TPTP Problem File: SWW475

TPTP Problem File: SWW475_3.p

%------------------------------------------------------------------------------
% File     : SWW475_3 : TPTP v8.2.0. Released v5.3.0.
% Domain   : Software Verification
% Problem  : Java type soundness line 22, 1000 axioms selected
% Version  : Especial.
% English  :

% Refs     : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
%          : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source   : [Bla11]
% Names    : jinja_1000_tff_l22 [Bla11]

% Status   : Theorem
% Rating   : 1.00 v5.5.0, 0.75 v5.4.0, 1.00 v5.3.0
% Syntax   : Number of formulae    : 1739 ( 422 unt; 524 typ;   0 def)
%            Number of atoms       : 3014 ( 905 equ)
%            Maximal formula atoms :   11 (   1 avg)
%            Number of connectives : 2481 ( 682   ~;  14   |;  80   &)
%                                         ( 166 <=>;1539  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   31 (   8 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of types       :  164 ( 163 usr)
%            Number of type conns  :  580 ( 316   >; 264   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  360 ( 360 usr;  45 con; 0-6 aty)
%            Number of variables   : 5948 (5823   !; 125   ?;5948   :)
% SPC      : TF0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2011-08-09 17:22:50
%------------------------------------------------------------------------------
%----Should-be-implicit typings (163)
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tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr,type,
    fun_Pr1329133739l_bool: $tType ).

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

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

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

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

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

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

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

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

tff(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__Olist_,type,
    produc469582463har_ty: $tType ).

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

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

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

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

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

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

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

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

tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J__033,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__034,type,
    produc1350825965t_char: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Type__Oty_J_,type,
    produc300386343har_ty: $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,
    produc463632231har_ty: $tType ).

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

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

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

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

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mt,type,
    produc2128539405al_val: $tType ).

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

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

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String,type,
    produc633474461t_char: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String_035,type,
    produc1404366365t_char: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Li,type,
    produc785809127har_ty: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Li_036,type,
    produc997054249t_char: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fu,type,
    produc940183837on_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_I,type,
    produc1367398613t_char: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr,type,
    produc228386305t_char: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__prod,type,
    produc1049221769al_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_,type,
    produc1454067869on_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_It,type,
    produc1464201097on_val: $tType ).

tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_It,type,
    produc319655913on_val: $tType ).

%----Explicit typings (361)
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__Option__Ooption_Itc__Type__Oty_J_000tc__fun_Itc__fun_Itc__prod,type,
    cOMBB_352765746t_char: ( fun_op1983271469ion_ty * fun_li688206603ion_ty ) > fun_li1301775111ion_ty ).

tff(sy_c_COMBB_000tc__Type__Oty_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List_,type,
    cOMBB_1888336841t_char: ( fun_ty_option_ty * fun_list_char_ty ) > fun_li688206603ion_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__prod_Itc__List__Olist_Itc__String__Ochar_,type,
    cOMBK_1944287343al_nat: fun_op637900998on_val ).

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

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

tff(sy_c_Exceptions_OClassCast,type,
    classCast: list_char ).

tff(sy_c_Exceptions_ONullPointer,type,
    nullPointer: list_char ).

tff(sy_c_Exceptions_OOutOfMemory,type,
    outOfMemory: list_char ).

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

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

tff(sy_c_Exceptions_Osys__xcpts,type,
    sys_xcpts: fun_list_char_bool ).

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

tff(sy_c_Expr_Obop_OAdd,type,
    add: bop ).

tff(sy_c_Expr_Obop_OEq,type,
    c_Expr_Obop_OEq: bop ).

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

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

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

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

tff(sy_c_Expr_Oexp_OCond_000tc__List__Olist_Itc__String__Ochar_J,type,
    cond_list_char: ( exp_list_char * exp_list_char * exp_list_char ) > exp_list_char ).

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

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

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

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

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

tff(sy_c_Expr_Oexp_OVal_000tc__List__Olist_Itc__String__Ochar_J,type,
    val_list_char: fun_va223928858t_char ).

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

tff(sy_c_Expr_Oexp_Onew_000tc__List__Olist_Itc__String__Ochar_J,type,
    new_list_char: list_char > exp_list_char ).

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

tff(sy_c_Expr_Ofv,type,
    fv: exp_list_char > fun_list_char_bool ).

tff(sy_c_Fun_Ocomp_000tc__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_037,type,
    fun_up1149430426on_val: ( fun_li1432931796on_val * list_char * option_val ) > fun_li1432931796on_val ).

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

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

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

tff(sy_c_Lattices_Osemilattice__sup__class_Osup_000tc__fun_Itc__List__Olist_Itc__Str,type,
    semila919158006r_bool: ( fun_list_char_bool * fun_list_char_bool ) > fun_list_char_bool ).

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

tff(sy_c_List_Oappend_000tc__List__Olist_Itc__String__Ochar_J,type,
    append_list_char: ( list_list_char * list_list_char ) > list_list_char ).

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

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

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

tff(sy_c_List_Oappend_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Type__O,type,
    append1373980413har_ty: ( list_P1940453997har_ty * list_P1940453997har_ty ) > list_P1940453997har_ty ).

tff(sy_c_List_Oappend_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_It,type,
    append814478020har_ty: ( list_P2098242612har_ty * list_P2098242612har_ty ) > list_P2098242612har_ty ).

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

tff(sy_c_List_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__Option__Ooption_Itc__Type__Oty_J,type,
    cons_option_ty: ( option_ty * list_option_ty ) > list_option_ty ).

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_OCons_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Typ,type,
    cons_P306092184har_ty: ( produc917948472har_ty * list_P1940453997har_ty ) > list_P1940453997har_ty ).

tff(sy_c_List_Olist_OCons_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__pro,type,
    cons_P1020158687har_ty: ( produc469582463har_ty * list_P2098242612har_ty ) > list_P2098242612har_ty ).

tff(sy_c_List_Olist_OCons_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_,type,
    cons_P796333129har_ty: ( produc245756905har_ty * list_P2023964830har_ty ) > list_P2023964830har_ty ).

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_Omap_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Type__Oty_,type,
    map_Pr1471044963har_ty: ( fun_Pr107226222har_ty * list_P1940453997har_ty ) > list_P2023964830har_ty ).

tff(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__,type,
    map_Pr1267419400har_ty: ( fun_Pr1566767763har_ty * list_P2023964830har_ty ) > list_P2098242612har_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_Map_Odom_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
    dom_list_char_val: fun_li1432931796on_val > fun_list_char_bool ).

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

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

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

tff(sy_c_Map_Omap__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__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_Oobj__ty,type,
    obj_ty: produc639455274on_val > ty ).

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

tff(sy_c_Option_Ooption_ONone_000tc__Nat__Onat,type,
    none_nat: option_nat ).

tff(sy_c_Option_Ooption_ONone_000tc__Type__Oty,type,
    none_ty: option_ty ).

tff(sy_c_Option_Ooption_ONone_000tc__Value__Oval,type,
    none_val: option_val ).

tff(sy_c_Option_Ooption_ONone_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_,type,
    none_P179726773on_val: option1479284511on_val ).

tff(sy_c_Option_Ooption_OSome_000tc__Nat__Onat,type,
    some_nat: fun_nat_option_nat ).

tff(sy_c_Option_Ooption_OSome_000tc__Type__Oty,type,
    some_ty: fun_ty_option_ty ).

tff(sy_c_Option_Ooption_OSome_000tc__Value__Oval,type,
    some_val: fun_val_option_val ).

tff(sy_c_Option_Ooption_OSome_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_,type,
    some_P948696889on_val: fun_Pr357631842on_val ).

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

tff(sy_c_Option_Othe_000tc__Value__Oval,type,
    the_val: fun_option_val_val ).

tff(sy_c_Option_Othe_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc_,type,
    the_Pr431167171on_val: fun_op498348476on_val ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__List__Olist_Itc__String__Oc,type,
    ord_le2092826700r_bool: ( fun_list_char_bool * fun_list_char_bool ) > bool ).

tff(sy_c_Product__Type_OPair_000tc__Expr__Obop_000tc__prod_Itc__Value__Oval_Mtc__Val,type,
    produc621191550al_val: ( bop * product_prod_val_val ) > produc1645268488al_val ).

tff(sy_c_Product__Type_OPair_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J,type,
    produc1259058957on_val: ( exp_list_char * produc12694297on_val ) > produc124828825on_val ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
    produc379668296on_val: ( list_exp_list_char * produc12694297on_val ) > produc2061676504on_val ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_,type,
    produc1147572817t_char: ( list_list_char * exp_list_char ) > produc809539159t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar__038,type,
    produc921874948t_char: ( list_list_char * produc220283002t_char ) > produc1285161482t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__List__Ol,type,
    produc5062597t_char: ( list_char * list_char ) > produc1278157519t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__Type__Ot,type,
    produc251930284har_ty: ( list_char * ty ) > produc917948472har_ty ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc_,type,
    produc823076510on_val: ( list_char * fun_Pr806764899on_val ) > produc639455274on_val ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc,type,
    produc1002914035har_ty: ( list_char * produc917948472har_ty ) > produc469582463har_ty ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Type__Oty_J_000tc__prod_Itc__Li,type,
    produc1909267824t_char: ( list_ty * produc662261637t_char ) > produc220283002t_char ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Value__Oval_J_000tc__Expr__Oexp,type,
    produc1916172923t_char: ( list_val * exp_list_char ) > produc662261637t_char ).

tff(sy_c_Product__Type_OPair_000tc__Value__Oval_000tc__Value__Oval,type,
    product_Pair_val_val: ( val * val ) > product_prod_val_val ).

tff(sy_c_Product__Type_OPair_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pro,type,
    produc899768717on_val: ( fun_na939144002on_val * fun_li1432931796on_val ) > produc12694297on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_,type,
    produc1924279125al_val: ( produc1645268488al_val * produc1645268488al_val ) > produc630464863al_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
    produc1441475159on_val: ( produc124828825on_val * produc124828825on_val ) > produc1102272487on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List_,type,
    produc1611380469on_val: ( produc2061676504on_val * produc2061676504on_val ) > produc430140671on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri,type,
    produc1897818327t_char: ( produc809539159t_char * produc809539159t_char ) > produc1534059751t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri_039,type,
    produc24551831t_char: ( produc1285161482t_char * produc1285161482t_char ) > produc349695911t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__,type,
    produc1265154397har_ty: ( produc1278157519t_char * ty ) > produc245756905har_ty ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___040,type,
    produc2080520419t_char: ( produc1278157519t_char * produc1278157519t_char ) > produc1350825965t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___041,type,
    produc1414300567har_ty: ( produc917948472har_ty * produc917948472har_ty ) > produc300386343har_ty ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___042,type,
    produc499151895on_val: ( produc639455274on_val * produc639455274on_val ) > produc87279271on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___043,type,
    produc2038128087har_ty: ( produc469582463har_ty * produc469582463har_ty ) > produc463632231har_ty ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod,type,
    produc57279289t_char: ( produc220283002t_char * produc220283002t_char ) > produc1406897475t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Ex,type,
    produc1299387215t_char: ( produc662261637t_char * produc662261637t_char ) > produc1826280281t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__,type,
    produc1244920211al_val: ( product_prod_val_val * product_prod_val_val ) > produc800118557al_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooptio,type,
    produc870913623on_val: ( produc12694297on_val * produc12694297on_val ) > produc409205479on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Va,type,
    produc370870787al_val: ( produc630464863al_val * produc630464863al_val ) > produc2128539405al_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_,type,
    produc1564932627on_val: ( produc1102272487on_val * produc1102272487on_val ) > produc231486621on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_,type,
    produc1951691075on_val: ( produc430140671on_val * produc430140671on_val ) > produc1466422861on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist,type,
    produc253822483t_char: ( produc1534059751t_char * produc1534059751t_char ) > produc633474461t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_044,type,
    produc1288549779t_char: ( produc349695911t_char * produc349695911t_char ) > produc1404366365t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Och,type,
    produc63273559har_ty: ( produc245756905har_ty * produc245756905har_ty ) > produc785809127har_ty ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Och_045,type,
    produc354099231t_char: ( produc1350825965t_char * produc1350825965t_char ) > produc997054249t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Och_046,type,
    produc434506131on_val: ( produc87279271on_val * produc87279271on_val ) > produc940183837on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J,type,
    produc913263563t_char: ( produc1406897475t_char * produc1406897475t_char ) > produc1367398613t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval,type,
    produc627518711t_char: ( produc1826280281t_char * produc1826280281t_char ) > produc228386305t_char ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval,type,
    produc94135935al_val: ( produc800118557al_val * produc800118557al_val ) > produc1049221769al_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Opti,type,
    produc935654419on_val: ( produc409205479on_val * produc409205479on_val ) > produc1454067869on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__Li,type,
    produc1729053055on_val: ( produc231486621on_val * produc231486621on_val ) > produc1464201097on_val ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__E,type,
    produc722767071on_val: ( produc1466422861on_val * produc1466422861on_val ) > produc319655913on_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_047,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__Type__O,type,
    produc2091768109y_bool: fun_Pr1127025070y_bool > fun_li634443788y_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__prod_It,type,
    produc166740340y_bool: fun_Pr758558581y_bool > fun_li800818899y_bool ).

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

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

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

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

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

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

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

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

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Str_048,type,
    produc17861502r_bool: fun_Pr1895638121r_bool > fun_Pr1794669603r_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_,type,
    produc1215659230y_bool: fun_Pr2102567903y_bool > fun_Pr1633645595y_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__049,type,
    produc715708746r_bool: fun_Pr1336847023r_bool > fun_Pr185059443r_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__050,type,
    produc1996970750l_bool: fun_Pr235369833l_bool > fun_Pr788853347l_bool ).

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

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

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

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

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

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

tff(sy_c_Product__Type_Ofst_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__,type,
    produc1230355531on_val: fun_Pr1940015747t_char ).

tff(sy_c_Product__Type_Ofst_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod,type,
    produc1517998010on_val: fun_Pr820147700on_val ).

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

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

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

tff(sy_c_Set_OCollect_000tc__Type__Oty,type,
    collect_ty: fun_ty_bool > fun_ty_bool ).

tff(sy_c_SmallStep_Oassigned,type,
    assigned: ( list_char * exp_list_char ) > bool ).

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

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

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

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

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

tff(sy_c_State_Ohp,type,
    hp: fun_Pr820147700on_val ).

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

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

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

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

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

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

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__List__Olist__051,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_052,type,
    transi1325206117har_ty: fun_Pr1670851305y_bool > fun_Pr1670851305y_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__String__Ocha_053,type,
    transi61620055on_val: fun_Pr235369833l_bool > fun_Pr235369833l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__String__Ocha_054,type,
    transi1158914604har_ty: fun_Pr1239516201y_bool > fun_Pr1239516201y_bool ).

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

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

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

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

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__Expr__Obop_Mtc__pro,type,
    transi486718450al_val: fun_Pr180697551l_bool > fun_Pr180697551l_bool ).

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

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

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Li,type,
    transi1630776058t_char: fun_Pr678067807r_bool > fun_Pr678067807r_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Li_055,type,
    transi2072254650t_char: fun_Pr1493019359r_bool > fun_Pr1493019359r_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__List__Olist_Itc__St,type,
    transi935089046har_ty: fun_Pr330025897y_bool > fun_Pr330025897y_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__List__Olist_Itc__St_056,type,
    transi15035776t_char: fun_Pr555864043r_bool > fun_Pr555864043r_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__List__Olist_Itc__St_057,type,
    transi1953049786on_val: fun_Pr1283539423l_bool > fun_Pr1283539423l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Ty,type,
    transi1452021206t_char: fun_Pr900028311r_bool > fun_Pr900028311r_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Va,type,
    transi1803333868t_char: fun_Pr4797123r_bool > fun_Pr4797123r_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__Value__Oval_Mtc__Va,type,
    transi1927461808al_val: fun_Pr1443979083l_bool > fun_Pr1443979083l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_,type,
    transi594096122on_val: fun_Pr27327839l_bool > fun_Pr27327839l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oex,type,
    transi678815536on_val: fun_Pr111684683l_bool > fun_Pr111684683l_bool ).

tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__prod_Itc__List__Oli,type,
    transi1751449568on_val: fun_Pr1329133739l_bool > fun_Pr1329133739l_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_Type_Ois__refT,type,
    is_refT: fun_ty_bool ).

tff(sy_c_Type_Othis,type,
    this: list_char ).

tff(sy_c_Type_Oty_OBoolean,type,
    boolean: ty ).

tff(sy_c_Type_Oty_OClass,type,
    class: fun_list_char_ty ).

tff(sy_c_Type_Oty_OInteger,type,
    integer: ty ).

tff(sy_c_Type_Oty_ONT,type,
    nt: ty ).

tff(sy_c_Type_Oty_OVoid,type,
    void: ty ).

tff(sy_c_Value_Othe__Addr,type,
    the_Addr: val > nat ).

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

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

tff(sy_c_Value_Oval_ONull,type,
    null: val ).

tff(sy_c_Value_Oval_OUnit,type,
    unit: val ).

tff(sy_c_WWellForm_Owwf__J__mdecl,type,
    wwf_J_mdecl: fun_li318226104r_bool ).

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

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

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

tff(sy_c_fFalse,type,
    fFalse: bool ).

tff(sy_c_fTrue,type,
    fTrue: bool ).

tff(sy_c_fequal_000tc__Value__Oval,type,
    fequal_val: fun_val_fun_val_bool ).

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

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

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

tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar,type,
    hAPP_l146377954l_bool: ( fun_li1372729616l_bool * list_exp_list_char ) > fun_Pr1696029455l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__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__058,type,
    hAPP_l217977712r_bool: ( fun_li1024794712r_bool * list_list_char ) > fun_Pr46158268r_bool ).

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

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

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__Type__Oty_Mtc_,type,
    hAPP_l1734756650y_bool: ( fun_li634443788y_bool * list_char ) > fun_ty_bool ).

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

tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__fun_Itc__prod__059,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__prod_Itc__List,type,
    hAPP_l1665608433y_bool: ( fun_li800818899y_bool * list_char ) > fun_Pr1127025070y_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__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__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__Option__Ooption_Itc__Type__Oty_J_000tc__fun_Itc__fun_Itc__prod_,type,
    hAPP_o534509643ion_ty: ( fun_op1983271469ion_ty * option_ty ) > fun_fu357191650ion_ty ).

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

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__fun_Itc__List__Olist_,type,
    hAPP_o538043682on_val: ( fun_op2076490582on_val * option_val ) > fun_li1432931796on_val ).

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

tff(sy_c_hAPP_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_060,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__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__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_,type,
    hAPP_f1033709212l_bool: ( fun_fu1693644106l_bool * fun_li1432931796on_val ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol,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_061,type,
    hAPP_f1175813647l_bool: ( fun_fu100249073l_bool * fun_na939144002on_val ) > fun_fu1693644106l_bool ).

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

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List___062,type,
    hAPP_f652398900ion_ty: ( fun_fu357191650ion_ty * fun_Pr806764899on_val ) > option_ty ).

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

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__Ova_063,type,
    hAPP_P323054207l_bool: ( fun_Pr1713170355l_bool * produc1645268488al_val ) > fun_Pr252072522l_bool ).

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

tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_064,type,
    hAPP_P1116729363l_bool: ( fun_Pr633696065l_bool * produc124828825on_val ) > fun_Pr680585871l_bool ).

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

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str_065,type,
    hAPP_P1183008383l_bool: ( fun_Pr597144499l_bool * produc2061676504on_val ) > fun_Pr248118298l_bool ).

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_066,type,
    hAPP_P1939418767r_bool: ( fun_Pr92408125r_bool * produc809539159t_char ) > fun_Pr1336948301r_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_067,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_068,type,
    hAPP_P1928969845r_bool: ( fun_Pr1794669603r_bool * produc1285161482t_char ) > fun_Pr227936640r_bool ).

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_069,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_070,type,
    hAPP_P1845004857y_bool: ( fun_Pr1633645595y_bool * produc1278157519t_char ) > fun_ty_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc_071,type,
    hAPP_P663876415r_bool: ( fun_Pr185059443r_bool * produc1278157519t_char ) > fun_Pr565113489r_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Type__Oty_J_000,type,
    hAPP_P748443392y_bool: ( fun_Pr1127025070y_bool * produc917948472har_ty ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Type__Oty_J_000_072,type,
    hAPP_P71962758har_ty: ( fun_Pr107226222har_ty * produc917948472har_ty ) > produc245756905har_ty ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__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_073,type,
    hAPP_P1789965269t_char: ( fun_Pr1940015747t_char * produc639455274on_val ) > list_char ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I_074,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_075,type,
    hAPP_P416784693l_bool: ( fun_Pr788853347l_bool * produc639455274on_val ) > fun_Pr315804320l_bool ).

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

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__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_076,type,
    hAPP_P1214880255r_bool: ( fun_Pr1074372915r_bool * produc220283002t_char ) > fun_Pr46158268r_bool ).

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_077,type,
    hAPP_P357098431r_bool: ( fun_Pr378536435r_bool * produc662261637t_char ) > fun_Pr827765831r_bool ).

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

tff(sy_c_hAPP_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_Itc__prod_I,type,
    hAPP_P1815899455l_bool: ( fun_Pr324760563l_bool * product_prod_val_val ) > fun_Pr2081272681l_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_078,type,
    hAPP_P703866694on_val: ( fun_Pr820147700on_val * produc12694297on_val ) > fun_na939144002on_val ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_079,type,
    hAPP_P1988153107l_bool: ( fun_Pr598845249l_bool * produc12694297on_val ) > fun_Pr1696029455l_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__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_080,type,
    hAPP_P2062527807l_bool: ( fun_Pr220980979l_bool * produc1102272487on_val ) > fun_Pr691271849l_bool ).

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_081,type,
    hAPP_P220718911l_bool: ( fun_Pr1511900787l_bool * produc430140671on_val ) > fun_Pr859510977l_bool ).

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_082,type,
    hAPP_P824029447r_bool: ( fun_Pr1895638121r_bool * produc349695911t_char ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List_,type,
    hAPP_P27757617y_bool: ( fun_Pr2102567903y_bool * produc245756905har_ty ) > bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__083,type,
    hAPP_P385447595har_ty: ( fun_Pr1566767763har_ty * produc245756905har_ty ) > produc469582463har_ty ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__084,type,
    hAPP_P2010574925r_bool: ( fun_Pr1336847023r_bool * produc1350825965t_char ) > bool ).

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

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

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

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

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

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

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

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

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

tff(sy_c_member_000tc__Nat__Onat,type,
    member_nat: ( nat * fun_nat_bool ) > bool ).

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

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Type__Oty_J,type,
    member503779467har_ty: ( produc917948472har_ty * fun_Pr1127025070y_bool ) > bool ).

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

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

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

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

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

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__085,type,
    member1420286996t_char: ( produc349695911t_char * fun_Pr1895638121r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis,type,
    member1783291580har_ty: ( produc245756905har_ty * fun_Pr2102567903y_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis_086,type,
    member794220506t_char: ( produc1350825965t_char * fun_Pr1336847023r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Typ,type,
    member119266708har_ty: ( produc300386343har_ty * fun_Pr1670851305y_bool ) > bool ).

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

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__pro,type,
    member1664419796har_ty: ( produc463632231har_ty * fun_Pr1239516201y_bool ) > bool ).

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

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

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

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

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value,type,
    member23198458al_val: ( produc2128539405al_val * fun_Pr180697551l_bool ) > bool ).

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

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

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_It,type,
    member902595210t_char: ( produc633474461t_char * fun_Pr678067807r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_It_087,type,
    member1934728458t_char: ( produc1404366365t_char * fun_Pr1493019359r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_,type,
    member1986596692har_ty: ( produc785809127har_ty * fun_Pr330025897y_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar__088,type,
    member1689070870t_char: ( produc997054249t_char * fun_Pr555864043r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar__089,type,
    member1114719754on_val: ( produc940183837on_val * fun_Pr1283539423l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mt,type,
    member371591362t_char: ( produc1367398613t_char * fun_Pr900028311r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_,type,
    member1105423342t_char: ( produc228386305t_char * fun_Pr4797123r_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_,type,
    member384848502al_val: ( produc1049221769al_val * fun_Pr1443979083l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option_,type,
    member2032527242on_val: ( produc1454067869on_val * fun_Pr27327839l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List_,type,
    member712690550on_val: ( produc1464201097on_val * fun_Pr111684683l_bool ) > bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr,type,
    member1837727190on_val: ( produc319655913on_val * fun_Pr1329133739l_bool ) > bool ).

tff(sy_v_E,type,
    e_1: fun_li688206603ion_ty ).

tff(sy_v_P,type,
    p: list_P1999446415t_char ).

tff(sy_v_T,type,
    t: ty ).

tff(sy_v_e,type,
    e: exp_list_char ).

tff(sy_v_e_H,type,
    e_2: exp_list_char ).

tff(sy_v_h,type,
    h_1: fun_na939144002on_val ).

tff(sy_v_h_H,type,
    h: fun_na939144002on_val ).

tff(sy_v_l,type,
    l_1: fun_li1432931796on_val ).

tff(sy_v_l_H,type,
    l: fun_li1432931796on_val ).

%----Relevant facts (1200)
tff(fact_0_prod__induct5,axiom,
    ! [X_2: produc1466422861on_val,Pa: fun_Pr302334223l_bool] :
      ( ! [A_1: produc430140671on_val,B_1: produc2061676504on_val,C_3: list_exp_list_char,D_1: fun_na939144002on_val,E_4: fun_li1432931796on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,produc1951691075on_val(A_1,produc1611380469on_val(B_1,produc379668296on_val(C_3,produc899768717on_val(D_1,E_4))))))
     => hBOOL(hAPP_P2028072621l_bool(Pa,X_2)) ) ).

tff(fact_1_prod__induct5,axiom,
    ! [X_2: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
      ( ! [A_1: produc1102272487on_val,B_1: produc124828825on_val,C_3: exp_list_char,D_1: fun_na939144002on_val,E_4: fun_li1432931796on_val] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_1,produc1441475159on_val(B_1,produc1259058957on_val(C_3,produc899768717on_val(D_1,E_4))))))
     => hBOOL(hAPP_P378063101l_bool(Pa,X_2)) ) ).

tff(fact_2_prod__induct5,axiom,
    ! [X_2: produc349695911t_char,Pa: fun_Pr1895638121r_bool] :
      ( ! [A_1: produc1285161482t_char,B_1: list_list_char,C_3: list_ty,D_1: list_val,E_4: exp_list_char] : hBOOL(hAPP_P824029447r_bool(Pa,produc24551831t_char(A_1,produc921874948t_char(B_1,produc1909267824t_char(C_3,produc1916172923t_char(D_1,E_4))))))
     => hBOOL(hAPP_P824029447r_bool(Pa,X_2)) ) ).

tff(fact_3_prod__cases5,axiom,
    ! [Y_1: produc1466422861on_val] :
      ~ ! [A_1: produc430140671on_val,B_1: produc2061676504on_val,C_3: list_exp_list_char,D_1: fun_na939144002on_val,E_4: fun_li1432931796on_val] : Y_1 != produc1951691075on_val(A_1,produc1611380469on_val(B_1,produc379668296on_val(C_3,produc899768717on_val(D_1,E_4)))) ).

tff(fact_4_prod__cases5,axiom,
    ! [Y_1: produc231486621on_val] :
      ~ ! [A_1: produc1102272487on_val,B_1: produc124828825on_val,C_3: exp_list_char,D_1: fun_na939144002on_val,E_4: fun_li1432931796on_val] : Y_1 != produc1564932627on_val(A_1,produc1441475159on_val(B_1,produc1259058957on_val(C_3,produc899768717on_val(D_1,E_4)))) ).

tff(fact_5_prod__cases5,axiom,
    ! [Y_6: produc349695911t_char] :
      ~ ! [A_1: produc1285161482t_char,B_1: list_list_char,C_3: list_ty,D_1: list_val,E_4: exp_list_char] : Y_6 != produc24551831t_char(A_1,produc921874948t_char(B_1,produc1909267824t_char(C_3,produc1916172923t_char(D_1,E_4)))) ).

tff(fact_6_prod__induct4,axiom,
    ! [X_2: produc1102272487on_val,Pa: fun_Pr691271849l_bool] :
      ( ! [A_1: produc124828825on_val,B_1: exp_list_char,C_3: fun_na939144002on_val,D_1: fun_li1432931796on_val] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A_1,produc1259058957on_val(B_1,produc899768717on_val(C_3,D_1)))))
     => hBOOL(hAPP_P282169671l_bool(Pa,X_2)) ) ).

tff(fact_7_prod__induct4,axiom,
    ! [X_2: produc430140671on_val,Pa: fun_Pr859510977l_bool] :
      ( ! [A_1: produc2061676504on_val,B_1: list_exp_list_char,C_3: fun_na939144002on_val,D_1: fun_li1432931796on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,produc1611380469on_val(A_1,produc379668296on_val(B_1,produc899768717on_val(C_3,D_1)))))
     => hBOOL(hAPP_P1333315679l_bool(Pa,X_2)) ) ).

tff(fact_8_prod__induct4,axiom,
    ! [X_2: produc1285161482t_char,Pa: fun_Pr227936640r_bool] :
      ( ! [A_1: list_list_char,B_1: list_ty,C_3: list_val,D_1: exp_list_char] : hBOOL(hAPP_P92196306r_bool(Pa,produc921874948t_char(A_1,produc1909267824t_char(B_1,produc1916172923t_char(C_3,D_1)))))
     => hBOOL(hAPP_P92196306r_bool(Pa,X_2)) ) ).

tff(fact_9_prod__induct4,axiom,
    ! [X_2: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
      ( ! [A_1: produc1102272487on_val,B_1: produc124828825on_val,C_3: exp_list_char,D_1: produc12694297on_val] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_1,produc1441475159on_val(B_1,produc1259058957on_val(C_3,D_1)))))
     => hBOOL(hAPP_P378063101l_bool(Pa,X_2)) ) ).

tff(fact_10_prod__induct4,axiom,
    ! [X_2: produc1466422861on_val,Pa: fun_Pr302334223l_bool] :
      ( ! [A_1: produc430140671on_val,B_1: produc2061676504on_val,C_3: list_exp_list_char,D_1: produc12694297on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,produc1951691075on_val(A_1,produc1611380469on_val(B_1,produc379668296on_val(C_3,D_1)))))
     => hBOOL(hAPP_P2028072621l_bool(Pa,X_2)) ) ).

tff(fact_11_prod__induct4,axiom,
    ! [X_2: produc349695911t_char,Pa: fun_Pr1895638121r_bool] :
      ( ! [A_1: produc1285161482t_char,B_1: list_list_char,C_3: list_ty,D_1: produc662261637t_char] : hBOOL(hAPP_P824029447r_bool(Pa,produc24551831t_char(A_1,produc921874948t_char(B_1,produc1909267824t_char(C_3,D_1)))))
     => hBOOL(hAPP_P824029447r_bool(Pa,X_2)) ) ).

tff(fact_12_prod__induct4,axiom,
    ! [X_2: produc1406897475t_char,Pa: fun_Pr1728267013r_bool] :
      ( ! [A_1: produc220283002t_char,B_1: list_ty,C_3: list_val,D_1: exp_list_char] : hBOOL(hAPP_P1240100515r_bool(Pa,produc57279289t_char(A_1,produc1909267824t_char(B_1,produc1916172923t_char(C_3,D_1)))))
     => hBOOL(hAPP_P1240100515r_bool(Pa,X_2)) ) ).

tff(fact_13_prod__induct4,axiom,
    ! [X_2: produc630464863al_val,Pa: fun_Pr897334561l_bool] :
      ( ! [A_1: produc1645268488al_val,B_1: bop,C_3: val,D_1: val] : hBOOL(hAPP_P738987199l_bool(Pa,produc1924279125al_val(A_1,produc621191550al_val(B_1,product_Pair_val_val(C_3,D_1)))))
     => hBOOL(hAPP_P738987199l_bool(Pa,X_2)) ) ).

tff(fact_14_prod__cases4,axiom,
    ! [Y_1: produc1102272487on_val] :
      ~ ! [A_1: produc124828825on_val,B_1: exp_list_char,C_3: fun_na939144002on_val,D_1: fun_li1432931796on_val] : Y_1 != produc1441475159on_val(A_1,produc1259058957on_val(B_1,produc899768717on_val(C_3,D_1))) ).

tff(fact_15_prod__cases4,axiom,
    ! [Y_1: produc430140671on_val] :
      ~ ! [A_1: produc2061676504on_val,B_1: list_exp_list_char,C_3: fun_na939144002on_val,D_1: fun_li1432931796on_val] : Y_1 != produc1611380469on_val(A_1,produc379668296on_val(B_1,produc899768717on_val(C_3,D_1))) ).

tff(fact_16_prod__cases4,axiom,
    ! [Y_5: produc1285161482t_char] :
      ~ ! [A_1: list_list_char,B_1: list_ty,C_3: list_val,D_1: exp_list_char] : Y_5 != produc921874948t_char(A_1,produc1909267824t_char(B_1,produc1916172923t_char(C_3,D_1))) ).

tff(fact_17_prod__cases4,axiom,
    ! [Y_1: produc231486621on_val] :
      ~ ! [A_1: produc1102272487on_val,B_1: produc124828825on_val,C_3: exp_list_char,D_1: produc12694297on_val] : Y_1 != produc1564932627on_val(A_1,produc1441475159on_val(B_1,produc1259058957on_val(C_3,D_1))) ).

tff(fact_18_prod__cases4,axiom,
    ! [Y_1: produc1466422861on_val] :
      ~ ! [A_1: produc430140671on_val,B_1: produc2061676504on_val,C_3: list_exp_list_char,D_1: produc12694297on_val] : Y_1 != produc1951691075on_val(A_1,produc1611380469on_val(B_1,produc379668296on_val(C_3,D_1))) ).

tff(fact_19_prod__cases4,axiom,
    ! [Y_5: produc349695911t_char] :
      ~ ! [A_1: produc1285161482t_char,B_1: list_list_char,C_3: list_ty,D_1: produc662261637t_char] : Y_5 != produc24551831t_char(A_1,produc921874948t_char(B_1,produc1909267824t_char(C_3,D_1))) ).

tff(fact_20_prod__cases4,axiom,
    ! [Y_5: produc1406897475t_char] :
      ~ ! [A_1: produc220283002t_char,B_1: list_ty,C_3: list_val,D_1: exp_list_char] : Y_5 != produc57279289t_char(A_1,produc1909267824t_char(B_1,produc1916172923t_char(C_3,D_1))) ).

tff(fact_21_prod__cases4,axiom,
    ! [Y_5: produc630464863al_val] :
      ~ ! [A_1: produc1645268488al_val,B_1: bop,C_3: val,D_1: val] : Y_5 != produc1924279125al_val(A_1,produc621191550al_val(B_1,product_Pair_val_val(C_3,D_1))) ).

tff(fact_22_red__hext__incr,axiom,
    ! [Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,La)),produc1259058957on_val(E_a,produc899768717on_val(H_a,L_a))),red(Pa)))
     => hBOOL(hext(Ha,H_a)) ) ).

tff(fact_23_prod__induct3,axiom,
    ! [X_2: produc469582463har_ty,Pa: fun_Pr758558581y_bool] :
      ( ! [A_1: list_char,B_1: list_char,C_3: ty] : hBOOL(hAPP_P831231943y_bool(Pa,produc1002914035har_ty(A_1,produc251930284har_ty(B_1,C_3))))
     => hBOOL(hAPP_P831231943y_bool(Pa,X_2)) ) ).

tff(fact_24_prod__induct3,axiom,
    ! [X_2: produc1102272487on_val,Pa: fun_Pr691271849l_bool] :
      ( ! [A_1: produc124828825on_val,B_1: exp_list_char,C_3: produc12694297on_val] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A_1,produc1259058957on_val(B_1,C_3))))
     => hBOOL(hAPP_P282169671l_bool(Pa,X_2)) ) ).

tff(fact_25_prod__induct3,axiom,
    ! [X_2: produc124828825on_val,Pa: fun_Pr680585871l_bool] :
      ( ! [A_1: exp_list_char,B_1: fun_na939144002on_val,C_3: fun_li1432931796on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A_1,produc899768717on_val(B_1,C_3))))
     => hBOOL(hAPP_P1708370145l_bool(Pa,X_2)) ) ).

tff(fact_26_prod__induct3,axiom,
    ! [X_2: produc430140671on_val,Pa: fun_Pr859510977l_bool] :
      ( ! [A_1: produc2061676504on_val,B_1: list_exp_list_char,C_3: produc12694297on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,produc1611380469on_val(A_1,produc379668296on_val(B_1,C_3))))
     => hBOOL(hAPP_P1333315679l_bool(Pa,X_2)) ) ).

tff(fact_27_prod__induct3,axiom,
    ! [X_2: produc2061676504on_val,Pa: fun_Pr248118298l_bool] :
      ( ! [A_1: list_exp_list_char,B_1: fun_na939144002on_val,C_3: fun_li1432931796on_val] : hBOOL(hAPP_P71593144l_bool(Pa,produc379668296on_val(A_1,produc899768717on_val(B_1,C_3))))
     => hBOOL(hAPP_P71593144l_bool(Pa,X_2)) ) ).

tff(fact_28_prod__induct3,axiom,
    ! [X_2: produc1285161482t_char,Pa: fun_Pr227936640r_bool] :
      ( ! [A_1: list_list_char,B_1: list_ty,C_3: produc662261637t_char] : hBOOL(hAPP_P92196306r_bool(Pa,produc921874948t_char(A_1,produc1909267824t_char(B_1,C_3))))
     => hBOOL(hAPP_P92196306r_bool(Pa,X_2)) ) ).

tff(fact_29_prod__induct3,axiom,
    ! [X_2: produc220283002t_char,Pa: fun_Pr46158268r_bool] :
      ( ! [A_1: list_ty,B_1: list_val,C_3: exp_list_char] : hBOOL(hAPP_P1907982426r_bool(Pa,produc1909267824t_char(A_1,produc1916172923t_char(B_1,C_3))))
     => hBOOL(hAPP_P1907982426r_bool(Pa,X_2)) ) ).

tff(fact_30_prod__induct3,axiom,
    ! [X_2: produc1645268488al_val,Pa: fun_Pr252072522l_bool] :
      ( ! [A_1: bop,B_1: val,C_3: val] : hBOOL(hAPP_P943837928l_bool(Pa,produc621191550al_val(A_1,product_Pair_val_val(B_1,C_3))))
     => hBOOL(hAPP_P943837928l_bool(Pa,X_2)) ) ).

tff(fact_31_prod__induct3,axiom,
    ! [X_2: produc231486621on_val,Pa: fun_Pr903661919l_bool] :
      ( ! [A_1: produc1102272487on_val,B_1: produc124828825on_val,C_3: produc124828825on_val] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_1,produc1441475159on_val(B_1,C_3))))
     => hBOOL(hAPP_P378063101l_bool(Pa,X_2)) ) ).

tff(fact_32_prod__induct3,axiom,
    ! [X_2: produc409205479on_val,Pa: fun_Pr693020585l_bool] :
      ( ! [A_1: produc12694297on_val,B_1: fun_na939144002on_val,C_3: fun_li1432931796on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,produc870913623on_val(A_1,produc899768717on_val(B_1,C_3))))
     => hBOOL(hAPP_P1221872711l_bool(Pa,X_2)) ) ).

tff(fact_33_prod__induct3,axiom,
    ! [X_2: produc1466422861on_val,Pa: fun_Pr302334223l_bool] :
      ( ! [A_1: produc430140671on_val,B_1: produc2061676504on_val,C_3: produc2061676504on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,produc1951691075on_val(A_1,produc1611380469on_val(B_1,C_3))))
     => hBOOL(hAPP_P2028072621l_bool(Pa,X_2)) ) ).

tff(fact_34_prod__induct3,axiom,
    ! [X_2: produc349695911t_char,Pa: fun_Pr1895638121r_bool] :
      ( ! [A_1: produc1285161482t_char,B_1: list_list_char,C_3: produc220283002t_char] : hBOOL(hAPP_P824029447r_bool(Pa,produc24551831t_char(A_1,produc921874948t_char(B_1,C_3))))
     => hBOOL(hAPP_P824029447r_bool(Pa,X_2)) ) ).

tff(fact_35_prod__induct3,axiom,
    ! [X_2: produc1406897475t_char,Pa: fun_Pr1728267013r_bool] :
      ( ! [A_1: produc220283002t_char,B_1: list_ty,C_3: produc662261637t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,produc57279289t_char(A_1,produc1909267824t_char(B_1,C_3))))
     => hBOOL(hAPP_P1240100515r_bool(Pa,X_2)) ) ).

tff(fact_36_prod__induct3,axiom,
    ! [X_2: produc1826280281t_char,Pa: fun_Pr1890037787r_bool] :
      ( ! [A_1: produc662261637t_char,B_1: list_val,C_3: exp_list_char] : hBOOL(hAPP_P1183499705r_bool(Pa,produc1299387215t_char(A_1,produc1916172923t_char(B_1,C_3))))
     => hBOOL(hAPP_P1183499705r_bool(Pa,X_2)) ) ).

tff(fact_37_prod__induct3,axiom,
    ! [X_2: produc630464863al_val,Pa: fun_Pr897334561l_bool] :
      ( ! [A_1: produc1645268488al_val,B_1: bop,C_3: product_prod_val_val] : hBOOL(hAPP_P738987199l_bool(Pa,produc1924279125al_val(A_1,produc621191550al_val(B_1,C_3))))
     => hBOOL(hAPP_P738987199l_bool(Pa,X_2)) ) ).

tff(fact_38_prod__induct3,axiom,
    ! [X_2: produc800118557al_val,Pa: fun_Pr832147423l_bool] :
      ( ! [A_1: product_prod_val_val,B_1: val,C_3: val] : hBOOL(hAPP_P2123002749l_bool(Pa,produc1244920211al_val(A_1,product_Pair_val_val(B_1,C_3))))
     => hBOOL(hAPP_P2123002749l_bool(Pa,X_2)) ) ).

tff(fact_39_prod__induct3,axiom,
    ! [X_2: produc87279271on_val,Pa: fun_Pr235369833l_bool] :
      ( ! [A_1: produc639455274on_val,B_1: list_char,C_3: fun_Pr806764899on_val] : hBOOL(hAPP_P124632071l_bool(Pa,produc499151895on_val(A_1,produc823076510on_val(B_1,C_3))))
     => hBOOL(hAPP_P124632071l_bool(Pa,X_2)) ) ).

tff(fact_40_prod__induct3,axiom,
    ! [X_2: produc1350825965t_char,Pa: fun_Pr1336847023r_bool] :
      ( ! [A_1: produc1278157519t_char,B_1: list_char,C_3: list_char] : hBOOL(hAPP_P2010574925r_bool(Pa,produc2080520419t_char(A_1,produc5062597t_char(B_1,C_3))))
     => hBOOL(hAPP_P2010574925r_bool(Pa,X_2)) ) ).

tff(fact_41_prod__induct3,axiom,
    ! [X_2: produc1534059751t_char,Pa: fun_Pr908866473r_bool] :
      ( ! [A_1: produc809539159t_char,B_1: list_list_char,C_3: exp_list_char] : hBOOL(hAPP_P1002912327r_bool(Pa,produc1897818327t_char(A_1,produc1147572817t_char(B_1,C_3))))
     => hBOOL(hAPP_P1002912327r_bool(Pa,X_2)) ) ).

tff(fact_42_prod__cases3,axiom,
    ! [Y_4: produc469582463har_ty] :
      ~ ! [A_1: list_char,B_1: list_char,C_3: ty] : Y_4 != produc1002914035har_ty(A_1,produc251930284har_ty(B_1,C_3)) ).

tff(fact_43_prod__cases3,axiom,
    ! [Y_1: produc1102272487on_val] :
      ~ ! [A_1: produc124828825on_val,B_1: exp_list_char,C_3: produc12694297on_val] : Y_1 != produc1441475159on_val(A_1,produc1259058957on_val(B_1,C_3)) ).

tff(fact_44_prod__cases3,axiom,
    ! [Y_1: produc124828825on_val] :
      ~ ! [A_1: exp_list_char,B_1: fun_na939144002on_val,C_3: fun_li1432931796on_val] : Y_1 != produc1259058957on_val(A_1,produc899768717on_val(B_1,C_3)) ).

tff(fact_45_prod__cases3,axiom,
    ! [Y_1: produc430140671on_val] :
      ~ ! [A_1: produc2061676504on_val,B_1: list_exp_list_char,C_3: produc12694297on_val] : Y_1 != produc1611380469on_val(A_1,produc379668296on_val(B_1,C_3)) ).

tff(fact_46_prod__cases3,axiom,
    ! [Y_1: produc2061676504on_val] :
      ~ ! [A_1: list_exp_list_char,B_1: fun_na939144002on_val,C_3: fun_li1432931796on_val] : Y_1 != produc379668296on_val(A_1,produc899768717on_val(B_1,C_3)) ).

tff(fact_47_prod__cases3,axiom,
    ! [Y_4: produc1285161482t_char] :
      ~ ! [A_1: list_list_char,B_1: list_ty,C_3: produc662261637t_char] : Y_4 != produc921874948t_char(A_1,produc1909267824t_char(B_1,C_3)) ).

tff(fact_48_prod__cases3,axiom,
    ! [Y_4: produc220283002t_char] :
      ~ ! [A_1: list_ty,B_1: list_val,C_3: exp_list_char] : Y_4 != produc1909267824t_char(A_1,produc1916172923t_char(B_1,C_3)) ).

tff(fact_49_prod__cases3,axiom,
    ! [Y_4: produc1645268488al_val] :
      ~ ! [A_1: bop,B_1: val,C_3: val] : Y_4 != produc621191550al_val(A_1,product_Pair_val_val(B_1,C_3)) ).

tff(fact_50_prod__cases3,axiom,
    ! [Y_1: produc231486621on_val] :
      ~ ! [A_1: produc1102272487on_val,B_1: produc124828825on_val,C_3: produc124828825on_val] : Y_1 != produc1564932627on_val(A_1,produc1441475159on_val(B_1,C_3)) ).

tff(fact_51_prod__cases3,axiom,
    ! [Y_1: produc409205479on_val] :
      ~ ! [A_1: produc12694297on_val,B_1: fun_na939144002on_val,C_3: fun_li1432931796on_val] : Y_1 != produc870913623on_val(A_1,produc899768717on_val(B_1,C_3)) ).

tff(fact_52_prod__cases3,axiom,
    ! [Y_1: produc1466422861on_val] :
      ~ ! [A_1: produc430140671on_val,B_1: produc2061676504on_val,C_3: produc2061676504on_val] : Y_1 != produc1951691075on_val(A_1,produc1611380469on_val(B_1,C_3)) ).

tff(fact_53_prod__cases3,axiom,
    ! [Y_4: produc349695911t_char] :
      ~ ! [A_1: produc1285161482t_char,B_1: list_list_char,C_3: produc220283002t_char] : Y_4 != produc24551831t_char(A_1,produc921874948t_char(B_1,C_3)) ).

tff(fact_54_prod__cases3,axiom,
    ! [Y_4: produc1406897475t_char] :
      ~ ! [A_1: produc220283002t_char,B_1: list_ty,C_3: produc662261637t_char] : Y_4 != produc57279289t_char(A_1,produc1909267824t_char(B_1,C_3)) ).

tff(fact_55_prod__cases3,axiom,
    ! [Y_4: produc1826280281t_char] :
      ~ ! [A_1: produc662261637t_char,B_1: list_val,C_3: exp_list_char] : Y_4 != produc1299387215t_char(A_1,produc1916172923t_char(B_1,C_3)) ).

tff(fact_56_prod__cases3,axiom,
    ! [Y_4: produc630464863al_val] :
      ~ ! [A_1: produc1645268488al_val,B_1: bop,C_3: product_prod_val_val] : Y_4 != produc1924279125al_val(A_1,produc621191550al_val(B_1,C_3)) ).

tff(fact_57_prod__cases3,axiom,
    ! [Y_4: produc800118557al_val] :
      ~ ! [A_1: product_prod_val_val,B_1: val,C_3: val] : Y_4 != produc1244920211al_val(A_1,product_Pair_val_val(B_1,C_3)) ).

tff(fact_58_prod__cases3,axiom,
    ! [Y_1: produc87279271on_val] :
      ~ ! [A_1: produc639455274on_val,B_1: list_char,C_3: fun_Pr806764899on_val] : Y_1 != produc499151895on_val(A_1,produc823076510on_val(B_1,C_3)) ).

tff(fact_59_prod__cases3,axiom,
    ! [Y_4: produc1350825965t_char] :
      ~ ! [A_1: produc1278157519t_char,B_1: list_char,C_3: list_char] : Y_4 != produc2080520419t_char(A_1,produc5062597t_char(B_1,C_3)) ).

tff(fact_60_prod__cases3,axiom,
    ! [Y_4: produc1534059751t_char] :
      ~ ! [A_1: produc809539159t_char,B_1: list_list_char,C_3: exp_list_char] : Y_4 != produc1897818327t_char(A_1,produc1147572817t_char(B_1,C_3)) ).

tff(fact_61_split__paired__All,axiom,
    ! [Pa: fun_Pr758558581y_bool] :
      ( ! [X1: produc469582463har_ty] : hBOOL(hAPP_P831231943y_bool(Pa,X1))
    <=> ! [A_1: list_char,B_1: produc917948472har_ty] : hBOOL(hAPP_P831231943y_bool(Pa,produc1002914035har_ty(A_1,B_1))) ) ).

tff(fact_62_split__paired__All,axiom,
    ! [Pa: fun_Pr2102567903y_bool] :
      ( ! [X1: produc245756905har_ty] : hBOOL(hAPP_P27757617y_bool(Pa,X1))
    <=> ! [A_1: produc1278157519t_char,B_1: ty] : hBOOL(hAPP_P27757617y_bool(Pa,produc1265154397har_ty(A_1,B_1))) ) ).

tff(fact_63_split__paired__All,axiom,
    ! [Pa: fun_Pr1127025070y_bool] :
      ( ! [X1: produc917948472har_ty] : hBOOL(hAPP_P748443392y_bool(Pa,X1))
    <=> ! [A_1: list_char,B_1: ty] : hBOOL(hAPP_P748443392y_bool(Pa,produc251930284har_ty(A_1,B_1))) ) ).

tff(fact_64_split__paired__All,axiom,
    ! [Pa: fun_Pr908866473r_bool] :
      ( ! [X1: produc1534059751t_char] : hBOOL(hAPP_P1002912327r_bool(Pa,X1))
    <=> ! [A_1: produc809539159t_char,B_1: produc809539159t_char] : hBOOL(hAPP_P1002912327r_bool(Pa,produc1897818327t_char(A_1,B_1))) ) ).

tff(fact_65_split__paired__All,axiom,
    ! [Pa: fun_Pr1336847023r_bool] :
      ( ! [X1: produc1350825965t_char] : hBOOL(hAPP_P2010574925r_bool(Pa,X1))
    <=> ! [A_1: produc1278157519t_char,B_1: produc1278157519t_char] : hBOOL(hAPP_P2010574925r_bool(Pa,produc2080520419t_char(A_1,B_1))) ) ).

tff(fact_66_split__paired__All,axiom,
    ! [Pa: fun_Pr235369833l_bool] :
      ( ! [X1: produc87279271on_val] : hBOOL(hAPP_P124632071l_bool(Pa,X1))
    <=> ! [A_1: produc639455274on_val,B_1: produc639455274on_val] : hBOOL(hAPP_P124632071l_bool(Pa,produc499151895on_val(A_1,B_1))) ) ).

tff(fact_67_split__paired__All,axiom,
    ! [Pa: fun_Pr832147423l_bool] :
      ( ! [X1: produc800118557al_val] : hBOOL(hAPP_P2123002749l_bool(Pa,X1))
    <=> ! [A_1: product_prod_val_val,B_1: product_prod_val_val] : hBOOL(hAPP_P2123002749l_bool(Pa,produc1244920211al_val(A_1,B_1))) ) ).

tff(fact_68_split__paired__All,axiom,
    ! [Pa: fun_Pr897334561l_bool] :
      ( ! [X1: produc630464863al_val] : hBOOL(hAPP_P738987199l_bool(Pa,X1))
    <=> ! [A_1: produc1645268488al_val,B_1: produc1645268488al_val] : hBOOL(hAPP_P738987199l_bool(Pa,produc1924279125al_val(A_1,B_1))) ) ).

tff(fact_69_split__paired__All,axiom,
    ! [Pa: fun_Pr1890037787r_bool] :
      ( ! [X1: produc1826280281t_char] : hBOOL(hAPP_P1183499705r_bool(Pa,X1))
    <=> ! [A_1: produc662261637t_char,B_1: produc662261637t_char] : hBOOL(hAPP_P1183499705r_bool(Pa,produc1299387215t_char(A_1,B_1))) ) ).

tff(fact_70_split__paired__All,axiom,
    ! [Pa: fun_Pr1728267013r_bool] :
      ( ! [X1: produc1406897475t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,X1))
    <=> ! [A_1: produc220283002t_char,B_1: produc220283002t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,produc57279289t_char(A_1,B_1))) ) ).

tff(fact_71_split__paired__All,axiom,
    ! [Pa: fun_Pr1895638121r_bool] :
      ( ! [X1: produc349695911t_char] : hBOOL(hAPP_P824029447r_bool(Pa,X1))
    <=> ! [A_1: produc1285161482t_char,B_1: produc1285161482t_char] : hBOOL(hAPP_P824029447r_bool(Pa,produc24551831t_char(A_1,B_1))) ) ).

tff(fact_72_split__paired__All,axiom,
    ! [Pa: fun_Pr302334223l_bool] :
      ( ! [X1: produc1466422861on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,X1))
    <=> ! [A_1: produc430140671on_val,B_1: produc430140671on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,produc1951691075on_val(A_1,B_1))) ) ).

tff(fact_73_split__paired__All,axiom,
    ! [Pa: fun_Pr693020585l_bool] :
      ( ! [X1: produc409205479on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,X1))
    <=> ! [A_1: produc12694297on_val,B_1: produc12694297on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,produc870913623on_val(A_1,B_1))) ) ).

tff(fact_74_split__paired__All,axiom,
    ! [Pa: fun_Pr903661919l_bool] :
      ( ! [X1: produc231486621on_val] : hBOOL(hAPP_P378063101l_bool(Pa,X1))
    <=> ! [A_1: produc1102272487on_val,B_1: produc1102272487on_val] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_1,B_1))) ) ).

tff(fact_75_split__paired__All,axiom,
    ! [Pa: fun_Pr691271849l_bool] :
      ( ! [X1: produc1102272487on_val] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
    <=> ! [A_1: produc124828825on_val,B_1: produc124828825on_val] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A_1,B_1))) ) ).

tff(fact_76_split__paired__All,axiom,
    ! [Pa: fun_Pr680585871l_bool] :
      ( ! [X1: produc124828825on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
    <=> ! [A_1: exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A_1,B_1))) ) ).

tff(fact_77_split__paired__All,axiom,
    ! [Pa: fun_Pr1696029455l_bool] :
      ( ! [X1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
    <=> ! [A_1: fun_na939144002on_val,B_1: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(Pa,produc899768717on_val(A_1,B_1))) ) ).

tff(fact_78_split__paired__All,axiom,
    ! [Pa: fun_Pr859510977l_bool] :
      ( ! [X1: produc430140671on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,X1))
    <=> ! [A_1: produc2061676504on_val,B_1: produc2061676504on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,produc1611380469on_val(A_1,B_1))) ) ).

tff(fact_79_split__paired__All,axiom,
    ! [Pa: fun_Pr248118298l_bool] :
      ( ! [X1: produc2061676504on_val] : hBOOL(hAPP_P71593144l_bool(Pa,X1))
    <=> ! [A_1: list_exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P71593144l_bool(Pa,produc379668296on_val(A_1,B_1))) ) ).

tff(fact_80_split__paired__All,axiom,
    ! [Pa: fun_Pr227936640r_bool] :
      ( ! [X1: produc1285161482t_char] : hBOOL(hAPP_P92196306r_bool(Pa,X1))
    <=> ! [A_1: list_list_char,B_1: produc220283002t_char] : hBOOL(hAPP_P92196306r_bool(Pa,produc921874948t_char(A_1,B_1))) ) ).

tff(fact_81_split__paired__All,axiom,
    ! [Pa: fun_Pr46158268r_bool] :
      ( ! [X1: produc220283002t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,X1))
    <=> ! [A_1: list_ty,B_1: produc662261637t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,produc1909267824t_char(A_1,B_1))) ) ).

tff(fact_82_split__paired__All,axiom,
    ! [Pa: fun_Pr827765831r_bool] :
      ( ! [X1: produc662261637t_char] : hBOOL(hAPP_P2118621157r_bool(Pa,X1))
    <=> ! [A_1: list_val,B_1: exp_list_char] : hBOOL(hAPP_P2118621157r_bool(Pa,produc1916172923t_char(A_1,B_1))) ) ).

tff(fact_83_split__paired__All,axiom,
    ! [Pa: fun_Pr252072522l_bool] :
      ( ! [X1: produc1645268488al_val] : hBOOL(hAPP_P943837928l_bool(Pa,X1))
    <=> ! [A_1: bop,B_1: product_prod_val_val] : hBOOL(hAPP_P943837928l_bool(Pa,produc621191550al_val(A_1,B_1))) ) ).

tff(fact_84_split__paired__All,axiom,
    ! [Pa: fun_Pr2081272681l_bool] :
      ( ! [X1: product_prod_val_val] : hBOOL(hAPP_P929938951l_bool(Pa,X1))
    <=> ! [A_1: val,B_1: val] : hBOOL(hAPP_P929938951l_bool(Pa,product_Pair_val_val(A_1,B_1))) ) ).

tff(fact_85_split__paired__All,axiom,
    ! [Pa: fun_Pr315804320l_bool] :
      ( ! [X1: produc639455274on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,X1))
    <=> ! [A_1: list_char,B_1: fun_Pr806764899on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,produc823076510on_val(A_1,B_1))) ) ).

tff(fact_86_split__paired__All,axiom,
    ! [Pa: fun_Pr565113489r_bool] :
      ( ! [X1: produc1278157519t_char] : hBOOL(hAPP_P449474095r_bool(Pa,X1))
    <=> ! [A_1: list_char,B_1: list_char] : hBOOL(hAPP_P449474095r_bool(Pa,produc5062597t_char(A_1,B_1))) ) ).

tff(fact_87_split__paired__All,axiom,
    ! [Pa: fun_Pr1336948301r_bool] :
      ( ! [X1: produc809539159t_char] : hBOOL(hAPP_P2014166431r_bool(Pa,X1))
    <=> ! [A_1: list_list_char,B_1: exp_list_char] : hBOOL(hAPP_P2014166431r_bool(Pa,produc1147572817t_char(A_1,B_1))) ) ).

