TPTP Problem File: SWW478^2.p
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%------------------------------------------------------------------------------
% File : SWW478^2 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Java type soundness line 479, 500 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : jinja_500_thf_l479 [Bla11]
% Status : Theorem
% Rating : 0.33 v8.1.0, 0.50 v7.5.0, 1.00 v7.2.0, 0.75 v7.1.0, 0.00 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.57 v6.1.0, 0.29 v6.0.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.80 v5.3.0
% Syntax : Number of formulae : 975 ( 234 unt; 274 typ; 0 def)
% Number of atoms : 1883 ( 517 equ; 8 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 8641 ( 219 ~; 5 |; 45 &;7585 @)
% ( 135 <=>; 638 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 10 avg)
% Number of types : 20 ( 19 usr)
% Number of type conns : 2183 (2183 >; 0 *; 0 +; 0 <<)
% Number of symbols : 260 ( 255 usr; 22 con; 0-5 aty)
% ( 7 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 2999 ( 54 ^;2891 !; 54 ?;2999 :)
% SPC : TH1_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 19:42:39
%------------------------------------------------------------------------------
%----Should-be-implicit typings (19)
thf(ty_ty_tc__Expr__Obop,type,
bop: $tType ).
thf(ty_ty_tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
exp_list_char: $tType ).
thf(ty_ty_tc__List__Olist_Itc__String__Ochar_J,type,
list_char: $tType ).
thf(ty_ty_tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_,type,
list_P1999446415t_char: $tType ).
thf(ty_ty_tc__Nat__Onat,type,
nat: $tType ).
thf(ty_ty_tc__Option__Ooption_I_062_Itc__List__Olist_Itc__String__Ochar_J_M_Eo_J_J,type,
option_list_char_o: $tType ).
thf(ty_ty_tc__Option__Ooption_Itc__Type__Oty_J,type,
option_ty: $tType ).
thf(ty_ty_tc__Option__Ooption_Itc__Value__Oval_J,type,
option_val: $tType ).
thf(ty_ty_tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_,type,
option1728594148on_val: $tType ).
thf(ty_ty_tc__Type__Oty,type,
ty: $tType ).
thf(ty_ty_tc__Value__Oval,type,
val: $tType ).
thf(ty_ty_tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol,type,
produc2090907612on_val: $tType ).
thf(ty_ty_tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_J,type,
produc1645268488al_val: $tType ).
thf(ty_ty_tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__prod,type,
produc1282892786on_val: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc__prod_Itc__List__,type,
produc2088785539on_val: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_Itc__Strin,type,
produc1278157519t_char: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__Olist_,type,
produc1013743697t_char: $tType ).
thf(ty_ty_tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J,type,
product_prod_val_val: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
produc1746408499on_val: $tType ).
%----Explicit typings (269)
thf(sy_c_BigStep_Oeval,type,
eval: list_P1999446415t_char > exp_list_char > produc2090907612on_val > exp_list_char > produc2090907612on_val > $o ).
thf(sy_c_BigStep_Ofinal_000tc__List__Olist_Itc__String__Ochar_J,type,
final_list_char: exp_list_char > $o ).
thf(sy_c_Conform_Oconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Oc,type,
conf_P373316194t_char: list_P1999446415t_char > ( nat > option1728594148on_val ) > val > ty > $o ).
thf(sy_c_Conform_Ohconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
hconf_97414254t_char: list_P1999446415t_char > ( nat > option1728594148on_val ) > $o ).
thf(sy_c_Conform_Olconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
lconf_496643946t_char: list_P1999446415t_char > ( nat > option1728594148on_val ) > ( list_char > option_val ) > ( list_char > option_ty ) > $o ).
thf(sy_c_Conform_Ooconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
oconf_1869808039t_char: list_P1999446415t_char > ( nat > option1728594148on_val ) > produc2088785539on_val > $o ).
thf(sy_c_Decl_Ois__class_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__,type,
is_cla570604648t_char: list_P1999446415t_char > list_char > $o ).
thf(sy_c_DefAss_O_092_060D_062_000tc__List__Olist_Itc__String__Ochar_J,type,
d_list_char: exp_list_char > option_list_char_o > $o ).
thf(sy_c_Exceptions_OClassCast,type,
classCast: list_char ).
thf(sy_c_Exceptions_ONullPointer,type,
nullPointer: list_char ).
thf(sy_c_Exceptions_Oaddr__of__sys__xcpt,type,
addr_of_sys_xcpt: list_char > nat ).
thf(sy_c_Expr_Obinop,type,
binop: produc1645268488al_val > option_val ).
thf(sy_c_Expr_Obop_OAdd,type,
add: bop ).
thf(sy_c_Expr_Obop_OEq,type,
c_Expr_Obop_OEq: bop ).
thf(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 ).
thf(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 ).
thf(sy_c_Expr_Oexp_OCast_000tc__List__Olist_Itc__String__Ochar_J,type,
cast_list_char: list_char > exp_list_char > exp_list_char ).
thf(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 ).
thf(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 ).
thf(sy_c_Expr_Oexp_OLAss_000tc__List__Olist_Itc__String__Ochar_J,type,
lAss_list_char: list_char > exp_list_char > exp_list_char ).
thf(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 ).
thf(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 ).
thf(sy_c_Expr_Oexp_OVal_000tc__List__Olist_Itc__String__Ochar_J,type,
val_list_char: val > exp_list_char ).
thf(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 ).
thf(sy_c_Expr_Oexp_Othrow_000tc__List__Olist_Itc__String__Ochar_J,type,
throw_list_char: exp_list_char > exp_list_char ).
thf(sy_c_Fun_Ofun__upd_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooptio,type,
fun_up405271663char_o: ( list_char > option_list_char_o ) > list_char > option_list_char_o > list_char > option_list_char_o ).
thf(sy_c_Fun_Ofun__upd_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooptio_001,type,
fun_up424764369ion_ty: ( list_char > option_ty ) > list_char > option_ty > list_char > option_ty ).
thf(sy_c_Fun_Ofun__upd_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooptio_002,type,
fun_up1149430426on_val: ( list_char > option_val ) > list_char > option_val > list_char > option_val ).
thf(sy_c_Fun_Ofun__upd_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooptio_003,type,
fun_up867733049on_val: ( list_char > option1728594148on_val ) > list_char > option1728594148on_val > list_char > option1728594148on_val ).
thf(sy_c_Fun_Ofun__upd_000tc__Nat__Onat_000tc__Option__Ooption_I_062_Itc__List__Olis,type,
fun_up412657745char_o: ( nat > option_list_char_o ) > nat > option_list_char_o > nat > option_list_char_o ).
thf(sy_c_Fun_Ofun__upd_000tc__Nat__Onat_000tc__Option__Ooption_Itc__Type__Oty_J,type,
fun_up421284275ion_ty: ( nat > option_ty ) > nat > option_ty > nat > option_ty ).
thf(sy_c_Fun_Ofun__upd_000tc__Nat__Onat_000tc__Option__Ooption_Itc__Value__Oval_J,type,
fun_up846528380on_val: ( nat > option_val ) > nat > option_val > nat > option_val ).
thf(sy_c_Fun_Ofun__upd_000tc__Nat__Onat_000tc__Option__Ooption_Itc__prod_Itc__List__,type,
fun_up1472480727on_val: ( nat > option1728594148on_val ) > nat > option1728594148on_val > nat > option1728594148on_val ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pr,type,
fun_up590200203char_o: ( produc2090907612on_val > option_list_char_o ) > produc2090907612on_val > option_list_char_o > produc2090907612on_val > option_list_char_o ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pr_004,type,
fun_up1313253613ion_ty: ( produc2090907612on_val > option_ty ) > produc2090907612on_val > option_ty > produc2090907612on_val > option_ty ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pr_005,type,
fun_up1458528694on_val: ( produc2090907612on_val > option_val ) > produc2090907612on_val > option_val > produc2090907612on_val > option_val ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pr_006,type,
fun_up224753181on_val: ( produc2090907612on_val > option1728594148on_val ) > produc2090907612on_val > option1728594148on_val > produc2090907612on_val > option1728594148on_val ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__V,type,
fun_up743641015char_o: ( produc1645268488al_val > option_list_char_o ) > produc1645268488al_val > option_list_char_o > produc1645268488al_val > option_list_char_o ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__V_007,type,
fun_up430376729ion_ty: ( produc1645268488al_val > option_ty ) > produc1645268488al_val > option_ty > produc1645268488al_val > option_ty ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__V_008,type,
fun_up1370188258on_val: ( produc1645268488al_val > option_val ) > produc1645268488al_val > option_val > produc1645268488al_val > option_val ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__V_009,type,
fun_up709865713on_val: ( produc1645268488al_val > option1728594148on_val ) > produc1645268488al_val > option1728594148on_val > produc1645268488al_val > option1728594148on_val ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och,type,
fun_up122360737char_o: ( produc1282892786on_val > option_list_char_o ) > produc1282892786on_val > option_list_char_o > produc1282892786on_val > option_list_char_o ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och_010,type,
fun_up951485699ion_ty: ( produc1282892786on_val > option_ty ) > produc1282892786on_val > option_ty > produc1282892786on_val > option_ty ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och_011,type,
fun_up1510380236on_val: ( produc1282892786on_val > option_val ) > produc1282892786on_val > option_val > produc1282892786on_val > option_val ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och_012,type,
fun_up881763975on_val: ( produc1282892786on_val > option1728594148on_val ) > produc1282892786on_val > option1728594148on_val > produc1282892786on_val > option1728594148on_val ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc__,type,
fun_up1138829106char_o: ( produc2088785539on_val > option_list_char_o ) > produc2088785539on_val > option_list_char_o > produc2088785539on_val > option_list_char_o ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc___013,type,
fun_up1537495444ion_ty: ( produc2088785539on_val > option_ty ) > produc2088785539on_val > option_ty > produc2088785539on_val > option_ty ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc___014,type,
fun_up305473245on_val: ( produc2088785539on_val > option_val ) > produc2088785539on_val > option_val > produc2088785539on_val > option_val ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc___015,type,
fun_up70099126on_val: ( produc2088785539on_val > option1728594148on_val ) > produc2088785539on_val > option1728594148on_val > produc2088785539on_val > option1728594148on_val ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__,type,
fun_up204312361on_val: ( produc1278157519t_char > option_val ) > produc1278157519t_char > option_val > produc1278157519t_char > option_val ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__Option,type,
fun_up179536214char_o: ( product_prod_val_val > option_list_char_o ) > product_prod_val_val > option_list_char_o > product_prod_val_val > option_list_char_o ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__Option_016,type,
fun_up638349240ion_ty: ( product_prod_val_val > option_ty ) > product_prod_val_val > option_ty > product_prod_val_val > option_ty ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__Option_017,type,
fun_up2650881on_val: ( product_prod_val_val > option_val ) > product_prod_val_val > option_val > product_prod_val_val > option_val ).
thf(sy_c_Fun_Ofun__upd_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__Option_018,type,
fun_up2110408082on_val: ( product_prod_val_val > option1728594148on_val ) > product_prod_val_val > option1728594148on_val > product_prod_val_val > option1728594148on_val ).
thf(sy_c_JWellForm_Owf__J__mdecl,type,
wf_J_mdecl: list_P1999446415t_char > list_char > produc1013743697t_char > $o ).
thf(sy_c_Map_Odom_000tc__List__Olist_Itc__String__Ochar_J_000_062_Itc__List__Olist_I,type,
dom_li115714383char_o: ( list_char > option_list_char_o ) > list_char > $o ).
thf(sy_c_Map_Odom_000tc__List__Olist_Itc__String__Ochar_J_000tc__Type__Oty,type,
dom_list_char_ty: ( list_char > option_ty ) > list_char > $o ).
thf(sy_c_Map_Odom_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
dom_list_char_val: ( list_char > option_val ) > list_char > $o ).
thf(sy_c_Map_Odom_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__List__Oli,type,
dom_li96736835on_val: ( list_char > option1728594148on_val ) > list_char > $o ).
thf(sy_c_Map_Odom_000tc__Nat__Onat_000_062_Itc__List__Olist_Itc__String__Ochar_J_M_E,type,
dom_nat_list_char_o: ( nat > option_list_char_o ) > nat > $o ).
thf(sy_c_Map_Odom_000tc__Nat__Onat_000tc__Type__Oty,type,
dom_nat_ty: ( nat > option_ty ) > nat > $o ).
thf(sy_c_Map_Odom_000tc__Nat__Onat_000tc__Value__Oval,type,
dom_nat_val: ( nat > option_val ) > nat > $o ).
thf(sy_c_Map_Odom_000tc__Nat__Onat_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J,type,
dom_na2045926843on_val: ( nat > option1728594148on_val ) > nat > $o ).
thf(sy_c_Map_Odom_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It,type,
dom_Pr1958353971char_o: ( produc2090907612on_val > option_list_char_o ) > produc2090907612on_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_019,type,
dom_Pr878896021val_ty: ( produc2090907612on_val > option_ty ) > produc2090907612on_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_020,type,
dom_Pr1333147486al_val: ( produc2090907612on_val > option_val ) > produc2090907612on_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_021,type,
dom_Pr1306915423on_val: ( produc2090907612on_val > option1728594148on_val ) > produc2090907612on_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value_,type,
dom_Pr1531186439char_o: ( produc1645268488al_val > option_list_char_o ) > produc1645268488al_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__022,type,
dom_Pr585943145val_ty: ( produc1645268488al_val > option_ty ) > produc1645268488al_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__023,type,
dom_Pr934474290al_val: ( produc1645268488al_val > option_val ) > produc1645268488al_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__024,type,
dom_Pr1903277195on_val: ( produc1645268488al_val > option1728594148on_val ) > produc1645268488al_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_,type,
dom_Pr373640349char_o: ( produc1282892786on_val > option_list_char_o ) > produc1282892786on_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J__025,type,
dom_Pr1290145279val_ty: ( produc1282892786on_val > option_ty ) > produc1282892786on_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J__026,type,
dom_Pr959892680al_val: ( produc1282892786on_val > option_val ) > produc1282892786on_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J__027,type,
dom_Pr1372035957on_val: ( produc1282892786on_val > option1728594148on_val ) > produc1282892786on_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc__prod_,type,
dom_Pr957742668char_o: ( produc2088785539on_val > option_list_char_o ) > produc2088785539on_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc__prod__028,type,
dom_Pr970344110val_ty: ( produc2088785539on_val > option_ty ) > produc2088785539on_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc__prod__029,type,
dom_Pr397909495al_val: ( produc2088785539on_val > option_val ) > produc2088785539on_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc__prod__030,type,
dom_Pr1058999302on_val: ( produc2088785539on_val > option1728594148on_val ) > produc2088785539on_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist,type,
dom_Pr695701035ar_val: ( produc1278157519t_char > option_val ) > produc1278157519t_char > $o ).
thf(sy_c_Map_Odom_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000_062_Itc__List_,type,
dom_Pr581342760char_o: ( product_prod_val_val > option_list_char_o ) > product_prod_val_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__Type__Oty,type,
dom_Pr1536367242val_ty: ( product_prod_val_val > option_ty ) > product_prod_val_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__Value__Oval,type,
dom_Pr1854948307al_val: ( product_prod_val_val > option_val ) > product_prod_val_val > $o ).
thf(sy_c_Map_Odom_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__prod_Itc__L,type,
dom_Pr283571498on_val: ( product_prod_val_val > option1728594148on_val ) > product_prod_val_val > $o ).
thf(sy_c_Map_Omap__add_000tc__List__Olist_Itc__String__Ochar_J_000_062_Itc__List__Ol,type,
map_ad1407104812char_o: ( list_char > option_list_char_o ) > ( list_char > option_list_char_o ) > list_char > option_list_char_o ).
thf(sy_c_Map_Omap__add_000tc__List__Olist_Itc__String__Ochar_J_000tc__Type__Oty,type,
map_add_list_char_ty: ( list_char > option_ty ) > ( list_char > option_ty ) > list_char > option_ty ).
thf(sy_c_Map_Omap__add_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
map_ad325961431ar_val: ( list_char > option_val ) > ( list_char > option_val ) > list_char > option_val ).
thf(sy_c_Map_Omap__add_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__List,type,
map_ad53467942on_val: ( list_char > option1728594148on_val ) > ( list_char > option1728594148on_val ) > list_char > option1728594148on_val ).
thf(sy_c_Map_Omap__add_000tc__Nat__Onat_000_062_Itc__List__Olist_Itc__String__Ochar_,type,
map_ad2090421050char_o: ( nat > option_list_char_o ) > ( nat > option_list_char_o ) > nat > option_list_char_o ).
thf(sy_c_Map_Omap__add_000tc__Nat__Onat_000tc__Type__Oty,type,
map_add_nat_ty: ( nat > option_ty ) > ( nat > option_ty ) > nat > option_ty ).
thf(sy_c_Map_Omap__add_000tc__Nat__Onat_000tc__Value__Oval,type,
map_add_nat_val: ( nat > option_val ) > ( nat > option_val ) > nat > option_val ).
thf(sy_c_Map_Omap__add_000tc__Nat__Onat_000tc__prod_Itc__List__Olist_Itc__String__Oc,type,
map_ad1851375512on_val: ( nat > option1728594148on_val ) > ( nat > option1728594148on_val ) > nat > option1728594148on_val ).
thf(sy_c_Map_Omap__add_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pr,type,
map_ad1905329424char_o: ( produc2090907612on_val > option_list_char_o ) > ( produc2090907612on_val > option_list_char_o ) > produc2090907612on_val > option_list_char_o ).
thf(sy_c_Map_Omap__add_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pr_031,type,
map_ad1576841586val_ty: ( produc2090907612on_val > option_ty ) > ( produc2090907612on_val > option_ty ) > produc2090907612on_val > option_ty ).
thf(sy_c_Map_Omap__add_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pr_032,type,
map_ad466413243al_val: ( produc2090907612on_val > option_val ) > ( produc2090907612on_val > option_val ) > produc2090907612on_val > option_val ).
thf(sy_c_Map_Omap__add_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pr_033,type,
map_ad815995970on_val: ( produc2090907612on_val > option1728594148on_val ) > ( produc2090907612on_val > option1728594148on_val ) > produc2090907612on_val > option1728594148on_val ).
thf(sy_c_Map_Omap__add_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__V,type,
map_ad440022500char_o: ( produc1645268488al_val > option_list_char_o ) > ( produc1645268488al_val > option_list_char_o ) > produc1645268488al_val > option_list_char_o ).
thf(sy_c_Map_Omap__add_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__V_034,type,
map_ad1877333574val_ty: ( produc1645268488al_val > option_ty ) > ( produc1645268488al_val > option_ty ) > produc1645268488al_val > option_ty ).
thf(sy_c_Map_Omap__add_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__V_035,type,
map_ad1808327055al_val: ( produc1645268488al_val > option_val ) > ( produc1645268488al_val > option_val ) > produc1645268488al_val > option_val ).
thf(sy_c_Map_Omap__add_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__V_036,type,
map_ad1824497262on_val: ( produc1645268488al_val > option1728594148on_val ) > ( produc1645268488al_val > option1728594148on_val ) > produc1645268488al_val > option1728594148on_val ).
thf(sy_c_Map_Omap__add_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och,type,
map_ad134899834char_o: ( produc1282892786on_val > option_list_char_o ) > ( produc1282892786on_val > option_list_char_o ) > produc1282892786on_val > option_list_char_o ).
thf(sy_c_Map_Omap__add_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och_037,type,
map_ad1914244828val_ty: ( produc1282892786on_val > option_ty ) > ( produc1282892786on_val > option_ty ) > produc1282892786on_val > option_ty ).
thf(sy_c_Map_Omap__add_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och_038,type,
map_ad1639788325al_val: ( produc1282892786on_val > option_val ) > ( produc1282892786on_val > option_val ) > produc1282892786on_val > option_val ).
thf(sy_c_Map_Omap__add_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Och_039,type,
map_ad1893716568on_val: ( produc1282892786on_val > option1728594148on_val ) > ( produc1282892786on_val > option1728594148on_val ) > produc1282892786on_val > option1728594148on_val ).
thf(sy_c_Map_Omap__add_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc__,type,
map_ad1510374185char_o: ( produc2088785539on_val > option_list_char_o ) > ( produc2088785539on_val > option_list_char_o ) > produc2088785539on_val > option_list_char_o ).
thf(sy_c_Map_Omap__add_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc___040,type,
map_ad775792779val_ty: ( produc2088785539on_val > option_ty ) > ( produc2088785539on_val > option_ty ) > produc2088785539on_val > option_ty ).
thf(sy_c_Map_Omap__add_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc___041,type,
map_ad2035409236al_val: ( produc2088785539on_val > option_val ) > ( produc2088785539on_val > option_val ) > produc2088785539on_val > option_val ).
thf(sy_c_Map_Omap__add_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc___042,type,
map_ad918921705on_val: ( produc2088785539on_val > option1728594148on_val ) > ( produc2088785539on_val > option1728594148on_val ) > produc2088785539on_val > option1728594148on_val ).
thf(sy_c_Map_Omap__add_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__,type,
map_ad1185064968ar_val: ( produc1278157519t_char > option_val ) > ( produc1278157519t_char > option_val ) > produc1278157519t_char > option_val ).
thf(sy_c_Map_Omap__add_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000_062_Itc__,type,
map_ad1233037829char_o: ( product_prod_val_val > option_list_char_o ) > ( product_prod_val_val > option_list_char_o ) > product_prod_val_val > option_list_char_o ).
thf(sy_c_Map_Omap__add_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__Type__,type,
map_ad1402016615val_ty: ( product_prod_val_val > option_ty ) > ( product_prod_val_val > option_ty ) > product_prod_val_val > option_ty ).
thf(sy_c_Map_Omap__add_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__Value_,type,
map_ad1139121712al_val: ( product_prod_val_val > option_val ) > ( product_prod_val_val > option_val ) > product_prod_val_val > option_val ).
thf(sy_c_Map_Omap__add_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__prod_I,type,
map_ad1570649101on_val: ( product_prod_val_val > option1728594148on_val ) > ( product_prod_val_val > option1728594148on_val ) > product_prod_val_val > option1728594148on_val ).
thf(sy_c_Objects_Ohext,type,
hext: ( nat > option1728594148on_val ) > ( nat > option1728594148on_val ) > $o ).
thf(sy_c_Option_Ooption_ONone_000tc__Value__Oval,type,
none_val: option_val ).
thf(sy_c_Option_Ooption_ONone_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_06,type,
none_P1260844216on_val: option1728594148on_val ).
thf(sy_c_Option_Ooption_OSome_000_062_Itc__List__Olist_Itc__String__Ochar_J_M_Eo_J,type,
some_list_char_o: ( list_char > $o ) > option_list_char_o ).
thf(sy_c_Option_Ooption_OSome_000tc__Type__Oty,type,
some_ty: ty > option_ty ).
thf(sy_c_Option_Ooption_OSome_000tc__Value__Oval,type,
some_val: val > option_val ).
thf(sy_c_Option_Ooption_OSome_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_06,type,
some_P451527732on_val: produc2088785539on_val > option1728594148on_val ).
thf(sy_c_Option_Othe_000tc__Value__Oval,type,
the_val: option_val > val ).
thf(sy_c_Product__Type_OPair_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I,type,
produc755559506on_val: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2090907612on_val ).
thf(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 ).
thf(sy_c_Product__Type_OPair_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J,type,
produc235638504on_val: exp_list_char > produc2090907612on_val > produc1282892786on_val ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000_062_Itc__pr,type,
produc926070009on_val: list_char > ( produc1278157519t_char > option_val ) > produc2088785539on_val ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__List__Ol,type,
produc5062597t_char: list_char > list_char > produc1278157519t_char ).
thf(sy_c_Product__Type_OPair_000tc__Value__Oval_000tc__Value__Oval,type,
product_Pair_val_val: val > val > product_prod_val_val ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
produc833389609on_val: produc1282892786on_val > produc1282892786on_val > produc1746408499on_val ).
thf(sy_c_Product__Type_Ocurry_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_,type,
produc1402621651_val_o: ( produc2090907612on_val > $o ) > ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__Expr__Obop_000tc__prod_Itc__Value__Oval_Mtc__Va,type,
produc275195559_val_o: ( produc1645268488al_val > $o ) > bop > product_prod_val_val > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_,type,
produc1287763389_val_o: ( produc1282892786on_val > $o ) > exp_list_char > produc2090907612on_val > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__String__Ochar_J_000_062_Itc__p,type,
produc1177570924_val_o: ( produc2088785539on_val > $o ) > list_char > ( produc1278157519t_char > option_val ) > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__String__Ochar_J_000tc__List__O,type,
produc1709467424char_o: ( produc1278157519t_char > $o ) > list_char > list_char > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__Value__Oval_000tc__Value__Oval_000_Eo,type,
produc575837646_val_o: ( product_prod_val_val > $o ) > val > val > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Stri,type,
produc803302844_val_o: ( produc1746408499on_val > $o ) > produc1282892786on_val > produc1282892786on_val > $o ).
thf(sy_c_Product__Type_Ointernal__split_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_,type,
produc575577405_val_o: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o ) > produc2090907612on_val > $o ).
thf(sy_c_Product__Type_Ointernal__split_000tc__Expr__Obop_000tc__prod_Itc__Value__Ov,type,
produc1476785425_val_o: ( bop > product_prod_val_val > $o ) > produc1645268488al_val > $o ).
thf(sy_c_Product__Type_Ointernal__split_000tc__Expr__Oexp_Itc__List__Olist_Itc__Stri,type,
produc900512295_val_o: ( exp_list_char > produc2090907612on_val > $o ) > produc1282892786on_val > $o ).
thf(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__String__Ochar_J_000_,type,
produc473466070_val_o: ( list_char > ( produc1278157519t_char > option_val ) > $o ) > produc2088785539on_val > $o ).
thf(sy_c_Product__Type_Ointernal__split_000tc__List__Olist_Itc__String__Ochar_J_000t,type,
produc1140826762char_o: ( list_char > list_char > $o ) > produc1278157519t_char > $o ).
thf(sy_c_Product__Type_Ointernal__split_000tc__Value__Oval_000tc__Value__Oval_000_Eo,type,
produc2001734200_val_o: ( val > val > $o ) > product_prod_val_val > $o ).
thf(sy_c_Product__Type_Ointernal__split_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist,type,
produc2006262054_val_o: ( produc1282892786on_val > produc1282892786on_val > $o ) > produc1746408499on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption,type,
produc546196114char_o: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > list_char > $o ) > produc2090907612on_val > list_char > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_043,type,
produc1075640496_nat_o: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > nat > $o ) > produc2090907612on_val > nat > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_044,type,
produc146628214_val_o: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2090907612on_val > $o ) > produc2090907612on_val > produc2090907612on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_045,type,
produc528569674_val_o: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1645268488al_val > $o ) > produc2090907612on_val > produc1645268488al_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_046,type,
produc74886368_val_o: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1282892786on_val > $o ) > produc2090907612on_val > produc1282892786on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_047,type,
produc1215095823_val_o: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2088785539on_val > $o ) > produc2090907612on_val > produc2088785539on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_048,type,
produc1880562923_val_o: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > product_prod_val_val > $o ) > produc2090907612on_val > product_prod_val_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_049,type,
produc252486962_val_o: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o ) > produc2090907612on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_050,type,
produc1442430405al_val: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1645268488al_val ) > produc2090907612on_val > produc1645268488al_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_051,type,
produc1016489647on_val: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1282892786on_val ) > produc2090907612on_val > produc1282892786on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_052,type,
produc2039683648on_val: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2088785539on_val ) > produc2090907612on_val > produc2088785539on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_053,type,
produc562949388t_char: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1278157519t_char ) > produc2090907612on_val > produc1278157519t_char ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_054,type,
produc794934116al_val: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > product_prod_val_val ) > produc2090907612on_val > product_prod_val_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_055,type,
produc1186953840on_val: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1746408499on_val ) > produc2090907612on_val > produc1746408499on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Obop_000tc__prod_Itc__Value__O,type,
produc1671601254char_o: ( bop > product_prod_val_val > list_char > $o ) > produc1645268488al_val > list_char > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Obop_000tc__prod_Itc__Value__O_056,type,
produc2010981340_nat_o: ( bop > product_prod_val_val > nat > $o ) > produc1645268488al_val > nat > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Obop_000tc__prod_Itc__Value__O_057,type,
produc1539816522_val_o: ( bop > product_prod_val_val > produc2090907612on_val > $o ) > produc1645268488al_val > produc2090907612on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Obop_000tc__prod_Itc__Value__O_058,type,
produc1554035486_val_o: ( bop > product_prod_val_val > produc1645268488al_val > $o ) > produc1645268488al_val > produc1645268488al_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Obop_000tc__prod_Itc__Value__O_059,type,
produc813528756_val_o: ( bop > product_prod_val_val > produc1282892786on_val > $o ) > produc1645268488al_val > produc1282892786on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Obop_000tc__prod_Itc__Value__O_060,type,
produc633541091_val_o: ( bop > product_prod_val_val > produc2088785539on_val > $o ) > produc1645268488al_val > produc2088785539on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Obop_000tc__prod_Itc__Value__O_061,type,
produc26920639_val_o: ( bop > product_prod_val_val > product_prod_val_val > $o ) > produc1645268488al_val > product_prod_val_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Obop_000tc__prod_Itc__Value__O_062,type,
produc1063861510_val_o: ( bop > product_prod_val_val > $o ) > produc1645268488al_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Obop_000tc__prod_Itc__Value__O_063,type,
produc1247631557on_val: ( bop > product_prod_val_val > produc2090907612on_val ) > produc1645268488al_val > produc2090907612on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Oexp_Itc__List__Olist_Itc__Str,type,
produc279240572char_o: ( exp_list_char > produc2090907612on_val > list_char > $o ) > produc1282892786on_val > list_char > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Oexp_Itc__List__Olist_Itc__Str_064,type,
produc1795400262_nat_o: ( exp_list_char > produc2090907612on_val > nat > $o ) > produc1282892786on_val > nat > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Oexp_Itc__List__Olist_Itc__Str_065,type,
produc1115879776_val_o: ( exp_list_char > produc2090907612on_val > produc2090907612on_val > $o ) > produc1282892786on_val > produc2090907612on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Oexp_Itc__List__Olist_Itc__Str_066,type,
produc156332084_val_o: ( exp_list_char > produc2090907612on_val > produc1645268488al_val > $o ) > produc1282892786on_val > produc1645268488al_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Oexp_Itc__List__Olist_Itc__Str_067,type,
produc68058570_val_o: ( exp_list_char > produc2090907612on_val > produc1282892786on_val > $o ) > produc1282892786on_val > produc1282892786on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Oexp_Itc__List__Olist_Itc__Str_068,type,
produc1552443129_val_o: ( exp_list_char > produc2090907612on_val > produc2088785539on_val > $o ) > produc1282892786on_val > produc2088785539on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Oexp_Itc__List__Olist_Itc__Str_069,type,
produc193813973_val_o: ( exp_list_char > produc2090907612on_val > product_prod_val_val > $o ) > produc1282892786on_val > product_prod_val_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Oexp_Itc__List__Olist_Itc__Str_070,type,
produc1835097372_val_o: ( exp_list_char > produc2090907612on_val > $o ) > produc1282892786on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Expr__Oexp_Itc__List__Olist_Itc__Str_071,type,
produc69760047on_val: ( exp_list_char > produc2090907612on_val > produc2090907612on_val ) > produc1282892786on_val > produc2090907612on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000,type,
produc1019934379char_o: ( list_char > ( produc1278157519t_char > option_val ) > list_char > $o ) > produc2088785539on_val > list_char > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_072,type,
produc1168407767_nat_o: ( list_char > ( produc1278157519t_char > option_val ) > nat > $o ) > produc2088785539on_val > nat > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_073,type,
produc371411343_val_o: ( list_char > ( produc1278157519t_char > option_val ) > produc2090907612on_val > $o ) > produc2088785539on_val > produc2090907612on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_074,type,
produc762675299_val_o: ( list_char > ( produc1278157519t_char > option_val ) > produc1645268488al_val > $o ) > produc2088785539on_val > produc1645268488al_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_075,type,
produc370364153_val_o: ( list_char > ( produc1278157519t_char > option_val ) > produc1282892786on_val > $o ) > produc2088785539on_val > produc1282892786on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_076,type,
produc250270504_val_o: ( list_char > ( produc1278157519t_char > option_val ) > produc2088785539on_val > $o ) > produc2088785539on_val > produc2088785539on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_077,type,
produc2105497348_val_o: ( list_char > ( produc1278157519t_char > option_val ) > product_prod_val_val > $o ) > produc2088785539on_val > product_prod_val_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_078,type,
produc765165771_val_o: ( list_char > ( produc1278157519t_char > option_val ) > $o ) > produc2088785539on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_079,type,
produc1349598016on_val: ( list_char > ( produc1278157519t_char > option_val ) > produc2090907612on_val ) > produc2088785539on_val > produc2090907612on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_080,type,
produc1602969823char_o: ( list_char > list_char > list_char > $o ) > produc1278157519t_char > list_char > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_081,type,
produc823420835_nat_o: ( list_char > list_char > nat > $o ) > produc1278157519t_char > nat > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_082,type,
produc1730830275_val_o: ( list_char > list_char > produc2090907612on_val > $o ) > produc1278157519t_char > produc2090907612on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_083,type,
produc967415447_val_o: ( list_char > list_char > produc1645268488al_val > $o ) > produc1278157519t_char > produc1645268488al_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_084,type,
produc1656516909_val_o: ( list_char > list_char > produc1282892786on_val > $o ) > produc1278157519t_char > produc1282892786on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_085,type,
produc584792412_val_o: ( list_char > list_char > produc2088785539on_val > $o ) > produc1278157519t_char > produc2088785539on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_086,type,
produc707156280_val_o: ( list_char > list_char > product_prod_val_val > $o ) > produc1278157519t_char > product_prod_val_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_087,type,
produc282231039char_o: ( list_char > list_char > $o ) > produc1278157519t_char > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__String__Ochar_J_000_088,type,
produc835075084on_val: ( list_char > list_char > produc2090907612on_val ) > produc1278157519t_char > produc2090907612on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Value__Oval_000tc__Value__Oval_000_0,type,
produc2042909709char_o: ( val > val > list_char > $o ) > product_prod_val_val > list_char > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Value__Oval_000tc__Value__Oval_000_0_089,type,
produc776580085_nat_o: ( val > val > nat > $o ) > product_prod_val_val > nat > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Value__Oval_000tc__Value__Oval_000_0_090,type,
produc1559655665_val_o: ( val > val > produc2090907612on_val > $o ) > product_prod_val_val > produc2090907612on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Value__Oval_000tc__Value__Oval_000_0_091,type,
produc1680944069_val_o: ( val > val > produc1645268488al_val > $o ) > product_prod_val_val > produc1645268488al_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Value__Oval_000tc__Value__Oval_000_0_092,type,
produc1702738011_val_o: ( val > val > produc1282892786on_val > $o ) > product_prod_val_val > produc1282892786on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Value__Oval_000tc__Value__Oval_000_0_093,type,
produc532727434_val_o: ( val > val > produc2088785539on_val > $o ) > product_prod_val_val > produc2088785539on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Value__Oval_000tc__Value__Oval_000_0_094,type,
produc844722278_val_o: ( val > val > product_prod_val_val > $o ) > product_prod_val_val > product_prod_val_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Value__Oval_000tc__Value__Oval_000_E,type,
produc9430317_val_o: ( val > val > $o ) > product_prod_val_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__Value__Oval_000tc__Value__Oval_000tc,type,
produc1893839198on_val: ( val > val > produc2090907612on_val ) > product_prod_val_val > produc2090907612on_val ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Expr__Oexp_Itc__List__Olis,type,
produc942102907char_o: ( produc1282892786on_val > produc1282892786on_val > list_char > $o ) > produc1746408499on_val > list_char > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Expr__Oexp_Itc__List__Olis_095,type,
produc1524362759_nat_o: ( produc1282892786on_val > produc1282892786on_val > nat > $o ) > produc1746408499on_val > nat > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Expr__Oexp_Itc__List__Olis_096,type,
produc793795679_val_o: ( produc1282892786on_val > produc1282892786on_val > produc2090907612on_val > $o ) > produc1746408499on_val > produc2090907612on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Expr__Oexp_Itc__List__Olis_097,type,
produc836145971_val_o: ( produc1282892786on_val > produc1282892786on_val > produc1645268488al_val > $o ) > produc1746408499on_val > produc1645268488al_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Expr__Oexp_Itc__List__Olis_098,type,
produc1798214089_val_o: ( produc1282892786on_val > produc1282892786on_val > produc1282892786on_val > $o ) > produc1746408499on_val > produc1282892786on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Expr__Oexp_Itc__List__Olis_099,type,
produc1122313720_val_o: ( produc1282892786on_val > produc1282892786on_val > produc2088785539on_val > $o ) > produc1746408499on_val > produc2088785539on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Expr__Oexp_Itc__List__Olis_100,type,
produc545397204_val_o: ( produc1282892786on_val > produc1282892786on_val > product_prod_val_val > $o ) > produc1746408499on_val > product_prod_val_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Expr__Oexp_Itc__List__Olis_101,type,
produc1624062875_val_o: ( produc1282892786on_val > produc1282892786on_val > $o ) > produc1746408499on_val > $o ).
thf(sy_c_Product__Type_Oprod_Oprod__case_000tc__prod_Itc__Expr__Oexp_Itc__List__Olis_102,type,
produc511181936on_val: ( produc1282892786on_val > produc1282892786on_val > produc2090907612on_val ) > produc1746408499on_val > produc2090907612on_val ).
thf(sy_c_SmallStep_Oassigned,type,
assigned: list_char > exp_list_char > $o ).
thf(sy_c_SmallStep_Ored,type,
red: list_P1999446415t_char > produc1746408499on_val > $o ).
thf(sy_c_SmallStep_Oredp,type,
redp: list_P1999446415t_char > exp_list_char > produc2090907612on_val > exp_list_char > produc2090907612on_val > $o ).
thf(sy_c_State_Ohp,type,
hp: produc2090907612on_val > nat > option1728594148on_val ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__List__Olist_Itc__String__Ochar_J,type,
transi1395422419t_char: ( produc1278157519t_char > $o ) > produc1278157519t_char > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_I,type,
transi2118771717on_val: ( produc1746408499on_val > $o ) > produc1746408499on_val > $o ).
thf(sy_c_Transitive__Closure_Ortranclp_000tc__List__Olist_Itc__String__Ochar_J,type,
transi1065307915t_char: ( list_char > list_char > $o ) > list_char > list_char > $o ).
thf(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 > list_char > $o ).
thf(sy_c_TypeRel_Osubcls1_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String_,type,
subcls851966956t_char: list_P1999446415t_char > produc1278157519t_char > $o ).
thf(sy_c_TypeRel_Osubcls1p_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String,type,
subcls744239332t_char: list_P1999446415t_char > list_char > list_char > $o ).
thf(sy_c_TypeRel_Owiden_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
widen_2090681816t_char: list_P1999446415t_char > ty > ty > $o ).
thf(sy_c_TypeSafe__Mirabelle__xxsvwfzwam_Osconf,type,
typeSa1102574168_sconf: list_P1999446415t_char > ( list_char > option_ty ) > produc2090907612on_val > $o ).
thf(sy_c_Type_Ois__refT,type,
is_refT: ty > $o ).
thf(sy_c_Type_Oty_OClass,type,
class: list_char > ty ).
thf(sy_c_Type_Oty_ONT,type,
nt: ty ).
thf(sy_c_Type_Oty_OVoid,type,
void: ty ).
thf(sy_c_Value_Oval_OAddr,type,
addr: nat > val ).
thf(sy_c_Value_Oval_OBool,type,
bool: $o > val ).
thf(sy_c_Value_Oval_ONull,type,
null: val ).
thf(sy_c_Value_Oval_OUnit,type,
unit: val ).
thf(sy_c_WWellForm_Owwf__J__mdecl,type,
wwf_J_mdecl: list_P1999446415t_char > list_char > produc1013743697t_char > $o ).
thf(sy_c_WellForm_Owf__prog_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Strin,type,
wf_pro755087577t_char: ( list_P1999446415t_char > list_char > produc1013743697t_char > $o ) > list_P1999446415t_char > $o ).
thf(sy_c_WellTypeRT_OWTrt,type,
wTrt: list_P1999446415t_char > ( nat > option1728594148on_val ) > ( list_char > option_ty ) > exp_list_char > ty > $o ).
thf(sy_c_member_000tc__List__Olist_Itc__String__Ochar_J,type,
member_list_char: list_char > ( list_char > $o ) > $o ).
thf(sy_c_member_000tc__Nat__Onat,type,
member_nat: nat > ( nat > $o ) > $o ).
thf(sy_c_member_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc_,type,
member1846553161on_val: produc2090907612on_val > ( produc2090907612on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__O,type,
member1417904245al_val: produc1645268488al_val > ( produc1645268488al_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_,type,
member1072200031on_val: produc1282892786on_val > ( produc1282892786on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc__prod_It,type,
member1374264560on_val: produc2088785539on_val > ( produc2088785539on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_I,type,
member1251428284t_char: produc1278157519t_char > ( produc1278157519t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J,type,
member649088532al_val: product_prod_val_val > ( product_prod_val_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__,type,
member1913460000on_val: produc1746408499on_val > ( produc1746408499on_val > $o ) > $o ).
thf(sy_v_E____,type,
e: list_char > option_ty ).
thf(sy_v_P,type,
p: list_P1999446415t_char ).
thf(sy_v_T_H____,type,
t: ty ).
thf(sy_v_T____,type,
t_1: ty ).
thf(sy_v_V____,type,
v_1: list_char ).
thf(sy_v_e_Ha____,type,
e_a: exp_list_char ).
thf(sy_v_ea____,type,
ea: exp_list_char ).
thf(sy_v_h_Ha____,type,
h_a: nat > option1728594148on_val ).
thf(sy_v_ha____,type,
ha: nat > option1728594148on_val ).
thf(sy_v_l_Ha____,type,
l_a: list_char > option_val ).
thf(sy_v_la____,type,
la: list_char > option_val ).
thf(sy_v_v_H____,type,
v_2: val ).
thf(sy_v_v____,type,
v: val ).
