TPTP Problem File: SWW478^3.p
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%------------------------------------------------------------------------------
% File : SWW478^3 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Java type soundness line 479, 1000 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : jinja_1000_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, 0.57 v5.5.0, 0.50 v5.4.0, 0.80 v5.3.0
% Syntax : Number of formulae : 1612 ( 400 unt; 411 typ; 0 def)
% Number of atoms : 3388 ( 925 equ; 11 cnn)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 16018 ( 533 ~; 30 |; 93 &;13621 @)
% ( 266 <=>;1415 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 11 avg)
% Number of types : 67 ( 66 usr)
% Number of type conns : 2671 (2671 >; 0 *; 0 +; 0 <<)
% Number of symbols : 353 ( 345 usr; 30 con; 0-7 aty)
% ( 44 !!; 16 ??; 0 @@+; 0 @@-)
% Number of variables : 5504 ( 111 ^;5339 !; 54 ?;5504 :)
% SPC : TH1_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 20:03:39
%------------------------------------------------------------------------------
%----Should-be-implicit typings (66)
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__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_J,type,
list_exp_list_char: $tType ).
thf(ty_ty_tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J,type,
list_list_char: $tType ).
thf(ty_ty_tc__List__Olist_Itc__Option__Ooption_Itc__Type__Oty_J_J,type,
list_option_ty: $tType ).
thf(ty_ty_tc__List__Olist_Itc__String__Ochar_J,type,
list_char: $tType ).
thf(ty_ty_tc__List__Olist_Itc__Type__Oty_J,type,
list_ty: $tType ).
thf(ty_ty_tc__List__Olist_Itc__Value__Oval_J,type,
list_val: $tType ).
thf(ty_ty_tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Type_,type,
list_P1940453997har_ty: $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__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod__001,type,
list_P341299826t_char: $tType ).
thf(ty_ty_tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_,type,
list_P2023964830har_ty: $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__Nat__Onat_J,type,
option_nat: $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__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_,type,
produc774316953on_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_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol_002,type,
produc1287081631on_val: $tType ).
thf(ty_ty_tc__prod_I_062_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__,type,
produc688860215on_val: $tType ).
thf(ty_ty_tc__prod_Itc__Expr__Obop_Mtc__Expr__Obop_J,type,
product_prod_bop_bop: $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__Expr,type,
produc2048519645t_char: $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__Expr__Oexp_Itc__List__Olist_Itc__String__Oc,type,
produc91527719t_char: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_003,type,
produc1180562163on_val: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__Exp,type,
produc809539159t_char: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__Lis,type,
produc1200003175t_char: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__pro,type,
produc1285161482t_char: $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__Type__Oty_J,type,
produc917948472har_ty: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__Olist_,type,
produc1971331930t_char: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__Olist__004,type,
produc1013743697t_char: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List__Olist__005,type,
produc952412819t_char: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__List__Olist_Itc__Type__Oty,type,
produc1420746395ist_ty: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Olist_Itc_,type,
produc220283002t_char: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__Type__Oty_Mtc__p,type,
produc1025221954t_char: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__List__Ol,type,
produc662261637t_char: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__List__Olist_Itc__Value__,type,
produc753553453st_val: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_,type,
produc450000425har_ty: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J__006,type,
produc2146869324t_char: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J__007,type,
produc244676007t_char: $tType ).
thf(ty_ty_tc__prod_Itc__Type__Oty_Mtc__prod_Itc__List__Olist_Itc__List__Olist_Itc__S,type,
produc1059328077t_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_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc,type,
produc1581780743on_val: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__,type,
produc630464863al_val: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
produc1746408499on_val: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__,type,
produc618524391on_val: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_,type,
produc1534059751t_char: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J__008,type,
produc349695911t_char: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc__prod_I,type,
produc1368416213on_val: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_,type,
produc245756905har_ty: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist__009,type,
produc1350825965t_char: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__Li,type,
produc84451751t_char: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__Li_010,type,
produc740765671t_char: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__,type,
produc1406897475t_char: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc,type,
produc1826280281t_char: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String,type,
produc494726439t_char: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__prod_Itc__Valu,type,
produc800118557al_val: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String_,type,
produc652964533on_val: $tType ).
thf(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__O,type,
produc1250491293on_val: $tType ).
%----Explicit typings (405)
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_Oevals,type,
evals: list_P1999446415t_char > list_exp_list_char > produc2090907612on_val > list_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_BigStep_Ofinals_000tc__List__Olist_Itc__String__Ochar_J,type,
finals_list_char: list_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_OOutOfMemory,type,
outOfMemory: list_char ).
thf(sy_c_Exceptions_Oaddr__of__sys__xcpt,type,
addr_of_sys_xcpt: list_char > nat ).
thf(sy_c_Exceptions_Opreallocated,type,
preallocated: ( nat > option1728594148on_val ) > $o ).
thf(sy_c_Exceptions_Osys__xcpts,type,
sys_xcpts: list_char > $o ).
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_OCall_000tc__List__Olist_Itc__String__Ochar_J,type,
call_list_char: exp_list_char > list_char > list_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_OCond_000tc__List__Olist_Itc__String__Ochar_J,type,
cond_list_char: exp_list_char > exp_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_Onew_000tc__List__Olist_Itc__String__Ochar_J,type,
new_list_char: 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_Expr_Ofv,type,
fv: exp_list_char > list_char > $o ).
thf(sy_c_Expr_Ofvs,type,
fvs: list_exp_list_char > list_char > $o ).
thf(sy_c_Fun_Ocomp_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__Value__Oval_000t,type,
comp_o1129292306t_char: ( option_val > val ) > ( list_char > option_val ) > list_char > val ).
thf(sy_c_Fun_Ofun__upd_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooptio,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_011,type,
fun_up1149430426on_val: ( list_char > option_val ) > list_char > option_val > list_char > 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_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_Ooverride__on_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Oo,type,
overri2012515291on_val: ( list_char > option_val ) > ( list_char > option_val ) > ( list_char > $o ) > list_char > option_val ).
thf(sy_c_JWellForm_Owf__J__mdecl,type,
wf_J_mdecl: list_P1999446415t_char > list_char > produc1013743697t_char > $o ).
thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__List__Olist_Itc__String,type,
semila2134664963char_o: ( list_char > $o ) > ( list_char > $o ) > list_char > $o ).
thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Nat__Onat_M_Eo_J,type,
semila848761471_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__prod_Itc__List__Olist_I,type,
semila880700084char_o: ( produc1278157519t_char > $o ) > ( produc1278157519t_char > $o ) > produc1278157519t_char > $o ).
thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__prod_Itc__List__Olist_I_012,type,
semila690474031char_o: ( produc1971331930t_char > $o ) > ( produc1971331930t_char > $o ) > produc1971331930t_char > $o ).
thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__prod_Itc__List__Olist_I_013,type,
semila1228900530char_o: ( produc1013743697t_char > $o ) > ( produc1013743697t_char > $o ) > produc1013743697t_char > $o ).
thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__prod_Itc__prod_Itc__Exp,type,
semila1505903696_val_o: ( produc1746408499on_val > $o ) > ( produc1746408499on_val > $o ) > produc1746408499on_val > $o ).
thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__prod_Itc__prod_Itc__Lis,type,
semila1566912796_val_o: ( produc618524391on_val > $o ) > ( produc618524391on_val > $o ) > produc618524391on_val > $o ).
thf(sy_c_List_Oappend_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
append_exp_list_char: list_exp_list_char > list_exp_list_char > list_exp_list_char ).
thf(sy_c_List_Odistinct_000tc__List__Olist_Itc__String__Ochar_J,type,
distinct_list_char: list_list_char > $o ).
thf(sy_c_List_Olist_OCons_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
cons_exp_list_char: exp_list_char > list_exp_list_char > list_exp_list_char ).
thf(sy_c_List_Olist_OCons_000tc__List__Olist_Itc__String__Ochar_J,type,
cons_list_char: list_char > list_list_char > list_list_char ).
thf(sy_c_List_Olist_OCons_000tc__Type__Oty,type,
cons_ty: ty > list_ty > list_ty ).
thf(sy_c_List_Olist_OCons_000tc__Value__Oval,type,
cons_val: val > list_val > list_val ).
thf(sy_c_List_Olist__all2_000tc__Type__Oty_000tc__Type__Oty,type,
list_all2_ty_ty: ( ty > ty > $o ) > list_ty > list_ty > $o ).
thf(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
map_list_char_val: ( list_char > val ) > list_list_char > list_val ).
thf(sy_c_List_Omap_000tc__Type__Oty_000tc__Option__Ooption_Itc__Type__Oty_J,type,
map_ty_option_ty: ( ty > option_ty ) > list_ty > list_option_ty ).
thf(sy_c_List_Omap_000tc__Value__Oval_000tc__Expr__Oexp_Itc__List__Olist_Itc__String,type,
map_va1934808527t_char: ( val > exp_list_char ) > list_val > list_exp_list_char ).
thf(sy_c_List_Omap_000tc__Value__Oval_000tc__Option__Ooption_Itc__Type__Oty_J,type,
map_val_option_ty: ( val > option_ty ) > list_val > list_option_ty ).
thf(sy_c_List_Oset_000tc__List__Olist_Itc__String__Ochar_J,type,
set_list_char: list_list_char > list_char > $o ).
thf(sy_c_List_Oset_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__,type,
set_Pr1494163115t_char: list_P1999446415t_char > produc1971331930t_char > $o ).
thf(sy_c_List_Oset_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc___014,type,
set_Pr2033386304t_char: list_P341299826t_char > produc1013743697t_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__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_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_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__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_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__upds_000tc__List__Olist_Itc__String__Ochar_J_000tc__Type__Oty,type,
map_up891053837har_ty: ( list_char > option_ty ) > list_list_char > list_ty > list_char > option_ty ).
thf(sy_c_Map_Omap__upds_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
map_up1085636310ar_val: ( list_char > option_val ) > list_list_char > list_val > list_char > option_val ).
thf(sy_c_Map_Orestrict__map_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Ov,type,
restri761823004ar_val: ( list_char > option_val ) > ( list_char > $o ) > list_char > option_val ).
thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_,type,
size_s1143674878t_char: list_exp_list_char > nat ).
thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__List__Olist_Itc__String__Och,type,
size_s2113983095t_char: list_list_char > nat ).
thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Type__Oty_J,type,
size_size_list_ty: list_ty > nat ).
thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Value__Oval_J,type,
size_size_list_val: list_val > nat ).
thf(sy_c_Objects_Ohext,type,
hext: ( nat > option1728594148on_val ) > ( nat > option1728594148on_val ) > $o ).
thf(sy_c_Objects_Oinit__fields,type,
init_fields: list_P2023964830har_ty > produc1278157519t_char > option_val ).
thf(sy_c_Objects_Onew__Addr,type,
new_Addr: ( nat > option1728594148on_val ) > option_nat ).
thf(sy_c_Objects_Otypeof__h,type,
typeof_h: ( nat > option1728594148on_val ) > val > option_ty ).
thf(sy_c_Option_Ooption_ONone_000_062_Itc__List__Olist_Itc__String__Ochar_J_M_Eo_J,type,
none_list_char_o: option_list_char_o ).
thf(sy_c_Option_Ooption_ONone_000tc__Nat__Onat,type,
none_nat: option_nat ).
thf(sy_c_Option_Ooption_ONone_000tc__Type__Oty,type,
none_ty: option_ty ).
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__Nat__Onat,type,
some_nat: nat > option_nat ).
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_Ooption_Ooption__case_000tc__Option__Ooption_Itc__Type__Oty_J_000tc_,type,
option857204770on_val: option_ty > ( produc2088785539on_val > option_ty ) > option1728594148on_val > option_ty ).
thf(sy_c_Option_Othe_000_062_Itc__List__Olist_Itc__String__Ochar_J_M_Eo_J,type,
the_list_char_o: option_list_char_o > list_char > $o ).
thf(sy_c_Option_Othe_000tc__Nat__Onat,type,
the_nat: option_nat > nat ).
thf(sy_c_Option_Othe_000tc__Type__Oty,type,
the_ty: option_ty > ty ).
thf(sy_c_Option_Othe_000tc__Value__Oval,type,
the_val: option_val > val ).
thf(sy_c_Option_Othe_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_Itc__pr,type,
the_Pr1885945130on_val: option1728594148on_val > produc2088785539on_val ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Nat__Onat_Mtc__Option__O,type,
ord_le1145603820_val_o: ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o ) > ( ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Expr__Obop_M_062_Itc__prod_Itc,type,
ord_le1352079040_val_o: ( bop > product_prod_val_val > $o ) > ( bop > product_prod_val_val > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Expr__Oexp_Itc__List__Olist_It,type,
ord_le1792911318_val_o: ( exp_list_char > produc2090907612on_val > $o ) > ( exp_list_char > produc2090907612on_val > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__List__Olist_Itc__Expr__Oexp_It,type,
ord_le636719503_val_o: ( list_exp_list_char > produc2090907612on_val > $o ) > ( list_exp_list_char > produc2090907612on_val > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__List__Olist_Itc__List__Olist_I,type,
ord_le84164651char_o: ( list_list_char > exp_list_char > $o ) > ( list_list_char > exp_list_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__List__Olist_Itc__List__Olist_I_015,type,
ord_le424140984char_o: ( list_list_char > produc220283002t_char > $o ) > ( list_list_char > produc220283002t_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__List__Olist_Itc__String__Ochar,type,
ord_le1726974981_val_o: ( list_char > ( produc1278157519t_char > option_val ) > $o ) > ( list_char > ( produc1278157519t_char > option_val ) > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__List__Olist_Itc__String__Ochar_016,type,
ord_le237460153char_o: ( list_char > list_char > $o ) > ( list_char > list_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__List__Olist_Itc__String__Ochar_017,type,
ord_le1501926550char_o: ( list_char > produc952412819t_char > $o ) > ( list_char > produc952412819t_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__List__Olist_Itc__String__Ochar_018,type,
ord_le694689975char_o: ( list_char > produc1025221954t_char > $o ) > ( list_char > produc1025221954t_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__List__Olist_Itc__String__Ochar_019,type,
ord_le1073847069char_o: ( list_char > produc2146869324t_char > $o ) > ( list_char > produc2146869324t_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__List__Olist_Itc__String__Ochar_020,type,
ord_le1777678169char_o: ( list_char > $o ) > ( list_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__List__Olist_Itc__Type__Oty_J_M,type,
ord_le1975270990char_o: ( list_ty > produc662261637t_char > $o ) > ( list_ty > produc662261637t_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__List__Olist_Itc__Value__Oval_J,type,
ord_le1480834691char_o: ( list_val > exp_list_char > $o ) > ( list_val > exp_list_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__List__Olist_Itc__prod_Itc__Lis,type,
ord_le1015080996char_o: ( list_P1940453997har_ty > list_P341299826t_char > $o ) > ( list_P1940453997har_ty > list_P341299826t_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Nat__Onat_M_Eo_J,type,
ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Value__Oval_M_062_Itc__Value__,type,
ord_le946822159_val_o: ( val > val > $o ) > ( val > val > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_I_062_Itc__Nat__Onat_Mtc_,type,
ord_le290925629_val_o: ( produc2090907612on_val > $o ) > ( produc2090907612on_val > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__Expr__Obop_Mtc__prod,type,
ord_le1019536145_val_o: ( produc1645268488al_val > $o ) > ( produc1645268488al_val > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__Expr__Oexp_Itc__List,type,
ord_le166837589_val_o: ( produc1282892786on_val > produc1282892786on_val > $o ) > ( produc1282892786on_val > produc1282892786on_val > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__Expr__Oexp_Itc__List_021,type,
ord_le900129703_val_o: ( produc1282892786on_val > $o ) > ( produc1282892786on_val > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__List__Olist_Itc__Exp,type,
ord_le1294853199_val_o: ( produc1180562163on_val > produc1180562163on_val > $o ) > ( produc1180562163on_val > produc1180562163on_val > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__List__Olist_Itc__Exp_022,type,
ord_le941641472_val_o: ( produc1180562163on_val > $o ) > ( produc1180562163on_val > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__List__Olist_Itc__Lis,type,
ord_le1754369948char_o: ( produc809539159t_char > $o ) > ( produc809539159t_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__List__Olist_Itc__Lis_023,type,
ord_le1356274601char_o: ( produc1285161482t_char > $o ) > ( produc1285161482t_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__List__Olist_Itc__Str,type,
ord_le719203798_val_o: ( produc2088785539on_val > $o ) > ( produc2088785539on_val > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__List__Olist_Itc__Str_024,type,
ord_le7825418char_o: ( produc1278157519t_char > $o ) > ( produc1278157519t_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__List__Olist_Itc__Str_025,type,
ord_le139275609char_o: ( produc1971331930t_char > $o ) > ( produc1971331930t_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__List__Olist_Itc__Str_026,type,
ord_le1156912648char_o: ( produc1013743697t_char > $o ) > ( produc1013743697t_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__List__Olist_Itc__Str_027,type,
ord_le1844608096char_o: ( produc952412819t_char > $o ) > ( produc952412819t_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__List__Olist_Itc__Typ,type,
ord_le1234751263char_o: ( produc220283002t_char > $o ) > ( produc220283002t_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__List__Olist_Itc__Val,type,
ord_le1298648532char_o: ( produc662261637t_char > $o ) > ( produc662261637t_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__List__Olist_Itc__pro,type,
ord_le2021326055char_o: ( produc2146869324t_char > $o ) > ( produc2146869324t_char > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__Value__Oval_Mtc__Val,type,
ord_le1101577138_val_o: ( product_prod_val_val > $o ) > ( product_prod_val_val > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__prod_Itc__Expr__Oexp,type,
ord_le1364969894_val_o: ( produc1746408499on_val > $o ) > ( produc1746408499on_val > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__prod_Itc__List__Olis,type,
ord_le559588722_val_o: ( produc618524391on_val > $o ) > ( produc618524391on_val > $o ) > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_000_Eo,type,
ord_less_eq_o: $o > $o > $o ).
thf(sy_c_Product__Type_OPair_000_062_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Opti,type,
produc1338265359on_val: ( list_char > option_val ) > ( list_char > option_val ) > produc774316953on_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_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I_028,type,
produc1208913941on_val: ( nat > option1728594148on_val ) > ( nat > option1728594148on_val ) > produc1287081631on_val ).
thf(sy_c_Product__Type_OPair_000_062_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J,type,
produc253229997on_val: ( produc1278157519t_char > option_val ) > ( produc1278157519t_char > option_val ) > produc688860215on_val ).
thf(sy_c_Product__Type_OPair_000tc__Expr__Obop_000tc__Expr__Obop,type,
product_Pair_bop_bop: bop > bop > product_prod_bop_bop ).
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,
produc943465171t_char: exp_list_char > exp_list_char > produc2048519645t_char ).
thf(sy_c_Product__Type_OPair_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_029,type,
produc235638504on_val: exp_list_char > produc2090907612on_val > produc1282892786on_val ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
produc1237966615t_char: list_exp_list_char > list_exp_list_char > produc91527719t_char ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc_030,type,
produc1302104557on_val: list_exp_list_char > produc2090907612on_val > produc1180562163on_val ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_,type,
produc1147572817t_char: list_list_char > exp_list_char > produc809539159t_char ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar__031,type,
produc2035944023t_char: list_list_char > list_list_char > produc1200003175t_char ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar__032,type,
produc921874948t_char: list_list_char > produc220283002t_char > produc1285161482t_char ).
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__List__Olist_Itc__String__Ochar_J_000tc__Type__Ot,type,
produc251930284har_ty: list_char > ty > produc917948472har_ty ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc,type,
produc822965838t_char: list_char > produc952412819t_char > produc1971331930t_char ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc_033,type,
produc1331140167t_char: list_char > produc1025221954t_char > produc1013743697t_char ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc_034,type,
produc1483578759t_char: list_char > produc2146869324t_char > produc952412819t_char ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_,type,
produc512429457ist_ty: list_ty > list_ty > produc1420746395ist_ty ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Type__Oty_J_000tc__prod_Itc__Li,type,
produc1909267824t_char: list_ty > produc662261637t_char > produc220283002t_char ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Type__Oty_J_000tc__prod_Itc__Ty,type,
produc2016959032t_char: list_ty > produc1059328077t_char > produc1025221954t_char ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Value__Oval_J_000tc__Expr__Oexp,type,
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thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olis,type,
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thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Stri,type,
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thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Stri_035,type,
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thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Stri_036,type,
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thf(sy_c_Product__Type_OPair_000tc__Type__Oty_000tc__prod_Itc__List__Olist_Itc__List,type,
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thf(sy_c_Product__Type_OPair_000tc__Value__Oval_000tc__Value__Oval,type,
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thf(sy_c_Product__Type_OPair_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_I,type,
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thf(sy_c_Product__Type_OPair_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_,type,
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thf(sy_c_Product__Type_OPair_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
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thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List_,type,
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thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri,type,
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thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri_037,type,
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thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062,type,
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thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__,type,
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thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___038,type,
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thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___039,type,
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thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc___040,type,
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thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod,type,
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thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Ex,type,
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thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist,type,
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thf(sy_c_Product__Type_OPair_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__,type,
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thf(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_,type,
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thf(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_,type,
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thf(sy_c_Product__Type_Ocurry_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_,type,
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thf(sy_c_Product__Type_Ocurry_000tc__Expr__Obop_000tc__prod_Itc__Value__Oval_Mtc__Va,type,
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thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_It,type,
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thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_041,type,
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thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__String__Ochar_J_000_062_Itc__p,type,
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thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__String__Ochar_J_000_062_Itc__p_042,type,
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thf(sy_c_TypeRel_OMethod_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__,type,
method1809630380t_char: list_P1999446415t_char > list_char > list_char > list_ty > ty > produc809539159t_char > 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__cbiupqffsr_Osconf,type,
typeSa816273224_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_Othis,type,
this: list_char ).
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_1: list_P1999446415t_char > ( nat > option1728594148on_val ) > ( list_char > option_ty ) > exp_list_char > ty > $o ).
thf(sy_c_WellTypeRT_OWTrts,type,
wTrts_1: list_P1999446415t_char > ( nat > option1728594148on_val ) > ( list_char > option_ty ) > list_exp_list_char > list_ty > $o ).
thf(sy_c_Wellfounded_Olex__prod_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pro,type,
lex_pr359407722on_val: ( produc1287081631on_val > $o ) > ( produc774316953on_val > $o ) > produc1581780743on_val > $o ).
thf(sy_c_Wellfounded_Olex__prod_000tc__Expr__Obop_000tc__prod_Itc__Value__Oval_Mtc__,type,
lex_pr1932514710al_val: ( product_prod_bop_bop > $o ) > ( produc800118557al_val > $o ) > produc630464863al_val > $o ).
thf(sy_c_Wellfounded_Olex__prod_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ocha,type,
lex_pr1492265728on_val: ( produc2048519645t_char > $o ) > ( produc1581780743on_val > $o ) > produc1746408499on_val > $o ).
thf(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_,type,
lex_pr855826389on_val: ( produc91527719t_char > $o ) > ( produc1581780743on_val > $o ) > produc618524391on_val > $o ).
thf(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__List__Olist_Itc__String__Och,type,
lex_pr1787105337t_char: ( produc1200003175t_char > $o ) > ( produc2048519645t_char > $o ) > produc1534059751t_char > $o ).
thf(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__List__Olist_Itc__String__Och_054,type,
lex_pr1876288492t_char: ( produc1200003175t_char > $o ) > ( produc1406897475t_char > $o ) > produc349695911t_char > $o ).
thf(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__String__Ochar_J_000_062_Itc_,type,
lex_pr697649425on_val: ( produc1278157519t_char > $o ) > ( produc688860215on_val > $o ) > produc1368416213on_val > $o ).
thf(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__String__Ochar_J_000tc__List_,type,
lex_pr280535005t_char: ( produc1278157519t_char > $o ) > ( produc1278157519t_char > $o ) > produc1350825965t_char > $o ).
thf(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_,type,
lex_pr1668767798t_char: ( produc1278157519t_char > $o ) > ( produc740765671t_char > $o ) > produc84451751t_char > $o ).
thf(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod__055,type,
lex_pr167435119t_char: ( produc1278157519t_char > $o ) > ( produc494726439t_char > $o ) > produc740765671t_char > $o ).
thf(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__Type__Oty_J_000tc__prod_Itc_,type,
lex_pr1588300168t_char: ( produc1420746395ist_ty > $o ) > ( produc1826280281t_char > $o ) > produc1406897475t_char > $o ).
thf(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__Value__Oval_J_000tc__Expr__O,type,
lex_pr307591827t_char: ( produc753553453st_val > $o ) > ( produc2048519645t_char > $o ) > produc1826280281t_char > $o ).
thf(sy_c_Wellfounded_Olex__prod_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__S,type,
lex_pr213428520t_char: ( produc450000425har_ty > $o ) > ( produc244676007t_char > $o ) > produc494726439t_char > $o ).
thf(sy_c_Wellfounded_Olex__prod_000tc__Value__Oval_000tc__Value__Oval,type,
lex_prod_val_val: ( product_prod_val_val > $o ) > ( product_prod_val_val > $o ) > produc800118557al_val > $o ).
thf(sy_c_Wellfounded_Olex__prod_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__St,type,
lex_pr296420417on_val: ( produc1746408499on_val > $o ) > ( produc1746408499on_val > $o ) > produc652964533on_val > $o ).
thf(sy_c_Wellfounded_Olex__prod_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__Li,type,
lex_pr1943870447on_val: ( produc618524391on_val > $o ) > ( produc618524391on_val > $o ) > produc1250491293on_val > $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__List__Olist_Itc__String__Ochar_J_Mtc__Option_,type,
member1838289030on_val: produc774316953on_val > ( produc774316953on_val > $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_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__056,type,
member112887436on_val: produc1287081631on_val > ( produc1287081631on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_I_062_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mt,type,
member1448924196on_val: produc688860215on_val > ( produc688860215on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__Expr__Obop_Mtc__Expr__Obop_J,type,
member978285664op_bop: product_prod_bop_bop > ( product_prod_bop_bop > $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,
member1199939018t_char: produc2048519645t_char > ( produc2048519645t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J__057,type,
member1072200031on_val: produc1282892786on_val > ( produc1282892786on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__S,type,
member894971540t_char: produc91527719t_char > ( produc91527719t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__S_058,type,
member1224782662on_val: produc1180562163on_val > ( produc1180562163on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J,type,
member1840112042t_char: produc809539159t_char > ( produc809539159t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_059,type,
member817832404t_char: produc1200003175t_char > ( produc1200003175t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_060,type,
member133545693t_char: produc1285161482t_char > ( produc1285161482t_char > $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__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__Lis,type,
member1467889965t_char: produc1971331930t_char > ( produc1971331930t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__Lis_061,type,
member1601084734t_char: produc1013743697t_char > ( produc1013743697t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__Lis_062,type,
member1771544038t_char: produc952412819t_char > ( produc952412819t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__List__Olist_Itc__,type,
member104734088ist_ty: produc1420746395ist_ty > ( produc1420746395ist_ty > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__O,type,
member140606439t_char: produc220283002t_char > ( produc220283002t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc_,type,
member699351154t_char: produc662261637t_char > ( produc662261637t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__List__Olist_Itc,type,
member273646106st_val: produc753553453st_val > ( produc753553453st_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String_,type,
member520253462har_ty: produc450000425har_ty > ( produc450000425har_ty > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__063,type,
member1379348767t_char: produc2146869324t_char > ( produc2146869324t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__064,type,
member1580476948t_char: produc244676007t_char > ( produc244676007t_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_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc_,type,
member565037556on_val: produc1581780743on_val > ( produc1581780743on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc,type,
member1732271180al_val: produc630464863al_val > ( produc630464863al_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_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Ol,type,
member2042188884on_val: produc618524391on_val > ( produc618524391on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String_,type,
member1999287380t_char: produc1534059751t_char > ( produc1534059751t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__065,type,
member1420286996t_char: produc349695911t_char > ( produc349695911t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062_It,type,
member1235075778on_val: produc1368416213on_val > ( produc1368416213on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Lis,type,
member794220506t_char: produc1350825965t_char > ( produc1350825965t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__pro,type,
member162552852t_char: produc84451751t_char > ( produc84451751t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__pro_066,type,
member1607118676t_char: produc740765671t_char > ( produc740765671t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_It,type,
member125098544t_char: produc1406897475t_char > ( produc1406897475t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr_,type,
member1161907014t_char: produc1826280281t_char > ( produc1826280281t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_It,type,
member1551446420t_char: produc494726439t_char > ( produc494726439t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__prod_,type,
member837208074al_val: produc800118557al_val > ( produc800118557al_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
member1714424482on_val: produc652964533on_val > ( produc652964533on_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc,type,
member1145216138on_val: produc1250491293on_val > ( produc1250491293on_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 (1200)
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_24: list_char > option_val,X_1: list_char] :
( ( fun_up1149430426on_val @ F_24 @ X_1 @ ( F_24 @ X_1 ) )
= F_24 ) ).
thf(fact_3_fun__upd__triv,axiom,
! [F_24: list_char > option_ty,X_1: list_char] :
( ( fun_up424764369ion_ty @ F_24 @ X_1 @ ( F_24 @ X_1 ) )
= F_24 ) ).
thf(fact_4_fun__upd__triv,axiom,
! [F_24: nat > option1728594148on_val,X_1: nat] :
( ( fun_up1472480727on_val @ F_24 @ X_1 @ ( F_24 @ X_1 ) )
= F_24 ) ).
thf(fact_5_fun__upd__triv,axiom,
! [F_24: produc1278157519t_char > option_val,X_1: produc1278157519t_char] :
( ( fun_up204312361on_val @ F_24 @ X_1 @ ( F_24 @ X_1 ) )
= F_24 ) ).
thf(fact_6_assms,axiom,
wf_pro755087577t_char @ wf_J_mdecl @ p ).
thf(fact_7_map__upd__Some__unfold,axiom,
! [M_17: list_char > option_val,A_79: list_char,B_46: val,X_41: list_char,Y_22: val] :
( ( ( fun_up1149430426on_val @ M_17 @ A_79 @ ( some_val @ B_46 ) @ X_41 )
= ( some_val @ Y_22 ) )
<=> ( ( ( X_41 = A_79 )
& ( B_46 = Y_22 ) )
| ( ( X_41 != A_79 )
& ( ( M_17 @ X_41 )
= ( some_val @ Y_22 ) ) ) ) ) ).
thf(fact_8_map__upd__Some__unfold,axiom,
! [M_17: list_char > option_ty,A_79: list_char,B_46: ty,X_41: list_char,Y_22: ty] :
( ( ( fun_up424764369ion_ty @ M_17 @ A_79 @ ( some_ty @ B_46 ) @ X_41 )
= ( some_ty @ Y_22 ) )
<=> ( ( ( X_41 = A_79 )
& ( B_46 = Y_22 ) )
| ( ( X_41 != A_79 )
& ( ( M_17 @ X_41 )
= ( some_ty @ Y_22 ) ) ) ) ) ).
thf(fact_9_map__upd__Some__unfold,axiom,
! [M_17: nat > option1728594148on_val,A_79: nat,B_46: produc2088785539on_val,X_41: nat,Y_22: produc2088785539on_val] :
( ( ( fun_up1472480727on_val @ M_17 @ A_79 @ ( some_P451527732on_val @ B_46 ) @ X_41 )
= ( some_P451527732on_val @ Y_22 ) )
<=> ( ( ( X_41 = A_79 )
& ( B_46 = Y_22 ) )
| ( ( X_41 != A_79 )
& ( ( M_17 @ X_41 )
= ( some_P451527732on_val @ Y_22 ) ) ) ) ) ).
thf(fact_10_map__upd__Some__unfold,axiom,
! [M_17: produc1278157519t_char > option_val,A_79: produc1278157519t_char,B_46: val,X_41: produc1278157519t_char,Y_22: val] :
( ( ( fun_up204312361on_val @ M_17 @ A_79 @ ( some_val @ B_46 ) @ X_41 )
= ( some_val @ Y_22 ) )
<=> ( ( ( X_41 = A_79 )
& ( B_46 = Y_22 ) )
| ( ( X_41 != A_79 )
& ( ( M_17 @ X_41 )
= ( some_val @ Y_22 ) ) ) ) ) ).
thf(fact_11_map__upd__triv,axiom,
! [T_15: list_char > option_val,K_5: list_char,X_40: val] :
( ( ( T_15 @ K_5 )
= ( some_val @ X_40 ) )
=> ( ( fun_up1149430426on_val @ T_15 @ K_5 @ ( some_val @ X_40 ) )
= T_15 ) ) ).
thf(fact_12_map__upd__triv,axiom,
! [T_15: list_char > option_ty,K_5: list_char,X_40: ty] :
( ( ( T_15 @ K_5 )
= ( some_ty @ X_40 ) )
=> ( ( fun_up424764369ion_ty @ T_15 @ K_5 @ ( some_ty @ X_40 ) )
= T_15 ) ) ).
thf(fact_13_map__upd__triv,axiom,
! [T_15: nat > option1728594148on_val,K_5: nat,X_40: produc2088785539on_val] :
( ( ( T_15 @ K_5 )
= ( some_P451527732on_val @ X_40 ) )
=> ( ( fun_up1472480727on_val @ T_15 @ K_5 @ ( some_P451527732on_val @ X_40 ) )
= T_15 ) ) ).
thf(fact_14_map__upd__triv,axiom,
! [T_15: produc1278157519t_char > option_val,K_5: produc1278157519t_char,X_40: val] :
( ( ( T_15 @ K_5 )
= ( some_val @ X_40 ) )
=> ( ( fun_up204312361on_val @ T_15 @ K_5 @ ( some_val @ X_40 ) )
= T_15 ) ) ).
thf(fact_15_map__upd__eqD1,axiom,
! [M_16: list_char > option_val,A_78: list_char,X_39: val,N_4: list_char > option_val,Y_21: val] :
( ( ( fun_up1149430426on_val @ M_16 @ A_78 @ ( some_val @ X_39 ) )
= ( fun_up1149430426on_val @ N_4 @ A_78 @ ( some_val @ Y_21 ) ) )
=> ( X_39 = Y_21 ) ) ).
thf(fact_16_map__upd__eqD1,axiom,
! [M_16: list_char > option_ty,A_78: list_char,X_39: ty,N_4: list_char > option_ty,Y_21: ty] :
( ( ( fun_up424764369ion_ty @ M_16 @ A_78 @ ( some_ty @ X_39 ) )
= ( fun_up424764369ion_ty @ N_4 @ A_78 @ ( some_ty @ Y_21 ) ) )
=> ( X_39 = Y_21 ) ) ).
thf(fact_17_map__upd__eqD1,axiom,
! [M_16: nat > option1728594148on_val,A_78: nat,X_39: produc2088785539on_val,N_4: nat > option1728594148on_val,Y_21: produc2088785539on_val] :
( ( ( fun_up1472480727on_val @ M_16 @ A_78 @ ( some_P451527732on_val @ X_39 ) )
= ( fun_up1472480727on_val @ N_4 @ A_78 @ ( some_P451527732on_val @ Y_21 ) ) )
=> ( X_39 = Y_21 ) ) ).
thf(fact_18_map__upd__eqD1,axiom,
! [M_16: produc1278157519t_char > option_val,A_78: produc1278157519t_char,X_39: val,N_4: produc1278157519t_char > option_val,Y_21: val] :
( ( ( fun_up204312361on_val @ M_16 @ A_78 @ ( some_val @ X_39 ) )
= ( fun_up204312361on_val @ N_4 @ A_78 @ ( some_val @ Y_21 ) ) )
=> ( X_39 = Y_21 ) ) ).
thf(fact_19_InitBlockRed_I2_J,axiom,
! [T: ty,E_2: list_char > option_ty] :
( ( typeSa816273224_sconf @ p @ E_2 @ ( produc755559506on_val @ ha @ ( fun_up1149430426on_val @ la @ v_1 @ ( some_val @ v ) ) ) )
=> ( ( wTrt_1 @ p @ ha @ E_2 @ ea @ T )
=> ? [T_7: ty] :
( ( wTrt_1 @ p @ h_a @ E_2 @ e_a @ T_7 )
& ( widen_2090681816t_char @ p @ T_7 @ T ) ) ) ) ).
thf(fact_20_prod__induct5,axiom,
! [X_38: produc1250491293on_val,P_30: produc1250491293on_val > $o] :
( ! [A_1: produc618524391on_val,B_14: produc1180562163on_val,C_20: list_exp_list_char,D_3: nat > option1728594148on_val,E_4: list_char > option_val] : ( P_30 @ ( produc1347028499on_val @ A_1 @ ( produc747700183on_val @ B_14 @ ( produc1302104557on_val @ C_20 @ ( produc755559506on_val @ D_3 @ E_4 ) ) ) ) )
=> ( P_30 @ X_38 ) ) ).
thf(fact_21_prod__induct5,axiom,
! [X_38: produc652964533on_val,P_30: produc652964533on_val > $o] :
( ! [A_1: produc1746408499on_val,B_14: produc1282892786on_val,C_20: exp_list_char,D_3: nat > option1728594148on_val,E_4: list_char > option_val] : ( P_30 @ ( produc345758123on_val @ A_1 @ ( produc833389609on_val @ B_14 @ ( produc235638504on_val @ C_20 @ ( produc755559506on_val @ D_3 @ E_4 ) ) ) ) )
=> ( P_30 @ X_38 ) ) ).
thf(fact_22_prod__induct5,axiom,
! [X_38: produc349695911t_char,P_30: produc349695911t_char > $o] :
( ! [A_1: produc1285161482t_char,B_14: list_list_char,C_20: list_ty,D_3: list_val,E_4: exp_list_char] : ( P_30 @ ( produc24551831t_char @ A_1 @ ( produc921874948t_char @ B_14 @ ( produc1909267824t_char @ C_20 @ ( produc1916172923t_char @ D_3 @ E_4 ) ) ) ) )
=> ( P_30 @ X_38 ) ) ).
thf(fact_23_prod__induct5,axiom,
! [X_38: produc84451751t_char,P_30: produc84451751t_char > $o] :
( ! [A_1: produc1971331930t_char,B_14: list_char,C_20: list_char,D_3: list_P1940453997har_ty,E_4: list_P341299826t_char] : ( P_30 @ ( produc1641293463t_char @ A_1 @ ( produc822965838t_char @ B_14 @ ( produc1483578759t_char @ C_20 @ ( produc1152259904t_char @ D_3 @ E_4 ) ) ) ) )
=> ( P_30 @ X_38 ) ) ).
thf(fact_24_prod__induct5,axiom,
! [X_38: produc1013743697t_char,P_30: produc1013743697t_char > $o] :
( ! [A_1: list_char,B_14: list_ty,C_20: ty,D_3: list_list_char,E_4: exp_list_char] : ( P_30 @ ( produc1331140167t_char @ A_1 @ ( produc2016959032t_char @ B_14 @ ( produc1545444669t_char @ C_20 @ ( produc1147572817t_char @ D_3 @ E_4 ) ) ) ) )
=> ( P_30 @ X_38 ) ) ).
thf(fact_25_prod__cases5,axiom,
! [Y_20: produc1250491293on_val] :
~ ! [A_1: produc618524391on_val,B_14: produc1180562163on_val,C_20: list_exp_list_char,D_3: nat > option1728594148on_val,E_4: list_char > option_val] :
( Y_20
!= ( produc1347028499on_val @ A_1 @ ( produc747700183on_val @ B_14 @ ( produc1302104557on_val @ C_20 @ ( produc755559506on_val @ D_3 @ E_4 ) ) ) ) ) ).
thf(fact_26_prod__cases5,axiom,
! [Y_20: produc652964533on_val] :
~ ! [A_1: produc1746408499on_val,B_14: produc1282892786on_val,C_20: exp_list_char,D_3: nat > option1728594148on_val,E_4: list_char > option_val] :
( Y_20
!= ( produc345758123on_val @ A_1 @ ( produc833389609on_val @ B_14 @ ( produc235638504on_val @ C_20 @ ( produc755559506on_val @ D_3 @ E_4 ) ) ) ) ) ).
thf(fact_27_prod__cases5,axiom,
! [Y_20: produc349695911t_char] :
~ ! [A_1: produc1285161482t_char,B_14: list_list_char,C_20: list_ty,D_3: list_val,E_4: exp_list_char] :
( Y_20
!= ( produc24551831t_char @ A_1 @ ( produc921874948t_char @ B_14 @ ( produc1909267824t_char @ C_20 @ ( produc1916172923t_char @ D_3 @ E_4 ) ) ) ) ) ).
thf(fact_28_prod__cases5,axiom,
! [Y_20: produc84451751t_char] :
~ ! [A_1: produc1971331930t_char,B_14: list_char,C_20: list_char,D_3: list_P1940453997har_ty,E_4: list_P341299826t_char] :
( Y_20
!= ( produc1641293463t_char @ A_1 @ ( produc822965838t_char @ B_14 @ ( produc1483578759t_char @ C_20 @ ( produc1152259904t_char @ D_3 @ E_4 ) ) ) ) ) ).
thf(fact_29_prod__cases5,axiom,
! [Y_20: produc1013743697t_char] :
~ ! [A_1: list_char,B_14: list_ty,C_20: ty,D_3: list_list_char,E_4: exp_list_char] :
( Y_20
!= ( produc1331140167t_char @ A_1 @ ( produc2016959032t_char @ B_14 @ ( produc1545444669t_char @ C_20 @ ( produc1147572817t_char @ D_3 @ E_4 ) ) ) ) ) ).
thf(fact_30_prod__induct4,axiom,
! [X_37: produc1013743697t_char,P_29: produc1013743697t_char > $o] :
( ! [A_1: list_char,B_14: list_ty,C_20: ty,D_3: produc809539159t_char] : ( P_29 @ ( produc1331140167t_char @ A_1 @ ( produc2016959032t_char @ B_14 @ ( produc1545444669t_char @ C_20 @ D_3 ) ) ) )
=> ( P_29 @ X_37 ) ) ).
thf(fact_31_prod__induct4,axiom,
! [X_37: produc1746408499on_val,P_29: produc1746408499on_val > $o] :
( ! [A_1: produc1282892786on_val,B_14: exp_list_char,C_20: nat > option1728594148on_val,D_3: list_char > option_val] : ( P_29 @ ( produc833389609on_val @ A_1 @ ( produc235638504on_val @ B_14 @ ( produc755559506on_val @ C_20 @ D_3 ) ) ) )
=> ( P_29 @ X_37 ) ) ).
thf(fact_32_prod__induct4,axiom,
! [X_37: produc618524391on_val,P_29: produc618524391on_val > $o] :
( ! [A_1: produc1180562163on_val,B_14: list_exp_list_char,C_20: nat > option1728594148on_val,D_3: list_char > option_val] : ( P_29 @ ( produc747700183on_val @ A_1 @ ( produc1302104557on_val @ B_14 @ ( produc755559506on_val @ C_20 @ D_3 ) ) ) )
=> ( P_29 @ X_37 ) ) ).
thf(fact_33_prod__induct4,axiom,
! [X_37: produc1285161482t_char,P_29: produc1285161482t_char > $o] :
( ! [A_1: list_list_char,B_14: list_ty,C_20: list_val,D_3: exp_list_char] : ( P_29 @ ( produc921874948t_char @ A_1 @ ( produc1909267824t_char @ B_14 @ ( produc1916172923t_char @ C_20 @ D_3 ) ) ) )
=> ( P_29 @ X_37 ) ) ).
thf(fact_34_prod__induct4,axiom,
! [X_37: produc1971331930t_char,P_29: produc1971331930t_char > $o] :
( ! [A_1: list_char,B_14: list_char,C_20: list_P1940453997har_ty,D_3: list_P341299826t_char] : ( P_29 @ ( produc822965838t_char @ A_1 @ ( produc1483578759t_char @ B_14 @ ( produc1152259904t_char @ C_20 @ D_3 ) ) ) )
=> ( P_29 @ X_37 ) ) ).
thf(fact_35_prod__induct4,axiom,
! [X_37: produc652964533on_val,P_29: produc652964533on_val > $o] :
( ! [A_1: produc1746408499on_val,B_14: produc1282892786on_val,C_20: exp_list_char,D_3: produc2090907612on_val] : ( P_29 @ ( produc345758123on_val @ A_1 @ ( produc833389609on_val @ B_14 @ ( produc235638504on_val @ C_20 @ D_3 ) ) ) )
=> ( P_29 @ X_37 ) ) ).
thf(fact_36_prod__induct4,axiom,
! [X_37: produc630464863al_val,P_29: produc630464863al_val > $o] :
( ! [A_1: produc1645268488al_val,B_14: bop,C_20: val,D_3: val] : ( P_29 @ ( produc1924279125al_val @ A_1 @ ( produc621191550al_val @ B_14 @ ( product_Pair_val_val @ C_20 @ D_3 ) ) ) )
=> ( P_29 @ X_37 ) ) ).
thf(fact_37_prod__induct4,axiom,
! [X_37: produc1250491293on_val,P_29: produc1250491293on_val > $o] :
( ! [A_1: produc618524391on_val,B_14: produc1180562163on_val,C_20: list_exp_list_char,D_3: produc2090907612on_val] : ( P_29 @ ( produc1347028499on_val @ A_1 @ ( produc747700183on_val @ B_14 @ ( produc1302104557on_val @ C_20 @ D_3 ) ) ) )
=> ( P_29 @ X_37 ) ) ).
thf(fact_38_prod__induct4,axiom,
! [X_37: produc349695911t_char,P_29: produc349695911t_char > $o] :
( ! [A_1: produc1285161482t_char,B_14: list_list_char,C_20: list_ty,D_3: produc662261637t_char] : ( P_29 @ ( produc24551831t_char @ A_1 @ ( produc921874948t_char @ B_14 @ ( produc1909267824t_char @ C_20 @ D_3 ) ) ) )
=> ( P_29 @ X_37 ) ) ).
thf(fact_39_prod__induct4,axiom,
! [X_37: produc1406897475t_char,P_29: produc1406897475t_char > $o] :
( ! [A_1: produc220283002t_char,B_14: list_ty,C_20: list_val,D_3: exp_list_char] : ( P_29 @ ( produc57279289t_char @ A_1 @ ( produc1909267824t_char @ B_14 @ ( produc1916172923t_char @ C_20 @ D_3 ) ) ) )
=> ( P_29 @ X_37 ) ) ).
thf(fact_40_prod__induct4,axiom,
! [X_37: produc84451751t_char,P_29: produc84451751t_char > $o] :
( ! [A_1: produc1971331930t_char,B_14: list_char,C_20: list_char,D_3: produc2146869324t_char] : ( P_29 @ ( produc1641293463t_char @ A_1 @ ( produc822965838t_char @ B_14 @ ( produc1483578759t_char @ C_20 @ D_3 ) ) ) )
=> ( P_29 @ X_37 ) ) ).
thf(fact_41_prod__induct4,axiom,
! [X_37: produc740765671t_char,P_29: produc740765671t_char > $o] :
( ! [A_1: produc952412819t_char,B_14: list_char,C_20: list_P1940453997har_ty,D_3: list_P341299826t_char] : ( P_29 @ ( produc1431439831t_char @ A_1 @ ( produc1483578759t_char @ B_14 @ ( produc1152259904t_char @ C_20 @ D_3 ) ) ) )
=> ( P_29 @ X_37 ) ) ).
thf(fact_42_prod__cases4,axiom,
! [Y_19: produc1013743697t_char] :
~ ! [A_1: list_char,B_14: list_ty,C_20: ty,D_3: produc809539159t_char] :
( Y_19
!= ( produc1331140167t_char @ A_1 @ ( produc2016959032t_char @ B_14 @ ( produc1545444669t_char @ C_20 @ D_3 ) ) ) ) ).
thf(fact_43_prod__cases4,axiom,
! [Y_19: produc1746408499on_val] :
~ ! [A_1: produc1282892786on_val,B_14: exp_list_char,C_20: nat > option1728594148on_val,D_3: list_char > option_val] :
( Y_19
!= ( produc833389609on_val @ A_1 @ ( produc235638504on_val @ B_14 @ ( produc755559506on_val @ C_20 @ D_3 ) ) ) ) ).
thf(fact_44_prod__cases4,axiom,
! [Y_19: produc618524391on_val] :
~ ! [A_1: produc1180562163on_val,B_14: list_exp_list_char,C_20: nat > option1728594148on_val,D_3: list_char > option_val] :
( Y_19
!= ( produc747700183on_val @ A_1 @ ( produc1302104557on_val @ B_14 @ ( produc755559506on_val @ C_20 @ D_3 ) ) ) ) ).
thf(fact_45_prod__cases4,axiom,
! [Y_19: produc1285161482t_char] :
~ ! [A_1: list_list_char,B_14: list_ty,C_20: list_val,D_3: exp_list_char] :
( Y_19
!= ( produc921874948t_char @ A_1 @ ( produc1909267824t_char @ B_14 @ ( produc1916172923t_char @ C_20 @ D_3 ) ) ) ) ).
thf(fact_46_prod__cases4,axiom,
! [Y_19: produc1971331930t_char] :
~ ! [A_1: list_char,B_14: list_char,C_20: list_P1940453997har_ty,D_3: list_P341299826t_char] :
( Y_19
!= ( produc822965838t_char @ A_1 @ ( produc1483578759t_char @ B_14 @ ( produc1152259904t_char @ C_20 @ D_3 ) ) ) ) ).
thf(fact_47_prod__cases4,axiom,
! [Y_19: produc652964533on_val] :
~ ! [A_1: produc1746408499on_val,B_14: produc1282892786on_val,C_20: exp_list_char,D_3: produc2090907612on_val] :
( Y_19
!= ( produc345758123on_val @ A_1 @ ( produc833389609on_val @ B_14 @ ( produc235638504on_val @ C_20 @ D_3 ) ) ) ) ).
thf(fact_48_prod__cases4,axiom,
! [Y_19: produc630464863al_val] :
~ ! [A_1: produc1645268488al_val,B_14: bop,C_20: val,D_3: val] :
( Y_19
!= ( produc1924279125al_val @ A_1 @ ( produc621191550al_val @ B_14 @ ( product_Pair_val_val @ C_20 @ D_3 ) ) ) ) ).
thf(fact_49_prod__cases4,axiom,
! [Y_19: produc1250491293on_val] :
~ ! [A_1: produc618524391on_val,B_14: produc1180562163on_val,C_20: list_exp_list_char,D_3: produc2090907612on_val] :
( Y_19
!= ( produc1347028499on_val @ A_1 @ ( produc747700183on_val @ B_14 @ ( produc1302104557on_val @ C_20 @ D_3 ) ) ) ) ).
thf(fact_50_prod__cases4,axiom,
! [Y_19: produc349695911t_char] :
~ ! [A_1: produc1285161482t_char,B_14: list_list_char,C_20: list_ty,D_3: produc662261637t_char] :
( Y_19
!= ( produc24551831t_char @ A_1 @ ( produc921874948t_char @ B_14 @ ( produc1909267824t_char @ C_20 @ D_3 ) ) ) ) ).
thf(fact_51_prod__cases4,axiom,
! [Y_19: produc1406897475t_char] :
~ ! [A_1: produc220283002t_char,B_14: list_ty,C_20: list_val,D_3: exp_list_char] :
( Y_19
!= ( produc57279289t_char @ A_1 @ ( produc1909267824t_char @ B_14 @ ( produc1916172923t_char @ C_20 @ D_3 ) ) ) ) ).
thf(fact_52_prod__cases4,axiom,
! [Y_19: produc84451751t_char] :
~ ! [A_1: produc1971331930t_char,B_14: list_char,C_20: list_char,D_3: produc2146869324t_char] :
( Y_19
!= ( produc1641293463t_char @ A_1 @ ( produc822965838t_char @ B_14 @ ( produc1483578759t_char @ C_20 @ D_3 ) ) ) ) ).
thf(fact_53_prod__cases4,axiom,
! [Y_19: produc740765671t_char] :
~ ! [A_1: produc952412819t_char,B_14: list_char,C_20: list_P1940453997har_ty,D_3: list_P341299826t_char] :
( Y_19
!= ( produc1431439831t_char @ A_1 @ ( produc1483578759t_char @ B_14 @ ( produc1152259904t_char @ C_20 @ D_3 ) ) ) ) ).
thf(fact_54_InitBlockRed_I4_J,axiom,
typeSa816273224_sconf @ p @ e @ ( produc755559506on_val @ ha @ la ) ).
thf(fact_55_Pair__inject,axiom,
! [A_77: list_char,B_45: ty,A_76: list_char,B_44: ty] :
( ( ( produc251930284har_ty @ A_77 @ B_45 )
= ( produc251930284har_ty @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_56_Pair__inject,axiom,
! [A_77: produc1278157519t_char,B_45: ty,A_76: produc1278157519t_char,B_44: ty] :
( ( ( produc1265154397har_ty @ A_77 @ B_45 )
= ( produc1265154397har_ty @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_57_Pair__inject,axiom,
! [A_77: list_char,B_45: produc1025221954t_char,A_76: list_char,B_44: produc1025221954t_char] :
( ( ( produc1331140167t_char @ A_77 @ B_45 )
= ( produc1331140167t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_58_Pair__inject,axiom,
! [A_77: produc809539159t_char,B_45: produc809539159t_char,A_76: produc809539159t_char,B_44: produc809539159t_char] :
( ( ( produc1897818327t_char @ A_77 @ B_45 )
= ( produc1897818327t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_59_Pair__inject,axiom,
! [A_77: produc2146869324t_char,B_45: produc2146869324t_char,A_76: produc2146869324t_char,B_44: produc2146869324t_char] :
( ( ( produc635935767t_char @ A_77 @ B_45 )
= ( produc635935767t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_60_Pair__inject,axiom,
! [A_77: produc952412819t_char,B_45: produc952412819t_char,A_76: produc952412819t_char,B_44: produc952412819t_char] :
( ( ( produc1431439831t_char @ A_77 @ B_45 )
= ( produc1431439831t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_61_Pair__inject,axiom,
! [A_77: produc1971331930t_char,B_45: produc1971331930t_char,A_76: produc1971331930t_char,B_44: produc1971331930t_char] :
( ( ( produc1641293463t_char @ A_77 @ B_45 )
= ( produc1641293463t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_62_Pair__inject,axiom,
! [A_77: produc662261637t_char,B_45: produc662261637t_char,A_76: produc662261637t_char,B_44: produc662261637t_char] :
( ( ( produc1299387215t_char @ A_77 @ B_45 )
= ( produc1299387215t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_63_Pair__inject,axiom,
! [A_77: produc220283002t_char,B_45: produc220283002t_char,A_76: produc220283002t_char,B_44: produc220283002t_char] :
( ( ( produc57279289t_char @ A_77 @ B_45 )
= ( produc57279289t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_64_Pair__inject,axiom,
! [A_77: produc1285161482t_char,B_45: produc1285161482t_char,A_76: produc1285161482t_char,B_44: produc1285161482t_char] :
( ( ( produc24551831t_char @ A_77 @ B_45 )
= ( produc24551831t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_65_Pair__inject,axiom,
! [A_77: produc618524391on_val,B_45: produc618524391on_val,A_76: produc618524391on_val,B_44: produc618524391on_val] :
( ( ( produc1347028499on_val @ A_77 @ B_45 )
= ( produc1347028499on_val @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_66_Pair__inject,axiom,
! [A_77: product_prod_val_val,B_45: product_prod_val_val,A_76: product_prod_val_val,B_44: product_prod_val_val] :
( ( ( produc1244920211al_val @ A_77 @ B_45 )
= ( produc1244920211al_val @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_67_Pair__inject,axiom,
! [A_77: produc1645268488al_val,B_45: produc1645268488al_val,A_76: produc1645268488al_val,B_44: produc1645268488al_val] :
( ( ( produc1924279125al_val @ A_77 @ B_45 )
= ( produc1924279125al_val @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_68_Pair__inject,axiom,
! [A_77: produc1278157519t_char,B_45: produc1278157519t_char,A_76: produc1278157519t_char,B_44: produc1278157519t_char] :
( ( ( produc2080520419t_char @ A_77 @ B_45 )
= ( produc2080520419t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_69_Pair__inject,axiom,
! [A_77: produc2088785539on_val,B_45: produc2088785539on_val,A_76: produc2088785539on_val,B_44: produc2088785539on_val] :
( ( ( produc1773146955on_val @ A_77 @ B_45 )
= ( produc1773146955on_val @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_70_Pair__inject,axiom,
! [A_77: produc2090907612on_val,B_45: produc2090907612on_val,A_76: produc2090907612on_val,B_44: produc2090907612on_val] :
( ( ( produc259392253on_val @ A_77 @ B_45 )
= ( produc259392253on_val @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_71_Pair__inject,axiom,
! [A_77: produc1746408499on_val,B_45: produc1746408499on_val,A_76: produc1746408499on_val,B_44: produc1746408499on_val] :
( ( ( produc345758123on_val @ A_77 @ B_45 )
= ( produc345758123on_val @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_72_Pair__inject,axiom,
! [A_77: list_exp_list_char,B_45: list_exp_list_char,A_76: list_exp_list_char,B_44: list_exp_list_char] :
( ( ( produc1237966615t_char @ A_77 @ B_45 )
= ( produc1237966615t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_73_Pair__inject,axiom,
! [A_77: exp_list_char,B_45: exp_list_char,A_76: exp_list_char,B_44: exp_list_char] :
( ( ( produc943465171t_char @ A_77 @ B_45 )
= ( produc943465171t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_74_Pair__inject,axiom,
! [A_77: list_list_char,B_45: list_list_char,A_76: list_list_char,B_44: list_list_char] :
( ( ( produc2035944023t_char @ A_77 @ B_45 )
= ( produc2035944023t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_75_Pair__inject,axiom,
! [A_77: list_P1940453997har_ty,B_45: list_P1940453997har_ty,A_76: list_P1940453997har_ty,B_44: list_P1940453997har_ty] :
( ( ( produc1860789535har_ty @ A_77 @ B_45 )
= ( produc1860789535har_ty @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_76_Pair__inject,axiom,
! [A_77: list_P341299826t_char,B_45: list_P341299826t_char,A_76: list_P341299826t_char,B_44: list_P341299826t_char] :
( ( ( produc436875159t_char @ A_77 @ B_45 )
= ( produc436875159t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_77_Pair__inject,axiom,
! [A_77: list_val,B_45: list_val,A_76: list_val,B_44: list_val] :
( ( ( produc2078839843st_val @ A_77 @ B_45 )
= ( produc2078839843st_val @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_78_Pair__inject,axiom,
! [A_77: list_ty,B_45: list_ty,A_76: list_ty,B_44: list_ty] :
( ( ( produc512429457ist_ty @ A_77 @ B_45 )
= ( produc512429457ist_ty @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_79_Pair__inject,axiom,
! [A_77: bop,B_45: bop,A_76: bop,B_44: bop] :
( ( ( product_Pair_bop_bop @ A_77 @ B_45 )
= ( product_Pair_bop_bop @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_80_Pair__inject,axiom,
! [A_77: produc1278157519t_char > option_val,B_45: produc1278157519t_char > option_val,A_76: produc1278157519t_char > option_val,B_44: produc1278157519t_char > option_val] :
( ( ( produc253229997on_val @ A_77 @ B_45 )
= ( produc253229997on_val @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_81_Pair__inject,axiom,
! [A_77: nat > option1728594148on_val,B_45: nat > option1728594148on_val,A_76: nat > option1728594148on_val,B_44: nat > option1728594148on_val] :
( ( ( produc1208913941on_val @ A_77 @ B_45 )
= ( produc1208913941on_val @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_82_Pair__inject,axiom,
! [A_77: list_char > option_val,B_45: list_char > option_val,A_76: list_char > option_val,B_44: list_char > option_val] :
( ( ( produc1338265359on_val @ A_77 @ B_45 )
= ( produc1338265359on_val @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_83_Pair__inject,axiom,
! [A_77: produc1282892786on_val,B_45: produc1282892786on_val,A_76: produc1282892786on_val,B_44: produc1282892786on_val] :
( ( ( produc833389609on_val @ A_77 @ B_45 )
= ( produc833389609on_val @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_84_Pair__inject,axiom,
! [A_77: exp_list_char,B_45: produc2090907612on_val,A_76: exp_list_char,B_44: produc2090907612on_val] :
( ( ( produc235638504on_val @ A_77 @ B_45 )
= ( produc235638504on_val @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_85_Pair__inject,axiom,
! [A_77: nat > option1728594148on_val,B_45: list_char > option_val,A_76: nat > option1728594148on_val,B_44: list_char > option_val] :
( ( ( produc755559506on_val @ A_77 @ B_45 )
= ( produc755559506on_val @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_86_Pair__inject,axiom,
! [A_77: list_char,B_45: produc1278157519t_char > option_val,A_76: list_char,B_44: produc1278157519t_char > option_val] :
( ( ( produc926070009on_val @ A_77 @ B_45 )
= ( produc926070009on_val @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_87_Pair__inject,axiom,
! [A_77: list_char,B_45: list_char,A_76: list_char,B_44: list_char] :
( ( ( produc5062597t_char @ A_77 @ B_45 )
= ( produc5062597t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_88_Pair__inject,axiom,
! [A_77: bop,B_45: product_prod_val_val,A_76: bop,B_44: product_prod_val_val] :
( ( ( produc621191550al_val @ A_77 @ B_45 )
= ( produc621191550al_val @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_89_Pair__inject,axiom,
! [A_77: val,B_45: val,A_76: val,B_44: val] :
( ( ( product_Pair_val_val @ A_77 @ B_45 )
= ( product_Pair_val_val @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_90_Pair__inject,axiom,
! [A_77: produc1180562163on_val,B_45: produc1180562163on_val,A_76: produc1180562163on_val,B_44: produc1180562163on_val] :
( ( ( produc747700183on_val @ A_77 @ B_45 )
= ( produc747700183on_val @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_91_Pair__inject,axiom,
! [A_77: list_exp_list_char,B_45: produc2090907612on_val,A_76: list_exp_list_char,B_44: produc2090907612on_val] :
( ( ( produc1302104557on_val @ A_77 @ B_45 )
= ( produc1302104557on_val @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_92_Pair__inject,axiom,
! [A_77: list_list_char,B_45: produc220283002t_char,A_76: list_list_char,B_44: produc220283002t_char] :
( ( ( produc921874948t_char @ A_77 @ B_45 )
= ( produc921874948t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_93_Pair__inject,axiom,
! [A_77: list_ty,B_45: produc662261637t_char,A_76: list_ty,B_44: produc662261637t_char] :
( ( ( produc1909267824t_char @ A_77 @ B_45 )
= ( produc1909267824t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_94_Pair__inject,axiom,
! [A_77: list_val,B_45: exp_list_char,A_76: list_val,B_44: exp_list_char] :
( ( ( produc1916172923t_char @ A_77 @ B_45 )
= ( produc1916172923t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_95_Pair__inject,axiom,
! [A_77: list_char,B_45: produc952412819t_char,A_76: list_char,B_44: produc952412819t_char] :
( ( ( produc822965838t_char @ A_77 @ B_45 )
= ( produc822965838t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_96_Pair__inject,axiom,
! [A_77: list_char,B_45: produc2146869324t_char,A_76: list_char,B_44: produc2146869324t_char] :
( ( ( produc1483578759t_char @ A_77 @ B_45 )
= ( produc1483578759t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_97_Pair__inject,axiom,
! [A_77: list_P1940453997har_ty,B_45: list_P341299826t_char,A_76: list_P1940453997har_ty,B_44: list_P341299826t_char] :
( ( ( produc1152259904t_char @ A_77 @ B_45 )
= ( produc1152259904t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_98_Pair__inject,axiom,
! [A_77: list_list_char,B_45: exp_list_char,A_76: list_list_char,B_44: exp_list_char] :
( ( ( produc1147572817t_char @ A_77 @ B_45 )
= ( produc1147572817t_char @ A_76 @ B_44 ) )
=> ~ ( ( A_77 = A_76 )
=> ( B_45 != B_44 ) ) ) ).
