y_3: option_nat] :
      ( ( Y_3 != none_nat )
     => ~ ! [A_1: nat] : Y_3 != hAPP_nat_option_nat(some_nat,A_1) ) ).

tff(fact_791_option_Oexhaust,axiom,
    ! [Y_3: option_ty] :
      ( ( Y_3 != none_ty )
     => ~ ! [A_1: ty] : Y_3 != hAPP_ty_option_ty(some_ty,A_1) ) ).

tff(fact_792_option_Oexhaust,axiom,
    ! [Y_2: option1479284511on_val] :
      ( ( Y_2 != none_P179726773on_val )
     => ~ ! [A_1: produc639455274on_val] : Y_2 != hAPP_P1510515380on_val(some_P948696889on_val,A_1) ) ).

tff(fact_793_option_Oexhaust,axiom,
    ! [Y_3: option_val] :
      ( ( Y_3 != none_val )
     => ~ ! [A_1: val] : Y_3 != hAPP_val_option_val(some_val,A_1) ) ).

tff(fact_794_option_Oexhaust,axiom,
    ! [Y_2: option466449911r_bool] :
      ( ( Y_2 != none_f478147469r_bool )
     => ~ ! [A_1: fun_list_char_bool] : Y_2 != hAPP_f363827556r_bool(some_f80346385r_bool,A_1) ) ).

tff(fact_795_order__refl,axiom,
    ! [X_2: fun_list_char_bool] : hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(X_2),X_2)) ).

tff(fact_796_rtrancl__induct,axiom,
    ! [Pa: fun_Pr248118298l_bool,A: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),Y_1)),transi374442731on_val(R_1)))
             => ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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_797_rtrancl__induct,axiom,
    ! [Pa: fun_list_char_bool,A: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(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(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),Y_1)),transi1395422419t_char(R_1)))
             => ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(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_798_rtrancl__induct,axiom,
    ! [Pa: fun_Pr680585871l_bool,A: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),Y_1)),transi2024712006on_val(R_1)))
             => ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_799_rtrancl__induct,axiom,
    ! [Pa: fun_val_bool,A: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(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(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),Y_1)),transi935034983cl_val(R_1)))
             => ( hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(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_800_pred__subset__eq2,axiom,
    ! [R_2: fun_Pr70170387r_bool,S_4: fun_Pr70170387r_bool] :
      ( hBOOL(hAPP_f1931964053l_bool(ord_le2008677227r_bool(hAPP_f1209019955r_bool(hAPP_f521496323r_bool(cOMBC_654453230r_bool,hAPP_f732843907r_bool(hAPP_f1563448447r_bool(cOMBB_1490692730t_char,cOMBC_390659185l_bool),hAPP_f1868463117l_bool(hAPP_f1365840271l_bool(cOMBB_1705938036t_char,hAPP_f1937828171l_bool(cOMBB_1681501894t_char,member1601084734t_char)),produc1331140167t_char))),R_2)),hAPP_f1209019955r_bool(hAPP_f521496323r_bool(cOMBC_654453230r_bool,hAPP_f732843907r_bool(hAPP_f1563448447r_bool(cOMBB_1490692730t_char,cOMBC_390659185l_bool),hAPP_f1868463117l_bool(hAPP_f1365840271l_bool(cOMBB_1705938036t_char,hAPP_f1937828171l_bool(cOMBB_1681501894t_char,member1601084734t_char)),produc1331140167t_char))),S_4)))
    <=> hBOOL(hAPP_f483496539l_bool(ord_le1987888477r_bool(R_2),S_4)) ) ).

tff(fact_801_pred__subset__eq2,axiom,
    ! [R_2: fun_Pr1861226704r_bool,S_4: fun_Pr1861226704r_bool] :
      ( hBOOL(hAPP_f1795246582l_bool(ord_le735260024r_bool(hAPP_f2025561243r_bool(hAPP_f1500560577r_bool(cOMBC_1784597444r_bool,hAPP_f29105311r_bool(hAPP_f953097879r_bool(cOMBB_672864638t_char,cOMBC_1338332465l_bool),hAPP_f333583909l_bool(hAPP_f1407048615l_bool(cOMBB_741416308t_char,hAPP_f937861397l_bool(cOMBB_1520154591t_char,member1467889965t_char)),produc822965838t_char))),R_2)),hAPP_f2025561243r_bool(hAPP_f1500560577r_bool(cOMBC_1784597444r_bool,hAPP_f29105311r_bool(hAPP_f953097879r_bool(cOMBB_672864638t_char,cOMBC_1338332465l_bool),hAPP_f333583909l_bool(hAPP_f1407048615l_bool(cOMBB_741416308t_char,hAPP_f937861397l_bool(cOMBB_1520154591t_char,member1467889965t_char)),produc822965838t_char))),S_4)))
    <=> hBOOL(hAPP_f515912112l_bool(ord_le117566470r_bool(R_2),S_4)) ) ).

tff(fact_802_pred__subset__eq2,axiom,
    ! [R_2: fun_Pr859510977l_bool,S_4: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f861853459l_bool(ord_le1270183657l_bool(hAPP_f447422815l_bool(hAPP_f2052909183l_bool(cOMBC_766524526l_bool,hAPP_f1427871743l_bool(hAPP_f32926423l_bool(cOMBB_779086262on_val,cOMBC_1491642377l_bool),hAPP_f1082373989l_bool(hAPP_f869803751l_bool(cOMBB_555068556on_val,hAPP_f810261999l_bool(cOMBB_1034324152on_val,member875476972on_val)),produc1611380469on_val))),R_2)),hAPP_f447422815l_bool(hAPP_f2052909183l_bool(cOMBC_766524526l_bool,hAPP_f1427871743l_bool(hAPP_f32926423l_bool(cOMBB_779086262on_val,cOMBC_1491642377l_bool),hAPP_f1082373989l_bool(hAPP_f869803751l_bool(cOMBB_555068556on_val,hAPP_f810261999l_bool(cOMBB_1034324152on_val,member875476972on_val)),produc1611380469on_val))),S_4)))
    <=> hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(R_2),S_4)) ) ).

tff(fact_803_pred__subset__eq2,axiom,
    ! [R_2: fun_Pr565113489r_bool,S_4: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f1776419603l_bool(ord_le1871967977r_bool(hAPP_f344506159r_bool(hAPP_f447563647r_bool(cOMBC_389248878r_bool,hAPP_f1032444159r_bool(hAPP_f254182519r_bool(cOMBB_1551681790t_char,cOMBC_1603044337l_bool),hAPP_f1764180741l_bool(hAPP_f247798919l_bool(cOMBB_526805108t_char,hAPP_f144783951l_bool(cOMBB_1586673472t_char,member1251428284t_char)),produc5062597t_char))),R_2)),hAPP_f344506159r_bool(hAPP_f447563647r_bool(cOMBC_389248878r_bool,hAPP_f1032444159r_bool(hAPP_f254182519r_bool(cOMBB_1551681790t_char,cOMBC_1603044337l_bool),hAPP_f1764180741l_bool(hAPP_f247798919l_bool(cOMBB_526805108t_char,hAPP_f144783951l_bool(cOMBB_1586673472t_char,member1251428284t_char)),produc5062597t_char))),S_4)))
    <=> hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(R_2),S_4)) ) ).

tff(fact_804_pred__subset__eq2,axiom,
    ! [R_2: fun_Pr691271849l_bool,S_4: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f434955681l_bool(ord_le1050317687l_bool(hAPP_f1200025813l_bool(hAPP_f1089788553l_bool(cOMBC_967917532l_bool,hAPP_f2095325577l_bool(hAPP_f1135930489l_bool(cOMBB_1223415373on_val,cOMBC_1608987946l_bool),hAPP_f1204100177l_bool(hAPP_f2026692601l_bool(cOMBB_1977588741on_val,hAPP_f1510763001l_bool(cOMBB_565412073on_val,member773094996on_val)),produc1441475159on_val))),R_2)),hAPP_f1200025813l_bool(hAPP_f1089788553l_bool(cOMBC_967917532l_bool,hAPP_f2095325577l_bool(hAPP_f1135930489l_bool(cOMBB_1223415373on_val,cOMBC_1608987946l_bool),hAPP_f1204100177l_bool(hAPP_f2026692601l_bool(cOMBB_1977588741on_val,hAPP_f1510763001l_bool(cOMBB_565412073on_val,member773094996on_val)),produc1441475159on_val))),S_4)))
    <=> hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(R_2),S_4)) ) ).

tff(fact_805_pred__subset__eq2,axiom,
    ! [R_2: fun_Pr1336948301r_bool,S_4: fun_Pr1336948301r_bool] :
      ( hBOOL(hAPP_f539072365l_bool(ord_le176694639r_bool(hAPP_f2091926485r_bool(hAPP_f1820115955r_bool(cOMBC_790582442r_bool,hAPP_f2059406941r_bool(hAPP_f108089737r_bool(cOMBB_2143526097t_char,cOMBC_220519196l_bool),hAPP_f165071409l_bool(hAPP_f1174637065l_bool(cOMBB_33167485t_char,hAPP_f380623487l_bool(cOMBB_1033145403t_char,member1840112042t_char)),produc1147572817t_char))),R_2)),hAPP_f2091926485r_bool(hAPP_f1820115955r_bool(cOMBC_790582442r_bool,hAPP_f2059406941r_bool(hAPP_f108089737r_bool(cOMBB_2143526097t_char,cOMBC_220519196l_bool),hAPP_f165071409l_bool(hAPP_f1174637065l_bool(cOMBB_33167485t_char,hAPP_f380623487l_bool(cOMBB_1033145403t_char,member1840112042t_char)),produc1147572817t_char))),S_4)))
    <=> hBOOL(hAPP_f82569901l_bool(ord_le715555971r_bool(R_2),S_4)) ) ).

tff(fact_806_pred__subset__eq2,axiom,
    ! [R_2: fun_Pr1669461698r_bool,S_4: fun_Pr1669461698r_bool] :
      ( hBOOL(hAPP_f1409772418l_bool(ord_le458107652r_bool(hAPP_f306469557r_bool(hAPP_f197435839r_bool(cOMBC_886773442r_bool,hAPP_f1749915625r_bool(hAPP_f842743203r_bool(cOMBB_657296617har_ty,cOMBC_1407716098l_bool),hAPP_f935003377l_bool(hAPP_f162154931l_bool(cOMBB_859890145har_ty,hAPP_f1847120981l_bool(cOMBB_1035649854t_char,member1379348767t_char)),produc1152259904t_char))),R_2)),hAPP_f306469557r_bool(hAPP_f197435839r_bool(cOMBC_886773442r_bool,hAPP_f1749915625r_bool(hAPP_f842743203r_bool(cOMBB_657296617har_ty,cOMBC_1407716098l_bool),hAPP_f935003377l_bool(hAPP_f162154931l_bool(cOMBB_859890145har_ty,hAPP_f1847120981l_bool(cOMBB_1035649854t_char,member1379348767t_char)),produc1152259904t_char))),S_4)))
    <=> hBOOL(hAPP_f1161798306l_bool(ord_le1734858744r_bool(R_2),S_4)) ) ).

tff(fact_807_pred__subset__eq2,axiom,
    ! [R_2: fun_Pr1898949769r_bool,S_4: fun_Pr1898949769r_bool] :
      ( hBOOL(hAPP_f1520735791l_bool(ord_le1151384881r_bool(hAPP_f719350875r_bool(hAPP_f2133563379r_bool(cOMBC_1025440566r_bool,hAPP_f1957374161r_bool(hAPP_f304993943r_bool(cOMBB_847828016t_char,cOMBC_516637475l_bool),hAPP_f1817350437l_bool(hAPP_f614662951l_bool(cOMBB_1558246132t_char,hAPP_f251669717l_bool(cOMBB_773661144t_char,member1771544038t_char)),produc1483578759t_char))),R_2)),hAPP_f719350875r_bool(hAPP_f2133563379r_bool(cOMBC_1025440566r_bool,hAPP_f1957374161r_bool(hAPP_f304993943r_bool(cOMBB_847828016t_char,cOMBC_516637475l_bool),hAPP_f1817350437l_bool(hAPP_f614662951l_bool(cOMBB_1558246132t_char,hAPP_f251669717l_bool(cOMBB_773661144t_char,member1771544038t_char)),produc1483578759t_char))),S_4)))
    <=> hBOOL(hAPP_f2050077417l_bool(ord_le725666495r_bool(R_2),S_4)) ) ).

tff(fact_808_pred__subset__eq2,axiom,
    ! [R_2: fun_Pr827765831r_bool,S_4: fun_Pr827765831r_bool] :
      ( hBOOL(hAPP_f1118567467l_bool(ord_le989574145r_bool(hAPP_f1051205629r_bool(hAPP_f987862447r_bool(cOMBC_1387630958r_bool,hAPP_f1449341487r_bool(hAPP_f1823921107r_bool(cOMBB_308691073st_val,cOMBC_818212448l_bool),hAPP_f2118054305l_bool(hAPP_f1687138147l_bool(cOMBB_2078271971st_val,hAPP_f1612138403l_bool(cOMBB_961360819t_char,member699351154t_char)),produc1916172923t_char))),R_2)),hAPP_f1051205629r_bool(hAPP_f987862447r_bool(cOMBC_1387630958r_bool,hAPP_f1449341487r_bool(hAPP_f1823921107r_bool(cOMBB_308691073st_val,cOMBC_818212448l_bool),hAPP_f2118054305l_bool(hAPP_f1687138147l_bool(cOMBB_2078271971st_val,hAPP_f1612138403l_bool(cOMBB_961360819t_char,member699351154t_char)),produc1916172923t_char))),S_4)))
    <=> hBOOL(hAPP_f1314764175l_bool(ord_le1852058257r_bool(R_2),S_4)) ) ).

tff(fact_809_pred__subset__eq2,axiom,
    ! [R_2: fun_Pr46158268r_bool,S_4: fun_Pr46158268r_bool] :
      ( hBOOL(hAPP_f1889282162l_bool(ord_le1449176264r_bool(hAPP_f2071340985r_bool(hAPP_f133320957r_bool(cOMBC_1127703214r_bool,hAPP_f1608277885r_bool(hAPP_f1134248971r_bool(cOMBB_338473166ist_ty,cOMBC_1365742487l_bool),hAPP_f2047757465l_bool(hAPP_f466945179l_bool(cOMBB_68065882ist_ty,hAPP_f693085049l_bool(cOMBB_147773915t_char,member140606439t_char)),produc1909267824t_char))),R_2)),hAPP_f2071340985r_bool(hAPP_f133320957r_bool(cOMBC_1127703214r_bool,hAPP_f1608277885r_bool(hAPP_f1134248971r_bool(cOMBB_338473166ist_ty,cOMBC_1365742487l_bool),hAPP_f2047757465l_bool(hAPP_f466945179l_bool(cOMBB_68065882ist_ty,hAPP_f693085049l_bool(cOMBB_147773915t_char,member140606439t_char)),produc1909267824t_char))),S_4)))
    <=> hBOOL(hAPP_f1746574980l_bool(ord_le1218729222r_bool(R_2),S_4)) ) ).

tff(fact_810_pred__subset__eq2,axiom,
    ! [R_2: fun_Pr227936640r_bool,S_4: fun_Pr227936640r_bool] :
      ( hBOOL(hAPP_f998390560l_bool(ord_le817953186r_bool(hAPP_f1044627221r_bool(hAPP_f308875635r_bool(cOMBC_1718404842r_bool,hAPP_f531187933r_bool(hAPP_f179418505r_bool(cOMBB_550632017t_char,cOMBC_407285762l_bool),hAPP_f1136362289l_bool(hAPP_f1736484361l_bool(cOMBB_2042763133t_char,hAPP_f1715733055l_bool(cOMBB_123628846t_char,member133545693t_char)),produc921874948t_char))),R_2)),hAPP_f1044627221r_bool(hAPP_f308875635r_bool(cOMBC_1718404842r_bool,hAPP_f531187933r_bool(hAPP_f179418505r_bool(cOMBB_550632017t_char,cOMBC_407285762l_bool),hAPP_f1136362289l_bool(hAPP_f1736484361l_bool(cOMBB_2042763133t_char,hAPP_f1715733055l_bool(cOMBB_123628846t_char,member133545693t_char)),produc921874948t_char))),S_4)))
    <=> hBOOL(hAPP_f1780084320l_bool(ord_le1579844278r_bool(R_2),S_4)) ) ).

tff(fact_811_pred__subset__eq2,axiom,
    ! [R_2: fun_Pr248118298l_bool,S_4: fun_Pr248118298l_bool] :
      ( hBOOL(hAPP_f2041029616l_bool(ord_le285175110l_bool(hAPP_f844901525l_bool(hAPP_f348508809l_bool(cOMBC_622308798l_bool,hAPP_f1149562121l_bool(hAPP_f1850037271l_bool(cOMBB_773375802t_char,cOMBC_2141828763l_bool),hAPP_f1752856401l_bool(hAPP_f552300311l_bool(cOMBB_1270208498t_char,hAPP_f1564338425l_bool(cOMBB_1078680455on_val,member1972431429on_val)),produc379668296on_val))),R_2)),hAPP_f844901525l_bool(hAPP_f348508809l_bool(cOMBC_622308798l_bool,hAPP_f1149562121l_bool(hAPP_f1850037271l_bool(cOMBB_773375802t_char,cOMBC_2141828763l_bool),hAPP_f1752856401l_bool(hAPP_f552300311l_bool(cOMBB_1270208498t_char,hAPP_f1564338425l_bool(cOMBB_1078680455on_val,member1972431429on_val)),produc379668296on_val))),S_4)))
    <=> hBOOL(hAPP_f837795298l_bool(ord_le1461833060l_bool(R_2),S_4)) ) ).

tff(fact_812_pred__subset__eq2,axiom,
    ! [R_2: fun_Pr2081272681l_bool,S_4: fun_Pr2081272681l_bool] :
      ( hBOOL(hAPP_f2071159779l_bool(ord_le408082617l_bool(hAPP_f198821591l_bool(hAPP_f1880802701l_bool(cOMBC_1979963740l_bool,hAPP_f1859053709l_bool(hAPP_f400269243l_bool(cOMBB_1701031980ol_val,cOMBC_331963401l_bool),hAPP_f293485653l_bool(hAPP_f565735867l_bool(cOMBB_815843940ol_val,hAPP_f183649339l_bool(cOMBB_2078984970ol_val,member649088532al_val)),product_Pair_val_val))),R_2)),hAPP_f198821591l_bool(hAPP_f1880802701l_bool(cOMBC_1979963740l_bool,hAPP_f1859053709l_bool(hAPP_f400269243l_bool(cOMBB_1701031980ol_val,cOMBC_331963401l_bool),hAPP_f293485653l_bool(hAPP_f565735867l_bool(cOMBB_815843940ol_val,hAPP_f183649339l_bool(cOMBB_2078984970ol_val,member649088532al_val)),product_Pair_val_val))),S_4)))
    <=> hBOOL(hAPP_f2028441009l_bool(ord_le310098611l_bool(R_2),S_4)) ) ).