tff(fact_88_Pair__eq,axiom,
    ! [A: list_char,B: produc917948472har_ty,A_3: list_char,B_4: produc917948472har_ty] :
      ( ( produc1002914035har_ty(A,B) = produc1002914035har_ty(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_89_Pair__eq,axiom,
    ! [A: produc1278157519t_char,B: ty,A_3: produc1278157519t_char,B_4: ty] :
      ( ( produc1265154397har_ty(A,B) = produc1265154397har_ty(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_90_Pair__eq,axiom,
    ! [A: list_char,B: ty,A_3: list_char,B_4: ty] :
      ( ( produc251930284har_ty(A,B) = produc251930284har_ty(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_91_Pair__eq,axiom,
    ! [A: produc809539159t_char,B: produc809539159t_char,A_3: produc809539159t_char,B_4: produc809539159t_char] :
      ( ( produc1897818327t_char(A,B) = produc1897818327t_char(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_92_Pair__eq,axiom,
    ! [A: produc1278157519t_char,B: produc1278157519t_char,A_3: produc1278157519t_char,B_4: produc1278157519t_char] :
      ( ( produc2080520419t_char(A,B) = produc2080520419t_char(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_93_Pair__eq,axiom,
    ! [A: produc639455274on_val,B: produc639455274on_val,A_3: produc639455274on_val,B_4: produc639455274on_val] :
      ( ( produc499151895on_val(A,B) = produc499151895on_val(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_94_Pair__eq,axiom,
    ! [A: product_prod_val_val,B: product_prod_val_val,A_3: product_prod_val_val,B_4: product_prod_val_val] :
      ( ( produc1244920211al_val(A,B) = produc1244920211al_val(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_95_Pair__eq,axiom,
    ! [A: produc1645268488al_val,B: produc1645268488al_val,A_3: produc1645268488al_val,B_4: produc1645268488al_val] :
      ( ( produc1924279125al_val(A,B) = produc1924279125al_val(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_96_Pair__eq,axiom,
    ! [A: produc662261637t_char,B: produc662261637t_char,A_3: produc662261637t_char,B_4: produc662261637t_char] :
      ( ( produc1299387215t_char(A,B) = produc1299387215t_char(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_97_Pair__eq,axiom,
    ! [A: produc220283002t_char,B: produc220283002t_char,A_3: produc220283002t_char,B_4: produc220283002t_char] :
      ( ( produc57279289t_char(A,B) = produc57279289t_char(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_98_Pair__eq,axiom,
    ! [A: produc1285161482t_char,B: produc1285161482t_char,A_3: produc1285161482t_char,B_4: produc1285161482t_char] :
      ( ( produc24551831t_char(A,B) = produc24551831t_char(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_99_Pair__eq,axiom,
    ! [A: produc430140671on_val,B: produc430140671on_val,A_3: produc430140671on_val,B_4: produc430140671on_val] :
      ( ( produc1951691075on_val(A,B) = produc1951691075on_val(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_100_Pair__eq,axiom,
    ! [A: produc12694297on_val,B: produc12694297on_val,A_3: produc12694297on_val,B_4: produc12694297on_val] :
      ( ( produc870913623on_val(A,B) = produc870913623on_val(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_101_Pair__eq,axiom,
    ! [A: produc1102272487on_val,B: produc1102272487on_val,A_3: produc1102272487on_val,B_4: produc1102272487on_val] :
      ( ( produc1564932627on_val(A,B) = produc1564932627on_val(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_102_Pair__eq,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,A_3: produc124828825on_val,B_4: produc124828825on_val] :
      ( ( produc1441475159on_val(A,B) = produc1441475159on_val(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_103_Pair__eq,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,A_3: exp_list_char,B_4: produc12694297on_val] :
      ( ( produc1259058957on_val(A,B) = produc1259058957on_val(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_104_Pair__eq,axiom,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,A_3: fun_na939144002on_val,B_4: fun_li1432931796on_val] :
      ( ( produc899768717on_val(A,B) = produc899768717on_val(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_105_Pair__eq,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,A_3: produc2061676504on_val,B_4: produc2061676504on_val] :
      ( ( produc1611380469on_val(A,B) = produc1611380469on_val(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_106_Pair__eq,axiom,
    ! [A: list_exp_list_char,B: produc12694297on_val,A_3: list_exp_list_char,B_4: produc12694297on_val] :
      ( ( produc379668296on_val(A,B) = produc379668296on_val(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_107_Pair__eq,axiom,
    ! [A: list_list_char,B: produc220283002t_char,A_3: list_list_char,B_4: produc220283002t_char] :
      ( ( produc921874948t_char(A,B) = produc921874948t_char(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_108_Pair__eq,axiom,
    ! [A: list_ty,B: produc662261637t_char,A_3: list_ty,B_4: produc662261637t_char] :
      ( ( produc1909267824t_char(A,B) = produc1909267824t_char(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_109_Pair__eq,axiom,
    ! [A: list_val,B: exp_list_char,A_3: list_val,B_4: exp_list_char] :
      ( ( produc1916172923t_char(A,B) = produc1916172923t_char(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_110_Pair__eq,axiom,
    ! [A: bop,B: product_prod_val_val,A_3: bop,B_4: product_prod_val_val] :
      ( ( produc621191550al_val(A,B) = produc621191550al_val(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_111_Pair__eq,axiom,
    ! [A: val,B: val,A_3: val,B_4: val] :
      ( ( product_Pair_val_val(A,B) = product_Pair_val_val(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_112_Pair__eq,axiom,
    ! [A: list_char,B: fun_Pr806764899on_val,A_3: list_char,B_4: fun_Pr806764899on_val] :
      ( ( produc823076510on_val(A,B) = produc823076510on_val(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_113_Pair__eq,axiom,
    ! [A: list_char,B: list_char,A_3: list_char,B_4: list_char] :
      ( ( produc5062597t_char(A,B) = produc5062597t_char(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_114_Pair__eq,axiom,
    ! [A: list_list_char,B: exp_list_char,A_3: list_list_char,B_4: exp_list_char] :
      ( ( produc1147572817t_char(A,B) = produc1147572817t_char(A_3,B_4) )
    <=> ( ( A = A_3 )
        & ( B = B_4 ) ) ) ).

tff(fact_115_Pair__inject,axiom,
    ! [A_78: list_char,B_3: produc917948472har_ty,A_77: list_char,B_2: produc917948472har_ty] :
      ( ( produc1002914035har_ty(A_78,B_3) = produc1002914035har_ty(A_77,B_2) )
     => ~ ( ( A_78 = A_77 )
         => ( B_3 != B_2 ) ) ) ).

tff(fact_116_Pair__inject,axiom,
    ! [A_78: produc1278157519t_char,B_3: ty,A_77: produc1278157519t_char,B_2: ty] :
      ( ( produc1265154397har_ty(A_78,B_3) = produc1265154397har_ty(A_77,B_2) )
     => ~ ( ( A_78 = A_77 )
         => ( B_3 != B_2 ) ) ) ).

tff(fact_117_Pair__inject,axiom,
    ! [A_78: list_char,B_3: ty,A_77: list_char,B_2: ty] :
      ( ( produc251930284har_ty(A_78,B_3) = produc251930284har_ty(A_77,B_2) )
     => ~ ( ( A_78 = A_77 )
         => ( B_3 != B_2 ) ) ) ).

tff(fact_118_Pair__inject,axiom,
    ! [A_78: produc809539159t_char,B_3: produc809539159t_char,A_77: produc809539159t_char,B_2: produc809539159t_char] :
      ( ( produc1897818327t_char(A_78,B_3) = produc1897818327t_char(A_77,B_2) )
     => ~ ( ( A_78 = A_77 )
         => ( B_3 != B_2 ) ) ) ).

tff(fact_119_Pair__inject,axiom,
    ! [A_78: produc1278157519t_char,B_3: produc1278157519t_char,A_77: produc1278157519t_char,B_2: produc1278157519t_char] :
      ( ( produc2080520419t_char(A_78,B_3) = produc2080520419t_char(A_77,B_2) )
     => ~ ( ( A_78 = A_77 )
         => ( B_3 != B_2 ) ) ) ).

tff(fact_120_Pair__inject,axiom,
    ! [A: produc639455274on_val,B: produc639455274on_val,A_3: produc639455274on_val,B_4: produc639455274on_val] :
      ( ( produc499151895on_val(A,B) = produc499151895on_val(A_3,B_4) )
     => ~ ( ( A = A_3 )
         => ( B != B_4 ) ) ) ).

tff(fact_121_Pair__inject,axiom,
    ! [A_78: product_prod_val_val,B_3: product_prod_val_val,A_77: product_prod_val_val,B_2: product_prod_val_val] :
      ( ( produc1244920211al_val(A_78,B_3) = produc1244920211al_val(A_77,B_2) )
     => ~ ( ( A_78 = A_77 )
         => ( B_3 != B_2 ) ) ) ).

tff(fact_122_Pair__inject,axiom,
    ! [A_78: produc1645268488al_val,B_3: produc1645268488al_val,A_77: produc1645268488al_val,B_2: produc1645268488al_val] :
      ( ( produc1924279125al_val(A_78,B_3) = produc1924279125al_val(A_77,B_2) )
     => ~ ( ( A_78 = A_77 )
         => ( B_3 != B_2 ) ) ) ).

tff(fact_123_Pair__inject,axiom,
    ! [A_78: produc662261637t_char,B_3: produc662261637t_char,A_77: produc662261637t_char,B_2: produc662261637t_char] :
      ( ( produc1299387215t_char(A_78,B_3) = produc1299387215t_char(A_77,B_2) )
     => ~ ( ( A_78 = A_77 )
         => ( B_3 != B_2 ) ) ) ).

tff(fact_124_Pair__inject,axiom,
    ! [A_78: produc220283002t_char,B_3: produc220283002t_char,A_77: produc220283002t_char,B_2: produc220283002t_char] :
      ( ( produc57279289t_char(A_78,B_3) = produc57279289t_char(A_77,B_2) )
     => ~ ( ( A_78 = A_77 )
         => ( B_3 != B_2 ) ) ) ).

tff(fact_125_Pair__inject,axiom,
    ! [A_78: produc1285161482t_char,B_3: produc1285161482t_char,A_77: produc1285161482t_char,B_2: produc1285161482t_char] :
      ( ( produc24551831t_char(A_78,B_3) = produc24551831t_char(A_77,B_2) )
     => ~ ( ( A_78 = A_77 )
         => ( B_3 != B_2 ) ) ) ).

tff(fact_126_Pair__inject,axiom,
    ! [A: produc430140671on_val,B: produc430140671on_val,A_3: produc430140671on_val,B_4: produc430140671on_val] :
      ( ( produc1951691075on_val(A,B) = produc1951691075on_val(A_3,B_4) )
     => ~ ( ( A = A_3 )
         => ( B != B_4 ) ) ) ).

tff(fact_127_Pair__inject,axiom,
    ! [A: produc12694297on_val,B: produc12694297on_val,A_3: produc12694297on_val,B_4: produc12694297on_val] :
      ( ( produc870913623on_val(A,B) = produc870913623on_val(A_3,B_4) )
     => ~ ( ( A = A_3 )
         => ( B != B_4 ) ) ) ).

tff(fact_128_Pair__inject,axiom,
    ! [A: produc1102272487on_val,B: produc1102272487on_val,A_3: produc1102272487on_val,B_4: produc1102272487on_val] :
      ( ( produc1564932627on_val(A,B) = produc1564932627on_val(A_3,B_4) )
     => ~ ( ( A = A_3 )
         => ( B != B_4 ) ) ) ).

tff(fact_129_Pair__inject,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,A_3: produc124828825on_val,B_4: produc124828825on_val] :
      ( ( produc1441475159on_val(A,B) = produc1441475159on_val(A_3,B_4) )
     => ~ ( ( A = A_3 )
         => ( B != B_4 ) ) ) ).

tff(fact_130_Pair__inject,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,A_3: exp_list_char,B_4: produc12694297on_val] :
      ( ( produc1259058957on_val(A,B) = produc1259058957on_val(A_3,B_4) )
     => ~ ( ( A = A_3 )
         => ( B != B_4 ) ) ) ).

tff(fact_131_Pair__inject,axiom,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,A_3: fun_na939144002on_val,B_4: fun_li1432931796on_val] :
      ( ( produc899768717on_val(A,B) = produc899768717on_val(A_3,B_4) )
     => ~ ( ( A = A_3 )
         => ( B != B_4 ) ) ) ).

tff(fact_132_Pair__inject,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,A_3: produc2061676504on_val,B_4: produc2061676504on_val] :
      ( ( produc1611380469on_val(A,B) = produc1611380469on_val(A_3,B_4) )
     => ~ ( ( A = A_3 )
         => ( B != B_4 ) ) ) ).

tff(fact_133_Pair__inject,axiom,
    ! [A: list_exp_list_char,B: produc12694297on_val,A_3: list_exp_list_char,B_4: produc12694297on_val] :
      ( ( produc379668296on_val(A,B) = produc379668296on_val(A_3,B_4) )
     => ~ ( ( A = A_3 )
         => ( B != B_4 ) ) ) ).

tff(fact_134_Pair__inject,axiom,
    ! [A_78: list_list_char,B_3: produc220283002t_char,A_77: list_list_char,B_2: produc220283002t_char] :
      ( ( produc921874948t_char(A_78,B_3) = produc921874948t_char(A_77,B_2) )
     => ~ ( ( A_78 = A_77 )
         => ( B_3 != B_2 ) ) ) ).

tff(fact_135_Pair__inject,axiom,
    ! [A_78: list_ty,B_3: produc662261637t_char,A_77: list_ty,B_2: produc662261637t_char] :
      ( ( produc1909267824t_char(A_78,B_3) = produc1909267824t_char(A_77,B_2) )
     => ~ ( ( A_78 = A_77 )
         => ( B_3 != B_2 ) ) ) ).

tff(fact_136_Pair__inject,axiom,
    ! [A_78: list_val,B_3: exp_list_char,A_77: list_val,B_2: exp_list_char] :
      ( ( produc1916172923t_char(A_78,B_3) = produc1916172923t_char(A_77,B_2) )
     => ~ ( ( A_78 = A_77 )
         => ( B_3 != B_2 ) ) ) ).

tff(fact_137_Pair__inject,axiom,
    ! [A_78: bop,B_3: product_prod_val_val,A_77: bop,B_2: product_prod_val_val] :
      ( ( produc621191550al_val(A_78,B_3) = produc621191550al_val(A_77,B_2) )
     => ~ ( ( A_78 = A_77 )
         => ( B_3 != B_2 ) ) ) ).

tff(fact_138_Pair__inject,axiom,
    ! [A_78: val,B_3: val,A_77: val,B_2: val] :
      ( ( product_Pair_val_val(A_78,B_3) = product_Pair_val_val(A_77,B_2) )
     => ~ ( ( A_78 = A_77 )
         => ( B_3 != B_2 ) ) ) ).

tff(fact_139_Pair__inject,axiom,
    ! [A: list_char,B: fun_Pr806764899on_val,A_3: list_char,B_4: fun_Pr806764899on_val] :
      ( ( produc823076510on_val(A,B) = produc823076510on_val(A_3,B_4) )
     => ~ ( ( A = A_3 )
         => ( B != B_4 ) ) ) ).

tff(fact_140_Pair__inject,axiom,
    ! [A_78: list_char,B_3: list_char,A_77: list_char,B_2: list_char] :
      ( ( produc5062597t_char(A_78,B_3) = produc5062597t_char(A_77,B_2) )
     => ~ ( ( A_78 = A_77 )
         => ( B_3 != B_2 ) ) ) ).

tff(fact_141_Pair__inject,axiom,
    ! [A_78: list_list_char,B_3: exp_list_char,A_77: list_list_char,B_2: exp_list_char] :
      ( ( produc1147572817t_char(A_78,B_3) = produc1147572817t_char(A_77,B_2) )
     => ~ ( ( A_78 = A_77 )
         => ( B_3 != B_2 ) ) ) ).

tff(fact_142_hext__refl,axiom,
    ! [Ha: fun_na939144002on_val] : hBOOL(hext(Ha,Ha)) ).

tff(fact_143_WTrt__hext__mono,axiom,
    ! [H_a: fun_na939144002on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),T_3))
     => ( hBOOL(hext(Ha,H_a))
       => hBOOL(hAPP_ty_bool(wTrt(Pa,H_a,E_1,Ea),T_3)) ) ) ).

tff(fact_144_red__lcl__add,axiom,
    ! [L_0: fun_li1432931796on_val,Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,La)),produc1259058957on_val(E_a,produc899768717on_val(H_a,L_a))),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,map_ad325961431ar_val(L_0,La))),produc1259058957on_val(E_a,produc899768717on_val(H_a,map_ad325961431ar_val(L_0,L_a)))),red(Pa))) ) ).

tff(fact_145_prod_Oexhaust,axiom,
    ! [Y_3: produc469582463har_ty] :
      ~ ! [A_1: list_char,B_1: produc917948472har_ty] : Y_3 != produc1002914035har_ty(A_1,B_1) ).

tff(fact_146_prod_Oexhaust,axiom,
    ! [Y_3: produc245756905har_ty] :
      ~ ! [A_1: produc1278157519t_char,B_1: ty] : Y_3 != produc1265154397har_ty(A_1,B_1) ).

tff(fact_147_prod_Oexhaust,axiom,
    ! [Y_3: produc917948472har_ty] :
      ~ ! [A_1: list_char,B_1: ty] : Y_3 != produc251930284har_ty(A_1,B_1) ).

tff(fact_148_prod_Oexhaust,axiom,
    ! [Y_3: produc1534059751t_char] :
      ~ ! [A_1: produc809539159t_char,B_1: produc809539159t_char] : Y_3 != produc1897818327t_char(A_1,B_1) ).

tff(fact_149_prod_Oexhaust,axiom,
    ! [Y_3: produc1350825965t_char] :
      ~ ! [A_1: produc1278157519t_char,B_1: produc1278157519t_char] : Y_3 != produc2080520419t_char(A_1,B_1) ).

tff(fact_150_prod_Oexhaust,axiom,
    ! [Y_1: produc87279271on_val] :
      ~ ! [A_1: produc639455274on_val,B_1: produc639455274on_val] : Y_1 != produc499151895on_val(A_1,B_1) ).

tff(fact_151_prod_Oexhaust,axiom,
    ! [Y_3: produc800118557al_val] :
      ~ ! [A_1: product_prod_val_val,B_1: product_prod_val_val] : Y_3 != produc1244920211al_val(A_1,B_1) ).

tff(fact_152_prod_Oexhaust,axiom,
    ! [Y_3: produc630464863al_val] :
      ~ ! [A_1: produc1645268488al_val,B_1: produc1645268488al_val] : Y_3 != produc1924279125al_val(A_1,B_1) ).

tff(fact_153_prod_Oexhaust,axiom,
    ! [Y_3: produc1826280281t_char] :
      ~ ! [A_1: produc662261637t_char,B_1: produc662261637t_char] : Y_3 != produc1299387215t_char(A_1,B_1) ).

tff(fact_154_prod_Oexhaust,axiom,
    ! [Y_3: produc1406897475t_char] :
      ~ ! [A_1: produc220283002t_char,B_1: produc220283002t_char] : Y_3 != produc57279289t_char(A_1,B_1) ).

tff(fact_155_prod_Oexhaust,axiom,
    ! [Y_3: produc349695911t_char] :
      ~ ! [A_1: produc1285161482t_char,B_1: produc1285161482t_char] : Y_3 != produc24551831t_char(A_1,B_1) ).

tff(fact_156_prod_Oexhaust,axiom,
    ! [Y_1: produc1466422861on_val] :
      ~ ! [A_1: produc430140671on_val,B_1: produc430140671on_val] : Y_1 != produc1951691075on_val(A_1,B_1) ).

tff(fact_157_prod_Oexhaust,axiom,
    ! [Y_1: produc409205479on_val] :
      ~ ! [A_1: produc12694297on_val,B_1: produc12694297on_val] : Y_1 != produc870913623on_val(A_1,B_1) ).

tff(fact_158_prod_Oexhaust,axiom,
    ! [Y_1: produc231486621on_val] :
      ~ ! [A_1: produc1102272487on_val,B_1: produc1102272487on_val] : Y_1 != produc1564932627on_val(A_1,B_1) ).

tff(fact_159_prod_Oexhaust,axiom,
    ! [Y_1: produc1102272487on_val] :
      ~ ! [A_1: produc124828825on_val,B_1: produc124828825on_val] : Y_1 != produc1441475159on_val(A_1,B_1) ).

tff(fact_160_prod_Oexhaust,axiom,
    ! [Y_1: produc124828825on_val] :
      ~ ! [A_1: exp_list_char,B_1: produc12694297on_val] : Y_1 != produc1259058957on_val(A_1,B_1) ).

tff(fact_161_prod_Oexhaust,axiom,
    ! [Y_1: produc12694297on_val] :
      ~ ! [A_1: fun_na939144002on_val,B_1: fun_li1432931796on_val] : Y_1 != produc899768717on_val(A_1,B_1) ).

tff(fact_162_prod_Oexhaust,axiom,
    ! [Y_1: produc430140671on_val] :
      ~ ! [A_1: produc2061676504on_val,B_1: produc2061676504on_val] : Y_1 != produc1611380469on_val(A_1,B_1) ).

tff(fact_163_prod_Oexhaust,axiom,
    ! [Y_1: produc2061676504on_val] :
      ~ ! [A_1: list_exp_list_char,B_1: produc12694297on_val] : Y_1 != produc379668296on_val(A_1,B_1) ).

tff(fact_164_prod_Oexhaust,axiom,
    ! [Y_3: produc1285161482t_char] :
      ~ ! [A_1: list_list_char,B_1: produc220283002t_char] : Y_3 != produc921874948t_char(A_1,B_1) ).

tff(fact_165_prod_Oexhaust,axiom,
    ! [Y_3: produc220283002t_char] :
      ~ ! [A_1: list_ty,B_1: produc662261637t_char] : Y_3 != produc1909267824t_char(A_1,B_1) ).

tff(fact_166_prod_Oexhaust,axiom,
    ! [Y_3: produc662261637t_char] :
      ~ ! [A_1: list_val,B_1: exp_list_char] : Y_3 != produc1916172923t_char(A_1,B_1) ).

tff(fact_167_prod_Oexhaust,axiom,
    ! [Y_3: produc1645268488al_val] :
      ~ ! [A_1: bop,B_1: product_prod_val_val] : Y_3 != produc621191550al_val(A_1,B_1) ).

tff(fact_168_prod_Oexhaust,axiom,
    ! [Y_3: product_prod_val_val] :
      ~ ! [A_1: val,B_1: val] : Y_3 != product_Pair_val_val(A_1,B_1) ).

tff(fact_169_prod_Oexhaust,axiom,
    ! [Y_1: produc639455274on_val] :
      ~ ! [A_1: list_char,B_1: fun_Pr806764899on_val] : Y_1 != produc823076510on_val(A_1,B_1) ).

tff(fact_170_prod_Oexhaust,axiom,
    ! [Y_3: produc1278157519t_char] :
      ~ ! [A_1: list_char,B_1: list_char] : Y_3 != produc5062597t_char(A_1,B_1) ).

tff(fact_171_prod_Oexhaust,axiom,
    ! [Y_3: produc809539159t_char] :
      ~ ! [A_1: list_list_char,B_1: exp_list_char] : Y_3 != produc1147572817t_char(A_1,B_1) ).

tff(fact_172_PairE,axiom,
    ! [P_2: produc469582463har_ty] :
      ~ ! [X_1: list_char,Y_2: produc917948472har_ty] : P_2 != produc1002914035har_ty(X_1,Y_2) ).

tff(fact_173_PairE,axiom,
    ! [P_2: produc245756905har_ty] :
      ~ ! [X_1: produc1278157519t_char,Y_2: ty] : P_2 != produc1265154397har_ty(X_1,Y_2) ).

tff(fact_174_PairE,axiom,
    ! [P_2: produc917948472har_ty] :
      ~ ! [X_1: list_char,Y_2: ty] : P_2 != produc251930284har_ty(X_1,Y_2) ).

tff(fact_175_PairE,axiom,
    ! [P_2: produc1534059751t_char] :
      ~ ! [X_1: produc809539159t_char,Y_2: produc809539159t_char] : P_2 != produc1897818327t_char(X_1,Y_2) ).

tff(fact_176_PairE,axiom,
    ! [P_2: produc1350825965t_char] :
      ~ ! [X_1: produc1278157519t_char,Y_2: produc1278157519t_char] : P_2 != produc2080520419t_char(X_1,Y_2) ).

tff(fact_177_PairE,axiom,
    ! [P_1: produc87279271on_val] :
      ~ ! [X_1: produc639455274on_val,Y_2: produc639455274on_val] : P_1 != produc499151895on_val(X_1,Y_2) ).

tff(fact_178_PairE,axiom,
    ! [P_2: produc800118557al_val] :
      ~ ! [X_1: product_prod_val_val,Y_2: product_prod_val_val] : P_2 != produc1244920211al_val(X_1,Y_2) ).

tff(fact_179_PairE,axiom,
    ! [P_2: produc630464863al_val] :
      ~ ! [X_1: produc1645268488al_val,Y_2: produc1645268488al_val] : P_2 != produc1924279125al_val(X_1,Y_2) ).

tff(fact_180_PairE,axiom,
    ! [P_2: produc1826280281t_char] :
      ~ ! [X_1: produc662261637t_char,Y_2: produc662261637t_char] : P_2 != produc1299387215t_char(X_1,Y_2) ).

tff(fact_181_PairE,axiom,
    ! [P_2: produc1406897475t_char] :
      ~ ! [X_1: produc220283002t_char,Y_2: produc220283002t_char] : P_2 != produc57279289t_char(X_1,Y_2) ).

tff(fact_182_PairE,axiom,
    ! [P_2: produc349695911t_char] :
      ~ ! [X_1: produc1285161482t_char,Y_2: produc1285161482t_char] : P_2 != produc24551831t_char(X_1,Y_2) ).

tff(fact_183_PairE,axiom,
    ! [P_1: produc1466422861on_val] :
      ~ ! [X_1: produc430140671on_val,Y_2: produc430140671on_val] : P_1 != produc1951691075on_val(X_1,Y_2) ).

tff(fact_184_PairE,axiom,
    ! [P_1: produc409205479on_val] :
      ~ ! [X_1: produc12694297on_val,Y_2: produc12694297on_val] : P_1 != produc870913623on_val(X_1,Y_2) ).

tff(fact_185_PairE,axiom,
    ! [P_1: produc231486621on_val] :
      ~ ! [X_1: produc1102272487on_val,Y_2: produc1102272487on_val] : P_1 != produc1564932627on_val(X_1,Y_2) ).

tff(fact_186_PairE,axiom,
    ! [P_1: produc1102272487on_val] :
      ~ ! [X_1: produc124828825on_val,Y_2: produc124828825on_val] : P_1 != produc1441475159on_val(X_1,Y_2) ).

tff(fact_187_PairE,axiom,
    ! [P_1: produc124828825on_val] :
      ~ ! [X_1: exp_list_char,Y_2: produc12694297on_val] : P_1 != produc1259058957on_val(X_1,Y_2) ).

tff(fact_188_PairE,axiom,
    ! [P_1: produc12694297on_val] :
      ~ ! [X_1: fun_na939144002on_val,Y_2: fun_li1432931796on_val] : P_1 != produc899768717on_val(X_1,Y_2) ).

tff(fact_189_PairE,axiom,
    ! [P_1: produc430140671on_val] :
      ~ ! [X_1: produc2061676504on_val,Y_2: produc2061676504on_val] : P_1 != produc1611380469on_val(X_1,Y_2) ).

tff(fact_190_PairE,axiom,
    ! [P_1: produc2061676504on_val] :
      ~ ! [X_1: list_exp_list_char,Y_2: produc12694297on_val] : P_1 != produc379668296on_val(X_1,Y_2) ).

tff(fact_191_PairE,axiom,
    ! [P_2: produc1285161482t_char] :
      ~ ! [X_1: list_list_char,Y_2: produc220283002t_char] : P_2 != produc921874948t_char(X_1,Y_2) ).

tff(fact_192_PairE,axiom,
    ! [P_2: produc220283002t_char] :
      ~ ! [X_1: list_ty,Y_2: produc662261637t_char] : P_2 != produc1909267824t_char(X_1,Y_2) ).

tff(fact_193_PairE,axiom,
    ! [P_2: produc662261637t_char] :
      ~ ! [X_1: list_val,Y_2: exp_list_char] : P_2 != produc1916172923t_char(X_1,Y_2) ).

tff(fact_194_PairE,axiom,
    ! [P_2: produc1645268488al_val] :
      ~ ! [X_1: bop,Y_2: product_prod_val_val] : P_2 != produc621191550al_val(X_1,Y_2) ).

tff(fact_195_PairE,axiom,
    ! [P_2: product_prod_val_val] :
      ~ ! [X_1: val,Y_2: val] : P_2 != product_Pair_val_val(X_1,Y_2) ).

tff(fact_196_PairE,axiom,
    ! [P_1: produc639455274on_val] :
      ~ ! [X_1: list_char,Y_2: fun_Pr806764899on_val] : P_1 != produc823076510on_val(X_1,Y_2) ).

tff(fact_197_PairE,axiom,
    ! [P_2: produc1278157519t_char] :
      ~ ! [X_1: list_char,Y_2: list_char] : P_2 != produc5062597t_char(X_1,Y_2) ).

tff(fact_198_PairE,axiom,
    ! [P_2: produc809539159t_char] :
      ~ ! [X_1: list_list_char,Y_2: exp_list_char] : P_2 != produc1147572817t_char(X_1,Y_2) ).

tff(fact_199_split__paired__Ex,axiom,
    ! [Pa: fun_Pr758558581y_bool] :
      ( ? [X1: produc469582463har_ty] : hBOOL(hAPP_P831231943y_bool(Pa,X1))
    <=> ? [A_1: list_char,B_1: produc917948472har_ty] : hBOOL(hAPP_P831231943y_bool(Pa,produc1002914035har_ty(A_1,B_1))) ) ).

tff(fact_200_split__paired__Ex,axiom,
    ! [Pa: fun_Pr2102567903y_bool] :
      ( ? [X1: produc245756905har_ty] : hBOOL(hAPP_P27757617y_bool(Pa,X1))
    <=> ? [A_1: produc1278157519t_char,B_1: ty] : hBOOL(hAPP_P27757617y_bool(Pa,produc1265154397har_ty(A_1,B_1))) ) ).

tff(fact_201_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1127025070y_bool] :
      ( ? [X1: produc917948472har_ty] : hBOOL(hAPP_P748443392y_bool(Pa,X1))
    <=> ? [A_1: list_char,B_1: ty] : hBOOL(hAPP_P748443392y_bool(Pa,produc251930284har_ty(A_1,B_1))) ) ).

tff(fact_202_split__paired__Ex,axiom,
    ! [Pa: fun_Pr908866473r_bool] :
      ( ? [X1: produc1534059751t_char] : hBOOL(hAPP_P1002912327r_bool(Pa,X1))
    <=> ? [A_1: produc809539159t_char,B_1: produc809539159t_char] : hBOOL(hAPP_P1002912327r_bool(Pa,produc1897818327t_char(A_1,B_1))) ) ).

tff(fact_203_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1336847023r_bool] :
      ( ? [X1: produc1350825965t_char] : hBOOL(hAPP_P2010574925r_bool(Pa,X1))
    <=> ? [A_1: produc1278157519t_char,B_1: produc1278157519t_char] : hBOOL(hAPP_P2010574925r_bool(Pa,produc2080520419t_char(A_1,B_1))) ) ).

tff(fact_204_split__paired__Ex,axiom,
    ! [Pa: fun_Pr235369833l_bool] :
      ( ? [X1: produc87279271on_val] : hBOOL(hAPP_P124632071l_bool(Pa,X1))
    <=> ? [A_1: produc639455274on_val,B_1: produc639455274on_val] : hBOOL(hAPP_P124632071l_bool(Pa,produc499151895on_val(A_1,B_1))) ) ).

tff(fact_205_split__paired__Ex,axiom,
    ! [Pa: fun_Pr832147423l_bool] :
      ( ? [X1: produc800118557al_val] : hBOOL(hAPP_P2123002749l_bool(Pa,X1))
    <=> ? [A_1: product_prod_val_val,B_1: product_prod_val_val] : hBOOL(hAPP_P2123002749l_bool(Pa,produc1244920211al_val(A_1,B_1))) ) ).

tff(fact_206_split__paired__Ex,axiom,
    ! [Pa: fun_Pr897334561l_bool] :
      ( ? [X1: produc630464863al_val] : hBOOL(hAPP_P738987199l_bool(Pa,X1))
    <=> ? [A_1: produc1645268488al_val,B_1: produc1645268488al_val] : hBOOL(hAPP_P738987199l_bool(Pa,produc1924279125al_val(A_1,B_1))) ) ).

tff(fact_207_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1890037787r_bool] :
      ( ? [X1: produc1826280281t_char] : hBOOL(hAPP_P1183499705r_bool(Pa,X1))
    <=> ? [A_1: produc662261637t_char,B_1: produc662261637t_char] : hBOOL(hAPP_P1183499705r_bool(Pa,produc1299387215t_char(A_1,B_1))) ) ).

tff(fact_208_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1728267013r_bool] :
      ( ? [X1: produc1406897475t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,X1))
    <=> ? [A_1: produc220283002t_char,B_1: produc220283002t_char] : hBOOL(hAPP_P1240100515r_bool(Pa,produc57279289t_char(A_1,B_1))) ) ).

tff(fact_209_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1895638121r_bool] :
      ( ? [X1: produc349695911t_char] : hBOOL(hAPP_P824029447r_bool(Pa,X1))
    <=> ? [A_1: produc1285161482t_char,B_1: produc1285161482t_char] : hBOOL(hAPP_P824029447r_bool(Pa,produc24551831t_char(A_1,B_1))) ) ).

tff(fact_210_split__paired__Ex,axiom,
    ! [Pa: fun_Pr302334223l_bool] :
      ( ? [X1: produc1466422861on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,X1))
    <=> ? [A_1: produc430140671on_val,B_1: produc430140671on_val] : hBOOL(hAPP_P2028072621l_bool(Pa,produc1951691075on_val(A_1,B_1))) ) ).

tff(fact_211_split__paired__Ex,axiom,
    ! [Pa: fun_Pr693020585l_bool] :
      ( ? [X1: produc409205479on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,X1))
    <=> ? [A_1: produc12694297on_val,B_1: produc12694297on_val] : hBOOL(hAPP_P1221872711l_bool(Pa,produc870913623on_val(A_1,B_1))) ) ).

tff(fact_212_split__paired__Ex,axiom,
    ! [Pa: fun_Pr903661919l_bool] :
      ( ? [X1: produc231486621on_val] : hBOOL(hAPP_P378063101l_bool(Pa,X1))
    <=> ? [A_1: produc1102272487on_val,B_1: produc1102272487on_val] : hBOOL(hAPP_P378063101l_bool(Pa,produc1564932627on_val(A_1,B_1))) ) ).

tff(fact_213_split__paired__Ex,axiom,
    ! [Pa: fun_Pr691271849l_bool] :
      ( ? [X1: produc1102272487on_val] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
    <=> ? [A_1: produc124828825on_val,B_1: produc124828825on_val] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A_1,B_1))) ) ).

tff(fact_214_split__paired__Ex,axiom,
    ! [Pa: fun_Pr680585871l_bool] :
      ( ? [X1: produc124828825on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
    <=> ? [A_1: exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A_1,B_1))) ) ).

tff(fact_215_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1696029455l_bool] :
      ( ? [X1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
    <=> ? [A_1: fun_na939144002on_val,B_1: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(Pa,produc899768717on_val(A_1,B_1))) ) ).

tff(fact_216_split__paired__Ex,axiom,
    ! [Pa: fun_Pr859510977l_bool] :
      ( ? [X1: produc430140671on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,X1))
    <=> ? [A_1: produc2061676504on_val,B_1: produc2061676504on_val] : hBOOL(hAPP_P1333315679l_bool(Pa,produc1611380469on_val(A_1,B_1))) ) ).

tff(fact_217_split__paired__Ex,axiom,
    ! [Pa: fun_Pr248118298l_bool] :
      ( ? [X1: produc2061676504on_val] : hBOOL(hAPP_P71593144l_bool(Pa,X1))
    <=> ? [A_1: list_exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P71593144l_bool(Pa,produc379668296on_val(A_1,B_1))) ) ).

tff(fact_218_split__paired__Ex,axiom,
    ! [Pa: fun_Pr227936640r_bool] :
      ( ? [X1: produc1285161482t_char] : hBOOL(hAPP_P92196306r_bool(Pa,X1))
    <=> ? [A_1: list_list_char,B_1: produc220283002t_char] : hBOOL(hAPP_P92196306r_bool(Pa,produc921874948t_char(A_1,B_1))) ) ).

tff(fact_219_split__paired__Ex,axiom,
    ! [Pa: fun_Pr46158268r_bool] :
      ( ? [X1: produc220283002t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,X1))
    <=> ? [A_1: list_ty,B_1: produc662261637t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,produc1909267824t_char(A_1,B_1))) ) ).

tff(fact_220_split__paired__Ex,axiom,
    ! [Pa: fun_Pr827765831r_bool] :
      ( ? [X1: produc662261637t_char] : hBOOL(hAPP_P2118621157r_bool(Pa,X1))
    <=> ? [A_1: list_val,B_1: exp_list_char] : hBOOL(hAPP_P2118621157r_bool(Pa,produc1916172923t_char(A_1,B_1))) ) ).

tff(fact_221_split__paired__Ex,axiom,
    ! [Pa: fun_Pr252072522l_bool] :
      ( ? [X1: produc1645268488al_val] : hBOOL(hAPP_P943837928l_bool(Pa,X1))
    <=> ? [A_1: bop,B_1: product_prod_val_val] : hBOOL(hAPP_P943837928l_bool(Pa,produc621191550al_val(A_1,B_1))) ) ).

tff(fact_222_split__paired__Ex,axiom,
    ! [Pa: fun_Pr2081272681l_bool] :
      ( ? [X1: product_prod_val_val] : hBOOL(hAPP_P929938951l_bool(Pa,X1))
    <=> ? [A_1: val,B_1: val] : hBOOL(hAPP_P929938951l_bool(Pa,product_Pair_val_val(A_1,B_1))) ) ).

tff(fact_223_split__paired__Ex,axiom,
    ! [Pa: fun_Pr315804320l_bool] :
      ( ? [X1: produc639455274on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,X1))
    <=> ? [A_1: list_char,B_1: fun_Pr806764899on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,produc823076510on_val(A_1,B_1))) ) ).

tff(fact_224_split__paired__Ex,axiom,
    ! [Pa: fun_Pr565113489r_bool] :
      ( ? [X1: produc1278157519t_char] : hBOOL(hAPP_P449474095r_bool(Pa,X1))
    <=> ? [A_1: list_char,B_1: list_char] : hBOOL(hAPP_P449474095r_bool(Pa,produc5062597t_char(A_1,B_1))) ) ).

tff(fact_225_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1336948301r_bool] :
      ( ? [X1: produc809539159t_char] : hBOOL(hAPP_P2014166431r_bool(Pa,X1))
    <=> ? [A_1: list_list_char,B_1: exp_list_char] : hBOOL(hAPP_P2014166431r_bool(Pa,produc1147572817t_char(A_1,B_1))) ) ).

tff(fact_226_hext__trans,axiom,
    ! [H_4: fun_na939144002on_val,Ha: fun_na939144002on_val,H_a: fun_na939144002on_val] :
      ( hBOOL(hext(Ha,H_a))
     => ( hBOOL(hext(H_a,H_4))
       => hBOOL(hext(Ha,H_4)) ) ) ).

tff(fact_227_curryI,axiom,
    ! [F_1: fun_Pr758558581y_bool,A: list_char,B: produc917948472har_ty] :
      ( hBOOL(hAPP_P831231943y_bool(F_1,produc1002914035har_ty(A,B)))
     => hBOOL(hAPP_P748443392y_bool(hAPP_l1665608433y_bool(produc166740340y_bool(F_1),A),B)) ) ).

tff(fact_228_curryI,axiom,
    ! [F_1: fun_Pr2102567903y_bool,A: produc1278157519t_char,B: ty] :
      ( hBOOL(hAPP_P27757617y_bool(F_1,produc1265154397har_ty(A,B)))
     => hBOOL(hAPP_ty_bool(hAPP_P1845004857y_bool(produc1215659230y_bool(F_1),A),B)) ) ).

tff(fact_229_curryI,axiom,
    ! [F_1: fun_Pr1127025070y_bool,A: list_char,B: ty] :
      ( hBOOL(hAPP_P748443392y_bool(F_1,produc251930284har_ty(A,B)))
     => hBOOL(hAPP_ty_bool(hAPP_l1734756650y_bool(produc2091768109y_bool(F_1),A),B)) ) ).

tff(fact_230_curryI,axiom,
    ! [F_1: fun_Pr908866473r_bool,A: produc809539159t_char,B: produc809539159t_char] :
      ( hBOOL(hAPP_P1002912327r_bool(F_1,produc1897818327t_char(A,B)))
     => hBOOL(hAPP_P2014166431r_bool(hAPP_P1939418767r_bool(produc1295142846r_bool(F_1),A),B)) ) ).

tff(fact_231_curryI,axiom,
    ! [F_1: fun_Pr1336847023r_bool,A: produc1278157519t_char,B: produc1278157519t_char] :
      ( hBOOL(hAPP_P2010574925r_bool(F_1,produc2080520419t_char(A,B)))
     => hBOOL(hAPP_P449474095r_bool(hAPP_P663876415r_bool(produc715708746r_bool(F_1),A),B)) ) ).

tff(fact_232_curryI,axiom,
    ! [F_1: fun_Pr235369833l_bool,A: produc639455274on_val,B: produc639455274on_val] :
      ( hBOOL(hAPP_P124632071l_bool(F_1,produc499151895on_val(A,B)))
     => hBOOL(hAPP_P1235399154l_bool(hAPP_P416784693l_bool(produc1996970750l_bool(F_1),A),B)) ) ).

tff(fact_233_curryI,axiom,
    ! [F_1: fun_Pr832147423l_bool,A: product_prod_val_val,B: product_prod_val_val] :
      ( hBOOL(hAPP_P2123002749l_bool(F_1,produc1244920211al_val(A,B)))
     => hBOOL(hAPP_P929938951l_bool(hAPP_P1815899455l_bool(produc1034940666l_bool(F_1),A),B)) ) ).

tff(fact_234_curryI,axiom,
    ! [F_1: fun_Pr897334561l_bool,A: produc1645268488al_val,B: produc1645268488al_val] :
      ( hBOOL(hAPP_P738987199l_bool(F_1,produc1924279125al_val(A,B)))
     => hBOOL(hAPP_P943837928l_bool(hAPP_P323054207l_bool(produc1969754044l_bool(F_1),A),B)) ) ).

tff(fact_235_curryI,axiom,
    ! [F_1: fun_Pr1890037787r_bool,A: produc662261637t_char,B: produc662261637t_char] :
      ( hBOOL(hAPP_P1183499705r_bool(F_1,produc1299387215t_char(A,B)))
     => hBOOL(hAPP_P2118621157r_bool(hAPP_P357098431r_bool(produc1535899062r_bool(F_1),A),B)) ) ).

tff(fact_236_curryI,axiom,
    ! [F_1: fun_Pr1728267013r_bool,A: produc220283002t_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P1240100515r_bool(F_1,produc57279289t_char(A,B)))
     => hBOOL(hAPP_P1907982426r_bool(hAPP_P1214880255r_bool(produc1268552608r_bool(F_1),A),B)) ) ).

tff(fact_237_curryI,axiom,
    ! [F_1: fun_Pr1895638121r_bool,A: produc1285161482t_char,B: produc1285161482t_char] :
      ( hBOOL(hAPP_P824029447r_bool(F_1,produc24551831t_char(A,B)))
     => hBOOL(hAPP_P92196306r_bool(hAPP_P1928969845r_bool(produc17861502r_bool(F_1),A),B)) ) ).

tff(fact_238_curryI,axiom,
    ! [F_1: fun_Pr302334223l_bool,A: produc430140671on_val,B: produc430140671on_val] :
      ( hBOOL(hAPP_P2028072621l_bool(F_1,produc1951691075on_val(A,B)))
     => hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(produc971707818l_bool(F_1),A),B)) ) ).

tff(fact_239_curryI,axiom,
    ! [F_1: fun_Pr693020585l_bool,A: produc12694297on_val,B: produc12694297on_val] :
      ( hBOOL(hAPP_P1221872711l_bool(F_1,produc870913623on_val(A,B)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(produc1073654846l_bool(F_1),A),B)) ) ).

tff(fact_240_curryI,axiom,
    ! [F_1: fun_Pr903661919l_bool,A: produc1102272487on_val,B: produc1102272487on_val] :
      ( hBOOL(hAPP_P378063101l_bool(F_1,produc1564932627on_val(A,B)))
     => hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(produc1497005946l_bool(F_1),A),B)) ) ).

tff(fact_241_curryI,axiom,
    ! [F_1: fun_Pr691271849l_bool,A: produc124828825on_val,B: produc124828825on_val] :
      ( hBOOL(hAPP_P282169671l_bool(F_1,produc1441475159on_val(A,B)))
     => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F_1),A),B)) ) ).

tff(fact_242_curryI,axiom,
    ! [F_1: fun_Pr680585871l_bool,A: exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P1708370145l_bool(F_1,produc1259058957on_val(A,B)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F_1),A),B)) ) ).

tff(fact_243_curryI,axiom,
    ! [F_1: fun_Pr1696029455l_bool,A: fun_na939144002on_val,B: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(F_1,produc899768717on_val(A,B)))
     => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F_1),A),B)) ) ).

tff(fact_244_curryI,axiom,
    ! [F_1: fun_Pr859510977l_bool,A: produc2061676504on_val,B: produc2061676504on_val] :
      ( hBOOL(hAPP_P1333315679l_bool(F_1,produc1611380469on_val(A,B)))
     => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(produc2053127004l_bool(F_1),A),B)) ) ).

tff(fact_245_curryI,axiom,
    ! [F_1: fun_Pr248118298l_bool,A: list_exp_list_char,B: produc12694297on_val] :
      ( hBOOL(hAPP_P71593144l_bool(F_1,produc379668296on_val(A,B)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(produc1838470831l_bool(F_1),A),B)) ) ).

tff(fact_246_curryI,axiom,
    ! [F_1: fun_Pr227936640r_bool,A: list_list_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P92196306r_bool(F_1,produc921874948t_char(A,B)))
     => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F_1),A),B)) ) ).

tff(fact_247_curryI,axiom,
    ! [F_1: fun_Pr46158268r_bool,A: list_ty,B: produc662261637t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(F_1,produc1909267824t_char(A,B)))
     => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F_1),A),B)) ) ).

tff(fact_248_curryI,axiom,
    ! [F_1: fun_Pr827765831r_bool,A: list_val,B: exp_list_char] :
      ( hBOOL(hAPP_P2118621157r_bool(F_1,produc1916172923t_char(A,B)))
     => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F_1),A),B)) ) ).

tff(fact_249_curryI,axiom,
    ! [F_1: fun_Pr252072522l_bool,A: bop,B: product_prod_val_val] :
      ( hBOOL(hAPP_P943837928l_bool(F_1,produc621191550al_val(A,B)))
     => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(produc1555310053l_bool(F_1),A),B)) ) ).

tff(fact_250_curryI,axiom,
    ! [F_1: fun_Pr2081272681l_bool,A: val,B: val] :
      ( hBOOL(hAPP_P929938951l_bool(F_1,product_Pair_val_val(A,B)))
     => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(produc886919678l_bool(F_1),A),B)) ) ).

tff(fact_251_curryI,axiom,
    ! [F_1: fun_Pr315804320l_bool,A: list_char,B: fun_Pr806764899on_val] :
      ( hBOOL(hAPP_P1235399154l_bool(F_1,produc823076510on_val(A,B)))
     => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F_1),A),B)) ) ).

tff(fact_252_curryI,axiom,
    ! [F_1: fun_Pr565113489r_bool,A: list_char,B: list_char] :
      ( hBOOL(hAPP_P449474095r_bool(F_1,produc5062597t_char(A,B)))
     => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(produc95371820r_bool(F_1),A),B)) ) ).

tff(fact_253_curryI,axiom,
    ! [F_1: fun_Pr1336948301r_bool,A: list_list_char,B: exp_list_char] :
      ( hBOOL(hAPP_P2014166431r_bool(F_1,produc1147572817t_char(A,B)))
     => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(produc288369490r_bool(F_1),A),B)) ) ).

tff(fact_254_reds__hext__incr,axiom,
    ! [Esa: list_exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,Es_a: list_exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Esa,produc899768717on_val(Ha,La)),produc379668296on_val(Es_a,produc899768717on_val(H_a,L_a))),reds(Pa)))
     => hBOOL(hext(Ha,H_a)) ) ).

tff(fact_255_red__reds_OTryRed,axiom,
    ! [C: list_char,V: list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(tryCatch_list_char(Ea,C,V,E_2),S_1),produc1259058957on_val(tryCatch_list_char(E_a,C,V,E_2),S)),red(Pa))) ) ).

tff(fact_256_curryD,axiom,
    ! [F_1: fun_Pr758558581y_bool,A: list_char,B: produc917948472har_ty] :
      ( hBOOL(hAPP_P748443392y_bool(hAPP_l1665608433y_bool(produc166740340y_bool(F_1),A),B))
     => hBOOL(hAPP_P831231943y_bool(F_1,produc1002914035har_ty(A,B))) ) ).

tff(fact_257_curryD,axiom,
    ! [F_1: fun_Pr2102567903y_bool,A: produc1278157519t_char,B: ty] :
      ( hBOOL(hAPP_ty_bool(hAPP_P1845004857y_bool(produc1215659230y_bool(F_1),A),B))
     => hBOOL(hAPP_P27757617y_bool(F_1,produc1265154397har_ty(A,B))) ) ).

tff(fact_258_curryD,axiom,
    ! [F_1: fun_Pr1127025070y_bool,A: list_char,B: ty] :
      ( hBOOL(hAPP_ty_bool(hAPP_l1734756650y_bool(produc2091768109y_bool(F_1),A),B))
     => hBOOL(hAPP_P748443392y_bool(F_1,produc251930284har_ty(A,B))) ) ).

tff(fact_259_curryD,axiom,
    ! [F_1: fun_Pr908866473r_bool,A: produc809539159t_char,B: produc809539159t_char] :
      ( hBOOL(hAPP_P2014166431r_bool(hAPP_P1939418767r_bool(produc1295142846r_bool(F_1),A),B))
     => hBOOL(hAPP_P1002912327r_bool(F_1,produc1897818327t_char(A,B))) ) ).

tff(fact_260_curryD,axiom,
    ! [F_1: fun_Pr1336847023r_bool,A: produc1278157519t_char,B: produc1278157519t_char] :
      ( hBOOL(hAPP_P449474095r_bool(hAPP_P663876415r_bool(produc715708746r_bool(F_1),A),B))
     => hBOOL(hAPP_P2010574925r_bool(F_1,produc2080520419t_char(A,B))) ) ).

tff(fact_261_curryD,axiom,
    ! [F_1: fun_Pr235369833l_bool,A: produc639455274on_val,B: produc639455274on_val] :
      ( hBOOL(hAPP_P1235399154l_bool(hAPP_P416784693l_bool(produc1996970750l_bool(F_1),A),B))
     => hBOOL(hAPP_P124632071l_bool(F_1,produc499151895on_val(A,B))) ) ).

tff(fact_262_curryD,axiom,
    ! [F_1: fun_Pr832147423l_bool,A: product_prod_val_val,B: product_prod_val_val] :
      ( hBOOL(hAPP_P929938951l_bool(hAPP_P1815899455l_bool(produc1034940666l_bool(F_1),A),B))
     => hBOOL(hAPP_P2123002749l_bool(F_1,produc1244920211al_val(A,B))) ) ).

tff(fact_263_curryD,axiom,
    ! [F_1: fun_Pr897334561l_bool,A: produc1645268488al_val,B: produc1645268488al_val] :
      ( hBOOL(hAPP_P943837928l_bool(hAPP_P323054207l_bool(produc1969754044l_bool(F_1),A),B))
     => hBOOL(hAPP_P738987199l_bool(F_1,produc1924279125al_val(A,B))) ) ).

tff(fact_264_curryD,axiom,
    ! [F_1: fun_Pr1890037787r_bool,A: produc662261637t_char,B: produc662261637t_char] :
      ( hBOOL(hAPP_P2118621157r_bool(hAPP_P357098431r_bool(produc1535899062r_bool(F_1),A),B))
     => hBOOL(hAPP_P1183499705r_bool(F_1,produc1299387215t_char(A,B))) ) ).

tff(fact_265_curryD,axiom,
    ! [F_1: fun_Pr1728267013r_bool,A: produc220283002t_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(hAPP_P1214880255r_bool(produc1268552608r_bool(F_1),A),B))
     => hBOOL(hAPP_P1240100515r_bool(F_1,produc57279289t_char(A,B))) ) ).

tff(fact_266_curryD,axiom,
    ! [F_1: fun_Pr1895638121r_bool,A: produc1285161482t_char,B: produc1285161482t_char] :
      ( hBOOL(hAPP_P92196306r_bool(hAPP_P1928969845r_bool(produc17861502r_bool(F_1),A),B))
     => hBOOL(hAPP_P824029447r_bool(F_1,produc24551831t_char(A,B))) ) ).

tff(fact_267_curryD,axiom,
    ! [F_1: fun_Pr302334223l_bool,A: produc430140671on_val,B: produc430140671on_val] :
      ( hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(produc971707818l_bool(F_1),A),B))
     => hBOOL(hAPP_P2028072621l_bool(F_1,produc1951691075on_val(A,B))) ) ).

tff(fact_268_curryD,axiom,
    ! [F_1: fun_Pr693020585l_bool,A: produc12694297on_val,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(produc1073654846l_bool(F_1),A),B))
     => hBOOL(hAPP_P1221872711l_bool(F_1,produc870913623on_val(A,B))) ) ).

tff(fact_269_curryD,axiom,
    ! [F_1: fun_Pr903661919l_bool,A: produc1102272487on_val,B: produc1102272487on_val] :
      ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(produc1497005946l_bool(F_1),A),B))
     => hBOOL(hAPP_P378063101l_bool(F_1,produc1564932627on_val(A,B))) ) ).

tff(fact_270_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,produc1441475159on_val(A,B))) ) ).

tff(fact_271_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,produc1259058957on_val(A,B))) ) ).

tff(fact_272_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,produc899768717on_val(A,B))) ) ).

tff(fact_273_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,produc1611380469on_val(A,B))) ) ).

tff(fact_274_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,produc379668296on_val(A,B))) ) ).

tff(fact_275_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,produc921874948t_char(A,B))) ) ).

tff(fact_276_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,produc1909267824t_char(A,B))) ) ).

tff(fact_277_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,produc1916172923t_char(A,B))) ) ).

tff(fact_278_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,produc621191550al_val(A,B))) ) ).

tff(fact_279_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,product_Pair_val_val(A,B))) ) ).

tff(fact_280_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,produc823076510on_val(A,B))) ) ).

tff(fact_281_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,produc5062597t_char(A,B))) ) ).

tff(fact_282_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,produc1147572817t_char(A,B))) ) ).

tff(fact_283_curryE,axiom,
    ! [F_1: fun_Pr758558581y_bool,A: list_char,B: produc917948472har_ty] :
      ( hBOOL(hAPP_P748443392y_bool(hAPP_l1665608433y_bool(produc166740340y_bool(F_1),A),B))
     => hBOOL(hAPP_P831231943y_bool(F_1,produc1002914035har_ty(A,B))) ) ).

tff(fact_284_curryE,axiom,
    ! [F_1: fun_Pr2102567903y_bool,A: produc1278157519t_char,B: ty] :
      ( hBOOL(hAPP_ty_bool(hAPP_P1845004857y_bool(produc1215659230y_bool(F_1),A),B))
     => hBOOL(hAPP_P27757617y_bool(F_1,produc1265154397har_ty(A,B))) ) ).

tff(fact_285_curryE,axiom,
    ! [F_1: fun_Pr1127025070y_bool,A: list_char,B: ty] :
      ( hBOOL(hAPP_ty_bool(hAPP_l1734756650y_bool(produc2091768109y_bool(F_1),A),B))
     => hBOOL(hAPP_P748443392y_bool(F_1,produc251930284har_ty(A,B))) ) ).

tff(fact_286_curryE,axiom,
    ! [F_1: fun_Pr908866473r_bool,A: produc809539159t_char,B: produc809539159t_char] :
      ( hBOOL(hAPP_P2014166431r_bool(hAPP_P1939418767r_bool(produc1295142846r_bool(F_1),A),B))
     => hBOOL(hAPP_P1002912327r_bool(F_1,produc1897818327t_char(A,B))) ) ).

tff(fact_287_curryE,axiom,
    ! [F_1: fun_Pr1336847023r_bool,A: produc1278157519t_char,B: produc1278157519t_char] :
      ( hBOOL(hAPP_P449474095r_bool(hAPP_P663876415r_bool(produc715708746r_bool(F_1),A),B))
     => hBOOL(hAPP_P2010574925r_bool(F_1,produc2080520419t_char(A,B))) ) ).

tff(fact_288_curryE,axiom,
    ! [F_1: fun_Pr235369833l_bool,A: produc639455274on_val,B: produc639455274on_val] :
      ( hBOOL(hAPP_P1235399154l_bool(hAPP_P416784693l_bool(produc1996970750l_bool(F_1),A),B))
     => hBOOL(hAPP_P124632071l_bool(F_1,produc499151895on_val(A,B))) ) ).

tff(fact_289_curryE,axiom,
    ! [F_1: fun_Pr832147423l_bool,A: product_prod_val_val,B: product_prod_val_val] :
      ( hBOOL(hAPP_P929938951l_bool(hAPP_P1815899455l_bool(produc1034940666l_bool(F_1),A),B))
     => hBOOL(hAPP_P2123002749l_bool(F_1,produc1244920211al_val(A,B))) ) ).

tff(fact_290_curryE,axiom,
    ! [F_1: fun_Pr897334561l_bool,A: produc1645268488al_val,B: produc1645268488al_val] :
      ( hBOOL(hAPP_P943837928l_bool(hAPP_P323054207l_bool(produc1969754044l_bool(F_1),A),B))
     => hBOOL(hAPP_P738987199l_bool(F_1,produc1924279125al_val(A,B))) ) ).

tff(fact_291_curryE,axiom,
    ! [F_1: fun_Pr1890037787r_bool,A: produc662261637t_char,B: produc662261637t_char] :
      ( hBOOL(hAPP_P2118621157r_bool(hAPP_P357098431r_bool(produc1535899062r_bool(F_1),A),B))
     => hBOOL(hAPP_P1183499705r_bool(F_1,produc1299387215t_char(A,B))) ) ).

tff(fact_292_curryE,axiom,
    ! [F_1: fun_Pr1728267013r_bool,A: produc220283002t_char,B: produc220283002t_char] :
      ( hBOOL(hAPP_P1907982426r_bool(hAPP_P1214880255r_bool(produc1268552608r_bool(F_1),A),B))
     => hBOOL(hAPP_P1240100515r_bool(F_1,produc57279289t_char(A,B))) ) ).

tff(fact_293_curryE,axiom,
    ! [F_1: fun_Pr1895638121r_bool,A: produc1285161482t_char,B: produc1285161482t_char] :
      ( hBOOL(hAPP_P92196306r_bool(hAPP_P1928969845r_bool(produc17861502r_bool(F_1),A),B))
     => hBOOL(hAPP_P824029447r_bool(F_1,produc24551831t_char(A,B))) ) ).

tff(fact_294_curryE,axiom,
    ! [F_1: fun_Pr302334223l_bool,A: produc430140671on_val,B: produc430140671on_val] :
      ( hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(produc971707818l_bool(F_1),A),B))
     => hBOOL(hAPP_P2028072621l_bool(F_1,produc1951691075on_val(A,B))) ) ).

tff(fact_295_curryE,axiom,
    ! [F_1: fun_Pr693020585l_bool,A: produc12694297on_val,B: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(produc1073654846l_bool(F_1),A),B))
     => hBOOL(hAPP_P1221872711l_bool(F_1,produc870913623on_val(A,B))) ) ).

tff(fact_296_curryE,axiom,
    ! [F_1: fun_Pr903661919l_bool,A: produc1102272487on_val,B: produc1102272487on_val] :
      ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(produc1497005946l_bool(F_1),A),B))
     => hBOOL(hAPP_P378063101l_bool(F_1,produc1564932627on_val(A,B))) ) ).

tff(fact_297_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,produc1441475159on_val(A,B))) ) ).

tff(fact_298_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,produc1259058957on_val(A,B))) ) ).

tff(fact_299_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,produc899768717on_val(A,B))) ) ).

tff(fact_300_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,produc1611380469on_val(A,B))) ) ).