thf(fact_99_Pair__eq,axiom,
! [A_75: list_char,B_43: ty,A_74: list_char,B_42: ty] :
( ( ( produc251930284har_ty @ A_75 @ B_43 )
= ( produc251930284har_ty @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_100_Pair__eq,axiom,
! [A_75: produc1278157519t_char,B_43: ty,A_74: produc1278157519t_char,B_42: ty] :
( ( ( produc1265154397har_ty @ A_75 @ B_43 )
= ( produc1265154397har_ty @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_101_Pair__eq,axiom,
! [A_75: list_char,B_43: produc1025221954t_char,A_74: list_char,B_42: produc1025221954t_char] :
( ( ( produc1331140167t_char @ A_75 @ B_43 )
= ( produc1331140167t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_102_Pair__eq,axiom,
! [A_75: produc809539159t_char,B_43: produc809539159t_char,A_74: produc809539159t_char,B_42: produc809539159t_char] :
( ( ( produc1897818327t_char @ A_75 @ B_43 )
= ( produc1897818327t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_103_Pair__eq,axiom,
! [A_75: produc2146869324t_char,B_43: produc2146869324t_char,A_74: produc2146869324t_char,B_42: produc2146869324t_char] :
( ( ( produc635935767t_char @ A_75 @ B_43 )
= ( produc635935767t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_104_Pair__eq,axiom,
! [A_75: produc952412819t_char,B_43: produc952412819t_char,A_74: produc952412819t_char,B_42: produc952412819t_char] :
( ( ( produc1431439831t_char @ A_75 @ B_43 )
= ( produc1431439831t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_105_Pair__eq,axiom,
! [A_75: produc1971331930t_char,B_43: produc1971331930t_char,A_74: produc1971331930t_char,B_42: produc1971331930t_char] :
( ( ( produc1641293463t_char @ A_75 @ B_43 )
= ( produc1641293463t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_106_Pair__eq,axiom,
! [A_75: produc662261637t_char,B_43: produc662261637t_char,A_74: produc662261637t_char,B_42: produc662261637t_char] :
( ( ( produc1299387215t_char @ A_75 @ B_43 )
= ( produc1299387215t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_107_Pair__eq,axiom,
! [A_75: produc220283002t_char,B_43: produc220283002t_char,A_74: produc220283002t_char,B_42: produc220283002t_char] :
( ( ( produc57279289t_char @ A_75 @ B_43 )
= ( produc57279289t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_108_Pair__eq,axiom,
! [A_75: produc1285161482t_char,B_43: produc1285161482t_char,A_74: produc1285161482t_char,B_42: produc1285161482t_char] :
( ( ( produc24551831t_char @ A_75 @ B_43 )
= ( produc24551831t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_109_Pair__eq,axiom,
! [A_75: produc618524391on_val,B_43: produc618524391on_val,A_74: produc618524391on_val,B_42: produc618524391on_val] :
( ( ( produc1347028499on_val @ A_75 @ B_43 )
= ( produc1347028499on_val @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_110_Pair__eq,axiom,
! [A_75: product_prod_val_val,B_43: product_prod_val_val,A_74: product_prod_val_val,B_42: product_prod_val_val] :
( ( ( produc1244920211al_val @ A_75 @ B_43 )
= ( produc1244920211al_val @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_111_Pair__eq,axiom,
! [A_75: produc1645268488al_val,B_43: produc1645268488al_val,A_74: produc1645268488al_val,B_42: produc1645268488al_val] :
( ( ( produc1924279125al_val @ A_75 @ B_43 )
= ( produc1924279125al_val @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_112_Pair__eq,axiom,
! [A_75: produc1278157519t_char,B_43: produc1278157519t_char,A_74: produc1278157519t_char,B_42: produc1278157519t_char] :
( ( ( produc2080520419t_char @ A_75 @ B_43 )
= ( produc2080520419t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_113_Pair__eq,axiom,
! [A_75: produc2088785539on_val,B_43: produc2088785539on_val,A_74: produc2088785539on_val,B_42: produc2088785539on_val] :
( ( ( produc1773146955on_val @ A_75 @ B_43 )
= ( produc1773146955on_val @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_114_Pair__eq,axiom,
! [A_75: produc2090907612on_val,B_43: produc2090907612on_val,A_74: produc2090907612on_val,B_42: produc2090907612on_val] :
( ( ( produc259392253on_val @ A_75 @ B_43 )
= ( produc259392253on_val @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_115_Pair__eq,axiom,
! [A_75: produc1746408499on_val,B_43: produc1746408499on_val,A_74: produc1746408499on_val,B_42: produc1746408499on_val] :
( ( ( produc345758123on_val @ A_75 @ B_43 )
= ( produc345758123on_val @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_116_Pair__eq,axiom,
! [A_75: list_exp_list_char,B_43: list_exp_list_char,A_74: list_exp_list_char,B_42: list_exp_list_char] :
( ( ( produc1237966615t_char @ A_75 @ B_43 )
= ( produc1237966615t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_117_Pair__eq,axiom,
! [A_75: exp_list_char,B_43: exp_list_char,A_74: exp_list_char,B_42: exp_list_char] :
( ( ( produc943465171t_char @ A_75 @ B_43 )
= ( produc943465171t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_118_Pair__eq,axiom,
! [A_75: list_list_char,B_43: list_list_char,A_74: list_list_char,B_42: list_list_char] :
( ( ( produc2035944023t_char @ A_75 @ B_43 )
= ( produc2035944023t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_119_Pair__eq,axiom,
! [A_75: list_P1940453997har_ty,B_43: list_P1940453997har_ty,A_74: list_P1940453997har_ty,B_42: list_P1940453997har_ty] :
( ( ( produc1860789535har_ty @ A_75 @ B_43 )
= ( produc1860789535har_ty @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_120_Pair__eq,axiom,
! [A_75: list_P341299826t_char,B_43: list_P341299826t_char,A_74: list_P341299826t_char,B_42: list_P341299826t_char] :
( ( ( produc436875159t_char @ A_75 @ B_43 )
= ( produc436875159t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_121_Pair__eq,axiom,
! [A_75: list_val,B_43: list_val,A_74: list_val,B_42: list_val] :
( ( ( produc2078839843st_val @ A_75 @ B_43 )
= ( produc2078839843st_val @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_122_Pair__eq,axiom,
! [A_75: list_ty,B_43: list_ty,A_74: list_ty,B_42: list_ty] :
( ( ( produc512429457ist_ty @ A_75 @ B_43 )
= ( produc512429457ist_ty @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_123_Pair__eq,axiom,
! [A_75: bop,B_43: bop,A_74: bop,B_42: bop] :
( ( ( product_Pair_bop_bop @ A_75 @ B_43 )
= ( product_Pair_bop_bop @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_124_Pair__eq,axiom,
! [A_75: produc1278157519t_char > option_val,B_43: produc1278157519t_char > option_val,A_74: produc1278157519t_char > option_val,B_42: produc1278157519t_char > option_val] :
( ( ( produc253229997on_val @ A_75 @ B_43 )
= ( produc253229997on_val @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_125_Pair__eq,axiom,
! [A_75: nat > option1728594148on_val,B_43: nat > option1728594148on_val,A_74: nat > option1728594148on_val,B_42: nat > option1728594148on_val] :
( ( ( produc1208913941on_val @ A_75 @ B_43 )
= ( produc1208913941on_val @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_126_Pair__eq,axiom,
! [A_75: list_char > option_val,B_43: list_char > option_val,A_74: list_char > option_val,B_42: list_char > option_val] :
( ( ( produc1338265359on_val @ A_75 @ B_43 )
= ( produc1338265359on_val @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_127_Pair__eq,axiom,
! [A_75: produc1282892786on_val,B_43: produc1282892786on_val,A_74: produc1282892786on_val,B_42: produc1282892786on_val] :
( ( ( produc833389609on_val @ A_75 @ B_43 )
= ( produc833389609on_val @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_128_Pair__eq,axiom,
! [A_75: exp_list_char,B_43: produc2090907612on_val,A_74: exp_list_char,B_42: produc2090907612on_val] :
( ( ( produc235638504on_val @ A_75 @ B_43 )
= ( produc235638504on_val @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_129_Pair__eq,axiom,
! [A_75: nat > option1728594148on_val,B_43: list_char > option_val,A_74: nat > option1728594148on_val,B_42: list_char > option_val] :
( ( ( produc755559506on_val @ A_75 @ B_43 )
= ( produc755559506on_val @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_130_Pair__eq,axiom,
! [A_75: list_char,B_43: produc1278157519t_char > option_val,A_74: list_char,B_42: produc1278157519t_char > option_val] :
( ( ( produc926070009on_val @ A_75 @ B_43 )
= ( produc926070009on_val @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_131_Pair__eq,axiom,
! [A_75: list_char,B_43: list_char,A_74: list_char,B_42: list_char] :
( ( ( produc5062597t_char @ A_75 @ B_43 )
= ( produc5062597t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_132_Pair__eq,axiom,
! [A_75: bop,B_43: product_prod_val_val,A_74: bop,B_42: product_prod_val_val] :
( ( ( produc621191550al_val @ A_75 @ B_43 )
= ( produc621191550al_val @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_133_Pair__eq,axiom,
! [A_75: val,B_43: val,A_74: val,B_42: val] :
( ( ( product_Pair_val_val @ A_75 @ B_43 )
= ( product_Pair_val_val @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_134_Pair__eq,axiom,
! [A_75: produc1180562163on_val,B_43: produc1180562163on_val,A_74: produc1180562163on_val,B_42: produc1180562163on_val] :
( ( ( produc747700183on_val @ A_75 @ B_43 )
= ( produc747700183on_val @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_135_Pair__eq,axiom,
! [A_75: list_exp_list_char,B_43: produc2090907612on_val,A_74: list_exp_list_char,B_42: produc2090907612on_val] :
( ( ( produc1302104557on_val @ A_75 @ B_43 )
= ( produc1302104557on_val @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_136_Pair__eq,axiom,
! [A_75: list_list_char,B_43: produc220283002t_char,A_74: list_list_char,B_42: produc220283002t_char] :
( ( ( produc921874948t_char @ A_75 @ B_43 )
= ( produc921874948t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_137_Pair__eq,axiom,
! [A_75: list_ty,B_43: produc662261637t_char,A_74: list_ty,B_42: produc662261637t_char] :
( ( ( produc1909267824t_char @ A_75 @ B_43 )
= ( produc1909267824t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_138_Pair__eq,axiom,
! [A_75: list_val,B_43: exp_list_char,A_74: list_val,B_42: exp_list_char] :
( ( ( produc1916172923t_char @ A_75 @ B_43 )
= ( produc1916172923t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_139_Pair__eq,axiom,
! [A_75: list_char,B_43: produc952412819t_char,A_74: list_char,B_42: produc952412819t_char] :
( ( ( produc822965838t_char @ A_75 @ B_43 )
= ( produc822965838t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_140_Pair__eq,axiom,
! [A_75: list_char,B_43: produc2146869324t_char,A_74: list_char,B_42: produc2146869324t_char] :
( ( ( produc1483578759t_char @ A_75 @ B_43 )
= ( produc1483578759t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_141_Pair__eq,axiom,
! [A_75: list_P1940453997har_ty,B_43: list_P341299826t_char,A_74: list_P1940453997har_ty,B_42: list_P341299826t_char] :
( ( ( produc1152259904t_char @ A_75 @ B_43 )
= ( produc1152259904t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_142_Pair__eq,axiom,
! [A_75: list_list_char,B_43: exp_list_char,A_74: list_list_char,B_42: exp_list_char] :
( ( ( produc1147572817t_char @ A_75 @ B_43 )
= ( produc1147572817t_char @ A_74 @ B_42 ) )
<=> ( ( A_75 = A_74 )
& ( B_43 = B_42 ) ) ) ).
thf(fact_143_split__paired__All,axiom,
! [P_28: produc917948472har_ty > $o] :
( ( !! @ produc917948472har_ty @ P_28 )
<=> ! [A_1: list_char,B_14: ty] : ( P_28 @ ( produc251930284har_ty @ A_1 @ B_14 ) ) ) ).
thf(fact_144_split__paired__All,axiom,
! [P_28: produc245756905har_ty > $o] :
( ( !! @ produc245756905har_ty @ P_28 )
<=> ! [A_1: produc1278157519t_char,B_14: ty] : ( P_28 @ ( produc1265154397har_ty @ A_1 @ B_14 ) ) ) ).
thf(fact_145_split__paired__All,axiom,
! [P_28: produc1013743697t_char > $o] :
( ( !! @ produc1013743697t_char @ P_28 )
<=> ! [A_1: list_char,B_14: produc1025221954t_char] : ( P_28 @ ( produc1331140167t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_146_split__paired__All,axiom,
! [P_28: produc1534059751t_char > $o] :
( ( !! @ produc1534059751t_char @ P_28 )
<=> ! [A_1: produc809539159t_char,B_14: produc809539159t_char] : ( P_28 @ ( produc1897818327t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_147_split__paired__All,axiom,
! [P_28: produc494726439t_char > $o] :
( ( !! @ produc494726439t_char @ P_28 )
<=> ! [A_1: produc2146869324t_char,B_14: produc2146869324t_char] : ( P_28 @ ( produc635935767t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_148_split__paired__All,axiom,
! [P_28: produc740765671t_char > $o] :
( ( !! @ produc740765671t_char @ P_28 )
<=> ! [A_1: produc952412819t_char,B_14: produc952412819t_char] : ( P_28 @ ( produc1431439831t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_149_split__paired__All,axiom,
! [P_28: produc84451751t_char > $o] :
( ( !! @ produc84451751t_char @ P_28 )
<=> ! [A_1: produc1971331930t_char,B_14: produc1971331930t_char] : ( P_28 @ ( produc1641293463t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_150_split__paired__All,axiom,
! [P_28: produc1826280281t_char > $o] :
( ( !! @ produc1826280281t_char @ P_28 )
<=> ! [A_1: produc662261637t_char,B_14: produc662261637t_char] : ( P_28 @ ( produc1299387215t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_151_split__paired__All,axiom,
! [P_28: produc1406897475t_char > $o] :
( ( !! @ produc1406897475t_char @ P_28 )
<=> ! [A_1: produc220283002t_char,B_14: produc220283002t_char] : ( P_28 @ ( produc57279289t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_152_split__paired__All,axiom,
! [P_28: produc349695911t_char > $o] :
( ( !! @ produc349695911t_char @ P_28 )
<=> ! [A_1: produc1285161482t_char,B_14: produc1285161482t_char] : ( P_28 @ ( produc24551831t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_153_split__paired__All,axiom,
! [P_28: produc1250491293on_val > $o] :
( ( !! @ produc1250491293on_val @ P_28 )
<=> ! [A_1: produc618524391on_val,B_14: produc618524391on_val] : ( P_28 @ ( produc1347028499on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_154_split__paired__All,axiom,
! [P_28: produc800118557al_val > $o] :
( ( !! @ produc800118557al_val @ P_28 )
<=> ! [A_1: product_prod_val_val,B_14: product_prod_val_val] : ( P_28 @ ( produc1244920211al_val @ A_1 @ B_14 ) ) ) ).
thf(fact_155_split__paired__All,axiom,
! [P_28: produc630464863al_val > $o] :
( ( !! @ produc630464863al_val @ P_28 )
<=> ! [A_1: produc1645268488al_val,B_14: produc1645268488al_val] : ( P_28 @ ( produc1924279125al_val @ A_1 @ B_14 ) ) ) ).
thf(fact_156_split__paired__All,axiom,
! [P_28: produc1350825965t_char > $o] :
( ( !! @ produc1350825965t_char @ P_28 )
<=> ! [A_1: produc1278157519t_char,B_14: produc1278157519t_char] : ( P_28 @ ( produc2080520419t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_157_split__paired__All,axiom,
! [P_28: produc1368416213on_val > $o] :
( ( !! @ produc1368416213on_val @ P_28 )
<=> ! [A_1: produc2088785539on_val,B_14: produc2088785539on_val] : ( P_28 @ ( produc1773146955on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_158_split__paired__All,axiom,
! [P_28: produc1581780743on_val > $o] :
( ( !! @ produc1581780743on_val @ P_28 )
<=> ! [A_1: produc2090907612on_val,B_14: produc2090907612on_val] : ( P_28 @ ( produc259392253on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_159_split__paired__All,axiom,
! [P_28: produc652964533on_val > $o] :
( ( !! @ produc652964533on_val @ P_28 )
<=> ! [A_1: produc1746408499on_val,B_14: produc1746408499on_val] : ( P_28 @ ( produc345758123on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_160_split__paired__All,axiom,
! [P_28: produc91527719t_char > $o] :
( ( !! @ produc91527719t_char @ P_28 )
<=> ! [A_1: list_exp_list_char,B_14: list_exp_list_char] : ( P_28 @ ( produc1237966615t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_161_split__paired__All,axiom,
! [P_28: produc2048519645t_char > $o] :
( ( !! @ produc2048519645t_char @ P_28 )
<=> ! [A_1: exp_list_char,B_14: exp_list_char] : ( P_28 @ ( produc943465171t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_162_split__paired__All,axiom,
! [P_28: produc1200003175t_char > $o] :
( ( !! @ produc1200003175t_char @ P_28 )
<=> ! [A_1: list_list_char,B_14: list_list_char] : ( P_28 @ ( produc2035944023t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_163_split__paired__All,axiom,
! [P_28: produc450000425har_ty > $o] :
( ( !! @ produc450000425har_ty @ P_28 )
<=> ! [A_1: list_P1940453997har_ty,B_14: list_P1940453997har_ty] : ( P_28 @ ( produc1860789535har_ty @ A_1 @ B_14 ) ) ) ).
thf(fact_164_split__paired__All,axiom,
! [P_28: produc244676007t_char > $o] :
( ( !! @ produc244676007t_char @ P_28 )
<=> ! [A_1: list_P341299826t_char,B_14: list_P341299826t_char] : ( P_28 @ ( produc436875159t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_165_split__paired__All,axiom,
! [P_28: produc753553453st_val > $o] :
( ( !! @ produc753553453st_val @ P_28 )
<=> ! [A_1: list_val,B_14: list_val] : ( P_28 @ ( produc2078839843st_val @ A_1 @ B_14 ) ) ) ).
thf(fact_166_split__paired__All,axiom,
! [P_28: produc1420746395ist_ty > $o] :
( ( !! @ produc1420746395ist_ty @ P_28 )
<=> ! [A_1: list_ty,B_14: list_ty] : ( P_28 @ ( produc512429457ist_ty @ A_1 @ B_14 ) ) ) ).
thf(fact_167_split__paired__All,axiom,
! [P_28: product_prod_bop_bop > $o] :
( ( !! @ product_prod_bop_bop @ P_28 )
<=> ! [A_1: bop,B_14: bop] : ( P_28 @ ( product_Pair_bop_bop @ A_1 @ B_14 ) ) ) ).
thf(fact_168_split__paired__All,axiom,
! [P_28: produc688860215on_val > $o] :
( ( !! @ produc688860215on_val @ P_28 )
<=> ! [A_1: produc1278157519t_char > option_val,B_14: produc1278157519t_char > option_val] : ( P_28 @ ( produc253229997on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_169_split__paired__All,axiom,
! [P_28: produc1287081631on_val > $o] :
( ( !! @ produc1287081631on_val @ P_28 )
<=> ! [A_1: nat > option1728594148on_val,B_14: nat > option1728594148on_val] : ( P_28 @ ( produc1208913941on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_170_split__paired__All,axiom,
! [P_28: produc774316953on_val > $o] :
( ( !! @ produc774316953on_val @ P_28 )
<=> ! [A_1: list_char > option_val,B_14: list_char > option_val] : ( P_28 @ ( produc1338265359on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_171_split__paired__All,axiom,
! [P_28: produc1746408499on_val > $o] :
( ( !! @ produc1746408499on_val @ P_28 )
<=> ! [A_1: produc1282892786on_val,B_14: produc1282892786on_val] : ( P_28 @ ( produc833389609on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_172_split__paired__All,axiom,
! [P_28: produc1282892786on_val > $o] :
( ( !! @ produc1282892786on_val @ P_28 )
<=> ! [A_1: exp_list_char,B_14: produc2090907612on_val] : ( P_28 @ ( produc235638504on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_173_split__paired__All,axiom,
! [P_28: produc2090907612on_val > $o] :
( ( !! @ produc2090907612on_val @ P_28 )
<=> ! [A_1: nat > option1728594148on_val,B_14: list_char > option_val] : ( P_28 @ ( produc755559506on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_174_split__paired__All,axiom,
! [P_28: produc2088785539on_val > $o] :
( ( !! @ produc2088785539on_val @ P_28 )
<=> ! [A_1: list_char,B_14: produc1278157519t_char > option_val] : ( P_28 @ ( produc926070009on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_175_split__paired__All,axiom,
! [P_28: produc1278157519t_char > $o] :
( ( !! @ produc1278157519t_char @ P_28 )
<=> ! [A_1: list_char,B_14: list_char] : ( P_28 @ ( produc5062597t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_176_split__paired__All,axiom,
! [P_28: produc1645268488al_val > $o] :
( ( !! @ produc1645268488al_val @ P_28 )
<=> ! [A_1: bop,B_14: product_prod_val_val] : ( P_28 @ ( produc621191550al_val @ A_1 @ B_14 ) ) ) ).
thf(fact_177_split__paired__All,axiom,
! [P_28: product_prod_val_val > $o] :
( ( !! @ product_prod_val_val @ P_28 )
<=> ! [A_1: val,B_14: val] : ( P_28 @ ( product_Pair_val_val @ A_1 @ B_14 ) ) ) ).
thf(fact_178_split__paired__All,axiom,
! [P_28: produc618524391on_val > $o] :
( ( !! @ produc618524391on_val @ P_28 )
<=> ! [A_1: produc1180562163on_val,B_14: produc1180562163on_val] : ( P_28 @ ( produc747700183on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_179_split__paired__All,axiom,
! [P_28: produc1180562163on_val > $o] :
( ( !! @ produc1180562163on_val @ P_28 )
<=> ! [A_1: list_exp_list_char,B_14: produc2090907612on_val] : ( P_28 @ ( produc1302104557on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_180_split__paired__All,axiom,
! [P_28: produc1285161482t_char > $o] :
( ( !! @ produc1285161482t_char @ P_28 )
<=> ! [A_1: list_list_char,B_14: produc220283002t_char] : ( P_28 @ ( produc921874948t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_181_split__paired__All,axiom,
! [P_28: produc220283002t_char > $o] :
( ( !! @ produc220283002t_char @ P_28 )
<=> ! [A_1: list_ty,B_14: produc662261637t_char] : ( P_28 @ ( produc1909267824t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_182_split__paired__All,axiom,
! [P_28: produc662261637t_char > $o] :
( ( !! @ produc662261637t_char @ P_28 )
<=> ! [A_1: list_val,B_14: exp_list_char] : ( P_28 @ ( produc1916172923t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_183_split__paired__All,axiom,
! [P_28: produc1971331930t_char > $o] :
( ( !! @ produc1971331930t_char @ P_28 )
<=> ! [A_1: list_char,B_14: produc952412819t_char] : ( P_28 @ ( produc822965838t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_184_split__paired__All,axiom,
! [P_28: produc952412819t_char > $o] :
( ( !! @ produc952412819t_char @ P_28 )
<=> ! [A_1: list_char,B_14: produc2146869324t_char] : ( P_28 @ ( produc1483578759t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_185_split__paired__All,axiom,
! [P_28: produc2146869324t_char > $o] :
( ( !! @ produc2146869324t_char @ P_28 )
<=> ! [A_1: list_P1940453997har_ty,B_14: list_P341299826t_char] : ( P_28 @ ( produc1152259904t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_186_split__paired__All,axiom,
! [P_28: produc809539159t_char > $o] :
( ( !! @ produc809539159t_char @ P_28 )
<=> ! [A_1: list_list_char,B_14: exp_list_char] : ( P_28 @ ( produc1147572817t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_187_fun__upd__def,axiom,
! [F_23: list_char > option_val,B_41: option_val,A_73: list_char,X: list_char] :
( ( ( X = A_73 )
=> ( ( fun_up1149430426on_val @ F_23 @ A_73 @ B_41 @ X )
= B_41 ) )
& ( ( X != A_73 )
=> ( ( fun_up1149430426on_val @ F_23 @ A_73 @ B_41 @ X )
= ( F_23 @ X ) ) ) ) ).
thf(fact_188_fun__upd__def,axiom,
! [F_23: list_char > option_ty,B_41: option_ty,A_73: list_char,X: list_char] :
( ( ( X = A_73 )
=> ( ( fun_up424764369ion_ty @ F_23 @ A_73 @ B_41 @ X )
= B_41 ) )
& ( ( X != A_73 )
=> ( ( fun_up424764369ion_ty @ F_23 @ A_73 @ B_41 @ X )
= ( F_23 @ X ) ) ) ) ).
thf(fact_189_fun__upd__def,axiom,
! [F_23: nat > option1728594148on_val,B_41: option1728594148on_val,A_73: nat,X: nat] :
( ( ( X = A_73 )
=> ( ( fun_up1472480727on_val @ F_23 @ A_73 @ B_41 @ X )
= B_41 ) )
& ( ( X != A_73 )
=> ( ( fun_up1472480727on_val @ F_23 @ A_73 @ B_41 @ X )
= ( F_23 @ X ) ) ) ) ).
thf(fact_190_fun__upd__def,axiom,
! [F_23: produc1278157519t_char > option_val,B_41: option_val,A_73: produc1278157519t_char,X: produc1278157519t_char] :
( ( ( X = A_73 )
=> ( ( fun_up204312361on_val @ F_23 @ A_73 @ B_41 @ X )
= B_41 ) )
& ( ( X != A_73 )
=> ( ( fun_up204312361on_val @ F_23 @ A_73 @ B_41 @ X )
= ( F_23 @ X ) ) ) ) ).
thf(fact_191_fun__upd__idem,axiom,
! [F_22: list_char > option_val,X_36: list_char,Y_18: option_val] :
( ( ( F_22 @ X_36 )
= Y_18 )
=> ( ( fun_up1149430426on_val @ F_22 @ X_36 @ Y_18 )
= F_22 ) ) ).
thf(fact_192_fun__upd__idem,axiom,
! [F_22: list_char > option_ty,X_36: list_char,Y_18: option_ty] :
( ( ( F_22 @ X_36 )
= Y_18 )
=> ( ( fun_up424764369ion_ty @ F_22 @ X_36 @ Y_18 )
= F_22 ) ) ).
thf(fact_193_fun__upd__idem,axiom,
! [F_22: nat > option1728594148on_val,X_36: nat,Y_18: option1728594148on_val] :
( ( ( F_22 @ X_36 )
= Y_18 )
=> ( ( fun_up1472480727on_val @ F_22 @ X_36 @ Y_18 )
= F_22 ) ) ).
thf(fact_194_fun__upd__idem,axiom,
! [F_22: produc1278157519t_char > option_val,X_36: produc1278157519t_char,Y_18: option_val] :
( ( ( F_22 @ X_36 )
= Y_18 )
=> ( ( fun_up204312361on_val @ F_22 @ X_36 @ Y_18 )
= F_22 ) ) ).
thf(fact_195_fun__upd__other,axiom,
! [F_21: list_char > option_val,Y_17: option_val,Z_7: list_char,X_35: list_char] :
( ( Z_7 != X_35 )
=> ( ( fun_up1149430426on_val @ F_21 @ X_35 @ Y_17 @ Z_7 )
= ( F_21 @ Z_7 ) ) ) ).
thf(fact_196_fun__upd__other,axiom,
! [F_21: list_char > option_ty,Y_17: option_ty,Z_7: list_char,X_35: list_char] :
( ( Z_7 != X_35 )
=> ( ( fun_up424764369ion_ty @ F_21 @ X_35 @ Y_17 @ Z_7 )
= ( F_21 @ Z_7 ) ) ) ).
thf(fact_197_fun__upd__other,axiom,
! [F_21: nat > option1728594148on_val,Y_17: option1728594148on_val,Z_7: nat,X_35: nat] :
( ( Z_7 != X_35 )
=> ( ( fun_up1472480727on_val @ F_21 @ X_35 @ Y_17 @ Z_7 )
= ( F_21 @ Z_7 ) ) ) ).
thf(fact_198_fun__upd__other,axiom,
! [F_21: produc1278157519t_char > option_val,Y_17: option_val,Z_7: produc1278157519t_char,X_35: produc1278157519t_char] :
( ( Z_7 != X_35 )
=> ( ( fun_up204312361on_val @ F_21 @ X_35 @ Y_17 @ Z_7 )
= ( F_21 @ Z_7 ) ) ) ).
thf(fact_199_fun__upd__twist,axiom,
! [M_15: list_char > option_val,B_40: option_val,D_2: option_val,A_72: list_char,C_21: list_char] :
( ( A_72 != C_21 )
=> ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ M_15 @ A_72 @ B_40 ) @ C_21 @ D_2 )
= ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ M_15 @ C_21 @ D_2 ) @ A_72 @ B_40 ) ) ) ).
thf(fact_200_fun__upd__twist,axiom,
! [M_15: list_char > option_ty,B_40: option_ty,D_2: option_ty,A_72: list_char,C_21: list_char] :
( ( A_72 != C_21 )
=> ( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ M_15 @ A_72 @ B_40 ) @ C_21 @ D_2 )
= ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ M_15 @ C_21 @ D_2 ) @ A_72 @ B_40 ) ) ) ).
thf(fact_201_fun__upd__twist,axiom,
! [M_15: nat > option1728594148on_val,B_40: option1728594148on_val,D_2: option1728594148on_val,A_72: nat,C_21: nat] :
( ( A_72 != C_21 )
=> ( ( fun_up1472480727on_val @ ( fun_up1472480727on_val @ M_15 @ A_72 @ B_40 ) @ C_21 @ D_2 )
= ( fun_up1472480727on_val @ ( fun_up1472480727on_val @ M_15 @ C_21 @ D_2 ) @ A_72 @ B_40 ) ) ) ).
thf(fact_202_fun__upd__twist,axiom,
! [M_15: produc1278157519t_char > option_val,B_40: option_val,D_2: option_val,A_72: produc1278157519t_char,C_21: produc1278157519t_char] :
( ( A_72 != C_21 )
=> ( ( fun_up204312361on_val @ ( fun_up204312361on_val @ M_15 @ A_72 @ B_40 ) @ C_21 @ D_2 )
= ( fun_up204312361on_val @ ( fun_up204312361on_val @ M_15 @ C_21 @ D_2 ) @ A_72 @ B_40 ) ) ) ).
thf(fact_203_fun__upd__apply,axiom,
! [F_20: list_char > option_val,Y_16: option_val,Z_6: list_char,X_34: list_char] :
( ( ( Z_6 = X_34 )
=> ( ( fun_up1149430426on_val @ F_20 @ X_34 @ Y_16 @ Z_6 )
= Y_16 ) )
& ( ( Z_6 != X_34 )
=> ( ( fun_up1149430426on_val @ F_20 @ X_34 @ Y_16 @ Z_6 )
= ( F_20 @ Z_6 ) ) ) ) ).
thf(fact_204_fun__upd__apply,axiom,
! [F_20: list_char > option_ty,Y_16: option_ty,Z_6: list_char,X_34: list_char] :
( ( ( Z_6 = X_34 )
=> ( ( fun_up424764369ion_ty @ F_20 @ X_34 @ Y_16 @ Z_6 )
= Y_16 ) )
& ( ( Z_6 != X_34 )
=> ( ( fun_up424764369ion_ty @ F_20 @ X_34 @ Y_16 @ Z_6 )
= ( F_20 @ Z_6 ) ) ) ) ).
thf(fact_205_fun__upd__apply,axiom,
! [F_20: nat > option1728594148on_val,Y_16: option1728594148on_val,Z_6: nat,X_34: nat] :
( ( ( Z_6 = X_34 )
=> ( ( fun_up1472480727on_val @ F_20 @ X_34 @ Y_16 @ Z_6 )
= Y_16 ) )
& ( ( Z_6 != X_34 )
=> ( ( fun_up1472480727on_val @ F_20 @ X_34 @ Y_16 @ Z_6 )
= ( F_20 @ Z_6 ) ) ) ) ).
thf(fact_206_fun__upd__apply,axiom,
! [F_20: produc1278157519t_char > option_val,Y_16: option_val,Z_6: produc1278157519t_char,X_34: produc1278157519t_char] :
( ( ( Z_6 = X_34 )
=> ( ( fun_up204312361on_val @ F_20 @ X_34 @ Y_16 @ Z_6 )
= Y_16 ) )
& ( ( Z_6 != X_34 )
=> ( ( fun_up204312361on_val @ F_20 @ X_34 @ Y_16 @ Z_6 )
= ( F_20 @ Z_6 ) ) ) ) ).
thf(fact_207_fun__upd__same,axiom,
! [F_19: list_char > option_val,X_33: list_char,Y_15: option_val] :
( ( fun_up1149430426on_val @ F_19 @ X_33 @ Y_15 @ X_33 )
= Y_15 ) ).
thf(fact_208_fun__upd__same,axiom,
! [F_19: list_char > option_ty,X_33: list_char,Y_15: option_ty] :
( ( fun_up424764369ion_ty @ F_19 @ X_33 @ Y_15 @ X_33 )
= Y_15 ) ).
thf(fact_209_fun__upd__same,axiom,
! [F_19: nat > option1728594148on_val,X_33: nat,Y_15: option1728594148on_val] :
( ( fun_up1472480727on_val @ F_19 @ X_33 @ Y_15 @ X_33 )
= Y_15 ) ).
thf(fact_210_fun__upd__same,axiom,
! [F_19: produc1278157519t_char > option_val,X_33: produc1278157519t_char,Y_15: option_val] :
( ( fun_up204312361on_val @ F_19 @ X_33 @ Y_15 @ X_33 )
= Y_15 ) ).
thf(fact_211_fun__upd__upd,axiom,
! [F_18: list_char > option_val,X_32: list_char,Y_14: option_val,Z_5: option_val] :
( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ F_18 @ X_32 @ Y_14 ) @ X_32 @ Z_5 )
= ( fun_up1149430426on_val @ F_18 @ X_32 @ Z_5 ) ) ).
thf(fact_212_fun__upd__upd,axiom,
! [F_18: list_char > option_ty,X_32: list_char,Y_14: option_ty,Z_5: option_ty] :
( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ F_18 @ X_32 @ Y_14 ) @ X_32 @ Z_5 )
= ( fun_up424764369ion_ty @ F_18 @ X_32 @ Z_5 ) ) ).
thf(fact_213_fun__upd__upd,axiom,
! [F_18: nat > option1728594148on_val,X_32: nat,Y_14: option1728594148on_val,Z_5: option1728594148on_val] :
( ( fun_up1472480727on_val @ ( fun_up1472480727on_val @ F_18 @ X_32 @ Y_14 ) @ X_32 @ Z_5 )
= ( fun_up1472480727on_val @ F_18 @ X_32 @ Z_5 ) ) ).
thf(fact_214_fun__upd__upd,axiom,
! [F_18: produc1278157519t_char > option_val,X_32: produc1278157519t_char,Y_14: option_val,Z_5: option_val] :
( ( fun_up204312361on_val @ ( fun_up204312361on_val @ F_18 @ X_32 @ Y_14 ) @ X_32 @ Z_5 )
= ( fun_up204312361on_val @ F_18 @ X_32 @ Z_5 ) ) ).
thf(fact_215_fun__upd__idem__iff,axiom,
! [F_17: list_char > option_val,X_31: list_char,Y_13: option_val] :
( ( ( fun_up1149430426on_val @ F_17 @ X_31 @ Y_13 )
= F_17 )
<=> ( ( F_17 @ X_31 )
= Y_13 ) ) ).
thf(fact_216_fun__upd__idem__iff,axiom,
! [F_17: list_char > option_ty,X_31: list_char,Y_13: option_ty] :
( ( ( fun_up424764369ion_ty @ F_17 @ X_31 @ Y_13 )
= F_17 )
<=> ( ( F_17 @ X_31 )
= Y_13 ) ) ).
thf(fact_217_fun__upd__idem__iff,axiom,
! [F_17: nat > option1728594148on_val,X_31: nat,Y_13: option1728594148on_val] :
( ( ( fun_up1472480727on_val @ F_17 @ X_31 @ Y_13 )
= F_17 )
<=> ( ( F_17 @ X_31 )
= Y_13 ) ) ).
thf(fact_218_fun__upd__idem__iff,axiom,
! [F_17: produc1278157519t_char > option_val,X_31: produc1278157519t_char,Y_13: option_val] :
( ( ( fun_up204312361on_val @ F_17 @ X_31 @ Y_13 )
= F_17 )
<=> ( ( F_17 @ X_31 )
= Y_13 ) ) ).
thf(fact_219_widen__refl,axiom,
! [P_27: list_P1999446415t_char,T_14: ty] : ( widen_2090681816t_char @ P_27 @ T_14 @ T_14 ) ).
thf(fact_220_red__preserves__hconf,axiom,
! [E_2: list_char > option_ty,T: ty,E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) ) @ ( red @ P ) )
=> ( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ T )
=> ( ( hconf_97414254t_char @ P @ H_1 )
=> ( hconf_97414254t_char @ P @ H ) ) ) ) ).
thf(fact_221_red__preserves__lconf,axiom,
! [E_2: list_char > option_ty,T: ty,E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) ) @ ( red @ P ) )
=> ( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ T )
=> ( ( lconf_496643946t_char @ P @ H_1 @ L_1 @ E_2 )
=> ( lconf_496643946t_char @ P @ H @ L @ E_2 ) ) ) ) ).
thf(fact_222_prod__cases3,axiom,
! [Y_12: produc1013743697t_char] :
~ ! [A_1: list_char,B_14: list_ty,C_20: produc1059328077t_char] :
( Y_12
!= ( produc1331140167t_char @ A_1 @ ( produc2016959032t_char @ B_14 @ C_20 ) ) ) ).
thf(fact_223_prod__cases3,axiom,
! [Y_12: produc1746408499on_val] :
~ ! [A_1: produc1282892786on_val,B_14: exp_list_char,C_20: produc2090907612on_val] :
( Y_12
!= ( produc833389609on_val @ A_1 @ ( produc235638504on_val @ B_14 @ C_20 ) ) ) ).
thf(fact_224_prod__cases3,axiom,
! [Y_12: produc1282892786on_val] :
~ ! [A_1: exp_list_char,B_14: nat > option1728594148on_val,C_20: list_char > option_val] :
( Y_12
!= ( produc235638504on_val @ A_1 @ ( produc755559506on_val @ B_14 @ C_20 ) ) ) ).
thf(fact_225_prod__cases3,axiom,
! [Y_12: produc1645268488al_val] :
~ ! [A_1: bop,B_14: val,C_20: val] :
( Y_12
!= ( produc621191550al_val @ A_1 @ ( product_Pair_val_val @ B_14 @ C_20 ) ) ) ).
thf(fact_226_prod__cases3,axiom,
! [Y_12: produc618524391on_val] :
~ ! [A_1: produc1180562163on_val,B_14: list_exp_list_char,C_20: produc2090907612on_val] :
( Y_12
!= ( produc747700183on_val @ A_1 @ ( produc1302104557on_val @ B_14 @ C_20 ) ) ) ).
thf(fact_227_prod__cases3,axiom,
! [Y_12: produc1180562163on_val] :
~ ! [A_1: list_exp_list_char,B_14: nat > option1728594148on_val,C_20: list_char > option_val] :
( Y_12
!= ( produc1302104557on_val @ A_1 @ ( produc755559506on_val @ B_14 @ C_20 ) ) ) ).
thf(fact_228_prod__cases3,axiom,
! [Y_12: produc1285161482t_char] :
~ ! [A_1: list_list_char,B_14: list_ty,C_20: produc662261637t_char] :
( Y_12
!= ( produc921874948t_char @ A_1 @ ( produc1909267824t_char @ B_14 @ C_20 ) ) ) ).
thf(fact_229_prod__cases3,axiom,
! [Y_12: produc220283002t_char] :
~ ! [A_1: list_ty,B_14: list_val,C_20: exp_list_char] :
( Y_12
!= ( produc1909267824t_char @ A_1 @ ( produc1916172923t_char @ B_14 @ C_20 ) ) ) ).
thf(fact_230_prod__cases3,axiom,
! [Y_12: produc1971331930t_char] :
~ ! [A_1: list_char,B_14: list_char,C_20: produc2146869324t_char] :
( Y_12
!= ( produc822965838t_char @ A_1 @ ( produc1483578759t_char @ B_14 @ C_20 ) ) ) ).
thf(fact_231_prod__cases3,axiom,
! [Y_12: produc952412819t_char] :
~ ! [A_1: list_char,B_14: list_P1940453997har_ty,C_20: list_P341299826t_char] :
( Y_12
!= ( produc1483578759t_char @ A_1 @ ( produc1152259904t_char @ B_14 @ C_20 ) ) ) ).
thf(fact_232_prod__cases3,axiom,
! [Y_12: produc652964533on_val] :
~ ! [A_1: produc1746408499on_val,B_14: produc1282892786on_val,C_20: produc1282892786on_val] :
( Y_12
!= ( produc345758123on_val @ A_1 @ ( produc833389609on_val @ B_14 @ C_20 ) ) ) ).
thf(fact_233_prod__cases3,axiom,
! [Y_12: produc1581780743on_val] :
~ ! [A_1: produc2090907612on_val,B_14: nat > option1728594148on_val,C_20: list_char > option_val] :
( Y_12
!= ( produc259392253on_val @ A_1 @ ( produc755559506on_val @ B_14 @ C_20 ) ) ) ).
thf(fact_234_prod__cases3,axiom,
! [Y_12: produc1368416213on_val] :
~ ! [A_1: produc2088785539on_val,B_14: list_char,C_20: produc1278157519t_char > option_val] :
( Y_12
!= ( produc1773146955on_val @ A_1 @ ( produc926070009on_val @ B_14 @ C_20 ) ) ) ).
thf(fact_235_prod__cases3,axiom,
! [Y_12: produc1350825965t_char] :
~ ! [A_1: produc1278157519t_char,B_14: list_char,C_20: list_char] :
( Y_12
!= ( produc2080520419t_char @ A_1 @ ( produc5062597t_char @ B_14 @ C_20 ) ) ) ).
thf(fact_236_prod__cases3,axiom,
! [Y_12: produc630464863al_val] :
~ ! [A_1: produc1645268488al_val,B_14: bop,C_20: product_prod_val_val] :
( Y_12
!= ( produc1924279125al_val @ A_1 @ ( produc621191550al_val @ B_14 @ C_20 ) ) ) ).
thf(fact_237_prod__cases3,axiom,
! [Y_12: produc800118557al_val] :
~ ! [A_1: product_prod_val_val,B_14: val,C_20: val] :
( Y_12
!= ( produc1244920211al_val @ A_1 @ ( product_Pair_val_val @ B_14 @ C_20 ) ) ) ).
thf(fact_238_prod__cases3,axiom,
! [Y_12: produc1250491293on_val] :
~ ! [A_1: produc618524391on_val,B_14: produc1180562163on_val,C_20: produc1180562163on_val] :
( Y_12
!= ( produc1347028499on_val @ A_1 @ ( produc747700183on_val @ B_14 @ C_20 ) ) ) ).
thf(fact_239_prod__cases3,axiom,
! [Y_12: produc349695911t_char] :
~ ! [A_1: produc1285161482t_char,B_14: list_list_char,C_20: produc220283002t_char] :
( Y_12
!= ( produc24551831t_char @ A_1 @ ( produc921874948t_char @ B_14 @ C_20 ) ) ) ).
thf(fact_240_prod__cases3,axiom,
! [Y_12: produc1406897475t_char] :
~ ! [A_1: produc220283002t_char,B_14: list_ty,C_20: produc662261637t_char] :
( Y_12
!= ( produc57279289t_char @ A_1 @ ( produc1909267824t_char @ B_14 @ C_20 ) ) ) ).
thf(fact_241_prod__cases3,axiom,
! [Y_12: produc1826280281t_char] :
~ ! [A_1: produc662261637t_char,B_14: list_val,C_20: exp_list_char] :
( Y_12
!= ( produc1299387215t_char @ A_1 @ ( produc1916172923t_char @ B_14 @ C_20 ) ) ) ).
thf(fact_242_prod__cases3,axiom,
! [Y_12: produc84451751t_char] :
~ ! [A_1: produc1971331930t_char,B_14: list_char,C_20: produc952412819t_char] :
( Y_12
!= ( produc1641293463t_char @ A_1 @ ( produc822965838t_char @ B_14 @ C_20 ) ) ) ).
thf(fact_243_prod__cases3,axiom,
! [Y_12: produc740765671t_char] :
~ ! [A_1: produc952412819t_char,B_14: list_char,C_20: produc2146869324t_char] :
( Y_12
!= ( produc1431439831t_char @ A_1 @ ( produc1483578759t_char @ B_14 @ C_20 ) ) ) ).
thf(fact_244_prod__cases3,axiom,
! [Y_12: produc494726439t_char] :
~ ! [A_1: produc2146869324t_char,B_14: list_P1940453997har_ty,C_20: list_P341299826t_char] :
( Y_12
!= ( produc635935767t_char @ A_1 @ ( produc1152259904t_char @ B_14 @ C_20 ) ) ) ).
thf(fact_245_prod__cases3,axiom,
! [Y_12: produc1534059751t_char] :
~ ! [A_1: produc809539159t_char,B_14: list_list_char,C_20: exp_list_char] :
( Y_12
!= ( produc1897818327t_char @ A_1 @ ( produc1147572817t_char @ B_14 @ C_20 ) ) ) ).
thf(fact_246_prod__induct3,axiom,
! [X_30: produc1013743697t_char,P_26: produc1013743697t_char > $o] :
( ! [A_1: list_char,B_14: list_ty,C_20: produc1059328077t_char] : ( P_26 @ ( produc1331140167t_char @ A_1 @ ( produc2016959032t_char @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_247_prod__induct3,axiom,
! [X_30: produc1746408499on_val,P_26: produc1746408499on_val > $o] :
( ! [A_1: produc1282892786on_val,B_14: exp_list_char,C_20: produc2090907612on_val] : ( P_26 @ ( produc833389609on_val @ A_1 @ ( produc235638504on_val @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_248_prod__induct3,axiom,
! [X_30: produc1282892786on_val,P_26: produc1282892786on_val > $o] :
( ! [A_1: exp_list_char,B_14: nat > option1728594148on_val,C_20: list_char > option_val] : ( P_26 @ ( produc235638504on_val @ A_1 @ ( produc755559506on_val @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_249_prod__induct3,axiom,
! [X_30: produc1645268488al_val,P_26: produc1645268488al_val > $o] :
( ! [A_1: bop,B_14: val,C_20: val] : ( P_26 @ ( produc621191550al_val @ A_1 @ ( product_Pair_val_val @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_250_prod__induct3,axiom,
! [X_30: produc618524391on_val,P_26: produc618524391on_val > $o] :
( ! [A_1: produc1180562163on_val,B_14: list_exp_list_char,C_20: produc2090907612on_val] : ( P_26 @ ( produc747700183on_val @ A_1 @ ( produc1302104557on_val @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_251_prod__induct3,axiom,
! [X_30: produc1180562163on_val,P_26: produc1180562163on_val > $o] :
( ! [A_1: list_exp_list_char,B_14: nat > option1728594148on_val,C_20: list_char > option_val] : ( P_26 @ ( produc1302104557on_val @ A_1 @ ( produc755559506on_val @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_252_prod__induct3,axiom,
! [X_30: produc1285161482t_char,P_26: produc1285161482t_char > $o] :
( ! [A_1: list_list_char,B_14: list_ty,C_20: produc662261637t_char] : ( P_26 @ ( produc921874948t_char @ A_1 @ ( produc1909267824t_char @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_253_prod__induct3,axiom,
! [X_30: produc220283002t_char,P_26: produc220283002t_char > $o] :
( ! [A_1: list_ty,B_14: list_val,C_20: exp_list_char] : ( P_26 @ ( produc1909267824t_char @ A_1 @ ( produc1916172923t_char @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_254_prod__induct3,axiom,
! [X_30: produc1971331930t_char,P_26: produc1971331930t_char > $o] :
( ! [A_1: list_char,B_14: list_char,C_20: produc2146869324t_char] : ( P_26 @ ( produc822965838t_char @ A_1 @ ( produc1483578759t_char @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_255_prod__induct3,axiom,
! [X_30: produc952412819t_char,P_26: produc952412819t_char > $o] :
( ! [A_1: list_char,B_14: list_P1940453997har_ty,C_20: list_P341299826t_char] : ( P_26 @ ( produc1483578759t_char @ A_1 @ ( produc1152259904t_char @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_256_prod__induct3,axiom,
! [X_30: produc652964533on_val,P_26: produc652964533on_val > $o] :
( ! [A_1: produc1746408499on_val,B_14: produc1282892786on_val,C_20: produc1282892786on_val] : ( P_26 @ ( produc345758123on_val @ A_1 @ ( produc833389609on_val @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_257_prod__induct3,axiom,
! [X_30: produc1581780743on_val,P_26: produc1581780743on_val > $o] :
( ! [A_1: produc2090907612on_val,B_14: nat > option1728594148on_val,C_20: list_char > option_val] : ( P_26 @ ( produc259392253on_val @ A_1 @ ( produc755559506on_val @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_258_prod__induct3,axiom,
! [X_30: produc1368416213on_val,P_26: produc1368416213on_val > $o] :
( ! [A_1: produc2088785539on_val,B_14: list_char,C_20: produc1278157519t_char > option_val] : ( P_26 @ ( produc1773146955on_val @ A_1 @ ( produc926070009on_val @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_259_prod__induct3,axiom,
! [X_30: produc1350825965t_char,P_26: produc1350825965t_char > $o] :
( ! [A_1: produc1278157519t_char,B_14: list_char,C_20: list_char] : ( P_26 @ ( produc2080520419t_char @ A_1 @ ( produc5062597t_char @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_260_prod__induct3,axiom,
! [X_30: produc630464863al_val,P_26: produc630464863al_val > $o] :
( ! [A_1: produc1645268488al_val,B_14: bop,C_20: product_prod_val_val] : ( P_26 @ ( produc1924279125al_val @ A_1 @ ( produc621191550al_val @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_261_prod__induct3,axiom,
! [X_30: produc800118557al_val,P_26: produc800118557al_val > $o] :
( ! [A_1: product_prod_val_val,B_14: val,C_20: val] : ( P_26 @ ( produc1244920211al_val @ A_1 @ ( product_Pair_val_val @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_262_prod__induct3,axiom,
! [X_30: produc1250491293on_val,P_26: produc1250491293on_val > $o] :
( ! [A_1: produc618524391on_val,B_14: produc1180562163on_val,C_20: produc1180562163on_val] : ( P_26 @ ( produc1347028499on_val @ A_1 @ ( produc747700183on_val @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_263_prod__induct3,axiom,
! [X_30: produc349695911t_char,P_26: produc349695911t_char > $o] :
( ! [A_1: produc1285161482t_char,B_14: list_list_char,C_20: produc220283002t_char] : ( P_26 @ ( produc24551831t_char @ A_1 @ ( produc921874948t_char @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_264_prod__induct3,axiom,
! [X_30: produc1406897475t_char,P_26: produc1406897475t_char > $o] :
( ! [A_1: produc220283002t_char,B_14: list_ty,C_20: produc662261637t_char] : ( P_26 @ ( produc57279289t_char @ A_1 @ ( produc1909267824t_char @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_265_prod__induct3,axiom,
! [X_30: produc1826280281t_char,P_26: produc1826280281t_char > $o] :
( ! [A_1: produc662261637t_char,B_14: list_val,C_20: exp_list_char] : ( P_26 @ ( produc1299387215t_char @ A_1 @ ( produc1916172923t_char @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_266_prod__induct3,axiom,
! [X_30: produc84451751t_char,P_26: produc84451751t_char > $o] :
( ! [A_1: produc1971331930t_char,B_14: list_char,C_20: produc952412819t_char] : ( P_26 @ ( produc1641293463t_char @ A_1 @ ( produc822965838t_char @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_267_prod__induct3,axiom,
! [X_30: produc740765671t_char,P_26: produc740765671t_char > $o] :
( ! [A_1: produc952412819t_char,B_14: list_char,C_20: produc2146869324t_char] : ( P_26 @ ( produc1431439831t_char @ A_1 @ ( produc1483578759t_char @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_268_prod__induct3,axiom,
! [X_30: produc494726439t_char,P_26: produc494726439t_char > $o] :
( ! [A_1: produc2146869324t_char,B_14: list_P1940453997har_ty,C_20: list_P341299826t_char] : ( P_26 @ ( produc635935767t_char @ A_1 @ ( produc1152259904t_char @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_269_prod__induct3,axiom,
! [X_30: produc1534059751t_char,P_26: produc1534059751t_char > $o] :
( ! [A_1: produc809539159t_char,B_14: list_list_char,C_20: exp_list_char] : ( P_26 @ ( produc1897818327t_char @ A_1 @ ( produc1147572817t_char @ B_14 @ C_20 ) ) )
=> ( P_26 @ X_30 ) ) ).
thf(fact_270_red__preserves__sconf,axiom,
! [E_2: list_char > option_ty,T: ty,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( red @ P ) )
=> ( ( wTrt_1 @ P @ ( hp @ S ) @ E_2 @ E_1 @ T )
=> ( ( typeSa816273224_sconf @ P @ E_2 @ S )
=> ( typeSa816273224_sconf @ P @ E_2 @ S_2 ) ) ) ) ).