%----Relevant facts (700)
thf(fact_0_InitBlockRed_I3_J,axiom,
( ( l_a @ v_1 )
= ( some_val @ v_2 ) ) ).
thf(fact_1_InitBlockRed_I1_J,axiom,
member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ea @ ( produc755559506on_val @ ha @ ( fun_up1149430426on_val @ la @ v_1 @ ( some_val @ v ) ) ) ) @ ( produc235638504on_val @ e_a @ ( produc755559506on_val @ h_a @ l_a ) ) ) @ ( red @ p ) ).
thf(fact_2_fun__upd__triv,axiom,
! [F_21: list_char > option_val,X: list_char] :
( ( fun_up1149430426on_val @ F_21 @ X @ ( F_21 @ X ) )
= F_21 ) ).
thf(fact_3_fun__upd__triv,axiom,
! [F_21: list_char > option_ty,X: list_char] :
( ( fun_up424764369ion_ty @ F_21 @ X @ ( F_21 @ X ) )
= F_21 ) ).
thf(fact_4_fun__upd__triv,axiom,
! [F_21: nat > option1728594148on_val,X: nat] :
( ( fun_up1472480727on_val @ F_21 @ X @ ( F_21 @ X ) )
= F_21 ) ).
thf(fact_5_fun__upd__triv,axiom,
! [F_21: produc1278157519t_char > option_val,X: produc1278157519t_char] :
( ( fun_up204312361on_val @ F_21 @ X @ ( F_21 @ X ) )
= F_21 ) ).
thf(fact_6_assms,axiom,
wf_pro755087577t_char @ wf_J_mdecl @ p ).
thf(fact_7_map__upd__Some__unfold,axiom,
! [M_9: list_char > option_val,A_45: list_char,B_20: val,X_15: list_char,Y_13: val] :
( ( ( fun_up1149430426on_val @ M_9 @ A_45 @ ( some_val @ B_20 ) @ X_15 )
= ( some_val @ Y_13 ) )
<=> ( ( ( X_15 = A_45 )
& ( B_20 = Y_13 ) )
| ( ( X_15 != A_45 )
& ( ( M_9 @ X_15 )
= ( some_val @ Y_13 ) ) ) ) ) ).
thf(fact_8_map__upd__Some__unfold,axiom,
! [M_9: list_char > option_ty,A_45: list_char,B_20: ty,X_15: list_char,Y_13: ty] :
( ( ( fun_up424764369ion_ty @ M_9 @ A_45 @ ( some_ty @ B_20 ) @ X_15 )
= ( some_ty @ Y_13 ) )
<=> ( ( ( X_15 = A_45 )
& ( B_20 = Y_13 ) )
| ( ( X_15 != A_45 )
& ( ( M_9 @ X_15 )
= ( some_ty @ Y_13 ) ) ) ) ) ).
thf(fact_9_map__upd__Some__unfold,axiom,
! [M_9: nat > option1728594148on_val,A_45: nat,B_20: produc2088785539on_val,X_15: nat,Y_13: produc2088785539on_val] :
( ( ( fun_up1472480727on_val @ M_9 @ A_45 @ ( some_P451527732on_val @ B_20 ) @ X_15 )
= ( some_P451527732on_val @ Y_13 ) )
<=> ( ( ( X_15 = A_45 )
& ( B_20 = Y_13 ) )
| ( ( X_15 != A_45 )
& ( ( M_9 @ X_15 )
= ( some_P451527732on_val @ Y_13 ) ) ) ) ) ).
thf(fact_10_map__upd__Some__unfold,axiom,
! [M_9: produc1278157519t_char > option_val,A_45: produc1278157519t_char,B_20: val,X_15: produc1278157519t_char,Y_13: val] :
( ( ( fun_up204312361on_val @ M_9 @ A_45 @ ( some_val @ B_20 ) @ X_15 )
= ( some_val @ Y_13 ) )
<=> ( ( ( X_15 = A_45 )
& ( B_20 = Y_13 ) )
| ( ( X_15 != A_45 )
& ( ( M_9 @ X_15 )
= ( some_val @ Y_13 ) ) ) ) ) ).
thf(fact_11_map__upd__triv,axiom,
! [T_13: list_char > option_val,K_1: list_char,X_14: val] :
( ( ( T_13 @ K_1 )
= ( some_val @ X_14 ) )
=> ( ( fun_up1149430426on_val @ T_13 @ K_1 @ ( some_val @ X_14 ) )
= T_13 ) ) ).
thf(fact_12_map__upd__triv,axiom,
! [T_13: list_char > option_ty,K_1: list_char,X_14: ty] :
( ( ( T_13 @ K_1 )
= ( some_ty @ X_14 ) )
=> ( ( fun_up424764369ion_ty @ T_13 @ K_1 @ ( some_ty @ X_14 ) )
= T_13 ) ) ).
thf(fact_13_map__upd__triv,axiom,
! [T_13: nat > option1728594148on_val,K_1: nat,X_14: produc2088785539on_val] :
( ( ( T_13 @ K_1 )
= ( some_P451527732on_val @ X_14 ) )
=> ( ( fun_up1472480727on_val @ T_13 @ K_1 @ ( some_P451527732on_val @ X_14 ) )
= T_13 ) ) ).
thf(fact_14_map__upd__triv,axiom,
! [T_13: produc1278157519t_char > option_val,K_1: produc1278157519t_char,X_14: val] :
( ( ( T_13 @ K_1 )
= ( some_val @ X_14 ) )
=> ( ( fun_up204312361on_val @ T_13 @ K_1 @ ( some_val @ X_14 ) )
= T_13 ) ) ).
thf(fact_15_map__upd__eqD1,axiom,
! [M_8: list_char > option_val,A_44: list_char,X_13: val,N_1: list_char > option_val,Y_12: val] :
( ( ( fun_up1149430426on_val @ M_8 @ A_44 @ ( some_val @ X_13 ) )
= ( fun_up1149430426on_val @ N_1 @ A_44 @ ( some_val @ Y_12 ) ) )
=> ( X_13 = Y_12 ) ) ).
thf(fact_16_map__upd__eqD1,axiom,
! [M_8: list_char > option_ty,A_44: list_char,X_13: ty,N_1: list_char > option_ty,Y_12: ty] :
( ( ( fun_up424764369ion_ty @ M_8 @ A_44 @ ( some_ty @ X_13 ) )
= ( fun_up424764369ion_ty @ N_1 @ A_44 @ ( some_ty @ Y_12 ) ) )
=> ( X_13 = Y_12 ) ) ).
thf(fact_17_map__upd__eqD1,axiom,
! [M_8: nat > option1728594148on_val,A_44: nat,X_13: produc2088785539on_val,N_1: nat > option1728594148on_val,Y_12: produc2088785539on_val] :
( ( ( fun_up1472480727on_val @ M_8 @ A_44 @ ( some_P451527732on_val @ X_13 ) )
= ( fun_up1472480727on_val @ N_1 @ A_44 @ ( some_P451527732on_val @ Y_12 ) ) )
=> ( X_13 = Y_12 ) ) ).
thf(fact_18_map__upd__eqD1,axiom,
! [M_8: produc1278157519t_char > option_val,A_44: produc1278157519t_char,X_13: val,N_1: produc1278157519t_char > option_val,Y_12: val] :
( ( ( fun_up204312361on_val @ M_8 @ A_44 @ ( some_val @ X_13 ) )
= ( fun_up204312361on_val @ N_1 @ A_44 @ ( some_val @ Y_12 ) ) )
=> ( X_13 = Y_12 ) ) ).
thf(fact_19_InitBlockRed_I2_J,axiom,
! [T: ty,E_4: list_char > option_ty] :
( ( typeSa1102574168_sconf @ p @ E_4 @ ( produc755559506on_val @ ha @ ( fun_up1149430426on_val @ la @ v_1 @ ( some_val @ v ) ) ) )
=> ( ( wTrt @ p @ ha @ E_4 @ ea @ T )
=> ? [T_3: ty] :
( ( wTrt @ p @ h_a @ E_4 @ e_a @ T_3 )
& ( widen_2090681816t_char @ p @ T_3 @ T ) ) ) ) ).
thf(fact_20_prod__induct4,axiom,
! [X_12: produc1746408499on_val,P_22: produc1746408499on_val > $o] :
( ! [A: produc1282892786on_val,B_1: exp_list_char,C_11: nat > option1728594148on_val,D_2: list_char > option_val] : ( P_22 @ ( produc833389609on_val @ A @ ( produc235638504on_val @ B_1 @ ( produc755559506on_val @ C_11 @ D_2 ) ) ) )
=> ( P_22 @ X_12 ) ) ).
thf(fact_21_prod__cases4,axiom,
! [Y_11: produc1746408499on_val] :
~ ! [A: produc1282892786on_val,B_1: exp_list_char,C_11: nat > option1728594148on_val,D_2: list_char > option_val] :
( Y_11
!= ( produc833389609on_val @ A @ ( produc235638504on_val @ B_1 @ ( produc755559506on_val @ C_11 @ D_2 ) ) ) ) ).
thf(fact_22_InitBlockRed_I4_J,axiom,
typeSa1102574168_sconf @ p @ e @ ( produc755559506on_val @ ha @ la ) ).
thf(fact_23_Pair__inject,axiom,
! [A_43: produc1282892786on_val,B_19: produc1282892786on_val,A_42: produc1282892786on_val,B_18: produc1282892786on_val] :
( ( ( produc833389609on_val @ A_43 @ B_19 )
= ( produc833389609on_val @ A_42 @ B_18 ) )
=> ~ ( ( A_43 = A_42 )
=> ( B_19 != B_18 ) ) ) ).
thf(fact_24_Pair__inject,axiom,
! [A_43: exp_list_char,B_19: produc2090907612on_val,A_42: exp_list_char,B_18: produc2090907612on_val] :
( ( ( produc235638504on_val @ A_43 @ B_19 )
= ( produc235638504on_val @ A_42 @ B_18 ) )
=> ~ ( ( A_43 = A_42 )
=> ( B_19 != B_18 ) ) ) ).
thf(fact_25_Pair__inject,axiom,
! [A_43: nat > option1728594148on_val,B_19: list_char > option_val,A_42: nat > option1728594148on_val,B_18: list_char > option_val] :
( ( ( produc755559506on_val @ A_43 @ B_19 )
= ( produc755559506on_val @ A_42 @ B_18 ) )
=> ~ ( ( A_43 = A_42 )
=> ( B_19 != B_18 ) ) ) ).
thf(fact_26_Pair__inject,axiom,
! [A_43: list_char,B_19: produc1278157519t_char > option_val,A_42: list_char,B_18: produc1278157519t_char > option_val] :
( ( ( produc926070009on_val @ A_43 @ B_19 )
= ( produc926070009on_val @ A_42 @ B_18 ) )
=> ~ ( ( A_43 = A_42 )
=> ( B_19 != B_18 ) ) ) ).
thf(fact_27_Pair__inject,axiom,
! [A_43: list_char,B_19: list_char,A_42: list_char,B_18: list_char] :
( ( ( produc5062597t_char @ A_43 @ B_19 )
= ( produc5062597t_char @ A_42 @ B_18 ) )
=> ~ ( ( A_43 = A_42 )
=> ( B_19 != B_18 ) ) ) ).
thf(fact_28_Pair__inject,axiom,
! [A_43: bop,B_19: product_prod_val_val,A_42: bop,B_18: product_prod_val_val] :
( ( ( produc621191550al_val @ A_43 @ B_19 )
= ( produc621191550al_val @ A_42 @ B_18 ) )
=> ~ ( ( A_43 = A_42 )
=> ( B_19 != B_18 ) ) ) ).
thf(fact_29_Pair__inject,axiom,
! [A_43: val,B_19: val,A_42: val,B_18: val] :
( ( ( product_Pair_val_val @ A_43 @ B_19 )
= ( product_Pair_val_val @ A_42 @ B_18 ) )
=> ~ ( ( A_43 = A_42 )
=> ( B_19 != B_18 ) ) ) ).
thf(fact_30_Pair__eq,axiom,
! [A_41: produc1282892786on_val,B_17: produc1282892786on_val,A_40: produc1282892786on_val,B_16: produc1282892786on_val] :
( ( ( produc833389609on_val @ A_41 @ B_17 )
= ( produc833389609on_val @ A_40 @ B_16 ) )
<=> ( ( A_41 = A_40 )
& ( B_17 = B_16 ) ) ) ).
thf(fact_31_Pair__eq,axiom,
! [A_41: exp_list_char,B_17: produc2090907612on_val,A_40: exp_list_char,B_16: produc2090907612on_val] :
( ( ( produc235638504on_val @ A_41 @ B_17 )
= ( produc235638504on_val @ A_40 @ B_16 ) )
<=> ( ( A_41 = A_40 )
& ( B_17 = B_16 ) ) ) ).
thf(fact_32_Pair__eq,axiom,
! [A_41: nat > option1728594148on_val,B_17: list_char > option_val,A_40: nat > option1728594148on_val,B_16: list_char > option_val] :
( ( ( produc755559506on_val @ A_41 @ B_17 )
= ( produc755559506on_val @ A_40 @ B_16 ) )
<=> ( ( A_41 = A_40 )
& ( B_17 = B_16 ) ) ) ).
thf(fact_33_Pair__eq,axiom,
! [A_41: list_char,B_17: produc1278157519t_char > option_val,A_40: list_char,B_16: produc1278157519t_char > option_val] :
( ( ( produc926070009on_val @ A_41 @ B_17 )
= ( produc926070009on_val @ A_40 @ B_16 ) )
<=> ( ( A_41 = A_40 )
& ( B_17 = B_16 ) ) ) ).
thf(fact_34_Pair__eq,axiom,
! [A_41: list_char,B_17: list_char,A_40: list_char,B_16: list_char] :
( ( ( produc5062597t_char @ A_41 @ B_17 )
= ( produc5062597t_char @ A_40 @ B_16 ) )
<=> ( ( A_41 = A_40 )
& ( B_17 = B_16 ) ) ) ).
thf(fact_35_Pair__eq,axiom,
! [A_41: bop,B_17: product_prod_val_val,A_40: bop,B_16: product_prod_val_val] :
( ( ( produc621191550al_val @ A_41 @ B_17 )
= ( produc621191550al_val @ A_40 @ B_16 ) )
<=> ( ( A_41 = A_40 )
& ( B_17 = B_16 ) ) ) ).
thf(fact_36_Pair__eq,axiom,
! [A_41: val,B_17: val,A_40: val,B_16: val] :
( ( ( product_Pair_val_val @ A_41 @ B_17 )
= ( product_Pair_val_val @ A_40 @ B_16 ) )
<=> ( ( A_41 = A_40 )
& ( B_17 = B_16 ) ) ) ).
thf(fact_37_split__paired__All,axiom,
! [P_21: produc1746408499on_val > $o] :
( ( !! @ produc1746408499on_val @ P_21 )
<=> ! [A: produc1282892786on_val,B_1: produc1282892786on_val] : ( P_21 @ ( produc833389609on_val @ A @ B_1 ) ) ) ).
thf(fact_38_split__paired__All,axiom,
! [P_21: produc1282892786on_val > $o] :
( ( !! @ produc1282892786on_val @ P_21 )
<=> ! [A: exp_list_char,B_1: produc2090907612on_val] : ( P_21 @ ( produc235638504on_val @ A @ B_1 ) ) ) ).
thf(fact_39_split__paired__All,axiom,
! [P_21: produc2090907612on_val > $o] :
( ( !! @ produc2090907612on_val @ P_21 )
<=> ! [A: nat > option1728594148on_val,B_1: list_char > option_val] : ( P_21 @ ( produc755559506on_val @ A @ B_1 ) ) ) ).
thf(fact_40_split__paired__All,axiom,
! [P_21: produc2088785539on_val > $o] :
( ( !! @ produc2088785539on_val @ P_21 )
<=> ! [A: list_char,B_1: produc1278157519t_char > option_val] : ( P_21 @ ( produc926070009on_val @ A @ B_1 ) ) ) ).
thf(fact_41_split__paired__All,axiom,
! [P_21: produc1278157519t_char > $o] :
( ( !! @ produc1278157519t_char @ P_21 )
<=> ! [A: list_char,B_1: list_char] : ( P_21 @ ( produc5062597t_char @ A @ B_1 ) ) ) ).
thf(fact_42_split__paired__All,axiom,
! [P_21: produc1645268488al_val > $o] :
( ( !! @ produc1645268488al_val @ P_21 )
<=> ! [A: bop,B_1: product_prod_val_val] : ( P_21 @ ( produc621191550al_val @ A @ B_1 ) ) ) ).
thf(fact_43_split__paired__All,axiom,
! [P_21: product_prod_val_val > $o] :
( ( !! @ product_prod_val_val @ P_21 )
<=> ! [A: val,B_1: val] : ( P_21 @ ( product_Pair_val_val @ A @ B_1 ) ) ) ).
thf(fact_44_fun__upd__def,axiom,
! [F_20: list_char > option_val,B_15: option_val,A_39: list_char,X_1: list_char] :
( ( ( X_1 = A_39 )
=> ( ( fun_up1149430426on_val @ F_20 @ A_39 @ B_15 @ X_1 )
= B_15 ) )
& ( ( X_1 != A_39 )
=> ( ( fun_up1149430426on_val @ F_20 @ A_39 @ B_15 @ X_1 )
= ( F_20 @ X_1 ) ) ) ) ).
thf(fact_45_fun__upd__def,axiom,
! [F_20: list_char > option_ty,B_15: option_ty,A_39: list_char,X_1: list_char] :
( ( ( X_1 = A_39 )
=> ( ( fun_up424764369ion_ty @ F_20 @ A_39 @ B_15 @ X_1 )
= B_15 ) )
& ( ( X_1 != A_39 )
=> ( ( fun_up424764369ion_ty @ F_20 @ A_39 @ B_15 @ X_1 )
= ( F_20 @ X_1 ) ) ) ) ).
thf(fact_46_fun__upd__def,axiom,
! [F_20: nat > option1728594148on_val,B_15: option1728594148on_val,A_39: nat,X_1: nat] :
( ( ( X_1 = A_39 )
=> ( ( fun_up1472480727on_val @ F_20 @ A_39 @ B_15 @ X_1 )
= B_15 ) )
& ( ( X_1 != A_39 )
=> ( ( fun_up1472480727on_val @ F_20 @ A_39 @ B_15 @ X_1 )
= ( F_20 @ X_1 ) ) ) ) ).
thf(fact_47_fun__upd__def,axiom,
! [F_20: produc1278157519t_char > option_val,B_15: option_val,A_39: produc1278157519t_char,X_1: produc1278157519t_char] :
( ( ( X_1 = A_39 )
=> ( ( fun_up204312361on_val @ F_20 @ A_39 @ B_15 @ X_1 )
= B_15 ) )
& ( ( X_1 != A_39 )
=> ( ( fun_up204312361on_val @ F_20 @ A_39 @ B_15 @ X_1 )
= ( F_20 @ X_1 ) ) ) ) ).
thf(fact_48_fun__upd__idem,axiom,
! [F_19: list_char > option_val,X_11: list_char,Y_10: option_val] :
( ( ( F_19 @ X_11 )
= Y_10 )
=> ( ( fun_up1149430426on_val @ F_19 @ X_11 @ Y_10 )
= F_19 ) ) ).
thf(fact_49_fun__upd__idem,axiom,
! [F_19: list_char > option_ty,X_11: list_char,Y_10: option_ty] :
( ( ( F_19 @ X_11 )
= Y_10 )
=> ( ( fun_up424764369ion_ty @ F_19 @ X_11 @ Y_10 )
= F_19 ) ) ).
thf(fact_50_fun__upd__idem,axiom,
! [F_19: nat > option1728594148on_val,X_11: nat,Y_10: option1728594148on_val] :
( ( ( F_19 @ X_11 )
= Y_10 )
=> ( ( fun_up1472480727on_val @ F_19 @ X_11 @ Y_10 )
= F_19 ) ) ).
thf(fact_51_fun__upd__idem,axiom,
! [F_19: produc1278157519t_char > option_val,X_11: produc1278157519t_char,Y_10: option_val] :
( ( ( F_19 @ X_11 )
= Y_10 )
=> ( ( fun_up204312361on_val @ F_19 @ X_11 @ Y_10 )
= F_19 ) ) ).
thf(fact_52_fun__upd__other,axiom,
! [F_18: list_char > option_val,Y_9: option_val,Z_5: list_char,X_10: list_char] :
( ( Z_5 != X_10 )
=> ( ( fun_up1149430426on_val @ F_18 @ X_10 @ Y_9 @ Z_5 )
= ( F_18 @ Z_5 ) ) ) ).
thf(fact_53_fun__upd__other,axiom,
! [F_18: list_char > option_ty,Y_9: option_ty,Z_5: list_char,X_10: list_char] :
( ( Z_5 != X_10 )
=> ( ( fun_up424764369ion_ty @ F_18 @ X_10 @ Y_9 @ Z_5 )
= ( F_18 @ Z_5 ) ) ) ).
thf(fact_54_fun__upd__other,axiom,
! [F_18: nat > option1728594148on_val,Y_9: option1728594148on_val,Z_5: nat,X_10: nat] :
( ( Z_5 != X_10 )
=> ( ( fun_up1472480727on_val @ F_18 @ X_10 @ Y_9 @ Z_5 )
= ( F_18 @ Z_5 ) ) ) ).
thf(fact_55_fun__upd__other,axiom,
! [F_18: produc1278157519t_char > option_val,Y_9: option_val,Z_5: produc1278157519t_char,X_10: produc1278157519t_char] :
( ( Z_5 != X_10 )
=> ( ( fun_up204312361on_val @ F_18 @ X_10 @ Y_9 @ Z_5 )
= ( F_18 @ Z_5 ) ) ) ).
thf(fact_56_fun__upd__twist,axiom,
! [M_7: list_char > option_val,B_14: option_val,D_1: option_val,A_38: list_char,C_12: list_char] :
( ( A_38 != C_12 )
=> ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ M_7 @ A_38 @ B_14 ) @ C_12 @ D_1 )
= ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ M_7 @ C_12 @ D_1 ) @ A_38 @ B_14 ) ) ) ).
thf(fact_57_fun__upd__twist,axiom,
! [M_7: list_char > option_ty,B_14: option_ty,D_1: option_ty,A_38: list_char,C_12: list_char] :
( ( A_38 != C_12 )
=> ( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ M_7 @ A_38 @ B_14 ) @ C_12 @ D_1 )
= ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ M_7 @ C_12 @ D_1 ) @ A_38 @ B_14 ) ) ) ).
thf(fact_58_fun__upd__twist,axiom,
! [M_7: nat > option1728594148on_val,B_14: option1728594148on_val,D_1: option1728594148on_val,A_38: nat,C_12: nat] :
( ( A_38 != C_12 )
=> ( ( fun_up1472480727on_val @ ( fun_up1472480727on_val @ M_7 @ A_38 @ B_14 ) @ C_12 @ D_1 )
= ( fun_up1472480727on_val @ ( fun_up1472480727on_val @ M_7 @ C_12 @ D_1 ) @ A_38 @ B_14 ) ) ) ).
thf(fact_59_fun__upd__twist,axiom,
! [M_7: produc1278157519t_char > option_val,B_14: option_val,D_1: option_val,A_38: produc1278157519t_char,C_12: produc1278157519t_char] :
( ( A_38 != C_12 )
=> ( ( fun_up204312361on_val @ ( fun_up204312361on_val @ M_7 @ A_38 @ B_14 ) @ C_12 @ D_1 )
= ( fun_up204312361on_val @ ( fun_up204312361on_val @ M_7 @ C_12 @ D_1 ) @ A_38 @ B_14 ) ) ) ).
thf(fact_60_fun__upd__apply,axiom,
! [F_17: list_char > option_val,Y_8: option_val,Z_4: list_char,X_9: list_char] :
( ( ( Z_4 = X_9 )
=> ( ( fun_up1149430426on_val @ F_17 @ X_9 @ Y_8 @ Z_4 )
= Y_8 ) )
& ( ( Z_4 != X_9 )
=> ( ( fun_up1149430426on_val @ F_17 @ X_9 @ Y_8 @ Z_4 )
= ( F_17 @ Z_4 ) ) ) ) ).
thf(fact_61_fun__upd__apply,axiom,
! [F_17: list_char > option_ty,Y_8: option_ty,Z_4: list_char,X_9: list_char] :
( ( ( Z_4 = X_9 )
=> ( ( fun_up424764369ion_ty @ F_17 @ X_9 @ Y_8 @ Z_4 )
= Y_8 ) )
& ( ( Z_4 != X_9 )
=> ( ( fun_up424764369ion_ty @ F_17 @ X_9 @ Y_8 @ Z_4 )
= ( F_17 @ Z_4 ) ) ) ) ).
thf(fact_62_fun__upd__apply,axiom,
! [F_17: nat > option1728594148on_val,Y_8: option1728594148on_val,Z_4: nat,X_9: nat] :
( ( ( Z_4 = X_9 )
=> ( ( fun_up1472480727on_val @ F_17 @ X_9 @ Y_8 @ Z_4 )
= Y_8 ) )
& ( ( Z_4 != X_9 )
=> ( ( fun_up1472480727on_val @ F_17 @ X_9 @ Y_8 @ Z_4 )
= ( F_17 @ Z_4 ) ) ) ) ).
thf(fact_63_fun__upd__apply,axiom,
! [F_17: produc1278157519t_char > option_val,Y_8: option_val,Z_4: produc1278157519t_char,X_9: produc1278157519t_char] :
( ( ( Z_4 = X_9 )
=> ( ( fun_up204312361on_val @ F_17 @ X_9 @ Y_8 @ Z_4 )
= Y_8 ) )
& ( ( Z_4 != X_9 )
=> ( ( fun_up204312361on_val @ F_17 @ X_9 @ Y_8 @ Z_4 )
= ( F_17 @ Z_4 ) ) ) ) ).
thf(fact_64_fun__upd__same,axiom,
! [F_16: list_char > option_val,X_8: list_char,Y_7: option_val] :
( ( fun_up1149430426on_val @ F_16 @ X_8 @ Y_7 @ X_8 )
= Y_7 ) ).
thf(fact_65_fun__upd__same,axiom,
! [F_16: list_char > option_ty,X_8: list_char,Y_7: option_ty] :
( ( fun_up424764369ion_ty @ F_16 @ X_8 @ Y_7 @ X_8 )
= Y_7 ) ).
thf(fact_66_fun__upd__same,axiom,
! [F_16: nat > option1728594148on_val,X_8: nat,Y_7: option1728594148on_val] :
( ( fun_up1472480727on_val @ F_16 @ X_8 @ Y_7 @ X_8 )
= Y_7 ) ).
thf(fact_67_fun__upd__same,axiom,
! [F_16: produc1278157519t_char > option_val,X_8: produc1278157519t_char,Y_7: option_val] :
( ( fun_up204312361on_val @ F_16 @ X_8 @ Y_7 @ X_8 )
= Y_7 ) ).
thf(fact_68_fun__upd__upd,axiom,
! [F_15: list_char > option_val,X_7: list_char,Y_6: option_val,Z_3: option_val] :
( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ F_15 @ X_7 @ Y_6 ) @ X_7 @ Z_3 )
= ( fun_up1149430426on_val @ F_15 @ X_7 @ Z_3 ) ) ).
thf(fact_69_fun__upd__upd,axiom,
! [F_15: list_char > option_ty,X_7: list_char,Y_6: option_ty,Z_3: option_ty] :
( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ F_15 @ X_7 @ Y_6 ) @ X_7 @ Z_3 )
= ( fun_up424764369ion_ty @ F_15 @ X_7 @ Z_3 ) ) ).
thf(fact_70_fun__upd__upd,axiom,
! [F_15: nat > option1728594148on_val,X_7: nat,Y_6: option1728594148on_val,Z_3: option1728594148on_val] :
( ( fun_up1472480727on_val @ ( fun_up1472480727on_val @ F_15 @ X_7 @ Y_6 ) @ X_7 @ Z_3 )
= ( fun_up1472480727on_val @ F_15 @ X_7 @ Z_3 ) ) ).
thf(fact_71_fun__upd__upd,axiom,
! [F_15: produc1278157519t_char > option_val,X_7: produc1278157519t_char,Y_6: option_val,Z_3: option_val] :
( ( fun_up204312361on_val @ ( fun_up204312361on_val @ F_15 @ X_7 @ Y_6 ) @ X_7 @ Z_3 )
= ( fun_up204312361on_val @ F_15 @ X_7 @ Z_3 ) ) ).
thf(fact_72_fun__upd__idem__iff,axiom,
! [F_14: list_char > option_val,X_6: list_char,Y_5: option_val] :
( ( ( fun_up1149430426on_val @ F_14 @ X_6 @ Y_5 )
= F_14 )
<=> ( ( F_14 @ X_6 )
= Y_5 ) ) ).
thf(fact_73_fun__upd__idem__iff,axiom,
! [F_14: list_char > option_ty,X_6: list_char,Y_5: option_ty] :
( ( ( fun_up424764369ion_ty @ F_14 @ X_6 @ Y_5 )
= F_14 )
<=> ( ( F_14 @ X_6 )
= Y_5 ) ) ).
thf(fact_74_fun__upd__idem__iff,axiom,
! [F_14: nat > option1728594148on_val,X_6: nat,Y_5: option1728594148on_val] :
( ( ( fun_up1472480727on_val @ F_14 @ X_6 @ Y_5 )
= F_14 )
<=> ( ( F_14 @ X_6 )
= Y_5 ) ) ).
thf(fact_75_fun__upd__idem__iff,axiom,
! [F_14: produc1278157519t_char > option_val,X_6: produc1278157519t_char,Y_5: option_val] :
( ( ( fun_up204312361on_val @ F_14 @ X_6 @ Y_5 )
= F_14 )
<=> ( ( F_14 @ X_6 )
= Y_5 ) ) ).
thf(fact_76_widen__refl,axiom,
! [P_20: list_P1999446415t_char,T_12: ty] : ( widen_2090681816t_char @ P_20 @ T_12 @ T_12 ) ).
thf(fact_77_red__preserves__hconf,axiom,
! [E_4: list_char > option_ty,T: ty,E_1: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,E: exp_list_char,H_4: nat > option1728594148on_val,L_4: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_4 @ L_4 ) ) ) @ ( red @ P ) )
=> ( ( wTrt @ P @ H @ E_4 @ E_1 @ T )
=> ( ( hconf_97414254t_char @ P @ H )
=> ( hconf_97414254t_char @ P @ H_4 ) ) ) ) ).
thf(fact_78_red__preserves__lconf,axiom,
! [E_4: list_char > option_ty,T: ty,E_1: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,E: exp_list_char,H_4: nat > option1728594148on_val,L_4: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_4 @ L_4 ) ) ) @ ( red @ P ) )
=> ( ( wTrt @ P @ H @ E_4 @ E_1 @ T )
=> ( ( lconf_496643946t_char @ P @ H @ L @ E_4 )
=> ( lconf_496643946t_char @ P @ H_4 @ L_4 @ E_4 ) ) ) ) ).
thf(fact_79_prod__cases3,axiom,
! [Y_4: produc1746408499on_val] :
~ ! [A: produc1282892786on_val,B_1: exp_list_char,C_11: produc2090907612on_val] :
( Y_4
!= ( produc833389609on_val @ A @ ( produc235638504on_val @ B_1 @ C_11 ) ) ) ).
thf(fact_80_prod__cases3,axiom,
! [Y_4: produc1282892786on_val] :
~ ! [A: exp_list_char,B_1: nat > option1728594148on_val,C_11: list_char > option_val] :
( Y_4
!= ( produc235638504on_val @ A @ ( produc755559506on_val @ B_1 @ C_11 ) ) ) ).
thf(fact_81_prod__cases3,axiom,
! [Y_4: produc1645268488al_val] :
~ ! [A: bop,B_1: val,C_11: val] :
( Y_4
!= ( produc621191550al_val @ A @ ( product_Pair_val_val @ B_1 @ C_11 ) ) ) ).
thf(fact_82_prod__induct3,axiom,
! [X_5: produc1746408499on_val,P_19: produc1746408499on_val > $o] :
( ! [A: produc1282892786on_val,B_1: exp_list_char,C_11: produc2090907612on_val] : ( P_19 @ ( produc833389609on_val @ A @ ( produc235638504on_val @ B_1 @ C_11 ) ) )
=> ( P_19 @ X_5 ) ) ).
thf(fact_83_prod__induct3,axiom,
! [X_5: produc1282892786on_val,P_19: produc1282892786on_val > $o] :
( ! [A: exp_list_char,B_1: nat > option1728594148on_val,C_11: list_char > option_val] : ( P_19 @ ( produc235638504on_val @ A @ ( produc755559506on_val @ B_1 @ C_11 ) ) )
=> ( P_19 @ X_5 ) ) ).
thf(fact_84_prod__induct3,axiom,
! [X_5: produc1645268488al_val,P_19: produc1645268488al_val > $o] :
( ! [A: bop,B_1: val,C_11: val] : ( P_19 @ ( produc621191550al_val @ A @ ( product_Pair_val_val @ B_1 @ C_11 ) ) )
=> ( P_19 @ X_5 ) ) ).
thf(fact_85_red__preserves__sconf,axiom,
! [E_4: list_char > option_ty,T: ty,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( red @ P ) )
=> ( ( wTrt @ P @ ( hp @ S_2 ) @ E_4 @ E_1 @ T )
=> ( ( typeSa1102574168_sconf @ P @ E_4 @ S_2 )
=> ( typeSa1102574168_sconf @ P @ E_4 @ S ) ) ) ) ).
thf(fact_86_pred__equals__eq2,axiom,
! [S_6: produc1282892786on_val > $o,R: produc1282892786on_val > $o] :
( ! [X_1: exp_list_char,Xa: produc2090907612on_val] :
( ( member1072200031on_val @ ( produc235638504on_val @ X_1 @ Xa ) @ R )
<=> ( member1072200031on_val @ ( produc235638504on_val @ X_1 @ Xa ) @ S_6 ) )
<=> ( R = S_6 ) ) ).