tff(fact_301_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,produc379668296on_val(A,B))) ) ).

tff(fact_302_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,produc921874948t_char(A,B))) ) ).

tff(fact_303_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,produc1909267824t_char(A,B))) ) ).

tff(fact_304_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,produc1916172923t_char(A,B))) ) ).

tff(fact_305_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,produc621191550al_val(A,B))) ) ).

tff(fact_306_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,product_Pair_val_val(A,B))) ) ).

tff(fact_307_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,produc823076510on_val(A,B))) ) ).

tff(fact_308_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,produc5062597t_char(A,B))) ) ).

tff(fact_309_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,produc1147572817t_char(A,B))) ) ).

tff(fact_310_curry__conv,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,produc1441475159on_val(A,B))) ) ).

tff(fact_311_curry__conv,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,produc1259058957on_val(A,B))) ) ).

tff(fact_312_curry__conv,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,produc899768717on_val(A,B))) ) ).

tff(fact_313_curry__conv,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,produc1611380469on_val(A,B))) ) ).

tff(fact_314_curry__conv,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,produc379668296on_val(A,B))) ) ).

tff(fact_315_curry__conv,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,produc921874948t_char(A,B))) ) ).

tff(fact_316_curry__conv,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,produc1909267824t_char(A,B))) ) ).

tff(fact_317_curry__conv,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,produc1916172923t_char(A,B))) ) ).

tff(fact_318_curry__conv,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,produc621191550al_val(A,B))) ) ).

tff(fact_319_curry__conv,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,product_Pair_val_val(A,B))) ) ).

tff(fact_320_curry__conv,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,produc823076510on_val(A,B))) ) ).

tff(fact_321_curry__conv,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,produc5062597t_char(A,B))) ) ).

tff(fact_322_curry__conv,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,produc1147572817t_char(A,B))) ) ).

tff(fact_323_red__reds_OListRed1,axiom,
    ! [Esa: list_exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(cons_exp_list_char(Ea,Esa),S_1),produc379668296on_val(cons_exp_list_char(E_a,Esa),S)),reds(Pa))) ) ).

tff(fact_324_Red__lcl__add,axiom,
    ! [L_0: fun_li1432931796on_val,Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,La)),produc1259058957on_val(E_a,produc899768717on_val(H_a,L_a))),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,map_ad325961431ar_val(L_0,La))),produc1259058957on_val(E_a,produc899768717on_val(H_a,map_ad325961431ar_val(L_0,L_a)))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_325_red__reds_ORedTry,axiom,
    ! [V_1: val,C: list_char,V: list_char,E_2: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(tryCatch_list_char(hAPP_v834067052t_char(val_list_char,V_1),C,V,E_2),S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),S_1)),red(Pa))) ).

tff(fact_326_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_327_exp_Osimps_I15_J,axiom,
    ! [Exp1_81: exp_list_char,List_3: list_char,A: list_char,Exp2_81: exp_list_char,Exp1_80: exp_list_char,List_2: list_char,A_3: list_char,Exp2_80: exp_list_char] :
      ( ( tryCatch_list_char(Exp1_81,List_3,A,Exp2_81) = tryCatch_list_char(Exp1_80,List_2,A_3,Exp2_80) )
    <=> ( ( Exp1_81 = Exp1_80 )
        & ( List_3 = List_2 )
        & ( A = A_3 )
        & ( Exp2_81 = Exp2_80 ) ) ) ).

tff(fact_328_red__reds_OFAccRed,axiom,
    ! [F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAcc_list_char(Ea,F,D),S_1),produc1259058957on_val(fAcc_list_char(E_a,F,D),S)),red(Pa))) ) ).

tff(fact_329_red__reds_OCastRed,axiom,
    ! [C: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cast_list_char(C,Ea),S_1),produc1259058957on_val(cast_list_char(C,E_a),S)),red(Pa))) ) ).

tff(fact_330_red__reds_OCondRed,axiom,
    ! [E_1_1: exp_list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cond_list_char(Ea,E_1_1,E_2),S_1),produc1259058957on_val(cond_list_char(E_a,E_1_1,E_2),S)),red(Pa))) ) ).

tff(fact_331_red__reds_OCallParams,axiom,
    ! [V_1: val,M: list_char,Esa: list_exp_list_char,S_1: produc12694297on_val,Es_a: list_exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Esa,S_1),produc379668296on_val(Es_a,S)),reds(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(call_list_char(hAPP_v834067052t_char(val_list_char,V_1),M,Esa),S_1),produc1259058957on_val(call_list_char(hAPP_v834067052t_char(val_list_char,V_1),M,Es_a),S)),red(Pa))) ) ).

tff(fact_332_red__reds_OBinOpRed1,axiom,
    ! [Bop: bop,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(binOp_list_char(Ea,Bop,E_2),S_1),produc1259058957on_val(binOp_list_char(E_a,Bop,E_2),S)),red(Pa))) ) ).

tff(fact_333_red__reds_OCallObj,axiom,
    ! [M: list_char,Esa: list_exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(call_list_char(Ea,M,Esa),S_1),produc1259058957on_val(call_list_char(E_a,M,Esa),S)),red(Pa))) ) ).

tff(fact_334_exp_Osimps_I45_J,axiom,
    ! [Val_25: val,List_51: list_char,Exp_145: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_25) != cast_list_char(List_51,Exp_145) ).

tff(fact_335_exp_Osimps_I80_J,axiom,
    ! [Val_24: val,Exp_144: exp_list_char,List1_73: list_char,List2_73: list_exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_24) != call_list_char(Exp_144,List1_73,List2_73) ).

tff(fact_336_exp_Osimps_I86_J,axiom,
    ! [Val_23: val,Exp1_145: exp_list_char,Exp2_145: exp_list_char,Exp3_25: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_23) != cond_list_char(Exp1_145,Exp2_145,Exp3_25) ).

tff(fact_337_exp_Osimps_I76_J,axiom,
    ! [Val_22: val,Exp_143: exp_list_char,List1_72: list_char,List2_72: list_char] : hAPP_v834067052t_char(val_list_char,Val_22) != fAcc_list_char(Exp_143,List1_72,List2_72) ).

tff(fact_338_exp_Osimps_I70_J,axiom,
    ! [Val_21: val,Exp1_144: exp_list_char,Bop_25: bop,Exp2_144: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_21) != binOp_list_char(Exp1_144,Bop_25,Exp2_144) ).

tff(fact_339_exp_Osimps_I44_J,axiom,
    ! [List_50: list_char,Exp_142: exp_list_char,Val_20: val] : cast_list_char(List_50,Exp_142) != hAPP_v834067052t_char(val_list_char,Val_20) ).

tff(fact_340_exp_Osimps_I56_J,axiom,
    ! [List_49: list_char,Exp_141: exp_list_char,Exp_140: exp_list_char,List1_71: list_char,List2_71: list_exp_list_char] : cast_list_char(List_49,Exp_141) != call_list_char(Exp_140,List1_71,List2_71) ).

tff(fact_341_exp_Osimps_I62_J,axiom,
    ! [List_48: list_char,Exp_139: exp_list_char,Exp1_143: exp_list_char,Exp2_143: exp_list_char,Exp3_24: exp_list_char] : cast_list_char(List_48,Exp_139) != cond_list_char(Exp1_143,Exp2_143,Exp3_24) ).

tff(fact_342_exp_Osimps_I52_J,axiom,
    ! [List_47: list_char,Exp_138: exp_list_char,Exp_137: exp_list_char,List1_70: list_char,List2_70: list_char] : cast_list_char(List_47,Exp_138) != fAcc_list_char(Exp_137,List1_70,List2_70) ).

tff(fact_343_exp_Osimps_I46_J,axiom,
    ! [List_46: list_char,Exp_136: exp_list_char,Exp1_142: exp_list_char,Bop_24: bop,Exp2_142: exp_list_char] : cast_list_char(List_46,Exp_136) != binOp_list_char(Exp1_142,Bop_24,Exp2_142) ).

tff(fact_344_exp_Osimps_I81_J,axiom,
    ! [Exp_135: exp_list_char,List1_69: list_char,List2_69: list_exp_list_char,Val_19: val] : call_list_char(Exp_135,List1_69,List2_69) != hAPP_v834067052t_char(val_list_char,Val_19) ).

tff(fact_345_exp_Osimps_I87_J,axiom,
    ! [Exp1_141: exp_list_char,Exp2_141: exp_list_char,Exp3_23: exp_list_char,Val_18: val] : cond_list_char(Exp1_141,Exp2_141,Exp3_23) != hAPP_v834067052t_char(val_list_char,Val_18) ).

tff(fact_346_exp_Osimps_I77_J,axiom,
    ! [Exp_134: exp_list_char,List1_68: list_char,List2_68: list_char,Val_17: val] : fAcc_list_char(Exp_134,List1_68,List2_68) != hAPP_v834067052t_char(val_list_char,Val_17) ).

tff(fact_347_exp_Osimps_I71_J,axiom,
    ! [Exp1_140: exp_list_char,Bop_23: bop,Exp2_140: exp_list_char,Val_16: val] : binOp_list_char(Exp1_140,Bop_23,Exp2_140) != hAPP_v834067052t_char(val_list_char,Val_16) ).

tff(fact_348_exp_Osimps_I57_J,axiom,
    ! [Exp_133: exp_list_char,List1_67: list_char,List2_67: list_exp_list_char,List_45: list_char,Exp_132: exp_list_char] : call_list_char(Exp_133,List1_67,List2_67) != cast_list_char(List_45,Exp_132) ).

tff(fact_349_exp_Osimps_I63_J,axiom,
    ! [Exp1_139: exp_list_char,Exp2_139: exp_list_char,Exp3_22: exp_list_char,List_44: list_char,Exp_131: exp_list_char] : cond_list_char(Exp1_139,Exp2_139,Exp3_22) != cast_list_char(List_44,Exp_131) ).

tff(fact_350_exp_Osimps_I53_J,axiom,
    ! [Exp_130: exp_list_char,List1_66: list_char,List2_66: list_char,List_43: list_char,Exp_129: exp_list_char] : fAcc_list_char(Exp_130,List1_66,List2_66) != cast_list_char(List_43,Exp_129) ).

tff(fact_351_exp_Osimps_I47_J,axiom,
    ! [Exp1_138: exp_list_char,Bop_22: bop,Exp2_138: exp_list_char,List_42: list_char,Exp_128: exp_list_char] : binOp_list_char(Exp1_138,Bop_22,Exp2_138) != cast_list_char(List_42,Exp_128) ).

tff(fact_352_exp_Osimps_I188_J,axiom,
    ! [Exp_127: exp_list_char,List1_65: list_char,List2_65: list_exp_list_char,Exp1_137: exp_list_char,Exp2_137: exp_list_char,Exp3_21: exp_list_char] : call_list_char(Exp_127,List1_65,List2_65) != cond_list_char(Exp1_137,Exp2_137,Exp3_21) ).

tff(fact_353_exp_Osimps_I157_J,axiom,
    ! [Exp_126: exp_list_char,List1_64: list_char,List2_64: list_exp_list_char,Exp_125: exp_list_char,List1_63: list_char,List2_63: list_char] : call_list_char(Exp_126,List1_64,List2_64) != fAcc_list_char(Exp_125,List1_63,List2_63) ).

tff(fact_354_exp_Osimps_I103_J,axiom,
    ! [Exp_124: exp_list_char,List1_62: list_char,List2_62: list_exp_list_char,Exp1_136: exp_list_char,Bop_21: bop,Exp2_136: exp_list_char] : call_list_char(Exp_124,List1_62,List2_62) != binOp_list_char(Exp1_136,Bop_21,Exp2_136) ).

tff(fact_355_exp_Osimps_I189_J,axiom,
    ! [Exp1_135: exp_list_char,Exp2_135: exp_list_char,Exp3_20: exp_list_char,Exp_123: exp_list_char,List1_61: list_char,List2_61: list_exp_list_char] : cond_list_char(Exp1_135,Exp2_135,Exp3_20) != call_list_char(Exp_123,List1_61,List2_61) ).

tff(fact_356_exp_Osimps_I163_J,axiom,
    ! [Exp1_134: exp_list_char,Exp2_134: exp_list_char,Exp3_19: exp_list_char,Exp_122: exp_list_char,List1_60: list_char,List2_60: list_char] : cond_list_char(Exp1_134,Exp2_134,Exp3_19) != fAcc_list_char(Exp_122,List1_60,List2_60) ).

tff(fact_357_exp_Osimps_I109_J,axiom,
    ! [Exp1_133: exp_list_char,Exp2_133: exp_list_char,Exp3_18: exp_list_char,Exp1_132: exp_list_char,Bop_20: bop,Exp2_132: exp_list_char] : cond_list_char(Exp1_133,Exp2_133,Exp3_18) != binOp_list_char(Exp1_132,Bop_20,Exp2_132) ).

tff(fact_358_exp_Osimps_I156_J,axiom,
    ! [Exp_121: exp_list_char,List1_59: list_char,List2_59: list_char,Exp_120: exp_list_char,List1_58: list_char,List2_58: list_exp_list_char] : fAcc_list_char(Exp_121,List1_59,List2_59) != call_list_char(Exp_120,List1_58,List2_58) ).

tff(fact_359_exp_Osimps_I162_J,axiom,
    ! [Exp_119: exp_list_char,List1_57: list_char,List2_57: list_char,Exp1_131: exp_list_char,Exp2_131: exp_list_char,Exp3_17: exp_list_char] : fAcc_list_char(Exp_119,List1_57,List2_57) != cond_list_char(Exp1_131,Exp2_131,Exp3_17) ).

tff(fact_360_exp_Osimps_I99_J,axiom,
    ! [Exp_118: exp_list_char,List1_56: list_char,List2_56: list_char,Exp1_130: exp_list_char,Bop_19: bop,Exp2_130: exp_list_char] : fAcc_list_char(Exp_118,List1_56,List2_56) != binOp_list_char(Exp1_130,Bop_19,Exp2_130) ).

tff(fact_361_exp_Osimps_I102_J,axiom,
    ! [Exp1_129: exp_list_char,Bop_18: bop,Exp2_129: exp_list_char,Exp_117: exp_list_char,List1_55: list_char,List2_55: list_exp_list_char] : binOp_list_char(Exp1_129,Bop_18,Exp2_129) != call_list_char(Exp_117,List1_55,List2_55) ).

tff(fact_362_exp_Osimps_I108_J,axiom,
    ! [Exp1_128: exp_list_char,Bop_17: bop,Exp2_128: exp_list_char,Exp1_127: exp_list_char,Exp2_127: exp_list_char,Exp3_16: exp_list_char] : binOp_list_char(Exp1_128,Bop_17,Exp2_128) != cond_list_char(Exp1_127,Exp2_127,Exp3_16) ).

tff(fact_363_exp_Osimps_I98_J,axiom,
    ! [Exp1_126: exp_list_char,Bop_16: bop,Exp2_126: exp_list_char,Exp_116: exp_list_char,List1_54: list_char,List2_54: list_char] : binOp_list_char(Exp1_126,Bop_16,Exp2_126) != fAcc_list_char(Exp_116,List1_54,List2_54) ).

tff(fact_364_exp_Osimps_I3_J,axiom,
    ! [Val_15: val,Val_14: val] :
      ( ( hAPP_v834067052t_char(val_list_char,Val_15) = hAPP_v834067052t_char(val_list_char,Val_14) )
    <=> ( Val_15 = Val_14 ) ) ).

tff(fact_365_exp_Osimps_I2_J,axiom,
    ! [List_3: list_char,Exp_35: exp_list_char,List_2: list_char,Exp_34: exp_list_char] :
      ( ( cast_list_char(List_3,Exp_35) = cast_list_char(List_2,Exp_34) )
    <=> ( ( List_3 = List_2 )
        & ( Exp_35 = Exp_34 ) ) ) ).

tff(fact_366_exp_Osimps_I9_J,axiom,
    ! [Exp_35: exp_list_char,List1_41: list_char,List2_41: list_exp_list_char,Exp_34: exp_list_char,List1_40: list_char,List2_40: list_exp_list_char] :
      ( ( call_list_char(Exp_35,List1_41,List2_41) = call_list_char(Exp_34,List1_40,List2_40) )
    <=> ( ( Exp_35 = Exp_34 )
        & ( List1_41 = List1_40 )
        & ( List2_41 = List2_40 ) ) ) ).

tff(fact_367_exp_Osimps_I12_J,axiom,
    ! [Exp1_81: exp_list_char,Exp2_81: exp_list_char,Exp3_15: exp_list_char,Exp1_80: exp_list_char,Exp2_80: exp_list_char,Exp3_14: exp_list_char] :
      ( ( cond_list_char(Exp1_81,Exp2_81,Exp3_15) = cond_list_char(Exp1_80,Exp2_80,Exp3_14) )
    <=> ( ( Exp1_81 = Exp1_80 )
        & ( Exp2_81 = Exp2_80 )
        & ( Exp3_15 = Exp3_14 ) ) ) ).

tff(fact_368_exp_Osimps_I7_J,axiom,
    ! [Exp_35: exp_list_char,List1_41: list_char,List2_41: list_char,Exp_34: exp_list_char,List1_40: list_char,List2_40: list_char] :
      ( ( fAcc_list_char(Exp_35,List1_41,List2_41) = fAcc_list_char(Exp_34,List1_40,List2_40) )
    <=> ( ( Exp_35 = Exp_34 )
        & ( List1_41 = List1_40 )
        & ( List2_41 = List2_40 ) ) ) ).

tff(fact_369_exp_Osimps_I4_J,axiom,
    ! [Exp1_81: exp_list_char,Bop: bop,Exp2_81: exp_list_char,Exp1_80: exp_list_char,Bop_15: bop,Exp2_80: exp_list_char] :
      ( ( binOp_list_char(Exp1_81,Bop,Exp2_81) = binOp_list_char(Exp1_80,Bop_15,Exp2_80) )
    <=> ( ( Exp1_81 = Exp1_80 )
        & ( Bop = Bop_15 )
        & ( Exp2_81 = Exp2_80 ) ) ) ).

tff(fact_370_exp_Osimps_I92_J,axiom,
    ! [Val_13: val,Exp1_125: exp_list_char,List_41: list_char,A_76: list_char,Exp2_125: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_13) != tryCatch_list_char(Exp1_125,List_41,A_76,Exp2_125) ).

tff(fact_371_mem__def,axiom,
    ! [X_2: produc917948472har_ty,A_75: fun_Pr1127025070y_bool] :
      ( hBOOL(member503779467har_ty(X_2,A_75))
    <=> hBOOL(hAPP_P748443392y_bool(A_75,X_2)) ) ).

tff(fact_372_mem__def,axiom,
    ! [X_2: produc245756905har_ty,A_75: fun_Pr2102567903y_bool] :
      ( hBOOL(member1783291580har_ty(X_2,A_75))
    <=> hBOOL(hAPP_P27757617y_bool(A_75,X_2)) ) ).

tff(fact_373_mem__def,axiom,
    ! [X_2: product_prod_val_val,A_75: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(X_2,A_75))
    <=> hBOOL(hAPP_P929938951l_bool(A_75,X_2)) ) ).

tff(fact_374_mem__def,axiom,
    ! [X_2: produc1534059751t_char,A_75: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(X_2,A_75))
    <=> hBOOL(hAPP_P1002912327r_bool(A_75,X_2)) ) ).

tff(fact_375_mem__def,axiom,
    ! [X_2: produc1350825965t_char,A_75: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(X_2,A_75))
    <=> hBOOL(hAPP_P2010574925r_bool(A_75,X_2)) ) ).

tff(fact_376_mem__def,axiom,
    ! [X_2: produc87279271on_val,A_75: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(X_2,A_75))
    <=> hBOOL(hAPP_P124632071l_bool(A_75,X_2)) ) ).

tff(fact_377_mem__def,axiom,
    ! [X_2: produc800118557al_val,A_75: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(X_2,A_75))
    <=> hBOOL(hAPP_P2123002749l_bool(A_75,X_2)) ) ).

tff(fact_378_mem__def,axiom,
    ! [X_2: produc630464863al_val,A_75: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(X_2,A_75))
    <=> hBOOL(hAPP_P738987199l_bool(A_75,X_2)) ) ).

tff(fact_379_mem__def,axiom,
    ! [X_2: produc1826280281t_char,A_75: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(X_2,A_75))
    <=> hBOOL(hAPP_P1183499705r_bool(A_75,X_2)) ) ).

tff(fact_380_mem__def,axiom,
    ! [X_2: produc1406897475t_char,A_75: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(X_2,A_75))
    <=> hBOOL(hAPP_P1240100515r_bool(A_75,X_2)) ) ).

tff(fact_381_mem__def,axiom,
    ! [X_2: produc349695911t_char,A_75: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(X_2,A_75))
    <=> hBOOL(hAPP_P824029447r_bool(A_75,X_2)) ) ).

tff(fact_382_mem__def,axiom,
    ! [X_2: produc1466422861on_val,A_75: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(X_2,A_75))
    <=> hBOOL(hAPP_P2028072621l_bool(A_75,X_2)) ) ).

tff(fact_383_mem__def,axiom,
    ! [X_2: produc409205479on_val,A_75: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(X_2,A_75))
    <=> hBOOL(hAPP_P1221872711l_bool(A_75,X_2)) ) ).

tff(fact_384_mem__def,axiom,
    ! [X_2: produc231486621on_val,A_75: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(X_2,A_75))
    <=> hBOOL(hAPP_P378063101l_bool(A_75,X_2)) ) ).

tff(fact_385_mem__def,axiom,
    ! [X_2: produc1102272487on_val,A_75: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(X_2,A_75))
    <=> hBOOL(hAPP_P282169671l_bool(A_75,X_2)) ) ).

tff(fact_386_mem__def,axiom,
    ! [X_2: produc430140671on_val,A_75: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(X_2,A_75))
    <=> hBOOL(hAPP_P1333315679l_bool(A_75,X_2)) ) ).

tff(fact_387_mem__def,axiom,
    ! [X_2: produc1278157519t_char,A_75: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(X_2,A_75))
    <=> hBOOL(hAPP_P449474095r_bool(A_75,X_2)) ) ).

tff(fact_388_mem__def,axiom,
    ! [X_2: list_char,A_75: fun_list_char_bool] :
      ( hBOOL(member_list_char(X_2,A_75))
    <=> hBOOL(hAPP_list_char_bool(A_75,X_2)) ) ).

tff(fact_389_mem__def,axiom,
    ! [X_2: nat,A_75: fun_nat_bool] :
      ( hBOOL(member_nat(X_2,A_75))
    <=> hBOOL(hAPP_nat_bool(A_75,X_2)) ) ).

tff(fact_390_Collect__def,axiom,
    ! [Pa: fun_ty_bool] : collect_ty(Pa) = Pa ).

tff(fact_391_exp_Osimps_I93_J,axiom,
    ! [Exp1_124: exp_list_char,List_40: list_char,A_74: list_char,Exp2_124: exp_list_char,Val_12: val] : tryCatch_list_char(Exp1_124,List_40,A_74,Exp2_124) != hAPP_v834067052t_char(val_list_char,Val_12) ).

tff(fact_392_exp_Osimps_I68_J,axiom,
    ! [List_39: list_char,Exp_115: exp_list_char,Exp1_123: exp_list_char,List_38: list_char,A_73: list_char,Exp2_123: exp_list_char] : cast_list_char(List_39,Exp_115) != tryCatch_list_char(Exp1_123,List_38,A_73,Exp2_123) ).

tff(fact_393_exp_Osimps_I194_J,axiom,
    ! [Exp_114: exp_list_char,List1_53: list_char,List2_53: list_exp_list_char,Exp1_122: exp_list_char,List_37: list_char,A_72: list_char,Exp2_122: exp_list_char] : call_list_char(Exp_114,List1_53,List2_53) != tryCatch_list_char(Exp1_122,List_37,A_72,Exp2_122) ).

tff(fact_394_exp_Osimps_I218_J,axiom,
    ! [Exp1_121: exp_list_char,Exp2_121: exp_list_char,Exp3_13: exp_list_char,Exp1_120: exp_list_char,List_36: list_char,A_71: list_char,Exp2_120: exp_list_char] : cond_list_char(Exp1_121,Exp2_121,Exp3_13) != tryCatch_list_char(Exp1_120,List_36,A_71,Exp2_120) ).

tff(fact_395_exp_Osimps_I168_J,axiom,
    ! [Exp_113: exp_list_char,List1_52: list_char,List2_52: list_char,Exp1_119: exp_list_char,List_35: list_char,A_70: list_char,Exp2_119: exp_list_char] : fAcc_list_char(Exp_113,List1_52,List2_52) != tryCatch_list_char(Exp1_119,List_35,A_70,Exp2_119) ).

tff(fact_396_exp_Osimps_I114_J,axiom,
    ! [Exp1_118: exp_list_char,Bop_14: bop,Exp2_118: exp_list_char,Exp1_117: exp_list_char,List_34: list_char,A_69: list_char,Exp2_117: exp_list_char] : binOp_list_char(Exp1_118,Bop_14,Exp2_118) != tryCatch_list_char(Exp1_117,List_34,A_69,Exp2_117) ).

tff(fact_397_exp_Osimps_I69_J,axiom,
    ! [Exp1_116: exp_list_char,List_33: list_char,A_68: list_char,Exp2_116: exp_list_char,List_32: list_char,Exp_112: exp_list_char] : tryCatch_list_char(Exp1_116,List_33,A_68,Exp2_116) != cast_list_char(List_32,Exp_112) ).

tff(fact_398_exp_Osimps_I195_J,axiom,
    ! [Exp1_115: exp_list_char,List_31: list_char,A_67: list_char,Exp2_115: exp_list_char,Exp_111: exp_list_char,List1_51: list_char,List2_51: list_exp_list_char] : tryCatch_list_char(Exp1_115,List_31,A_67,Exp2_115) != call_list_char(Exp_111,List1_51,List2_51) ).

tff(fact_399_exp_Osimps_I219_J,axiom,
    ! [Exp1_114: exp_list_char,List_30: list_char,A_66: list_char,Exp2_114: exp_list_char,Exp1_113: exp_list_char,Exp2_113: exp_list_char,Exp3_12: exp_list_char] : tryCatch_list_char(Exp1_114,List_30,A_66,Exp2_114) != cond_list_char(Exp1_113,Exp2_113,Exp3_12) ).

tff(fact_400_exp_Osimps_I169_J,axiom,
    ! [Exp1_112: exp_list_char,List_29: list_char,A_65: list_char,Exp2_112: exp_list_char,Exp_110: exp_list_char,List1_50: list_char,List2_50: list_char] : tryCatch_list_char(Exp1_112,List_29,A_65,Exp2_112) != fAcc_list_char(Exp_110,List1_50,List2_50) ).

tff(fact_401_exp_Osimps_I115_J,axiom,
    ! [Exp1_111: exp_list_char,List_28: list_char,A_64: list_char,Exp2_111: exp_list_char,Exp1_110: exp_list_char,Bop_13: bop,Exp2_110: exp_list_char] : tryCatch_list_char(Exp1_111,List_28,A_64,Exp2_111) != binOp_list_char(Exp1_110,Bop_13,Exp2_110) ).

tff(fact_402_red__reds_OBinOpRed2,axiom,
    ! [V_1_1: val,Bop: bop,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_1),Bop,Ea),S_1),produc1259058957on_val(binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_1),Bop,E_a),S)),red(Pa))) ) ).

tff(fact_403_red__reds_OListRed2,axiom,
    ! [V_1: val,Esa: list_exp_list_char,S_1: produc12694297on_val,Es_a: list_exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Esa,S_1),produc379668296on_val(Es_a,S)),reds(Pa)))
     => hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Esa),S_1),produc379668296on_val(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Es_a),S)),reds(Pa))) ) ).

tff(fact_404_TryRedsVal,axiom,
    ! [C: list_char,V: list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,V_1: val,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(tryCatch_list_char(Ea,C,V,E_2),S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_405_BinOp2Reds,axiom,
    ! [V_1: val,Bop: bop,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Bop,Ea),S_1),produc1259058957on_val(binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Bop,E_a),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_406_TryReds,axiom,
    ! [C: list_char,V: list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(tryCatch_list_char(Ea,C,V,E_2),S_1),produc1259058957on_val(tryCatch_list_char(E_a,C,V,E_2),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_407_FAccReds,axiom,
    ! [F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAcc_list_char(Ea,F,D),S_1),produc1259058957on_val(fAcc_list_char(E_a,F,D),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_408_CondReds,axiom,
    ! [E_1_1: exp_list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cond_list_char(Ea,E_1_1,E_2),S_1),produc1259058957on_val(cond_list_char(E_a,E_1_1,E_2),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_409_CastReds,axiom,
    ! [C: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cast_list_char(C,Ea),S_1),produc1259058957on_val(cast_list_char(C,E_a),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_410_BinOp1Reds,axiom,
    ! [Bop: bop,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(binOp_list_char(Ea,Bop,E_2),S_1),produc1259058957on_val(binOp_list_char(E_a,Bop,E_2),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_411_CallRedsObj,axiom,
    ! [M: list_char,Esa: list_exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(call_list_char(Ea,M,Esa),S_1),produc1259058957on_val(call_list_char(E_a,M,Esa),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_412_rtrancl_Ortrancl__refl,axiom,
    ! [A: produc809539159t_char,R_1: fun_Pr908866473r_bool] : hBOOL(member1999287380t_char(produc1897818327t_char(A,A),transi198989188t_char(R_1))) ).

tff(fact_413_rtrancl_Ortrancl__refl,axiom,
    ! [A: produc1278157519t_char,R_1: fun_Pr1336847023r_bool] : hBOOL(member794220506t_char(produc2080520419t_char(A,A),transi1095029602t_char(R_1))) ).

tff(fact_414_rtrancl_Ortrancl__refl,axiom,
    ! [A: produc639455274on_val,R_1: fun_Pr235369833l_bool] : hBOOL(member1322055188on_val(produc499151895on_val(A,A),transi61620055on_val(R_1))) ).

tff(fact_415_rtrancl_Ortrancl__refl,axiom,
    ! [A: product_prod_val_val,R_1: fun_Pr832147423l_bool] : hBOOL(member837208074al_val(produc1244920211al_val(A,A),transi1423755450al_val(R_1))) ).

tff(fact_416_rtrancl_Ortrancl__refl,axiom,
    ! [A: produc1645268488al_val,R_1: fun_Pr897334561l_bool] : hBOOL(member1732271180al_val(produc1924279125al_val(A,A),transi1906258203al_val(R_1))) ).

tff(fact_417_rtrancl_Ortrancl__refl,axiom,
    ! [A: produc662261637t_char,R_1: fun_Pr1890037787r_bool] : hBOOL(member1161907014t_char(produc1299387215t_char(A,A),transi1789604888t_char(R_1))) ).

tff(fact_418_rtrancl_Ortrancl__refl,axiom,
    ! [A: produc220283002t_char,R_1: fun_Pr1728267013r_bool] : hBOOL(member125098544t_char(produc57279289t_char(A,A),transi1257872013t_char(R_1))) ).

tff(fact_419_rtrancl_Ortrancl__refl,axiom,
    ! [A: produc1285161482t_char,R_1: fun_Pr1895638121r_bool] : hBOOL(member1420286996t_char(produc24551831t_char(A,A),transi122195895t_char(R_1))) ).

tff(fact_420_rtrancl_Ortrancl__refl,axiom,
    ! [A: produc430140671on_val,R_1: fun_Pr302334223l_bool] : hBOOL(member88670778on_val(produc1951691075on_val(A,A),transi208336786on_val(R_1))) ).

tff(fact_421_rtrancl_Ortrancl__refl,axiom,
    ! [A: produc12694297on_val,R_1: fun_Pr693020585l_bool] : hBOOL(member563141460on_val(produc870913623on_val(A,A),transi921647814on_val(R_1))) ).

tff(fact_422_rtrancl_Ortrancl__refl,axiom,
    ! [A: produc1102272487on_val,R_1: fun_Pr903661919l_bool] : hBOOL(member808015754on_val(produc1564932627on_val(A,A),transi910771962on_val(R_1))) ).

tff(fact_423_rtrancl_Ortrancl__refl,axiom,
    ! [A: val,R_1: fun_Pr2081272681l_bool] : hBOOL(member649088532al_val(product_Pair_val_val(A,A),transi935034983cl_val(R_1))) ).

tff(fact_424_rtrancl_Ortrancl__refl,axiom,
    ! [A: produc124828825on_val,R_1: fun_Pr691271849l_bool] : hBOOL(member773094996on_val(produc1441475159on_val(A,A),transi2024712006on_val(R_1))) ).

tff(fact_425_rtrancl_Ortrancl__refl,axiom,
    ! [A: produc2061676504on_val,R_1: fun_Pr859510977l_bool] : hBOOL(member875476972on_val(produc1611380469on_val(A,A),transi374442731on_val(R_1))) ).

tff(fact_426_rtrancl_Ortrancl__refl,axiom,
    ! [A: list_char,R_1: fun_Pr565113489r_bool] : hBOOL(member1251428284t_char(produc5062597t_char(A,A),transi1395422419t_char(R_1))) ).

tff(fact_427_r__into__rtrancl,axiom,
    ! [P_1: product_prod_val_val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(P_1,R_1))
     => hBOOL(member649088532al_val(P_1,transi935034983cl_val(R_1))) ) ).

tff(fact_428_r__into__rtrancl,axiom,
    ! [P_1: produc1534059751t_char,R_1: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(P_1,R_1))
     => hBOOL(member1999287380t_char(P_1,transi198989188t_char(R_1))) ) ).

tff(fact_429_r__into__rtrancl,axiom,
    ! [P_1: produc1350825965t_char,R_1: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(P_1,R_1))
     => hBOOL(member794220506t_char(P_1,transi1095029602t_char(R_1))) ) ).

tff(fact_430_r__into__rtrancl,axiom,
    ! [P_1: produc87279271on_val,R_1: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(P_1,R_1))
     => hBOOL(member1322055188on_val(P_1,transi61620055on_val(R_1))) ) ).

tff(fact_431_r__into__rtrancl,axiom,
    ! [P_1: produc800118557al_val,R_1: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(P_1,R_1))
     => hBOOL(member837208074al_val(P_1,transi1423755450al_val(R_1))) ) ).

tff(fact_432_r__into__rtrancl,axiom,
    ! [P_1: produc630464863al_val,R_1: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(P_1,R_1))
     => hBOOL(member1732271180al_val(P_1,transi1906258203al_val(R_1))) ) ).

tff(fact_433_r__into__rtrancl,axiom,
    ! [P_1: produc1826280281t_char,R_1: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(P_1,R_1))
     => hBOOL(member1161907014t_char(P_1,transi1789604888t_char(R_1))) ) ).

tff(fact_434_r__into__rtrancl,axiom,
    ! [P_1: produc1406897475t_char,R_1: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(P_1,R_1))
     => hBOOL(member125098544t_char(P_1,transi1257872013t_char(R_1))) ) ).

tff(fact_435_r__into__rtrancl,axiom,
    ! [P_1: produc349695911t_char,R_1: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(P_1,R_1))
     => hBOOL(member1420286996t_char(P_1,transi122195895t_char(R_1))) ) ).

tff(fact_436_r__into__rtrancl,axiom,
    ! [P_1: produc1466422861on_val,R_1: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(P_1,R_1))
     => hBOOL(member88670778on_val(P_1,transi208336786on_val(R_1))) ) ).

tff(fact_437_r__into__rtrancl,axiom,
    ! [P_1: produc409205479on_val,R_1: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(P_1,R_1))
     => hBOOL(member563141460on_val(P_1,transi921647814on_val(R_1))) ) ).

tff(fact_438_r__into__rtrancl,axiom,
    ! [P_1: produc231486621on_val,R_1: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(P_1,R_1))
     => hBOOL(member808015754on_val(P_1,transi910771962on_val(R_1))) ) ).

tff(fact_439_r__into__rtrancl,axiom,
    ! [P_1: produc1102272487on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(P_1,R_1))
     => hBOOL(member773094996on_val(P_1,transi2024712006on_val(R_1))) ) ).

tff(fact_440_r__into__rtrancl,axiom,
    ! [P_1: produc430140671on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(P_1,R_1))
     => hBOOL(member875476972on_val(P_1,transi374442731on_val(R_1))) ) ).

tff(fact_441_r__into__rtrancl,axiom,
    ! [P_1: produc1278157519t_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(P_1,R_1))
     => hBOOL(member1251428284t_char(P_1,transi1395422419t_char(R_1))) ) ).

tff(fact_442_rtrancl__trans,axiom,
    ! [C_1: produc809539159t_char,A: produc809539159t_char,B: produc809539159t_char,R_1: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(produc1897818327t_char(A,B),transi198989188t_char(R_1)))
     => ( hBOOL(member1999287380t_char(produc1897818327t_char(B,C_1),transi198989188t_char(R_1)))
       => hBOOL(member1999287380t_char(produc1897818327t_char(A,C_1),transi198989188t_char(R_1))) ) ) ).

tff(fact_443_rtrancl__trans,axiom,
    ! [C_1: produc1278157519t_char,A: produc1278157519t_char,B: produc1278157519t_char,R_1: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(produc2080520419t_char(A,B),transi1095029602t_char(R_1)))
     => ( hBOOL(member794220506t_char(produc2080520419t_char(B,C_1),transi1095029602t_char(R_1)))
       => hBOOL(member794220506t_char(produc2080520419t_char(A,C_1),transi1095029602t_char(R_1))) ) ) ).

tff(fact_444_rtrancl__trans,axiom,
    ! [C_1: produc639455274on_val,A: produc639455274on_val,B: produc639455274on_val,R_1: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(produc499151895on_val(A,B),transi61620055on_val(R_1)))
     => ( hBOOL(member1322055188on_val(produc499151895on_val(B,C_1),transi61620055on_val(R_1)))
       => hBOOL(member1322055188on_val(produc499151895on_val(A,C_1),transi61620055on_val(R_1))) ) ) ).

tff(fact_445_rtrancl__trans,axiom,
    ! [C_1: product_prod_val_val,A: product_prod_val_val,B: product_prod_val_val,R_1: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(produc1244920211al_val(A,B),transi1423755450al_val(R_1)))
     => ( hBOOL(member837208074al_val(produc1244920211al_val(B,C_1),transi1423755450al_val(R_1)))
       => hBOOL(member837208074al_val(produc1244920211al_val(A,C_1),transi1423755450al_val(R_1))) ) ) ).

tff(fact_446_rtrancl__trans,axiom,
    ! [C_1: produc1645268488al_val,A: produc1645268488al_val,B: produc1645268488al_val,R_1: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(produc1924279125al_val(A,B),transi1906258203al_val(R_1)))
     => ( hBOOL(member1732271180al_val(produc1924279125al_val(B,C_1),transi1906258203al_val(R_1)))
       => hBOOL(member1732271180al_val(produc1924279125al_val(A,C_1),transi1906258203al_val(R_1))) ) ) ).

tff(fact_447_rtrancl__trans,axiom,
    ! [C_1: produc662261637t_char,A: produc662261637t_char,B: produc662261637t_char,R_1: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(produc1299387215t_char(A,B),transi1789604888t_char(R_1)))
     => ( hBOOL(member1161907014t_char(produc1299387215t_char(B,C_1),transi1789604888t_char(R_1)))
       => hBOOL(member1161907014t_char(produc1299387215t_char(A,C_1),transi1789604888t_char(R_1))) ) ) ).

tff(fact_448_rtrancl__trans,axiom,
    ! [C_1: produc220283002t_char,A: produc220283002t_char,B: produc220283002t_char,R_1: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(produc57279289t_char(A,B),transi1257872013t_char(R_1)))
     => ( hBOOL(member125098544t_char(produc57279289t_char(B,C_1),transi1257872013t_char(R_1)))
       => hBOOL(member125098544t_char(produc57279289t_char(A,C_1),transi1257872013t_char(R_1))) ) ) ).

tff(fact_449_rtrancl__trans,axiom,
    ! [C_1: produc1285161482t_char,A: produc1285161482t_char,B: produc1285161482t_char,R_1: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(produc24551831t_char(A,B),transi122195895t_char(R_1)))
     => ( hBOOL(member1420286996t_char(produc24551831t_char(B,C_1),transi122195895t_char(R_1)))
       => hBOOL(member1420286996t_char(produc24551831t_char(A,C_1),transi122195895t_char(R_1))) ) ) ).

tff(fact_450_rtrancl__trans,axiom,
    ! [C_1: produc430140671on_val,A: produc430140671on_val,B: produc430140671on_val,R_1: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(A,B),transi208336786on_val(R_1)))
     => ( hBOOL(member88670778on_val(produc1951691075on_val(B,C_1),transi208336786on_val(R_1)))
       => hBOOL(member88670778on_val(produc1951691075on_val(A,C_1),transi208336786on_val(R_1))) ) ) ).

tff(fact_451_rtrancl__trans,axiom,
    ! [C_1: produc12694297on_val,A: produc12694297on_val,B: produc12694297on_val,R_1: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(A,B),transi921647814on_val(R_1)))
     => ( hBOOL(member563141460on_val(produc870913623on_val(B,C_1),transi921647814on_val(R_1)))
       => hBOOL(member563141460on_val(produc870913623on_val(A,C_1),transi921647814on_val(R_1))) ) ) ).

tff(fact_452_rtrancl__trans,axiom,
    ! [C_1: produc1102272487on_val,A: produc1102272487on_val,B: produc1102272487on_val,R_1: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(A,B),transi910771962on_val(R_1)))
     => ( hBOOL(member808015754on_val(produc1564932627on_val(B,C_1),transi910771962on_val(R_1)))
       => hBOOL(member808015754on_val(produc1564932627on_val(A,C_1),transi910771962on_val(R_1))) ) ) ).

tff(fact_453_rtrancl__trans,axiom,
    ! [C_1: val,A: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(product_Pair_val_val(A,B),transi935034983cl_val(R_1)))
     => ( hBOOL(member649088532al_val(product_Pair_val_val(B,C_1),transi935034983cl_val(R_1)))
       => hBOOL(member649088532al_val(product_Pair_val_val(A,C_1),transi935034983cl_val(R_1))) ) ) ).

tff(fact_454_rtrancl__trans,axiom,
    ! [C_1: produc124828825on_val,A: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(A,B),transi2024712006on_val(R_1)))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(B,C_1),transi2024712006on_val(R_1)))
       => hBOOL(member773094996on_val(produc1441475159on_val(A,C_1),transi2024712006on_val(R_1))) ) ) ).

tff(fact_455_rtrancl__trans,axiom,
    ! [C_1: produc2061676504on_val,A: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(A,B),transi374442731on_val(R_1)))
     => ( hBOOL(member875476972on_val(produc1611380469on_val(B,C_1),transi374442731on_val(R_1)))
       => hBOOL(member875476972on_val(produc1611380469on_val(A,C_1),transi374442731on_val(R_1))) ) ) ).

tff(fact_456_rtrancl__trans,axiom,
    ! [C_1: list_char,A: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(produc5062597t_char(A,B),transi1395422419t_char(R_1)))
     => ( hBOOL(member1251428284t_char(produc5062597t_char(B,C_1),transi1395422419t_char(R_1)))
       => hBOOL(member1251428284t_char(produc5062597t_char(A,C_1),transi1395422419t_char(R_1))) ) ) ).

tff(fact_457_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr2081272681l_bool] : transi935034983cl_val(transi935034983cl_val(R_1)) = transi935034983cl_val(R_1) ).

tff(fact_458_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr908866473r_bool] : transi198989188t_char(transi198989188t_char(R_1)) = transi198989188t_char(R_1) ).

tff(fact_459_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr1336847023r_bool] : transi1095029602t_char(transi1095029602t_char(R_1)) = transi1095029602t_char(R_1) ).

tff(fact_460_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr235369833l_bool] : transi61620055on_val(transi61620055on_val(R_1)) = transi61620055on_val(R_1) ).

tff(fact_461_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr832147423l_bool] : transi1423755450al_val(transi1423755450al_val(R_1)) = transi1423755450al_val(R_1) ).

tff(fact_462_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr897334561l_bool] : transi1906258203al_val(transi1906258203al_val(R_1)) = transi1906258203al_val(R_1) ).

tff(fact_463_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr1890037787r_bool] : transi1789604888t_char(transi1789604888t_char(R_1)) = transi1789604888t_char(R_1) ).

tff(fact_464_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr1728267013r_bool] : transi1257872013t_char(transi1257872013t_char(R_1)) = transi1257872013t_char(R_1) ).

tff(fact_465_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr1895638121r_bool] : transi122195895t_char(transi122195895t_char(R_1)) = transi122195895t_char(R_1) ).

tff(fact_466_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr302334223l_bool] : transi208336786on_val(transi208336786on_val(R_1)) = transi208336786on_val(R_1) ).

tff(fact_467_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr693020585l_bool] : transi921647814on_val(transi921647814on_val(R_1)) = transi921647814on_val(R_1) ).

tff(fact_468_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr903661919l_bool] : transi910771962on_val(transi910771962on_val(R_1)) = transi910771962on_val(R_1) ).

tff(fact_469_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr691271849l_bool] : transi2024712006on_val(transi2024712006on_val(R_1)) = transi2024712006on_val(R_1) ).

tff(fact_470_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr859510977l_bool] : transi374442731on_val(transi374442731on_val(R_1)) = transi374442731on_val(R_1) ).

tff(fact_471_rtrancl__idemp,axiom,
    ! [R_1: fun_Pr565113489r_bool] : transi1395422419t_char(transi1395422419t_char(R_1)) = transi1395422419t_char(R_1) ).

tff(fact_472_ListReds2,axiom,
    ! [V_1: val,Esa: list_exp_list_char,S_1: produc12694297on_val,Es_a: list_exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Esa,S_1),produc379668296on_val(Es_a,S)),transi374442731on_val(reds(Pa))))
     => hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Esa),S_1),produc379668296on_val(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Es_a),S)),transi374442731on_val(reds(Pa)))) ) ).

tff(fact_473_ListReds1,axiom,
    ! [Esa: list_exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(cons_exp_list_char(Ea,Esa),S_1),produc379668296on_val(cons_exp_list_char(E_a,Esa),S)),transi374442731on_val(reds(Pa)))) ) ).

tff(fact_474_ListRedsVal,axiom,
    ! [Esa: list_exp_list_char,Es_a: list_exp_list_char,S_2_1: produc12694297on_val,Ea: exp_list_char,S_0: produc12694297on_val,V_1: val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_0),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Esa,S_1_1),produc379668296on_val(Es_a,S_2_1)),transi374442731on_val(reds(Pa))))
       => hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(cons_exp_list_char(Ea,Esa),S_0),produc379668296on_val(cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Es_a),S_2_1)),transi374442731on_val(reds(Pa)))) ) ) ).

tff(fact_475_CallRedsParams,axiom,
    ! [V_1: val,M: list_char,Esa: list_exp_list_char,S_1: produc12694297on_val,Es_a: list_exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Esa,S_1),produc379668296on_val(Es_a,S)),transi374442731on_val(reds(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(call_list_char(hAPP_v834067052t_char(val_list_char,V_1),M,Esa),S_1),produc1259058957on_val(call_list_char(hAPP_v834067052t_char(val_list_char,V_1),M,Es_a),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_476_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc809539159t_char,A: produc809539159t_char,B: produc809539159t_char,R_1: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(produc1897818327t_char(A,B),R_1))
     => ( hBOOL(member1999287380t_char(produc1897818327t_char(B,C_1),transi198989188t_char(R_1)))
       => hBOOL(member1999287380t_char(produc1897818327t_char(A,C_1),transi198989188t_char(R_1))) ) ) ).

tff(fact_477_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc1278157519t_char,A: produc1278157519t_char,B: produc1278157519t_char,R_1: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(produc2080520419t_char(A,B),R_1))
     => ( hBOOL(member794220506t_char(produc2080520419t_char(B,C_1),transi1095029602t_char(R_1)))
       => hBOOL(member794220506t_char(produc2080520419t_char(A,C_1),transi1095029602t_char(R_1))) ) ) ).

tff(fact_478_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc639455274on_val,A: produc639455274on_val,B: produc639455274on_val,R_1: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(produc499151895on_val(A,B),R_1))
     => ( hBOOL(member1322055188on_val(produc499151895on_val(B,C_1),transi61620055on_val(R_1)))
       => hBOOL(member1322055188on_val(produc499151895on_val(A,C_1),transi61620055on_val(R_1))) ) ) ).

tff(fact_479_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: product_prod_val_val,A: product_prod_val_val,B: product_prod_val_val,R_1: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(produc1244920211al_val(A,B),R_1))
     => ( hBOOL(member837208074al_val(produc1244920211al_val(B,C_1),transi1423755450al_val(R_1)))
       => hBOOL(member837208074al_val(produc1244920211al_val(A,C_1),transi1423755450al_val(R_1))) ) ) ).

tff(fact_480_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc1645268488al_val,A: produc1645268488al_val,B: produc1645268488al_val,R_1: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(produc1924279125al_val(A,B),R_1))
     => ( hBOOL(member1732271180al_val(produc1924279125al_val(B,C_1),transi1906258203al_val(R_1)))
       => hBOOL(member1732271180al_val(produc1924279125al_val(A,C_1),transi1906258203al_val(R_1))) ) ) ).

tff(fact_481_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc662261637t_char,A: produc662261637t_char,B: produc662261637t_char,R_1: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(produc1299387215t_char(A,B),R_1))
     => ( hBOOL(member1161907014t_char(produc1299387215t_char(B,C_1),transi1789604888t_char(R_1)))
       => hBOOL(member1161907014t_char(produc1299387215t_char(A,C_1),transi1789604888t_char(R_1))) ) ) ).

tff(fact_482_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc220283002t_char,A: produc220283002t_char,B: produc220283002t_char,R_1: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(produc57279289t_char(A,B),R_1))
     => ( hBOOL(member125098544t_char(produc57279289t_char(B,C_1),transi1257872013t_char(R_1)))
       => hBOOL(member125098544t_char(produc57279289t_char(A,C_1),transi1257872013t_char(R_1))) ) ) ).

tff(fact_483_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc1285161482t_char,A: produc1285161482t_char,B: produc1285161482t_char,R_1: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(produc24551831t_char(A,B),R_1))
     => ( hBOOL(member1420286996t_char(produc24551831t_char(B,C_1),transi122195895t_char(R_1)))
       => hBOOL(member1420286996t_char(produc24551831t_char(A,C_1),transi122195895t_char(R_1))) ) ) ).

tff(fact_484_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc430140671on_val,A: produc430140671on_val,B: produc430140671on_val,R_1: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(A,B),R_1))
     => ( hBOOL(member88670778on_val(produc1951691075on_val(B,C_1),transi208336786on_val(R_1)))
       => hBOOL(member88670778on_val(produc1951691075on_val(A,C_1),transi208336786on_val(R_1))) ) ) ).

tff(fact_485_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc12694297on_val,A: produc12694297on_val,B: produc12694297on_val,R_1: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(A,B),R_1))
     => ( hBOOL(member563141460on_val(produc870913623on_val(B,C_1),transi921647814on_val(R_1)))
       => hBOOL(member563141460on_val(produc870913623on_val(A,C_1),transi921647814on_val(R_1))) ) ) ).

tff(fact_486_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc1102272487on_val,A: produc1102272487on_val,B: produc1102272487on_val,R_1: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(A,B),R_1))
     => ( hBOOL(member808015754on_val(produc1564932627on_val(B,C_1),transi910771962on_val(R_1)))
       => hBOOL(member808015754on_val(produc1564932627on_val(A,C_1),transi910771962on_val(R_1))) ) ) ).

tff(fact_487_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: val,A: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(product_Pair_val_val(A,B),R_1))
     => ( hBOOL(member649088532al_val(product_Pair_val_val(B,C_1),transi935034983cl_val(R_1)))
       => hBOOL(member649088532al_val(product_Pair_val_val(A,C_1),transi935034983cl_val(R_1))) ) ) ).

tff(fact_488_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc124828825on_val,A: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(A,B),R_1))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(B,C_1),transi2024712006on_val(R_1)))
       => hBOOL(member773094996on_val(produc1441475159on_val(A,C_1),transi2024712006on_val(R_1))) ) ) ).

tff(fact_489_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: produc2061676504on_val,A: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(A,B),R_1))
     => ( hBOOL(member875476972on_val(produc1611380469on_val(B,C_1),transi374442731on_val(R_1)))
       => hBOOL(member875476972on_val(produc1611380469on_val(A,C_1),transi374442731on_val(R_1))) ) ) ).

tff(fact_490_converse__rtrancl__into__rtrancl,axiom,
    ! [C_1: list_char,A: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(produc5062597t_char(A,B),R_1))
     => ( hBOOL(member1251428284t_char(produc5062597t_char(B,C_1),transi1395422419t_char(R_1)))
       => hBOOL(member1251428284t_char(produc5062597t_char(A,C_1),transi1395422419t_char(R_1))) ) ) ).

tff(fact_491_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc809539159t_char,A: produc809539159t_char,B: produc809539159t_char,R_1: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(produc1897818327t_char(A,B),transi198989188t_char(R_1)))
     => ( hBOOL(member1999287380t_char(produc1897818327t_char(B,C_1),R_1))
       => hBOOL(member1999287380t_char(produc1897818327t_char(A,C_1),transi198989188t_char(R_1))) ) ) ).

tff(fact_492_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc1278157519t_char,A: produc1278157519t_char,B: produc1278157519t_char,R_1: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(produc2080520419t_char(A,B),transi1095029602t_char(R_1)))
     => ( hBOOL(member794220506t_char(produc2080520419t_char(B,C_1),R_1))
       => hBOOL(member794220506t_char(produc2080520419t_char(A,C_1),transi1095029602t_char(R_1))) ) ) ).

tff(fact_493_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc639455274on_val,A: produc639455274on_val,B: produc639455274on_val,R_1: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(produc499151895on_val(A,B),transi61620055on_val(R_1)))
     => ( hBOOL(member1322055188on_val(produc499151895on_val(B,C_1),R_1))
       => hBOOL(member1322055188on_val(produc499151895on_val(A,C_1),transi61620055on_val(R_1))) ) ) ).

tff(fact_494_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: product_prod_val_val,A: product_prod_val_val,B: product_prod_val_val,R_1: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(produc1244920211al_val(A,B),transi1423755450al_val(R_1)))
     => ( hBOOL(member837208074al_val(produc1244920211al_val(B,C_1),R_1))
       => hBOOL(member837208074al_val(produc1244920211al_val(A,C_1),transi1423755450al_val(R_1))) ) ) ).

tff(fact_495_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc1645268488al_val,A: produc1645268488al_val,B: produc1645268488al_val,R_1: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(produc1924279125al_val(A,B),transi1906258203al_val(R_1)))
     => ( hBOOL(member1732271180al_val(produc1924279125al_val(B,C_1),R_1))
       => hBOOL(member1732271180al_val(produc1924279125al_val(A,C_1),transi1906258203al_val(R_1))) ) ) ).

tff(fact_496_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc662261637t_char,A: produc662261637t_char,B: produc662261637t_char,R_1: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(produc1299387215t_char(A,B),transi1789604888t_char(R_1)))
     => ( hBOOL(member1161907014t_char(produc1299387215t_char(B,C_1),R_1))
       => hBOOL(member1161907014t_char(produc1299387215t_char(A,C_1),transi1789604888t_char(R_1))) ) ) ).

tff(fact_497_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc220283002t_char,A: produc220283002t_char,B: produc220283002t_char,R_1: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(produc57279289t_char(A,B),transi1257872013t_char(R_1)))
     => ( hBOOL(member125098544t_char(produc57279289t_char(B,C_1),R_1))
       => hBOOL(member125098544t_char(produc57279289t_char(A,C_1),transi1257872013t_char(R_1))) ) ) ).

tff(fact_498_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc1285161482t_char,A: produc1285161482t_char,B: produc1285161482t_char,R_1: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(produc24551831t_char(A,B),transi122195895t_char(R_1)))
     => ( hBOOL(member1420286996t_char(produc24551831t_char(B,C_1),R_1))
       => hBOOL(member1420286996t_char(produc24551831t_char(A,C_1),transi122195895t_char(R_1))) ) ) ).

tff(fact_499_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc430140671on_val,A: produc430140671on_val,B: produc430140671on_val,R_1: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(A,B),transi208336786on_val(R_1)))
     => ( hBOOL(member88670778on_val(produc1951691075on_val(B,C_1),R_1))
       => hBOOL(member88670778on_val(produc1951691075on_val(A,C_1),transi208336786on_val(R_1))) ) ) ).

tff(fact_500_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc12694297on_val,A: produc12694297on_val,B: produc12694297on_val,R_1: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(A,B),transi921647814on_val(R_1)))
     => ( hBOOL(member563141460on_val(produc870913623on_val(B,C_1),R_1))
       => hBOOL(member563141460on_val(produc870913623on_val(A,C_1),transi921647814on_val(R_1))) ) ) ).

tff(fact_501_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc1102272487on_val,A: produc1102272487on_val,B: produc1102272487on_val,R_1: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(A,B),transi910771962on_val(R_1)))
     => ( hBOOL(member808015754on_val(produc1564932627on_val(B,C_1),R_1))
       => hBOOL(member808015754on_val(produc1564932627on_val(A,C_1),transi910771962on_val(R_1))) ) ) ).

tff(fact_502_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: val,A: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(product_Pair_val_val(A,B),transi935034983cl_val(R_1)))
     => ( hBOOL(member649088532al_val(product_Pair_val_val(B,C_1),R_1))
       => hBOOL(member649088532al_val(product_Pair_val_val(A,C_1),transi935034983cl_val(R_1))) ) ) ).

tff(fact_503_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc124828825on_val,A: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(A,B),transi2024712006on_val(R_1)))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(B,C_1),R_1))
       => hBOOL(member773094996on_val(produc1441475159on_val(A,C_1),transi2024712006on_val(R_1))) ) ) ).

tff(fact_504_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: produc2061676504on_val,A: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(A,B),transi374442731on_val(R_1)))
     => ( hBOOL(member875476972on_val(produc1611380469on_val(B,C_1),R_1))
       => hBOOL(member875476972on_val(produc1611380469on_val(A,C_1),transi374442731on_val(R_1))) ) ) ).

tff(fact_505_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [C_1: list_char,A: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(produc5062597t_char(A,B),transi1395422419t_char(R_1)))
     => ( hBOOL(member1251428284t_char(produc5062597t_char(B,C_1),R_1))
       => hBOOL(member1251428284t_char(produc5062597t_char(A,C_1),transi1395422419t_char(R_1))) ) ) ).