thf(fact_271_pred__equals__eq2,axiom,
! [S_12: produc91527719t_char > $o,R_19: produc91527719t_char > $o] :
( ! [X: list_exp_list_char,Xa: list_exp_list_char] :
( ( member894971540t_char @ ( produc1237966615t_char @ X @ Xa ) @ R_19 )
<=> ( member894971540t_char @ ( produc1237966615t_char @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_272_pred__equals__eq2,axiom,
! [S_12: produc2048519645t_char > $o,R_19: produc2048519645t_char > $o] :
( ! [X: exp_list_char,Xa: exp_list_char] :
( ( member1199939018t_char @ ( produc943465171t_char @ X @ Xa ) @ R_19 )
<=> ( member1199939018t_char @ ( produc943465171t_char @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_273_pred__equals__eq2,axiom,
! [S_12: produc1200003175t_char > $o,R_19: produc1200003175t_char > $o] :
( ! [X: list_list_char,Xa: list_list_char] :
( ( member817832404t_char @ ( produc2035944023t_char @ X @ Xa ) @ R_19 )
<=> ( member817832404t_char @ ( produc2035944023t_char @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_274_pred__equals__eq2,axiom,
! [S_12: produc450000425har_ty > $o,R_19: produc450000425har_ty > $o] :
( ! [X: list_P1940453997har_ty,Xa: list_P1940453997har_ty] :
( ( member520253462har_ty @ ( produc1860789535har_ty @ X @ Xa ) @ R_19 )
<=> ( member520253462har_ty @ ( produc1860789535har_ty @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_275_pred__equals__eq2,axiom,
! [S_12: produc244676007t_char > $o,R_19: produc244676007t_char > $o] :
( ! [X: list_P341299826t_char,Xa: list_P341299826t_char] :
( ( member1580476948t_char @ ( produc436875159t_char @ X @ Xa ) @ R_19 )
<=> ( member1580476948t_char @ ( produc436875159t_char @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_276_pred__equals__eq2,axiom,
! [S_12: produc753553453st_val > $o,R_19: produc753553453st_val > $o] :
( ! [X: list_val,Xa: list_val] :
( ( member273646106st_val @ ( produc2078839843st_val @ X @ Xa ) @ R_19 )
<=> ( member273646106st_val @ ( produc2078839843st_val @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_277_pred__equals__eq2,axiom,
! [S_12: produc1420746395ist_ty > $o,R_19: produc1420746395ist_ty > $o] :
( ! [X: list_ty,Xa: list_ty] :
( ( member104734088ist_ty @ ( produc512429457ist_ty @ X @ Xa ) @ R_19 )
<=> ( member104734088ist_ty @ ( produc512429457ist_ty @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_278_pred__equals__eq2,axiom,
! [S_12: product_prod_bop_bop > $o,R_19: product_prod_bop_bop > $o] :
( ! [X: bop,Xa: bop] :
( ( member978285664op_bop @ ( product_Pair_bop_bop @ X @ Xa ) @ R_19 )
<=> ( member978285664op_bop @ ( product_Pair_bop_bop @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_279_pred__equals__eq2,axiom,
! [S_12: produc688860215on_val > $o,R_19: produc688860215on_val > $o] :
( ! [X: produc1278157519t_char > option_val,Xa: produc1278157519t_char > option_val] :
( ( member1448924196on_val @ ( produc253229997on_val @ X @ Xa ) @ R_19 )
<=> ( member1448924196on_val @ ( produc253229997on_val @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_280_pred__equals__eq2,axiom,
! [S_12: produc1287081631on_val > $o,R_19: produc1287081631on_val > $o] :
( ! [X: nat > option1728594148on_val,Xa: nat > option1728594148on_val] :
( ( member112887436on_val @ ( produc1208913941on_val @ X @ Xa ) @ R_19 )
<=> ( member112887436on_val @ ( produc1208913941on_val @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_281_pred__equals__eq2,axiom,
! [S_12: produc774316953on_val > $o,R_19: produc774316953on_val > $o] :
( ! [X: list_char > option_val,Xa: list_char > option_val] :
( ( member1838289030on_val @ ( produc1338265359on_val @ X @ Xa ) @ R_19 )
<=> ( member1838289030on_val @ ( produc1338265359on_val @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_282_pred__equals__eq2,axiom,
! [S_12: produc1282892786on_val > $o,R_19: produc1282892786on_val > $o] :
( ! [X: exp_list_char,Xa: produc2090907612on_val] :
( ( member1072200031on_val @ ( produc235638504on_val @ X @ Xa ) @ R_19 )
<=> ( member1072200031on_val @ ( produc235638504on_val @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_283_pred__equals__eq2,axiom,
! [S_12: produc2090907612on_val > $o,R_19: produc2090907612on_val > $o] :
( ! [X: nat > option1728594148on_val,Xa: list_char > option_val] :
( ( member1846553161on_val @ ( produc755559506on_val @ X @ Xa ) @ R_19 )
<=> ( member1846553161on_val @ ( produc755559506on_val @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_284_pred__equals__eq2,axiom,
! [S_12: produc2088785539on_val > $o,R_19: produc2088785539on_val > $o] :
( ! [X: list_char,Xa: produc1278157519t_char > option_val] :
( ( member1374264560on_val @ ( produc926070009on_val @ X @ Xa ) @ R_19 )
<=> ( member1374264560on_val @ ( produc926070009on_val @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_285_pred__equals__eq2,axiom,
! [S_12: produc1645268488al_val > $o,R_19: produc1645268488al_val > $o] :
( ! [X: bop,Xa: product_prod_val_val] :
( ( member1417904245al_val @ ( produc621191550al_val @ X @ Xa ) @ R_19 )
<=> ( member1417904245al_val @ ( produc621191550al_val @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_286_pred__equals__eq2,axiom,
! [S_12: product_prod_val_val > $o,R_19: product_prod_val_val > $o] :
( ! [X: val,Xa: val] :
( ( member649088532al_val @ ( product_Pair_val_val @ X @ Xa ) @ R_19 )
<=> ( member649088532al_val @ ( product_Pair_val_val @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_287_pred__equals__eq2,axiom,
! [S_12: produc1180562163on_val > $o,R_19: produc1180562163on_val > $o] :
( ! [X: list_exp_list_char,Xa: produc2090907612on_val] :
( ( member1224782662on_val @ ( produc1302104557on_val @ X @ Xa ) @ R_19 )
<=> ( member1224782662on_val @ ( produc1302104557on_val @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_288_pred__equals__eq2,axiom,
! [S_12: produc1285161482t_char > $o,R_19: produc1285161482t_char > $o] :
( ! [X: list_list_char,Xa: produc220283002t_char] :
( ( member133545693t_char @ ( produc921874948t_char @ X @ Xa ) @ R_19 )
<=> ( member133545693t_char @ ( produc921874948t_char @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_289_pred__equals__eq2,axiom,
! [S_12: produc220283002t_char > $o,R_19: produc220283002t_char > $o] :
( ! [X: list_ty,Xa: produc662261637t_char] :
( ( member140606439t_char @ ( produc1909267824t_char @ X @ Xa ) @ R_19 )
<=> ( member140606439t_char @ ( produc1909267824t_char @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_290_pred__equals__eq2,axiom,
! [S_12: produc662261637t_char > $o,R_19: produc662261637t_char > $o] :
( ! [X: list_val,Xa: exp_list_char] :
( ( member699351154t_char @ ( produc1916172923t_char @ X @ Xa ) @ R_19 )
<=> ( member699351154t_char @ ( produc1916172923t_char @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_291_pred__equals__eq2,axiom,
! [S_12: produc952412819t_char > $o,R_19: produc952412819t_char > $o] :
( ! [X: list_char,Xa: produc2146869324t_char] :
( ( member1771544038t_char @ ( produc1483578759t_char @ X @ Xa ) @ R_19 )
<=> ( member1771544038t_char @ ( produc1483578759t_char @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_292_pred__equals__eq2,axiom,
! [S_12: produc2146869324t_char > $o,R_19: produc2146869324t_char > $o] :
( ! [X: list_P1940453997har_ty,Xa: list_P341299826t_char] :
( ( member1379348767t_char @ ( produc1152259904t_char @ X @ Xa ) @ R_19 )
<=> ( member1379348767t_char @ ( produc1152259904t_char @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_293_pred__equals__eq2,axiom,
! [S_12: produc809539159t_char > $o,R_19: produc809539159t_char > $o] :
( ! [X: list_list_char,Xa: exp_list_char] :
( ( member1840112042t_char @ ( produc1147572817t_char @ X @ Xa ) @ R_19 )
<=> ( member1840112042t_char @ ( produc1147572817t_char @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_294_pred__equals__eq2,axiom,
! [S_12: produc1746408499on_val > $o,R_19: produc1746408499on_val > $o] :
( ! [X: produc1282892786on_val,Xa: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ X @ Xa ) @ R_19 )
<=> ( member1913460000on_val @ ( produc833389609on_val @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_295_pred__equals__eq2,axiom,
! [S_12: produc1278157519t_char > $o,R_19: produc1278157519t_char > $o] :
( ! [X: list_char,Xa: list_char] :
( ( member1251428284t_char @ ( produc5062597t_char @ X @ Xa ) @ R_19 )
<=> ( member1251428284t_char @ ( produc5062597t_char @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_296_pred__equals__eq2,axiom,
! [S_12: produc618524391on_val > $o,R_19: produc618524391on_val > $o] :
( ! [X: produc1180562163on_val,Xa: produc1180562163on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ X @ Xa ) @ R_19 )
<=> ( member2042188884on_val @ ( produc747700183on_val @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_297_pred__equals__eq2,axiom,
! [S_12: produc1971331930t_char > $o,R_19: produc1971331930t_char > $o] :
( ! [X: list_char,Xa: produc952412819t_char] :
( ( member1467889965t_char @ ( produc822965838t_char @ X @ Xa ) @ R_19 )
<=> ( member1467889965t_char @ ( produc822965838t_char @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_298_pred__equals__eq2,axiom,
! [S_12: produc1013743697t_char > $o,R_19: produc1013743697t_char > $o] :
( ! [X: list_char,Xa: produc1025221954t_char] :
( ( member1601084734t_char @ ( produc1331140167t_char @ X @ Xa ) @ R_19 )
<=> ( member1601084734t_char @ ( produc1331140167t_char @ X @ Xa ) @ S_12 ) )
<=> ( R_19 = S_12 ) ) ).
thf(fact_299_prod_Oexhaust,axiom,
! [Y_11: produc809539159t_char] :
~ ! [A_1: list_list_char,B_14: exp_list_char] :
( Y_11
!= ( produc1147572817t_char @ A_1 @ B_14 ) ) ).
thf(fact_300_prod_Oexhaust,axiom,
! [Y_11: produc2146869324t_char] :
~ ! [A_1: list_P1940453997har_ty,B_14: list_P341299826t_char] :
( Y_11
!= ( produc1152259904t_char @ A_1 @ B_14 ) ) ).
thf(fact_301_prod_Oexhaust,axiom,
! [Y_11: produc952412819t_char] :
~ ! [A_1: list_char,B_14: produc2146869324t_char] :
( Y_11
!= ( produc1483578759t_char @ A_1 @ B_14 ) ) ).
thf(fact_302_prod_Oexhaust,axiom,
! [Y_11: produc1971331930t_char] :
~ ! [A_1: list_char,B_14: produc952412819t_char] :
( Y_11
!= ( produc822965838t_char @ A_1 @ B_14 ) ) ).
thf(fact_303_prod_Oexhaust,axiom,
! [Y_11: produc662261637t_char] :
~ ! [A_1: list_val,B_14: exp_list_char] :
( Y_11
!= ( produc1916172923t_char @ A_1 @ B_14 ) ) ).
thf(fact_304_prod_Oexhaust,axiom,
! [Y_11: produc220283002t_char] :
~ ! [A_1: list_ty,B_14: produc662261637t_char] :
( Y_11
!= ( produc1909267824t_char @ A_1 @ B_14 ) ) ).
thf(fact_305_prod_Oexhaust,axiom,
! [Y_11: produc1285161482t_char] :
~ ! [A_1: list_list_char,B_14: produc220283002t_char] :
( Y_11
!= ( produc921874948t_char @ A_1 @ B_14 ) ) ).
thf(fact_306_prod_Oexhaust,axiom,
! [Y_11: produc1180562163on_val] :
~ ! [A_1: list_exp_list_char,B_14: produc2090907612on_val] :
( Y_11
!= ( produc1302104557on_val @ A_1 @ B_14 ) ) ).
thf(fact_307_prod_Oexhaust,axiom,
! [Y_11: produc618524391on_val] :
~ ! [A_1: produc1180562163on_val,B_14: produc1180562163on_val] :
( Y_11
!= ( produc747700183on_val @ A_1 @ B_14 ) ) ).
thf(fact_308_prod_Oexhaust,axiom,
! [Y_11: product_prod_val_val] :
~ ! [A_1: val,B_14: val] :
( Y_11
!= ( product_Pair_val_val @ A_1 @ B_14 ) ) ).
thf(fact_309_prod_Oexhaust,axiom,
! [Y_11: produc1645268488al_val] :
~ ! [A_1: bop,B_14: product_prod_val_val] :
( Y_11
!= ( produc621191550al_val @ A_1 @ B_14 ) ) ).
thf(fact_310_prod_Oexhaust,axiom,
! [Y_11: produc1278157519t_char] :
~ ! [A_1: list_char,B_14: list_char] :
( Y_11
!= ( produc5062597t_char @ A_1 @ B_14 ) ) ).
thf(fact_311_prod_Oexhaust,axiom,
! [Y_11: produc2088785539on_val] :
~ ! [A_1: list_char,B_14: produc1278157519t_char > option_val] :
( Y_11
!= ( produc926070009on_val @ A_1 @ B_14 ) ) ).
thf(fact_312_prod_Oexhaust,axiom,
! [Y_11: produc2090907612on_val] :
~ ! [A_1: nat > option1728594148on_val,B_14: list_char > option_val] :
( Y_11
!= ( produc755559506on_val @ A_1 @ B_14 ) ) ).
thf(fact_313_prod_Oexhaust,axiom,
! [Y_11: produc1282892786on_val] :
~ ! [A_1: exp_list_char,B_14: produc2090907612on_val] :
( Y_11
!= ( produc235638504on_val @ A_1 @ B_14 ) ) ).
thf(fact_314_prod_Oexhaust,axiom,
! [Y_11: produc1746408499on_val] :
~ ! [A_1: produc1282892786on_val,B_14: produc1282892786on_val] :
( Y_11
!= ( produc833389609on_val @ A_1 @ B_14 ) ) ).
thf(fact_315_PairE,axiom,
! [P_25: produc809539159t_char] :
~ ! [X: list_list_char,Y_1: exp_list_char] :
( P_25
!= ( produc1147572817t_char @ X @ Y_1 ) ) ).
thf(fact_316_PairE,axiom,
! [P_25: produc2146869324t_char] :
~ ! [X: list_P1940453997har_ty,Y_1: list_P341299826t_char] :
( P_25
!= ( produc1152259904t_char @ X @ Y_1 ) ) ).
thf(fact_317_PairE,axiom,
! [P_25: produc952412819t_char] :
~ ! [X: list_char,Y_1: produc2146869324t_char] :
( P_25
!= ( produc1483578759t_char @ X @ Y_1 ) ) ).
thf(fact_318_PairE,axiom,
! [P_25: produc1971331930t_char] :
~ ! [X: list_char,Y_1: produc952412819t_char] :
( P_25
!= ( produc822965838t_char @ X @ Y_1 ) ) ).
thf(fact_319_PairE,axiom,
! [P_25: produc662261637t_char] :
~ ! [X: list_val,Y_1: exp_list_char] :
( P_25
!= ( produc1916172923t_char @ X @ Y_1 ) ) ).
thf(fact_320_PairE,axiom,
! [P_25: produc220283002t_char] :
~ ! [X: list_ty,Y_1: produc662261637t_char] :
( P_25
!= ( produc1909267824t_char @ X @ Y_1 ) ) ).
thf(fact_321_PairE,axiom,
! [P_25: produc1285161482t_char] :
~ ! [X: list_list_char,Y_1: produc220283002t_char] :
( P_25
!= ( produc921874948t_char @ X @ Y_1 ) ) ).
thf(fact_322_PairE,axiom,
! [P_25: produc1180562163on_val] :
~ ! [X: list_exp_list_char,Y_1: produc2090907612on_val] :
( P_25
!= ( produc1302104557on_val @ X @ Y_1 ) ) ).
thf(fact_323_PairE,axiom,
! [P_25: produc618524391on_val] :
~ ! [X: produc1180562163on_val,Y_1: produc1180562163on_val] :
( P_25
!= ( produc747700183on_val @ X @ Y_1 ) ) ).
thf(fact_324_PairE,axiom,
! [P_25: product_prod_val_val] :
~ ! [X: val,Y_1: val] :
( P_25
!= ( product_Pair_val_val @ X @ Y_1 ) ) ).
thf(fact_325_PairE,axiom,
! [P_25: produc1645268488al_val] :
~ ! [X: bop,Y_1: product_prod_val_val] :
( P_25
!= ( produc621191550al_val @ X @ Y_1 ) ) ).
thf(fact_326_PairE,axiom,
! [P_25: produc1278157519t_char] :
~ ! [X: list_char,Y_1: list_char] :
( P_25
!= ( produc5062597t_char @ X @ Y_1 ) ) ).
thf(fact_327_PairE,axiom,
! [P_25: produc2088785539on_val] :
~ ! [X: list_char,Y_1: produc1278157519t_char > option_val] :
( P_25
!= ( produc926070009on_val @ X @ Y_1 ) ) ).
thf(fact_328_PairE,axiom,
! [P_25: produc2090907612on_val] :
~ ! [X: nat > option1728594148on_val,Y_1: list_char > option_val] :
( P_25
!= ( produc755559506on_val @ X @ Y_1 ) ) ).
thf(fact_329_PairE,axiom,
! [P_25: produc1282892786on_val] :
~ ! [X: exp_list_char,Y_1: produc2090907612on_val] :
( P_25
!= ( produc235638504on_val @ X @ Y_1 ) ) ).
thf(fact_330_PairE,axiom,
! [P_25: produc1746408499on_val] :
~ ! [X: produc1282892786on_val,Y_1: produc1282892786on_val] :
( P_25
!= ( produc833389609on_val @ X @ Y_1 ) ) ).
thf(fact_331_split__paired__Ex,axiom,
! [P_24: produc809539159t_char > $o] :
( ( ?? @ produc809539159t_char @ P_24 )
<=> ? [A_1: list_list_char,B_14: exp_list_char] : ( P_24 @ ( produc1147572817t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_332_split__paired__Ex,axiom,
! [P_24: produc2146869324t_char > $o] :
( ( ?? @ produc2146869324t_char @ P_24 )
<=> ? [A_1: list_P1940453997har_ty,B_14: list_P341299826t_char] : ( P_24 @ ( produc1152259904t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_333_split__paired__Ex,axiom,
! [P_24: produc952412819t_char > $o] :
( ( ?? @ produc952412819t_char @ P_24 )
<=> ? [A_1: list_char,B_14: produc2146869324t_char] : ( P_24 @ ( produc1483578759t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_334_split__paired__Ex,axiom,
! [P_24: produc1971331930t_char > $o] :
( ( ?? @ produc1971331930t_char @ P_24 )
<=> ? [A_1: list_char,B_14: produc952412819t_char] : ( P_24 @ ( produc822965838t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_335_split__paired__Ex,axiom,
! [P_24: produc662261637t_char > $o] :
( ( ?? @ produc662261637t_char @ P_24 )
<=> ? [A_1: list_val,B_14: exp_list_char] : ( P_24 @ ( produc1916172923t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_336_split__paired__Ex,axiom,
! [P_24: produc220283002t_char > $o] :
( ( ?? @ produc220283002t_char @ P_24 )
<=> ? [A_1: list_ty,B_14: produc662261637t_char] : ( P_24 @ ( produc1909267824t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_337_split__paired__Ex,axiom,
! [P_24: produc1285161482t_char > $o] :
( ( ?? @ produc1285161482t_char @ P_24 )
<=> ? [A_1: list_list_char,B_14: produc220283002t_char] : ( P_24 @ ( produc921874948t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_338_split__paired__Ex,axiom,
! [P_24: produc1180562163on_val > $o] :
( ( ?? @ produc1180562163on_val @ P_24 )
<=> ? [A_1: list_exp_list_char,B_14: produc2090907612on_val] : ( P_24 @ ( produc1302104557on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_339_split__paired__Ex,axiom,
! [P_24: produc618524391on_val > $o] :
( ( ?? @ produc618524391on_val @ P_24 )
<=> ? [A_1: produc1180562163on_val,B_14: produc1180562163on_val] : ( P_24 @ ( produc747700183on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_340_split__paired__Ex,axiom,
! [P_24: product_prod_val_val > $o] :
( ( ?? @ product_prod_val_val @ P_24 )
<=> ? [A_1: val,B_14: val] : ( P_24 @ ( product_Pair_val_val @ A_1 @ B_14 ) ) ) ).
thf(fact_341_split__paired__Ex,axiom,
! [P_24: produc1645268488al_val > $o] :
( ( ?? @ produc1645268488al_val @ P_24 )
<=> ? [A_1: bop,B_14: product_prod_val_val] : ( P_24 @ ( produc621191550al_val @ A_1 @ B_14 ) ) ) ).
thf(fact_342_split__paired__Ex,axiom,
! [P_24: produc1278157519t_char > $o] :
( ( ?? @ produc1278157519t_char @ P_24 )
<=> ? [A_1: list_char,B_14: list_char] : ( P_24 @ ( produc5062597t_char @ A_1 @ B_14 ) ) ) ).
thf(fact_343_split__paired__Ex,axiom,
! [P_24: produc2088785539on_val > $o] :
( ( ?? @ produc2088785539on_val @ P_24 )
<=> ? [A_1: list_char,B_14: produc1278157519t_char > option_val] : ( P_24 @ ( produc926070009on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_344_split__paired__Ex,axiom,
! [P_24: produc2090907612on_val > $o] :
( ( ?? @ produc2090907612on_val @ P_24 )
<=> ? [A_1: nat > option1728594148on_val,B_14: list_char > option_val] : ( P_24 @ ( produc755559506on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_345_split__paired__Ex,axiom,
! [P_24: produc1282892786on_val > $o] :
( ( ?? @ produc1282892786on_val @ P_24 )
<=> ? [A_1: exp_list_char,B_14: produc2090907612on_val] : ( P_24 @ ( produc235638504on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_346_split__paired__Ex,axiom,
! [P_24: produc1746408499on_val > $o] :
( ( ?? @ produc1746408499on_val @ P_24 )
<=> ? [A_1: produc1282892786on_val,B_14: produc1282892786on_val] : ( P_24 @ ( produc833389609on_val @ A_1 @ B_14 ) ) ) ).
thf(fact_347_widen__trans,axiom,
! [T_13: ty,P_23: list_P1999446415t_char,S_11: ty,U_1: ty] :
( ( widen_2090681816t_char @ P_23 @ S_11 @ U_1 )
=> ( ( widen_2090681816t_char @ P_23 @ U_1 @ T_13 )
=> ( widen_2090681816t_char @ P_23 @ S_11 @ T_13 ) ) ) ).
thf(fact_348_InitBlockRed_I5_J,axiom,
wTrt_1 @ 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_349_sconf__def,axiom,
! [P: list_P1999446415t_char,E_2: list_char > option_ty,S: produc2090907612on_val] :
( ( typeSa816273224_sconf @ P @ E_2 @ S )
<=> ( produc252486962_val_o
@ ^ [H_4: nat > option1728594148on_val,L_4: list_char > option_val] : ( (&) @ ( hconf_97414254t_char @ P @ H_4 ) @ ( lconf_496643946t_char @ P @ H_4 @ L_4 @ E_2 ) )
@ S ) ) ).
thf(fact_350_red__hext__incr,axiom,
! [E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) ) @ ( red @ P ) )
=> ( hext @ H_1 @ H ) ) ).
thf(fact_351_red__preserves__defass,axiom,
! [E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L: 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_1 @ L_1 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) ) @ ( red @ P ) )
=> ( ( d_list_char @ E_1 @ ( some_list_char_o @ ( dom_list_char_val @ L_1 ) ) )
=> ( d_list_char @ E @ ( some_list_char_o @ ( dom_list_char_val @ L ) ) ) ) ) ) ).
thf(fact_352_option_Oinject,axiom,
! [A_71: nat,A_70: nat] :
( ( ( some_nat @ A_71 )
= ( some_nat @ A_70 ) )
<=> ( A_71 = A_70 ) ) ).
thf(fact_353_option_Oinject,axiom,
! [A_71: produc2088785539on_val,A_70: produc2088785539on_val] :
( ( ( some_P451527732on_val @ A_71 )
= ( some_P451527732on_val @ A_70 ) )
<=> ( A_71 = A_70 ) ) ).
thf(fact_354_option_Oinject,axiom,
! [A_71: ty,A_70: ty] :
( ( ( some_ty @ A_71 )
= ( some_ty @ A_70 ) )
<=> ( A_71 = A_70 ) ) ).
thf(fact_355_option_Oinject,axiom,
! [A_71: list_char > $o,A_70: list_char > $o] :
( ( ( some_list_char_o @ A_71 )
= ( some_list_char_o @ A_70 ) )
<=> ( A_71 = A_70 ) ) ).
thf(fact_356_option_Oinject,axiom,
! [A_71: val,A_70: val] :
( ( ( some_val @ A_71 )
= ( some_val @ A_70 ) )
<=> ( A_71 = A_70 ) ) ).
thf(fact_357_curryI,axiom,
! [F_16: produc809539159t_char > $o,A_69: list_list_char,B_39: exp_list_char] :
( ( F_16 @ ( produc1147572817t_char @ A_69 @ B_39 ) )
=> ( produc1404278138char_o @ F_16 @ A_69 @ B_39 ) ) ).
thf(fact_358_curryI,axiom,
! [F_16: produc2146869324t_char > $o,A_69: list_P1940453997har_ty,B_39: list_P341299826t_char] :
( ( F_16 @ ( produc1152259904t_char @ A_69 @ B_39 ) )
=> ( produc2107091019char_o @ F_16 @ A_69 @ B_39 ) ) ).
thf(fact_359_curryI,axiom,
! [F_16: produc952412819t_char > $o,A_69: list_char,B_39: produc2146869324t_char] :
( ( F_16 @ ( produc1483578759t_char @ A_69 @ B_39 ) )
=> ( produc325775556char_o @ F_16 @ A_69 @ B_39 ) ) ).
thf(fact_360_curryI,axiom,
! [F_16: produc1971331930t_char > $o,A_69: list_char,B_39: produc952412819t_char] :
( ( F_16 @ ( produc822965838t_char @ A_69 @ B_39 ) )
=> ( produc1383007933char_o @ F_16 @ A_69 @ B_39 ) ) ).
thf(fact_361_curryI,axiom,
! [F_16: produc662261637t_char > $o,A_69: list_val,B_39: exp_list_char] :
( ( F_16 @ ( produc1916172923t_char @ A_69 @ B_39 ) )
=> ( produc1072551658char_o @ F_16 @ A_69 @ B_39 ) ) ).
thf(fact_362_curryI,axiom,
! [F_16: produc220283002t_char > $o,A_69: list_ty,B_39: produc662261637t_char] :
( ( F_16 @ ( produc1909267824t_char @ A_69 @ B_39 ) )
=> ( produc786676533char_o @ F_16 @ A_69 @ B_39 ) ) ).
thf(fact_363_curryI,axiom,
! [F_16: produc1285161482t_char > $o,A_69: list_list_char,B_39: produc220283002t_char] :
( ( F_16 @ ( produc921874948t_char @ A_69 @ B_39 ) )
=> ( produc193646727char_o @ F_16 @ A_69 @ B_39 ) ) ).
thf(fact_364_curryI,axiom,
! [F_16: produc1180562163on_val > $o,A_69: list_exp_list_char,B_39: produc2090907612on_val] :
( ( F_16 @ ( produc1302104557on_val @ A_69 @ B_39 ) )
=> ( produc618849246_val_o @ F_16 @ A_69 @ B_39 ) ) ).
thf(fact_365_curryI,axiom,
! [F_16: produc618524391on_val > $o,A_69: produc1180562163on_val,B_39: produc1180562163on_val] :
( ( F_16 @ ( produc747700183on_val @ A_69 @ B_39 ) )
=> ( produc551782158_val_o @ F_16 @ A_69 @ B_39 ) ) ).
thf(fact_366_curryI,axiom,
! [F_16: product_prod_val_val > $o,A_69: val,B_39: val] :
( ( F_16 @ ( product_Pair_val_val @ A_69 @ B_39 ) )
=> ( produc575837646_val_o @ F_16 @ A_69 @ B_39 ) ) ).
thf(fact_367_curryI,axiom,
! [F_16: produc1645268488al_val > $o,A_69: bop,B_39: product_prod_val_val] :
( ( F_16 @ ( produc621191550al_val @ A_69 @ B_39 ) )
=> ( produc275195559_val_o @ F_16 @ A_69 @ B_39 ) ) ).
thf(fact_368_curryI,axiom,
! [F_16: produc1278157519t_char > $o,A_69: list_char,B_39: list_char] :
( ( F_16 @ ( produc5062597t_char @ A_69 @ B_39 ) )
=> ( produc1709467424char_o @ F_16 @ A_69 @ B_39 ) ) ).
thf(fact_369_curryI,axiom,
! [F_16: produc2088785539on_val > $o,A_69: list_char,B_39: produc1278157519t_char > option_val] :
( ( F_16 @ ( produc926070009on_val @ A_69 @ B_39 ) )
=> ( produc1177570924_val_o @ F_16 @ A_69 @ B_39 ) ) ).
thf(fact_370_curryI,axiom,
! [F_16: produc2090907612on_val > $o,A_69: nat > option1728594148on_val,B_39: list_char > option_val] :
( ( F_16 @ ( produc755559506on_val @ A_69 @ B_39 ) )
=> ( produc1402621651_val_o @ F_16 @ A_69 @ B_39 ) ) ).
thf(fact_371_curryI,axiom,
! [F_16: produc1282892786on_val > $o,A_69: exp_list_char,B_39: produc2090907612on_val] :
( ( F_16 @ ( produc235638504on_val @ A_69 @ B_39 ) )
=> ( produc1287763389_val_o @ F_16 @ A_69 @ B_39 ) ) ).
thf(fact_372_curryI,axiom,
! [F_16: produc1746408499on_val > $o,A_69: produc1282892786on_val,B_39: produc1282892786on_val] :
( ( F_16 @ ( produc833389609on_val @ A_69 @ B_39 ) )
=> ( produc803302844_val_o @ F_16 @ A_69 @ B_39 ) ) ).
thf(fact_373_red__lcl__add,axiom,
! [L_0: list_char > option_val,E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ ( map_ad325961431ar_val @ L_0 @ L_1 ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ ( map_ad325961431ar_val @ L_0 @ L ) ) ) ) @ ( red @ P ) ) ) ).
thf(fact_374_lconf__upd,axiom,
! [V_12: list_char,V_11: val,T_12: ty,P_22: list_P1999446415t_char,H_16: nat > option1728594148on_val,L_8: list_char > option_val,E_11: list_char > option_ty] :
( ( lconf_496643946t_char @ P_22 @ H_16 @ L_8 @ E_11 )
=> ( ( conf_P373316194t_char @ P_22 @ H_16 @ V_11 @ T_12 )
=> ( ( ( E_11 @ V_12 )
= ( some_ty @ T_12 ) )
=> ( lconf_496643946t_char @ P_22 @ H_16 @ ( fun_up1149430426on_val @ L_8 @ V_12 @ ( some_val @ V_11 ) ) @ E_11 ) ) ) ) ).
thf(fact_375_lconf__upd2,axiom,
! [V_10: list_char,V_9: val,T_11: ty,P_21: list_P1999446415t_char,H_15: nat > option1728594148on_val,L_7: list_char > option_val,E_10: list_char > option_ty] :
( ( lconf_496643946t_char @ P_21 @ H_15 @ L_7 @ E_10 )
=> ( ( conf_P373316194t_char @ P_21 @ H_15 @ V_9 @ T_11 )
=> ( lconf_496643946t_char @ P_21 @ H_15 @ ( fun_up1149430426on_val @ L_7 @ V_10 @ ( some_val @ V_9 ) ) @ ( fun_up424764369ion_ty @ E_10 @ V_10 @ ( some_ty @ T_11 ) ) ) ) ) ).
thf(fact_376_in__lex__prod,axiom,
! [A_68: list_exp_list_char,B_38: produc2090907612on_val,A_67: list_exp_list_char,B_37: produc2090907612on_val,R_18: produc91527719t_char > $o,S_10: produc1581780743on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ A_68 @ B_38 ) @ ( produc1302104557on_val @ A_67 @ B_37 ) ) @ ( lex_pr855826389on_val @ R_18 @ S_10 ) )
<=> ( ( member894971540t_char @ ( produc1237966615t_char @ A_68 @ A_67 ) @ R_18 )
| ( ( A_68 = A_67 )
& ( member565037556on_val @ ( produc259392253on_val @ B_38 @ B_37 ) @ S_10 ) ) ) ) ).
thf(fact_377_in__lex__prod,axiom,
! [A_68: exp_list_char,B_38: produc2090907612on_val,A_67: exp_list_char,B_37: produc2090907612on_val,R_18: produc2048519645t_char > $o,S_10: produc1581780743on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ A_68 @ B_38 ) @ ( produc235638504on_val @ A_67 @ B_37 ) ) @ ( lex_pr1492265728on_val @ R_18 @ S_10 ) )
<=> ( ( member1199939018t_char @ ( produc943465171t_char @ A_68 @ A_67 ) @ R_18 )
| ( ( A_68 = A_67 )
& ( member565037556on_val @ ( produc259392253on_val @ B_38 @ B_37 ) @ S_10 ) ) ) ) ).
thf(fact_378_in__lex__prod,axiom,
! [A_68: list_list_char,B_38: exp_list_char,A_67: list_list_char,B_37: exp_list_char,R_18: produc1200003175t_char > $o,S_10: produc2048519645t_char > $o] :
( ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ A_68 @ B_38 ) @ ( produc1147572817t_char @ A_67 @ B_37 ) ) @ ( lex_pr1787105337t_char @ R_18 @ S_10 ) )
<=> ( ( member817832404t_char @ ( produc2035944023t_char @ A_68 @ A_67 ) @ R_18 )
| ( ( A_68 = A_67 )
& ( member1199939018t_char @ ( produc943465171t_char @ B_38 @ B_37 ) @ S_10 ) ) ) ) ).
thf(fact_379_in__lex__prod,axiom,
! [A_68: list_P1940453997har_ty,B_38: list_P341299826t_char,A_67: list_P1940453997har_ty,B_37: list_P341299826t_char,R_18: produc450000425har_ty > $o,S_10: produc244676007t_char > $o] :
( ( member1551446420t_char @ ( produc635935767t_char @ ( produc1152259904t_char @ A_68 @ B_38 ) @ ( produc1152259904t_char @ A_67 @ B_37 ) ) @ ( lex_pr213428520t_char @ R_18 @ S_10 ) )
<=> ( ( member520253462har_ty @ ( produc1860789535har_ty @ A_68 @ A_67 ) @ R_18 )
| ( ( A_68 = A_67 )
& ( member1580476948t_char @ ( produc436875159t_char @ B_38 @ B_37 ) @ S_10 ) ) ) ) ).
thf(fact_380_in__lex__prod,axiom,
! [A_68: list_char,B_38: produc2146869324t_char,A_67: list_char,B_37: produc2146869324t_char,R_18: produc1278157519t_char > $o,S_10: produc494726439t_char > $o] :
( ( member1607118676t_char @ ( produc1431439831t_char @ ( produc1483578759t_char @ A_68 @ B_38 ) @ ( produc1483578759t_char @ A_67 @ B_37 ) ) @ ( lex_pr167435119t_char @ R_18 @ S_10 ) )
<=> ( ( member1251428284t_char @ ( produc5062597t_char @ A_68 @ A_67 ) @ R_18 )
| ( ( A_68 = A_67 )
& ( member1551446420t_char @ ( produc635935767t_char @ B_38 @ B_37 ) @ S_10 ) ) ) ) ).
thf(fact_381_in__lex__prod,axiom,
! [A_68: list_char,B_38: produc952412819t_char,A_67: list_char,B_37: produc952412819t_char,R_18: produc1278157519t_char > $o,S_10: produc740765671t_char > $o] :
( ( member162552852t_char @ ( produc1641293463t_char @ ( produc822965838t_char @ A_68 @ B_38 ) @ ( produc822965838t_char @ A_67 @ B_37 ) ) @ ( lex_pr1668767798t_char @ R_18 @ S_10 ) )
<=> ( ( member1251428284t_char @ ( produc5062597t_char @ A_68 @ A_67 ) @ R_18 )
| ( ( A_68 = A_67 )
& ( member1607118676t_char @ ( produc1431439831t_char @ B_38 @ B_37 ) @ S_10 ) ) ) ) ).
thf(fact_382_in__lex__prod,axiom,
! [A_68: list_val,B_38: exp_list_char,A_67: list_val,B_37: exp_list_char,R_18: produc753553453st_val > $o,S_10: produc2048519645t_char > $o] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ A_68 @ B_38 ) @ ( produc1916172923t_char @ A_67 @ B_37 ) ) @ ( lex_pr307591827t_char @ R_18 @ S_10 ) )
<=> ( ( member273646106st_val @ ( produc2078839843st_val @ A_68 @ A_67 ) @ R_18 )
| ( ( A_68 = A_67 )
& ( member1199939018t_char @ ( produc943465171t_char @ B_38 @ B_37 ) @ S_10 ) ) ) ) ).
thf(fact_383_in__lex__prod,axiom,
! [A_68: list_ty,B_38: produc662261637t_char,A_67: list_ty,B_37: produc662261637t_char,R_18: produc1420746395ist_ty > $o,S_10: produc1826280281t_char > $o] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ A_68 @ B_38 ) @ ( produc1909267824t_char @ A_67 @ B_37 ) ) @ ( lex_pr1588300168t_char @ R_18 @ S_10 ) )
<=> ( ( member104734088ist_ty @ ( produc512429457ist_ty @ A_68 @ A_67 ) @ R_18 )
| ( ( A_68 = A_67 )
& ( member1161907014t_char @ ( produc1299387215t_char @ B_38 @ B_37 ) @ S_10 ) ) ) ) ).
thf(fact_384_in__lex__prod,axiom,
! [A_68: list_list_char,B_38: produc220283002t_char,A_67: list_list_char,B_37: produc220283002t_char,R_18: produc1200003175t_char > $o,S_10: produc1406897475t_char > $o] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ A_68 @ B_38 ) @ ( produc921874948t_char @ A_67 @ B_37 ) ) @ ( lex_pr1876288492t_char @ R_18 @ S_10 ) )
<=> ( ( member817832404t_char @ ( produc2035944023t_char @ A_68 @ A_67 ) @ R_18 )
| ( ( A_68 = A_67 )
& ( member125098544t_char @ ( produc57279289t_char @ B_38 @ B_37 ) @ S_10 ) ) ) ) ).
thf(fact_385_in__lex__prod,axiom,
! [A_68: produc1180562163on_val,B_38: produc1180562163on_val,A_67: produc1180562163on_val,B_37: produc1180562163on_val,R_18: produc618524391on_val > $o,S_10: produc618524391on_val > $o] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ A_68 @ B_38 ) @ ( produc747700183on_val @ A_67 @ B_37 ) ) @ ( lex_pr1943870447on_val @ R_18 @ S_10 ) )
<=> ( ( member2042188884on_val @ ( produc747700183on_val @ A_68 @ A_67 ) @ R_18 )
| ( ( A_68 = A_67 )
& ( member2042188884on_val @ ( produc747700183on_val @ B_38 @ B_37 ) @ S_10 ) ) ) ) ).
thf(fact_386_in__lex__prod,axiom,
! [A_68: val,B_38: val,A_67: val,B_37: val,R_18: product_prod_val_val > $o,S_10: product_prod_val_val > $o] :
( ( member837208074al_val @ ( produc1244920211al_val @ ( product_Pair_val_val @ A_68 @ B_38 ) @ ( product_Pair_val_val @ A_67 @ B_37 ) ) @ ( lex_prod_val_val @ R_18 @ S_10 ) )
<=> ( ( member649088532al_val @ ( product_Pair_val_val @ A_68 @ A_67 ) @ R_18 )
| ( ( A_68 = A_67 )
& ( member649088532al_val @ ( product_Pair_val_val @ B_38 @ B_37 ) @ S_10 ) ) ) ) ).
thf(fact_387_in__lex__prod,axiom,
! [A_68: bop,B_38: product_prod_val_val,A_67: bop,B_37: product_prod_val_val,R_18: product_prod_bop_bop > $o,S_10: produc800118557al_val > $o] :
( ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ A_68 @ B_38 ) @ ( produc621191550al_val @ A_67 @ B_37 ) ) @ ( lex_pr1932514710al_val @ R_18 @ S_10 ) )
<=> ( ( member978285664op_bop @ ( product_Pair_bop_bop @ A_68 @ A_67 ) @ R_18 )
| ( ( A_68 = A_67 )
& ( member837208074al_val @ ( produc1244920211al_val @ B_38 @ B_37 ) @ S_10 ) ) ) ) ).
thf(fact_388_in__lex__prod,axiom,
! [A_68: list_char,B_38: list_char,A_67: list_char,B_37: list_char,R_18: produc1278157519t_char > $o,S_10: produc1278157519t_char > $o] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ A_68 @ B_38 ) @ ( produc5062597t_char @ A_67 @ B_37 ) ) @ ( lex_pr280535005t_char @ R_18 @ S_10 ) )
<=> ( ( member1251428284t_char @ ( produc5062597t_char @ A_68 @ A_67 ) @ R_18 )
| ( ( A_68 = A_67 )
& ( member1251428284t_char @ ( produc5062597t_char @ B_38 @ B_37 ) @ S_10 ) ) ) ) ).
thf(fact_389_in__lex__prod,axiom,
! [A_68: list_char,B_38: produc1278157519t_char > option_val,A_67: list_char,B_37: produc1278157519t_char > option_val,R_18: produc1278157519t_char > $o,S_10: produc688860215on_val > $o] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ A_68 @ B_38 ) @ ( produc926070009on_val @ A_67 @ B_37 ) ) @ ( lex_pr697649425on_val @ R_18 @ S_10 ) )
<=> ( ( member1251428284t_char @ ( produc5062597t_char @ A_68 @ A_67 ) @ R_18 )
| ( ( A_68 = A_67 )
& ( member1448924196on_val @ ( produc253229997on_val @ B_38 @ B_37 ) @ S_10 ) ) ) ) ).
thf(fact_390_in__lex__prod,axiom,
! [A_68: nat > option1728594148on_val,B_38: list_char > option_val,A_67: nat > option1728594148on_val,B_37: list_char > option_val,R_18: produc1287081631on_val > $o,S_10: produc774316953on_val > $o] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ A_68 @ B_38 ) @ ( produc755559506on_val @ A_67 @ B_37 ) ) @ ( lex_pr359407722on_val @ R_18 @ S_10 ) )
<=> ( ( member112887436on_val @ ( produc1208913941on_val @ A_68 @ A_67 ) @ R_18 )
| ( ( A_68 = A_67 )
& ( member1838289030on_val @ ( produc1338265359on_val @ B_38 @ B_37 ) @ S_10 ) ) ) ) ).
thf(fact_391_in__lex__prod,axiom,
! [A_68: produc1282892786on_val,B_38: produc1282892786on_val,A_67: produc1282892786on_val,B_37: produc1282892786on_val,R_18: produc1746408499on_val > $o,S_10: produc1746408499on_val > $o] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ A_68 @ B_38 ) @ ( produc833389609on_val @ A_67 @ B_37 ) ) @ ( lex_pr296420417on_val @ R_18 @ S_10 ) )
<=> ( ( member1913460000on_val @ ( produc833389609on_val @ A_68 @ A_67 ) @ R_18 )
| ( ( A_68 = A_67 )
& ( member1913460000on_val @ ( produc833389609on_val @ B_38 @ B_37 ) @ S_10 ) ) ) ) ).
thf(fact_392_prod__caseI,axiom,
! [F1_1: list_list_char > exp_list_char > $o,A_66: list_list_char,B_36: exp_list_char] :
( ( F1_1 @ A_66 @ B_36 )
=> ( produc1596287579char_o @ F1_1 @ ( produc1147572817t_char @ A_66 @ B_36 ) ) ) ).
thf(fact_393_prod__caseI,axiom,
! [F1_1: list_P1940453997har_ty > list_P341299826t_char > $o,A_66: list_P1940453997har_ty,B_36: list_P341299826t_char] :
( ( F1_1 @ A_66 @ B_36 )
=> ( produc875422124char_o @ F1_1 @ ( produc1152259904t_char @ A_66 @ B_36 ) ) ) ).
thf(fact_394_prod__caseI,axiom,
! [F1_1: list_char > produc2146869324t_char > $o,A_66: list_char,B_36: produc2146869324t_char] :
( ( F1_1 @ A_66 @ B_36 )
=> ( produc781483429char_o @ F1_1 @ ( produc1483578759t_char @ A_66 @ B_36 ) ) ) ).
thf(fact_395_prod__caseI,axiom,
! [F1_1: list_char > produc952412819t_char > $o,A_66: list_char,B_36: produc952412819t_char] :
( ( F1_1 @ A_66 @ B_36 )
=> ( produc1519396638char_o @ F1_1 @ ( produc822965838t_char @ A_66 @ B_36 ) ) ) ).
thf(fact_396_prod__caseI,axiom,
! [F1_1: list_val > exp_list_char > $o,A_66: list_val,B_36: exp_list_char] :
( ( F1_1 @ A_66 @ B_36 )
=> ( produc525137097char_o @ F1_1 @ ( produc1916172923t_char @ A_66 @ B_36 ) ) ) ).
thf(fact_397_prod__caseI,axiom,
! [F1_1: list_ty > produc662261637t_char > $o,A_66: list_ty,B_36: produc662261637t_char] :
( ( F1_1 @ A_66 @ B_36 )
=> ( produc861054100char_o @ F1_1 @ ( produc1909267824t_char @ A_66 @ B_36 ) ) ) ).
thf(fact_398_prod__caseI,axiom,
! [F1_1: list_list_char > produc220283002t_char > $o,A_66: list_list_char,B_36: produc220283002t_char] :
( ( F1_1 @ A_66 @ B_36 )
=> ( produc1530867176char_o @ F1_1 @ ( produc921874948t_char @ A_66 @ B_36 ) ) ) ).
thf(fact_399_prod__caseI,axiom,
! [F1_1: list_exp_list_char > produc2090907612on_val > $o,A_66: list_exp_list_char,B_36: produc2090907612on_val] :
( ( F1_1 @ A_66 @ B_36 )
=> ( produc1841295295_val_o @ F1_1 @ ( produc1302104557on_val @ A_66 @ B_36 ) ) ) ).
thf(fact_400_prod__caseI,axiom,
! [F1_1: produc1180562163on_val > produc1180562163on_val > $o,A_66: produc1180562163on_val,B_36: produc1180562163on_val] :
( ( F1_1 @ A_66 @ B_36 )
=> ( produc2136448621_val_o @ F1_1 @ ( produc747700183on_val @ A_66 @ B_36 ) ) ) ).
thf(fact_401_prod__caseI,axiom,
! [F1_1: val > val > $o,A_66: val,B_36: val] :
( ( F1_1 @ A_66 @ B_36 )
=> ( produc9430317_val_o @ F1_1 @ ( product_Pair_val_val @ A_66 @ B_36 ) ) ) ).
thf(fact_402_prod__caseI,axiom,
! [F1_1: bop > product_prod_val_val > $o,A_66: bop,B_36: product_prod_val_val] :
( ( F1_1 @ A_66 @ B_36 )
=> ( produc1063861510_val_o @ F1_1 @ ( produc621191550al_val @ A_66 @ B_36 ) ) ) ).
thf(fact_403_prod__caseI,axiom,
! [F1_1: list_char > list_char > $o,A_66: list_char,B_36: list_char] :
( ( F1_1 @ A_66 @ B_36 )
=> ( produc282231039char_o @ F1_1 @ ( produc5062597t_char @ A_66 @ B_36 ) ) ) ).
thf(fact_404_prod__caseI,axiom,
! [F1_1: list_char > ( produc1278157519t_char > option_val ) > $o,A_66: list_char,B_36: produc1278157519t_char > option_val] :
( ( F1_1 @ A_66 @ B_36 )
=> ( produc765165771_val_o @ F1_1 @ ( produc926070009on_val @ A_66 @ B_36 ) ) ) ).
thf(fact_405_prod__caseI,axiom,
! [F1_1: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,A_66: nat > option1728594148on_val,B_36: list_char > option_val] :
( ( F1_1 @ A_66 @ B_36 )
=> ( produc252486962_val_o @ F1_1 @ ( produc755559506on_val @ A_66 @ B_36 ) ) ) ).
thf(fact_406_prod__caseI,axiom,
! [F1_1: exp_list_char > produc2090907612on_val > $o,A_66: exp_list_char,B_36: produc2090907612on_val] :
( ( F1_1 @ A_66 @ B_36 )
=> ( produc1835097372_val_o @ F1_1 @ ( produc235638504on_val @ A_66 @ B_36 ) ) ) ).
thf(fact_407_prod__caseI,axiom,
! [F1_1: produc1282892786on_val > produc1282892786on_val > $o,A_66: produc1282892786on_val,B_36: produc1282892786on_val] :
( ( F1_1 @ A_66 @ B_36 )
=> ( produc1624062875_val_o @ F1_1 @ ( produc833389609on_val @ A_66 @ B_36 ) ) ) ).
thf(fact_408_splitI,axiom,
! [F_15: list_list_char > exp_list_char > $o,A_65: list_list_char,B_35: exp_list_char] :
( ( F_15 @ A_65 @ B_35 )
=> ( produc1596287579char_o @ F_15 @ ( produc1147572817t_char @ A_65 @ B_35 ) ) ) ).
thf(fact_409_splitI,axiom,
! [F_15: list_P1940453997har_ty > list_P341299826t_char > $o,A_65: list_P1940453997har_ty,B_35: list_P341299826t_char] :
( ( F_15 @ A_65 @ B_35 )
=> ( produc875422124char_o @ F_15 @ ( produc1152259904t_char @ A_65 @ B_35 ) ) ) ).
thf(fact_410_splitI,axiom,
! [F_15: list_char > produc2146869324t_char > $o,A_65: list_char,B_35: produc2146869324t_char] :
( ( F_15 @ A_65 @ B_35 )
=> ( produc781483429char_o @ F_15 @ ( produc1483578759t_char @ A_65 @ B_35 ) ) ) ).
thf(fact_411_splitI,axiom,
! [F_15: list_char > produc952412819t_char > $o,A_65: list_char,B_35: produc952412819t_char] :
( ( F_15 @ A_65 @ B_35 )
=> ( produc1519396638char_o @ F_15 @ ( produc822965838t_char @ A_65 @ B_35 ) ) ) ).
thf(fact_412_splitI,axiom,
! [F_15: list_val > exp_list_char > $o,A_65: list_val,B_35: exp_list_char] :
( ( F_15 @ A_65 @ B_35 )
=> ( produc525137097char_o @ F_15 @ ( produc1916172923t_char @ A_65 @ B_35 ) ) ) ).
thf(fact_413_splitI,axiom,
! [F_15: list_ty > produc662261637t_char > $o,A_65: list_ty,B_35: produc662261637t_char] :
( ( F_15 @ A_65 @ B_35 )
=> ( produc861054100char_o @ F_15 @ ( produc1909267824t_char @ A_65 @ B_35 ) ) ) ).
thf(fact_414_splitI,axiom,
! [F_15: list_list_char > produc220283002t_char > $o,A_65: list_list_char,B_35: produc220283002t_char] :
( ( F_15 @ A_65 @ B_35 )
=> ( produc1530867176char_o @ F_15 @ ( produc921874948t_char @ A_65 @ B_35 ) ) ) ).
thf(fact_415_splitI,axiom,
! [F_15: list_exp_list_char > produc2090907612on_val > $o,A_65: list_exp_list_char,B_35: produc2090907612on_val] :
( ( F_15 @ A_65 @ B_35 )
=> ( produc1841295295_val_o @ F_15 @ ( produc1302104557on_val @ A_65 @ B_35 ) ) ) ).
thf(fact_416_splitI,axiom,
! [F_15: produc1180562163on_val > produc1180562163on_val > $o,A_65: produc1180562163on_val,B_35: produc1180562163on_val] :
( ( F_15 @ A_65 @ B_35 )
=> ( produc2136448621_val_o @ F_15 @ ( produc747700183on_val @ A_65 @ B_35 ) ) ) ).
thf(fact_417_splitI,axiom,
! [F_15: val > val > $o,A_65: val,B_35: val] :
( ( F_15 @ A_65 @ B_35 )
=> ( produc9430317_val_o @ F_15 @ ( product_Pair_val_val @ A_65 @ B_35 ) ) ) ).
thf(fact_418_splitI,axiom,
! [F_15: bop > product_prod_val_val > $o,A_65: bop,B_35: product_prod_val_val] :
( ( F_15 @ A_65 @ B_35 )
=> ( produc1063861510_val_o @ F_15 @ ( produc621191550al_val @ A_65 @ B_35 ) ) ) ).
thf(fact_419_splitI,axiom,
! [F_15: list_char > list_char > $o,A_65: list_char,B_35: list_char] :
( ( F_15 @ A_65 @ B_35 )
=> ( produc282231039char_o @ F_15 @ ( produc5062597t_char @ A_65 @ B_35 ) ) ) ).
thf(fact_420_splitI,axiom,
! [F_15: list_char > ( produc1278157519t_char > option_val ) > $o,A_65: list_char,B_35: produc1278157519t_char > option_val] :
( ( F_15 @ A_65 @ B_35 )
=> ( produc765165771_val_o @ F_15 @ ( produc926070009on_val @ A_65 @ B_35 ) ) ) ).
thf(fact_421_splitI,axiom,
! [F_15: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,A_65: nat > option1728594148on_val,B_35: list_char > option_val] :
( ( F_15 @ A_65 @ B_35 )
=> ( produc252486962_val_o @ F_15 @ ( produc755559506on_val @ A_65 @ B_35 ) ) ) ).
thf(fact_422_splitI,axiom,
! [F_15: exp_list_char > produc2090907612on_val > $o,A_65: exp_list_char,B_35: produc2090907612on_val] :
( ( F_15 @ A_65 @ B_35 )
=> ( produc1835097372_val_o @ F_15 @ ( produc235638504on_val @ A_65 @ B_35 ) ) ) ).
thf(fact_423_splitI,axiom,
! [F_15: produc1282892786on_val > produc1282892786on_val > $o,A_65: produc1282892786on_val,B_35: produc1282892786on_val] :
( ( F_15 @ A_65 @ B_35 )
=> ( produc1624062875_val_o @ F_15 @ ( produc833389609on_val @ A_65 @ B_35 ) ) ) ).
thf(fact_424_map__add__dom__app__simps_I1_J,axiom,
! [L1_2: nat > option1728594148on_val,M_14: nat,L2_2: nat > option1728594148on_val] :
( ( member_nat @ M_14 @ ( dom_na2045926843on_val @ L2_2 ) )
=> ( ( map_ad1851375512on_val @ L1_2 @ L2_2 @ M_14 )
= ( L2_2 @ M_14 ) ) ) ).
thf(fact_425_map__add__dom__app__simps_I1_J,axiom,
! [L1_2: list_char > option_val,M_14: list_char,L2_2: list_char > option_val] :
( ( member_list_char @ M_14 @ ( dom_list_char_val @ L2_2 ) )
=> ( ( map_ad325961431ar_val @ L1_2 @ L2_2 @ M_14 )
= ( L2_2 @ M_14 ) ) ) ).
thf(fact_426_split__weak__cong,axiom,
! [C_19: list_char > ( produc1278157519t_char > option_val ) > option_ty,P_20: produc2088785539on_val,Q_4: produc2088785539on_val] :
( ( P_20 = Q_4 )
=> ( ( produc863160906ion_ty @ C_19 @ P_20 )
= ( produc863160906ion_ty @ C_19 @ Q_4 ) ) ) ).
thf(fact_427_split__weak__cong,axiom,
! [C_19: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,P_20: produc2090907612on_val,Q_4: produc2090907612on_val] :
( ( P_20 = Q_4 )
=> ( ( produc252486962_val_o @ C_19 @ P_20 )
<=> ( produc252486962_val_o @ C_19 @ Q_4 ) ) ) ).
thf(fact_428_map__add__dom__app__simps_I3_J,axiom,
! [L1_1: nat > option1728594148on_val,M_13: nat,L2_1: nat > option1728594148on_val] :
( ~ ( member_nat @ M_13 @ ( dom_na2045926843on_val @ L2_1 ) )
=> ( ( map_ad1851375512on_val @ L1_1 @ L2_1 @ M_13 )
= ( L1_1 @ M_13 ) ) ) ).
thf(fact_429_map__add__dom__app__simps_I3_J,axiom,
! [L1_1: list_char > option_val,M_13: list_char,L2_1: list_char > option_val] :
( ~ ( member_list_char @ M_13 @ ( dom_list_char_val @ L2_1 ) )
=> ( ( map_ad325961431ar_val @ L1_1 @ L2_1 @ M_13 )
= ( L1_1 @ M_13 ) ) ) ).
thf(fact_430_map__add__dom__app__simps_I2_J,axiom,
! [L2: nat > option1728594148on_val,M_12: nat,L1: nat > option1728594148on_val] :
( ~ ( member_nat @ M_12 @ ( dom_na2045926843on_val @ L1 ) )
=> ( ( map_ad1851375512on_val @ L1 @ L2 @ M_12 )
= ( L2 @ M_12 ) ) ) ).
thf(fact_431_map__add__dom__app__simps_I2_J,axiom,
! [L2: list_char > option_val,M_12: list_char,L1: list_char > option_val] :
( ~ ( member_list_char @ M_12 @ ( dom_list_char_val @ L1 ) )
=> ( ( map_ad325961431ar_val @ L1 @ L2 @ M_12 )
= ( L2 @ M_12 ) ) ) ).
thf(fact_432_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_433_split__curry,axiom,
! [F_14: produc2088785539on_val > option_ty] :
( ( produc863160906ion_ty @ ( produc1673424105ion_ty @ F_14 ) )
= F_14 ) ).
thf(fact_434_split__curry,axiom,
! [F_14: produc2090907612on_val > $o] :
( ( produc252486962_val_o @ ( produc1402621651_val_o @ F_14 ) )
= F_14 ) ).
thf(fact_435_curry__split,axiom,
! [F_13: list_char > ( produc1278157519t_char > option_val ) > option_ty] :
( ( produc1673424105ion_ty @ ( produc863160906ion_ty @ F_13 ) )
= F_13 ) ).
thf(fact_436_curry__split,axiom,
! [F_13: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o] :
( ( produc1402621651_val_o @ ( produc252486962_val_o @ F_13 ) )
= F_13 ) ).
thf(fact_437_split__part,axiom,
! [P_19: $o,Q_3: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,X: produc2090907612on_val] :
( ( produc252486962_val_o
@ ^ [A_1: nat > option1728594148on_val,B_14: list_char > option_val] : ( (&) @ P_19 @ ( Q_3 @ A_1 @ B_14 ) )
@ X )
<=> ( P_19
& ( produc252486962_val_o @ Q_3 @ X ) ) ) ).
thf(fact_438_red__reds_ORedInitBlock,axiom,
! [V_1: list_char,T: ty,V: val,U: val,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ ( val_list_char @ U ) ) ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ U ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_439_conf__widen,axiom,
! [T_10: ty,P_18: list_P1999446415t_char,H_14: nat > option1728594148on_val,V_8: val,T_9: ty] :
( ( conf_P373316194t_char @ P_18 @ H_14 @ V_8 @ T_9 )
=> ( ( widen_2090681816t_char @ P_18 @ T_9 @ T_10 )
=> ( conf_P373316194t_char @ P_18 @ H_14 @ V_8 @ T_10 ) ) ) ).
thf(fact_440_splitD,axiom,
! [F_12: list_list_char > exp_list_char > $o,A_64: list_list_char,B_34: exp_list_char] :
( ( produc1596287579char_o @ F_12 @ ( produc1147572817t_char @ A_64 @ B_34 ) )
=> ( F_12 @ A_64 @ B_34 ) ) ).
thf(fact_441_splitD,axiom,
! [F_12: list_P1940453997har_ty > list_P341299826t_char > $o,A_64: list_P1940453997har_ty,B_34: list_P341299826t_char] :
( ( produc875422124char_o @ F_12 @ ( produc1152259904t_char @ A_64 @ B_34 ) )
=> ( F_12 @ A_64 @ B_34 ) ) ).
thf(fact_442_splitD,axiom,
! [F_12: list_char > produc2146869324t_char > $o,A_64: list_char,B_34: produc2146869324t_char] :
( ( produc781483429char_o @ F_12 @ ( produc1483578759t_char @ A_64 @ B_34 ) )
=> ( F_12 @ A_64 @ B_34 ) ) ).
thf(fact_443_splitD,axiom,
! [F_12: list_char > produc952412819t_char > $o,A_64: list_char,B_34: produc952412819t_char] :
( ( produc1519396638char_o @ F_12 @ ( produc822965838t_char @ A_64 @ B_34 ) )
=> ( F_12 @ A_64 @ B_34 ) ) ).
thf(fact_444_splitD,axiom,
! [F_12: list_val > exp_list_char > $o,A_64: list_val,B_34: exp_list_char] :
( ( produc525137097char_o @ F_12 @ ( produc1916172923t_char @ A_64 @ B_34 ) )
=> ( F_12 @ A_64 @ B_34 ) ) ).
thf(fact_445_splitD,axiom,
! [F_12: list_ty > produc662261637t_char > $o,A_64: list_ty,B_34: produc662261637t_char] :
( ( produc861054100char_o @ F_12 @ ( produc1909267824t_char @ A_64 @ B_34 ) )
=> ( F_12 @ A_64 @ B_34 ) ) ).
thf(fact_446_splitD,axiom,
! [F_12: list_list_char > produc220283002t_char > $o,A_64: list_list_char,B_34: produc220283002t_char] :
( ( produc1530867176char_o @ F_12 @ ( produc921874948t_char @ A_64 @ B_34 ) )
=> ( F_12 @ A_64 @ B_34 ) ) ).
thf(fact_447_splitD,axiom,
! [F_12: list_exp_list_char > produc2090907612on_val > $o,A_64: list_exp_list_char,B_34: produc2090907612on_val] :
( ( produc1841295295_val_o @ F_12 @ ( produc1302104557on_val @ A_64 @ B_34 ) )
=> ( F_12 @ A_64 @ B_34 ) ) ).
thf(fact_448_splitD,axiom,
! [F_12: produc1180562163on_val > produc1180562163on_val > $o,A_64: produc1180562163on_val,B_34: produc1180562163on_val] :
( ( produc2136448621_val_o @ F_12 @ ( produc747700183on_val @ A_64 @ B_34 ) )
=> ( F_12 @ A_64 @ B_34 ) ) ).
thf(fact_449_splitD,axiom,
! [F_12: val > val > $o,A_64: val,B_34: val] :
( ( produc9430317_val_o @ F_12 @ ( product_Pair_val_val @ A_64 @ B_34 ) )
=> ( F_12 @ A_64 @ B_34 ) ) ).
thf(fact_450_splitD,axiom,
! [F_12: bop > product_prod_val_val > $o,A_64: bop,B_34: product_prod_val_val] :
( ( produc1063861510_val_o @ F_12 @ ( produc621191550al_val @ A_64 @ B_34 ) )
=> ( F_12 @ A_64 @ B_34 ) ) ).
thf(fact_451_splitD,axiom,
! [F_12: list_char > list_char > $o,A_64: list_char,B_34: list_char] :
( ( produc282231039char_o @ F_12 @ ( produc5062597t_char @ A_64 @ B_34 ) )
=> ( F_12 @ A_64 @ B_34 ) ) ).
thf(fact_452_splitD,axiom,
! [F_12: list_char > ( produc1278157519t_char > option_val ) > $o,A_64: list_char,B_34: produc1278157519t_char > option_val] :
( ( produc765165771_val_o @ F_12 @ ( produc926070009on_val @ A_64 @ B_34 ) )
=> ( F_12 @ A_64 @ B_34 ) ) ).
thf(fact_453_splitD,axiom,
! [F_12: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,A_64: nat > option1728594148on_val,B_34: list_char > option_val] :
( ( produc252486962_val_o @ F_12 @ ( produc755559506on_val @ A_64 @ B_34 ) )
=> ( F_12 @ A_64 @ B_34 ) ) ).
thf(fact_454_splitD,axiom,
! [F_12: exp_list_char > produc2090907612on_val > $o,A_64: exp_list_char,B_34: produc2090907612on_val] :
( ( produc1835097372_val_o @ F_12 @ ( produc235638504on_val @ A_64 @ B_34 ) )
=> ( F_12 @ A_64 @ B_34 ) ) ).
thf(fact_455_splitD,axiom,
! [F_12: produc1282892786on_val > produc1282892786on_val > $o,A_64: produc1282892786on_val,B_34: produc1282892786on_val] :
( ( produc1624062875_val_o @ F_12 @ ( produc833389609on_val @ A_64 @ B_34 ) )
=> ( F_12 @ A_64 @ B_34 ) ) ).
thf(fact_456_lconf__hext,axiom,
! [H_13: nat > option1728594148on_val,P_17: list_P1999446415t_char,H_12: nat > option1728594148on_val,L_6: list_char > option_val,E_9: list_char > option_ty] :
( ( lconf_496643946t_char @ P_17 @ H_12 @ L_6 @ E_9 )
=> ( ( hext @ H_12 @ H_13 )
=> ( lconf_496643946t_char @ P_17 @ H_13 @ L_6 @ E_9 ) ) ) ).