tff(fact_813_pred__subset__eq2,axiom,
    ! [R_2: fun_Pr252072522l_bool,S_4: fun_Pr252072522l_bool] :
      ( hBOOL(hAPP_f1776070952l_bool(ord_le1725884030l_bool(hAPP_f257113085l_bool(hAPP_f1100052969l_bool(cOMBC_199425070l_bool,hAPP_f2100207721l_bool(hAPP_f1374595987l_bool(cOMBB_761748254ol_bop,cOMBC_813705475l_bool),hAPP_f866074145l_bool(hAPP_f877616419l_bool(cOMBB_1458388806ol_bop,hAPP_f62511709l_bool(cOMBB_2139740953al_val,member1417904245al_val)),produc621191550al_val))),R_2)),hAPP_f257113085l_bool(hAPP_f1100052969l_bool(cOMBC_199425070l_bool,hAPP_f2100207721l_bool(hAPP_f1374595987l_bool(cOMBB_761748254ol_bop,cOMBC_813705475l_bool),hAPP_f866074145l_bool(hAPP_f877616419l_bool(cOMBB_1458388806ol_bop,hAPP_f62511709l_bool(cOMBB_2139740953al_val,member1417904245al_val)),produc621191550al_val))),S_4)))
    <=> hBOOL(hAPP_f742333458l_bool(ord_le1467847572l_bool(R_2),S_4)) ) ).

tff(fact_814_pred__subset__eq2,axiom,
    ! [R_2: fun_Pr315804320l_bool,S_4: fun_Pr315804320l_bool] :
      ( hBOOL(hAPP_f678833350l_bool(ord_le188521288l_bool(hAPP_f2080627739l_bool(hAPP_f350189921l_bool(cOMBC_1535683812l_bool,hAPP_f1094343359l_bool(hAPP_f876671127l_bool(cOMBB_1200577438t_char,cOMBC_317789649l_bool),hAPP_f1370205989l_bool(hAPP_f1406462375l_bool(cOMBB_109816436t_char,hAPP_f919000597l_bool(cOMBB_1153773871on_val,member1542417277on_val)),produc823076510on_val))),R_2)),hAPP_f2080627739l_bool(hAPP_f350189921l_bool(cOMBC_1535683812l_bool,hAPP_f1094343359l_bool(hAPP_f876671127l_bool(cOMBB_1200577438t_char,cOMBC_317789649l_bool),hAPP_f1370205989l_bool(hAPP_f1406462375l_bool(cOMBB_109816436t_char,hAPP_f919000597l_bool(cOMBB_1153773871on_val,member1542417277on_val)),produc823076510on_val))),S_4)))
    <=> hBOOL(hAPP_f1134950784l_bool(ord_le1744419030l_bool(R_2),S_4)) ) ).

tff(fact_815_pred__subset__eq2,axiom,
    ! [R_2: fun_Pr1696029455l_bool,S_4: fun_Pr1696029455l_bool] :
      ( hBOOL(hAPP_f1450446905l_bool(ord_le125655867l_bool(hAPP_f47713631l_bool(hAPP_f77033475l_bool(cOMBC_1317565126l_bool,hAPP_f1250221913l_bool(hAPP_f1860331535l_bool(cOMBB_2084052674on_val,cOMBC_1518234801l_bool),hAPP_f1670595613l_bool(hAPP_f1472899487l_bool(cOMBB_588525814on_val,hAPP_f1168269397l_bool(cOMBB_1293776864on_val,member763590124on_val)),produc899768717on_val))),R_2)),hAPP_f47713631l_bool(hAPP_f77033475l_bool(cOMBC_1317565126l_bool,hAPP_f1250221913l_bool(hAPP_f1860331535l_bool(cOMBB_2084052674on_val,cOMBC_1518234801l_bool),hAPP_f1670595613l_bool(hAPP_f1472899487l_bool(cOMBB_588525814on_val,hAPP_f1168269397l_bool(cOMBB_1293776864on_val,member763590124on_val)),produc899768717on_val))),S_4)))
    <=> hBOOL(hAPP_f966411375l_bool(ord_le1908998213l_bool(R_2),S_4)) ) ).

tff(fact_816_pred__subset__eq2,axiom,
    ! [R_2: fun_Pr680585871l_bool,S_4: fun_Pr680585871l_bool] :
      ( hBOOL(hAPP_f570766339l_bool(ord_le1080391173l_bool(hAPP_f989077673l_bool(hAPP_f40682957l_bool(cOMBC_562612496l_bool,hAPP_f1475571983l_bool(hAPP_f1946480059l_bool(cOMBB_673739729t_char,cOMBC_1585774710l_bool),hAPP_f1614195593l_bool(hAPP_f705562443l_bool(cOMBB_507006011t_char,hAPP_f1639555093l_bool(cOMBB_985659173on_val,member840932460on_val)),produc1259058957on_val))),R_2)),hAPP_f989077673l_bool(hAPP_f40682957l_bool(cOMBC_562612496l_bool,hAPP_f1475571983l_bool(hAPP_f1946480059l_bool(cOMBB_673739729t_char,cOMBC_1585774710l_bool),hAPP_f1614195593l_bool(hAPP_f705562443l_bool(cOMBB_507006011t_char,hAPP_f1639555093l_bool(cOMBB_985659173on_val,member840932460on_val)),produc1259058957on_val))),S_4)))
    <=> hBOOL(hAPP_f91506671l_bool(ord_le1668954565l_bool(R_2),S_4)) ) ).

tff(fact_817_xt1_I6_J,axiom,
    ! [Z_1: fun_list_char_bool,Y_2: fun_list_char_bool,X_2: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Y_2),X_2))
     => ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Z_1),Y_2))
       => hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Z_1),X_2)) ) ) ).

tff(fact_818_xt1_I5_J,axiom,
    ! [Y_2: fun_list_char_bool,X_2: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Y_2),X_2))
     => ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(X_2),Y_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_819_order__trans,axiom,
    ! [Z_1: fun_list_char_bool,X_2: fun_list_char_bool,Y_2: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(X_2),Y_2))
     => ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Y_2),Z_1))
       => hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(X_2),Z_1)) ) ) ).

tff(fact_820_order__antisym,axiom,
    ! [X_2: fun_list_char_bool,Y_2: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(X_2),Y_2))
     => ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Y_2),X_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_821_xt1_I4_J,axiom,
    ! [C_2: fun_list_char_bool,B: fun_list_char_bool,A: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(B),A))
     => ( ( B = C_2 )
       => hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(C_2),A)) ) ) ).

tff(fact_822_ord__le__eq__trans,axiom,
    ! [C_2: fun_list_char_bool,A: fun_list_char_bool,B: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A),B))
     => ( ( B = C_2 )
       => hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A),C_2)) ) ) ).

tff(fact_823_xt1_I3_J,axiom,
    ! [C_2: fun_list_char_bool,A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( A = B )
     => ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(C_2),B))
       => hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(C_2),A)) ) ) ).

tff(fact_824_ord__eq__le__trans,axiom,
    ! [C_2: fun_list_char_bool,A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( A = B )
     => ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(B),C_2))
       => hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A),C_2)) ) ) ).

tff(fact_825_order__antisym__conv,axiom,
    ! [Y_2: fun_list_char_bool,X_2: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Y_2),X_2))
     => ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_826_order__eq__refl,axiom,
    ! [X_2: fun_list_char_bool,Y_2: fun_list_char_bool] :
      ( ( X_2 = Y_2 )
     => hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(X_2),Y_2)) ) ).

tff(fact_827_order__eq__iff,axiom,
    ! [X_2: fun_list_char_bool,Y_2: fun_list_char_bool] :
      ( ( X_2 = Y_2 )
    <=> ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(X_2),Y_2))
        & hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Y_2),X_2)) ) ) ).

tff(fact_828_le__funE,axiom,
    ! [X_2: list_char,F_1: fun_list_char_bool,G: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(F_1),G))
     => hBOOL(hAPP_bool_bool(ord_less_eq_bool(hAPP_list_char_bool(F_1,X_2)),hAPP_list_char_bool(G,X_2))) ) ).

tff(fact_829_le__funD,axiom,
    ! [X_2: list_char,F_1: fun_list_char_bool,G: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(F_1),G))
     => hBOOL(hAPP_bool_bool(ord_less_eq_bool(hAPP_list_char_bool(F_1,X_2)),hAPP_list_char_bool(G,X_2))) ) ).

tff(fact_830_le__fun__def,axiom,
    ! [F_1: fun_list_char_bool,G: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(F_1),G))
    <=> ! [X_1: list_char] : hBOOL(hAPP_bool_bool(ord_less_eq_bool(hAPP_list_char_bool(F_1,X_1)),hAPP_list_char_bool(G,X_1))) ) ).

tff(fact_831_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_832_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_833_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_f986089162l_bool(ord_le2092826700r_bool(fv(E_b)),fv(Eb))) ) ) ).

tff(fact_834_rtranclE,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B)),transi374442731on_val(R_1)))
     => ( ( A != B )
       => ~ ! [Y_1: produc2061676504on_val] :
              ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),Y_1)),transi374442731on_val(R_1)))
             => ~ hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Y_1),B)),R_1)) ) ) ) ).

tff(fact_835_rtranclE,axiom,
    ! [A: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B)),transi1395422419t_char(R_1)))
     => ( ( A != B )
       => ~ ! [Y_1: list_char] :
              ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),Y_1)),transi1395422419t_char(R_1)))
             => ~ hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Y_1),B)),R_1)) ) ) ) ).

tff(fact_836_rtranclE,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B)),transi2024712006on_val(R_1)))
     => ( ( A != B )
       => ~ ! [Y_1: produc124828825on_val] :
              ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),Y_1)),transi2024712006on_val(R_1)))
             => ~ hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Y_1),B)),R_1)) ) ) ) ).

tff(fact_837_rtranclE,axiom,
    ! [A: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B)),transi935034983cl_val(R_1)))
     => ( ( A != B )
       => ~ ! [Y_1: val] :
              ( hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),Y_1)),transi935034983cl_val(R_1)))
             => ~ hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Y_1),B)),R_1)) ) ) ) ).

tff(fact_838_converse__rtranclE,axiom,
    ! [X_2: produc2061676504on_val,Z_1: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,X_2),Y_1)),R_1))
             => ~ hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Y_1),Z_1)),transi374442731on_val(R_1))) ) ) ) ).

tff(fact_839_converse__rtranclE,axiom,
    ! [X_2: list_char,Z_1: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(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(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_2),Y_1)),R_1))
             => ~ hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Y_1),Z_1)),transi1395422419t_char(R_1))) ) ) ) ).

tff(fact_840_converse__rtranclE,axiom,
    ! [X_2: produc124828825on_val,Z_1: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X_2),Y_1)),R_1))
             => ~ hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Y_1),Z_1)),transi2024712006on_val(R_1))) ) ) ) ).

tff(fact_841_converse__rtranclE,axiom,
    ! [X_2: val,Z_1: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(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(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_2),Y_1)),R_1))
             => ~ hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Y_1),Z_1)),transi935034983cl_val(R_1))) ) ) ) ).

tff(fact_842_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr248118298l_bool,A: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Y_1),Z)),R_1))
             => ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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_843_converse__rtrancl__induct,axiom,
    ! [Pa: fun_list_char_bool,A: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(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(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Y_1),Z)),R_1))
             => ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(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_844_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr680585871l_bool,A: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Y_1),Z)),R_1))
             => ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_845_converse__rtrancl__induct,axiom,
    ! [Pa: fun_val_bool,A: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(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(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Y_1),Z)),R_1))
             => ( hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(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_846_le__funI,axiom,
    ! [F_1: fun_list_char_bool,G: fun_list_char_bool] :
      ( ! [X_1: list_char] : hBOOL(hAPP_bool_bool(ord_less_eq_bool(hAPP_list_char_bool(F_1,X_1)),hAPP_list_char_bool(G,X_1)))
     => hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(F_1),G)) ) ).

tff(fact_847_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_848_eval__notfree__unchanged,axiom,
    ! [Va_1: 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(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,Va_1),fv(Eb)))
       => ( hAPP_l207779698on_val(L_b,Va_1) = hAPP_l207779698on_val(Lb,Va_1) ) ) ) ).

tff(fact_849_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_850_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_851_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_852_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_853_LAss,axiom,
    ! [L_b: fun_li1432931796on_val,Va_1: list_char,Pa: list_P1999446415t_char,Eb: exp_list_char,S_0: produc12694297on_val,Va: 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,Va)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)))
     => ( ( L_b = fun_up1149430426on_val(Lb,Va_1,hAPP_val_option_val(some_val,Va)) )
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,lAss_list_char(Va_1,Eb),S_0),hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),L_b))) ) ) ).

tff(fact_854_Block,axiom,
    ! [Ta: ty,Pa: list_P1999446415t_char,E_0: exp_list_char,H_0: fun_na939144002on_val,L_0: fun_li1432931796on_val,Va_1: list_char,E_1_1: exp_list_char,H_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_0,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),fun_up1149430426on_val(L_0,Va_1,none_val))),E_1_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,block_list_char(Va_1,Ta,E_0),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),L_0)),E_1_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),fun_up1149430426on_val(L_1_1,Va_1,hAPP_l207779698on_val(L_0,Va_1))))) ) ).

tff(fact_855_eval__lcl__incr,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,H_0: fun_na939144002on_val,L_0: fun_li1432931796on_val,E_b: exp_list_char,H_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),L_0)),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1)))
     => hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(dom_list_char_val(L_0)),dom_list_char_val(L_1_1))) ) ).

tff(fact_856_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_857_Seq,axiom,
    ! [E_1_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,Va: val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_0,S_0),hAPP_v834067052t_char(val_list_char,Va)),S_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_1),E_2),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,seq_list_char(E_0,E_1_1),S_0),E_2),S_2_1)) ) ) ).

tff(fact_858_Reds__dom__lcl,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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f986089162l_bool(ord_le2092826700r_bool(dom_list_char_val(L_b)),semila919158006r_bool(dom_list_char_val(Lb),fv(Eb)))) ) ) ).

tff(fact_859_UnE,axiom,
    ! [C_2: produc1013743697t_char,A_2: fun_Pr70170387r_bool,B_1: fun_Pr70170387r_bool] :
      ( hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,C_2),semila1731249415r_bool(A_2,B_1)))
     => ( ~ hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,C_2),A_2))
       => hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,C_2),B_1)) ) ) ).

tff(fact_860_UnE,axiom,
    ! [C_2: produc1971331930t_char,A_2: fun_Pr1861226704r_bool,B_1: fun_Pr1861226704r_bool] :
      ( hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,C_2),semila1346223580r_bool(A_2,B_1)))
     => ( ~ hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,C_2),A_2))
       => hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,C_2),B_1)) ) ) ).

tff(fact_861_UnE,axiom,
    ! [C_2: produc430140671on_val,A_2: fun_Pr859510977l_bool,B_1: fun_Pr859510977l_bool] :
      ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,C_2),semila449273525l_bool(A_2,B_1)))
     => ( ~ hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,C_2),A_2))
       => hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,C_2),B_1)) ) ) ).

tff(fact_862_UnE,axiom,
    ! [C_2: nat,A_2: fun_nat_bool,B_1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),semila465093516t_bool(A_2,B_1)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_1)) ) ) ).

tff(fact_863_UnE,axiom,
    ! [C_2: produc1278157519t_char,A_2: fun_Pr565113489r_bool,B_1: fun_Pr565113489r_bool] :
      ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,C_2),semila1168318597r_bool(A_2,B_1)))
     => ( ~ hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,C_2),A_2))
       => hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,C_2),B_1)) ) ) ).

tff(fact_864_UnE,axiom,
    ! [C_2: list_char,A_2: fun_list_char_bool,B_1: fun_list_char_bool] :
      ( hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C_2),semila919158006r_bool(A_2,B_1)))
     => ( ~ hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C_2),A_2))
       => hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C_2),B_1)) ) ) ).

tff(fact_865_UnE,axiom,
    ! [C_2: produc1102272487on_val,A_2: fun_Pr691271849l_bool,B_1: fun_Pr691271849l_bool] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,C_2),semila751111325l_bool(A_2,B_1)))
     => ( ~ hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,C_2),A_2))
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,C_2),B_1)) ) ) ).

tff(fact_866_UnCI,axiom,
    ! [A_2: fun_Pr70170387r_bool,C_2: produc1013743697t_char,B_1: fun_Pr70170387r_bool] :
      ( ( ~ hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,C_2),B_1))
       => hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,C_2),A_2)) )
     => hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,C_2),semila1731249415r_bool(A_2,B_1))) ) ).

tff(fact_867_UnCI,axiom,
    ! [A_2: fun_Pr1861226704r_bool,C_2: produc1971331930t_char,B_1: fun_Pr1861226704r_bool] :
      ( ( ~ hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,C_2),B_1))
       => hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,C_2),A_2)) )
     => hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,C_2),semila1346223580r_bool(A_2,B_1))) ) ).

tff(fact_868_UnCI,axiom,
    ! [A_2: fun_Pr859510977l_bool,C_2: produc430140671on_val,B_1: fun_Pr859510977l_bool] :
      ( ( ~ hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,C_2),B_1))
       => hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,C_2),A_2)) )
     => hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,C_2),semila449273525l_bool(A_2,B_1))) ) ).

tff(fact_869_UnCI,axiom,
    ! [A_2: fun_nat_bool,C_2: nat,B_1: fun_nat_bool] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_2)) )
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),semila465093516t_bool(A_2,B_1))) ) ).

tff(fact_870_UnCI,axiom,
    ! [A_2: fun_Pr565113489r_bool,C_2: produc1278157519t_char,B_1: fun_Pr565113489r_bool] :
      ( ( ~ hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,C_2),B_1))
       => hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,C_2),A_2)) )
     => hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,C_2),semila1168318597r_bool(A_2,B_1))) ) ).

tff(fact_871_UnCI,axiom,
    ! [A_2: fun_list_char_bool,C_2: list_char,B_1: fun_list_char_bool] :
      ( ( ~ hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C_2),B_1))
       => hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C_2),A_2)) )
     => hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C_2),semila919158006r_bool(A_2,B_1))) ) ).