tff(fact_506_rtrancl__induct2,axiom,
    ! [Pa: fun_li800818899y_bool,Ax: list_char,Ay: produc917948472har_ty,Bx: list_char,By: produc917948472har_ty,R_1: fun_Pr1239516201y_bool] :
      ( hBOOL(member1664419796har_ty(produc2038128087har_ty(produc1002914035har_ty(Ax,Ay),produc1002914035har_ty(Bx,By)),transi1158914604har_ty(R_1)))
     => ( hBOOL(hAPP_P748443392y_bool(hAPP_l1665608433y_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_char,B_1: produc917948472har_ty,Aa: list_char,Ba: produc917948472har_ty] :
              ( hBOOL(member1664419796har_ty(produc2038128087har_ty(produc1002914035har_ty(Ax,Ay),produc1002914035har_ty(A_1,B_1)),transi1158914604har_ty(R_1)))
             => ( hBOOL(member1664419796har_ty(produc2038128087har_ty(produc1002914035har_ty(A_1,B_1),produc1002914035har_ty(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P748443392y_bool(hAPP_l1665608433y_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P748443392y_bool(hAPP_l1665608433y_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P748443392y_bool(hAPP_l1665608433y_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_507_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr1633645595y_bool,Ax: produc1278157519t_char,Ay: ty,Bx: produc1278157519t_char,By: ty,R_1: fun_Pr330025897y_bool] :
      ( hBOOL(member1986596692har_ty(produc63273559har_ty(produc1265154397har_ty(Ax,Ay),produc1265154397har_ty(Bx,By)),transi935089046har_ty(R_1)))
     => ( hBOOL(hAPP_ty_bool(hAPP_P1845004857y_bool(Pa,Ax),Ay))
       => ( ! [A_1: produc1278157519t_char,B_1: ty,Aa: produc1278157519t_char,Ba: ty] :
              ( hBOOL(member1986596692har_ty(produc63273559har_ty(produc1265154397har_ty(Ax,Ay),produc1265154397har_ty(A_1,B_1)),transi935089046har_ty(R_1)))
             => ( hBOOL(member1986596692har_ty(produc63273559har_ty(produc1265154397har_ty(A_1,B_1),produc1265154397har_ty(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_ty_bool(hAPP_P1845004857y_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_ty_bool(hAPP_P1845004857y_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_ty_bool(hAPP_P1845004857y_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_508_rtrancl__induct2,axiom,
    ! [Pa: fun_li634443788y_bool,Ax: list_char,Ay: ty,Bx: list_char,By: ty,R_1: fun_Pr1670851305y_bool] :
      ( hBOOL(member119266708har_ty(produc1414300567har_ty(produc251930284har_ty(Ax,Ay),produc251930284har_ty(Bx,By)),transi1325206117har_ty(R_1)))
     => ( hBOOL(hAPP_ty_bool(hAPP_l1734756650y_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_char,B_1: ty,Aa: list_char,Ba: ty] :
              ( hBOOL(member119266708har_ty(produc1414300567har_ty(produc251930284har_ty(Ax,Ay),produc251930284har_ty(A_1,B_1)),transi1325206117har_ty(R_1)))
             => ( hBOOL(member119266708har_ty(produc1414300567har_ty(produc251930284har_ty(A_1,B_1),produc251930284har_ty(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_ty_bool(hAPP_l1734756650y_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_ty_bool(hAPP_l1734756650y_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_ty_bool(hAPP_l1734756650y_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_509_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr92408125r_bool,Ax: produc809539159t_char,Ay: produc809539159t_char,Bx: produc809539159t_char,By: produc809539159t_char,R_1: fun_Pr678067807r_bool] :
      ( hBOOL(member902595210t_char(produc253822483t_char(produc1897818327t_char(Ax,Ay),produc1897818327t_char(Bx,By)),transi1630776058t_char(R_1)))
     => ( hBOOL(hAPP_P2014166431r_bool(hAPP_P1939418767r_bool(Pa,Ax),Ay))
       => ( ! [A_1: produc809539159t_char,B_1: produc809539159t_char,Aa: produc809539159t_char,Ba: produc809539159t_char] :
              ( hBOOL(member902595210t_char(produc253822483t_char(produc1897818327t_char(Ax,Ay),produc1897818327t_char(A_1,B_1)),transi1630776058t_char(R_1)))
             => ( hBOOL(member902595210t_char(produc253822483t_char(produc1897818327t_char(A_1,B_1),produc1897818327t_char(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P2014166431r_bool(hAPP_P1939418767r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P2014166431r_bool(hAPP_P1939418767r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P2014166431r_bool(hAPP_P1939418767r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_510_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr185059443r_bool,Ax: produc1278157519t_char,Ay: produc1278157519t_char,Bx: produc1278157519t_char,By: produc1278157519t_char,R_1: fun_Pr555864043r_bool] :
      ( hBOOL(member1689070870t_char(produc354099231t_char(produc2080520419t_char(Ax,Ay),produc2080520419t_char(Bx,By)),transi15035776t_char(R_1)))
     => ( hBOOL(hAPP_P449474095r_bool(hAPP_P663876415r_bool(Pa,Ax),Ay))
       => ( ! [A_1: produc1278157519t_char,B_1: produc1278157519t_char,Aa: produc1278157519t_char,Ba: produc1278157519t_char] :
              ( hBOOL(member1689070870t_char(produc354099231t_char(produc2080520419t_char(Ax,Ay),produc2080520419t_char(A_1,B_1)),transi15035776t_char(R_1)))
             => ( hBOOL(member1689070870t_char(produc354099231t_char(produc2080520419t_char(A_1,B_1),produc2080520419t_char(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P449474095r_bool(hAPP_P663876415r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P449474095r_bool(hAPP_P663876415r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P449474095r_bool(hAPP_P663876415r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_511_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr788853347l_bool,Ax: produc639455274on_val,Ay: produc639455274on_val,Bx: produc639455274on_val,By: produc639455274on_val,R_1: fun_Pr1283539423l_bool] :
      ( hBOOL(member1114719754on_val(produc434506131on_val(produc499151895on_val(Ax,Ay),produc499151895on_val(Bx,By)),transi1953049786on_val(R_1)))
     => ( hBOOL(hAPP_P1235399154l_bool(hAPP_P416784693l_bool(Pa,Ax),Ay))
       => ( ! [A_1: produc639455274on_val,B_1: produc639455274on_val,Aa: produc639455274on_val,Ba: produc639455274on_val] :
              ( hBOOL(member1114719754on_val(produc434506131on_val(produc499151895on_val(Ax,Ay),produc499151895on_val(A_1,B_1)),transi1953049786on_val(R_1)))
             => ( hBOOL(member1114719754on_val(produc434506131on_val(produc499151895on_val(A_1,B_1),produc499151895on_val(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P1235399154l_bool(hAPP_P416784693l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P1235399154l_bool(hAPP_P416784693l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P1235399154l_bool(hAPP_P416784693l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_512_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr324760563l_bool,Ax: product_prod_val_val,Ay: product_prod_val_val,Bx: product_prod_val_val,By: product_prod_val_val,R_1: fun_Pr1443979083l_bool] :
      ( hBOOL(member384848502al_val(produc94135935al_val(produc1244920211al_val(Ax,Ay),produc1244920211al_val(Bx,By)),transi1927461808al_val(R_1)))
     => ( hBOOL(hAPP_P929938951l_bool(hAPP_P1815899455l_bool(Pa,Ax),Ay))
       => ( ! [A_1: product_prod_val_val,B_1: product_prod_val_val,Aa: product_prod_val_val,Ba: product_prod_val_val] :
              ( hBOOL(member384848502al_val(produc94135935al_val(produc1244920211al_val(Ax,Ay),produc1244920211al_val(A_1,B_1)),transi1927461808al_val(R_1)))
             => ( hBOOL(member384848502al_val(produc94135935al_val(produc1244920211al_val(A_1,B_1),produc1244920211al_val(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P929938951l_bool(hAPP_P1815899455l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P929938951l_bool(hAPP_P1815899455l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P929938951l_bool(hAPP_P1815899455l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_513_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr1713170355l_bool,Ax: produc1645268488al_val,Ay: produc1645268488al_val,Bx: produc1645268488al_val,By: produc1645268488al_val,R_1: fun_Pr180697551l_bool] :
      ( hBOOL(member23198458al_val(produc370870787al_val(produc1924279125al_val(Ax,Ay),produc1924279125al_val(Bx,By)),transi486718450al_val(R_1)))
     => ( hBOOL(hAPP_P943837928l_bool(hAPP_P323054207l_bool(Pa,Ax),Ay))
       => ( ! [A_1: produc1645268488al_val,B_1: produc1645268488al_val,Aa: produc1645268488al_val,Ba: produc1645268488al_val] :
              ( hBOOL(member23198458al_val(produc370870787al_val(produc1924279125al_val(Ax,Ay),produc1924279125al_val(A_1,B_1)),transi486718450al_val(R_1)))
             => ( hBOOL(member23198458al_val(produc370870787al_val(produc1924279125al_val(A_1,B_1),produc1924279125al_val(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P943837928l_bool(hAPP_P323054207l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P943837928l_bool(hAPP_P323054207l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P943837928l_bool(hAPP_P323054207l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_514_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr378536435r_bool,Ax: produc662261637t_char,Ay: produc662261637t_char,Bx: produc662261637t_char,By: produc662261637t_char,R_1: fun_Pr4797123r_bool] :
      ( hBOOL(member1105423342t_char(produc627518711t_char(produc1299387215t_char(Ax,Ay),produc1299387215t_char(Bx,By)),transi1803333868t_char(R_1)))
     => ( hBOOL(hAPP_P2118621157r_bool(hAPP_P357098431r_bool(Pa,Ax),Ay))
       => ( ! [A_1: produc662261637t_char,B_1: produc662261637t_char,Aa: produc662261637t_char,Ba: produc662261637t_char] :
              ( hBOOL(member1105423342t_char(produc627518711t_char(produc1299387215t_char(Ax,Ay),produc1299387215t_char(A_1,B_1)),transi1803333868t_char(R_1)))
             => ( hBOOL(member1105423342t_char(produc627518711t_char(produc1299387215t_char(A_1,B_1),produc1299387215t_char(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P2118621157r_bool(hAPP_P357098431r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P2118621157r_bool(hAPP_P357098431r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P2118621157r_bool(hAPP_P357098431r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_515_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr1074372915r_bool,Ax: produc220283002t_char,Ay: produc220283002t_char,Bx: produc220283002t_char,By: produc220283002t_char,R_1: fun_Pr900028311r_bool] :
      ( hBOOL(member371591362t_char(produc913263563t_char(produc57279289t_char(Ax,Ay),produc57279289t_char(Bx,By)),transi1452021206t_char(R_1)))
     => ( hBOOL(hAPP_P1907982426r_bool(hAPP_P1214880255r_bool(Pa,Ax),Ay))
       => ( ! [A_1: produc220283002t_char,B_1: produc220283002t_char,Aa: produc220283002t_char,Ba: produc220283002t_char] :
              ( hBOOL(member371591362t_char(produc913263563t_char(produc57279289t_char(Ax,Ay),produc57279289t_char(A_1,B_1)),transi1452021206t_char(R_1)))
             => ( hBOOL(member371591362t_char(produc913263563t_char(produc57279289t_char(A_1,B_1),produc57279289t_char(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P1907982426r_bool(hAPP_P1214880255r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P1907982426r_bool(hAPP_P1214880255r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P1907982426r_bool(hAPP_P1214880255r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_516_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr1794669603r_bool,Ax: produc1285161482t_char,Ay: produc1285161482t_char,Bx: produc1285161482t_char,By: produc1285161482t_char,R_1: fun_Pr1493019359r_bool] :
      ( hBOOL(member1934728458t_char(produc1288549779t_char(produc24551831t_char(Ax,Ay),produc24551831t_char(Bx,By)),transi2072254650t_char(R_1)))
     => ( hBOOL(hAPP_P92196306r_bool(hAPP_P1928969845r_bool(Pa,Ax),Ay))
       => ( ! [A_1: produc1285161482t_char,B_1: produc1285161482t_char,Aa: produc1285161482t_char,Ba: produc1285161482t_char] :
              ( hBOOL(member1934728458t_char(produc1288549779t_char(produc24551831t_char(Ax,Ay),produc24551831t_char(A_1,B_1)),transi2072254650t_char(R_1)))
             => ( hBOOL(member1934728458t_char(produc1288549779t_char(produc24551831t_char(A_1,B_1),produc24551831t_char(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P92196306r_bool(hAPP_P1928969845r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P92196306r_bool(hAPP_P1928969845r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P92196306r_bool(hAPP_P1928969845r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_517_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr1511900787l_bool,Ax: produc430140671on_val,Ay: produc430140671on_val,Bx: produc430140671on_val,By: produc430140671on_val,R_1: fun_Pr1329133739l_bool] :
      ( hBOOL(member1837727190on_val(produc722767071on_val(produc1951691075on_val(Ax,Ay),produc1951691075on_val(Bx,By)),transi1751449568on_val(R_1)))
     => ( hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(Pa,Ax),Ay))
       => ( ! [A_1: produc430140671on_val,B_1: produc430140671on_val,Aa: produc430140671on_val,Ba: produc430140671on_val] :
              ( hBOOL(member1837727190on_val(produc722767071on_val(produc1951691075on_val(Ax,Ay),produc1951691075on_val(A_1,B_1)),transi1751449568on_val(R_1)))
             => ( hBOOL(member1837727190on_val(produc722767071on_val(produc1951691075on_val(A_1,B_1),produc1951691075on_val(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_518_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr598845249l_bool,Ax: produc12694297on_val,Ay: produc12694297on_val,Bx: produc12694297on_val,By: produc12694297on_val,R_1: fun_Pr27327839l_bool] :
      ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Ax,Ay),produc870913623on_val(Bx,By)),transi594096122on_val(R_1)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Ax),Ay))
       => ( ! [A_1: produc12694297on_val,B_1: produc12694297on_val,Aa: produc12694297on_val,Ba: produc12694297on_val] :
              ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Ax,Ay),produc870913623on_val(A_1,B_1)),transi594096122on_val(R_1)))
             => ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(A_1,B_1),produc870913623on_val(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_519_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr220980979l_bool,Ax: produc1102272487on_val,Ay: produc1102272487on_val,Bx: produc1102272487on_val,By: produc1102272487on_val,R_1: fun_Pr111684683l_bool] :
      ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Ax,Ay),produc1564932627on_val(Bx,By)),transi678815536on_val(R_1)))
     => ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Ax),Ay))
       => ( ! [A_1: produc1102272487on_val,B_1: produc1102272487on_val,Aa: produc1102272487on_val,Ba: produc1102272487on_val] :
              ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Ax,Ay),produc1564932627on_val(A_1,B_1)),transi678815536on_val(R_1)))
             => ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(A_1,B_1),produc1564932627on_val(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_520_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr633696065l_bool,Ax: produc124828825on_val,Ay: produc124828825on_val,Bx: produc124828825on_val,By: produc124828825on_val,R_1: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(Bx,By)),transi910771962on_val(R_1)))
     => ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay))
       => ( ! [A_1: produc124828825on_val,B_1: produc124828825on_val,Aa: produc124828825on_val,Ba: produc124828825on_val] :
              ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(A_1,B_1)),transi910771962on_val(R_1)))
             => ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A_1,B_1),produc1441475159on_val(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_521_rtrancl__induct2,axiom,
    ! [Pa: fun_fu100249073l_bool,Ax: fun_na939144002on_val,Ay: fun_li1432931796on_val,Bx: fun_na939144002on_val,By: fun_li1432931796on_val,R_1: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(Bx,By)),transi921647814on_val(R_1)))
     => ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay))
       => ( ! [A_1: fun_na939144002on_val,B_1: fun_li1432931796on_val,Aa: fun_na939144002on_val,Ba: fun_li1432931796on_val] :
              ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(A_1,B_1)),transi921647814on_val(R_1)))
             => ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A_1,B_1),produc899768717on_val(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_522_rtrancl__induct2,axiom,
    ! [Pa: fun_Pr597144499l_bool,Ax: produc2061676504on_val,Ay: produc2061676504on_val,Bx: produc2061676504on_val,By: produc2061676504on_val,R_1: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(produc1611380469on_val(Ax,Ay),produc1611380469on_val(Bx,By)),transi208336786on_val(R_1)))
     => ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Ax),Ay))
       => ( ! [A_1: produc2061676504on_val,B_1: produc2061676504on_val,Aa: produc2061676504on_val,Ba: produc2061676504on_val] :
              ( hBOOL(member88670778on_val(produc1951691075on_val(produc1611380469on_val(Ax,Ay),produc1611380469on_val(A_1,B_1)),transi208336786on_val(R_1)))
             => ( hBOOL(member88670778on_val(produc1951691075on_val(produc1611380469on_val(A_1,B_1),produc1611380469on_val(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_523_rtrancl__induct2,axiom,
    ! [Pa: fun_li1024794712r_bool,Ax: list_list_char,Ay: produc220283002t_char,Bx: list_list_char,By: produc220283002t_char,R_1: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Ax,Ay),produc921874948t_char(Bx,By)),transi122195895t_char(R_1)))
     => ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_list_char,B_1: produc220283002t_char,Aa: list_list_char,Ba: produc220283002t_char] :
              ( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Ax,Ay),produc921874948t_char(A_1,B_1)),transi122195895t_char(R_1)))
             => ( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(A_1,B_1),produc921874948t_char(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_524_rtrancl__induct2,axiom,
    ! [Pa: fun_li887890578r_bool,Ax: list_ty,Ay: produc662261637t_char,Bx: list_ty,By: produc662261637t_char,R_1: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Ax,Ay),produc1909267824t_char(Bx,By)),transi1257872013t_char(R_1)))
     => ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_ty,B_1: produc662261637t_char,Aa: list_ty,Ba: produc662261637t_char] :
              ( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Ax,Ay),produc1909267824t_char(A_1,B_1)),transi1257872013t_char(R_1)))
             => ( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(A_1,B_1),produc1909267824t_char(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_525_rtrancl__induct2,axiom,
    ! [Pa: fun_li826105035r_bool,Ax: list_val,Ay: exp_list_char,Bx: list_val,By: exp_list_char,R_1: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Ax,Ay),produc1916172923t_char(Bx,By)),transi1789604888t_char(R_1)))
     => ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_val,B_1: exp_list_char,Aa: list_val,Ba: exp_list_char] :
              ( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Ax,Ay),produc1916172923t_char(A_1,B_1)),transi1789604888t_char(R_1)))
             => ( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(A_1,B_1),produc1916172923t_char(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_526_rtrancl__induct2,axiom,
    ! [Pa: fun_bo1454185032l_bool,Ax: bop,Ay: product_prod_val_val,Bx: bop,By: product_prod_val_val,R_1: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(produc1924279125al_val(produc621191550al_val(Ax,Ay),produc621191550al_val(Bx,By)),transi1906258203al_val(R_1)))
     => ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Ax),Ay))
       => ( ! [A_1: bop,B_1: product_prod_val_val,Aa: bop,Ba: product_prod_val_val] :
              ( hBOOL(member1732271180al_val(produc1924279125al_val(produc621191550al_val(Ax,Ay),produc621191550al_val(A_1,B_1)),transi1906258203al_val(R_1)))
             => ( hBOOL(member1732271180al_val(produc1924279125al_val(produc621191550al_val(A_1,B_1),produc621191550al_val(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_527_rtrancl__induct2,axiom,
    ! [Pa: fun_val_fun_val_bool,Ax: val,Ay: val,Bx: val,By: val,R_1: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(produc1244920211al_val(product_Pair_val_val(Ax,Ay),product_Pair_val_val(Bx,By)),transi1423755450al_val(R_1)))
     => ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Ax),Ay))
       => ( ! [A_1: val,B_1: val,Aa: val,Ba: val] :
              ( hBOOL(member837208074al_val(produc1244920211al_val(product_Pair_val_val(Ax,Ay),product_Pair_val_val(A_1,B_1)),transi1423755450al_val(R_1)))
             => ( hBOOL(member837208074al_val(produc1244920211al_val(product_Pair_val_val(A_1,B_1),product_Pair_val_val(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_528_rtrancl__induct2,axiom,
    ! [Pa: fun_li823162622l_bool,Ax: list_char,Ay: fun_Pr806764899on_val,Bx: list_char,By: fun_Pr806764899on_val,R_1: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Ax,Ay),produc823076510on_val(Bx,By)),transi61620055on_val(R_1)))
     => ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_char,B_1: fun_Pr806764899on_val,Aa: list_char,Ba: fun_Pr806764899on_val] :
              ( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Ax,Ay),produc823076510on_val(A_1,B_1)),transi61620055on_val(R_1)))
             => ( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(A_1,B_1),produc823076510on_val(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_529_rtrancl__induct2,axiom,
    ! [Pa: fun_li860735411r_bool,Ax: list_char,Ay: list_char,Bx: list_char,By: list_char,R_1: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(produc2080520419t_char(produc5062597t_char(Ax,Ay),produc5062597t_char(Bx,By)),transi1095029602t_char(R_1)))
     => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_char,B_1: list_char,Aa: list_char,Ba: list_char] :
              ( hBOOL(member794220506t_char(produc2080520419t_char(produc5062597t_char(Ax,Ay),produc5062597t_char(A_1,B_1)),transi1095029602t_char(R_1)))
             => ( hBOOL(member794220506t_char(produc2080520419t_char(produc5062597t_char(A_1,B_1),produc5062597t_char(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_530_rtrancl__induct2,axiom,
    ! [Pa: fun_li221477r_bool,Ax: list_list_char,Ay: exp_list_char,Bx: list_list_char,By: exp_list_char,R_1: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(produc1897818327t_char(produc1147572817t_char(Ax,Ay),produc1147572817t_char(Bx,By)),transi198989188t_char(R_1)))
     => ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_list_char,B_1: exp_list_char,Aa: list_list_char,Ba: exp_list_char] :
              ( hBOOL(member1999287380t_char(produc1897818327t_char(produc1147572817t_char(Ax,Ay),produc1147572817t_char(A_1,B_1)),transi198989188t_char(R_1)))
             => ( hBOOL(member1999287380t_char(produc1897818327t_char(produc1147572817t_char(A_1,B_1),produc1147572817t_char(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_531_rtrancl__induct2,axiom,
    ! [Pa: fun_ex1201926843l_bool,Ax: exp_list_char,Ay: produc12694297on_val,Bx: exp_list_char,By: produc12694297on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(Bx,By)),transi2024712006on_val(R_1)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay))
       => ( ! [A_1: exp_list_char,B_1: produc12694297on_val,Aa: exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(A_1,B_1)),transi2024712006on_val(R_1)))
             => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A_1,B_1),produc1259058957on_val(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_532_rtrancl__induct2,axiom,
    ! [Pa: fun_li1372729616l_bool,Ax: list_exp_list_char,Ay: produc12694297on_val,Bx: list_exp_list_char,By: produc12694297on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Ax,Ay),produc379668296on_val(Bx,By)),transi374442731on_val(R_1)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Ax),Ay))
       => ( ! [A_1: list_exp_list_char,B_1: produc12694297on_val,Aa: list_exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Ax,Ay),produc379668296on_val(A_1,B_1)),transi374442731on_val(R_1)))
             => ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(A_1,B_1),produc379668296on_val(Aa,Ba)),R_1))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,A_1),B_1))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Aa),Ba)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Bx),By)) ) ) ) ).

tff(fact_533_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li800818899y_bool,Ax: list_char,Ay: produc917948472har_ty,Bx: list_char,By: produc917948472har_ty,R_1: fun_Pr1239516201y_bool] :
      ( hBOOL(member1664419796har_ty(produc2038128087har_ty(produc1002914035har_ty(Ax,Ay),produc1002914035har_ty(Bx,By)),transi1158914604har_ty(R_1)))
     => ( hBOOL(hAPP_P748443392y_bool(hAPP_l1665608433y_bool(Pa,Bx),By))
       => ( ! [A_1: list_char,B_1: produc917948472har_ty,Aa: list_char,Ba: produc917948472har_ty] :
              ( hBOOL(member1664419796har_ty(produc2038128087har_ty(produc1002914035har_ty(A_1,B_1),produc1002914035har_ty(Aa,Ba)),R_1))
             => ( hBOOL(member1664419796har_ty(produc2038128087har_ty(produc1002914035har_ty(Aa,Ba),produc1002914035har_ty(Bx,By)),transi1158914604har_ty(R_1)))
               => ( hBOOL(hAPP_P748443392y_bool(hAPP_l1665608433y_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P748443392y_bool(hAPP_l1665608433y_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P748443392y_bool(hAPP_l1665608433y_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_534_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr1633645595y_bool,Ax: produc1278157519t_char,Ay: ty,Bx: produc1278157519t_char,By: ty,R_1: fun_Pr330025897y_bool] :
      ( hBOOL(member1986596692har_ty(produc63273559har_ty(produc1265154397har_ty(Ax,Ay),produc1265154397har_ty(Bx,By)),transi935089046har_ty(R_1)))
     => ( hBOOL(hAPP_ty_bool(hAPP_P1845004857y_bool(Pa,Bx),By))
       => ( ! [A_1: produc1278157519t_char,B_1: ty,Aa: produc1278157519t_char,Ba: ty] :
              ( hBOOL(member1986596692har_ty(produc63273559har_ty(produc1265154397har_ty(A_1,B_1),produc1265154397har_ty(Aa,Ba)),R_1))
             => ( hBOOL(member1986596692har_ty(produc63273559har_ty(produc1265154397har_ty(Aa,Ba),produc1265154397har_ty(Bx,By)),transi935089046har_ty(R_1)))
               => ( hBOOL(hAPP_ty_bool(hAPP_P1845004857y_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_ty_bool(hAPP_P1845004857y_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_ty_bool(hAPP_P1845004857y_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_535_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li634443788y_bool,Ax: list_char,Ay: ty,Bx: list_char,By: ty,R_1: fun_Pr1670851305y_bool] :
      ( hBOOL(member119266708har_ty(produc1414300567har_ty(produc251930284har_ty(Ax,Ay),produc251930284har_ty(Bx,By)),transi1325206117har_ty(R_1)))
     => ( hBOOL(hAPP_ty_bool(hAPP_l1734756650y_bool(Pa,Bx),By))
       => ( ! [A_1: list_char,B_1: ty,Aa: list_char,Ba: ty] :
              ( hBOOL(member119266708har_ty(produc1414300567har_ty(produc251930284har_ty(A_1,B_1),produc251930284har_ty(Aa,Ba)),R_1))
             => ( hBOOL(member119266708har_ty(produc1414300567har_ty(produc251930284har_ty(Aa,Ba),produc251930284har_ty(Bx,By)),transi1325206117har_ty(R_1)))
               => ( hBOOL(hAPP_ty_bool(hAPP_l1734756650y_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_ty_bool(hAPP_l1734756650y_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_ty_bool(hAPP_l1734756650y_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_536_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr92408125r_bool,Ax: produc809539159t_char,Ay: produc809539159t_char,Bx: produc809539159t_char,By: produc809539159t_char,R_1: fun_Pr678067807r_bool] :
      ( hBOOL(member902595210t_char(produc253822483t_char(produc1897818327t_char(Ax,Ay),produc1897818327t_char(Bx,By)),transi1630776058t_char(R_1)))
     => ( hBOOL(hAPP_P2014166431r_bool(hAPP_P1939418767r_bool(Pa,Bx),By))
       => ( ! [A_1: produc809539159t_char,B_1: produc809539159t_char,Aa: produc809539159t_char,Ba: produc809539159t_char] :
              ( hBOOL(member902595210t_char(produc253822483t_char(produc1897818327t_char(A_1,B_1),produc1897818327t_char(Aa,Ba)),R_1))
             => ( hBOOL(member902595210t_char(produc253822483t_char(produc1897818327t_char(Aa,Ba),produc1897818327t_char(Bx,By)),transi1630776058t_char(R_1)))
               => ( hBOOL(hAPP_P2014166431r_bool(hAPP_P1939418767r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P2014166431r_bool(hAPP_P1939418767r_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P2014166431r_bool(hAPP_P1939418767r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_537_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr185059443r_bool,Ax: produc1278157519t_char,Ay: produc1278157519t_char,Bx: produc1278157519t_char,By: produc1278157519t_char,R_1: fun_Pr555864043r_bool] :
      ( hBOOL(member1689070870t_char(produc354099231t_char(produc2080520419t_char(Ax,Ay),produc2080520419t_char(Bx,By)),transi15035776t_char(R_1)))
     => ( hBOOL(hAPP_P449474095r_bool(hAPP_P663876415r_bool(Pa,Bx),By))
       => ( ! [A_1: produc1278157519t_char,B_1: produc1278157519t_char,Aa: produc1278157519t_char,Ba: produc1278157519t_char] :
              ( hBOOL(member1689070870t_char(produc354099231t_char(produc2080520419t_char(A_1,B_1),produc2080520419t_char(Aa,Ba)),R_1))
             => ( hBOOL(member1689070870t_char(produc354099231t_char(produc2080520419t_char(Aa,Ba),produc2080520419t_char(Bx,By)),transi15035776t_char(R_1)))
               => ( hBOOL(hAPP_P449474095r_bool(hAPP_P663876415r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P449474095r_bool(hAPP_P663876415r_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P449474095r_bool(hAPP_P663876415r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_538_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr788853347l_bool,Ax: produc639455274on_val,Ay: produc639455274on_val,Bx: produc639455274on_val,By: produc639455274on_val,R_1: fun_Pr1283539423l_bool] :
      ( hBOOL(member1114719754on_val(produc434506131on_val(produc499151895on_val(Ax,Ay),produc499151895on_val(Bx,By)),transi1953049786on_val(R_1)))
     => ( hBOOL(hAPP_P1235399154l_bool(hAPP_P416784693l_bool(Pa,Bx),By))
       => ( ! [A_1: produc639455274on_val,B_1: produc639455274on_val,Aa: produc639455274on_val,Ba: produc639455274on_val] :
              ( hBOOL(member1114719754on_val(produc434506131on_val(produc499151895on_val(A_1,B_1),produc499151895on_val(Aa,Ba)),R_1))
             => ( hBOOL(member1114719754on_val(produc434506131on_val(produc499151895on_val(Aa,Ba),produc499151895on_val(Bx,By)),transi1953049786on_val(R_1)))
               => ( hBOOL(hAPP_P1235399154l_bool(hAPP_P416784693l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P1235399154l_bool(hAPP_P416784693l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P1235399154l_bool(hAPP_P416784693l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_539_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr324760563l_bool,Ax: product_prod_val_val,Ay: product_prod_val_val,Bx: product_prod_val_val,By: product_prod_val_val,R_1: fun_Pr1443979083l_bool] :
      ( hBOOL(member384848502al_val(produc94135935al_val(produc1244920211al_val(Ax,Ay),produc1244920211al_val(Bx,By)),transi1927461808al_val(R_1)))
     => ( hBOOL(hAPP_P929938951l_bool(hAPP_P1815899455l_bool(Pa,Bx),By))
       => ( ! [A_1: product_prod_val_val,B_1: product_prod_val_val,Aa: product_prod_val_val,Ba: product_prod_val_val] :
              ( hBOOL(member384848502al_val(produc94135935al_val(produc1244920211al_val(A_1,B_1),produc1244920211al_val(Aa,Ba)),R_1))
             => ( hBOOL(member384848502al_val(produc94135935al_val(produc1244920211al_val(Aa,Ba),produc1244920211al_val(Bx,By)),transi1927461808al_val(R_1)))
               => ( hBOOL(hAPP_P929938951l_bool(hAPP_P1815899455l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P929938951l_bool(hAPP_P1815899455l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P929938951l_bool(hAPP_P1815899455l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_540_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr1713170355l_bool,Ax: produc1645268488al_val,Ay: produc1645268488al_val,Bx: produc1645268488al_val,By: produc1645268488al_val,R_1: fun_Pr180697551l_bool] :
      ( hBOOL(member23198458al_val(produc370870787al_val(produc1924279125al_val(Ax,Ay),produc1924279125al_val(Bx,By)),transi486718450al_val(R_1)))
     => ( hBOOL(hAPP_P943837928l_bool(hAPP_P323054207l_bool(Pa,Bx),By))
       => ( ! [A_1: produc1645268488al_val,B_1: produc1645268488al_val,Aa: produc1645268488al_val,Ba: produc1645268488al_val] :
              ( hBOOL(member23198458al_val(produc370870787al_val(produc1924279125al_val(A_1,B_1),produc1924279125al_val(Aa,Ba)),R_1))
             => ( hBOOL(member23198458al_val(produc370870787al_val(produc1924279125al_val(Aa,Ba),produc1924279125al_val(Bx,By)),transi486718450al_val(R_1)))
               => ( hBOOL(hAPP_P943837928l_bool(hAPP_P323054207l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P943837928l_bool(hAPP_P323054207l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P943837928l_bool(hAPP_P323054207l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_541_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr378536435r_bool,Ax: produc662261637t_char,Ay: produc662261637t_char,Bx: produc662261637t_char,By: produc662261637t_char,R_1: fun_Pr4797123r_bool] :
      ( hBOOL(member1105423342t_char(produc627518711t_char(produc1299387215t_char(Ax,Ay),produc1299387215t_char(Bx,By)),transi1803333868t_char(R_1)))
     => ( hBOOL(hAPP_P2118621157r_bool(hAPP_P357098431r_bool(Pa,Bx),By))
       => ( ! [A_1: produc662261637t_char,B_1: produc662261637t_char,Aa: produc662261637t_char,Ba: produc662261637t_char] :
              ( hBOOL(member1105423342t_char(produc627518711t_char(produc1299387215t_char(A_1,B_1),produc1299387215t_char(Aa,Ba)),R_1))
             => ( hBOOL(member1105423342t_char(produc627518711t_char(produc1299387215t_char(Aa,Ba),produc1299387215t_char(Bx,By)),transi1803333868t_char(R_1)))
               => ( hBOOL(hAPP_P2118621157r_bool(hAPP_P357098431r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P2118621157r_bool(hAPP_P357098431r_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P2118621157r_bool(hAPP_P357098431r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_542_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr1074372915r_bool,Ax: produc220283002t_char,Ay: produc220283002t_char,Bx: produc220283002t_char,By: produc220283002t_char,R_1: fun_Pr900028311r_bool] :
      ( hBOOL(member371591362t_char(produc913263563t_char(produc57279289t_char(Ax,Ay),produc57279289t_char(Bx,By)),transi1452021206t_char(R_1)))
     => ( hBOOL(hAPP_P1907982426r_bool(hAPP_P1214880255r_bool(Pa,Bx),By))
       => ( ! [A_1: produc220283002t_char,B_1: produc220283002t_char,Aa: produc220283002t_char,Ba: produc220283002t_char] :
              ( hBOOL(member371591362t_char(produc913263563t_char(produc57279289t_char(A_1,B_1),produc57279289t_char(Aa,Ba)),R_1))
             => ( hBOOL(member371591362t_char(produc913263563t_char(produc57279289t_char(Aa,Ba),produc57279289t_char(Bx,By)),transi1452021206t_char(R_1)))
               => ( hBOOL(hAPP_P1907982426r_bool(hAPP_P1214880255r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P1907982426r_bool(hAPP_P1214880255r_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P1907982426r_bool(hAPP_P1214880255r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_543_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr1794669603r_bool,Ax: produc1285161482t_char,Ay: produc1285161482t_char,Bx: produc1285161482t_char,By: produc1285161482t_char,R_1: fun_Pr1493019359r_bool] :
      ( hBOOL(member1934728458t_char(produc1288549779t_char(produc24551831t_char(Ax,Ay),produc24551831t_char(Bx,By)),transi2072254650t_char(R_1)))
     => ( hBOOL(hAPP_P92196306r_bool(hAPP_P1928969845r_bool(Pa,Bx),By))
       => ( ! [A_1: produc1285161482t_char,B_1: produc1285161482t_char,Aa: produc1285161482t_char,Ba: produc1285161482t_char] :
              ( hBOOL(member1934728458t_char(produc1288549779t_char(produc24551831t_char(A_1,B_1),produc24551831t_char(Aa,Ba)),R_1))
             => ( hBOOL(member1934728458t_char(produc1288549779t_char(produc24551831t_char(Aa,Ba),produc24551831t_char(Bx,By)),transi2072254650t_char(R_1)))
               => ( hBOOL(hAPP_P92196306r_bool(hAPP_P1928969845r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P92196306r_bool(hAPP_P1928969845r_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P92196306r_bool(hAPP_P1928969845r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_544_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr1511900787l_bool,Ax: produc430140671on_val,Ay: produc430140671on_val,Bx: produc430140671on_val,By: produc430140671on_val,R_1: fun_Pr1329133739l_bool] :
      ( hBOOL(member1837727190on_val(produc722767071on_val(produc1951691075on_val(Ax,Ay),produc1951691075on_val(Bx,By)),transi1751449568on_val(R_1)))
     => ( hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(Pa,Bx),By))
       => ( ! [A_1: produc430140671on_val,B_1: produc430140671on_val,Aa: produc430140671on_val,Ba: produc430140671on_val] :
              ( hBOOL(member1837727190on_val(produc722767071on_val(produc1951691075on_val(A_1,B_1),produc1951691075on_val(Aa,Ba)),R_1))
             => ( hBOOL(member1837727190on_val(produc722767071on_val(produc1951691075on_val(Aa,Ba),produc1951691075on_val(Bx,By)),transi1751449568on_val(R_1)))
               => ( hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P1333315679l_bool(hAPP_P220718911l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_545_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr598845249l_bool,Ax: produc12694297on_val,Ay: produc12694297on_val,Bx: produc12694297on_val,By: produc12694297on_val,R_1: fun_Pr27327839l_bool] :
      ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Ax,Ay),produc870913623on_val(Bx,By)),transi594096122on_val(R_1)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Bx),By))
       => ( ! [A_1: produc12694297on_val,B_1: produc12694297on_val,Aa: produc12694297on_val,Ba: produc12694297on_val] :
              ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(A_1,B_1),produc870913623on_val(Aa,Ba)),R_1))
             => ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Aa,Ba),produc870913623on_val(Bx,By)),transi594096122on_val(R_1)))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_P1988153107l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_546_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr220980979l_bool,Ax: produc1102272487on_val,Ay: produc1102272487on_val,Bx: produc1102272487on_val,By: produc1102272487on_val,R_1: fun_Pr111684683l_bool] :
      ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Ax,Ay),produc1564932627on_val(Bx,By)),transi678815536on_val(R_1)))
     => ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Bx),By))
       => ( ! [A_1: produc1102272487on_val,B_1: produc1102272487on_val,Aa: produc1102272487on_val,Ba: produc1102272487on_val] :
              ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(A_1,B_1),produc1564932627on_val(Aa,Ba)),R_1))
             => ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Aa,Ba),produc1564932627on_val(Bx,By)),transi678815536on_val(R_1)))
               => ( hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P282169671l_bool(hAPP_P2062527807l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_547_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr633696065l_bool,Ax: produc124828825on_val,Ay: produc124828825on_val,Bx: produc124828825on_val,By: produc124828825on_val,R_1: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(Bx,By)),transi910771962on_val(R_1)))
     => ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By))
       => ( ! [A_1: produc124828825on_val,B_1: produc124828825on_val,Aa: produc124828825on_val,Ba: produc124828825on_val] :
              ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A_1,B_1),produc1441475159on_val(Aa,Ba)),R_1))
             => ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Aa,Ba),produc1441475159on_val(Bx,By)),transi910771962on_val(R_1)))
               => ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_548_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_fu100249073l_bool,Ax: fun_na939144002on_val,Ay: fun_li1432931796on_val,Bx: fun_na939144002on_val,By: fun_li1432931796on_val,R_1: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(Bx,By)),transi921647814on_val(R_1)))
     => ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By))
       => ( ! [A_1: fun_na939144002on_val,B_1: fun_li1432931796on_val,Aa: fun_na939144002on_val,Ba: fun_li1432931796on_val] :
              ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A_1,B_1),produc899768717on_val(Aa,Ba)),R_1))
             => ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Aa,Ba),produc899768717on_val(Bx,By)),transi921647814on_val(R_1)))
               => ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_549_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_Pr597144499l_bool,Ax: produc2061676504on_val,Ay: produc2061676504on_val,Bx: produc2061676504on_val,By: produc2061676504on_val,R_1: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(produc1611380469on_val(Ax,Ay),produc1611380469on_val(Bx,By)),transi208336786on_val(R_1)))
     => ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Bx),By))
       => ( ! [A_1: produc2061676504on_val,B_1: produc2061676504on_val,Aa: produc2061676504on_val,Ba: produc2061676504on_val] :
              ( hBOOL(member88670778on_val(produc1951691075on_val(produc1611380469on_val(A_1,B_1),produc1611380469on_val(Aa,Ba)),R_1))
             => ( hBOOL(member88670778on_val(produc1951691075on_val(produc1611380469on_val(Aa,Ba),produc1611380469on_val(Bx,By)),transi208336786on_val(R_1)))
               => ( hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_550_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li1024794712r_bool,Ax: list_list_char,Ay: produc220283002t_char,Bx: list_list_char,By: produc220283002t_char,R_1: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Ax,Ay),produc921874948t_char(Bx,By)),transi122195895t_char(R_1)))
     => ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Bx),By))
       => ( ! [A_1: list_list_char,B_1: produc220283002t_char,Aa: list_list_char,Ba: produc220283002t_char] :
              ( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(A_1,B_1),produc921874948t_char(Aa,Ba)),R_1))
             => ( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Aa,Ba),produc921874948t_char(Bx,By)),transi122195895t_char(R_1)))
               => ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_551_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li887890578r_bool,Ax: list_ty,Ay: produc662261637t_char,Bx: list_ty,By: produc662261637t_char,R_1: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Ax,Ay),produc1909267824t_char(Bx,By)),transi1257872013t_char(R_1)))
     => ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Bx),By))
       => ( ! [A_1: list_ty,B_1: produc662261637t_char,Aa: list_ty,Ba: produc662261637t_char] :
              ( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(A_1,B_1),produc1909267824t_char(Aa,Ba)),R_1))
             => ( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Aa,Ba),produc1909267824t_char(Bx,By)),transi1257872013t_char(R_1)))
               => ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_552_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li826105035r_bool,Ax: list_val,Ay: exp_list_char,Bx: list_val,By: exp_list_char,R_1: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Ax,Ay),produc1916172923t_char(Bx,By)),transi1789604888t_char(R_1)))
     => ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Bx),By))
       => ( ! [A_1: list_val,B_1: exp_list_char,Aa: list_val,Ba: exp_list_char] :
              ( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(A_1,B_1),produc1916172923t_char(Aa,Ba)),R_1))
             => ( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Aa,Ba),produc1916172923t_char(Bx,By)),transi1789604888t_char(R_1)))
               => ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_553_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_bo1454185032l_bool,Ax: bop,Ay: product_prod_val_val,Bx: bop,By: product_prod_val_val,R_1: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(produc1924279125al_val(produc621191550al_val(Ax,Ay),produc621191550al_val(Bx,By)),transi1906258203al_val(R_1)))
     => ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Bx),By))
       => ( ! [A_1: bop,B_1: product_prod_val_val,Aa: bop,Ba: product_prod_val_val] :
              ( hBOOL(member1732271180al_val(produc1924279125al_val(produc621191550al_val(A_1,B_1),produc621191550al_val(Aa,Ba)),R_1))
             => ( hBOOL(member1732271180al_val(produc1924279125al_val(produc621191550al_val(Aa,Ba),produc621191550al_val(Bx,By)),transi1906258203al_val(R_1)))
               => ( hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_554_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_val_fun_val_bool,Ax: val,Ay: val,Bx: val,By: val,R_1: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(produc1244920211al_val(product_Pair_val_val(Ax,Ay),product_Pair_val_val(Bx,By)),transi1423755450al_val(R_1)))
     => ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Bx),By))
       => ( ! [A_1: val,B_1: val,Aa: val,Ba: val] :
              ( hBOOL(member837208074al_val(produc1244920211al_val(product_Pair_val_val(A_1,B_1),product_Pair_val_val(Aa,Ba)),R_1))
             => ( hBOOL(member837208074al_val(produc1244920211al_val(product_Pair_val_val(Aa,Ba),product_Pair_val_val(Bx,By)),transi1423755450al_val(R_1)))
               => ( hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_555_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li823162622l_bool,Ax: list_char,Ay: fun_Pr806764899on_val,Bx: list_char,By: fun_Pr806764899on_val,R_1: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Ax,Ay),produc823076510on_val(Bx,By)),transi61620055on_val(R_1)))
     => ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Bx),By))
       => ( ! [A_1: list_char,B_1: fun_Pr806764899on_val,Aa: list_char,Ba: fun_Pr806764899on_val] :
              ( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(A_1,B_1),produc823076510on_val(Aa,Ba)),R_1))
             => ( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Aa,Ba),produc823076510on_val(Bx,By)),transi61620055on_val(R_1)))
               => ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_556_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li860735411r_bool,Ax: list_char,Ay: list_char,Bx: list_char,By: list_char,R_1: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(produc2080520419t_char(produc5062597t_char(Ax,Ay),produc5062597t_char(Bx,By)),transi1095029602t_char(R_1)))
     => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Bx),By))
       => ( ! [A_1: list_char,B_1: list_char,Aa: list_char,Ba: list_char] :
              ( hBOOL(member794220506t_char(produc2080520419t_char(produc5062597t_char(A_1,B_1),produc5062597t_char(Aa,Ba)),R_1))
             => ( hBOOL(member794220506t_char(produc2080520419t_char(produc5062597t_char(Aa,Ba),produc5062597t_char(Bx,By)),transi1095029602t_char(R_1)))
               => ( hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_557_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li221477r_bool,Ax: list_list_char,Ay: exp_list_char,Bx: list_list_char,By: exp_list_char,R_1: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(produc1897818327t_char(produc1147572817t_char(Ax,Ay),produc1147572817t_char(Bx,By)),transi198989188t_char(R_1)))
     => ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Bx),By))
       => ( ! [A_1: list_list_char,B_1: exp_list_char,Aa: list_list_char,Ba: exp_list_char] :
              ( hBOOL(member1999287380t_char(produc1897818327t_char(produc1147572817t_char(A_1,B_1),produc1147572817t_char(Aa,Ba)),R_1))
             => ( hBOOL(member1999287380t_char(produc1897818327t_char(produc1147572817t_char(Aa,Ba),produc1147572817t_char(Bx,By)),transi198989188t_char(R_1)))
               => ( hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_558_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_ex1201926843l_bool,Ax: exp_list_char,Ay: produc12694297on_val,Bx: exp_list_char,By: produc12694297on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(Bx,By)),transi2024712006on_val(R_1)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By))
       => ( ! [A_1: exp_list_char,B_1: produc12694297on_val,Aa: exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A_1,B_1),produc1259058957on_val(Aa,Ba)),R_1))
             => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Aa,Ba),produc1259058957on_val(Bx,By)),transi2024712006on_val(R_1)))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_559_converse__rtrancl__induct2,axiom,
    ! [Pa: fun_li1372729616l_bool,Ax: list_exp_list_char,Ay: produc12694297on_val,Bx: list_exp_list_char,By: produc12694297on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Ax,Ay),produc379668296on_val(Bx,By)),transi374442731on_val(R_1)))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Bx),By))
       => ( ! [A_1: list_exp_list_char,B_1: produc12694297on_val,Aa: list_exp_list_char,Ba: produc12694297on_val] :
              ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(A_1,B_1),produc379668296on_val(Aa,Ba)),R_1))
             => ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Aa,Ba),produc379668296on_val(Bx,By)),transi374442731on_val(R_1)))
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Aa),Ba))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,A_1),B_1)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Ax),Ay)) ) ) ) ).

tff(fact_560_converse__rtranclE2,axiom,
    ! [Xa_1: list_char,Xb_1: produc917948472har_ty,Za: list_char,Zb: produc917948472har_ty,R_1: fun_Pr1239516201y_bool] :
      ( hBOOL(member1664419796har_ty(produc2038128087har_ty(produc1002914035har_ty(Xa_1,Xb_1),produc1002914035har_ty(Za,Zb)),transi1158914604har_ty(R_1)))
     => ( ( produc1002914035har_ty(Xa_1,Xb_1) != produc1002914035har_ty(Za,Zb) )
       => ~ ! [A_1: list_char,B_1: produc917948472har_ty] :
              ( hBOOL(member1664419796har_ty(produc2038128087har_ty(produc1002914035har_ty(Xa_1,Xb_1),produc1002914035har_ty(A_1,B_1)),R_1))
             => ~ hBOOL(member1664419796har_ty(produc2038128087har_ty(produc1002914035har_ty(A_1,B_1),produc1002914035har_ty(Za,Zb)),transi1158914604har_ty(R_1))) ) ) ) ).

tff(fact_561_converse__rtranclE2,axiom,
    ! [Xa_1: produc1278157519t_char,Xb_1: ty,Za: produc1278157519t_char,Zb: ty,R_1: fun_Pr330025897y_bool] :
      ( hBOOL(member1986596692har_ty(produc63273559har_ty(produc1265154397har_ty(Xa_1,Xb_1),produc1265154397har_ty(Za,Zb)),transi935089046har_ty(R_1)))
     => ( ( produc1265154397har_ty(Xa_1,Xb_1) != produc1265154397har_ty(Za,Zb) )
       => ~ ! [A_1: produc1278157519t_char,B_1: ty] :
              ( hBOOL(member1986596692har_ty(produc63273559har_ty(produc1265154397har_ty(Xa_1,Xb_1),produc1265154397har_ty(A_1,B_1)),R_1))
             => ~ hBOOL(member1986596692har_ty(produc63273559har_ty(produc1265154397har_ty(A_1,B_1),produc1265154397har_ty(Za,Zb)),transi935089046har_ty(R_1))) ) ) ) ).

tff(fact_562_converse__rtranclE2,axiom,
    ! [Xa_1: list_char,Xb_1: ty,Za: list_char,Zb: ty,R_1: fun_Pr1670851305y_bool] :
      ( hBOOL(member119266708har_ty(produc1414300567har_ty(produc251930284har_ty(Xa_1,Xb_1),produc251930284har_ty(Za,Zb)),transi1325206117har_ty(R_1)))
     => ( ( produc251930284har_ty(Xa_1,Xb_1) != produc251930284har_ty(Za,Zb) )
       => ~ ! [A_1: list_char,B_1: ty] :
              ( hBOOL(member119266708har_ty(produc1414300567har_ty(produc251930284har_ty(Xa_1,Xb_1),produc251930284har_ty(A_1,B_1)),R_1))
             => ~ hBOOL(member119266708har_ty(produc1414300567har_ty(produc251930284har_ty(A_1,B_1),produc251930284har_ty(Za,Zb)),transi1325206117har_ty(R_1))) ) ) ) ).

tff(fact_563_converse__rtranclE2,axiom,
    ! [Xa_1: produc809539159t_char,Xb_1: produc809539159t_char,Za: produc809539159t_char,Zb: produc809539159t_char,R_1: fun_Pr678067807r_bool] :
      ( hBOOL(member902595210t_char(produc253822483t_char(produc1897818327t_char(Xa_1,Xb_1),produc1897818327t_char(Za,Zb)),transi1630776058t_char(R_1)))
     => ( ( produc1897818327t_char(Xa_1,Xb_1) != produc1897818327t_char(Za,Zb) )
       => ~ ! [A_1: produc809539159t_char,B_1: produc809539159t_char] :
              ( hBOOL(member902595210t_char(produc253822483t_char(produc1897818327t_char(Xa_1,Xb_1),produc1897818327t_char(A_1,B_1)),R_1))
             => ~ hBOOL(member902595210t_char(produc253822483t_char(produc1897818327t_char(A_1,B_1),produc1897818327t_char(Za,Zb)),transi1630776058t_char(R_1))) ) ) ) ).

tff(fact_564_converse__rtranclE2,axiom,
    ! [Xa_1: produc1278157519t_char,Xb_1: produc1278157519t_char,Za: produc1278157519t_char,Zb: produc1278157519t_char,R_1: fun_Pr555864043r_bool] :
      ( hBOOL(member1689070870t_char(produc354099231t_char(produc2080520419t_char(Xa_1,Xb_1),produc2080520419t_char(Za,Zb)),transi15035776t_char(R_1)))
     => ( ( produc2080520419t_char(Xa_1,Xb_1) != produc2080520419t_char(Za,Zb) )
       => ~ ! [A_1: produc1278157519t_char,B_1: produc1278157519t_char] :
              ( hBOOL(member1689070870t_char(produc354099231t_char(produc2080520419t_char(Xa_1,Xb_1),produc2080520419t_char(A_1,B_1)),R_1))
             => ~ hBOOL(member1689070870t_char(produc354099231t_char(produc2080520419t_char(A_1,B_1),produc2080520419t_char(Za,Zb)),transi15035776t_char(R_1))) ) ) ) ).

tff(fact_565_converse__rtranclE2,axiom,
    ! [Xa_1: produc639455274on_val,Xb_1: produc639455274on_val,Za: produc639455274on_val,Zb: produc639455274on_val,R_1: fun_Pr1283539423l_bool] :
      ( hBOOL(member1114719754on_val(produc434506131on_val(produc499151895on_val(Xa_1,Xb_1),produc499151895on_val(Za,Zb)),transi1953049786on_val(R_1)))
     => ( ( produc499151895on_val(Xa_1,Xb_1) != produc499151895on_val(Za,Zb) )
       => ~ ! [A_1: produc639455274on_val,B_1: produc639455274on_val] :
              ( hBOOL(member1114719754on_val(produc434506131on_val(produc499151895on_val(Xa_1,Xb_1),produc499151895on_val(A_1,B_1)),R_1))
             => ~ hBOOL(member1114719754on_val(produc434506131on_val(produc499151895on_val(A_1,B_1),produc499151895on_val(Za,Zb)),transi1953049786on_val(R_1))) ) ) ) ).

tff(fact_566_converse__rtranclE2,axiom,
    ! [Xa_1: product_prod_val_val,Xb_1: product_prod_val_val,Za: product_prod_val_val,Zb: product_prod_val_val,R_1: fun_Pr1443979083l_bool] :
      ( hBOOL(member384848502al_val(produc94135935al_val(produc1244920211al_val(Xa_1,Xb_1),produc1244920211al_val(Za,Zb)),transi1927461808al_val(R_1)))
     => ( ( produc1244920211al_val(Xa_1,Xb_1) != produc1244920211al_val(Za,Zb) )
       => ~ ! [A_1: product_prod_val_val,B_1: product_prod_val_val] :
              ( hBOOL(member384848502al_val(produc94135935al_val(produc1244920211al_val(Xa_1,Xb_1),produc1244920211al_val(A_1,B_1)),R_1))
             => ~ hBOOL(member384848502al_val(produc94135935al_val(produc1244920211al_val(A_1,B_1),produc1244920211al_val(Za,Zb)),transi1927461808al_val(R_1))) ) ) ) ).

tff(fact_567_converse__rtranclE2,axiom,
    ! [Xa_1: produc1645268488al_val,Xb_1: produc1645268488al_val,Za: produc1645268488al_val,Zb: produc1645268488al_val,R_1: fun_Pr180697551l_bool] :
      ( hBOOL(member23198458al_val(produc370870787al_val(produc1924279125al_val(Xa_1,Xb_1),produc1924279125al_val(Za,Zb)),transi486718450al_val(R_1)))
     => ( ( produc1924279125al_val(Xa_1,Xb_1) != produc1924279125al_val(Za,Zb) )
       => ~ ! [A_1: produc1645268488al_val,B_1: produc1645268488al_val] :
              ( hBOOL(member23198458al_val(produc370870787al_val(produc1924279125al_val(Xa_1,Xb_1),produc1924279125al_val(A_1,B_1)),R_1))
             => ~ hBOOL(member23198458al_val(produc370870787al_val(produc1924279125al_val(A_1,B_1),produc1924279125al_val(Za,Zb)),transi486718450al_val(R_1))) ) ) ) ).

tff(fact_568_converse__rtranclE2,axiom,
    ! [Xa_1: produc662261637t_char,Xb_1: produc662261637t_char,Za: produc662261637t_char,Zb: produc662261637t_char,R_1: fun_Pr4797123r_bool] :
      ( hBOOL(member1105423342t_char(produc627518711t_char(produc1299387215t_char(Xa_1,Xb_1),produc1299387215t_char(Za,Zb)),transi1803333868t_char(R_1)))
     => ( ( produc1299387215t_char(Xa_1,Xb_1) != produc1299387215t_char(Za,Zb) )
       => ~ ! [A_1: produc662261637t_char,B_1: produc662261637t_char] :
              ( hBOOL(member1105423342t_char(produc627518711t_char(produc1299387215t_char(Xa_1,Xb_1),produc1299387215t_char(A_1,B_1)),R_1))
             => ~ hBOOL(member1105423342t_char(produc627518711t_char(produc1299387215t_char(A_1,B_1),produc1299387215t_char(Za,Zb)),transi1803333868t_char(R_1))) ) ) ) ).

tff(fact_569_converse__rtranclE2,axiom,
    ! [Xa_1: produc220283002t_char,Xb_1: produc220283002t_char,Za: produc220283002t_char,Zb: produc220283002t_char,R_1: fun_Pr900028311r_bool] :
      ( hBOOL(member371591362t_char(produc913263563t_char(produc57279289t_char(Xa_1,Xb_1),produc57279289t_char(Za,Zb)),transi1452021206t_char(R_1)))
     => ( ( produc57279289t_char(Xa_1,Xb_1) != produc57279289t_char(Za,Zb) )
       => ~ ! [A_1: produc220283002t_char,B_1: produc220283002t_char] :
              ( hBOOL(member371591362t_char(produc913263563t_char(produc57279289t_char(Xa_1,Xb_1),produc57279289t_char(A_1,B_1)),R_1))
             => ~ hBOOL(member371591362t_char(produc913263563t_char(produc57279289t_char(A_1,B_1),produc57279289t_char(Za,Zb)),transi1452021206t_char(R_1))) ) ) ) ).

tff(fact_570_converse__rtranclE2,axiom,
    ! [Xa_1: produc1285161482t_char,Xb_1: produc1285161482t_char,Za: produc1285161482t_char,Zb: produc1285161482t_char,R_1: fun_Pr1493019359r_bool] :
      ( hBOOL(member1934728458t_char(produc1288549779t_char(produc24551831t_char(Xa_1,Xb_1),produc24551831t_char(Za,Zb)),transi2072254650t_char(R_1)))
     => ( ( produc24551831t_char(Xa_1,Xb_1) != produc24551831t_char(Za,Zb) )
       => ~ ! [A_1: produc1285161482t_char,B_1: produc1285161482t_char] :
              ( hBOOL(member1934728458t_char(produc1288549779t_char(produc24551831t_char(Xa_1,Xb_1),produc24551831t_char(A_1,B_1)),R_1))
             => ~ hBOOL(member1934728458t_char(produc1288549779t_char(produc24551831t_char(A_1,B_1),produc24551831t_char(Za,Zb)),transi2072254650t_char(R_1))) ) ) ) ).

tff(fact_571_converse__rtranclE2,axiom,
    ! [Xa_1: produc430140671on_val,Xb_1: produc430140671on_val,Za: produc430140671on_val,Zb: produc430140671on_val,R_1: fun_Pr1329133739l_bool] :
      ( hBOOL(member1837727190on_val(produc722767071on_val(produc1951691075on_val(Xa_1,Xb_1),produc1951691075on_val(Za,Zb)),transi1751449568on_val(R_1)))
     => ( ( produc1951691075on_val(Xa_1,Xb_1) != produc1951691075on_val(Za,Zb) )
       => ~ ! [A_1: produc430140671on_val,B_1: produc430140671on_val] :
              ( hBOOL(member1837727190on_val(produc722767071on_val(produc1951691075on_val(Xa_1,Xb_1),produc1951691075on_val(A_1,B_1)),R_1))
             => ~ hBOOL(member1837727190on_val(produc722767071on_val(produc1951691075on_val(A_1,B_1),produc1951691075on_val(Za,Zb)),transi1751449568on_val(R_1))) ) ) ) ).

tff(fact_572_converse__rtranclE2,axiom,
    ! [Xa_1: produc12694297on_val,Xb_1: produc12694297on_val,Za: produc12694297on_val,Zb: produc12694297on_val,R_1: fun_Pr27327839l_bool] :
      ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Xa_1,Xb_1),produc870913623on_val(Za,Zb)),transi594096122on_val(R_1)))
     => ( ( produc870913623on_val(Xa_1,Xb_1) != produc870913623on_val(Za,Zb) )
       => ~ ! [A_1: produc12694297on_val,B_1: produc12694297on_val] :
              ( hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(Xa_1,Xb_1),produc870913623on_val(A_1,B_1)),R_1))
             => ~ hBOOL(member2032527242on_val(produc935654419on_val(produc870913623on_val(A_1,B_1),produc870913623on_val(Za,Zb)),transi594096122on_val(R_1))) ) ) ) ).

tff(fact_573_converse__rtranclE2,axiom,
    ! [Xa_1: produc1102272487on_val,Xb_1: produc1102272487on_val,Za: produc1102272487on_val,Zb: produc1102272487on_val,R_1: fun_Pr111684683l_bool] :
      ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Xa_1,Xb_1),produc1564932627on_val(Za,Zb)),transi678815536on_val(R_1)))
     => ( ( produc1564932627on_val(Xa_1,Xb_1) != produc1564932627on_val(Za,Zb) )
       => ~ ! [A_1: produc1102272487on_val,B_1: produc1102272487on_val] :
              ( hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(Xa_1,Xb_1),produc1564932627on_val(A_1,B_1)),R_1))
             => ~ hBOOL(member712690550on_val(produc1729053055on_val(produc1564932627on_val(A_1,B_1),produc1564932627on_val(Za,Zb)),transi678815536on_val(R_1))) ) ) ) ).

