TPTP Problem File: SWW476^2.p
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%------------------------------------------------------------------------------
% File : SWW476^2 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Java type soundness line 197, 500 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : jinja_500_thf_l197 [Bla11]
% Status : Theorem
% Rating : 1.00 v5.3.0
% Syntax : Number of formulae : 974 ( 253 unt; 269 typ; 0 def)
% Number of atoms : 1899 ( 570 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 9737 ( 327 ~; 2 |; 29 &;8372 @)
% ( 96 <=>; 863 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 11 avg)
% Number of types : 44 ( 43 usr)
% Number of type conns : 1413 (1413 >; 0 *; 0 +; 0 <<)
% Number of symbols : 231 ( 226 usr; 16 con; 0-7 aty)
% ( 24 !!; 24 ??; 0 @@+; 0 @@-)
% Number of variables : 3375 ( 0 ^;3305 !; 70 ?;3375 :)
% SPC : TH1_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 19:28:58
%------------------------------------------------------------------------------
%----Should-be-implicit typings (43)
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__Option__Ooption_Itc__Value__Oval_J_J,type,
list_option_val: $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__List_,type,
list_P1916372464t_char: $tType ).
thf(ty_ty_tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_,type,
list_P1999446415t_char: $tType ).
thf(ty_ty_tc__List__Olist_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__,type,
list_P1964248404on_val: $tType ).
thf(ty_ty_tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__,type,
list_P1314671880on_val: $tType ).
thf(ty_ty_tc__Nat__Onat,type,
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__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol,type,
produc2090907612on_val: $tType ).
thf(ty_ty_tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_J,type,
produc1645268488al_val: $tType ).
thf(ty_ty_tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__prod,type,
produc1282892786on_val: $tType ).
thf(ty_ty_tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc,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__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__Type__Oty_J_Mtc__prod_Itc__List__Olist_Itc_,type,
produc220283002t_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__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__001,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,
produc1350825965t_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__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 (274)
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_Exceptions_OClassCast,type,
classCast: list_char ).
thf(sy_c_Exceptions_ONullPointer,type,
nullPointer: list_char ).
thf(sy_c_Exceptions_Oaddr__of__sys__xcpt,type,
addr_of_sys_xcpt: list_char > nat ).
thf(sy_c_Expr_Obinop,type,
binop: produc1645268488al_val > option_val ).
thf(sy_c_Expr_Obop_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_OFAcc_000tc__List__Olist_Itc__String__Ochar_J,type,
fAcc_list_char: exp_list_char > list_char > list_char > exp_list_char ).
thf(sy_c_Expr_Oexp_OFAss_000tc__List__Olist_Itc__String__Ochar_J,type,
fAss_list_char: exp_list_char > list_char > list_char > exp_list_char > exp_list_char ).
thf(sy_c_Expr_Oexp_OLAss_000tc__List__Olist_Itc__String__Ochar_J,type,
lAss_list_char: list_char > exp_list_char > exp_list_char ).
thf(sy_c_Expr_Oexp_OSeq_000tc__List__Olist_Itc__String__Ochar_J,type,
seq_list_char: exp_list_char > exp_list_char > exp_list_char ).
thf(sy_c_Expr_Oexp_OTryCatch_000tc__List__Olist_Itc__String__Ochar_J,type,
tryCatch_list_char: exp_list_char > list_char > list_char > exp_list_char > exp_list_char ).
thf(sy_c_Expr_Oexp_OVal_000tc__List__Olist_Itc__String__Ochar_J,type,
val_list_char: val > exp_list_char ).
thf(sy_c_Expr_Oexp_OWhile_000tc__List__Olist_Itc__String__Ochar_J,type,
while_list_char: exp_list_char > exp_list_char > exp_list_char ).
thf(sy_c_Expr_Oexp_Othrow_000tc__List__Olist_Itc__String__Ochar_J,type,
throw_list_char: exp_list_char > exp_list_char ).
thf(sy_c_Fun_Ocomp_000tc__List__Olist_Itc__Option__Ooption_Itc__Value__Oval_J_J_000t,type,
comp_l1825390573t_char: ( list_option_val > list_val ) > ( list_list_char > list_option_val ) > list_list_char > list_val ).