thf(fact_457_red__reds_ORedSeq,axiom,
! [V: val,E_2_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ ( val_list_char @ V ) @ E_2_1 ) @ S ) @ ( produc235638504on_val @ E_2_1 @ S ) ) @ ( red @ P ) ) ).
thf(fact_458_map__add__upd__left,axiom,
! [E1: nat > option1728594148on_val,U1: produc2088785539on_val,M_11: nat,E2: nat > option1728594148on_val] :
( ~ ( member_nat @ M_11 @ ( dom_na2045926843on_val @ E2 ) )
=> ( ( map_ad1851375512on_val @ ( fun_up1472480727on_val @ E1 @ M_11 @ ( some_P451527732on_val @ U1 ) ) @ E2 )
= ( fun_up1472480727on_val @ ( map_ad1851375512on_val @ E1 @ E2 ) @ M_11 @ ( some_P451527732on_val @ U1 ) ) ) ) ).
thf(fact_459_map__add__upd__left,axiom,
! [E1: list_char > option_val,U1: val,M_11: list_char,E2: list_char > option_val] :
( ~ ( member_list_char @ M_11 @ ( dom_list_char_val @ E2 ) )
=> ( ( map_ad325961431ar_val @ ( fun_up1149430426on_val @ E1 @ M_11 @ ( some_val @ U1 ) ) @ E2 )
= ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ E1 @ E2 ) @ M_11 @ ( some_val @ U1 ) ) ) ) ).
thf(fact_460_map__add__upd__left,axiom,
! [E1: produc1278157519t_char > option_val,U1: val,M_11: produc1278157519t_char,E2: produc1278157519t_char > option_val] :
( ~ ( member1251428284t_char @ M_11 @ ( dom_Pr695701035ar_val @ E2 ) )
=> ( ( map_ad1185064968ar_val @ ( fun_up204312361on_val @ E1 @ M_11 @ ( some_val @ U1 ) ) @ E2 )
= ( fun_up204312361on_val @ ( map_ad1185064968ar_val @ E1 @ E2 ) @ M_11 @ ( some_val @ U1 ) ) ) ) ).
thf(fact_461_map__add__upd__left,axiom,
! [E1: list_char > option_ty,U1: ty,M_11: list_char,E2: list_char > option_ty] :
( ~ ( member_list_char @ M_11 @ ( dom_list_char_ty @ E2 ) )
=> ( ( map_add_list_char_ty @ ( fun_up424764369ion_ty @ E1 @ M_11 @ ( some_ty @ U1 ) ) @ E2 )
= ( fun_up424764369ion_ty @ ( map_add_list_char_ty @ E1 @ E2 ) @ M_11 @ ( some_ty @ U1 ) ) ) ) ).
thf(fact_462_red__reds_ORedBlock,axiom,
! [V_1: list_char,T: ty,U: val,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_1 @ T @ ( val_list_char @ U ) ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ U ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_463_domI,axiom,
! [M_10: nat > option1728594148on_val,A_63: nat,B_33: produc2088785539on_val] :
( ( ( M_10 @ A_63 )
= ( some_P451527732on_val @ B_33 ) )
=> ( member_nat @ A_63 @ ( dom_na2045926843on_val @ M_10 ) ) ) ).
thf(fact_464_domI,axiom,
! [M_10: list_char > option_val,A_63: list_char,B_33: val] :
( ( ( M_10 @ A_63 )
= ( some_val @ B_33 ) )
=> ( member_list_char @ A_63 @ ( dom_list_char_val @ M_10 ) ) ) ).
thf(fact_465_red__reds_OInitBlockRed,axiom,
! [T: ty,V_4: val,E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,V_1: list_char,V: val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ ( fun_up1149430426on_val @ L_1 @ V_1 @ ( some_val @ V ) ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) ) @ ( red @ P ) )
=> ( ( ( L @ V_1 )
= ( some_val @ V_4 ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ E_1 ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V_4 ) ) @ E ) ) @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_1 @ ( L_1 @ V_1 ) ) ) ) ) @ ( red @ P ) ) ) ) ).
thf(fact_466_prod_Osimps_I2_J,axiom,
! [F1: list_char > ( produc1278157519t_char > option_val ) > option_ty,A_62: list_char,B_32: produc1278157519t_char > option_val] :
( ( produc863160906ion_ty @ F1 @ ( produc926070009on_val @ A_62 @ B_32 ) )
= ( F1 @ A_62 @ B_32 ) ) ).
thf(fact_467_prod_Osimps_I2_J,axiom,
! [F1: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,A_62: nat > option1728594148on_val,B_32: list_char > option_val] :
( ( produc252486962_val_o @ F1 @ ( produc755559506on_val @ A_62 @ B_32 ) )
<=> ( F1 @ A_62 @ B_32 ) ) ).
thf(fact_468_split__conv,axiom,
! [F_11: list_char > ( produc1278157519t_char > option_val ) > option_ty,A_61: list_char,B_31: produc1278157519t_char > option_val] :
( ( produc863160906ion_ty @ F_11 @ ( produc926070009on_val @ A_61 @ B_31 ) )
= ( F_11 @ A_61 @ B_31 ) ) ).
thf(fact_469_split__conv,axiom,
! [F_11: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,A_61: nat > option1728594148on_val,B_31: list_char > option_val] :
( ( produc252486962_val_o @ F_11 @ ( produc755559506on_val @ A_61 @ B_31 ) )
<=> ( F_11 @ A_61 @ B_31 ) ) ).
thf(fact_470_map__add__find__right,axiom,
! [M_9: list_char > option_val,N_3: list_char > option_val,K_4: list_char,Xx: val] :
( ( ( N_3 @ K_4 )
= ( some_val @ Xx ) )
=> ( ( map_ad325961431ar_val @ M_9 @ N_3 @ K_4 )
= ( some_val @ Xx ) ) ) ).
thf(fact_471_mem__def,axiom,
! [X_29: produc1013743697t_char,A_60: produc1013743697t_char > $o] :
( ( member1601084734t_char @ X_29 @ A_60 )
<=> ( A_60 @ X_29 ) ) ).
thf(fact_472_mem__def,axiom,
! [X_29: produc1971331930t_char,A_60: produc1971331930t_char > $o] :
( ( member1467889965t_char @ X_29 @ A_60 )
<=> ( A_60 @ X_29 ) ) ).
thf(fact_473_mem__def,axiom,
! [X_29: produc618524391on_val,A_60: produc618524391on_val > $o] :
( ( member2042188884on_val @ X_29 @ A_60 )
<=> ( A_60 @ X_29 ) ) ).
thf(fact_474_mem__def,axiom,
! [X_29: nat,A_60: nat > $o] :
( ( member_nat @ X_29 @ A_60 )
<=> ( A_60 @ X_29 ) ) ).
thf(fact_475_mem__def,axiom,
! [X_29: produc1278157519t_char,A_60: produc1278157519t_char > $o] :
( ( member1251428284t_char @ X_29 @ A_60 )
<=> ( A_60 @ X_29 ) ) ).
thf(fact_476_mem__def,axiom,
! [X_29: list_char,A_60: list_char > $o] :
( ( member_list_char @ X_29 @ A_60 )
<=> ( A_60 @ X_29 ) ) ).
thf(fact_477_mem__def,axiom,
! [X_29: produc1746408499on_val,A_60: produc1746408499on_val > $o] :
( ( member1913460000on_val @ X_29 @ A_60 )
<=> ( A_60 @ X_29 ) ) ).
thf(fact_478_split__eta,axiom,
! [F_10: produc2088785539on_val > option_ty] :
( ( produc863160906ion_ty
@ ^ [X: list_char,Y_1: produc1278157519t_char > option_val] : ( F_10 @ ( produc926070009on_val @ X @ Y_1 ) ) )
= F_10 ) ).
thf(fact_479_split__eta,axiom,
! [F_10: produc2090907612on_val > $o] :
( ( produc252486962_val_o
@ ^ [X: nat > option1728594148on_val,Y_1: list_char > option_val] : ( F_10 @ ( produc755559506on_val @ X @ Y_1 ) ) )
= F_10 ) ).
thf(fact_480_red__reds_OLAssRed,axiom,
! [V_1: list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V_1 @ E_1 ) @ S ) @ ( produc235638504on_val @ ( lAss_list_char @ V_1 @ E ) @ S_2 ) ) @ ( red @ P ) ) ) ).
thf(fact_481_red__reds_OSeqRed,axiom,
! [E_2_1: exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ E_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( seq_list_char @ E @ E_2_1 ) @ S_2 ) ) @ ( red @ P ) ) ) ).
thf(fact_482_curryE,axiom,
! [F_9: produc809539159t_char > $o,A_59: list_list_char,B_30: exp_list_char] :
( ( produc1404278138char_o @ F_9 @ A_59 @ B_30 )
=> ( F_9 @ ( produc1147572817t_char @ A_59 @ B_30 ) ) ) ).
thf(fact_483_curryE,axiom,
! [F_9: produc2146869324t_char > $o,A_59: list_P1940453997har_ty,B_30: list_P341299826t_char] :
( ( produc2107091019char_o @ F_9 @ A_59 @ B_30 )
=> ( F_9 @ ( produc1152259904t_char @ A_59 @ B_30 ) ) ) ).
thf(fact_484_curryE,axiom,
! [F_9: produc952412819t_char > $o,A_59: list_char,B_30: produc2146869324t_char] :
( ( produc325775556char_o @ F_9 @ A_59 @ B_30 )
=> ( F_9 @ ( produc1483578759t_char @ A_59 @ B_30 ) ) ) ).
thf(fact_485_curryE,axiom,
! [F_9: produc1971331930t_char > $o,A_59: list_char,B_30: produc952412819t_char] :
( ( produc1383007933char_o @ F_9 @ A_59 @ B_30 )
=> ( F_9 @ ( produc822965838t_char @ A_59 @ B_30 ) ) ) ).
thf(fact_486_curryE,axiom,
! [F_9: produc662261637t_char > $o,A_59: list_val,B_30: exp_list_char] :
( ( produc1072551658char_o @ F_9 @ A_59 @ B_30 )
=> ( F_9 @ ( produc1916172923t_char @ A_59 @ B_30 ) ) ) ).
thf(fact_487_curryE,axiom,
! [F_9: produc220283002t_char > $o,A_59: list_ty,B_30: produc662261637t_char] :
( ( produc786676533char_o @ F_9 @ A_59 @ B_30 )
=> ( F_9 @ ( produc1909267824t_char @ A_59 @ B_30 ) ) ) ).
thf(fact_488_curryE,axiom,
! [F_9: produc1285161482t_char > $o,A_59: list_list_char,B_30: produc220283002t_char] :
( ( produc193646727char_o @ F_9 @ A_59 @ B_30 )
=> ( F_9 @ ( produc921874948t_char @ A_59 @ B_30 ) ) ) ).
thf(fact_489_curryE,axiom,
! [F_9: produc1180562163on_val > $o,A_59: list_exp_list_char,B_30: produc2090907612on_val] :
( ( produc618849246_val_o @ F_9 @ A_59 @ B_30 )
=> ( F_9 @ ( produc1302104557on_val @ A_59 @ B_30 ) ) ) ).
thf(fact_490_curryE,axiom,
! [F_9: produc618524391on_val > $o,A_59: produc1180562163on_val,B_30: produc1180562163on_val] :
( ( produc551782158_val_o @ F_9 @ A_59 @ B_30 )
=> ( F_9 @ ( produc747700183on_val @ A_59 @ B_30 ) ) ) ).
thf(fact_491_curryE,axiom,
! [F_9: product_prod_val_val > $o,A_59: val,B_30: val] :
( ( produc575837646_val_o @ F_9 @ A_59 @ B_30 )
=> ( F_9 @ ( product_Pair_val_val @ A_59 @ B_30 ) ) ) ).
thf(fact_492_curryE,axiom,
! [F_9: produc1645268488al_val > $o,A_59: bop,B_30: product_prod_val_val] :
( ( produc275195559_val_o @ F_9 @ A_59 @ B_30 )
=> ( F_9 @ ( produc621191550al_val @ A_59 @ B_30 ) ) ) ).
thf(fact_493_curryE,axiom,
! [F_9: produc1278157519t_char > $o,A_59: list_char,B_30: list_char] :
( ( produc1709467424char_o @ F_9 @ A_59 @ B_30 )
=> ( F_9 @ ( produc5062597t_char @ A_59 @ B_30 ) ) ) ).
thf(fact_494_curryE,axiom,
! [F_9: produc2088785539on_val > $o,A_59: list_char,B_30: produc1278157519t_char > option_val] :
( ( produc1177570924_val_o @ F_9 @ A_59 @ B_30 )
=> ( F_9 @ ( produc926070009on_val @ A_59 @ B_30 ) ) ) ).
thf(fact_495_curryE,axiom,
! [F_9: produc2090907612on_val > $o,A_59: nat > option1728594148on_val,B_30: list_char > option_val] :
( ( produc1402621651_val_o @ F_9 @ A_59 @ B_30 )
=> ( F_9 @ ( produc755559506on_val @ A_59 @ B_30 ) ) ) ).
thf(fact_496_curryE,axiom,
! [F_9: produc1282892786on_val > $o,A_59: exp_list_char,B_30: produc2090907612on_val] :
( ( produc1287763389_val_o @ F_9 @ A_59 @ B_30 )
=> ( F_9 @ ( produc235638504on_val @ A_59 @ B_30 ) ) ) ).
thf(fact_497_curryE,axiom,
! [F_9: produc1746408499on_val > $o,A_59: produc1282892786on_val,B_30: produc1282892786on_val] :
( ( produc803302844_val_o @ F_9 @ A_59 @ B_30 )
=> ( F_9 @ ( produc833389609on_val @ A_59 @ B_30 ) ) ) ).
thf(fact_498_curryD,axiom,
! [F_8: produc809539159t_char > $o,A_58: list_list_char,B_29: exp_list_char] :
( ( produc1404278138char_o @ F_8 @ A_58 @ B_29 )
=> ( F_8 @ ( produc1147572817t_char @ A_58 @ B_29 ) ) ) ).
thf(fact_499_curryD,axiom,
! [F_8: produc2146869324t_char > $o,A_58: list_P1940453997har_ty,B_29: list_P341299826t_char] :
( ( produc2107091019char_o @ F_8 @ A_58 @ B_29 )
=> ( F_8 @ ( produc1152259904t_char @ A_58 @ B_29 ) ) ) ).
thf(fact_500_curryD,axiom,
! [F_8: produc952412819t_char > $o,A_58: list_char,B_29: produc2146869324t_char] :
( ( produc325775556char_o @ F_8 @ A_58 @ B_29 )
=> ( F_8 @ ( produc1483578759t_char @ A_58 @ B_29 ) ) ) ).
thf(fact_501_curryD,axiom,
! [F_8: produc1971331930t_char > $o,A_58: list_char,B_29: produc952412819t_char] :
( ( produc1383007933char_o @ F_8 @ A_58 @ B_29 )
=> ( F_8 @ ( produc822965838t_char @ A_58 @ B_29 ) ) ) ).
thf(fact_502_curryD,axiom,
! [F_8: produc662261637t_char > $o,A_58: list_val,B_29: exp_list_char] :
( ( produc1072551658char_o @ F_8 @ A_58 @ B_29 )
=> ( F_8 @ ( produc1916172923t_char @ A_58 @ B_29 ) ) ) ).
thf(fact_503_curryD,axiom,
! [F_8: produc220283002t_char > $o,A_58: list_ty,B_29: produc662261637t_char] :
( ( produc786676533char_o @ F_8 @ A_58 @ B_29 )
=> ( F_8 @ ( produc1909267824t_char @ A_58 @ B_29 ) ) ) ).
thf(fact_504_curryD,axiom,
! [F_8: produc1285161482t_char > $o,A_58: list_list_char,B_29: produc220283002t_char] :
( ( produc193646727char_o @ F_8 @ A_58 @ B_29 )
=> ( F_8 @ ( produc921874948t_char @ A_58 @ B_29 ) ) ) ).
thf(fact_505_curryD,axiom,
! [F_8: produc1180562163on_val > $o,A_58: list_exp_list_char,B_29: produc2090907612on_val] :
( ( produc618849246_val_o @ F_8 @ A_58 @ B_29 )
=> ( F_8 @ ( produc1302104557on_val @ A_58 @ B_29 ) ) ) ).
thf(fact_506_curryD,axiom,
! [F_8: produc618524391on_val > $o,A_58: produc1180562163on_val,B_29: produc1180562163on_val] :
( ( produc551782158_val_o @ F_8 @ A_58 @ B_29 )
=> ( F_8 @ ( produc747700183on_val @ A_58 @ B_29 ) ) ) ).
thf(fact_507_curryD,axiom,
! [F_8: product_prod_val_val > $o,A_58: val,B_29: val] :
( ( produc575837646_val_o @ F_8 @ A_58 @ B_29 )
=> ( F_8 @ ( product_Pair_val_val @ A_58 @ B_29 ) ) ) ).
thf(fact_508_curryD,axiom,
! [F_8: produc1645268488al_val > $o,A_58: bop,B_29: product_prod_val_val] :
( ( produc275195559_val_o @ F_8 @ A_58 @ B_29 )
=> ( F_8 @ ( produc621191550al_val @ A_58 @ B_29 ) ) ) ).
thf(fact_509_curryD,axiom,
! [F_8: produc1278157519t_char > $o,A_58: list_char,B_29: list_char] :
( ( produc1709467424char_o @ F_8 @ A_58 @ B_29 )
=> ( F_8 @ ( produc5062597t_char @ A_58 @ B_29 ) ) ) ).
thf(fact_510_curryD,axiom,
! [F_8: produc2088785539on_val > $o,A_58: list_char,B_29: produc1278157519t_char > option_val] :
( ( produc1177570924_val_o @ F_8 @ A_58 @ B_29 )
=> ( F_8 @ ( produc926070009on_val @ A_58 @ B_29 ) ) ) ).
thf(fact_511_curryD,axiom,
! [F_8: produc2090907612on_val > $o,A_58: nat > option1728594148on_val,B_29: list_char > option_val] :
( ( produc1402621651_val_o @ F_8 @ A_58 @ B_29 )
=> ( F_8 @ ( produc755559506on_val @ A_58 @ B_29 ) ) ) ).
thf(fact_512_curryD,axiom,
! [F_8: produc1282892786on_val > $o,A_58: exp_list_char,B_29: produc2090907612on_val] :
( ( produc1287763389_val_o @ F_8 @ A_58 @ B_29 )
=> ( F_8 @ ( produc235638504on_val @ A_58 @ B_29 ) ) ) ).
thf(fact_513_curryD,axiom,
! [F_8: produc1746408499on_val > $o,A_58: produc1282892786on_val,B_29: produc1282892786on_val] :
( ( produc803302844_val_o @ F_8 @ A_58 @ B_29 )
=> ( F_8 @ ( produc833389609on_val @ A_58 @ B_29 ) ) ) ).
thf(fact_514_map__add__upd,axiom,
! [F_7: produc1278157519t_char > option_val,G_5: produc1278157519t_char > option_val,X_28: produc1278157519t_char,Y_10: val] :
( ( map_ad1185064968ar_val @ F_7 @ ( fun_up204312361on_val @ G_5 @ X_28 @ ( some_val @ Y_10 ) ) )
= ( fun_up204312361on_val @ ( map_ad1185064968ar_val @ F_7 @ G_5 ) @ X_28 @ ( some_val @ Y_10 ) ) ) ).
thf(fact_515_map__add__upd,axiom,
! [F_7: nat > option1728594148on_val,G_5: nat > option1728594148on_val,X_28: nat,Y_10: produc2088785539on_val] :
( ( map_ad1851375512on_val @ F_7 @ ( fun_up1472480727on_val @ G_5 @ X_28 @ ( some_P451527732on_val @ Y_10 ) ) )
= ( fun_up1472480727on_val @ ( map_ad1851375512on_val @ F_7 @ G_5 ) @ X_28 @ ( some_P451527732on_val @ Y_10 ) ) ) ).
thf(fact_516_map__add__upd,axiom,
! [F_7: list_char > option_ty,G_5: list_char > option_ty,X_28: list_char,Y_10: ty] :
( ( map_add_list_char_ty @ F_7 @ ( fun_up424764369ion_ty @ G_5 @ X_28 @ ( some_ty @ Y_10 ) ) )
= ( fun_up424764369ion_ty @ ( map_add_list_char_ty @ F_7 @ G_5 ) @ X_28 @ ( some_ty @ Y_10 ) ) ) ).
thf(fact_517_map__add__upd,axiom,
! [F_7: list_char > option_val,G_5: list_char > option_val,X_28: list_char,Y_10: val] :
( ( map_ad325961431ar_val @ F_7 @ ( fun_up1149430426on_val @ G_5 @ X_28 @ ( some_val @ Y_10 ) ) )
= ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ F_7 @ G_5 ) @ X_28 @ ( some_val @ Y_10 ) ) ) ).
thf(fact_518_internal__split__def,axiom,
produc1576476927ion_ty = produc863160906ion_ty ).
thf(fact_519_internal__split__def,axiom,
produc575577405_val_o = produc252486962_val_o ).
thf(fact_520_WTrtBlock,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,V_1: list_char,T: ty,E_1: exp_list_char,T_5: ty] :
( ( wTrt_1 @ P @ H_1 @ ( fun_up424764369ion_ty @ E_2 @ V_1 @ ( some_ty @ T ) ) @ E_1 @ T_5 )
=> ( wTrt_1 @ P @ H_1 @ E_2 @ ( block_list_char @ V_1 @ T @ E_1 ) @ T_5 ) ) ).
thf(fact_521_splitE,axiom,
! [C_18: list_list_char > exp_list_char > $o,P_16: produc809539159t_char] :
( ( produc1596287579char_o @ C_18 @ P_16 )
=> ~ ! [X: list_list_char,Y_1: exp_list_char] :
( ( P_16
= ( produc1147572817t_char @ X @ Y_1 ) )
=> ~ ( C_18 @ X @ Y_1 ) ) ) ).
thf(fact_522_splitE,axiom,
! [C_18: list_P1940453997har_ty > list_P341299826t_char > $o,P_16: produc2146869324t_char] :
( ( produc875422124char_o @ C_18 @ P_16 )
=> ~ ! [X: list_P1940453997har_ty,Y_1: list_P341299826t_char] :
( ( P_16
= ( produc1152259904t_char @ X @ Y_1 ) )
=> ~ ( C_18 @ X @ Y_1 ) ) ) ).
thf(fact_523_splitE,axiom,
! [C_18: list_char > produc2146869324t_char > $o,P_16: produc952412819t_char] :
( ( produc781483429char_o @ C_18 @ P_16 )
=> ~ ! [X: list_char,Y_1: produc2146869324t_char] :
( ( P_16
= ( produc1483578759t_char @ X @ Y_1 ) )
=> ~ ( C_18 @ X @ Y_1 ) ) ) ).
thf(fact_524_splitE,axiom,
! [C_18: list_char > produc952412819t_char > $o,P_16: produc1971331930t_char] :
( ( produc1519396638char_o @ C_18 @ P_16 )
=> ~ ! [X: list_char,Y_1: produc952412819t_char] :
( ( P_16
= ( produc822965838t_char @ X @ Y_1 ) )
=> ~ ( C_18 @ X @ Y_1 ) ) ) ).
thf(fact_525_splitE,axiom,
! [C_18: list_val > exp_list_char > $o,P_16: produc662261637t_char] :
( ( produc525137097char_o @ C_18 @ P_16 )
=> ~ ! [X: list_val,Y_1: exp_list_char] :
( ( P_16
= ( produc1916172923t_char @ X @ Y_1 ) )
=> ~ ( C_18 @ X @ Y_1 ) ) ) ).
thf(fact_526_splitE,axiom,
! [C_18: list_ty > produc662261637t_char > $o,P_16: produc220283002t_char] :
( ( produc861054100char_o @ C_18 @ P_16 )
=> ~ ! [X: list_ty,Y_1: produc662261637t_char] :
( ( P_16
= ( produc1909267824t_char @ X @ Y_1 ) )
=> ~ ( C_18 @ X @ Y_1 ) ) ) ).
thf(fact_527_splitE,axiom,
! [C_18: list_list_char > produc220283002t_char > $o,P_16: produc1285161482t_char] :
( ( produc1530867176char_o @ C_18 @ P_16 )
=> ~ ! [X: list_list_char,Y_1: produc220283002t_char] :
( ( P_16
= ( produc921874948t_char @ X @ Y_1 ) )
=> ~ ( C_18 @ X @ Y_1 ) ) ) ).
thf(fact_528_splitE,axiom,
! [C_18: list_exp_list_char > produc2090907612on_val > $o,P_16: produc1180562163on_val] :
( ( produc1841295295_val_o @ C_18 @ P_16 )
=> ~ ! [X: list_exp_list_char,Y_1: produc2090907612on_val] :
( ( P_16
= ( produc1302104557on_val @ X @ Y_1 ) )
=> ~ ( C_18 @ X @ Y_1 ) ) ) ).
thf(fact_529_splitE,axiom,
! [C_18: produc1180562163on_val > produc1180562163on_val > $o,P_16: produc618524391on_val] :
( ( produc2136448621_val_o @ C_18 @ P_16 )
=> ~ ! [X: produc1180562163on_val,Y_1: produc1180562163on_val] :
( ( P_16
= ( produc747700183on_val @ X @ Y_1 ) )
=> ~ ( C_18 @ X @ Y_1 ) ) ) ).
thf(fact_530_splitE,axiom,
! [C_18: val > val > $o,P_16: product_prod_val_val] :
( ( produc9430317_val_o @ C_18 @ P_16 )
=> ~ ! [X: val,Y_1: val] :
( ( P_16
= ( product_Pair_val_val @ X @ Y_1 ) )
=> ~ ( C_18 @ X @ Y_1 ) ) ) ).
thf(fact_531_splitE,axiom,
! [C_18: bop > product_prod_val_val > $o,P_16: produc1645268488al_val] :
( ( produc1063861510_val_o @ C_18 @ P_16 )
=> ~ ! [X: bop,Y_1: product_prod_val_val] :
( ( P_16
= ( produc621191550al_val @ X @ Y_1 ) )
=> ~ ( C_18 @ X @ Y_1 ) ) ) ).
thf(fact_532_splitE,axiom,
! [C_18: list_char > list_char > $o,P_16: produc1278157519t_char] :
( ( produc282231039char_o @ C_18 @ P_16 )
=> ~ ! [X: list_char,Y_1: list_char] :
( ( P_16
= ( produc5062597t_char @ X @ Y_1 ) )
=> ~ ( C_18 @ X @ Y_1 ) ) ) ).
thf(fact_533_splitE,axiom,
! [C_18: list_char > ( produc1278157519t_char > option_val ) > $o,P_16: produc2088785539on_val] :
( ( produc765165771_val_o @ C_18 @ P_16 )
=> ~ ! [X: list_char,Y_1: produc1278157519t_char > option_val] :
( ( P_16
= ( produc926070009on_val @ X @ Y_1 ) )
=> ~ ( C_18 @ X @ Y_1 ) ) ) ).
thf(fact_534_splitE,axiom,
! [C_18: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,P_16: produc2090907612on_val] :
( ( produc252486962_val_o @ C_18 @ P_16 )
=> ~ ! [X: nat > option1728594148on_val,Y_1: list_char > option_val] :
( ( P_16
= ( produc755559506on_val @ X @ Y_1 ) )
=> ~ ( C_18 @ X @ Y_1 ) ) ) ).
thf(fact_535_splitE,axiom,
! [C_18: exp_list_char > produc2090907612on_val > $o,P_16: produc1282892786on_val] :
( ( produc1835097372_val_o @ C_18 @ P_16 )
=> ~ ! [X: exp_list_char,Y_1: produc2090907612on_val] :
( ( P_16
= ( produc235638504on_val @ X @ Y_1 ) )
=> ~ ( C_18 @ X @ Y_1 ) ) ) ).
thf(fact_536_splitE,axiom,
! [C_18: produc1282892786on_val > produc1282892786on_val > $o,P_16: produc1746408499on_val] :
( ( produc1624062875_val_o @ C_18 @ P_16 )
=> ~ ! [X: produc1282892786on_val,Y_1: produc1282892786on_val] :
( ( P_16
= ( produc833389609on_val @ X @ Y_1 ) )
=> ~ ( C_18 @ X @ Y_1 ) ) ) ).
thf(fact_537_splitI2,axiom,
! [C_17: list_list_char > exp_list_char > $o,P_15: produc809539159t_char] :
( ! [A_1: list_list_char,B_14: exp_list_char] :
( ( P_15
= ( produc1147572817t_char @ A_1 @ B_14 ) )
=> ( C_17 @ A_1 @ B_14 ) )
=> ( produc1596287579char_o @ C_17 @ P_15 ) ) ).
thf(fact_538_splitI2,axiom,
! [C_17: list_P1940453997har_ty > list_P341299826t_char > $o,P_15: produc2146869324t_char] :
( ! [A_1: list_P1940453997har_ty,B_14: list_P341299826t_char] :
( ( P_15
= ( produc1152259904t_char @ A_1 @ B_14 ) )
=> ( C_17 @ A_1 @ B_14 ) )
=> ( produc875422124char_o @ C_17 @ P_15 ) ) ).
thf(fact_539_splitI2,axiom,
! [C_17: list_char > produc2146869324t_char > $o,P_15: produc952412819t_char] :
( ! [A_1: list_char,B_14: produc2146869324t_char] :
( ( P_15
= ( produc1483578759t_char @ A_1 @ B_14 ) )
=> ( C_17 @ A_1 @ B_14 ) )
=> ( produc781483429char_o @ C_17 @ P_15 ) ) ).
thf(fact_540_splitI2,axiom,
! [C_17: list_char > produc952412819t_char > $o,P_15: produc1971331930t_char] :
( ! [A_1: list_char,B_14: produc952412819t_char] :
( ( P_15
= ( produc822965838t_char @ A_1 @ B_14 ) )
=> ( C_17 @ A_1 @ B_14 ) )
=> ( produc1519396638char_o @ C_17 @ P_15 ) ) ).
thf(fact_541_splitI2,axiom,
! [C_17: list_val > exp_list_char > $o,P_15: produc662261637t_char] :
( ! [A_1: list_val,B_14: exp_list_char] :
( ( P_15
= ( produc1916172923t_char @ A_1 @ B_14 ) )
=> ( C_17 @ A_1 @ B_14 ) )
=> ( produc525137097char_o @ C_17 @ P_15 ) ) ).
thf(fact_542_splitI2,axiom,
! [C_17: list_ty > produc662261637t_char > $o,P_15: produc220283002t_char] :
( ! [A_1: list_ty,B_14: produc662261637t_char] :
( ( P_15
= ( produc1909267824t_char @ A_1 @ B_14 ) )
=> ( C_17 @ A_1 @ B_14 ) )
=> ( produc861054100char_o @ C_17 @ P_15 ) ) ).
thf(fact_543_splitI2,axiom,
! [C_17: list_list_char > produc220283002t_char > $o,P_15: produc1285161482t_char] :
( ! [A_1: list_list_char,B_14: produc220283002t_char] :
( ( P_15
= ( produc921874948t_char @ A_1 @ B_14 ) )
=> ( C_17 @ A_1 @ B_14 ) )
=> ( produc1530867176char_o @ C_17 @ P_15 ) ) ).
thf(fact_544_splitI2,axiom,
! [C_17: list_exp_list_char > produc2090907612on_val > $o,P_15: produc1180562163on_val] :
( ! [A_1: list_exp_list_char,B_14: produc2090907612on_val] :
( ( P_15
= ( produc1302104557on_val @ A_1 @ B_14 ) )
=> ( C_17 @ A_1 @ B_14 ) )
=> ( produc1841295295_val_o @ C_17 @ P_15 ) ) ).
thf(fact_545_splitI2,axiom,
! [C_17: produc1180562163on_val > produc1180562163on_val > $o,P_15: produc618524391on_val] :
( ! [A_1: produc1180562163on_val,B_14: produc1180562163on_val] :
( ( P_15
= ( produc747700183on_val @ A_1 @ B_14 ) )
=> ( C_17 @ A_1 @ B_14 ) )
=> ( produc2136448621_val_o @ C_17 @ P_15 ) ) ).
thf(fact_546_splitI2,axiom,
! [C_17: val > val > $o,P_15: product_prod_val_val] :
( ! [A_1: val,B_14: val] :
( ( P_15
= ( product_Pair_val_val @ A_1 @ B_14 ) )
=> ( C_17 @ A_1 @ B_14 ) )
=> ( produc9430317_val_o @ C_17 @ P_15 ) ) ).
thf(fact_547_splitI2,axiom,
! [C_17: bop > product_prod_val_val > $o,P_15: produc1645268488al_val] :
( ! [A_1: bop,B_14: product_prod_val_val] :
( ( P_15
= ( produc621191550al_val @ A_1 @ B_14 ) )
=> ( C_17 @ A_1 @ B_14 ) )
=> ( produc1063861510_val_o @ C_17 @ P_15 ) ) ).
thf(fact_548_splitI2,axiom,
! [C_17: list_char > list_char > $o,P_15: produc1278157519t_char] :
( ! [A_1: list_char,B_14: list_char] :
( ( P_15
= ( produc5062597t_char @ A_1 @ B_14 ) )
=> ( C_17 @ A_1 @ B_14 ) )
=> ( produc282231039char_o @ C_17 @ P_15 ) ) ).
thf(fact_549_splitI2,axiom,
! [C_17: list_char > ( produc1278157519t_char > option_val ) > $o,P_15: produc2088785539on_val] :
( ! [A_1: list_char,B_14: produc1278157519t_char > option_val] :
( ( P_15
= ( produc926070009on_val @ A_1 @ B_14 ) )
=> ( C_17 @ A_1 @ B_14 ) )
=> ( produc765165771_val_o @ C_17 @ P_15 ) ) ).
thf(fact_550_splitI2,axiom,
! [C_17: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,P_15: produc2090907612on_val] :
( ! [A_1: nat > option1728594148on_val,B_14: list_char > option_val] :
( ( P_15
= ( produc755559506on_val @ A_1 @ B_14 ) )
=> ( C_17 @ A_1 @ B_14 ) )
=> ( produc252486962_val_o @ C_17 @ P_15 ) ) ).
thf(fact_551_splitI2,axiom,
! [C_17: exp_list_char > produc2090907612on_val > $o,P_15: produc1282892786on_val] :
( ! [A_1: exp_list_char,B_14: produc2090907612on_val] :
( ( P_15
= ( produc235638504on_val @ A_1 @ B_14 ) )
=> ( C_17 @ A_1 @ B_14 ) )
=> ( produc1835097372_val_o @ C_17 @ P_15 ) ) ).
thf(fact_552_splitI2,axiom,
! [C_17: produc1282892786on_val > produc1282892786on_val > $o,P_15: produc1746408499on_val] :
( ! [A_1: produc1282892786on_val,B_14: produc1282892786on_val] :
( ( P_15
= ( produc833389609on_val @ A_1 @ B_14 ) )
=> ( C_17 @ A_1 @ B_14 ) )
=> ( produc1624062875_val_o @ C_17 @ P_15 ) ) ).
thf(fact_553_WTrtSeq,axiom,
! [E_2_1: exp_list_char,T_2_2: ty,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1_1: exp_list_char,T_1_1: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1_1 @ T_1_1 )
=> ( ( wTrt_1 @ P @ H_1 @ E_2 @ E_2_1 @ T_2_2 )
=> ( wTrt_1 @ P @ H_1 @ E_2 @ ( seq_list_char @ E_1_1 @ E_2_1 ) @ T_2_2 ) ) ) ).
thf(fact_554_lconf__def,axiom,
! [P_14: list_P1999446415t_char,H_11: nat > option1728594148on_val,L_5: list_char > option_val,E_8: list_char > option_ty] :
( ( lconf_496643946t_char @ P_14 @ H_11 @ L_5 @ E_8 )
<=> ! [V_7: list_char,V_2: val] :
( ( ( L_5 @ V_7 )
= ( some_val @ V_2 ) )
=> ? [T_4: ty] :
( ( ( E_8 @ V_7 )
= ( some_ty @ T_4 ) )
& ( conf_P373316194t_char @ P_14 @ H_11 @ V_2 @ T_4 ) ) ) ) ).
thf(fact_555_red__reds_ORedLAss,axiom,
! [V_1: list_char,V: val,H_1: nat > option1728594148on_val,L_1: list_char > option_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ ( val_list_char @ unit ) @ ( produc755559506on_val @ H_1 @ ( fun_up1149430426on_val @ L_1 @ V_1 @ ( some_val @ V ) ) ) ) ) @ ( red @ P ) ) ).
thf(fact_556_hext__refl,axiom,
! [H_1: nat > option1728594148on_val] : ( hext @ H_1 @ H_1 ) ).
thf(fact_557_cond__split__eta,axiom,
! [F_6: list_char > ( produc1278157519t_char > option_val ) > option_ty,G_4: produc2088785539on_val > option_ty] :
( ! [X: list_char,Y_1: produc1278157519t_char > option_val] :
( ( F_6 @ X @ Y_1 )
= ( G_4 @ ( produc926070009on_val @ X @ Y_1 ) ) )
=> ( ( produc863160906ion_ty @ F_6 )
= G_4 ) ) ).
thf(fact_558_cond__split__eta,axiom,
! [G_4: produc2090907612on_val > $o,F_6: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o] :
( ! [X: nat > option1728594148on_val,Y_1: list_char > option_val] :
( ( F_6 @ X @ Y_1 )
<=> ( G_4 @ ( produc755559506on_val @ X @ Y_1 ) ) )
=> ( ( produc252486962_val_o @ F_6 )
= G_4 ) ) ).
thf(fact_559_domD,axiom,
! [A_57: nat,M_8: nat > option1728594148on_val] :
( ( member_nat @ A_57 @ ( dom_na2045926843on_val @ M_8 ) )
=> ? [B_14: produc2088785539on_val] :
( ( M_8 @ A_57 )
= ( some_P451527732on_val @ B_14 ) ) ) ).
thf(fact_560_domD,axiom,
! [A_57: list_char,M_8: list_char > option_val] :
( ( member_list_char @ A_57 @ ( dom_list_char_val @ M_8 ) )
=> ? [B_14: val] :
( ( M_8 @ A_57 )
= ( some_val @ B_14 ) ) ) ).
thf(fact_561_splitE2,axiom,
! [Q_2: option_ty > $o,P_13: list_char > ( produc1278157519t_char > option_val ) > option_ty,Z_4: produc2088785539on_val] :
( ( Q_2 @ ( produc863160906ion_ty @ P_13 @ Z_4 ) )
=> ~ ! [X: list_char,Y_1: produc1278157519t_char > option_val] :
( ( Z_4
= ( produc926070009on_val @ X @ Y_1 ) )
=> ~ ( Q_2 @ ( P_13 @ X @ Y_1 ) ) ) ) ).
thf(fact_562_splitE2,axiom,
! [Q_2: $o > $o,P_13: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,Z_4: produc2090907612on_val] :
( ( Q_2 @ ( produc252486962_val_o @ P_13 @ Z_4 ) )
=> ~ ! [X: nat > option1728594148on_val,Y_1: list_char > option_val] :
( ( Z_4
= ( produc755559506on_val @ X @ Y_1 ) )
=> ~ ( Q_2 @ ( P_13 @ X @ Y_1 ) ) ) ) ).
thf(fact_563_WTrt__hext__mono,axiom,
! [H: nat > option1728594148on_val,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,T: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ T )
=> ( ( hext @ H_1 @ H )
=> ( wTrt_1 @ P @ H @ E_2 @ E_1 @ T ) ) ) ).
thf(fact_564_hext__upd__obj,axiom,
! [Fs_4: produc1278157519t_char > option_val,H_1: nat > option1728594148on_val,A: nat,C: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( H_1 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( hext @ H_1 @ ( fun_up1472480727on_val @ H_1 @ A @ ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs_4 ) ) ) ) ) ).
thf(fact_565_hext__trans,axiom,
! [H_10: nat > option1728594148on_val,H_1: nat > option1728594148on_val,H: nat > option1728594148on_val] :
( ( hext @ H_1 @ H )
=> ( ( hext @ H @ H_10 )
=> ( hext @ H_1 @ H_10 ) ) ) ).
thf(fact_566_hext__objD,axiom,
! [A: nat,C: list_char,Fs: produc1278157519t_char > option_val,H_1: nat > option1728594148on_val,H: nat > option1728594148on_val] :
( ( hext @ H_1 @ H )
=> ( ( ( H_1 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ? [Fs_6: produc1278157519t_char > option_val] :
( ( H @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs_6 ) ) ) ) ) ).
thf(fact_567_hext__def,axiom,
! [H_1: nat > option1728594148on_val,H: nat > option1728594148on_val] :
( ( hext @ H_1 @ H )
<=> ! [A_1: nat,C_1: list_char,Fs_1: produc1278157519t_char > option_val] :
( ( ( H_1 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs_1 ) ) )
=> ? [Fs_6: produc1278157519t_char > option_val] :
( ( H @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs_6 ) ) ) ) ) ).
thf(fact_568__092_060D_062___092_060D_062s_Osimps_I6_J,axiom,
! [V_6: list_char,E_7: exp_list_char,A_56: option_list_char_o] :
( ( d_list_char @ ( lAss_list_char @ V_6 @ E_7 ) @ A_56 )
<=> ( d_list_char @ E_7 @ A_56 ) ) ).
thf(fact_569_exp_Osimps_I143_J,axiom,
! [A_55: list_char,Ty_7: ty,Exp_15: exp_list_char,A_54: list_char,Exp_14: exp_list_char] :
( ( block_list_char @ A_55 @ Ty_7 @ Exp_15 )
!= ( lAss_list_char @ A_54 @ Exp_14 ) ) ).
thf(fact_570_exp_Osimps_I196_J,axiom,
! [A_53: list_char,Ty_6: ty,Exp_13: exp_list_char,Exp1_7: exp_list_char,Exp2_7: exp_list_char] :
( ( block_list_char @ A_53 @ Ty_6 @ Exp_13 )
!= ( seq_list_char @ Exp1_7 @ Exp2_7 ) ) ).
thf(fact_571_exp_Osimps_I142_J,axiom,
! [A_52: list_char,Exp_12: exp_list_char,A_51: list_char,Ty_5: ty,Exp_11: exp_list_char] :
( ( lAss_list_char @ A_52 @ Exp_12 )
!= ( block_list_char @ A_51 @ Ty_5 @ Exp_11 ) ) ).
thf(fact_572_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_573_exp_Osimps_I11_J,axiom,
! [Exp1_6: exp_list_char,Exp2_6: exp_list_char,Exp1_5: exp_list_char,Exp2_5: exp_list_char] :
( ( ( seq_list_char @ Exp1_6 @ Exp2_6 )
= ( seq_list_char @ Exp1_5 @ Exp2_5 ) )
<=> ( ( Exp1_6 = Exp1_5 )
& ( Exp2_6 = Exp2_5 ) ) ) ).
thf(fact_574_exp_Osimps_I6_J,axiom,
! [A_50: list_char,Exp_10: exp_list_char,A_49: list_char,Exp_9: exp_list_char] :
( ( ( lAss_list_char @ A_50 @ Exp_10 )
= ( lAss_list_char @ A_49 @ Exp_9 ) )
<=> ( ( A_50 = A_49 )
& ( Exp_10 = Exp_9 ) ) ) ).
thf(fact_575_exp_Osimps_I10_J,axiom,
! [A_48: list_char,Ty_4: ty,Exp_8: exp_list_char,A_47: list_char,Ty_3: ty,Exp_7: exp_list_char] :
( ( ( block_list_char @ A_48 @ Ty_4 @ Exp_8 )
= ( block_list_char @ A_47 @ Ty_3 @ Exp_7 ) )
<=> ( ( A_48 = A_47 )
& ( Ty_4 = Ty_3 )
& ( Exp_8 = Exp_7 ) ) ) ).
thf(fact_576_exp_Osimps_I84_J,axiom,
! [Val_5: val,Exp1_4: exp_list_char,Exp2_4: exp_list_char] :
( ( val_list_char @ Val_5 )
!= ( seq_list_char @ Exp1_4 @ Exp2_4 ) ) ).
thf(fact_577_exp_Osimps_I74_J,axiom,
! [Val_4: val,A_46: list_char,Exp_6: exp_list_char] :
( ( val_list_char @ Val_4 )
!= ( lAss_list_char @ A_46 @ Exp_6 ) ) ).
thf(fact_578_exp_Osimps_I85_J,axiom,
! [Exp1_3: exp_list_char,Exp2_3: exp_list_char,Val_3: val] :
( ( seq_list_char @ Exp1_3 @ Exp2_3 )
!= ( val_list_char @ Val_3 ) ) ).
thf(fact_579_exp_Osimps_I75_J,axiom,
! [A_45: list_char,Exp_5: exp_list_char,Val_2: val] :
( ( lAss_list_char @ A_45 @ Exp_5 )
!= ( val_list_char @ Val_2 ) ) ).
thf(fact_580_exp_Osimps_I82_J,axiom,
! [Val_1: val,A_44: list_char,Ty_2: ty,Exp_4: exp_list_char] :
( ( val_list_char @ Val_1 )
!= ( block_list_char @ A_44 @ Ty_2 @ Exp_4 ) ) ).
thf(fact_581_exp_Osimps_I83_J,axiom,
! [A_43: list_char,Ty_1: ty,Exp_3: exp_list_char,Val: val] :
( ( block_list_char @ A_43 @ Ty_1 @ Exp_3 )
!= ( val_list_char @ Val ) ) ).
thf(fact_582__092_060D_062___092_060D_062s_Osimps_I3_J,axiom,
! [V_5: val,A_42: option_list_char_o] : ( d_list_char @ ( val_list_char @ V_5 ) @ A_42 ) ).
thf(fact_583_exp_Osimps_I145_J,axiom,
! [Exp1_2: exp_list_char,Exp2_2: exp_list_char,A_41: list_char,Exp_2: exp_list_char] :
( ( seq_list_char @ Exp1_2 @ Exp2_2 )
!= ( lAss_list_char @ A_41 @ Exp_2 ) ) ).
thf(fact_584_exp_Osimps_I144_J,axiom,
! [A_40: list_char,Exp_1: exp_list_char,Exp1_1: exp_list_char,Exp2_1: exp_list_char] :
( ( lAss_list_char @ A_40 @ Exp_1 )
!= ( seq_list_char @ Exp1_1 @ Exp2_1 ) ) ).
thf(fact_585_exp_Osimps_I197_J,axiom,
! [Exp1: exp_list_char,Exp2: exp_list_char,A_39: list_char,Ty: ty,Exp: exp_list_char] :
( ( seq_list_char @ Exp1 @ Exp2 )
!= ( block_list_char @ A_39 @ Ty @ Exp ) ) ).
thf(fact_586_hconf__upd__obj,axiom,
! [Fs_8: produc1278157519t_char > option_val,A_38: nat,C_16: list_char,Fs_7: produc1278157519t_char > option_val,P_12: list_P1999446415t_char,H_9: nat > option1728594148on_val] :
( ( hconf_97414254t_char @ P_12 @ H_9 )
=> ( ( ( H_9 @ A_38 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_16 @ Fs_7 ) ) )
=> ( ( oconf_1869808039t_char @ P_12 @ H_9 @ ( produc926070009on_val @ C_16 @ Fs_8 ) )
=> ( hconf_97414254t_char @ P_12 @ ( fun_up1472480727on_val @ H_9 @ A_38 @ ( some_P451527732on_val @ ( produc926070009on_val @ C_16 @ Fs_8 ) ) ) ) ) ) ) ).
thf(fact_587_redp__redsp_OInitBlockRed,axiom,
! [T: ty,V_4: val,P: list_P1999446415t_char,E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,V_1: list_char,V: val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val] :
( ( redp @ P @ E_1 @ ( produc755559506on_val @ H_1 @ ( fun_up1149430426on_val @ L_1 @ V_1 @ ( some_val @ V ) ) ) @ E @ ( produc755559506on_val @ H @ L ) )
=> ( ( ( L @ V_1 )
= ( some_val @ V_4 ) )
=> ( redp @ P @ ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ E_1 ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) @ ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V_4 ) ) @ E ) ) @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_1 @ ( L_1 @ V_1 ) ) ) ) ) ) ).
thf(fact_588_red__reds_OBlockRedSome,axiom,
! [T: ty,V: val,E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,V_1: list_char,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ ( fun_up1149430426on_val @ L_1 @ V_1 @ none_val ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) ) @ ( red @ P ) )
=> ( ( ( L @ V_1 )
= ( some_val @ V ) )
=> ( ~ ( assigned @ V_1 @ E_1 )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_1 @ T @ E_1 ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ E ) ) @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_1 @ ( L_1 @ V_1 ) ) ) ) ) @ ( red @ P ) ) ) ) ) ).
thf(fact_589_WTrtLAss,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_1: exp_list_char,T_5: ty,E_2: list_char > option_ty,V_1: list_char,T: ty] :
( ( ( E_2 @ V_1 )
= ( some_ty @ T ) )
=> ( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ T_5 )
=> ( ( widen_2090681816t_char @ P @ T_5 @ T )
=> ( wTrt_1 @ P @ H_1 @ E_2 @ ( lAss_list_char @ V_1 @ E_1 ) @ void ) ) ) ) ).
thf(fact_590_LAssRedsVal,axiom,
! [V_1: list_char,E_1: exp_list_char,S: produc2090907612on_val,V: val,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ ( produc755559506on_val @ H @ L ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V_1 @ E_1 ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ unit ) @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_1 @ ( some_val @ V ) ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_591_hextI,axiom,
! [H: nat > option1728594148on_val,H_1: nat > option1728594148on_val] :
( ! [A_1: nat,C_1: list_char,Fs_1: produc1278157519t_char > option_val] :
( ( ( H_1 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs_1 ) ) )
=> ? [Fs_6: produc1278157519t_char > option_val] :
( ( H @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs_6 ) ) ) )
=> ( hext @ H_1 @ H ) ) ).
thf(fact_592_redp__redsp_ORedLAss,axiom,
! [P: list_P1999446415t_char,V_1: list_char,V: val,H_1: nat > option1728594148on_val,L_1: list_char > option_val] : ( redp @ P @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) @ ( val_list_char @ unit ) @ ( produc755559506on_val @ H_1 @ ( fun_up1149430426on_val @ L_1 @ V_1 @ ( some_val @ V ) ) ) ) ).
thf(fact_593_red__lcl__incr,axiom,
! [E_1: exp_list_char,H_0: nat > option1728594148on_val,L_0: list_char > option_val,E: exp_list_char,H_1_1: nat > option1728594148on_val,L_1_1: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_0 @ L_0 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H_1_1 @ L_1_1 ) ) ) @ ( red @ P ) )
=> ( ord_le1777678169char_o @ ( dom_list_char_val @ L_0 ) @ ( dom_list_char_val @ L_1_1 ) ) ) ).
thf(fact_594_lconf__empty,axiom,
! [P_11: list_P1999446415t_char,H_8: nat > option1728594148on_val,E_6: list_char > option_ty] :
( lconf_496643946t_char @ P_11 @ H_8
@ ^ [X: list_char] : none_val
@ E_6 ) ).
thf(fact_595_rev__predicate1D,axiom,
! [Q_1: list_char > $o,P_10: list_char > $o,X_27: list_char] :
( ( P_10 @ X_27 )
=> ( ( ord_le1777678169char_o @ P_10 @ Q_1 )
=> ( Q_1 @ X_27 ) ) ) ).
thf(fact_596_predicate1D,axiom,
! [X_26: list_char,P_9: list_char > $o,Q: list_char > $o] :
( ( ord_le1777678169char_o @ P_9 @ Q )
=> ( ( P_9 @ X_26 )
=> ( Q @ X_26 ) ) ) ).
thf(fact_597_pred__subset__eq,axiom,
! [R_17: produc1013743697t_char > $o,S_9: produc1013743697t_char > $o] :
( ( ord_le1156912648char_o
@ ^ [X: produc1013743697t_char] : ( member1601084734t_char @ X @ R_17 )
@ ^ [X: produc1013743697t_char] : ( member1601084734t_char @ X @ S_9 ) )
<=> ( ord_le1156912648char_o @ R_17 @ S_9 ) ) ).
thf(fact_598_pred__subset__eq,axiom,
! [R_17: produc1971331930t_char > $o,S_9: produc1971331930t_char > $o] :
( ( ord_le139275609char_o
@ ^ [X: produc1971331930t_char] : ( member1467889965t_char @ X @ R_17 )
@ ^ [X: produc1971331930t_char] : ( member1467889965t_char @ X @ S_9 ) )
<=> ( ord_le139275609char_o @ R_17 @ S_9 ) ) ).
thf(fact_599_pred__subset__eq,axiom,
! [R_17: produc618524391on_val > $o,S_9: produc618524391on_val > $o] :
( ( ord_le559588722_val_o
@ ^ [X: produc618524391on_val] : ( member2042188884on_val @ X @ R_17 )
@ ^ [X: produc618524391on_val] : ( member2042188884on_val @ X @ S_9 ) )
<=> ( ord_le559588722_val_o @ R_17 @ S_9 ) ) ).
thf(fact_600_pred__subset__eq,axiom,
! [R_17: nat > $o,S_9: nat > $o] :
( ( ord_less_eq_nat_o
@ ^ [X: nat] : ( member_nat @ X @ R_17 )
@ ^ [X: nat] : ( member_nat @ X @ S_9 ) )
<=> ( ord_less_eq_nat_o @ R_17 @ S_9 ) ) ).
thf(fact_601_pred__subset__eq,axiom,
! [R_17: produc1278157519t_char > $o,S_9: produc1278157519t_char > $o] :
( ( ord_le7825418char_o
@ ^ [X: produc1278157519t_char] : ( member1251428284t_char @ X @ R_17 )
@ ^ [X: produc1278157519t_char] : ( member1251428284t_char @ X @ S_9 ) )
<=> ( ord_le7825418char_o @ R_17 @ S_9 ) ) ).
thf(fact_602_pred__subset__eq,axiom,
! [R_17: list_char > $o,S_9: list_char > $o] :
( ( ord_le1777678169char_o
@ ^ [X: list_char] : ( member_list_char @ X @ R_17 )
@ ^ [X: list_char] : ( member_list_char @ X @ S_9 ) )
<=> ( ord_le1777678169char_o @ R_17 @ S_9 ) ) ).
thf(fact_603_pred__subset__eq,axiom,
! [R_17: produc1746408499on_val > $o,S_9: produc1746408499on_val > $o] :
( ( ord_le1364969894_val_o
@ ^ [X: produc1746408499on_val] : ( member1913460000on_val @ X @ R_17 )
@ ^ [X: produc1746408499on_val] : ( member1913460000on_val @ X @ S_9 ) )
<=> ( ord_le1364969894_val_o @ R_17 @ S_9 ) ) ).
thf(fact_604_option_Osimps_I2_J,axiom,
! [A_37: nat] :
( none_nat
!= ( some_nat @ A_37 ) ) ).
thf(fact_605_option_Osimps_I2_J,axiom,
! [A_37: ty] :
( none_ty
!= ( some_ty @ A_37 ) ) ).
thf(fact_606_option_Osimps_I2_J,axiom,
! [A_37: produc2088785539on_val] :
( none_P1260844216on_val
!= ( some_P451527732on_val @ A_37 ) ) ).
thf(fact_607_option_Osimps_I2_J,axiom,
! [A_37: val] :
( none_val
!= ( some_val @ A_37 ) ) ).
thf(fact_608_option_Osimps_I2_J,axiom,
! [A_37: list_char > $o] :
( none_list_char_o
!= ( some_list_char_o @ A_37 ) ) ).
thf(fact_609_option_Osimps_I3_J,axiom,
! [A_36: nat] :
( ( some_nat @ A_36 )
!= none_nat ) ).
thf(fact_610_option_Osimps_I3_J,axiom,
! [A_36: ty] :
( ( some_ty @ A_36 )
!= none_ty ) ).
thf(fact_611_option_Osimps_I3_J,axiom,
! [A_36: produc2088785539on_val] :
( ( some_P451527732on_val @ A_36 )
!= none_P1260844216on_val ) ).
thf(fact_612_option_Osimps_I3_J,axiom,
! [A_36: val] :
( ( some_val @ A_36 )
!= none_val ) ).
thf(fact_613_option_Osimps_I3_J,axiom,
! [A_36: list_char > $o] :
( ( some_list_char_o @ A_36 )
!= none_list_char_o ) ).
thf(fact_614_not__Some__eq,axiom,
! [X_25: option_nat] :
( ! [Y_1: nat] :
( X_25
!= ( some_nat @ Y_1 ) )
<=> ( X_25 = none_nat ) ) ).
thf(fact_615_not__Some__eq,axiom,
! [X_25: option_ty] :
( ! [Y_1: ty] :
( X_25
!= ( some_ty @ Y_1 ) )
<=> ( X_25 = none_ty ) ) ).
thf(fact_616_not__Some__eq,axiom,
! [X_25: option1728594148on_val] :
( ! [Y_1: produc2088785539on_val] :
( X_25
!= ( some_P451527732on_val @ Y_1 ) )
<=> ( X_25 = none_P1260844216on_val ) ) ).
thf(fact_617_not__Some__eq,axiom,
! [X_25: option_val] :
( ! [Y_1: val] :
( X_25
!= ( some_val @ Y_1 ) )
<=> ( X_25 = none_val ) ) ).
thf(fact_618_not__Some__eq,axiom,
! [X_25: option_list_char_o] :
( ! [Y_1: list_char > $o] :
( X_25
!= ( some_list_char_o @ Y_1 ) )
<=> ( X_25 = none_list_char_o ) ) ).
thf(fact_619_not__None__eq,axiom,
! [X_24: option_nat] :
( ( X_24 != none_nat )
<=> ? [Y_1: nat] :
( X_24
= ( some_nat @ Y_1 ) ) ) ).
thf(fact_620_not__None__eq,axiom,
! [X_24: option_ty] :
( ( X_24 != none_ty )
<=> ? [Y_1: ty] :
( X_24
= ( some_ty @ Y_1 ) ) ) ).
thf(fact_621_not__None__eq,axiom,
! [X_24: option1728594148on_val] :
( ( X_24 != none_P1260844216on_val )
<=> ? [Y_1: produc2088785539on_val] :
( X_24
= ( some_P451527732on_val @ Y_1 ) ) ) ).
thf(fact_622_not__None__eq,axiom,
! [X_24: option_val] :
( ( X_24 != none_val )
<=> ? [Y_1: val] :
( X_24
= ( some_val @ Y_1 ) ) ) ).
thf(fact_623_not__None__eq,axiom,
! [X_24: option_list_char_o] :
( ( X_24 != none_list_char_o )
<=> ? [Y_1: list_char > $o] :
( X_24
= ( some_list_char_o @ Y_1 ) ) ) ).
thf(fact_624_redp__redsp_OLAssRed,axiom,
! [V_1: list_char,P: list_P1999446415t_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S @ E @ S_2 )
=> ( redp @ P @ ( lAss_list_char @ V_1 @ E_1 ) @ S @ ( lAss_list_char @ V_1 @ E ) @ S_2 ) ) ).
thf(fact_625_redp__redsp_OSeqRed,axiom,
! [E_2_1: exp_list_char,P: list_P1999446415t_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S @ E @ S_2 )
=> ( redp @ P @ ( seq_list_char @ E_1 @ E_2_1 ) @ S @ ( seq_list_char @ E @ E_2_1 ) @ S_2 ) ) ).
thf(fact_626_dom__def,axiom,
! [M_7: nat > option1728594148on_val] :
( ( dom_na2045926843on_val @ M_7 )
= ( collect_nat
@ ^ [A_1: nat] :
( (~)
@ ( ( M_7 @ A_1 )
= none_P1260844216on_val ) ) ) ) ).
thf(fact_627_dom__def,axiom,
! [M_7: list_char > option_val] :
( ( dom_list_char_val @ M_7 )
= ( collect_list_char
@ ^ [A_1: list_char] :
( (~)
@ ( ( M_7 @ A_1 )
= none_val ) ) ) ) ).
thf(fact_628_domIff,axiom,
! [A_35: nat,M_6: nat > option1728594148on_val] :
( ( member_nat @ A_35 @ ( dom_na2045926843on_val @ M_6 ) )
<=> ( ( M_6 @ A_35 )
!= none_P1260844216on_val ) ) ).
thf(fact_629_domIff,axiom,
! [A_35: list_char,M_6: list_char > option_val] :
( ( member_list_char @ A_35 @ ( dom_list_char_val @ M_6 ) )
<=> ( ( M_6 @ A_35 )
!= none_val ) ) ).
thf(fact_630_redp__redsp_OBlockRedNone,axiom,
! [T: ty,P: list_P1999446415t_char,E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,V_1: list_char,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val] :
( ( redp @ P @ E_1 @ ( produc755559506on_val @ H_1 @ ( fun_up1149430426on_val @ L_1 @ V_1 @ none_val ) ) @ E @ ( produc755559506on_val @ H @ L ) )
=> ( ( ( L @ V_1 )
= none_val )
=> ( ~ ( assigned @ V_1 @ E_1 )
=> ( redp @ P @ ( block_list_char @ V_1 @ T @ E_1 ) @ ( produc755559506on_val @ H_1 @ L_1 ) @ ( block_list_char @ V_1 @ T @ E ) @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_1 @ ( L_1 @ V_1 ) ) ) ) ) ) ) ).