tff(fact_574_converse__rtranclE2,axiom,
    ! [Xa_1: produc124828825on_val,Xb_1: produc124828825on_val,Za: produc124828825on_val,Zb: produc124828825on_val,R_1: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Xa_1,Xb_1),produc1441475159on_val(Za,Zb)),transi910771962on_val(R_1)))
     => ( ( produc1441475159on_val(Xa_1,Xb_1) != produc1441475159on_val(Za,Zb) )
       => ~ ! [A_1: produc124828825on_val,B_1: produc124828825on_val] :
              ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Xa_1,Xb_1),produc1441475159on_val(A_1,B_1)),R_1))
             => ~ hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A_1,B_1),produc1441475159on_val(Za,Zb)),transi910771962on_val(R_1))) ) ) ) ).

tff(fact_575_converse__rtranclE2,axiom,
    ! [Xa_1: fun_na939144002on_val,Xb_1: fun_li1432931796on_val,Za: fun_na939144002on_val,Zb: fun_li1432931796on_val,R_1: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Xa_1,Xb_1),produc899768717on_val(Za,Zb)),transi921647814on_val(R_1)))
     => ( ( produc899768717on_val(Xa_1,Xb_1) != produc899768717on_val(Za,Zb) )
       => ~ ! [A_1: fun_na939144002on_val,B_1: fun_li1432931796on_val] :
              ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Xa_1,Xb_1),produc899768717on_val(A_1,B_1)),R_1))
             => ~ hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A_1,B_1),produc899768717on_val(Za,Zb)),transi921647814on_val(R_1))) ) ) ) ).

tff(fact_576_converse__rtranclE2,axiom,
    ! [Xa_1: produc2061676504on_val,Xb_1: produc2061676504on_val,Za: produc2061676504on_val,Zb: produc2061676504on_val,R_1: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(produc1611380469on_val(Xa_1,Xb_1),produc1611380469on_val(Za,Zb)),transi208336786on_val(R_1)))
     => ( ( produc1611380469on_val(Xa_1,Xb_1) != produc1611380469on_val(Za,Zb) )
       => ~ ! [A_1: produc2061676504on_val,B_1: produc2061676504on_val] :
              ( hBOOL(member88670778on_val(produc1951691075on_val(produc1611380469on_val(Xa_1,Xb_1),produc1611380469on_val(A_1,B_1)),R_1))
             => ~ hBOOL(member88670778on_val(produc1951691075on_val(produc1611380469on_val(A_1,B_1),produc1611380469on_val(Za,Zb)),transi208336786on_val(R_1))) ) ) ) ).

tff(fact_577_converse__rtranclE2,axiom,
    ! [Xa_1: list_list_char,Xb_1: produc220283002t_char,Za: list_list_char,Zb: produc220283002t_char,R_1: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Xa_1,Xb_1),produc921874948t_char(Za,Zb)),transi122195895t_char(R_1)))
     => ( ( produc921874948t_char(Xa_1,Xb_1) != produc921874948t_char(Za,Zb) )
       => ~ ! [A_1: list_list_char,B_1: produc220283002t_char] :
              ( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Xa_1,Xb_1),produc921874948t_char(A_1,B_1)),R_1))
             => ~ hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(A_1,B_1),produc921874948t_char(Za,Zb)),transi122195895t_char(R_1))) ) ) ) ).

tff(fact_578_converse__rtranclE2,axiom,
    ! [Xa_1: list_ty,Xb_1: produc662261637t_char,Za: list_ty,Zb: produc662261637t_char,R_1: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Xa_1,Xb_1),produc1909267824t_char(Za,Zb)),transi1257872013t_char(R_1)))
     => ( ( produc1909267824t_char(Xa_1,Xb_1) != produc1909267824t_char(Za,Zb) )
       => ~ ! [A_1: list_ty,B_1: produc662261637t_char] :
              ( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Xa_1,Xb_1),produc1909267824t_char(A_1,B_1)),R_1))
             => ~ hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(A_1,B_1),produc1909267824t_char(Za,Zb)),transi1257872013t_char(R_1))) ) ) ) ).

tff(fact_579_converse__rtranclE2,axiom,
    ! [Xa_1: list_val,Xb_1: exp_list_char,Za: list_val,Zb: exp_list_char,R_1: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Xa_1,Xb_1),produc1916172923t_char(Za,Zb)),transi1789604888t_char(R_1)))
     => ( ( produc1916172923t_char(Xa_1,Xb_1) != produc1916172923t_char(Za,Zb) )
       => ~ ! [A_1: list_val,B_1: exp_list_char] :
              ( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Xa_1,Xb_1),produc1916172923t_char(A_1,B_1)),R_1))
             => ~ hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(A_1,B_1),produc1916172923t_char(Za,Zb)),transi1789604888t_char(R_1))) ) ) ) ).

tff(fact_580_converse__rtranclE2,axiom,
    ! [Xa_1: bop,Xb_1: product_prod_val_val,Za: bop,Zb: product_prod_val_val,R_1: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(produc1924279125al_val(produc621191550al_val(Xa_1,Xb_1),produc621191550al_val(Za,Zb)),transi1906258203al_val(R_1)))
     => ( ( produc621191550al_val(Xa_1,Xb_1) != produc621191550al_val(Za,Zb) )
       => ~ ! [A_1: bop,B_1: product_prod_val_val] :
              ( hBOOL(member1732271180al_val(produc1924279125al_val(produc621191550al_val(Xa_1,Xb_1),produc621191550al_val(A_1,B_1)),R_1))
             => ~ hBOOL(member1732271180al_val(produc1924279125al_val(produc621191550al_val(A_1,B_1),produc621191550al_val(Za,Zb)),transi1906258203al_val(R_1))) ) ) ) ).

tff(fact_581_converse__rtranclE2,axiom,
    ! [Xa_1: val,Xb_1: val,Za: val,Zb: val,R_1: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(produc1244920211al_val(product_Pair_val_val(Xa_1,Xb_1),product_Pair_val_val(Za,Zb)),transi1423755450al_val(R_1)))
     => ( ( product_Pair_val_val(Xa_1,Xb_1) != product_Pair_val_val(Za,Zb) )
       => ~ ! [A_1: val,B_1: val] :
              ( hBOOL(member837208074al_val(produc1244920211al_val(product_Pair_val_val(Xa_1,Xb_1),product_Pair_val_val(A_1,B_1)),R_1))
             => ~ hBOOL(member837208074al_val(produc1244920211al_val(product_Pair_val_val(A_1,B_1),product_Pair_val_val(Za,Zb)),transi1423755450al_val(R_1))) ) ) ) ).

tff(fact_582_converse__rtranclE2,axiom,
    ! [Xa_1: list_char,Xb_1: fun_Pr806764899on_val,Za: list_char,Zb: fun_Pr806764899on_val,R_1: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Xa_1,Xb_1),produc823076510on_val(Za,Zb)),transi61620055on_val(R_1)))
     => ( ( produc823076510on_val(Xa_1,Xb_1) != produc823076510on_val(Za,Zb) )
       => ~ ! [A_1: list_char,B_1: fun_Pr806764899on_val] :
              ( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Xa_1,Xb_1),produc823076510on_val(A_1,B_1)),R_1))
             => ~ hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(A_1,B_1),produc823076510on_val(Za,Zb)),transi61620055on_val(R_1))) ) ) ) ).

tff(fact_583_converse__rtranclE2,axiom,
    ! [Xa_1: list_char,Xb_1: list_char,Za: list_char,Zb: list_char,R_1: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(produc2080520419t_char(produc5062597t_char(Xa_1,Xb_1),produc5062597t_char(Za,Zb)),transi1095029602t_char(R_1)))
     => ( ( produc5062597t_char(Xa_1,Xb_1) != produc5062597t_char(Za,Zb) )
       => ~ ! [A_1: list_char,B_1: list_char] :
              ( hBOOL(member794220506t_char(produc2080520419t_char(produc5062597t_char(Xa_1,Xb_1),produc5062597t_char(A_1,B_1)),R_1))
             => ~ hBOOL(member794220506t_char(produc2080520419t_char(produc5062597t_char(A_1,B_1),produc5062597t_char(Za,Zb)),transi1095029602t_char(R_1))) ) ) ) ).

tff(fact_584_converse__rtranclE2,axiom,
    ! [Xa_1: list_list_char,Xb_1: exp_list_char,Za: list_list_char,Zb: exp_list_char,R_1: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(produc1897818327t_char(produc1147572817t_char(Xa_1,Xb_1),produc1147572817t_char(Za,Zb)),transi198989188t_char(R_1)))
     => ( ( produc1147572817t_char(Xa_1,Xb_1) != produc1147572817t_char(Za,Zb) )
       => ~ ! [A_1: list_list_char,B_1: exp_list_char] :
              ( hBOOL(member1999287380t_char(produc1897818327t_char(produc1147572817t_char(Xa_1,Xb_1),produc1147572817t_char(A_1,B_1)),R_1))
             => ~ hBOOL(member1999287380t_char(produc1897818327t_char(produc1147572817t_char(A_1,B_1),produc1147572817t_char(Za,Zb)),transi198989188t_char(R_1))) ) ) ) ).

tff(fact_585_converse__rtranclE2,axiom,
    ! [Xa_1: exp_list_char,Xb_1: produc12694297on_val,Za: exp_list_char,Zb: produc12694297on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Xa_1,Xb_1),produc1259058957on_val(Za,Zb)),transi2024712006on_val(R_1)))
     => ( ( produc1259058957on_val(Xa_1,Xb_1) != produc1259058957on_val(Za,Zb) )
       => ~ ! [A_1: exp_list_char,B_1: produc12694297on_val] :
              ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Xa_1,Xb_1),produc1259058957on_val(A_1,B_1)),R_1))
             => ~ hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A_1,B_1),produc1259058957on_val(Za,Zb)),transi2024712006on_val(R_1))) ) ) ) ).

tff(fact_586_converse__rtranclE2,axiom,
    ! [Xa_1: list_exp_list_char,Xb_1: produc12694297on_val,Za: list_exp_list_char,Zb: produc12694297on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Xa_1,Xb_1),produc379668296on_val(Za,Zb)),transi374442731on_val(R_1)))
     => ( ( produc379668296on_val(Xa_1,Xb_1) != produc379668296on_val(Za,Zb) )
       => ~ ! [A_1: list_exp_list_char,B_1: produc12694297on_val] :
              ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Xa_1,Xb_1),produc379668296on_val(A_1,B_1)),R_1))
             => ~ hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(A_1,B_1),produc379668296on_val(Za,Zb)),transi374442731on_val(R_1))) ) ) ) ).

tff(fact_587_rtrancl__induct,axiom,
    ! [Pa: fun_Pr1336948301r_bool,A: produc809539159t_char,B: produc809539159t_char,R_1: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(produc1897818327t_char(A,B),transi198989188t_char(R_1)))
     => ( hBOOL(hAPP_P2014166431r_bool(Pa,A))
       => ( ! [Y_2: produc809539159t_char,Z: produc809539159t_char] :
              ( hBOOL(member1999287380t_char(produc1897818327t_char(A,Y_2),transi198989188t_char(R_1)))
             => ( hBOOL(member1999287380t_char(produc1897818327t_char(Y_2,Z),R_1))
               => ( hBOOL(hAPP_P2014166431r_bool(Pa,Y_2))
                 => hBOOL(hAPP_P2014166431r_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P2014166431r_bool(Pa,B)) ) ) ) ).

tff(fact_588_rtrancl__induct,axiom,
    ! [Pa: fun_Pr565113489r_bool,A: produc1278157519t_char,B: produc1278157519t_char,R_1: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(produc2080520419t_char(A,B),transi1095029602t_char(R_1)))
     => ( hBOOL(hAPP_P449474095r_bool(Pa,A))
       => ( ! [Y_2: produc1278157519t_char,Z: produc1278157519t_char] :
              ( hBOOL(member794220506t_char(produc2080520419t_char(A,Y_2),transi1095029602t_char(R_1)))
             => ( hBOOL(member794220506t_char(produc2080520419t_char(Y_2,Z),R_1))
               => ( hBOOL(hAPP_P449474095r_bool(Pa,Y_2))
                 => hBOOL(hAPP_P449474095r_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P449474095r_bool(Pa,B)) ) ) ) ).

tff(fact_589_rtrancl__induct,axiom,
    ! [Pa: fun_Pr315804320l_bool,A: produc639455274on_val,B: produc639455274on_val,R_1: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(produc499151895on_val(A,B),transi61620055on_val(R_1)))
     => ( hBOOL(hAPP_P1235399154l_bool(Pa,A))
       => ( ! [Y_2: produc639455274on_val,Z: produc639455274on_val] :
              ( hBOOL(member1322055188on_val(produc499151895on_val(A,Y_2),transi61620055on_val(R_1)))
             => ( hBOOL(member1322055188on_val(produc499151895on_val(Y_2,Z),R_1))
               => ( hBOOL(hAPP_P1235399154l_bool(Pa,Y_2))
                 => hBOOL(hAPP_P1235399154l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P1235399154l_bool(Pa,B)) ) ) ) ).

tff(fact_590_rtrancl__induct,axiom,
    ! [Pa: fun_Pr2081272681l_bool,A: product_prod_val_val,B: product_prod_val_val,R_1: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(produc1244920211al_val(A,B),transi1423755450al_val(R_1)))
     => ( hBOOL(hAPP_P929938951l_bool(Pa,A))
       => ( ! [Y_2: product_prod_val_val,Z: product_prod_val_val] :
              ( hBOOL(member837208074al_val(produc1244920211al_val(A,Y_2),transi1423755450al_val(R_1)))
             => ( hBOOL(member837208074al_val(produc1244920211al_val(Y_2,Z),R_1))
               => ( hBOOL(hAPP_P929938951l_bool(Pa,Y_2))
                 => hBOOL(hAPP_P929938951l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P929938951l_bool(Pa,B)) ) ) ) ).

tff(fact_591_rtrancl__induct,axiom,
    ! [Pa: fun_Pr252072522l_bool,A: produc1645268488al_val,B: produc1645268488al_val,R_1: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(produc1924279125al_val(A,B),transi1906258203al_val(R_1)))
     => ( hBOOL(hAPP_P943837928l_bool(Pa,A))
       => ( ! [Y_2: produc1645268488al_val,Z: produc1645268488al_val] :
              ( hBOOL(member1732271180al_val(produc1924279125al_val(A,Y_2),transi1906258203al_val(R_1)))
             => ( hBOOL(member1732271180al_val(produc1924279125al_val(Y_2,Z),R_1))
               => ( hBOOL(hAPP_P943837928l_bool(Pa,Y_2))
                 => hBOOL(hAPP_P943837928l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P943837928l_bool(Pa,B)) ) ) ) ).

tff(fact_592_rtrancl__induct,axiom,
    ! [Pa: fun_Pr827765831r_bool,A: produc662261637t_char,B: produc662261637t_char,R_1: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(produc1299387215t_char(A,B),transi1789604888t_char(R_1)))
     => ( hBOOL(hAPP_P2118621157r_bool(Pa,A))
       => ( ! [Y_2: produc662261637t_char,Z: produc662261637t_char] :
              ( hBOOL(member1161907014t_char(produc1299387215t_char(A,Y_2),transi1789604888t_char(R_1)))
             => ( hBOOL(member1161907014t_char(produc1299387215t_char(Y_2,Z),R_1))
               => ( hBOOL(hAPP_P2118621157r_bool(Pa,Y_2))
                 => hBOOL(hAPP_P2118621157r_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P2118621157r_bool(Pa,B)) ) ) ) ).

tff(fact_593_rtrancl__induct,axiom,
    ! [Pa: fun_Pr46158268r_bool,A: produc220283002t_char,B: produc220283002t_char,R_1: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(produc57279289t_char(A,B),transi1257872013t_char(R_1)))
     => ( hBOOL(hAPP_P1907982426r_bool(Pa,A))
       => ( ! [Y_2: produc220283002t_char,Z: produc220283002t_char] :
              ( hBOOL(member125098544t_char(produc57279289t_char(A,Y_2),transi1257872013t_char(R_1)))
             => ( hBOOL(member125098544t_char(produc57279289t_char(Y_2,Z),R_1))
               => ( hBOOL(hAPP_P1907982426r_bool(Pa,Y_2))
                 => hBOOL(hAPP_P1907982426r_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P1907982426r_bool(Pa,B)) ) ) ) ).

tff(fact_594_rtrancl__induct,axiom,
    ! [Pa: fun_Pr227936640r_bool,A: produc1285161482t_char,B: produc1285161482t_char,R_1: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(produc24551831t_char(A,B),transi122195895t_char(R_1)))
     => ( hBOOL(hAPP_P92196306r_bool(Pa,A))
       => ( ! [Y_2: produc1285161482t_char,Z: produc1285161482t_char] :
              ( hBOOL(member1420286996t_char(produc24551831t_char(A,Y_2),transi122195895t_char(R_1)))
             => ( hBOOL(member1420286996t_char(produc24551831t_char(Y_2,Z),R_1))
               => ( hBOOL(hAPP_P92196306r_bool(Pa,Y_2))
                 => hBOOL(hAPP_P92196306r_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P92196306r_bool(Pa,B)) ) ) ) ).

tff(fact_595_rtrancl__induct,axiom,
    ! [Pa: fun_Pr859510977l_bool,A: produc430140671on_val,B: produc430140671on_val,R_1: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(A,B),transi208336786on_val(R_1)))
     => ( hBOOL(hAPP_P1333315679l_bool(Pa,A))
       => ( ! [Y_2: produc430140671on_val,Z: produc430140671on_val] :
              ( hBOOL(member88670778on_val(produc1951691075on_val(A,Y_2),transi208336786on_val(R_1)))
             => ( hBOOL(member88670778on_val(produc1951691075on_val(Y_2,Z),R_1))
               => ( hBOOL(hAPP_P1333315679l_bool(Pa,Y_2))
                 => hBOOL(hAPP_P1333315679l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P1333315679l_bool(Pa,B)) ) ) ) ).

tff(fact_596_rtrancl__induct,axiom,
    ! [Pa: fun_Pr1696029455l_bool,A: produc12694297on_val,B: produc12694297on_val,R_1: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(A,B),transi921647814on_val(R_1)))
     => ( hBOOL(hAPP_P159683425l_bool(Pa,A))
       => ( ! [Y_2: produc12694297on_val,Z: produc12694297on_val] :
              ( hBOOL(member563141460on_val(produc870913623on_val(A,Y_2),transi921647814on_val(R_1)))
             => ( hBOOL(member563141460on_val(produc870913623on_val(Y_2,Z),R_1))
               => ( hBOOL(hAPP_P159683425l_bool(Pa,Y_2))
                 => hBOOL(hAPP_P159683425l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(Pa,B)) ) ) ) ).

tff(fact_597_rtrancl__induct,axiom,
    ! [Pa: fun_Pr691271849l_bool,A: produc1102272487on_val,B: produc1102272487on_val,R_1: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(A,B),transi910771962on_val(R_1)))
     => ( hBOOL(hAPP_P282169671l_bool(Pa,A))
       => ( ! [Y_2: produc1102272487on_val,Z: produc1102272487on_val] :
              ( hBOOL(member808015754on_val(produc1564932627on_val(A,Y_2),transi910771962on_val(R_1)))
             => ( hBOOL(member808015754on_val(produc1564932627on_val(Y_2,Z),R_1))
               => ( hBOOL(hAPP_P282169671l_bool(Pa,Y_2))
                 => hBOOL(hAPP_P282169671l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P282169671l_bool(Pa,B)) ) ) ) ).

tff(fact_598_rtrancl__induct,axiom,
    ! [Pa: fun_val_bool,A: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(product_Pair_val_val(A,B),transi935034983cl_val(R_1)))
     => ( hBOOL(hAPP_val_bool(Pa,A))
       => ( ! [Y_2: val,Z: val] :
              ( hBOOL(member649088532al_val(product_Pair_val_val(A,Y_2),transi935034983cl_val(R_1)))
             => ( hBOOL(member649088532al_val(product_Pair_val_val(Y_2,Z),R_1))
               => ( hBOOL(hAPP_val_bool(Pa,Y_2))
                 => hBOOL(hAPP_val_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_val_bool(Pa,B)) ) ) ) ).

tff(fact_599_rtrancl__induct,axiom,
    ! [Pa: fun_Pr680585871l_bool,A: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(A,B),transi2024712006on_val(R_1)))
     => ( hBOOL(hAPP_P1708370145l_bool(Pa,A))
       => ( ! [Y_2: produc124828825on_val,Z: produc124828825on_val] :
              ( hBOOL(member773094996on_val(produc1441475159on_val(A,Y_2),transi2024712006on_val(R_1)))
             => ( hBOOL(member773094996on_val(produc1441475159on_val(Y_2,Z),R_1))
               => ( hBOOL(hAPP_P1708370145l_bool(Pa,Y_2))
                 => hBOOL(hAPP_P1708370145l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(Pa,B)) ) ) ) ).

tff(fact_600_rtrancl__induct,axiom,
    ! [Pa: fun_Pr248118298l_bool,A: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(A,B),transi374442731on_val(R_1)))
     => ( hBOOL(hAPP_P71593144l_bool(Pa,A))
       => ( ! [Y_2: produc2061676504on_val,Z: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(produc1611380469on_val(A,Y_2),transi374442731on_val(R_1)))
             => ( hBOOL(member875476972on_val(produc1611380469on_val(Y_2,Z),R_1))
               => ( hBOOL(hAPP_P71593144l_bool(Pa,Y_2))
                 => hBOOL(hAPP_P71593144l_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(Pa,B)) ) ) ) ).

tff(fact_601_rtrancl__induct,axiom,
    ! [Pa: fun_list_char_bool,A: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(produc5062597t_char(A,B),transi1395422419t_char(R_1)))
     => ( hBOOL(hAPP_list_char_bool(Pa,A))
       => ( ! [Y_2: list_char,Z: list_char] :
              ( hBOOL(member1251428284t_char(produc5062597t_char(A,Y_2),transi1395422419t_char(R_1)))
             => ( hBOOL(member1251428284t_char(produc5062597t_char(Y_2,Z),R_1))
               => ( hBOOL(hAPP_list_char_bool(Pa,Y_2))
                 => hBOOL(hAPP_list_char_bool(Pa,Z)) ) ) )
         => hBOOL(hAPP_list_char_bool(Pa,B)) ) ) ) ).

tff(fact_602_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr1336948301r_bool,A: produc809539159t_char,B: produc809539159t_char,R_1: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(produc1897818327t_char(A,B),transi198989188t_char(R_1)))
     => ( hBOOL(hAPP_P2014166431r_bool(Pa,B))
       => ( ! [Y_2: produc809539159t_char,Z: produc809539159t_char] :
              ( hBOOL(member1999287380t_char(produc1897818327t_char(Y_2,Z),R_1))
             => ( hBOOL(member1999287380t_char(produc1897818327t_char(Z,B),transi198989188t_char(R_1)))
               => ( hBOOL(hAPP_P2014166431r_bool(Pa,Z))
                 => hBOOL(hAPP_P2014166431r_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_P2014166431r_bool(Pa,A)) ) ) ) ).

tff(fact_603_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr565113489r_bool,A: produc1278157519t_char,B: produc1278157519t_char,R_1: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(produc2080520419t_char(A,B),transi1095029602t_char(R_1)))
     => ( hBOOL(hAPP_P449474095r_bool(Pa,B))
       => ( ! [Y_2: produc1278157519t_char,Z: produc1278157519t_char] :
              ( hBOOL(member794220506t_char(produc2080520419t_char(Y_2,Z),R_1))
             => ( hBOOL(member794220506t_char(produc2080520419t_char(Z,B),transi1095029602t_char(R_1)))
               => ( hBOOL(hAPP_P449474095r_bool(Pa,Z))
                 => hBOOL(hAPP_P449474095r_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_P449474095r_bool(Pa,A)) ) ) ) ).

tff(fact_604_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr315804320l_bool,A: produc639455274on_val,B: produc639455274on_val,R_1: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(produc499151895on_val(A,B),transi61620055on_val(R_1)))
     => ( hBOOL(hAPP_P1235399154l_bool(Pa,B))
       => ( ! [Y_2: produc639455274on_val,Z: produc639455274on_val] :
              ( hBOOL(member1322055188on_val(produc499151895on_val(Y_2,Z),R_1))
             => ( hBOOL(member1322055188on_val(produc499151895on_val(Z,B),transi61620055on_val(R_1)))
               => ( hBOOL(hAPP_P1235399154l_bool(Pa,Z))
                 => hBOOL(hAPP_P1235399154l_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_P1235399154l_bool(Pa,A)) ) ) ) ).

tff(fact_605_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr2081272681l_bool,A: product_prod_val_val,B: product_prod_val_val,R_1: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(produc1244920211al_val(A,B),transi1423755450al_val(R_1)))
     => ( hBOOL(hAPP_P929938951l_bool(Pa,B))
       => ( ! [Y_2: product_prod_val_val,Z: product_prod_val_val] :
              ( hBOOL(member837208074al_val(produc1244920211al_val(Y_2,Z),R_1))
             => ( hBOOL(member837208074al_val(produc1244920211al_val(Z,B),transi1423755450al_val(R_1)))
               => ( hBOOL(hAPP_P929938951l_bool(Pa,Z))
                 => hBOOL(hAPP_P929938951l_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_P929938951l_bool(Pa,A)) ) ) ) ).

tff(fact_606_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr252072522l_bool,A: produc1645268488al_val,B: produc1645268488al_val,R_1: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(produc1924279125al_val(A,B),transi1906258203al_val(R_1)))
     => ( hBOOL(hAPP_P943837928l_bool(Pa,B))
       => ( ! [Y_2: produc1645268488al_val,Z: produc1645268488al_val] :
              ( hBOOL(member1732271180al_val(produc1924279125al_val(Y_2,Z),R_1))
             => ( hBOOL(member1732271180al_val(produc1924279125al_val(Z,B),transi1906258203al_val(R_1)))
               => ( hBOOL(hAPP_P943837928l_bool(Pa,Z))
                 => hBOOL(hAPP_P943837928l_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_P943837928l_bool(Pa,A)) ) ) ) ).

tff(fact_607_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr827765831r_bool,A: produc662261637t_char,B: produc662261637t_char,R_1: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(produc1299387215t_char(A,B),transi1789604888t_char(R_1)))
     => ( hBOOL(hAPP_P2118621157r_bool(Pa,B))
       => ( ! [Y_2: produc662261637t_char,Z: produc662261637t_char] :
              ( hBOOL(member1161907014t_char(produc1299387215t_char(Y_2,Z),R_1))
             => ( hBOOL(member1161907014t_char(produc1299387215t_char(Z,B),transi1789604888t_char(R_1)))
               => ( hBOOL(hAPP_P2118621157r_bool(Pa,Z))
                 => hBOOL(hAPP_P2118621157r_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_P2118621157r_bool(Pa,A)) ) ) ) ).

tff(fact_608_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr46158268r_bool,A: produc220283002t_char,B: produc220283002t_char,R_1: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(produc57279289t_char(A,B),transi1257872013t_char(R_1)))
     => ( hBOOL(hAPP_P1907982426r_bool(Pa,B))
       => ( ! [Y_2: produc220283002t_char,Z: produc220283002t_char] :
              ( hBOOL(member125098544t_char(produc57279289t_char(Y_2,Z),R_1))
             => ( hBOOL(member125098544t_char(produc57279289t_char(Z,B),transi1257872013t_char(R_1)))
               => ( hBOOL(hAPP_P1907982426r_bool(Pa,Z))
                 => hBOOL(hAPP_P1907982426r_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_P1907982426r_bool(Pa,A)) ) ) ) ).

tff(fact_609_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr227936640r_bool,A: produc1285161482t_char,B: produc1285161482t_char,R_1: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(produc24551831t_char(A,B),transi122195895t_char(R_1)))
     => ( hBOOL(hAPP_P92196306r_bool(Pa,B))
       => ( ! [Y_2: produc1285161482t_char,Z: produc1285161482t_char] :
              ( hBOOL(member1420286996t_char(produc24551831t_char(Y_2,Z),R_1))
             => ( hBOOL(member1420286996t_char(produc24551831t_char(Z,B),transi122195895t_char(R_1)))
               => ( hBOOL(hAPP_P92196306r_bool(Pa,Z))
                 => hBOOL(hAPP_P92196306r_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_P92196306r_bool(Pa,A)) ) ) ) ).

tff(fact_610_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr859510977l_bool,A: produc430140671on_val,B: produc430140671on_val,R_1: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(A,B),transi208336786on_val(R_1)))
     => ( hBOOL(hAPP_P1333315679l_bool(Pa,B))
       => ( ! [Y_2: produc430140671on_val,Z: produc430140671on_val] :
              ( hBOOL(member88670778on_val(produc1951691075on_val(Y_2,Z),R_1))
             => ( hBOOL(member88670778on_val(produc1951691075on_val(Z,B),transi208336786on_val(R_1)))
               => ( hBOOL(hAPP_P1333315679l_bool(Pa,Z))
                 => hBOOL(hAPP_P1333315679l_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_P1333315679l_bool(Pa,A)) ) ) ) ).

tff(fact_611_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr1696029455l_bool,A: produc12694297on_val,B: produc12694297on_val,R_1: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(A,B),transi921647814on_val(R_1)))
     => ( hBOOL(hAPP_P159683425l_bool(Pa,B))
       => ( ! [Y_2: produc12694297on_val,Z: produc12694297on_val] :
              ( hBOOL(member563141460on_val(produc870913623on_val(Y_2,Z),R_1))
             => ( hBOOL(member563141460on_val(produc870913623on_val(Z,B),transi921647814on_val(R_1)))
               => ( hBOOL(hAPP_P159683425l_bool(Pa,Z))
                 => hBOOL(hAPP_P159683425l_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_P159683425l_bool(Pa,A)) ) ) ) ).

tff(fact_612_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr691271849l_bool,A: produc1102272487on_val,B: produc1102272487on_val,R_1: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(A,B),transi910771962on_val(R_1)))
     => ( hBOOL(hAPP_P282169671l_bool(Pa,B))
       => ( ! [Y_2: produc1102272487on_val,Z: produc1102272487on_val] :
              ( hBOOL(member808015754on_val(produc1564932627on_val(Y_2,Z),R_1))
             => ( hBOOL(member808015754on_val(produc1564932627on_val(Z,B),transi910771962on_val(R_1)))
               => ( hBOOL(hAPP_P282169671l_bool(Pa,Z))
                 => hBOOL(hAPP_P282169671l_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_P282169671l_bool(Pa,A)) ) ) ) ).

tff(fact_613_converse__rtrancl__induct,axiom,
    ! [Pa: fun_val_bool,A: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(product_Pair_val_val(A,B),transi935034983cl_val(R_1)))
     => ( hBOOL(hAPP_val_bool(Pa,B))
       => ( ! [Y_2: val,Z: val] :
              ( hBOOL(member649088532al_val(product_Pair_val_val(Y_2,Z),R_1))
             => ( hBOOL(member649088532al_val(product_Pair_val_val(Z,B),transi935034983cl_val(R_1)))
               => ( hBOOL(hAPP_val_bool(Pa,Z))
                 => hBOOL(hAPP_val_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_val_bool(Pa,A)) ) ) ) ).

tff(fact_614_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr680585871l_bool,A: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(A,B),transi2024712006on_val(R_1)))
     => ( hBOOL(hAPP_P1708370145l_bool(Pa,B))
       => ( ! [Y_2: produc124828825on_val,Z: produc124828825on_val] :
              ( hBOOL(member773094996on_val(produc1441475159on_val(Y_2,Z),R_1))
             => ( hBOOL(member773094996on_val(produc1441475159on_val(Z,B),transi2024712006on_val(R_1)))
               => ( hBOOL(hAPP_P1708370145l_bool(Pa,Z))
                 => hBOOL(hAPP_P1708370145l_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_P1708370145l_bool(Pa,A)) ) ) ) ).

tff(fact_615_converse__rtrancl__induct,axiom,
    ! [Pa: fun_Pr248118298l_bool,A: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(A,B),transi374442731on_val(R_1)))
     => ( hBOOL(hAPP_P71593144l_bool(Pa,B))
       => ( ! [Y_2: produc2061676504on_val,Z: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(produc1611380469on_val(Y_2,Z),R_1))
             => ( hBOOL(member875476972on_val(produc1611380469on_val(Z,B),transi374442731on_val(R_1)))
               => ( hBOOL(hAPP_P71593144l_bool(Pa,Z))
                 => hBOOL(hAPP_P71593144l_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_P71593144l_bool(Pa,A)) ) ) ) ).

tff(fact_616_converse__rtrancl__induct,axiom,
    ! [Pa: fun_list_char_bool,A: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(produc5062597t_char(A,B),transi1395422419t_char(R_1)))
     => ( hBOOL(hAPP_list_char_bool(Pa,B))
       => ( ! [Y_2: list_char,Z: list_char] :
              ( hBOOL(member1251428284t_char(produc5062597t_char(Y_2,Z),R_1))
             => ( hBOOL(member1251428284t_char(produc5062597t_char(Z,B),transi1395422419t_char(R_1)))
               => ( hBOOL(hAPP_list_char_bool(Pa,Z))
                 => hBOOL(hAPP_list_char_bool(Pa,Y_2)) ) ) )
         => hBOOL(hAPP_list_char_bool(Pa,A)) ) ) ) ).

tff(fact_617_converse__rtranclE,axiom,
    ! [X_2: produc809539159t_char,Z_1: produc809539159t_char,R_1: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(produc1897818327t_char(X_2,Z_1),transi198989188t_char(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: produc809539159t_char] :
              ( hBOOL(member1999287380t_char(produc1897818327t_char(X_2,Y_2),R_1))
             => ~ hBOOL(member1999287380t_char(produc1897818327t_char(Y_2,Z_1),transi198989188t_char(R_1))) ) ) ) ).

tff(fact_618_converse__rtranclE,axiom,
    ! [X_2: produc1278157519t_char,Z_1: produc1278157519t_char,R_1: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(produc2080520419t_char(X_2,Z_1),transi1095029602t_char(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: produc1278157519t_char] :
              ( hBOOL(member794220506t_char(produc2080520419t_char(X_2,Y_2),R_1))
             => ~ hBOOL(member794220506t_char(produc2080520419t_char(Y_2,Z_1),transi1095029602t_char(R_1))) ) ) ) ).

tff(fact_619_converse__rtranclE,axiom,
    ! [X_2: produc639455274on_val,Z_1: produc639455274on_val,R_1: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(produc499151895on_val(X_2,Z_1),transi61620055on_val(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: produc639455274on_val] :
              ( hBOOL(member1322055188on_val(produc499151895on_val(X_2,Y_2),R_1))
             => ~ hBOOL(member1322055188on_val(produc499151895on_val(Y_2,Z_1),transi61620055on_val(R_1))) ) ) ) ).

tff(fact_620_converse__rtranclE,axiom,
    ! [X_2: product_prod_val_val,Z_1: product_prod_val_val,R_1: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(produc1244920211al_val(X_2,Z_1),transi1423755450al_val(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: product_prod_val_val] :
              ( hBOOL(member837208074al_val(produc1244920211al_val(X_2,Y_2),R_1))
             => ~ hBOOL(member837208074al_val(produc1244920211al_val(Y_2,Z_1),transi1423755450al_val(R_1))) ) ) ) ).

tff(fact_621_converse__rtranclE,axiom,
    ! [X_2: produc1645268488al_val,Z_1: produc1645268488al_val,R_1: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(produc1924279125al_val(X_2,Z_1),transi1906258203al_val(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: produc1645268488al_val] :
              ( hBOOL(member1732271180al_val(produc1924279125al_val(X_2,Y_2),R_1))
             => ~ hBOOL(member1732271180al_val(produc1924279125al_val(Y_2,Z_1),transi1906258203al_val(R_1))) ) ) ) ).

tff(fact_622_converse__rtranclE,axiom,
    ! [X_2: produc662261637t_char,Z_1: produc662261637t_char,R_1: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(produc1299387215t_char(X_2,Z_1),transi1789604888t_char(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: produc662261637t_char] :
              ( hBOOL(member1161907014t_char(produc1299387215t_char(X_2,Y_2),R_1))
             => ~ hBOOL(member1161907014t_char(produc1299387215t_char(Y_2,Z_1),transi1789604888t_char(R_1))) ) ) ) ).

tff(fact_623_converse__rtranclE,axiom,
    ! [X_2: produc220283002t_char,Z_1: produc220283002t_char,R_1: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(produc57279289t_char(X_2,Z_1),transi1257872013t_char(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: produc220283002t_char] :
              ( hBOOL(member125098544t_char(produc57279289t_char(X_2,Y_2),R_1))
             => ~ hBOOL(member125098544t_char(produc57279289t_char(Y_2,Z_1),transi1257872013t_char(R_1))) ) ) ) ).

tff(fact_624_converse__rtranclE,axiom,
    ! [X_2: produc1285161482t_char,Z_1: produc1285161482t_char,R_1: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(produc24551831t_char(X_2,Z_1),transi122195895t_char(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: produc1285161482t_char] :
              ( hBOOL(member1420286996t_char(produc24551831t_char(X_2,Y_2),R_1))
             => ~ hBOOL(member1420286996t_char(produc24551831t_char(Y_2,Z_1),transi122195895t_char(R_1))) ) ) ) ).

tff(fact_625_converse__rtranclE,axiom,
    ! [X_2: produc430140671on_val,Z_1: produc430140671on_val,R_1: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(X_2,Z_1),transi208336786on_val(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: produc430140671on_val] :
              ( hBOOL(member88670778on_val(produc1951691075on_val(X_2,Y_2),R_1))
             => ~ hBOOL(member88670778on_val(produc1951691075on_val(Y_2,Z_1),transi208336786on_val(R_1))) ) ) ) ).

tff(fact_626_converse__rtranclE,axiom,
    ! [X_2: produc12694297on_val,Z_1: produc12694297on_val,R_1: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(X_2,Z_1),transi921647814on_val(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: produc12694297on_val] :
              ( hBOOL(member563141460on_val(produc870913623on_val(X_2,Y_2),R_1))
             => ~ hBOOL(member563141460on_val(produc870913623on_val(Y_2,Z_1),transi921647814on_val(R_1))) ) ) ) ).

tff(fact_627_converse__rtranclE,axiom,
    ! [X_2: produc1102272487on_val,Z_1: produc1102272487on_val,R_1: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(X_2,Z_1),transi910771962on_val(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: produc1102272487on_val] :
              ( hBOOL(member808015754on_val(produc1564932627on_val(X_2,Y_2),R_1))
             => ~ hBOOL(member808015754on_val(produc1564932627on_val(Y_2,Z_1),transi910771962on_val(R_1))) ) ) ) ).

tff(fact_628_converse__rtranclE,axiom,
    ! [X_2: val,Z_1: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(product_Pair_val_val(X_2,Z_1),transi935034983cl_val(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: val] :
              ( hBOOL(member649088532al_val(product_Pair_val_val(X_2,Y_2),R_1))
             => ~ hBOOL(member649088532al_val(product_Pair_val_val(Y_2,Z_1),transi935034983cl_val(R_1))) ) ) ) ).

tff(fact_629_converse__rtranclE,axiom,
    ! [X_2: produc124828825on_val,Z_1: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(X_2,Z_1),transi2024712006on_val(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: produc124828825on_val] :
              ( hBOOL(member773094996on_val(produc1441475159on_val(X_2,Y_2),R_1))
             => ~ hBOOL(member773094996on_val(produc1441475159on_val(Y_2,Z_1),transi2024712006on_val(R_1))) ) ) ) ).

tff(fact_630_converse__rtranclE,axiom,
    ! [X_2: produc2061676504on_val,Z_1: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(X_2,Z_1),transi374442731on_val(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(produc1611380469on_val(X_2,Y_2),R_1))
             => ~ hBOOL(member875476972on_val(produc1611380469on_val(Y_2,Z_1),transi374442731on_val(R_1))) ) ) ) ).

tff(fact_631_converse__rtranclE,axiom,
    ! [X_2: list_char,Z_1: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(produc5062597t_char(X_2,Z_1),transi1395422419t_char(R_1)))
     => ( ( X_2 != Z_1 )
       => ~ ! [Y_2: list_char] :
              ( hBOOL(member1251428284t_char(produc5062597t_char(X_2,Y_2),R_1))
             => ~ hBOOL(member1251428284t_char(produc5062597t_char(Y_2,Z_1),transi1395422419t_char(R_1))) ) ) ) ).

tff(fact_632_rtranclE,axiom,
    ! [A: produc809539159t_char,B: produc809539159t_char,R_1: fun_Pr908866473r_bool] :
      ( hBOOL(member1999287380t_char(produc1897818327t_char(A,B),transi198989188t_char(R_1)))
     => ( ( A != B )
       => ~ ! [Y_2: produc809539159t_char] :
              ( hBOOL(member1999287380t_char(produc1897818327t_char(A,Y_2),transi198989188t_char(R_1)))
             => ~ hBOOL(member1999287380t_char(produc1897818327t_char(Y_2,B),R_1)) ) ) ) ).

tff(fact_633_rtranclE,axiom,
    ! [A: produc1278157519t_char,B: produc1278157519t_char,R_1: fun_Pr1336847023r_bool] :
      ( hBOOL(member794220506t_char(produc2080520419t_char(A,B),transi1095029602t_char(R_1)))
     => ( ( A != B )
       => ~ ! [Y_2: produc1278157519t_char] :
              ( hBOOL(member794220506t_char(produc2080520419t_char(A,Y_2),transi1095029602t_char(R_1)))
             => ~ hBOOL(member794220506t_char(produc2080520419t_char(Y_2,B),R_1)) ) ) ) ).

tff(fact_634_rtranclE,axiom,
    ! [A: produc639455274on_val,B: produc639455274on_val,R_1: fun_Pr235369833l_bool] :
      ( hBOOL(member1322055188on_val(produc499151895on_val(A,B),transi61620055on_val(R_1)))
     => ( ( A != B )
       => ~ ! [Y_2: produc639455274on_val] :
              ( hBOOL(member1322055188on_val(produc499151895on_val(A,Y_2),transi61620055on_val(R_1)))
             => ~ hBOOL(member1322055188on_val(produc499151895on_val(Y_2,B),R_1)) ) ) ) ).

tff(fact_635_rtranclE,axiom,
    ! [A: product_prod_val_val,B: product_prod_val_val,R_1: fun_Pr832147423l_bool] :
      ( hBOOL(member837208074al_val(produc1244920211al_val(A,B),transi1423755450al_val(R_1)))
     => ( ( A != B )
       => ~ ! [Y_2: product_prod_val_val] :
              ( hBOOL(member837208074al_val(produc1244920211al_val(A,Y_2),transi1423755450al_val(R_1)))
             => ~ hBOOL(member837208074al_val(produc1244920211al_val(Y_2,B),R_1)) ) ) ) ).

tff(fact_636_rtranclE,axiom,
    ! [A: produc1645268488al_val,B: produc1645268488al_val,R_1: fun_Pr897334561l_bool] :
      ( hBOOL(member1732271180al_val(produc1924279125al_val(A,B),transi1906258203al_val(R_1)))
     => ( ( A != B )
       => ~ ! [Y_2: produc1645268488al_val] :
              ( hBOOL(member1732271180al_val(produc1924279125al_val(A,Y_2),transi1906258203al_val(R_1)))
             => ~ hBOOL(member1732271180al_val(produc1924279125al_val(Y_2,B),R_1)) ) ) ) ).

tff(fact_637_rtranclE,axiom,
    ! [A: produc662261637t_char,B: produc662261637t_char,R_1: fun_Pr1890037787r_bool] :
      ( hBOOL(member1161907014t_char(produc1299387215t_char(A,B),transi1789604888t_char(R_1)))
     => ( ( A != B )
       => ~ ! [Y_2: produc662261637t_char] :
              ( hBOOL(member1161907014t_char(produc1299387215t_char(A,Y_2),transi1789604888t_char(R_1)))
             => ~ hBOOL(member1161907014t_char(produc1299387215t_char(Y_2,B),R_1)) ) ) ) ).

tff(fact_638_rtranclE,axiom,
    ! [A: produc220283002t_char,B: produc220283002t_char,R_1: fun_Pr1728267013r_bool] :
      ( hBOOL(member125098544t_char(produc57279289t_char(A,B),transi1257872013t_char(R_1)))
     => ( ( A != B )
       => ~ ! [Y_2: produc220283002t_char] :
              ( hBOOL(member125098544t_char(produc57279289t_char(A,Y_2),transi1257872013t_char(R_1)))
             => ~ hBOOL(member125098544t_char(produc57279289t_char(Y_2,B),R_1)) ) ) ) ).

tff(fact_639_rtranclE,axiom,
    ! [A: produc1285161482t_char,B: produc1285161482t_char,R_1: fun_Pr1895638121r_bool] :
      ( hBOOL(member1420286996t_char(produc24551831t_char(A,B),transi122195895t_char(R_1)))
     => ( ( A != B )
       => ~ ! [Y_2: produc1285161482t_char] :
              ( hBOOL(member1420286996t_char(produc24551831t_char(A,Y_2),transi122195895t_char(R_1)))
             => ~ hBOOL(member1420286996t_char(produc24551831t_char(Y_2,B),R_1)) ) ) ) ).

tff(fact_640_rtranclE,axiom,
    ! [A: produc430140671on_val,B: produc430140671on_val,R_1: fun_Pr302334223l_bool] :
      ( hBOOL(member88670778on_val(produc1951691075on_val(A,B),transi208336786on_val(R_1)))
     => ( ( A != B )
       => ~ ! [Y_2: produc430140671on_val] :
              ( hBOOL(member88670778on_val(produc1951691075on_val(A,Y_2),transi208336786on_val(R_1)))
             => ~ hBOOL(member88670778on_val(produc1951691075on_val(Y_2,B),R_1)) ) ) ) ).

tff(fact_641_rtranclE,axiom,
    ! [A: produc12694297on_val,B: produc12694297on_val,R_1: fun_Pr693020585l_bool] :
      ( hBOOL(member563141460on_val(produc870913623on_val(A,B),transi921647814on_val(R_1)))
     => ( ( A != B )
       => ~ ! [Y_2: produc12694297on_val] :
              ( hBOOL(member563141460on_val(produc870913623on_val(A,Y_2),transi921647814on_val(R_1)))
             => ~ hBOOL(member563141460on_val(produc870913623on_val(Y_2,B),R_1)) ) ) ) ).

tff(fact_642_rtranclE,axiom,
    ! [A: produc1102272487on_val,B: produc1102272487on_val,R_1: fun_Pr903661919l_bool] :
      ( hBOOL(member808015754on_val(produc1564932627on_val(A,B),transi910771962on_val(R_1)))
     => ( ( A != B )
       => ~ ! [Y_2: produc1102272487on_val] :
              ( hBOOL(member808015754on_val(produc1564932627on_val(A,Y_2),transi910771962on_val(R_1)))
             => ~ hBOOL(member808015754on_val(produc1564932627on_val(Y_2,B),R_1)) ) ) ) ).

tff(fact_643_rtranclE,axiom,
    ! [A: val,B: val,R_1: fun_Pr2081272681l_bool] :
      ( hBOOL(member649088532al_val(product_Pair_val_val(A,B),transi935034983cl_val(R_1)))
     => ( ( A != B )
       => ~ ! [Y_2: val] :
              ( hBOOL(member649088532al_val(product_Pair_val_val(A,Y_2),transi935034983cl_val(R_1)))
             => ~ hBOOL(member649088532al_val(product_Pair_val_val(Y_2,B),R_1)) ) ) ) ).

tff(fact_644_rtranclE,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,R_1: fun_Pr691271849l_bool] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(A,B),transi2024712006on_val(R_1)))
     => ( ( A != B )
       => ~ ! [Y_2: produc124828825on_val] :
              ( hBOOL(member773094996on_val(produc1441475159on_val(A,Y_2),transi2024712006on_val(R_1)))
             => ~ hBOOL(member773094996on_val(produc1441475159on_val(Y_2,B),R_1)) ) ) ) ).

tff(fact_645_rtranclE,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,R_1: fun_Pr859510977l_bool] :
      ( hBOOL(member875476972on_val(produc1611380469on_val(A,B),transi374442731on_val(R_1)))
     => ( ( A != B )
       => ~ ! [Y_2: produc2061676504on_val] :
              ( hBOOL(member875476972on_val(produc1611380469on_val(A,Y_2),transi374442731on_val(R_1)))
             => ~ hBOOL(member875476972on_val(produc1611380469on_val(Y_2,B),R_1)) ) ) ) ).

tff(fact_646_rtranclE,axiom,
    ! [A: list_char,B: list_char,R_1: fun_Pr565113489r_bool] :
      ( hBOOL(member1251428284t_char(produc5062597t_char(A,B),transi1395422419t_char(R_1)))
     => ( ( A != B )
       => ~ ! [Y_2: list_char] :
              ( hBOOL(member1251428284t_char(produc5062597t_char(A,Y_2),transi1395422419t_char(R_1)))
             => ~ hBOOL(member1251428284t_char(produc5062597t_char(Y_2,B),R_1)) ) ) ) ).

tff(fact_647_CondReds2T,axiom,
    ! [E_2: exp_list_char,E_1_1: exp_list_char,E_a: exp_list_char,S_2_1: produc12694297on_val,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_0),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,bool_1(fTrue)),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_1_1,S_1_1),produc1259058957on_val(E_a,S_2_1)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cond_list_char(Ea,E_1_1,E_2),S_0),produc1259058957on_val(E_a,S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_648_CondReds2F,axiom,
    ! [E_1_1: exp_list_char,E_2: exp_list_char,E_a: exp_list_char,S_2_1: produc12694297on_val,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_0),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,bool_1(fFalse)),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_2,S_1_1),produc1259058957on_val(E_a,S_2_1)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cond_list_char(Ea,E_1_1,E_2),S_0),produc1259058957on_val(E_a,S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_649_CastRedsNull,axiom,
    ! [C: list_char,Ea: exp_list_char,S_1: produc12694297on_val,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,null),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cast_list_char(C,Ea),S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,null),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_650_red__reds_ORedCastNull,axiom,
    ! [C: list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cast_list_char(C,hAPP_v834067052t_char(val_list_char,null)),S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,null),S_1)),red(Pa))) ).

tff(fact_651_red__reds_ORedCondF,axiom,
    ! [E_1_1: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cond_list_char(hAPP_v834067052t_char(val_list_char,bool_1(fFalse)),E_1_1,E_2),S_1),produc1259058957on_val(E_2,S_1)),red(Pa))) ).

tff(fact_652_red__reds_ORedCondT,axiom,
    ! [E_1_1: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cond_list_char(hAPP_v834067052t_char(val_list_char,bool_1(fTrue)),E_1_1,E_2),S_1),produc1259058957on_val(E_1_1,S_1)),red(Pa))) ).

tff(fact_653_val_Osimps_I12_J,axiom,
    ! [Bool_1: bool] : null != bool_1(Bool_1) ).

tff(fact_654_val_Osimps_I13_J,axiom,
    ! [Bool_1: bool] : bool_1(Bool_1) != null ).

tff(fact_655_WhileTReds,axiom,
    ! [Ea: exp_list_char,S_3: produc12694297on_val,C_1: exp_list_char,V_1_1: val,S_2_1: produc12694297on_val,B: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(B,S_0),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,bool_1(fTrue)),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(C_1,S_1_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1_1),S_2_1)),transi2024712006on_val(red(Pa))))
       => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(while_list_char(B,C_1),S_2_1),produc1259058957on_val(Ea,S_3)),transi2024712006on_val(red(Pa))))
         => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(while_list_char(B,C_1),S_0),produc1259058957on_val(Ea,S_3)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_656_BinOpRedsThrow2,axiom,
    ! [Bop: bop,E_2: exp_list_char,Ea: exp_list_char,S_2_1: produc12694297on_val,E_1_1: exp_list_char,S_0: produc12694297on_val,V_1_1: val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_1_1,S_0),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1_1),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_2,S_1_1),produc1259058957on_val(throw_list_char(Ea),S_2_1)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(binOp_list_char(E_1_1,Bop,E_2),S_0),produc1259058957on_val(throw_list_char(Ea),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_657_FAccRedsThrow,axiom,
    ! [F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val,A: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(throw_list_char(A),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAcc_list_char(Ea,F,D),S_1),produc1259058957on_val(throw_list_char(A),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_658_CondRedsThrow,axiom,
    ! [E_1_1: exp_list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,A: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(throw_list_char(A),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cond_list_char(Ea,E_1_1,E_2),S_1),produc1259058957on_val(throw_list_char(A),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_659_CastRedsThrow,axiom,
    ! [C: list_char,Ea: exp_list_char,S_1: produc12694297on_val,A: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(throw_list_char(A),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cast_list_char(C,Ea),S_1),produc1259058957on_val(throw_list_char(A),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_660_BinOpRedsThrow1,axiom,
    ! [Bop: bop,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(throw_list_char(E_a),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(binOp_list_char(Ea,Bop,E_2),S_1),produc1259058957on_val(throw_list_char(E_a),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_661_CallRedsThrowObj,axiom,
    ! [M: list_char,Esa: list_exp_list_char,Ea: exp_list_char,S0: produc12694297on_val,A: exp_list_char,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S0),produc1259058957on_val(throw_list_char(A),S_1_1)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(call_list_char(Ea,M,Esa),S0),produc1259058957on_val(throw_list_char(A),S_1_1)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_662_exp_Osimps_I221_J,axiom,
    ! [Exp_109: exp_list_char,Exp1_109: exp_list_char,Exp2_109: exp_list_char] : throw_list_char(Exp_109) != while_list_char(Exp1_109,Exp2_109) ).

tff(fact_663_exp_Osimps_I220_J,axiom,
    ! [Exp1_108: exp_list_char,Exp2_108: exp_list_char,Exp_108: exp_list_char] : while_list_char(Exp1_108,Exp2_108) != throw_list_char(Exp_108) ).

tff(fact_664_exp_Osimps_I14_J,axiom,
    ! [Exp_35: exp_list_char,Exp_34: exp_list_char] :
      ( ( throw_list_char(Exp_35) = throw_list_char(Exp_34) )
    <=> ( Exp_35 = Exp_34 ) ) ).

tff(fact_665_exp_Osimps_I13_J,axiom,
    ! [Exp1_81: exp_list_char,Exp2_81: exp_list_char,Exp1_80: exp_list_char,Exp2_80: exp_list_char] :
      ( ( while_list_char(Exp1_81,Exp2_81) = while_list_char(Exp1_80,Exp2_80) )
    <=> ( ( Exp1_81 = Exp1_80 )
        & ( Exp2_81 = Exp2_80 ) ) ) ).

tff(fact_666_exp_Osimps_I91_J,axiom,
    ! [Exp_107: exp_list_char,Val_11: val] : throw_list_char(Exp_107) != hAPP_v834067052t_char(val_list_char,Val_11) ).

tff(fact_667_exp_Osimps_I90_J,axiom,
    ! [Val_10: val,Exp_106: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_10) != throw_list_char(Exp_106) ).

tff(fact_668_exp_Osimps_I89_J,axiom,
    ! [Exp1_107: exp_list_char,Exp2_107: exp_list_char,Val_9: val] : while_list_char(Exp1_107,Exp2_107) != hAPP_v834067052t_char(val_list_char,Val_9) ).

tff(fact_669_exp_Osimps_I88_J,axiom,
    ! [Val_8: val,Exp1_106: exp_list_char,Exp2_106: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_8) != while_list_char(Exp1_106,Exp2_106) ).

tff(fact_670_exp_Osimps_I192_J,axiom,
    ! [Exp_105: exp_list_char,List1_49: list_char,List2_49: list_exp_list_char,Exp_104: exp_list_char] : call_list_char(Exp_105,List1_49,List2_49) != throw_list_char(Exp_104) ).

tff(fact_671_exp_Osimps_I193_J,axiom,
    ! [Exp_103: exp_list_char,Exp_102: exp_list_char,List1_48: list_char,List2_48: list_exp_list_char] : throw_list_char(Exp_103) != call_list_char(Exp_102,List1_48,List2_48) ).

tff(fact_672_exp_Osimps_I112_J,axiom,
    ! [Exp1_105: exp_list_char,Bop_12: bop,Exp2_105: exp_list_char,Exp_101: exp_list_char] : binOp_list_char(Exp1_105,Bop_12,Exp2_105) != throw_list_char(Exp_101) ).

tff(fact_673_exp_Osimps_I113_J,axiom,
    ! [Exp_100: exp_list_char,Exp1_104: exp_list_char,Bop_11: bop,Exp2_104: exp_list_char] : throw_list_char(Exp_100) != binOp_list_char(Exp1_104,Bop_11,Exp2_104) ).

tff(fact_674_exp_Osimps_I216_J,axiom,
    ! [Exp1_103: exp_list_char,Exp2_103: exp_list_char,Exp3_11: exp_list_char,Exp_99: exp_list_char] : cond_list_char(Exp1_103,Exp2_103,Exp3_11) != throw_list_char(Exp_99) ).

tff(fact_675_exp_Osimps_I66_J,axiom,
    ! [List_27: list_char,Exp_98: exp_list_char,Exp_97: exp_list_char] : cast_list_char(List_27,Exp_98) != throw_list_char(Exp_97) ).

tff(fact_676_exp_Osimps_I217_J,axiom,
    ! [Exp_96: exp_list_char,Exp1_102: exp_list_char,Exp2_102: exp_list_char,Exp3_10: exp_list_char] : throw_list_char(Exp_96) != cond_list_char(Exp1_102,Exp2_102,Exp3_10) ).

tff(fact_677_exp_Osimps_I67_J,axiom,
    ! [Exp_95: exp_list_char,List_26: list_char,Exp_94: exp_list_char] : throw_list_char(Exp_95) != cast_list_char(List_26,Exp_94) ).

tff(fact_678_exp_Osimps_I166_J,axiom,
    ! [Exp_93: exp_list_char,List1_47: list_char,List2_47: list_char,Exp_92: exp_list_char] : fAcc_list_char(Exp_93,List1_47,List2_47) != throw_list_char(Exp_92) ).

tff(fact_679_exp_Osimps_I167_J,axiom,
    ! [Exp_91: exp_list_char,Exp_90: exp_list_char,List1_46: list_char,List2_46: list_char] : throw_list_char(Exp_91) != fAcc_list_char(Exp_90,List1_46,List2_46) ).

tff(fact_680_exp_Osimps_I225_J,axiom,
    ! [Exp1_101: exp_list_char,List_25: list_char,A_63: list_char,Exp2_101: exp_list_char,Exp_89: exp_list_char] : tryCatch_list_char(Exp1_101,List_25,A_63,Exp2_101) != throw_list_char(Exp_89) ).

tff(fact_681_exp_Osimps_I224_J,axiom,
    ! [Exp_88: exp_list_char,Exp1_100: exp_list_char,List_24: list_char,A_62: list_char,Exp2_100: exp_list_char] : throw_list_char(Exp_88) != tryCatch_list_char(Exp1_100,List_24,A_62,Exp2_100) ).

tff(fact_682_exp_Osimps_I190_J,axiom,
    ! [Exp_87: exp_list_char,List1_45: list_char,List2_45: list_exp_list_char,Exp1_99: exp_list_char,Exp2_99: exp_list_char] : call_list_char(Exp_87,List1_45,List2_45) != while_list_char(Exp1_99,Exp2_99) ).

tff(fact_683_exp_Osimps_I191_J,axiom,
    ! [Exp1_98: exp_list_char,Exp2_98: exp_list_char,Exp_86: exp_list_char,List1_44: list_char,List2_44: list_exp_list_char] : while_list_char(Exp1_98,Exp2_98) != call_list_char(Exp_86,List1_44,List2_44) ).