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_002,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_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__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_,type,
list_a52822260ion_ty: ( exp_list_char > option_ty > $o ) > list_exp_list_char > list_option_ty > $o ).
thf(sy_c_List_Olist__all2_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Oop,type,
list_a1834344429ion_ty: ( list_char > option_ty > $o ) > list_list_char > list_option_ty > $o ).
thf(sy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Expr__Oexp_,type,
list_a283687028t_char: ( option_ty > exp_list_char > $o ) > list_option_ty > list_exp_list_char > $o ).
thf(sy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist,type,
list_a839443437t_char: ( option_ty > list_char > $o ) > list_option_ty > list_list_char > $o ).
thf(sy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Type__Oty,type,
list_a2039389316_ty_ty: ( option_ty > ty > $o ) > list_option_ty > list_ty > $o ).
thf(sy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Value__Oval,type,
list_a1073113293ty_val: ( option_ty > val > $o ) > list_option_ty > list_val > $o ).
thf(sy_c_List_Olist__all2_000tc__Type__Oty_000tc__Option__Ooption_Itc__Type__Oty_J,type,
list_a1880637950ion_ty: ( ty > option_ty > $o ) > list_ty > list_option_ty > $o ).
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_Olist__all2_000tc__Value__Oval_000tc__Option__Ooption_Itc__Type__Oty_J,type,
list_a1462908359ion_ty: ( val > option_ty > $o ) > list_val > list_option_ty > $o ).
thf(sy_c_List_Olist__all2_000tc__Value__Oval_000tc__Type__Oty,type,
list_all2_val_ty: ( val > ty > $o ) > list_val > list_ty > $o ).
thf(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__,type,
map_ex2109939687t_char: ( exp_list_char > list_char ) > list_exp_list_char > list_list_char ).
thf(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___003,type,
map_ex1548475405ion_ty: ( exp_list_char > option_ty ) > list_exp_list_char > list_option_ty ).
thf(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___004,type,
map_ex1598883030on_val: ( exp_list_char > option_val ) > list_exp_list_char > list_option_val ).
thf(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___005,type,
map_ex740158547ar_val: ( exp_list_char > val ) > list_exp_list_char > list_val ).
thf(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___006,type,
map_ex230966390t_char: ( exp_list_char > produc1278157519t_char ) > list_exp_list_char > list_P1916372464t_char ).
thf(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___007,type,
map_ex920537562on_val: ( exp_list_char > produc1746408499on_val ) > list_exp_list_char > list_P1964248404on_val ).
thf(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___008,type,
map_ex939917838on_val: ( exp_list_char > produc618524391on_val ) > list_exp_list_char > list_P1314671880on_val ).
thf(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__List__Olist_Itc__S,type,
map_li1333403488t_char: ( list_char > list_char ) > list_list_char > list_list_char ).
thf(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooption_It,type,
map_li771939206ion_ty: ( list_char > option_ty ) > list_list_char > list_option_ty ).
thf(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooption_It_009,type,
map_li50976719on_val: ( list_char > option_val ) > list_list_char > list_option_val ).
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__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__List__Ol,type,
map_li239070063t_char: ( list_char > produc1278157519t_char ) > list_list_char > list_P1916372464t_char ).
thf(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__prod_Itc,type,
map_li772299987on_val: ( list_char > produc1746408499on_val ) > list_list_char > list_P1964248404on_val ).
thf(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__prod_Itc_010,type,
map_li1565673351on_val: ( list_char > produc618524391on_val ) > list_list_char > list_P1314671880on_val ).
thf(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Expr__Oexp_Itc__Li,type,
map_op1779340173t_char: ( option_ty > exp_list_char ) > list_option_ty > list_exp_list_char ).
thf(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist_Itc__S,type,
map_op1924521862t_char: ( option_ty > list_char ) > list_option_ty > list_list_char ).
thf(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Option__Ooption_It,type,
map_op1363057580ion_ty: ( option_ty > option_ty ) > list_option_ty > list_option_ty ).
thf(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Type__Oty,type,
map_option_ty_ty: ( option_ty > ty ) > list_option_ty > list_ty ).
thf(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Value__Oval,type,
map_option_ty_val: ( option_ty > val ) > list_option_ty > list_val ).
thf(sy_c_List_Omap_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__Value__Oval,type,
map_option_val_val: ( option_val > val ) > list_option_val > list_val ).
thf(sy_c_List_Omap_000tc__Type__Oty_000tc__List__Olist_Itc__String__Ochar_J,type,
map_ty_list_char: ( ty > list_char ) > list_ty > list_list_char ).