thf(fact_631_map__add__None,axiom,
! [M_5: list_char > option_val,N_2: list_char > option_val,K_3: list_char] :
( ( ( map_ad325961431ar_val @ M_5 @ N_2 @ K_3 )
= none_val )
<=> ( ( ( N_2 @ K_3 )
= none_val )
& ( ( M_5 @ K_3 )
= none_val ) ) ) ).
thf(fact_632_empty__upd__none,axiom,
! [X_23: produc1278157519t_char,X: produc1278157519t_char] :
( ( fun_up204312361on_val
@ ^ [Y_1: produc1278157519t_char] : none_val
@ X_23
@ none_val
@ X )
= none_val ) ).
thf(fact_633_empty__upd__none,axiom,
! [X_23: nat,X: nat] :
( ( fun_up1472480727on_val
@ ^ [Y_1: nat] : none_P1260844216on_val
@ X_23
@ none_P1260844216on_val
@ X )
= none_P1260844216on_val ) ).
thf(fact_634_empty__upd__none,axiom,
! [X_23: list_char,X: list_char] :
( ( fun_up424764369ion_ty
@ ^ [Y_1: list_char] : none_ty
@ X_23
@ none_ty
@ X )
= none_ty ) ).
thf(fact_635_empty__upd__none,axiom,
! [X_23: list_char,X: list_char] :
( ( fun_up1149430426on_val
@ ^ [Y_1: list_char] : none_val
@ X_23
@ none_val
@ X )
= none_val ) ).
thf(fact_636_map__add__empty,axiom,
! [M_4: list_char > option_val] :
( ( map_ad325961431ar_val @ M_4
@ ^ [X: list_char] : none_val )
= M_4 ) ).
thf(fact_637_empty__map__add,axiom,
! [M_3: list_char > option_val] :
( ( map_ad325961431ar_val
@ ^ [X: list_char] : none_val
@ M_3 )
= M_3 ) ).
thf(fact_638_redp__redsp_ORedSeq,axiom,
! [P: list_P1999446415t_char,V: val,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( seq_list_char @ ( val_list_char @ V ) @ E_2_1 ) @ S @ E_2_1 @ S ) ).
thf(fact_639_map__upd__nonempty,axiom,
! [T_8: produc1278157519t_char > option_val,K_2: produc1278157519t_char,X_22: val] :
~ ! [X: produc1278157519t_char] :
( ( fun_up204312361on_val @ T_8 @ K_2 @ ( some_val @ X_22 ) @ X )
= none_val ) ).
thf(fact_640_map__upd__nonempty,axiom,
! [T_8: nat > option1728594148on_val,K_2: nat,X_22: produc2088785539on_val] :
~ ! [X: nat] :
( ( fun_up1472480727on_val @ T_8 @ K_2 @ ( some_P451527732on_val @ X_22 ) @ X )
= none_P1260844216on_val ) ).
thf(fact_641_map__upd__nonempty,axiom,
! [T_8: list_char > option_ty,K_2: list_char,X_22: ty] :
~ ! [X: list_char] :
( ( fun_up424764369ion_ty @ T_8 @ K_2 @ ( some_ty @ X_22 ) @ X )
= none_ty ) ).
thf(fact_642_map__upd__nonempty,axiom,
! [T_8: list_char > option_val,K_2: list_char,X_22: val] :
~ ! [X: list_char] :
( ( fun_up1149430426on_val @ T_8 @ K_2 @ ( some_val @ X_22 ) @ X )
= none_val ) ).
thf(fact_643_redp__redsp_ORedBlock,axiom,
! [P: list_P1999446415t_char,V_1: list_char,T: ty,U: val,S: produc2090907612on_val] : ( redp @ P @ ( block_list_char @ V_1 @ T @ ( val_list_char @ U ) ) @ S @ ( val_list_char @ U ) @ S ) ).
thf(fact_644_map__add__SomeD,axiom,
! [M_2: list_char > option_val,N_1: list_char > option_val,K_1: list_char,X_21: val] :
( ( ( map_ad325961431ar_val @ M_2 @ N_1 @ K_1 )
= ( some_val @ X_21 ) )
=> ( ( ( N_1 @ K_1 )
= ( some_val @ X_21 ) )
| ( ( ( N_1 @ K_1 )
= none_val )
& ( ( M_2 @ K_1 )
= ( some_val @ X_21 ) ) ) ) ) ).
thf(fact_645_map__add__Some__iff,axiom,
! [M_1: list_char > option_val,N: list_char > option_val,K: list_char,X_20: val] :
( ( ( map_ad325961431ar_val @ M_1 @ N @ K )
= ( some_val @ X_20 ) )
<=> ( ( ( N @ K )
= ( some_val @ X_20 ) )
| ( ( ( N @ K )
= none_val )
& ( ( M_1 @ K )
= ( some_val @ X_20 ) ) ) ) ) ).
thf(fact_646_SeqReds,axiom,
! [E_2_1: exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ E_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( seq_list_char @ E @ E_2_1 ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_647_LAssReds,axiom,
! [V_1: list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V_1 @ E_1 ) @ S ) @ ( produc235638504on_val @ ( lAss_list_char @ V_1 @ E ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_648_redp__redsp_OBlockRedSome,axiom,
! [T: ty,V: val,P: list_P1999446415t_char,E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,V_1: list_char,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val] :
( ( redp @ P @ E_1 @ ( produc755559506on_val @ H_1 @ ( fun_up1149430426on_val @ L_1 @ V_1 @ none_val ) ) @ E @ ( produc755559506on_val @ H @ L ) )
=> ( ( ( L @ V_1 )
= ( some_val @ V ) )
=> ( ~ ( assigned @ V_1 @ E_1 )
=> ( redp @ P @ ( block_list_char @ V_1 @ T @ E_1 ) @ ( produc755559506on_val @ H_1 @ L_1 ) @ ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ E ) ) @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_1 @ ( L_1 @ V_1 ) ) ) ) ) ) ) ).
thf(fact_649_SeqReds2,axiom,
! [E_2_1: exp_list_char,E_2_2: exp_list_char,S_2_1: produc2090907612on_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1_2: 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_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2_1 @ S_1 ) @ ( produc235638504on_val @ E_2_2 @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ E_1_1 @ E_2_1 ) @ S_0 ) @ ( produc235638504on_val @ E_2_2 @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_650_redp__red__eq,axiom,
! [P: list_P1999446415t_char,X: exp_list_char,Xa: produc2090907612on_val,Xb: exp_list_char,Xc: produc2090907612on_val] :
( ( redp @ P @ X @ Xa @ Xb @ Xc )
<=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ X @ Xa ) @ ( produc235638504on_val @ Xb @ Xc ) ) @ ( red @ P ) ) ) ).
thf(fact_651_hconfD,axiom,
! [A_34: nat,Obj_1: produc2088785539on_val,P_8: list_P1999446415t_char,H_7: nat > option1728594148on_val] :
( ( hconf_97414254t_char @ P_8 @ H_7 )
=> ( ( ( H_7 @ A_34 )
= ( some_P451527732on_val @ Obj_1 ) )
=> ( oconf_1869808039t_char @ P_8 @ H_7 @ Obj_1 ) ) ) ).
thf(fact_652_redp__redsp_ORedInitBlock,axiom,
! [P: list_P1999446415t_char,V_1: list_char,T: ty,V: val,U: val,S: produc2090907612on_val] : ( redp @ P @ ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ ( val_list_char @ U ) ) ) @ S @ ( val_list_char @ U ) @ S ) ).
thf(fact_653_red__reds_OBlockRedNone,axiom,
! [T: ty,E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,V_1: list_char,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ ( fun_up1149430426on_val @ L_1 @ V_1 @ none_val ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) ) @ ( red @ P ) )
=> ( ( ( L @ V_1 )
= none_val )
=> ( ~ ( assigned @ V_1 @ E_1 )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_1 @ T @ E_1 ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ ( block_list_char @ V_1 @ T @ E ) @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_1 @ ( L_1 @ V_1 ) ) ) ) ) @ ( red @ P ) ) ) ) ) ).
thf(fact_654_Red__lcl__add,axiom,
! [L_0: list_char > option_val,E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ ( map_ad325961431ar_val @ L_0 @ L_1 ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ ( map_ad325961431ar_val @ L_0 @ L ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_655_WTrt__elim__cases_I1_J,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,V: list_char,E_1: exp_list_char,T: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ ( lAss_list_char @ V @ E_1 ) @ T )
=> ~ ( ( T = void )
=> ! [T_4: ty] :
( ( ( E_2 @ V )
= ( some_ty @ T_4 ) )
=> ! [T_7: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ T_7 )
=> ~ ( widen_2090681816t_char @ P @ T_7 @ T_4 ) ) ) ) ) ).
thf(fact_656_InitBlockReds,axiom,
! [T: ty,E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,V_1: list_char,V: val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ ( fun_up1149430426on_val @ L_1 @ V_1 @ ( some_val @ V ) ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ E_1 ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ ( the_val @ ( L @ V_1 ) ) ) ) @ E ) ) @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_1 @ ( L_1 @ V_1 ) ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_657_InitBlockRedsFinal,axiom,
! [T: ty,E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,V_1: list_char,V: val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ ( fun_up1149430426on_val @ L_1 @ V_1 @ ( some_val @ V ) ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( final_list_char @ E )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ E_1 ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L @ V_1 @ ( L_1 @ V_1 ) ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_658_assigned__def,axiom,
! [V_1: list_char,E_1: exp_list_char] :
( ( assigned @ V_1 @ E_1 )
<=> ? [V_2: val,E_3: exp_list_char] :
( E_1
= ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V_2 ) ) @ E_3 ) ) ) ).
thf(fact_659_rtrancl_Ortrancl__refl,axiom,
! [A_33: produc1180562163on_val,R_16: produc618524391on_val > $o] : ( member2042188884on_val @ ( produc747700183on_val @ A_33 @ A_33 ) @ ( transi808828192on_val @ R_16 ) ) ).
thf(fact_660_rtrancl_Ortrancl__refl,axiom,
! [A_33: list_char,R_16: produc1278157519t_char > $o] : ( member1251428284t_char @ ( produc5062597t_char @ A_33 @ A_33 ) @ ( transi1395422419t_char @ R_16 ) ) ).
thf(fact_661_rtrancl_Ortrancl__refl,axiom,
! [A_33: produc1282892786on_val,R_16: produc1746408499on_val > $o] : ( member1913460000on_val @ ( produc833389609on_val @ A_33 @ A_33 ) @ ( transi2118771717on_val @ R_16 ) ) ).
thf(fact_662_rtrancl_Ortrancl__refl,axiom,
! [A_33: val,R_16: product_prod_val_val > $o] : ( member649088532al_val @ ( product_Pair_val_val @ A_33 @ A_33 ) @ ( transi935034983cl_val @ R_16 ) ) ).
thf(fact_663_BlockRedsFinal,axiom,
! [T: ty,H_0: nat > option1728594148on_val,L_0: list_char > option_val,V_1: list_char,E_0: exp_list_char,S_0: produc2090907612on_val,E_2_1: exp_list_char,H_2: nat > option1728594148on_val,L_2_1: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_0 @ S_0 ) @ ( produc235638504on_val @ E_2_1 @ ( produc755559506on_val @ H_2 @ L_2_1 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( final_list_char @ E_2_1 )
=> ( ( S_0
= ( produc755559506on_val @ H_0 @ ( fun_up1149430426on_val @ L_0 @ V_1 @ none_val ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_1 @ T @ E_0 ) @ ( produc755559506on_val @ H_0 @ L_0 ) ) @ ( produc235638504on_val @ E_2_1 @ ( produc755559506on_val @ H_2 @ ( fun_up1149430426on_val @ L_2_1 @ V_1 @ ( L_0 @ V_1 ) ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_664_oconf__fupd,axiom,
! [Fs_5: produc1278157519t_char > option_val,H_6: nat > option1728594148on_val,V_3: val,P_7: list_P1999446415t_char,C_15: list_char,F_5: list_char,T_6: ty,D_1: list_char] :
( ( has_fi1183600461t_char @ P_7 @ C_15 @ F_5 @ T_6 @ D_1 )
=> ( ( conf_P373316194t_char @ P_7 @ H_6 @ V_3 @ T_6 )
=> ( ( oconf_1869808039t_char @ P_7 @ H_6 @ ( produc926070009on_val @ C_15 @ Fs_5 ) )
=> ( oconf_1869808039t_char @ P_7 @ H_6 @ ( produc926070009on_val @ C_15 @ ( fun_up204312361on_val @ Fs_5 @ ( produc5062597t_char @ F_5 @ D_1 ) @ ( some_val @ V_3 ) ) ) ) ) ) ) ).
thf(fact_665_r__into__rtrancl,axiom,
! [P_6: produc618524391on_val,R_15: produc618524391on_val > $o] :
( ( member2042188884on_val @ P_6 @ R_15 )
=> ( member2042188884on_val @ P_6 @ ( transi808828192on_val @ R_15 ) ) ) ).
thf(fact_666_r__into__rtrancl,axiom,
! [P_6: produc1278157519t_char,R_15: produc1278157519t_char > $o] :
( ( member1251428284t_char @ P_6 @ R_15 )
=> ( member1251428284t_char @ P_6 @ ( transi1395422419t_char @ R_15 ) ) ) ).
thf(fact_667_r__into__rtrancl,axiom,
! [P_6: produc1746408499on_val,R_15: produc1746408499on_val > $o] :
( ( member1913460000on_val @ P_6 @ R_15 )
=> ( member1913460000on_val @ P_6 @ ( transi2118771717on_val @ R_15 ) ) ) ).
thf(fact_668_equalityI,axiom,
! [A_32: list_char > $o,B_28: list_char > $o] :
( ( ord_le1777678169char_o @ A_32 @ B_28 )
=> ( ( ord_le1777678169char_o @ B_28 @ A_32 )
=> ( A_32 = B_28 ) ) ) ).
thf(fact_669_subsetD,axiom,
! [C_14: produc1013743697t_char,A_31: produc1013743697t_char > $o,B_27: produc1013743697t_char > $o] :
( ( ord_le1156912648char_o @ A_31 @ B_27 )
=> ( ( member1601084734t_char @ C_14 @ A_31 )
=> ( member1601084734t_char @ C_14 @ B_27 ) ) ) ).
thf(fact_670_subsetD,axiom,
! [C_14: produc1971331930t_char,A_31: produc1971331930t_char > $o,B_27: produc1971331930t_char > $o] :
( ( ord_le139275609char_o @ A_31 @ B_27 )
=> ( ( member1467889965t_char @ C_14 @ A_31 )
=> ( member1467889965t_char @ C_14 @ B_27 ) ) ) ).
thf(fact_671_subsetD,axiom,
! [C_14: produc618524391on_val,A_31: produc618524391on_val > $o,B_27: produc618524391on_val > $o] :
( ( ord_le559588722_val_o @ A_31 @ B_27 )
=> ( ( member2042188884on_val @ C_14 @ A_31 )
=> ( member2042188884on_val @ C_14 @ B_27 ) ) ) ).
thf(fact_672_subsetD,axiom,
! [C_14: nat,A_31: nat > $o,B_27: nat > $o] :
( ( ord_less_eq_nat_o @ A_31 @ B_27 )
=> ( ( member_nat @ C_14 @ A_31 )
=> ( member_nat @ C_14 @ B_27 ) ) ) ).
thf(fact_673_subsetD,axiom,
! [C_14: produc1278157519t_char,A_31: produc1278157519t_char > $o,B_27: produc1278157519t_char > $o] :
( ( ord_le7825418char_o @ A_31 @ B_27 )
=> ( ( member1251428284t_char @ C_14 @ A_31 )
=> ( member1251428284t_char @ C_14 @ B_27 ) ) ) ).
thf(fact_674_subsetD,axiom,
! [C_14: list_char,A_31: list_char > $o,B_27: list_char > $o] :
( ( ord_le1777678169char_o @ A_31 @ B_27 )
=> ( ( member_list_char @ C_14 @ A_31 )
=> ( member_list_char @ C_14 @ B_27 ) ) ) ).
thf(fact_675_subsetD,axiom,
! [C_14: produc1746408499on_val,A_31: produc1746408499on_val > $o,B_27: produc1746408499on_val > $o] :
( ( ord_le1364969894_val_o @ A_31 @ B_27 )
=> ( ( member1913460000on_val @ C_14 @ A_31 )
=> ( member1913460000on_val @ C_14 @ B_27 ) ) ) ).
thf(fact_676_rtrancl__mono,axiom,
! [R_14: produc618524391on_val > $o,S_8: produc618524391on_val > $o] :
( ( ord_le559588722_val_o @ R_14 @ S_8 )
=> ( ord_le559588722_val_o @ ( transi808828192on_val @ R_14 ) @ ( transi808828192on_val @ S_8 ) ) ) ).
thf(fact_677_rtrancl__mono,axiom,
! [R_14: produc1278157519t_char > $o,S_8: produc1278157519t_char > $o] :
( ( ord_le7825418char_o @ R_14 @ S_8 )
=> ( ord_le7825418char_o @ ( transi1395422419t_char @ R_14 ) @ ( transi1395422419t_char @ S_8 ) ) ) ).
thf(fact_678_rtrancl__mono,axiom,
! [R_14: produc1746408499on_val > $o,S_8: produc1746408499on_val > $o] :
( ( ord_le1364969894_val_o @ R_14 @ S_8 )
=> ( ord_le1364969894_val_o @ ( transi2118771717on_val @ R_14 ) @ ( transi2118771717on_val @ S_8 ) ) ) ).
thf(fact_679_rtrancl__subset,axiom,
! [R_13: produc618524391on_val > $o,S_7: produc618524391on_val > $o] :
( ( ord_le559588722_val_o @ R_13 @ S_7 )
=> ( ( ord_le559588722_val_o @ S_7 @ ( transi808828192on_val @ R_13 ) )
=> ( ( transi808828192on_val @ S_7 )
= ( transi808828192on_val @ R_13 ) ) ) ) ).
thf(fact_680_rtrancl__subset,axiom,
! [R_13: produc1278157519t_char > $o,S_7: produc1278157519t_char > $o] :
( ( ord_le7825418char_o @ R_13 @ S_7 )
=> ( ( ord_le7825418char_o @ S_7 @ ( transi1395422419t_char @ R_13 ) )
=> ( ( transi1395422419t_char @ S_7 )
= ( transi1395422419t_char @ R_13 ) ) ) ) ).
thf(fact_681_rtrancl__subset,axiom,
! [R_13: produc1746408499on_val > $o,S_7: produc1746408499on_val > $o] :
( ( ord_le1364969894_val_o @ R_13 @ S_7 )
=> ( ( ord_le1364969894_val_o @ S_7 @ ( transi2118771717on_val @ R_13 ) )
=> ( ( transi2118771717on_val @ S_7 )
= ( transi2118771717on_val @ R_13 ) ) ) ) ).
thf(fact_682_rtrancl__subset__rtrancl,axiom,
! [R_12: produc618524391on_val > $o,S_6: produc618524391on_val > $o] :
( ( ord_le559588722_val_o @ R_12 @ ( transi808828192on_val @ S_6 ) )
=> ( ord_le559588722_val_o @ ( transi808828192on_val @ R_12 ) @ ( transi808828192on_val @ S_6 ) ) ) ).
thf(fact_683_rtrancl__subset__rtrancl,axiom,
! [R_12: produc1278157519t_char > $o,S_6: produc1278157519t_char > $o] :
( ( ord_le7825418char_o @ R_12 @ ( transi1395422419t_char @ S_6 ) )
=> ( ord_le7825418char_o @ ( transi1395422419t_char @ R_12 ) @ ( transi1395422419t_char @ S_6 ) ) ) ).
thf(fact_684_rtrancl__subset__rtrancl,axiom,
! [R_12: produc1746408499on_val > $o,S_6: produc1746408499on_val > $o] :
( ( ord_le1364969894_val_o @ R_12 @ ( transi2118771717on_val @ S_6 ) )
=> ( ord_le1364969894_val_o @ ( transi2118771717on_val @ R_12 ) @ ( transi2118771717on_val @ S_6 ) ) ) ).
thf(fact_685_the_Osimps,axiom,
! [X_19: val] :
( ( the_val @ ( some_val @ X_19 ) )
= X_19 ) ).
thf(fact_686_the_Osimps,axiom,
! [X_19: nat] :
( ( the_nat @ ( some_nat @ X_19 ) )
= X_19 ) ).
thf(fact_687_the_Osimps,axiom,
! [X_19: produc2088785539on_val] :
( ( the_Pr1885945130on_val @ ( some_P451527732on_val @ X_19 ) )
= X_19 ) ).
thf(fact_688_the_Osimps,axiom,
! [X_19: ty] :
( ( the_ty @ ( some_ty @ X_19 ) )
= X_19 ) ).
thf(fact_689_the_Osimps,axiom,
! [X_19: list_char > $o] :
( ( the_list_char_o @ ( some_list_char_o @ X_19 ) )
= X_19 ) ).
thf(fact_690_subset__refl,axiom,
! [A_30: list_char > $o] : ( ord_le1777678169char_o @ A_30 @ A_30 ) ).
thf(fact_691_set__eq__subset,axiom,
! [A_29: list_char > $o,B_26: list_char > $o] :
( ( A_29 = B_26 )
<=> ( ( ord_le1777678169char_o @ A_29 @ B_26 )
& ( ord_le1777678169char_o @ B_26 @ A_29 ) ) ) ).
thf(fact_692_equalityD1,axiom,
! [A_28: list_char > $o,B_25: list_char > $o] :
( ( A_28 = B_25 )
=> ( ord_le1777678169char_o @ A_28 @ B_25 ) ) ).
thf(fact_693_equalityD2,axiom,
! [A_27: list_char > $o,B_24: list_char > $o] :
( ( A_27 = B_24 )
=> ( ord_le1777678169char_o @ B_24 @ A_27 ) ) ).
thf(fact_694_in__mono,axiom,
! [X_18: produc1013743697t_char,A_26: produc1013743697t_char > $o,B_23: produc1013743697t_char > $o] :
( ( ord_le1156912648char_o @ A_26 @ B_23 )
=> ( ( member1601084734t_char @ X_18 @ A_26 )
=> ( member1601084734t_char @ X_18 @ B_23 ) ) ) ).
thf(fact_695_in__mono,axiom,
! [X_18: produc1971331930t_char,A_26: produc1971331930t_char > $o,B_23: produc1971331930t_char > $o] :
( ( ord_le139275609char_o @ A_26 @ B_23 )
=> ( ( member1467889965t_char @ X_18 @ A_26 )
=> ( member1467889965t_char @ X_18 @ B_23 ) ) ) ).
thf(fact_696_in__mono,axiom,
! [X_18: produc618524391on_val,A_26: produc618524391on_val > $o,B_23: produc618524391on_val > $o] :
( ( ord_le559588722_val_o @ A_26 @ B_23 )
=> ( ( member2042188884on_val @ X_18 @ A_26 )
=> ( member2042188884on_val @ X_18 @ B_23 ) ) ) ).
thf(fact_697_in__mono,axiom,
! [X_18: nat,A_26: nat > $o,B_23: nat > $o] :
( ( ord_less_eq_nat_o @ A_26 @ B_23 )
=> ( ( member_nat @ X_18 @ A_26 )
=> ( member_nat @ X_18 @ B_23 ) ) ) ).
thf(fact_698_in__mono,axiom,
! [X_18: produc1278157519t_char,A_26: produc1278157519t_char > $o,B_23: produc1278157519t_char > $o] :
( ( ord_le7825418char_o @ A_26 @ B_23 )
=> ( ( member1251428284t_char @ X_18 @ A_26 )
=> ( member1251428284t_char @ X_18 @ B_23 ) ) ) ).
thf(fact_699_in__mono,axiom,
! [X_18: list_char,A_26: list_char > $o,B_23: list_char > $o] :
( ( ord_le1777678169char_o @ A_26 @ B_23 )
=> ( ( member_list_char @ X_18 @ A_26 )
=> ( member_list_char @ X_18 @ B_23 ) ) ) ).
thf(fact_700_in__mono,axiom,
! [X_18: produc1746408499on_val,A_26: produc1746408499on_val > $o,B_23: produc1746408499on_val > $o] :
( ( ord_le1364969894_val_o @ A_26 @ B_23 )
=> ( ( member1913460000on_val @ X_18 @ A_26 )
=> ( member1913460000on_val @ X_18 @ B_23 ) ) ) ).
thf(fact_701_set__rev__mp,axiom,
! [B_22: produc1013743697t_char > $o,X_17: produc1013743697t_char,A_25: produc1013743697t_char > $o] :
( ( member1601084734t_char @ X_17 @ A_25 )
=> ( ( ord_le1156912648char_o @ A_25 @ B_22 )
=> ( member1601084734t_char @ X_17 @ B_22 ) ) ) ).
thf(fact_702_set__rev__mp,axiom,
! [B_22: produc1971331930t_char > $o,X_17: produc1971331930t_char,A_25: produc1971331930t_char > $o] :
( ( member1467889965t_char @ X_17 @ A_25 )
=> ( ( ord_le139275609char_o @ A_25 @ B_22 )
=> ( member1467889965t_char @ X_17 @ B_22 ) ) ) ).
thf(fact_703_set__rev__mp,axiom,
! [B_22: produc618524391on_val > $o,X_17: produc618524391on_val,A_25: produc618524391on_val > $o] :
( ( member2042188884on_val @ X_17 @ A_25 )
=> ( ( ord_le559588722_val_o @ A_25 @ B_22 )
=> ( member2042188884on_val @ X_17 @ B_22 ) ) ) ).
thf(fact_704_set__rev__mp,axiom,
! [B_22: nat > $o,X_17: nat,A_25: nat > $o] :
( ( member_nat @ X_17 @ A_25 )
=> ( ( ord_less_eq_nat_o @ A_25 @ B_22 )
=> ( member_nat @ X_17 @ B_22 ) ) ) ).
thf(fact_705_set__rev__mp,axiom,
! [B_22: produc1278157519t_char > $o,X_17: produc1278157519t_char,A_25: produc1278157519t_char > $o] :
( ( member1251428284t_char @ X_17 @ A_25 )
=> ( ( ord_le7825418char_o @ A_25 @ B_22 )
=> ( member1251428284t_char @ X_17 @ B_22 ) ) ) ).
thf(fact_706_set__rev__mp,axiom,
! [B_22: list_char > $o,X_17: list_char,A_25: list_char > $o] :
( ( member_list_char @ X_17 @ A_25 )
=> ( ( ord_le1777678169char_o @ A_25 @ B_22 )
=> ( member_list_char @ X_17 @ B_22 ) ) ) ).
thf(fact_707_set__rev__mp,axiom,
! [B_22: produc1746408499on_val > $o,X_17: produc1746408499on_val,A_25: produc1746408499on_val > $o] :
( ( member1913460000on_val @ X_17 @ A_25 )
=> ( ( ord_le1364969894_val_o @ A_25 @ B_22 )
=> ( member1913460000on_val @ X_17 @ B_22 ) ) ) ).
thf(fact_708_set__mp,axiom,
! [X_16: produc1013743697t_char,A_24: produc1013743697t_char > $o,B_21: produc1013743697t_char > $o] :
( ( ord_le1156912648char_o @ A_24 @ B_21 )
=> ( ( member1601084734t_char @ X_16 @ A_24 )
=> ( member1601084734t_char @ X_16 @ B_21 ) ) ) ).
thf(fact_709_set__mp,axiom,
! [X_16: produc1971331930t_char,A_24: produc1971331930t_char > $o,B_21: produc1971331930t_char > $o] :
( ( ord_le139275609char_o @ A_24 @ B_21 )
=> ( ( member1467889965t_char @ X_16 @ A_24 )
=> ( member1467889965t_char @ X_16 @ B_21 ) ) ) ).
thf(fact_710_set__mp,axiom,
! [X_16: produc618524391on_val,A_24: produc618524391on_val > $o,B_21: produc618524391on_val > $o] :
( ( ord_le559588722_val_o @ A_24 @ B_21 )
=> ( ( member2042188884on_val @ X_16 @ A_24 )
=> ( member2042188884on_val @ X_16 @ B_21 ) ) ) ).
thf(fact_711_set__mp,axiom,
! [X_16: nat,A_24: nat > $o,B_21: nat > $o] :
( ( ord_less_eq_nat_o @ A_24 @ B_21 )
=> ( ( member_nat @ X_16 @ A_24 )
=> ( member_nat @ X_16 @ B_21 ) ) ) ).
thf(fact_712_set__mp,axiom,
! [X_16: produc1278157519t_char,A_24: produc1278157519t_char > $o,B_21: produc1278157519t_char > $o] :
( ( ord_le7825418char_o @ A_24 @ B_21 )
=> ( ( member1251428284t_char @ X_16 @ A_24 )
=> ( member1251428284t_char @ X_16 @ B_21 ) ) ) ).
thf(fact_713_set__mp,axiom,
! [X_16: list_char,A_24: list_char > $o,B_21: list_char > $o] :
( ( ord_le1777678169char_o @ A_24 @ B_21 )
=> ( ( member_list_char @ X_16 @ A_24 )
=> ( member_list_char @ X_16 @ B_21 ) ) ) ).
thf(fact_714_set__mp,axiom,
! [X_16: produc1746408499on_val,A_24: produc1746408499on_val > $o,B_21: produc1746408499on_val > $o] :
( ( ord_le1364969894_val_o @ A_24 @ B_21 )
=> ( ( member1913460000on_val @ X_16 @ A_24 )
=> ( member1913460000on_val @ X_16 @ B_21 ) ) ) ).
thf(fact_715_subset__trans,axiom,
! [C_13: list_char > $o,A_23: list_char > $o,B_20: list_char > $o] :
( ( ord_le1777678169char_o @ A_23 @ B_20 )
=> ( ( ord_le1777678169char_o @ B_20 @ C_13 )
=> ( ord_le1777678169char_o @ A_23 @ C_13 ) ) ) ).
thf(fact_716_equalityE,axiom,
! [A_22: list_char > $o,B_19: list_char > $o] :
( ( A_22 = B_19 )
=> ~ ( ( ord_le1777678169char_o @ A_22 @ B_19 )
=> ~ ( ord_le1777678169char_o @ B_19 @ A_22 ) ) ) ).
thf(fact_717_hext__new,axiom,
! [X_1: produc2088785539on_val,H_1: nat > option1728594148on_val,A: nat] :
( ( ( H_1 @ A )
= none_P1260844216on_val )
=> ( hext @ H_1 @ ( fun_up1472480727on_val @ H_1 @ A @ ( some_P451527732on_val @ X_1 ) ) ) ) ).
thf(fact_718_rtrancl__idemp,axiom,
! [R_11: produc618524391on_val > $o] :
( ( transi808828192on_val @ ( transi808828192on_val @ R_11 ) )
= ( transi808828192on_val @ R_11 ) ) ).
thf(fact_719_rtrancl__idemp,axiom,
! [R_11: produc1278157519t_char > $o] :
( ( transi1395422419t_char @ ( transi1395422419t_char @ R_11 ) )
= ( transi1395422419t_char @ R_11 ) ) ).
thf(fact_720_rtrancl__idemp,axiom,
! [R_11: produc1746408499on_val > $o] :
( ( transi2118771717on_val @ ( transi2118771717on_val @ R_11 ) )
= ( transi2118771717on_val @ R_11 ) ) ).
thf(fact_721_hconf__new,axiom,
! [Obj: produc2088785539on_val,A_21: nat,P_5: list_P1999446415t_char,H_5: nat > option1728594148on_val] :
( ( hconf_97414254t_char @ P_5 @ H_5 )
=> ( ( ( H_5 @ A_21 )
= none_P1260844216on_val )
=> ( ( oconf_1869808039t_char @ P_5 @ H_5 @ Obj )
=> ( hconf_97414254t_char @ P_5 @ ( fun_up1472480727on_val @ H_5 @ A_21 @ ( some_P451527732on_val @ Obj ) ) ) ) ) ) ).
thf(fact_722_converse__rtrancl__into__rtrancl,axiom,
! [C_12: produc1180562163on_val,A_20: produc1180562163on_val,B_18: produc1180562163on_val,R_10: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_20 @ B_18 ) @ R_10 )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ B_18 @ C_12 ) @ ( transi808828192on_val @ R_10 ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ A_20 @ C_12 ) @ ( transi808828192on_val @ R_10 ) ) ) ) ).
thf(fact_723_converse__rtrancl__into__rtrancl,axiom,
! [C_12: list_char,A_20: list_char,B_18: list_char,R_10: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_20 @ B_18 ) @ R_10 )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ B_18 @ C_12 ) @ ( transi1395422419t_char @ R_10 ) )
=> ( member1251428284t_char @ ( produc5062597t_char @ A_20 @ C_12 ) @ ( transi1395422419t_char @ R_10 ) ) ) ) ).
thf(fact_724_converse__rtrancl__into__rtrancl,axiom,
! [C_12: produc1282892786on_val,A_20: produc1282892786on_val,B_18: produc1282892786on_val,R_10: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_20 @ B_18 ) @ R_10 )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ B_18 @ C_12 ) @ ( transi2118771717on_val @ R_10 ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ A_20 @ C_12 ) @ ( transi2118771717on_val @ R_10 ) ) ) ) ).
thf(fact_725_converse__rtrancl__into__rtrancl,axiom,
! [C_12: val,A_20: val,B_18: val,R_10: product_prod_val_val > $o] :
( ( member649088532al_val @ ( product_Pair_val_val @ A_20 @ B_18 ) @ R_10 )
=> ( ( member649088532al_val @ ( product_Pair_val_val @ B_18 @ C_12 ) @ ( transi935034983cl_val @ R_10 ) )
=> ( member649088532al_val @ ( product_Pair_val_val @ A_20 @ C_12 ) @ ( transi935034983cl_val @ R_10 ) ) ) ) ).
thf(fact_726_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_11: produc1180562163on_val,A_19: produc1180562163on_val,B_17: produc1180562163on_val,R_9: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_19 @ B_17 ) @ ( transi808828192on_val @ R_9 ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ B_17 @ C_11 ) @ R_9 )
=> ( member2042188884on_val @ ( produc747700183on_val @ A_19 @ C_11 ) @ ( transi808828192on_val @ R_9 ) ) ) ) ).
thf(fact_727_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_11: list_char,A_19: list_char,B_17: list_char,R_9: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_19 @ B_17 ) @ ( transi1395422419t_char @ R_9 ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ B_17 @ C_11 ) @ R_9 )
=> ( member1251428284t_char @ ( produc5062597t_char @ A_19 @ C_11 ) @ ( transi1395422419t_char @ R_9 ) ) ) ) ).
thf(fact_728_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_11: produc1282892786on_val,A_19: produc1282892786on_val,B_17: produc1282892786on_val,R_9: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_19 @ B_17 ) @ ( transi2118771717on_val @ R_9 ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ B_17 @ C_11 ) @ R_9 )
=> ( member1913460000on_val @ ( produc833389609on_val @ A_19 @ C_11 ) @ ( transi2118771717on_val @ R_9 ) ) ) ) ).
thf(fact_729_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_11: val,A_19: val,B_17: val,R_9: product_prod_val_val > $o] :
( ( member649088532al_val @ ( product_Pair_val_val @ A_19 @ B_17 ) @ ( transi935034983cl_val @ R_9 ) )
=> ( ( member649088532al_val @ ( product_Pair_val_val @ B_17 @ C_11 ) @ R_9 )
=> ( member649088532al_val @ ( product_Pair_val_val @ A_19 @ C_11 ) @ ( transi935034983cl_val @ R_9 ) ) ) ) ).
thf(fact_730_rtrancl__trans,axiom,
! [C_10: produc1180562163on_val,A_18: produc1180562163on_val,B_16: produc1180562163on_val,R_8: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_18 @ B_16 ) @ ( transi808828192on_val @ R_8 ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ B_16 @ C_10 ) @ ( transi808828192on_val @ R_8 ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ A_18 @ C_10 ) @ ( transi808828192on_val @ R_8 ) ) ) ) ).
thf(fact_731_rtrancl__trans,axiom,
! [C_10: list_char,A_18: list_char,B_16: list_char,R_8: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_18 @ B_16 ) @ ( transi1395422419t_char @ R_8 ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ B_16 @ C_10 ) @ ( transi1395422419t_char @ R_8 ) )
=> ( member1251428284t_char @ ( produc5062597t_char @ A_18 @ C_10 ) @ ( transi1395422419t_char @ R_8 ) ) ) ) ).
thf(fact_732_rtrancl__trans,axiom,
! [C_10: produc1282892786on_val,A_18: produc1282892786on_val,B_16: produc1282892786on_val,R_8: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_18 @ B_16 ) @ ( transi2118771717on_val @ R_8 ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ B_16 @ C_10 ) @ ( transi2118771717on_val @ R_8 ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ A_18 @ C_10 ) @ ( transi2118771717on_val @ R_8 ) ) ) ) ).
thf(fact_733_rtrancl__trans,axiom,
! [C_10: val,A_18: val,B_16: val,R_8: product_prod_val_val > $o] :
( ( member649088532al_val @ ( product_Pair_val_val @ A_18 @ B_16 ) @ ( transi935034983cl_val @ R_8 ) )
=> ( ( member649088532al_val @ ( product_Pair_val_val @ B_16 @ C_10 ) @ ( transi935034983cl_val @ R_8 ) )
=> ( member649088532al_val @ ( product_Pair_val_val @ A_18 @ C_10 ) @ ( transi935034983cl_val @ R_8 ) ) ) ) ).
thf(fact_734_subsetI,axiom,
! [B_15: produc1013743697t_char > $o,A_17: produc1013743697t_char > $o] :
( ! [X: produc1013743697t_char] :
( ( member1601084734t_char @ X @ A_17 )
=> ( member1601084734t_char @ X @ B_15 ) )
=> ( ord_le1156912648char_o @ A_17 @ B_15 ) ) ).
thf(fact_735_subsetI,axiom,
! [B_15: produc1971331930t_char > $o,A_17: produc1971331930t_char > $o] :
( ! [X: produc1971331930t_char] :
( ( member1467889965t_char @ X @ A_17 )
=> ( member1467889965t_char @ X @ B_15 ) )
=> ( ord_le139275609char_o @ A_17 @ B_15 ) ) ).
thf(fact_736_subsetI,axiom,
! [B_15: produc618524391on_val > $o,A_17: produc618524391on_val > $o] :
( ! [X: produc618524391on_val] :
( ( member2042188884on_val @ X @ A_17 )
=> ( member2042188884on_val @ X @ B_15 ) )
=> ( ord_le559588722_val_o @ A_17 @ B_15 ) ) ).
thf(fact_737_subsetI,axiom,
! [B_15: nat > $o,A_17: nat > $o] :
( ! [X: nat] :
( ( member_nat @ X @ A_17 )
=> ( member_nat @ X @ B_15 ) )
=> ( ord_less_eq_nat_o @ A_17 @ B_15 ) ) ).
thf(fact_738_subsetI,axiom,
! [B_15: produc1278157519t_char > $o,A_17: produc1278157519t_char > $o] :
( ! [X: produc1278157519t_char] :
( ( member1251428284t_char @ X @ A_17 )
=> ( member1251428284t_char @ X @ B_15 ) )
=> ( ord_le7825418char_o @ A_17 @ B_15 ) ) ).
thf(fact_739_subsetI,axiom,
! [B_15: list_char > $o,A_17: list_char > $o] :
( ! [X: list_char] :
( ( member_list_char @ X @ A_17 )
=> ( member_list_char @ X @ B_15 ) )
=> ( ord_le1777678169char_o @ A_17 @ B_15 ) ) ).
thf(fact_740_subsetI,axiom,
! [B_15: produc1746408499on_val > $o,A_17: produc1746408499on_val > $o] :
( ! [X: produc1746408499on_val] :
( ( member1913460000on_val @ X @ A_17 )
=> ( member1913460000on_val @ X @ B_15 ) )
=> ( ord_le1364969894_val_o @ A_17 @ B_15 ) ) ).
thf(fact_741_converse__rtranclE2,axiom,
! [Xa_1: list_exp_list_char,Xb_1: produc2090907612on_val,Za: list_exp_list_char,Zb: produc2090907612on_val,R_7: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Xa_1 @ Xb_1 ) @ ( produc1302104557on_val @ Za @ Zb ) ) @ ( transi808828192on_val @ R_7 ) )
=> ( ( ( produc1302104557on_val @ Xa_1 @ Xb_1 )
!= ( produc1302104557on_val @ Za @ Zb ) )
=> ~ ! [A_1: list_exp_list_char,B_14: produc2090907612on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Xa_1 @ Xb_1 ) @ ( produc1302104557on_val @ A_1 @ B_14 ) ) @ R_7 )
=> ~ ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ A_1 @ B_14 ) @ ( produc1302104557on_val @ Za @ Zb ) ) @ ( transi808828192on_val @ R_7 ) ) ) ) ) ).
thf(fact_742_converse__rtranclE2,axiom,
! [Xa_1: exp_list_char,Xb_1: produc2090907612on_val,Za: exp_list_char,Zb: produc2090907612on_val,R_7: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Xa_1 @ Xb_1 ) @ ( produc235638504on_val @ Za @ Zb ) ) @ ( transi2118771717on_val @ R_7 ) )
=> ( ( ( produc235638504on_val @ Xa_1 @ Xb_1 )
!= ( produc235638504on_val @ Za @ Zb ) )
=> ~ ! [A_1: exp_list_char,B_14: produc2090907612on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Xa_1 @ Xb_1 ) @ ( produc235638504on_val @ A_1 @ B_14 ) ) @ R_7 )
=> ~ ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ A_1 @ B_14 ) @ ( produc235638504on_val @ Za @ Zb ) ) @ ( transi2118771717on_val @ R_7 ) ) ) ) ) ).
thf(fact_743_converse__rtranclE2,axiom,
! [Xa_1: list_list_char,Xb_1: exp_list_char,Za: list_list_char,Zb: exp_list_char,R_7: produc1534059751t_char > $o] :
( ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ Xa_1 @ Xb_1 ) @ ( produc1147572817t_char @ Za @ Zb ) ) @ ( transi198989188t_char @ R_7 ) )
=> ( ( ( produc1147572817t_char @ Xa_1 @ Xb_1 )
!= ( produc1147572817t_char @ Za @ Zb ) )
=> ~ ! [A_1: list_list_char,B_14: exp_list_char] :
( ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ Xa_1 @ Xb_1 ) @ ( produc1147572817t_char @ A_1 @ B_14 ) ) @ R_7 )
=> ~ ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ A_1 @ B_14 ) @ ( produc1147572817t_char @ Za @ Zb ) ) @ ( transi198989188t_char @ R_7 ) ) ) ) ) ).
thf(fact_744_converse__rtranclE2,axiom,
! [Xa_1: list_P1940453997har_ty,Xb_1: list_P341299826t_char,Za: list_P1940453997har_ty,Zb: list_P341299826t_char,R_7: produc494726439t_char > $o] :
( ( member1551446420t_char @ ( produc635935767t_char @ ( produc1152259904t_char @ Xa_1 @ Xb_1 ) @ ( produc1152259904t_char @ Za @ Zb ) ) @ ( transi772168185t_char @ R_7 ) )
=> ( ( ( produc1152259904t_char @ Xa_1 @ Xb_1 )
!= ( produc1152259904t_char @ Za @ Zb ) )
=> ~ ! [A_1: list_P1940453997har_ty,B_14: list_P341299826t_char] :
( ( member1551446420t_char @ ( produc635935767t_char @ ( produc1152259904t_char @ Xa_1 @ Xb_1 ) @ ( produc1152259904t_char @ A_1 @ B_14 ) ) @ R_7 )
=> ~ ( member1551446420t_char @ ( produc635935767t_char @ ( produc1152259904t_char @ A_1 @ B_14 ) @ ( produc1152259904t_char @ Za @ Zb ) ) @ ( transi772168185t_char @ R_7 ) ) ) ) ) ).
thf(fact_745_converse__rtranclE2,axiom,
! [Xa_1: list_char,Xb_1: produc2146869324t_char,Za: list_char,Zb: produc2146869324t_char,R_7: produc740765671t_char > $o] :
( ( member1607118676t_char @ ( produc1431439831t_char @ ( produc1483578759t_char @ Xa_1 @ Xb_1 ) @ ( produc1483578759t_char @ Za @ Zb ) ) @ ( transi2005320128t_char @ R_7 ) )
=> ( ( ( produc1483578759t_char @ Xa_1 @ Xb_1 )
!= ( produc1483578759t_char @ Za @ Zb ) )
=> ~ ! [A_1: list_char,B_14: produc2146869324t_char] :
( ( member1607118676t_char @ ( produc1431439831t_char @ ( produc1483578759t_char @ Xa_1 @ Xb_1 ) @ ( produc1483578759t_char @ A_1 @ B_14 ) ) @ R_7 )
=> ~ ( member1607118676t_char @ ( produc1431439831t_char @ ( produc1483578759t_char @ A_1 @ B_14 ) @ ( produc1483578759t_char @ Za @ Zb ) ) @ ( transi2005320128t_char @ R_7 ) ) ) ) ) ).
thf(fact_746_converse__rtranclE2,axiom,
! [Xa_1: list_char,Xb_1: produc952412819t_char,Za: list_char,Zb: produc952412819t_char,R_7: produc84451751t_char > $o] :
( ( member162552852t_char @ ( produc1641293463t_char @ ( produc822965838t_char @ Xa_1 @ Xb_1 ) @ ( produc822965838t_char @ Za @ Zb ) ) @ ( transi1123801095t_char @ R_7 ) )
=> ( ( ( produc822965838t_char @ Xa_1 @ Xb_1 )
!= ( produc822965838t_char @ Za @ Zb ) )
=> ~ ! [A_1: list_char,B_14: produc952412819t_char] :
( ( member162552852t_char @ ( produc1641293463t_char @ ( produc822965838t_char @ Xa_1 @ Xb_1 ) @ ( produc822965838t_char @ A_1 @ B_14 ) ) @ R_7 )
=> ~ ( member162552852t_char @ ( produc1641293463t_char @ ( produc822965838t_char @ A_1 @ B_14 ) @ ( produc822965838t_char @ Za @ Zb ) ) @ ( transi1123801095t_char @ R_7 ) ) ) ) ) ).
thf(fact_747_converse__rtranclE2,axiom,
! [Xa_1: list_val,Xb_1: exp_list_char,Za: list_val,Zb: exp_list_char,R_7: produc1826280281t_char > $o] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Xa_1 @ Xb_1 ) @ ( produc1916172923t_char @ Za @ Zb ) ) @ ( transi1789604888t_char @ R_7 ) )
=> ( ( ( produc1916172923t_char @ Xa_1 @ Xb_1 )
!= ( produc1916172923t_char @ Za @ Zb ) )
=> ~ ! [A_1: list_val,B_14: exp_list_char] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Xa_1 @ Xb_1 ) @ ( produc1916172923t_char @ A_1 @ B_14 ) ) @ R_7 )
=> ~ ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ A_1 @ B_14 ) @ ( produc1916172923t_char @ Za @ Zb ) ) @ ( transi1789604888t_char @ R_7 ) ) ) ) ) ).
thf(fact_748_converse__rtranclE2,axiom,
! [Xa_1: list_ty,Xb_1: produc662261637t_char,Za: list_ty,Zb: produc662261637t_char,R_7: produc1406897475t_char > $o] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Xa_1 @ Xb_1 ) @ ( produc1909267824t_char @ Za @ Zb ) ) @ ( transi1257872013t_char @ R_7 ) )
=> ( ( ( produc1909267824t_char @ Xa_1 @ Xb_1 )
!= ( produc1909267824t_char @ Za @ Zb ) )
=> ~ ! [A_1: list_ty,B_14: produc662261637t_char] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Xa_1 @ Xb_1 ) @ ( produc1909267824t_char @ A_1 @ B_14 ) ) @ R_7 )
=> ~ ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ A_1 @ B_14 ) @ ( produc1909267824t_char @ Za @ Zb ) ) @ ( transi1257872013t_char @ R_7 ) ) ) ) ) ).
thf(fact_749_converse__rtranclE2,axiom,
! [Xa_1: list_list_char,Xb_1: produc220283002t_char,Za: list_list_char,Zb: produc220283002t_char,R_7: produc349695911t_char > $o] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Xa_1 @ Xb_1 ) @ ( produc921874948t_char @ Za @ Zb ) ) @ ( transi122195895t_char @ R_7 ) )
=> ( ( ( produc921874948t_char @ Xa_1 @ Xb_1 )
!= ( produc921874948t_char @ Za @ Zb ) )
=> ~ ! [A_1: list_list_char,B_14: produc220283002t_char] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Xa_1 @ Xb_1 ) @ ( produc921874948t_char @ A_1 @ B_14 ) ) @ R_7 )
=> ~ ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ A_1 @ B_14 ) @ ( produc921874948t_char @ Za @ Zb ) ) @ ( transi122195895t_char @ R_7 ) ) ) ) ) ).
thf(fact_750_converse__rtranclE2,axiom,
! [Xa_1: produc1180562163on_val,Xb_1: produc1180562163on_val,Za: produc1180562163on_val,Zb: produc1180562163on_val,R_7: produc1250491293on_val > $o] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ Xa_1 @ Xb_1 ) @ ( produc747700183on_val @ Za @ Zb ) ) @ ( transi1457397498on_val @ R_7 ) )
=> ( ( ( produc747700183on_val @ Xa_1 @ Xb_1 )
!= ( produc747700183on_val @ Za @ Zb ) )
=> ~ ! [A_1: produc1180562163on_val,B_14: produc1180562163on_val] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ Xa_1 @ Xb_1 ) @ ( produc747700183on_val @ A_1 @ B_14 ) ) @ R_7 )
=> ~ ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ A_1 @ B_14 ) @ ( produc747700183on_val @ Za @ Zb ) ) @ ( transi1457397498on_val @ R_7 ) ) ) ) ) ).
thf(fact_751_converse__rtranclE2,axiom,
! [Xa_1: val,Xb_1: val,Za: val,Zb: val,R_7: produc800118557al_val > $o] :
( ( member837208074al_val @ ( produc1244920211al_val @ ( product_Pair_val_val @ Xa_1 @ Xb_1 ) @ ( product_Pair_val_val @ Za @ Zb ) ) @ ( transi1423755450al_val @ R_7 ) )
=> ( ( ( product_Pair_val_val @ Xa_1 @ Xb_1 )
!= ( product_Pair_val_val @ Za @ Zb ) )
=> ~ ! [A_1: val,B_14: val] :
( ( member837208074al_val @ ( produc1244920211al_val @ ( product_Pair_val_val @ Xa_1 @ Xb_1 ) @ ( product_Pair_val_val @ A_1 @ B_14 ) ) @ R_7 )
=> ~ ( member837208074al_val @ ( produc1244920211al_val @ ( product_Pair_val_val @ A_1 @ B_14 ) @ ( product_Pair_val_val @ Za @ Zb ) ) @ ( transi1423755450al_val @ R_7 ) ) ) ) ) ).
thf(fact_752_converse__rtranclE2,axiom,
! [Xa_1: bop,Xb_1: product_prod_val_val,Za: bop,Zb: product_prod_val_val,R_7: produc630464863al_val > $o] :
( ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ Xa_1 @ Xb_1 ) @ ( produc621191550al_val @ Za @ Zb ) ) @ ( transi1906258203al_val @ R_7 ) )
=> ( ( ( produc621191550al_val @ Xa_1 @ Xb_1 )
!= ( produc621191550al_val @ Za @ Zb ) )
=> ~ ! [A_1: bop,B_14: product_prod_val_val] :
( ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ Xa_1 @ Xb_1 ) @ ( produc621191550al_val @ A_1 @ B_14 ) ) @ R_7 )
=> ~ ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ A_1 @ B_14 ) @ ( produc621191550al_val @ Za @ Zb ) ) @ ( transi1906258203al_val @ R_7 ) ) ) ) ) ).
thf(fact_753_converse__rtranclE2,axiom,
! [Xa_1: list_char,Xb_1: list_char,Za: list_char,Zb: list_char,R_7: produc1350825965t_char > $o] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ Xa_1 @ Xb_1 ) @ ( produc5062597t_char @ Za @ Zb ) ) @ ( transi1095029602t_char @ R_7 ) )
=> ( ( ( produc5062597t_char @ Xa_1 @ Xb_1 )
!= ( produc5062597t_char @ Za @ Zb ) )
=> ~ ! [A_1: list_char,B_14: list_char] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ Xa_1 @ Xb_1 ) @ ( produc5062597t_char @ A_1 @ B_14 ) ) @ R_7 )
=> ~ ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ A_1 @ B_14 ) @ ( produc5062597t_char @ Za @ Zb ) ) @ ( transi1095029602t_char @ R_7 ) ) ) ) ) ).
thf(fact_754_converse__rtranclE2,axiom,
! [Xa_1: list_char,Xb_1: produc1278157519t_char > option_val,Za: list_char,Zb: produc1278157519t_char > option_val,R_7: produc1368416213on_val > $o] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Xa_1 @ Xb_1 ) @ ( produc926070009on_val @ Za @ Zb ) ) @ ( transi1669211542on_val @ R_7 ) )
=> ( ( ( produc926070009on_val @ Xa_1 @ Xb_1 )
!= ( produc926070009on_val @ Za @ Zb ) )
=> ~ ! [A_1: list_char,B_14: produc1278157519t_char > option_val] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Xa_1 @ Xb_1 ) @ ( produc926070009on_val @ A_1 @ B_14 ) ) @ R_7 )
=> ~ ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ A_1 @ B_14 ) @ ( produc926070009on_val @ Za @ Zb ) ) @ ( transi1669211542on_val @ R_7 ) ) ) ) ) ).
thf(fact_755_converse__rtranclE2,axiom,
! [Xa_1: nat > option1728594148on_val,Xb_1: list_char > option_val,Za: nat > option1728594148on_val,Zb: list_char > option_val,R_7: produc1581780743on_val > $o] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Xa_1 @ Xb_1 ) @ ( produc755559506on_val @ Za @ Zb ) ) @ ( transi466770671on_val @ R_7 ) )
=> ( ( ( produc755559506on_val @ Xa_1 @ Xb_1 )
!= ( produc755559506on_val @ Za @ Zb ) )
=> ~ ! [A_1: nat > option1728594148on_val,B_14: list_char > option_val] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Xa_1 @ Xb_1 ) @ ( produc755559506on_val @ A_1 @ B_14 ) ) @ R_7 )
=> ~ ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ A_1 @ B_14 ) @ ( produc755559506on_val @ Za @ Zb ) ) @ ( transi466770671on_val @ R_7 ) ) ) ) ) ).
thf(fact_756_converse__rtranclE2,axiom,
! [Xa_1: produc1282892786on_val,Xb_1: produc1282892786on_val,Za: produc1282892786on_val,Zb: produc1282892786on_val,R_7: produc652964533on_val > $o] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Xa_1 @ Xb_1 ) @ ( produc833389609on_val @ Za @ Zb ) ) @ ( transi130214086on_val @ R_7 ) )
=> ( ( ( produc833389609on_val @ Xa_1 @ Xb_1 )
!= ( produc833389609on_val @ Za @ Zb ) )
=> ~ ! [A_1: produc1282892786on_val,B_14: produc1282892786on_val] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Xa_1 @ Xb_1 ) @ ( produc833389609on_val @ A_1 @ B_14 ) ) @ R_7 )
=> ~ ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ A_1 @ B_14 ) @ ( produc833389609on_val @ Za @ Zb ) ) @ ( transi130214086on_val @ R_7 ) ) ) ) ) ).