tff(fact_872_UnCI,axiom,
    ! [A_2: fun_Pr691271849l_bool,C_2: produc1102272487on_val,B_1: fun_Pr691271849l_bool] :
      ( ( ~ hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,C_2),B_1))
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,C_2),A_2)) )
     => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,C_2),semila751111325l_bool(A_2,B_1))) ) ).

tff(fact_873_sup1E,axiom,
    ! [A_2: fun_list_char_bool,B_1: fun_list_char_bool,X_2: list_char] :
      ( hBOOL(hAPP_list_char_bool(semila919158006r_bool(A_2,B_1),X_2))
     => ( ~ hBOOL(hAPP_list_char_bool(A_2,X_2))
       => hBOOL(hAPP_list_char_bool(B_1,X_2)) ) ) ).

tff(fact_874_sup1CI,axiom,
    ! [A_2: fun_list_char_bool,B_1: fun_list_char_bool,X_2: list_char] :
      ( ( ~ hBOOL(hAPP_list_char_bool(B_1,X_2))
       => hBOOL(hAPP_list_char_bool(A_2,X_2)) )
     => hBOOL(hAPP_list_char_bool(semila919158006r_bool(A_2,B_1),X_2)) ) ).

tff(fact_875_Un__absorb,axiom,
    ! [A_2: fun_list_char_bool] : semila919158006r_bool(A_2,A_2) = A_2 ).

tff(fact_876_Un__def,axiom,
    ! [A_2: fun_Pr70170387r_bool,B_1: fun_Pr70170387r_bool] : semila1731249415r_bool(A_2,B_1) = collec1387638140t_char(cOMBS_1743887558l_bool(hAPP_f1985672189l_bool(hAPP_f1169733153l_bool(cOMBB_565990871t_char,fdisj),hAPP_f1853572245r_bool(hAPP_f1933376467r_bool(cOMBC_36589090l_bool,member1601084734t_char),A_2)),hAPP_f1853572245r_bool(hAPP_f1933376467r_bool(cOMBC_36589090l_bool,member1601084734t_char),B_1))) ).

tff(fact_877_Un__def,axiom,
    ! [A_2: fun_Pr1861226704r_bool,B_1: fun_Pr1861226704r_bool] : semila1346223580r_bool(A_2,B_1) = collec1583467887t_char(cOMBS_635570165l_bool(hAPP_f561246575l_bool(hAPP_f321462169l_bool(cOMBB_808210516t_char,fdisj),hAPP_f1666729379r_bool(hAPP_f1020753317r_bool(cOMBC_1297648632l_bool,member1467889965t_char),A_2)),hAPP_f1666729379r_bool(hAPP_f1020753317r_bool(cOMBC_1297648632l_bool,member1467889965t_char),B_1))) ).

tff(fact_878_Un__def,axiom,
    ! [A_2: fun_Pr859510977l_bool,B_1: fun_Pr859510977l_bool] : semila449273525l_bool(A_2,B_1) = collec2087910442on_val(cOMBS_1218320756l_bool(hAPP_f914702973l_bool(hAPP_f1600936353l_bool(cOMBB_1617503877on_val,fdisj),hAPP_f1856968213l_bool(hAPP_f677078775l_bool(cOMBC_475083938l_bool,member875476972on_val),A_2)),hAPP_f1856968213l_bool(hAPP_f677078775l_bool(cOMBC_475083938l_bool,member875476972on_val),B_1))) ).

tff(fact_879_Un__def,axiom,
    ! [A_2: fun_nat_bool,B_1: fun_nat_bool] : semila465093516t_bool(A_2,B_1) = collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fdisj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A_2)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),B_1))) ).

tff(fact_880_Un__def,axiom,
    ! [A_2: fun_Pr565113489r_bool,B_1: fun_Pr565113489r_bool] : semila1168318597r_bool(A_2,B_1) = collec1797130234t_char(cOMBS_350755140l_bool(hAPP_f644972157l_bool(hAPP_f722872225l_bool(cOMBB_1643767893t_char,fdisj),hAPP_f112056853r_bool(hAPP_f1876889431r_bool(cOMBC_148995234l_bool,member1251428284t_char),A_2)),hAPP_f112056853r_bool(hAPP_f1876889431r_bool(cOMBC_148995234l_bool,member1251428284t_char),B_1))) ).

tff(fact_881_Un__def,axiom,
    ! [A_2: fun_list_char_bool,B_1: fun_list_char_bool] : semila919158006r_bool(A_2,B_1) = collect_list_char(cOMBS_1502238389l_bool(hAPP_f1163760061l_bool(hAPP_f1157863905l_bool(cOMBB_984708934t_char,fdisj),hAPP_f1371002581r_bool(hAPP_f522372661r_bool(cOMBC_892477410l_bool,member_list_char),A_2)),hAPP_f1371002581r_bool(hAPP_f522372661r_bool(cOMBC_892477410l_bool,member_list_char),B_1))) ).

tff(fact_882_Un__def,axiom,
    ! [A_2: fun_Pr691271849l_bool,B_1: fun_Pr691271849l_bool] : semila751111325l_bool(A_2,B_1) = collec718040978on_val(cOMBS_1319864284l_bool(hAPP_f379976829l_bool(hAPP_f606945057l_bool(cOMBB_705522285on_val,fdisj),hAPP_f2036784149l_bool(hAPP_f1720452391l_bool(cOMBC_1021753250l_bool,member773094996on_val),A_2)),hAPP_f2036784149l_bool(hAPP_f1720452391l_bool(cOMBC_1021753250l_bool,member773094996on_val),B_1))) ).

tff(fact_883_Un__commute,axiom,
    ! [A_2: fun_list_char_bool,B_1: fun_list_char_bool] : semila919158006r_bool(A_2,B_1) = semila919158006r_bool(B_1,A_2) ).

tff(fact_884_fv__fvs_Osimps_I11_J,axiom,
    ! [E_1_1: exp_list_char,E_2: exp_list_char] : fv(seq_list_char(E_1_1,E_2)) = semila919158006r_bool(fv(E_1_1),fv(E_2)) ).

tff(fact_885_eval__cases_I2_J,axiom,
    ! [Pa: list_P1999446415t_char,Va: 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,Va),S),E_b),S_2))
     => ~ ( ( E_b = hAPP_v834067052t_char(val_list_char,Va) )
         => ( S_2 != S ) ) ) ).

tff(fact_886_Val,axiom,
    ! [Pa: list_P1999446415t_char,Va: val,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,hAPP_v834067052t_char(val_list_char,Va),S),hAPP_v834067052t_char(val_list_char,Va)),S)) ).

tff(fact_887_Red__dom__lcl,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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_f986089162l_bool(ord_le2092826700r_bool(dom_list_char_val(L_b)),semila919158006r_bool(dom_list_char_val(Lb),fv(Eb)))) ) ).

tff(fact_888_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_889_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_890_eval__cases_I8_J,axiom,
    ! [Pa: list_P1999446415t_char,Va_1: list_char,Ta: ty,E_1_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(Va_1,Ta,E_1_1),S),E_b),S_2))
     => ~ ! [H_0_1: fun_na939144002on_val,L_0_1: fun_li1432931796on_val] :
            ( ( S = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0_1),L_0_1) )
           => ! [H_1_1: fun_na939144002on_val,L_1_2: fun_li1432931796on_val] :
                ( ( S_2 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1_1),fun_up1149430426on_val(L_1_2,Va_1,hAPP_l207779698on_val(L_0_1,Va_1))) )
               => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0_1),fun_up1149430426on_val(L_0_1,Va_1,none_val))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1_1),L_1_2))) ) ) ) ).

tff(fact_891_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(hAPP_f986089162l_bool(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_892_FAssRedsVal,axiom,
    ! [F: list_char,D: list_char,C: list_char,Fs: fun_Pr806764899on_val,E_2: exp_list_char,Va: val,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,E_1_1: exp_list_char,S_0: produc12694297on_val,A: nat,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va)),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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(E_1_1,F,D,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,fun_up2041264236on_val(H_2,A,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,F),D),hAPP_val_option_val(some_val,Va)))))),L_2)))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_893_redp__redsp_OFAssRed1,axiom,
    ! [F: list_char,D: 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,F,D,E_2),S),fAss_list_char(E_b,F,D,E_2)),S_2)) ) ).

tff(fact_894_redp__redsp_OFAssRed2,axiom,
    ! [Va: val,F: list_char,D: 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,Va),F,D,Eb),S),fAss_list_char(hAPP_v834067052t_char(val_list_char,Va),F,D,E_b)),S_2)) ) ).

tff(fact_895_fv__fvs_Osimps_I8_J,axiom,
    ! [E_1_1: exp_list_char,F: list_char,D: list_char,E_2: exp_list_char] : fv(fAss_list_char(E_1_1,F,D,E_2)) = semila919158006r_bool(fv(E_1_1),fv(E_2)) ).

tff(fact_896_red__reds_OFAssRed1,axiom,
    ! [F: list_char,D: 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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(Eb,F,D,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(E_b,F,D,E_2)),S_2))),red(Pa))) ) ).

tff(fact_897_red__reds_OFAssRed2,axiom,
    ! [Va: val,F: list_char,D: list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va),F,D,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,Va),F,D,E_b)),S_2))),red(Pa))) ) ).

tff(fact_898_FAssReds1,axiom,
    ! [F: list_char,D: 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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(Eb,F,D,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(E_b,F,D,E_2)),S_2))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_899_FAssReds2,axiom,
    ! [Va: val,F: list_char,D: list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va),F,D,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,Va),F,D,E_b)),S_2))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_900_FAss,axiom,
    ! [H_2_1: fun_na939144002on_val,Fs_2: fun_Pr806764899on_val,F: list_char,D: list_char,C: list_char,Fs: fun_Pr806764899on_val,E_2: exp_list_char,Va: val,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,Pa: list_P1999446415t_char,E_1_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_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,Va)),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,F),D),hAPP_val_option_val(some_val,Va)) )
           => ( ( 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_1,F,D,E_2),S_0),hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2_1),L_2))) ) ) ) ) ) ).

tff(fact_901_redp__redsp_ORedFAss,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,Va: 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)),F,D,hAPP_v834067052t_char(val_list_char,Va)),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,F),D),hAPP_val_option_val(some_val,Va)))))),Lb))) ) ).

tff(fact_902_red__reds_ORedFAss,axiom,
    ! [F: list_char,D: list_char,Va: 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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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)),F,D,hAPP_v834067052t_char(val_list_char,Va))),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,F),D),hAPP_val_option_val(some_val,Va)))))),Lb)))),red(Pa))) ) ).

tff(fact_903_FAccRedsVal,axiom,
    ! [F: list_char,D: list_char,Va: 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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(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,F),D)) = hAPP_val_option_val(some_val,Va) )
         => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(Eb,F,D)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),S_2))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_904_red__reds_ORedFAcc,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,Va: val,S: produc12694297on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) )
     => ( ( hAPP_P2094403585on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D)) = hAPP_val_option_val(some_val,Va) )
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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)),F,D)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),S))),red(Pa))) ) ) ).

tff(fact_905_redp__redsp_ORedFAcc,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,Va: val,S: produc12694297on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) )
     => ( ( hAPP_P2094403585on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D)) = hAPP_val_option_val(some_val,Va) )
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),F,D),S),hAPP_v834067052t_char(val_list_char,Va)),S)) ) ) ).

tff(fact_906_FAcc,axiom,
    ! [F: list_char,D: list_char,Va: 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,F),D)) = hAPP_val_option_val(some_val,Va) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAcc_list_char(Eb,F,D),S_0),hAPP_v834067052t_char(val_list_char,Va)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))) ) ) ) ).

tff(fact_907_red__reds_OInitBlockThrow,axiom,
    ! [Va_1: list_char,Ta: ty,Va: val,A: nat,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),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_908_redp__redsp_OFAccThrow,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,F: list_char,D: list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(throw_list_char(Eb),F,D),S),throw_list_char(Eb)),S)) ).

tff(fact_909_eval__evals_OFAccThrow,axiom,
    ! [F: list_char,D: 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,F,D),S_0),throw_list_char(E_b)),S_1)) ) ).

tff(fact_910_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_911_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_912_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_913_fv__fvs_Osimps_I14_J,axiom,
    ! [Eb: exp_list_char] : fv(throw_list_char(Eb)) = fv(Eb) ).

tff(fact_914_redp__redsp_OFAccRed,axiom,
    ! [F: list_char,D: 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,F,D),S),fAcc_list_char(E_b,F,D)),S_2)) ) ).

tff(fact_915_fv__fvs_Osimps_I7_J,axiom,
    ! [Eb: exp_list_char,F: list_char,D: list_char] : fv(fAcc_list_char(Eb,F,D)) = fv(Eb) ).

tff(fact_916_red__reds_OFAccThrow,axiom,
    ! [Eb: exp_list_char,F: list_char,D: list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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),F,D)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S))),red(Pa))) ).

tff(fact_917_FAccRedsThrow,axiom,
    ! [F: list_char,D: list_char,Eb: exp_list_char,S: produc12694297on_val,A: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(Eb,F,D)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_918_eval__evals_OSeqThrow,axiom,
    ! [E_1_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_1),S_0),throw_list_char(Eb)),S_1)) ) ).

tff(fact_919_eval__evals_OLAssThrow,axiom,
    ! [Va_1: 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(Va_1,Eb),S_0),throw_list_char(E_b)),S_1)) ) ).

tff(fact_920_eval__evals_OFAssThrow1,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,E_1_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_1,S_0),throw_list_char(E_b)),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAss_list_char(E_1_1,F,D,E_2),S_0),throw_list_char(E_b)),S_1)) ) ).

tff(fact_921_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_922_redp__redsp_OLAssThrow,axiom,
    ! [Pa: list_P1999446415t_char,Va_1: list_char,Eb: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(Va_1,throw_list_char(Eb)),S),throw_list_char(Eb)),S)) ).

tff(fact_923_redp__redsp_OFAssThrow1,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,F: list_char,D: 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),F,D,E_2),S),throw_list_char(Eb)),S)) ).

tff(fact_924_red__reds_OThrowThrow,axiom,
    ! [Eb: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_925_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_f1453283057l_bool(hAPP_P1303341961l_bool(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_926_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_927_eval__evals_OFAssThrow2,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,E_b: exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc12694297on_val,Va: val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,Va)),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_1,F,D,E_2),S_0),throw_list_char(E_b)),S_2_1)) ) ) ).

tff(fact_928_red__reds_OFAccRed,axiom,
    ! [F: list_char,D: list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(Eb,F,D)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(E_b,F,D)),S_2))),red(Pa))) ) ).

tff(fact_929_redp__redsp_OFAssThrow2,axiom,
    ! [Pa: list_P1999446415t_char,Va: val,F: list_char,D: 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,Va),F,D,throw_list_char(Eb)),S),throw_list_char(Eb)),S)) ).

tff(fact_930_ThrowReds,axiom,
    ! [Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_931_ThrowRedsThrow,axiom,
    ! [Eb: exp_list_char,S: produc12694297on_val,A: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_932_red__reds_OLAssThrow,axiom,
    ! [Va_1: list_char,Eb: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,throw_list_char(Eb))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S))),red(Pa))) ).

tff(fact_933_red__reds_OSeqThrow,axiom,
    ! [Eb: exp_list_char,E_2: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_934_red__reds_OFAssThrow1,axiom,
    ! [Eb: exp_list_char,F: list_char,D: list_char,E_2: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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),F,D,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S))),red(Pa))) ).

tff(fact_935_redp__redsp_OBlockThrow,axiom,
    ! [Pa: list_P1999446415t_char,Va_1: list_char,Ta: ty,A: nat,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,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_936_FAccReds,axiom,
    ! [F: list_char,D: list_char,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(Eb,F,D)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(E_b,F,D)),S_2))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_937_red__reds_OFAssThrow2,axiom,
    ! [Va: val,F: list_char,D: list_char,Eb: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va),F,D,throw_list_char(Eb))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S))),red(Pa))) ).

tff(fact_938_LAssRedsThrow,axiom,
    ! [Va_1: list_char,Eb: exp_list_char,S: produc12694297on_val,A: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_939_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_940_FAssRedsThrow1,axiom,
    ! [F: list_char,D: 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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(Eb,F,D,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E_b)),S_2))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_941_FAssRedsThrow2,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,Eb: exp_list_char,S_2_1: produc12694297on_val,E_1_1: exp_list_char,S_0: produc12694297on_val,Va: val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),S_1))),transi2024712006on_val(red(Pa))))
     => ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(E_1_1,F,D,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_942_red__reds_OBlockThrow,axiom,
    ! [Va_1: list_char,Ta: ty,A: nat,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,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_943_redp__redsp_OInitBlockThrow,axiom,
    ! [Pa: list_P1999446415t_char,Va_1: list_char,Ta: ty,Va: val,A: nat,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),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_944_eval__cases_I4_J,axiom,
    ! [Pa: list_P1999446415t_char,Va_1: 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(Va_1,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,Va_1,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_1: exp_list_char] :
              ( ( E_b = throw_list_char(E_1) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),throw_list_char(E_1)),S_2)) ) ) ) ).

tff(fact_945_eval__cases_I9_J,axiom,
    ! [Pa: list_P1999446415t_char,E_1_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_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_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_4: exp_list_char] :
              ( ( E_b = throw_list_char(E_4) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S),throw_list_char(E_4)),S_2)) ) ) ) ).

tff(fact_946_val_Osimps_I10_J,axiom,
    ! [Nat_1: nat] : unit != addr(Nat_1) ).

tff(fact_947_val_Osimps_I11_J,axiom,
    ! [Nat_1: nat] : addr(Nat_1) != unit ).

tff(fact_948_val_Osimps_I3_J,axiom,
    ! [Nat_2: nat,Nat: nat] :
      ( ( addr(Nat_2) = addr(Nat) )
    <=> ( Nat_2 = Nat ) ) ).

tff(fact_949_TryCatchRedsFinal,axiom,
    ! [E_2: exp_list_char,Va_1: list_char,E_2_1: exp_list_char,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,C: list_char,D: list_char,Fs: fun_Pr806764899on_val,E_1_1: exp_list_char,S_0: produc12694297on_val,A: nat,H_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_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),L_1_1)))),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(H_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) )
       => ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa))))
         => ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),fun_up1149430426on_val(L_1_1,Va_1,hAPP_val_option_val(some_val,addr(A)))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2)))),transi2024712006on_val(red(Pa))))
           => ( hBOOL(final_list_char(E_2_1))
             => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(E_1_1,C,Va_1,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),fun_up1149430426on_val(L_2,Va_1,hAPP_l207779698on_val(L_1_1,Va_1)))))),transi2024712006on_val(red(Pa)))) ) ) ) ) ) ).