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__Type__Oty_000tc__Option__Ooption_Itc__Value__Oval_J,type,
map_ty_option_val: ( ty > option_val ) > list_ty > list_option_val ).
thf(sy_c_List_Omap_000tc__Type__Oty_000tc__Value__Oval,type,
map_ty_val: ( ty > val ) > list_ty > list_val ).
thf(sy_c_List_Omap_000tc__Type__Oty_000tc__prod_Itc__List__Olist_Itc__String__Ochar_,type,
map_ty1751634702t_char: ( ty > produc1278157519t_char ) > list_ty > list_P1916372464t_char ).
thf(sy_c_List_Omap_000tc__Type__Oty_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List_,type,
map_ty908261490on_val: ( ty > produc1746408499on_val ) > list_ty > list_P1964248404on_val ).
thf(sy_c_List_Omap_000tc__Type__Oty_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr,type,
map_ty804687014on_val: ( ty > produc618524391on_val ) > list_ty > list_P1314671880on_val ).
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__List__Olist_Itc__String__Ochar_J,type,
map_val_list_char: ( val > list_char ) > list_val > list_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_Omap_000tc__Value__Oval_000tc__Option__Ooption_Itc__Value__Oval_J,type,
map_val_option_val: ( val > option_val ) > list_val > list_option_val ).
thf(sy_c_List_Omap_000tc__Value__Oval_000tc__Value__Oval,type,
map_val_val: ( val > val ) > list_val > list_val ).
thf(sy_c_List_Omap_000tc__Value__Oval_000tc__prod_Itc__List__Olist_Itc__String__Ocha,type,
map_va234578647t_char: ( val > produc1278157519t_char ) > list_val > list_P1916372464t_char ).
thf(sy_c_List_Omap_000tc__Value__Oval_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__Lis,type,
map_va32158779on_val: ( val > produc1746408499on_val ) > list_val > list_P1964248404on_val ).
thf(sy_c_List_Omap_000tc__Value__Oval_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Ex,type,
map_va426754799on_val: ( val > produc618524391on_val ) > list_val > list_P1314671880on_val ).
thf(sy_c_List_Omap_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olis,type,
map_Pr361633150t_char: ( produc1278157519t_char > produc1278157519t_char ) > list_P1916372464t_char > list_P1916372464t_char ).
thf(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
map_Pr816758342on_val: ( produc1746408499on_val > produc1746408499on_val ) > list_P1964248404on_val > list_P1964248404on_val ).
thf(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List_,type,
map_Pr1978321326on_val: ( produc618524391on_val > produc618524391on_val ) > list_P1314671880on_val > list_P1314671880on_val ).
thf(sy_c_List_Oset_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
set_exp_list_char: list_exp_list_char > exp_list_char > $o ).
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__Option__Ooption_Itc__Type__Oty_J,type,
set_option_ty: list_option_ty > option_ty > $o ).
thf(sy_c_List_Oset_000tc__Type__Oty,type,
set_ty: list_ty > ty > $o ).
thf(sy_c_List_Oset_000tc__Value__Oval,type,
set_val: list_val > val > $o ).
thf(sy_c_List_Oset_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olis,type,
set_Pr550895038t_char: list_P1916372464t_char > produc1278157519t_char > $o ).
thf(sy_c_List_Oset_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
set_Pr1184195362on_val: list_P1964248404on_val > produc1746408499on_val > $o ).
thf(sy_c_List_Oset_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List_,type,
set_Pr333999958on_val: list_P1314671880on_val > produc618524391on_val > $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__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_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__Option__Ooption_Itc__Type__O,type,
size_s1050794909ion_ty: list_option_ty > nat ).
thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Option__Ooption_Itc__Value__,type,
size_s1595297126on_val: list_option_val > 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_Nat_Osize__class_Osize_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__S,type,
size_s1010401542t_char: list_P1916372464t_char > nat ).
thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__prod_Itc__prod_Itc__Expr__Oe,type,
size_s350851178on_val: list_P1964248404on_val > nat ).