thf(fact_757_converse__rtrancl__induct2,axiom,
! [P_4: list_exp_list_char > produc2090907612on_val > $o,Ax_1: list_exp_list_char,Ay_1: produc2090907612on_val,Bx_1: list_exp_list_char,By_1: produc2090907612on_val,R_6: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Ax_1 @ Ay_1 ) @ ( produc1302104557on_val @ Bx_1 @ By_1 ) ) @ ( transi808828192on_val @ R_6 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: list_exp_list_char,B_14: produc2090907612on_val,Aa: list_exp_list_char,Ba: produc2090907612on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ A_1 @ B_14 ) @ ( produc1302104557on_val @ Aa @ Ba ) ) @ R_6 )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Aa @ Ba ) @ ( produc1302104557on_val @ Bx_1 @ By_1 ) ) @ ( transi808828192on_val @ R_6 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_14 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_758_converse__rtrancl__induct2,axiom,
! [P_4: exp_list_char > produc2090907612on_val > $o,Ax_1: exp_list_char,Ay_1: produc2090907612on_val,Bx_1: exp_list_char,By_1: produc2090907612on_val,R_6: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Ax_1 @ Ay_1 ) @ ( produc235638504on_val @ Bx_1 @ By_1 ) ) @ ( transi2118771717on_val @ R_6 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: exp_list_char,B_14: produc2090907612on_val,Aa: exp_list_char,Ba: produc2090907612on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ A_1 @ B_14 ) @ ( produc235638504on_val @ Aa @ Ba ) ) @ R_6 )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Aa @ Ba ) @ ( produc235638504on_val @ Bx_1 @ By_1 ) ) @ ( transi2118771717on_val @ R_6 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_14 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_759_converse__rtrancl__induct2,axiom,
! [P_4: list_list_char > exp_list_char > $o,Ax_1: list_list_char,Ay_1: exp_list_char,Bx_1: list_list_char,By_1: exp_list_char,R_6: produc1534059751t_char > $o] :
( ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ Ax_1 @ Ay_1 ) @ ( produc1147572817t_char @ Bx_1 @ By_1 ) ) @ ( transi198989188t_char @ R_6 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: list_list_char,B_14: exp_list_char,Aa: list_list_char,Ba: exp_list_char] :
( ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ A_1 @ B_14 ) @ ( produc1147572817t_char @ Aa @ Ba ) ) @ R_6 )
=> ( ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ Aa @ Ba ) @ ( produc1147572817t_char @ Bx_1 @ By_1 ) ) @ ( transi198989188t_char @ R_6 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_14 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_760_converse__rtrancl__induct2,axiom,
! [P_4: list_P1940453997har_ty > list_P341299826t_char > $o,Ax_1: list_P1940453997har_ty,Ay_1: list_P341299826t_char,Bx_1: list_P1940453997har_ty,By_1: list_P341299826t_char,R_6: produc494726439t_char > $o] :
( ( member1551446420t_char @ ( produc635935767t_char @ ( produc1152259904t_char @ Ax_1 @ Ay_1 ) @ ( produc1152259904t_char @ Bx_1 @ By_1 ) ) @ ( transi772168185t_char @ R_6 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: list_P1940453997har_ty,B_14: list_P341299826t_char,Aa: list_P1940453997har_ty,Ba: list_P341299826t_char] :
( ( member1551446420t_char @ ( produc635935767t_char @ ( produc1152259904t_char @ A_1 @ B_14 ) @ ( produc1152259904t_char @ Aa @ Ba ) ) @ R_6 )
=> ( ( member1551446420t_char @ ( produc635935767t_char @ ( produc1152259904t_char @ Aa @ Ba ) @ ( produc1152259904t_char @ Bx_1 @ By_1 ) ) @ ( transi772168185t_char @ R_6 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_14 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_761_converse__rtrancl__induct2,axiom,
! [P_4: list_char > produc2146869324t_char > $o,Ax_1: list_char,Ay_1: produc2146869324t_char,Bx_1: list_char,By_1: produc2146869324t_char,R_6: produc740765671t_char > $o] :
( ( member1607118676t_char @ ( produc1431439831t_char @ ( produc1483578759t_char @ Ax_1 @ Ay_1 ) @ ( produc1483578759t_char @ Bx_1 @ By_1 ) ) @ ( transi2005320128t_char @ R_6 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: list_char,B_14: produc2146869324t_char,Aa: list_char,Ba: produc2146869324t_char] :
( ( member1607118676t_char @ ( produc1431439831t_char @ ( produc1483578759t_char @ A_1 @ B_14 ) @ ( produc1483578759t_char @ Aa @ Ba ) ) @ R_6 )
=> ( ( member1607118676t_char @ ( produc1431439831t_char @ ( produc1483578759t_char @ Aa @ Ba ) @ ( produc1483578759t_char @ Bx_1 @ By_1 ) ) @ ( transi2005320128t_char @ R_6 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_14 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_762_converse__rtrancl__induct2,axiom,
! [P_4: list_char > produc952412819t_char > $o,Ax_1: list_char,Ay_1: produc952412819t_char,Bx_1: list_char,By_1: produc952412819t_char,R_6: produc84451751t_char > $o] :
( ( member162552852t_char @ ( produc1641293463t_char @ ( produc822965838t_char @ Ax_1 @ Ay_1 ) @ ( produc822965838t_char @ Bx_1 @ By_1 ) ) @ ( transi1123801095t_char @ R_6 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: list_char,B_14: produc952412819t_char,Aa: list_char,Ba: produc952412819t_char] :
( ( member162552852t_char @ ( produc1641293463t_char @ ( produc822965838t_char @ A_1 @ B_14 ) @ ( produc822965838t_char @ Aa @ Ba ) ) @ R_6 )
=> ( ( member162552852t_char @ ( produc1641293463t_char @ ( produc822965838t_char @ Aa @ Ba ) @ ( produc822965838t_char @ Bx_1 @ By_1 ) ) @ ( transi1123801095t_char @ R_6 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_14 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_763_converse__rtrancl__induct2,axiom,
! [P_4: list_val > exp_list_char > $o,Ax_1: list_val,Ay_1: exp_list_char,Bx_1: list_val,By_1: exp_list_char,R_6: produc1826280281t_char > $o] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Ax_1 @ Ay_1 ) @ ( produc1916172923t_char @ Bx_1 @ By_1 ) ) @ ( transi1789604888t_char @ R_6 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: list_val,B_14: exp_list_char,Aa: list_val,Ba: exp_list_char] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ A_1 @ B_14 ) @ ( produc1916172923t_char @ Aa @ Ba ) ) @ R_6 )
=> ( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Aa @ Ba ) @ ( produc1916172923t_char @ Bx_1 @ By_1 ) ) @ ( transi1789604888t_char @ R_6 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_14 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_764_converse__rtrancl__induct2,axiom,
! [P_4: list_ty > produc662261637t_char > $o,Ax_1: list_ty,Ay_1: produc662261637t_char,Bx_1: list_ty,By_1: produc662261637t_char,R_6: produc1406897475t_char > $o] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Ax_1 @ Ay_1 ) @ ( produc1909267824t_char @ Bx_1 @ By_1 ) ) @ ( transi1257872013t_char @ R_6 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: list_ty,B_14: produc662261637t_char,Aa: list_ty,Ba: produc662261637t_char] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ A_1 @ B_14 ) @ ( produc1909267824t_char @ Aa @ Ba ) ) @ R_6 )
=> ( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Aa @ Ba ) @ ( produc1909267824t_char @ Bx_1 @ By_1 ) ) @ ( transi1257872013t_char @ R_6 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_14 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_765_converse__rtrancl__induct2,axiom,
! [P_4: list_list_char > produc220283002t_char > $o,Ax_1: list_list_char,Ay_1: produc220283002t_char,Bx_1: list_list_char,By_1: produc220283002t_char,R_6: produc349695911t_char > $o] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Ax_1 @ Ay_1 ) @ ( produc921874948t_char @ Bx_1 @ By_1 ) ) @ ( transi122195895t_char @ R_6 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: list_list_char,B_14: produc220283002t_char,Aa: list_list_char,Ba: produc220283002t_char] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ A_1 @ B_14 ) @ ( produc921874948t_char @ Aa @ Ba ) ) @ R_6 )
=> ( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Aa @ Ba ) @ ( produc921874948t_char @ Bx_1 @ By_1 ) ) @ ( transi122195895t_char @ R_6 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_14 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_766_converse__rtrancl__induct2,axiom,
! [P_4: produc1180562163on_val > produc1180562163on_val > $o,Ax_1: produc1180562163on_val,Ay_1: produc1180562163on_val,Bx_1: produc1180562163on_val,By_1: produc1180562163on_val,R_6: produc1250491293on_val > $o] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ Ax_1 @ Ay_1 ) @ ( produc747700183on_val @ Bx_1 @ By_1 ) ) @ ( transi1457397498on_val @ R_6 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: produc1180562163on_val,B_14: produc1180562163on_val,Aa: produc1180562163on_val,Ba: produc1180562163on_val] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ A_1 @ B_14 ) @ ( produc747700183on_val @ Aa @ Ba ) ) @ R_6 )
=> ( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ Aa @ Ba ) @ ( produc747700183on_val @ Bx_1 @ By_1 ) ) @ ( transi1457397498on_val @ R_6 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_14 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_767_converse__rtrancl__induct2,axiom,
! [P_4: val > val > $o,Ax_1: val,Ay_1: val,Bx_1: val,By_1: val,R_6: produc800118557al_val > $o] :
( ( member837208074al_val @ ( produc1244920211al_val @ ( product_Pair_val_val @ Ax_1 @ Ay_1 ) @ ( product_Pair_val_val @ Bx_1 @ By_1 ) ) @ ( transi1423755450al_val @ R_6 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: val,B_14: val,Aa: val,Ba: val] :
( ( member837208074al_val @ ( produc1244920211al_val @ ( product_Pair_val_val @ A_1 @ B_14 ) @ ( product_Pair_val_val @ Aa @ Ba ) ) @ R_6 )
=> ( ( member837208074al_val @ ( produc1244920211al_val @ ( product_Pair_val_val @ Aa @ Ba ) @ ( product_Pair_val_val @ Bx_1 @ By_1 ) ) @ ( transi1423755450al_val @ R_6 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_14 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_768_converse__rtrancl__induct2,axiom,
! [P_4: bop > product_prod_val_val > $o,Ax_1: bop,Ay_1: product_prod_val_val,Bx_1: bop,By_1: product_prod_val_val,R_6: produc630464863al_val > $o] :
( ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ Ax_1 @ Ay_1 ) @ ( produc621191550al_val @ Bx_1 @ By_1 ) ) @ ( transi1906258203al_val @ R_6 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: bop,B_14: product_prod_val_val,Aa: bop,Ba: product_prod_val_val] :
( ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ A_1 @ B_14 ) @ ( produc621191550al_val @ Aa @ Ba ) ) @ R_6 )
=> ( ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ Aa @ Ba ) @ ( produc621191550al_val @ Bx_1 @ By_1 ) ) @ ( transi1906258203al_val @ R_6 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_14 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_769_converse__rtrancl__induct2,axiom,
! [P_4: list_char > list_char > $o,Ax_1: list_char,Ay_1: list_char,Bx_1: list_char,By_1: list_char,R_6: produc1350825965t_char > $o] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ Ax_1 @ Ay_1 ) @ ( produc5062597t_char @ Bx_1 @ By_1 ) ) @ ( transi1095029602t_char @ R_6 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: list_char,B_14: list_char,Aa: list_char,Ba: list_char] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ A_1 @ B_14 ) @ ( produc5062597t_char @ Aa @ Ba ) ) @ R_6 )
=> ( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ Aa @ Ba ) @ ( produc5062597t_char @ Bx_1 @ By_1 ) ) @ ( transi1095029602t_char @ R_6 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_14 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_770_converse__rtrancl__induct2,axiom,
! [P_4: list_char > ( produc1278157519t_char > option_val ) > $o,Ax_1: list_char,Ay_1: produc1278157519t_char > option_val,Bx_1: list_char,By_1: produc1278157519t_char > option_val,R_6: produc1368416213on_val > $o] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Ax_1 @ Ay_1 ) @ ( produc926070009on_val @ Bx_1 @ By_1 ) ) @ ( transi1669211542on_val @ R_6 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: list_char,B_14: produc1278157519t_char > option_val,Aa: list_char,Ba: produc1278157519t_char > option_val] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ A_1 @ B_14 ) @ ( produc926070009on_val @ Aa @ Ba ) ) @ R_6 )
=> ( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Aa @ Ba ) @ ( produc926070009on_val @ Bx_1 @ By_1 ) ) @ ( transi1669211542on_val @ R_6 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_14 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_771_converse__rtrancl__induct2,axiom,
! [P_4: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,Ax_1: nat > option1728594148on_val,Ay_1: list_char > option_val,Bx_1: nat > option1728594148on_val,By_1: list_char > option_val,R_6: produc1581780743on_val > $o] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Ax_1 @ Ay_1 ) @ ( produc755559506on_val @ Bx_1 @ By_1 ) ) @ ( transi466770671on_val @ R_6 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: nat > option1728594148on_val,B_14: list_char > option_val,Aa: nat > option1728594148on_val,Ba: list_char > option_val] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ A_1 @ B_14 ) @ ( produc755559506on_val @ Aa @ Ba ) ) @ R_6 )
=> ( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Aa @ Ba ) @ ( produc755559506on_val @ Bx_1 @ By_1 ) ) @ ( transi466770671on_val @ R_6 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_14 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_772_converse__rtrancl__induct2,axiom,
! [P_4: produc1282892786on_val > produc1282892786on_val > $o,Ax_1: produc1282892786on_val,Ay_1: produc1282892786on_val,Bx_1: produc1282892786on_val,By_1: produc1282892786on_val,R_6: produc652964533on_val > $o] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Ax_1 @ Ay_1 ) @ ( produc833389609on_val @ Bx_1 @ By_1 ) ) @ ( transi130214086on_val @ R_6 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: produc1282892786on_val,B_14: produc1282892786on_val,Aa: produc1282892786on_val,Ba: produc1282892786on_val] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ A_1 @ B_14 ) @ ( produc833389609on_val @ Aa @ Ba ) ) @ R_6 )
=> ( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Aa @ Ba ) @ ( produc833389609on_val @ Bx_1 @ By_1 ) ) @ ( transi130214086on_val @ R_6 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_14 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_773_rtrancl__induct2,axiom,
! [P_3: list_exp_list_char > produc2090907612on_val > $o,Ax: list_exp_list_char,Ay: produc2090907612on_val,Bx: list_exp_list_char,By: produc2090907612on_val,R_5: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Ax @ Ay ) @ ( produc1302104557on_val @ Bx @ By ) ) @ ( transi808828192on_val @ R_5 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: list_exp_list_char,B_14: produc2090907612on_val,Aa: list_exp_list_char,Ba: produc2090907612on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Ax @ Ay ) @ ( produc1302104557on_val @ A_1 @ B_14 ) ) @ ( transi808828192on_val @ R_5 ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ A_1 @ B_14 ) @ ( produc1302104557on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( P_3 @ A_1 @ B_14 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_774_rtrancl__induct2,axiom,
! [P_3: exp_list_char > produc2090907612on_val > $o,Ax: exp_list_char,Ay: produc2090907612on_val,Bx: exp_list_char,By: produc2090907612on_val,R_5: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Ax @ Ay ) @ ( produc235638504on_val @ Bx @ By ) ) @ ( transi2118771717on_val @ R_5 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: exp_list_char,B_14: produc2090907612on_val,Aa: exp_list_char,Ba: produc2090907612on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Ax @ Ay ) @ ( produc235638504on_val @ A_1 @ B_14 ) ) @ ( transi2118771717on_val @ R_5 ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ A_1 @ B_14 ) @ ( produc235638504on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( P_3 @ A_1 @ B_14 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_775_rtrancl__induct2,axiom,
! [P_3: list_list_char > exp_list_char > $o,Ax: list_list_char,Ay: exp_list_char,Bx: list_list_char,By: exp_list_char,R_5: produc1534059751t_char > $o] :
( ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ Ax @ Ay ) @ ( produc1147572817t_char @ Bx @ By ) ) @ ( transi198989188t_char @ R_5 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: list_list_char,B_14: exp_list_char,Aa: list_list_char,Ba: exp_list_char] :
( ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ Ax @ Ay ) @ ( produc1147572817t_char @ A_1 @ B_14 ) ) @ ( transi198989188t_char @ R_5 ) )
=> ( ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ A_1 @ B_14 ) @ ( produc1147572817t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( P_3 @ A_1 @ B_14 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_776_rtrancl__induct2,axiom,
! [P_3: list_P1940453997har_ty > list_P341299826t_char > $o,Ax: list_P1940453997har_ty,Ay: list_P341299826t_char,Bx: list_P1940453997har_ty,By: list_P341299826t_char,R_5: produc494726439t_char > $o] :
( ( member1551446420t_char @ ( produc635935767t_char @ ( produc1152259904t_char @ Ax @ Ay ) @ ( produc1152259904t_char @ Bx @ By ) ) @ ( transi772168185t_char @ R_5 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: list_P1940453997har_ty,B_14: list_P341299826t_char,Aa: list_P1940453997har_ty,Ba: list_P341299826t_char] :
( ( member1551446420t_char @ ( produc635935767t_char @ ( produc1152259904t_char @ Ax @ Ay ) @ ( produc1152259904t_char @ A_1 @ B_14 ) ) @ ( transi772168185t_char @ R_5 ) )
=> ( ( member1551446420t_char @ ( produc635935767t_char @ ( produc1152259904t_char @ A_1 @ B_14 ) @ ( produc1152259904t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( P_3 @ A_1 @ B_14 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_777_rtrancl__induct2,axiom,
! [P_3: list_char > produc2146869324t_char > $o,Ax: list_char,Ay: produc2146869324t_char,Bx: list_char,By: produc2146869324t_char,R_5: produc740765671t_char > $o] :
( ( member1607118676t_char @ ( produc1431439831t_char @ ( produc1483578759t_char @ Ax @ Ay ) @ ( produc1483578759t_char @ Bx @ By ) ) @ ( transi2005320128t_char @ R_5 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: list_char,B_14: produc2146869324t_char,Aa: list_char,Ba: produc2146869324t_char] :
( ( member1607118676t_char @ ( produc1431439831t_char @ ( produc1483578759t_char @ Ax @ Ay ) @ ( produc1483578759t_char @ A_1 @ B_14 ) ) @ ( transi2005320128t_char @ R_5 ) )
=> ( ( member1607118676t_char @ ( produc1431439831t_char @ ( produc1483578759t_char @ A_1 @ B_14 ) @ ( produc1483578759t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( P_3 @ A_1 @ B_14 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_778_rtrancl__induct2,axiom,
! [P_3: list_char > produc952412819t_char > $o,Ax: list_char,Ay: produc952412819t_char,Bx: list_char,By: produc952412819t_char,R_5: produc84451751t_char > $o] :
( ( member162552852t_char @ ( produc1641293463t_char @ ( produc822965838t_char @ Ax @ Ay ) @ ( produc822965838t_char @ Bx @ By ) ) @ ( transi1123801095t_char @ R_5 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: list_char,B_14: produc952412819t_char,Aa: list_char,Ba: produc952412819t_char] :
( ( member162552852t_char @ ( produc1641293463t_char @ ( produc822965838t_char @ Ax @ Ay ) @ ( produc822965838t_char @ A_1 @ B_14 ) ) @ ( transi1123801095t_char @ R_5 ) )
=> ( ( member162552852t_char @ ( produc1641293463t_char @ ( produc822965838t_char @ A_1 @ B_14 ) @ ( produc822965838t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( P_3 @ A_1 @ B_14 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_779_rtrancl__induct2,axiom,
! [P_3: list_val > exp_list_char > $o,Ax: list_val,Ay: exp_list_char,Bx: list_val,By: exp_list_char,R_5: produc1826280281t_char > $o] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Ax @ Ay ) @ ( produc1916172923t_char @ Bx @ By ) ) @ ( transi1789604888t_char @ R_5 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: list_val,B_14: exp_list_char,Aa: list_val,Ba: exp_list_char] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Ax @ Ay ) @ ( produc1916172923t_char @ A_1 @ B_14 ) ) @ ( transi1789604888t_char @ R_5 ) )
=> ( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ A_1 @ B_14 ) @ ( produc1916172923t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( P_3 @ A_1 @ B_14 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_780_rtrancl__induct2,axiom,
! [P_3: list_ty > produc662261637t_char > $o,Ax: list_ty,Ay: produc662261637t_char,Bx: list_ty,By: produc662261637t_char,R_5: produc1406897475t_char > $o] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Ax @ Ay ) @ ( produc1909267824t_char @ Bx @ By ) ) @ ( transi1257872013t_char @ R_5 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: list_ty,B_14: produc662261637t_char,Aa: list_ty,Ba: produc662261637t_char] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Ax @ Ay ) @ ( produc1909267824t_char @ A_1 @ B_14 ) ) @ ( transi1257872013t_char @ R_5 ) )
=> ( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ A_1 @ B_14 ) @ ( produc1909267824t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( P_3 @ A_1 @ B_14 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_781_rtrancl__induct2,axiom,
! [P_3: list_list_char > produc220283002t_char > $o,Ax: list_list_char,Ay: produc220283002t_char,Bx: list_list_char,By: produc220283002t_char,R_5: produc349695911t_char > $o] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Ax @ Ay ) @ ( produc921874948t_char @ Bx @ By ) ) @ ( transi122195895t_char @ R_5 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: list_list_char,B_14: produc220283002t_char,Aa: list_list_char,Ba: produc220283002t_char] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Ax @ Ay ) @ ( produc921874948t_char @ A_1 @ B_14 ) ) @ ( transi122195895t_char @ R_5 ) )
=> ( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ A_1 @ B_14 ) @ ( produc921874948t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( P_3 @ A_1 @ B_14 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_782_rtrancl__induct2,axiom,
! [P_3: produc1180562163on_val > produc1180562163on_val > $o,Ax: produc1180562163on_val,Ay: produc1180562163on_val,Bx: produc1180562163on_val,By: produc1180562163on_val,R_5: produc1250491293on_val > $o] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ Ax @ Ay ) @ ( produc747700183on_val @ Bx @ By ) ) @ ( transi1457397498on_val @ R_5 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: produc1180562163on_val,B_14: produc1180562163on_val,Aa: produc1180562163on_val,Ba: produc1180562163on_val] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ Ax @ Ay ) @ ( produc747700183on_val @ A_1 @ B_14 ) ) @ ( transi1457397498on_val @ R_5 ) )
=> ( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ A_1 @ B_14 ) @ ( produc747700183on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( P_3 @ A_1 @ B_14 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_783_rtrancl__induct2,axiom,
! [P_3: val > val > $o,Ax: val,Ay: val,Bx: val,By: val,R_5: produc800118557al_val > $o] :
( ( member837208074al_val @ ( produc1244920211al_val @ ( product_Pair_val_val @ Ax @ Ay ) @ ( product_Pair_val_val @ Bx @ By ) ) @ ( transi1423755450al_val @ R_5 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: val,B_14: val,Aa: val,Ba: val] :
( ( member837208074al_val @ ( produc1244920211al_val @ ( product_Pair_val_val @ Ax @ Ay ) @ ( product_Pair_val_val @ A_1 @ B_14 ) ) @ ( transi1423755450al_val @ R_5 ) )
=> ( ( member837208074al_val @ ( produc1244920211al_val @ ( product_Pair_val_val @ A_1 @ B_14 ) @ ( product_Pair_val_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( P_3 @ A_1 @ B_14 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_784_rtrancl__induct2,axiom,
! [P_3: bop > product_prod_val_val > $o,Ax: bop,Ay: product_prod_val_val,Bx: bop,By: product_prod_val_val,R_5: produc630464863al_val > $o] :
( ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ Ax @ Ay ) @ ( produc621191550al_val @ Bx @ By ) ) @ ( transi1906258203al_val @ R_5 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: bop,B_14: product_prod_val_val,Aa: bop,Ba: product_prod_val_val] :
( ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ Ax @ Ay ) @ ( produc621191550al_val @ A_1 @ B_14 ) ) @ ( transi1906258203al_val @ R_5 ) )
=> ( ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ A_1 @ B_14 ) @ ( produc621191550al_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( P_3 @ A_1 @ B_14 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_785_rtrancl__induct2,axiom,
! [P_3: list_char > list_char > $o,Ax: list_char,Ay: list_char,Bx: list_char,By: list_char,R_5: produc1350825965t_char > $o] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ Ax @ Ay ) @ ( produc5062597t_char @ Bx @ By ) ) @ ( transi1095029602t_char @ R_5 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: list_char,B_14: list_char,Aa: list_char,Ba: list_char] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ Ax @ Ay ) @ ( produc5062597t_char @ A_1 @ B_14 ) ) @ ( transi1095029602t_char @ R_5 ) )
=> ( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ A_1 @ B_14 ) @ ( produc5062597t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( P_3 @ A_1 @ B_14 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_786_rtrancl__induct2,axiom,
! [P_3: list_char > ( produc1278157519t_char > option_val ) > $o,Ax: list_char,Ay: produc1278157519t_char > option_val,Bx: list_char,By: produc1278157519t_char > option_val,R_5: produc1368416213on_val > $o] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Ax @ Ay ) @ ( produc926070009on_val @ Bx @ By ) ) @ ( transi1669211542on_val @ R_5 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: list_char,B_14: produc1278157519t_char > option_val,Aa: list_char,Ba: produc1278157519t_char > option_val] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Ax @ Ay ) @ ( produc926070009on_val @ A_1 @ B_14 ) ) @ ( transi1669211542on_val @ R_5 ) )
=> ( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ A_1 @ B_14 ) @ ( produc926070009on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( P_3 @ A_1 @ B_14 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_787_rtrancl__induct2,axiom,
! [P_3: ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o,Ax: nat > option1728594148on_val,Ay: list_char > option_val,Bx: nat > option1728594148on_val,By: list_char > option_val,R_5: produc1581780743on_val > $o] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Ax @ Ay ) @ ( produc755559506on_val @ Bx @ By ) ) @ ( transi466770671on_val @ R_5 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: nat > option1728594148on_val,B_14: list_char > option_val,Aa: nat > option1728594148on_val,Ba: list_char > option_val] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Ax @ Ay ) @ ( produc755559506on_val @ A_1 @ B_14 ) ) @ ( transi466770671on_val @ R_5 ) )
=> ( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ A_1 @ B_14 ) @ ( produc755559506on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( P_3 @ A_1 @ B_14 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_788_rtrancl__induct2,axiom,
! [P_3: produc1282892786on_val > produc1282892786on_val > $o,Ax: produc1282892786on_val,Ay: produc1282892786on_val,Bx: produc1282892786on_val,By: produc1282892786on_val,R_5: produc652964533on_val > $o] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Ax @ Ay ) @ ( produc833389609on_val @ Bx @ By ) ) @ ( transi130214086on_val @ R_5 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: produc1282892786on_val,B_14: produc1282892786on_val,Aa: produc1282892786on_val,Ba: produc1282892786on_val] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Ax @ Ay ) @ ( produc833389609on_val @ A_1 @ B_14 ) ) @ ( transi130214086on_val @ R_5 ) )
=> ( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ A_1 @ B_14 ) @ ( produc833389609on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( P_3 @ A_1 @ B_14 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_789_progress,axiom,
! [L_1: list_char > option_val,E_2: list_char > option_ty,E_1: exp_list_char,T: ty,H_1: nat > option1728594148on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( hconf_97414254t_char @ P @ H_1 )
=> ( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ T )
=> ( ( d_list_char @ E_1 @ ( some_list_char_o @ ( dom_list_char_val @ L_1 ) ) )
=> ( ~ ( final_list_char @ E_1 )
=> ? [E_3: exp_list_char,S_5: produc2090907612on_val] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ E_3 @ S_5 ) ) @ ( red @ P ) ) ) ) ) ) ) ).
thf(fact_790_option_Oexhaust,axiom,
! [Y_9: option_nat] :
( ( Y_9 != none_nat )
=> ~ ! [A_1: nat] :
( Y_9
!= ( some_nat @ A_1 ) ) ) ).
thf(fact_791_option_Oexhaust,axiom,
! [Y_9: option_ty] :
( ( Y_9 != none_ty )
=> ~ ! [A_1: ty] :
( Y_9
!= ( some_ty @ A_1 ) ) ) ).
thf(fact_792_option_Oexhaust,axiom,
! [Y_9: option1728594148on_val] :
( ( Y_9 != none_P1260844216on_val )
=> ~ ! [A_1: produc2088785539on_val] :
( Y_9
!= ( some_P451527732on_val @ A_1 ) ) ) ).
thf(fact_793_option_Oexhaust,axiom,
! [Y_9: option_val] :
( ( Y_9 != none_val )
=> ~ ! [A_1: val] :
( Y_9
!= ( some_val @ A_1 ) ) ) ).
thf(fact_794_option_Oexhaust,axiom,
! [Y_9: option_list_char_o] :
( ( Y_9 != none_list_char_o )
=> ~ ! [A_1: list_char > $o] :
( Y_9
!= ( some_list_char_o @ A_1 ) ) ) ).
thf(fact_795_order__refl,axiom,
! [X_15: list_char > $o] : ( ord_le1777678169char_o @ X_15 @ X_15 ) ).
thf(fact_796_rtrancl__induct,axiom,
! [P_2: produc1180562163on_val > $o,A_16: produc1180562163on_val,B_13: produc1180562163on_val,R_4: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_16 @ B_13 ) @ ( transi808828192on_val @ R_4 ) )
=> ( ( P_2 @ A_16 )
=> ( ! [Y_1: produc1180562163on_val,Z: produc1180562163on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_16 @ Y_1 ) @ ( transi808828192on_val @ R_4 ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ Y_1 @ Z ) @ R_4 )
=> ( ( P_2 @ Y_1 )
=> ( P_2 @ Z ) ) ) )
=> ( P_2 @ B_13 ) ) ) ) ).
thf(fact_797_rtrancl__induct,axiom,
! [P_2: list_char > $o,A_16: list_char,B_13: list_char,R_4: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_16 @ B_13 ) @ ( transi1395422419t_char @ R_4 ) )
=> ( ( P_2 @ A_16 )
=> ( ! [Y_1: list_char,Z: list_char] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_16 @ Y_1 ) @ ( transi1395422419t_char @ R_4 ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ Y_1 @ Z ) @ R_4 )
=> ( ( P_2 @ Y_1 )
=> ( P_2 @ Z ) ) ) )
=> ( P_2 @ B_13 ) ) ) ) ).
thf(fact_798_rtrancl__induct,axiom,
! [P_2: produc1282892786on_val > $o,A_16: produc1282892786on_val,B_13: produc1282892786on_val,R_4: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_16 @ B_13 ) @ ( transi2118771717on_val @ R_4 ) )
=> ( ( P_2 @ A_16 )
=> ( ! [Y_1: produc1282892786on_val,Z: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_16 @ Y_1 ) @ ( transi2118771717on_val @ R_4 ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ Y_1 @ Z ) @ R_4 )
=> ( ( P_2 @ Y_1 )
=> ( P_2 @ Z ) ) ) )
=> ( P_2 @ B_13 ) ) ) ) ).
thf(fact_799_rtrancl__induct,axiom,
! [P_2: val > $o,A_16: val,B_13: val,R_4: product_prod_val_val > $o] :
( ( member649088532al_val @ ( product_Pair_val_val @ A_16 @ B_13 ) @ ( transi935034983cl_val @ R_4 ) )
=> ( ( P_2 @ A_16 )
=> ( ! [Y_1: val,Z: val] :
( ( member649088532al_val @ ( product_Pair_val_val @ A_16 @ Y_1 ) @ ( transi935034983cl_val @ R_4 ) )
=> ( ( member649088532al_val @ ( product_Pair_val_val @ Y_1 @ Z ) @ R_4 )
=> ( ( P_2 @ Y_1 )
=> ( P_2 @ Z ) ) ) )
=> ( P_2 @ B_13 ) ) ) ) ).
thf(fact_800_pred__subset__eq2,axiom,
! [R_3: produc1013743697t_char > $o,S_4: produc1013743697t_char > $o] :
( ( ord_le694689975char_o
@ ^ [X: list_char,Y_1: produc1025221954t_char] : ( member1601084734t_char @ ( produc1331140167t_char @ X @ Y_1 ) @ R_3 )
@ ^ [X: list_char,Y_1: produc1025221954t_char] : ( member1601084734t_char @ ( produc1331140167t_char @ X @ Y_1 ) @ S_4 ) )
<=> ( ord_le1156912648char_o @ R_3 @ S_4 ) ) ).
thf(fact_801_pred__subset__eq2,axiom,
! [R_3: produc1971331930t_char > $o,S_4: produc1971331930t_char > $o] :
( ( ord_le1501926550char_o
@ ^ [X: list_char,Y_1: produc952412819t_char] : ( member1467889965t_char @ ( produc822965838t_char @ X @ Y_1 ) @ R_3 )
@ ^ [X: list_char,Y_1: produc952412819t_char] : ( member1467889965t_char @ ( produc822965838t_char @ X @ Y_1 ) @ S_4 ) )
<=> ( ord_le139275609char_o @ R_3 @ S_4 ) ) ).
thf(fact_802_pred__subset__eq2,axiom,
! [R_3: produc618524391on_val > $o,S_4: produc618524391on_val > $o] :
( ( ord_le1294853199_val_o
@ ^ [X: produc1180562163on_val,Y_1: produc1180562163on_val] : ( member2042188884on_val @ ( produc747700183on_val @ X @ Y_1 ) @ R_3 )
@ ^ [X: produc1180562163on_val,Y_1: produc1180562163on_val] : ( member2042188884on_val @ ( produc747700183on_val @ X @ Y_1 ) @ S_4 ) )
<=> ( ord_le559588722_val_o @ R_3 @ S_4 ) ) ).
thf(fact_803_pred__subset__eq2,axiom,
! [R_3: produc1278157519t_char > $o,S_4: produc1278157519t_char > $o] :
( ( ord_le237460153char_o
@ ^ [X: list_char,Y_1: list_char] : ( member1251428284t_char @ ( produc5062597t_char @ X @ Y_1 ) @ R_3 )
@ ^ [X: list_char,Y_1: list_char] : ( member1251428284t_char @ ( produc5062597t_char @ X @ Y_1 ) @ S_4 ) )
<=> ( ord_le7825418char_o @ R_3 @ S_4 ) ) ).
thf(fact_804_pred__subset__eq2,axiom,
! [R_3: produc1746408499on_val > $o,S_4: produc1746408499on_val > $o] :
( ( ord_le166837589_val_o
@ ^ [X: produc1282892786on_val,Y_1: produc1282892786on_val] : ( member1913460000on_val @ ( produc833389609on_val @ X @ Y_1 ) @ R_3 )
@ ^ [X: produc1282892786on_val,Y_1: produc1282892786on_val] : ( member1913460000on_val @ ( produc833389609on_val @ X @ Y_1 ) @ S_4 ) )
<=> ( ord_le1364969894_val_o @ R_3 @ S_4 ) ) ).
thf(fact_805_pred__subset__eq2,axiom,
! [R_3: produc809539159t_char > $o,S_4: produc809539159t_char > $o] :
( ( ord_le84164651char_o
@ ^ [X: list_list_char,Y_1: exp_list_char] : ( member1840112042t_char @ ( produc1147572817t_char @ X @ Y_1 ) @ R_3 )
@ ^ [X: list_list_char,Y_1: exp_list_char] : ( member1840112042t_char @ ( produc1147572817t_char @ X @ Y_1 ) @ S_4 ) )
<=> ( ord_le1754369948char_o @ R_3 @ S_4 ) ) ).
thf(fact_806_pred__subset__eq2,axiom,
! [R_3: produc2146869324t_char > $o,S_4: produc2146869324t_char > $o] :
( ( ord_le1015080996char_o
@ ^ [X: list_P1940453997har_ty,Y_1: list_P341299826t_char] : ( member1379348767t_char @ ( produc1152259904t_char @ X @ Y_1 ) @ R_3 )
@ ^ [X: list_P1940453997har_ty,Y_1: list_P341299826t_char] : ( member1379348767t_char @ ( produc1152259904t_char @ X @ Y_1 ) @ S_4 ) )
<=> ( ord_le2021326055char_o @ R_3 @ S_4 ) ) ).
thf(fact_807_pred__subset__eq2,axiom,
! [R_3: produc952412819t_char > $o,S_4: produc952412819t_char > $o] :
( ( ord_le1073847069char_o
@ ^ [X: list_char,Y_1: produc2146869324t_char] : ( member1771544038t_char @ ( produc1483578759t_char @ X @ Y_1 ) @ R_3 )
@ ^ [X: list_char,Y_1: produc2146869324t_char] : ( member1771544038t_char @ ( produc1483578759t_char @ X @ Y_1 ) @ S_4 ) )
<=> ( ord_le1844608096char_o @ R_3 @ S_4 ) ) ).
thf(fact_808_pred__subset__eq2,axiom,
! [R_3: produc662261637t_char > $o,S_4: produc662261637t_char > $o] :
( ( ord_le1480834691char_o
@ ^ [X: list_val,Y_1: exp_list_char] : ( member699351154t_char @ ( produc1916172923t_char @ X @ Y_1 ) @ R_3 )
@ ^ [X: list_val,Y_1: exp_list_char] : ( member699351154t_char @ ( produc1916172923t_char @ X @ Y_1 ) @ S_4 ) )
<=> ( ord_le1298648532char_o @ R_3 @ S_4 ) ) ).
thf(fact_809_pred__subset__eq2,axiom,
! [R_3: produc220283002t_char > $o,S_4: produc220283002t_char > $o] :
( ( ord_le1975270990char_o
@ ^ [X: list_ty,Y_1: produc662261637t_char] : ( member140606439t_char @ ( produc1909267824t_char @ X @ Y_1 ) @ R_3 )
@ ^ [X: list_ty,Y_1: produc662261637t_char] : ( member140606439t_char @ ( produc1909267824t_char @ X @ Y_1 ) @ S_4 ) )
<=> ( ord_le1234751263char_o @ R_3 @ S_4 ) ) ).
thf(fact_810_pred__subset__eq2,axiom,
! [R_3: produc1285161482t_char > $o,S_4: produc1285161482t_char > $o] :
( ( ord_le424140984char_o
@ ^ [X: list_list_char,Y_1: produc220283002t_char] : ( member133545693t_char @ ( produc921874948t_char @ X @ Y_1 ) @ R_3 )
@ ^ [X: list_list_char,Y_1: produc220283002t_char] : ( member133545693t_char @ ( produc921874948t_char @ X @ Y_1 ) @ S_4 ) )
<=> ( ord_le1356274601char_o @ R_3 @ S_4 ) ) ).
thf(fact_811_pred__subset__eq2,axiom,
! [R_3: produc1180562163on_val > $o,S_4: produc1180562163on_val > $o] :
( ( ord_le636719503_val_o
@ ^ [X: list_exp_list_char,Y_1: produc2090907612on_val] : ( member1224782662on_val @ ( produc1302104557on_val @ X @ Y_1 ) @ R_3 )
@ ^ [X: list_exp_list_char,Y_1: produc2090907612on_val] : ( member1224782662on_val @ ( produc1302104557on_val @ X @ Y_1 ) @ S_4 ) )
<=> ( ord_le941641472_val_o @ R_3 @ S_4 ) ) ).
thf(fact_812_pred__subset__eq2,axiom,
! [R_3: product_prod_val_val > $o,S_4: product_prod_val_val > $o] :
( ( ord_le946822159_val_o
@ ^ [X: val,Y_1: val] : ( member649088532al_val @ ( product_Pair_val_val @ X @ Y_1 ) @ R_3 )
@ ^ [X: val,Y_1: val] : ( member649088532al_val @ ( product_Pair_val_val @ X @ Y_1 ) @ S_4 ) )
<=> ( ord_le1101577138_val_o @ R_3 @ S_4 ) ) ).
thf(fact_813_pred__subset__eq2,axiom,
! [R_3: produc1645268488al_val > $o,S_4: produc1645268488al_val > $o] :
( ( ord_le1352079040_val_o
@ ^ [X: bop,Y_1: product_prod_val_val] : ( member1417904245al_val @ ( produc621191550al_val @ X @ Y_1 ) @ R_3 )
@ ^ [X: bop,Y_1: product_prod_val_val] : ( member1417904245al_val @ ( produc621191550al_val @ X @ Y_1 ) @ S_4 ) )
<=> ( ord_le1019536145_val_o @ R_3 @ S_4 ) ) ).
thf(fact_814_pred__subset__eq2,axiom,
! [R_3: produc2088785539on_val > $o,S_4: produc2088785539on_val > $o] :
( ( ord_le1726974981_val_o
@ ^ [X: list_char,Y_1: produc1278157519t_char > option_val] : ( member1374264560on_val @ ( produc926070009on_val @ X @ Y_1 ) @ R_3 )
@ ^ [X: list_char,Y_1: produc1278157519t_char > option_val] : ( member1374264560on_val @ ( produc926070009on_val @ X @ Y_1 ) @ S_4 ) )
<=> ( ord_le719203798_val_o @ R_3 @ S_4 ) ) ).
thf(fact_815_pred__subset__eq2,axiom,
! [R_3: produc2090907612on_val > $o,S_4: produc2090907612on_val > $o] :
( ( ord_le1145603820_val_o
@ ^ [X: nat > option1728594148on_val,Y_1: list_char > option_val] : ( member1846553161on_val @ ( produc755559506on_val @ X @ Y_1 ) @ R_3 )
@ ^ [X: nat > option1728594148on_val,Y_1: list_char > option_val] : ( member1846553161on_val @ ( produc755559506on_val @ X @ Y_1 ) @ S_4 ) )
<=> ( ord_le290925629_val_o @ R_3 @ S_4 ) ) ).
thf(fact_816_pred__subset__eq2,axiom,
! [R_3: produc1282892786on_val > $o,S_4: produc1282892786on_val > $o] :
( ( ord_le1792911318_val_o
@ ^ [X: exp_list_char,Y_1: produc2090907612on_val] : ( member1072200031on_val @ ( produc235638504on_val @ X @ Y_1 ) @ R_3 )
@ ^ [X: exp_list_char,Y_1: produc2090907612on_val] : ( member1072200031on_val @ ( produc235638504on_val @ X @ Y_1 ) @ S_4 ) )
<=> ( ord_le900129703_val_o @ R_3 @ S_4 ) ) ).
thf(fact_817_xt1_I6_J,axiom,
! [Z_3: list_char > $o,Y_8: list_char > $o,X_14: list_char > $o] :
( ( ord_le1777678169char_o @ Y_8 @ X_14 )
=> ( ( ord_le1777678169char_o @ Z_3 @ Y_8 )
=> ( ord_le1777678169char_o @ Z_3 @ X_14 ) ) ) ).
thf(fact_818_xt1_I5_J,axiom,
! [Y_7: list_char > $o,X_13: list_char > $o] :
( ( ord_le1777678169char_o @ Y_7 @ X_13 )
=> ( ( ord_le1777678169char_o @ X_13 @ Y_7 )
=> ( X_13 = Y_7 ) ) ) ).
thf(fact_819_order__trans,axiom,
! [Z_2: list_char > $o,X_12: list_char > $o,Y_6: list_char > $o] :
( ( ord_le1777678169char_o @ X_12 @ Y_6 )
=> ( ( ord_le1777678169char_o @ Y_6 @ Z_2 )
=> ( ord_le1777678169char_o @ X_12 @ Z_2 ) ) ) ).
thf(fact_820_order__antisym,axiom,
! [X_11: list_char > $o,Y_5: list_char > $o] :
( ( ord_le1777678169char_o @ X_11 @ Y_5 )
=> ( ( ord_le1777678169char_o @ Y_5 @ X_11 )
=> ( X_11 = Y_5 ) ) ) ).
thf(fact_821_xt1_I4_J,axiom,
! [C_9: list_char > $o,B_12: list_char > $o,A_15: list_char > $o] :
( ( ord_le1777678169char_o @ B_12 @ A_15 )
=> ( ( B_12 = C_9 )
=> ( ord_le1777678169char_o @ C_9 @ A_15 ) ) ) ).
thf(fact_822_ord__le__eq__trans,axiom,
! [C_8: list_char > $o,A_14: list_char > $o,B_11: list_char > $o] :
( ( ord_le1777678169char_o @ A_14 @ B_11 )
=> ( ( B_11 = C_8 )
=> ( ord_le1777678169char_o @ A_14 @ C_8 ) ) ) ).
thf(fact_823_xt1_I3_J,axiom,
! [C_7: list_char > $o,A_13: list_char > $o,B_10: list_char > $o] :
( ( A_13 = B_10 )
=> ( ( ord_le1777678169char_o @ C_7 @ B_10 )
=> ( ord_le1777678169char_o @ C_7 @ A_13 ) ) ) ).
thf(fact_824_ord__eq__le__trans,axiom,
! [C_6: list_char > $o,A_12: list_char > $o,B_9: list_char > $o] :
( ( A_12 = B_9 )
=> ( ( ord_le1777678169char_o @ B_9 @ C_6 )
=> ( ord_le1777678169char_o @ A_12 @ C_6 ) ) ) ).
thf(fact_825_order__antisym__conv,axiom,
! [Y_4: list_char > $o,X_10: list_char > $o] :
( ( ord_le1777678169char_o @ Y_4 @ X_10 )
=> ( ( ord_le1777678169char_o @ X_10 @ Y_4 )
<=> ( X_10 = Y_4 ) ) ) ).
thf(fact_826_order__eq__refl,axiom,
! [X_9: list_char > $o,Y_3: list_char > $o] :
( ( X_9 = Y_3 )
=> ( ord_le1777678169char_o @ X_9 @ Y_3 ) ) ).
thf(fact_827_order__eq__iff,axiom,
! [X_8: list_char > $o,Y_2: list_char > $o] :
( ( X_8 = Y_2 )
<=> ( ( ord_le1777678169char_o @ X_8 @ Y_2 )
& ( ord_le1777678169char_o @ Y_2 @ X_8 ) ) ) ).
thf(fact_828_le__funE,axiom,
! [X_7: list_char,F_4: list_char > $o,G_3: list_char > $o] :
( ( ord_le1777678169char_o @ F_4 @ G_3 )
=> ( ord_less_eq_o @ ( F_4 @ X_7 ) @ ( G_3 @ X_7 ) ) ) ).
thf(fact_829_le__funD,axiom,
! [X_6: list_char,F_3: list_char > $o,G_2: list_char > $o] :
( ( ord_le1777678169char_o @ F_3 @ G_2 )
=> ( ord_less_eq_o @ ( F_3 @ X_6 ) @ ( G_2 @ X_6 ) ) ) ).
thf(fact_830_le__fun__def,axiom,
! [F_2: list_char > $o,G_1: list_char > $o] :
( ( ord_le1777678169char_o @ F_2 @ G_1 )
<=> ! [X: list_char] : ( ord_less_eq_o @ ( F_2 @ X ) @ ( G_1 @ X ) ) ) ).
thf(fact_831_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_832_wf__mdecl__wwf__mdecl,axiom,
! [P: list_P1999446415t_char,C: list_char,Md: produc1013743697t_char] :
( ( wf_J_mdecl @ P @ C @ Md )
=> ( wwf_J_mdecl @ P @ C @ Md ) ) ).
thf(fact_833_Red__fv,axiom,
! [E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) ) @ ( red @ P ) )
=> ( ord_le1777678169char_o @ ( fv @ E ) @ ( fv @ E_1 ) ) ) ) ).
thf(fact_834_rtranclE,axiom,
! [A_11: produc1180562163on_val,B_8: produc1180562163on_val,R_2: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_11 @ B_8 ) @ ( transi808828192on_val @ R_2 ) )
=> ( ( A_11 != B_8 )
=> ~ ! [Y_1: produc1180562163on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_11 @ Y_1 ) @ ( transi808828192on_val @ R_2 ) )
=> ~ ( member2042188884on_val @ ( produc747700183on_val @ Y_1 @ B_8 ) @ R_2 ) ) ) ) ).
thf(fact_835_rtranclE,axiom,
! [A_11: list_char,B_8: list_char,R_2: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_11 @ B_8 ) @ ( transi1395422419t_char @ R_2 ) )
=> ( ( A_11 != B_8 )
=> ~ ! [Y_1: list_char] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_11 @ Y_1 ) @ ( transi1395422419t_char @ R_2 ) )
=> ~ ( member1251428284t_char @ ( produc5062597t_char @ Y_1 @ B_8 ) @ R_2 ) ) ) ) ).
thf(fact_836_rtranclE,axiom,
! [A_11: produc1282892786on_val,B_8: produc1282892786on_val,R_2: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_11 @ B_8 ) @ ( transi2118771717on_val @ R_2 ) )
=> ( ( A_11 != B_8 )
=> ~ ! [Y_1: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_11 @ Y_1 ) @ ( transi2118771717on_val @ R_2 ) )
=> ~ ( member1913460000on_val @ ( produc833389609on_val @ Y_1 @ B_8 ) @ R_2 ) ) ) ) ).
thf(fact_837_rtranclE,axiom,
! [A_11: val,B_8: val,R_2: product_prod_val_val > $o] :
( ( member649088532al_val @ ( product_Pair_val_val @ A_11 @ B_8 ) @ ( transi935034983cl_val @ R_2 ) )
=> ( ( A_11 != B_8 )
=> ~ ! [Y_1: val] :
( ( member649088532al_val @ ( product_Pair_val_val @ A_11 @ Y_1 ) @ ( transi935034983cl_val @ R_2 ) )
=> ~ ( member649088532al_val @ ( product_Pair_val_val @ Y_1 @ B_8 ) @ R_2 ) ) ) ) ).
thf(fact_838_converse__rtranclE,axiom,
! [X_5: produc1180562163on_val,Z_1: produc1180562163on_val,R_1: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ X_5 @ Z_1 ) @ ( transi808828192on_val @ R_1 ) )
=> ( ( X_5 != Z_1 )
=> ~ ! [Y_1: produc1180562163on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ X_5 @ Y_1 ) @ R_1 )
=> ~ ( member2042188884on_val @ ( produc747700183on_val @ Y_1 @ Z_1 ) @ ( transi808828192on_val @ R_1 ) ) ) ) ) ).
thf(fact_839_converse__rtranclE,axiom,
! [X_5: list_char,Z_1: list_char,R_1: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ X_5 @ Z_1 ) @ ( transi1395422419t_char @ R_1 ) )
=> ( ( X_5 != Z_1 )
=> ~ ! [Y_1: list_char] :
( ( member1251428284t_char @ ( produc5062597t_char @ X_5 @ Y_1 ) @ R_1 )
=> ~ ( member1251428284t_char @ ( produc5062597t_char @ Y_1 @ Z_1 ) @ ( transi1395422419t_char @ R_1 ) ) ) ) ) ).
thf(fact_840_converse__rtranclE,axiom,
! [X_5: produc1282892786on_val,Z_1: produc1282892786on_val,R_1: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ X_5 @ Z_1 ) @ ( transi2118771717on_val @ R_1 ) )
=> ( ( X_5 != Z_1 )
=> ~ ! [Y_1: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ X_5 @ Y_1 ) @ R_1 )
=> ~ ( member1913460000on_val @ ( produc833389609on_val @ Y_1 @ Z_1 ) @ ( transi2118771717on_val @ R_1 ) ) ) ) ) ).
thf(fact_841_converse__rtranclE,axiom,
! [X_5: val,Z_1: val,R_1: product_prod_val_val > $o] :
( ( member649088532al_val @ ( product_Pair_val_val @ X_5 @ Z_1 ) @ ( transi935034983cl_val @ R_1 ) )
=> ( ( X_5 != Z_1 )
=> ~ ! [Y_1: val] :
( ( member649088532al_val @ ( product_Pair_val_val @ X_5 @ Y_1 ) @ R_1 )
=> ~ ( member649088532al_val @ ( product_Pair_val_val @ Y_1 @ Z_1 ) @ ( transi935034983cl_val @ R_1 ) ) ) ) ) ).
thf(fact_842_converse__rtrancl__induct,axiom,
! [P_1: produc1180562163on_val > $o,A_10: produc1180562163on_val,B_7: produc1180562163on_val,R: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_10 @ B_7 ) @ ( transi808828192on_val @ R ) )
=> ( ( P_1 @ B_7 )
=> ( ! [Y_1: produc1180562163on_val,Z: produc1180562163on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ Y_1 @ Z ) @ R )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ Z @ B_7 ) @ ( transi808828192on_val @ R ) )
=> ( ( P_1 @ Z )
=> ( P_1 @ Y_1 ) ) ) )
=> ( P_1 @ A_10 ) ) ) ) ).
thf(fact_843_converse__rtrancl__induct,axiom,
! [P_1: list_char > $o,A_10: list_char,B_7: list_char,R: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_10 @ B_7 ) @ ( transi1395422419t_char @ R ) )
=> ( ( P_1 @ B_7 )
=> ( ! [Y_1: list_char,Z: list_char] :
( ( member1251428284t_char @ ( produc5062597t_char @ Y_1 @ Z ) @ R )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ Z @ B_7 ) @ ( transi1395422419t_char @ R ) )
=> ( ( P_1 @ Z )
=> ( P_1 @ Y_1 ) ) ) )
=> ( P_1 @ A_10 ) ) ) ) ).
thf(fact_844_converse__rtrancl__induct,axiom,
! [P_1: produc1282892786on_val > $o,A_10: produc1282892786on_val,B_7: produc1282892786on_val,R: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_10 @ B_7 ) @ ( transi2118771717on_val @ R ) )
=> ( ( P_1 @ B_7 )
=> ( ! [Y_1: produc1282892786on_val,Z: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ Y_1 @ Z ) @ R )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ Z @ B_7 ) @ ( transi2118771717on_val @ R ) )
=> ( ( P_1 @ Z )
=> ( P_1 @ Y_1 ) ) ) )
=> ( P_1 @ A_10 ) ) ) ) ).
thf(fact_845_converse__rtrancl__induct,axiom,
! [P_1: val > $o,A_10: val,B_7: val,R: product_prod_val_val > $o] :
( ( member649088532al_val @ ( product_Pair_val_val @ A_10 @ B_7 ) @ ( transi935034983cl_val @ R ) )
=> ( ( P_1 @ B_7 )
=> ( ! [Y_1: val,Z: val] :
( ( member649088532al_val @ ( product_Pair_val_val @ Y_1 @ Z ) @ R )
=> ( ( member649088532al_val @ ( product_Pair_val_val @ Z @ B_7 ) @ ( transi935034983cl_val @ R ) )
=> ( ( P_1 @ Z )
=> ( P_1 @ Y_1 ) ) ) )
=> ( P_1 @ A_10 ) ) ) ) ).
thf(fact_846_le__funI,axiom,
! [F_1: list_char > $o,G: list_char > $o] :
( ! [X: list_char] : ( ord_less_eq_o @ ( F_1 @ X ) @ ( G @ X ) )
=> ( ord_le1777678169char_o @ F_1 @ G ) ) ).
thf(fact_847_big__iff__small,axiom,
! [E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( eval @ P @ E_1 @ S @ E @ S_2 )
<=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
& ( final_list_char @ E ) ) ) ) ).
thf(fact_848_eval__notfree__unchanged,axiom,
! [V_1: list_char,P: list_P1999446415t_char,E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val] :
( ( eval @ P @ E_1 @ ( produc755559506on_val @ H_1 @ L_1 ) @ E @ ( produc755559506on_val @ H @ L ) )
=> ( ~ ( member_list_char @ V_1 @ ( fv @ E_1 ) )
=> ( ( L @ V_1 )
= ( L_1 @ V_1 ) ) ) ) ).
thf(fact_849_extend__1__eval,axiom,
! [E: exp_list_char,S_2: produc2090907612on_val,E_1: exp_list_char,S: produc2090907612on_val,E_5: 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 ) @ ( produc235638504on_val @ E_5 @ S_3 ) ) @ ( red @ P ) )
=> ( ( eval @ P @ E_5 @ S_3 @ E @ S_2 )
=> ( eval @ P @ E_1 @ S @ E @ S_2 ) ) ) ) ).
thf(fact_850_big__by__small,axiom,
! [E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( eval @ P @ E_1 @ S @ E @ S_2 )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_851_extend__eval,axiom,
! [E: exp_list_char,S_2: produc2090907612on_val,E_1: exp_list_char,S: produc2090907612on_val,E_5: 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 ) @ ( produc235638504on_val @ E_5 @ S_3 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( eval @ P @ E_5 @ S_3 @ E @ S_2 )
=> ( eval @ P @ E_1 @ S @ E @ S_2 ) ) ) ) ).
thf(fact_852_small__by__big,axiom,
! [E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( final_list_char @ E )
=> ( eval @ P @ E_1 @ S @ E @ S_2 ) ) ) ) ).
thf(fact_853_LAss,axiom,
! [L: list_char > option_val,V_1: list_char,P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,V: val,H_1: nat > option1728594148on_val,L_1: list_char > option_val] :
( ( eval @ P @ E_1 @ S_0 @ ( val_list_char @ V ) @ ( produc755559506on_val @ H_1 @ L_1 ) )
=> ( ( L
= ( fun_up1149430426on_val @ L_1 @ V_1 @ ( some_val @ V ) ) )
=> ( eval @ P @ ( lAss_list_char @ V_1 @ E_1 ) @ S_0 @ ( val_list_char @ unit ) @ ( produc755559506on_val @ H_1 @ L ) ) ) ) ).
thf(fact_854_Block,axiom,
! [T: ty,P: list_P1999446415t_char,E_0: exp_list_char,H_0: nat > option1728594148on_val,L_0: list_char > option_val,V_1: list_char,E_1_1: exp_list_char,H_1_1: nat > option1728594148on_val,L_1_1: list_char > option_val] :
( ( eval @ P @ E_0 @ ( produc755559506on_val @ H_0 @ ( fun_up1149430426on_val @ L_0 @ V_1 @ none_val ) ) @ E_1_1 @ ( produc755559506on_val @ H_1_1 @ L_1_1 ) )
=> ( eval @ P @ ( block_list_char @ V_1 @ T @ E_0 ) @ ( produc755559506on_val @ H_0 @ L_0 ) @ E_1_1 @ ( produc755559506on_val @ H_1_1 @ ( fun_up1149430426on_val @ L_1_1 @ V_1 @ ( L_0 @ V_1 ) ) ) ) ) ).
thf(fact_855_eval__lcl__incr,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,H_0: nat > option1728594148on_val,L_0: list_char > option_val,E: exp_list_char,H_1_1: nat > option1728594148on_val,L_1_1: list_char > option_val] :
( ( eval @ P @ E_1 @ ( produc755559506on_val @ H_0 @ L_0 ) @ E @ ( produc755559506on_val @ H_1_1 @ L_1_1 ) )
=> ( ord_le1777678169char_o @ ( dom_list_char_val @ L_0 ) @ ( dom_list_char_val @ L_1_1 ) ) ) ).
thf(fact_856_eval__hext,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val] :
( ( eval @ P @ E_1 @ ( produc755559506on_val @ H_1 @ L_1 ) @ E @ ( produc755559506on_val @ H @ L ) )
=> ( hext @ H_1 @ H ) ) ).
thf(fact_857_Seq,axiom,
! [E_1_1: exp_list_char,E_2_1: 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_1 @ S_2_1 )
=> ( eval @ P @ ( seq_list_char @ E_0 @ E_1_1 ) @ S_0 @ E_2_1 @ S_2_1 ) ) ) ).
thf(fact_858_Reds__dom__lcl,axiom,
! [E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ord_le1777678169char_o @ ( dom_list_char_val @ L ) @ ( semila2134664963char_o @ ( dom_list_char_val @ L_1 ) @ ( fv @ E_1 ) ) ) ) ) ).
thf(fact_859_UnE,axiom,
! [C_5: produc1013743697t_char,A_9: produc1013743697t_char > $o,B_6: produc1013743697t_char > $o] :
( ( member1601084734t_char @ C_5 @ ( semila1228900530char_o @ A_9 @ B_6 ) )
=> ( ~ ( member1601084734t_char @ C_5 @ A_9 )
=> ( member1601084734t_char @ C_5 @ B_6 ) ) ) ).
thf(fact_860_UnE,axiom,
! [C_5: produc1971331930t_char,A_9: produc1971331930t_char > $o,B_6: produc1971331930t_char > $o] :
( ( member1467889965t_char @ C_5 @ ( semila690474031char_o @ A_9 @ B_6 ) )
=> ( ~ ( member1467889965t_char @ C_5 @ A_9 )
=> ( member1467889965t_char @ C_5 @ B_6 ) ) ) ).
thf(fact_861_UnE,axiom,
! [C_5: produc618524391on_val,A_9: produc618524391on_val > $o,B_6: produc618524391on_val > $o] :
( ( member2042188884on_val @ C_5 @ ( semila1566912796_val_o @ A_9 @ B_6 ) )
=> ( ~ ( member2042188884on_val @ C_5 @ A_9 )
=> ( member2042188884on_val @ C_5 @ B_6 ) ) ) ).
thf(fact_862_UnE,axiom,
! [C_5: nat,A_9: nat > $o,B_6: nat > $o] :
( ( member_nat @ C_5 @ ( semila848761471_nat_o @ A_9 @ B_6 ) )
=> ( ~ ( member_nat @ C_5 @ A_9 )
=> ( member_nat @ C_5 @ B_6 ) ) ) ).
thf(fact_863_UnE,axiom,
! [C_5: produc1278157519t_char,A_9: produc1278157519t_char > $o,B_6: produc1278157519t_char > $o] :
( ( member1251428284t_char @ C_5 @ ( semila880700084char_o @ A_9 @ B_6 ) )
=> ( ~ ( member1251428284t_char @ C_5 @ A_9 )
=> ( member1251428284t_char @ C_5 @ B_6 ) ) ) ).
thf(fact_864_UnE,axiom,
! [C_5: list_char,A_9: list_char > $o,B_6: list_char > $o] :
( ( member_list_char @ C_5 @ ( semila2134664963char_o @ A_9 @ B_6 ) )
=> ( ~ ( member_list_char @ C_5 @ A_9 )
=> ( member_list_char @ C_5 @ B_6 ) ) ) ).
thf(fact_865_UnE,axiom,
! [C_5: produc1746408499on_val,A_9: produc1746408499on_val > $o,B_6: produc1746408499on_val > $o] :
( ( member1913460000on_val @ C_5 @ ( semila1505903696_val_o @ A_9 @ B_6 ) )
=> ( ~ ( member1913460000on_val @ C_5 @ A_9 )
=> ( member1913460000on_val @ C_5 @ B_6 ) ) ) ).
thf(fact_866_UnCI,axiom,
! [A_8: produc1013743697t_char > $o,C_4: produc1013743697t_char,B_5: produc1013743697t_char > $o] :
( ( ~ ( member1601084734t_char @ C_4 @ B_5 )
=> ( member1601084734t_char @ C_4 @ A_8 ) )
=> ( member1601084734t_char @ C_4 @ ( semila1228900530char_o @ A_8 @ B_5 ) ) ) ).
thf(fact_867_UnCI,axiom,
! [A_8: produc1971331930t_char > $o,C_4: produc1971331930t_char,B_5: produc1971331930t_char > $o] :
( ( ~ ( member1467889965t_char @ C_4 @ B_5 )
=> ( member1467889965t_char @ C_4 @ A_8 ) )
=> ( member1467889965t_char @ C_4 @ ( semila690474031char_o @ A_8 @ B_5 ) ) ) ).
thf(fact_868_UnCI,axiom,
! [A_8: produc618524391on_val > $o,C_4: produc618524391on_val,B_5: produc618524391on_val > $o] :
( ( ~ ( member2042188884on_val @ C_4 @ B_5 )
=> ( member2042188884on_val @ C_4 @ A_8 ) )
=> ( member2042188884on_val @ C_4 @ ( semila1566912796_val_o @ A_8 @ B_5 ) ) ) ).
thf(fact_869_UnCI,axiom,
! [A_8: nat > $o,C_4: nat,B_5: nat > $o] :
( ( ~ ( member_nat @ C_4 @ B_5 )
=> ( member_nat @ C_4 @ A_8 ) )
=> ( member_nat @ C_4 @ ( semila848761471_nat_o @ A_8 @ B_5 ) ) ) ).
thf(fact_870_UnCI,axiom,
! [A_8: produc1278157519t_char > $o,C_4: produc1278157519t_char,B_5: produc1278157519t_char > $o] :
( ( ~ ( member1251428284t_char @ C_4 @ B_5 )
=> ( member1251428284t_char @ C_4 @ A_8 ) )
=> ( member1251428284t_char @ C_4 @ ( semila880700084char_o @ A_8 @ B_5 ) ) ) ).
thf(fact_871_UnCI,axiom,
! [A_8: list_char > $o,C_4: list_char,B_5: list_char > $o] :
( ( ~ ( member_list_char @ C_4 @ B_5 )
=> ( member_list_char @ C_4 @ A_8 ) )
=> ( member_list_char @ C_4 @ ( semila2134664963char_o @ A_8 @ B_5 ) ) ) ).
thf(fact_872_UnCI,axiom,
! [A_8: produc1746408499on_val > $o,C_4: produc1746408499on_val,B_5: produc1746408499on_val > $o] :
( ( ~ ( member1913460000on_val @ C_4 @ B_5 )
=> ( member1913460000on_val @ C_4 @ A_8 ) )
=> ( member1913460000on_val @ C_4 @ ( semila1505903696_val_o @ A_8 @ B_5 ) ) ) ).
thf(fact_873_sup1E,axiom,
! [A_7: list_char > $o,B_4: list_char > $o,X_4: list_char] :
( ( semila2134664963char_o @ A_7 @ B_4 @ X_4 )
=> ( ~ ( A_7 @ X_4 )
=> ( B_4 @ X_4 ) ) ) ).
thf(fact_874_sup1CI,axiom,
! [A_6: list_char > $o,B_3: list_char > $o,X_3: list_char] :
( ( ~ ( B_3 @ X_3 )
=> ( A_6 @ X_3 ) )
=> ( semila2134664963char_o @ A_6 @ B_3 @ X_3 ) ) ).
thf(fact_875_Un__absorb,axiom,
! [A_5: list_char > $o] :
( ( semila2134664963char_o @ A_5 @ A_5 )
= A_5 ) ).
thf(fact_876_Un__def,axiom,
! [A_4: produc1013743697t_char > $o,B_2: produc1013743697t_char > $o] :
( ( semila1228900530char_o @ A_4 @ B_2 )
= ( collec1387638140t_char
@ ^ [X: produc1013743697t_char] : ( (|) @ ( member1601084734t_char @ X @ A_4 ) @ ( member1601084734t_char @ X @ B_2 ) ) ) ) ).