thf(fact_87_pred__equals__eq2,axiom,
! [S_6: produc2090907612on_val > $o,R: produc2090907612on_val > $o] :
( ! [X_1: nat > option1728594148on_val,Xa: list_char > option_val] :
( ( member1846553161on_val @ ( produc755559506on_val @ X_1 @ Xa ) @ R )
<=> ( member1846553161on_val @ ( produc755559506on_val @ X_1 @ Xa ) @ S_6 ) )
<=> ( R = S_6 ) ) ).
thf(fact_88_pred__equals__eq2,axiom,
! [S_6: produc2088785539on_val > $o,R: produc2088785539on_val > $o] :
( ! [X_1: list_char,Xa: produc1278157519t_char > option_val] :
( ( member1374264560on_val @ ( produc926070009on_val @ X_1 @ Xa ) @ R )
<=> ( member1374264560on_val @ ( produc926070009on_val @ X_1 @ Xa ) @ S_6 ) )
<=> ( R = S_6 ) ) ).
thf(fact_89_pred__equals__eq2,axiom,
! [S_6: produc1645268488al_val > $o,R: produc1645268488al_val > $o] :
( ! [X_1: bop,Xa: product_prod_val_val] :
( ( member1417904245al_val @ ( produc621191550al_val @ X_1 @ Xa ) @ R )
<=> ( member1417904245al_val @ ( produc621191550al_val @ X_1 @ Xa ) @ S_6 ) )
<=> ( R = S_6 ) ) ).
thf(fact_90_pred__equals__eq2,axiom,
! [S_6: product_prod_val_val > $o,R: product_prod_val_val > $o] :
( ! [X_1: val,Xa: val] :
( ( member649088532al_val @ ( product_Pair_val_val @ X_1 @ Xa ) @ R )
<=> ( member649088532al_val @ ( product_Pair_val_val @ X_1 @ Xa ) @ S_6 ) )
<=> ( R = S_6 ) ) ).
thf(fact_91_pred__equals__eq2,axiom,
! [S_6: produc1746408499on_val > $o,R: produc1746408499on_val > $o] :
( ! [X_1: produc1282892786on_val,Xa: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ X_1 @ Xa ) @ R )
<=> ( member1913460000on_val @ ( produc833389609on_val @ X_1 @ Xa ) @ S_6 ) )
<=> ( R = S_6 ) ) ).
thf(fact_92_pred__equals__eq2,axiom,
! [S_6: produc1278157519t_char > $o,R: produc1278157519t_char > $o] :
( ! [X_1: list_char,Xa: list_char] :
( ( member1251428284t_char @ ( produc5062597t_char @ X_1 @ Xa ) @ R )
<=> ( member1251428284t_char @ ( produc5062597t_char @ X_1 @ Xa ) @ S_6 ) )
<=> ( R = S_6 ) ) ).
thf(fact_93_prod_Oexhaust,axiom,
! [Y_3: produc1746408499on_val] :
~ ! [A: produc1282892786on_val,B_1: produc1282892786on_val] :
( Y_3
!= ( produc833389609on_val @ A @ B_1 ) ) ).
thf(fact_94_prod_Oexhaust,axiom,
! [Y_3: produc1282892786on_val] :
~ ! [A: exp_list_char,B_1: produc2090907612on_val] :
( Y_3
!= ( produc235638504on_val @ A @ B_1 ) ) ).
thf(fact_95_prod_Oexhaust,axiom,
! [Y_3: produc2090907612on_val] :
~ ! [A: nat > option1728594148on_val,B_1: list_char > option_val] :
( Y_3
!= ( produc755559506on_val @ A @ B_1 ) ) ).
thf(fact_96_prod_Oexhaust,axiom,
! [Y_3: produc2088785539on_val] :
~ ! [A: list_char,B_1: produc1278157519t_char > option_val] :
( Y_3
!= ( produc926070009on_val @ A @ B_1 ) ) ).
thf(fact_97_prod_Oexhaust,axiom,
! [Y_3: produc1278157519t_char] :
~ ! [A: list_char,B_1: list_char] :
( Y_3
!= ( produc5062597t_char @ A @ B_1 ) ) ).
thf(fact_98_prod_Oexhaust,axiom,
! [Y_3: produc1645268488al_val] :
~ ! [A: bop,B_1: product_prod_val_val] :
( Y_3
!= ( produc621191550al_val @ A @ B_1 ) ) ).
thf(fact_99_prod_Oexhaust,axiom,
! [Y_3: product_prod_val_val] :
~ ! [A: val,B_1: val] :
( Y_3
!= ( product_Pair_val_val @ A @ B_1 ) ) ).
thf(fact_100_PairE,axiom,
! [P_18: produc1746408499on_val] :
~ ! [X_1: produc1282892786on_val,Y_1: produc1282892786on_val] :
( P_18
!= ( produc833389609on_val @ X_1 @ Y_1 ) ) ).
thf(fact_101_PairE,axiom,
! [P_18: produc1282892786on_val] :
~ ! [X_1: exp_list_char,Y_1: produc2090907612on_val] :
( P_18
!= ( produc235638504on_val @ X_1 @ Y_1 ) ) ).
thf(fact_102_PairE,axiom,
! [P_18: produc2090907612on_val] :
~ ! [X_1: nat > option1728594148on_val,Y_1: list_char > option_val] :
( P_18
!= ( produc755559506on_val @ X_1 @ Y_1 ) ) ).
thf(fact_103_PairE,axiom,
! [P_18: produc2088785539on_val] :
~ ! [X_1: list_char,Y_1: produc1278157519t_char > option_val] :
( P_18
!= ( produc926070009on_val @ X_1 @ Y_1 ) ) ).
thf(fact_104_PairE,axiom,
! [P_18: produc1278157519t_char] :
~ ! [X_1: list_char,Y_1: list_char] :
( P_18
!= ( produc5062597t_char @ X_1 @ Y_1 ) ) ).
thf(fact_105_PairE,axiom,
! [P_18: produc1645268488al_val] :
~ ! [X_1: bop,Y_1: product_prod_val_val] :
( P_18
!= ( produc621191550al_val @ X_1 @ Y_1 ) ) ).
thf(fact_106_PairE,axiom,
! [P_18: product_prod_val_val] :
~ ! [X_1: val,Y_1: val] :
( P_18
!= ( product_Pair_val_val @ X_1 @ Y_1 ) ) ).
thf(fact_107_split__paired__Ex,axiom,
! [P_17: produc1746408499on_val > $o] :
( ( ?? @ produc1746408499on_val @ P_17 )
<=> ? [A: produc1282892786on_val,B_1: produc1282892786on_val] : ( P_17 @ ( produc833389609on_val @ A @ B_1 ) ) ) ).
thf(fact_108_split__paired__Ex,axiom,
! [P_17: produc1282892786on_val > $o] :
( ( ?? @ produc1282892786on_val @ P_17 )
<=> ? [A: exp_list_char,B_1: produc2090907612on_val] : ( P_17 @ ( produc235638504on_val @ A @ B_1 ) ) ) ).
thf(fact_109_split__paired__Ex,axiom,
! [P_17: produc2090907612on_val > $o] :
( ( ?? @ produc2090907612on_val @ P_17 )
<=> ? [A: nat > option1728594148on_val,B_1: list_char > option_val] : ( P_17 @ ( produc755559506on_val @ A @ B_1 ) ) ) ).
thf(fact_110_split__paired__Ex,axiom,
! [P_17: produc2088785539on_val > $o] :
( ( ?? @ produc2088785539on_val @ P_17 )
<=> ? [A: list_char,B_1: produc1278157519t_char > option_val] : ( P_17 @ ( produc926070009on_val @ A @ B_1 ) ) ) ).
thf(fact_111_split__paired__Ex,axiom,
! [P_17: produc1278157519t_char > $o] :
( ( ?? @ produc1278157519t_char @ P_17 )
<=> ? [A: list_char,B_1: list_char] : ( P_17 @ ( produc5062597t_char @ A @ B_1 ) ) ) ).
thf(fact_112_split__paired__Ex,axiom,
! [P_17: produc1645268488al_val > $o] :
( ( ?? @ produc1645268488al_val @ P_17 )
<=> ? [A: bop,B_1: product_prod_val_val] : ( P_17 @ ( produc621191550al_val @ A @ B_1 ) ) ) ).
thf(fact_113_split__paired__Ex,axiom,
! [P_17: product_prod_val_val > $o] :
( ( ?? @ product_prod_val_val @ P_17 )
<=> ? [A: val,B_1: val] : ( P_17 @ ( product_Pair_val_val @ A @ B_1 ) ) ) ).
thf(fact_114_widen__trans,axiom,
! [T_11: ty,P_16: list_P1999446415t_char,S_5: ty,U_1: ty] :
( ( widen_2090681816t_char @ P_16 @ S_5 @ U_1 )
=> ( ( widen_2090681816t_char @ P_16 @ U_1 @ T_11 )
=> ( widen_2090681816t_char @ P_16 @ S_5 @ T_11 ) ) ) ).
thf(fact_115_InitBlockRed_I5_J,axiom,
wTrt @ p @ ha @ e @ ( block_list_char @ v_1 @ t_1 @ ( seq_list_char @ ( lAss_list_char @ v_1 @ ( val_list_char @ v ) ) @ ea ) ) @ t ).
thf(fact_116_internal__split__conv,axiom,
! [C_10: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,A_37: nat > option1728594148on_val,B_13: list_char > option_val] :
( ( produc575577405_val_o @ C_10 @ ( produc755559506on_val @ A_37 @ B_13 ) )
<=> ( C_10 @ A_37 @ B_13 ) ) ).
thf(fact_117_sconf__def,axiom,
! [P: list_P1999446415t_char,E_4: list_char > option_ty,S_2: produc2090907612on_val] :
( ( typeSa1102574168_sconf @ P @ E_4 @ S_2 )
<=> ( produc252486962_val_o
@ ^ [H_3: nat > option1728594148on_val,L_3: list_char > option_val] : ( (&) @ ( hconf_97414254t_char @ P @ H_3 ) @ ( lconf_496643946t_char @ P @ H_3 @ L_3 @ E_4 ) )
@ S_2 ) ) ).
thf(fact_118_red__hext__incr,axiom,
! [E_1: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,E: exp_list_char,H_4: nat > option1728594148on_val,L_4: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_4 @ L_4 ) ) ) @ ( red @ P ) )
=> ( hext @ H @ H_4 ) ) ).
thf(fact_119_curry__def,axiom,
! [X_1: produc1746408499on_val > $o,Xa: produc1282892786on_val,Xb: produc1282892786on_val] :
( ( produc803302844_val_o @ X_1 @ Xa @ Xb )
<=> ( X_1 @ ( produc833389609on_val @ Xa @ Xb ) ) ) ).
thf(fact_120_curry__def,axiom,
! [X_1: produc1282892786on_val > $o,Xa: exp_list_char,Xb: produc2090907612on_val] :
( ( produc1287763389_val_o @ X_1 @ Xa @ Xb )
<=> ( X_1 @ ( produc235638504on_val @ Xa @ Xb ) ) ) ).
thf(fact_121_curry__def,axiom,
! [X_1: produc2090907612on_val > $o,Xa: nat > option1728594148on_val,Xb: list_char > option_val] :
( ( produc1402621651_val_o @ X_1 @ Xa @ Xb )
<=> ( X_1 @ ( produc755559506on_val @ Xa @ Xb ) ) ) ).
thf(fact_122_curry__def,axiom,
! [X_1: produc2088785539on_val > $o,Xa: list_char,Xb: produc1278157519t_char > option_val] :
( ( produc1177570924_val_o @ X_1 @ Xa @ Xb )
<=> ( X_1 @ ( produc926070009on_val @ Xa @ Xb ) ) ) ).
thf(fact_123_curry__def,axiom,
! [X_1: produc1278157519t_char > $o,Xa: list_char,Xb: list_char] :
( ( produc1709467424char_o @ X_1 @ Xa @ Xb )
<=> ( X_1 @ ( produc5062597t_char @ Xa @ Xb ) ) ) ).
thf(fact_124_curry__def,axiom,
! [X_1: produc1645268488al_val > $o,Xa: bop,Xb: product_prod_val_val] :
( ( produc275195559_val_o @ X_1 @ Xa @ Xb )
<=> ( X_1 @ ( produc621191550al_val @ Xa @ Xb ) ) ) ).
thf(fact_125_curry__def,axiom,
! [X_1: product_prod_val_val > $o,Xa: val,Xb: val] :
( ( produc575837646_val_o @ X_1 @ Xa @ Xb )
<=> ( X_1 @ ( product_Pair_val_val @ Xa @ Xb ) ) ) ).
thf(fact_126_red__preserves__defass,axiom,
! [E_1: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,E: exp_list_char,H_4: nat > option1728594148on_val,L_4: list_char > option_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wf_J_mdecl @ P )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_4 @ L_4 ) ) ) @ ( red @ P ) )
=> ( ( d_list_char @ E_1 @ ( some_list_char_o @ ( dom_list_char_val @ L ) ) )
=> ( d_list_char @ E @ ( some_list_char_o @ ( dom_list_char_val @ L_4 ) ) ) ) ) ) ).
thf(fact_127_option_Oinject,axiom,
! [A_36: val,A_35: val] :
( ( ( some_val @ A_36 )
= ( some_val @ A_35 ) )
<=> ( A_36 = A_35 ) ) ).
thf(fact_128_option_Oinject,axiom,
! [A_36: list_char > $o,A_35: list_char > $o] :
( ( ( some_list_char_o @ A_36 )
= ( some_list_char_o @ A_35 ) )
<=> ( A_36 = A_35 ) ) ).
thf(fact_129_option_Oinject,axiom,
! [A_36: ty,A_35: ty] :
( ( ( some_ty @ A_36 )
= ( some_ty @ A_35 ) )
<=> ( A_36 = A_35 ) ) ).
thf(fact_130_option_Oinject,axiom,
! [A_36: produc2088785539on_val,A_35: produc2088785539on_val] :
( ( ( some_P451527732on_val @ A_36 )
= ( some_P451527732on_val @ A_35 ) )
<=> ( A_36 = A_35 ) ) ).
thf(fact_131_curryI,axiom,
! [F_13: produc1746408499on_val > $o,A_34: produc1282892786on_val,B_12: produc1282892786on_val] :
( ( F_13 @ ( produc833389609on_val @ A_34 @ B_12 ) )
=> ( produc803302844_val_o @ F_13 @ A_34 @ B_12 ) ) ).
thf(fact_132_curryI,axiom,
! [F_13: produc1282892786on_val > $o,A_34: exp_list_char,B_12: produc2090907612on_val] :
( ( F_13 @ ( produc235638504on_val @ A_34 @ B_12 ) )
=> ( produc1287763389_val_o @ F_13 @ A_34 @ B_12 ) ) ).
thf(fact_133_curryI,axiom,
! [F_13: produc2090907612on_val > $o,A_34: nat > option1728594148on_val,B_12: list_char > option_val] :
( ( F_13 @ ( produc755559506on_val @ A_34 @ B_12 ) )
=> ( produc1402621651_val_o @ F_13 @ A_34 @ B_12 ) ) ).
thf(fact_134_curryI,axiom,
! [F_13: produc2088785539on_val > $o,A_34: list_char,B_12: produc1278157519t_char > option_val] :
( ( F_13 @ ( produc926070009on_val @ A_34 @ B_12 ) )
=> ( produc1177570924_val_o @ F_13 @ A_34 @ B_12 ) ) ).
thf(fact_135_curryI,axiom,
! [F_13: produc1278157519t_char > $o,A_34: list_char,B_12: list_char] :
( ( F_13 @ ( produc5062597t_char @ A_34 @ B_12 ) )
=> ( produc1709467424char_o @ F_13 @ A_34 @ B_12 ) ) ).
thf(fact_136_curryI,axiom,
! [F_13: produc1645268488al_val > $o,A_34: bop,B_12: product_prod_val_val] :
( ( F_13 @ ( produc621191550al_val @ A_34 @ B_12 ) )
=> ( produc275195559_val_o @ F_13 @ A_34 @ B_12 ) ) ).
thf(fact_137_curryI,axiom,
! [F_13: product_prod_val_val > $o,A_34: val,B_12: val] :
( ( F_13 @ ( product_Pair_val_val @ A_34 @ B_12 ) )
=> ( produc575837646_val_o @ F_13 @ A_34 @ B_12 ) ) ).
thf(fact_138_red__lcl__add,axiom,
! [L_0_1: list_char > option_val,E_1: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,E: exp_list_char,H_4: nat > option1728594148on_val,L_4: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_4 @ L_4 ) ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ ( map_ad325961431ar_val @ L_0_1 @ L ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_4 @ ( map_ad325961431ar_val @ L_0_1 @ L_4 ) ) ) ) @ ( red @ P ) ) ) ).
thf(fact_139_lconf__upd,axiom,
! [V_14: list_char,V_13: val,T_10: ty,P_15: list_P1999446415t_char,H_15: nat > option1728594148on_val,L_8: list_char > option_val,E_11: list_char > option_ty] :
( ( lconf_496643946t_char @ P_15 @ H_15 @ L_8 @ E_11 )
=> ( ( conf_P373316194t_char @ P_15 @ H_15 @ V_13 @ T_10 )
=> ( ( ( E_11 @ V_14 )
= ( some_ty @ T_10 ) )
=> ( lconf_496643946t_char @ P_15 @ H_15 @ ( fun_up1149430426on_val @ L_8 @ V_14 @ ( some_val @ V_13 ) ) @ E_11 ) ) ) ) ).
thf(fact_140_prod__caseI,axiom,
! [F1_1: produc1282892786on_val > produc1282892786on_val > $o,A_33: produc1282892786on_val,B_11: produc1282892786on_val] :
( ( F1_1 @ A_33 @ B_11 )
=> ( produc1624062875_val_o @ F1_1 @ ( produc833389609on_val @ A_33 @ B_11 ) ) ) ).
thf(fact_141_prod__caseI,axiom,
! [F1_1: exp_list_char > produc2090907612on_val > $o,A_33: exp_list_char,B_11: produc2090907612on_val] :
( ( F1_1 @ A_33 @ B_11 )
=> ( produc1835097372_val_o @ F1_1 @ ( produc235638504on_val @ A_33 @ B_11 ) ) ) ).
thf(fact_142_prod__caseI,axiom,
! [F1_1: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,A_33: nat > option1728594148on_val,B_11: list_char > option_val] :
( ( F1_1 @ A_33 @ B_11 )
=> ( produc252486962_val_o @ F1_1 @ ( produc755559506on_val @ A_33 @ B_11 ) ) ) ).
thf(fact_143_prod__caseI,axiom,
! [F1_1: list_char > ( produc1278157519t_char > option_val ) > $o,A_33: list_char,B_11: produc1278157519t_char > option_val] :
( ( F1_1 @ A_33 @ B_11 )
=> ( produc765165771_val_o @ F1_1 @ ( produc926070009on_val @ A_33 @ B_11 ) ) ) ).
thf(fact_144_prod__caseI,axiom,
! [F1_1: list_char > list_char > $o,A_33: list_char,B_11: list_char] :
( ( F1_1 @ A_33 @ B_11 )
=> ( produc282231039char_o @ F1_1 @ ( produc5062597t_char @ A_33 @ B_11 ) ) ) ).
thf(fact_145_prod__caseI,axiom,
! [F1_1: bop > product_prod_val_val > $o,A_33: bop,B_11: product_prod_val_val] :
( ( F1_1 @ A_33 @ B_11 )
=> ( produc1063861510_val_o @ F1_1 @ ( produc621191550al_val @ A_33 @ B_11 ) ) ) ).
thf(fact_146_prod__caseI,axiom,
! [F1_1: val > val > $o,A_33: val,B_11: val] :
( ( F1_1 @ A_33 @ B_11 )
=> ( produc9430317_val_o @ F1_1 @ ( product_Pair_val_val @ A_33 @ B_11 ) ) ) ).
thf(fact_147_splitI,axiom,
! [F_12: produc1282892786on_val > produc1282892786on_val > $o,A_32: produc1282892786on_val,B_10: produc1282892786on_val] :
( ( F_12 @ A_32 @ B_10 )
=> ( produc1624062875_val_o @ F_12 @ ( produc833389609on_val @ A_32 @ B_10 ) ) ) ).
thf(fact_148_splitI,axiom,
! [F_12: exp_list_char > produc2090907612on_val > $o,A_32: exp_list_char,B_10: produc2090907612on_val] :
( ( F_12 @ A_32 @ B_10 )
=> ( produc1835097372_val_o @ F_12 @ ( produc235638504on_val @ A_32 @ B_10 ) ) ) ).
thf(fact_149_splitI,axiom,
! [F_12: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,A_32: nat > option1728594148on_val,B_10: list_char > option_val] :
( ( F_12 @ A_32 @ B_10 )
=> ( produc252486962_val_o @ F_12 @ ( produc755559506on_val @ A_32 @ B_10 ) ) ) ).
thf(fact_150_splitI,axiom,
! [F_12: list_char > ( produc1278157519t_char > option_val ) > $o,A_32: list_char,B_10: produc1278157519t_char > option_val] :
( ( F_12 @ A_32 @ B_10 )
=> ( produc765165771_val_o @ F_12 @ ( produc926070009on_val @ A_32 @ B_10 ) ) ) ).
thf(fact_151_splitI,axiom,
! [F_12: list_char > list_char > $o,A_32: list_char,B_10: list_char] :
( ( F_12 @ A_32 @ B_10 )
=> ( produc282231039char_o @ F_12 @ ( produc5062597t_char @ A_32 @ B_10 ) ) ) ).
thf(fact_152_splitI,axiom,
! [F_12: bop > product_prod_val_val > $o,A_32: bop,B_10: product_prod_val_val] :
( ( F_12 @ A_32 @ B_10 )
=> ( produc1063861510_val_o @ F_12 @ ( produc621191550al_val @ A_32 @ B_10 ) ) ) ).
thf(fact_153_splitI,axiom,
! [F_12: val > val > $o,A_32: val,B_10: val] :
( ( F_12 @ A_32 @ B_10 )
=> ( produc9430317_val_o @ F_12 @ ( product_Pair_val_val @ A_32 @ B_10 ) ) ) ).
thf(fact_154_conf__hext,axiom,
! [P_14: list_P1999446415t_char,V_12: val,T_9: ty,H_14: nat > option1728594148on_val,H_13: nat > option1728594148on_val] :
( ( hext @ H_14 @ H_13 )
=> ( ( conf_P373316194t_char @ P_14 @ H_14 @ V_12 @ T_9 )
=> ( conf_P373316194t_char @ P_14 @ H_13 @ V_12 @ T_9 ) ) ) ).
thf(fact_155_conf__upd__obj,axiom,
! [P_13: list_P1999446415t_char,Fs_7: produc1278157519t_char > option_val,X_4: val,T_8: ty,H_12: nat > option1728594148on_val,A_31: nat,C_9: list_char,Fs_6: produc1278157519t_char > option_val] :
( ( ( H_12 @ A_31 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_9 @ Fs_6 ) ) )
=> ( ( conf_P373316194t_char @ P_13 @ ( fun_up1472480727on_val @ H_12 @ A_31 @ ( some_P451527732on_val @ ( produc926070009on_val @ C_9 @ Fs_7 ) ) ) @ X_4 @ T_8 )
<=> ( conf_P373316194t_char @ P_13 @ H_12 @ X_4 @ T_8 ) ) ) ).
thf(fact_156_map__add__dom__app__simps_I1_J,axiom,
! [L1_2: nat > option1728594148on_val,M_6: nat,L2_2: nat > option1728594148on_val] :
( ( member_nat @ M_6 @ ( dom_na2045926843on_val @ L2_2 ) )
=> ( ( map_ad1851375512on_val @ L1_2 @ L2_2 @ M_6 )
= ( L2_2 @ M_6 ) ) ) ).
thf(fact_157_map__add__dom__app__simps_I1_J,axiom,
! [L1_2: list_char > option_ty,M_6: list_char,L2_2: list_char > option_ty] :
( ( member_list_char @ M_6 @ ( dom_list_char_ty @ L2_2 ) )
=> ( ( map_add_list_char_ty @ L1_2 @ L2_2 @ M_6 )
= ( L2_2 @ M_6 ) ) ) ).
thf(fact_158_map__add__dom__app__simps_I1_J,axiom,
! [L1_2: produc1278157519t_char > option_val,M_6: produc1278157519t_char,L2_2: produc1278157519t_char > option_val] :
( ( member1251428284t_char @ M_6 @ ( dom_Pr695701035ar_val @ L2_2 ) )
=> ( ( map_ad1185064968ar_val @ L1_2 @ L2_2 @ M_6 )
= ( L2_2 @ M_6 ) ) ) ).
thf(fact_159_map__add__dom__app__simps_I1_J,axiom,
! [L1_2: list_char > option_val,M_6: list_char,L2_2: list_char > option_val] :
( ( member_list_char @ M_6 @ ( dom_list_char_val @ L2_2 ) )
=> ( ( map_ad325961431ar_val @ L1_2 @ L2_2 @ M_6 )
= ( L2_2 @ M_6 ) ) ) ).
thf(fact_160_split__weak__cong,axiom,
! [C_8: val > val > $o,P_12: product_prod_val_val,Q_2: product_prod_val_val] :
( ( P_12 = Q_2 )
=> ( ( produc9430317_val_o @ C_8 @ P_12 )
<=> ( produc9430317_val_o @ C_8 @ Q_2 ) ) ) ).
thf(fact_161_split__weak__cong,axiom,
! [C_8: bop > product_prod_val_val > $o,P_12: produc1645268488al_val,Q_2: produc1645268488al_val] :
( ( P_12 = Q_2 )
=> ( ( produc1063861510_val_o @ C_8 @ P_12 )
<=> ( produc1063861510_val_o @ C_8 @ Q_2 ) ) ) ).
thf(fact_162_split__weak__cong,axiom,
! [C_8: list_char > list_char > $o,P_12: produc1278157519t_char,Q_2: produc1278157519t_char] :
( ( P_12 = Q_2 )
=> ( ( produc282231039char_o @ C_8 @ P_12 )
<=> ( produc282231039char_o @ C_8 @ Q_2 ) ) ) ).
thf(fact_163_split__weak__cong,axiom,
! [C_8: list_char > ( produc1278157519t_char > option_val ) > $o,P_12: produc2088785539on_val,Q_2: produc2088785539on_val] :
( ( P_12 = Q_2 )
=> ( ( produc765165771_val_o @ C_8 @ P_12 )
<=> ( produc765165771_val_o @ C_8 @ Q_2 ) ) ) ).
thf(fact_164_split__weak__cong,axiom,
! [C_8: exp_list_char > produc2090907612on_val > $o,P_12: produc1282892786on_val,Q_2: produc1282892786on_val] :
( ( P_12 = Q_2 )
=> ( ( produc1835097372_val_o @ C_8 @ P_12 )
<=> ( produc1835097372_val_o @ C_8 @ Q_2 ) ) ) ).
thf(fact_165_split__weak__cong,axiom,
! [C_8: produc1282892786on_val > produc1282892786on_val > $o,P_12: produc1746408499on_val,Q_2: produc1746408499on_val] :
( ( P_12 = Q_2 )
=> ( ( produc1624062875_val_o @ C_8 @ P_12 )
<=> ( produc1624062875_val_o @ C_8 @ Q_2 ) ) ) ).
thf(fact_166_split__weak__cong,axiom,
! [C_8: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,P_12: produc2090907612on_val,Q_2: produc2090907612on_val] :
( ( P_12 = Q_2 )
=> ( ( produc252486962_val_o @ C_8 @ P_12 )
<=> ( produc252486962_val_o @ C_8 @ Q_2 ) ) ) ).
thf(fact_167_map__add__dom__app__simps_I3_J,axiom,
! [L1_1: nat > option1728594148on_val,M_5: nat,L2_1: nat > option1728594148on_val] :
( ~ ( member_nat @ M_5 @ ( dom_na2045926843on_val @ L2_1 ) )
=> ( ( map_ad1851375512on_val @ L1_1 @ L2_1 @ M_5 )
= ( L1_1 @ M_5 ) ) ) ).
thf(fact_168_map__add__dom__app__simps_I3_J,axiom,
! [L1_1: list_char > option_ty,M_5: list_char,L2_1: list_char > option_ty] :
( ~ ( member_list_char @ M_5 @ ( dom_list_char_ty @ L2_1 ) )
=> ( ( map_add_list_char_ty @ L1_1 @ L2_1 @ M_5 )
= ( L1_1 @ M_5 ) ) ) ).
thf(fact_169_map__add__dom__app__simps_I3_J,axiom,
! [L1_1: produc1278157519t_char > option_val,M_5: produc1278157519t_char,L2_1: produc1278157519t_char > option_val] :
( ~ ( member1251428284t_char @ M_5 @ ( dom_Pr695701035ar_val @ L2_1 ) )
=> ( ( map_ad1185064968ar_val @ L1_1 @ L2_1 @ M_5 )
= ( L1_1 @ M_5 ) ) ) ).
thf(fact_170_map__add__dom__app__simps_I3_J,axiom,
! [L1_1: list_char > option_val,M_5: list_char,L2_1: list_char > option_val] :
( ~ ( member_list_char @ M_5 @ ( dom_list_char_val @ L2_1 ) )
=> ( ( map_ad325961431ar_val @ L1_1 @ L2_1 @ M_5 )
= ( L1_1 @ M_5 ) ) ) ).
thf(fact_171_map__add__dom__app__simps_I2_J,axiom,
! [L2: nat > option1728594148on_val,M_4: nat,L1: nat > option1728594148on_val] :
( ~ ( member_nat @ M_4 @ ( dom_na2045926843on_val @ L1 ) )
=> ( ( map_ad1851375512on_val @ L1 @ L2 @ M_4 )
= ( L2 @ M_4 ) ) ) ).
thf(fact_172_map__add__dom__app__simps_I2_J,axiom,
! [L2: list_char > option_ty,M_4: list_char,L1: list_char > option_ty] :
( ~ ( member_list_char @ M_4 @ ( dom_list_char_ty @ L1 ) )
=> ( ( map_add_list_char_ty @ L1 @ L2 @ M_4 )
= ( L2 @ M_4 ) ) ) ).
thf(fact_173_map__add__dom__app__simps_I2_J,axiom,
! [L2: produc1278157519t_char > option_val,M_4: produc1278157519t_char,L1: produc1278157519t_char > option_val] :
( ~ ( member1251428284t_char @ M_4 @ ( dom_Pr695701035ar_val @ L1 ) )
=> ( ( map_ad1185064968ar_val @ L1 @ L2 @ M_4 )
= ( L2 @ M_4 ) ) ) ).
thf(fact_174_map__add__dom__app__simps_I2_J,axiom,
! [L2: list_char > option_val,M_4: list_char,L1: list_char > option_val] :
( ~ ( member_list_char @ M_4 @ ( dom_list_char_val @ L1 ) )
=> ( ( map_ad325961431ar_val @ L1 @ L2 @ M_4 )
= ( L2 @ M_4 ) ) ) ).
thf(fact_175_internal__split__def,axiom,
produc2001734200_val_o = produc9430317_val_o ).
thf(fact_176_internal__split__def,axiom,
produc1476785425_val_o = produc1063861510_val_o ).
thf(fact_177_internal__split__def,axiom,
produc1140826762char_o = produc282231039char_o ).
thf(fact_178_internal__split__def,axiom,
produc473466070_val_o = produc765165771_val_o ).
thf(fact_179_internal__split__def,axiom,
produc900512295_val_o = produc1835097372_val_o ).
thf(fact_180_internal__split__def,axiom,
produc2006262054_val_o = produc1624062875_val_o ).
thf(fact_181_internal__split__def,axiom,
produc575577405_val_o = produc252486962_val_o ).
thf(fact_182_map__add__assoc,axiom,
! [M1: produc1278157519t_char > option_val,M2: produc1278157519t_char > option_val,M3: produc1278157519t_char > option_val] :
( ( map_ad1185064968ar_val @ M1 @ ( map_ad1185064968ar_val @ M2 @ M3 ) )
= ( map_ad1185064968ar_val @ ( map_ad1185064968ar_val @ M1 @ M2 ) @ M3 ) ) ).
thf(fact_183_map__add__assoc,axiom,
! [M1: nat > option1728594148on_val,M2: nat > option1728594148on_val,M3: nat > option1728594148on_val] :
( ( map_ad1851375512on_val @ M1 @ ( map_ad1851375512on_val @ M2 @ M3 ) )
= ( map_ad1851375512on_val @ ( map_ad1851375512on_val @ M1 @ M2 ) @ M3 ) ) ).
thf(fact_184_map__add__assoc,axiom,
! [M1: list_char > option_ty,M2: list_char > option_ty,M3: list_char > option_ty] :
( ( map_add_list_char_ty @ M1 @ ( map_add_list_char_ty @ M2 @ M3 ) )
= ( map_add_list_char_ty @ ( map_add_list_char_ty @ M1 @ M2 ) @ M3 ) ) ).
thf(fact_185_map__add__assoc,axiom,
! [M1: list_char > option_val,M2: list_char > option_val,M3: list_char > option_val] :
( ( map_ad325961431ar_val @ M1 @ ( map_ad325961431ar_val @ M2 @ M3 ) )
= ( map_ad325961431ar_val @ ( map_ad325961431ar_val @ M1 @ M2 ) @ M3 ) ) ).
thf(fact_186_split__twice,axiom,
! [F_11: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,G_2: val > val > produc2090907612on_val,P_11: product_prod_val_val] :
( ( produc252486962_val_o @ F_11 @ ( produc1893839198on_val @ G_2 @ P_11 ) )
<=> ( produc9430317_val_o
@ ^ [X_1: val,Y_1: val] : ( produc252486962_val_o @ F_11 @ ( G_2 @ X_1 @ Y_1 ) )
@ P_11 ) ) ).
thf(fact_187_split__twice,axiom,
! [F_11: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,G_2: bop > product_prod_val_val > produc2090907612on_val,P_11: produc1645268488al_val] :
( ( produc252486962_val_o @ F_11 @ ( produc1247631557on_val @ G_2 @ P_11 ) )
<=> ( produc1063861510_val_o
@ ^ [X_1: bop,Y_1: product_prod_val_val] : ( produc252486962_val_o @ F_11 @ ( G_2 @ X_1 @ Y_1 ) )
@ P_11 ) ) ).
thf(fact_188_split__twice,axiom,
! [F_11: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,G_2: list_char > list_char > produc2090907612on_val,P_11: produc1278157519t_char] :
( ( produc252486962_val_o @ F_11 @ ( produc835075084on_val @ G_2 @ P_11 ) )
<=> ( produc282231039char_o
@ ^ [X_1: list_char,Y_1: list_char] : ( produc252486962_val_o @ F_11 @ ( G_2 @ X_1 @ Y_1 ) )
@ P_11 ) ) ).
thf(fact_189_split__twice,axiom,
! [F_11: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,G_2: list_char > ( produc1278157519t_char > option_val ) > produc2090907612on_val,P_11: produc2088785539on_val] :
( ( produc252486962_val_o @ F_11 @ ( produc1349598016on_val @ G_2 @ P_11 ) )
<=> ( produc765165771_val_o
@ ^ [X_1: list_char,Y_1: produc1278157519t_char > option_val] : ( produc252486962_val_o @ F_11 @ ( G_2 @ X_1 @ Y_1 ) )
@ P_11 ) ) ).
thf(fact_190_split__twice,axiom,
! [F_11: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,G_2: exp_list_char > produc2090907612on_val > produc2090907612on_val,P_11: produc1282892786on_val] :
( ( produc252486962_val_o @ F_11 @ ( produc69760047on_val @ G_2 @ P_11 ) )
<=> ( produc1835097372_val_o
@ ^ [X_1: exp_list_char,Y_1: produc2090907612on_val] : ( produc252486962_val_o @ F_11 @ ( G_2 @ X_1 @ Y_1 ) )
@ P_11 ) ) ).
thf(fact_191_split__twice,axiom,
! [F_11: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,G_2: produc1282892786on_val > produc1282892786on_val > produc2090907612on_val,P_11: produc1746408499on_val] :
( ( produc252486962_val_o @ F_11 @ ( produc511181936on_val @ G_2 @ P_11 ) )
<=> ( produc1624062875_val_o
@ ^ [X_1: produc1282892786on_val,Y_1: produc1282892786on_val] : ( produc252486962_val_o @ F_11 @ ( G_2 @ X_1 @ Y_1 ) )
@ P_11 ) ) ).
thf(fact_192_split__twice,axiom,
! [F_11: val > val > $o,G_2: ( nat > option1728594148on_val ) > ( list_char > option_val ) > product_prod_val_val,P_11: produc2090907612on_val] :
( ( produc9430317_val_o @ F_11 @ ( produc794934116al_val @ G_2 @ P_11 ) )
<=> ( produc252486962_val_o
@ ^ [X_1: nat > option1728594148on_val,Y_1: list_char > option_val] : ( produc9430317_val_o @ F_11 @ ( G_2 @ X_1 @ Y_1 ) )
@ P_11 ) ) ).
thf(fact_193_split__twice,axiom,
! [F_11: bop > product_prod_val_val > $o,G_2: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1645268488al_val,P_11: produc2090907612on_val] :
( ( produc1063861510_val_o @ F_11 @ ( produc1442430405al_val @ G_2 @ P_11 ) )
<=> ( produc252486962_val_o
@ ^ [X_1: nat > option1728594148on_val,Y_1: list_char > option_val] : ( produc1063861510_val_o @ F_11 @ ( G_2 @ X_1 @ Y_1 ) )
@ P_11 ) ) ).
thf(fact_194_split__twice,axiom,
! [F_11: list_char > list_char > $o,G_2: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1278157519t_char,P_11: produc2090907612on_val] :
( ( produc282231039char_o @ F_11 @ ( produc562949388t_char @ G_2 @ P_11 ) )
<=> ( produc252486962_val_o
@ ^ [X_1: nat > option1728594148on_val,Y_1: list_char > option_val] : ( produc282231039char_o @ F_11 @ ( G_2 @ X_1 @ Y_1 ) )
@ P_11 ) ) ).