thf(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__prod_Itc__prod_Itc__List__Ol,type,
size_s658972446on_val: list_P1314671880on_val > nat ).
thf(sy_c_Objects_Ohext,type,
hext: ( nat > option1728594148on_val ) > ( nat > option1728594148on_val ) > $o ).
thf(sy_c_Objects_Otypeof__h,type,
typeof_h: ( nat > option1728594148on_val ) > val > option_ty ).
thf(sy_c_Option_Ooption_OSome_000tc__Type__Oty,type,
some_ty: ty > option_ty ).
thf(sy_c_Option_Ooption_OSome_000tc__Value__Oval,type,
some_val: val > option_val ).
thf(sy_c_Option_Ooption_OSome_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_06,type,
some_P451527732on_val: produc2088785539on_val > option1728594148on_val ).
thf(sy_c_Option_Othe_000tc__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_Product__Type_OPair_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_I,type,
produc755559506on_val: ( nat > option1728594148on_val ) > ( list_char > option_val ) > produc2090907612on_val ).
thf(sy_c_Product__Type_OPair_000tc__Expr__Obop_000tc__prod_Itc__Value__Oval_Mtc__Val,type,
produc621191550al_val: bop > product_prod_val_val > produc1645268488al_val ).
thf(sy_c_Product__Type_OPair_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J,type,
produc235638504on_val: exp_list_char > produc2090907612on_val > produc1282892786on_val ).
thf(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc,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__011,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__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__Value__Oval_J_000tc__Expr__Oexp,type,
produc1916172923t_char: list_val > exp_list_char > produc662261637t_char ).
thf(sy_c_Product__Type_OPair_000tc__Value__Oval_000tc__Value__Oval,type,
product_Pair_val_val: val > val > product_prod_val_val ).
thf(sy_c_Product__Type_OPair_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_I,type,
produc259392253on_val: produc2090907612on_val > produc2090907612on_val > produc1581780743on_val ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_,type,
produc1924279125al_val: produc1645268488al_val > produc1645268488al_val > produc630464863al_val ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
produc833389609on_val: produc1282892786on_val > produc1282892786on_val > produc1746408499on_val ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List_,type,
produc747700183on_val: produc1180562163on_val > produc1180562163on_val > produc618524391on_val ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri,type,
produc1897818327t_char: produc809539159t_char > produc809539159t_char > produc1534059751t_char ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri_012,type,
produc24551831t_char: produc1285161482t_char > produc1285161482t_char > produc349695911t_char ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_062,type,
produc1773146955on_val: produc2088785539on_val > produc2088785539on_val > produc1368416213on_val ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__,type,
produc2080520419t_char: produc1278157519t_char > produc1278157519t_char > produc1350825965t_char ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod,type,
produc57279289t_char: produc220283002t_char > produc220283002t_char > produc1406897475t_char ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Ex,type,
produc1299387215t_char: produc662261637t_char > produc662261637t_char > produc1826280281t_char ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__,type,
produc1244920211al_val: product_prod_val_val > product_prod_val_val > produc800118557al_val ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_,type,
produc345758123on_val: produc1746408499on_val > produc1746408499on_val > produc652964533on_val ).
thf(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_,type,
produc1347028499on_val: produc618524391on_val > produc618524391on_val > produc1250491293on_val ).