tff(fact_684_exp_Osimps_I110_J,axiom,
    ! [Exp1_97: exp_list_char,Bop_10: bop,Exp2_97: exp_list_char,Exp1_96: exp_list_char,Exp2_96: exp_list_char] : binOp_list_char(Exp1_97,Bop_10,Exp2_97) != while_list_char(Exp1_96,Exp2_96) ).

tff(fact_685_exp_Osimps_I111_J,axiom,
    ! [Exp1_95: exp_list_char,Exp2_95: exp_list_char,Exp1_94: exp_list_char,Bop_9: bop,Exp2_94: exp_list_char] : while_list_char(Exp1_95,Exp2_95) != binOp_list_char(Exp1_94,Bop_9,Exp2_94) ).

tff(fact_686_exp_Osimps_I214_J,axiom,
    ! [Exp1_93: exp_list_char,Exp2_93: exp_list_char,Exp3_9: exp_list_char,Exp1_92: exp_list_char,Exp2_92: exp_list_char] : cond_list_char(Exp1_93,Exp2_93,Exp3_9) != while_list_char(Exp1_92,Exp2_92) ).

tff(fact_687_exp_Osimps_I215_J,axiom,
    ! [Exp1_91: exp_list_char,Exp2_91: exp_list_char,Exp1_90: exp_list_char,Exp2_90: exp_list_char,Exp3_8: exp_list_char] : while_list_char(Exp1_91,Exp2_91) != cond_list_char(Exp1_90,Exp2_90,Exp3_8) ).

tff(fact_688_exp_Osimps_I65_J,axiom,
    ! [Exp1_89: exp_list_char,Exp2_89: exp_list_char,List_23: list_char,Exp_85: exp_list_char] : while_list_char(Exp1_89,Exp2_89) != cast_list_char(List_23,Exp_85) ).

tff(fact_689_exp_Osimps_I64_J,axiom,
    ! [List_22: list_char,Exp_84: exp_list_char,Exp1_88: exp_list_char,Exp2_88: exp_list_char] : cast_list_char(List_22,Exp_84) != while_list_char(Exp1_88,Exp2_88) ).

tff(fact_690_exp_Osimps_I164_J,axiom,
    ! [Exp_83: exp_list_char,List1_43: list_char,List2_43: list_char,Exp1_87: exp_list_char,Exp2_87: exp_list_char] : fAcc_list_char(Exp_83,List1_43,List2_43) != while_list_char(Exp1_87,Exp2_87) ).

tff(fact_691_exp_Osimps_I165_J,axiom,
    ! [Exp1_86: exp_list_char,Exp2_86: exp_list_char,Exp_82: exp_list_char,List1_42: list_char,List2_42: list_char] : while_list_char(Exp1_86,Exp2_86) != fAcc_list_char(Exp_82,List1_42,List2_42) ).

tff(fact_692_exp_Osimps_I223_J,axiom,
    ! [Exp1_85: exp_list_char,List_21: list_char,A_61: list_char,Exp2_85: exp_list_char,Exp1_84: exp_list_char,Exp2_84: exp_list_char] : tryCatch_list_char(Exp1_85,List_21,A_61,Exp2_85) != while_list_char(Exp1_84,Exp2_84) ).

tff(fact_693_exp_Osimps_I222_J,axiom,
    ! [Exp1_83: exp_list_char,Exp2_83: exp_list_char,Exp1_82: exp_list_char,List_20: list_char,A_60: list_char,Exp2_82: exp_list_char] : while_list_char(Exp1_83,Exp2_83) != tryCatch_list_char(Exp1_82,List_20,A_60,Exp2_82) ).

tff(fact_694_WhileRedsThrow,axiom,
    ! [C_1: exp_list_char,B: exp_list_char,S_1: produc12694297on_val,Ea: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(B,S_1),produc1259058957on_val(throw_list_char(Ea),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(while_list_char(B,C_1),S_1),produc1259058957on_val(throw_list_char(Ea),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_695_red__reds_OThrowThrow,axiom,
    ! [Ea: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(throw_list_char(throw_list_char(Ea)),S_1),produc1259058957on_val(throw_list_char(Ea),S_1)),red(Pa))) ).

tff(fact_696_red__reds_OThrowRed,axiom,
    ! [Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(throw_list_char(Ea),S_1),produc1259058957on_val(throw_list_char(E_a),S)),red(Pa))) ) ).

tff(fact_697_WhileTRedsThrow,axiom,
    ! [C_1: exp_list_char,Ea: exp_list_char,S_2_1: produc12694297on_val,B: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(B,S_0),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,bool_1(fTrue)),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(C_1,S_1_1),produc1259058957on_val(throw_list_char(Ea),S_2_1)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(while_list_char(B,C_1),S_0),produc1259058957on_val(throw_list_char(Ea),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_698_val_Osimps_I1_J,axiom,
    ! [Bool: bool,Bool_1: bool] :
      ( ( bool_1(Bool) = bool_1(Bool_1) )
    <=> ( hBOOL(Bool)
      <=> hBOOL(Bool_1) ) ) ).

tff(fact_699_ThrowReds,axiom,
    ! [Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(throw_list_char(Ea),S_1),produc1259058957on_val(throw_list_char(E_a),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_700_ThrowRedsThrow,axiom,
    ! [Ea: exp_list_char,S_1: produc12694297on_val,A: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(throw_list_char(A),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(throw_list_char(Ea),S_1),produc1259058957on_val(throw_list_char(A),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_701_red__reds_OCallThrowObj,axiom,
    ! [Ea: exp_list_char,M: list_char,Esa: list_exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(call_list_char(throw_list_char(Ea),M,Esa),S_1),produc1259058957on_val(throw_list_char(Ea),S_1)),red(Pa))) ).

tff(fact_702_red__reds_OBinOpThrow1,axiom,
    ! [Ea: exp_list_char,Bop: bop,E_2: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(binOp_list_char(throw_list_char(Ea),Bop,E_2),S_1),produc1259058957on_val(throw_list_char(Ea),S_1)),red(Pa))) ).

tff(fact_703_red__reds_OCastThrow,axiom,
    ! [C: list_char,Ea: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cast_list_char(C,throw_list_char(Ea)),S_1),produc1259058957on_val(throw_list_char(Ea),S_1)),red(Pa))) ).

tff(fact_704_red__reds_OCondThrow,axiom,
    ! [Ea: exp_list_char,E_1_1: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cond_list_char(throw_list_char(Ea),E_1_1,E_2),S_1),produc1259058957on_val(throw_list_char(Ea),S_1)),red(Pa))) ).

tff(fact_705_red__reds_OFAccThrow,axiom,
    ! [Ea: exp_list_char,F: list_char,D: list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAcc_list_char(throw_list_char(Ea),F,D),S_1),produc1259058957on_val(throw_list_char(Ea),S_1)),red(Pa))) ).

tff(fact_706_red__reds_OBinOpThrow2,axiom,
    ! [V_1_1: val,Bop: bop,Ea: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_1),Bop,throw_list_char(Ea)),S_1),produc1259058957on_val(throw_list_char(Ea),S_1)),red(Pa))) ).

tff(fact_707_WhileFReds,axiom,
    ! [C_1: exp_list_char,B: exp_list_char,S_1: produc12694297on_val,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(B,S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,bool_1(fFalse)),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(while_list_char(B,C_1),S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,unit),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_708_WTrtThrow,axiom,
    ! [T_3: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,T_r: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),T_r))
     => ( hBOOL(hAPP_ty_bool(is_refT,T_r))
       => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,throw_list_char(Ea)),T_3)) ) ) ).

tff(fact_709_FAssRedsThrow2,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,Ea: exp_list_char,S_2_1: produc12694297on_val,E_1_1: exp_list_char,S_0: produc12694297on_val,V_1: val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_1_1,S_0),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_2,S_1_1),produc1259058957on_val(throw_list_char(Ea),S_2_1)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(E_1_1,F,D,E_2),S_0),produc1259058957on_val(throw_list_char(Ea),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_710_CallRedsThrowParams,axiom,
    ! [M: list_char,Esa: list_exp_list_char,Vs_1_1: list_val,A: exp_list_char,Es_2_1: list_exp_list_char,S_2_1: produc12694297on_val,Ea: exp_list_char,S0: produc12694297on_val,V_1: val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S0),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Esa,S_1_1),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_1)),S_2_1)),transi374442731on_val(reds(Pa))))
       => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(call_list_char(Ea,M,Esa),S0),produc1259058957on_val(throw_list_char(A),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_711_FAssRedsThrow1,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(throw_list_char(E_a),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(Ea,F,D,E_2),S_1),produc1259058957on_val(throw_list_char(E_a),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_712_FAssReds2,axiom,
    ! [V_1: val,F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(hAPP_v834067052t_char(val_list_char,V_1),F,D,Ea),S_1),produc1259058957on_val(fAss_list_char(hAPP_v834067052t_char(val_list_char,V_1),F,D,E_a),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_713_red__reds_OFAssThrow2,axiom,
    ! [V_1: val,F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(hAPP_v834067052t_char(val_list_char,V_1),F,D,throw_list_char(Ea)),S_1),produc1259058957on_val(throw_list_char(Ea),S_1)),red(Pa))) ).

tff(fact_714_LAssRedsThrow,axiom,
    ! [V: list_char,Ea: exp_list_char,S_1: produc12694297on_val,A: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(throw_list_char(A),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(lAss_list_char(V,Ea),S_1),produc1259058957on_val(throw_list_char(A),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_715_SeqRedsThrow,axiom,
    ! [E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(throw_list_char(E_a),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(seq_list_char(Ea,E_2),S_1),produc1259058957on_val(throw_list_char(E_a),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_716_WTrtSeq,axiom,
    ! [E_2: exp_list_char,T_2_2: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,E_1_1: exp_list_char,T_1_2: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_1_1),T_1_2))
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_2),T_2_2))
       => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,seq_list_char(E_1_1,E_2)),T_2_2)) ) ) ).

tff(fact_717_exp_Osimps_I8_J,axiom,
    ! [Exp1_81: exp_list_char,List1_41: list_char,List2_41: list_char,Exp2_81: exp_list_char,Exp1_80: exp_list_char,List1_40: list_char,List2_40: list_char,Exp2_80: exp_list_char] :
      ( ( fAss_list_char(Exp1_81,List1_41,List2_41,Exp2_81) = fAss_list_char(Exp1_80,List1_40,List2_40,Exp2_80) )
    <=> ( ( Exp1_81 = Exp1_80 )
        & ( List1_41 = List1_40 )
        & ( List2_41 = List2_40 )
        & ( Exp2_81 = Exp2_80 ) ) ) ).

tff(fact_718_exp_Osimps_I6_J,axiom,
    ! [A: list_char,Exp_35: exp_list_char,A_3: list_char,Exp_34: exp_list_char] :
      ( ( lAss_list_char(A,Exp_35) = lAss_list_char(A_3,Exp_34) )
    <=> ( ( A = A_3 )
        & ( Exp_35 = Exp_34 ) ) ) ).

tff(fact_719_exp_Osimps_I11_J,axiom,
    ! [Exp1_81: exp_list_char,Exp2_81: exp_list_char,Exp1_80: exp_list_char,Exp2_80: exp_list_char] :
      ( ( seq_list_char(Exp1_81,Exp2_81) = seq_list_char(Exp1_80,Exp2_80) )
    <=> ( ( Exp1_81 = Exp1_80 )
        & ( Exp2_81 = Exp2_80 ) ) ) ).

tff(fact_720_exp_Osimps_I139_J,axiom,
    ! [Exp1_79: exp_list_char,List1_39: list_char,List2_39: list_char,Exp2_79: exp_list_char,A_59: list_char,Exp_81: exp_list_char] : fAss_list_char(Exp1_79,List1_39,List2_39,Exp2_79) != lAss_list_char(A_59,Exp_81) ).

tff(fact_721_exp_Osimps_I174_J,axiom,
    ! [Exp1_78: exp_list_char,List1_38: list_char,List2_38: list_char,Exp2_78: exp_list_char,Exp1_77: exp_list_char,Exp2_77: exp_list_char] : fAss_list_char(Exp1_78,List1_38,List2_38,Exp2_78) != seq_list_char(Exp1_77,Exp2_77) ).

tff(fact_722_exp_Osimps_I138_J,axiom,
    ! [A_58: list_char,Exp_80: exp_list_char,Exp1_76: exp_list_char,List1_37: list_char,List2_37: list_char,Exp2_76: exp_list_char] : lAss_list_char(A_58,Exp_80) != fAss_list_char(Exp1_76,List1_37,List2_37,Exp2_76) ).

tff(fact_723_exp_Osimps_I175_J,axiom,
    ! [Exp1_75: exp_list_char,Exp2_75: exp_list_char,Exp1_74: exp_list_char,List1_36: list_char,List2_36: list_char,Exp2_74: exp_list_char] : seq_list_char(Exp1_75,Exp2_75) != fAss_list_char(Exp1_74,List1_36,List2_36,Exp2_74) ).

tff(fact_724_exp_Osimps_I144_J,axiom,
    ! [A_57: list_char,Exp_79: exp_list_char,Exp1_73: exp_list_char,Exp2_73: exp_list_char] : lAss_list_char(A_57,Exp_79) != seq_list_char(Exp1_73,Exp2_73) ).

tff(fact_725_exp_Osimps_I145_J,axiom,
    ! [Exp1_72: exp_list_char,Exp2_72: exp_list_char,A_56: list_char,Exp_78: exp_list_char] : seq_list_char(Exp1_72,Exp2_72) != lAss_list_char(A_56,Exp_78) ).

tff(fact_726_exp_Osimps_I84_J,axiom,
    ! [Val_7: val,Exp1_71: exp_list_char,Exp2_71: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_7) != seq_list_char(Exp1_71,Exp2_71) ).

tff(fact_727_exp_Osimps_I74_J,axiom,
    ! [Val_6: val,A_55: list_char,Exp_77: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_6) != lAss_list_char(A_55,Exp_77) ).

tff(fact_728_exp_Osimps_I78_J,axiom,
    ! [Val_5: val,Exp1_70: exp_list_char,List1_35: list_char,List2_35: list_char,Exp2_70: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val_5) != fAss_list_char(Exp1_70,List1_35,List2_35,Exp2_70) ).

tff(fact_729_exp_Osimps_I85_J,axiom,
    ! [Exp1_69: exp_list_char,Exp2_69: exp_list_char,Val_4: val] : seq_list_char(Exp1_69,Exp2_69) != hAPP_v834067052t_char(val_list_char,Val_4) ).

tff(fact_730_exp_Osimps_I75_J,axiom,
    ! [A_54: list_char,Exp_76: exp_list_char,Val_3: val] : lAss_list_char(A_54,Exp_76) != hAPP_v834067052t_char(val_list_char,Val_3) ).

tff(fact_731_exp_Osimps_I79_J,axiom,
    ! [Exp1_68: exp_list_char,List1_34: list_char,List2_34: list_char,Exp2_68: exp_list_char,Val_2: val] : fAss_list_char(Exp1_68,List1_34,List2_34,Exp2_68) != hAPP_v834067052t_char(val_list_char,Val_2) ).

tff(fact_732_exp_Osimps_I180_J,axiom,
    ! [Exp1_67: exp_list_char,List1_33: list_char,List2_33: list_char,Exp2_67: exp_list_char,Exp_75: exp_list_char] : fAss_list_char(Exp1_67,List1_33,List2_33,Exp2_67) != throw_list_char(Exp_75) ).

tff(fact_733_exp_Osimps_I150_J,axiom,
    ! [A_53: list_char,Exp_74: exp_list_char,Exp_73: exp_list_char] : lAss_list_char(A_53,Exp_74) != throw_list_char(Exp_73) ).

tff(fact_734_exp_Osimps_I210_J,axiom,
    ! [Exp1_66: exp_list_char,Exp2_66: exp_list_char,Exp_72: exp_list_char] : seq_list_char(Exp1_66,Exp2_66) != throw_list_char(Exp_72) ).

tff(fact_735_exp_Osimps_I181_J,axiom,
    ! [Exp_71: exp_list_char,Exp1_65: exp_list_char,List1_32: list_char,List2_32: list_char,Exp2_65: exp_list_char] : throw_list_char(Exp_71) != fAss_list_char(Exp1_65,List1_32,List2_32,Exp2_65) ).

tff(fact_736_exp_Osimps_I151_J,axiom,
    ! [Exp_70: exp_list_char,A_52: list_char,Exp_69: exp_list_char] : throw_list_char(Exp_70) != lAss_list_char(A_52,Exp_69) ).

tff(fact_737_exp_Osimps_I211_J,axiom,
    ! [Exp_68: exp_list_char,Exp1_64: exp_list_char,Exp2_64: exp_list_char] : throw_list_char(Exp_68) != seq_list_char(Exp1_64,Exp2_64) ).

tff(fact_738_exp_Osimps_I187_J,axiom,
    ! [Exp1_63: exp_list_char,Exp2_63: exp_list_char,Exp_67: exp_list_char,List1_31: list_char,List2_31: list_exp_list_char] : seq_list_char(Exp1_63,Exp2_63) != call_list_char(Exp_67,List1_31,List2_31) ).

tff(fact_739_exp_Osimps_I140_J,axiom,
    ! [A_51: list_char,Exp_66: exp_list_char,Exp_65: exp_list_char,List1_30: list_char,List2_30: list_exp_list_char] : lAss_list_char(A_51,Exp_66) != call_list_char(Exp_65,List1_30,List2_30) ).

tff(fact_740_exp_Osimps_I186_J,axiom,
    ! [Exp_64: exp_list_char,List1_29: list_char,List2_29: list_exp_list_char,Exp1_62: exp_list_char,Exp2_62: exp_list_char] : call_list_char(Exp_64,List1_29,List2_29) != seq_list_char(Exp1_62,Exp2_62) ).

tff(fact_741_exp_Osimps_I141_J,axiom,
    ! [Exp_63: exp_list_char,List1_28: list_char,List2_28: list_exp_list_char,A_50: list_char,Exp_62: exp_list_char] : call_list_char(Exp_63,List1_28,List2_28) != lAss_list_char(A_50,Exp_62) ).

tff(fact_742_exp_Osimps_I171_J,axiom,
    ! [Exp_61: exp_list_char,List1_27: list_char,List2_27: list_exp_list_char,Exp1_61: exp_list_char,List1_26: list_char,List2_26: list_char,Exp2_61: exp_list_char] : call_list_char(Exp_61,List1_27,List2_27) != fAss_list_char(Exp1_61,List1_26,List2_26,Exp2_61) ).

tff(fact_743_exp_Osimps_I170_J,axiom,
    ! [Exp1_60: exp_list_char,List1_25: list_char,List2_25: list_char,Exp2_60: exp_list_char,Exp_60: exp_list_char,List1_24: list_char,List2_24: list_exp_list_char] : fAss_list_char(Exp1_60,List1_25,List2_25,Exp2_60) != call_list_char(Exp_60,List1_24,List2_24) ).

tff(fact_744_exp_Osimps_I107_J,axiom,
    ! [Exp1_59: exp_list_char,Exp2_59: exp_list_char,Exp1_58: exp_list_char,Bop_8: bop,Exp2_58: exp_list_char] : seq_list_char(Exp1_59,Exp2_59) != binOp_list_char(Exp1_58,Bop_8,Exp2_58) ).

tff(fact_745_exp_Osimps_I97_J,axiom,
    ! [A_49: list_char,Exp_59: exp_list_char,Exp1_57: exp_list_char,Bop_7: bop,Exp2_57: exp_list_char] : lAss_list_char(A_49,Exp_59) != binOp_list_char(Exp1_57,Bop_7,Exp2_57) ).

tff(fact_746_exp_Osimps_I106_J,axiom,
    ! [Exp1_56: exp_list_char,Bop_6: bop,Exp2_56: exp_list_char,Exp1_55: exp_list_char,Exp2_55: exp_list_char] : binOp_list_char(Exp1_56,Bop_6,Exp2_56) != seq_list_char(Exp1_55,Exp2_55) ).

tff(fact_747_exp_Osimps_I96_J,axiom,
    ! [Exp1_54: exp_list_char,Bop_5: bop,Exp2_54: exp_list_char,A_48: list_char,Exp_58: exp_list_char] : binOp_list_char(Exp1_54,Bop_5,Exp2_54) != lAss_list_char(A_48,Exp_58) ).

tff(fact_748_exp_Osimps_I100_J,axiom,
    ! [Exp1_53: exp_list_char,Bop_4: bop,Exp2_53: exp_list_char,Exp1_52: exp_list_char,List1_23: list_char,List2_23: list_char,Exp2_52: exp_list_char] : binOp_list_char(Exp1_53,Bop_4,Exp2_53) != fAss_list_char(Exp1_52,List1_23,List2_23,Exp2_52) ).

tff(fact_749_exp_Osimps_I101_J,axiom,
    ! [Exp1_51: exp_list_char,List1_22: list_char,List2_22: list_char,Exp2_51: exp_list_char,Exp1_50: exp_list_char,Bop_3: bop,Exp2_50: exp_list_char] : fAss_list_char(Exp1_51,List1_22,List2_22,Exp2_51) != binOp_list_char(Exp1_50,Bop_3,Exp2_50) ).

tff(fact_750_exp_Osimps_I61_J,axiom,
    ! [Exp1_49: exp_list_char,Exp2_49: exp_list_char,List_19: list_char,Exp_57: exp_list_char] : seq_list_char(Exp1_49,Exp2_49) != cast_list_char(List_19,Exp_57) ).

tff(fact_751_exp_Osimps_I60_J,axiom,
    ! [List_18: list_char,Exp_56: exp_list_char,Exp1_48: exp_list_char,Exp2_48: exp_list_char] : cast_list_char(List_18,Exp_56) != seq_list_char(Exp1_48,Exp2_48) ).

tff(fact_752_exp_Osimps_I50_J,axiom,
    ! [List_17: list_char,Exp_55: exp_list_char,A_47: list_char,Exp_54: exp_list_char] : cast_list_char(List_17,Exp_55) != lAss_list_char(A_47,Exp_54) ).

tff(fact_753_exp_Osimps_I51_J,axiom,
    ! [A_46: list_char,Exp_53: exp_list_char,List_16: list_char,Exp_52: exp_list_char] : lAss_list_char(A_46,Exp_53) != cast_list_char(List_16,Exp_52) ).

tff(fact_754_exp_Osimps_I206_J,axiom,
    ! [Exp1_47: exp_list_char,Exp2_47: exp_list_char,Exp1_46: exp_list_char,Exp2_46: exp_list_char,Exp3_7: exp_list_char] : seq_list_char(Exp1_47,Exp2_47) != cond_list_char(Exp1_46,Exp2_46,Exp3_7) ).

tff(fact_755_exp_Osimps_I146_J,axiom,
    ! [A_45: list_char,Exp_51: exp_list_char,Exp1_45: exp_list_char,Exp2_45: exp_list_char,Exp3_6: exp_list_char] : lAss_list_char(A_45,Exp_51) != cond_list_char(Exp1_45,Exp2_45,Exp3_6) ).

tff(fact_756_exp_Osimps_I54_J,axiom,
    ! [List_15: list_char,Exp_50: exp_list_char,Exp1_44: exp_list_char,List1_21: list_char,List2_21: list_char,Exp2_44: exp_list_char] : cast_list_char(List_15,Exp_50) != fAss_list_char(Exp1_44,List1_21,List2_21,Exp2_44) ).

tff(fact_757_exp_Osimps_I207_J,axiom,
    ! [Exp1_43: exp_list_char,Exp2_43: exp_list_char,Exp3_5: exp_list_char,Exp1_42: exp_list_char,Exp2_42: exp_list_char] : cond_list_char(Exp1_43,Exp2_43,Exp3_5) != seq_list_char(Exp1_42,Exp2_42) ).

tff(fact_758_exp_Osimps_I147_J,axiom,
    ! [Exp1_41: exp_list_char,Exp2_41: exp_list_char,Exp3_4: exp_list_char,A_44: list_char,Exp_49: exp_list_char] : cond_list_char(Exp1_41,Exp2_41,Exp3_4) != lAss_list_char(A_44,Exp_49) ).

tff(fact_759_exp_Osimps_I177_J,axiom,
    ! [Exp1_40: exp_list_char,Exp2_40: exp_list_char,Exp3_3: exp_list_char,Exp1_39: exp_list_char,List1_20: list_char,List2_20: list_char,Exp2_39: exp_list_char] : cond_list_char(Exp1_40,Exp2_40,Exp3_3) != fAss_list_char(Exp1_39,List1_20,List2_20,Exp2_39) ).

tff(fact_760_exp_Osimps_I55_J,axiom,
    ! [Exp1_38: exp_list_char,List1_19: list_char,List2_19: list_char,Exp2_38: exp_list_char,List_14: list_char,Exp_48: exp_list_char] : fAss_list_char(Exp1_38,List1_19,List2_19,Exp2_38) != cast_list_char(List_14,Exp_48) ).

tff(fact_761_exp_Osimps_I176_J,axiom,
    ! [Exp1_37: exp_list_char,List1_18: list_char,List2_18: list_char,Exp2_37: exp_list_char,Exp1_36: exp_list_char,Exp2_36: exp_list_char,Exp3_2: exp_list_char] : fAss_list_char(Exp1_37,List1_18,List2_18,Exp2_37) != cond_list_char(Exp1_36,Exp2_36,Exp3_2) ).

tff(fact_762_exp_Osimps_I161_J,axiom,
    ! [Exp1_35: exp_list_char,Exp2_35: exp_list_char,Exp_47: exp_list_char,List1_17: list_char,List2_17: list_char] : seq_list_char(Exp1_35,Exp2_35) != fAcc_list_char(Exp_47,List1_17,List2_17) ).

tff(fact_763_exp_Osimps_I136_J,axiom,
    ! [A_43: list_char,Exp_46: exp_list_char,Exp_45: exp_list_char,List1_16: list_char,List2_16: list_char] : lAss_list_char(A_43,Exp_46) != fAcc_list_char(Exp_45,List1_16,List2_16) ).

tff(fact_764_exp_Osimps_I160_J,axiom,
    ! [Exp_44: exp_list_char,List1_15: list_char,List2_15: list_char,Exp1_34: exp_list_char,Exp2_34: exp_list_char] : fAcc_list_char(Exp_44,List1_15,List2_15) != seq_list_char(Exp1_34,Exp2_34) ).

tff(fact_765_exp_Osimps_I137_J,axiom,
    ! [Exp_43: exp_list_char,List1_14: list_char,List2_14: list_char,A_42: list_char,Exp_42: exp_list_char] : fAcc_list_char(Exp_43,List1_14,List2_14) != lAss_list_char(A_42,Exp_42) ).

tff(fact_766_exp_Osimps_I154_J,axiom,
    ! [Exp_41: exp_list_char,List1_13: list_char,List2_13: list_char,Exp1_33: exp_list_char,List1_12: list_char,List2_12: list_char,Exp2_33: exp_list_char] : fAcc_list_char(Exp_41,List1_13,List2_13) != fAss_list_char(Exp1_33,List1_12,List2_12,Exp2_33) ).

tff(fact_767_exp_Osimps_I155_J,axiom,
    ! [Exp1_32: exp_list_char,List1_11: list_char,List2_11: list_char,Exp2_32: exp_list_char,Exp_40: exp_list_char,List1_10: list_char,List2_10: list_char] : fAss_list_char(Exp1_32,List1_11,List2_11,Exp2_32) != fAcc_list_char(Exp_40,List1_10,List2_10) ).

tff(fact_768_exp_Osimps_I212_J,axiom,
    ! [Exp1_31: exp_list_char,Exp2_31: exp_list_char,Exp1_30: exp_list_char,List_13: list_char,A_41: list_char,Exp2_30: exp_list_char] : seq_list_char(Exp1_31,Exp2_31) != tryCatch_list_char(Exp1_30,List_13,A_41,Exp2_30) ).

tff(fact_769_exp_Osimps_I152_J,axiom,
    ! [A_40: list_char,Exp_39: exp_list_char,Exp1_29: exp_list_char,List_12: list_char,A_39: list_char,Exp2_29: exp_list_char] : lAss_list_char(A_40,Exp_39) != tryCatch_list_char(Exp1_29,List_12,A_39,Exp2_29) ).

tff(fact_770_exp_Osimps_I213_J,axiom,
    ! [Exp1_28: exp_list_char,List_11: list_char,A_38: list_char,Exp2_28: exp_list_char,Exp1_27: exp_list_char,Exp2_27: exp_list_char] : tryCatch_list_char(Exp1_28,List_11,A_38,Exp2_28) != seq_list_char(Exp1_27,Exp2_27) ).

tff(fact_771_exp_Osimps_I153_J,axiom,
    ! [Exp1_26: exp_list_char,List_10: list_char,A_37: list_char,Exp2_26: exp_list_char,A_36: list_char,Exp_38: exp_list_char] : tryCatch_list_char(Exp1_26,List_10,A_37,Exp2_26) != lAss_list_char(A_36,Exp_38) ).

tff(fact_772_exp_Osimps_I182_J,axiom,
    ! [Exp1_25: exp_list_char,List1_9: list_char,List2_9: list_char,Exp2_25: exp_list_char,Exp1_24: exp_list_char,List_9: list_char,A_35: list_char,Exp2_24: exp_list_char] : fAss_list_char(Exp1_25,List1_9,List2_9,Exp2_25) != tryCatch_list_char(Exp1_24,List_9,A_35,Exp2_24) ).

tff(fact_773_exp_Osimps_I183_J,axiom,
    ! [Exp1_23: exp_list_char,List_8: list_char,A_34: list_char,Exp2_23: exp_list_char,Exp1_22: exp_list_char,List1_8: list_char,List2_8: list_char,Exp2_22: exp_list_char] : tryCatch_list_char(Exp1_23,List_8,A_34,Exp2_23) != fAss_list_char(Exp1_22,List1_8,List2_8,Exp2_22) ).

tff(fact_774_exp_Osimps_I178_J,axiom,
    ! [Exp1_21: exp_list_char,List1_7: list_char,List2_7: list_char,Exp2_21: exp_list_char,Exp1_20: exp_list_char,Exp2_20: exp_list_char] : fAss_list_char(Exp1_21,List1_7,List2_7,Exp2_21) != while_list_char(Exp1_20,Exp2_20) ).

tff(fact_775_exp_Osimps_I179_J,axiom,
    ! [Exp1_19: exp_list_char,Exp2_19: exp_list_char,Exp1_18: exp_list_char,List1_6: list_char,List2_6: list_char,Exp2_18: exp_list_char] : while_list_char(Exp1_19,Exp2_19) != fAss_list_char(Exp1_18,List1_6,List2_6,Exp2_18) ).

tff(fact_776_exp_Osimps_I149_J,axiom,
    ! [Exp1_17: exp_list_char,Exp2_17: exp_list_char,A_33: list_char,Exp_37: exp_list_char] : while_list_char(Exp1_17,Exp2_17) != lAss_list_char(A_33,Exp_37) ).

tff(fact_777_exp_Osimps_I209_J,axiom,
    ! [Exp1_16: exp_list_char,Exp2_16: exp_list_char,Exp1_15: exp_list_char,Exp2_15: exp_list_char] : while_list_char(Exp1_16,Exp2_16) != seq_list_char(Exp1_15,Exp2_15) ).

tff(fact_778_exp_Osimps_I148_J,axiom,
    ! [A_32: list_char,Exp_36: exp_list_char,Exp1_14: exp_list_char,Exp2_14: exp_list_char] : lAss_list_char(A_32,Exp_36) != while_list_char(Exp1_14,Exp2_14) ).

tff(fact_779_exp_Osimps_I208_J,axiom,
    ! [Exp1_13: exp_list_char,Exp2_13: exp_list_char,Exp1_12: exp_list_char,Exp2_12: exp_list_char] : seq_list_char(Exp1_13,Exp2_13) != while_list_char(Exp1_12,Exp2_12) ).

tff(fact_780_val_Osimps_I5_J,axiom,
    null != unit ).

tff(fact_781_val_Osimps_I4_J,axiom,
    unit != null ).

tff(fact_782_val_Osimps_I6_J,axiom,
    ! [Bool_1: bool] : unit != bool_1(Bool_1) ).

tff(fact_783_val_Osimps_I7_J,axiom,
    ! [Bool_1: bool] : bool_1(Bool_1) != unit ).

tff(fact_784_red__reds_OLAssRed,axiom,
    ! [V: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(lAss_list_char(V,Ea),S_1),produc1259058957on_val(lAss_list_char(V,E_a),S)),red(Pa))) ) ).

tff(fact_785_red__reds_OSeqRed,axiom,
    ! [E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(seq_list_char(Ea,E_2),S_1),produc1259058957on_val(seq_list_char(E_a,E_2),S)),red(Pa))) ) ).

tff(fact_786_red__reds_OFAssRed1,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(Ea,F,D,E_2),S_1),produc1259058957on_val(fAss_list_char(E_a,F,D,E_2),S)),red(Pa))) ) ).

tff(fact_787_red__reds_OCallThrowParams,axiom,
    ! [V_1: val,M: list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char,Esa: list_exp_list_char,Vs_1: list_val,Ea: 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(Ea),Es_a)) )
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(call_list_char(hAPP_v834067052t_char(val_list_char,V_1),M,Esa),S_1),produc1259058957on_val(throw_list_char(Ea),S_1)),red(Pa))) ) ).

tff(fact_788_red__reds_ORedWhile,axiom,
    ! [B: exp_list_char,C_1: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(while_list_char(B,C_1),S_1),produc1259058957on_val(cond_list_char(B,seq_list_char(C_1,while_list_char(B,C_1)),hAPP_v834067052t_char(val_list_char,unit)),S_1)),red(Pa))) ).

tff(fact_789_red__reds_ORedSeq,axiom,
    ! [V_1: val,E_2: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(seq_list_char(hAPP_v834067052t_char(val_list_char,V_1),E_2),S_1),produc1259058957on_val(E_2,S_1)),red(Pa))) ).

tff(fact_790_red__reds_OSeqThrow,axiom,
    ! [Ea: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(seq_list_char(throw_list_char(Ea),E_2),S_1),produc1259058957on_val(throw_list_char(Ea),S_1)),red(Pa))) ).

tff(fact_791_red__reds_OLAssThrow,axiom,
    ! [V: list_char,Ea: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(lAss_list_char(V,throw_list_char(Ea)),S_1),produc1259058957on_val(throw_list_char(Ea),S_1)),red(Pa))) ).

tff(fact_792_LAssReds,axiom,
    ! [V: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(lAss_list_char(V,Ea),S_1),produc1259058957on_val(lAss_list_char(V,E_a),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_793_SeqReds,axiom,
    ! [E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(seq_list_char(Ea,E_2),S_1),produc1259058957on_val(seq_list_char(E_a,E_2),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_794_red__reds_OFAssRed2,axiom,
    ! [V_1: val,F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),red(Pa)))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(hAPP_v834067052t_char(val_list_char,V_1),F,D,Ea),S_1),produc1259058957on_val(fAss_list_char(hAPP_v834067052t_char(val_list_char,V_1),F,D,E_a),S)),red(Pa))) ) ).

tff(fact_795_red__reds_OFAssThrow1,axiom,
    ! [Ea: exp_list_char,F: list_char,D: list_char,E_2: exp_list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(throw_list_char(Ea),F,D,E_2),S_1),produc1259058957on_val(throw_list_char(Ea),S_1)),red(Pa))) ).

tff(fact_796_FAssReds1,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(Ea,F,D,E_2),S_1),produc1259058957on_val(fAss_list_char(E_a,F,D,E_2),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_797_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_1: val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_1_1,S_0),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1_1),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_2,S_1_1),produc1259058957on_val(E_2_1,S_2_1)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(seq_list_char(E_1_1,E_2),S_0),produc1259058957on_val(E_2_1,S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_798_WTrt__elim__cases_I4_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,throw_list_char(Ea)),T_3))
     => ~ ! [T_r_1: ty] :
            ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),T_r_1))
           => ~ hBOOL(hAPP_ty_bool(is_refT,T_r_1)) ) ) ).

tff(fact_799_map__append,axiom,
    ! [F_1: fun_Pr1566767763har_ty,Xs: list_P2023964830har_ty,Ys: list_P2023964830har_ty] : map_Pr1267419400har_ty(F_1,append590652462har_ty(Xs,Ys)) = append814478020har_ty(map_Pr1267419400har_ty(F_1,Xs),map_Pr1267419400har_ty(F_1,Ys)) ).

tff(fact_800_map__append,axiom,
    ! [F_1: fun_Pr107226222har_ty,Xs: list_P1940453997har_ty,Ys: list_P1940453997har_ty] : map_Pr1471044963har_ty(F_1,append1373980413har_ty(Xs,Ys)) = append590652462har_ty(map_Pr1471044963har_ty(F_1,Xs),map_Pr1471044963har_ty(F_1,Ys)) ).

tff(fact_801_map__append,axiom,
    ! [F_1: fun_list_char_val,Xs: list_list_char,Ys: list_list_char] : map_list_char_val(F_1,append_list_char(Xs,Ys)) = append_val(map_list_char_val(F_1,Xs),map_list_char_val(F_1,Ys)) ).

tff(fact_802_map__append,axiom,
    ! [F_1: fun_ty_option_ty,Xs: list_ty,Ys: list_ty] : map_ty_option_ty(F_1,append_ty(Xs,Ys)) = append_option_ty(map_ty_option_ty(F_1,Xs),map_ty_option_ty(F_1,Ys)) ).

tff(fact_803_map__append,axiom,
    ! [F_1: fun_val_option_ty,Xs: list_val,Ys: list_val] : map_val_option_ty(F_1,append_val(Xs,Ys)) = append_option_ty(map_val_option_ty(F_1,Xs),map_val_option_ty(F_1,Ys)) ).

tff(fact_804_map__append,axiom,
    ! [F_1: fun_va223928858t_char,Xs: list_val,Ys: list_val] : map_va1934808527t_char(F_1,append_val(Xs,Ys)) = append_exp_list_char(map_va1934808527t_char(F_1,Xs),map_va1934808527t_char(F_1,Ys)) ).

tff(fact_805_Cons__eq__appendI,axiom,
    ! [Xs_6: list_P2023964830har_ty,Zs_4: list_P2023964830har_ty,X_6: produc245756905har_ty,Xs1_1: list_P2023964830har_ty,Ys_4: list_P2023964830har_ty] :
      ( ( cons_P796333129har_ty(X_6,Xs1_1) = Ys_4 )
     => ( ( Xs_6 = append590652462har_ty(Xs1_1,Zs_4) )
       => ( cons_P796333129har_ty(X_6,Xs_6) = append590652462har_ty(Ys_4,Zs_4) ) ) ) ).

tff(fact_806_Cons__eq__appendI,axiom,
    ! [Xs_6: list_exp_list_char,Zs_4: list_exp_list_char,X_6: exp_list_char,Xs1_1: list_exp_list_char,Ys_4: list_exp_list_char] :
      ( ( cons_exp_list_char(X_6,Xs1_1) = Ys_4 )
     => ( ( Xs_6 = append_exp_list_char(Xs1_1,Zs_4) )
       => ( cons_exp_list_char(X_6,Xs_6) = append_exp_list_char(Ys_4,Zs_4) ) ) ) ).

tff(fact_807_Cons__eq__appendI,axiom,
    ! [Xs_6: list_val,Zs_4: list_val,X_6: val,Xs1_1: list_val,Ys_4: list_val] :
      ( ( cons_val(X_6,Xs1_1) = Ys_4 )
     => ( ( Xs_6 = append_val(Xs1_1,Zs_4) )
       => ( cons_val(X_6,Xs_6) = append_val(Ys_4,Zs_4) ) ) ) ).

tff(fact_808_Cons__eq__appendI,axiom,
    ! [Xs_6: list_ty,Zs_4: list_ty,X_6: ty,Xs1_1: list_ty,Ys_4: list_ty] :
      ( ( cons_ty(X_6,Xs1_1) = Ys_4 )
     => ( ( Xs_6 = append_ty(Xs1_1,Zs_4) )
       => ( cons_ty(X_6,Xs_6) = append_ty(Ys_4,Zs_4) ) ) ) ).

tff(fact_809_Cons__eq__appendI,axiom,
    ! [Xs_6: list_list_char,Zs_4: list_list_char,X_6: list_char,Xs1_1: list_list_char,Ys_4: list_list_char] :
      ( ( cons_list_char(X_6,Xs1_1) = Ys_4 )
     => ( ( Xs_6 = append_list_char(Xs1_1,Zs_4) )
       => ( cons_list_char(X_6,Xs_6) = append_list_char(Ys_4,Zs_4) ) ) ) ).

tff(fact_810_append__Cons,axiom,
    ! [X_5: produc245756905har_ty,Xs_5: list_P2023964830har_ty,Ys_3: list_P2023964830har_ty] : append590652462har_ty(cons_P796333129har_ty(X_5,Xs_5),Ys_3) = cons_P796333129har_ty(X_5,append590652462har_ty(Xs_5,Ys_3)) ).

tff(fact_811_append__Cons,axiom,
    ! [X_5: exp_list_char,Xs_5: list_exp_list_char,Ys_3: list_exp_list_char] : append_exp_list_char(cons_exp_list_char(X_5,Xs_5),Ys_3) = cons_exp_list_char(X_5,append_exp_list_char(Xs_5,Ys_3)) ).

tff(fact_812_append__Cons,axiom,
    ! [X_5: val,Xs_5: list_val,Ys_3: list_val] : append_val(cons_val(X_5,Xs_5),Ys_3) = cons_val(X_5,append_val(Xs_5,Ys_3)) ).

tff(fact_813_append__Cons,axiom,
    ! [X_5: ty,Xs_5: list_ty,Ys_3: list_ty] : append_ty(cons_ty(X_5,Xs_5),Ys_3) = cons_ty(X_5,append_ty(Xs_5,Ys_3)) ).

tff(fact_814_append__Cons,axiom,
    ! [X_5: list_char,Xs_5: list_list_char,Ys_3: list_list_char] : append_list_char(cons_list_char(X_5,Xs_5),Ys_3) = cons_list_char(X_5,append_list_char(Xs_5,Ys_3)) ).

tff(fact_815_map_Osimps_I2_J,axiom,
    ! [F_1: fun_Pr1566767763har_ty,X_2: produc245756905har_ty,Xs: list_P2023964830har_ty] : map_Pr1267419400har_ty(F_1,cons_P796333129har_ty(X_2,Xs)) = cons_P1020158687har_ty(hAPP_P385447595har_ty(F_1,X_2),map_Pr1267419400har_ty(F_1,Xs)) ).

tff(fact_816_map_Osimps_I2_J,axiom,
    ! [F_1: fun_Pr107226222har_ty,X_2: produc917948472har_ty,Xs: list_P1940453997har_ty] : map_Pr1471044963har_ty(F_1,cons_P306092184har_ty(X_2,Xs)) = cons_P796333129har_ty(hAPP_P71962758har_ty(F_1,X_2),map_Pr1471044963har_ty(F_1,Xs)) ).

tff(fact_817_map_Osimps_I2_J,axiom,
    ! [F_1: fun_list_char_val,X_2: list_char,Xs: list_list_char] : map_list_char_val(F_1,cons_list_char(X_2,Xs)) = cons_val(hAPP_list_char_val(F_1,X_2),map_list_char_val(F_1,Xs)) ).

tff(fact_818_map_Osimps_I2_J,axiom,
    ! [F_1: fun_ty_option_ty,X_2: ty,Xs: list_ty] : map_ty_option_ty(F_1,cons_ty(X_2,Xs)) = cons_option_ty(hAPP_ty_option_ty(F_1,X_2),map_ty_option_ty(F_1,Xs)) ).

tff(fact_819_map_Osimps_I2_J,axiom,
    ! [F_1: fun_val_option_ty,X_2: val,Xs: list_val] : map_val_option_ty(F_1,cons_val(X_2,Xs)) = cons_option_ty(hAPP_val_option_ty(F_1,X_2),map_val_option_ty(F_1,Xs)) ).

tff(fact_820_map_Osimps_I2_J,axiom,
    ! [F_1: fun_va223928858t_char,X_2: val,Xs: list_val] : map_va1934808527t_char(F_1,cons_val(X_2,Xs)) = cons_exp_list_char(hAPP_v834067052t_char(F_1,X_2),map_va1934808527t_char(F_1,Xs)) ).

tff(fact_821_redp__redsp_OCallThrowParams,axiom,
    ! [Pa: list_P1999446415t_char,V_1: val,M: list_char,S_1: produc12694297on_val,Esa: list_exp_list_char,Vs_1: list_val,Ea: 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(Ea),Es_a)) )
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(hAPP_v834067052t_char(val_list_char,V_1),M,Esa),S_1),throw_list_char(Ea)),S_1)) ) ).

tff(fact_822_red__reds_ORedInitBlock,axiom,
    ! [V: list_char,T_3: ty,V_1: val,U: val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(block_list_char(V,T_3,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),hAPP_v834067052t_char(val_list_char,U))),S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,U),S_1)),red(Pa))) ).

tff(fact_823_finals__app__map,axiom,
    ! [Vs_1: list_val,Esa: list_exp_list_char] :
      ( hBOOL(finals_list_char(append_exp_list_char(map_va1934808527t_char(val_list_char,Vs_1),Esa)))
    <=> hBOOL(finals_list_char(Esa)) ) ).

tff(fact_824_exp_Osimps_I10_J,axiom,
    ! [A: list_char,Ty_25: ty,Exp_35: exp_list_char,A_3: list_char,Ty_24: ty,Exp_34: exp_list_char] :
      ( ( block_list_char(A,Ty_25,Exp_35) = block_list_char(A_3,Ty_24,Exp_34) )
    <=> ( ( A = A_3 )
        & ( Ty_25 = Ty_24 )
        & ( Exp_35 = Exp_34 ) ) ) ).

tff(fact_825_redp__redsp_ORedBlock,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,T_3: ty,U: val,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V,T_3,hAPP_v834067052t_char(val_list_char,U)),S_1),hAPP_v834067052t_char(val_list_char,U)),S_1)) ).

tff(fact_826_redp__redsp_OThrowThrow,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,throw_list_char(throw_list_char(Ea)),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_827_redp__redsp_OThrowRed,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E_a),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,throw_list_char(Ea),S_1),throw_list_char(E_a)),S)) ) ).

tff(fact_828_redp__redsp_OSeqRed,axiom,
    ! [E_2: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E_a),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(Ea,E_2),S_1),seq_list_char(E_a,E_2)),S)) ) ).

tff(fact_829_redp__redsp_OLAssRed,axiom,
    ! [V: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E_a),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(V,Ea),S_1),lAss_list_char(V,E_a)),S)) ) ).

tff(fact_830_redp__redsp_OCallObj,axiom,
    ! [M: list_char,Esa: list_exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E_a),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(Ea,M,Esa),S_1),call_list_char(E_a,M,Esa)),S)) ) ).

tff(fact_831_redp__redsp_OFAssRed1,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E_a),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(Ea,F,D,E_2),S_1),fAss_list_char(E_a,F,D,E_2)),S)) ) ).

tff(fact_832_redp__redsp_OBinOpRed1,axiom,
    ! [Bop: bop,E_2: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E_a),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(Ea,Bop,E_2),S_1),binOp_list_char(E_a,Bop,E_2)),S)) ) ).

tff(fact_833_redp__redsp_OCastRed,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E_a),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,Ea),S_1),cast_list_char(C,E_a)),S)) ) ).

tff(fact_834_redp__redsp_OCondRed,axiom,
    ! [E_1_1: exp_list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E_a),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cond_list_char(Ea,E_1_1,E_2),S_1),cond_list_char(E_a,E_1_1,E_2)),S)) ) ).

tff(fact_835_redp__redsp_OFAccRed,axiom,
    ! [F: list_char,D: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E_a),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(Ea,F,D),S_1),fAcc_list_char(E_a,F,D)),S)) ) ).

tff(fact_836_redp__redsp_OTryRed,axiom,
    ! [C: list_char,V: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E_a),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,tryCatch_list_char(Ea,C,V,E_2),S_1),tryCatch_list_char(E_a,C,V,E_2)),S)) ) ).

tff(fact_837_exp_Osimps_I83_J,axiom,
    ! [A_31: list_char,Ty_23: ty,Exp_33: exp_list_char,Val_1: val] : block_list_char(A_31,Ty_23,Exp_33) != hAPP_v834067052t_char(val_list_char,Val_1) ).

tff(fact_838_exp_Osimps_I82_J,axiom,
    ! [Val: val,A_30: list_char,Ty_22: ty,Exp_32: exp_list_char] : hAPP_v834067052t_char(val_list_char,Val) != block_list_char(A_30,Ty_22,Exp_32) ).

tff(fact_839_exp_Osimps_I203_J,axiom,
    ! [Exp_31: exp_list_char,A_29: list_char,Ty_21: ty,Exp_30: exp_list_char] : throw_list_char(Exp_31) != block_list_char(A_29,Ty_21,Exp_30) ).

tff(fact_840_exp_Osimps_I202_J,axiom,
    ! [A_28: list_char,Ty_20: ty,Exp_29: exp_list_char,Exp_28: exp_list_char] : block_list_char(A_28,Ty_20,Exp_29) != throw_list_char(Exp_28) ).

tff(fact_841_exp_Osimps_I197_J,axiom,
    ! [Exp1_11: exp_list_char,Exp2_11: exp_list_char,A_27: list_char,Ty_19: ty,Exp_27: exp_list_char] : seq_list_char(Exp1_11,Exp2_11) != block_list_char(A_27,Ty_19,Exp_27) ).

tff(fact_842_exp_Osimps_I142_J,axiom,
    ! [A_26: list_char,Exp_26: exp_list_char,A_25: list_char,Ty_18: ty,Exp_25: exp_list_char] : lAss_list_char(A_26,Exp_26) != block_list_char(A_25,Ty_18,Exp_25) ).

tff(fact_843_exp_Osimps_I196_J,axiom,
    ! [A_24: list_char,Ty_17: ty,Exp_24: exp_list_char,Exp1_10: exp_list_char,Exp2_10: exp_list_char] : block_list_char(A_24,Ty_17,Exp_24) != seq_list_char(Exp1_10,Exp2_10) ).

tff(fact_844_exp_Osimps_I143_J,axiom,
    ! [A_23: list_char,Ty_16: ty,Exp_23: exp_list_char,A_22: list_char,Exp_22: exp_list_char] : block_list_char(A_23,Ty_16,Exp_23) != lAss_list_char(A_22,Exp_22) ).

tff(fact_845_exp_Osimps_I185_J,axiom,
    ! [A_21: list_char,Ty_15: ty,Exp_21: exp_list_char,Exp_20: exp_list_char,List1_5: list_char,List2_5: list_exp_list_char] : block_list_char(A_21,Ty_15,Exp_21) != call_list_char(Exp_20,List1_5,List2_5) ).

tff(fact_846_exp_Osimps_I184_J,axiom,
    ! [Exp_19: exp_list_char,List1_4: list_char,List2_4: list_exp_list_char,A_20: list_char,Ty_14: ty,Exp_18: exp_list_char] : call_list_char(Exp_19,List1_4,List2_4) != block_list_char(A_20,Ty_14,Exp_18) ).

tff(fact_847_exp_Osimps_I173_J,axiom,
    ! [A_19: list_char,Ty_13: ty,Exp_17: exp_list_char,Exp1_9: exp_list_char,List1_3: list_char,List2_3: list_char,Exp2_9: exp_list_char] : block_list_char(A_19,Ty_13,Exp_17) != fAss_list_char(Exp1_9,List1_3,List2_3,Exp2_9) ).

tff(fact_848_exp_Osimps_I172_J,axiom,
    ! [Exp1_8: exp_list_char,List1_2: list_char,List2_2: list_char,Exp2_8: exp_list_char,A_18: list_char,Ty_12: ty,Exp_16: exp_list_char] : fAss_list_char(Exp1_8,List1_2,List2_2,Exp2_8) != block_list_char(A_18,Ty_12,Exp_16) ).

tff(fact_849_exp_Osimps_I105_J,axiom,
    ! [A_17: list_char,Ty_11: ty,Exp_15: exp_list_char,Exp1_7: exp_list_char,Bop_2: bop,Exp2_7: exp_list_char] : block_list_char(A_17,Ty_11,Exp_15) != binOp_list_char(Exp1_7,Bop_2,Exp2_7) ).

tff(fact_850_exp_Osimps_I104_J,axiom,
    ! [Exp1_6: exp_list_char,Bop_1: bop,Exp2_6: exp_list_char,A_16: list_char,Ty_10: ty,Exp_14: exp_list_char] : binOp_list_char(Exp1_6,Bop_1,Exp2_6) != block_list_char(A_16,Ty_10,Exp_14) ).

tff(fact_851_exp_Osimps_I198_J,axiom,
    ! [A_15: list_char,Ty_9: ty,Exp_13: exp_list_char,Exp1_5: exp_list_char,Exp2_5: exp_list_char,Exp3_1: exp_list_char] : block_list_char(A_15,Ty_9,Exp_13) != cond_list_char(Exp1_5,Exp2_5,Exp3_1) ).

tff(fact_852_exp_Osimps_I199_J,axiom,
    ! [Exp1_4: exp_list_char,Exp2_4: exp_list_char,Exp3: exp_list_char,A_14: list_char,Ty_8: ty,Exp_12: exp_list_char] : cond_list_char(Exp1_4,Exp2_4,Exp3) != block_list_char(A_14,Ty_8,Exp_12) ).

tff(fact_853_exp_Osimps_I59_J,axiom,
    ! [A_13: list_char,Ty_7: ty,Exp_11: exp_list_char,List_7: list_char,Exp_10: exp_list_char] : block_list_char(A_13,Ty_7,Exp_11) != cast_list_char(List_7,Exp_10) ).

tff(fact_854_exp_Osimps_I58_J,axiom,
    ! [List_6: list_char,Exp_9: exp_list_char,A_12: list_char,Ty_6: ty,Exp_8: exp_list_char] : cast_list_char(List_6,Exp_9) != block_list_char(A_12,Ty_6,Exp_8) ).

tff(fact_855_exp_Osimps_I159_J,axiom,
    ! [A_11: list_char,Ty_5: ty,Exp_7: exp_list_char,Exp_6: exp_list_char,List1_1: list_char,List2_1: list_char] : block_list_char(A_11,Ty_5,Exp_7) != fAcc_list_char(Exp_6,List1_1,List2_1) ).

tff(fact_856_exp_Osimps_I158_J,axiom,
    ! [Exp_5: exp_list_char,List1: list_char,List2: list_char,A_10: list_char,Ty_4: ty,Exp_4: exp_list_char] : fAcc_list_char(Exp_5,List1,List2) != block_list_char(A_10,Ty_4,Exp_4) ).

tff(fact_857_exp_Osimps_I201_J,axiom,
    ! [Exp1_3: exp_list_char,Exp2_3: exp_list_char,A_9: list_char,Ty_3: ty,Exp_3: exp_list_char] : while_list_char(Exp1_3,Exp2_3) != block_list_char(A_9,Ty_3,Exp_3) ).

tff(fact_858_exp_Osimps_I200_J,axiom,
    ! [A_8: list_char,Ty_2: ty,Exp_2: exp_list_char,Exp1_2: exp_list_char,Exp2_2: exp_list_char] : block_list_char(A_8,Ty_2,Exp_2) != while_list_char(Exp1_2,Exp2_2) ).

tff(fact_859_exp_Osimps_I205_J,axiom,
    ! [Exp1_1: exp_list_char,List_5: list_char,A_7: list_char,Exp2_1: exp_list_char,A_6: list_char,Ty_1: ty,Exp_1: exp_list_char] : tryCatch_list_char(Exp1_1,List_5,A_7,Exp2_1) != block_list_char(A_6,Ty_1,Exp_1) ).

tff(fact_860_exp_Osimps_I204_J,axiom,
    ! [A_5: list_char,Ty: ty,Exp: exp_list_char,Exp1: exp_list_char,List_4: list_char,A_4: list_char,Exp2: exp_list_char] : block_list_char(A_5,Ty,Exp) != tryCatch_list_char(Exp1,List_4,A_4,Exp2) ).

tff(fact_861_redp__redsp_ORedInitBlock,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,T_3: ty,V_1: val,U: val,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V,T_3,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),hAPP_v834067052t_char(val_list_char,U))),S_1),hAPP_v834067052t_char(val_list_char,U)),S_1)) ).

tff(fact_862_redp__redsp_ORedSeq,axiom,
    ! [Pa: list_P1999446415t_char,V_1: val,E_2: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(hAPP_v834067052t_char(val_list_char,V_1),E_2),S_1),E_2),S_1)) ).

tff(fact_863_redp__redsp_OFAssRed2,axiom,
    ! [V_1: val,F: list_char,D: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E_a),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,V_1),F,D,Ea),S_1),fAss_list_char(hAPP_v834067052t_char(val_list_char,V_1),F,D,E_a)),S)) ) ).

tff(fact_864_redp__redsp_OBinOpRed2,axiom,
    ! [V_1_1: val,Bop: bop,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E_a),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_1),Bop,Ea),S_1),binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_1),Bop,E_a)),S)) ) ).

tff(fact_865_redp__redsp_OSeqThrow,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(throw_list_char(Ea),E_2),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_866_redp__redsp_OLAssThrow,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,Ea: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(V,throw_list_char(Ea)),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_867_redp__redsp_OCallThrowObj,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,M: list_char,Esa: list_exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(throw_list_char(Ea),M,Esa),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_868_redp__redsp_OFAssThrow1,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,F: list_char,D: list_char,E_2: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(throw_list_char(Ea),F,D,E_2),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_869_redp__redsp_OBinOpThrow1,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,Bop: bop,E_2: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(throw_list_char(Ea),Bop,E_2),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_870_redp__redsp_OCondThrow,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,E_1_1: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cond_list_char(throw_list_char(Ea),E_1_1,E_2),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_871_redp__redsp_OCastThrow,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,Ea: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,throw_list_char(Ea)),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_872_redp__redsp_ORedTry,axiom,
    ! [Pa: list_P1999446415t_char,V_1: val,C: list_char,V: list_char,E_2: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,tryCatch_list_char(hAPP_v834067052t_char(val_list_char,V_1),C,V,E_2),S_1),hAPP_v834067052t_char(val_list_char,V_1)),S_1)) ).

tff(fact_873_redp__redsp_OFAccThrow,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,F: list_char,D: list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(throw_list_char(Ea),F,D),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_874_redp__redsp_OFAssThrow2,axiom,
    ! [Pa: list_P1999446415t_char,V_1: val,F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,V_1),F,D,throw_list_char(Ea)),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_875_redp__redsp_OBinOpThrow2,axiom,
    ! [Pa: list_P1999446415t_char,V_1_1: val,Bop: bop,Ea: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_1),Bop,throw_list_char(Ea)),S_1),throw_list_char(Ea)),S_1)) ).

tff(fact_876_redp__redsp_ORedCastNull,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,hAPP_v834067052t_char(val_list_char,null)),S_1),hAPP_v834067052t_char(val_list_char,null)),S_1)) ).

tff(fact_877_redp__redsp_ORedCondT,axiom,
    ! [Pa: list_P1999446415t_char,E_1_1: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cond_list_char(hAPP_v834067052t_char(val_list_char,bool_1(fTrue)),E_1_1,E_2),S_1),E_1_1),S_1)) ).

tff(fact_878_redp__redsp_ORedCondF,axiom,
    ! [Pa: list_P1999446415t_char,E_1_1: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cond_list_char(hAPP_v834067052t_char(val_list_char,bool_1(fFalse)),E_1_1,E_2),S_1),E_2),S_1)) ).

tff(fact_879_list_Oinject,axiom,
    ! [A: val,List_3: list_val,A_3: val,List_2: list_val] :
      ( ( cons_val(A,List_3) = cons_val(A_3,List_2) )
    <=> ( ( A = A_3 )
        & ( List_3 = List_2 ) ) ) ).