thf(fact_195_split__twice,axiom,
! [F_11: list_char > ( produc1278157519t_char > option_val ) > $o,G_2: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2088785539on_val,P_11: produc2090907612on_val] :
( ( produc765165771_val_o @ F_11 @ ( produc2039683648on_val @ G_2 @ P_11 ) )
<=> ( produc252486962_val_o
@ ^ [X_1: nat > option1728594148on_val,Y_1: list_char > option_val] : ( produc765165771_val_o @ F_11 @ ( G_2 @ X_1 @ Y_1 ) )
@ P_11 ) ) ).
thf(fact_196_split__twice,axiom,
! [F_11: exp_list_char > produc2090907612on_val > $o,G_2: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1282892786on_val,P_11: produc2090907612on_val] :
( ( produc1835097372_val_o @ F_11 @ ( produc1016489647on_val @ G_2 @ P_11 ) )
<=> ( produc252486962_val_o
@ ^ [X_1: nat > option1728594148on_val,Y_1: list_char > option_val] : ( produc1835097372_val_o @ F_11 @ ( G_2 @ X_1 @ Y_1 ) )
@ P_11 ) ) ).
thf(fact_197_split__twice,axiom,
! [F_11: produc1282892786on_val > produc1282892786on_val > $o,G_2: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1746408499on_val,P_11: produc2090907612on_val] :
( ( produc1624062875_val_o @ F_11 @ ( produc1186953840on_val @ G_2 @ P_11 ) )
<=> ( produc252486962_val_o
@ ^ [X_1: nat > option1728594148on_val,Y_1: list_char > option_val] : ( produc1624062875_val_o @ F_11 @ ( G_2 @ X_1 @ Y_1 ) )
@ P_11 ) ) ).
thf(fact_198_split__curry,axiom,
! [F_10: product_prod_val_val > $o] :
( ( produc9430317_val_o @ ( produc575837646_val_o @ F_10 ) )
= F_10 ) ).
thf(fact_199_split__curry,axiom,
! [F_10: produc1645268488al_val > $o] :
( ( produc1063861510_val_o @ ( produc275195559_val_o @ F_10 ) )
= F_10 ) ).
thf(fact_200_split__curry,axiom,
! [F_10: produc1278157519t_char > $o] :
( ( produc282231039char_o @ ( produc1709467424char_o @ F_10 ) )
= F_10 ) ).
thf(fact_201_split__curry,axiom,
! [F_10: produc2088785539on_val > $o] :
( ( produc765165771_val_o @ ( produc1177570924_val_o @ F_10 ) )
= F_10 ) ).
thf(fact_202_split__curry,axiom,
! [F_10: produc1282892786on_val > $o] :
( ( produc1835097372_val_o @ ( produc1287763389_val_o @ F_10 ) )
= F_10 ) ).
thf(fact_203_split__curry,axiom,
! [F_10: produc1746408499on_val > $o] :
( ( produc1624062875_val_o @ ( produc803302844_val_o @ F_10 ) )
= F_10 ) ).
thf(fact_204_split__curry,axiom,
! [F_10: produc2090907612on_val > $o] :
( ( produc252486962_val_o @ ( produc1402621651_val_o @ F_10 ) )
= F_10 ) ).
thf(fact_205_curry__split,axiom,
! [F_9: val > val > $o] :
( ( produc575837646_val_o @ ( produc9430317_val_o @ F_9 ) )
= F_9 ) ).
thf(fact_206_curry__split,axiom,
! [F_9: bop > product_prod_val_val > $o] :
( ( produc275195559_val_o @ ( produc1063861510_val_o @ F_9 ) )
= F_9 ) ).
thf(fact_207_curry__split,axiom,
! [F_9: list_char > list_char > $o] :
( ( produc1709467424char_o @ ( produc282231039char_o @ F_9 ) )
= F_9 ) ).
thf(fact_208_curry__split,axiom,
! [F_9: list_char > ( produc1278157519t_char > option_val ) > $o] :
( ( produc1177570924_val_o @ ( produc765165771_val_o @ F_9 ) )
= F_9 ) ).
thf(fact_209_curry__split,axiom,
! [F_9: exp_list_char > produc2090907612on_val > $o] :
( ( produc1287763389_val_o @ ( produc1835097372_val_o @ F_9 ) )
= F_9 ) ).
thf(fact_210_curry__split,axiom,
! [F_9: produc1282892786on_val > produc1282892786on_val > $o] :
( ( produc803302844_val_o @ ( produc1624062875_val_o @ F_9 ) )
= F_9 ) ).
thf(fact_211_curry__split,axiom,
! [F_9: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o] :
( ( produc1402621651_val_o @ ( produc252486962_val_o @ F_9 ) )
= F_9 ) ).
thf(fact_212_split__part,axiom,
! [P_10: $o,Q_1: val > val > $o,X_1: product_prod_val_val] :
( ( produc9430317_val_o
@ ^ [A: val,B_1: val] : ( (&) @ P_10 @ ( Q_1 @ A @ B_1 ) )
@ X_1 )
<=> ( P_10
& ( produc9430317_val_o @ Q_1 @ X_1 ) ) ) ).
thf(fact_213_split__part,axiom,
! [P_10: $o,Q_1: bop > product_prod_val_val > $o,X_1: produc1645268488al_val] :
( ( produc1063861510_val_o
@ ^ [A: bop,B_1: product_prod_val_val] : ( (&) @ P_10 @ ( Q_1 @ A @ B_1 ) )
@ X_1 )
<=> ( P_10
& ( produc1063861510_val_o @ Q_1 @ X_1 ) ) ) ).
thf(fact_214_split__part,axiom,
! [P_10: $o,Q_1: list_char > list_char > $o,X_1: produc1278157519t_char] :
( ( produc282231039char_o
@ ^ [A: list_char,B_1: list_char] : ( (&) @ P_10 @ ( Q_1 @ A @ B_1 ) )
@ X_1 )
<=> ( P_10
& ( produc282231039char_o @ Q_1 @ X_1 ) ) ) ).
thf(fact_215_split__part,axiom,
! [P_10: $o,Q_1: list_char > ( produc1278157519t_char > option_val ) > $o,X_1: produc2088785539on_val] :
( ( produc765165771_val_o
@ ^ [A: list_char,B_1: produc1278157519t_char > option_val] : ( (&) @ P_10 @ ( Q_1 @ A @ B_1 ) )
@ X_1 )
<=> ( P_10
& ( produc765165771_val_o @ Q_1 @ X_1 ) ) ) ).
thf(fact_216_split__part,axiom,
! [P_10: $o,Q_1: exp_list_char > produc2090907612on_val > $o,X_1: produc1282892786on_val] :
( ( produc1835097372_val_o
@ ^ [A: exp_list_char,B_1: produc2090907612on_val] : ( (&) @ P_10 @ ( Q_1 @ A @ B_1 ) )
@ X_1 )
<=> ( P_10
& ( produc1835097372_val_o @ Q_1 @ X_1 ) ) ) ).
thf(fact_217_split__part,axiom,
! [P_10: $o,Q_1: produc1282892786on_val > produc1282892786on_val > $o,X_1: produc1746408499on_val] :
( ( produc1624062875_val_o
@ ^ [A: produc1282892786on_val,B_1: produc1282892786on_val] : ( (&) @ P_10 @ ( Q_1 @ A @ B_1 ) )
@ X_1 )
<=> ( P_10
& ( produc1624062875_val_o @ Q_1 @ X_1 ) ) ) ).
thf(fact_218_split__part,axiom,
! [P_10: $o,Q_1: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,X_1: produc2090907612on_val] :
( ( produc252486962_val_o
@ ^ [A: nat > option1728594148on_val,B_1: list_char > option_val] : ( (&) @ P_10 @ ( Q_1 @ A @ B_1 ) )
@ X_1 )
<=> ( P_10
& ( produc252486962_val_o @ Q_1 @ X_1 ) ) ) ).
thf(fact_219_red__reds_ORedInitBlock,axiom,
! [V_4: list_char,T: ty,V: val,U: val,S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_4 @ T @ ( seq_list_char @ ( lAss_list_char @ V_4 @ ( val_list_char @ V ) ) @ ( val_list_char @ U ) ) ) @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ U ) @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_220_conf__widen,axiom,
! [T_7: ty,P_9: list_P1999446415t_char,H_11: nat > option1728594148on_val,V_11: val,T_6: ty] :
( ( conf_P373316194t_char @ P_9 @ H_11 @ V_11 @ T_6 )
=> ( ( widen_2090681816t_char @ P_9 @ T_6 @ T_7 )
=> ( conf_P373316194t_char @ P_9 @ H_11 @ V_11 @ T_7 ) ) ) ).
thf(fact_221_splitD,axiom,
! [F_8: produc1282892786on_val > produc1282892786on_val > $o,A_30: produc1282892786on_val,B_9: produc1282892786on_val] :
( ( produc1624062875_val_o @ F_8 @ ( produc833389609on_val @ A_30 @ B_9 ) )
=> ( F_8 @ A_30 @ B_9 ) ) ).
thf(fact_222_splitD,axiom,
! [F_8: exp_list_char > produc2090907612on_val > $o,A_30: exp_list_char,B_9: produc2090907612on_val] :
( ( produc1835097372_val_o @ F_8 @ ( produc235638504on_val @ A_30 @ B_9 ) )
=> ( F_8 @ A_30 @ B_9 ) ) ).
thf(fact_223_splitD,axiom,
! [F_8: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,A_30: nat > option1728594148on_val,B_9: list_char > option_val] :
( ( produc252486962_val_o @ F_8 @ ( produc755559506on_val @ A_30 @ B_9 ) )
=> ( F_8 @ A_30 @ B_9 ) ) ).
thf(fact_224_splitD,axiom,
! [F_8: list_char > ( produc1278157519t_char > option_val ) > $o,A_30: list_char,B_9: produc1278157519t_char > option_val] :
( ( produc765165771_val_o @ F_8 @ ( produc926070009on_val @ A_30 @ B_9 ) )
=> ( F_8 @ A_30 @ B_9 ) ) ).
thf(fact_225_splitD,axiom,
! [F_8: list_char > list_char > $o,A_30: list_char,B_9: list_char] :
( ( produc282231039char_o @ F_8 @ ( produc5062597t_char @ A_30 @ B_9 ) )
=> ( F_8 @ A_30 @ B_9 ) ) ).
thf(fact_226_splitD,axiom,
! [F_8: bop > product_prod_val_val > $o,A_30: bop,B_9: product_prod_val_val] :
( ( produc1063861510_val_o @ F_8 @ ( produc621191550al_val @ A_30 @ B_9 ) )
=> ( F_8 @ A_30 @ B_9 ) ) ).
thf(fact_227_splitD,axiom,
! [F_8: val > val > $o,A_30: val,B_9: val] :
( ( produc9430317_val_o @ F_8 @ ( product_Pair_val_val @ A_30 @ B_9 ) )
=> ( F_8 @ A_30 @ B_9 ) ) ).
thf(fact_228_lconf__hext,axiom,
! [H_10: nat > option1728594148on_val,P_8: list_P1999446415t_char,H_9: nat > option1728594148on_val,L_7: list_char > option_val,E_10: list_char > option_ty] :
( ( lconf_496643946t_char @ P_8 @ H_9 @ L_7 @ E_10 )
=> ( ( hext @ H_9 @ H_10 )
=> ( lconf_496643946t_char @ P_8 @ H_10 @ L_7 @ E_10 ) ) ) ).
thf(fact_229_red__reds_ORedSeq,axiom,
! [V: val,E_2: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ ( val_list_char @ V ) @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ E_2 @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_230_map__add__upd__left,axiom,
! [E1: nat > option_val,U1: val,M_3: nat,E2: nat > option_val] :
( ~ ( member_nat @ M_3 @ ( dom_nat_val @ E2 ) )
=> ( ( map_add_nat_val @ ( fun_up846528380on_val @ E1 @ M_3 @ ( some_val @ U1 ) ) @ E2 )
= ( fun_up846528380on_val @ ( map_add_nat_val @ E1 @ E2 ) @ M_3 @ ( some_val @ U1 ) ) ) ) ).
thf(fact_231_map__add__upd__left,axiom,
! [E1: product_prod_val_val > option_val,U1: val,M_3: product_prod_val_val,E2: product_prod_val_val > option_val] :
( ~ ( member649088532al_val @ M_3 @ ( dom_Pr1854948307al_val @ E2 ) )
=> ( ( map_ad1139121712al_val @ ( fun_up2650881on_val @ E1 @ M_3 @ ( some_val @ U1 ) ) @ E2 )
= ( fun_up2650881on_val @ ( map_ad1139121712al_val @ E1 @ E2 ) @ M_3 @ ( some_val @ U1 ) ) ) ) ).
thf(fact_232_map__add__upd__left,axiom,
! [E1: produc1645268488al_val > option_val,U1: val,M_3: produc1645268488al_val,E2: produc1645268488al_val > option_val] :
( ~ ( member1417904245al_val @ M_3 @ ( dom_Pr934474290al_val @ E2 ) )
=> ( ( map_ad1808327055al_val @ ( fun_up1370188258on_val @ E1 @ M_3 @ ( some_val @ U1 ) ) @ E2 )
= ( fun_up1370188258on_val @ ( map_ad1808327055al_val @ E1 @ E2 ) @ M_3 @ ( some_val @ U1 ) ) ) ) ).
thf(fact_233_map__add__upd__left,axiom,
! [E1: produc2088785539on_val > option_val,U1: val,M_3: produc2088785539on_val,E2: produc2088785539on_val > option_val] :
( ~ ( member1374264560on_val @ M_3 @ ( dom_Pr397909495al_val @ E2 ) )
=> ( ( map_ad2035409236al_val @ ( fun_up305473245on_val @ E1 @ M_3 @ ( some_val @ U1 ) ) @ E2 )
= ( fun_up305473245on_val @ ( map_ad2035409236al_val @ E1 @ E2 ) @ M_3 @ ( some_val @ U1 ) ) ) ) ).
thf(fact_234_map__add__upd__left,axiom,
! [E1: produc2090907612on_val > option_val,U1: val,M_3: produc2090907612on_val,E2: produc2090907612on_val > option_val] :
( ~ ( member1846553161on_val @ M_3 @ ( dom_Pr1333147486al_val @ E2 ) )
=> ( ( map_ad466413243al_val @ ( fun_up1458528694on_val @ E1 @ M_3 @ ( some_val @ U1 ) ) @ E2 )
= ( fun_up1458528694on_val @ ( map_ad466413243al_val @ E1 @ E2 ) @ M_3 @ ( some_val @ U1 ) ) ) ) ).
thf(fact_235_map__add__upd__left,axiom,
! [E1: produc1282892786on_val > option_val,U1: val,M_3: produc1282892786on_val,E2: produc1282892786on_val > option_val] :
( ~ ( member1072200031on_val @ M_3 @ ( dom_Pr959892680al_val @ E2 ) )
=> ( ( map_ad1639788325al_val @ ( fun_up1510380236on_val @ E1 @ M_3 @ ( some_val @ U1 ) ) @ E2 )
= ( fun_up1510380236on_val @ ( map_ad1639788325al_val @ E1 @ E2 ) @ M_3 @ ( some_val @ U1 ) ) ) ) ).
thf(fact_236_map__add__upd__left,axiom,
! [E1: list_char > option_list_char_o,U1: list_char > $o,M_3: list_char,E2: list_char > option_list_char_o] :
( ~ ( member_list_char @ M_3 @ ( dom_li115714383char_o @ E2 ) )
=> ( ( map_ad1407104812char_o @ ( fun_up405271663char_o @ E1 @ M_3 @ ( some_list_char_o @ U1 ) ) @ E2 )
= ( fun_up405271663char_o @ ( map_ad1407104812char_o @ E1 @ E2 ) @ M_3 @ ( some_list_char_o @ U1 ) ) ) ) ).
thf(fact_237_map__add__upd__left,axiom,
! [E1: nat > option_list_char_o,U1: list_char > $o,M_3: nat,E2: nat > option_list_char_o] :
( ~ ( member_nat @ M_3 @ ( dom_nat_list_char_o @ E2 ) )
=> ( ( map_ad2090421050char_o @ ( fun_up412657745char_o @ E1 @ M_3 @ ( some_list_char_o @ U1 ) ) @ E2 )
= ( fun_up412657745char_o @ ( map_ad2090421050char_o @ E1 @ E2 ) @ M_3 @ ( some_list_char_o @ U1 ) ) ) ) ).
thf(fact_238_map__add__upd__left,axiom,
! [E1: product_prod_val_val > option_list_char_o,U1: list_char > $o,M_3: product_prod_val_val,E2: product_prod_val_val > option_list_char_o] :
( ~ ( member649088532al_val @ M_3 @ ( dom_Pr581342760char_o @ E2 ) )
=> ( ( map_ad1233037829char_o @ ( fun_up179536214char_o @ E1 @ M_3 @ ( some_list_char_o @ U1 ) ) @ E2 )
= ( fun_up179536214char_o @ ( map_ad1233037829char_o @ E1 @ E2 ) @ M_3 @ ( some_list_char_o @ U1 ) ) ) ) ).
thf(fact_239_map__add__upd__left,axiom,
! [E1: produc1645268488al_val > option_list_char_o,U1: list_char > $o,M_3: produc1645268488al_val,E2: produc1645268488al_val > option_list_char_o] :
( ~ ( member1417904245al_val @ M_3 @ ( dom_Pr1531186439char_o @ E2 ) )
=> ( ( map_ad440022500char_o @ ( fun_up743641015char_o @ E1 @ M_3 @ ( some_list_char_o @ U1 ) ) @ E2 )
= ( fun_up743641015char_o @ ( map_ad440022500char_o @ E1 @ E2 ) @ M_3 @ ( some_list_char_o @ U1 ) ) ) ) ).
thf(fact_240_map__add__upd__left,axiom,
! [E1: produc2088785539on_val > option_list_char_o,U1: list_char > $o,M_3: produc2088785539on_val,E2: produc2088785539on_val > option_list_char_o] :
( ~ ( member1374264560on_val @ M_3 @ ( dom_Pr957742668char_o @ E2 ) )
=> ( ( map_ad1510374185char_o @ ( fun_up1138829106char_o @ E1 @ M_3 @ ( some_list_char_o @ U1 ) ) @ E2 )
= ( fun_up1138829106char_o @ ( map_ad1510374185char_o @ E1 @ E2 ) @ M_3 @ ( some_list_char_o @ U1 ) ) ) ) ).
thf(fact_241_map__add__upd__left,axiom,
! [E1: produc2090907612on_val > option_list_char_o,U1: list_char > $o,M_3: produc2090907612on_val,E2: produc2090907612on_val > option_list_char_o] :
( ~ ( member1846553161on_val @ M_3 @ ( dom_Pr1958353971char_o @ E2 ) )
=> ( ( map_ad1905329424char_o @ ( fun_up590200203char_o @ E1 @ M_3 @ ( some_list_char_o @ U1 ) ) @ E2 )
= ( fun_up590200203char_o @ ( map_ad1905329424char_o @ E1 @ E2 ) @ M_3 @ ( some_list_char_o @ U1 ) ) ) ) ).
thf(fact_242_map__add__upd__left,axiom,
! [E1: produc1282892786on_val > option_list_char_o,U1: list_char > $o,M_3: produc1282892786on_val,E2: produc1282892786on_val > option_list_char_o] :
( ~ ( member1072200031on_val @ M_3 @ ( dom_Pr373640349char_o @ E2 ) )
=> ( ( map_ad134899834char_o @ ( fun_up122360737char_o @ E1 @ M_3 @ ( some_list_char_o @ U1 ) ) @ E2 )
= ( fun_up122360737char_o @ ( map_ad134899834char_o @ E1 @ E2 ) @ M_3 @ ( some_list_char_o @ U1 ) ) ) ) ).
thf(fact_243_map__add__upd__left,axiom,
! [E1: nat > option_ty,U1: ty,M_3: nat,E2: nat > option_ty] :
( ~ ( member_nat @ M_3 @ ( dom_nat_ty @ E2 ) )
=> ( ( map_add_nat_ty @ ( fun_up421284275ion_ty @ E1 @ M_3 @ ( some_ty @ U1 ) ) @ E2 )
= ( fun_up421284275ion_ty @ ( map_add_nat_ty @ E1 @ E2 ) @ M_3 @ ( some_ty @ U1 ) ) ) ) ).
thf(fact_244_map__add__upd__left,axiom,
! [E1: product_prod_val_val > option_ty,U1: ty,M_3: product_prod_val_val,E2: product_prod_val_val > option_ty] :
( ~ ( member649088532al_val @ M_3 @ ( dom_Pr1536367242val_ty @ E2 ) )
=> ( ( map_ad1402016615val_ty @ ( fun_up638349240ion_ty @ E1 @ M_3 @ ( some_ty @ U1 ) ) @ E2 )
= ( fun_up638349240ion_ty @ ( map_ad1402016615val_ty @ E1 @ E2 ) @ M_3 @ ( some_ty @ U1 ) ) ) ) ).
thf(fact_245_map__add__upd__left,axiom,
! [E1: produc1645268488al_val > option_ty,U1: ty,M_3: produc1645268488al_val,E2: produc1645268488al_val > option_ty] :
( ~ ( member1417904245al_val @ M_3 @ ( dom_Pr585943145val_ty @ E2 ) )
=> ( ( map_ad1877333574val_ty @ ( fun_up430376729ion_ty @ E1 @ M_3 @ ( some_ty @ U1 ) ) @ E2 )
= ( fun_up430376729ion_ty @ ( map_ad1877333574val_ty @ E1 @ E2 ) @ M_3 @ ( some_ty @ U1 ) ) ) ) ).
thf(fact_246_map__add__upd__left,axiom,
! [E1: produc2088785539on_val > option_ty,U1: ty,M_3: produc2088785539on_val,E2: produc2088785539on_val > option_ty] :
( ~ ( member1374264560on_val @ M_3 @ ( dom_Pr970344110val_ty @ E2 ) )
=> ( ( map_ad775792779val_ty @ ( fun_up1537495444ion_ty @ E1 @ M_3 @ ( some_ty @ U1 ) ) @ E2 )
= ( fun_up1537495444ion_ty @ ( map_ad775792779val_ty @ E1 @ E2 ) @ M_3 @ ( some_ty @ U1 ) ) ) ) ).
thf(fact_247_map__add__upd__left,axiom,
! [E1: produc2090907612on_val > option_ty,U1: ty,M_3: produc2090907612on_val,E2: produc2090907612on_val > option_ty] :
( ~ ( member1846553161on_val @ M_3 @ ( dom_Pr878896021val_ty @ E2 ) )
=> ( ( map_ad1576841586val_ty @ ( fun_up1313253613ion_ty @ E1 @ M_3 @ ( some_ty @ U1 ) ) @ E2 )
= ( fun_up1313253613ion_ty @ ( map_ad1576841586val_ty @ E1 @ E2 ) @ M_3 @ ( some_ty @ U1 ) ) ) ) ).
thf(fact_248_map__add__upd__left,axiom,
! [E1: produc1282892786on_val > option_ty,U1: ty,M_3: produc1282892786on_val,E2: produc1282892786on_val > option_ty] :
( ~ ( member1072200031on_val @ M_3 @ ( dom_Pr1290145279val_ty @ E2 ) )
=> ( ( map_ad1914244828val_ty @ ( fun_up951485699ion_ty @ E1 @ M_3 @ ( some_ty @ U1 ) ) @ E2 )
= ( fun_up951485699ion_ty @ ( map_ad1914244828val_ty @ E1 @ E2 ) @ M_3 @ ( some_ty @ U1 ) ) ) ) ).
thf(fact_249_map__add__upd__left,axiom,
! [E1: list_char > option1728594148on_val,U1: produc2088785539on_val,M_3: list_char,E2: list_char > option1728594148on_val] :
( ~ ( member_list_char @ M_3 @ ( dom_li96736835on_val @ E2 ) )
=> ( ( map_ad53467942on_val @ ( fun_up867733049on_val @ E1 @ M_3 @ ( some_P451527732on_val @ U1 ) ) @ E2 )
= ( fun_up867733049on_val @ ( map_ad53467942on_val @ E1 @ E2 ) @ M_3 @ ( some_P451527732on_val @ U1 ) ) ) ) ).
thf(fact_250_map__add__upd__left,axiom,
! [E1: product_prod_val_val > option1728594148on_val,U1: produc2088785539on_val,M_3: product_prod_val_val,E2: product_prod_val_val > option1728594148on_val] :
( ~ ( member649088532al_val @ M_3 @ ( dom_Pr283571498on_val @ E2 ) )
=> ( ( map_ad1570649101on_val @ ( fun_up2110408082on_val @ E1 @ M_3 @ ( some_P451527732on_val @ U1 ) ) @ E2 )
= ( fun_up2110408082on_val @ ( map_ad1570649101on_val @ E1 @ E2 ) @ M_3 @ ( some_P451527732on_val @ U1 ) ) ) ) ).
thf(fact_251_map__add__upd__left,axiom,
! [E1: produc1645268488al_val > option1728594148on_val,U1: produc2088785539on_val,M_3: produc1645268488al_val,E2: produc1645268488al_val > option1728594148on_val] :
( ~ ( member1417904245al_val @ M_3 @ ( dom_Pr1903277195on_val @ E2 ) )
=> ( ( map_ad1824497262on_val @ ( fun_up709865713on_val @ E1 @ M_3 @ ( some_P451527732on_val @ U1 ) ) @ E2 )
= ( fun_up709865713on_val @ ( map_ad1824497262on_val @ E1 @ E2 ) @ M_3 @ ( some_P451527732on_val @ U1 ) ) ) ) ).
thf(fact_252_map__add__upd__left,axiom,
! [E1: produc2088785539on_val > option1728594148on_val,U1: produc2088785539on_val,M_3: produc2088785539on_val,E2: produc2088785539on_val > option1728594148on_val] :
( ~ ( member1374264560on_val @ M_3 @ ( dom_Pr1058999302on_val @ E2 ) )
=> ( ( map_ad918921705on_val @ ( fun_up70099126on_val @ E1 @ M_3 @ ( some_P451527732on_val @ U1 ) ) @ E2 )
= ( fun_up70099126on_val @ ( map_ad918921705on_val @ E1 @ E2 ) @ M_3 @ ( some_P451527732on_val @ U1 ) ) ) ) ).
thf(fact_253_map__add__upd__left,axiom,
! [E1: produc2090907612on_val > option1728594148on_val,U1: produc2088785539on_val,M_3: produc2090907612on_val,E2: produc2090907612on_val > option1728594148on_val] :
( ~ ( member1846553161on_val @ M_3 @ ( dom_Pr1306915423on_val @ E2 ) )
=> ( ( map_ad815995970on_val @ ( fun_up224753181on_val @ E1 @ M_3 @ ( some_P451527732on_val @ U1 ) ) @ E2 )
= ( fun_up224753181on_val @ ( map_ad815995970on_val @ E1 @ E2 ) @ M_3 @ ( some_P451527732on_val @ U1 ) ) ) ) ).
thf(fact_254_map__add__upd__left,axiom,
! [E1: produc1282892786on_val > option1728594148on_val,U1: produc2088785539on_val,M_3: produc1282892786on_val,E2: produc1282892786on_val > option1728594148on_val] :
( ~ ( member1072200031on_val @ M_3 @ ( dom_Pr1372035957on_val @ E2 ) )
=> ( ( map_ad1893716568on_val @ ( fun_up881763975on_val @ E1 @ M_3 @ ( some_P451527732on_val @ U1 ) ) @ E2 )
= ( fun_up881763975on_val @ ( map_ad1893716568on_val @ E1 @ E2 ) @ M_3 @ ( some_P451527732on_val @ U1 ) ) ) ) ).
thf(fact_255_map__add__upd__left,axiom,
! [E1: list_char > option_ty,U1: ty,M_3: list_char,E2: list_char > option_ty] :
( ~ ( member_list_char @ M_3 @ ( dom_list_char_ty @ E2 ) )
=> ( ( map_add_list_char_ty @ ( fun_up424764369ion_ty @ E1 @ M_3 @ ( some_ty @ U1 ) ) @ E2 )
= ( fun_up424764369ion_ty @ ( map_add_list_char_ty @ E1 @ E2 ) @ M_3 @ ( some_ty @ U1 ) ) ) ) ).
thf(fact_256_map__add__upd__left,axiom,
! [E1: nat > option1728594148on_val,U1: produc2088785539on_val,M_3: nat,E2: nat > option1728594148on_val] :
( ~ ( member_nat @ M_3 @ ( dom_na2045926843on_val @ E2 ) )
=> ( ( map_ad1851375512on_val @ ( fun_up1472480727on_val @ E1 @ M_3 @ ( some_P451527732on_val @ U1 ) ) @ E2 )
= ( fun_up1472480727on_val @ ( map_ad1851375512on_val @ E1 @ E2 ) @ M_3 @ ( some_P451527732on_val @ U1 ) ) ) ) ).
thf(fact_257_map__add__upd__left,axiom,
! [E1: produc1278157519t_char > option_val,U1: val,M_3: produc1278157519t_char,E2: produc1278157519t_char > option_val] :
( ~ ( member1251428284t_char @ M_3 @ ( dom_Pr695701035ar_val @ E2 ) )
=> ( ( map_ad1185064968ar_val @ ( fun_up204312361on_val @ E1 @ M_3 @ ( some_val @ U1 ) ) @ E2 )
= ( fun_up204312361on_val @ ( map_ad1185064968ar_val @ E1 @ E2 ) @ M_3 @ ( some_val @ U1 ) ) ) ) ).
thf(fact_258_map__add__upd__left,axiom,
! [E1: list_char > option_val,U1: val,M_3: list_char,E2: list_char > option_val] :
( ~ ( member_list_char @ M_3 @ ( dom_list_char_val @ E2 ) )
=> ( ( map_ad325961431ar_val @ ( fun_up1149430426on_val @ E1 @ M_3 @ ( some_val @ U1 ) ) @ E2 )
= ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ E1 @ E2 ) @ M_3 @ ( some_val @ U1 ) ) ) ) ).
thf(fact_259_red__reds_ORedBlock,axiom,
! [V_4: list_char,T: ty,U: val,S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_4 @ T @ ( val_list_char @ U ) ) @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ U ) @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_260_domI,axiom,
! [M_2: nat > option_val,A_29: nat,B_8: val] :
( ( ( M_2 @ A_29 )
= ( some_val @ B_8 ) )
=> ( member_nat @ A_29 @ ( dom_nat_val @ M_2 ) ) ) ).
thf(fact_261_domI,axiom,
! [M_2: product_prod_val_val > option_val,A_29: product_prod_val_val,B_8: val] :
( ( ( M_2 @ A_29 )
= ( some_val @ B_8 ) )
=> ( member649088532al_val @ A_29 @ ( dom_Pr1854948307al_val @ M_2 ) ) ) ).
thf(fact_262_domI,axiom,
! [M_2: produc1645268488al_val > option_val,A_29: produc1645268488al_val,B_8: val] :
( ( ( M_2 @ A_29 )
= ( some_val @ B_8 ) )
=> ( member1417904245al_val @ A_29 @ ( dom_Pr934474290al_val @ M_2 ) ) ) ).
thf(fact_263_domI,axiom,
! [M_2: produc2088785539on_val > option_val,A_29: produc2088785539on_val,B_8: val] :
( ( ( M_2 @ A_29 )
= ( some_val @ B_8 ) )
=> ( member1374264560on_val @ A_29 @ ( dom_Pr397909495al_val @ M_2 ) ) ) ).
thf(fact_264_domI,axiom,
! [M_2: produc2090907612on_val > option_val,A_29: produc2090907612on_val,B_8: val] :
( ( ( M_2 @ A_29 )
= ( some_val @ B_8 ) )
=> ( member1846553161on_val @ A_29 @ ( dom_Pr1333147486al_val @ M_2 ) ) ) ).
thf(fact_265_domI,axiom,
! [M_2: produc1282892786on_val > option_val,A_29: produc1282892786on_val,B_8: val] :
( ( ( M_2 @ A_29 )
= ( some_val @ B_8 ) )
=> ( member1072200031on_val @ A_29 @ ( dom_Pr959892680al_val @ M_2 ) ) ) ).
thf(fact_266_domI,axiom,
! [M_2: list_char > option_list_char_o,A_29: list_char,B_8: list_char > $o] :
( ( ( M_2 @ A_29 )
= ( some_list_char_o @ B_8 ) )
=> ( member_list_char @ A_29 @ ( dom_li115714383char_o @ M_2 ) ) ) ).
thf(fact_267_domI,axiom,
! [M_2: nat > option_list_char_o,A_29: nat,B_8: list_char > $o] :
( ( ( M_2 @ A_29 )
= ( some_list_char_o @ B_8 ) )
=> ( member_nat @ A_29 @ ( dom_nat_list_char_o @ M_2 ) ) ) ).
thf(fact_268_domI,axiom,
! [M_2: product_prod_val_val > option_list_char_o,A_29: product_prod_val_val,B_8: list_char > $o] :
( ( ( M_2 @ A_29 )
= ( some_list_char_o @ B_8 ) )
=> ( member649088532al_val @ A_29 @ ( dom_Pr581342760char_o @ M_2 ) ) ) ).
thf(fact_269_domI,axiom,
! [M_2: produc1645268488al_val > option_list_char_o,A_29: produc1645268488al_val,B_8: list_char > $o] :
( ( ( M_2 @ A_29 )
= ( some_list_char_o @ B_8 ) )
=> ( member1417904245al_val @ A_29 @ ( dom_Pr1531186439char_o @ M_2 ) ) ) ).
thf(fact_270_domI,axiom,
! [M_2: produc2088785539on_val > option_list_char_o,A_29: produc2088785539on_val,B_8: list_char > $o] :
( ( ( M_2 @ A_29 )
= ( some_list_char_o @ B_8 ) )
=> ( member1374264560on_val @ A_29 @ ( dom_Pr957742668char_o @ M_2 ) ) ) ).
thf(fact_271_domI,axiom,
! [M_2: produc2090907612on_val > option_list_char_o,A_29: produc2090907612on_val,B_8: list_char > $o] :
( ( ( M_2 @ A_29 )
= ( some_list_char_o @ B_8 ) )
=> ( member1846553161on_val @ A_29 @ ( dom_Pr1958353971char_o @ M_2 ) ) ) ).
thf(fact_272_domI,axiom,
! [M_2: produc1282892786on_val > option_list_char_o,A_29: produc1282892786on_val,B_8: list_char > $o] :
( ( ( M_2 @ A_29 )
= ( some_list_char_o @ B_8 ) )
=> ( member1072200031on_val @ A_29 @ ( dom_Pr373640349char_o @ M_2 ) ) ) ).
thf(fact_273_domI,axiom,
! [M_2: list_char > option_ty,A_29: list_char,B_8: ty] :
( ( ( M_2 @ A_29 )
= ( some_ty @ B_8 ) )
=> ( member_list_char @ A_29 @ ( dom_list_char_ty @ M_2 ) ) ) ).
thf(fact_274_domI,axiom,
! [M_2: nat > option_ty,A_29: nat,B_8: ty] :
( ( ( M_2 @ A_29 )
= ( some_ty @ B_8 ) )
=> ( member_nat @ A_29 @ ( dom_nat_ty @ M_2 ) ) ) ).
thf(fact_275_domI,axiom,
! [M_2: product_prod_val_val > option_ty,A_29: product_prod_val_val,B_8: ty] :
( ( ( M_2 @ A_29 )
= ( some_ty @ B_8 ) )
=> ( member649088532al_val @ A_29 @ ( dom_Pr1536367242val_ty @ M_2 ) ) ) ).
thf(fact_276_domI,axiom,
! [M_2: produc1645268488al_val > option_ty,A_29: produc1645268488al_val,B_8: ty] :
( ( ( M_2 @ A_29 )
= ( some_ty @ B_8 ) )
=> ( member1417904245al_val @ A_29 @ ( dom_Pr585943145val_ty @ M_2 ) ) ) ).
thf(fact_277_domI,axiom,
! [M_2: produc2088785539on_val > option_ty,A_29: produc2088785539on_val,B_8: ty] :
( ( ( M_2 @ A_29 )
= ( some_ty @ B_8 ) )
=> ( member1374264560on_val @ A_29 @ ( dom_Pr970344110val_ty @ M_2 ) ) ) ).
thf(fact_278_domI,axiom,
! [M_2: produc2090907612on_val > option_ty,A_29: produc2090907612on_val,B_8: ty] :
( ( ( M_2 @ A_29 )
= ( some_ty @ B_8 ) )
=> ( member1846553161on_val @ A_29 @ ( dom_Pr878896021val_ty @ M_2 ) ) ) ).
thf(fact_279_domI,axiom,
! [M_2: produc1282892786on_val > option_ty,A_29: produc1282892786on_val,B_8: ty] :
( ( ( M_2 @ A_29 )
= ( some_ty @ B_8 ) )
=> ( member1072200031on_val @ A_29 @ ( dom_Pr1290145279val_ty @ M_2 ) ) ) ).
thf(fact_280_domI,axiom,
! [M_2: nat > option1728594148on_val,A_29: nat,B_8: produc2088785539on_val] :
( ( ( M_2 @ A_29 )
= ( some_P451527732on_val @ B_8 ) )
=> ( member_nat @ A_29 @ ( dom_na2045926843on_val @ M_2 ) ) ) ).
thf(fact_281_domI,axiom,
! [M_2: list_char > option1728594148on_val,A_29: list_char,B_8: produc2088785539on_val] :
( ( ( M_2 @ A_29 )
= ( some_P451527732on_val @ B_8 ) )
=> ( member_list_char @ A_29 @ ( dom_li96736835on_val @ M_2 ) ) ) ).
thf(fact_282_domI,axiom,
! [M_2: product_prod_val_val > option1728594148on_val,A_29: product_prod_val_val,B_8: produc2088785539on_val] :
( ( ( M_2 @ A_29 )
= ( some_P451527732on_val @ B_8 ) )
=> ( member649088532al_val @ A_29 @ ( dom_Pr283571498on_val @ M_2 ) ) ) ).
thf(fact_283_domI,axiom,
! [M_2: produc1645268488al_val > option1728594148on_val,A_29: produc1645268488al_val,B_8: produc2088785539on_val] :
( ( ( M_2 @ A_29 )
= ( some_P451527732on_val @ B_8 ) )
=> ( member1417904245al_val @ A_29 @ ( dom_Pr1903277195on_val @ M_2 ) ) ) ).