thf(sy_c_Product__Type_Ocurry_000_062_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_,type,
produc1402621651_val_o: ( produc2090907612on_val > $o ) > ( nat > option1728594148on_val ) > ( list_char > option_val ) > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__Expr__Obop_000tc__prod_Itc__Value__Oval_Mtc__Va,type,
produc275195559_val_o: ( produc1645268488al_val > $o ) > bop > product_prod_val_val > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_,type,
produc1287763389_val_o: ( produc1282892786on_val > $o ) > exp_list_char > produc2090907612on_val > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_It,type,
produc618849246_val_o: ( produc1180562163on_val > $o ) > list_exp_list_char > produc2090907612on_val > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar,type,
produc1404278138char_o: ( produc809539159t_char > $o ) > list_list_char > exp_list_char > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_013,type,
produc193646727char_o: ( produc1285161482t_char > $o ) > list_list_char > produc220283002t_char > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__String__Ochar_J_000_062_Itc__p,type,
produc1177570924_val_o: ( produc2088785539on_val > $o ) > list_char > ( produc1278157519t_char > option_val ) > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__String__Ochar_J_000tc__List__O,type,
produc1709467424char_o: ( produc1278157519t_char > $o ) > list_char > list_char > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Type__Oty_J_000tc__prod_Itc__L,type,
produc786676533char_o: ( produc220283002t_char > $o ) > list_ty > produc662261637t_char > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Value__Oval_J_000tc__Expr__Oex,type,
produc1072551658char_o: ( produc662261637t_char > $o ) > list_val > exp_list_char > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__Value__Oval_000tc__Value__Oval_000_Eo,type,
produc575837646_val_o: ( product_prod_val_val > $o ) > val > val > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__Ooption_,type,
produc1959713768_val_o: ( produc1581780743on_val > $o ) > produc2090907612on_val > produc2090907612on_val > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval,type,
produc1498697104_val_o: ( produc630464863al_val > $o ) > produc1645268488al_val > produc1645268488al_val > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Stri,type,
produc803302844_val_o: ( produc1746408499on_val > $o ) > produc1282892786on_val > produc1282892786on_val > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List,type,
produc551782158_val_o: ( produc618524391on_val > $o ) > produc1180562163on_val > produc1180562163on_val > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Str,type,
produc810272782char_o: ( produc1534059751t_char > $o ) > produc809539159t_char > produc809539159t_char > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Str_014,type,
produc261176398char_o: ( produc349695911t_char > $o ) > produc1285161482t_char > produc1285161482t_char > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_M_06,type,
produc1333173274_val_o: ( produc1368416213on_val > $o ) > produc2088785539on_val > produc2088785539on_val > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_,type,
produc1255505282char_o: ( produc1350825965t_char > $o ) > produc1278157519t_char > produc1278157519t_char > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__pro,type,
produc1560057516char_o: ( produc1406897475t_char > $o ) > produc220283002t_char > produc220283002t_char > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__E,type,
produc1625470998char_o: ( produc1826280281t_char > $o ) > produc662261637t_char > produc662261637t_char > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc_,type,
produc1669808594_val_o: ( produc800118557al_val > $o ) > product_prod_val_val > product_prod_val_val > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist,type,
produc1882616506_val_o: ( produc652964533on_val > $o ) > produc1746408499on_val > produc1746408499on_val > $o ).
thf(sy_c_Product__Type_Ocurry_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp,type,
produc317637970_val_o: ( produc1250491293on_val > $o ) > produc618524391on_val > produc618524391on_val > $o ).
thf(sy_c_SmallStep_Oblocks,type,
blocks: produc1285161482t_char > exp_list_char ).
thf(sy_c_SmallStep_Ored,type,
red: list_P1999446415t_char > produc1746408499on_val > $o ).
thf(sy_c_SmallStep_Oredp,type,
redp: list_P1999446415t_char > exp_list_char > produc2090907612on_val > exp_list_char > produc2090907612on_val > $o ).
thf(sy_c_SmallStep_Oreds,type,
reds: list_P1999446415t_char > produc618524391on_val > $o ).
thf(sy_c_SmallStep_Oredsp,type,
redsp: list_P1999446415t_char > list_exp_list_char > produc2090907612on_val > list_exp_list_char > produc2090907612on_val > $o ).