tff(fact_950_WTrtThrow,axiom,
    ! [Ta: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,T_r: ty] :
      ( hBOOL(wTrt_1(Pa,Hb,Ea,Eb,T_r))
     => ( hBOOL(is_refT(T_r))
       => hBOOL(wTrt_1(Pa,Hb,Ea,throw_list_char(Eb),Ta)) ) ) ).

tff(fact_951_BinOpRedsThrow2,axiom,
    ! [Bop: bop,E_2: exp_list_char,Eb: exp_list_char,S_2_1: produc12694297on_val,E_1_1: exp_list_char,S_0: produc12694297on_val,V_1_2: val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(E_1_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_952_TryRedsFail,axiom,
    ! [Va_1: list_char,E_2: exp_list_char,C: list_char,D: list_char,Fs: fun_Pr806764899on_val,E_1_1: exp_list_char,S: produc12694297on_val,A: nat,Hb: fun_na939144002on_val,Lb: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_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,D),Fs)) )
       => ( ~ hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(E_1_1,C,Va_1,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_953_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_954_redp__redsp_OTryRed,axiom,
    ! [C: list_char,Va_1: 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,Va_1,E_2),S),tryCatch_list_char(E_b,C,Va_1,E_2)),S_2)) ) ).

tff(fact_955_eval__evals_OBinOpThrow1,axiom,
    ! [Bop: bop,E_2: exp_list_char,Pa: list_P1999446415t_char,E_1_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_1,S_0),throw_list_char(Eb)),S_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,binOp_list_char(E_1_1,Bop,E_2),S_0),throw_list_char(Eb)),S_1)) ) ).

tff(fact_956_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_957_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_958_Try,axiom,
    ! [C: list_char,Va_1: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,E_1_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_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_1,C,Va_1,E_2),S_0),hAPP_v834067052t_char(val_list_char,V_1_2)),S_1)) ) ).

tff(fact_959_redp__redsp_ORedTry,axiom,
    ! [Pa: list_P1999446415t_char,Va: val,C: list_char,Va_1: 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,Va),C,Va_1,E_2),S),hAPP_v834067052t_char(val_list_char,Va)),S)) ).

tff(fact_960_fv__fvs_Osimps_I4_J,axiom,
    ! [E_1_1: exp_list_char,Bop: bop,E_2: exp_list_char] : fv(binOp_list_char(E_1_1,Bop,E_2)) = semila919158006r_bool(fv(E_1_1),fv(E_2)) ).

tff(fact_961_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_f1453283057l_bool(hAPP_P1303341961l_bool(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_962_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_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_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_1,Bop,E_2),S_0),throw_list_char(Eb)),S_2_1)) ) ) ).

tff(fact_963_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_964_red__reds_OTryRed,axiom,
    ! [C: list_char,Va_1: 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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(Eb,C,Va_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(E_b,C,Va_1,E_2)),S_2))),red(Pa))) ) ).

tff(fact_965_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_f1453283057l_bool(hAPP_P1303341961l_bool(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_966_red__reds_OBinOpThrow1,axiom,
    ! [Eb: exp_list_char,Bop: bop,E_2: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_967_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_968_red__reds_ORedTry,axiom,
    ! [Va: val,C: list_char,Va_1: list_char,E_2: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va),C,Va_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),S))),red(Pa))) ).

tff(fact_969_TryReds,axiom,
    ! [C: list_char,Va_1: 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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(Eb,C,Va_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(E_b,C,Va_1,E_2)),S_2))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_970_TryThrow,axiom,
    ! [Va_1: list_char,E_2: exp_list_char,C: list_char,D: list_char,Fs: fun_Pr806764899on_val,Pa: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc12694297on_val,A: nat,H_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1)))
     => ( ( hAPP_n546249108on_val(H_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) )
       => ( ~ hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,tryCatch_list_char(E_1_1,C,Va_1,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),L_1_1))) ) ) ) ).

tff(fact_971_red__reds_OBinOpThrow2,axiom,
    ! [V_1_2: val,Bop: bop,Eb: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_972_BinOp2Reds,axiom,
    ! [Va: val,Bop: bop,Eb: exp_list_char,S: produc12694297on_val,E_b: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va),Bop,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(hAPP_v834067052t_char(val_list_char,Va),Bop,E_b)),S_2))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_973_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_974_TryRedsVal,axiom,
    ! [C: list_char,Va_1: list_char,E_2: exp_list_char,Eb: exp_list_char,S: produc12694297on_val,Va: val,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va)),S_2))),transi2024712006on_val(red(Pa))))
     => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(Eb,C,Va_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),S_2))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_975_red__reds_ORedTryFail,axiom,
    ! [Va_1: list_char,E_2: exp_list_char,C: list_char,Pa: list_P1999446415t_char,S: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) )
     => ( ~ hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa))))
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va_1,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_976_TryCatch,axiom,
    ! [E_2: exp_list_char,Va_1: list_char,E_2_1: exp_list_char,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,C: list_char,D: list_char,Fs: fun_Pr806764899on_val,Pa: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc12694297on_val,A: nat,H_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1)))
     => ( ( hAPP_n546249108on_val(H_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) )
       => ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa))))
         => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),fun_up1149430426on_val(L_1_1,Va_1,hAPP_val_option_val(some_val,addr(A))))),E_2_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2)))
           => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,tryCatch_list_char(E_1_1,C,Va_1,E_2),S_0),E_2_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),fun_up1149430426on_val(L_2,Va_1,hAPP_l207779698on_val(L_1_1,Va_1))))) ) ) ) ) ).

tff(fact_977_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(wTrt_1(Pa,Hb,Ea,throw_list_char(Eb),Ta))
     => ~ ! [T_r_1: ty] :
            ( hBOOL(wTrt_1(Pa,Hb,Ea,Eb,T_r_1))
           => ~ hBOOL(is_refT(T_r_1)) ) ) ).

tff(fact_978_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_979_red__reds_ORedTryCatch,axiom,
    ! [Va_1: list_char,E_2: exp_list_char,C: list_char,Pa: list_P1999446415t_char,S: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) )
     => ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa))))
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,hAPP_list_char_ty(class,C),seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,addr(A))),E_2))),S))),red(Pa))) ) ) ).

tff(fact_980_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_981_CastRedsAddr,axiom,
    ! [C: list_char,D: list_char,Fs: fun_Pr806764899on_val,Eb: exp_list_char,S: produc12694297on_val,A: nat,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hp(S_2),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) )
       => ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_982_WTrtTry,axiom,
    ! [Va_1: list_char,C: list_char,E_2: exp_list_char,T_2_2: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1_1: exp_list_char,T_1_1: ty] :
      ( hBOOL(wTrt_1(Pa,Hb,Ea,E_1_1,T_1_1))
     => ( hBOOL(wTrt_1(Pa,Hb,fun_up424764369ion_ty(Ea,Va_1,hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,C))),E_2,T_2_2))
       => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_1),T_2_2))
         => hBOOL(wTrt_1(Pa,Hb,Ea,tryCatch_list_char(E_1_1,C,Va_1,E_2),T_2_2)) ) ) ) ).

tff(fact_983_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_984_fv__fvs_Osimps_I2_J,axiom,
    ! [C: list_char,Eb: exp_list_char] : fv(cast_list_char(C,Eb)) = fv(Eb) ).

tff(fact_985_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_986_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_987_WTrtFAcc,axiom,
    ! [F: list_char,Ta: ty,D: list_char,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,C: list_char] :
      ( hBOOL(wTrt_1(Pa,Hb,Ea,Eb,hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,F,Ta),D))
       => hBOOL(wTrt_1(Pa,Hb,Ea,fAcc_list_char(Eb,F,D),Ta)) ) ) ).

tff(fact_988_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_f1453283057l_bool(hAPP_P1303341961l_bool(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_989_red__reds_OCastThrow,axiom,
    ! [C: list_char,Eb: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_990_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_991_WTrtFAss,axiom,
    ! [E_2: exp_list_char,T_2_2: ty,F: list_char,Ta: ty,D: list_char,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1_1: exp_list_char,C: list_char] :
      ( hBOOL(wTrt_1(Pa,Hb,Ea,E_1_1,hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,F,Ta),D))
       => ( hBOOL(wTrt_1(Pa,Hb,Ea,E_2,T_2_2))
         => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_2),Ta))
           => hBOOL(wTrt_1(Pa,Hb,Ea,fAss_list_char(E_1_1,F,D,E_2),void)) ) ) ) ) ).

tff(fact_992_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_993_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_994_Cast,axiom,
    ! [C: list_char,D: 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,D),Fs)) )
       => ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,Eb),S_0),hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))) ) ) ) ).

tff(fact_995_red__reds_ORedCast,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,S: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) )
     => ( hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa))))
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_996_WTrt__elim__cases_I5_J,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1_1: exp_list_char,C: list_char,Va_1: list_char,E_2: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt_1(Pa,Hb,Ea,tryCatch_list_char(E_1_1,C,Va_1,E_2),Ta))
     => ~ ! [T_1_2: ty] :
            ( hBOOL(wTrt_1(Pa,Hb,Ea,E_1_1,T_1_2))
           => ( hBOOL(wTrt_1(Pa,Hb,fun_up424764369ion_ty(Ea,Va_1,hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,C))),E_2,Ta))
             => ~ hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_2),Ta)) ) ) ) ).

tff(fact_997_final__addrE,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,C: list_char] :
      ( hBOOL(wTrt_1(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_998_BinOpRedsVal,axiom,
    ! [Bop: bop,Va: val,E_2: exp_list_char,V_2_1: val,S_2_1: produc12694297on_val,E_1_1: exp_list_char,S_0: produc12694297on_val,V_1_2: val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1)),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_1))) = hAPP_val_option_val(some_val,Va) )
         => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(E_1_1,Bop,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),S_2_1))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_999_CastRedsFail,axiom,
    ! [C: list_char,D: list_char,Fs: fun_Pr806764899on_val,Eb: exp_list_char,S: produc12694297on_val,A: nat,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hp(S_2),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) )
       => ( ~ hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1000_BinOp,axiom,
    ! [Bop: bop,Va: val,E_2: exp_list_char,V_2_1: val,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,E_1_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_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_1)),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_1))) = hAPP_val_option_val(some_val,Va) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,binOp_list_char(E_1_1,Bop,E_2),S_0),hAPP_v834067052t_char(val_list_char,Va)),S_2_1)) ) ) ) ).

tff(fact_1001_redp__redsp_ORedBinOp,axiom,
    ! [Pa: list_P1999446415t_char,S: produc12694297on_val,Bop: bop,V_1_2: val,V_2_1: val,Va: 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_1))) = hAPP_val_option_val(some_val,Va) )
     => 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_1)),S),hAPP_v834067052t_char(val_list_char,Va)),S)) ) ).

tff(fact_1002_CastFail,axiom,
    ! [C: list_char,D: 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,D),Fs)) )
       => ( ~ hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,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_1003_red__reds_ORedCastFail,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,S: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) )
     => ( ~ hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa))))
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1004_red__reds_ORedBinOp,axiom,
    ! [S: produc12694297on_val,Pa: list_P1999446415t_char,Bop: bop,V_1_2: val,V_2_1: val,Va: 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_1))) = hAPP_val_option_val(some_val,Va) )
     => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),S))),red(Pa))) ) ).

tff(fact_1005_eval__cases_I3_J,axiom,
    ! [Pa: list_P1999446415t_char,E_1_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_1,Bop,E_2),S),E_b),S_2))
     => ( ! [V_1_1: 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_1,S),hAPP_v834067052t_char(val_list_char,V_1_1)),S_1_1))
             => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_1),hAPP_v834067052t_char(val_list_char,V_2_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_1),V_2_3))) != hAPP_val_option_val(some_val,V_2) ) ) ) )
       => ( ! [E_4: exp_list_char] :
              ( ( E_b = throw_list_char(E_4) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S),throw_list_char(E_4)),S_2)) )
         => ~ ! [V_1_1: val,S_1_1: produc12694297on_val,E_4: exp_list_char] :
                ( ( E_b = throw_list_char(E_4) )
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S),hAPP_v834067052t_char(val_list_char,V_1_1)),S_1_1))
                 => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_1),throw_list_char(E_4)),S_2)) ) ) ) ) ) ).

tff(fact_1006_binop_Osimps_I7_J,axiom,
    ! [V_1_3: val] : binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_3),unit))) = none_val ).

tff(fact_1007_binop_Osimps_I3_J,axiom,
    ! [V_2_2: val] : binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,unit),V_2_2))) = none_val ).

tff(fact_1008_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_1009_WTrtVal,axiom,
    ! [Pa: list_P1999446415t_char,Ea: fun_li688206603ion_ty,Hb: fun_na939144002on_val,Va: val,Ta: ty] :
      ( ( hAPP_val_option_ty(typeof_h(Hb),Va) = hAPP_ty_option_ty(some_ty,Ta) )
     => hBOOL(wTrt_1(Pa,Hb,Ea,hAPP_v834067052t_char(val_list_char,Va),Ta)) ) ).

tff(fact_1010_hext__typeof__mono,axiom,
    ! [Va: val,Ta: ty,Hb: fun_na939144002on_val,H_b: fun_na939144002on_val] :
      ( hBOOL(hext(Hb,H_b))
     => ( ( hAPP_val_option_ty(typeof_h(Hb),Va) = hAPP_ty_option_ty(some_ty,Ta) )
       => ( hAPP_val_option_ty(typeof_h(H_b),Va) = hAPP_ty_option_ty(some_ty,Ta) ) ) ) ).

tff(fact_1011_typeof__lit__typeof,axiom,
    ! [Hb: fun_na939144002on_val,Va: val,Ta: ty] :
      ( ( hAPP_val_option_ty(typeof_h(hAPP_o1576581476on_val(cOMBK_1944287343al_nat,none_P179726773on_val)),Va) = hAPP_ty_option_ty(some_ty,Ta) )
     => ( hAPP_val_option_ty(typeof_h(Hb),Va) = hAPP_ty_option_ty(some_ty,Ta) ) ) ).

tff(fact_1012_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_1013_binop_Osimps_I6_J,axiom,
    ! [V: nat,V_2_2: val] : binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,addr(V)),V_2_2))) = none_val ).

tff(fact_1014_binop_Osimps_I10_J,axiom,
    ! [V_1_3: val,V: nat] : binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_3),addr(V)))) = none_val ).

tff(fact_1015_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_1016_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_1017_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_1018_WTrt_H__WTrts_H_Ointros_I16_J,axiom,
    ! [Ea: fun_li688206603ion_ty,Va_1: list_char,E_2: exp_list_char,T_2_2: ty,Pa: list_P1999446415t_char,Ta: ty,Hb: fun_na939144002on_val,Va: val,T_1_1: ty] :
      ( ( hAPP_val_option_ty(typeof_h(Hb),Va) = hAPP_ty_option_ty(some_ty,T_1_1) )
     => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_1),Ta))
       => ( hBOOL(wTrt(Pa,Hb,fun_up424764369ion_ty(Ea,Va_1,hAPP_ty_option_ty(some_ty,Ta)),E_2,T_2_2))
         => hBOOL(wTrt(Pa,Hb,Ea,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),E_2)),T_2_2)) ) ) ) ).

tff(fact_1019_WTrt_H__WTrts_H_Ointros_I3_J,axiom,
    ! [Pa: list_P1999446415t_char,Ea: fun_li688206603ion_ty,Hb: fun_na939144002on_val,Va: val,Ta: ty] :
      ( ( hAPP_val_option_ty(typeof_h(Hb),Va) = hAPP_ty_option_ty(some_ty,Ta) )
     => hBOOL(wTrt(Pa,Hb,Ea,hAPP_v834067052t_char(val_list_char,Va),Ta)) ) ).

tff(fact_1020_WTrt_H__WTrts_H_Ointros_I18_J,axiom,
    ! [E_2: exp_list_char,T_2_2: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1_1: exp_list_char,T_1_1: ty] :
      ( hBOOL(wTrt(Pa,Hb,Ea,E_1_1,T_1_1))
     => ( hBOOL(wTrt(Pa,Hb,Ea,E_2,T_2_2))
       => hBOOL(wTrt(Pa,Hb,Ea,seq_list_char(E_1_1,E_2),T_2_2)) ) ) ).

tff(fact_1021_wt__wt_H,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt_1(Pa,Hb,Ea,Eb,Ta))
     => hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta)) ) ).

tff(fact_1022_wt_H__wt,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta))
     => hBOOL(wTrt_1(Pa,Hb,Ea,Eb,Ta)) ) ).

tff(fact_1023_wt_H__iff__wt,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta))
    <=> hBOOL(wTrt_1(Pa,Hb,Ea,Eb,Ta)) ) ).

tff(fact_1024_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(wTrt(Pa,Hb,Ea,Eb,T_r))
     => ( hBOOL(is_refT(T_r))
       => hBOOL(wTrt(Pa,Hb,Ea,throw_list_char(Eb),Ta)) ) ) ).

tff(fact_1025_WTrt_H__WTrts_H_Ointros_I8_J,axiom,
    ! [F: list_char,Ta: ty,D: list_char,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,C: list_char] :
      ( hBOOL(wTrt(Pa,Hb,Ea,Eb,hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,F,Ta),D))
       => hBOOL(wTrt(Pa,Hb,Ea,fAcc_list_char(Eb,F,D),Ta)) ) ) ).

tff(fact_1026_WTrt_H__WTrts_H_Ointros_I17_J,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Va_1: list_char,Ta: ty,Eb: exp_list_char,T_a: ty] :
      ( hBOOL(wTrt(Pa,Hb,fun_up424764369ion_ty(Ea,Va_1,hAPP_ty_option_ty(some_ty,Ta)),Eb,T_a))
     => ( ~ hBOOL(assigned(Va_1,Eb))
       => hBOOL(wTrt(Pa,Hb,Ea,block_list_char(Va_1,Ta,Eb),T_a)) ) ) ).

tff(fact_1027_WTrt_H__WTrts_H_Ointros_I22_J,axiom,
    ! [Va_1: list_char,C: list_char,E_2: exp_list_char,T_2_2: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1_1: exp_list_char,T_1_1: ty] :
      ( hBOOL(wTrt(Pa,Hb,Ea,E_1_1,T_1_1))
     => ( hBOOL(wTrt(Pa,Hb,fun_up424764369ion_ty(Ea,Va_1,hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,C))),E_2,T_2_2))
       => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_1),T_2_2))
         => hBOOL(wTrt(Pa,Hb,Ea,tryCatch_list_char(E_1_1,C,Va_1,E_2),T_2_2)) ) ) ) ).