thf(fact_284_domI,axiom,
! [M_2: produc2088785539on_val > option1728594148on_val,A_29: produc2088785539on_val,B_8: produc2088785539on_val] :
( ( ( M_2 @ A_29 )
= ( some_P451527732on_val @ B_8 ) )
=> ( member1374264560on_val @ A_29 @ ( dom_Pr1058999302on_val @ M_2 ) ) ) ).
thf(fact_285_domI,axiom,
! [M_2: produc2090907612on_val > option1728594148on_val,A_29: produc2090907612on_val,B_8: produc2088785539on_val] :
( ( ( M_2 @ A_29 )
= ( some_P451527732on_val @ B_8 ) )
=> ( member1846553161on_val @ A_29 @ ( dom_Pr1306915423on_val @ M_2 ) ) ) ).
thf(fact_286_domI,axiom,
! [M_2: produc1282892786on_val > option1728594148on_val,A_29: produc1282892786on_val,B_8: produc2088785539on_val] :
( ( ( M_2 @ A_29 )
= ( some_P451527732on_val @ B_8 ) )
=> ( member1072200031on_val @ A_29 @ ( dom_Pr1372035957on_val @ M_2 ) ) ) ).
thf(fact_287_domI,axiom,
! [M_2: produc1278157519t_char > option_val,A_29: produc1278157519t_char,B_8: val] :
( ( ( M_2 @ A_29 )
= ( some_val @ B_8 ) )
=> ( member1251428284t_char @ A_29 @ ( dom_Pr695701035ar_val @ M_2 ) ) ) ).
thf(fact_288_domI,axiom,
! [M_2: list_char > option_val,A_29: list_char,B_8: val] :
( ( ( M_2 @ A_29 )
= ( some_val @ B_8 ) )
=> ( member_list_char @ A_29 @ ( dom_list_char_val @ M_2 ) ) ) ).
thf(fact_289_red__reds_OInitBlockRed,axiom,
! [T: ty,V_5: val,E_1: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,V_4: list_char,V: val,E: exp_list_char,H_4: nat > option1728594148on_val,L_4: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_4 @ ( some_val @ V ) ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_4 @ L_4 ) ) ) @ ( red @ P ) )
=> ( ( ( L_4 @ V_4 )
= ( some_val @ V_5 ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_4 @ T @ ( seq_list_char @ ( lAss_list_char @ V_4 @ ( val_list_char @ V ) ) @ E_1 ) ) @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ ( block_list_char @ V_4 @ T @ ( seq_list_char @ ( lAss_list_char @ V_4 @ ( val_list_char @ V_5 ) ) @ E ) ) @ ( produc755559506on_val @ H_4 @ ( fun_up1149430426on_val @ L_4 @ V_4 @ ( L @ V_4 ) ) ) ) ) @ ( red @ P ) ) ) ) ).
thf(fact_290_prod_Osimps_I2_J,axiom,
! [F1: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,A_28: nat > option1728594148on_val,B_7: list_char > option_val] :
( ( produc252486962_val_o @ F1 @ ( produc755559506on_val @ A_28 @ B_7 ) )
<=> ( F1 @ A_28 @ B_7 ) ) ).
thf(fact_291_prod_Osimps_I2_J,axiom,
! [F1: produc1282892786on_val > produc1282892786on_val > $o,A_28: produc1282892786on_val,B_7: produc1282892786on_val] :
( ( produc1624062875_val_o @ F1 @ ( produc833389609on_val @ A_28 @ B_7 ) )
<=> ( F1 @ A_28 @ B_7 ) ) ).
thf(fact_292_prod_Osimps_I2_J,axiom,
! [F1: exp_list_char > produc2090907612on_val > $o,A_28: exp_list_char,B_7: produc2090907612on_val] :
( ( produc1835097372_val_o @ F1 @ ( produc235638504on_val @ A_28 @ B_7 ) )
<=> ( F1 @ A_28 @ B_7 ) ) ).
thf(fact_293_prod_Osimps_I2_J,axiom,
! [F1: list_char > ( produc1278157519t_char > option_val ) > $o,A_28: list_char,B_7: produc1278157519t_char > option_val] :
( ( produc765165771_val_o @ F1 @ ( produc926070009on_val @ A_28 @ B_7 ) )
<=> ( F1 @ A_28 @ B_7 ) ) ).
thf(fact_294_prod_Osimps_I2_J,axiom,
! [F1: list_char > list_char > $o,A_28: list_char,B_7: list_char] :
( ( produc282231039char_o @ F1 @ ( produc5062597t_char @ A_28 @ B_7 ) )
<=> ( F1 @ A_28 @ B_7 ) ) ).
thf(fact_295_prod_Osimps_I2_J,axiom,
! [F1: bop > product_prod_val_val > $o,A_28: bop,B_7: product_prod_val_val] :
( ( produc1063861510_val_o @ F1 @ ( produc621191550al_val @ A_28 @ B_7 ) )
<=> ( F1 @ A_28 @ B_7 ) ) ).
thf(fact_296_prod_Osimps_I2_J,axiom,
! [F1: val > val > $o,A_28: val,B_7: val] :
( ( produc9430317_val_o @ F1 @ ( product_Pair_val_val @ A_28 @ B_7 ) )
<=> ( F1 @ A_28 @ B_7 ) ) ).
thf(fact_297_split__conv,axiom,
! [F_7: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,A_27: nat > option1728594148on_val,B_6: list_char > option_val] :
( ( produc252486962_val_o @ F_7 @ ( produc755559506on_val @ A_27 @ B_6 ) )
<=> ( F_7 @ A_27 @ B_6 ) ) ).
thf(fact_298_split__conv,axiom,
! [F_7: produc1282892786on_val > produc1282892786on_val > $o,A_27: produc1282892786on_val,B_6: produc1282892786on_val] :
( ( produc1624062875_val_o @ F_7 @ ( produc833389609on_val @ A_27 @ B_6 ) )
<=> ( F_7 @ A_27 @ B_6 ) ) ).
thf(fact_299_split__conv,axiom,
! [F_7: exp_list_char > produc2090907612on_val > $o,A_27: exp_list_char,B_6: produc2090907612on_val] :
( ( produc1835097372_val_o @ F_7 @ ( produc235638504on_val @ A_27 @ B_6 ) )
<=> ( F_7 @ A_27 @ B_6 ) ) ).
thf(fact_300_split__conv,axiom,
! [F_7: list_char > ( produc1278157519t_char > option_val ) > $o,A_27: list_char,B_6: produc1278157519t_char > option_val] :
( ( produc765165771_val_o @ F_7 @ ( produc926070009on_val @ A_27 @ B_6 ) )
<=> ( F_7 @ A_27 @ B_6 ) ) ).
thf(fact_301_split__conv,axiom,
! [F_7: list_char > list_char > $o,A_27: list_char,B_6: list_char] :
( ( produc282231039char_o @ F_7 @ ( produc5062597t_char @ A_27 @ B_6 ) )
<=> ( F_7 @ A_27 @ B_6 ) ) ).
thf(fact_302_split__conv,axiom,
! [F_7: bop > product_prod_val_val > $o,A_27: bop,B_6: product_prod_val_val] :
( ( produc1063861510_val_o @ F_7 @ ( produc621191550al_val @ A_27 @ B_6 ) )
<=> ( F_7 @ A_27 @ B_6 ) ) ).
thf(fact_303_split__conv,axiom,
! [F_7: val > val > $o,A_27: val,B_6: val] :
( ( produc9430317_val_o @ F_7 @ ( product_Pair_val_val @ A_27 @ B_6 ) )
<=> ( F_7 @ A_27 @ B_6 ) ) ).
thf(fact_304_map__add__find__right,axiom,
! [M_1: produc1278157519t_char > option_val,N: produc1278157519t_char > option_val,K: produc1278157519t_char,Xx: val] :
( ( ( N @ K )
= ( some_val @ Xx ) )
=> ( ( map_ad1185064968ar_val @ M_1 @ N @ K )
= ( some_val @ Xx ) ) ) ).
thf(fact_305_map__add__find__right,axiom,
! [M_1: list_char > option_ty,N: list_char > option_ty,K: list_char,Xx: ty] :
( ( ( N @ K )
= ( some_ty @ Xx ) )
=> ( ( map_add_list_char_ty @ M_1 @ N @ K )
= ( some_ty @ Xx ) ) ) ).
thf(fact_306_map__add__find__right,axiom,
! [M_1: nat > option1728594148on_val,N: nat > option1728594148on_val,K: nat,Xx: produc2088785539on_val] :
( ( ( N @ K )
= ( some_P451527732on_val @ Xx ) )
=> ( ( map_ad1851375512on_val @ M_1 @ N @ K )
= ( some_P451527732on_val @ Xx ) ) ) ).
thf(fact_307_map__add__find__right,axiom,
! [M_1: list_char > option_val,N: list_char > option_val,K: list_char,Xx: val] :
( ( ( N @ K )
= ( some_val @ Xx ) )
=> ( ( map_ad325961431ar_val @ M_1 @ N @ K )
= ( some_val @ Xx ) ) ) ).
thf(fact_308_split__eta,axiom,
! [F_6: produc2090907612on_val > $o] :
( ( produc252486962_val_o
@ ^ [X_1: nat > option1728594148on_val,Y_1: list_char > option_val] : ( F_6 @ ( produc755559506on_val @ X_1 @ Y_1 ) ) )
= F_6 ) ).
thf(fact_309_split__eta,axiom,
! [F_6: produc1746408499on_val > $o] :
( ( produc1624062875_val_o
@ ^ [X_1: produc1282892786on_val,Y_1: produc1282892786on_val] : ( F_6 @ ( produc833389609on_val @ X_1 @ Y_1 ) ) )
= F_6 ) ).
thf(fact_310_split__eta,axiom,
! [F_6: produc1282892786on_val > $o] :
( ( produc1835097372_val_o
@ ^ [X_1: exp_list_char,Y_1: produc2090907612on_val] : ( F_6 @ ( produc235638504on_val @ X_1 @ Y_1 ) ) )
= F_6 ) ).
thf(fact_311_split__eta,axiom,
! [F_6: produc2088785539on_val > $o] :
( ( produc765165771_val_o
@ ^ [X_1: list_char,Y_1: produc1278157519t_char > option_val] : ( F_6 @ ( produc926070009on_val @ X_1 @ Y_1 ) ) )
= F_6 ) ).
thf(fact_312_split__eta,axiom,
! [F_6: produc1278157519t_char > $o] :
( ( produc282231039char_o
@ ^ [X_1: list_char,Y_1: list_char] : ( F_6 @ ( produc5062597t_char @ X_1 @ Y_1 ) ) )
= F_6 ) ).
thf(fact_313_split__eta,axiom,
! [F_6: produc1645268488al_val > $o] :
( ( produc1063861510_val_o
@ ^ [X_1: bop,Y_1: product_prod_val_val] : ( F_6 @ ( produc621191550al_val @ X_1 @ Y_1 ) ) )
= F_6 ) ).
thf(fact_314_split__eta,axiom,
! [F_6: product_prod_val_val > $o] :
( ( produc9430317_val_o
@ ^ [X_1: val,Y_1: val] : ( F_6 @ ( product_Pair_val_val @ X_1 @ Y_1 ) ) )
= F_6 ) ).
thf(fact_315_mem__def,axiom,
! [X_3: list_char,A_26: list_char > $o] :
( ( member_list_char @ X_3 @ A_26 )
<=> ( A_26 @ X_3 ) ) ).
thf(fact_316_mem__def,axiom,
! [X_3: nat,A_26: nat > $o] :
( ( member_nat @ X_3 @ A_26 )
<=> ( A_26 @ X_3 ) ) ).
thf(fact_317_mem__def,axiom,
! [X_3: product_prod_val_val,A_26: product_prod_val_val > $o] :
( ( member649088532al_val @ X_3 @ A_26 )
<=> ( A_26 @ X_3 ) ) ).
thf(fact_318_mem__def,axiom,
! [X_3: produc1645268488al_val,A_26: produc1645268488al_val > $o] :
( ( member1417904245al_val @ X_3 @ A_26 )
<=> ( A_26 @ X_3 ) ) ).
thf(fact_319_mem__def,axiom,
! [X_3: produc2088785539on_val,A_26: produc2088785539on_val > $o] :
( ( member1374264560on_val @ X_3 @ A_26 )
<=> ( A_26 @ X_3 ) ) ).
thf(fact_320_mem__def,axiom,
! [X_3: produc2090907612on_val,A_26: produc2090907612on_val > $o] :
( ( member1846553161on_val @ X_3 @ A_26 )
<=> ( A_26 @ X_3 ) ) ).
thf(fact_321_mem__def,axiom,
! [X_3: produc1282892786on_val,A_26: produc1282892786on_val > $o] :
( ( member1072200031on_val @ X_3 @ A_26 )
<=> ( A_26 @ X_3 ) ) ).
thf(fact_322_mem__def,axiom,
! [X_3: produc1746408499on_val,A_26: produc1746408499on_val > $o] :
( ( member1913460000on_val @ X_3 @ A_26 )
<=> ( A_26 @ X_3 ) ) ).
thf(fact_323_mem__def,axiom,
! [X_3: produc1278157519t_char,A_26: produc1278157519t_char > $o] :
( ( member1251428284t_char @ X_3 @ A_26 )
<=> ( A_26 @ X_3 ) ) ).
thf(fact_324_red__reds_OLAssRed,axiom,
! [V_4: list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V_4 @ E_1 ) @ S_2 ) @ ( produc235638504on_val @ ( lAss_list_char @ V_4 @ E ) @ S ) ) @ ( red @ P ) ) ) ).
thf(fact_325_red__reds_OSeqRed,axiom,
! [E_2: exp_list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ E_1 @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( seq_list_char @ E @ E_2 ) @ S ) ) @ ( red @ P ) ) ) ).
thf(fact_326_curryE,axiom,
! [F_5: produc1746408499on_val > $o,A_25: produc1282892786on_val,B_5: produc1282892786on_val] :
( ( produc803302844_val_o @ F_5 @ A_25 @ B_5 )
=> ( F_5 @ ( produc833389609on_val @ A_25 @ B_5 ) ) ) ).
thf(fact_327_curryE,axiom,
! [F_5: produc1282892786on_val > $o,A_25: exp_list_char,B_5: produc2090907612on_val] :
( ( produc1287763389_val_o @ F_5 @ A_25 @ B_5 )
=> ( F_5 @ ( produc235638504on_val @ A_25 @ B_5 ) ) ) ).
thf(fact_328_curryE,axiom,
! [F_5: produc2090907612on_val > $o,A_25: nat > option1728594148on_val,B_5: list_char > option_val] :
( ( produc1402621651_val_o @ F_5 @ A_25 @ B_5 )
=> ( F_5 @ ( produc755559506on_val @ A_25 @ B_5 ) ) ) ).
thf(fact_329_curryE,axiom,
! [F_5: produc2088785539on_val > $o,A_25: list_char,B_5: produc1278157519t_char > option_val] :
( ( produc1177570924_val_o @ F_5 @ A_25 @ B_5 )
=> ( F_5 @ ( produc926070009on_val @ A_25 @ B_5 ) ) ) ).
thf(fact_330_curryE,axiom,
! [F_5: produc1278157519t_char > $o,A_25: list_char,B_5: list_char] :
( ( produc1709467424char_o @ F_5 @ A_25 @ B_5 )
=> ( F_5 @ ( produc5062597t_char @ A_25 @ B_5 ) ) ) ).
thf(fact_331_curryE,axiom,
! [F_5: produc1645268488al_val > $o,A_25: bop,B_5: product_prod_val_val] :
( ( produc275195559_val_o @ F_5 @ A_25 @ B_5 )
=> ( F_5 @ ( produc621191550al_val @ A_25 @ B_5 ) ) ) ).
thf(fact_332_curryE,axiom,
! [F_5: product_prod_val_val > $o,A_25: val,B_5: val] :
( ( produc575837646_val_o @ F_5 @ A_25 @ B_5 )
=> ( F_5 @ ( product_Pair_val_val @ A_25 @ B_5 ) ) ) ).
thf(fact_333_curryD,axiom,
! [F_4: produc1746408499on_val > $o,A_24: produc1282892786on_val,B_4: produc1282892786on_val] :
( ( produc803302844_val_o @ F_4 @ A_24 @ B_4 )
=> ( F_4 @ ( produc833389609on_val @ A_24 @ B_4 ) ) ) ).
thf(fact_334_curryD,axiom,
! [F_4: produc1282892786on_val > $o,A_24: exp_list_char,B_4: produc2090907612on_val] :
( ( produc1287763389_val_o @ F_4 @ A_24 @ B_4 )
=> ( F_4 @ ( produc235638504on_val @ A_24 @ B_4 ) ) ) ).
thf(fact_335_curryD,axiom,
! [F_4: produc2090907612on_val > $o,A_24: nat > option1728594148on_val,B_4: list_char > option_val] :
( ( produc1402621651_val_o @ F_4 @ A_24 @ B_4 )
=> ( F_4 @ ( produc755559506on_val @ A_24 @ B_4 ) ) ) ).
thf(fact_336_curryD,axiom,
! [F_4: produc2088785539on_val > $o,A_24: list_char,B_4: produc1278157519t_char > option_val] :
( ( produc1177570924_val_o @ F_4 @ A_24 @ B_4 )
=> ( F_4 @ ( produc926070009on_val @ A_24 @ B_4 ) ) ) ).
thf(fact_337_curryD,axiom,
! [F_4: produc1278157519t_char > $o,A_24: list_char,B_4: list_char] :
( ( produc1709467424char_o @ F_4 @ A_24 @ B_4 )
=> ( F_4 @ ( produc5062597t_char @ A_24 @ B_4 ) ) ) ).
thf(fact_338_curryD,axiom,
! [F_4: produc1645268488al_val > $o,A_24: bop,B_4: product_prod_val_val] :
( ( produc275195559_val_o @ F_4 @ A_24 @ B_4 )
=> ( F_4 @ ( produc621191550al_val @ A_24 @ B_4 ) ) ) ).
thf(fact_339_curryD,axiom,
! [F_4: product_prod_val_val > $o,A_24: val,B_4: val] :
( ( produc575837646_val_o @ F_4 @ A_24 @ B_4 )
=> ( F_4 @ ( product_Pair_val_val @ A_24 @ B_4 ) ) ) ).
thf(fact_340_map__add__upd,axiom,
! [F_3: list_char > option_val,G_1: list_char > option_val,X_2: list_char,Y_2: val] :
( ( map_ad325961431ar_val @ F_3 @ ( fun_up1149430426on_val @ G_1 @ X_2 @ ( some_val @ Y_2 ) ) )
= ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ F_3 @ G_1 ) @ X_2 @ ( some_val @ Y_2 ) ) ) ).
thf(fact_341_map__add__upd,axiom,
! [F_3: list_char > option_ty,G_1: list_char > option_ty,X_2: list_char,Y_2: ty] :
( ( map_add_list_char_ty @ F_3 @ ( fun_up424764369ion_ty @ G_1 @ X_2 @ ( some_ty @ Y_2 ) ) )
= ( fun_up424764369ion_ty @ ( map_add_list_char_ty @ F_3 @ G_1 ) @ X_2 @ ( some_ty @ Y_2 ) ) ) ).
thf(fact_342_map__add__upd,axiom,
! [F_3: nat > option1728594148on_val,G_1: nat > option1728594148on_val,X_2: nat,Y_2: produc2088785539on_val] :
( ( map_ad1851375512on_val @ F_3 @ ( fun_up1472480727on_val @ G_1 @ X_2 @ ( some_P451527732on_val @ Y_2 ) ) )
= ( fun_up1472480727on_val @ ( map_ad1851375512on_val @ F_3 @ G_1 ) @ X_2 @ ( some_P451527732on_val @ Y_2 ) ) ) ).
thf(fact_343_map__add__upd,axiom,
! [F_3: produc1278157519t_char > option_val,G_1: produc1278157519t_char > option_val,X_2: produc1278157519t_char,Y_2: val] :
( ( map_ad1185064968ar_val @ F_3 @ ( fun_up204312361on_val @ G_1 @ X_2 @ ( some_val @ Y_2 ) ) )
= ( fun_up204312361on_val @ ( map_ad1185064968ar_val @ F_3 @ G_1 ) @ X_2 @ ( some_val @ Y_2 ) ) ) ).
thf(fact_344_curry__conv,axiom,
! [F_2: produc1746408499on_val > $o,A_23: produc1282892786on_val,B_3: produc1282892786on_val] :
( ( produc803302844_val_o @ F_2 @ A_23 @ B_3 )
<=> ( F_2 @ ( produc833389609on_val @ A_23 @ B_3 ) ) ) ).
thf(fact_345_curry__conv,axiom,
! [F_2: produc1282892786on_val > $o,A_23: exp_list_char,B_3: produc2090907612on_val] :
( ( produc1287763389_val_o @ F_2 @ A_23 @ B_3 )
<=> ( F_2 @ ( produc235638504on_val @ A_23 @ B_3 ) ) ) ).
thf(fact_346_curry__conv,axiom,
! [F_2: produc2090907612on_val > $o,A_23: nat > option1728594148on_val,B_3: list_char > option_val] :
( ( produc1402621651_val_o @ F_2 @ A_23 @ B_3 )
<=> ( F_2 @ ( produc755559506on_val @ A_23 @ B_3 ) ) ) ).
thf(fact_347_curry__conv,axiom,
! [F_2: produc2088785539on_val > $o,A_23: list_char,B_3: produc1278157519t_char > option_val] :
( ( produc1177570924_val_o @ F_2 @ A_23 @ B_3 )
<=> ( F_2 @ ( produc926070009on_val @ A_23 @ B_3 ) ) ) ).
thf(fact_348_curry__conv,axiom,
! [F_2: produc1278157519t_char > $o,A_23: list_char,B_3: list_char] :
( ( produc1709467424char_o @ F_2 @ A_23 @ B_3 )
<=> ( F_2 @ ( produc5062597t_char @ A_23 @ B_3 ) ) ) ).
thf(fact_349_curry__conv,axiom,
! [F_2: produc1645268488al_val > $o,A_23: bop,B_3: product_prod_val_val] :
( ( produc275195559_val_o @ F_2 @ A_23 @ B_3 )
<=> ( F_2 @ ( produc621191550al_val @ A_23 @ B_3 ) ) ) ).
thf(fact_350_curry__conv,axiom,
! [F_2: product_prod_val_val > $o,A_23: val,B_3: val] :
( ( produc575837646_val_o @ F_2 @ A_23 @ B_3 )
<=> ( F_2 @ ( product_Pair_val_val @ A_23 @ B_3 ) ) ) ).
thf(fact_351_lconf__upd2,axiom,
! [V_10: list_char,V_9: val,T_5: ty,P_7: list_P1999446415t_char,H_8: nat > option1728594148on_val,L_6: list_char > option_val,E_9: list_char > option_ty] :
( ( lconf_496643946t_char @ P_7 @ H_8 @ L_6 @ E_9 )
=> ( ( conf_P373316194t_char @ P_7 @ H_8 @ V_9 @ T_5 )
=> ( lconf_496643946t_char @ P_7 @ H_8 @ ( fun_up1149430426on_val @ L_6 @ V_10 @ ( some_val @ V_9 ) ) @ ( fun_up424764369ion_ty @ E_9 @ V_10 @ ( some_ty @ T_5 ) ) ) ) ) ).
thf(fact_352_WTrtBlock,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_4: list_char > option_ty,V_4: list_char,T: ty,E_1: exp_list_char,T_4: ty] :
( ( wTrt @ P @ H @ ( fun_up424764369ion_ty @ E_4 @ V_4 @ ( some_ty @ T ) ) @ E_1 @ T_4 )
=> ( wTrt @ P @ H @ E_4 @ ( block_list_char @ V_4 @ T @ E_1 ) @ T_4 ) ) ).
thf(fact_353_splitE,axiom,
! [C_7: produc1282892786on_val > produc1282892786on_val > $o,P_6: produc1746408499on_val] :
( ( produc1624062875_val_o @ C_7 @ P_6 )
=> ~ ! [X_1: produc1282892786on_val,Y_1: produc1282892786on_val] :
( ( P_6
= ( produc833389609on_val @ X_1 @ Y_1 ) )
=> ~ ( C_7 @ X_1 @ Y_1 ) ) ) ).
thf(fact_354_splitE,axiom,
! [C_7: exp_list_char > produc2090907612on_val > $o,P_6: produc1282892786on_val] :
( ( produc1835097372_val_o @ C_7 @ P_6 )
=> ~ ! [X_1: exp_list_char,Y_1: produc2090907612on_val] :
( ( P_6
= ( produc235638504on_val @ X_1 @ Y_1 ) )
=> ~ ( C_7 @ X_1 @ Y_1 ) ) ) ).
thf(fact_355_splitE,axiom,
! [C_7: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,P_6: produc2090907612on_val] :
( ( produc252486962_val_o @ C_7 @ P_6 )
=> ~ ! [X_1: nat > option1728594148on_val,Y_1: list_char > option_val] :
( ( P_6
= ( produc755559506on_val @ X_1 @ Y_1 ) )
=> ~ ( C_7 @ X_1 @ Y_1 ) ) ) ).
thf(fact_356_splitE,axiom,
! [C_7: list_char > ( produc1278157519t_char > option_val ) > $o,P_6: produc2088785539on_val] :
( ( produc765165771_val_o @ C_7 @ P_6 )
=> ~ ! [X_1: list_char,Y_1: produc1278157519t_char > option_val] :
( ( P_6
= ( produc926070009on_val @ X_1 @ Y_1 ) )
=> ~ ( C_7 @ X_1 @ Y_1 ) ) ) ).
thf(fact_357_splitE,axiom,
! [C_7: list_char > list_char > $o,P_6: produc1278157519t_char] :
( ( produc282231039char_o @ C_7 @ P_6 )
=> ~ ! [X_1: list_char,Y_1: list_char] :
( ( P_6
= ( produc5062597t_char @ X_1 @ Y_1 ) )
=> ~ ( C_7 @ X_1 @ Y_1 ) ) ) ).
thf(fact_358_splitE,axiom,
! [C_7: bop > product_prod_val_val > $o,P_6: produc1645268488al_val] :
( ( produc1063861510_val_o @ C_7 @ P_6 )
=> ~ ! [X_1: bop,Y_1: product_prod_val_val] :
( ( P_6
= ( produc621191550al_val @ X_1 @ Y_1 ) )
=> ~ ( C_7 @ X_1 @ Y_1 ) ) ) ).
thf(fact_359_splitE,axiom,
! [C_7: val > val > $o,P_6: product_prod_val_val] :
( ( produc9430317_val_o @ C_7 @ P_6 )
=> ~ ! [X_1: val,Y_1: val] :
( ( P_6
= ( product_Pair_val_val @ X_1 @ Y_1 ) )
=> ~ ( C_7 @ X_1 @ Y_1 ) ) ) ).
thf(fact_360_splitI2,axiom,
! [C_6: produc1282892786on_val > produc1282892786on_val > $o,P_5: produc1746408499on_val] :
( ! [A: produc1282892786on_val,B_1: produc1282892786on_val] :
( ( P_5
= ( produc833389609on_val @ A @ B_1 ) )
=> ( C_6 @ A @ B_1 ) )
=> ( produc1624062875_val_o @ C_6 @ P_5 ) ) ).
thf(fact_361_splitI2,axiom,
! [C_6: exp_list_char > produc2090907612on_val > $o,P_5: produc1282892786on_val] :
( ! [A: exp_list_char,B_1: produc2090907612on_val] :
( ( P_5
= ( produc235638504on_val @ A @ B_1 ) )
=> ( C_6 @ A @ B_1 ) )
=> ( produc1835097372_val_o @ C_6 @ P_5 ) ) ).
thf(fact_362_splitI2,axiom,
! [C_6: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,P_5: produc2090907612on_val] :
( ! [A: nat > option1728594148on_val,B_1: list_char > option_val] :
( ( P_5
= ( produc755559506on_val @ A @ B_1 ) )
=> ( C_6 @ A @ B_1 ) )
=> ( produc252486962_val_o @ C_6 @ P_5 ) ) ).
thf(fact_363_splitI2,axiom,
! [C_6: list_char > ( produc1278157519t_char > option_val ) > $o,P_5: produc2088785539on_val] :
( ! [A: list_char,B_1: produc1278157519t_char > option_val] :
( ( P_5
= ( produc926070009on_val @ A @ B_1 ) )
=> ( C_6 @ A @ B_1 ) )
=> ( produc765165771_val_o @ C_6 @ P_5 ) ) ).
thf(fact_364_splitI2,axiom,
! [C_6: list_char > list_char > $o,P_5: produc1278157519t_char] :
( ! [A: list_char,B_1: list_char] :
( ( P_5
= ( produc5062597t_char @ A @ B_1 ) )
=> ( C_6 @ A @ B_1 ) )
=> ( produc282231039char_o @ C_6 @ P_5 ) ) ).
thf(fact_365_splitI2,axiom,
! [C_6: bop > product_prod_val_val > $o,P_5: produc1645268488al_val] :
( ! [A: bop,B_1: product_prod_val_val] :
( ( P_5
= ( produc621191550al_val @ A @ B_1 ) )
=> ( C_6 @ A @ B_1 ) )
=> ( produc1063861510_val_o @ C_6 @ P_5 ) ) ).
thf(fact_366_splitI2,axiom,
! [C_6: val > val > $o,P_5: product_prod_val_val] :
( ! [A: val,B_1: val] :
( ( P_5
= ( product_Pair_val_val @ A @ B_1 ) )
=> ( C_6 @ A @ B_1 ) )
=> ( produc9430317_val_o @ C_6 @ P_5 ) ) ).
thf(fact_367_WTrtSeq,axiom,
! [E_2: exp_list_char,T_2_1: ty,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_4: list_char > option_ty,E_1_1: exp_list_char,T_1_2: ty] :
( ( wTrt @ P @ H @ E_4 @ E_1_1 @ T_1_2 )
=> ( ( wTrt @ P @ H @ E_4 @ E_2 @ T_2_1 )
=> ( wTrt @ P @ H @ E_4 @ ( seq_list_char @ E_1_1 @ E_2 ) @ T_2_1 ) ) ) ).
thf(fact_368_lconf__def,axiom,
! [P_4: list_P1999446415t_char,H_7: nat > option1728594148on_val,L_5: list_char > option_val,E_8: list_char > option_ty] :
( ( lconf_496643946t_char @ P_4 @ H_7 @ L_5 @ E_8 )
<=> ! [V_8: list_char,V_3: val] :
( ( ( L_5 @ V_8 )
= ( some_val @ V_3 ) )
=> ? [T_1: ty] :
( ( ( E_8 @ V_8 )
= ( some_ty @ T_1 ) )
& ( conf_P373316194t_char @ P_4 @ H_7 @ V_3 @ T_1 ) ) ) ) ).
thf(fact_369_red__reds_ORedLAss,axiom,
! [V_4: list_char,V: val,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V_4 @ ( val_list_char @ V ) ) @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ ( val_list_char @ unit ) @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_4 @ ( some_val @ V ) ) ) ) ) @ ( red @ P ) ) ).
thf(fact_370_hext__refl,axiom,
! [H: nat > option1728594148on_val] : ( hext @ H @ H ) ).
thf(fact_371_cond__split__eta,axiom,
! [G: produc2090907612on_val > $o,F_1: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o] :
( ! [X_1: nat > option1728594148on_val,Y_1: list_char > option_val] :
( ( F_1 @ X_1 @ Y_1 )
<=> ( G @ ( produc755559506on_val @ X_1 @ Y_1 ) ) )
=> ( ( produc252486962_val_o @ F_1 )
= G ) ) ).
thf(fact_372_cond__split__eta,axiom,
! [G: produc1746408499on_val > $o,F_1: produc1282892786on_val > produc1282892786on_val > $o] :
( ! [X_1: produc1282892786on_val,Y_1: produc1282892786on_val] :
( ( F_1 @ X_1 @ Y_1 )
<=> ( G @ ( produc833389609on_val @ X_1 @ Y_1 ) ) )
=> ( ( produc1624062875_val_o @ F_1 )
= G ) ) ).
thf(fact_373_cond__split__eta,axiom,
! [G: produc1282892786on_val > $o,F_1: exp_list_char > produc2090907612on_val > $o] :
( ! [X_1: exp_list_char,Y_1: produc2090907612on_val] :
( ( F_1 @ X_1 @ Y_1 )
<=> ( G @ ( produc235638504on_val @ X_1 @ Y_1 ) ) )
=> ( ( produc1835097372_val_o @ F_1 )
= G ) ) ).
thf(fact_374_cond__split__eta,axiom,
! [G: produc2088785539on_val > $o,F_1: list_char > ( produc1278157519t_char > option_val ) > $o] :
( ! [X_1: list_char,Y_1: produc1278157519t_char > option_val] :
( ( F_1 @ X_1 @ Y_1 )
<=> ( G @ ( produc926070009on_val @ X_1 @ Y_1 ) ) )
=> ( ( produc765165771_val_o @ F_1 )
= G ) ) ).
thf(fact_375_cond__split__eta,axiom,
! [G: produc1278157519t_char > $o,F_1: list_char > list_char > $o] :
( ! [X_1: list_char,Y_1: list_char] :
( ( F_1 @ X_1 @ Y_1 )
<=> ( G @ ( produc5062597t_char @ X_1 @ Y_1 ) ) )
=> ( ( produc282231039char_o @ F_1 )
= G ) ) ).
thf(fact_376_cond__split__eta,axiom,
! [G: produc1645268488al_val > $o,F_1: bop > product_prod_val_val > $o] :
( ! [X_1: bop,Y_1: product_prod_val_val] :
( ( F_1 @ X_1 @ Y_1 )
<=> ( G @ ( produc621191550al_val @ X_1 @ Y_1 ) ) )
=> ( ( produc1063861510_val_o @ F_1 )
= G ) ) ).
thf(fact_377_cond__split__eta,axiom,
! [G: product_prod_val_val > $o,F_1: val > val > $o] :
( ! [X_1: val,Y_1: val] :
( ( F_1 @ X_1 @ Y_1 )
<=> ( G @ ( product_Pair_val_val @ X_1 @ Y_1 ) ) )
=> ( ( produc9430317_val_o @ F_1 )
= G ) ) ).
thf(fact_378_domD,axiom,
! [A_22: nat,M: nat > option_val] :
( ( member_nat @ A_22 @ ( dom_nat_val @ M ) )
=> ? [B_1: val] :
( ( M @ A_22 )
= ( some_val @ B_1 ) ) ) ).
thf(fact_379_domD,axiom,
! [A_22: product_prod_val_val,M: product_prod_val_val > option_val] :
( ( member649088532al_val @ A_22 @ ( dom_Pr1854948307al_val @ M ) )
=> ? [B_1: val] :
( ( M @ A_22 )
= ( some_val @ B_1 ) ) ) ).
thf(fact_380_domD,axiom,
! [A_22: produc1645268488al_val,M: produc1645268488al_val > option_val] :
( ( member1417904245al_val @ A_22 @ ( dom_Pr934474290al_val @ M ) )
=> ? [B_1: val] :
( ( M @ A_22 )
= ( some_val @ B_1 ) ) ) ).
thf(fact_381_domD,axiom,
! [A_22: produc2088785539on_val,M: produc2088785539on_val > option_val] :
( ( member1374264560on_val @ A_22 @ ( dom_Pr397909495al_val @ M ) )
=> ? [B_1: val] :
( ( M @ A_22 )
= ( some_val @ B_1 ) ) ) ).
thf(fact_382_domD,axiom,
! [A_22: produc2090907612on_val,M: produc2090907612on_val > option_val] :
( ( member1846553161on_val @ A_22 @ ( dom_Pr1333147486al_val @ M ) )
=> ? [B_1: val] :
( ( M @ A_22 )
= ( some_val @ B_1 ) ) ) ).
thf(fact_383_domD,axiom,
! [A_22: produc1282892786on_val,M: produc1282892786on_val > option_val] :
( ( member1072200031on_val @ A_22 @ ( dom_Pr959892680al_val @ M ) )
=> ? [B_1: val] :
( ( M @ A_22 )
= ( some_val @ B_1 ) ) ) ).
thf(fact_384_domD,axiom,
! [A_22: list_char,M: list_char > option_list_char_o] :
( ( member_list_char @ A_22 @ ( dom_li115714383char_o @ M ) )
=> ? [B_1: list_char > $o] :
( ( M @ A_22 )
= ( some_list_char_o @ B_1 ) ) ) ).
thf(fact_385_domD,axiom,
! [A_22: nat,M: nat > option_list_char_o] :
( ( member_nat @ A_22 @ ( dom_nat_list_char_o @ M ) )
=> ? [B_1: list_char > $o] :
( ( M @ A_22 )
= ( some_list_char_o @ B_1 ) ) ) ).
thf(fact_386_domD,axiom,
! [A_22: product_prod_val_val,M: product_prod_val_val > option_list_char_o] :
( ( member649088532al_val @ A_22 @ ( dom_Pr581342760char_o @ M ) )
=> ? [B_1: list_char > $o] :
( ( M @ A_22 )
= ( some_list_char_o @ B_1 ) ) ) ).
thf(fact_387_domD,axiom,
! [A_22: produc1645268488al_val,M: produc1645268488al_val > option_list_char_o] :
( ( member1417904245al_val @ A_22 @ ( dom_Pr1531186439char_o @ M ) )
=> ? [B_1: list_char > $o] :
( ( M @ A_22 )
= ( some_list_char_o @ B_1 ) ) ) ).
thf(fact_388_domD,axiom,
! [A_22: produc2088785539on_val,M: produc2088785539on_val > option_list_char_o] :
( ( member1374264560on_val @ A_22 @ ( dom_Pr957742668char_o @ M ) )
=> ? [B_1: list_char > $o] :
( ( M @ A_22 )
= ( some_list_char_o @ B_1 ) ) ) ).
thf(fact_389_domD,axiom,
! [A_22: produc2090907612on_val,M: produc2090907612on_val > option_list_char_o] :
( ( member1846553161on_val @ A_22 @ ( dom_Pr1958353971char_o @ M ) )
=> ? [B_1: list_char > $o] :
( ( M @ A_22 )
= ( some_list_char_o @ B_1 ) ) ) ).