thf(fact_877_Un__def,axiom,
! [A_4: produc1971331930t_char > $o,B_2: produc1971331930t_char > $o] :
( ( semila690474031char_o @ A_4 @ B_2 )
= ( collec1583467887t_char
@ ^ [X: produc1971331930t_char] : ( (|) @ ( member1467889965t_char @ X @ A_4 ) @ ( member1467889965t_char @ X @ B_2 ) ) ) ) ).
thf(fact_878_Un__def,axiom,
! [A_4: produc618524391on_val > $o,B_2: produc618524391on_val > $o] :
( ( semila1566912796_val_o @ A_4 @ B_2 )
= ( collec507727762on_val
@ ^ [X: produc618524391on_val] : ( (|) @ ( member2042188884on_val @ X @ A_4 ) @ ( member2042188884on_val @ X @ B_2 ) ) ) ) ).
thf(fact_879_Un__def,axiom,
! [A_4: nat > $o,B_2: nat > $o] :
( ( semila848761471_nat_o @ A_4 @ B_2 )
= ( collect_nat
@ ^ [X: nat] : ( (|) @ ( member_nat @ X @ A_4 ) @ ( member_nat @ X @ B_2 ) ) ) ) ).
thf(fact_880_Un__def,axiom,
! [A_4: produc1278157519t_char > $o,B_2: produc1278157519t_char > $o] :
( ( semila880700084char_o @ A_4 @ B_2 )
= ( collec1797130234t_char
@ ^ [X: produc1278157519t_char] : ( (|) @ ( member1251428284t_char @ X @ A_4 ) @ ( member1251428284t_char @ X @ B_2 ) ) ) ) ).
thf(fact_881_Un__def,axiom,
! [A_4: list_char > $o,B_2: list_char > $o] :
( ( semila2134664963char_o @ A_4 @ B_2 )
= ( collect_list_char
@ ^ [X: list_char] : ( (|) @ ( member_list_char @ X @ A_4 ) @ ( member_list_char @ X @ B_2 ) ) ) ) ).
thf(fact_882_Un__def,axiom,
! [A_4: produc1746408499on_val > $o,B_2: produc1746408499on_val > $o] :
( ( semila1505903696_val_o @ A_4 @ B_2 )
= ( collec1451572574on_val
@ ^ [X: produc1746408499on_val] : ( (|) @ ( member1913460000on_val @ X @ A_4 ) @ ( member1913460000on_val @ X @ B_2 ) ) ) ) ).
thf(fact_883_Un__commute,axiom,
! [A_3: list_char > $o,B_1: list_char > $o] :
( ( semila2134664963char_o @ A_3 @ B_1 )
= ( semila2134664963char_o @ B_1 @ A_3 ) ) ).
thf(fact_884_fv__fvs_Osimps_I11_J,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char] :
( ( fv @ ( seq_list_char @ E_1_1 @ E_2_1 ) )
= ( semila2134664963char_o @ ( fv @ E_1_1 ) @ ( fv @ E_2_1 ) ) ) ).
thf(fact_885_eval__cases_I2_J,axiom,
! [P: list_P1999446415t_char,V: val,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( eval @ P @ ( val_list_char @ V ) @ S @ E @ S_2 )
=> ~ ( ( E
= ( val_list_char @ V ) )
=> ( S_2 != S ) ) ) ).
thf(fact_886_Val,axiom,
! [P: list_P1999446415t_char,V: val,S: produc2090907612on_val] : ( eval @ P @ ( val_list_char @ V ) @ S @ ( val_list_char @ V ) @ S ) ).
thf(fact_887_Red__dom__lcl,axiom,
! [E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) ) @ ( red @ P ) )
=> ( ord_le1777678169char_o @ ( dom_list_char_val @ L ) @ ( semila2134664963char_o @ ( dom_list_char_val @ L_1 ) @ ( fv @ E_1 ) ) ) ) ).
thf(fact_888_eval__final,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( eval @ P @ E_1 @ S @ E @ S_2 )
=> ( final_list_char @ E ) ) ).
thf(fact_889_eval__finalId,axiom,
! [P: list_P1999446415t_char,S: produc2090907612on_val,E_1: exp_list_char] :
( ( final_list_char @ E_1 )
=> ( eval @ P @ E_1 @ S @ E_1 @ S ) ) ).
thf(fact_890_eval__cases_I8_J,axiom,
! [P: list_P1999446415t_char,V_1: list_char,T: ty,E_1_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( eval @ P @ ( block_list_char @ V_1 @ T @ E_1_1 ) @ S @ E @ S_2 )
=> ~ ! [H_0_1: nat > option1728594148on_val,L_0_1: list_char > option_val] :
( ( S
= ( produc755559506on_val @ H_0_1 @ L_0_1 ) )
=> ! [H_1_2: nat > option1728594148on_val,L_1_2: list_char > option_val] :
( ( S_2
= ( produc755559506on_val @ H_1_2 @ ( fun_up1149430426on_val @ L_1_2 @ V_1 @ ( L_0_1 @ V_1 ) ) ) )
=> ~ ( eval @ P @ E_1_1 @ ( produc755559506on_val @ H_0_1 @ ( fun_up1149430426on_val @ L_0_1 @ V_1 @ none_val ) ) @ E @ ( produc755559506on_val @ H_1_2 @ L_1_2 ) ) ) ) ) ).
thf(fact_891_eval__restrict__lcl,axiom,
! [W: list_char > $o,E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( eval @ P @ E_1 @ ( produc755559506on_val @ H_1 @ L_1 ) @ E @ ( produc755559506on_val @ H @ L ) )
=> ( ( ord_le1777678169char_o @ ( fv @ E_1 ) @ W )
=> ( eval @ P @ E_1 @ ( produc755559506on_val @ H_1 @ ( restri761823004ar_val @ L_1 @ W ) ) @ E @ ( produc755559506on_val @ H @ ( restri761823004ar_val @ L @ W ) ) ) ) ) ) ).
thf(fact_892_FAssRedsVal,axiom,
! [F: list_char,D: list_char,C: list_char,Fs: produc1278157519t_char > option_val,E_2_1: exp_list_char,V: val,H_2: nat > option1728594148on_val,L_2_1: list_char > option_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,A: 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 ) ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2_1 @ S_1 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ ( produc755559506on_val @ H_2 @ L_2_1 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) )
= ( H_2 @ A ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2_1 ) @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ unit ) @ ( produc755559506on_val @ ( fun_up1472480727on_val @ H_2 @ A @ ( some_P451527732on_val @ ( produc926070009on_val @ C @ ( fun_up204312361on_val @ Fs @ ( produc5062597t_char @ F @ D ) @ ( some_val @ V ) ) ) ) ) @ L_2_1 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_893_redp__redsp_OFAssRed1,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,P: list_P1999446415t_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S @ E @ S_2 )
=> ( redp @ P @ ( fAss_list_char @ E_1 @ F @ D @ E_2_1 ) @ S @ ( fAss_list_char @ E @ F @ D @ E_2_1 ) @ S_2 ) ) ).
thf(fact_894_redp__redsp_OFAssRed2,axiom,
! [V: val,F: list_char,D: list_char,P: list_P1999446415t_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S @ E @ S_2 )
=> ( redp @ P @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ E_1 ) @ S @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ E ) @ S_2 ) ) ).
thf(fact_895_fv__fvs_Osimps_I8_J,axiom,
! [E_1_1: exp_list_char,F: list_char,D: list_char,E_2_1: exp_list_char] :
( ( fv @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2_1 ) )
= ( semila2134664963char_o @ ( fv @ E_1_1 ) @ ( fv @ E_2_1 ) ) ) ).
thf(fact_896_red__reds_OFAssRed1,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ E_1 @ F @ D @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( fAss_list_char @ E @ F @ D @ E_2_1 ) @ S_2 ) ) @ ( red @ P ) ) ) ).
thf(fact_897_red__reds_OFAssRed2,axiom,
! [V: val,F: list_char,D: list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ E_1 ) @ S ) @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ E ) @ S_2 ) ) @ ( red @ P ) ) ) ).
thf(fact_898_FAssReds1,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ E_1 @ F @ D @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( fAss_list_char @ E @ F @ D @ E_2_1 ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_899_FAssReds2,axiom,
! [V: val,F: list_char,D: list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ E_1 ) @ S ) @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ E ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_900_FAss,axiom,
! [H_2_1: nat > option1728594148on_val,Fs_4: produc1278157519t_char > option_val,F: list_char,D: list_char,C: list_char,Fs: produc1278157519t_char > option_val,E_2_1: exp_list_char,V: val,H_2: nat > option1728594148on_val,L_2_1: list_char > option_val,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,A: nat,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ ( addr @ A ) ) @ S_1 )
=> ( ( eval @ P @ E_2_1 @ S_1 @ ( val_list_char @ V ) @ ( produc755559506on_val @ H_2 @ L_2_1 ) )
=> ( ( ( H_2 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( ( Fs_4
= ( fun_up204312361on_val @ Fs @ ( produc5062597t_char @ F @ D ) @ ( some_val @ V ) ) )
=> ( ( H_2_1
= ( fun_up1472480727on_val @ H_2 @ A @ ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs_4 ) ) ) )
=> ( eval @ P @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2_1 ) @ S_0 @ ( val_list_char @ unit ) @ ( produc755559506on_val @ H_2_1 @ L_2_1 ) ) ) ) ) ) ) ).
thf(fact_901_redp__redsp_ORedFAss,axiom,
! [P: list_P1999446415t_char,F: list_char,D: list_char,V: val,L_1: list_char > option_val,H_1: nat > option1728594148on_val,A: nat,C: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( H_1 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( redp @ P @ ( fAss_list_char @ ( val_list_char @ ( addr @ A ) ) @ F @ D @ ( val_list_char @ V ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) @ ( val_list_char @ unit ) @ ( produc755559506on_val @ ( fun_up1472480727on_val @ H_1 @ A @ ( some_P451527732on_val @ ( produc926070009on_val @ C @ ( fun_up204312361on_val @ Fs @ ( produc5062597t_char @ F @ D ) @ ( some_val @ V ) ) ) ) ) @ L_1 ) ) ) ).
thf(fact_902_red__reds_ORedFAss,axiom,
! [F: list_char,D: list_char,V: val,L_1: list_char > option_val,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,A: nat,C: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( H_1 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ ( addr @ A ) ) @ F @ D @ ( val_list_char @ V ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ ( val_list_char @ unit ) @ ( produc755559506on_val @ ( fun_up1472480727on_val @ H_1 @ A @ ( some_P451527732on_val @ ( produc926070009on_val @ C @ ( fun_up204312361on_val @ Fs @ ( produc5062597t_char @ F @ D ) @ ( some_val @ V ) ) ) ) ) @ L_1 ) ) ) @ ( red @ P ) ) ) ).
thf(fact_903_FAccRedsVal,axiom,
! [F: list_char,D: list_char,V: val,C: list_char,Fs: produc1278157519t_char > option_val,E_1: exp_list_char,S: produc2090907612on_val,A: nat,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ ( val_list_char @ ( addr @ A ) ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( hp @ S_2 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( ( ( Fs @ ( produc5062597t_char @ F @ D ) )
= ( some_val @ V ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E_1 @ F @ D ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_904_red__reds_ORedFAcc,axiom,
! [P: list_P1999446415t_char,F: list_char,D: list_char,V: val,S: produc2090907612on_val,A: nat,C: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( ( ( Fs @ ( produc5062597t_char @ F @ D ) )
= ( some_val @ V ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ ( val_list_char @ ( addr @ A ) ) @ F @ D ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S ) ) @ ( red @ P ) ) ) ) ).
thf(fact_905_redp__redsp_ORedFAcc,axiom,
! [P: list_P1999446415t_char,F: list_char,D: list_char,V: val,S: produc2090907612on_val,A: nat,C: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( ( ( Fs @ ( produc5062597t_char @ F @ D ) )
= ( some_val @ V ) )
=> ( redp @ P @ ( fAcc_list_char @ ( val_list_char @ ( addr @ A ) ) @ F @ D ) @ S @ ( val_list_char @ V ) @ S ) ) ) ).
thf(fact_906_FAcc,axiom,
! [F: list_char,D: list_char,V: val,C: list_char,Fs: produc1278157519t_char > option_val,P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,A: nat,H_1: nat > option1728594148on_val,L_1: list_char > option_val] :
( ( eval @ P @ E_1 @ S_0 @ ( val_list_char @ ( addr @ A ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) )
=> ( ( ( H_1 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ 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_1 @ L_1 ) ) ) ) ) ).
thf(fact_907_red__reds_OInitBlockThrow,axiom,
! [V_1: list_char,T: ty,V: val,A: nat,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_908_redp__redsp_OFAccThrow,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,F: list_char,D: list_char,S: produc2090907612on_val] : ( redp @ P @ ( fAcc_list_char @ ( throw_list_char @ E_1 ) @ F @ D ) @ S @ ( throw_list_char @ E_1 ) @ S ) ).
thf(fact_909_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_910_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_911_redp__redsp_OThrowThrow,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( throw_list_char @ ( throw_list_char @ E_1 ) ) @ S @ ( throw_list_char @ E_1 ) @ S ) ).
thf(fact_912_redp__redsp_OThrowRed,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S @ E @ S_2 )
=> ( redp @ P @ ( throw_list_char @ E_1 ) @ S @ ( throw_list_char @ E ) @ S_2 ) ) ).
thf(fact_913_fv__fvs_Osimps_I14_J,axiom,
! [E_1: exp_list_char] :
( ( fv @ ( throw_list_char @ E_1 ) )
= ( fv @ E_1 ) ) ).
thf(fact_914_redp__redsp_OFAccRed,axiom,
! [F: list_char,D: list_char,P: list_P1999446415t_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S @ E @ S_2 )
=> ( redp @ P @ ( fAcc_list_char @ E_1 @ F @ D ) @ S @ ( fAcc_list_char @ E @ F @ D ) @ S_2 ) ) ).
thf(fact_915_fv__fvs_Osimps_I7_J,axiom,
! [E_1: exp_list_char,F: list_char,D: list_char] :
( ( fv @ ( fAcc_list_char @ E_1 @ F @ D ) )
= ( fv @ E_1 ) ) ).
thf(fact_916_red__reds_OFAccThrow,axiom,
! [E_1: exp_list_char,F: list_char,D: list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ ( throw_list_char @ E_1 ) @ F @ D ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_917_FAccRedsThrow,axiom,
! [F: list_char,D: list_char,E_1: exp_list_char,S: produc2090907612on_val,A: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E_1 @ F @ D ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_918_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_919_eval__evals_OLAssThrow,axiom,
! [V_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 @ ( lAss_list_char @ V_1 @ E_1 ) @ S_0 @ ( throw_list_char @ E ) @ S_1 ) ) ).
thf(fact_920_eval__evals_OFAssThrow1,axiom,
! [F: list_char,D: list_char,E_2_1: 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_1 ) @ S_0 @ ( throw_list_char @ E ) @ S_1 ) ) ).
thf(fact_921_redp__redsp_OSeqThrow,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( seq_list_char @ ( throw_list_char @ E_1 ) @ E_2_1 ) @ S @ ( throw_list_char @ E_1 ) @ S ) ).
thf(fact_922_redp__redsp_OLAssThrow,axiom,
! [P: list_P1999446415t_char,V_1: list_char,E_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( lAss_list_char @ V_1 @ ( throw_list_char @ E_1 ) ) @ S @ ( throw_list_char @ E_1 ) @ S ) ).
thf(fact_923_redp__redsp_OFAssThrow1,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,F: list_char,D: list_char,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( fAss_list_char @ ( throw_list_char @ E_1 ) @ F @ D @ E_2_1 ) @ S @ ( throw_list_char @ E_1 ) @ S ) ).
thf(fact_924_red__reds_OThrowThrow,axiom,
! [E_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ ( throw_list_char @ E_1 ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_925_red__reds_OThrowRed,axiom,
! [E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_2 ) ) @ ( red @ P ) ) ) ).
thf(fact_926_Throw,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,A: nat,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1 @ S_0 @ ( val_list_char @ ( addr @ A ) ) @ S_1 )
=> ( eval @ P @ ( throw_list_char @ E_1 ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ S_1 ) ) ).
thf(fact_927_eval__evals_OFAssThrow2,axiom,
! [F: list_char,D: list_char,E_2_1: 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_1 @ S_1 @ ( throw_list_char @ E ) @ S_2_1 )
=> ( eval @ P @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2_1 ) @ S_0 @ ( throw_list_char @ E ) @ S_2_1 ) ) ) ).
thf(fact_928_red__reds_OFAccRed,axiom,
! [F: list_char,D: list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E_1 @ F @ D ) @ S ) @ ( produc235638504on_val @ ( fAcc_list_char @ E @ F @ D ) @ S_2 ) ) @ ( red @ P ) ) ) ).
thf(fact_929_redp__redsp_OFAssThrow2,axiom,
! [P: list_P1999446415t_char,V: val,F: list_char,D: list_char,E_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( fAss_list_char @ ( val_list_char @ V ) @ F @ D @ ( throw_list_char @ E_1 ) ) @ S @ ( throw_list_char @ E_1 ) @ S ) ).
thf(fact_930_ThrowReds,axiom,
! [E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_931_ThrowRedsThrow,axiom,
! [E_1: exp_list_char,S: produc2090907612on_val,A: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_932_red__reds_OLAssThrow,axiom,
! [V_1: list_char,E_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V_1 @ ( throw_list_char @ E_1 ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_933_red__reds_OSeqThrow,axiom,
! [E_1: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ ( throw_list_char @ E_1 ) @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_934_red__reds_OFAssThrow1,axiom,
! [E_1: exp_list_char,F: list_char,D: list_char,E_2_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ ( throw_list_char @ E_1 ) @ F @ D @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_935_redp__redsp_OBlockThrow,axiom,
! [P: list_P1999446415t_char,V_1: list_char,T: ty,A: nat,S: produc2090907612on_val] : ( redp @ P @ ( block_list_char @ V_1 @ T @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) ) @ S @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ S ) ).
thf(fact_936_FAccReds,axiom,
! [F: list_char,D: list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E_1 @ F @ D ) @ S ) @ ( produc235638504on_val @ ( fAcc_list_char @ E @ F @ D ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_937_red__reds_OFAssThrow2,axiom,
! [V: val,F: list_char,D: list_char,E_1: exp_list_char,S: 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 ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_938_LAssRedsThrow,axiom,
! [V_1: list_char,E_1: exp_list_char,S: produc2090907612on_val,A: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V_1 @ E_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_939_SeqRedsThrow,axiom,
! [E_2_1: exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ E_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_940_FAssRedsThrow1,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ E_1 @ F @ D @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_941_FAssRedsThrow2,axiom,
! [F: list_char,D: list_char,E_2_1: 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_1 @ 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_1 ) @ S_0 ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_942_red__reds_OBlockThrow,axiom,
! [V_1: list_char,T: ty,A: nat,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( block_list_char @ V_1 @ T @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_943_redp__redsp_OInitBlockThrow,axiom,
! [P: list_P1999446415t_char,V_1: list_char,T: ty,V: val,A: nat,S: produc2090907612on_val] : ( redp @ P @ ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) ) ) @ S @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ S ) ).
thf(fact_944_eval__cases_I4_J,axiom,
! [P: list_P1999446415t_char,V_1: list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( eval @ P @ ( lAss_list_char @ V_1 @ E_1 ) @ S @ E @ S_2 )
=> ( ( ( E
= ( val_list_char @ unit ) )
=> ! [V_2: val,H_4: nat > option1728594148on_val,L_4: list_char > option_val] :
( ( S_2
= ( produc755559506on_val @ H_4 @ ( fun_up1149430426on_val @ L_4 @ V_1 @ ( some_val @ V_2 ) ) ) )
=> ~ ( eval @ P @ E_1 @ S @ ( val_list_char @ V_2 ) @ ( produc755559506on_val @ H_4 @ L_4 ) ) ) )
=> ~ ! [E_3: exp_list_char] :
( ( E
= ( throw_list_char @ E_3 ) )
=> ~ ( eval @ P @ E_1 @ S @ ( throw_list_char @ E_3 ) @ S_2 ) ) ) ) ).
thf(fact_945_eval__cases_I9_J,axiom,
! [P: list_P1999446415t_char,E_1_1: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( eval @ P @ ( seq_list_char @ E_1_1 @ E_2_1 ) @ S @ E @ S_2 )
=> ( ! [V_2: val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S @ ( val_list_char @ V_2 ) @ S_1_1 )
=> ~ ( eval @ P @ E_2_1 @ S_1_1 @ E @ S_2 ) )
=> ~ ! [E_4: exp_list_char] :
( ( E
= ( throw_list_char @ E_4 ) )
=> ~ ( eval @ P @ E_1_1 @ S @ ( throw_list_char @ E_4 ) @ S_2 ) ) ) ) ).
thf(fact_946_val_Osimps_I10_J,axiom,
! [Nat: nat] :
( unit
!= ( addr @ Nat ) ) ).
thf(fact_947_val_Osimps_I11_J,axiom,
! [Nat: nat] :
( ( addr @ Nat )
!= unit ) ).
thf(fact_948_val_Osimps_I3_J,axiom,
! [Nat_1: nat,Nat: nat] :
( ( ( addr @ Nat_1 )
= ( addr @ Nat ) )
<=> ( Nat_1 = Nat ) ) ).
thf(fact_949_TryCatchRedsFinal,axiom,
! [E_2_1: exp_list_char,V_1: list_char,E_2_2: exp_list_char,H_2: nat > option1728594148on_val,L_2_1: list_char > option_val,C: list_char,D: list_char,Fs: produc1278157519t_char > option_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,A: nat,H_1_1: nat > option1728594148on_val,L_1_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 ) ) ) @ ( produc755559506on_val @ H_1_1 @ L_1_1 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( H_1_1 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ D @ C ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2_1 @ ( produc755559506on_val @ H_1_1 @ ( fun_up1149430426on_val @ L_1_1 @ V_1 @ ( some_val @ ( addr @ A ) ) ) ) ) @ ( produc235638504on_val @ E_2_2 @ ( produc755559506on_val @ H_2 @ L_2_1 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( final_list_char @ E_2_2 )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ E_1_1 @ C @ V_1 @ E_2_1 ) @ S_0 ) @ ( produc235638504on_val @ E_2_2 @ ( produc755559506on_val @ H_2 @ ( fun_up1149430426on_val @ L_2_1 @ V_1 @ ( L_1_1 @ V_1 ) ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ) ) ).
thf(fact_950_WTrtThrow,axiom,
! [T: ty,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,T_r: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ T_r )
=> ( ( is_refT @ T_r )
=> ( wTrt_1 @ P @ H_1 @ E_2 @ ( throw_list_char @ E_1 ) @ T ) ) ) ).
thf(fact_951_BinOpRedsThrow2,axiom,
! [Bop: bop,E_2_1: 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_2: 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_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2_1 @ 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_1 ) @ S_0 ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_952_TryRedsFail,axiom,
! [V_1: list_char,E_2_1: exp_list_char,C: list_char,D: list_char,Fs: produc1278157519t_char > option_val,E_1_1: exp_list_char,S: produc2090907612on_val,A: 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 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( H_1 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ~ ( member1251428284t_char @ ( produc5062597t_char @ D @ C ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ E_1_1 @ C @ V_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_953_redp__redsp_OBinOpRed1,axiom,
! [Bop: bop,E_2_1: exp_list_char,P: list_P1999446415t_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S @ E @ S_2 )
=> ( redp @ P @ ( binOp_list_char @ E_1 @ Bop @ E_2_1 ) @ S @ ( binOp_list_char @ E @ Bop @ E_2_1 ) @ S_2 ) ) ).
thf(fact_954_redp__redsp_OTryRed,axiom,
! [C: list_char,V_1: list_char,E_2_1: exp_list_char,P: list_P1999446415t_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S @ E @ S_2 )
=> ( redp @ P @ ( tryCatch_list_char @ E_1 @ C @ V_1 @ E_2_1 ) @ S @ ( tryCatch_list_char @ E @ C @ V_1 @ E_2_1 ) @ S_2 ) ) ).
thf(fact_955_eval__evals_OBinOpThrow1,axiom,
! [Bop: bop,E_2_1: 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_1 ) @ S_0 @ ( throw_list_char @ E_1 ) @ S_1 ) ) ).
thf(fact_956_redp__redsp_OBinOpRed2,axiom,
! [V_1_2: val,Bop: bop,P: list_P1999446415t_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S @ E @ S_2 )
=> ( redp @ P @ ( binOp_list_char @ ( val_list_char @ V_1_2 ) @ Bop @ E_1 ) @ S @ ( binOp_list_char @ ( val_list_char @ V_1_2 ) @ Bop @ E ) @ S_2 ) ) ).
thf(fact_957_redp__redsp_OBinOpThrow1,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,Bop: bop,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( binOp_list_char @ ( throw_list_char @ E_1 ) @ Bop @ E_2_1 ) @ S @ ( throw_list_char @ E_1 ) @ S ) ).
thf(fact_958_Try,axiom,
! [C: list_char,V_1: list_char,E_2_1: exp_list_char,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1_2: val,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ V_1_2 ) @ S_1 )
=> ( eval @ P @ ( tryCatch_list_char @ E_1_1 @ C @ V_1 @ E_2_1 ) @ S_0 @ ( val_list_char @ V_1_2 ) @ S_1 ) ) ).
thf(fact_959_redp__redsp_ORedTry,axiom,
! [P: list_P1999446415t_char,V: val,C: list_char,V_1: list_char,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( tryCatch_list_char @ ( val_list_char @ V ) @ C @ V_1 @ E_2_1 ) @ S @ ( val_list_char @ V ) @ S ) ).
thf(fact_960_fv__fvs_Osimps_I4_J,axiom,
! [E_1_1: exp_list_char,Bop: bop,E_2_1: exp_list_char] :
( ( fv @ ( binOp_list_char @ E_1_1 @ Bop @ E_2_1 ) )
= ( semila2134664963char_o @ ( fv @ E_1_1 ) @ ( fv @ E_2_1 ) ) ) ).
thf(fact_961_red__reds_OBinOpRed1,axiom,
! [Bop: bop,E_2_1: exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ E_1 @ Bop @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( binOp_list_char @ E @ Bop @ E_2_1 ) @ S_2 ) ) @ ( red @ P ) ) ) ).
thf(fact_962_eval__evals_OBinOpThrow2,axiom,
! [Bop: bop,E_2_1: 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_2: val,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ V_1_2 ) @ S_1 )
=> ( ( eval @ P @ E_2_1 @ S_1 @ ( throw_list_char @ E_1 ) @ S_2_1 )
=> ( eval @ P @ ( binOp_list_char @ E_1_1 @ Bop @ E_2_1 ) @ S_0 @ ( throw_list_char @ E_1 ) @ S_2_1 ) ) ) ).
thf(fact_963_redp__redsp_OBinOpThrow2,axiom,
! [P: list_P1999446415t_char,V_1_2: val,Bop: bop,E_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( binOp_list_char @ ( val_list_char @ V_1_2 ) @ Bop @ ( throw_list_char @ E_1 ) ) @ S @ ( throw_list_char @ E_1 ) @ S ) ).
thf(fact_964_red__reds_OTryRed,axiom,
! [C: list_char,V_1: list_char,E_2_1: exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ E_1 @ C @ V_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( tryCatch_list_char @ E @ C @ V_1 @ E_2_1 ) @ S_2 ) ) @ ( red @ P ) ) ) ).
thf(fact_965_red__reds_OBinOpRed2,axiom,
! [V_1_2: val,Bop: bop,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V_1_2 ) @ Bop @ E_1 ) @ S ) @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V_1_2 ) @ Bop @ E ) @ S_2 ) ) @ ( red @ P ) ) ) ).
thf(fact_966_red__reds_OBinOpThrow1,axiom,
! [E_1: exp_list_char,Bop: bop,E_2_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ ( throw_list_char @ E_1 ) @ Bop @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_967_BinOp1Reds,axiom,
! [Bop: bop,E_2_1: exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ E_1 @ Bop @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( binOp_list_char @ E @ Bop @ E_2_1 ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_968_red__reds_ORedTry,axiom,
! [V: val,C: list_char,V_1: list_char,E_2_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ ( val_list_char @ V ) @ C @ V_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_969_TryReds,axiom,
! [C: list_char,V_1: list_char,E_2_1: exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ E_1 @ C @ V_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( tryCatch_list_char @ E @ C @ V_1 @ E_2_1 ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_970_TryThrow,axiom,
! [V_1: list_char,E_2_1: exp_list_char,C: 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: nat,H_1_1: nat > option1728594148on_val,L_1_1: list_char > option_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ ( produc755559506on_val @ H_1_1 @ L_1_1 ) )
=> ( ( ( H_1_1 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ~ ( member1251428284t_char @ ( produc5062597t_char @ D @ C ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( eval @ P @ ( tryCatch_list_char @ E_1_1 @ C @ V_1 @ E_2_1 ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ ( produc755559506on_val @ H_1_1 @ L_1_1 ) ) ) ) ) ).
thf(fact_971_red__reds_OBinOpThrow2,axiom,
! [V_1_2: val,Bop: bop,E_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V_1_2 ) @ Bop @ ( throw_list_char @ E_1 ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_972_BinOp2Reds,axiom,
! [V: val,Bop: bop,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V ) @ Bop @ E_1 ) @ S ) @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V ) @ Bop @ E ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_973_BinOpRedsThrow1,axiom,
! [Bop: bop,E_2_1: exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ E_1 @ Bop @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_974_TryRedsVal,axiom,
! [C: list_char,V_1: list_char,E_2_1: exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,V: val,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ E_1 @ C @ V_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_975_red__reds_ORedTryFail,axiom,
! [V_1: list_char,E_2_1: exp_list_char,C: list_char,P: list_P1999446415t_char,S: produc2090907612on_val,A: nat,D: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ~ ( member1251428284t_char @ ( produc5062597t_char @ D @ C ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ C @ V_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ S ) ) @ ( red @ P ) ) ) ) ).
thf(fact_976_TryCatch,axiom,
! [E_2_1: exp_list_char,V_1: list_char,E_2_2: exp_list_char,H_2: nat > option1728594148on_val,L_2_1: list_char > option_val,C: 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: nat,H_1_1: nat > option1728594148on_val,L_1_1: list_char > option_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ ( produc755559506on_val @ H_1_1 @ L_1_1 ) )
=> ( ( ( H_1_1 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ D @ C ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( ( eval @ P @ E_2_1 @ ( produc755559506on_val @ H_1_1 @ ( fun_up1149430426on_val @ L_1_1 @ V_1 @ ( some_val @ ( addr @ A ) ) ) ) @ E_2_2 @ ( produc755559506on_val @ H_2 @ L_2_1 ) )
=> ( eval @ P @ ( tryCatch_list_char @ E_1_1 @ C @ V_1 @ E_2_1 ) @ S_0 @ E_2_2 @ ( produc755559506on_val @ H_2 @ ( fun_up1149430426on_val @ L_2_1 @ V_1 @ ( L_1_1 @ V_1 ) ) ) ) ) ) ) ) ).
thf(fact_977_WTrt__elim__cases_I4_J,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,T: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ ( throw_list_char @ E_1 ) @ T )
=> ~ ! [T_r_1: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ T_r_1 )
=> ~ ( is_refT @ T_r_1 ) ) ) ).
thf(fact_978_preallocated__new,axiom,
! [X_2: produc2088785539on_val,A_2: nat,H_1: nat > option1728594148on_val] :
( ( preallocated @ H_1 )
=> ( ( ( H_1 @ A_2 )
= none_P1260844216on_val )
=> ( preallocated @ ( fun_up1472480727on_val @ H_1 @ A_2 @ ( some_P451527732on_val @ X_2 ) ) ) ) ) ).
thf(fact_979_red__reds_ORedTryCatch,axiom,
! [V_1: list_char,E_2_1: exp_list_char,C: list_char,P: list_P1999446415t_char,S: produc2090907612on_val,A: nat,D: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ D @ C ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ C @ V_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( block_list_char @ V_1 @ ( class @ C ) @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ ( addr @ A ) ) ) @ E_2_1 ) ) @ S ) ) @ ( red @ P ) ) ) ) ).
thf(fact_980_preallocated__upd__obj,axiom,
! [Fs_3: produc1278157519t_char > option_val,A_2: nat,C_3: list_char,Fs_2: produc1278157519t_char > option_val,H_1: nat > option1728594148on_val] :
( ( preallocated @ H_1 )
=> ( ( ( H_1 @ A_2 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_3 @ Fs_2 ) ) )
=> ( preallocated @ ( fun_up1472480727on_val @ H_1 @ A_2 @ ( some_P451527732on_val @ ( produc926070009on_val @ C_3 @ Fs_3 ) ) ) ) ) ) ).
thf(fact_981_CastRedsAddr,axiom,
! [C: list_char,D: list_char,Fs: produc1278157519t_char > option_val,E_1: exp_list_char,S: produc2090907612on_val,A: nat,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ ( val_list_char @ ( addr @ A ) ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( hp @ S_2 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ D @ C ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ E_1 ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ ( addr @ A ) ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_982_WTrtTry,axiom,
! [V_1: list_char,C: list_char,E_2_1: exp_list_char,T_2_2: ty,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1_1: exp_list_char,T_1_1: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1_1 @ T_1_1 )
=> ( ( wTrt_1 @ P @ H_1 @ ( fun_up424764369ion_ty @ E_2 @ V_1 @ ( some_ty @ ( class @ C ) ) ) @ E_2_1 @ T_2_2 )
=> ( ( widen_2090681816t_char @ P @ T_1_1 @ T_2_2 )
=> ( wTrt_1 @ P @ H_1 @ E_2 @ ( tryCatch_list_char @ E_1_1 @ C @ V_1 @ E_2_1 ) @ T_2_2 ) ) ) ) ).
thf(fact_983_redp__redsp_OCastRed,axiom,
! [C: list_char,P: list_P1999446415t_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S @ E @ S_2 )
=> ( redp @ P @ ( cast_list_char @ C @ E_1 ) @ S @ ( cast_list_char @ C @ E ) @ S_2 ) ) ).
thf(fact_984_fv__fvs_Osimps_I2_J,axiom,
! [C: list_char,E_1: exp_list_char] :
( ( fv @ ( cast_list_char @ C @ E_1 ) )
= ( fv @ E_1 ) ) ).
thf(fact_985_eval__evals_OCastThrow,axiom,
! [C: 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 @ E_1 ) @ S_0 @ ( throw_list_char @ E ) @ S_1 ) ) ).
thf(fact_986_redp__redsp_OCastThrow,axiom,
! [P: list_P1999446415t_char,C: list_char,E_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( cast_list_char @ C @ ( throw_list_char @ E_1 ) ) @ S @ ( throw_list_char @ E_1 ) @ S ) ).
thf(fact_987_WTrtFAcc,axiom,
! [F: list_char,T: ty,D: list_char,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,C: list_char] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ ( class @ C ) )
=> ( ( has_fi1183600461t_char @ P @ C @ F @ T @ D )
=> ( wTrt_1 @ P @ H_1 @ E_2 @ ( fAcc_list_char @ E_1 @ F @ D ) @ T ) ) ) ).
thf(fact_988_red__reds_OCastRed,axiom,
! [C: list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ E_1 ) @ S ) @ ( produc235638504on_val @ ( cast_list_char @ C @ E ) @ S_2 ) ) @ ( red @ P ) ) ) ).
thf(fact_989_red__reds_OCastThrow,axiom,
! [C: list_char,E_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ ( throw_list_char @ E_1 ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_990_CastReds,axiom,
! [C: list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ E_1 ) @ S ) @ ( produc235638504on_val @ ( cast_list_char @ C @ E ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_991_WTrtFAss,axiom,
! [E_2_1: exp_list_char,T_2_2: ty,F: list_char,T: ty,D: list_char,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1_1: exp_list_char,C: list_char] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1_1 @ ( class @ C ) )
=> ( ( has_fi1183600461t_char @ P @ C @ F @ T @ D )
=> ( ( wTrt_1 @ P @ H_1 @ E_2 @ E_2_1 @ T_2_2 )
=> ( ( widen_2090681816t_char @ P @ T_2_2 @ T )
=> ( wTrt_1 @ P @ H_1 @ E_2 @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2_1 ) @ void ) ) ) ) ) ).
thf(fact_992_CastRedsThrow,axiom,
! [C: list_char,E_1: exp_list_char,S: produc2090907612on_val,A: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ E_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_993_preallocated__hext,axiom,
! [H: nat > option1728594148on_val,H_1: nat > option1728594148on_val] :
( ( preallocated @ H_1 )
=> ( ( hext @ H_1 @ H )
=> ( preallocated @ H ) ) ) ).
thf(fact_994_Cast,axiom,
! [C: list_char,D: list_char,Fs: produc1278157519t_char > option_val,P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,A: nat,H_1: nat > option1728594148on_val,L_1: list_char > option_val] :
( ( eval @ P @ E_1 @ S_0 @ ( val_list_char @ ( addr @ A ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) )
=> ( ( ( H_1 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ D @ C ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( eval @ P @ ( cast_list_char @ C @ E_1 ) @ S_0 @ ( val_list_char @ ( addr @ A ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) ) ) ) ).
thf(fact_995_red__reds_ORedCast,axiom,
! [C: list_char,P: list_P1999446415t_char,S: produc2090907612on_val,A: nat,D: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ D @ C ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ ( val_list_char @ ( addr @ A ) ) ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ ( addr @ A ) ) @ S ) ) @ ( red @ P ) ) ) ) ).
thf(fact_996_WTrt__elim__cases_I5_J,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1_1: exp_list_char,C: list_char,V_1: list_char,E_2_1: exp_list_char,T: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ ( tryCatch_list_char @ E_1_1 @ C @ V_1 @ E_2_1 ) @ T )
=> ~ ! [T_1_2: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1_1 @ T_1_2 )
=> ( ( wTrt_1 @ P @ H_1 @ ( fun_up424764369ion_ty @ E_2 @ V_1 @ ( some_ty @ ( class @ C ) ) ) @ E_2_1 @ T )
=> ~ ( widen_2090681816t_char @ P @ T_1_2 @ T ) ) ) ) ).
thf(fact_997_final__addrE,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,C: list_char] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ ( class @ C ) )
=> ( ( final_list_char @ E_1 )
=> ( ! [A_1: nat] :
( E_1
!= ( val_list_char @ ( addr @ A_1 ) ) )
=> ~ ! [A_1: nat] :
( E_1
!= ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) ) ) ) ) ).
thf(fact_998_BinOpRedsVal,axiom,
! [Bop: bop,V: val,E_2_1: exp_list_char,V_2_1: val,S_2_1: produc2090907612on_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1_2: 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_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2_1 @ S_1 ) @ ( produc235638504on_val @ ( val_list_char @ V_2_1 ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( binop @ ( produc621191550al_val @ Bop @ ( product_Pair_val_val @ V_1_2 @ V_2_1 ) ) )
= ( some_val @ V ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ E_1_1 @ Bop @ E_2_1 ) @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_999_CastRedsFail,axiom,
! [C: list_char,D: list_char,Fs: produc1278157519t_char > option_val,E_1: exp_list_char,S: produc2090907612on_val,A: nat,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ ( val_list_char @ ( addr @ A ) ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( hp @ S_2 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ~ ( member1251428284t_char @ ( produc5062597t_char @ D @ C ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ E_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_1000_BinOp,axiom,
! [Bop: bop,V: val,E_2_1: exp_list_char,V_2_1: val,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1_2: val,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ V_1_2 ) @ S_1 )
=> ( ( eval @ P @ E_2_1 @ S_1 @ ( val_list_char @ V_2_1 ) @ S_2_1 )
=> ( ( ( binop @ ( produc621191550al_val @ Bop @ ( product_Pair_val_val @ V_1_2 @ V_2_1 ) ) )
= ( some_val @ V ) )
=> ( eval @ P @ ( binOp_list_char @ E_1_1 @ Bop @ E_2_1 ) @ S_0 @ ( val_list_char @ V ) @ S_2_1 ) ) ) ) ).
thf(fact_1001_redp__redsp_ORedBinOp,axiom,
! [P: list_P1999446415t_char,S: produc2090907612on_val,Bop: bop,V_1_2: val,V_2_1: val,V: val] :
( ( ( binop @ ( produc621191550al_val @ Bop @ ( product_Pair_val_val @ V_1_2 @ V_2_1 ) ) )
= ( some_val @ V ) )
=> ( redp @ P @ ( binOp_list_char @ ( val_list_char @ V_1_2 ) @ Bop @ ( val_list_char @ V_2_1 ) ) @ S @ ( val_list_char @ V ) @ S ) ) ).
thf(fact_1002_CastFail,axiom,
! [C: list_char,D: list_char,Fs: produc1278157519t_char > option_val,P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,A: nat,H_1: nat > option1728594148on_val,L_1: list_char > option_val] :
( ( eval @ P @ E_1 @ S_0 @ ( val_list_char @ ( addr @ A ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) )
=> ( ( ( H_1 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ~ ( member1251428284t_char @ ( produc5062597t_char @ D @ C ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( eval @ P @ ( cast_list_char @ C @ E_1 ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) ) ) ) ).
thf(fact_1003_red__reds_ORedCastFail,axiom,
! [C: list_char,P: list_P1999446415t_char,S: produc2090907612on_val,A: nat,D: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ~ ( member1251428284t_char @ ( produc5062597t_char @ D @ C ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ ( val_list_char @ ( addr @ A ) ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) @ S ) ) @ ( red @ P ) ) ) ) ).
thf(fact_1004_red__reds_ORedBinOp,axiom,
! [S: produc2090907612on_val,P: list_P1999446415t_char,Bop: bop,V_1_2: val,V_2_1: val,V: val] :
( ( ( binop @ ( produc621191550al_val @ Bop @ ( product_Pair_val_val @ V_1_2 @ V_2_1 ) ) )
= ( some_val @ V ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V_1_2 ) @ Bop @ ( val_list_char @ V_2_1 ) ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S ) ) @ ( red @ P ) ) ) ).
thf(fact_1005_eval__cases_I3_J,axiom,
! [P: list_P1999446415t_char,E_1_1: exp_list_char,Bop: bop,E_2_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( eval @ P @ ( binOp_list_char @ E_1_1 @ Bop @ E_2_1 ) @ S @ E @ S_2 )
=> ( ! [V_1_1: val,S_1_1: produc2090907612on_val,V_2_2: val,V_2: val] :
( ( E
= ( val_list_char @ V_2 ) )
=> ( ( eval @ P @ E_1_1 @ S @ ( val_list_char @ V_1_1 ) @ S_1_1 )
=> ( ( eval @ P @ E_2_1 @ S_1_1 @ ( val_list_char @ V_2_2 ) @ S_2 )
=> ( ( binop @ ( produc621191550al_val @ Bop @ ( product_Pair_val_val @ V_1_1 @ V_2_2 ) ) )
!= ( some_val @ V_2 ) ) ) ) )
=> ( ! [E_4: exp_list_char] :
( ( E
= ( throw_list_char @ E_4 ) )
=> ~ ( eval @ P @ E_1_1 @ S @ ( throw_list_char @ E_4 ) @ S_2 ) )
=> ~ ! [V_1_1: val,S_1_1: produc2090907612on_val,E_4: exp_list_char] :
( ( E
= ( throw_list_char @ E_4 ) )
=> ( ( eval @ P @ E_1_1 @ S @ ( val_list_char @ V_1_1 ) @ S_1_1 )
=> ~ ( eval @ P @ E_2_1 @ S_1_1 @ ( throw_list_char @ E_4 ) @ S_2 ) ) ) ) ) ) ).
thf(fact_1006_binop_Osimps_I7_J,axiom,
! [V_1_2: val] :
( ( binop @ ( produc621191550al_val @ add @ ( product_Pair_val_val @ V_1_2 @ unit ) ) )
= none_val ) ).
thf(fact_1007_binop_Osimps_I3_J,axiom,
! [V_2_1: val] :
( ( binop @ ( produc621191550al_val @ add @ ( product_Pair_val_val @ unit @ V_2_1 ) ) )
= none_val ) ).
thf(fact_1008_typeof__ClassCast,axiom,
! [H_1: nat > option1728594148on_val] :
( ( preallocated @ H_1 )
=> ( ( typeof_h @ H_1 @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) )
= ( some_ty @ ( class @ classCast ) ) ) ) ).
thf(fact_1009_WTrtVal,axiom,
! [P: list_P1999446415t_char,E_2: list_char > option_ty,H_1: nat > option1728594148on_val,V: val,T: ty] :
( ( ( typeof_h @ H_1 @ V )
= ( some_ty @ T ) )
=> ( wTrt_1 @ P @ H_1 @ E_2 @ ( val_list_char @ V ) @ T ) ) ).
thf(fact_1010_hext__typeof__mono,axiom,
! [V: val,T: ty,H_1: nat > option1728594148on_val,H: nat > option1728594148on_val] :
( ( hext @ H_1 @ H )
=> ( ( ( typeof_h @ H_1 @ V )
= ( some_ty @ T ) )
=> ( ( typeof_h @ H @ V )
= ( some_ty @ T ) ) ) ) ).
thf(fact_1011_typeof__lit__typeof,axiom,
! [H_1: nat > option1728594148on_val,V: val,T: ty] :
( ( ( typeof_h
@ ^ [X: nat] : none_P1260844216on_val
@ V )
= ( some_ty @ T ) )
=> ( ( typeof_h @ H_1 @ V )
= ( some_ty @ T ) ) ) ).
thf(fact_1012_typeof__h_Osimps_I1_J,axiom,
! [H_1: nat > option1728594148on_val] :
( ( typeof_h @ H_1 @ unit )
= ( some_ty @ void ) ) ).
thf(fact_1013_binop_Osimps_I6_J,axiom,
! [V: nat,V_2_1: val] :
( ( binop @ ( produc621191550al_val @ add @ ( product_Pair_val_val @ ( addr @ V ) @ V_2_1 ) ) )
= none_val ) ).
thf(fact_1014_binop_Osimps_I10_J,axiom,
! [V_1_2: val,V: nat] :
( ( binop @ ( produc621191550al_val @ add @ ( product_Pair_val_val @ V_1_2 @ ( addr @ V ) ) ) )
= none_val ) ).
thf(fact_1015_typeof__OutOfMemory,axiom,
! [H_1: nat > option1728594148on_val] :
( ( preallocated @ H_1 )
=> ( ( typeof_h @ H_1 @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) )
= ( some_ty @ ( class @ outOfMemory ) ) ) ) ).
thf(fact_1016_typeof__NullPointer,axiom,
! [H_1: nat > option1728594148on_val] :
( ( preallocated @ H_1 )
=> ( ( typeof_h @ H_1 @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) )
= ( some_ty @ ( class @ nullPointer ) ) ) ) ).
thf(fact_1017_typeof__h_Osimps_I5_J,axiom,
! [H_1: nat > option1728594148on_val,A: nat] :
( ( typeof_h @ H_1 @ ( addr @ A ) )
= ( option857204770on_val @ none_ty
@ ( produc863160906ion_ty
@ ^ [C_1: list_char,Fs_1: produc1278157519t_char > option_val] : ( some_ty @ ( class @ C_1 ) ) )
@ ( H_1 @ A ) ) ) ).
thf(fact_1018_WTrt_H__WTrts_H_Ointros_I16_J,axiom,
! [E_2: list_char > option_ty,V_1: list_char,E_2_1: exp_list_char,T_2_2: ty,P: list_P1999446415t_char,T: ty,H_1: nat > option1728594148on_val,V: val,T_1_1: ty] :
( ( ( typeof_h @ H_1 @ V )
= ( some_ty @ T_1_1 ) )
=> ( ( widen_2090681816t_char @ P @ T_1_1 @ T )
=> ( ( wTrt @ P @ H_1 @ ( fun_up424764369ion_ty @ E_2 @ V_1 @ ( some_ty @ T ) ) @ E_2_1 @ T_2_2 )
=> ( wTrt @ P @ H_1 @ E_2 @ ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ E_2_1 ) ) @ T_2_2 ) ) ) ) ).
thf(fact_1019_WTrt_H__WTrts_H_Ointros_I3_J,axiom,
! [P: list_P1999446415t_char,E_2: list_char > option_ty,H_1: nat > option1728594148on_val,V: val,T: ty] :
( ( ( typeof_h @ H_1 @ V )
= ( some_ty @ T ) )
=> ( wTrt @ P @ H_1 @ E_2 @ ( val_list_char @ V ) @ T ) ) ).
thf(fact_1020_WTrt_H__WTrts_H_Ointros_I18_J,axiom,
! [E_2_1: exp_list_char,T_2_2: ty,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1_1: exp_list_char,T_1_1: ty] :
( ( wTrt @ P @ H_1 @ E_2 @ E_1_1 @ T_1_1 )
=> ( ( wTrt @ P @ H_1 @ E_2 @ E_2_1 @ T_2_2 )
=> ( wTrt @ P @ H_1 @ E_2 @ ( seq_list_char @ E_1_1 @ E_2_1 ) @ T_2_2 ) ) ) ).
thf(fact_1021_wt__wt_H,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,T: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ T )
=> ( wTrt @ P @ H_1 @ E_2 @ E_1 @ T ) ) ).
thf(fact_1022_wt_H__wt,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,T: ty] :
( ( wTrt @ P @ H_1 @ E_2 @ E_1 @ T )
=> ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ T ) ) ).
thf(fact_1023_wt_H__iff__wt,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,T: ty] :
( ( wTrt @ P @ H_1 @ E_2 @ E_1 @ T )
<=> ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ T ) ) ).
thf(fact_1024_WTrt_H__WTrts_H_Ointros_I21_J,axiom,
! [T: ty,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,T_r: ty] :
( ( wTrt @ P @ H_1 @ E_2 @ E_1 @ T_r )
=> ( ( is_refT @ T_r )
=> ( wTrt @ P @ H_1 @ E_2 @ ( throw_list_char @ E_1 ) @ T ) ) ) ).
thf(fact_1025_WTrt_H__WTrts_H_Ointros_I8_J,axiom,
! [F: list_char,T: ty,D: list_char,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,C: list_char] :
( ( wTrt @ P @ H_1 @ E_2 @ E_1 @ ( class @ C ) )
=> ( ( has_fi1183600461t_char @ P @ C @ F @ T @ D )
=> ( wTrt @ P @ H_1 @ E_2 @ ( fAcc_list_char @ E_1 @ F @ D ) @ T ) ) ) ).
thf(fact_1026_WTrt_H__WTrts_H_Ointros_I17_J,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,V_1: list_char,T: ty,E_1: exp_list_char,T_5: ty] :
( ( wTrt @ P @ H_1 @ ( fun_up424764369ion_ty @ E_2 @ V_1 @ ( some_ty @ T ) ) @ E_1 @ T_5 )
=> ( ~ ( assigned @ V_1 @ E_1 )
=> ( wTrt @ P @ H_1 @ E_2 @ ( block_list_char @ V_1 @ T @ E_1 ) @ T_5 ) ) ) ).
thf(fact_1027_WTrt_H__WTrts_H_Ointros_I22_J,axiom,
! [V_1: list_char,C: list_char,E_2_1: exp_list_char,T_2_2: ty,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1_1: exp_list_char,T_1_1: ty] :
( ( wTrt @ P @ H_1 @ E_2 @ E_1_1 @ T_1_1 )
=> ( ( wTrt @ P @ H_1 @ ( fun_up424764369ion_ty @ E_2 @ V_1 @ ( some_ty @ ( class @ C ) ) ) @ E_2_1 @ T_2_2 )
=> ( ( widen_2090681816t_char @ P @ T_1_1 @ T_2_2 )
=> ( wTrt @ P @ H_1 @ E_2 @ ( tryCatch_list_char @ E_1_1 @ C @ V_1 @ E_2_1 ) @ T_2_2 ) ) ) ) ).
thf(fact_1028_WTrt_H__WTrts_H_Ointros_I10_J,axiom,
! [E_2_1: exp_list_char,T_2_2: ty,F: list_char,T: ty,D: list_char,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1_1: exp_list_char,C: list_char] :
( ( wTrt @ P @ H_1 @ E_2 @ E_1_1 @ ( class @ C ) )
=> ( ( has_fi1183600461t_char @ P @ C @ F @ T @ D )
=> ( ( wTrt @ P @ H_1 @ E_2 @ E_2_1 @ T_2_2 )
=> ( ( widen_2090681816t_char @ P @ T_2_2 @ T )
=> ( wTrt @ P @ H_1 @ E_2 @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2_1 ) @ void ) ) ) ) ) ).
thf(fact_1029_FAccRedsNull,axiom,
! [F: list_char,D: list_char,E_1: exp_list_char,S: produc2090907612on_val,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E_1 @ F @ D ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_1030_FAssRedsNull,axiom,
! [F: list_char,D: list_char,E_2_1: 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_1 @ 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_1 ) @ 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_1031_red__reds_ORedFAccNull,axiom,
! [F: list_char,D: list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ ( val_list_char @ null ) @ F @ D ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_1032_val_Osimps_I5_J,axiom,
null != unit ).
thf(fact_1033_val_Osimps_I4_J,axiom,
unit != null ).
thf(fact_1034_val_Osimps_I16_J,axiom,
! [Nat: nat] :
( null
!= ( addr @ Nat ) ) ).
thf(fact_1035_val_Osimps_I17_J,axiom,
! [Nat: nat] :
( ( addr @ Nat )
!= null ) ).
thf(fact_1036_CastNull,axiom,
! [C: 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 @ E_1 ) @ S_0 @ ( val_list_char @ null ) @ S_1 ) ) ).
thf(fact_1037_redp__redsp_ORedCastNull,axiom,
! [P: list_P1999446415t_char,C: list_char,S: produc2090907612on_val] : ( redp @ P @ ( cast_list_char @ C @ ( val_list_char @ null ) ) @ S @ ( val_list_char @ null ) @ S ) ).
thf(fact_1038_red__reds_ORedCastNull,axiom,
! [C: list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ ( val_list_char @ null ) ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_1039_CastRedsNull,axiom,
! [C: list_char,E_1: exp_list_char,S: produc2090907612on_val,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ E_1 ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_1040_binop_Osimps_I8_J,axiom,
! [V_1_2: val] :
( ( binop @ ( produc621191550al_val @ add @ ( product_Pair_val_val @ V_1_2 @ null ) ) )
= none_val ) ).
thf(fact_1041_binop_Osimps_I4_J,axiom,
! [V_2_1: val] :
( ( binop @ ( produc621191550al_val @ add @ ( product_Pair_val_val @ null @ V_2_1 ) ) )
= none_val ) ).
thf(fact_1042_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_1043_redp__redsp_ORedThrowNull,axiom,
! [P: list_P1999446415t_char,S: produc2090907612on_val] : ( redp @ P @ ( throw_list_char @ ( val_list_char @ null ) ) @ S @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ).
thf(fact_1044_FAssNull,axiom,
! [F: list_char,D: list_char,E_2_1: 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_1 @ S_1 @ ( val_list_char @ V ) @ S_2_1 )
=> ( eval @ P @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2_1 ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_2_1 ) ) ) ).
thf(fact_1045_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_1046_redp__redsp_ORedFAssNull,axiom,
! [P: list_P1999446415t_char,F: list_char,D: list_char,V: val,S: produc2090907612on_val] : ( redp @ P @ ( fAss_list_char @ ( val_list_char @ null ) @ F @ D @ ( val_list_char @ V ) ) @ S @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ).
thf(fact_1047_redp__redsp_ORedFAccNull,axiom,
! [P: list_P1999446415t_char,F: list_char,D: list_char,S: produc2090907612on_val] : ( redp @ P @ ( fAcc_list_char @ ( val_list_char @ null ) @ F @ D ) @ S @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ).
thf(fact_1048_red__reds_ORedThrowNull,axiom,
! [S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ null ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_1049_ThrowRedsNull,axiom,
! [E_1: exp_list_char,S: produc2090907612on_val,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_1050_red__reds_ORedFAssNull,axiom,
! [F: list_char,D: list_char,V: val,S: 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 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_1051_finalRefE,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,T: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ T )
=> ( ( is_refT @ T )
=> ( ( final_list_char @ E_1 )
=> ( ( E_1
!= ( val_list_char @ null ) )
=> ( ( ? [A_1: nat] :
( E_1
= ( val_list_char @ ( addr @ A_1 ) ) )
=> ! [C_1: list_char] :
( T
!= ( class @ C_1 ) ) )
=> ~ ! [A_1: nat] :
( E_1
!= ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) ) ) ) ) ) ) ).
thf(fact_1052_eval__cases_I12_J,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( eval @ P @ ( throw_list_char @ E_1 ) @ S @ E @ S_2 )
=> ( ! [A_1: nat] :
( ( E
= ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) )
=> ~ ( eval @ P @ E_1 @ S @ ( val_list_char @ ( addr @ A_1 ) ) @ S_2 ) )
=> ( ( ( E
= ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) )
=> ~ ( eval @ P @ E_1 @ S @ ( val_list_char @ null ) @ S_2 ) )
=> ~ ! [E_3: exp_list_char] :
( ( E
= ( throw_list_char @ E_3 ) )
=> ~ ( eval @ P @ E_1 @ S @ ( throw_list_char @ E_3 ) @ S_2 ) ) ) ) ) ).
thf(fact_1053_redp__redsp_ORedTryCatch,axiom,
! [V_1: list_char,E_2_1: exp_list_char,P: list_P1999446415t_char,C: list_char,S: produc2090907612on_val,A: nat,D: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ( transi1065307915t_char @ ( subcls744239332t_char @ P ) @ D @ C )
=> ( redp @ P @ ( tryCatch_list_char @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ C @ V_1 @ E_2_1 ) @ S @ ( block_list_char @ V_1 @ ( class @ C ) @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ ( addr @ A ) ) ) @ E_2_1 ) ) @ S ) ) ) ).
thf(fact_1054_redp__redsp_ORedCast,axiom,
! [P: list_P1999446415t_char,C: list_char,S: produc2090907612on_val,A: nat,D: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ( transi1065307915t_char @ ( subcls744239332t_char @ P ) @ D @ C )
=> ( redp @ P @ ( cast_list_char @ C @ ( val_list_char @ ( addr @ A ) ) ) @ S @ ( val_list_char @ ( addr @ A ) ) @ S ) ) ) ).
thf(fact_1055_redp__redsp_ORedTryFail,axiom,
! [V_1: list_char,E_2_1: exp_list_char,P: list_P1999446415t_char,C: list_char,S: produc2090907612on_val,A: nat,D: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ~ ( transi1065307915t_char @ ( subcls744239332t_char @ P ) @ D @ C )
=> ( redp @ P @ ( tryCatch_list_char @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ C @ V_1 @ E_2_1 ) @ S @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ S ) ) ) ).
thf(fact_1056_redp__redsp_ORedCastFail,axiom,
! [P: list_P1999446415t_char,C: list_char,S: produc2090907612on_val,A: nat,D: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ D @ Fs ) ) )
=> ( ~ ( transi1065307915t_char @ ( subcls744239332t_char @ P ) @ D @ C )
=> ( redp @ P @ ( cast_list_char @ C @ ( val_list_char @ ( addr @ A ) ) ) @ S @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) @ S ) ) ) ).
thf(fact_1057_WTrtCast,axiom,
! [C: list_char,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,T: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ T )
=> ( ( is_refT @ T )
=> ( ( is_cla570604648t_char @ P @ C )
=> ( wTrt_1 @ P @ H_1 @ E_2 @ ( cast_list_char @ C @ E_1 ) @ ( class @ C ) ) ) ) ) ).
thf(fact_1058_ty_Osimps_I9_J,axiom,
! [List: list_char] :
( ( class @ List )
!= void ) ).
thf(fact_1059_ty_Osimps_I8_J,axiom,
! [List: list_char] :
( void
!= ( class @ List ) ) ).
thf(fact_1060_ty_Oinject,axiom,
! [List_1: list_char,List: list_char] :
( ( ( class @ List_1 )
= ( class @ List ) )
<=> ( List_1 = List ) ) ).
thf(fact_1061_WTrt_H__WTrts_H_Ointros_I2_J,axiom,
! [C: list_char,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,T: ty] :
( ( wTrt @ P @ H_1 @ E_2 @ E_1 @ T )
=> ( ( is_refT @ T )
=> ( ( is_cla570604648t_char @ P @ C )
=> ( wTrt @ P @ H_1 @ E_2 @ ( cast_list_char @ C @ E_1 ) @ ( class @ C ) ) ) ) ) ).
thf(fact_1062_WTrt__elim__cases_I6_J,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,D: list_char,E_1: exp_list_char,T: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ ( cast_list_char @ D @ E_1 ) @ T )
=> ~ ( ( T
= ( class @ D ) )
=> ! [T_4: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ T_4 )
=> ( ( is_refT @ T_4 )
=> ~ ( is_cla570604648t_char @ P @ D ) ) ) ) ) ).
thf(fact_1063_sys__xcpts__cases,axiom,
! [P: list_char > $o,C: list_char] :
( ( member_list_char @ C @ sys_xcpts )
=> ( ( P @ nullPointer )
=> ( ( P @ outOfMemory )
=> ( ( P @ classCast )
=> ( P @ C ) ) ) ) ) ).