tff(fact_1028_WTrt_H__WTrts_H_Ointros_I10_J,axiom,
    ! [E_2: exp_list_char,T_2_2: ty,F: list_char,Ta: ty,D: list_char,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1_1: exp_list_char,C: list_char] :
      ( hBOOL(wTrt(Pa,Hb,Ea,E_1_1,hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,F,Ta),D))
       => ( hBOOL(wTrt(Pa,Hb,Ea,E_2,T_2_2))
         => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_2),Ta))
           => hBOOL(wTrt(Pa,Hb,Ea,fAss_list_char(E_1_1,F,D,E_2),void)) ) ) ) ) ).

tff(fact_1029_FAccRedsNull,axiom,
    ! [F: list_char,D: list_char,Eb: exp_list_char,S: produc12694297on_val,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(Eb,F,D)),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_1030_FAssRedsNull,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,Va: val,S_2_1: produc12694297on_val,E_1_1: exp_list_char,S_0: produc12694297on_val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va)),S_2_1))),transi2024712006on_val(red(Pa))))
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(E_1_1,F,D,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2_1))),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_1031_red__reds_ORedFAccNull,axiom,
    ! [F: list_char,D: list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(hAPP_v834067052t_char(val_list_char,null),F,D)),S)),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_1032_val_Osimps_I5_J,axiom,
    null != unit ).

tff(fact_1033_val_Osimps_I4_J,axiom,
    unit != null ).

tff(fact_1034_val_Osimps_I16_J,axiom,
    ! [Nat_1: nat] : null != addr(Nat_1) ).

tff(fact_1035_val_Osimps_I17_J,axiom,
    ! [Nat_1: nat] : addr(Nat_1) != null ).

tff(fact_1036_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_1037_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_1038_red__reds_ORedCastNull,axiom,
    ! [C: list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1039_CastRedsNull,axiom,
    ! [C: list_char,Eb: exp_list_char,S: produc12694297on_val,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1040_binop_Osimps_I8_J,axiom,
    ! [V_1_3: val] : binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_3),null))) = none_val ).

tff(fact_1041_binop_Osimps_I4_J,axiom,
    ! [V_2_2: val] : binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,null),V_2_2))) = none_val ).

tff(fact_1042_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_1043_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_1044_FAssNull,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,Va: val,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc12694297on_val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1),hAPP_v834067052t_char(val_list_char,Va)),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAss_list_char(E_1_1,F,D,E_2),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2_1)) ) ) ).

tff(fact_1045_FAccNull,axiom,
    ! [F: list_char,D: 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,F,D),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_1)) ) ).

tff(fact_1046_redp__redsp_ORedFAssNull,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,Va: val,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,null),F,D,hAPP_v834067052t_char(val_list_char,Va)),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S)) ).

tff(fact_1047_redp__redsp_ORedFAccNull,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(hAPP_v834067052t_char(val_list_char,null),F,D),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S)) ).

tff(fact_1048_red__reds_ORedThrowNull,axiom,
    ! [S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1049_ThrowRedsNull,axiom,
    ! [Eb: exp_list_char,S: produc12694297on_val,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1050_red__reds_ORedFAssNull,axiom,
    ! [F: list_char,D: list_char,Va: val,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,null),F,D,hAPP_v834067052t_char(val_list_char,Va))),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_1051_finalRefE,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt_1(Pa,Hb,Ea,Eb,Ta))
     => ( hBOOL(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_1: list_char] : Ta != hAPP_list_char_ty(class,C_1) )
             => ~ ! [A_1: nat] : Eb != throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))) ) ) ) ) ) ).

tff(fact_1052_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_1: exp_list_char] :
                ( ( E_b = throw_list_char(E_1) )
               => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),throw_list_char(E_1)),S_2)) ) ) ) ) ).

tff(fact_1053_redp__redsp_ORedTryCatch,axiom,
    ! [Va_1: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,C: list_char,S: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) )
     => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(transi1065307915t_char(subcls744239332t_char(Pa)),D),C))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,tryCatch_list_char(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))),C,Va_1,E_2),S),block_list_char(Va_1,hAPP_list_char_ty(class,C),seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,addr(A))),E_2))),S)) ) ) ).

tff(fact_1054_redp__redsp_ORedCast,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,S: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) )
     => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(transi1065307915t_char(subcls744239332t_char(Pa)),D),C))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,hAPP_v834067052t_char(val_list_char,addr(A))),S),hAPP_v834067052t_char(val_list_char,addr(A))),S)) ) ) ).

tff(fact_1055_redp__redsp_ORedTryFail,axiom,
    ! [Va_1: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,C: list_char,S: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) )
     => ( ~ hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(transi1065307915t_char(subcls744239332t_char(Pa)),D),C))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,tryCatch_list_char(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))),C,Va_1,E_2),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S)) ) ) ).

tff(fact_1056_redp__redsp_ORedCastFail,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,S: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) )
     => ( ~ hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(transi1065307915t_char(subcls744239332t_char(Pa)),D),C))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,hAPP_v834067052t_char(val_list_char,addr(A))),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(classCast))))),S)) ) ) ).

tff(fact_1057_WTrtCast,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt_1(Pa,Hb,Ea,Eb,Ta))
     => ( hBOOL(is_refT(Ta))
       => ( hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C))
         => hBOOL(wTrt_1(Pa,Hb,Ea,cast_list_char(C,Eb),hAPP_list_char_ty(class,C))) ) ) ) ).

tff(fact_1058_ty_Osimps_I9_J,axiom,
    ! [List: list_char] : hAPP_list_char_ty(class,List) != void ).

tff(fact_1059_ty_Osimps_I8_J,axiom,
    ! [List: list_char] : void != hAPP_list_char_ty(class,List) ).

tff(fact_1060_ty_Oinject,axiom,
    ! [List_2: list_char,List_1: list_char] :
      ( ( hAPP_list_char_ty(class,List_2) = hAPP_list_char_ty(class,List_1) )
    <=> ( List_2 = List_1 ) ) ).

tff(fact_1061_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(wTrt(Pa,Hb,Ea,Eb,Ta))
     => ( hBOOL(is_refT(Ta))
       => ( hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C))
         => hBOOL(wTrt(Pa,Hb,Ea,cast_list_char(C,Eb),hAPP_list_char_ty(class,C))) ) ) ) ).

tff(fact_1062_WTrt__elim__cases_I6_J,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,D: list_char,Eb: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt_1(Pa,Hb,Ea,cast_list_char(D,Eb),Ta))
     => ~ ( ( Ta = hAPP_list_char_ty(class,D) )
         => ! [T_4: ty] :
              ( hBOOL(wTrt_1(Pa,Hb,Ea,Eb,T_4))
             => ( hBOOL(is_refT(T_4))
               => ~ hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),D)) ) ) ) ) ).

tff(fact_1063_sys__xcpts__cases,axiom,
    ! [Pa: fun_list_char_bool,C: list_char] :
      ( hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(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_1064_binop_Osimps_I9_J,axiom,
    ! [V_1_2: val,Va: 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(Va)))) = none_val ).

tff(fact_1065_val_Osimps_I21_J,axiom,
    ! [Nat: nat,Bool_1: bool] : addr(Nat) != bool_1(Bool_1) ).

tff(fact_1066_val_Osimps_I20_J,axiom,
    ! [Bool_1: bool,Nat: nat] : bool_1(Bool_1) != addr(Nat) ).

tff(fact_1067_val_Osimps_I1_J,axiom,
    ! [Bool_1: bool,Bool: bool] :
      ( ( bool_1(Bool_1) = bool_1(Bool) )
    <=> ( hBOOL(Bool_1)
      <=> hBOOL(Bool) ) ) ).

tff(fact_1068_val_Osimps_I6_J,axiom,
    ! [Bool: bool] : unit != bool_1(Bool) ).

tff(fact_1069_val_Osimps_I7_J,axiom,
    ! [Bool: bool] : bool_1(Bool) != unit ).

tff(fact_1070_val_Osimps_I12_J,axiom,
    ! [Bool: bool] : null != bool_1(Bool) ).

tff(fact_1071_val_Osimps_I13_J,axiom,
    ! [Bool: bool] : bool_1(Bool) != null ).

tff(fact_1072_preallocated__dom,axiom,
    ! [C: list_char,Hb: fun_na939144002on_val] :
      ( hBOOL(preallocated(Hb))
     => ( hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C),sys_xcpts))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,addr_of_sys_xcpt(C)),dom_na996029170on_val(Hb))) ) ) ).

tff(fact_1073_binop_Osimps_I5_J,axiom,
    ! [Va: bool,V_2_1: val] : binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,bool_1(Va)),V_2_1))) = none_val ).

tff(fact_1074_preallocatedE,axiom,
    ! [Pa: fun_fu311765169r_bool,C: list_char,Hb: fun_na939144002on_val] :
      ( hBOOL(preallocated(Hb))
     => ( hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(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_1075_preallocatedD,axiom,
    ! [C: list_char,Hb: fun_na939144002on_val] :
      ( hBOOL(preallocated(Hb))
     => ( hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(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_1076_preallocated__def,axiom,
    ! [Hb: fun_na939144002on_val] :
      ( hBOOL(preallocated(Hb))
    <=> ! [X_1: list_char] :
          ( hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(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_1077_binop_Osimps_I1_J,axiom,
    ! [V_1_2: val,V_2_1: 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_1))) = hAPP_val_option_val(some_val,bool_1(hAPP_val_bool(hAPP_v1392248405l_bool(fequal_val,V_1_2),V_2_1))) ).

tff(fact_1078_WhileFReds,axiom,
    ! [C_2: exp_list_char,B: exp_list_char,S: produc12694297on_val,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,while_list_char(B,C_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,unit)),S_2))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1079_WhileCondThrow,axiom,
    ! [C_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,while_list_char(Eb,C_2),S_0),throw_list_char(E_b)),S_1)) ) ).

tff(fact_1080_bop_Oexhaust,axiom,
    ! [Y: bop] :
      ( ( Y != c_Expr_Obop_OEq )
     => ( Y = add ) ) ).

tff(fact_1081_bop_Osimps_I2_J,axiom,
    add != c_Expr_Obop_OEq ).

tff(fact_1082_bop_Osimps_I1_J,axiom,
    c_Expr_Obop_OEq != add ).

tff(fact_1083_fv__fvs_Osimps_I13_J,axiom,
    ! [B: exp_list_char,Eb: exp_list_char] : fv(while_list_char(B,Eb)) = semila919158006r_bool(fv(B),fv(Eb)) ).

tff(fact_1084_WhileT,axiom,
    ! [E_3: exp_list_char,S_3_1: produc12694297on_val,C_2: exp_list_char,V_1_2: val,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,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_2,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_2),S_2_1),E_3),S_3_1))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Eb,C_2),S_0),E_3),S_3_1)) ) ) ) ).

tff(fact_1085_WhileBodyThrow,axiom,
    ! [C_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(fTrue))),S_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_2,S_1),throw_list_char(E_b)),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Eb,C_2),S_0),throw_list_char(E_b)),S_2_1)) ) ) ).

tff(fact_1086_WhileF,axiom,
    ! [C_2: 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_2),S_0),hAPP_v834067052t_char(val_list_char,unit)),S_1)) ) ).

tff(fact_1087_WhileRedsThrow,axiom,
    ! [C_2: exp_list_char,B: exp_list_char,S: produc12694297on_val,Eb: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,while_list_char(B,C_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S_2))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1088_WhileTReds,axiom,
    ! [Eb: exp_list_char,S_3_1: produc12694297on_val,C_2: exp_list_char,V_1_2: val,S_2_1: produc12694297on_val,B: exp_list_char,S_0: produc12694297on_val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_2),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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,while_list_char(B,C_2)),S_2_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S_3_1))),transi2024712006on_val(red(Pa))))
         => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,while_list_char(B,C_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S_3_1))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1089_WhileTRedsThrow,axiom,
    ! [C_2: 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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_2),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S_2_1))),transi2024712006on_val(red(Pa))))
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,while_list_char(B,C_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S_2_1))),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_1090_eval__cases_I11_J,axiom,
    ! [Pa: list_P1999446415t_char,B: exp_list_char,C_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,while_list_char(B,C_2),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_1: val,S_2_2: produc12694297on_val] :
                  ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_2,S_1_1),hAPP_v834067052t_char(val_list_char,V_1_1)),S_2_2))
                 => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(B,C_2),S_2_2),E_b),S_2)) ) )
         => ( ! [E_1: exp_list_char] :
                ( ( E_b = throw_list_char(E_1) )
               => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,B,S),throw_list_char(E_1)),S_2)) )
           => ~ ! [S_1_1: produc12694297on_val,E_1: exp_list_char] :
                  ( ( E_b = throw_list_char(E_1) )
                 => ( 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_2,S_1_1),throw_list_char(E_1)),S_2)) ) ) ) ) ) ) ).

tff(fact_1091_red__reds_ORedWhile,axiom,
    ! [B: exp_list_char,C_2: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,while_list_char(B,C_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(B,seq_list_char(C_2,while_list_char(B,C_2)),hAPP_v834067052t_char(val_list_char,unit))),S))),red(Pa))) ).

tff(fact_1092_redp__redsp_OCondRed,axiom,
    ! [E_1_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_1,E_2),S),cond_list_char(E_b,E_1_1,E_2)),S_2)) ) ).

tff(fact_1093_eval__evals_OCondThrow,axiom,
    ! [E_1_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_1,E_2),S_0),throw_list_char(E_b)),S_1)) ) ).

tff(fact_1094_redp__redsp_OCondThrow,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,E_1_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_1,E_2),S),throw_list_char(Eb)),S)) ).

tff(fact_1095_fv__fvs_Osimps_I12_J,axiom,
    ! [B: exp_list_char,E_1_1: exp_list_char,E_2: exp_list_char] : fv(cond_list_char(B,E_1_1,E_2)) = semila919158006r_bool(semila919158006r_bool(fv(B),fv(E_1_1)),fv(E_2)) ).

tff(fact_1096_red__reds_OCondRed,axiom,
    ! [E_1_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(Eb,E_1_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(E_b,E_1_1,E_2)),S_2))),red(Pa))) ) ).

tff(fact_1097_CondF,axiom,
    ! [E_1_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_1,E_2),S_0),E_b),S_2_1)) ) ) ).

tff(fact_1098_CondT,axiom,
    ! [E_2: exp_list_char,E_1_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_1,S_1),E_b),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(Eb,E_1_1,E_2),S_0),E_b),S_2_1)) ) ) ).

tff(fact_1099_redp__redsp_ORedCondF,axiom,
    ! [Pa: list_P1999446415t_char,E_1_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_1,E_2),S),E_2),S)) ).

tff(fact_1100_redp__redsp_ORedCondT,axiom,
    ! [Pa: list_P1999446415t_char,E_1_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_1,E_2),S),E_1_1),S)) ).

tff(fact_1101_red__reds_OCondThrow,axiom,
    ! [Eb: exp_list_char,E_1_1: exp_list_char,E_2: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S))),red(Pa))) ).

tff(fact_1102_CondReds,axiom,
    ! [E_1_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(Eb,E_1_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(E_b,E_1_1,E_2)),S_2))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1103_CondRedsThrow,axiom,
    ! [E_1_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(Eb,E_1_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1104_red__reds_ORedCondT,axiom,
    ! [E_1_1: exp_list_char,E_2: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_1),S))),red(Pa))) ).

tff(fact_1105_red__reds_ORedCondF,axiom,
    ! [E_1_1: exp_list_char,E_2: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S))),red(Pa))) ).

tff(fact_1106_unfold__while,axiom,
    ! [Pa: list_P1999446415t_char,B: exp_list_char,C_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,while_list_char(B,C_2),S),E_b),S_2))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(B,seq_list_char(C_2,while_list_char(B,C_2)),hAPP_v834067052t_char(val_list_char,unit)),S),E_b),S_2)) ) ).

tff(fact_1107_redp__redsp_ORedWhile,axiom,
    ! [Pa: list_P1999446415t_char,B: exp_list_char,C_2: exp_list_char,S: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,while_list_char(B,C_2),S),cond_list_char(B,seq_list_char(C_2,while_list_char(B,C_2)),hAPP_v834067052t_char(val_list_char,unit))),S)) ).

tff(fact_1108_CondReds2T,axiom,
    ! [E_2: exp_list_char,E_1_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_1),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2_1))),transi2024712006on_val(red(Pa))))
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(Eb,E_1_1,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2_1))),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_1109_CondReds2F,axiom,
    ! [E_1_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(Eb,E_1_1,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2_1))),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_1110_ty_Osimps_I20_J,axiom,
    ! [List: list_char] : nt != hAPP_list_char_ty(class,List) ).

tff(fact_1111_ty_Osimps_I21_J,axiom,
    ! [List: list_char] : hAPP_list_char_ty(class,List) != nt ).

tff(fact_1112_ty_Osimps_I7_J,axiom,
    nt != void ).

tff(fact_1113_ty_Osimps_I6_J,axiom,
    void != nt ).

tff(fact_1114_WTrtFAccNT,axiom,
    ! [F: list_char,D: list_char,Ta: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char] :
      ( hBOOL(wTrt_1(Pa,Hb,Ea,Eb,nt))
     => hBOOL(wTrt_1(Pa,Hb,Ea,fAcc_list_char(Eb,F,D),Ta)) ) ).

tff(fact_1115_WTrt_H__WTrts_H_Ointros_I9_J,axiom,
    ! [F: list_char,D: list_char,Ta: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char] :
      ( hBOOL(wTrt(Pa,Hb,Ea,Eb,nt))
     => hBOOL(wTrt(Pa,Hb,Ea,fAcc_list_char(Eb,F,D),Ta)) ) ).

tff(fact_1116_is__refT__def,axiom,
    ! [Ta: ty] :
      ( hBOOL(is_refT(Ta))
    <=> ( ( Ta = nt )
        | ? [C_1: list_char] : Ta = hAPP_list_char_ty(class,C_1) ) ) ).

tff(fact_1117_WTrtFAssNT,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,T_2_2: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1_1: exp_list_char] :
      ( hBOOL(wTrt_1(Pa,Hb,Ea,E_1_1,nt))
     => ( hBOOL(wTrt_1(Pa,Hb,Ea,E_2,T_2_2))
       => hBOOL(wTrt_1(Pa,Hb,Ea,fAss_list_char(E_1_1,F,D,E_2),void)) ) ) ).