tff(fact_880_list_Oinject,axiom,
    ! [A: ty,List_3: list_ty,A_3: ty,List_2: list_ty] :
      ( ( cons_ty(A,List_3) = cons_ty(A_3,List_2) )
    <=> ( ( A = A_3 )
        & ( List_3 = List_2 ) ) ) ).

tff(fact_881_list_Oinject,axiom,
    ! [A: list_char,List_3: list_list_char,A_3: list_char,List_2: list_list_char] :
      ( ( cons_list_char(A,List_3) = cons_list_char(A_3,List_2) )
    <=> ( ( A = A_3 )
        & ( List_3 = List_2 ) ) ) ).

tff(fact_882_list_Oinject,axiom,
    ! [A: exp_list_char,List_3: list_exp_list_char,A_3: exp_list_char,List_2: list_exp_list_char] :
      ( ( cons_exp_list_char(A,List_3) = cons_exp_list_char(A_3,List_2) )
    <=> ( ( A = A_3 )
        & ( List_3 = List_2 ) ) ) ).

tff(fact_883_not__Cons__self2,axiom,
    ! [X_4: val,Xs_4: list_val] : cons_val(X_4,Xs_4) != Xs_4 ).

tff(fact_884_not__Cons__self2,axiom,
    ! [X_4: ty,Xs_4: list_ty] : cons_ty(X_4,Xs_4) != Xs_4 ).

tff(fact_885_not__Cons__self2,axiom,
    ! [X_4: list_char,Xs_4: list_list_char] : cons_list_char(X_4,Xs_4) != Xs_4 ).

tff(fact_886_not__Cons__self2,axiom,
    ! [X_4: exp_list_char,Xs_4: list_exp_list_char] : cons_exp_list_char(X_4,Xs_4) != Xs_4 ).

tff(fact_887_not__Cons__self,axiom,
    ! [Xs_3: list_val,X_3: val] : Xs_3 != cons_val(X_3,Xs_3) ).

tff(fact_888_not__Cons__self,axiom,
    ! [Xs_3: list_ty,X_3: ty] : Xs_3 != cons_ty(X_3,Xs_3) ).

tff(fact_889_not__Cons__self,axiom,
    ! [Xs_3: list_list_char,X_3: list_char] : Xs_3 != cons_list_char(X_3,Xs_3) ).

tff(fact_890_not__Cons__self,axiom,
    ! [Xs_3: list_exp_list_char,X_3: exp_list_char] : Xs_3 != cons_exp_list_char(X_3,Xs_3) ).

tff(fact_891_append__eq__appendI,axiom,
    ! [Ys_2: list_P2023964830har_ty,Us_1: list_P2023964830har_ty,Xs_2: list_P2023964830har_ty,Xs1: list_P2023964830har_ty,Zs_3: list_P2023964830har_ty] :
      ( ( append590652462har_ty(Xs_2,Xs1) = Zs_3 )
     => ( ( Ys_2 = append590652462har_ty(Xs1,Us_1) )
       => ( append590652462har_ty(Xs_2,Ys_2) = append590652462har_ty(Zs_3,Us_1) ) ) ) ).

tff(fact_892_append__eq__appendI,axiom,
    ! [Ys_2: list_exp_list_char,Us_1: list_exp_list_char,Xs_2: list_exp_list_char,Xs1: list_exp_list_char,Zs_3: list_exp_list_char] :
      ( ( append_exp_list_char(Xs_2,Xs1) = Zs_3 )
     => ( ( Ys_2 = append_exp_list_char(Xs1,Us_1) )
       => ( append_exp_list_char(Xs_2,Ys_2) = append_exp_list_char(Zs_3,Us_1) ) ) ) ).

tff(fact_893_append__same__eq,axiom,
    ! [Ys: list_P2023964830har_ty,Xs: list_P2023964830har_ty,Zs_2: list_P2023964830har_ty] :
      ( ( append590652462har_ty(Ys,Xs) = append590652462har_ty(Zs_2,Xs) )
    <=> ( Ys = Zs_2 ) ) ).

tff(fact_894_append__same__eq,axiom,
    ! [Ys: list_exp_list_char,Xs: list_exp_list_char,Zs_2: list_exp_list_char] :
      ( ( append_exp_list_char(Ys,Xs) = append_exp_list_char(Zs_2,Xs) )
    <=> ( Ys = Zs_2 ) ) ).

tff(fact_895_same__append__eq,axiom,
    ! [Xs: list_P2023964830har_ty,Ys: list_P2023964830har_ty,Zs_2: list_P2023964830har_ty] :
      ( ( append590652462har_ty(Xs,Ys) = append590652462har_ty(Xs,Zs_2) )
    <=> ( Ys = Zs_2 ) ) ).

tff(fact_896_same__append__eq,axiom,
    ! [Xs: list_exp_list_char,Ys: list_exp_list_char,Zs_2: list_exp_list_char] :
      ( ( append_exp_list_char(Xs,Ys) = append_exp_list_char(Xs,Zs_2) )
    <=> ( Ys = Zs_2 ) ) ).

tff(fact_897_append__eq__append__conv2,axiom,
    ! [Xs: list_P2023964830har_ty,Ys: list_P2023964830har_ty,Zs_2: list_P2023964830har_ty,Ts_3: list_P2023964830har_ty] :
      ( ( append590652462har_ty(Xs,Ys) = append590652462har_ty(Zs_2,Ts_3) )
    <=> ? [Us: list_P2023964830har_ty] :
          ( ( ( Xs = append590652462har_ty(Zs_2,Us) )
            & ( append590652462har_ty(Us,Ys) = Ts_3 ) )
          | ( ( append590652462har_ty(Xs,Us) = Zs_2 )
            & ( Ys = append590652462har_ty(Us,Ts_3) ) ) ) ) ).

tff(fact_898_append__eq__append__conv2,axiom,
    ! [Xs: list_exp_list_char,Ys: list_exp_list_char,Zs_2: list_exp_list_char,Ts_3: list_exp_list_char] :
      ( ( append_exp_list_char(Xs,Ys) = append_exp_list_char(Zs_2,Ts_3) )
    <=> ? [Us: list_exp_list_char] :
          ( ( ( Xs = append_exp_list_char(Zs_2,Us) )
            & ( append_exp_list_char(Us,Ys) = Ts_3 ) )
          | ( ( append_exp_list_char(Xs,Us) = Zs_2 )
            & ( Ys = append_exp_list_char(Us,Ts_3) ) ) ) ) ).

tff(fact_899_append__assoc,axiom,
    ! [Xs_1: list_P2023964830har_ty,Ys_1: list_P2023964830har_ty,Zs_1: list_P2023964830har_ty] : append590652462har_ty(append590652462har_ty(Xs_1,Ys_1),Zs_1) = append590652462har_ty(Xs_1,append590652462har_ty(Ys_1,Zs_1)) ).

tff(fact_900_append__assoc,axiom,
    ! [Xs_1: list_exp_list_char,Ys_1: list_exp_list_char,Zs_1: list_exp_list_char] : append_exp_list_char(append_exp_list_char(Xs_1,Ys_1),Zs_1) = append_exp_list_char(Xs_1,append_exp_list_char(Ys_1,Zs_1)) ).

tff(fact_901_red__reds_ORedBlock,axiom,
    ! [V: list_char,T_3: ty,U: val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(block_list_char(V,T_3,hAPP_v834067052t_char(val_list_char,U)),S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,U),S_1)),red(Pa))) ).

tff(fact_902_redp__redsp_ORedWhile,axiom,
    ! [Pa: list_P1999446415t_char,B: exp_list_char,C_1: exp_list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,while_list_char(B,C_1),S_1),cond_list_char(B,seq_list_char(C_1,while_list_char(B,C_1)),hAPP_v834067052t_char(val_list_char,unit))),S_1)) ).

tff(fact_903_not__finals__ConsI,axiom,
    ! [Es_2: list_exp_list_char,E_7: exp_list_char] :
      ( ~ hBOOL(final_list_char(E_7))
     => ~ hBOOL(finals_list_char(cons_exp_list_char(E_7,Es_2))) ) ).

tff(fact_904_Cons__eq__map__conv,axiom,
    ! [X_2: produc469582463har_ty,Xs: list_P2098242612har_ty,F_1: fun_Pr1566767763har_ty,Ys: list_P2023964830har_ty] :
      ( ( cons_P1020158687har_ty(X_2,Xs) = map_Pr1267419400har_ty(F_1,Ys) )
    <=> ? [Z: produc245756905har_ty,Zs: list_P2023964830har_ty] :
          ( ( Ys = cons_P796333129har_ty(Z,Zs) )
          & ( X_2 = hAPP_P385447595har_ty(F_1,Z) )
          & ( Xs = map_Pr1267419400har_ty(F_1,Zs) ) ) ) ).

tff(fact_905_Cons__eq__map__conv,axiom,
    ! [X_2: produc245756905har_ty,Xs: list_P2023964830har_ty,F_1: fun_Pr107226222har_ty,Ys: list_P1940453997har_ty] :
      ( ( cons_P796333129har_ty(X_2,Xs) = map_Pr1471044963har_ty(F_1,Ys) )
    <=> ? [Z: produc917948472har_ty,Zs: list_P1940453997har_ty] :
          ( ( Ys = cons_P306092184har_ty(Z,Zs) )
          & ( X_2 = hAPP_P71962758har_ty(F_1,Z) )
          & ( Xs = map_Pr1471044963har_ty(F_1,Zs) ) ) ) ).

tff(fact_906_Cons__eq__map__conv,axiom,
    ! [X_2: val,Xs: list_val,F_1: fun_list_char_val,Ys: list_list_char] :
      ( ( cons_val(X_2,Xs) = map_list_char_val(F_1,Ys) )
    <=> ? [Z: list_char,Zs: list_list_char] :
          ( ( Ys = cons_list_char(Z,Zs) )
          & ( X_2 = hAPP_list_char_val(F_1,Z) )
          & ( Xs = map_list_char_val(F_1,Zs) ) ) ) ).

tff(fact_907_Cons__eq__map__conv,axiom,
    ! [X_2: option_ty,Xs: list_option_ty,F_1: fun_ty_option_ty,Ys: list_ty] :
      ( ( cons_option_ty(X_2,Xs) = map_ty_option_ty(F_1,Ys) )
    <=> ? [Z: ty,Zs: list_ty] :
          ( ( Ys = cons_ty(Z,Zs) )
          & ( X_2 = hAPP_ty_option_ty(F_1,Z) )
          & ( Xs = map_ty_option_ty(F_1,Zs) ) ) ) ).

tff(fact_908_Cons__eq__map__conv,axiom,
    ! [X_2: option_ty,Xs: list_option_ty,F_1: fun_val_option_ty,Ys: list_val] :
      ( ( cons_option_ty(X_2,Xs) = map_val_option_ty(F_1,Ys) )
    <=> ? [Z: val,Zs: list_val] :
          ( ( Ys = cons_val(Z,Zs) )
          & ( X_2 = hAPP_val_option_ty(F_1,Z) )
          & ( Xs = map_val_option_ty(F_1,Zs) ) ) ) ).

tff(fact_909_Cons__eq__map__conv,axiom,
    ! [X_2: exp_list_char,Xs: list_exp_list_char,F_1: fun_va223928858t_char,Ys: list_val] :
      ( ( cons_exp_list_char(X_2,Xs) = map_va1934808527t_char(F_1,Ys) )
    <=> ? [Z: val,Zs: list_val] :
          ( ( Ys = cons_val(Z,Zs) )
          & ( X_2 = hAPP_v834067052t_char(F_1,Z) )
          & ( Xs = map_va1934808527t_char(F_1,Zs) ) ) ) ).

tff(fact_910_map__eq__Cons__conv,axiom,
    ! [F_1: fun_Pr1566767763har_ty,Xs: list_P2023964830har_ty,Y_1: produc469582463har_ty,Ys: list_P2098242612har_ty] :
      ( ( map_Pr1267419400har_ty(F_1,Xs) = cons_P1020158687har_ty(Y_1,Ys) )
    <=> ? [Z: produc245756905har_ty,Zs: list_P2023964830har_ty] :
          ( ( Xs = cons_P796333129har_ty(Z,Zs) )
          & ( hAPP_P385447595har_ty(F_1,Z) = Y_1 )
          & ( map_Pr1267419400har_ty(F_1,Zs) = Ys ) ) ) ).

tff(fact_911_map__eq__Cons__conv,axiom,
    ! [F_1: fun_Pr107226222har_ty,Xs: list_P1940453997har_ty,Y_1: produc245756905har_ty,Ys: list_P2023964830har_ty] :
      ( ( map_Pr1471044963har_ty(F_1,Xs) = cons_P796333129har_ty(Y_1,Ys) )
    <=> ? [Z: produc917948472har_ty,Zs: list_P1940453997har_ty] :
          ( ( Xs = cons_P306092184har_ty(Z,Zs) )
          & ( hAPP_P71962758har_ty(F_1,Z) = Y_1 )
          & ( map_Pr1471044963har_ty(F_1,Zs) = Ys ) ) ) ).

tff(fact_912_map__eq__Cons__conv,axiom,
    ! [F_1: fun_list_char_val,Xs: list_list_char,Y_1: val,Ys: list_val] :
      ( ( map_list_char_val(F_1,Xs) = cons_val(Y_1,Ys) )
    <=> ? [Z: list_char,Zs: list_list_char] :
          ( ( Xs = cons_list_char(Z,Zs) )
          & ( hAPP_list_char_val(F_1,Z) = Y_1 )
          & ( map_list_char_val(F_1,Zs) = Ys ) ) ) ).

tff(fact_913_map__eq__Cons__conv,axiom,
    ! [F_1: fun_ty_option_ty,Xs: list_ty,Y_1: option_ty,Ys: list_option_ty] :
      ( ( map_ty_option_ty(F_1,Xs) = cons_option_ty(Y_1,Ys) )
    <=> ? [Z: ty,Zs: list_ty] :
          ( ( Xs = cons_ty(Z,Zs) )
          & ( hAPP_ty_option_ty(F_1,Z) = Y_1 )
          & ( map_ty_option_ty(F_1,Zs) = Ys ) ) ) ).

tff(fact_914_map__eq__Cons__conv,axiom,
    ! [F_1: fun_val_option_ty,Xs: list_val,Y_1: option_ty,Ys: list_option_ty] :
      ( ( map_val_option_ty(F_1,Xs) = cons_option_ty(Y_1,Ys) )
    <=> ? [Z: val,Zs: list_val] :
          ( ( Xs = cons_val(Z,Zs) )
          & ( hAPP_val_option_ty(F_1,Z) = Y_1 )
          & ( map_val_option_ty(F_1,Zs) = Ys ) ) ) ).

tff(fact_915_map__eq__Cons__conv,axiom,
    ! [F_1: fun_va223928858t_char,Xs: list_val,Y_1: exp_list_char,Ys: list_exp_list_char] :
      ( ( map_va1934808527t_char(F_1,Xs) = cons_exp_list_char(Y_1,Ys) )
    <=> ? [Z: val,Zs: list_val] :
          ( ( Xs = cons_val(Z,Zs) )
          & ( hAPP_v834067052t_char(F_1,Z) = Y_1 )
          & ( map_va1934808527t_char(F_1,Zs) = Ys ) ) ) ).

tff(fact_916_blocks_Osimps_I1_J,axiom,
    ! [V_6: list_char,Vs_4: list_list_char,T_4: ty,Ts_2: list_ty,V_3: val,Vs_3: list_val,E_6: exp_list_char] : blocks(produc921874948t_char(cons_list_char(V_6,Vs_4),produc1909267824t_char(cons_ty(T_4,Ts_2),produc1916172923t_char(cons_val(V_3,Vs_3),E_6)))) = block_list_char(V_6,T_4,seq_list_char(lAss_list_char(V_6,hAPP_v834067052t_char(val_list_char,V_3)),blocks(produc921874948t_char(Vs_4,produc1909267824t_char(Ts_2,produc1916172923t_char(Vs_3,E_6)))))) ).

tff(fact_917_red__reds_OInitBlockThrow,axiom,
    ! [V: list_char,T_3: ty,V_1: val,A: nat,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(block_list_char(V,T_3,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))))),S_1),produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))),S_1)),red(Pa))) ).

tff(fact_918_redp__redsp_OCallParams,axiom,
    ! [V_1: val,M: list_char,Pa: list_P1999446415t_char,Esa: list_exp_list_char,S_1: produc12694297on_val,Es_a: list_exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,Esa,S_1),Es_a),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(hAPP_v834067052t_char(val_list_char,V_1),M,Esa),S_1),call_list_char(hAPP_v834067052t_char(val_list_char,V_1),M,Es_a)),S)) ) ).

tff(fact_919_val_Osimps_I3_J,axiom,
    ! [Nat_2: nat,Nat_1: nat] :
      ( ( addr(Nat_2) = addr(Nat_1) )
    <=> ( Nat_2 = Nat_1 ) ) ).

tff(fact_920_val_Osimps_I16_J,axiom,
    ! [Nat: nat] : null != addr(Nat) ).

tff(fact_921_val_Osimps_I17_J,axiom,
    ! [Nat: nat] : addr(Nat) != null ).

tff(fact_922_val_Osimps_I21_J,axiom,
    ! [Nat_1: nat,Bool: bool] : addr(Nat_1) != bool_1(Bool) ).

tff(fact_923_val_Osimps_I20_J,axiom,
    ! [Bool: bool,Nat_1: nat] : bool_1(Bool) != addr(Nat_1) ).

tff(fact_924_val_Osimps_I11_J,axiom,
    ! [Nat: nat] : addr(Nat) != unit ).

tff(fact_925_val_Osimps_I10_J,axiom,
    ! [Nat: nat] : unit != addr(Nat) ).

tff(fact_926_final__def,axiom,
    ! [Ea: exp_list_char] :
      ( hBOOL(final_list_char(Ea))
    <=> ( ? [V_4: val] : Ea = hAPP_v834067052t_char(val_list_char,V_4)
        | ? [A_1: nat] : Ea = throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))) ) ) ).

tff(fact_927_redp__redsp_OBlockThrow,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,T_3: ty,A: nat,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V,T_3,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S_1),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S_1)) ).

tff(fact_928_redp__redsp_OListRed2,axiom,
    ! [V_1: val,Pa: list_P1999446415t_char,Esa: list_exp_list_char,S_1: produc12694297on_val,Es_a: list_exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,Esa,S_1),Es_a),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Esa),S_1),cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Es_a)),S)) ) ).

tff(fact_929_redp__redsp_OListRed1,axiom,
    ! [Esa: list_exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,S_1),E_a),S))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,cons_exp_list_char(Ea,Esa),S_1),cons_exp_list_char(E_a,Esa)),S)) ) ).

tff(fact_930_red__reds_OBlockThrow,axiom,
    ! [V: list_char,T_3: ty,A: nat,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(block_list_char(V,T_3,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S_1),produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))),S_1)),red(Pa))) ).

tff(fact_931_redp__redsp_OInitBlockThrow,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,T_3: ty,V_1: val,A: nat,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V,T_3,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))))),S_1),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S_1)) ).

tff(fact_932_finals__def,axiom,
    ! [Esa: list_exp_list_char] :
      ( hBOOL(finals_list_char(Esa))
    <=> ( ? [Vs_2: list_val] : Esa = map_va1934808527t_char(val_list_char,Vs_2)
        | ? [Vs_2: list_val,A_1: nat,Es_1: list_exp_list_char] : Esa = append_exp_list_char(map_va1934808527t_char(val_list_char,Vs_2),cons_exp_list_char(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))),Es_1)) ) ) ).

tff(fact_933_CallRedsNull,axiom,
    ! [M: list_char,Esa: list_exp_list_char,Vs_1: list_val,S_2_1: produc12694297on_val,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_0),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,null),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Esa,S_1_1),produc379668296on_val(map_va1934808527t_char(val_list_char,Vs_1),S_2_1)),transi374442731on_val(reds(Pa))))
       => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(call_list_char(Ea,M,Esa),S_0),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_934_finalE,axiom,
    ! [E_5: exp_list_char] :
      ( hBOOL(final_list_char(E_5))
     => ( ! [V_4: val] : E_5 != hAPP_v834067052t_char(val_list_char,V_4)
       => ~ ! [A_1: nat] : E_5 != throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))) ) ) ).

tff(fact_935_WTrtCons,axiom,
    ! [Esa: list_exp_list_char,Ts: list_ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),T_3))
     => ( hBOOL(wTrts(Pa,Ha,E_1,Esa,Ts))
       => hBOOL(wTrts(Pa,Ha,E_1,cons_exp_list_char(Ea,Esa),cons_ty(T_3,Ts))) ) ) ).

tff(fact_936_red__reds_ORedCallNull,axiom,
    ! [M: list_char,Vs_1: list_val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(call_list_char(hAPP_v834067052t_char(val_list_char,null),M,map_va1934808527t_char(val_list_char,Vs_1)),S_1),produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer)))),S_1)),red(Pa))) ).

tff(fact_937_WTrts__hext__mono,axiom,
    ! [H_a: fun_na939144002on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Esa: list_exp_list_char,Ts: list_ty] :
      ( hBOOL(wTrts(Pa,Ha,E_1,Esa,Ts))
     => ( hBOOL(hext(Ha,H_a))
       => hBOOL(wTrts(Pa,H_a,E_1,Esa,Ts)) ) ) ).

tff(fact_938_redp__redsp_ORedThrowNull,axiom,
    ! [Pa: list_P1999446415t_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,throw_list_char(hAPP_v834067052t_char(val_list_char,null)),S_1),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_1)) ).

tff(fact_939_redp__redsp_ORedFAssNull,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,V_1: val,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,null),F,D,hAPP_v834067052t_char(val_list_char,V_1)),S_1),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_1)) ).

tff(fact_940_redp__redsp_ORedFAccNull,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(hAPP_v834067052t_char(val_list_char,null),F,D),S_1),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_1)) ).

tff(fact_941_red__reds_ORedThrowNull,axiom,
    ! [S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,null)),S_1),produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer)))),S_1)),red(Pa))) ).

tff(fact_942_redp__redsp_ORedCallNull,axiom,
    ! [Pa: list_P1999446415t_char,M: list_char,Vs_1: list_val,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(hAPP_v834067052t_char(val_list_char,null),M,map_va1934808527t_char(val_list_char,Vs_1)),S_1),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_1)) ).

tff(fact_943_ThrowRedsNull,axiom,
    ! [Ea: exp_list_char,S_1: produc12694297on_val,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,null),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(throw_list_char(Ea),S_1),produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer)))),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_944_red__reds_ORedFAssNull,axiom,
    ! [F: list_char,D: list_char,V_1: val,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(hAPP_v834067052t_char(val_list_char,null),F,D,hAPP_v834067052t_char(val_list_char,V_1)),S_1),produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer)))),S_1)),red(Pa))) ).

tff(fact_945_red__reds_ORedFAccNull,axiom,
    ! [F: list_char,D: list_char,S_1: produc12694297on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAcc_list_char(hAPP_v834067052t_char(val_list_char,null),F,D),S_1),produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer)))),S_1)),red(Pa))) ).

tff(fact_946_FAssRedsNull,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,V_1: val,S_2_1: produc12694297on_val,E_1_1: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_1_1,S_0),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,null),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_2,S_1_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),S_2_1)),transi2024712006on_val(red(Pa))))
       => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(E_1_1,F,D,E_2),S_0),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_947_FAccRedsNull,axiom,
    ! [F: list_char,D: list_char,Ea: exp_list_char,S_1: produc12694297on_val,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,null),S)),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAcc_list_char(Ea,F,D),S_1),produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer)))),S)),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_948_FAccNull,axiom,
    ! [F: list_char,D: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAcc_list_char(Ea,F,D),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_1_1)) ) ).

tff(fact_949_FAssNull,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,V_1: val,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_1),hAPP_v834067052t_char(val_list_char,V_1)),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAss_list_char(E_1_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_950_ThrowNull,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(Ea),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_1_1)) ) ).

tff(fact_951_the__Addr_Osimps,axiom,
    ! [A_2: nat] : the_Addr(addr(A_2)) = A_2 ).

tff(fact_952_unfold__while,axiom,
    ! [Pa: list_P1999446415t_char,B: exp_list_char,C_1: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(B,C_1),S_1),E_a),S))
    <=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(B,seq_list_char(C_1,while_list_char(B,C_1)),hAPP_v834067052t_char(val_list_char,unit)),S_1),E_a),S)) ) ).

tff(fact_953_eval__evals_OThrowThrow,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E_a: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E_a)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(Ea),S_0),throw_list_char(E_a)),S_1_1)) ) ).

tff(fact_954_Val,axiom,
    ! [Pa: list_P1999446415t_char,V_1: val,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,hAPP_v834067052t_char(val_list_char,V_1),S_1),hAPP_v834067052t_char(val_list_char,V_1)),S_1)) ).

tff(fact_955_eval__cases_I2_J,axiom,
    ! [Pa: list_P1999446415t_char,V_1: val,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,hAPP_v834067052t_char(val_list_char,V_1),S_1),E_a),S))
     => ~ ( ( E_a = hAPP_v834067052t_char(val_list_char,V_1) )
         => ( S != S_1 ) ) ) ).

tff(fact_956_eval__finalId,axiom,
    ! [Pa: list_P1999446415t_char,S_1: produc12694297on_val,Ea: exp_list_char] :
      ( hBOOL(final_list_char(Ea))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),Ea),S_1)) ) ).

tff(fact_957_eval__final,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),E_a),S))
     => hBOOL(final_list_char(E_a)) ) ).

tff(fact_958_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,V_1: val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_0,S_0),hAPP_v834067052t_char(val_list_char,V_1)),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_1_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_959_eval__evals_OSeqThrow,axiom,
    ! [E_1_1: exp_list_char,Pa: list_P1999446415t_char,E_0: exp_list_char,S_0: produc12694297on_val,Ea: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_0,S_0),throw_list_char(Ea)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,seq_list_char(E_0,E_1_1),S_0),throw_list_char(Ea)),S_1_1)) ) ).

tff(fact_960_eval__evals_OLAssThrow,axiom,
    ! [V: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E_a: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E_a)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,lAss_list_char(V,Ea),S_0),throw_list_char(E_a)),S_1_1)) ) ).

tff(fact_961_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_a: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),throw_list_char(E_a)),S_1_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_a)),S_1_1)) ) ).

tff(fact_962_CallObjThrow,axiom,
    ! [M: list_char,Ps: list_exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E_a: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E_a)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,call_list_char(Ea,M,Ps),S_0),throw_list_char(E_a)),S_1_1)) ) ).

tff(fact_963_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,Ea: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),throw_list_char(Ea)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,binOp_list_char(E_1_1,Bop,E_2),S_0),throw_list_char(Ea)),S_1_1)) ) ).

tff(fact_964_eval__evals_OCastThrow,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E_a: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E_a)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,Ea),S_0),throw_list_char(E_a)),S_1_1)) ) ).

tff(fact_965_eval__evals_OCondThrow,axiom,
    ! [E_1_1: exp_list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E_a: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E_a)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(Ea,E_1_1,E_2),S_0),throw_list_char(E_a)),S_1_1)) ) ).

tff(fact_966_Try,axiom,
    ! [C: list_char,V: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc12694297on_val,V_1_1: val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,V_1_1)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,tryCatch_list_char(E_1_1,C,V,E_2),S_0),hAPP_v834067052t_char(val_list_char,V_1_1)),S_1_1)) ) ).

tff(fact_967_eval__evals_OFAccThrow,axiom,
    ! [F: list_char,D: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E_a: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E_a)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAcc_list_char(Ea,F,D),S_0),throw_list_char(E_a)),S_1_1)) ) ).

tff(fact_968_WhileCondThrow,axiom,
    ! [C_1: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E_a: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E_a)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Ea,C_1),S_0),throw_list_char(E_a)),S_1_1)) ) ).

tff(fact_969_eval__hext,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,produc899768717on_val(Ha,La)),E_a),produc899768717on_val(H_a,L_a)))
     => hBOOL(hext(Ha,H_a)) ) ).

tff(fact_970_Throw,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,A: nat,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(Ea),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S_1_1)) ) ).

tff(fact_971_eval__evals_OFAssThrow2,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,E_a: exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc12694297on_val,V_1: val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,V_1)),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_1),throw_list_char(E_a)),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_a)),S_2_1)) ) ) ).

tff(fact_972_eval__evals_OBinOpThrow2,axiom,
    ! [Bop: bop,E_2: exp_list_char,Ea: exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc12694297on_val,V_1_1: val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,V_1_1)),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_1),throw_list_char(Ea)),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(Ea)),S_2_1)) ) ) ).

tff(fact_973_CastNull,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,Ea),S_0),hAPP_v834067052t_char(val_list_char,null)),S_1_1)) ) ).

tff(fact_974_CondT,axiom,
    ! [E_2: exp_list_char,E_1_1: exp_list_char,E_a: exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_1_1),E_a),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(Ea,E_1_1,E_2),S_0),E_a),S_2_1)) ) ) ).

tff(fact_975_CondF,axiom,
    ! [E_1_1: exp_list_char,E_2: exp_list_char,E_a: exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,bool_1(fFalse))),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_1),E_a),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(Ea,E_1_1,E_2),S_0),E_a),S_2_1)) ) ) ).

tff(fact_976_WhileT,axiom,
    ! [E_3_1: exp_list_char,S_3: produc12694297on_val,C_1: exp_list_char,V_1_1: val,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_1,S_1_1),hAPP_v834067052t_char(val_list_char,V_1_1)),S_2_1))
       => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Ea,C_1),S_2_1),E_3_1),S_3))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Ea,C_1),S_0),E_3_1),S_3)) ) ) ) ).

tff(fact_977_WhileBodyThrow,axiom,
    ! [C_1: exp_list_char,E_a: exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_1,S_1_1),throw_list_char(E_a)),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Ea,C_1),S_0),throw_list_char(E_a)),S_2_1)) ) ) ).

tff(fact_978_WhileF,axiom,
    ! [C_1: exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,bool_1(fFalse))),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Ea,C_1),S_0),hAPP_v834067052t_char(val_list_char,unit)),S_1_1)) ) ).

tff(fact_979_eval__cases_I12_J,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(Ea),S_1),E_a),S))
     => ( ! [A_1: nat] :
            ( ( E_a = throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))) )
           => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),hAPP_v834067052t_char(val_list_char,addr(A_1))),S)) )
       => ( ( ( E_a = throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer)))) )
           => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),hAPP_v834067052t_char(val_list_char,null)),S)) )
         => ~ ! [E_3: exp_list_char] :
                ( ( E_a = throw_list_char(E_3) )
               => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),throw_list_char(E_3)),S)) ) ) ) ) ).

tff(fact_980_CallNull,axiom,
    ! [M: list_char,Ps: list_exp_list_char,Vs_1: list_val,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Ps,S_1_1),map_va1934808527t_char(val_list_char,Vs_1)),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,call_list_char(Ea,M,Ps),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2_1)) ) ) ).

tff(fact_981_CallParamsThrow,axiom,
    ! [M: list_char,Esa: list_exp_list_char,Vs_1: list_val,Ex: exp_list_char,Es_a: list_exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,V_1: val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,V_1)),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S_1_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(Ea,M,Esa),S_0),throw_list_char(Ex)),S_2_1)) ) ) ).

tff(fact_982_list__eval__Throw,axiom,
    ! [Vs_1: list_val,Es_a: list_exp_list_char,Pa: list_P1999446415t_char,X_2: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(X_2),S_1),E_a),S))
     => 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_1),append_exp_list_char(map_va1934808527t_char(val_list_char,Vs_1),cons_exp_list_char(E_a,Es_a))),S)) ) ).

tff(fact_983_eval__cases_I11_J,axiom,
    ! [Pa: list_P1999446415t_char,B: exp_list_char,C_1: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(B,C_1),S_1),E_a),S))
     => ( ( ( E_a = hAPP_v834067052t_char(val_list_char,unit) )
         => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,B,S_1),hAPP_v834067052t_char(val_list_char,bool_1(fFalse))),S)) )
       => ( ! [S_1_2: produc12694297on_val] :
              ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,B,S_1),hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1_2))
             => ! [V_1_3: val,S_2_2: produc12694297on_val] :
                  ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_1,S_1_2),hAPP_v834067052t_char(val_list_char,V_1_3)),S_2_2))
                 => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(B,C_1),S_2_2),E_a),S)) ) )
         => ( ! [E_3: exp_list_char] :
                ( ( E_a = throw_list_char(E_3) )
               => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,B,S_1),throw_list_char(E_3)),S)) )
           => ~ ! [S_1_2: produc12694297on_val,E_3: exp_list_char] :
                  ( ( E_a = throw_list_char(E_3) )
                 => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,B,S_1),hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1_2))
                   => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_1,S_1_2),throw_list_char(E_3)),S)) ) ) ) ) ) ) ).

tff(fact_984_eval__finalsId,axiom,
    ! [Pa: list_P1999446415t_char,S_1: produc12694297on_val,Esa: list_exp_list_char] :
      ( hBOOL(finals_list_char(Esa))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S_1),Esa),S_1)) ) ).

tff(fact_985_evals__final,axiom,
    ! [Pa: list_P1999446415t_char,Esa: list_exp_list_char,S_1: produc12694297on_val,Es_a: list_exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S_1),Es_a),S))
     => hBOOL(finals_list_char(Es_a)) ) ).

tff(fact_986_evals__hext,axiom,
    ! [Pa: list_P1999446415t_char,Esa: list_exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,Es_a: list_exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,produc899768717on_val(Ha,La)),Es_a),produc899768717on_val(H_a,L_a)))
     => hBOOL(hext(Ha,H_a)) ) ).

tff(fact_987_eval__evals_OCons,axiom,
    ! [Esa: list_exp_list_char,Es_a: list_exp_list_char,S_2_1: produc12694297on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,V_1: val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,V_1)),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S_1_1),Es_a),S_2_1))
       => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,cons_exp_list_char(Ea,Esa),S_0),cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_1),Es_a)),S_2_1)) ) ) ).

tff(fact_988_ConsThrow,axiom,
    ! [Esa: list_exp_list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,E_a: exp_list_char,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),throw_list_char(E_a)),S_1_1))
     => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,cons_exp_list_char(Ea,Esa),S_0),cons_exp_list_char(throw_list_char(E_a),Esa)),S_1_1)) ) ).

tff(fact_989_evals__cases_I2_J,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,Esa: list_exp_list_char,S_1: produc12694297on_val,E_a: list_exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,cons_exp_list_char(Ea,Esa),S_1),E_a),S))
     => ( ! [V_4: val,S_1_2: produc12694297on_val,Es_1: list_exp_list_char] :
            ( ( E_a = cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_4),Es_1) )
           => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),hAPP_v834067052t_char(val_list_char,V_4)),S_1_2))
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S_1_2),Es_1),S)) ) )
       => ~ ! [E_3: exp_list_char] :
              ( ( E_a = cons_exp_list_char(throw_list_char(E_3),Esa) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),throw_list_char(E_3)),S)) ) ) ) ).

tff(fact_990_eval__cases_I9_J,axiom,
    ! [Pa: list_P1999446415t_char,E_1_1: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,seq_list_char(E_1_1,E_2),S_1),E_a),S))
     => ( ! [V_4: val,S_1_2: produc12694297on_val] :
            ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_1),hAPP_v834067052t_char(val_list_char,V_4)),S_1_2))
           => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_2),E_a),S)) )
       => ~ ! [E_4: exp_list_char] :
              ( ( E_a = throw_list_char(E_4) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_1),throw_list_char(E_4)),S)) ) ) ) ).

tff(fact_991_eval__cases_I10_J,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,E_1_1: exp_list_char,E_2: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(Ea,E_1_1,E_2),S_1),E_a),S))
     => ( ! [S_1_2: produc12694297on_val] :
            ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),hAPP_v834067052t_char(val_list_char,bool_1(fTrue))),S_1_2))
           => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_1_2),E_a),S)) )
       => ( ! [S_1_2: produc12694297on_val] :
              ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),hAPP_v834067052t_char(val_list_char,bool_1(fFalse))),S_1_2))
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_2),E_a),S)) )
         => ~ ! [E_3: exp_list_char] :
                ( ( E_a = throw_list_char(E_3) )
               => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),throw_list_char(E_3)),S)) ) ) ) ) ).

tff(fact_992_InitBlockRedsFinal,axiom,
    ! [T_3: ty,Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,V: list_char,V_1: val,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,fun_up1149430426on_val(La,V,hAPP_val_option_val(some_val,V_1)))),produc1259058957on_val(E_a,produc899768717on_val(H_a,L_a))),transi2024712006on_val(red(Pa))))
     => ( hBOOL(final_list_char(E_a))
       => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(block_list_char(V,T_3,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),Ea)),produc899768717on_val(Ha,La)),produc1259058957on_val(E_a,produc899768717on_val(H_a,fun_up1149430426on_val(L_a,V,hAPP_l207779698on_val(La,V))))),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_993_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_994_map__add__upd,axiom,
    ! [F_1: fun_Pr806764899on_val,G: fun_Pr806764899on_val,X_2: produc1278157519t_char,Y_1: val] : map_ad1185064968ar_val(F_1,fun_up204312361on_val(G,X_2,hAPP_val_option_val(some_val,Y_1))) = fun_up204312361on_val(map_ad1185064968ar_val(F_1,G),X_2,hAPP_val_option_val(some_val,Y_1)) ).

tff(fact_995_map__add__upd,axiom,
    ! [F_1: fun_na939144002on_val,G: fun_na939144002on_val,X_2: nat,Y_1: produc639455274on_val] : map_ad61982421on_val(F_1,fun_up2041264236on_val(G,X_2,hAPP_P1510515380on_val(some_P948696889on_val,Y_1))) = fun_up2041264236on_val(map_ad61982421on_val(F_1,G),X_2,hAPP_P1510515380on_val(some_P948696889on_val,Y_1)) ).

tff(fact_996_map__add__upd,axiom,
    ! [F_1: fun_li688206603ion_ty,G: fun_li688206603ion_ty,X_2: list_char,Y_1: ty] : map_add_list_char_ty(F_1,fun_up424764369ion_ty(G,X_2,hAPP_ty_option_ty(some_ty,Y_1))) = fun_up424764369ion_ty(map_add_list_char_ty(F_1,G),X_2,hAPP_ty_option_ty(some_ty,Y_1)) ).

tff(fact_997_map__add__upd,axiom,
    ! [F_1: fun_li1432931796on_val,G: fun_li1432931796on_val,X_2: list_char,Y_1: val] : map_ad325961431ar_val(F_1,fun_up1149430426on_val(G,X_2,hAPP_val_option_val(some_val,Y_1))) = fun_up1149430426on_val(map_ad325961431ar_val(F_1,G),X_2,hAPP_val_option_val(some_val,Y_1)) ).

tff(fact_998_map__upd__eqD1,axiom,
    ! [M_1: fun_Pr806764899on_val,A: produc1278157519t_char,X_2: val,N: fun_Pr806764899on_val,Y_1: 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_1)) )
     => ( X_2 = Y_1 ) ) ).

tff(fact_999_map__upd__eqD1,axiom,
    ! [M_1: fun_na939144002on_val,A: nat,X_2: produc639455274on_val,N: fun_na939144002on_val,Y_1: 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_1)) )
     => ( X_2 = Y_1 ) ) ).

tff(fact_1000_map__upd__eqD1,axiom,
    ! [M_1: fun_li688206603ion_ty,A: list_char,X_2: ty,N: fun_li688206603ion_ty,Y_1: 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_1)) )
     => ( X_2 = Y_1 ) ) ).

tff(fact_1001_map__upd__eqD1,axiom,
    ! [M_1: fun_li1432931796on_val,A: list_char,X_2: val,N: fun_li1432931796on_val,Y_1: 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_1)) )
     => ( X_2 = Y_1 ) ) ).

tff(fact_1002_map__upd__triv,axiom,
    ! [T_1: fun_li688206603ion_ty,K: list_char,X_2: ty] :
      ( ( hAPP_l512744617ion_ty(T_1,K) = hAPP_ty_option_ty(some_ty,X_2) )
     => ( fun_up424764369ion_ty(T_1,K,hAPP_ty_option_ty(some_ty,X_2)) = T_1 ) ) ).

tff(fact_1003_map__upd__triv,axiom,
    ! [T_1: fun_li1432931796on_val,K: list_char,X_2: val] :
      ( ( hAPP_l207779698on_val(T_1,K) = hAPP_val_option_val(some_val,X_2) )
     => ( fun_up1149430426on_val(T_1,K,hAPP_val_option_val(some_val,X_2)) = T_1 ) ) ).

tff(fact_1004_LAss,axiom,
    ! [L_a: fun_li1432931796on_val,V: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,V_1: val,Ha: fun_na939144002on_val,La: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,V_1)),produc899768717on_val(Ha,La)))
     => ( ( L_a = fun_up1149430426on_val(La,V,hAPP_val_option_val(some_val,V_1)) )
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,lAss_list_char(V,Ea),S_0),hAPP_v834067052t_char(val_list_char,unit)),produc899768717on_val(Ha,L_a))) ) ) ).

tff(fact_1005_redp__redsp_ORedLAss,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,V_1: val,Ha: fun_na939144002on_val,La: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),produc899768717on_val(Ha,La)),hAPP_v834067052t_char(val_list_char,unit)),produc899768717on_val(Ha,fun_up1149430426on_val(La,V,hAPP_val_option_val(some_val,V_1))))) ).

tff(fact_1006_redp__redsp_OInitBlockRed,axiom,
    ! [T_3: ty,V_5: val,Pa: list_P1999446415t_char,Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,V: list_char,V_1: val,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,produc899768717on_val(Ha,fun_up1149430426on_val(La,V,hAPP_val_option_val(some_val,V_1)))),E_a),produc899768717on_val(H_a,L_a)))
     => ( ( hAPP_l207779698on_val(L_a,V) = hAPP_val_option_val(some_val,V_5) )
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V,T_3,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),Ea)),produc899768717on_val(Ha,La)),block_list_char(V,T_3,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_5)),E_a))),produc899768717on_val(H_a,fun_up1149430426on_val(L_a,V,hAPP_l207779698on_val(La,V))))) ) ) ).

tff(fact_1007_red__reds_ORedLAss,axiom,
    ! [V: list_char,V_1: val,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,Pa: list_P1999446415t_char] : hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),produc899768717on_val(Ha,La)),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,unit),produc899768717on_val(Ha,fun_up1149430426on_val(La,V,hAPP_val_option_val(some_val,V_1))))),red(Pa))) ).

tff(fact_1008_LAssRedsVal,axiom,
    ! [V: list_char,Ea: exp_list_char,S_1: produc12694297on_val,V_1: val,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),produc899768717on_val(H_a,L_a))),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(lAss_list_char(V,Ea),S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,unit),produc899768717on_val(H_a,fun_up1149430426on_val(L_a,V,hAPP_val_option_val(some_val,V_1))))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1009_red__reds_OInitBlockRed,axiom,
    ! [T_3: ty,V_5: val,Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,V: list_char,V_1: val,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,fun_up1149430426on_val(La,V,hAPP_val_option_val(some_val,V_1)))),produc1259058957on_val(E_a,produc899768717on_val(H_a,L_a))),red(Pa)))
     => ( ( hAPP_l207779698on_val(L_a,V) = hAPP_val_option_val(some_val,V_5) )
       => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(block_list_char(V,T_3,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),Ea)),produc899768717on_val(Ha,La)),produc1259058957on_val(block_list_char(V,T_3,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_5)),E_a)),produc899768717on_val(H_a,fun_up1149430426on_val(L_a,V,hAPP_l207779698on_val(La,V))))),red(Pa))) ) ) ).

tff(fact_1010_InitBlockReds,axiom,
    ! [T_3: ty,Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,V: list_char,V_1: val,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,fun_up1149430426on_val(La,V,hAPP_val_option_val(some_val,V_1)))),produc1259058957on_val(E_a,produc899768717on_val(H_a,L_a))),transi2024712006on_val(red(Pa))))
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(block_list_char(V,T_3,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),Ea)),produc899768717on_val(Ha,La)),produc1259058957on_val(block_list_char(V,T_3,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,hAPP_option_val_val(the_val,hAPP_l207779698on_val(L_a,V)))),E_a)),produc899768717on_val(H_a,fun_up1149430426on_val(L_a,V,hAPP_l207779698on_val(La,V))))),transi2024712006on_val(red(Pa)))) ) ).

tff(fact_1011_eval__cases_I4_J,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,lAss_list_char(V,Ea),S_1),E_a),S))
     => ( ( ( E_a = hAPP_v834067052t_char(val_list_char,unit) )
         => ! [V_4: val,H: fun_na939144002on_val,L_5: fun_li1432931796on_val] :
              ( ( S = produc899768717on_val(H,fun_up1149430426on_val(L_5,V,hAPP_val_option_val(some_val,V_4))) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),hAPP_v834067052t_char(val_list_char,V_4)),produc899768717on_val(H,L_5))) ) )
       => ~ ! [E_3: exp_list_char] :
              ( ( E_a = throw_list_char(E_3) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),throw_list_char(E_3)),S)) ) ) ) ).

tff(fact_1012_BinOpRedsVal,axiom,
    ! [Bop: bop,V_1: 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_1: val,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_1_1,S_0),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1_1),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_2,S_1_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_2_1),S_2_1)),transi2024712006on_val(red(Pa))))
       => ( ( binop(produc621191550al_val(Bop,product_Pair_val_val(V_1_1,V_2_1))) = hAPP_val_option_val(some_val,V_1) )
         => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(binOp_list_char(E_1_1,Bop,E_2),S_0),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),S_2_1)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1013_red__reds_ORedBinOp,axiom,
    ! [S_1: produc12694297on_val,Pa: list_P1999446415t_char,Bop: bop,V_1_1: val,V_2_1: val,V_1: val] :
      ( ( binop(produc621191550al_val(Bop,product_Pair_val_val(V_1_1,V_2_1))) = hAPP_val_option_val(some_val,V_1) )
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_1),Bop,hAPP_v834067052t_char(val_list_char,V_2_1)),S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),S_1)),red(Pa))) ) ).

tff(fact_1014_WTrtBlock,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,V: list_char,T_3: ty,Ea: exp_list_char,T_7: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,fun_up424764369ion_ty(E_1,V,hAPP_ty_option_ty(some_ty,T_3)),Ea),T_7))
     => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,block_list_char(V,T_3,Ea)),T_7)) ) ).

tff(fact_1015_hext__upd__obj,axiom,
    ! [Fs_2: fun_Pr806764899on_val,Ha: fun_na939144002on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs)) )
     => hBOOL(hext(Ha,fun_up2041264236on_val(Ha,A,hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs_2))))) ) ).

tff(fact_1016_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,V_1: 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_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_1),hAPP_v834067052t_char(val_list_char,V_1)),produc899768717on_val(H_2,L_2)))
       => ( ( hAPP_n546249108on_val(H_2,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs)) )
         => ( ( Fs_2 = fun_up204312361on_val(Fs,produc5062597t_char(F,D),hAPP_val_option_val(some_val,V_1)) )
           => ( ( H_2_1 = fun_up2041264236on_val(H_2,A,hAPP_P1510515380on_val(some_P948696889on_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)),produc899768717on_val(H_2_1,L_2))) ) ) ) ) ) ).

tff(fact_1017_redp__redsp_ORedFAss,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,V_1: val,La: fun_li1432931796on_val,Ha: fun_na939144002on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs)) )
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),F,D,hAPP_v834067052t_char(val_list_char,V_1)),produc899768717on_val(Ha,La)),hAPP_v834067052t_char(val_list_char,unit)),produc899768717on_val(fun_up2041264236on_val(Ha,A,hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,fun_up204312361on_val(Fs,produc5062597t_char(F,D),hAPP_val_option_val(some_val,V_1))))),La))) ) ).

tff(fact_1018_red__reds_ORedFAss,axiom,
    ! [F: list_char,D: list_char,V_1: val,La: fun_li1432931796on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs)) )
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),F,D,hAPP_v834067052t_char(val_list_char,V_1)),produc899768717on_val(Ha,La)),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,unit),produc899768717on_val(fun_up2041264236on_val(Ha,A,hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,fun_up204312361on_val(Fs,produc5062597t_char(F,D),hAPP_val_option_val(some_val,V_1))))),La))),red(Pa))) ) ).

tff(fact_1019_FAssRedsVal,axiom,
    ! [F: list_char,D: list_char,C: list_char,Fs: fun_Pr806764899on_val,E_2: exp_list_char,V_1: val,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,E_1_1: exp_list_char,S_0: produc12694297on_val,A: nat,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_1_1,S_0),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,addr(A)),S_1_1)),transi2024712006on_val(red(Pa))))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_2,S_1_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),produc899768717on_val(H_2,L_2))),transi2024712006on_val(red(Pa))))
       => ( ( hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs)) = hAPP_n546249108on_val(H_2,A) )
         => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAss_list_char(E_1_1,F,D,E_2),S_0),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,unit),produc899768717on_val(fun_up2041264236on_val(H_2,A,hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,fun_up204312361on_val(Fs,produc5062597t_char(F,D),hAPP_val_option_val(some_val,V_1))))),L_2))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1020_FAcc,axiom,
    ! [F: list_char,D: list_char,V_1: val,C: list_char,Fs: fun_Pr806764899on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,A: nat,Ha: fun_na939144002on_val,La: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),produc899768717on_val(Ha,La)))
     => ( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs)) )
       => ( ( hAPP_P2094403585on_val(Fs,produc5062597t_char(F,D)) = hAPP_val_option_val(some_val,V_1) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAcc_list_char(Ea,F,D),S_0),hAPP_v834067052t_char(val_list_char,V_1)),produc899768717on_val(Ha,La))) ) ) ) ).

tff(fact_1021_BinOp,axiom,
    ! [Bop: bop,V_1: 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_1: val,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,V_1_1)),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_1),hAPP_v834067052t_char(val_list_char,V_2_1)),S_2_1))
       => ( ( binop(produc621191550al_val(Bop,product_Pair_val_val(V_1_1,V_2_1))) = hAPP_val_option_val(some_val,V_1) )
         => 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,V_1)),S_2_1)) ) ) ) ).

tff(fact_1022_redp__redsp_ORedBinOp,axiom,
    ! [Pa: list_P1999446415t_char,S_1: produc12694297on_val,Bop: bop,V_1_1: val,V_2_1: val,V_1: val] :
      ( ( binop(produc621191550al_val(Bop,product_Pair_val_val(V_1_1,V_2_1))) = hAPP_val_option_val(some_val,V_1) )
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_1),Bop,hAPP_v834067052t_char(val_list_char,V_2_1)),S_1),hAPP_v834067052t_char(val_list_char,V_1)),S_1)) ) ).

tff(fact_1023_TryCatchRedsFinal,axiom,
    ! [E_2: exp_list_char,V: 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: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_1_1,S_0),produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))),produc899768717on_val(H_1,L_1))),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(H_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(D,Fs)) )
       => ( hBOOL(member1251428284t_char(produc5062597t_char(D,C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_2,produc899768717on_val(H_1,fun_up1149430426on_val(L_1,V,hAPP_val_option_val(some_val,addr(A))))),produc1259058957on_val(E_2_1,produc899768717on_val(H_2,L_2))),transi2024712006on_val(red(Pa))))
           => ( hBOOL(final_list_char(E_2_1))
             => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(tryCatch_list_char(E_1_1,C,V,E_2),S_0),produc1259058957on_val(E_2_1,produc899768717on_val(H_2,fun_up1149430426on_val(L_2,V,hAPP_l207779698on_val(L_1,V))))),transi2024712006on_val(red(Pa)))) ) ) ) ) ) ).

tff(fact_1024_FAccRedsVal,axiom,
    ! [F: list_char,D: list_char,V_1: val,C: list_char,Fs: fun_Pr806764899on_val,Ea: exp_list_char,S_1: produc12694297on_val,A: nat,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,addr(A)),S)),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S),A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs)) )
       => ( ( hAPP_P2094403585on_val(Fs,produc5062597t_char(F,D)) = hAPP_val_option_val(some_val,V_1) )
         => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAcc_list_char(Ea,F,D),S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),S)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1025_eval__cases_I3_J,axiom,
    ! [Pa: list_P1999446415t_char,E_1_1: exp_list_char,Bop: bop,E_2: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,binOp_list_char(E_1_1,Bop,E_2),S_1),E_a),S))
     => ( ! [V_1_3: val,S_1_2: produc12694297on_val,V_2_2: val,V_4: val] :
            ( ( E_a = hAPP_v834067052t_char(val_list_char,V_4) )
           => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_1),hAPP_v834067052t_char(val_list_char,V_1_3)),S_1_2))
             => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_2),hAPP_v834067052t_char(val_list_char,V_2_2)),S))
               => ( binop(produc621191550al_val(Bop,product_Pair_val_val(V_1_3,V_2_2))) != hAPP_val_option_val(some_val,V_4) ) ) ) )
       => ( ! [E_4: exp_list_char] :
              ( ( E_a = throw_list_char(E_4) )
             => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_1),throw_list_char(E_4)),S)) )
         => ~ ! [V_1_3: val,S_1_2: produc12694297on_val,E_4: exp_list_char] :
                ( ( E_a = throw_list_char(E_4) )
               => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_1),hAPP_v834067052t_char(val_list_char,V_1_3)),S_1_2))
                 => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_2),throw_list_char(E_4)),S)) ) ) ) ) ) ).

tff(fact_1026_red__reds_ORedFAcc,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,V_1: val,S_1: produc12694297on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs)) )
     => ( ( hAPP_P2094403585on_val(Fs,produc5062597t_char(F,D)) = hAPP_val_option_val(some_val,V_1) )
       => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(fAcc_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),F,D),S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),S_1)),red(Pa))) ) ) ).

tff(fact_1027_red__reds_ORedCast,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,S_1: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(D,Fs)) )
     => ( hBOOL(member1251428284t_char(produc5062597t_char(D,C),transi1395422419t_char(subcls851966956t_char(Pa))))
       => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cast_list_char(C,hAPP_v834067052t_char(val_list_char,addr(A))),S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,addr(A)),S_1)),red(Pa))) ) ) ).

tff(fact_1028_red__reds_ORedTryFail,axiom,
    ! [V: list_char,E_2: exp_list_char,C: list_char,Pa: list_P1999446415t_char,S_1: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(D,Fs)) )
     => ( ~ hBOOL(member1251428284t_char(produc5062597t_char(D,C),transi1395422419t_char(subcls851966956t_char(Pa))))
       => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(tryCatch_list_char(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))),C,V,E_2),S_1),produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))),S_1)),red(Pa))) ) ) ).

tff(fact_1029_CastRedsAddr,axiom,
    ! [C: list_char,D: list_char,Fs: fun_Pr806764899on_val,Ea: exp_list_char,S_1: produc12694297on_val,A: nat,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,addr(A)),S)),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S),A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(D,Fs)) )
       => ( hBOOL(member1251428284t_char(produc5062597t_char(D,C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cast_list_char(C,Ea),S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,addr(A)),S)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1030_Cast,axiom,
    ! [C: list_char,D: list_char,Fs: fun_Pr806764899on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,A: nat,Ha: fun_na939144002on_val,La: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),produc899768717on_val(Ha,La)))
     => ( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(D,Fs)) )
       => ( hBOOL(member1251428284t_char(produc5062597t_char(D,C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,Ea),S_0),hAPP_v834067052t_char(val_list_char,addr(A))),produc899768717on_val(Ha,La))) ) ) ) ).

tff(fact_1031_TryThrow,axiom,
    ! [V: 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: 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)))),produc899768717on_val(H_1,L_1)))
     => ( ( hAPP_n546249108on_val(H_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(D,Fs)) )
       => ( ~ hBOOL(member1251428284t_char(produc5062597t_char(D,C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,tryCatch_list_char(E_1_1,C,V,E_2),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),produc899768717on_val(H_1,L_1))) ) ) ) ).

tff(fact_1032_redp__redsp_ORedFAcc,axiom,
    ! [Pa: list_P1999446415t_char,F: list_char,D: list_char,V_1: val,S_1: produc12694297on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs)) )
     => ( ( hAPP_P2094403585on_val(Fs,produc5062597t_char(F,D)) = hAPP_val_option_val(some_val,V_1) )
       => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),F,D),S_1),hAPP_v834067052t_char(val_list_char,V_1)),S_1)) ) ) ).

tff(fact_1033_TryCatch,axiom,
    ! [E_2: exp_list_char,V: 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: 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)))),produc899768717on_val(H_1,L_1)))
     => ( ( hAPP_n546249108on_val(H_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(D,Fs)) )
       => ( hBOOL(member1251428284t_char(produc5062597t_char(D,C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,produc899768717on_val(H_1,fun_up1149430426on_val(L_1,V,hAPP_val_option_val(some_val,addr(A))))),E_2_1),produc899768717on_val(H_2,L_2)))
           => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,tryCatch_list_char(E_1_1,C,V,E_2),S_0),E_2_1),produc899768717on_val(H_2,fun_up1149430426on_val(L_2,V,hAPP_l207779698on_val(L_1,V))))) ) ) ) ) ).

tff(fact_1034_TryRedsFail,axiom,
    ! [V: list_char,E_2: exp_list_char,C: list_char,D: list_char,Fs: fun_Pr806764899on_val,E_1_1: exp_list_char,S_1: produc12694297on_val,A: nat,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_1_1,S_1),produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))),produc899768717on_val(Ha,La))),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(D,Fs)) )
       => ( ~ hBOOL(member1251428284t_char(produc5062597t_char(D,C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(tryCatch_list_char(E_1_1,C,V,E_2),S_1),produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))),produc899768717on_val(Ha,La))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1035_CastRedsFail,axiom,
    ! [C: list_char,D: list_char,Fs: fun_Pr806764899on_val,Ea: exp_list_char,S_1: produc12694297on_val,A: nat,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,addr(A)),S)),transi2024712006on_val(red(Pa))))
     => ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S),A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(D,Fs)) )
       => ( ~ hBOOL(member1251428284t_char(produc5062597t_char(D,C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cast_list_char(C,Ea),S_1),produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(classCast)))),S)),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1036_red__reds_ORedCastFail,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,S_1: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(D,Fs)) )
     => ( ~ hBOOL(member1251428284t_char(produc5062597t_char(D,C),transi1395422419t_char(subcls851966956t_char(Pa))))
       => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(cast_list_char(C,hAPP_v834067052t_char(val_list_char,addr(A))),S_1),produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(classCast)))),S_1)),red(Pa))) ) ) ).

tff(fact_1037_CastFail,axiom,
    ! [C: list_char,D: list_char,Fs: fun_Pr806764899on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,S_0: produc12694297on_val,A: nat,Ha: fun_na939144002on_val,La: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),produc899768717on_val(Ha,La)))
     => ( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(D,Fs)) )
       => ( ~ hBOOL(member1251428284t_char(produc5062597t_char(D,C),transi1395422419t_char(subcls851966956t_char(Pa))))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,Ea),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(classCast))))),produc899768717on_val(Ha,La))) ) ) ) ).

tff(fact_1038_red__reds_ORedTryCatch,axiom,
    ! [V: list_char,E_2: exp_list_char,C: list_char,Pa: list_P1999446415t_char,S_1: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(D,Fs)) )
     => ( hBOOL(member1251428284t_char(produc5062597t_char(D,C),transi1395422419t_char(subcls851966956t_char(Pa))))
       => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(tryCatch_list_char(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))),C,V,E_2),S_1),produc1259058957on_val(block_list_char(V,hAPP_list_char_ty(class,C),seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,addr(A))),E_2)),S_1)),red(Pa))) ) ) ).

tff(fact_1039_hext__def,axiom,
    ! [Ha: fun_na939144002on_val,H_a: fun_na939144002on_val] :
      ( hBOOL(hext(Ha,H_a))
    <=> ! [A_1: nat,C_2: list_char,Fs_1: fun_Pr806764899on_val] :
          ( ( hAPP_n546249108on_val(Ha,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C_2,Fs_1)) )
         => ? [Fs_3: fun_Pr806764899on_val] : hAPP_n546249108on_val(H_a,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C_2,Fs_3)) ) ) ).