thf(fact_1064_binop_Osimps_I9_J,axiom,
! [V_1_2: val,V: $o] :
( ( binop @ ( produc621191550al_val @ add @ ( product_Pair_val_val @ V_1_2 @ ( bool @ V ) ) ) )
= none_val ) ).
thf(fact_1065_val_Osimps_I21_J,axiom,
! [Nat: nat,Bool_1: $o] :
( ( addr @ Nat )
!= ( bool @ Bool_1 ) ) ).
thf(fact_1066_val_Osimps_I20_J,axiom,
! [Bool_1: $o,Nat: nat] :
( ( bool @ Bool_1 )
!= ( addr @ Nat ) ) ).
thf(fact_1067_val_Osimps_I1_J,axiom,
! [Bool_1: $o,Bool: $o] :
( ( ( bool @ Bool_1 )
= ( bool @ Bool ) )
<=> ( Bool_1
<=> Bool ) ) ).
thf(fact_1068_val_Osimps_I6_J,axiom,
! [Bool: $o] :
( unit
!= ( bool @ Bool ) ) ).
thf(fact_1069_val_Osimps_I7_J,axiom,
! [Bool: $o] :
( ( bool @ Bool )
!= unit ) ).
thf(fact_1070_val_Osimps_I12_J,axiom,
! [Bool: $o] :
( null
!= ( bool @ Bool ) ) ).
thf(fact_1071_val_Osimps_I13_J,axiom,
! [Bool: $o] :
( ( bool @ Bool )
!= null ) ).
thf(fact_1072_preallocated__dom,axiom,
! [C: list_char,H_1: nat > option1728594148on_val] :
( ( preallocated @ H_1 )
=> ( ( member_list_char @ C @ sys_xcpts )
=> ( member_nat @ ( addr_of_sys_xcpt @ C ) @ ( dom_na2045926843on_val @ H_1 ) ) ) ) ).
thf(fact_1073_binop_Osimps_I5_J,axiom,
! [V: $o,V_2_1: val] :
( ( binop @ ( produc621191550al_val @ add @ ( product_Pair_val_val @ ( bool @ V ) @ V_2_1 ) ) )
= none_val ) ).
thf(fact_1074_preallocatedE,axiom,
! [P: ( nat > option1728594148on_val ) > list_char > $o,C: list_char,H_1: nat > option1728594148on_val] :
( ( preallocated @ H_1 )
=> ( ( member_list_char @ C @ sys_xcpts )
=> ( ! [Fs_1: produc1278157519t_char > option_val] :
( ( ( H_1 @ ( addr_of_sys_xcpt @ C ) )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs_1 ) ) )
=> ( P @ H_1 @ C ) )
=> ( P @ H_1 @ C ) ) ) ) ).
thf(fact_1075_preallocatedD,axiom,
! [C: list_char,H_1: nat > option1728594148on_val] :
( ( preallocated @ H_1 )
=> ( ( member_list_char @ C @ sys_xcpts )
=> ? [Fs_1: produc1278157519t_char > option_val] :
( ( H_1 @ ( addr_of_sys_xcpt @ C ) )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs_1 ) ) ) ) ) ).
thf(fact_1076_preallocated__def,axiom,
! [H_1: nat > option1728594148on_val] :
( ( preallocated @ H_1 )
<=> ! [X: list_char] :
( ( member_list_char @ X @ sys_xcpts )
=> ? [Fs_1: produc1278157519t_char > option_val] :
( ( H_1 @ ( addr_of_sys_xcpt @ X ) )
= ( some_P451527732on_val @ ( produc926070009on_val @ X @ Fs_1 ) ) ) ) ) ).
thf(fact_1077_binop_Osimps_I1_J,axiom,
! [V_1_2: val,V_2_1: val] :
( ( binop @ ( produc621191550al_val @ c_Expr_Obop_OEq @ ( product_Pair_val_val @ V_1_2 @ V_2_1 ) ) )
= ( some_val @ ( bool @ ( V_1_2 = V_2_1 ) ) ) ) ).
thf(fact_1078_WhileFReds,axiom,
! [C_2: exp_list_char,B: exp_list_char,S: produc2090907612on_val,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ B @ S ) @ ( produc235638504on_val @ ( val_list_char @ ( bool @ $false ) ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( while_list_char @ B @ C_2 ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ unit ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_1079_WhileCondThrow,axiom,
! [C_2: 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_2 ) @ S_0 @ ( throw_list_char @ E ) @ S_1 ) ) ).
thf(fact_1080_bop_Oexhaust,axiom,
! [Y: bop] :
( ( Y != c_Expr_Obop_OEq )
=> ( Y = add ) ) ).
thf(fact_1081_bop_Osimps_I2_J,axiom,
add != c_Expr_Obop_OEq ).
thf(fact_1082_bop_Osimps_I1_J,axiom,
c_Expr_Obop_OEq != add ).
thf(fact_1083_fv__fvs_Osimps_I13_J,axiom,
! [B: exp_list_char,E_1: exp_list_char] :
( ( fv @ ( while_list_char @ B @ E_1 ) )
= ( semila2134664963char_o @ ( fv @ B ) @ ( fv @ E_1 ) ) ) ).
thf(fact_1084_WhileT,axiom,
! [E_3_1: exp_list_char,S_3_1: produc2090907612on_val,C_2: exp_list_char,V_1_2: val,S_2_1: produc2090907612on_val,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 @ ( bool @ $true ) ) @ S_1 )
=> ( ( eval @ P @ C_2 @ S_1 @ ( val_list_char @ V_1_2 ) @ S_2_1 )
=> ( ( eval @ P @ ( while_list_char @ E_1 @ C_2 ) @ S_2_1 @ E_3_1 @ S_3_1 )
=> ( eval @ P @ ( while_list_char @ E_1 @ C_2 ) @ S_0 @ E_3_1 @ S_3_1 ) ) ) ) ).
thf(fact_1085_WhileBodyThrow,axiom,
! [C_2: exp_list_char,E: exp_list_char,S_2_1: produc2090907612on_val,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 @ ( bool @ $true ) ) @ S_1 )
=> ( ( eval @ P @ C_2 @ S_1 @ ( throw_list_char @ E ) @ S_2_1 )
=> ( eval @ P @ ( while_list_char @ E_1 @ C_2 ) @ S_0 @ ( throw_list_char @ E ) @ S_2_1 ) ) ) ).
thf(fact_1086_WhileF,axiom,
! [C_2: exp_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 @ ( bool @ $false ) ) @ S_1 )
=> ( eval @ P @ ( while_list_char @ E_1 @ C_2 ) @ S_0 @ ( val_list_char @ unit ) @ S_1 ) ) ).
thf(fact_1087_WhileRedsThrow,axiom,
! [C_2: exp_list_char,B: exp_list_char,S: produc2090907612on_val,E_1: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ B @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( while_list_char @ B @ C_2 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_1088_WhileTReds,axiom,
! [E_1: exp_list_char,S_3_1: produc2090907612on_val,C_2: exp_list_char,V_1_2: val,S_2_1: produc2090907612on_val,B: exp_list_char,S_0: produc2090907612on_val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ B @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ ( bool @ $true ) ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ C_2 @ S_1 ) @ ( produc235638504on_val @ ( val_list_char @ V_1_2 ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( while_list_char @ B @ C_2 ) @ S_2_1 ) @ ( produc235638504on_val @ E_1 @ S_3_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( while_list_char @ B @ C_2 ) @ S_0 ) @ ( produc235638504on_val @ E_1 @ S_3_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_1089_WhileTRedsThrow,axiom,
! [C_2: exp_list_char,E_1: exp_list_char,S_2_1: produc2090907612on_val,B: exp_list_char,S_0: produc2090907612on_val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ B @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ ( bool @ $true ) ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ C_2 @ S_1 ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( while_list_char @ B @ C_2 ) @ S_0 ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_1090_eval__cases_I11_J,axiom,
! [P: list_P1999446415t_char,B: exp_list_char,C_2: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( eval @ P @ ( while_list_char @ B @ C_2 ) @ S @ E @ S_2 )
=> ( ( ( E
= ( val_list_char @ unit ) )
=> ~ ( eval @ P @ B @ S @ ( val_list_char @ ( bool @ $false ) ) @ S_2 ) )
=> ( ! [S_1_1: produc2090907612on_val] :
( ( eval @ P @ B @ S @ ( val_list_char @ ( bool @ $true ) ) @ S_1_1 )
=> ! [V_1_1: val,S_2_2: produc2090907612on_val] :
( ( eval @ P @ C_2 @ S_1_1 @ ( val_list_char @ V_1_1 ) @ S_2_2 )
=> ~ ( eval @ P @ ( while_list_char @ B @ C_2 ) @ S_2_2 @ E @ S_2 ) ) )
=> ( ! [E_3: exp_list_char] :
( ( E
= ( throw_list_char @ E_3 ) )
=> ~ ( eval @ P @ B @ S @ ( throw_list_char @ E_3 ) @ S_2 ) )
=> ~ ! [S_1_1: produc2090907612on_val,E_3: exp_list_char] :
( ( E
= ( throw_list_char @ E_3 ) )
=> ( ( eval @ P @ B @ S @ ( val_list_char @ ( bool @ $true ) ) @ S_1_1 )
=> ~ ( eval @ P @ C_2 @ S_1_1 @ ( throw_list_char @ E_3 ) @ S_2 ) ) ) ) ) ) ) ).
thf(fact_1091_red__reds_ORedWhile,axiom,
! [B: exp_list_char,C_2: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( while_list_char @ B @ C_2 ) @ S ) @ ( produc235638504on_val @ ( cond_list_char @ B @ ( seq_list_char @ C_2 @ ( while_list_char @ B @ C_2 ) ) @ ( val_list_char @ unit ) ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_1092_redp__redsp_OCondRed,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,P: list_P1999446415t_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S @ E @ S_2 )
=> ( redp @ P @ ( cond_list_char @ E_1 @ E_1_1 @ E_2_1 ) @ S @ ( cond_list_char @ E @ E_1_1 @ E_2_1 ) @ S_2 ) ) ).
thf(fact_1093_eval__evals_OCondThrow,axiom,
! [E_1_1: exp_list_char,E_2_1: 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 @ ( cond_list_char @ E_1 @ E_1_1 @ E_2_1 ) @ S_0 @ ( throw_list_char @ E ) @ S_1 ) ) ).
thf(fact_1094_redp__redsp_OCondThrow,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,E_1_1: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( cond_list_char @ ( throw_list_char @ E_1 ) @ E_1_1 @ E_2_1 ) @ S @ ( throw_list_char @ E_1 ) @ S ) ).
thf(fact_1095_fv__fvs_Osimps_I12_J,axiom,
! [B: exp_list_char,E_1_1: exp_list_char,E_2_1: exp_list_char] :
( ( fv @ ( cond_list_char @ B @ E_1_1 @ E_2_1 ) )
= ( semila2134664963char_o @ ( semila2134664963char_o @ ( fv @ B ) @ ( fv @ E_1_1 ) ) @ ( fv @ E_2_1 ) ) ) ).
thf(fact_1096_red__reds_OCondRed,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cond_list_char @ E_1 @ E_1_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( cond_list_char @ E @ E_1_1 @ E_2_1 ) @ S_2 ) ) @ ( red @ P ) ) ) ).
thf(fact_1097_CondF,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,E: exp_list_char,S_2_1: produc2090907612on_val,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 @ ( bool @ $false ) ) @ S_1 )
=> ( ( eval @ P @ E_2_1 @ S_1 @ E @ S_2_1 )
=> ( eval @ P @ ( cond_list_char @ E_1 @ E_1_1 @ E_2_1 ) @ S_0 @ E @ S_2_1 ) ) ) ).
thf(fact_1098_CondT,axiom,
! [E_2_1: exp_list_char,E_1_1: exp_list_char,E: exp_list_char,S_2_1: produc2090907612on_val,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 @ ( bool @ $true ) ) @ S_1 )
=> ( ( eval @ P @ E_1_1 @ S_1 @ E @ S_2_1 )
=> ( eval @ P @ ( cond_list_char @ E_1 @ E_1_1 @ E_2_1 ) @ S_0 @ E @ S_2_1 ) ) ) ).
thf(fact_1099_redp__redsp_ORedCondF,axiom,
! [P: list_P1999446415t_char,E_1_1: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( cond_list_char @ ( val_list_char @ ( bool @ $false ) ) @ E_1_1 @ E_2_1 ) @ S @ E_2_1 @ S ) ).
thf(fact_1100_redp__redsp_ORedCondT,axiom,
! [P: list_P1999446415t_char,E_1_1: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( cond_list_char @ ( val_list_char @ ( bool @ $true ) ) @ E_1_1 @ E_2_1 ) @ S @ E_1_1 @ S ) ).
thf(fact_1101_red__reds_OCondThrow,axiom,
! [E_1: exp_list_char,E_1_1: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cond_list_char @ ( throw_list_char @ E_1 ) @ E_1_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_1102_CondReds,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cond_list_char @ E_1 @ E_1_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( cond_list_char @ E @ E_1_1 @ E_2_1 ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_1103_CondRedsThrow,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,A: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cond_list_char @ E_1 @ E_1_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_1104_red__reds_ORedCondT,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cond_list_char @ ( val_list_char @ ( bool @ $true ) ) @ E_1_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ E_1_1 @ S ) ) @ ( red @ P ) ) ).
thf(fact_1105_red__reds_ORedCondF,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cond_list_char @ ( val_list_char @ ( bool @ $false ) ) @ E_1_1 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ E_2_1 @ S ) ) @ ( red @ P ) ) ).
thf(fact_1106_unfold__while,axiom,
! [P: list_P1999446415t_char,B: exp_list_char,C_2: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( eval @ P @ ( while_list_char @ B @ C_2 ) @ S @ E @ S_2 )
<=> ( eval @ P @ ( cond_list_char @ B @ ( seq_list_char @ C_2 @ ( while_list_char @ B @ C_2 ) ) @ ( val_list_char @ unit ) ) @ S @ E @ S_2 ) ) ).
thf(fact_1107_redp__redsp_ORedWhile,axiom,
! [P: list_P1999446415t_char,B: exp_list_char,C_2: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( while_list_char @ B @ C_2 ) @ S @ ( cond_list_char @ B @ ( seq_list_char @ C_2 @ ( while_list_char @ B @ C_2 ) ) @ ( val_list_char @ unit ) ) @ S ) ).
thf(fact_1108_CondReds2T,axiom,
! [E_2_1: exp_list_char,E_1_1: exp_list_char,E: exp_list_char,S_2_1: produc2090907612on_val,E_1: exp_list_char,S_0: produc2090907612on_val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ ( bool @ $true ) ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1_1 @ S_1 ) @ ( produc235638504on_val @ E @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cond_list_char @ E_1 @ E_1_1 @ E_2_1 ) @ S_0 ) @ ( produc235638504on_val @ E @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_1109_CondReds2F,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,E: exp_list_char,S_2_1: produc2090907612on_val,E_1: exp_list_char,S_0: produc2090907612on_val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ ( bool @ $false ) ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2_1 @ S_1 ) @ ( produc235638504on_val @ E @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cond_list_char @ E_1 @ E_1_1 @ E_2_1 ) @ S_0 ) @ ( produc235638504on_val @ E @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_1110_ty_Osimps_I20_J,axiom,
! [List: list_char] :
( nt
!= ( class @ List ) ) ).
thf(fact_1111_ty_Osimps_I21_J,axiom,
! [List: list_char] :
( ( class @ List )
!= nt ) ).
thf(fact_1112_ty_Osimps_I7_J,axiom,
nt != void ).
thf(fact_1113_ty_Osimps_I6_J,axiom,
void != nt ).
thf(fact_1114_WTrtFAccNT,axiom,
! [F: list_char,D: list_char,T: ty,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ nt )
=> ( wTrt_1 @ P @ H_1 @ E_2 @ ( fAcc_list_char @ E_1 @ F @ D ) @ T ) ) ).
thf(fact_1115_WTrt_H__WTrts_H_Ointros_I9_J,axiom,
! [F: list_char,D: list_char,T: ty,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char] :
( ( wTrt @ P @ H_1 @ E_2 @ E_1 @ nt )
=> ( wTrt @ P @ H_1 @ E_2 @ ( fAcc_list_char @ E_1 @ F @ D ) @ T ) ) ).
thf(fact_1116_is__refT__def,axiom,
! [T: ty] :
( ( is_refT @ T )
<=> ( ( T = nt )
| ? [C_1: list_char] :
( T
= ( class @ C_1 ) ) ) ) ).
thf(fact_1117_WTrtFAssNT,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,T_2_2: ty,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1_1: exp_list_char] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1_1 @ nt )
=> ( ( wTrt_1 @ P @ H_1 @ E_2 @ E_2_1 @ T_2_2 )
=> ( wTrt_1 @ P @ H_1 @ E_2 @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2_1 ) @ void ) ) ) ).
thf(fact_1118_WTrt_H__WTrts_H_Ointros_I11_J,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,T_2_2: ty,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1_1: exp_list_char] :
( ( wTrt @ P @ H_1 @ E_2 @ E_1_1 @ nt )
=> ( ( wTrt @ P @ H_1 @ E_2 @ E_2_1 @ T_2_2 )
=> ( wTrt @ P @ H_1 @ E_2 @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2_1 ) @ void ) ) ) ).
thf(fact_1119_typeof__h_Osimps_I2_J,axiom,
! [H_1: nat > option1728594148on_val] :
( ( typeof_h @ H_1 @ null )
= ( some_ty @ nt ) ) ).
thf(fact_1120_WTrt__elim__cases_I7_J,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,F: list_char,D: list_char,T: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ ( fAcc_list_char @ E_1 @ F @ D ) @ T )
=> ( ! [C_1: list_char] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ ( class @ C_1 ) )
=> ~ ( has_fi1183600461t_char @ P @ C_1 @ F @ T @ D ) )
=> ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ nt ) ) ) ).
thf(fact_1121_WTrt__elim__cases_I8_J,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,F: list_char,D: list_char,V: exp_list_char,T: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ ( fAss_list_char @ E_1 @ F @ D @ V ) @ T )
=> ( ( ( T = void )
=> ! [C_1: list_char] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ ( class @ C_1 ) )
=> ! [T_4: ty] :
( ( has_fi1183600461t_char @ P @ C_1 @ F @ T_4 @ D )
=> ! [T_2_1: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ V @ T_2_1 )
=> ~ ( widen_2090681816t_char @ P @ T_2_1 @ T_4 ) ) ) ) )
=> ~ ( ( T = void )
=> ( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ nt )
=> ! [T_2_1: ty] :
~ ( wTrt_1 @ P @ H_1 @ E_2 @ V @ T_2_1 ) ) ) ) ) ).
thf(fact_1122_refTE,axiom,
! [T: ty] :
( ( is_refT @ T )
=> ( ( T != nt )
=> ~ ! [C_1: list_char] :
( T
!= ( class @ C_1 ) ) ) ) ).
thf(fact_1123_eval__cases_I10_J,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,E_1_1: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( eval @ P @ ( cond_list_char @ E_1 @ E_1_1 @ E_2_1 ) @ S @ E @ S_2 )
=> ( ! [S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_1 @ S @ ( val_list_char @ ( bool @ $true ) ) @ S_1_1 )
=> ~ ( eval @ P @ E_1_1 @ S_1_1 @ E @ S_2 ) )
=> ( ! [S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_1 @ S @ ( val_list_char @ ( bool @ $false ) ) @ S_1_1 )
=> ~ ( eval @ P @ E_2_1 @ S_1_1 @ E @ S_2 ) )
=> ~ ! [E_3: exp_list_char] :
( ( E
= ( throw_list_char @ E_3 ) )
=> ~ ( eval @ P @ E_1 @ S @ ( throw_list_char @ E_3 ) @ S_2 ) ) ) ) ) ).
thf(fact_1124_red__reds_ORedNewFail,axiom,
! [C: list_char,L_1: list_char > option_val,P: list_P1999446415t_char,H_1: nat > option1728594148on_val] :
( ( ( new_Addr @ H_1 )
= none_nat )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( new_list_char @ C ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) ) @ ( red @ P ) ) ) ).
thf(fact_1125_WTrtNew,axiom,
! [H_1: nat > option1728594148on_val,E_2: list_char > option_ty,P: list_P1999446415t_char,C: list_char] :
( ( is_cla570604648t_char @ P @ C )
=> ( wTrt_1 @ P @ H_1 @ E_2 @ ( new_list_char @ C ) @ ( class @ C ) ) ) ).
thf(fact_1126_WTrt__elim__cases_I10_J,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,C: list_char,T: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ ( new_list_char @ C ) @ T )
=> ~ ( ( T
= ( class @ C ) )
=> ~ ( is_cla570604648t_char @ P @ C ) ) ) ).
thf(fact_1127_new__Addr__SomeD,axiom,
! [H_1: nat > option1728594148on_val,A: nat] :
( ( ( new_Addr @ H_1 )
= ( some_nat @ A ) )
=> ( ( H_1 @ A )
= none_P1260844216on_val ) ) ).
thf(fact_1128_WTrt_H__WTrts_H_Ointros_I1_J,axiom,
! [H_1: nat > option1728594148on_val,E_2: list_char > option_ty,P: list_P1999446415t_char,C: list_char] :
( ( is_cla570604648t_char @ P @ C )
=> ( wTrt @ P @ H_1 @ E_2 @ ( new_list_char @ C ) @ ( class @ C ) ) ) ).
thf(fact_1129_NewFail,axiom,
! [P: list_P1999446415t_char,C: list_char,L_1: list_char > option_val,H_1: nat > option1728594148on_val] :
( ( ( new_Addr @ H_1 )
= none_nat )
=> ( eval @ P @ ( new_list_char @ C ) @ ( produc755559506on_val @ H_1 @ L_1 ) @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) ) ).
thf(fact_1130_redp__redsp_ORedNewFail,axiom,
! [P: list_P1999446415t_char,C: list_char,L_1: list_char > option_val,H_1: nat > option1728594148on_val] :
( ( ( new_Addr @ H_1 )
= none_nat )
=> ( redp @ P @ ( new_list_char @ C ) @ ( produc755559506on_val @ H_1 @ L_1 ) @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) ) ).
thf(fact_1131_red__reds_ORedNew,axiom,
! [L_1: list_char > option_val,H: nat > option1728594148on_val,P: list_P1999446415t_char,C: list_char,FDTs: list_P2023964830har_ty,H_1: nat > option1728594148on_val,A: nat] :
( ( ( new_Addr @ H_1 )
= ( some_nat @ A ) )
=> ( ( fields1147507508t_char @ P @ C @ FDTs )
=> ( ( H
= ( fun_up1472480727on_val @ H_1 @ A @ ( some_P451527732on_val @ ( produc926070009on_val @ C @ ( init_fields @ FDTs ) ) ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( new_list_char @ C ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ ( val_list_char @ ( addr @ A ) ) @ ( produc755559506on_val @ H @ L_1 ) ) ) @ ( red @ P ) ) ) ) ) ).
thf(fact_1132_redp__redsp_ORedNew,axiom,
! [L_1: list_char > option_val,H: nat > option1728594148on_val,P: list_P1999446415t_char,C: list_char,FDTs: list_P2023964830har_ty,H_1: nat > option1728594148on_val,A: nat] :
( ( ( new_Addr @ H_1 )
= ( some_nat @ A ) )
=> ( ( fields1147507508t_char @ P @ C @ FDTs )
=> ( ( H
= ( fun_up1472480727on_val @ H_1 @ A @ ( some_P451527732on_val @ ( produc926070009on_val @ C @ ( init_fields @ FDTs ) ) ) ) )
=> ( redp @ P @ ( new_list_char @ C ) @ ( produc755559506on_val @ H_1 @ L_1 ) @ ( val_list_char @ ( addr @ A ) ) @ ( produc755559506on_val @ H @ L_1 ) ) ) ) ) ).
thf(fact_1133_New,axiom,
! [L_1: list_char > option_val,H: nat > option1728594148on_val,P: list_P1999446415t_char,C: list_char,FDTs: list_P2023964830har_ty,H_1: nat > option1728594148on_val,A: nat] :
( ( ( new_Addr @ H_1 )
= ( some_nat @ A ) )
=> ( ( fields1147507508t_char @ P @ C @ FDTs )
=> ( ( H
= ( fun_up1472480727on_val @ H_1 @ A @ ( some_P451527732on_val @ ( produc926070009on_val @ C @ ( init_fields @ FDTs ) ) ) ) )
=> ( eval @ P @ ( new_list_char @ C ) @ ( produc755559506on_val @ H_1 @ L_1 ) @ ( val_list_char @ ( addr @ A ) ) @ ( produc755559506on_val @ H @ L_1 ) ) ) ) ) ).
thf(fact_1134_red__reds_ORedCallNull,axiom,
! [M: list_char,Vs_1: list_val,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ ( val_list_char @ null ) @ M @ ( map_va1934808527t_char @ val_list_char @ Vs_1 ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_1135_redp__redsp_ORedCallNull,axiom,
! [P: list_P1999446415t_char,M: list_char,Vs_1: list_val,S: produc2090907612on_val] : ( redp @ P @ ( call_list_char @ ( val_list_char @ null ) @ M @ ( map_va1934808527t_char @ val_list_char @ Vs_1 ) ) @ S @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ).
thf(fact_1136_CallObjThrow,axiom,
! [M: list_char,Ps: list_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 @ ( call_list_char @ E_1 @ M @ Ps ) @ S_0 @ ( throw_list_char @ E ) @ S_1 ) ) ).
thf(fact_1137_redp__redsp_OCallObj,axiom,
! [M: list_char,Es: list_exp_list_char,P: list_P1999446415t_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S @ E @ S_2 )
=> ( redp @ P @ ( call_list_char @ E_1 @ M @ Es ) @ S @ ( call_list_char @ E @ M @ Es ) @ S_2 ) ) ).
thf(fact_1138_redp__redsp_OCallThrowObj,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,M: list_char,Es: list_exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( call_list_char @ ( throw_list_char @ E_1 ) @ M @ Es ) @ S @ ( throw_list_char @ E_1 ) @ S ) ).
thf(fact_1139_red__reds_OCallObj,axiom,
! [M: list_char,Es: list_exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ E_1 @ M @ Es ) @ S ) @ ( produc235638504on_val @ ( call_list_char @ E @ M @ Es ) @ S_2 ) ) @ ( red @ P ) ) ) ).
thf(fact_1140_red__reds_OCallThrowObj,axiom,
! [E_1: exp_list_char,M: list_char,Es: list_exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ ( throw_list_char @ E_1 ) @ M @ Es ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_1141_CallRedsObj,axiom,
! [M: list_char,Es: list_exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ E_1 @ M @ Es ) @ S ) @ ( produc235638504on_val @ ( call_list_char @ E @ M @ Es ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_1142_CallRedsThrowObj,axiom,
! [M: list_char,Es: list_exp_list_char,E_1: exp_list_char,S0: produc2090907612on_val,A: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S0 ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ E_1 @ M @ Es ) @ S0 ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_1143_CallRedsNull,axiom,
! [M: list_char,Es: list_exp_list_char,Vs_1: list_val,S_2_1: produc2090907612on_val,E_1: exp_list_char,S_0: produc2090907612on_val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S_1 ) @ ( produc1302104557on_val @ ( map_va1934808527t_char @ val_list_char @ Vs_1 ) @ S_2_1 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ E_1 @ M @ Es ) @ 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_1144_CallNull,axiom,
! [M: list_char,Ps: list_exp_list_char,Vs_1: list_val,S_2_1: produc2090907612on_val,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 )
=> ( ( evals @ P @ Ps @ S_1 @ ( map_va1934808527t_char @ val_list_char @ Vs_1 ) @ S_2_1 )
=> ( eval @ P @ ( call_list_char @ E_1 @ M @ Ps ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_2_1 ) ) ) ).
thf(fact_1145_extend__1__evals,axiom,
! [Es_1: list_exp_list_char,T_3: produc2090907612on_val,Es: list_exp_list_char,T_2: produc2090907612on_val,Es_3: list_exp_list_char,T_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ T_2 ) @ ( produc1302104557on_val @ Es_3 @ T_1 ) ) @ ( reds @ P ) )
=> ( ( evals @ P @ Es_3 @ T_1 @ Es_1 @ T_3 )
=> ( evals @ P @ Es @ T_2 @ Es_1 @ T_3 ) ) ) ) ).
thf(fact_1146_extend__evals,axiom,
! [Es_1: list_exp_list_char,S_2: produc2090907612on_val,Es: list_exp_list_char,S: produc2090907612on_val,Es_3: list_exp_list_char,S_3: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_3 @ S_3 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) )
=> ( ( evals @ P @ Es_3 @ S_3 @ Es_1 @ S_2 )
=> ( evals @ P @ Es @ S @ Es_1 @ S_2 ) ) ) ) ).
thf(fact_1147_bigs__by__smalls,axiom,
! [Es: list_exp_list_char,S: produc2090907612on_val,Es_1: list_exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( evals @ P @ Es @ S @ Es_1 @ S_2 )
=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_1 @ S_2 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) ) ) ) ).
thf(fact_1148_evals__hext,axiom,
! [P: list_P1999446415t_char,Es: list_exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,Es_1: list_exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val] :
( ( evals @ P @ Es @ ( produc755559506on_val @ H_1 @ L_1 ) @ Es_1 @ ( produc755559506on_val @ H @ L ) )
=> ( hext @ H_1 @ H ) ) ).
thf(fact_1149_reds__hext__incr,axiom,
! [Es: list_exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,Es_1: list_exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc1302104557on_val @ Es_1 @ ( produc755559506on_val @ H @ L ) ) ) @ ( reds @ P ) )
=> ( hext @ H_1 @ H ) ) ).
thf(fact_1150_evals__lcl__incr,axiom,
! [P: list_P1999446415t_char,Es: list_exp_list_char,H_0: nat > option1728594148on_val,L_0: list_char > option_val,Es_1: list_exp_list_char,H_1_1: nat > option1728594148on_val,L_1_1: list_char > option_val] :
( ( evals @ P @ Es @ ( produc755559506on_val @ H_0 @ L_0 ) @ Es_1 @ ( produc755559506on_val @ H_1_1 @ L_1_1 ) )
=> ( ord_le1777678169char_o @ ( dom_list_char_val @ L_0 ) @ ( dom_list_char_val @ L_1_1 ) ) ) ).
thf(fact_1151_red__reds_OCallParams,axiom,
! [V: val,M: list_char,Es: list_exp_list_char,S: produc2090907612on_val,Es_1: list_exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_1 @ S_2 ) ) @ ( reds @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ ( val_list_char @ V ) @ M @ Es ) @ S ) @ ( produc235638504on_val @ ( call_list_char @ ( val_list_char @ V ) @ M @ Es_1 ) @ S_2 ) ) @ ( red @ P ) ) ) ).
thf(fact_1152_CallRedsParams,axiom,
! [V: val,M: list_char,Es: list_exp_list_char,S: produc2090907612on_val,Es_1: list_exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_1 @ S_2 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ ( val_list_char @ V ) @ M @ Es ) @ S ) @ ( produc235638504on_val @ ( call_list_char @ ( val_list_char @ V ) @ M @ Es_1 ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_1153_CallRedsThrowParams,axiom,
! [M: list_char,Es: list_exp_list_char,Vs_1_1: list_val,A: exp_list_char,Es_2_1: list_exp_list_char,S_2_1: produc2090907612on_val,E_1: exp_list_char,S0: produc2090907612on_val,V: val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S0 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S_1 ) @ ( produc1302104557on_val @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ Vs_1_1 ) @ ( cons_exp_list_char @ ( throw_list_char @ A ) @ Es_2_1 ) ) @ S_2_1 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ E_1 @ M @ Es ) @ S0 ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_2_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_1154_fv__fvs_Osimps_I9_J,axiom,
! [E_1: exp_list_char,M: list_char,Es: list_exp_list_char] :
( ( fv @ ( call_list_char @ E_1 @ M @ Es ) )
= ( semila2134664963char_o @ ( fv @ E_1 ) @ ( fvs @ Es ) ) ) ).
thf(fact_1155_fv__fvs_Osimps_I17_J,axiom,
! [E_1: exp_list_char,Es: list_exp_list_char] :
( ( fvs @ ( cons_exp_list_char @ E_1 @ Es ) )
= ( semila2134664963char_o @ ( fv @ E_1 ) @ ( fvs @ Es ) ) ) ).
thf(fact_1156_eval__evals_OCons,axiom,
! [Es: list_exp_list_char,Es_1: list_exp_list_char,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,V: val,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1 @ S_0 @ ( val_list_char @ V ) @ S_1 )
=> ( ( evals @ P @ Es @ S_1 @ Es_1 @ S_2_1 )
=> ( evals @ P @ ( cons_exp_list_char @ E_1 @ Es ) @ S_0 @ ( cons_exp_list_char @ ( val_list_char @ V ) @ Es_1 ) @ S_2_1 ) ) ) ).
thf(fact_1157_ConsThrow,axiom,
! [Es: list_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 )
=> ( evals @ P @ ( cons_exp_list_char @ E_1 @ Es ) @ S_0 @ ( cons_exp_list_char @ ( throw_list_char @ E ) @ Es ) @ S_1 ) ) ).
thf(fact_1158_red__reds_OListRed2,axiom,
! [V: val,Es: list_exp_list_char,S: produc2090907612on_val,Es_1: list_exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_1 @ S_2 ) ) @ ( reds @ P ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ ( cons_exp_list_char @ ( val_list_char @ V ) @ Es ) @ S ) @ ( produc1302104557on_val @ ( cons_exp_list_char @ ( val_list_char @ V ) @ Es_1 ) @ S_2 ) ) @ ( reds @ P ) ) ) ).
thf(fact_1159_redp__redsp_OCallThrowParams,axiom,
! [P: list_P1999446415t_char,V: val,M: list_char,S: produc2090907612on_val,Es: list_exp_list_char,Vs_1: list_val,E_1: exp_list_char,Es_1: list_exp_list_char] :
( ( Es
= ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ Vs_1 ) @ ( cons_exp_list_char @ ( throw_list_char @ E_1 ) @ Es_1 ) ) )
=> ( redp @ P @ ( call_list_char @ ( val_list_char @ V ) @ M @ Es ) @ S @ ( throw_list_char @ E_1 ) @ S ) ) ).
thf(fact_1160_list__eval__Throw,axiom,
! [Vs_1: list_val,Es_1: list_exp_list_char,P: list_P1999446415t_char,X_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( eval @ P @ ( throw_list_char @ X_1 ) @ S @ E @ S_2 )
=> ( evals @ P @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ Vs_1 ) @ ( cons_exp_list_char @ ( throw_list_char @ X_1 ) @ Es_1 ) ) @ S @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ Vs_1 ) @ ( cons_exp_list_char @ E @ Es_1 ) ) @ S_2 ) ) ).
thf(fact_1161_ListReds2,axiom,
! [V: val,Es: list_exp_list_char,S: produc2090907612on_val,Es_1: list_exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_1 @ S_2 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ ( cons_exp_list_char @ ( val_list_char @ V ) @ Es ) @ S ) @ ( produc1302104557on_val @ ( cons_exp_list_char @ ( val_list_char @ V ) @ Es_1 ) @ S_2 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) ) ) ).
thf(fact_1162_red__reds_OListRed1,axiom,
! [Es: list_exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( red @ P ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ ( cons_exp_list_char @ E_1 @ Es ) @ S ) @ ( produc1302104557on_val @ ( cons_exp_list_char @ E @ Es ) @ S_2 ) ) @ ( reds @ P ) ) ) ).
thf(fact_1163_CallParamsThrow,axiom,
! [M: list_char,Es: list_exp_list_char,Vs_1: list_val,Ex: exp_list_char,Es_1: list_exp_list_char,S_2_1: produc2090907612on_val,P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,V: val,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1 @ S_0 @ ( val_list_char @ V ) @ S_1 )
=> ( ( evals @ P @ Es @ S_1 @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ Vs_1 ) @ ( cons_exp_list_char @ ( throw_list_char @ Ex ) @ Es_1 ) ) @ S_2_1 )
=> ( eval @ P @ ( call_list_char @ E_1 @ M @ Es ) @ S_0 @ ( throw_list_char @ Ex ) @ S_2_1 ) ) ) ).
thf(fact_1164_red__reds_OCallThrowParams,axiom,
! [V: val,M: list_char,S: produc2090907612on_val,P: list_P1999446415t_char,Es: list_exp_list_char,Vs_1: list_val,E_1: exp_list_char,Es_1: list_exp_list_char] :
( ( Es
= ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ Vs_1 ) @ ( cons_exp_list_char @ ( throw_list_char @ E_1 ) @ Es_1 ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ ( val_list_char @ V ) @ M @ Es ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_1 ) @ S ) ) @ ( red @ P ) ) ) ).
thf(fact_1165_ListReds1,axiom,
! [Es: list_exp_list_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S ) @ ( produc235638504on_val @ E @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ ( cons_exp_list_char @ E_1 @ Es ) @ S ) @ ( produc1302104557on_val @ ( cons_exp_list_char @ E @ Es ) @ S_2 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) ) ) ).
thf(fact_1166_ListRedsVal,axiom,
! [Es: list_exp_list_char,Es_1: list_exp_list_char,S_2_1: produc2090907612on_val,E_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 @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ V ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S_1 ) @ ( produc1302104557on_val @ Es_1 @ S_2_1 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ ( cons_exp_list_char @ E_1 @ Es ) @ S_0 ) @ ( produc1302104557on_val @ ( cons_exp_list_char @ ( val_list_char @ V ) @ Es_1 ) @ S_2_1 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) ) ) ) ).
thf(fact_1167_evals__cases_I2_J,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,Es: list_exp_list_char,S: produc2090907612on_val,E: list_exp_list_char,S_2: produc2090907612on_val] :
( ( evals @ P @ ( cons_exp_list_char @ E_1 @ Es ) @ S @ E @ S_2 )
=> ( ! [V_2: val,S_1_1: produc2090907612on_val,Es_2: list_exp_list_char] :
( ( E
= ( cons_exp_list_char @ ( val_list_char @ V_2 ) @ Es_2 ) )
=> ( ( eval @ P @ E_1 @ S @ ( val_list_char @ V_2 ) @ S_1_1 )
=> ~ ( evals @ P @ Es @ S_1_1 @ Es_2 @ S_2 ) ) )
=> ~ ! [E_3: exp_list_char] :
( ( E
= ( cons_exp_list_char @ ( throw_list_char @ E_3 ) @ Es ) )
=> ~ ( eval @ P @ E_1 @ S @ ( throw_list_char @ E_3 ) @ S_2 ) ) ) ) ).
thf(fact_1168_evals__final,axiom,
! [P: list_P1999446415t_char,Es: list_exp_list_char,S: produc2090907612on_val,Es_1: list_exp_list_char,S_2: produc2090907612on_val] :
( ( evals @ P @ Es @ S @ Es_1 @ S_2 )
=> ( finals_list_char @ Es_1 ) ) ).
thf(fact_1169_eval__finalsId,axiom,
! [P: list_P1999446415t_char,S: produc2090907612on_val,Es: list_exp_list_char] :
( ( finals_list_char @ Es )
=> ( evals @ P @ Es @ S @ Es @ S ) ) ).
thf(fact_1170_reds__preserves__sconf,axiom,
! [E_2: list_char > option_ty,Ts: list_ty,Es: list_exp_list_char,S: produc2090907612on_val,Es_1: list_exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_1 @ S_2 ) ) @ ( reds @ P ) )
=> ( ( wTrts_1 @ P @ ( hp @ S ) @ E_2 @ Es @ Ts )
=> ( ( typeSa816273224_sconf @ P @ E_2 @ S )
=> ( typeSa816273224_sconf @ P @ E_2 @ S_2 ) ) ) ) ).
thf(fact_1171_WTrtCons,axiom,
! [Es: list_exp_list_char,Ts: list_ty,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,T: ty] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ T )
=> ( ( wTrts_1 @ P @ H_1 @ E_2 @ Es @ Ts )
=> ( wTrts_1 @ P @ H_1 @ E_2 @ ( cons_exp_list_char @ E_1 @ Es ) @ ( cons_ty @ T @ Ts ) ) ) ) ).
thf(fact_1172_WTrts__hext__mono,axiom,
! [H: nat > option1728594148on_val,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,Es: list_exp_list_char,Ts: list_ty] :
( ( wTrts_1 @ P @ H_1 @ E_2 @ Es @ Ts )
=> ( ( hext @ H_1 @ H )
=> ( wTrts_1 @ P @ H @ E_2 @ Es @ Ts ) ) ) ).
thf(fact_1173_WTrtCallNT,axiom,
! [M: list_char,T: ty,Es: list_exp_list_char,Ts: list_ty,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ nt )
=> ( ( wTrts_1 @ P @ H_1 @ E_2 @ Es @ Ts )
=> ( wTrt_1 @ P @ H_1 @ E_2 @ ( call_list_char @ E_1 @ M @ Es ) @ T ) ) ) ).
thf(fact_1174_WTrts__Val,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,Vs_1: list_val,Ts: list_ty] :
( ( wTrts_1 @ P @ H_1 @ E_2 @ ( map_va1934808527t_char @ val_list_char @ Vs_1 ) @ Ts )
<=> ( ( map_val_option_ty @ ( typeof_h @ H_1 ) @ Vs_1 )
= ( map_ty_option_ty @ some_ty @ Ts ) ) ) ).
thf(fact_1175_reds__preserves__hconf,axiom,
! [E_2: list_char > option_ty,Ts: list_ty,Es: list_exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,Es_1: list_exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc1302104557on_val @ Es_1 @ ( produc755559506on_val @ H @ L ) ) ) @ ( reds @ P ) )
=> ( ( wTrts_1 @ P @ H_1 @ E_2 @ Es @ Ts )
=> ( ( hconf_97414254t_char @ P @ H_1 )
=> ( hconf_97414254t_char @ P @ H ) ) ) ) ).
thf(fact_1176_reds__preserves__lconf,axiom,
! [E_2: list_char > option_ty,Ts: list_ty,Es: list_exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,Es_1: list_exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc1302104557on_val @ Es_1 @ ( produc755559506on_val @ H @ L ) ) ) @ ( reds @ P ) )
=> ( ( wTrts_1 @ P @ H_1 @ E_2 @ Es @ Ts )
=> ( ( lconf_496643946t_char @ P @ H_1 @ L_1 @ E_2 )
=> ( lconf_496643946t_char @ P @ H @ L @ E_2 ) ) ) ) ).
thf(fact_1177_redsp__reds__eq,axiom,
! [P: list_P1999446415t_char,X: list_exp_list_char,Xa: produc2090907612on_val,Xb: list_exp_list_char,Xc: produc2090907612on_val] :
( ( redsp @ P @ X @ Xa @ Xb @ Xc )
<=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ X @ Xa ) @ ( produc1302104557on_val @ Xb @ Xc ) ) @ ( reds @ P ) ) ) ).
thf(fact_1178_blocks_Osimps_I1_J,axiom,
! [V_1: list_char,Vs: list_list_char,T: ty,Ts: list_ty,V: val,Vs_1: list_val,E_1: exp_list_char] :
( ( blocks @ ( produc921874948t_char @ ( cons_list_char @ V_1 @ Vs ) @ ( produc1909267824t_char @ ( cons_ty @ T @ Ts ) @ ( produc1916172923t_char @ ( cons_val @ V @ Vs_1 ) @ E_1 ) ) ) )
= ( block_list_char @ V_1 @ T @ ( seq_list_char @ ( lAss_list_char @ V_1 @ ( val_list_char @ V ) ) @ ( blocks @ ( produc921874948t_char @ Vs @ ( produc1909267824t_char @ Ts @ ( produc1916172923t_char @ Vs_1 @ E_1 ) ) ) ) ) ) ) ).
thf(fact_1179_redp__redsp_OListRed2,axiom,
! [V: val,P: list_P1999446415t_char,Es: list_exp_list_char,S: produc2090907612on_val,Es_1: list_exp_list_char,S_2: produc2090907612on_val] :
( ( redsp @ P @ Es @ S @ Es_1 @ S_2 )
=> ( redsp @ P @ ( cons_exp_list_char @ ( val_list_char @ V ) @ Es ) @ S @ ( cons_exp_list_char @ ( val_list_char @ V ) @ Es_1 ) @ S_2 ) ) ).
thf(fact_1180_redp__redsp_OListRed1,axiom,
! [Es: list_exp_list_char,P: list_P1999446415t_char,E_1: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_2: produc2090907612on_val] :
( ( redp @ P @ E_1 @ S @ E @ S_2 )
=> ( redsp @ P @ ( cons_exp_list_char @ E_1 @ Es ) @ S @ ( cons_exp_list_char @ E @ Es ) @ S_2 ) ) ).
thf(fact_1181_redp__redsp_OCallParams,axiom,
! [V: val,M: list_char,P: list_P1999446415t_char,Es: list_exp_list_char,S: produc2090907612on_val,Es_1: list_exp_list_char,S_2: produc2090907612on_val] :
( ( redsp @ P @ Es @ S @ Es_1 @ S_2 )
=> ( redp @ P @ ( call_list_char @ ( val_list_char @ V ) @ M @ Es ) @ S @ ( call_list_char @ ( val_list_char @ V ) @ M @ Es_1 ) @ S_2 ) ) ).
thf(fact_1182_wf__J__prog__wf__J__mdecl,axiom,
! [Jmdcl: produc1013743697t_char,C: list_char,D: list_char,Fds: list_P1940453997har_ty,Mths: list_P341299826t_char,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wf_J_mdecl @ P )
=> ( ( member1467889965t_char @ ( produc822965838t_char @ C @ ( produc1483578759t_char @ D @ ( produc1152259904t_char @ Fds @ Mths ) ) ) @ ( set_Pr1494163115t_char @ P ) )
=> ( ( member1601084734t_char @ Jmdcl @ ( set_Pr2033386304t_char @ Mths ) )
=> ( wf_J_mdecl @ P @ C @ Jmdcl ) ) ) ) ).
thf(fact_1183_CallRedsFinal,axiom,
! [Ef: exp_list_char,H_3: nat > option1728594148on_val,L_3_1: list_char > option_val,L_2_2: list_char > option_val,M: list_char,Ts: list_ty,T: ty,Pns: list_list_char,Body: exp_list_char,D: list_char,C: list_char,Fs: produc1278157519t_char > option_val,Es: list_exp_list_char,Vs_1: list_val,H_2: nat > option1728594148on_val,L_2_1: list_char > option_val,E_1: exp_list_char,S_0: produc2090907612on_val,A: nat,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( wf_pro755087577t_char @ wwf_J_mdecl @ P )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ ( addr @ A ) ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S_1 ) @ ( produc1302104557on_val @ ( map_va1934808527t_char @ val_list_char @ Vs_1 ) @ ( produc755559506on_val @ H_2 @ L_2_1 ) ) ) @ ( transi808828192on_val @ ( reds @ P ) ) )
=> ( ( ( H_2 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( ( method1809630380t_char @ P @ C @ M @ Ts @ T @ ( produc1147572817t_char @ Pns @ Body ) @ D )
=> ( ( ( size_size_list_val @ Vs_1 )
= ( size_s2113983095t_char @ Pns ) )
=> ( ( L_2_2
= ( map_up1085636310ar_val
@ ( fun_up1149430426on_val
@ ^ [X: list_char] : none_val
@ this
@ ( some_val @ ( addr @ A ) ) )
@ Pns
@ Vs_1 ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Body @ ( produc755559506on_val @ H_2 @ L_2_2 ) ) @ ( produc235638504on_val @ Ef @ ( produc755559506on_val @ H_3 @ L_3_1 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( final_list_char @ Ef )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ E_1 @ M @ Es ) @ S_0 ) @ ( produc235638504on_val @ Ef @ ( produc755559506on_val @ H_3 @ L_2_1 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(fact_1184_Call,axiom,
! [E: exp_list_char,H_3: nat > option1728594148on_val,L_3_1: list_char > option_val,L_2_2: list_char > option_val,M: list_char,Ts: list_ty,T: ty,Pns: list_list_char,Body: exp_list_char,D: list_char,C: list_char,Fs: produc1278157519t_char > option_val,Ps: list_exp_list_char,Vs_1: list_val,H_2: nat > option1728594148on_val,L_2_1: list_char > option_val,P: list_P1999446415t_char,E_1: exp_list_char,S_0: produc2090907612on_val,A: nat,S_1: produc2090907612on_val] :
( ( eval @ P @ E_1 @ S_0 @ ( val_list_char @ ( addr @ A ) ) @ S_1 )
=> ( ( evals @ P @ Ps @ S_1 @ ( map_va1934808527t_char @ val_list_char @ Vs_1 ) @ ( produc755559506on_val @ H_2 @ L_2_1 ) )
=> ( ( ( H_2 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( ( method1809630380t_char @ P @ C @ M @ Ts @ T @ ( produc1147572817t_char @ Pns @ Body ) @ D )
=> ( ( ( size_size_list_val @ Vs_1 )
= ( size_s2113983095t_char @ Pns ) )
=> ( ( L_2_2
= ( map_up1085636310ar_val
@ ( fun_up1149430426on_val
@ ^ [X: list_char] : none_val
@ this
@ ( some_val @ ( addr @ A ) ) )
@ Pns
@ Vs_1 ) )
=> ( ( eval @ P @ Body @ ( produc755559506on_val @ H_2 @ L_2_2 ) @ E @ ( produc755559506on_val @ H_3 @ L_3_1 ) )
=> ( eval @ P @ ( call_list_char @ E_1 @ M @ Ps ) @ S_0 @ E @ ( produc755559506on_val @ H_3 @ L_2_1 ) ) ) ) ) ) ) ) ) ).
thf(fact_1185_red__reds_ORedCall,axiom,
! [Vs_1: list_val,P: list_P1999446415t_char,M: list_char,Ts: list_ty,T: ty,Pns: list_list_char,Body: exp_list_char,D: list_char,S: produc2090907612on_val,A: nat,C: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( ( method1809630380t_char @ P @ C @ M @ Ts @ T @ ( produc1147572817t_char @ Pns @ Body ) @ D )
=> ( ( ( size_size_list_val @ Vs_1 )
= ( size_s2113983095t_char @ Pns ) )
=> ( ( ( size_size_list_ty @ Ts )
= ( size_s2113983095t_char @ Pns ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ ( val_list_char @ ( addr @ A ) ) @ M @ ( map_va1934808527t_char @ val_list_char @ Vs_1 ) ) @ S ) @ ( produc235638504on_val @ ( blocks @ ( produc921874948t_char @ ( cons_list_char @ this @ Pns ) @ ( produc1909267824t_char @ ( cons_ty @ ( class @ D ) @ Ts ) @ ( produc1916172923t_char @ ( cons_val @ ( addr @ A ) @ Vs_1 ) @ Body ) ) ) ) @ S ) ) @ ( red @ P ) ) ) ) ) ) ).
thf(fact_1186_redp__redsp_ORedCall,axiom,
! [Vs_1: list_val,P: list_P1999446415t_char,M: list_char,Ts: list_ty,T: ty,Pns: list_list_char,Body: exp_list_char,D: list_char,S: produc2090907612on_val,A: nat,C: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( hp @ S @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( ( method1809630380t_char @ P @ C @ M @ Ts @ T @ ( produc1147572817t_char @ Pns @ Body ) @ D )
=> ( ( ( size_size_list_val @ Vs_1 )
= ( size_s2113983095t_char @ Pns ) )
=> ( ( ( size_size_list_ty @ Ts )
= ( size_s2113983095t_char @ Pns ) )
=> ( redp @ P @ ( call_list_char @ ( val_list_char @ ( addr @ A ) ) @ M @ ( map_va1934808527t_char @ val_list_char @ Vs_1 ) ) @ S @ ( blocks @ ( produc921874948t_char @ ( cons_list_char @ this @ Pns ) @ ( produc1909267824t_char @ ( cons_ty @ ( class @ D ) @ Ts ) @ ( produc1916172923t_char @ ( cons_val @ ( addr @ A ) @ Vs_1 ) @ Body ) ) ) ) @ S ) ) ) ) ) ).
thf(fact_1187_WTrts__same__length,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,Es: list_exp_list_char,Ts: list_ty] :
( ( wTrts_1 @ P @ H_1 @ E_2 @ Es @ Ts )
=> ( ( size_s1143674878t_char @ Es )
= ( size_size_list_ty @ Ts ) ) ) ).
thf(fact_1188_blocksFinal,axiom,
! [H_1: nat > option1728594148on_val,L_1: list_char > option_val,P: list_P1999446415t_char,E_1: exp_list_char,Vs_1: list_val,Vs: list_list_char,Ts: list_ty] :
( ( ( size_s2113983095t_char @ Vs )
= ( size_size_list_ty @ Ts ) )
=> ( ( ( size_size_list_val @ Vs_1 )
= ( size_size_list_ty @ Ts ) )
=> ( ( final_list_char @ E_1 )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( blocks @ ( produc921874948t_char @ Vs @ ( produc1909267824t_char @ Ts @ ( produc1916172923t_char @ Vs_1 @ E_1 ) ) ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ L_1 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_1189_blocksEval,axiom,
! [P: list_P1999446415t_char,E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,Vs_1: list_val,Ps: list_list_char,Ts: list_ty] :
( ( ( size_s2113983095t_char @ Ps )
= ( size_size_list_ty @ Ts ) )
=> ( ( ( size_s2113983095t_char @ Ps )
= ( size_size_list_val @ Vs_1 ) )
=> ( ( eval @ P @ ( blocks @ ( produc921874948t_char @ Ps @ ( produc1909267824t_char @ Ts @ ( produc1916172923t_char @ Vs_1 @ E_1 ) ) ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) @ E @ ( produc755559506on_val @ H @ L ) )
=> ? [L_3: list_char > option_val] : ( eval @ P @ E_1 @ ( produc755559506on_val @ H_1 @ ( map_up1085636310ar_val @ L_1 @ Ps @ Vs_1 ) ) @ E @ ( produc755559506on_val @ H @ L_3 ) ) ) ) ) ).
thf(fact_1190_wt__blocks,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,T: ty,Vs_1: list_val,Vs: list_list_char,Ts: list_ty] :
( ( ( size_s2113983095t_char @ Vs )
= ( size_size_list_ty @ Ts ) )
=> ( ( ( size_size_list_val @ Vs_1 )
= ( size_size_list_ty @ Ts ) )
=> ( ( wTrt_1 @ P @ H_1 @ E_2 @ ( blocks @ ( produc921874948t_char @ Vs @ ( produc1909267824t_char @ Ts @ ( produc1916172923t_char @ Vs_1 @ E_1 ) ) ) ) @ T )
<=> ( ( wTrt_1 @ P @ H_1 @ ( map_up891053837har_ty @ E_2 @ Vs @ Ts ) @ E_1 @ T )
& ? [Ts_2: list_ty] :
( ( ( map_val_option_ty @ ( typeof_h @ H_1 ) @ Vs_1 )
= ( map_ty_option_ty @ some_ty @ Ts_2 ) )
& ( list_all2_ty_ty @ ( widen_2090681816t_char @ P ) @ Ts_2 @ Ts ) ) ) ) ) ) ).
thf(fact_1191_WTrtCall,axiom,
! [Es: list_exp_list_char,Ts_1: list_ty,M: list_char,Ts: list_ty,T: ty,Pns: list_list_char,Body: exp_list_char,D: list_char,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,C: list_char] :
( ( wTrt_1 @ P @ H_1 @ E_2 @ E_1 @ ( class @ C ) )
=> ( ( method1809630380t_char @ P @ C @ M @ Ts @ T @ ( produc1147572817t_char @ Pns @ Body ) @ D )
=> ( ( wTrts_1 @ P @ H_1 @ E_2 @ Es @ Ts_1 )
=> ( ( list_all2_ty_ty @ ( widen_2090681816t_char @ P ) @ Ts_1 @ Ts )
=> ( wTrt_1 @ P @ H_1 @ E_2 @ ( call_list_char @ E_1 @ M @ Es ) @ T ) ) ) ) ) ).
thf(fact_1192_WTrt_H__WTrts_H_Ointros_I12_J,axiom,
! [Es: list_exp_list_char,Ts_1: list_ty,M: list_char,Ts: list_ty,T: ty,Pns: list_list_char,Body: exp_list_char,D: list_char,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,C: list_char] :
( ( wTrt @ P @ H_1 @ E_2 @ E_1 @ ( class @ C ) )
=> ( ( method1809630380t_char @ P @ C @ M @ Ts @ T @ ( produc1147572817t_char @ Pns @ Body ) @ D )
=> ( ( wTrts @ P @ H_1 @ E_2 @ Es @ Ts_1 )
=> ( ( list_all2_ty_ty @ ( widen_2090681816t_char @ P ) @ Ts_1 @ Ts )
=> ( wTrt @ P @ H_1 @ E_2 @ ( call_list_char @ E_1 @ M @ Es ) @ T ) ) ) ) ) ).
thf(fact_1193_wts_H__iff__wts,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,Es: list_exp_list_char,Ts: list_ty] :
( ( wTrts @ P @ H_1 @ E_2 @ Es @ Ts )
<=> ( wTrts_1 @ P @ H_1 @ E_2 @ Es @ Ts ) ) ).
thf(fact_1194_wts_H__wts,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,Es: list_exp_list_char,Ts: list_ty] :
( ( wTrts @ P @ H_1 @ E_2 @ Es @ Ts )
=> ( wTrts_1 @ P @ H_1 @ E_2 @ Es @ Ts ) ) ).
thf(fact_1195_wts__wts_H,axiom,
! [P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,Es: list_exp_list_char,Ts: list_ty] :
( ( wTrts_1 @ P @ H_1 @ E_2 @ Es @ Ts )
=> ( wTrts @ P @ H_1 @ E_2 @ Es @ Ts ) ) ).
thf(fact_1196_WTrt_H__WTrts_H_Ointros_I13_J,axiom,
! [M: list_char,T: ty,Es: list_exp_list_char,Ts: list_ty,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char] :
( ( wTrt @ P @ H_1 @ E_2 @ E_1 @ nt )
=> ( ( wTrts @ P @ H_1 @ E_2 @ Es @ Ts )
=> ( wTrt @ P @ H_1 @ E_2 @ ( call_list_char @ E_1 @ M @ Es ) @ T ) ) ) ).
thf(fact_1197_WTrt_H__WTrts_H_Ointros_I15_J,axiom,
! [Es: list_exp_list_char,Ts: list_ty,P: list_P1999446415t_char,H_1: nat > option1728594148on_val,E_2: list_char > option_ty,E_1: exp_list_char,T: ty] :
( ( wTrt @ P @ H_1 @ E_2 @ E_1 @ T )
=> ( ( wTrts @ P @ H_1 @ E_2 @ Es @ Ts )
=> ( wTrts @ P @ H_1 @ E_2 @ ( cons_exp_list_char @ E_1 @ Es ) @ ( cons_ty @ T @ Ts ) ) ) ) ).
thf(fact_1198_blocksRedsFinal,axiom,
! [L_2: list_char > option_val,E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char,Vs_1: list_val,Vs: list_list_char,Ts: list_ty] :
( ( ( size_s2113983095t_char @ Vs )
= ( size_size_list_ty @ Ts ) )
=> ( ( ( size_size_list_val @ Vs_1 )
= ( size_size_list_ty @ Ts ) )
=> ( ( distinct_list_char @ Vs )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ ( map_up1085636310ar_val @ L_1 @ Vs @ Vs_1 ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( final_list_char @ E )
=> ( ( L_2
= ( overri2012515291on_val @ L @ L_1 @ ( set_list_char @ Vs ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( blocks @ ( produc921874948t_char @ Vs @ ( produc1909267824t_char @ Ts @ ( produc1916172923t_char @ Vs_1 @ E_1 ) ) ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L_2 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ) ) ) ).
thf(fact_1199_blocksReds,axiom,
! [E_1: exp_list_char,H_1: nat > option1728594148on_val,L_1: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L: list_char > option_val,P: list_P1999446415t_char,Vs_1: list_val,Vs: list_list_char,Ts: list_ty] :
( ( ( size_s2113983095t_char @ Vs )
= ( size_size_list_ty @ Ts ) )
=> ( ( ( size_size_list_val @ Vs_1 )
= ( size_size_list_ty @ Ts ) )
=> ( ( distinct_list_char @ Vs )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1 @ ( produc755559506on_val @ H_1 @ ( map_up1085636310ar_val @ L_1 @ Vs @ Vs_1 ) ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( blocks @ ( produc921874948t_char @ Vs @ ( produc1909267824t_char @ Ts @ ( produc1916172923t_char @ Vs_1 @ E_1 ) ) ) ) @ ( produc755559506on_val @ H_1 @ L_1 ) ) @ ( produc235638504on_val @ ( blocks @ ( produc921874948t_char @ Vs @ ( produc1909267824t_char @ Ts @ ( produc1916172923t_char @ ( map_list_char_val @ ( comp_o1129292306t_char @ the_val @ L ) @ Vs ) @ E ) ) ) ) @ ( produc755559506on_val @ H @ ( overri2012515291on_val @ L @ L_1 @ ( set_list_char @ Vs ) ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ) ).
%----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 ) ).
%------------------------------------------------------------------------------