tff(fact_1118_WTrt_H__WTrts_H_Ointros_I11_J,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,T_2_2: ty,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,E_1_1: exp_list_char] :
      ( hBOOL(wTrt(Pa,Hb,Ea,E_1_1,nt))
     => ( hBOOL(wTrt(Pa,Hb,Ea,E_2,T_2_2))
       => hBOOL(wTrt(Pa,Hb,Ea,fAss_list_char(E_1_1,F,D,E_2),void)) ) ) ).

tff(fact_1119_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_1120_WTrt__elim__cases_I7_J,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,F: list_char,D: list_char,Ta: ty] :
      ( hBOOL(wTrt_1(Pa,Hb,Ea,fAcc_list_char(Eb,F,D),Ta))
     => ( ! [C_1: list_char] :
            ( hBOOL(wTrt_1(Pa,Hb,Ea,Eb,hAPP_list_char_ty(class,C_1)))
           => ~ hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C_1,F,Ta),D)) )
       => hBOOL(wTrt_1(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,F: list_char,D: list_char,Va: exp_list_char,Ta: ty] :
      ( hBOOL(wTrt_1(Pa,Hb,Ea,fAss_list_char(Eb,F,D,Va),Ta))
     => ( ( ( Ta = void )
         => ! [C_1: list_char] :
              ( hBOOL(wTrt_1(Pa,Hb,Ea,Eb,hAPP_list_char_ty(class,C_1)))
             => ! [T_4: ty] :
                  ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C_1,F,T_4),D))
                 => ! [T_2_1: ty] :
                      ( hBOOL(wTrt_1(Pa,Hb,Ea,Va,T_2_1))
                     => ~ hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_1),T_4)) ) ) ) )
       => ~ ( ( Ta = void )
           => ( hBOOL(wTrt_1(Pa,Hb,Ea,Eb,nt))
             => ! [T_2_1: ty] : ~ hBOOL(wTrt_1(Pa,Hb,Ea,Va,T_2_1)) ) ) ) ) ).

tff(fact_1122_refTE,axiom,
    ! [T: ty] :
      ( hBOOL(is_refT(T))
     => ( ( T != nt )
       => ~ ! [C_1: list_char] : T != hAPP_list_char_ty(class,C_1) ) ) ).

tff(fact_1123_eval__cases_I10_J,axiom,
    ! [Pa: list_P1999446415t_char,Eb: exp_list_char,E_1_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_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_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_1: exp_list_char] :
                ( ( E_b = throw_list_char(E_1) )
               => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),throw_list_char(E_1)),S_2)) ) ) ) ) ).

tff(fact_1124_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1125_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(wTrt_1(Pa,Hb,Ea,new_list_char(C),hAPP_list_char_ty(class,C))) ) ).

tff(fact_1126_WTrt__elim__cases_I10_J,axiom,
    ! [Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,C: list_char,Ta: ty] :
      ( hBOOL(wTrt_1(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_1127_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_1128_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(wTrt(Pa,Hb,Ea,new_list_char(C),hAPP_list_char_ty(class,C))) ) ).

tff(fact_1129_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_1130_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_1131_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),init_fields(FDTs)))) )
         => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1132_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),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_1133_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),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_1134_red__reds_ORedCallNull,axiom,
    ! [M: list_char,Vs_1: list_val,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,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_1135_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,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_1136_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_1137_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_1138_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_1139_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_f1453283057l_bool(hAPP_P1303341961l_bool(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_1140_red__reds_OCallThrowObj,axiom,
    ! [Eb: exp_list_char,M: list_char,Esa: list_exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1141_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1142_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1143_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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,map_va1934808527t_char(val_list_char,Vs_1)),S_2_1))),transi374442731on_val(reds(Pa))))
       => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1144_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),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_1145_extend__1__evals,axiom,
    ! [Es_a: list_exp_list_char,T_3: produc12694297on_val,Esa: list_exp_list_char,T_2: produc12694297on_val,Es_1: list_exp_list_char,T_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),T_2)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),T_1))),reds(Pa)))
       => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es_1,T_1),Es_a),T_3))
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,T_2),Es_a),T_3)) ) ) ) ).

tff(fact_1146_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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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_1147_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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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_1148_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_1149_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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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_1150_evals__lcl__incr,axiom,
    ! [Pa: list_P1999446415t_char,Esa: list_exp_list_char,H_0: fun_na939144002on_val,L_0: fun_li1432931796on_val,Es_a: list_exp_list_char,H_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),L_0)),Es_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1)))
     => hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(dom_list_char_val(L_0)),dom_list_char_val(L_1_1))) ) ).

tff(fact_1151_red__reds_OCallParams,axiom,
    ! [Va: 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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va),M,Esa)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(hAPP_v834067052t_char(val_list_char,Va),M,Es_a)),S_2))),red(Pa))) ) ).

tff(fact_1152_CallRedsParams,axiom,
    ! [Va: 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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va),M,Esa)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(hAPP_v834067052t_char(val_list_char,Va),M,Es_a)),S_2))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1153_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,Va: val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va)),S_1))),transi2024712006on_val(red(Pa))))
     => ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1154_fv__fvs_Osimps_I9_J,axiom,
    ! [Eb: exp_list_char,M: list_char,Esa: list_exp_list_char] : fv(call_list_char(Eb,M,Esa)) = semila919158006r_bool(fv(Eb),fvs(Esa)) ).

tff(fact_1155_fv__fvs_Osimps_I17_J,axiom,
    ! [Eb: exp_list_char,Esa: list_exp_list_char] : fvs(cons_exp_list_char(Eb,Esa)) = semila919158006r_bool(fv(Eb),fvs(Esa)) ).

tff(fact_1156_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,Va: val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,Va)),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,Va),Es_a)),S_2_1)) ) ) ).

tff(fact_1157_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_1158_red__reds_OListRed2,axiom,
    ! [Va: val,Esa: list_exp_list_char,S: produc12694297on_val,Es_a: list_exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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,Va),Esa)),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(hAPP_v834067052t_char(val_list_char,Va),Es_a)),S_2))),reds(Pa))) ) ).

tff(fact_1159_redp__redsp_OCallThrowParams,axiom,
    ! [Pa: list_P1999446415t_char,Va: 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(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,Va),M,Esa),S),throw_list_char(Eb)),S)) ) ).

tff(fact_1160_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(map_va1934808527t_char(val_list_char,Vs_1),cons_exp_list_char(throw_list_char(X_2),Es_a)),S),append_exp_list_char(map_va1934808527t_char(val_list_char,Vs_1),cons_exp_list_char(E_b,Es_a))),S_2)) ) ).

tff(fact_1161_ListReds2,axiom,
    ! [Va: val,Esa: list_exp_list_char,S: produc12694297on_val,Es_a: list_exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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,Va),Esa)),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(hAPP_v834067052t_char(val_list_char,Va),Es_a)),S_2))),transi374442731on_val(reds(Pa)))) ) ).

tff(fact_1162_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_f458849545l_bool(hAPP_P126004409l_bool(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_1163_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,Va: val,S_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,Va)),S_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S_1),append_exp_list_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_1164_red__reds_OCallThrowParams,axiom,
    ! [Va: 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(map_va1934808527t_char(val_list_char,Vs_1),cons_exp_list_char(throw_list_char(Eb),Es_a)) )
     => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va),M,Esa)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S))),red(Pa))) ) ).

tff(fact_1165_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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_1166_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,Va: val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,Va)),S_1))),transi2024712006on_val(red(Pa))))
     => ( hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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,Va),Es_a)),S_2_1))),transi374442731on_val(reds(Pa)))) ) ) ).

tff(fact_1167_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_1: exp_list_char] :
              ( ( E_b = cons_exp_list_char(throw_list_char(E_1),Esa) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),throw_list_char(E_1)),S_2)) ) ) ) ).

tff(fact_1168_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_1169_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_1170_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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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,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_1171_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(wTrt_1(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_1172_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_1173_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(wTrt_1(Pa,Hb,Ea,Eb,nt))
     => ( hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts))
       => hBOOL(wTrt_1(Pa,Hb,Ea,call_list_char(Eb,M,Esa),Ta)) ) ) ).

tff(fact_1174_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,map_va1934808527t_char(val_list_char,Vs_1),Ts))
    <=> ( map_val_option_ty(typeof_h(Hb),Vs_1) = map_ty_option_ty(some_ty,Ts) ) ) ).

tff(fact_1175_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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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_1176_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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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_1177_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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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_1178_blocks_Osimps_I1_J,axiom,
    ! [V_1: list_char,Vs_3: list_list_char,T: ty,Ts_3: list_ty,V: val,Vs_2: list_val,E: exp_list_char] : blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,cons_list_char(V_1,Vs_3)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,cons_ty(T,Ts_3)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,cons_val(V,Vs_2)),E)))) = block_list_char(V_1,T,seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,V)),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)))))) ).

tff(fact_1179_redp__redsp_OListRed2,axiom,
    ! [Va: 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,Va),Esa),S),cons_exp_list_char(hAPP_v834067052t_char(val_list_char,Va),Es_a)),S_2)) ) ).

tff(fact_1180_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_1181_redp__redsp_OCallParams,axiom,
    ! [Va: 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,Va),M,Esa),S),call_list_char(hAPP_v834067052t_char(val_list_char,Va),M,Es_a)),S_2)) ) ).

tff(fact_1182_wf__J__prog__wf__J__mdecl,axiom,
    ! [Jmdcl: produc1013743697t_char,C: list_char,D: list_char,Fds: list_P1940453997har_ty,Mths: list_P341299826t_char,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wf_J_mdecl,Pa))
     => ( hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,C),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,D),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Fds),Mths)))),set_Pr1494163115t_char(Pa)))
       => ( hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(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_1183_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,D: 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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f458849545l_bool(hAPP_P126004409l_bool(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,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)),D))
             => ( ( 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_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1184_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,D: 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),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)),D))
           => ( ( 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_1185_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,D: list_char,S: produc12694297on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(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)),D))
       => ( ( size_size_list_val(Vs_1) = size_s2113983095t_char(Pns) )
         => ( ( size_size_list_ty(Ts) = size_s2113983095t_char(Pns) )
           => hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,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,D),Ts)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,cons_val(addr(A),Vs_1)),Body))))),S))),red(Pa))) ) ) ) ) ).

tff(fact_1186_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,D: list_char,S: produc12694297on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(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)),D))
       => ( ( 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,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,D),Ts)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,cons_val(addr(A),Vs_1)),Body))))),S)) ) ) ) ) ).

tff(fact_1187_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_1188_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1189_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_1190_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(wTrt_1(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(wTrt_1(Pa,Hb,map_up891053837har_ty(Ea,Vs,Ts),Eb,Ta))
            & ? [Ts_2: list_ty] :
                ( ( map_val_option_ty(typeof_h(Hb),Vs_1) = map_ty_option_ty(some_ty,Ts_2) )
                & hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_2,Ts)) ) ) ) ) ) ).

tff(fact_1191_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,D: list_char,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,C: list_char] :
      ( hBOOL(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)),D))
       => ( hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts_1))
         => ( hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_1,Ts))
           => hBOOL(wTrt_1(Pa,Hb,Ea,call_list_char(Eb,M,Esa),Ta)) ) ) ) ) ).

tff(fact_1192_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,D: list_char,Pa: list_P1999446415t_char,Hb: fun_na939144002on_val,Ea: fun_li688206603ion_ty,Eb: exp_list_char,C: list_char] :
      ( hBOOL(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)),D))
       => ( hBOOL(wTrts(Pa,Hb,Ea,Esa,Ts_1))
         => ( hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_1,Ts))
           => hBOOL(wTrt(Pa,Hb,Ea,call_list_char(Eb,M,Esa),Ta)) ) ) ) ) ).

tff(fact_1193_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_1194_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_1195_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_1196_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(wTrt(Pa,Hb,Ea,Eb,nt))
     => ( hBOOL(wTrts(Pa,Hb,Ea,Esa,Ts))
       => hBOOL(wTrt(Pa,Hb,Ea,call_list_char(Eb,M,Esa),Ta)) ) ) ).

tff(fact_1197_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(wTrt(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_1198_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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_1199_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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(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,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)))) ) ) ) ) ).

%----Helper facts (149)
tff(help_fNot_1_1_U,axiom,
    ! [P: bool] :
      ( ~ hBOOL(hAPP_bool_bool(fNot,P))
      | ~ hBOOL(P) ) ).

tff(help_fNot_2_1_U,axiom,
    ! [P: bool] :
      ( hBOOL(P)
      | hBOOL(hAPP_bool_bool(fNot,P)) ) ).

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_fdisj_1_1_U,axiom,
    ! [Q: bool,P: bool] :
      ( ~ hBOOL(P)
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) ) ).

tff(help_fdisj_2_1_U,axiom,
    ! [P: bool,Q: bool] :
      ( ~ hBOOL(Q)
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) ) ).

tff(help_fdisj_3_1_U,axiom,
    ! [P: bool,Q: bool] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q))
      | hBOOL(P)
      | 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_fequal_1_1_fequal_000tc__Option__Ooption_Itc__Value__Oval_J_T,axiom,
    ! [X: option_val,Y: option_val] :
      ( ~ hBOOL(hAPP_option_val_bool(hAPP_o586881855l_bool(fequal_option_val,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__Option__Ooption_Itc__Value__Oval_J_T,axiom,
    ! [X: option_val,Y: option_val] :
      ( ( X != Y )
      | hBOOL(hAPP_option_val_bool(hAPP_o586881855l_bool(fequal_option_val,X),Y)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
    ! [P: fun_bool_bool,Q: fun_nat_bool,R: nat] : hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,P),Q),R) = hAPP_bool_bool(P,hAPP_nat_bool(Q,R)) ).

tff(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
    ! [P: fun_na1469252690l_bool,Q: fun_nat_bool,R: nat] : hAPP_nat_bool(cOMBS_nat_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__List__Olist_Itc_,axiom,
    ! [P: fun_bool_bool,Q: fun_list_char_bool,R: list_char] : hAPP_list_char_bool(hAPP_f1371002581r_bool(hAPP_f1861125939r_bool(cOMBB_1091123364t_char,P),Q),R) = hAPP_bool_bool(P,hAPP_list_char_bool(Q,R)) ).

tff(help_COMBS_1_1_COMBS_000tc__List__Olist_Itc__String__Ochar_J_000tc__HOL__Obool_0,axiom,
    ! [P: fun_li332530512l_bool,Q: fun_list_char_bool,R: list_char] : hAPP_list_char_bool(cOMBS_1502238389l_bool(P,Q),R) = hAPP_bool_bool(hAPP_l2010421276l_bool(P,R),hAPP_list_char_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
    ! [P: fun_na1436237685l_bool,Q: fun_nat_bool,R: nat] : hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
    ! [P: fun_bo1549164019l_bool,Q: fun_nat_bool,R: nat] : hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R)) ).

tff(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist_,axiom,
    ! [P: option_ty,Q: list_char] : hAPP_l512744617ion_ty(hAPP_o1240645474ion_ty(cOMBK_1294242658t_char,P),Q) = P ).

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_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Oopt,axiom,
    ! [P: fun_li511029026l_bool,Q: option_val,R: list_char] : hAPP_list_char_bool(hAPP_o453398608r_bool(hAPP_f399018025r_bool(cOMBC_442485623l_bool,P),Q),R) = hAPP_option_val_bool(hAPP_l1646953198l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_987,axiom,
    ! [P: fun_bo1549164019l_bool,Q: fun_list_char_bool,R: list_char] : hAPP_l2010421276l_bool(hAPP_f1163760061l_bool(hAPP_f1157863905l_bool(cOMBB_984708934t_char,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_list_char_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__Value__Oval_000tc__fun_Itc__prod_Itc__Value__Oval_Mt,axiom,
    ! [P: fun_va633994418l_bool,Q: fun_Pr2081272681l_bool,R: val] : hAPP_val_bool(hAPP_f1728541444l_bool(hAPP_f1764548711l_bool(cOMBC_331963401l_bool,P),Q),R) = hAPP_f2028441009l_bool(hAPP_v3604996l_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__Lis,axiom,
    ! [P: fun_li1362522525l_bool,Q: fun_list_char_bool,R: list_char] : hAPP_list_char_bool(hAPP_f1371002581r_bool(hAPP_f522372661r_bool(cOMBC_892477410l_bool,P),Q),R) = hAPP_f986089162l_bool(hAPP_l1903254203l_bool(P,R),Q) ).

tff(help_COMBS_1_1_COMBS_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List,axiom,
    ! [P: fun_Pr1475963649l_bool,Q: fun_Pr565113489r_bool,R: produc1278157519t_char] : hAPP_P449474095r_bool(cOMBS_350755140l_bool(P,Q),R) = hAPP_bool_bool(hAPP_P1457625805l_bool(P,R),hAPP_P449474095r_bool(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_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__prod_Itc__,axiom,
    ! [P: option_val,Q: produc1278157519t_char] : hAPP_P2094403585on_val(hAPP_o1269033393on_val(cOMBK_1867744698t_char,P),Q) = P ).

tff(help_COMBC_1_1_COMBC_000tc__Value__Oval_000tc__fun_Itc__prod_Itc__Value__Oval_Mt_988,axiom,
    ! [P: fun_va310403589l_bool,Q: fun_Pr2081272681l_bool,R: val] : hAPP_v1392248405l_bool(hAPP_f198821591l_bool(hAPP_f1880802701l_bool(cOMBC_1979963740l_bool,P),Q),R) = hAPP_f1728541444l_bool(hAPP_v1988122071l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__fun_Itc__O,axiom,
    ! [P: fun_op860648563l_bool,Q: fun_li1432931796on_val,R: list_char] : hAPP_l1646953198l_bool(hAPP_f396807521l_bool(hAPP_f926979333l_bool(cOMBB_1112666310t_char,P),Q),R) = hAPP_o586881855l_bool(P,hAPP_l207779698on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_989,axiom,
    ! [P: fun_bo1549164019l_bool,Q: fun_Pr565113489r_bool,R: produc1278157519t_char] : hAPP_P1457625805l_bool(hAPP_f644972157l_bool(hAPP_f722872225l_bool(cOMBB_1643767893t_char,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_P449474095r_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_,axiom,
    ! [P: fun_Pr1095905387l_bool,Q: fun_va1923334394al_val,R: val] : hAPP_v3604996l_bool(hAPP_f1394668591l_bool(hAPP_f183649339l_bool(cOMBB_2078984970ol_val,P),Q),R) = hAPP_P530382601l_bool(P,hAPP_v852496844al_val(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_,axiom,
    ! [P: fun_Pr1856441676l_bool,Q: fun_Pr252072522l_bool,R: product_prod_val_val] : hAPP_P929938951l_bool(hAPP_f1335946228l_bool(hAPP_f263393637l_bool(cOMBC_813705475l_bool,P),Q),R) = hAPP_f742333458l_bool(hAPP_P1614880106l_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro,axiom,
    ! [P: fun_li758413868l_bool,Q: fun_Pr565113489r_bool,R: list_char] : hAPP_list_char_bool(hAPP_f335969926r_bool(hAPP_f1367982615r_bool(cOMBC_1603044337l_bool,P),Q),R) = hAPP_f2106398425l_bool(hAPP_l553007690l_bool(P,R),Q) ).

tff(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__fun_Itc__pro,axiom,
    ! [P: option_ty,Q: fun_Pr806764899on_val] : hAPP_f652398900ion_ty(hAPP_o534509643ion_ty(cOMBK_184479553on_val,P),Q) = P ).

tff(help_COMBC_1_1_COMBC_000tc__Expr__Obop_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc_,axiom,
    ! [P: fun_bo655815611l_bool,Q: fun_Pr252072522l_bool,R: bop] : hAPP_b97269396l_bool(hAPP_f257113085l_bool(hAPP_f1100052969l_bool(cOMBC_199425070l_bool,P),Q),R) = hAPP_f1335946228l_bool(hAPP_b1257035143l_bool(P,R),Q) ).