tff(fact_1040_hext__objD,axiom,
    ! [A: nat,C: list_char,Fs: fun_Pr806764899on_val,Ha: fun_na939144002on_val,H_a: fun_na939144002on_val] :
      ( hBOOL(hext(Ha,H_a))
     => ( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs)) )
       => ? [Fs_3: fun_Pr806764899on_val] : hAPP_n546249108on_val(H_a,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs_3)) ) ) ).

tff(fact_1041_finalRefE,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),T_3))
     => ( hBOOL(hAPP_ty_bool(is_refT,T_3))
       => ( hBOOL(final_list_char(Ea))
         => ( ( Ea != hAPP_v834067052t_char(val_list_char,null) )
           => ( ( ? [A_1: nat] : Ea = hAPP_v834067052t_char(val_list_char,addr(A_1))
               => ! [C_2: list_char] : T_3 != hAPP_list_char_ty(class,C_2) )
             => ~ ! [A_1: nat] : Ea != throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))) ) ) ) ) ) ).

tff(fact_1042_binop_Osimps_I1_J,axiom,
    ! [V_1_1: val,V_2_1: val] : binop(produc621191550al_val(c_Expr_Obop_OEq,product_Pair_val_val(V_1_1,V_2_1))) = hAPP_val_option_val(some_val,bool_1(hAPP_val_bool(hAPP_v1392248405l_bool(fequal_val,V_1_1),V_2_1))) ).

tff(fact_1043_final__addrE,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,C: list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),hAPP_list_char_ty(class,C)))
     => ( hBOOL(final_list_char(Ea))
       => ( ! [A_1: nat] : Ea != hAPP_v834067052t_char(val_list_char,addr(A_1))
         => ~ ! [A_1: nat] : Ea != throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))) ) ) ) ).

tff(fact_1044_redp__redsp_ORedTryCatch,axiom,
    ! [V: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,C: list_char,S_1: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A) = hAPP_P1510515380on_val(some_P948696889on_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,V,E_2),S_1),block_list_char(V,hAPP_list_char_ty(class,C),seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,addr(A))),E_2))),S_1)) ) ) ).

tff(fact_1045_BlockRedsFinal,axiom,
    ! [T_3: ty,H_0: fun_na939144002on_val,L_0: fun_li1432931796on_val,V: list_char,E_0: exp_list_char,S_0: produc12694297on_val,E_2: exp_list_char,H_2: fun_na939144002on_val,L_2: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(E_0,S_0),produc1259058957on_val(E_2,produc899768717on_val(H_2,L_2))),transi2024712006on_val(red(Pa))))
     => ( hBOOL(final_list_char(E_2))
       => ( ( S_0 = produc899768717on_val(H_0,fun_up1149430426on_val(L_0,V,none_val)) )
         => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(block_list_char(V,T_3,E_0),produc899768717on_val(H_0,L_0)),produc1259058957on_val(E_2,produc899768717on_val(H_2,fun_up1149430426on_val(L_2,V,hAPP_l207779698on_val(L_0,V))))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1046_WTrtCast,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),T_3))
     => ( hBOOL(hAPP_ty_bool(is_refT,T_3))
       => ( hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C))
         => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,cast_list_char(C,Ea)),hAPP_list_char_ty(class,C))) ) ) ) ).

tff(fact_1047_Block,axiom,
    ! [T_3: ty,Pa: list_P1999446415t_char,E_0: exp_list_char,H_0: fun_na939144002on_val,L_0: fun_li1432931796on_val,V: list_char,E_1_1: exp_list_char,H_1: fun_na939144002on_val,L_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_0,produc899768717on_val(H_0,fun_up1149430426on_val(L_0,V,none_val))),E_1_1),produc899768717on_val(H_1,L_1)))
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,block_list_char(V,T_3,E_0),produc899768717on_val(H_0,L_0)),E_1_1),produc899768717on_val(H_1,fun_up1149430426on_val(L_1,V,hAPP_l207779698on_val(L_0,V))))) ) ).

tff(fact_1048_redp__redsp_ORedCast,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,S_1: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A) = hAPP_P1510515380on_val(some_P948696889on_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_1),hAPP_v834067052t_char(val_list_char,addr(A))),S_1)) ) ) ).

tff(fact_1049_redp__redsp_ORedTryFail,axiom,
    ! [V: list_char,E_2: exp_list_char,Pa: list_P1999446415t_char,C: list_char,S_1: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A) = hAPP_P1510515380on_val(some_P948696889on_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,V,E_2),S_1),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S_1)) ) ) ).

tff(fact_1050_redp__redsp_ORedCastFail,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,S_1: produc12694297on_val,A: nat,D: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A) = hAPP_P1510515380on_val(some_P948696889on_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_1),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(classCast))))),S_1)) ) ) ).

tff(fact_1051_WTrt__elim__cases_I6_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,D: list_char,Ea: exp_list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,cast_list_char(D,Ea)),T_3))
     => ~ ( ( T_3 = hAPP_list_char_ty(class,D) )
         => ! [T_5: ty] :
              ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),T_5))
             => ( hBOOL(hAPP_ty_bool(is_refT,T_5))
               => ~ hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),D)) ) ) ) ) ).

tff(fact_1052_red__reds_OBlockRedSome,axiom,
    ! [T_3: ty,V_1: val,Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,V: list_char,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,fun_up1149430426on_val(La,V,none_val))),produc1259058957on_val(E_a,produc899768717on_val(H_a,L_a))),red(Pa)))
     => ( ( hAPP_l207779698on_val(L_a,V) = hAPP_val_option_val(some_val,V_1) )
       => ( ~ hBOOL(assigned(V,Ea))
         => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(block_list_char(V,T_3,Ea),produc899768717on_val(Ha,La)),produc1259058957on_val(block_list_char(V,T_3,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),E_a)),produc899768717on_val(H_a,fun_up1149430426on_val(L_a,V,hAPP_l207779698on_val(La,V))))),red(Pa))) ) ) ) ).

tff(fact_1053_redp__redsp_OBlockRedSome,axiom,
    ! [T_3: ty,V_1: val,Pa: list_P1999446415t_char,Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,V: list_char,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,produc899768717on_val(Ha,fun_up1149430426on_val(La,V,none_val))),E_a),produc899768717on_val(H_a,L_a)))
     => ( ( hAPP_l207779698on_val(L_a,V) = hAPP_val_option_val(some_val,V_1) )
       => ( ~ hBOOL(assigned(V,Ea))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V,T_3,Ea),produc899768717on_val(Ha,La)),block_list_char(V,T_3,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),E_a))),produc899768717on_val(H_a,fun_up1149430426on_val(L_a,V,hAPP_l207779698on_val(La,V))))) ) ) ) ).

tff(fact_1054_eval__cases_I8_J,axiom,
    ! [Pa: list_P1999446415t_char,V: list_char,T_3: ty,E_1_1: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,block_list_char(V,T_3,E_1_1),S_1),E_a),S))
     => ~ ! [H_0_1: fun_na939144002on_val,L_0_1: fun_li1432931796on_val] :
            ( ( S_1 = produc899768717on_val(H_0_1,L_0_1) )
           => ! [H_1_1: fun_na939144002on_val,L_1_1: fun_li1432931796on_val] :
                ( ( S = produc899768717on_val(H_1_1,fun_up1149430426on_val(L_1_1,V,hAPP_l207779698on_val(L_0_1,V))) )
               => ~ hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,produc899768717on_val(H_0_1,fun_up1149430426on_val(L_0_1,V,none_val))),E_a),produc899768717on_val(H_1_1,L_1_1))) ) ) ) ).

tff(fact_1055_hext__new,axiom,
    ! [X_2: produc639455274on_val,Ha: fun_na939144002on_val,A: nat] :
      ( ( hAPP_n546249108on_val(Ha,A) = none_P179726773on_val )
     => hBOOL(hext(Ha,fun_up2041264236on_val(Ha,A,hAPP_P1510515380on_val(some_P948696889on_val,X_2)))) ) ).

tff(fact_1056_redp__redsp_OBlockRedNone,axiom,
    ! [T_3: ty,Pa: list_P1999446415t_char,Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,V: list_char,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Ea,produc899768717on_val(Ha,fun_up1149430426on_val(La,V,none_val))),E_a),produc899768717on_val(H_a,L_a)))
     => ( ( hAPP_l207779698on_val(L_a,V) = none_val )
       => ( ~ hBOOL(assigned(V,Ea))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(V,T_3,Ea),produc899768717on_val(Ha,La)),block_list_char(V,T_3,E_a)),produc899768717on_val(H_a,fun_up1149430426on_val(L_a,V,hAPP_l207779698on_val(La,V))))) ) ) ) ).

tff(fact_1057_red__reds_OBlockRedNone,axiom,
    ! [T_3: ty,Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,V: list_char,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,fun_up1149430426on_val(La,V,none_val))),produc1259058957on_val(E_a,produc899768717on_val(H_a,L_a))),red(Pa)))
     => ( ( hAPP_l207779698on_val(L_a,V) = none_val )
       => ( ~ hBOOL(assigned(V,Ea))
         => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(block_list_char(V,T_3,Ea),produc899768717on_val(Ha,La)),produc1259058957on_val(block_list_char(V,T_3,E_a),produc899768717on_val(H_a,fun_up1149430426on_val(L_a,V,hAPP_l207779698on_val(La,V))))),red(Pa))) ) ) ) ).

tff(fact_1058_assigned__def,axiom,
    ! [V: list_char,Ea: exp_list_char] :
      ( hBOOL(assigned(V,Ea))
    <=> ? [V_4: val,E_3: exp_list_char] : Ea = seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_4)),E_3) ) ).

tff(fact_1059_binop_Osimps_I3_J,axiom,
    ! [V_2: val] : binop(produc621191550al_val(add,product_Pair_val_val(unit,V_2))) = none_val ).

tff(fact_1060_binop_Osimps_I7_J,axiom,
    ! [V_1_2: val] : binop(produc621191550al_val(add,product_Pair_val_val(V_1_2,unit))) = none_val ).

tff(fact_1061_binop_Osimps_I5_J,axiom,
    ! [V_1: bool,V_2_1: val] : binop(produc621191550al_val(add,product_Pair_val_val(bool_1(V_1),V_2_1))) = none_val ).

tff(fact_1062_bop_Osimps_I1_J,axiom,
    c_Expr_Obop_OEq != add ).

tff(fact_1063_bop_Osimps_I2_J,axiom,
    add != c_Expr_Obop_OEq ).

tff(fact_1064_bop_Oexhaust,axiom,
    ! [Y: bop] :
      ( ( Y != c_Expr_Obop_OEq )
     => ( Y = add ) ) ).

tff(fact_1065_binop_Osimps_I10_J,axiom,
    ! [V_1_2: val,V_3: nat] : binop(produc621191550al_val(add,product_Pair_val_val(V_1_2,addr(V_3)))) = none_val ).

tff(fact_1066_binop_Osimps_I6_J,axiom,
    ! [V_3: nat,V_2: val] : binop(produc621191550al_val(add,product_Pair_val_val(addr(V_3),V_2))) = none_val ).

tff(fact_1067_binop_Osimps_I4_J,axiom,
    ! [V_2: val] : binop(produc621191550al_val(add,product_Pair_val_val(null,V_2))) = none_val ).

tff(fact_1068_binop_Osimps_I8_J,axiom,
    ! [V_1_2: val] : binop(produc621191550al_val(add,product_Pair_val_val(V_1_2,null))) = none_val ).

tff(fact_1069_binop_Osimps_I9_J,axiom,
    ! [V_1_1: val,V_1: bool] : binop(produc621191550al_val(add,product_Pair_val_val(V_1_1,bool_1(V_1)))) = none_val ).

tff(fact_1070_WTrtTry,axiom,
    ! [V: list_char,C: list_char,E_2: exp_list_char,T_2_2: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,E_1_1: exp_list_char,T_1_2: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_1_1),T_1_2))
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,fun_up424764369ion_ty(E_1,V,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_2),T_2_2))
         => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,tryCatch_list_char(E_1_1,C,V,E_2)),T_2_2)) ) ) ) ).

tff(fact_1071_hextI,axiom,
    ! [H_a: fun_na939144002on_val,Ha: fun_na939144002on_val] :
      ( ! [A_1: nat,C_2: list_char,Fs_1: fun_Pr806764899on_val] :
          ( ( hAPP_n546249108on_val(Ha,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C_2,Fs_1)) )
         => ? [Fs_3: fun_Pr806764899on_val] : hAPP_n546249108on_val(H_a,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C_2,Fs_3)) )
     => hBOOL(hext(Ha,H_a)) ) ).

tff(fact_1072_WTrts__Val,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Vs_1: list_val,Ts: list_ty] :
      ( hBOOL(wTrts(Pa,Ha,E_1,map_va1934808527t_char(val_list_char,Vs_1),Ts))
    <=> ( map_val_option_ty(typeof_h(Ha),Vs_1) = map_ty_option_ty(some_ty,Ts) ) ) ).

tff(fact_1073_WTrtVal,axiom,
    ! [Pa: list_P1999446415t_char,E_1: fun_li688206603ion_ty,Ha: fun_na939144002on_val,V_1: val,T_3: ty] :
      ( ( hAPP_val_option_ty(typeof_h(Ha),V_1) = hAPP_ty_option_ty(some_ty,T_3) )
     => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,hAPP_v834067052t_char(val_list_char,V_1)),T_3)) ) ).

tff(fact_1074_hext__typeof__mono,axiom,
    ! [V_1: val,T_3: ty,Ha: fun_na939144002on_val,H_a: fun_na939144002on_val] :
      ( hBOOL(hext(Ha,H_a))
     => ( ( hAPP_val_option_ty(typeof_h(Ha),V_1) = hAPP_ty_option_ty(some_ty,T_3) )
       => ( hAPP_val_option_ty(typeof_h(H_a),V_1) = hAPP_ty_option_ty(some_ty,T_3) ) ) ) ).

tff(fact_1075_WTrt__elim__cases_I5_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,E_1_1: exp_list_char,C: list_char,V: list_char,E_2: exp_list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,tryCatch_list_char(E_1_1,C,V,E_2)),T_3))
     => ~ ! [T_1_1: ty] :
            ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_1_1),T_1_1))
           => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,fun_up424764369ion_ty(E_1,V,hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,C))),E_2),T_3))
             => ~ hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_1),T_3)) ) ) ) ).

tff(fact_1076_WTrt_H__WTrts_H_Ointros_I16_J,axiom,
    ! [E_1: fun_li688206603ion_ty,V: list_char,E_2: exp_list_char,T_2_2: ty,Pa: list_P1999446415t_char,T_3: ty,Ha: fun_na939144002on_val,V_1: val,T_1_2: ty] :
      ( ( hAPP_val_option_ty(typeof_h(Ha),V_1) = hAPP_ty_option_ty(some_ty,T_1_2) )
     => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_2),T_3))
       => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,fun_up424764369ion_ty(E_1,V,hAPP_ty_option_ty(some_ty,T_3)),E_2),T_2_2))
         => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,block_list_char(V,T_3,seq_list_char(lAss_list_char(V,hAPP_v834067052t_char(val_list_char,V_1)),E_2))),T_2_2)) ) ) ) ).

tff(fact_1077_WTrt_H__WTrts_H_Ointros_I3_J,axiom,
    ! [Pa: list_P1999446415t_char,E_1: fun_li688206603ion_ty,Ha: fun_na939144002on_val,V_1: val,T_3: ty] :
      ( ( hAPP_val_option_ty(typeof_h(Ha),V_1) = hAPP_ty_option_ty(some_ty,T_3) )
     => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,hAPP_v834067052t_char(val_list_char,V_1)),T_3)) ) ).

tff(fact_1078_WTrt_H__WTrts_H_Ointros_I8_J,axiom,
    ! [F: list_char,T_3: ty,D: list_char,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,C: list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,Ea),hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,F,T_3),D))
       => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,fAcc_list_char(Ea,F,D)),T_3)) ) ) ).

tff(fact_1079_WTrt_H__WTrts_H_Ointros_I18_J,axiom,
    ! [E_2: exp_list_char,T_2_2: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,E_1_1: exp_list_char,T_1_2: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,E_1_1),T_1_2))
     => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,E_2),T_2_2))
       => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,seq_list_char(E_1_1,E_2)),T_2_2)) ) ) ).

tff(fact_1080_WTrt_H__WTrts_H_Ointros_I9_J,axiom,
    ! [F: list_char,D: list_char,T_3: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,Ea),nt))
     => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,fAcc_list_char(Ea,F,D)),T_3)) ) ).

tff(fact_1081_wt_H__iff__wt,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,Ea),T_3))
    <=> hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),T_3)) ) ).

tff(fact_1082_wt_H__wt,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,Ea),T_3))
     => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),T_3)) ) ).

tff(fact_1083_wt__wt_H,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),T_3))
     => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,Ea),T_3)) ) ).

tff(fact_1084_WTrt_H__WTrts_H_Ointros_I21_J,axiom,
    ! [T_3: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,T_r: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,Ea),T_r))
     => ( hBOOL(hAPP_ty_bool(is_refT,T_r))
       => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,throw_list_char(Ea)),T_3)) ) ) ).

tff(fact_1085_WTrtFAccNT,axiom,
    ! [F: list_char,D: list_char,T_3: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),nt))
     => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,fAcc_list_char(Ea,F,D)),T_3)) ) ).

tff(fact_1086_WTrtCallNT,axiom,
    ! [M: list_char,T_3: ty,Esa: list_exp_list_char,Ts: list_ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),nt))
     => ( hBOOL(wTrts(Pa,Ha,E_1,Esa,Ts))
       => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,call_list_char(Ea,M,Esa)),T_3)) ) ) ).

tff(fact_1087_typeof__h_Osimps_I2_J,axiom,
    ! [Ha: fun_na939144002on_val] : hAPP_val_option_ty(typeof_h(Ha),null) = hAPP_ty_option_ty(some_ty,nt) ).

tff(fact_1088_WTrt_H__WTrts_H_Ointros_I2_J,axiom,
    ! [C: list_char,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,Ea),T_3))
     => ( hBOOL(hAPP_ty_bool(is_refT,T_3))
       => ( hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C))
         => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,cast_list_char(C,Ea)),hAPP_list_char_ty(class,C))) ) ) ) ).

tff(fact_1089_WTrt_H__WTrts_H_Ointros_I17_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,V: list_char,T_3: ty,Ea: exp_list_char,T_7: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,fun_up424764369ion_ty(E_1,V,hAPP_ty_option_ty(some_ty,T_3)),Ea),T_7))
     => ( ~ hBOOL(assigned(V,Ea))
       => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,block_list_char(V,T_3,Ea)),T_7)) ) ) ).

tff(fact_1090_WTrt_H__WTrts_H_Ointros_I22_J,axiom,
    ! [V: list_char,C: list_char,E_2: exp_list_char,T_2_2: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,E_1_1: exp_list_char,T_1_2: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,E_1_1),T_1_2))
     => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,fun_up424764369ion_ty(E_1,V,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_2),T_2_2))
         => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,tryCatch_list_char(E_1_1,C,V,E_2)),T_2_2)) ) ) ) ).

tff(fact_1091_WTrtFAcc,axiom,
    ! [F: list_char,T_3: ty,D: list_char,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,C: list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,F,T_3),D))
       => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,fAcc_list_char(Ea,F,D)),T_3)) ) ) ).

tff(fact_1092_WTrt__elim__cases_I7_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,F: list_char,D: list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,fAcc_list_char(Ea,F,D)),T_3))
     => ( ! [C_2: list_char] :
            ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),hAPP_list_char_ty(class,C_2)))
           => ~ hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C_2,F,T_3),D)) )
       => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),nt)) ) ) ).

tff(fact_1093_is__refT__def,axiom,
    ! [T_3: ty] :
      ( hBOOL(hAPP_ty_bool(is_refT,T_3))
    <=> ( ( T_3 = nt )
        | ? [C_2: list_char] : T_3 = hAPP_list_char_ty(class,C_2) ) ) ).

tff(fact_1094_ty_Osimps_I20_J,axiom,
    ! [List_1: list_char] : nt != hAPP_list_char_ty(class,List_1) ).

tff(fact_1095_ty_Oinject,axiom,
    ! [List_3: list_char,List_2: list_char] :
      ( ( hAPP_list_char_ty(class,List_3) = hAPP_list_char_ty(class,List_2) )
    <=> ( List_3 = List_2 ) ) ).

tff(fact_1096_ty_Osimps_I21_J,axiom,
    ! [List_1: list_char] : hAPP_list_char_ty(class,List_1) != nt ).

tff(fact_1097_refTE,axiom,
    ! [T_4: ty] :
      ( hBOOL(hAPP_ty_bool(is_refT,T_4))
     => ( ( T_4 != nt )
       => ~ ! [C_2: list_char] : T_4 != hAPP_list_char_ty(class,C_2) ) ) ).

tff(fact_1098_WTrt_H__WTrts_H_Ointros_I10_J,axiom,
    ! [E_2: exp_list_char,T_2_2: ty,F: list_char,T_3: ty,D: list_char,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,E_1_1: exp_list_char,C: list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,E_1_1),hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,F,T_3),D))
       => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,E_2),T_2_2))
         => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_2),T_3))
           => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,fAss_list_char(E_1_1,F,D,E_2)),void)) ) ) ) ) ).

tff(fact_1099_WTrtFAss,axiom,
    ! [E_2: exp_list_char,T_2_2: ty,F: list_char,T_3: ty,D: list_char,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,E_1_1: exp_list_char,C: list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_1_1),hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,F,T_3),D))
       => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_2),T_2_2))
         => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_2),T_3))
           => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,fAss_list_char(E_1_1,F,D,E_2)),void)) ) ) ) ) ).

tff(fact_1100_typeof__ClassCast,axiom,
    ! [Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( hAPP_val_option_ty(typeof_h(Ha),addr(addr_of_sys_xcpt(classCast))) = hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,classCast)) ) ) ).

tff(fact_1101_WTrtLAss,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,Ea: exp_list_char,T_7: ty,E_1: fun_li688206603ion_ty,V: list_char,T_3: ty] :
      ( ( hAPP_l512744617ion_ty(E_1,V) = hAPP_ty_option_ty(some_ty,T_3) )
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),T_7))
       => ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_7),T_3))
         => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,lAss_list_char(V,Ea)),void)) ) ) ) ).

tff(fact_1102_ty_Osimps_I9_J,axiom,
    ! [List_1: list_char] : hAPP_list_char_ty(class,List_1) != void ).

tff(fact_1103_ty_Osimps_I8_J,axiom,
    ! [List_1: list_char] : void != hAPP_list_char_ty(class,List_1) ).

tff(fact_1104_preallocated__hext,axiom,
    ! [H_a: fun_na939144002on_val,Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( hBOOL(hext(Ha,H_a))
       => hBOOL(preallocated(H_a)) ) ) ).

tff(fact_1105_ty_Osimps_I7_J,axiom,
    nt != void ).

tff(fact_1106_ty_Osimps_I6_J,axiom,
    void != nt ).

tff(fact_1107_preallocated__upd__obj,axiom,
    ! [Fs_2: fun_Pr806764899on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val,Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs)) )
       => hBOOL(preallocated(fun_up2041264236on_val(Ha,A,hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs_2))))) ) ) ).

tff(fact_1108_preallocated__new,axiom,
    ! [X_2: produc639455274on_val,A: nat,Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( ( hAPP_n546249108on_val(Ha,A) = none_P179726773on_val )
       => hBOOL(preallocated(fun_up2041264236on_val(Ha,A,hAPP_P1510515380on_val(some_P948696889on_val,X_2)))) ) ) ).

tff(fact_1109_WTrtFAssNT,axiom,
    ! [F: list_char,D: list_char,E_2: exp_list_char,T_2_2: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,E_1_1: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_1_1),nt))
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_2),T_2_2))
       => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,fAss_list_char(E_1_1,F,D,E_2)),void)) ) ) ).

tff(fact_1110_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,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,E_1_1: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,E_1_1),nt))
     => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,E_2),T_2_2))
       => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,fAss_list_char(E_1_1,F,D,E_2)),void)) ) ) ).

tff(fact_1111_typeof__h_Osimps_I1_J,axiom,
    ! [Ha: fun_na939144002on_val] : hAPP_val_option_ty(typeof_h(Ha),unit) = hAPP_ty_option_ty(some_ty,void) ).

tff(fact_1112_typeof__NullPointer,axiom,
    ! [Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( hAPP_val_option_ty(typeof_h(Ha),addr(addr_of_sys_xcpt(nullPointer))) = hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,nullPointer)) ) ) ).

tff(fact_1113_WTrt__elim__cases_I1_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,V_1: list_char,Ea: exp_list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,lAss_list_char(V_1,Ea)),T_3))
     => ~ ( ( T_3 = void )
         => ! [T_5: ty] :
              ( ( hAPP_l512744617ion_ty(E_1,V_1) = hAPP_ty_option_ty(some_ty,T_5) )
             => ! [T_6: ty] :
                  ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),T_6))
                 => ~ hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_6),T_5)) ) ) ) ) ).

tff(fact_1114_WTrt__elim__cases_I8_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,F: list_char,D: list_char,V_1: exp_list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,fAss_list_char(Ea,F,D,V_1)),T_3))
     => ( ( ( T_3 = void )
         => ! [C_2: list_char] :
              ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),hAPP_list_char_ty(class,C_2)))
             => ! [T_5: ty] :
                  ( hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C_2,F,T_5),D))
                 => ! [T_2_1: ty] :
                      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,V_1),T_2_1))
                     => ~ hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_1),T_5)) ) ) ) )
       => ~ ( ( T_3 = void )
           => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),nt))
             => ! [T_2_1: ty] : ~ hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,V_1),T_2_1)) ) ) ) ) ).

tff(fact_1115_typeof__OutOfMemory,axiom,
    ! [Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( hAPP_val_option_ty(typeof_h(Ha),addr(addr_of_sys_xcpt(outOfMemory))) = hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,outOfMemory)) ) ) ).

tff(fact_1116_sys__xcpts__cases,axiom,
    ! [Pa: fun_list_char_bool,C: list_char] :
      ( hBOOL(member_list_char(C,sys_xcpts))
     => ( hBOOL(hAPP_list_char_bool(Pa,nullPointer))
       => ( hBOOL(hAPP_list_char_bool(Pa,outOfMemory))
         => ( hBOOL(hAPP_list_char_bool(Pa,classCast))
           => hBOOL(hAPP_list_char_bool(Pa,C)) ) ) ) ) ).

tff(fact_1117_red__reds_ORedNewFail,axiom,
    ! [C: list_char,La: fun_li1432931796on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val] :
      ( ( new_Addr(Ha) = none_nat )
     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(new_list_char(C),produc899768717on_val(Ha,La)),produc1259058957on_val(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(outOfMemory)))),produc899768717on_val(Ha,La))),red(Pa))) ) ).

tff(fact_1118_WTrtNew,axiom,
    ! [Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Pa: list_P1999446415t_char,C: list_char] :
      ( hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C))
     => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,new_list_char(C)),hAPP_list_char_ty(class,C))) ) ).

tff(fact_1119_WTrt__elim__cases_I10_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,C: list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,new_list_char(C)),T_3))
     => ~ ( ( T_3 = hAPP_list_char_ty(class,C) )
         => ~ hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C)) ) ) ).

tff(fact_1120_new__Addr__SomeD,axiom,
    ! [Ha: fun_na939144002on_val,A: nat] :
      ( ( new_Addr(Ha) = hAPP_nat_option_nat(some_nat,A) )
     => ( hAPP_n546249108on_val(Ha,A) = none_P179726773on_val ) ) ).

tff(fact_1121_WTrt_H__WTrts_H_Ointros_I1_J,axiom,
    ! [Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Pa: list_P1999446415t_char,C: list_char] :
      ( hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C))
     => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,new_list_char(C)),hAPP_list_char_ty(class,C))) ) ).

tff(fact_1122_NewFail,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,La: fun_li1432931796on_val,Ha: fun_na939144002on_val] :
      ( ( new_Addr(Ha) = none_nat )
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,new_list_char(C),produc899768717on_val(Ha,La)),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(outOfMemory))))),produc899768717on_val(Ha,La))) ) ).

tff(fact_1123_redp__redsp_ORedNewFail,axiom,
    ! [Pa: list_P1999446415t_char,C: list_char,La: fun_li1432931796on_val,Ha: fun_na939144002on_val] :
      ( ( new_Addr(Ha) = none_nat )
     => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,new_list_char(C),produc899768717on_val(Ha,La)),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(outOfMemory))))),produc899768717on_val(Ha,La))) ) ).

tff(fact_1124_preallocated__def,axiom,
    ! [Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
    <=> ! [X_1: list_char] :
          ( hBOOL(member_list_char(X_1,sys_xcpts))
         => ? [Fs_1: fun_Pr806764899on_val] : hAPP_n546249108on_val(Ha,addr_of_sys_xcpt(X_1)) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(X_1,Fs_1)) ) ) ).

tff(fact_1125_preallocatedD,axiom,
    ! [C: list_char,Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( hBOOL(member_list_char(C,sys_xcpts))
       => ? [Fs_1: fun_Pr806764899on_val] : hAPP_n546249108on_val(Ha,addr_of_sys_xcpt(C)) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs_1)) ) ) ).

tff(fact_1126_preallocatedE,axiom,
    ! [Pa: fun_fu311765169r_bool,C: list_char,Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( hBOOL(member_list_char(C,sys_xcpts))
       => ( ! [Fs_1: fun_Pr806764899on_val] :
              ( ( hAPP_n546249108on_val(Ha,addr_of_sys_xcpt(C)) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs_1)) )
             => hBOOL(hAPP_list_char_bool(hAPP_f388705405r_bool(Pa,Ha),C)) )
         => hBOOL(hAPP_list_char_bool(hAPP_f388705405r_bool(Pa,Ha),C)) ) ) ) ).

tff(fact_1127_red__reds_ORedNew,axiom,
    ! [La: fun_li1432931796on_val,H_a: fun_na939144002on_val,Pa: list_P1999446415t_char,C: list_char,FDTs: list_P2023964830har_ty,Ha: fun_na939144002on_val,A: nat] :
      ( ( new_Addr(Ha) = hAPP_nat_option_nat(some_nat,A) )
     => ( hBOOL(fields1147507508t_char(Pa,C,FDTs))
       => ( ( H_a = fun_up2041264236on_val(Ha,A,hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,init_fields(FDTs)))) )
         => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(new_list_char(C),produc899768717on_val(Ha,La)),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,addr(A)),produc899768717on_val(H_a,La))),red(Pa))) ) ) ) ).

tff(fact_1128_redp__redsp_ORedNew,axiom,
    ! [La: fun_li1432931796on_val,H_a: fun_na939144002on_val,Pa: list_P1999446415t_char,C: list_char,FDTs: list_P2023964830har_ty,Ha: fun_na939144002on_val,A: nat] :
      ( ( new_Addr(Ha) = hAPP_nat_option_nat(some_nat,A) )
     => ( hBOOL(fields1147507508t_char(Pa,C,FDTs))
       => ( ( H_a = fun_up2041264236on_val(Ha,A,hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,init_fields(FDTs)))) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,new_list_char(C),produc899768717on_val(Ha,La)),hAPP_v834067052t_char(val_list_char,addr(A))),produc899768717on_val(H_a,La))) ) ) ) ).

tff(fact_1129_New,axiom,
    ! [La: fun_li1432931796on_val,H_a: fun_na939144002on_val,Pa: list_P1999446415t_char,C: list_char,FDTs: list_P2023964830har_ty,Ha: fun_na939144002on_val,A: nat] :
      ( ( new_Addr(Ha) = hAPP_nat_option_nat(some_nat,A) )
     => ( hBOOL(fields1147507508t_char(Pa,C,FDTs))
       => ( ( H_a = fun_up2041264236on_val(Ha,A,hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,init_fields(FDTs)))) )
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,new_list_char(C),produc899768717on_val(Ha,La)),hAPP_v834067052t_char(val_list_char,addr(A))),produc899768717on_val(H_a,La))) ) ) ) ).

tff(fact_1130_WTrt_H__WTrts_H_Ointros_I15_J,axiom,
    ! [Esa: list_exp_list_char,Ts: list_ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,Ea),T_3))
     => ( hBOOL(wTrts_1(Pa,Ha,E_1,Esa,Ts))
       => hBOOL(wTrts_1(Pa,Ha,E_1,cons_exp_list_char(Ea,Esa),cons_ty(T_3,Ts))) ) ) ).

tff(fact_1131_WTrtBinOpEq,axiom,
    ! [E_2: exp_list_char,T_2_2: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,E_1_1: exp_list_char,T_1_2: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_1_1),T_1_2))
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_2),T_2_2))
       => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,binOp_list_char(E_1_1,c_Expr_Obop_OEq,E_2)),boolean)) ) ) ).

tff(fact_1132_WTrtCond,axiom,
    ! [T_3: ty,E_2: exp_list_char,T_2_2: ty,E_1_1: exp_list_char,T_1_2: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),boolean))
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_1_1),T_1_2))
       => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_2),T_2_2))
         => ( ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_2),T_2_2))
              | hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_2),T_1_2)) )
           => ( ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_2),T_2_2))
               => ( T_3 = T_2_2 ) )
             => ( ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_2),T_1_2))
                 => ( T_3 = T_1_2 ) )
               => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,cond_list_char(Ea,E_1_1,E_2)),T_3)) ) ) ) ) ) ) ).

tff(fact_1133_WTrtWhile,axiom,
    ! [C_1: exp_list_char,T_3: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),boolean))
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,C_1),T_3))
       => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,while_list_char(Ea,C_1)),void)) ) ) ).

tff(fact_1134_ty_Osimps_I3_J,axiom,
    boolean != void ).

tff(fact_1135_ty_Osimps_I2_J,axiom,
    void != boolean ).

tff(fact_1136_ty_Osimps_I12_J,axiom,
    boolean != nt ).

tff(fact_1137_ty_Osimps_I13_J,axiom,
    nt != boolean ).

tff(fact_1138_ty_Osimps_I15_J,axiom,
    ! [List_1: list_char] : hAPP_list_char_ty(class,List_1) != boolean ).

tff(fact_1139_ty_Osimps_I14_J,axiom,
    ! [List_1: list_char] : boolean != hAPP_list_char_ty(class,List_1) ).

tff(fact_1140_wts_H__iff__wts,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Esa: list_exp_list_char,Ts: list_ty] :
      ( hBOOL(wTrts_1(Pa,Ha,E_1,Esa,Ts))
    <=> hBOOL(wTrts(Pa,Ha,E_1,Esa,Ts)) ) ).

tff(fact_1141_wts_H__wts,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Esa: list_exp_list_char,Ts: list_ty] :
      ( hBOOL(wTrts_1(Pa,Ha,E_1,Esa,Ts))
     => hBOOL(wTrts(Pa,Ha,E_1,Esa,Ts)) ) ).

tff(fact_1142_wts__wts_H,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Esa: list_exp_list_char,Ts: list_ty] :
      ( hBOOL(wTrts(Pa,Ha,E_1,Esa,Ts))
     => hBOOL(wTrts_1(Pa,Ha,E_1,Esa,Ts)) ) ).

tff(fact_1143_WTrt_H__WTrts_H_Ointros_I19_J,axiom,
    ! [T_3: ty,E_2: exp_list_char,T_2_2: ty,E_1_1: exp_list_char,T_1_2: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,Ea),boolean))
     => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,E_1_1),T_1_2))
       => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,E_2),T_2_2))
         => ( ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_2),T_2_2))
              | hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_2),T_1_2)) )
           => ( ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_2),T_2_2))
               => ( T_3 = T_2_2 ) )
             => ( ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_2),T_1_2))
                 => ( T_3 = T_1_2 ) )
               => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,cond_list_char(Ea,E_1_1,E_2)),T_3)) ) ) ) ) ) ) ).

tff(fact_1144_WTrt_H__WTrts_H_Ointros_I20_J,axiom,
    ! [C_1: exp_list_char,T_3: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,Ea),boolean))
     => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,C_1),T_3))
       => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,while_list_char(Ea,C_1)),void)) ) ) ).

tff(fact_1145_typeof__h_Osimps_I3_J,axiom,
    ! [Ha: fun_na939144002on_val,B: bool] : hAPP_val_option_ty(typeof_h(Ha),bool_1(B)) = hAPP_ty_option_ty(some_ty,boolean) ).

tff(fact_1146_WTrt_H__WTrts_H_Ointros_I5_J,axiom,
    ! [E_2: exp_list_char,T_2_2: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,E_1_1: exp_list_char,T_1_2: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,E_1_1),T_1_2))
     => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,E_2),T_2_2))
       => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,binOp_list_char(E_1_1,c_Expr_Obop_OEq,E_2)),boolean)) ) ) ).

tff(fact_1147_WTrt_H__WTrts_H_Ointros_I13_J,axiom,
    ! [M: list_char,T_3: ty,Esa: list_exp_list_char,Ts: list_ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,Ea),nt))
     => ( hBOOL(wTrts_1(Pa,Ha,E_1,Esa,Ts))
       => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,call_list_char(Ea,M,Esa)),T_3)) ) ) ).

tff(fact_1148_WTrt__elim__cases_I3_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,C_1: exp_list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,while_list_char(Ea,C_1)),T_3))
     => ~ ( ( T_3 = void )
         => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),boolean))
           => ! [T_5: ty] : ~ hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,C_1),T_5)) ) ) ) ).

tff(fact_1149_WTrt__elim__cases_I2_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,E_1_1: exp_list_char,E_2: exp_list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,cond_list_char(Ea,E_1_1,E_2)),T_3))
     => ~ ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),boolean))
         => ! [T_1_1: ty] :
              ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_1_1),T_1_1))
             => ! [T_2_1: ty] :
                  ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_2),T_2_1))
                 => ( ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_1),T_2_1))
                      | hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_1),T_1_1)) )
                   => ( ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_1),T_2_1))
                       => ( T_3 = T_2_1 ) )
                     => ~ ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_1),T_1_1))
                         => ( T_3 = T_1_1 ) ) ) ) ) ) ) ) ).

tff(fact_1150_WTrt__elim__cases_I9_J,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,E_1_1: exp_list_char,Bop: bop,E_2: exp_list_char,T_3: ty] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,binOp_list_char(E_1_1,Bop,E_2)),T_3))
     => ( ( ( T_3 = boolean )
         => ( ? [T_1_1: ty] : hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_1_1),T_1_1))
           => ( ? [X1: ty] : hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_2),X1))
             => ( Bop != c_Expr_Obop_OEq ) ) ) )
       => ~ ( ( T_3 = integer )
           => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_1_1),integer))
             => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_2),integer))
               => ( Bop != add ) ) ) ) ) ) ).

tff(fact_1151_WTrtBinOpAdd,axiom,
    ! [E_2: exp_list_char,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,E_1_1: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_1_1),integer))
     => ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,E_2),integer))
       => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,binOp_list_char(E_1_1,add,E_2)),integer)) ) ) ).

tff(fact_1152_ty_Osimps_I10_J,axiom,
    boolean != integer ).

tff(fact_1153_ty_Osimps_I11_J,axiom,
    integer != boolean ).

tff(fact_1154_ty_Osimps_I18_J,axiom,
    ! [List_1: list_char] : integer != hAPP_list_char_ty(class,List_1) ).

tff(fact_1155_ty_Osimps_I19_J,axiom,
    ! [List_1: list_char] : hAPP_list_char_ty(class,List_1) != integer ).

tff(fact_1156_ty_Osimps_I17_J,axiom,
    nt != integer ).

tff(fact_1157_ty_Osimps_I16_J,axiom,
    integer != nt ).

tff(fact_1158_ty_Osimps_I4_J,axiom,
    void != integer ).

tff(fact_1159_ty_Osimps_I5_J,axiom,
    integer != void ).

tff(fact_1160_WTrt_H__WTrts_H_Ointros_I6_J,axiom,
    ! [E_2: exp_list_char,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,E_1_1: exp_list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,E_1_1),integer))
     => ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,E_2),integer))
       => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,binOp_list_char(E_1_1,add,E_2)),integer)) ) ) ).

tff(fact_1161_not__refTE,axiom,
    ! [T_4: ty] :
      ( ~ hBOOL(hAPP_ty_bool(is_refT,T_4))
     => ( ( T_4 = void )
        | ( T_4 = boolean )
        | ( T_4 = integer ) ) ) ).

tff(fact_1162_ty_Oexhaust,axiom,
    ! [Y: ty] :
      ( ( Y != void )
     => ( ( Y != boolean )
       => ( ( Y != integer )
         => ( ( Y != nt )
           => ~ ! [List: list_char] : Y != hAPP_list_char_ty(class,List) ) ) ) ) ).

tff(fact_1163_red__reds_ORedCall,axiom,
    ! [Vs_1: list_val,Pa: list_P1999446415t_char,M: list_char,Ts: list_ty,T_3: ty,Pns: list_list_char,Body: exp_list_char,D: list_char,S_1: produc12694297on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs)) )
     => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Ts,T_3,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(member773094996on_val(produc1441475159on_val(produc1259058957on_val(call_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),M,map_va1934808527t_char(val_list_char,Vs_1)),S_1),produc1259058957on_val(blocks(produc921874948t_char(cons_list_char(this,Pns),produc1909267824t_char(cons_ty(hAPP_list_char_ty(class,D),Ts),produc1916172923t_char(cons_val(addr(A),Vs_1),Body)))),S_1)),red(Pa))) ) ) ) ) ).

tff(fact_1164_blocksFinal,axiom,
    ! [Ha: fun_na939144002on_val,La: fun_li1432931796on_val,Pa: list_P1999446415t_char,Ea: 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(Ea))
         => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(blocks(produc921874948t_char(Vs,produc1909267824t_char(Ts,produc1916172923t_char(Vs_1,Ea)))),produc899768717on_val(Ha,La)),produc1259058957on_val(Ea,produc899768717on_val(Ha,La))),transi2024712006on_val(red(Pa)))) ) ) ) ).

tff(fact_1165_redp__redsp_ORedCall,axiom,
    ! [Vs_1: list_val,Pa: list_P1999446415t_char,M: list_char,Ts: list_ty,T_3: ty,Pns: list_list_char,Body: exp_list_char,D: list_char,S_1: produc12694297on_val,A: nat,C: list_char,Fs: fun_Pr806764899on_val] :
      ( ( hAPP_n546249108on_val(hAPP_P703866694on_val(hp,S_1),A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs)) )
     => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Ts,T_3,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_1),blocks(produc921874948t_char(cons_list_char(this,Pns),produc1909267824t_char(cons_ty(hAPP_list_char_ty(class,D),Ts),produc1916172923t_char(cons_val(addr(A),Vs_1),Body))))),S_1)) ) ) ) ) ).

tff(fact_1166_WTrts__same__length,axiom,
    ! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Esa: list_exp_list_char,Ts: list_ty] :
      ( hBOOL(wTrts(Pa,Ha,E_1,Esa,Ts))
     => ( size_s1143674878t_char(Esa) = size_size_list_ty(Ts) ) ) ).

tff(fact_1167_blocksEval,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: 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(produc921874948t_char(Ps,produc1909267824t_char(Ts,produc1916172923t_char(Vs_1,Ea)))),produc899768717on_val(Ha,La)),E_a),produc899768717on_val(H_a,L_a)))
         => ? [L_4: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,produc899768717on_val(Ha,map_up1085636310ar_val(La,Ps,Vs_1))),E_a),produc899768717on_val(H_a,L_4))) ) ) ) ).

tff(fact_1168_WTrt_H__WTrts_H_Ointros_I12_J,axiom,
    ! [Esa: list_exp_list_char,Ts_1: list_ty,M: list_char,Ts: list_ty,T_3: ty,Pns: list_list_char,Body: exp_list_char,D: list_char,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,C: list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,Ea),hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Ts,T_3,produc1147572817t_char(Pns,Body)),D))
       => ( hBOOL(wTrts_1(Pa,Ha,E_1,Esa,Ts_1))
         => ( hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_1,Ts))
           => hBOOL(hAPP_ty_bool(wTrt_1(Pa,Ha,E_1,call_list_char(Ea,M,Esa)),T_3)) ) ) ) ) ).

tff(fact_1169_WTrtCall,axiom,
    ! [Esa: list_exp_list_char,Ts_1: list_ty,M: list_char,Ts: list_ty,T_3: ty,Pns: list_list_char,Body: exp_list_char,D: list_char,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,C: list_char] :
      ( hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,Ea),hAPP_list_char_ty(class,C)))
     => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Ts,T_3,produc1147572817t_char(Pns,Body)),D))
       => ( hBOOL(wTrts(Pa,Ha,E_1,Esa,Ts_1))
         => ( hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_1,Ts))
           => hBOOL(hAPP_ty_bool(wTrt(Pa,Ha,E_1,call_list_char(Ea,M,Esa)),T_3)) ) ) ) ) ).

tff(fact_1170_Call,axiom,
    ! [E_a: 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,T_3: 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,Ea: exp_list_char,S_0: produc12694297on_val,A: nat,S_1_1: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),S_1_1))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Ps,S_1_1),map_va1934808527t_char(val_list_char,Vs_1)),produc899768717on_val(H_2,L_2)))
       => ( ( hAPP_n546249108on_val(H_2,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs)) )
         => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Ts,T_3,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,produc899768717on_val(H_2,L_2_1)),E_a),produc899768717on_val(H_3,L_3)))
                 => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,call_list_char(Ea,M,Ps),S_0),E_a),produc899768717on_val(H_3,L_2))) ) ) ) ) ) ) ) ).

tff(fact_1171_typeof__lit__typeof,axiom,
    ! [Ha: fun_na939144002on_val,V_1: val,T_3: ty] :
      ( ( hAPP_val_option_ty(typeof_h(hAPP_o1576581476on_val(cOMBK_1944287343al_nat,none_P179726773on_val)),V_1) = hAPP_ty_option_ty(some_ty,T_3) )
     => ( hAPP_val_option_ty(typeof_h(Ha),V_1) = hAPP_ty_option_ty(some_ty,T_3) ) ) ).

tff(fact_1172_redp__red__eq,axiom,
    ! [Pa: list_P1999446415t_char,X_1: exp_list_char,Xa: produc12694297on_val,Xb: exp_list_char,Xc: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,X_1,Xa),Xb),Xc))
    <=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(X_1,Xa),produc1259058957on_val(Xb,Xc)),red(Pa))) ) ).

tff(fact_1173_redsp__reds__eq,axiom,
    ! [Pa: list_P1999446415t_char,X_1: list_exp_list_char,Xa: produc12694297on_val,Xb: list_exp_list_char,Xc: produc12694297on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,X_1,Xa),Xb),Xc))
    <=> hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(X_1,Xa),produc379668296on_val(Xb,Xc)),reds(Pa))) ) ).

tff(fact_1174_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,T_3: 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,Ea: exp_list_char,S_0: produc12694297on_val,A: nat,S_1_1: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_0),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,addr(A)),S_1_1)),transi2024712006on_val(red(Pa))))
       => ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Esa,S_1_1),produc379668296on_val(map_va1934808527t_char(val_list_char,Vs_1),produc899768717on_val(H_2,L_2))),transi374442731on_val(reds(Pa))))
         => ( ( hAPP_n546249108on_val(H_2,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs)) )
           => ( hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Ts,T_3,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(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Body,produc899768717on_val(H_2,L_2_1)),produc1259058957on_val(Ef,produc899768717on_val(H_3,L_3))),transi2024712006on_val(red(Pa))))
                   => ( hBOOL(final_list_char(Ef))
                     => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(call_list_char(Ea,M,Esa),S_0),produc1259058957on_val(Ef,produc899768717on_val(H_3,L_2))),transi2024712006on_val(red(Pa)))) ) ) ) ) ) ) ) ) ) ).

tff(fact_1175_extend__1__eval,axiom,
    ! [E_a: exp_list_char,S: produc12694297on_val,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E,S_2)),red(Pa)))
       => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E,S_2),E_a),S))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),E_a),S)) ) ) ) ).

tff(fact_1176_extend__1__evals,axiom,
    ! [Es_a: list_exp_list_char,T_2: produc12694297on_val,Esa: list_exp_list_char,T_1: produc12694297on_val,Es: list_exp_list_char,T: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Esa,T_1),produc379668296on_val(Es,T)),reds(Pa)))
       => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es,T),Es_a),T_2))
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,T_1),Es_a),T_2)) ) ) ) ).

tff(fact_1177_big__by__small,axiom,
    ! [Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),E_a),S))
       => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa)))) ) ) ).

tff(fact_1178_extend__eval,axiom,
    ! [E_a: exp_list_char,S: produc12694297on_val,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E,S_2)),transi2024712006on_val(red(Pa))))
       => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E,S_2),E_a),S))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),E_a),S)) ) ) ) ).

tff(fact_1179_bigs__by__smalls,axiom,
    ! [Esa: list_exp_list_char,S_1: produc12694297on_val,Es_a: list_exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S_1),Es_a),S))
       => hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Esa,S_1),produc379668296on_val(Es_a,S)),transi374442731on_val(reds(Pa)))) ) ) ).

tff(fact_1180_extend__evals,axiom,
    ! [Es_a: list_exp_list_char,S: produc12694297on_val,Esa: list_exp_list_char,S_1: produc12694297on_val,Es: list_exp_list_char,S_2: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(member875476972on_val(produc1611380469on_val(produc379668296on_val(Esa,S_1),produc379668296on_val(Es,S_2)),transi374442731on_val(reds(Pa))))
       => ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es,S_2),Es_a),S))
         => hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S_1),Es_a),S)) ) ) ) ).

tff(fact_1181_small__by__big,axiom,
    ! [Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
       => ( hBOOL(final_list_char(E_a))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),E_a),S)) ) ) ) ).

tff(fact_1182_big__iff__small,axiom,
    ! [Ea: exp_list_char,S_1: produc12694297on_val,E_a: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),E_a),S))
      <=> ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E_a,S)),transi2024712006on_val(red(Pa))))
          & hBOOL(final_list_char(E_a)) ) ) ) ).

tff(fact_1183_typeof__h_Osimps_I5_J,axiom,
    ! [Ha: fun_na939144002on_val,A: nat] : hAPP_val_option_ty(typeof_h(Ha),addr(A)) = option1388193227on_val(none_ty,produc907433735ion_ty(cOMBB_352765746t_char(cOMBK_184479553on_val,cOMBB_1888336841t_char(some_ty,class))),hAPP_n546249108on_val(Ha,A)) ).

tff(fact_1184_blocksRedsFinal,axiom,
    ! [L: fun_li1432931796on_val,Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char,Vs_1: list_val,Vs: list_list_char,Ts: list_ty] :
      ( ( size_s2113983095t_char(Vs) = size_size_list_ty(Ts) )
     => ( ( size_size_list_val(Vs_1) = size_size_list_ty(Ts) )
       => ( hBOOL(distinct_list_char(Vs))
         => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,map_up1085636310ar_val(La,Vs,Vs_1))),produc1259058957on_val(E_a,produc899768717on_val(H_a,L_a))),transi2024712006on_val(red(Pa))))
           => ( hBOOL(final_list_char(E_a))
             => ( ( L = overri2012515291on_val(L_a,La,set_list_char(Vs)) )
               => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(blocks(produc921874948t_char(Vs,produc1909267824t_char(Ts,produc1916172923t_char(Vs_1,Ea)))),produc899768717on_val(Ha,La)),produc1259058957on_val(E_a,produc899768717on_val(H_a,L))),transi2024712006on_val(red(Pa)))) ) ) ) ) ) ) ).

tff(fact_1185_blocksReds,axiom,
    ! [Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char,Vs_1: list_val,Vs: list_list_char,Ts: list_ty] :
      ( ( size_s2113983095t_char(Vs) = size_size_list_ty(Ts) )
     => ( ( size_size_list_val(Vs_1) = size_size_list_ty(Ts) )
       => ( hBOOL(distinct_list_char(Vs))
         => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,map_up1085636310ar_val(La,Vs,Vs_1))),produc1259058957on_val(E_a,produc899768717on_val(H_a,L_a))),transi2024712006on_val(red(Pa))))
           => hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(blocks(produc921874948t_char(Vs,produc1909267824t_char(Ts,produc1916172923t_char(Vs_1,Ea)))),produc899768717on_val(Ha,La)),produc1259058957on_val(blocks(produc921874948t_char(Vs,produc1909267824t_char(Ts,produc1916172923t_char(map_list_char_val(comp_o1129292306t_char(the_val,L_a),Vs),E_a)))),produc899768717on_val(H_a,overri2012515291on_val(L_a,La,set_list_char(Vs))))),transi2024712006on_val(red(Pa)))) ) ) ) ) ).

tff(fact_1186_Red__fv,axiom,
    ! [Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,La)),produc1259058957on_val(E_a,produc899768717on_val(H_a,L_a))),red(Pa)))
       => hBOOL(ord_le2092826700r_bool(fv(E_a),fv(Ea))) ) ) ).

tff(fact_1187_fv__fvs_Osimps_I7_J,axiom,
    ! [Ea: exp_list_char,F: list_char,D: list_char] : fv(fAcc_list_char(Ea,F,D)) = fv(Ea) ).

tff(fact_1188_fv__fvs_Osimps_I14_J,axiom,
    ! [Ea: exp_list_char] : fv(throw_list_char(Ea)) = fv(Ea) ).

tff(fact_1189_fv__fvs_Osimps_I2_J,axiom,
    ! [C: list_char,Ea: exp_list_char] : fv(cast_list_char(C,Ea)) = fv(Ea) ).

tff(fact_1190_eval__notfree__unchanged,axiom,
    ! [V: list_char,Pa: list_P1999446415t_char,Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,produc899768717on_val(Ha,La)),E_a),produc899768717on_val(H_a,L_a)))
     => ( ~ hBOOL(member_list_char(V,fv(Ea)))
       => ( hAPP_l207779698on_val(L_a,V) = hAPP_l207779698on_val(La,V) ) ) ) ).

tff(fact_1191_eval__restrict__lcl,axiom,
    ! [W: fun_list_char_bool,Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,produc899768717on_val(Ha,La)),E_a),produc899768717on_val(H_a,L_a)))
       => ( hBOOL(ord_le2092826700r_bool(fv(Ea),W))
         => hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,produc899768717on_val(Ha,restri761823004ar_val(La,W))),E_a),produc899768717on_val(H_a,restri761823004ar_val(L_a,W)))) ) ) ) ).

tff(fact_1192_cname__of__xcp,axiom,
    ! [C: list_char,Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( hBOOL(member_list_char(C,sys_xcpts))
       => ( hAPP_P1789965269t_char(produc1230355531on_val,hAPP_o1977518472on_val(the_Pr431167171on_val,hAPP_n546249108on_val(Ha,addr_of_sys_xcpt(C)))) = C ) ) ) ).

tff(fact_1193_obj__ty__def,axiom,
    ! [Obj: produc639455274on_val] : obj_ty(Obj) = hAPP_list_char_ty(class,hAPP_P1789965269t_char(produc1230355531on_val,Obj)) ).

tff(fact_1194_hp__def,axiom,
    hp = produc1517998010on_val ).

tff(fact_1195_eval__lcl__incr,axiom,
    ! [Pa: list_P1999446415t_char,Ea: exp_list_char,H_0: fun_na939144002on_val,L_0: fun_li1432931796on_val,E_a: exp_list_char,H_1: fun_na939144002on_val,L_1: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,produc899768717on_val(H_0,L_0)),E_a),produc899768717on_val(H_1,L_1)))
     => hBOOL(ord_le2092826700r_bool(dom_list_char_val(L_0),dom_list_char_val(L_1))) ) ).

tff(fact_1196_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: fun_li1432931796on_val] :
      ( hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,produc899768717on_val(H_0,L_0)),Es_a),produc899768717on_val(H_1,L_1)))
     => hBOOL(ord_le2092826700r_bool(dom_list_char_val(L_0),dom_list_char_val(L_1))) ) ).

tff(fact_1197_preallocated__dom,axiom,
    ! [C: list_char,Ha: fun_na939144002on_val] :
      ( hBOOL(preallocated(Ha))
     => ( hBOOL(member_list_char(C,sys_xcpts))
       => hBOOL(member_nat(addr_of_sys_xcpt(C),dom_na996029170on_val(Ha))) ) ) ).

tff(fact_1198_red__lcl__incr,axiom,
    ! [Ea: exp_list_char,H_0: fun_na939144002on_val,L_0: fun_li1432931796on_val,E_a: exp_list_char,H_1: fun_na939144002on_val,L_1: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(H_0,L_0)),produc1259058957on_val(E_a,produc899768717on_val(H_1,L_1))),red(Pa)))
     => hBOOL(ord_le2092826700r_bool(dom_list_char_val(L_0),dom_list_char_val(L_1))) ) ).

tff(fact_1199_Reds__dom__lcl,axiom,
    ! [Ea: exp_list_char,Ha: fun_na939144002on_val,La: fun_li1432931796on_val,E_a: exp_list_char,H_a: fun_na939144002on_val,L_a: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
      ( hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa))
     => ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,La)),produc1259058957on_val(E_a,produc899768717on_val(H_a,L_a))),transi2024712006on_val(red(Pa))))
       => hBOOL(ord_le2092826700r_bool(dom_list_char_val(L_a),semila919158006r_bool(dom_list_char_val(La),fv(Ea)))) ) ) ).

%----Helper facts (11)
tff(help_fTrue_1_1_U,axiom,
    hBOOL(fTrue) ).

tff(help_fTrue_1_1_T,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_fFalse_1_1_U,axiom,
    ~ hBOOL(fFalse) ).

tff(help_fFalse_1_1_T,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_fequal_1_1_fequal_000tc__Value__Oval_T,axiom,
    ! [X: val,Y: val] :
      ( ~ hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(fequal_val,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__Value__Oval_T,axiom,
    ! [X: val,Y: val] :
      ( ( X != Y )
      | hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(fequal_val,X),Y)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__List__Olis,axiom,
    ! [P: option_val,Q: list_char] : hAPP_l207779698on_val(hAPP_o538043682on_val(cOMBK_1097134891t_char,P),Q) = P ).

tff(help_COMBB_1_1_COMBB_000tc__Type__Oty_000tc__Option__Ooption_Itc__Type__Oty_J_00,axiom,
    ! [P: fun_ty_option_ty,Q: fun_list_char_ty,R: list_char] : hAPP_l512744617ion_ty(cOMBB_1888336841t_char(P,Q),R) = hAPP_ty_option_ty(P,hAPP_list_char_ty(Q,R)) ).

tff(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__fun_Itc__pro,axiom,
    ! [P: option_ty,Q: fun_Pr806764899on_val] : hAPP_f652398900ion_ty(hAPP_o534509643ion_ty(cOMBK_184479553on_val,P),Q) = P ).

tff(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__Stri,axiom,
    ! [P: option1479284511on_val,Q: nat] : hAPP_n546249108on_val(hAPP_o1576581476on_val(cOMBK_1944287343al_nat,P),Q) = P ).

tff(help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__fun_Itc__fun,axiom,
    ! [P: fun_op1983271469ion_ty,Q: fun_li688206603ion_ty,R: list_char] : hAPP_l2000496933ion_ty(cOMBB_352765746t_char(P,Q),R) = hAPP_o534509643ion_ty(P,hAPP_l512744617ion_ty(Q,R)) ).

%----Conjectures (4)
tff(conj_0,hypothesis,
    hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(e,produc899768717on_val(h_1,l_1)),produc1259058957on_val(e_2,produc899768717on_val(h,l))),red(p))) ).

tff(conj_1,hypothesis,
    hBOOL(hAPP_ty_bool(wTrt(p,h_1,e_1,e),t)) ).

tff(conj_2,hypothesis,
    hBOOL(hconf_97414254t_char(p,h_1)) ).

tff(conj_3,conjecture,
    hBOOL(hconf_97414254t_char(p,h)) ).

%------------------------------------------------------------------------------