thf(fact_390_domD,axiom,
! [A_22: produc1282892786on_val,M: produc1282892786on_val > option_list_char_o] :
( ( member1072200031on_val @ A_22 @ ( dom_Pr373640349char_o @ M ) )
=> ? [B_1: list_char > $o] :
( ( M @ A_22 )
= ( some_list_char_o @ B_1 ) ) ) ).
thf(fact_391_domD,axiom,
! [A_22: list_char,M: list_char > option_ty] :
( ( member_list_char @ A_22 @ ( dom_list_char_ty @ M ) )
=> ? [B_1: ty] :
( ( M @ A_22 )
= ( some_ty @ B_1 ) ) ) ).
thf(fact_392_domD,axiom,
! [A_22: nat,M: nat > option_ty] :
( ( member_nat @ A_22 @ ( dom_nat_ty @ M ) )
=> ? [B_1: ty] :
( ( M @ A_22 )
= ( some_ty @ B_1 ) ) ) ).
thf(fact_393_domD,axiom,
! [A_22: product_prod_val_val,M: product_prod_val_val > option_ty] :
( ( member649088532al_val @ A_22 @ ( dom_Pr1536367242val_ty @ M ) )
=> ? [B_1: ty] :
( ( M @ A_22 )
= ( some_ty @ B_1 ) ) ) ).
thf(fact_394_domD,axiom,
! [A_22: produc1645268488al_val,M: produc1645268488al_val > option_ty] :
( ( member1417904245al_val @ A_22 @ ( dom_Pr585943145val_ty @ M ) )
=> ? [B_1: ty] :
( ( M @ A_22 )
= ( some_ty @ B_1 ) ) ) ).
thf(fact_395_domD,axiom,
! [A_22: produc2088785539on_val,M: produc2088785539on_val > option_ty] :
( ( member1374264560on_val @ A_22 @ ( dom_Pr970344110val_ty @ M ) )
=> ? [B_1: ty] :
( ( M @ A_22 )
= ( some_ty @ B_1 ) ) ) ).
thf(fact_396_domD,axiom,
! [A_22: produc2090907612on_val,M: produc2090907612on_val > option_ty] :
( ( member1846553161on_val @ A_22 @ ( dom_Pr878896021val_ty @ M ) )
=> ? [B_1: ty] :
( ( M @ A_22 )
= ( some_ty @ B_1 ) ) ) ).
thf(fact_397_domD,axiom,
! [A_22: produc1282892786on_val,M: produc1282892786on_val > option_ty] :
( ( member1072200031on_val @ A_22 @ ( dom_Pr1290145279val_ty @ M ) )
=> ? [B_1: ty] :
( ( M @ A_22 )
= ( some_ty @ B_1 ) ) ) ).
thf(fact_398_domD,axiom,
! [A_22: nat,M: nat > option1728594148on_val] :
( ( member_nat @ A_22 @ ( dom_na2045926843on_val @ M ) )
=> ? [B_1: produc2088785539on_val] :
( ( M @ A_22 )
= ( some_P451527732on_val @ B_1 ) ) ) ).
thf(fact_399_domD,axiom,
! [A_22: list_char,M: list_char > option1728594148on_val] :
( ( member_list_char @ A_22 @ ( dom_li96736835on_val @ M ) )
=> ? [B_1: produc2088785539on_val] :
( ( M @ A_22 )
= ( some_P451527732on_val @ B_1 ) ) ) ).
thf(fact_400_domD,axiom,
! [A_22: product_prod_val_val,M: product_prod_val_val > option1728594148on_val] :
( ( member649088532al_val @ A_22 @ ( dom_Pr283571498on_val @ M ) )
=> ? [B_1: produc2088785539on_val] :
( ( M @ A_22 )
= ( some_P451527732on_val @ B_1 ) ) ) ).
thf(fact_401_domD,axiom,
! [A_22: produc1645268488al_val,M: produc1645268488al_val > option1728594148on_val] :
( ( member1417904245al_val @ A_22 @ ( dom_Pr1903277195on_val @ M ) )
=> ? [B_1: produc2088785539on_val] :
( ( M @ A_22 )
= ( some_P451527732on_val @ B_1 ) ) ) ).
thf(fact_402_domD,axiom,
! [A_22: produc2088785539on_val,M: produc2088785539on_val > option1728594148on_val] :
( ( member1374264560on_val @ A_22 @ ( dom_Pr1058999302on_val @ M ) )
=> ? [B_1: produc2088785539on_val] :
( ( M @ A_22 )
= ( some_P451527732on_val @ B_1 ) ) ) ).
thf(fact_403_domD,axiom,
! [A_22: produc2090907612on_val,M: produc2090907612on_val > option1728594148on_val] :
( ( member1846553161on_val @ A_22 @ ( dom_Pr1306915423on_val @ M ) )
=> ? [B_1: produc2088785539on_val] :
( ( M @ A_22 )
= ( some_P451527732on_val @ B_1 ) ) ) ).
thf(fact_404_domD,axiom,
! [A_22: produc1282892786on_val,M: produc1282892786on_val > option1728594148on_val] :
( ( member1072200031on_val @ A_22 @ ( dom_Pr1372035957on_val @ M ) )
=> ? [B_1: produc2088785539on_val] :
( ( M @ A_22 )
= ( some_P451527732on_val @ B_1 ) ) ) ).
thf(fact_405_domD,axiom,
! [A_22: produc1278157519t_char,M: produc1278157519t_char > option_val] :
( ( member1251428284t_char @ A_22 @ ( dom_Pr695701035ar_val @ M ) )
=> ? [B_1: val] :
( ( M @ A_22 )
= ( some_val @ B_1 ) ) ) ).
thf(fact_406_domD,axiom,
! [A_22: list_char,M: list_char > option_val] :
( ( member_list_char @ A_22 @ ( dom_list_char_val @ M ) )
=> ? [B_1: val] :
( ( M @ A_22 )
= ( some_val @ B_1 ) ) ) ).
thf(fact_407_splitE2,axiom,
! [Q: $o > $o,P_3: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,Z_2: produc2090907612on_val] :
( ( Q @ ( produc252486962_val_o @ P_3 @ Z_2 ) )
=> ~ ! [X_1: nat > option1728594148on_val,Y_1: list_char > option_val] :
( ( Z_2
= ( produc755559506on_val @ X_1 @ Y_1 ) )
=> ~ ( Q @ ( P_3 @ X_1 @ Y_1 ) ) ) ) ).
thf(fact_408_splitE2,axiom,
! [Q: $o > $o,P_3: produc1282892786on_val > produc1282892786on_val > $o,Z_2: produc1746408499on_val] :
( ( Q @ ( produc1624062875_val_o @ P_3 @ Z_2 ) )
=> ~ ! [X_1: produc1282892786on_val,Y_1: produc1282892786on_val] :
( ( Z_2
= ( produc833389609on_val @ X_1 @ Y_1 ) )
=> ~ ( Q @ ( P_3 @ X_1 @ Y_1 ) ) ) ) ).
thf(fact_409_splitE2,axiom,
! [Q: $o > $o,P_3: exp_list_char > produc2090907612on_val > $o,Z_2: produc1282892786on_val] :
( ( Q @ ( produc1835097372_val_o @ P_3 @ Z_2 ) )
=> ~ ! [X_1: exp_list_char,Y_1: produc2090907612on_val] :
( ( Z_2
= ( produc235638504on_val @ X_1 @ Y_1 ) )
=> ~ ( Q @ ( P_3 @ X_1 @ Y_1 ) ) ) ) ).
thf(fact_410_splitE2,axiom,
! [Q: $o > $o,P_3: list_char > ( produc1278157519t_char > option_val ) > $o,Z_2: produc2088785539on_val] :
( ( Q @ ( produc765165771_val_o @ P_3 @ Z_2 ) )
=> ~ ! [X_1: list_char,Y_1: produc1278157519t_char > option_val] :
( ( Z_2
= ( produc926070009on_val @ X_1 @ Y_1 ) )
=> ~ ( Q @ ( P_3 @ X_1 @ Y_1 ) ) ) ) ).
thf(fact_411_splitE2,axiom,
! [Q: $o > $o,P_3: list_char > list_char > $o,Z_2: produc1278157519t_char] :
( ( Q @ ( produc282231039char_o @ P_3 @ Z_2 ) )
=> ~ ! [X_1: list_char,Y_1: list_char] :
( ( Z_2
= ( produc5062597t_char @ X_1 @ Y_1 ) )
=> ~ ( Q @ ( P_3 @ X_1 @ Y_1 ) ) ) ) ).
thf(fact_412_splitE2,axiom,
! [Q: $o > $o,P_3: bop > product_prod_val_val > $o,Z_2: produc1645268488al_val] :
( ( Q @ ( produc1063861510_val_o @ P_3 @ Z_2 ) )
=> ~ ! [X_1: bop,Y_1: product_prod_val_val] :
( ( Z_2
= ( produc621191550al_val @ X_1 @ Y_1 ) )
=> ~ ( Q @ ( P_3 @ X_1 @ Y_1 ) ) ) ) ).
thf(fact_413_splitE2,axiom,
! [Q: $o > $o,P_3: val > val > $o,Z_2: product_prod_val_val] :
( ( Q @ ( produc9430317_val_o @ P_3 @ Z_2 ) )
=> ~ ! [X_1: val,Y_1: val] :
( ( Z_2
= ( product_Pair_val_val @ X_1 @ Y_1 ) )
=> ~ ( Q @ ( P_3 @ X_1 @ Y_1 ) ) ) ) ).
thf(fact_414_mem__splitI,axiom,
! [Z_1: list_char,C_5: produc1282892786on_val > produc1282892786on_val > list_char > $o,A_21: produc1282892786on_val,B_2: produc1282892786on_val] :
( ( member_list_char @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member_list_char @ Z_1 @ ( produc942102907char_o @ C_5 @ ( produc833389609on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_415_mem__splitI,axiom,
! [Z_1: nat,C_5: produc1282892786on_val > produc1282892786on_val > nat > $o,A_21: produc1282892786on_val,B_2: produc1282892786on_val] :
( ( member_nat @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member_nat @ Z_1 @ ( produc1524362759_nat_o @ C_5 @ ( produc833389609on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_416_mem__splitI,axiom,
! [Z_1: product_prod_val_val,C_5: produc1282892786on_val > produc1282892786on_val > product_prod_val_val > $o,A_21: produc1282892786on_val,B_2: produc1282892786on_val] :
( ( member649088532al_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member649088532al_val @ Z_1 @ ( produc545397204_val_o @ C_5 @ ( produc833389609on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_417_mem__splitI,axiom,
! [Z_1: produc1645268488al_val,C_5: produc1282892786on_val > produc1282892786on_val > produc1645268488al_val > $o,A_21: produc1282892786on_val,B_2: produc1282892786on_val] :
( ( member1417904245al_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1417904245al_val @ Z_1 @ ( produc836145971_val_o @ C_5 @ ( produc833389609on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_418_mem__splitI,axiom,
! [Z_1: produc2088785539on_val,C_5: produc1282892786on_val > produc1282892786on_val > produc2088785539on_val > $o,A_21: produc1282892786on_val,B_2: produc1282892786on_val] :
( ( member1374264560on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1374264560on_val @ Z_1 @ ( produc1122313720_val_o @ C_5 @ ( produc833389609on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_419_mem__splitI,axiom,
! [Z_1: produc2090907612on_val,C_5: produc1282892786on_val > produc1282892786on_val > produc2090907612on_val > $o,A_21: produc1282892786on_val,B_2: produc1282892786on_val] :
( ( member1846553161on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1846553161on_val @ Z_1 @ ( produc793795679_val_o @ C_5 @ ( produc833389609on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_420_mem__splitI,axiom,
! [Z_1: produc1282892786on_val,C_5: produc1282892786on_val > produc1282892786on_val > produc1282892786on_val > $o,A_21: produc1282892786on_val,B_2: produc1282892786on_val] :
( ( member1072200031on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1072200031on_val @ Z_1 @ ( produc1798214089_val_o @ C_5 @ ( produc833389609on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_421_mem__splitI,axiom,
! [Z_1: list_char,C_5: exp_list_char > produc2090907612on_val > list_char > $o,A_21: exp_list_char,B_2: produc2090907612on_val] :
( ( member_list_char @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member_list_char @ Z_1 @ ( produc279240572char_o @ C_5 @ ( produc235638504on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_422_mem__splitI,axiom,
! [Z_1: nat,C_5: exp_list_char > produc2090907612on_val > nat > $o,A_21: exp_list_char,B_2: produc2090907612on_val] :
( ( member_nat @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member_nat @ Z_1 @ ( produc1795400262_nat_o @ C_5 @ ( produc235638504on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_423_mem__splitI,axiom,
! [Z_1: product_prod_val_val,C_5: exp_list_char > produc2090907612on_val > product_prod_val_val > $o,A_21: exp_list_char,B_2: produc2090907612on_val] :
( ( member649088532al_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member649088532al_val @ Z_1 @ ( produc193813973_val_o @ C_5 @ ( produc235638504on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_424_mem__splitI,axiom,
! [Z_1: produc1645268488al_val,C_5: exp_list_char > produc2090907612on_val > produc1645268488al_val > $o,A_21: exp_list_char,B_2: produc2090907612on_val] :
( ( member1417904245al_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1417904245al_val @ Z_1 @ ( produc156332084_val_o @ C_5 @ ( produc235638504on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_425_mem__splitI,axiom,
! [Z_1: produc2088785539on_val,C_5: exp_list_char > produc2090907612on_val > produc2088785539on_val > $o,A_21: exp_list_char,B_2: produc2090907612on_val] :
( ( member1374264560on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1374264560on_val @ Z_1 @ ( produc1552443129_val_o @ C_5 @ ( produc235638504on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_426_mem__splitI,axiom,
! [Z_1: produc2090907612on_val,C_5: exp_list_char > produc2090907612on_val > produc2090907612on_val > $o,A_21: exp_list_char,B_2: produc2090907612on_val] :
( ( member1846553161on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1846553161on_val @ Z_1 @ ( produc1115879776_val_o @ C_5 @ ( produc235638504on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_427_mem__splitI,axiom,
! [Z_1: produc1282892786on_val,C_5: exp_list_char > produc2090907612on_val > produc1282892786on_val > $o,A_21: exp_list_char,B_2: produc2090907612on_val] :
( ( member1072200031on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1072200031on_val @ Z_1 @ ( produc68058570_val_o @ C_5 @ ( produc235638504on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_428_mem__splitI,axiom,
! [Z_1: list_char,C_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > list_char > $o,A_21: nat > option1728594148on_val,B_2: list_char > option_val] :
( ( member_list_char @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member_list_char @ Z_1 @ ( produc546196114char_o @ C_5 @ ( produc755559506on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_429_mem__splitI,axiom,
! [Z_1: nat,C_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > nat > $o,A_21: nat > option1728594148on_val,B_2: list_char > option_val] :
( ( member_nat @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member_nat @ Z_1 @ ( produc1075640496_nat_o @ C_5 @ ( produc755559506on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_430_mem__splitI,axiom,
! [Z_1: product_prod_val_val,C_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > product_prod_val_val > $o,A_21: nat > option1728594148on_val,B_2: list_char > option_val] :
( ( member649088532al_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member649088532al_val @ Z_1 @ ( produc1880562923_val_o @ C_5 @ ( produc755559506on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_431_mem__splitI,axiom,
! [Z_1: produc1645268488al_val,C_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1645268488al_val > $o,A_21: nat > option1728594148on_val,B_2: list_char > option_val] :
( ( member1417904245al_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1417904245al_val @ Z_1 @ ( produc528569674_val_o @ C_5 @ ( produc755559506on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_432_mem__splitI,axiom,
! [Z_1: produc2088785539on_val,C_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2088785539on_val > $o,A_21: nat > option1728594148on_val,B_2: list_char > option_val] :
( ( member1374264560on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1374264560on_val @ Z_1 @ ( produc1215095823_val_o @ C_5 @ ( produc755559506on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_433_mem__splitI,axiom,
! [Z_1: produc2090907612on_val,C_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2090907612on_val > $o,A_21: nat > option1728594148on_val,B_2: list_char > option_val] :
( ( member1846553161on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1846553161on_val @ Z_1 @ ( produc146628214_val_o @ C_5 @ ( produc755559506on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_434_mem__splitI,axiom,
! [Z_1: produc1282892786on_val,C_5: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc1282892786on_val > $o,A_21: nat > option1728594148on_val,B_2: list_char > option_val] :
( ( member1072200031on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1072200031on_val @ Z_1 @ ( produc74886368_val_o @ C_5 @ ( produc755559506on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_435_mem__splitI,axiom,
! [Z_1: list_char,C_5: list_char > ( produc1278157519t_char > option_val ) > list_char > $o,A_21: list_char,B_2: produc1278157519t_char > option_val] :
( ( member_list_char @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member_list_char @ Z_1 @ ( produc1019934379char_o @ C_5 @ ( produc926070009on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_436_mem__splitI,axiom,
! [Z_1: nat,C_5: list_char > ( produc1278157519t_char > option_val ) > nat > $o,A_21: list_char,B_2: produc1278157519t_char > option_val] :
( ( member_nat @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member_nat @ Z_1 @ ( produc1168407767_nat_o @ C_5 @ ( produc926070009on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_437_mem__splitI,axiom,
! [Z_1: product_prod_val_val,C_5: list_char > ( produc1278157519t_char > option_val ) > product_prod_val_val > $o,A_21: list_char,B_2: produc1278157519t_char > option_val] :
( ( member649088532al_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member649088532al_val @ Z_1 @ ( produc2105497348_val_o @ C_5 @ ( produc926070009on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_438_mem__splitI,axiom,
! [Z_1: produc1645268488al_val,C_5: list_char > ( produc1278157519t_char > option_val ) > produc1645268488al_val > $o,A_21: list_char,B_2: produc1278157519t_char > option_val] :
( ( member1417904245al_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1417904245al_val @ Z_1 @ ( produc762675299_val_o @ C_5 @ ( produc926070009on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_439_mem__splitI,axiom,
! [Z_1: produc2088785539on_val,C_5: list_char > ( produc1278157519t_char > option_val ) > produc2088785539on_val > $o,A_21: list_char,B_2: produc1278157519t_char > option_val] :
( ( member1374264560on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1374264560on_val @ Z_1 @ ( produc250270504_val_o @ C_5 @ ( produc926070009on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_440_mem__splitI,axiom,
! [Z_1: produc2090907612on_val,C_5: list_char > ( produc1278157519t_char > option_val ) > produc2090907612on_val > $o,A_21: list_char,B_2: produc1278157519t_char > option_val] :
( ( member1846553161on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1846553161on_val @ Z_1 @ ( produc371411343_val_o @ C_5 @ ( produc926070009on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_441_mem__splitI,axiom,
! [Z_1: produc1282892786on_val,C_5: list_char > ( produc1278157519t_char > option_val ) > produc1282892786on_val > $o,A_21: list_char,B_2: produc1278157519t_char > option_val] :
( ( member1072200031on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1072200031on_val @ Z_1 @ ( produc370364153_val_o @ C_5 @ ( produc926070009on_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_442_mem__splitI,axiom,
! [Z_1: list_char,C_5: list_char > list_char > list_char > $o,A_21: list_char,B_2: list_char] :
( ( member_list_char @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member_list_char @ Z_1 @ ( produc1602969823char_o @ C_5 @ ( produc5062597t_char @ A_21 @ B_2 ) ) ) ) ).
thf(fact_443_mem__splitI,axiom,
! [Z_1: nat,C_5: list_char > list_char > nat > $o,A_21: list_char,B_2: list_char] :
( ( member_nat @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member_nat @ Z_1 @ ( produc823420835_nat_o @ C_5 @ ( produc5062597t_char @ A_21 @ B_2 ) ) ) ) ).
thf(fact_444_mem__splitI,axiom,
! [Z_1: product_prod_val_val,C_5: list_char > list_char > product_prod_val_val > $o,A_21: list_char,B_2: list_char] :
( ( member649088532al_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member649088532al_val @ Z_1 @ ( produc707156280_val_o @ C_5 @ ( produc5062597t_char @ A_21 @ B_2 ) ) ) ) ).
thf(fact_445_mem__splitI,axiom,
! [Z_1: produc1645268488al_val,C_5: list_char > list_char > produc1645268488al_val > $o,A_21: list_char,B_2: list_char] :
( ( member1417904245al_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1417904245al_val @ Z_1 @ ( produc967415447_val_o @ C_5 @ ( produc5062597t_char @ A_21 @ B_2 ) ) ) ) ).
thf(fact_446_mem__splitI,axiom,
! [Z_1: produc2088785539on_val,C_5: list_char > list_char > produc2088785539on_val > $o,A_21: list_char,B_2: list_char] :
( ( member1374264560on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1374264560on_val @ Z_1 @ ( produc584792412_val_o @ C_5 @ ( produc5062597t_char @ A_21 @ B_2 ) ) ) ) ).
thf(fact_447_mem__splitI,axiom,
! [Z_1: produc2090907612on_val,C_5: list_char > list_char > produc2090907612on_val > $o,A_21: list_char,B_2: list_char] :
( ( member1846553161on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1846553161on_val @ Z_1 @ ( produc1730830275_val_o @ C_5 @ ( produc5062597t_char @ A_21 @ B_2 ) ) ) ) ).
thf(fact_448_mem__splitI,axiom,
! [Z_1: produc1282892786on_val,C_5: list_char > list_char > produc1282892786on_val > $o,A_21: list_char,B_2: list_char] :
( ( member1072200031on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1072200031on_val @ Z_1 @ ( produc1656516909_val_o @ C_5 @ ( produc5062597t_char @ A_21 @ B_2 ) ) ) ) ).
thf(fact_449_mem__splitI,axiom,
! [Z_1: list_char,C_5: bop > product_prod_val_val > list_char > $o,A_21: bop,B_2: product_prod_val_val] :
( ( member_list_char @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member_list_char @ Z_1 @ ( produc1671601254char_o @ C_5 @ ( produc621191550al_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_450_mem__splitI,axiom,
! [Z_1: nat,C_5: bop > product_prod_val_val > nat > $o,A_21: bop,B_2: product_prod_val_val] :
( ( member_nat @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member_nat @ Z_1 @ ( produc2010981340_nat_o @ C_5 @ ( produc621191550al_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_451_mem__splitI,axiom,
! [Z_1: product_prod_val_val,C_5: bop > product_prod_val_val > product_prod_val_val > $o,A_21: bop,B_2: product_prod_val_val] :
( ( member649088532al_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member649088532al_val @ Z_1 @ ( produc26920639_val_o @ C_5 @ ( produc621191550al_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_452_mem__splitI,axiom,
! [Z_1: produc1645268488al_val,C_5: bop > product_prod_val_val > produc1645268488al_val > $o,A_21: bop,B_2: product_prod_val_val] :
( ( member1417904245al_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1417904245al_val @ Z_1 @ ( produc1554035486_val_o @ C_5 @ ( produc621191550al_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_453_mem__splitI,axiom,
! [Z_1: produc2088785539on_val,C_5: bop > product_prod_val_val > produc2088785539on_val > $o,A_21: bop,B_2: product_prod_val_val] :
( ( member1374264560on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1374264560on_val @ Z_1 @ ( produc633541091_val_o @ C_5 @ ( produc621191550al_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_454_mem__splitI,axiom,
! [Z_1: produc2090907612on_val,C_5: bop > product_prod_val_val > produc2090907612on_val > $o,A_21: bop,B_2: product_prod_val_val] :
( ( member1846553161on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1846553161on_val @ Z_1 @ ( produc1539816522_val_o @ C_5 @ ( produc621191550al_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_455_mem__splitI,axiom,
! [Z_1: produc1282892786on_val,C_5: bop > product_prod_val_val > produc1282892786on_val > $o,A_21: bop,B_2: product_prod_val_val] :
( ( member1072200031on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1072200031on_val @ Z_1 @ ( produc813528756_val_o @ C_5 @ ( produc621191550al_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_456_mem__splitI,axiom,
! [Z_1: list_char,C_5: val > val > list_char > $o,A_21: val,B_2: val] :
( ( member_list_char @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member_list_char @ Z_1 @ ( produc2042909709char_o @ C_5 @ ( product_Pair_val_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_457_mem__splitI,axiom,
! [Z_1: nat,C_5: val > val > nat > $o,A_21: val,B_2: val] :
( ( member_nat @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member_nat @ Z_1 @ ( produc776580085_nat_o @ C_5 @ ( product_Pair_val_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_458_mem__splitI,axiom,
! [Z_1: product_prod_val_val,C_5: val > val > product_prod_val_val > $o,A_21: val,B_2: val] :
( ( member649088532al_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member649088532al_val @ Z_1 @ ( produc844722278_val_o @ C_5 @ ( product_Pair_val_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_459_mem__splitI,axiom,
! [Z_1: produc1645268488al_val,C_5: val > val > produc1645268488al_val > $o,A_21: val,B_2: val] :
( ( member1417904245al_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1417904245al_val @ Z_1 @ ( produc1680944069_val_o @ C_5 @ ( product_Pair_val_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_460_mem__splitI,axiom,
! [Z_1: produc2088785539on_val,C_5: val > val > produc2088785539on_val > $o,A_21: val,B_2: val] :
( ( member1374264560on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1374264560on_val @ Z_1 @ ( produc532727434_val_o @ C_5 @ ( product_Pair_val_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_461_mem__splitI,axiom,
! [Z_1: produc2090907612on_val,C_5: val > val > produc2090907612on_val > $o,A_21: val,B_2: val] :
( ( member1846553161on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1846553161on_val @ Z_1 @ ( produc1559655665_val_o @ C_5 @ ( product_Pair_val_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_462_mem__splitI,axiom,
! [Z_1: produc1282892786on_val,C_5: val > val > produc1282892786on_val > $o,A_21: val,B_2: val] :
( ( member1072200031on_val @ Z_1 @ ( C_5 @ A_21 @ B_2 ) )
=> ( member1072200031on_val @ Z_1 @ ( produc1702738011_val_o @ C_5 @ ( product_Pair_val_val @ A_21 @ B_2 ) ) ) ) ).
thf(fact_463_hext__upd__obj,axiom,
! [Fs_1: produc1278157519t_char > option_val,H: nat > option1728594148on_val,A_1: nat,C_1: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( H @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs ) ) )
=> ( hext @ H @ ( fun_up1472480727on_val @ H @ A_1 @ ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs_1 ) ) ) ) ) ).
thf(fact_464_hext__trans,axiom,
! [H_6: nat > option1728594148on_val,H: nat > option1728594148on_val,H_4: nat > option1728594148on_val] :
( ( hext @ H @ H_4 )
=> ( ( hext @ H_4 @ H_6 )
=> ( hext @ H @ H_6 ) ) ) ).
thf(fact_465_WTrt__hext__mono,axiom,
! [H_4: nat > option1728594148on_val,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_4: list_char > option_ty,E_1: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_4 @ E_1 @ T )
=> ( ( hext @ H @ H_4 )
=> ( wTrt @ P @ H_4 @ E_4 @ E_1 @ T ) ) ) ).
thf(fact_466_hext__objD,axiom,
! [A_1: nat,C_1: list_char,Fs: produc1278157519t_char > option_val,H: nat > option1728594148on_val,H_4: nat > option1728594148on_val] :
( ( hext @ H @ H_4 )
=> ( ( ( H @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs ) ) )
=> ? [Fs_3: produc1278157519t_char > option_val] :
( ( H_4 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs_3 ) ) ) ) ) ).
thf(fact_467_hext__def,axiom,
! [H: nat > option1728594148on_val,H_4: nat > option1728594148on_val] :
( ( hext @ H @ H_4 )
<=> ! [A: nat,C_2: list_char,Fs_2: produc1278157519t_char > option_val] :
( ( ( H @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_2 @ Fs_2 ) ) )
=> ? [Fs_3: produc1278157519t_char > option_val] :
( ( H_4 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_2 @ Fs_3 ) ) ) ) ) ).
thf(fact_468_mem__splitI2,axiom,
! [Z: product_prod_val_val,C_4: val > val > product_prod_val_val > $o,P_2: product_prod_val_val] :
( ! [A: val,B_1: val] :
( ( P_2
= ( product_Pair_val_val @ A @ B_1 ) )
=> ( member649088532al_val @ Z @ ( C_4 @ A @ B_1 ) ) )
=> ( member649088532al_val @ Z @ ( produc844722278_val_o @ C_4 @ P_2 ) ) ) ).
thf(fact_469_mem__splitI2,axiom,
! [Z: produc1645268488al_val,C_4: val > val > produc1645268488al_val > $o,P_2: product_prod_val_val] :
( ! [A: val,B_1: val] :
( ( P_2
= ( product_Pair_val_val @ A @ B_1 ) )
=> ( member1417904245al_val @ Z @ ( C_4 @ A @ B_1 ) ) )
=> ( member1417904245al_val @ Z @ ( produc1680944069_val_o @ C_4 @ P_2 ) ) ) ).
thf(fact_470_mem__splitI2,axiom,
! [Z: produc2088785539on_val,C_4: val > val > produc2088785539on_val > $o,P_2: product_prod_val_val] :
( ! [A: val,B_1: val] :
( ( P_2
= ( product_Pair_val_val @ A @ B_1 ) )
=> ( member1374264560on_val @ Z @ ( C_4 @ A @ B_1 ) ) )
=> ( member1374264560on_val @ Z @ ( produc532727434_val_o @ C_4 @ P_2 ) ) ) ).
thf(fact_471_mem__splitI2,axiom,
! [Z: produc2090907612on_val,C_4: val > val > produc2090907612on_val > $o,P_2: product_prod_val_val] :
( ! [A: val,B_1: val] :
( ( P_2
= ( product_Pair_val_val @ A @ B_1 ) )
=> ( member1846553161on_val @ Z @ ( C_4 @ A @ B_1 ) ) )
=> ( member1846553161on_val @ Z @ ( produc1559655665_val_o @ C_4 @ P_2 ) ) ) ).
thf(fact_472_mem__splitI2,axiom,
! [Z: produc1282892786on_val,C_4: val > val > produc1282892786on_val > $o,P_2: product_prod_val_val] :
( ! [A: val,B_1: val] :
( ( P_2
= ( product_Pair_val_val @ A @ B_1 ) )
=> ( member1072200031on_val @ Z @ ( C_4 @ A @ B_1 ) ) )
=> ( member1072200031on_val @ Z @ ( produc1702738011_val_o @ C_4 @ P_2 ) ) ) ).
thf(fact_473__092_060D_062___092_060D_062s_Osimps_I6_J,axiom,
! [V_7: list_char,E_7: exp_list_char,A_20: option_list_char_o] :
( ( d_list_char @ ( lAss_list_char @ V_7 @ E_7 ) @ A_20 )
<=> ( d_list_char @ E_7 @ A_20 ) ) ).
thf(fact_474_exp_Osimps_I143_J,axiom,
! [A_19: list_char,Ty_7: ty,Exp_15: exp_list_char,A_18: list_char,Exp_14: exp_list_char] :
( ( block_list_char @ A_19 @ Ty_7 @ Exp_15 )
!= ( lAss_list_char @ A_18 @ Exp_14 ) ) ).
thf(fact_475_exp_Osimps_I3_J,axiom,
! [Val_7: val,Val_6: val] :
( ( ( val_list_char @ Val_7 )
= ( val_list_char @ Val_6 ) )
<=> ( Val_7 = Val_6 ) ) ).
thf(fact_476_exp_Osimps_I11_J,axiom,
! [Exp1_7: exp_list_char,Exp2_7: exp_list_char,Exp1_6: exp_list_char,Exp2_6: exp_list_char] :
( ( ( seq_list_char @ Exp1_7 @ Exp2_7 )
= ( seq_list_char @ Exp1_6 @ Exp2_6 ) )
<=> ( ( Exp1_7 = Exp1_6 )
& ( Exp2_7 = Exp2_6 ) ) ) ).
thf(fact_477_exp_Osimps_I6_J,axiom,
! [A_17: list_char,Exp_13: exp_list_char,A_16: list_char,Exp_12: exp_list_char] :
( ( ( lAss_list_char @ A_17 @ Exp_13 )
= ( lAss_list_char @ A_16 @ Exp_12 ) )
<=> ( ( A_17 = A_16 )
& ( Exp_13 = Exp_12 ) ) ) ).
thf(fact_478_exp_Osimps_I10_J,axiom,
! [A_15: list_char,Ty_6: ty,Exp_11: exp_list_char,A_14: list_char,Ty_5: ty,Exp_10: exp_list_char] :
( ( ( block_list_char @ A_15 @ Ty_6 @ Exp_11 )
= ( block_list_char @ A_14 @ Ty_5 @ Exp_10 ) )
<=> ( ( A_15 = A_14 )
& ( Ty_6 = Ty_5 )
& ( Exp_11 = Exp_10 ) ) ) ).
thf(fact_479_exp_Osimps_I84_J,axiom,
! [Val_5: val,Exp1_5: exp_list_char,Exp2_5: exp_list_char] :
( ( val_list_char @ Val_5 )
!= ( seq_list_char @ Exp1_5 @ Exp2_5 ) ) ).
thf(fact_480_exp_Osimps_I74_J,axiom,
! [Val_4: val,A_13: list_char,Exp_9: exp_list_char] :
( ( val_list_char @ Val_4 )
!= ( lAss_list_char @ A_13 @ Exp_9 ) ) ).
thf(fact_481_exp_Osimps_I85_J,axiom,
! [Exp1_4: exp_list_char,Exp2_4: exp_list_char,Val_3: val] :
( ( seq_list_char @ Exp1_4 @ Exp2_4 )
!= ( val_list_char @ Val_3 ) ) ).
thf(fact_482_exp_Osimps_I75_J,axiom,
! [A_12: list_char,Exp_8: exp_list_char,Val_2: val] :
( ( lAss_list_char @ A_12 @ Exp_8 )
!= ( val_list_char @ Val_2 ) ) ).
thf(fact_483_exp_Osimps_I82_J,axiom,
! [Val_1: val,A_11: list_char,Ty_4: ty,Exp_7: exp_list_char] :
( ( val_list_char @ Val_1 )
!= ( block_list_char @ A_11 @ Ty_4 @ Exp_7 ) ) ).
thf(fact_484_exp_Osimps_I83_J,axiom,
! [A_10: list_char,Ty_3: ty,Exp_6: exp_list_char,Val: val] :
( ( block_list_char @ A_10 @ Ty_3 @ Exp_6 )
!= ( val_list_char @ Val ) ) ).
thf(fact_485__092_060D_062___092_060D_062s_Osimps_I3_J,axiom,
! [V_6: val,A_9: option_list_char_o] : ( d_list_char @ ( val_list_char @ V_6 ) @ A_9 ) ).
thf(fact_486_exp_Osimps_I145_J,axiom,
! [Exp1_3: exp_list_char,Exp2_3: exp_list_char,A_8: list_char,Exp_5: exp_list_char] :
( ( seq_list_char @ Exp1_3 @ Exp2_3 )
!= ( lAss_list_char @ A_8 @ Exp_5 ) ) ).
thf(fact_487_exp_Osimps_I144_J,axiom,
! [A_7: list_char,Exp_4: exp_list_char,Exp1_2: exp_list_char,Exp2_2: exp_list_char] :
( ( lAss_list_char @ A_7 @ Exp_4 )
!= ( seq_list_char @ Exp1_2 @ Exp2_2 ) ) ).
thf(fact_488_exp_Osimps_I197_J,axiom,
! [Exp1_1: exp_list_char,Exp2_1: exp_list_char,A_6: list_char,Ty_2: ty,Exp_3: exp_list_char] :
( ( seq_list_char @ Exp1_1 @ Exp2_1 )
!= ( block_list_char @ A_6 @ Ty_2 @ Exp_3 ) ) ).
thf(fact_489_exp_Osimps_I142_J,axiom,
! [A_5: list_char,Exp_2: exp_list_char,A_4: list_char,Ty_1: ty,Exp_1: exp_list_char] :
( ( lAss_list_char @ A_5 @ Exp_2 )
!= ( block_list_char @ A_4 @ Ty_1 @ Exp_1 ) ) ).
thf(fact_490_exp_Osimps_I196_J,axiom,
! [A_3: list_char,Ty: ty,Exp: exp_list_char,Exp1: exp_list_char,Exp2: exp_list_char] :
( ( block_list_char @ A_3 @ Ty @ Exp )
!= ( seq_list_char @ Exp1 @ Exp2 ) ) ).
thf(fact_491_hconf__upd__obj,axiom,
! [Fs_5: produc1278157519t_char > option_val,A_2: nat,C_3: list_char,Fs_4: produc1278157519t_char > option_val,P_1: list_P1999446415t_char,H_5: nat > option1728594148on_val] :
( ( hconf_97414254t_char @ P_1 @ H_5 )
=> ( ( ( H_5 @ A_2 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_3 @ Fs_4 ) ) )
=> ( ( oconf_1869808039t_char @ P_1 @ H_5 @ ( produc926070009on_val @ C_3 @ Fs_5 ) )
=> ( hconf_97414254t_char @ P_1 @ ( fun_up1472480727on_val @ H_5 @ A_2 @ ( some_P451527732on_val @ ( produc926070009on_val @ C_3 @ Fs_5 ) ) ) ) ) ) ) ).
thf(fact_492_redp__redsp_OInitBlockRed,axiom,
! [T: ty,V_5: val,P: list_P1999446415t_char,E_1: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,V_4: list_char,V: val,E: exp_list_char,H_4: nat > option1728594148on_val,L_4: list_char > option_val] :
( ( redp @ P @ E_1 @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_4 @ ( some_val @ V ) ) ) @ E @ ( produc755559506on_val @ H_4 @ L_4 ) )
=> ( ( ( L_4 @ V_4 )
= ( some_val @ V_5 ) )
=> ( redp @ P @ ( block_list_char @ V_4 @ T @ ( seq_list_char @ ( lAss_list_char @ V_4 @ ( val_list_char @ V ) ) @ E_1 ) ) @ ( produc755559506on_val @ H @ L ) @ ( block_list_char @ V_4 @ T @ ( seq_list_char @ ( lAss_list_char @ V_4 @ ( val_list_char @ V_5 ) ) @ E ) ) @ ( produc755559506on_val @ H_4 @ ( fun_up1149430426on_val @ L_4 @ V_4 @ ( L @ V_4 ) ) ) ) ) ) ).