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_COMBC_1_1_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_0,axiom,
    ! [P: fun_ex1789610473l_bool,Q: fun_Pr827765831r_bool,R: exp_list_char] : hAPP_e544220455r_bool(hAPP_f1724656343r_bool(hAPP_f388097003r_bool(cOMBC_818212448l_bool,P),Q),R) = hAPP_f1314764175l_bool(hAPP_e53687815l_bool(P,R),Q) ).

tff(help_fequal_1_1_fequal_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__St,axiom,
    ! [X: option1479284511on_val,Y: option1479284511on_val] :
      ( ~ hBOOL(hAPP_o2007402111l_bool(hAPP_o1968908095l_bool(fequal1937332960on_val,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__St,axiom,
    ! [X: option1479284511on_val,Y: option1479284511on_val] :
      ( ( X != Y )
      | hBOOL(hAPP_o2007402111l_bool(hAPP_o1968908095l_bool(fequal1937332960on_val,X),Y)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_990,axiom,
    ! [P: fun_li248212255r_bool,Q: fun_Pr565113489r_bool,R: list_char] : hAPP_l1361600383r_bool(hAPP_f344506159r_bool(hAPP_f447563647r_bool(cOMBC_389248878r_bool,P),Q),R) = hAPP_f335969926r_bool(hAPP_l1335043179r_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Value__Oval_Mtc__prod_Itc__Value__Oval_Mtc_,axiom,
    ! [P: fun_fu1915524369l_bool,Q: fun_va959426509al_val,R: val] : hAPP_v417179479l_bool(hAPP_f293485653l_bool(hAPP_f565735867l_bool(cOMBB_815843940ol_val,P),Q),R) = hAPP_f1394668591l_bool(P,hAPP_v1519391al_val(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List,axiom,
    ! [P: fun_Pr534396731l_bool,Q: fun_Pr565113489r_bool,R: produc1278157519t_char] : hAPP_P449474095r_bool(hAPP_f112056853r_bool(hAPP_f1876889431r_bool(cOMBC_148995234l_bool,P),Q),R) = hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_0_991,axiom,
    ! [P: fun_ex535087353l_bool,Q: fun_Pr1336948301r_bool,R: exp_list_char] : hAPP_e544220455r_bool(hAPP_f1466436665r_bool(hAPP_f1766231913r_bool(cOMBC_220519196l_bool,P),Q),R) = hAPP_f82569901l_bool(hAPP_e1303556805l_bool(P,R),Q) ).

tff(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__Stri,axiom,
    ! [P: option1479284511on_val,Q: nat] : hAPP_n546249108on_val(hAPP_o1576581476on_val(cOMBK_1944287343al_nat,P),Q) = P ).

tff(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Option__Ooption_Itc__prod_Itc__List,axiom,
    ! [P: fun_na712147476l_bool,Q: option1479284511on_val,R: nat] : hAPP_nat_bool(hAPP_o1566711458t_bool(hAPP_f489569861t_bool(cOMBC_229530231l_bool,P),Q),R) = hAPP_o2007402111l_bool(hAPP_n95946796l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc_,axiom,
    ! [P: fun_Pr285446189l_bool,Q: fun_Pr1615326228al_val,R: product_prod_val_val] : hAPP_P1614880106l_bool(hAPP_f1646911885l_bool(hAPP_f62511709l_bool(cOMBB_2139740953al_val,P),Q),R) = hAPP_P1653675595l_bool(P,hAPP_P929466802al_val(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Value__Oval_J_000tc__fun_Itc__prod_,axiom,
    ! [P: fun_li968298881r_bool,Q: fun_Pr827765831r_bool,R: list_val] : hAPP_l1062423959r_bool(hAPP_f1051205629r_bool(hAPP_f987862447r_bool(cOMBC_1387630958r_bool,P),Q),R) = hAPP_f1724656343r_bool(hAPP_l296209613r_bool(P,R),Q) ).

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__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List,axiom,
    ! [P: fun_Pr534396731l_bool,Q: fun_li1857149300t_char,R: list_char] : hAPP_l553007690l_bool(hAPP_f558380429l_bool(hAPP_f144783951l_bool(cOMBB_1586673472t_char,P),Q),R) = hAPP_P1180869721l_bool(P,hAPP_l2100324114t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Value__Oval_Mtc__fun_Itc__fun_Itc__prod_Itc,axiom,
    ! [P: fun_fu600031817l_bool,Q: fun_va2018308997l_bool,R: val] : hAPP_v1988122071l_bool(hAPP_f1859053709l_bool(hAPP_f400269243l_bool(cOMBB_1701031980ol_val,P),Q),R) = hAPP_f1764548711l_bool(P,hAPP_v417179479l_bool(Q,R)) ).

tff(help_COMBS_1_1_COMBS_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod,axiom,
    ! [P: fun_Pr1361196031l_bool,Q: fun_Pr70170387r_bool,R: produc1013743697t_char] : hAPP_P1384137393r_bool(cOMBS_1743887558l_bool(P,Q),R) = hAPP_bool_bool(hAPP_P415257547l_bool(P,R),hAPP_P1384137393r_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_,axiom,
    ! [P: fun_li2102970087r_bool,Q: fun_Pr1336948301r_bool,R: list_list_char] : hAPP_l214204733r_bool(hAPP_f2091926485r_bool(hAPP_f1820115955r_bool(cOMBC_790582442r_bool,P),Q),R) = hAPP_f1466436665r_bool(hAPP_l753659065r_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_992,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_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__,axiom,
    ! [P: fun_Pr1869680796l_bool,Q: fun_Pr46158268r_bool,R: produc662261637t_char] : hAPP_P2118621157r_bool(hAPP_f1298720864r_bool(hAPP_f225832321r_bool(cOMBC_1365742487l_bool,P),Q),R) = hAPP_f1746574980l_bool(hAPP_P2028292026l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_993,axiom,
    ! [P: fun_bo1549164019l_bool,Q: fun_Pr70170387r_bool,R: produc1013743697t_char] : hAPP_P415257547l_bool(hAPP_f1985672189l_bool(hAPP_f1169733153l_bool(cOMBB_565990871t_char,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_P1384137393r_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__,axiom,
    ! [P: fun_Pr1253690279l_bool,Q: fun_ex588373425t_char,R: exp_list_char] : hAPP_e53687815l_bool(hAPP_f361629773l_bool(hAPP_f1612138403l_bool(cOMBB_961360819t_char,P),Q),R) = hAPP_P845017029l_bool(P,hAPP_e1752110927t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mt,axiom,
    ! [P: fun_fu847194997l_bool,Q: fun_bo1153317747al_val,R: bop] : hAPP_b406740087l_bool(hAPP_f866074145l_bool(hAPP_f877616419l_bool(cOMBB_1458388806ol_bop,P),Q),R) = hAPP_f1646911885l_bool(P,hAPP_b1229254591al_val(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Type__Oty_J_000tc__fun_Itc__prod_It,axiom,
    ! [P: fun_li1851424531r_bool,Q: fun_Pr46158268r_bool,R: list_ty] : hAPP_l1987619678r_bool(hAPP_f2071340985r_bool(hAPP_f133320957r_bool(cOMBC_1127703214r_bool,P),Q),R) = hAPP_f1298720864r_bool(hAPP_l96108383r_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__,axiom,
    ! [P: fun_Pr1777565493l_bool,Q: fun_ex303050433t_char,R: exp_list_char] : hAPP_e1303556805l_bool(hAPP_f901718717l_bool(hAPP_f380623487l_bool(cOMBB_1033145403t_char,P),Q),R) = hAPP_P1293136973l_bool(P,hAPP_e952791821t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_,axiom,
    ! [P: fun_fu453549301l_bool,Q: fun_li835958565t_char,R: list_char] : hAPP_l1425867561l_bool(hAPP_f1764180741l_bool(hAPP_f247798919l_bool(cOMBB_526805108t_char,P),Q),R) = hAPP_f558380429l_bool(P,hAPP_l208357873t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_,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_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_,axiom,
    ! [P: fun_fu1361433468l_bool,Q: fun_Pr315804320l_bool,R: fun_Pr806764899on_val] : hAPP_f1715346603l_bool(hAPP_f1579743228l_bool(hAPP_f1166017719l_bool(cOMBC_317789649l_bool,P),Q),R) = hAPP_f1134950784l_bool(hAPP_f749178132l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mt_994,axiom,
    ! [P: fun_fu1248515149l_bool,Q: fun_bo1312031403l_bool,R: bop] : hAPP_b1257035143l_bool(hAPP_f2100207721l_bool(hAPP_f1374595987l_bool(cOMBB_761748254ol_bop,P),Q),R) = hAPP_f263393637l_bool(P,hAPP_b406740087l_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc,axiom,
    ! [P: fun_Pr402119737l_bool,Q: fun_Pr227936640r_bool,R: produc220283002t_char] : hAPP_P1907982426r_bool(hAPP_f1874697593r_bool(hAPP_f1707979241r_bool(cOMBC_407285762l_bool,P),Q),R) = hAPP_f1780084320l_bool(hAPP_P1562529797l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_I,axiom,
    ! [P: fun_fu1125427583r_bool,Q: fun_li515230429l_bool,R: list_char] : hAPP_l1335043179r_bool(hAPP_f1032444159r_bool(hAPP_f254182519r_bool(cOMBB_1551681790t_char,P),Q),R) = hAPP_f1367982615r_bool(P,hAPP_l1425867561l_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_995,axiom,
    ! [P: fun_li1383188623l_bool,Q: fun_Pr315804320l_bool,R: list_char] : hAPP_l465799708l_bool(hAPP_f2080627739l_bool(hAPP_f350189921l_bool(cOMBC_1535683812l_bool,P),Q),R) = hAPP_f1579743228l_bool(hAPP_l1739862107l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc,axiom,
    ! [P: fun_fu1082830261l_bool,Q: fun_li1751446259t_char,R: list_val] : hAPP_l1842007287l_bool(hAPP_f2118054305l_bool(hAPP_f1687138147l_bool(cOMBB_2078271971st_val,P),Q),R) = hAPP_f361629773l_bool(P,hAPP_l1859255743t_char(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,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__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc,axiom,
    ! [P: fun_Pr1758548753l_bool,Q: fun_Pr1504659044t_char,R: produc662261637t_char] : hAPP_P2028292026l_bool(hAPP_f921434893l_bool(hAPP_f693085049l_bool(cOMBB_147773915t_char,P),Q),R) = hAPP_P1198052655l_bool(P,hAPP_P1392904962t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__Stri,axiom,
    ! [P: fun_op1529201523l_bool,Q: fun_na939144002on_val,R: nat] : hAPP_n95946796l_bool(hAPP_f1677329295l_bool(hAPP_f1611569977l_bool(cOMBB_731867268ol_nat,P),Q),R) = hAPP_o1968908095l_bool(P,hAPP_n546249108on_val(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_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio_996,axiom,
    ! [P: fun_fu1796901562l_bool,Q: fun_Pr1696029455l_bool,R: fun_li1432931796on_val] : hAPP_f1033709212l_bool(hAPP_f33142364l_bool(hAPP_f510152537l_bool(cOMBC_1518234801l_bool,P),Q),R) = hAPP_f966411375l_bool(hAPP_f720086610l_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J__997,axiom,
    ! [P: fun_li1077890343r_bool,Q: fun_Pr227936640r_bool,R: list_list_char] : hAPP_l217977712r_bool(hAPP_f1044627221r_bool(hAPP_f308875635r_bool(cOMBC_1718404842r_bool,P),Q),R) = hAPP_f1874697593r_bool(hAPP_l1783480313r_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_998,axiom,
    ! [P: fun_fu1888091987r_bool,Q: fun_li1225301163l_bool,R: list_val] : hAPP_l296209613r_bool(hAPP_f1449341487r_bool(hAPP_f1823921107r_bool(cOMBB_308691073st_val,P),Q),R) = hAPP_f388097003r_bool(P,hAPP_l1842007287l_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc_999,axiom,
    ! [P: fun_Pr665774896l_bool,Q: fun_Pr70170387r_bool,R: produc1025221954t_char] : hAPP_P1187139874r_bool(hAPP_f279818502r_bool(hAPP_f1419180947r_bool(cOMBC_390659185l_bool,P),Q),R) = hAPP_f483496539l_bool(hAPP_P1383068750l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_1000,axiom,
    ! [P: fun_fu1302866591l_bool,Q: fun_li1727207611t_char,R: list_list_char] : hAPP_l551544901l_bool(hAPP_f165071409l_bool(hAPP_f1174637065l_bool(cOMBB_33167485t_char,P),Q),R) = hAPP_f901718717l_bool(P,hAPP_l796364813t_char(Q,R)) ).

tff(help_COMBS_1_1_COMBS_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_1001,axiom,
    ! [P: fun_Pr1882154498l_bool,Q: fun_Pr1861226704r_bool,R: produc1971331930t_char] : hAPP_P1680401186r_bool(cOMBS_635570165l_bool(P,Q),R) = hAPP_bool_bool(hAPP_P1552072218l_bool(P,R),hAPP_P1680401186r_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_1002,axiom,
    ! [P: fun_bo1549164019l_bool,Q: fun_Pr1861226704r_bool,R: produc1971331930t_char] : hAPP_P1552072218l_bool(hAPP_f561246575l_bool(hAPP_f321462169l_bool(cOMBB_808210516t_char,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_P1680401186r_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc,axiom,
    ! [P: fun_fu114905943l_bool,Q: fun_fu250820942l_bool,R: fun_na939144002on_val] : hAPP_f1492320500l_bool(hAPP_f1523875321l_bool(hAPP_f592397849l_bool(cOMBB_1718333400on_val,P),Q),R) = hAPP_f1863694447l_bool(P,hAPP_f1145256474l_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_1003,axiom,
    ! [P: fun_li977323167r_bool,Q: fun_Pr70170387r_bool,R: list_char] : hAPP_l165010689r_bool(hAPP_f1209019955r_bool(hAPP_f521496323r_bool(cOMBC_654453230r_bool,P),Q),R) = hAPP_f279818502r_bool(hAPP_l2053770731r_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod,axiom,
    ! [P: fun_Pr1752471359l_bool,Q: fun_Pr70170387r_bool,R: produc1013743697t_char] : hAPP_P1384137393r_bool(hAPP_f1853572245r_bool(hAPP_f1933376467r_bool(cOMBC_36589090l_bool,P),Q),R) = hAPP_f483496539l_bool(hAPP_P7095645l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_1004,axiom,
    ! [P: fun_fu1223433803r_bool,Q: fun_li99597427l_bool,R: list_list_char] : hAPP_l753659065r_bool(hAPP_f2059406941r_bool(hAPP_f108089737r_bool(cOMBB_2143526097t_char,P),Q),R) = hAPP_f1766231913r_bool(P,hAPP_l551544901l_bool(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__fun__1005,axiom,
    ! [P: fun_Pr1372407413l_bool,Q: fun_fu1718160452on_val,R: fun_Pr806764899on_val] : hAPP_f749178132l_bool(hAPP_f1099622285l_bool(hAPP_f919000597l_bool(cOMBB_1153773871on_val,P),Q),R) = hAPP_P1217996045l_bool(P,hAPP_f900686428on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mt,axiom,
    ! [P: fun_fu1167149685l_bool,Q: fun_li1548633647t_char,R: list_ty] : hAPP_l1117138611l_bool(hAPP_f2047757465l_bool(hAPP_f466945179l_bool(cOMBB_68065882ist_ty,P),Q),R) = hAPP_f921434893l_bool(P,hAPP_l14371579t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String___1006,axiom,
    ! [P: fun_Pr1982141813l_bool,Q: fun_Pr141094017t_char,R: produc220283002t_char] : hAPP_P1562529797l_bool(hAPP_f1233028029l_bool(hAPP_f1715733055l_bool(cOMBB_123628846t_char,P),Q),R) = hAPP_P1472618637l_bool(P,hAPP_P767818445t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_1007,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__prod_Itc__List__Olist_Itc__Value__Oval_J_Mt_1008,axiom,
    ! [P: fun_fu1034987497r_bool,Q: fun_li1135330407l_bool,R: list_ty] : hAPP_l96108383r_bool(hAPP_f1608277885r_bool(hAPP_f1134248971r_bool(cOMBB_338473166ist_ty,P),Q),R) = hAPP_f225832321r_bool(P,hAPP_l1117138611l_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__,axiom,
    ! [P: fun_li1548711503l_bool,Q: fun_Pr1669461698r_bool,R: list_P341299826t_char] : hAPP_l902158906r_bool(hAPP_f605643693r_bool(hAPP_f841257045r_bool(cOMBC_1407716098l_bool,P),Q),R) = hAPP_f1161798306l_bool(hAPP_l213519975l_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_1009,axiom,
    ! [P: fun_fu114548717l_bool,Q: fun_Pr1696029455l_bool,R: fun_na939144002on_val] : hAPP_f1175813647l_bool(hAPP_f47713631l_bool(hAPP_f77033475l_bool(cOMBC_1317565126l_bool,P),Q),R) = hAPP_f33142364l_bool(hAPP_f893576377l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod,axiom,
    ! [P: fun_Pr1752471359l_bool,Q: fun_Pr165123960t_char,R: produc1025221954t_char] : hAPP_P1383068750l_bool(hAPP_f1239832973l_bool(hAPP_f1937828171l_bool(cOMBB_1681501894t_char,P),Q),R) = hAPP_P7095645l_bool(P,hAPP_P242904598t_char(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String___1010,axiom,
    ! [P: fun_li1774921427r_bool,Q: fun_Pr1669461698r_bool,R: list_P1940453997har_ty] : hAPP_l24694616r_bool(hAPP_f306469557r_bool(hAPP_f197435839r_bool(cOMBC_886773442r_bool,P),Q),R) = hAPP_f605643693r_bool(hAPP_l1129005983r_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__1011,axiom,
    ! [P: fun_fu1263594869l_bool,Q: fun_li1436431093on_val,R: list_char] : hAPP_l2111308793l_bool(hAPP_f1370205989l_bool(hAPP_f1406462375l_bool(cOMBB_109816436t_char,P),Q),R) = hAPP_f1099622285l_bool(P,hAPP_l1786340417on_val(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It,axiom,
    ! [P: fun_Pr966331573l_bool,Q: fun_Pr680585871l_bool,R: produc12694297on_val] : hAPP_P159683425l_bool(hAPP_f1175362209l_bool(hAPP_f101237475l_bool(cOMBC_1585774710l_bool,P),Q),R) = hAPP_f91506671l_bool(hAPP_P1609485901l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_1012,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_COMBC_1_1_COMBC_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_1013,axiom,
    ! [P: fun_Pr228183746l_bool,Q: fun_Pr248118298l_bool,R: produc12694297on_val] : hAPP_P159683425l_bool(hAPP_f1526206996l_bool(hAPP_f1467537159l_bool(cOMBC_2141828763l_bool,P),Q),R) = hAPP_f837795298l_bool(hAPP_P594889876l_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc,axiom,
    ! [P: fun_Pr1021761724l_bool,Q: fun_Pr1898949769r_bool,R: produc2146869324t_char] : hAPP_P828904212r_bool(hAPP_f764724814r_bool(hAPP_f1410576713r_bool(cOMBC_516637475l_bool,P),Q),R) = hAPP_f2050077417l_bool(hAPP_P1418247892l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_1014,axiom,
    ! [P: fun_Pr2070293557l_bool,Q: fun_fu1690035458on_val,R: fun_li1432931796on_val] : hAPP_f720086610l_bool(hAPP_f292637069l_bool(hAPP_f1168269397l_bool(cOMBB_1293776864on_val,P),Q),R) = hAPP_P998768845l_bool(P,hAPP_f1727192346on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__1015,axiom,
    ! [P: fun_fu49805983l_bool,Q: fun_li1000975661l_bool,R: list_char] : hAPP_l1739862107l_bool(hAPP_f1094343359l_bool(hAPP_f876671127l_bool(cOMBB_1200577438t_char,P),Q),R) = hAPP_f1166017719l_bool(P,hAPP_l2111308793l_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_0_1016,axiom,
    ! [P: fun_ex897949293l_bool,Q: fun_Pr680585871l_bool,R: exp_list_char] : hAPP_e1833980889l_bool(hAPP_f989077673l_bool(hAPP_f40682957l_bool(cOMBC_562612496l_bool,P),Q),R) = hAPP_f1175362209l_bool(hAPP_e1705922617l_bool(P,R),Q) ).

tff(help_COMBS_1_1_COMBS_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_,axiom,
    ! [P: fun_Pr1041696489l_bool,Q: fun_Pr691271849l_bool,R: produc1102272487on_val] : hAPP_P282169671l_bool(cOMBS_1319864284l_bool(P,Q),R) = hAPP_bool_bool(hAPP_P1402001845l_bool(P,R),hAPP_P282169671l_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_1017,axiom,
    ! [P: fun_li486265185r_bool,Q: fun_Pr1898949769r_bool,R: list_char] : hAPP_l1342015621r_bool(hAPP_f719350875r_bool(hAPP_f2133563379r_bool(cOMBC_1025440566r_bool,P),Q),R) = hAPP_f764724814r_bool(hAPP_l1988620845r_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc_,axiom,
    ! [P: fun_fu821374111l_bool,Q: fun_li455628155t_char,R: list_list_char] : hAPP_l1571522437l_bool(hAPP_f1136362289l_bool(hAPP_f1736484361l_bool(cOMBB_2042763133t_char,P),Q),R) = hAPP_f1233028029l_bool(P,hAPP_l1873467853t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_1018,axiom,
    ! [P: fun_bo1549164019l_bool,Q: fun_Pr691271849l_bool,R: produc1102272487on_val] : hAPP_P1402001845l_bool(hAPP_f379976829l_bool(hAPP_f606945057l_bool(cOMBB_705522285on_val,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_P282169671l_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__St,axiom,
    ! [P: fun_li1961812931l_bool,Q: fun_Pr248118298l_bool,R: list_exp_list_char] : hAPP_l146377954l_bool(hAPP_f844901525l_bool(hAPP_f348508809l_bool(cOMBC_622308798l_bool,P),Q),R) = hAPP_f1526206996l_bool(hAPP_l177734933l_bool(P,R),Q) ).

tff(help_COMBS_1_1_COMBS_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc_,axiom,
    ! [P: fun_Pr2072119505l_bool,Q: fun_Pr859510977l_bool,R: produc430140671on_val] : hAPP_P1333315679l_bool(cOMBS_1218320756l_bool(P,Q),R) = hAPP_bool_bool(hAPP_P895943837l_bool(P,R),hAPP_P1333315679l_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_1019,axiom,
    ! [P: fun_Pr655735548l_bool,Q: fun_Pr1861226704r_bool,R: produc952412819t_char] : hAPP_P659547099r_bool(hAPP_f658521820r_bool(hAPP_f454222487r_bool(cOMBC_1338332465l_bool,P),Q),R) = hAPP_f515912112l_bool(hAPP_P780018708l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_1020,axiom,
    ! [P: fun_bo1549164019l_bool,Q: fun_Pr859510977l_bool,R: produc430140671on_val] : hAPP_P895943837l_bool(hAPP_f914702973l_bool(hAPP_f1600936353l_bool(cOMBB_1617503877on_val,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_P1333315679l_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__1021,axiom,
    ! [P: fun_fu839442891r_bool,Q: fun_li404360883l_bool,R: list_list_char] : hAPP_l1783480313r_bool(hAPP_f531187933r_bool(hAPP_f179418505r_bool(cOMBB_550632017t_char,P),Q),R) = hAPP_f1707979241r_bool(P,hAPP_l1571522437l_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_1022,axiom,
    ! [P: fun_li1555920111r_bool,Q: fun_Pr1861226704r_bool,R: list_char] : hAPP_l2140727500r_bool(hAPP_f2025561243r_bool(hAPP_f1500560577r_bool(cOMBC_1784597444r_bool,P),Q),R) = hAPP_f658521820r_bool(hAPP_l923073979r_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_1023,axiom,
    ! [P: fun_Pr2054894453l_bool,Q: fun_Pr1861226704r_bool,R: produc1971331930t_char] : hAPP_P1680401186r_bool(hAPP_f1666729379r_bool(hAPP_f1020753317r_bool(cOMBC_1297648632l_bool,P),Q),R) = hAPP_f515912112l_bool(hAPP_P205570445l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__1024,axiom,
    ! [P: fun_fu748506869l_bool,Q: fun_li1093980969t_char,R: list_char] : hAPP_l1845912621l_bool(hAPP_f1868463117l_bool(hAPP_f1365840271l_bool(cOMBB_1705938036t_char,P),Q),R) = hAPP_f1239832973l_bool(P,hAPP_l1388836853t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc,axiom,
    ! [P: fun_Pr1300573173l_bool,Q: fun_li618628759t_char,R: list_P341299826t_char] : hAPP_l213519975l_bool(hAPP_f156692813l_bool(hAPP_f1847120981l_bool(cOMBB_1035649854t_char,P),Q),R) = hAPP_P1327510541l_bool(P,hAPP_l277216047t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__1025,axiom,
    ! [P: fun_fu1497625339r_bool,Q: fun_li429005281l_bool,R: list_char] : hAPP_l2053770731r_bool(hAPP_f732843907r_bool(hAPP_f1563448447r_bool(cOMBB_1490692730t_char,P),Q),R) = hAPP_f1419180947r_bool(P,hAPP_l1845912621l_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_1026,axiom,
    ! [P: fun_fu1608823157l_bool,Q: fun_fu1639641777on_val,R: fun_na939144002on_val] : hAPP_f613075253l_bool(hAPP_f1670595613l_bool(hAPP_f1472899487l_bool(cOMBB_588525814on_val,P),Q),R) = hAPP_f292637069l_bool(P,hAPP_f1849790461on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O,axiom,
    ! [P: fun_Pr1751899445l_bool,Q: fun_Pr231134077on_val,R: produc12694297on_val] : hAPP_P1609485901l_bool(hAPP_f826324045l_bool(hAPP_f1639555093l_bool(cOMBB_985659173on_val,P),Q),R) = hAPP_P2015860941l_bool(P,hAPP_P604205461on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_1027,axiom,
    ! [P: fun_fu735196737l_bool,Q: fun_fu1165575785l_bool,R: fun_na939144002on_val] : hAPP_f893576377l_bool(hAPP_f1250221913l_bool(hAPP_f1860331535l_bool(cOMBB_2084052674on_val,P),Q),R) = hAPP_f510152537l_bool(P,hAPP_f613075253l_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_1028,axiom,
    ! [P: fun_Pr1572485173l_bool,Q: fun_Pr32647428t_char,R: produc2146869324t_char] : hAPP_P1418247892l_bool(hAPP_f2037329933l_bool(hAPP_f251669717l_bool(cOMBB_773661144t_char,P),Q),R) = hAPP_P1517699917l_bool(P,hAPP_P1423780764t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli,axiom,
    ! [P: fun_Pr1964766157l_bool,Q: fun_Pr254484106on_val,R: produc12694297on_val] : hAPP_P594889876l_bool(hAPP_f375531599l_bool(hAPP_f1564338425l_bool(cOMBB_1078680455on_val,P),Q),R) = hAPP_P483670507l_bool(P,hAPP_P1963616220on_val(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O,axiom,
    ! [P: fun_Pr973229009l_bool,Q: fun_Pr691271849l_bool,R: produc124828825on_val] : hAPP_P1708370145l_bool(hAPP_f973018659l_bool(hAPP_f961387813l_bool(cOMBC_1608987946l_bool,P),Q),R) = hAPP_f1453283057l_bool(hAPP_P638161699l_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli,axiom,
    ! [P: fun_Pr730004340l_bool,Q: fun_Pr859510977l_bool,R: produc2061676504on_val] : hAPP_P71593144l_bool(hAPP_f1317381998l_bool(hAPP_f1734997943l_bool(cOMBC_1491642377l_bool,P),Q),R) = hAPP_f458849545l_bool(hAPP_P88824722l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_1029,axiom,
    ! [P: fun_Pr2054894453l_bool,Q: fun_Pr880942020t_char,R: produc952412819t_char] : hAPP_P780018708l_bool(hAPP_f1107475085l_bool(hAPP_f937861397l_bool(cOMBB_1520154591t_char,P),Q),R) = hAPP_P205570445l_bool(P,hAPP_P1224499548t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc_,axiom,
    ! [P: fun_fu2068145461l_bool,Q: fun_li1497997787t_char,R: list_P1940453997har_ty] : hAPP_l1536299231l_bool(hAPP_f935003377l_bool(hAPP_f162154931l_bool(cOMBB_859890145har_ty,P),Q),R) = hAPP_f156692813l_bool(P,hAPP_l352172327t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__1030,axiom,
    ! [P: fun_fu989111613r_bool,Q: fun_li1358910483l_bool,R: list_P1940453997har_ty] : hAPP_l1129005983r_bool(hAPP_f1749915625r_bool(hAPP_f842743203r_bool(cOMBB_657296617har_ty,P),Q),R) = hAPP_f841257045r_bool(P,hAPP_l1536299231l_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O,axiom,
    ! [P: fun_fu1816861237l_bool,Q: fun_ex977868519on_val,R: exp_list_char] : hAPP_e286792811l_bool(hAPP_f1614195593l_bool(hAPP_f705562443l_bool(cOMBB_507006011t_char,P),Q),R) = hAPP_f826324045l_bool(P,hAPP_e1659493427on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__,axiom,
    ! [P: fun_fu1331594741l_bool,Q: fun_li2006863797t_char,R: list_char] : hAPP_l810309945l_bool(hAPP_f1817350437l_bool(hAPP_f614662951l_bool(cOMBB_1558246132t_char,P),Q),R) = hAPP_f2037329933l_bool(P,hAPP_l309186817t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_1031,axiom,
    ! [P: fun_fu1525621451l_bool,Q: fun_ex1231581599l_bool,R: exp_list_char] : hAPP_e1705922617l_bool(hAPP_f1475571983l_bool(hAPP_f1946480059l_bool(cOMBB_673739729t_char,P),Q),R) = hAPP_f101237475l_bool(P,hAPP_e286792811l_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_1032,axiom,
    ! [P: fun_fu793340337l_bool,Q: fun_li856594443on_val,R: list_exp_list_char] : hAPP_l232580245l_bool(hAPP_f1752856401l_bool(hAPP_f552300311l_bool(cOMBB_1270208498t_char,P),Q),R) = hAPP_f375531599l_bool(P,hAPP_l1275479261on_val(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O_1033,axiom,
    ! [P: fun_Pr519971843l_bool,Q: fun_Pr691271849l_bool,R: produc124828825on_val] : hAPP_P1116729363l_bool(hAPP_f1200025813l_bool(hAPP_f1089788553l_bool(cOMBC_967917532l_bool,P),Q),R) = hAPP_f973018659l_bool(hAPP_P609938901l_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_,axiom,
    ! [P: fun_Pr243362283l_bool,Q: fun_Pr691271849l_bool,R: produc1102272487on_val] : hAPP_P282169671l_bool(hAPP_f2036784149l_bool(hAPP_f1720452391l_bool(cOMBC_1021753250l_bool,P),Q),R) = hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List___1034,axiom,
    ! [P: fun_fu935579185r_bool,Q: fun_li1927639661l_bool,R: list_char] : hAPP_l1988620845r_bool(hAPP_f1957374161r_bool(hAPP_f304993943r_bool(cOMBB_847828016t_char,P),Q),R) = hAPP_f1410576713r_bool(P,hAPP_l810309945l_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_1035,axiom,
    ! [P: fun_fu76765545l_bool,Q: fun_li616301379l_bool,R: list_exp_list_char] : hAPP_l177734933l_bool(hAPP_f1149562121l_bool(hAPP_f1850037271l_bool(cOMBB_773375802t_char,P),Q),R) = hAPP_f1467537159l_bool(P,hAPP_l232580245l_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli_1036,axiom,
    ! [P: fun_Pr164273135l_bool,Q: fun_Pr859510977l_bool,R: produc2061676504on_val] : hAPP_P1183008383l_bool(hAPP_f447422815l_bool(hAPP_f2052909183l_bool(cOMBC_766524526l_bool,P),Q),R) = hAPP_f1317381998l_bool(hAPP_P768428603l_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc_,axiom,
    ! [P: fun_Pr1441107355l_bool,Q: fun_Pr859510977l_bool,R: produc430140671on_val] : hAPP_P1333315679l_bool(hAPP_f1856968213l_bool(hAPP_f677078775l_bool(cOMBC_475083938l_bool,P),Q),R) = hAPP_f458849545l_bool(hAPP_P126004409l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_,axiom,
    ! [P: fun_fu696652149l_bool,Q: fun_li937397365t_char,R: list_char] : hAPP_l1591404153l_bool(hAPP_f333583909l_bool(hAPP_f1407048615l_bool(cOMBB_741416308t_char,P),Q),R) = hAPP_f1107475085l_bool(P,hAPP_l902950593t_char(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J__1037,axiom,
    ! [P: fun_fu1928247679r_bool,Q: fun_li95346349l_bool,R: list_char] : hAPP_l923073979r_bool(hAPP_f29105311r_bool(hAPP_f953097879r_bool(cOMBB_672864638t_char,P),Q),R) = hAPP_f454222487r_bool(P,hAPP_l1591404153l_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_,axiom,
    ! [P: fun_Pr243362283l_bool,Q: fun_Pr714818201on_val,R: produc124828825on_val] : hAPP_P638161699l_bool(hAPP_f762728813l_bool(hAPP_f1510763001l_bool(cOMBB_565412073on_val,P),Q),R) = hAPP_P1303341961l_bool(P,hAPP_P1886180715on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc_,axiom,
    ! [P: fun_Pr1441107355l_bool,Q: fun_Pr2075414204on_val,R: produc2061676504on_val] : hAPP_P88824722l_bool(hAPP_f1776493709l_bool(hAPP_f810261999l_bool(cOMBB_1034324152on_val,P),Q),R) = hAPP_P126004409l_bool(P,hAPP_P658340954on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__,axiom,
    ! [P: fun_fu1839421007l_bool,Q: fun_Pr1391347915on_val,R: produc124828825on_val] : hAPP_P527298901l_bool(hAPP_f1204100177l_bool(hAPP_f2026692601l_bool(cOMBB_1977588741on_val,P),Q),R) = hAPP_f762728813l_bool(P,hAPP_P1870962205on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___1038,axiom,
    ! [P: fun_fu1666573063l_bool,Q: fun_Pr2043111299l_bool,R: produc124828825on_val] : hAPP_P609938901l_bool(hAPP_f2095325577l_bool(hAPP_f1135930489l_bool(cOMBB_1223415373on_val,P),Q),R) = hAPP_f961387813l_bool(P,hAPP_P527298901l_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__,axiom,
    ! [P: fun_fu450552565l_bool,Q: fun_Pr1643560277on_val,R: produc2061676504on_val] : hAPP_P76086873l_bool(hAPP_f1082373989l_bool(hAPP_f869803751l_bool(cOMBB_555068556on_val,P),Q),R) = hAPP_f1776493709l_bool(P,hAPP_P1526035745on_val(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc___1039,axiom,
    ! [P: fun_fu1668998687l_bool,Q: fun_Pr1689395469l_bool,R: produc2061676504on_val] : hAPP_P768428603l_bool(hAPP_f1427871743l_bool(hAPP_f32926423l_bool(cOMBB_779086262on_val,P),Q),R) = hAPP_f1734997943l_bool(P,hAPP_P76086873l_bool(Q,R)) ).

%----Conjectures (1)
% tff(conj_0,conjecture,
%     hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),fun_up1149430426on_val(la,v_1,hAPP_val_option_val(some_val,v))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,e_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,h_a),l_a)))),red(p))) ).

%------------------------------------------------------------------------------