thf(fact_493_red__reds_OBlockRedSome,axiom,
! [T: ty,V: val,E_1: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,V_4: list_char,E: exp_list_char,H_4: nat > option1728594148on_val,L_4: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_4 @ none_val ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_4 @ L_4 ) ) ) @ ( red @ P ) )
=> ( ( ( L_4 @ V_4 )
= ( some_val @ V ) )
=> ( ~ ( assigned @ V_4 @ E_1 )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_4 @ T @ E_1 ) @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ ( block_list_char @ V_4 @ T @ ( seq_list_char @ ( lAss_list_char @ V_4 @ ( val_list_char @ V ) ) @ E ) ) @ ( produc755559506on_val @ H_4 @ ( fun_up1149430426on_val @ L_4 @ V_4 @ ( L @ V_4 ) ) ) ) ) @ ( red @ P ) ) ) ) ) ).
thf(fact_494_WTrtLAss,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: exp_list_char,T_4: ty,E_4: list_char > option_ty,V_4: list_char,T: ty] :
( ( ( E_4 @ V_4 )
= ( some_ty @ T ) )
=> ( ( wTrt @ P @ H @ E_4 @ E_1 @ T_4 )
=> ( ( widen_2090681816t_char @ P @ T_4 @ T )
=> ( wTrt @ P @ H @ E_4 @ ( lAss_list_char @ V_4 @ E_1 ) @ void ) ) ) ) ).
thf(fact_495_LAssRedsVal,axiom,
! [V_4: list_char,E_1: exp_list_char,S_2: produc2090907612on_val,V: val,H_4: nat > option1728594148on_val,L_4: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ ( produc755559506on_val @ H_4 @ L_4 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V_4 @ E_1 ) @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ unit ) @ ( produc755559506on_val @ H_4 @ ( fun_up1149430426on_val @ L_4 @ V_4 @ ( some_val @ V ) ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_496_hextI,axiom,
! [H_4: nat > option1728594148on_val,H: nat > option1728594148on_val] :
( ! [A: nat,C_2: list_char,Fs_2: produc1278157519t_char > option_val] :
( ( ( H @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_2 @ Fs_2 ) ) )
=> ? [Fs_3: produc1278157519t_char > option_val] :
( ( H_4 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_2 @ Fs_3 ) ) ) )
=> ( hext @ H @ H_4 ) ) ).
thf(fact_497_redp__redsp_ORedLAss,axiom,
! [P: list_P1999446415t_char,V_4: list_char,V: val,H: nat > option1728594148on_val,L: list_char > option_val] : ( redp @ P @ ( lAss_list_char @ V_4 @ ( val_list_char @ V ) ) @ ( produc755559506on_val @ H @ L ) @ ( val_list_char @ unit ) @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_4 @ ( some_val @ V ) ) ) ) ).
thf(fact_498_redp__redsp_OLAssRed,axiom,
! [V_4: list_char,P: list_P1999446415t_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S_2 @ E @ S )
=> ( redp @ P @ ( lAss_list_char @ V_4 @ E_1 ) @ S_2 @ ( lAss_list_char @ V_4 @ E ) @ S ) ) ).
thf(fact_499_redp__redsp_OSeqRed,axiom,
! [E_2: exp_list_char,P: list_P1999446415t_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S_2 @ E @ S )
=> ( redp @ P @ ( seq_list_char @ E_1 @ E_2 ) @ S_2 @ ( seq_list_char @ E @ E_2 ) @ S ) ) ).
thf(fact_500_redp__redsp_OBlockRedNone,axiom,
! [T: ty,P: list_P1999446415t_char,E_1: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,V_4: list_char,E: exp_list_char,H_4: nat > option1728594148on_val,L_4: list_char > option_val] :
( ( redp @ P @ E_1 @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_4 @ none_val ) ) @ E @ ( produc755559506on_val @ H_4 @ L_4 ) )
=> ( ( ( L_4 @ V_4 )
= none_val )
=> ( ~ ( assigned @ V_4 @ E_1 )
=> ( redp @ P @ ( block_list_char @ V_4 @ T @ E_1 ) @ ( produc755559506on_val @ H @ L ) @ ( block_list_char @ V_4 @ T @ E ) @ ( produc755559506on_val @ H_4 @ ( fun_up1149430426on_val @ L_4 @ V_4 @ ( L @ V_4 ) ) ) ) ) ) ) ).
thf(fact_501_redp__redsp_ORedSeq,axiom,
! [P: list_P1999446415t_char,V: val,E_2: exp_list_char,S_2: produc2090907612on_val] : ( redp @ P @ ( seq_list_char @ ( val_list_char @ V ) @ E_2 ) @ S_2 @ E_2 @ S_2 ) ).
thf(fact_502_redp__redsp_ORedBlock,axiom,
! [P: list_P1999446415t_char,V_4: list_char,T: ty,U: val,S_2: produc2090907612on_val] : ( redp @ P @ ( block_list_char @ V_4 @ T @ ( val_list_char @ U ) ) @ S_2 @ ( val_list_char @ U ) @ S_2 ) ).
thf(fact_503_SeqReds,axiom,
! [E_2: exp_list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ E_1 @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( seq_list_char @ E @ E_2 ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_504_LAssReds,axiom,
! [V_4: list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V_4 @ E_1 ) @ S_2 ) @ ( produc235638504on_val @ ( lAss_list_char @ V_4 @ E ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_505_redp__redsp_OBlockRedSome,axiom,
! [T: ty,V: val,P: list_P1999446415t_char,E_1: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,V_4: list_char,E: exp_list_char,H_4: nat > option1728594148on_val,L_4: list_char > option_val] :
( ( redp @ P @ E_1 @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_4 @ none_val ) ) @ E @ ( produc755559506on_val @ H_4 @ L_4 ) )
=> ( ( ( L_4 @ V_4 )
= ( some_val @ V ) )
=> ( ~ ( assigned @ V_4 @ E_1 )
=> ( redp @ P @ ( block_list_char @ V_4 @ T @ E_1 ) @ ( produc755559506on_val @ H @ L ) @ ( block_list_char @ V_4 @ T @ ( seq_list_char @ ( lAss_list_char @ V_4 @ ( val_list_char @ V ) ) @ E ) ) @ ( produc755559506on_val @ H_4 @ ( fun_up1149430426on_val @ L_4 @ V_4 @ ( L @ V_4 ) ) ) ) ) ) ) ).
thf(fact_506_SeqReds2,axiom,
! [E_2: exp_list_char,E_2_1: exp_list_char,S_2_1: produc2090907612on_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1: val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1_1 @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ V_1 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2 @ S_1 ) @ ( produc235638504on_val @ E_2_1 @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ E_1_1 @ E_2 ) @ S_0 ) @ ( produc235638504on_val @ E_2_1 @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_507_redp__red__eq,axiom,
! [P: list_P1999446415t_char,X_1: exp_list_char,Xa: produc2090907612on_val,Xb: exp_list_char,Xc: produc2090907612on_val] :
( ( redp @ P @ X_1 @ Xa @ Xb @ Xc )
<=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ X_1 @ Xa ) @ ( produc235638504on_val @ Xb @ Xc ) ) @ ( red @ P ) ) ) ).
thf(fact_508_redp__redsp_ORedInitBlock,axiom,
! [P: list_P1999446415t_char,V_4: list_char,T: ty,V: val,U: val,S_2: produc2090907612on_val] : ( redp @ P @ ( block_list_char @ V_4 @ T @ ( seq_list_char @ ( lAss_list_char @ V_4 @ ( val_list_char @ V ) ) @ ( val_list_char @ U ) ) ) @ S_2 @ ( val_list_char @ U ) @ S_2 ) ).
thf(fact_509_red__reds_OBlockRedNone,axiom,
! [T: ty,E_1: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,V_4: list_char,E: exp_list_char,H_4: nat > option1728594148on_val,L_4: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_4 @ none_val ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_4 @ L_4 ) ) ) @ ( red @ P ) )
=> ( ( ( L_4 @ V_4 )
= none_val )
=> ( ~ ( assigned @ V_4 @ E_1 )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_4 @ T @ E_1 ) @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ ( block_list_char @ V_4 @ T @ E ) @ ( produc755559506on_val @ H_4 @ ( fun_up1149430426on_val @ L_4 @ V_4 @ ( L @ V_4 ) ) ) ) ) @ ( red @ P ) ) ) ) ) ).
thf(fact_510_Red__lcl__add,axiom,
! [L_0_1: list_char > option_val,E_1: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,E: exp_list_char,H_4: nat > option1728594148on_val,L_4: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_4 @ L_4 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ ( map_ad325961431ar_val @ L_0_1 @ L ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_4 @ ( map_ad325961431ar_val @ L_0_1 @ L_4 ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_511_WTrt__elim__cases_I1_J,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_4: list_char > option_ty,V: list_char,E_1: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_4 @ ( lAss_list_char @ V @ E_1 ) @ T )
=> ~ ( ( T = void )
=> ! [T_1: ty] :
( ( ( E_4 @ V )
= ( some_ty @ T_1 ) )
=> ! [T_3: ty] :
( ( wTrt @ P @ H @ E_4 @ E_1 @ T_3 )
=> ~ ( widen_2090681816t_char @ P @ T_3 @ T_1 ) ) ) ) ) ).
thf(fact_512_InitBlockReds,axiom,
! [T: ty,E_1: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,V_4: list_char,V: val,E: exp_list_char,H_4: nat > option1728594148on_val,L_4: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_4 @ ( some_val @ V ) ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_4 @ L_4 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_4 @ T @ ( seq_list_char @ ( lAss_list_char @ V_4 @ ( val_list_char @ V ) ) @ E_1 ) ) @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ ( block_list_char @ V_4 @ T @ ( seq_list_char @ ( lAss_list_char @ V_4 @ ( val_list_char @ ( the_val @ ( L_4 @ V_4 ) ) ) ) @ E ) ) @ ( produc755559506on_val @ H_4 @ ( fun_up1149430426on_val @ L_4 @ V_4 @ ( L @ V_4 ) ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_513_InitBlockRedsFinal,axiom,
! [T: ty,E_1: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,V_4: list_char,V: val,E: exp_list_char,H_4: nat > option1728594148on_val,L_4: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_4 @ ( some_val @ V ) ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_4 @ L_4 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( final_list_char @ E )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_4 @ T @ ( seq_list_char @ ( lAss_list_char @ V_4 @ ( val_list_char @ V ) ) @ E_1 ) ) @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_4 @ ( fun_up1149430426on_val @ L_4 @ V_4 @ ( L @ V_4 ) ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_514_assigned__def,axiom,
! [V_4: list_char,E_1: exp_list_char] :
( ( assigned @ V_4 @ E_1 )
<=> ? [V_3: val,E_5: exp_list_char] :
( E_1
= ( seq_list_char @ ( lAss_list_char @ V_4 @ ( val_list_char @ V_3 ) ) @ E_5 ) ) ) ).
thf(fact_515_BlockRedsFinal,axiom,
! [T: ty,H_0_1: nat > option1728594148on_val,L_0_1: list_char > option_val,V_4: list_char,E_0: exp_list_char,S_0: produc2090907612on_val,E_2: exp_list_char,H_2: nat > option1728594148on_val,L_2: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_0 @ S_0 ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_2 @ L_2 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( final_list_char @ E_2 )
=> ( ( S_0
= ( produc755559506on_val @ H_0_1 @ ( fun_up1149430426on_val @ L_0_1 @ V_4 @ none_val ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_4 @ T @ E_0 ) @ ( produc755559506on_val @ H_0_1 @ L_0_1 ) ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_2 @ ( fun_up1149430426on_val @ L_2 @ V_4 @ ( L_0_1 @ V_4 ) ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_516_hext__new,axiom,
! [X: produc2088785539on_val,H: nat > option1728594148on_val,A_1: nat] :
( ( ( H @ A_1 )
= none_P1260844216on_val )
=> ( hext @ H @ ( fun_up1472480727on_val @ H @ A_1 @ ( some_P451527732on_val @ X ) ) ) ) ).
thf(fact_517_progress,axiom,
! [L: list_char > option_val,E_4: list_char > option_ty,E_1: exp_list_char,T: ty,H: nat > option1728594148on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( hconf_97414254t_char @ P @ H )
=> ( ( wTrt @ P @ H @ E_4 @ E_1 @ T )
=> ( ( d_list_char @ E_1 @ ( some_list_char_o @ ( dom_list_char_val @ L ) ) )
=> ( ~ ( final_list_char @ E_1 )
=> ? [E_5: exp_list_char,S_4: produc2090907612on_val] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ E_5 @ S_4 ) ) @ ( red @ P ) ) ) ) ) ) ) ).
thf(fact_518_wf__prog__wwf__prog,axiom,
! [P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wf_J_mdecl @ P )
=> ( wf_pro755087577t_char @ wwf_J_mdecl @ P ) ) ).
thf(fact_519_wf__mdecl__wwf__mdecl,axiom,
! [P: list_P1999446415t_char,C_1: list_char,Md: produc1013743697t_char] :
( ( wf_J_mdecl @ P @ C_1 @ Md )
=> ( wwf_J_mdecl @ P @ C_1 @ Md ) ) ).
thf(fact_520_small__by__big,axiom,
! [E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( final_list_char @ E )
=> ( eval @ P @ E_1 @ S_2 @ E @ S ) ) ) ) ).
thf(fact_521_big__iff__small,axiom,
! [E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( eval @ P @ E_1 @ S_2 @ E @ S )
<=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
& ( final_list_char @ E ) ) ) ) ).
thf(fact_522_FAssRedsVal,axiom,
! [F: list_char,D: list_char,C_1: list_char,Fs: produc1278157519t_char > option_val,E_2: exp_list_char,V: val,H_2: nat > option1728594148on_val,L_2: list_char > option_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,A_1: nat,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1_1 @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ ( addr @ A_1 ) ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2 @ S_1 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ ( produc755559506on_val @ H_2 @ L_2 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs ) )
= ( H_2 @ A_1 ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2 ) @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ unit ) @ ( produc755559506on_val @ ( fun_up1472480727on_val @ H_2 @ A_1 @ ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ ( fun_up204312361on_val @ Fs @ ( produc5062597t_char @ F @ D ) @ ( some_val @ V ) ) ) ) ) @ L_2 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_523_red__reds_ORedFAss,axiom,
! [F: list_char,D: list_char,V: val,L: list_char > option_val,P: list_P1999446415t_char,H: nat > option1728594148on_val,A_1: nat,C_1: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( H @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ ( addr @ A_1 ) ) @ F @ D @ ( val_list_char @ V ) ) @ ( produc755559506on_val @ H @ L ) ) @ ( produc235638504on_val @ ( val_list_char @ unit ) @ ( produc755559506on_val @ ( fun_up1472480727on_val @ H @ A_1 @ ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ ( fun_up204312361on_val @ Fs @ ( produc5062597t_char @ F @ D ) @ ( some_val @ V ) ) ) ) ) @ L ) ) ) @ ( red @ P ) ) ) ).
thf(fact_524_big__by__small,axiom,
! [E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( eval @ P @ E_1 @ S_2 @ E @ S )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_525_redp__redsp_OFAssRed1,axiom,
! [F: list_char,D: list_char,E_2: exp_list_char,P: list_P1999446415t_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S_2 @ E @ S )
=> ( redp @ P @ ( fAss_list_char @ E_1 @ F @ D @ E_2 ) @ S_2 @ ( fAss_list_char @ E @ F @ D @ E_2 ) @ S ) ) ).
thf(fact_526_redp__redsp_OFAssRed2,axiom,
! [V: val,F: list_char,D: list_char,P: list_P1999446415t_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S_2 @ E @ S )
=> ( redp @ P @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ E_1 ) @ S_2 @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ E ) @ S ) ) ).
thf(fact_527_red__reds_OFAssRed1,axiom,
! [F: list_char,D: list_char,E_2: exp_list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ E_1 @ F @ D @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( fAss_list_char @ E @ F @ D @ E_2 ) @ S ) ) @ ( red @ P ) ) ) ).
thf(fact_528_red__reds_OFAssRed2,axiom,
! [V: val,F: list_char,D: list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ E_1 ) @ S_2 ) @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ E ) @ S ) ) @ ( red @ P ) ) ) ).
thf(fact_529_FAssReds1,axiom,
! [F: list_char,D: list_char,E_2: exp_list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ E_1 @ F @ D @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( fAss_list_char @ E @ F @ D @ E_2 ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_530_extend__1__eval,axiom,
! [E: exp_list_char,S: produc2090907612on_val,E_1: exp_list_char,S_2: produc2090907612on_val,E_6: exp_list_char,S_3: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E_6 @ S_3 ) ) @ ( red @ P ) )
=> ( ( eval @ P @ E_6 @ S_3 @ E @ S )
=> ( eval @ P @ E_1 @ S_2 @ E @ S ) ) ) ) ).
thf(fact_531_FAssReds2,axiom,
! [V: val,F: list_char,D: list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ E_1 ) @ S_2 ) @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ E ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_532_redp__redsp_ORedFAss,axiom,
! [P: list_P1999446415t_char,F: list_char,D: list_char,V: val,L: list_char > option_val,H: nat > option1728594148on_val,A_1: nat,C_1: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( H @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs ) ) )
=> ( redp @ P @ ( fAss_list_char @ ( val_list_char @ ( addr @ A_1 ) ) @ F @ D @ ( val_list_char @ V ) ) @ ( produc755559506on_val @ H @ L ) @ ( val_list_char @ unit ) @ ( produc755559506on_val @ ( fun_up1472480727on_val @ H @ A_1 @ ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ ( fun_up204312361on_val @ Fs @ ( produc5062597t_char @ F @ D ) @ ( some_val @ V ) ) ) ) ) @ L ) ) ) ).
thf(fact_533_extend__eval,axiom,
! [E: exp_list_char,S: produc2090907612on_val,E_1: exp_list_char,S_2: produc2090907612on_val,E_6: exp_list_char,S_3: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E_6 @ S_3 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( eval @ P @ E_6 @ S_3 @ E @ S )
=> ( eval @ P @ E_1 @ S_2 @ E @ S ) ) ) ) ).
thf(fact_534_FAss,axiom,
! [H_2_1: nat > option1728594148on_val,Fs_1: produc1278157519t_char > option_val,F: list_char,D: list_char,C_1: list_char,Fs: produc1278157519t_char > option_val,E_2: exp_list_char,V: val,H_2: nat > option1728594148on_val,L_2: list_char > option_val,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,A_1: nat,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ ( addr @ A_1 ) ) @ S_1 )
=> ( ( eval @ P @ E_2 @ S_1 @ ( val_list_char @ V ) @ ( produc755559506on_val @ H_2 @ L_2 ) )
=> ( ( ( H_2 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs ) ) )
=> ( ( Fs_1
= ( fun_up204312361on_val @ Fs @ ( produc5062597t_char @ F @ D ) @ ( some_val @ V ) ) )
=> ( ( H_2_1
= ( fun_up1472480727on_val @ H_2 @ A_1 @ ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs_1 ) ) ) )
=> ( eval @ P @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2 ) @ S_0 @ ( val_list_char @ unit ) @ ( produc755559506on_val @ H_2_1 @ L_2 ) ) ) ) ) ) ) ).
thf(fact_535_LAss,axiom,
! [L_4: list_char > option_val,V_4: list_char,P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,V: val,H: nat > option1728594148on_val,L: list_char > option_val] :
( ( eval @ P @ E_1 @ S_0 @ ( val_list_char @ V ) @ ( produc755559506on_val @ H @ L ) )
=> ( ( L_4
= ( fun_up1149430426on_val @ L @ V_4 @ ( some_val @ V ) ) )
=> ( eval @ P @ ( lAss_list_char @ V_4 @ E_1 ) @ S_0 @ ( val_list_char @ unit ) @ ( produc755559506on_val @ H @ L_4 ) ) ) ) ).
thf(fact_536_Block,axiom,
! [T: ty,P: list_P1999446415t_char,E_0: exp_list_char,H_0_1: nat > option1728594148on_val,L_0_1: list_char > option_val,V_4: list_char,E_1_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val] :
( ( eval @ P @ E_0 @ ( produc755559506on_val @ H_0_1 @ ( fun_up1149430426on_val @ L_0_1 @ V_4 @ none_val ) ) @ E_1_1 @ ( produc755559506on_val @ H_1 @ L_1 ) )
=> ( eval @ P @ ( block_list_char @ V_4 @ T @ E_0 ) @ ( produc755559506on_val @ H_0_1 @ L_0_1 ) @ E_1_1 @ ( produc755559506on_val @ H_1 @ ( fun_up1149430426on_val @ L_1 @ V_4 @ ( L_0_1 @ V_4 ) ) ) ) ) ).
thf(fact_537_FAccRedsVal,axiom,
! [F: list_char,D: list_char,V: val,C_1: list_char,Fs: produc1278157519t_char > option_val,E_1: exp_list_char,S_2: produc2090907612on_val,A_1: nat,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ ( addr @ A_1 ) ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( hp @ S @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs ) ) )
=> ( ( ( Fs @ ( produc5062597t_char @ F @ D ) )
= ( some_val @ V ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E_1 @ F @ D ) @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_538_eval__hext,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,E: exp_list_char,H_4: nat > option1728594148on_val,L_4: list_char > option_val] :
( ( eval @ P @ E_1 @ ( produc755559506on_val @ H @ L ) @ E @ ( produc755559506on_val @ H_4 @ L_4 ) )
=> ( hext @ H @ H_4 ) ) ).
thf(fact_539_redp__redsp_OFAccRed,axiom,
! [F: list_char,D: list_char,P: list_P1999446415t_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S_2 @ E @ S )
=> ( redp @ P @ ( fAcc_list_char @ E_1 @ F @ D ) @ S_2 @ ( fAcc_list_char @ E @ F @ D ) @ S ) ) ).
thf(fact_540_red__reds_OFAccRed,axiom,
! [F: list_char,D: list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E_1 @ F @ D ) @ S_2 ) @ ( produc235638504on_val @ ( fAcc_list_char @ E @ F @ D ) @ S ) ) @ ( red @ P ) ) ) ).
thf(fact_541_FAccReds,axiom,
! [F: list_char,D: list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E_1 @ F @ D ) @ S_2 ) @ ( produc235638504on_val @ ( fAcc_list_char @ E @ F @ D ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_542_FAcc,axiom,
! [F: list_char,D: list_char,V: val,C_1: list_char,Fs: produc1278157519t_char > option_val,P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,A_1: nat,H: nat > option1728594148on_val,L: list_char > option_val] :
( ( eval @ P @ E_1 @ S_0 @ ( val_list_char @ ( addr @ A_1 ) ) @ ( produc755559506on_val @ H @ L ) )
=> ( ( ( H @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs ) ) )
=> ( ( ( Fs @ ( produc5062597t_char @ F @ D ) )
= ( some_val @ V ) )
=> ( eval @ P @ ( fAcc_list_char @ E_1 @ F @ D ) @ S_0 @ ( val_list_char @ V ) @ ( produc755559506on_val @ H @ L ) ) ) ) ) ).
thf(fact_543_Val,axiom,
! [P: list_P1999446415t_char,V: val,S_2: produc2090907612on_val] : ( eval @ P @ ( val_list_char @ V ) @ S_2 @ ( val_list_char @ V ) @ S_2 ) ).
thf(fact_544_eval__cases_I2_J,axiom,
! [P: list_P1999446415t_char,V: val,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( eval @ P @ ( val_list_char @ V ) @ S_2 @ E @ S )
=> ~ ( ( E
= ( val_list_char @ V ) )
=> ( S != S_2 ) ) ) ).
thf(fact_545_eval__final,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( eval @ P @ E_1 @ S_2 @ E @ S )
=> ( final_list_char @ E ) ) ).
thf(fact_546_eval__finalId,axiom,
! [P: list_P1999446415t_char,S_2: produc2090907612on_val,E_1: exp_list_char] :
( ( final_list_char @ E_1 )
=> ( eval @ P @ E_1 @ S_2 @ E_1 @ S_2 ) ) ).
thf(fact_547_redp__redsp_ORedFAcc,axiom,
! [P: list_P1999446415t_char,F: list_char,D: list_char,V: val,S_2: produc2090907612on_val,A_1: nat,C_1: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S_2 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs ) ) )
=> ( ( ( Fs @ ( produc5062597t_char @ F @ D ) )
= ( some_val @ V ) )
=> ( redp @ P @ ( fAcc_list_char @ ( val_list_char @ ( addr @ A_1 ) ) @ F @ D ) @ S_2 @ ( val_list_char @ V ) @ S_2 ) ) ) ).
thf(fact_548_red__reds_ORedFAcc,axiom,
! [P: list_P1999446415t_char,F: list_char,D: list_char,V: val,S_2: produc2090907612on_val,A_1: nat,C_1: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S_2 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs ) ) )
=> ( ( ( Fs @ ( produc5062597t_char @ F @ D ) )
= ( some_val @ V ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ ( val_list_char @ ( addr @ A_1 ) ) @ F @ D ) @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S_2 ) ) @ ( red @ P ) ) ) ) ).
thf(fact_549_Seq,axiom,
! [E_1_1: exp_list_char,E_2: exp_list_char,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E_0: exp_list_char,S_0: produc2090907612on_val,V: val,S_1: produc2090907612on_val] :
( ( eval @ P @ E_0 @ S_0 @ ( val_list_char @ V ) @ S_1 )
=> ( ( eval @ P @ E_1_1 @ S_1 @ E_2 @ S_2_1 )
=> ( eval @ P @ ( seq_list_char @ E_0 @ E_1_1 ) @ S_0 @ E_2 @ S_2_1 ) ) ) ).
thf(fact_550_eval__cases_I8_J,axiom,
! [P: list_P1999446415t_char,V_4: list_char,T: ty,E_1_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( eval @ P @ ( block_list_char @ V_4 @ T @ E_1_1 ) @ S_2 @ E @ S )
=> ~ ! [H_0: nat > option1728594148on_val,L_0: list_char > option_val] :
( ( S_2
= ( produc755559506on_val @ H_0 @ L_0 ) )
=> ! [H_1_1: nat > option1728594148on_val,L_1_1: list_char > option_val] :
( ( S
= ( produc755559506on_val @ H_1_1 @ ( fun_up1149430426on_val @ L_1_1 @ V_4 @ ( L_0 @ V_4 ) ) ) )
=> ~ ( eval @ P @ E_1_1 @ ( produc755559506on_val @ H_0 @ ( fun_up1149430426on_val @ L_0 @ V_4 @ none_val ) ) @ E @ ( produc755559506on_val @ H_1_1 @ L_1_1 ) ) ) ) ) ).
thf(fact_551_red__reds_OInitBlockThrow,axiom,
! [V_4: list_char,T: ty,V: val,A_1: nat,S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_4 @ T @ ( seq_list_char @ ( lAss_list_char @ V_4 @ ( val_list_char @ V ) ) @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) ) ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_552_val_Osimps_I11_J,axiom,
! [Nat: nat] :
( ( addr @ Nat )
!= unit ) ).
thf(fact_553_val_Osimps_I10_J,axiom,
! [Nat: nat] :
( unit
!= ( addr @ Nat ) ) ).
thf(fact_554_redp__redsp_OInitBlockThrow,axiom,
! [P: list_P1999446415t_char,V_4: list_char,T: ty,V: val,A_1: nat,S_2: produc2090907612on_val] : ( redp @ P @ ( block_list_char @ V_4 @ T @ ( seq_list_char @ ( lAss_list_char @ V_4 @ ( val_list_char @ V ) ) @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) ) ) @ S_2 @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) @ S_2 ) ).
thf(fact_555_eval__evals_OThrowThrow,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,E: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1 @ S_0 @ ( throw_list_char @ E ) @ S_1 )
=> ( eval @ P @ ( throw_list_char @ E_1 ) @ S_0 @ ( throw_list_char @ E ) @ S_1 ) ) ).
thf(fact_556_redp__redsp_OThrowRed,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S_2 @ E @ S )
=> ( redp @ P @ ( throw_list_char @ E_1 ) @ S_2 @ ( throw_list_char @ E ) @ S ) ) ).
thf(fact_557_redp__redsp_OThrowThrow,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,S_2: produc2090907612on_val] : ( redp @ P @ ( throw_list_char @ ( throw_list_char @ E_1 ) ) @ S_2 @ ( throw_list_char @ E_1 ) @ S_2 ) ).
thf(fact_558_eval__evals_OLAssThrow,axiom,
! [V_4: list_char,P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,E: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1 @ S_0 @ ( throw_list_char @ E ) @ S_1 )
=> ( eval @ P @ ( lAss_list_char @ V_4 @ E_1 ) @ S_0 @ ( throw_list_char @ E ) @ S_1 ) ) ).
thf(fact_559_eval__evals_OSeqThrow,axiom,
! [E_1_1: exp_list_char,P: list_P1999446415t_char,E_0: exp_list_char,S_0: produc2090907612on_val,E_1: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ E_0 @ S_0 @ ( throw_list_char @ E_1 ) @ S_1 )
=> ( eval @ P @ ( seq_list_char @ E_0 @ E_1_1 ) @ S_0 @ ( throw_list_char @ E_1 ) @ S_1 ) ) ).
thf(fact_560_eval__evals_OFAssThrow1,axiom,
! [F: list_char,D: list_char,E_2: exp_list_char,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,E: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( throw_list_char @ E ) @ S_1 )
=> ( eval @ P @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2 ) @ S_0 @ ( throw_list_char @ E ) @ S_1 ) ) ).
thf(fact_561_redp__redsp_OLAssThrow,axiom,
! [P: list_P1999446415t_char,V_4: list_char,E_1: exp_list_char,S_2: produc2090907612on_val] : ( redp @ P @ ( lAss_list_char @ V_4 @ ( throw_list_char @ E_1 ) ) @ S_2 @ ( throw_list_char @ E_1 ) @ S_2 ) ).
thf(fact_562_redp__redsp_OSeqThrow,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,E_2: exp_list_char,S_2: produc2090907612on_val] : ( redp @ P @ ( seq_list_char @ ( throw_list_char @ E_1 ) @ E_2 ) @ S_2 @ ( throw_list_char @ E_1 ) @ S_2 ) ).
thf(fact_563_eval__evals_OFAccThrow,axiom,
! [F: list_char,D: list_char,P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,E: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1 @ S_0 @ ( throw_list_char @ E ) @ S_1 )
=> ( eval @ P @ ( fAcc_list_char @ E_1 @ F @ D ) @ S_0 @ ( throw_list_char @ E ) @ S_1 ) ) ).
thf(fact_564_redp__redsp_OFAssThrow1,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,F: list_char,D: list_char,E_2: exp_list_char,S_2: produc2090907612on_val] : ( redp @ P @ ( fAss_list_char @ ( throw_list_char @ E_1 ) @ F @ D @ E_2 ) @ S_2 @ ( throw_list_char @ E_1 ) @ S_2 ) ).
thf(fact_565_redp__redsp_OFAccThrow,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,F: list_char,D: list_char,S_2: produc2090907612on_val] : ( redp @ P @ ( fAcc_list_char @ ( throw_list_char @ E_1 ) @ F @ D ) @ S_2 @ ( throw_list_char @ E_1 ) @ S_2 ) ).
thf(fact_566_red__reds_OThrowThrow,axiom,
! [E_1: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ ( throw_list_char @ E_1 ) ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_567_red__reds_OThrowRed,axiom,
! [E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ) ).
thf(fact_568_Throw,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,A_1: nat,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1 @ S_0 @ ( val_list_char @ ( addr @ A_1 ) ) @ S_1 )
=> ( eval @ P @ ( throw_list_char @ E_1 ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) @ S_1 ) ) ).
thf(fact_569_eval__evals_OFAssThrow2,axiom,
! [F: list_char,D: list_char,E_2: exp_list_char,E: exp_list_char,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,V: val,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ V ) @ S_1 )
=> ( ( eval @ P @ E_2 @ S_1 @ ( throw_list_char @ E ) @ S_2_1 )
=> ( eval @ P @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2 ) @ S_0 @ ( throw_list_char @ E ) @ S_2_1 ) ) ) ).
thf(fact_570_redp__redsp_OFAssThrow2,axiom,
! [P: list_P1999446415t_char,V: val,F: list_char,D: list_char,E_1: exp_list_char,S_2: produc2090907612on_val] : ( redp @ P @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ ( throw_list_char @ E_1 ) ) @ S_2 @ ( throw_list_char @ E_1 ) @ S_2 ) ).
thf(fact_571_val_Osimps_I3_J,axiom,
! [Nat_1: nat,Nat: nat] :
( ( ( addr @ Nat_1 )
= ( addr @ Nat ) )
<=> ( Nat_1 = Nat ) ) ).
thf(fact_572_ThrowReds,axiom,
! [E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_573_ThrowRedsThrow,axiom,
! [E_1: exp_list_char,S_2: produc2090907612on_val,A_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ A_1 ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ A_1 ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_574_red__reds_OLAssThrow,axiom,
! [V_4: list_char,E_1: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V_4 @ ( throw_list_char @ E_1 ) ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_575_red__reds_OSeqThrow,axiom,
! [E_1: exp_list_char,E_2: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ ( throw_list_char @ E_1 ) @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_576_red__reds_OFAssThrow1,axiom,
! [E_1: exp_list_char,F: list_char,D: list_char,E_2: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ ( throw_list_char @ E_1 ) @ F @ D @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_577_red__reds_OFAccThrow,axiom,
! [E_1: exp_list_char,F: list_char,D: list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ ( throw_list_char @ E_1 ) @ F @ D ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_578_redp__redsp_OBlockThrow,axiom,
! [P: list_P1999446415t_char,V_4: list_char,T: ty,A_1: nat,S_2: produc2090907612on_val] : ( redp @ P @ ( block_list_char @ V_4 @ T @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) ) @ S_2 @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) @ S_2 ) ).
thf(fact_579_red__reds_OFAssThrow2,axiom,
! [V: val,F: list_char,D: list_char,E_1: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ ( throw_list_char @ E_1 ) ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_580_LAssRedsThrow,axiom,
! [V_4: list_char,E_1: exp_list_char,S_2: produc2090907612on_val,A_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ A_1 ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V_4 @ E_1 ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ A_1 ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_581_SeqRedsThrow,axiom,
! [E_2: exp_list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ E_1 @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_582_FAssRedsThrow1,axiom,
! [F: list_char,D: list_char,E_2: exp_list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ E_1 @ F @ D @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_583_FAccRedsThrow,axiom,
! [F: list_char,D: list_char,E_1: exp_list_char,S_2: produc2090907612on_val,A_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ A_1 ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E_1 @ F @ D ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ A_1 ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_584_FAssRedsThrow2,axiom,
! [F: list_char,D: list_char,E_2: exp_list_char,E_1: exp_list_char,S_2_1: produc2090907612on_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,V: val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1_1 @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2 @ S_1 ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2 ) @ S_0 ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_585_red__reds_OBlockThrow,axiom,
! [V_4: list_char,T: ty,A_1: nat,S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_4 @ T @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_586_eval__cases_I4_J,axiom,
! [P: list_P1999446415t_char,V_4: list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( eval @ P @ ( lAss_list_char @ V_4 @ E_1 ) @ S_2 @ E @ S )
=> ( ( ( E
= ( val_list_char @ unit ) )
=> ! [V_3: val,H_3: nat > option1728594148on_val,L_3: list_char > option_val] :
( ( S
= ( produc755559506on_val @ H_3 @ ( fun_up1149430426on_val @ L_3 @ V_4 @ ( some_val @ V_3 ) ) ) )
=> ~ ( eval @ P @ E_1 @ S_2 @ ( val_list_char @ V_3 ) @ ( produc755559506on_val @ H_3 @ L_3 ) ) ) )
=> ~ ! [E_5: exp_list_char] :
( ( E
= ( throw_list_char @ E_5 ) )
=> ~ ( eval @ P @ E_1 @ S_2 @ ( throw_list_char @ E_5 ) @ S ) ) ) ) ).
thf(fact_587_eval__cases_I9_J,axiom,
! [P: list_P1999446415t_char,E_1_1: exp_list_char,E_2: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( eval @ P @ ( seq_list_char @ E_1_1 @ E_2 ) @ S_2 @ E @ S )
=> ( ! [V_3: val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_2 @ ( val_list_char @ V_3 ) @ S_1_1 )
=> ~ ( eval @ P @ E_2 @ S_1_1 @ E @ S ) )
=> ~ ! [E_3: exp_list_char] :
( ( E
= ( throw_list_char @ E_3 ) )
=> ~ ( eval @ P @ E_1_1 @ S_2 @ ( throw_list_char @ E_3 ) @ S ) ) ) ) ).
thf(fact_588_TryCatchRedsFinal,axiom,
! [E_2: exp_list_char,V_4: list_char,E_2_1: exp_list_char,H_2: nat > option1728594148on_val,L_2: list_char > option_val,C_1: list_char,D: list_char,Fs: produc1278157519t_char > option_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,A_1: nat,H_1: nat > option1728594148on_val,L_1: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1_1 @ S_0 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( H_1 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ D @ C_1 ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_1 @ ( fun_up1149430426on_val @ L_1 @ V_4 @ ( some_val @ ( addr @ A_1 ) ) ) ) ) @ ( produc235638504on_val @ E_2_1 @ ( produc755559506on_val @ H_2 @ L_2 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( final_list_char @ E_2_1 )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ E_1_1 @ C_1 @ V_4 @ E_2 ) @ S_0 ) @ ( produc235638504on_val @ E_2_1 @ ( produc755559506on_val @ H_2 @ ( fun_up1149430426on_val @ L_2 @ V_4 @ ( L_1 @ V_4 ) ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ) ) ).
thf(fact_589_redp__redsp_OTryRed,axiom,
! [C_1: list_char,V_4: list_char,E_2: exp_list_char,P: list_P1999446415t_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S_2 @ E @ S )
=> ( redp @ P @ ( tryCatch_list_char @ E_1 @ C_1 @ V_4 @ E_2 ) @ S_2 @ ( tryCatch_list_char @ E @ C_1 @ V_4 @ E_2 ) @ S ) ) ).
thf(fact_590_Try,axiom,
! [C_1: list_char,V_4: list_char,E_2: exp_list_char,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1: val,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ V_1 ) @ S_1 )
=> ( eval @ P @ ( tryCatch_list_char @ E_1_1 @ C_1 @ V_4 @ E_2 ) @ S_0 @ ( val_list_char @ V_1 ) @ S_1 ) ) ).
thf(fact_591_redp__redsp_ORedTry,axiom,
! [P: list_P1999446415t_char,V: val,C_1: list_char,V_4: list_char,E_2: exp_list_char,S_2: produc2090907612on_val] : ( redp @ P @ ( tryCatch_list_char @ ( val_list_char @ V ) @ C_1 @ V_4 @ E_2 ) @ S_2 @ ( val_list_char @ V ) @ S_2 ) ).
thf(fact_592_red__reds_OTryRed,axiom,
! [C_1: list_char,V_4: list_char,E_2: exp_list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ E_1 @ C_1 @ V_4 @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( tryCatch_list_char @ E @ C_1 @ V_4 @ E_2 ) @ S ) ) @ ( red @ P ) ) ) ).
thf(fact_593_red__reds_ORedTry,axiom,
! [V: val,C_1: list_char,V_4: list_char,E_2: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ ( val_list_char @ V ) @ C_1 @ V_4 @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_594_TryReds,axiom,
! [C_1: list_char,V_4: list_char,E_2: exp_list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ E_1 @ C_1 @ V_4 @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( tryCatch_list_char @ E @ C_1 @ V_4 @ E_2 ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_595_TryThrow,axiom,
! [V_4: list_char,E_2: exp_list_char,C_1: list_char,D: list_char,Fs: produc1278157519t_char > option_val,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,A_1: nat,H_1: nat > option1728594148on_val,L_1: list_char > option_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) )
=> ( ( ( H_1 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ~ ( member1251428284t_char @ ( produc5062597t_char @ D @ C_1 ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( eval @ P @ ( tryCatch_list_char @ E_1_1 @ C_1 @ V_4 @ E_2 ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) ) ) ) ).
thf(fact_596_TryRedsVal,axiom,
! [C_1: list_char,V_4: list_char,E_2: exp_list_char,E_1: exp_list_char,S_2: produc2090907612on_val,V: val,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ E_1 @ C_1 @ V_4 @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_597_red__reds_ORedTryFail,axiom,
! [V_4: list_char,E_2: exp_list_char,C_1: list_char,P: list_P1999446415t_char,S_2: produc2090907612on_val,A_1: nat,D: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S_2 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ~ ( member1251428284t_char @ ( produc5062597t_char @ D @ C_1 ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) @ C_1 @ V_4 @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) @ S_2 ) ) @ ( red @ P ) ) ) ) ).
thf(fact_598_TryCatch,axiom,
! [E_2: exp_list_char,V_4: list_char,E_2_1: exp_list_char,H_2: nat > option1728594148on_val,L_2: list_char > option_val,C_1: list_char,D: list_char,Fs: produc1278157519t_char > option_val,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,A_1: nat,H_1: nat > option1728594148on_val,L_1: list_char > option_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) )
=> ( ( ( H_1 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ D @ C_1 ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( ( eval @ P @ E_2 @ ( produc755559506on_val @ H_1 @ ( fun_up1149430426on_val @ L_1 @ V_4 @ ( some_val @ ( addr @ A_1 ) ) ) ) @ E_2_1 @ ( produc755559506on_val @ H_2 @ L_2 ) )
=> ( eval @ P @ ( tryCatch_list_char @ E_1_1 @ C_1 @ V_4 @ E_2 ) @ S_0 @ E_2_1 @ ( produc755559506on_val @ H_2 @ ( fun_up1149430426on_val @ L_2 @ V_4 @ ( L_1 @ V_4 ) ) ) ) ) ) ) ) ).
thf(fact_599_TryRedsFail,axiom,
! [V_4: list_char,E_2: exp_list_char,C_1: list_char,D: list_char,Fs: produc1278157519t_char > option_val,E_1_1: exp_list_char,S_2: produc2090907612on_val,A_1: nat,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1_1 @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) @ ( produc755559506on_val @ H @ L ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( H @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ~ ( member1251428284t_char @ ( produc5062597t_char @ D @ C_1 ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ E_1_1 @ C_1 @ V_4 @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) @ ( produc755559506on_val @ H @ L ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_600_red__reds_ORedTryCatch,axiom,
! [V_4: list_char,E_2: exp_list_char,C_1: list_char,P: list_P1999446415t_char,S_2: produc2090907612on_val,A_1: nat,D: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S_2 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ D @ C_1 ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) @ C_1 @ V_4 @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( block_list_char @ V_4 @ ( class @ C_1 ) @ ( seq_list_char @ ( lAss_list_char @ V_4 @ ( val_list_char @ ( addr @ A_1 ) ) ) @ E_2 ) ) @ S_2 ) ) @ ( red @ P ) ) ) ) ).
thf(fact_601_CastRedsAddr,axiom,
! [C_1: list_char,D: list_char,Fs: produc1278157519t_char > option_val,E_1: exp_list_char,S_2: produc2090907612on_val,A_1: nat,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ ( addr @ A_1 ) ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( hp @ S @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ D @ C_1 ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C_1 @ E_1 ) @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ ( addr @ A_1 ) ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_602_red__reds_ORedCast,axiom,
! [C_1: list_char,P: list_P1999446415t_char,S_2: produc2090907612on_val,A_1: nat,D: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S_2 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ D @ C_1 ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C_1 @ ( val_list_char @ ( addr @ A_1 ) ) ) @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ ( addr @ A_1 ) ) @ S_2 ) ) @ ( red @ P ) ) ) ) ).
thf(fact_603_WTrtTry,axiom,
! [V_4: list_char,C_1: list_char,E_2: exp_list_char,T_2_1: ty,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_4: list_char > option_ty,E_1_1: exp_list_char,T_1_2: ty] :
( ( wTrt @ P @ H @ E_4 @ E_1_1 @ T_1_2 )
=> ( ( wTrt @ P @ H @ ( fun_up424764369ion_ty @ E_4 @ V_4 @ ( some_ty @ ( class @ C_1 ) ) ) @ E_2 @ T_2_1 )
=> ( ( widen_2090681816t_char @ P @ T_1_2 @ T_2_1 )
=> ( wTrt @ P @ H @ E_4 @ ( tryCatch_list_char @ E_1_1 @ C_1 @ V_4 @ E_2 ) @ T_2_1 ) ) ) ) ).
thf(fact_604_redp__redsp_OCastRed,axiom,
! [C_1: list_char,P: list_P1999446415t_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S_2 @ E @ S )
=> ( redp @ P @ ( cast_list_char @ C_1 @ E_1 ) @ S_2 @ ( cast_list_char @ C_1 @ E ) @ S ) ) ).
thf(fact_605_eval__evals_OCastThrow,axiom,
! [C_1: list_char,P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,E: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1 @ S_0 @ ( throw_list_char @ E ) @ S_1 )
=> ( eval @ P @ ( cast_list_char @ C_1 @ E_1 ) @ S_0 @ ( throw_list_char @ E ) @ S_1 ) ) ).
thf(fact_606_redp__redsp_OCastThrow,axiom,
! [P: list_P1999446415t_char,C_1: list_char,E_1: exp_list_char,S_2: produc2090907612on_val] : ( redp @ P @ ( cast_list_char @ C_1 @ ( throw_list_char @ E_1 ) ) @ S_2 @ ( throw_list_char @ E_1 ) @ S_2 ) ).
thf(fact_607_WTrtFAcc,axiom,
! [F: list_char,T: ty,D: list_char,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_4: list_char > option_ty,E_1: exp_list_char,C_1: list_char] :
( ( wTrt @ P @ H @ E_4 @ E_1 @ ( class @ C_1 ) )
=> ( ( has_fi1183600461t_char @ P @ C_1 @ F @ T @ D )
=> ( wTrt @ P @ H @ E_4 @ ( fAcc_list_char @ E_1 @ F @ D ) @ T ) ) ) ).
thf(fact_608_red__reds_OCastRed,axiom,
! [C_1: list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C_1 @ E_1 ) @ S_2 ) @ ( produc235638504on_val @ ( cast_list_char @ C_1 @ E ) @ S ) ) @ ( red @ P ) ) ) ).
thf(fact_609_red__reds_OCastThrow,axiom,
! [C_1: list_char,E_1: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C_1 @ ( throw_list_char @ E_1 ) ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_610_CastReds,axiom,
! [C_1: list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C_1 @ E_1 ) @ S_2 ) @ ( produc235638504on_val @ ( cast_list_char @ C_1 @ E ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_611_WTrtFAss,axiom,
! [E_2: exp_list_char,T_2_1: ty,F: list_char,T: ty,D: list_char,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_4: list_char > option_ty,E_1_1: exp_list_char,C_1: list_char] :
( ( wTrt @ P @ H @ E_4 @ E_1_1 @ ( class @ C_1 ) )
=> ( ( has_fi1183600461t_char @ P @ C_1 @ F @ T @ D )
=> ( ( wTrt @ P @ H @ E_4 @ E_2 @ T_2_1 )
=> ( ( widen_2090681816t_char @ P @ T_2_1 @ T )
=> ( wTrt @ P @ H @ E_4 @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2 ) @ void ) ) ) ) ) ).
thf(fact_612_CastRedsThrow,axiom,
! [C_1: list_char,E_1: exp_list_char,S_2: produc2090907612on_val,A_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ A_1 ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C_1 @ E_1 ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ A_1 ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_613_Cast,axiom,
! [C_1: list_char,D: list_char,Fs: produc1278157519t_char > option_val,P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,A_1: nat,H: nat > option1728594148on_val,L: list_char > option_val] :
( ( eval @ P @ E_1 @ S_0 @ ( val_list_char @ ( addr @ A_1 ) ) @ ( produc755559506on_val @ H @ L ) )
=> ( ( ( H @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ D @ C_1 ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( eval @ P @ ( cast_list_char @ C_1 @ E_1 ) @ S_0 @ ( val_list_char @ ( addr @ A_1 ) ) @ ( produc755559506on_val @ H @ L ) ) ) ) ) ).
thf(fact_614_WTrt__elim__cases_I5_J,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_4: list_char > option_ty,E_1_1: exp_list_char,C_1: list_char,V_4: list_char,E_2: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_4 @ ( tryCatch_list_char @ E_1_1 @ C_1 @ V_4 @ E_2 ) @ T )
=> ~ ! [T_1_1: ty] :
( ( wTrt @ P @ H @ E_4 @ E_1_1 @ T_1_1 )
=> ( ( wTrt @ P @ H @ ( fun_up424764369ion_ty @ E_4 @ V_4 @ ( some_ty @ ( class @ C_1 ) ) ) @ E_2 @ T )
=> ~ ( widen_2090681816t_char @ P @ T_1_1 @ T ) ) ) ) ).
thf(fact_615_final__addrE,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_4: list_char > option_ty,E_1: exp_list_char,C_1: list_char] :
( ( wTrt @ P @ H @ E_4 @ E_1 @ ( class @ C_1 ) )
=> ( ( final_list_char @ E_1 )
=> ( ! [A: nat] :
( E_1
!= ( val_list_char @ ( addr @ A ) ) )
=> ~ ! [A: nat] :
( E_1
!= ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) ) ) ) ) ).
thf(fact_616_CastRedsFail,axiom,
! [C_1: list_char,D: list_char,Fs: produc1278157519t_char > option_val,E_1: exp_list_char,S_2: produc2090907612on_val,A_1: nat,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ ( addr @ A_1 ) ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( hp @ S @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ~ ( member1251428284t_char @ ( produc5062597t_char @ D @ C_1 ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C_1 @ E_1 ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_617_CastFail,axiom,
! [C_1: list_char,D: list_char,Fs: produc1278157519t_char > option_val,P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,A_1: nat,H: nat > option1728594148on_val,L: list_char > option_val] :
( ( eval @ P @ E_1 @ S_0 @ ( val_list_char @ ( addr @ A_1 ) ) @ ( produc755559506on_val @ H @ L ) )
=> ( ( ( H @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ~ ( member1251428284t_char @ ( produc5062597t_char @ D @ C_1 ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( eval @ P @ ( cast_list_char @ C_1 @ E_1 ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) @ ( produc755559506on_val @ H @ L ) ) ) ) ) ).
thf(fact_618_red__reds_ORedCastFail,axiom,
! [C_1: list_char,P: list_P1999446415t_char,S_2: produc2090907612on_val,A_1: nat,D: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S_2 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ~ ( member1251428284t_char @ ( produc5062597t_char @ D @ C_1 ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C_1 @ ( val_list_char @ ( addr @ A_1 ) ) ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) @ S_2 ) ) @ ( red @ P ) ) ) ) ).
thf(fact_619_redp__redsp_ORedTryCatch,axiom,
! [V_4: list_char,E_2: exp_list_char,P: list_P1999446415t_char,C_1: list_char,S_2: produc2090907612on_val,A_1: nat,D: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S_2 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ( transi1065307915t_char @ ( subcls744239332t_char @ P ) @ D @ C_1 )
=> ( redp @ P @ ( tryCatch_list_char @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) @ C_1 @ V_4 @ E_2 ) @ S_2 @ ( block_list_char @ V_4 @ ( class @ C_1 ) @ ( seq_list_char @ ( lAss_list_char @ V_4 @ ( val_list_char @ ( addr @ A_1 ) ) ) @ E_2 ) ) @ S_2 ) ) ) ).
thf(fact_620_redp__redsp_ORedCast,axiom,
! [P: list_P1999446415t_char,C_1: list_char,S_2: produc2090907612on_val,A_1: nat,D: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S_2 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ( transi1065307915t_char @ ( subcls744239332t_char @ P ) @ D @ C_1 )
=> ( redp @ P @ ( cast_list_char @ C_1 @ ( val_list_char @ ( addr @ A_1 ) ) ) @ S_2 @ ( val_list_char @ ( addr @ A_1 ) ) @ S_2 ) ) ) ).
thf(fact_621_redp__redsp_ORedTryFail,axiom,
! [V_4: list_char,E_2: exp_list_char,P: list_P1999446415t_char,C_1: list_char,S_2: produc2090907612on_val,A_1: nat,D: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S_2 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ~ ( transi1065307915t_char @ ( subcls744239332t_char @ P ) @ D @ C_1 )
=> ( redp @ P @ ( tryCatch_list_char @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) @ C_1 @ V_4 @ E_2 ) @ S_2 @ ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) @ S_2 ) ) ) ).
thf(fact_622_redp__redsp_ORedCastFail,axiom,
! [P: list_P1999446415t_char,C_1: list_char,S_2: produc2090907612on_val,A_1: nat,D: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S_2 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ~ ( transi1065307915t_char @ ( subcls744239332t_char @ P ) @ D @ C_1 )
=> ( redp @ P @ ( cast_list_char @ C_1 @ ( val_list_char @ ( addr @ A_1 ) ) ) @ S_2 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) @ S_2 ) ) ) ).
thf(fact_623_ty_Osimps_I8_J,axiom,
! [List: list_char] :
( void
!= ( class @ List ) ) ).
thf(fact_624_ty_Osimps_I9_J,axiom,
! [List: list_char] :
( ( class @ List )
!= void ) ).
thf(fact_625_ty_Oinject,axiom,
! [List_1: list_char,List: list_char] :
( ( ( class @ List_1 )
= ( class @ List ) )
<=> ( List_1 = List ) ) ).
thf(fact_626_CastRedsNull,axiom,
! [C_1: list_char,E_1: exp_list_char,S_2: produc2090907612on_val,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C_1 @ E_1 ) @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_627_ty_Osimps_I21_J,axiom,
! [List: list_char] :
( ( class @ List )
!= nt ) ).
thf(fact_628_ty_Osimps_I20_J,axiom,
! [List: list_char] :
( nt
!= ( class @ List ) ) ).
thf(fact_629_ty_Osimps_I6_J,axiom,
void != nt ).
thf(fact_630_ty_Osimps_I7_J,axiom,
nt != void ).
thf(fact_631_val_Osimps_I4_J,axiom,
unit != null ).
thf(fact_632_val_Osimps_I5_J,axiom,
null != unit ).
thf(fact_633_val_Osimps_I17_J,axiom,
! [Nat: nat] :
( ( addr @ Nat )
!= null ) ).
thf(fact_634_val_Osimps_I16_J,axiom,
! [Nat: nat] :
( null
!= ( addr @ Nat ) ) ).
thf(fact_635_WTrtFAccNT,axiom,
! [F: list_char,D: list_char,T: ty,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_4: list_char > option_ty,E_1: exp_list_char] :
( ( wTrt @ P @ H @ E_4 @ E_1 @ nt )
=> ( wTrt @ P @ H @ E_4 @ ( fAcc_list_char @ E_1 @ F @ D ) @ T ) ) ).
thf(fact_636_CastNull,axiom,
! [C_1: list_char,P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1 @ S_0 @ ( val_list_char @ null ) @ S_1 )
=> ( eval @ P @ ( cast_list_char @ C_1 @ E_1 ) @ S_0 @ ( val_list_char @ null ) @ S_1 ) ) ).
thf(fact_637_redp__redsp_ORedCastNull,axiom,
! [P: list_P1999446415t_char,C_1: list_char,S_2: produc2090907612on_val] : ( redp @ P @ ( cast_list_char @ C_1 @ ( val_list_char @ null ) ) @ S_2 @ ( val_list_char @ null ) @ S_2 ) ).
thf(fact_638_WTrtFAssNT,axiom,
! [F: list_char,D: list_char,E_2: exp_list_char,T_2_1: ty,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_4: list_char > option_ty,E_1_1: exp_list_char] :
( ( wTrt @ P @ H @ E_4 @ E_1_1 @ nt )
=> ( ( wTrt @ P @ H @ E_4 @ E_2 @ T_2_1 )
=> ( wTrt @ P @ H @ E_4 @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2 ) @ void ) ) ) ).
thf(fact_639_red__reds_ORedCastNull,axiom,
! [C_1: list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C_1 @ ( val_list_char @ null ) ) @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_640_WTrt__elim__cases_I7_J,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_4: list_char > option_ty,E_1: exp_list_char,F: list_char,D: list_char,T: ty] :
( ( wTrt @ P @ H @ E_4 @ ( fAcc_list_char @ E_1 @ F @ D ) @ T )
=> ( ! [C_2: list_char] :
( ( wTrt @ P @ H @ E_4 @ E_1 @ ( class @ C_2 ) )
=> ~ ( has_fi1183600461t_char @ P @ C_2 @ F @ T @ D ) )
=> ( wTrt @ P @ H @ E_4 @ E_1 @ nt ) ) ) ).
thf(fact_641_WTrt__elim__cases_I8_J,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_4: list_char > option_ty,E_1: exp_list_char,F: list_char,D: list_char,V: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_4 @ ( fAss_list_char @ E_1 @ F @ D @ V ) @ T )
=> ( ( ( T = void )
=> ! [C_2: list_char] :
( ( wTrt @ P @ H @ E_4 @ E_1 @ ( class @ C_2 ) )
=> ! [T_1: ty] :
( ( has_fi1183600461t_char @ P @ C_2 @ F @ T_1 @ D )
=> ! [T_2: ty] :
( ( wTrt @ P @ H @ E_4 @ V @ T_2 )
=> ~ ( widen_2090681816t_char @ P @ T_2 @ T_1 ) ) ) ) )
=> ~ ( ( T = void )
=> ( ( wTrt @ P @ H @ E_4 @ E_1 @ nt )
=> ! [T_2: ty] :
~ ( wTrt @ P @ H @ E_4 @ V @ T_2 ) ) ) ) ) ).
thf(fact_642_FAccRedsNull,axiom,
! [F: list_char,D: list_char,E_1: exp_list_char,S_2: produc2090907612on_val,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E_1 @ F @ D ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_643_ThrowNull,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1 @ S_0 @ ( val_list_char @ null ) @ S_1 )
=> ( eval @ P @ ( throw_list_char @ E_1 ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_1 ) ) ).
thf(fact_644_redp__redsp_ORedThrowNull,axiom,
! [P: list_P1999446415t_char,S_2: produc2090907612on_val] : ( redp @ P @ ( throw_list_char @ ( val_list_char @ null ) ) @ S_2 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_2 ) ).
thf(fact_645_FAssNull,axiom,
! [F: list_char,D: list_char,E_2: exp_list_char,V: val,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ null ) @ S_1 )
=> ( ( eval @ P @ E_2 @ S_1 @ ( val_list_char @ V ) @ S_2_1 )
=> ( eval @ P @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2 ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_2_1 ) ) ) ).
thf(fact_646_FAccNull,axiom,
! [F: list_char,D: list_char,P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1 @ S_0 @ ( val_list_char @ null ) @ S_1 )
=> ( eval @ P @ ( fAcc_list_char @ E_1 @ F @ D ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_1 ) ) ).
thf(fact_647_redp__redsp_ORedFAssNull,axiom,
! [P: list_P1999446415t_char,F: list_char,D: list_char,V: val,S_2: produc2090907612on_val] : ( redp @ P @ ( fAss_list_char @ ( val_list_char @ null ) @ F @ D @ ( val_list_char @ V ) ) @ S_2 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_2 ) ).
thf(fact_648_redp__redsp_ORedFAccNull,axiom,
! [P: list_P1999446415t_char,F: list_char,D: list_char,S_2: produc2090907612on_val] : ( redp @ P @ ( fAcc_list_char @ ( val_list_char @ null ) @ F @ D ) @ S_2 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_2 ) ).
thf(fact_649_red__reds_ORedThrowNull,axiom,
! [S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ null ) ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_650_ThrowRedsNull,axiom,
! [E_1: exp_list_char,S_2: produc2090907612on_val,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_651_red__reds_ORedFAssNull,axiom,
! [F: list_char,D: list_char,V: val,S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ null ) @ F @ D @ ( val_list_char @ V ) ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_652_red__reds_ORedFAccNull,axiom,
! [F: list_char,D: list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ ( val_list_char @ null ) @ F @ D ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_653_FAssRedsNull,axiom,
! [F: list_char,D: list_char,E_2: exp_list_char,V: val,S_2_1: produc2090907612on_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1_1 @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2 @ S_1 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2 ) @ S_0 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_654_eval__cases_I12_J,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( eval @ P @ ( throw_list_char @ E_1 ) @ S_2 @ E @ S )
=> ( ! [A: nat] :
( ( E
= ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) )
=> ~ ( eval @ P @ E_1 @ S_2 @ ( val_list_char @ ( addr @ A ) ) @ S ) )
=> ( ( ( E
= ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) )
=> ~ ( eval @ P @ E_1 @ S_2 @ ( val_list_char @ null ) @ S ) )
=> ~ ! [E_5: exp_list_char] :
( ( E
= ( throw_list_char @ E_5 ) )
=> ~ ( eval @ P @ E_1 @ S_2 @ ( throw_list_char @ E_5 ) @ S ) ) ) ) ) ).
thf(fact_655_finalRefE,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_4: list_char > option_ty,E_1: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_4 @ E_1 @ T )
=> ( ( is_refT @ T )
=> ( ( final_list_char @ E_1 )
=> ( ( E_1
!= ( val_list_char @ null ) )
=> ( ( ? [A: nat] :
( E_1
= ( val_list_char @ ( addr @ A ) ) )
=> ! [C_2: list_char] :
( T
!= ( class @ C_2 ) ) )
=> ~ ! [A: nat] :
( E_1
!= ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) ) ) ) ) ) ) ).
thf(fact_656_WTrtThrow,axiom,
! [T: ty,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_4: list_char > option_ty,E_1: exp_list_char,T_r_1: ty] :
( ( wTrt @ P @ H @ E_4 @ E_1 @ T_r_1 )
=> ( ( is_refT @ T_r_1 )
=> ( wTrt @ P @ H @ E_4 @ ( throw_list_char @ E_1 ) @ T ) ) ) ).
thf(fact_657_is__refT__def,axiom,
! [T: ty] :
( ( is_refT @ T )
<=> ( ( T = nt )
| ? [C_2: list_char] :
( T
= ( class @ C_2 ) ) ) ) ).
thf(fact_658_WTrt__elim__cases_I4_J,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_4: list_char > option_ty,E_1: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_4 @ ( throw_list_char @ E_1 ) @ T )
=> ~ ! [T_r: ty] :
( ( wTrt @ P @ H @ E_4 @ E_1 @ T_r )
=> ~ ( is_refT @ T_r ) ) ) ).
thf(fact_659_refTE,axiom,
! [T: ty] :
( ( is_refT @ T )
=> ( ( T != nt )
=> ~ ! [C_2: list_char] :
( T
!= ( class @ C_2 ) ) ) ) ).
thf(fact_660_WTrtCast,axiom,
! [C_1: list_char,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_4: list_char > option_ty,E_1: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_4 @ E_1 @ T )
=> ( ( is_refT @ T )
=> ( ( is_cla570604648t_char @ P @ C_1 )
=> ( wTrt @ P @ H @ E_4 @ ( cast_list_char @ C_1 @ E_1 ) @ ( class @ C_1 ) ) ) ) ) ).
thf(fact_661_BinOpRedsThrow2,axiom,
! [Bop: bop,E_2: exp_list_char,E_1: exp_list_char,S_2_1: produc2090907612on_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1: val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1_1 @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ V_1 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2 @ S_1 ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ E_1_1 @ Bop @ E_2 ) @ S_0 ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_662_eval__evals_OBinOpThrow1,axiom,
! [Bop: bop,E_2: exp_list_char,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,E_1: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( throw_list_char @ E_1 ) @ S_1 )
=> ( eval @ P @ ( binOp_list_char @ E_1_1 @ Bop @ E_2 ) @ S_0 @ ( throw_list_char @ E_1 ) @ S_1 ) ) ).
thf(fact_663_redp__redsp_OBinOpRed1,axiom,
! [Bop: bop,E_2: exp_list_char,P: list_P1999446415t_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S_2 @ E @ S )
=> ( redp @ P @ ( binOp_list_char @ E_1 @ Bop @ E_2 ) @ S_2 @ ( binOp_list_char @ E @ Bop @ E_2 ) @ S ) ) ).
thf(fact_664_redp__redsp_OBinOpThrow1,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,Bop: bop,E_2: exp_list_char,S_2: produc2090907612on_val] : ( redp @ P @ ( binOp_list_char @ ( throw_list_char @ E_1 ) @ Bop @ E_2 ) @ S_2 @ ( throw_list_char @ E_1 ) @ S_2 ) ).
thf(fact_665_redp__redsp_OBinOpRed2,axiom,
! [V_1: val,Bop: bop,P: list_P1999446415t_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S_2 @ E @ S )
=> ( redp @ P @ ( binOp_list_char @ ( val_list_char @ V_1 ) @ Bop @ E_1 ) @ S_2 @ ( binOp_list_char @ ( val_list_char @ V_1 ) @ Bop @ E ) @ S ) ) ).
thf(fact_666_red__reds_OBinOpRed1,axiom,
! [Bop: bop,E_2: exp_list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ E_1 @ Bop @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( binOp_list_char @ E @ Bop @ E_2 ) @ S ) ) @ ( red @ P ) ) ) ).
thf(fact_667_eval__evals_OBinOpThrow2,axiom,
! [Bop: bop,E_2: exp_list_char,E_1: exp_list_char,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1: val,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ V_1 ) @ S_1 )
=> ( ( eval @ P @ E_2 @ S_1 @ ( throw_list_char @ E_1 ) @ S_2_1 )
=> ( eval @ P @ ( binOp_list_char @ E_1_1 @ Bop @ E_2 ) @ S_0 @ ( throw_list_char @ E_1 ) @ S_2_1 ) ) ) ).
thf(fact_668_redp__redsp_OBinOpThrow2,axiom,
! [P: list_P1999446415t_char,V_1: val,Bop: bop,E_1: exp_list_char,S_2: produc2090907612on_val] : ( redp @ P @ ( binOp_list_char @ ( val_list_char @ V_1 ) @ Bop @ ( throw_list_char @ E_1 ) ) @ S_2 @ ( throw_list_char @ E_1 ) @ S_2 ) ).
thf(fact_669_red__reds_OBinOpRed2,axiom,
! [V_1: val,Bop: bop,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V_1 ) @ Bop @ E_1 ) @ S_2 ) @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V_1 ) @ Bop @ E ) @ S ) ) @ ( red @ P ) ) ) ).
thf(fact_670_red__reds_OBinOpThrow1,axiom,
! [E_1: exp_list_char,Bop: bop,E_2: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ ( throw_list_char @ E_1 ) @ Bop @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_671_BinOp1Reds,axiom,
! [Bop: bop,E_2: exp_list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ E_1 @ Bop @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( binOp_list_char @ E @ Bop @ E_2 ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_672_red__reds_OBinOpThrow2,axiom,
! [V_1: val,Bop: bop,E_1: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V_1 ) @ Bop @ ( throw_list_char @ E_1 ) ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2 ) ) @ ( red @ P ) ) ).
thf(fact_673_BinOp2Reds,axiom,
! [V: val,Bop: bop,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ E @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V ) @ Bop @ E_1 ) @ S_2 ) @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V ) @ Bop @ E ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_674_BinOpRedsThrow1,axiom,
! [Bop: bop,E_2: exp_list_char,E_1: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ E_1 @ Bop @ E_2 ) @ S_2 ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_675_WTrt__elim__cases_I6_J,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_4: list_char > option_ty,D: list_char,E_1: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_4 @ ( cast_list_char @ D @ E_1 ) @ T )
=> ~ ( ( T
= ( class @ D ) )
=> ! [T_1: ty] :
( ( wTrt @ P @ H @ E_4 @ E_1 @ T_1 )
=> ( ( is_refT @ T_1 )
=> ~ ( is_cla570604648t_char @ P @ D ) ) ) ) ) ).
thf(fact_676_BinOpRedsVal,axiom,
! [Bop: bop,V: val,E_2: exp_list_char,V_2: val,S_2_1: produc2090907612on_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1: val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1_1 @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ V_1 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2 @ S_1 ) @ ( produc235638504on_val @ ( val_list_char @ V_2 ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( binop @ ( produc621191550al_val @ Bop @ ( product_Pair_val_val @ V_1 @ V_2 ) ) )
= ( some_val @ V ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ E_1_1 @ Bop @ E_2 ) @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_677_BinOp,axiom,
! [Bop: bop,V: val,E_2: exp_list_char,V_2: val,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1: val,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ V_1 ) @ S_1 )
=> ( ( eval @ P @ E_2 @ S_1 @ ( val_list_char @ V_2 ) @ S_2_1 )
=> ( ( ( binop @ ( produc621191550al_val @ Bop @ ( product_Pair_val_val @ V_1 @ V_2 ) ) )
= ( some_val @ V ) )
=> ( eval @ P @ ( binOp_list_char @ E_1_1 @ Bop @ E_2 ) @ S_0 @ ( val_list_char @ V ) @ S_2_1 ) ) ) ) ).
thf(fact_678_redp__redsp_ORedBinOp,axiom,
! [P: list_P1999446415t_char,S_2: produc2090907612on_val,Bop: bop,V_1: val,V_2: val,V: val] :
( ( ( binop @ ( produc621191550al_val @ Bop @ ( product_Pair_val_val @ V_1 @ V_2 ) ) )
= ( some_val @ V ) )
=> ( redp @ P @ ( binOp_list_char @ ( val_list_char @ V_1 ) @ Bop @ ( val_list_char @ V_2 ) ) @ S_2 @ ( val_list_char @ V ) @ S_2 ) ) ).
thf(fact_679_red__reds_ORedBinOp,axiom,
! [S_2: produc2090907612on_val,P: list_P1999446415t_char,Bop: bop,V_1: val,V_2: val,V: val] :
( ( ( binop @ ( produc621191550al_val @ Bop @ ( product_Pair_val_val @ V_1 @ V_2 ) ) )
= ( some_val @ V ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V_1 ) @ Bop @ ( val_list_char @ V_2 ) ) @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S_2 ) ) @ ( red @ P ) ) ) ).
thf(fact_680_eval__cases_I3_J,axiom,
! [P: list_P1999446415t_char,E_1_1: exp_list_char,Bop: bop,E_2: exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S: produc2090907612on_val] :
( ( eval @ P @ ( binOp_list_char @ E_1_1 @ Bop @ E_2 ) @ S_2 @ E @ S )
=> ( ! [V_1_1: val,S_1_1: produc2090907612on_val,V_2_1: val,V_3: val] :
( ( E
= ( val_list_char @ V_3 ) )
=> ( ( eval @ P @ E_1_1 @ S_2 @ ( val_list_char @ V_1_1 ) @ S_1_1 )
=> ( ( eval @ P @ E_2 @ S_1_1 @ ( val_list_char @ V_2_1 ) @ S )
=> ( ( binop @ ( produc621191550al_val @ Bop @ ( product_Pair_val_val @ V_1_1 @ V_2_1 ) ) )
!= ( some_val @ V_3 ) ) ) ) )
=> ( ! [E_3: exp_list_char] :
( ( E
= ( throw_list_char @ E_3 ) )
=> ~ ( eval @ P @ E_1_1 @ S_2 @ ( throw_list_char @ E_3 ) @ S ) )
=> ~ ! [V_1_1: val,S_1_1: produc2090907612on_val,E_3: exp_list_char] :
( ( E
= ( throw_list_char @ E_3 ) )
=> ( ( eval @ P @ E_1_1 @ S_2 @ ( val_list_char @ V_1_1 ) @ S_1_1 )
=> ~ ( eval @ P @ E_2 @ S_1_1 @ ( throw_list_char @ E_3 ) @ S ) ) ) ) ) ) ).
thf(fact_681_binop_Osimps_I3_J,axiom,
! [V_2: val] :
( ( binop @ ( produc621191550al_val @ add @ ( product_Pair_val_val @ unit @ V_2 ) ) )
= none_val ) ).
thf(fact_682_binop_Osimps_I10_J,axiom,
! [V_1: val,V: nat] :
( ( binop @ ( produc621191550al_val @ add @ ( product_Pair_val_val @ V_1 @ ( addr @ V ) ) ) )
= none_val ) ).
thf(fact_683_binop_Osimps_I6_J,axiom,
! [V: nat,V_2: val] :
( ( binop @ ( produc621191550al_val @ add @ ( product_Pair_val_val @ ( addr @ V ) @ V_2 ) ) )
= none_val ) ).
thf(fact_684_binop_Osimps_I4_J,axiom,
! [V_2: val] :
( ( binop @ ( produc621191550al_val @ add @ ( product_Pair_val_val @ null @ V_2 ) ) )
= none_val ) ).
thf(fact_685_binop_Osimps_I8_J,axiom,
! [V_1: val] :
( ( binop @ ( produc621191550al_val @ add @ ( product_Pair_val_val @ V_1 @ null ) ) )
= none_val ) ).
thf(fact_686_binop_Osimps_I7_J,axiom,
! [V_1: val] :
( ( binop @ ( produc621191550al_val @ add @ ( product_Pair_val_val @ V_1 @ unit ) ) )
= none_val ) ).
thf(fact_687_binop_Osimps_I5_J,axiom,
! [V: $o,V_2: val] :
( ( binop @ ( produc621191550al_val @ add @ ( product_Pair_val_val @ ( bool @ V ) @ V_2 ) ) )
= none_val ) ).
thf(fact_688_binop_Osimps_I9_J,axiom,
! [V_1: val,V: $o] :
( ( binop @ ( produc621191550al_val @ add @ ( product_Pair_val_val @ V_1 @ ( bool @ V ) ) ) )
= none_val ) ).
thf(fact_689_val_Osimps_I12_J,axiom,
! [Bool_1: $o] :
( null
!= ( bool @ Bool_1 ) ) ).
thf(fact_690_val_Osimps_I13_J,axiom,
! [Bool_1: $o] :
( ( bool @ Bool_1 )
!= null ) ).
thf(fact_691_val_Osimps_I1_J,axiom,
! [Bool: $o,Bool_1: $o] :
( ( ( bool @ Bool )
= ( bool @ Bool_1 ) )
<=> ( Bool
<=> Bool_1 ) ) ).
thf(fact_692_val_Osimps_I6_J,axiom,
! [Bool_1: $o] :
( unit
!= ( bool @ Bool_1 ) ) ).
thf(fact_693_val_Osimps_I7_J,axiom,
! [Bool_1: $o] :
( ( bool @ Bool_1 )
!= unit ) ).
thf(fact_694_val_Osimps_I21_J,axiom,
! [Nat: nat,Bool: $o] :
( ( addr @ Nat )
!= ( bool @ Bool ) ) ).
thf(fact_695_val_Osimps_I20_J,axiom,
! [Bool: $o,Nat: nat] :
( ( bool @ Bool )
!= ( addr @ Nat ) ) ).
thf(fact_696_binop_Osimps_I1_J,axiom,
! [V_1: val,V_2: val] :
( ( binop @ ( produc621191550al_val @ c_Expr_Obop_OEq @ ( product_Pair_val_val @ V_1 @ V_2 ) ) )
= ( some_val @ ( bool @ ( V_1 = V_2 ) ) ) ) ).
thf(fact_697_WhileFReds,axiom,
! [C: exp_list_char,B: exp_list_char,S_2: produc2090907612on_val,S: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ B @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ ( bool @ $false ) ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( while_list_char @ B @ C ) @ S_2 ) @ ( produc235638504on_val @ ( val_list_char @ unit ) @ S ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_698_WhileCondThrow,axiom,
! [C: exp_list_char,P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,E: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1 @ S_0 @ ( throw_list_char @ E ) @ S_1 )
=> ( eval @ P @ ( while_list_char @ E_1 @ C ) @ S_0 @ ( throw_list_char @ E ) @ S_1 ) ) ).
thf(fact_699_bop_Oexhaust,axiom,
! [Y: bop] :
( ( Y != c_Expr_Obop_OEq )
=> ( Y = add ) ) ).
%----Conjectures (1)
thf(conj_0,conjecture,
member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ea @ ( produc755559506on_val @ ha @ ( fun_up1149430426on_val @ la @ v_1 @ ( some_val @ v ) ) ) ) @ ( produc235638504on_val @ e_a @ ( produc755559506on_val @ h_a @ l_a ) ) ) @ ( red @ p ) ).
%------------------------------------------------------------------------------