thf(sy_c_State_Ohp,type,
hp: produc2090907612on_val > nat > option1728594148on_val ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__List__Olist_Itc__String__Ochar_J,type,
transi1395422419t_char: ( produc1278157519t_char > $o ) > produc1278157519t_char > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__Value__Oval,type,
transi935034983cl_val: ( product_prod_val_val > $o ) > product_prod_val_val > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_I_062_Itc__Nat__Onat_Mtc__Option__,type,
transi466770671on_val: ( produc1581780743on_val > $o ) > produc1581780743on_val > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Val,type,
transi1906258203al_val: ( produc630464863al_val > $o ) > produc630464863al_val > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_I,type,
transi2118771717on_val: ( produc1746408499on_val > $o ) > produc1746408499on_val > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_I,type,
transi808828192on_val: ( produc618524391on_val > $o ) > produc618524391on_val > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__List__Olist_,type,
transi198989188t_char: ( produc1534059751t_char > $o ) > produc1534059751t_char > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__List__Olist__015,type,
transi122195895t_char: ( produc349695911t_char > $o ) > produc349695911t_char > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__String__Ocha,type,
transi1669211542on_val: ( produc1368416213on_val > $o ) > produc1368416213on_val > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__String__Ocha_016,type,
transi1095029602t_char: ( produc1350825965t_char > $o ) > produc1350825965t_char > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_,type,
transi1257872013t_char: ( produc1406897475t_char > $o ) > produc1406897475t_char > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__Value__Oval_,type,
transi1789604888t_char: ( produc1826280281t_char > $o ) > produc1826280281t_char > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_,type,
transi1423755450al_val: ( produc800118557al_val > $o ) > produc800118557al_val > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__Lis,type,
transi130214086on_val: ( produc652964533on_val > $o ) > produc652964533on_val > $o ).
thf(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Ex,type,
transi1457397498on_val: ( produc1250491293on_val > $o ) > produc1250491293on_val > $o ).
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_Osubcls1_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String_,type,
subcls851966956t_char: list_P1999446415t_char > produc1278157519t_char > $o ).
thf(sy_c_TypeRel_Owiden_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
widen_2090681816t_char: list_P1999446415t_char > ty > ty > $o ).
thf(sy_c_TypeSafe__Mirabelle__xxsvwfzwam_Osconf,type,
typeSa1102574168_sconf: list_P1999446415t_char > ( list_char > option_ty ) > produc2090907612on_val > $o ).
thf(sy_c_Type_Ois__refT,type,
is_refT: ty > $o ).
thf(sy_c_Type_Othis,type,
this: list_char ).
thf(sy_c_Type_Oty_OClass,type,
class: list_char > ty ).
thf(sy_c_Value_Odefault__val,type,
default_val: ty > val ).
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_WellTypeRT_OWTrt,type,
wTrt: list_P1999446415t_char > ( nat > option1728594148on_val ) > ( list_char > option_ty ) > exp_list_char > ty > $o ).
thf(sy_c_WellTypeRT_OWTrts,type,
wTrts: list_P1999446415t_char > ( nat > option1728594148on_val ) > ( list_char > option_ty ) > list_exp_list_char > list_ty > $o ).
thf(sy_c_fequal_000tc__Type__Oty,type,
fequal_ty: ty > ty > $o ).
thf(sy_c_member_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
member_exp_list_char: exp_list_char > ( exp_list_char > $o ) > $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__Option__Ooption_Itc__Type__Oty_J,type,
member_option_ty: option_ty > ( option_ty > $o ) > $o ).
thf(sy_c_member_000tc__Type__Oty,type,
member_ty: ty > ( ty > $o ) > $o ).
thf(sy_c_member_000tc__Value__Oval,type,
member_val: val > ( val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_I,type,
member1251428284t_char: produc1278157519t_char > ( produc1278157519t_char > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J,type,
member649088532al_val: product_prod_val_val > ( product_prod_val_val > $o ) > $o ).
thf(sy_c_member_000tc__prod_Itc__prod_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__017,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__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__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_1: list_char > option_ty ).
thf(sy_v_P,type,
p: list_P1999446415t_char ).
thf(sy_v_T,type,
t: ty ).
thf(sy_v_Ts,type,
ts: list_ty ).
thf(sy_v_Vs,type,
vs_1: list_list_char ).
thf(sy_v_e,type,
e: exp_list_char ).
thf(sy_v_h,type,
h: nat > option1728594148on_val ).
thf(sy_v_vs,type,
vs: list_val ).
%----Relevant facts (700)
thf(fact_0_widens__refl,axiom,
! [P: list_P1999446415t_char,Xs_16: list_ty] : ( list_all2_ty_ty @ ( widen_2090681816t_char @ P ) @ Xs_16 @ Xs_16 ) ).
thf(fact_1_widen__refl,axiom,
! [P_28: list_P1999446415t_char,T_12: ty] : ( widen_2090681816t_char @ P_28 @ T_12 @ T_12 ) ).
thf(fact_2_widens__trans,axiom,
! [Us: list_ty,P_27: list_P1999446415t_char,Ss: list_ty,Ts_8: list_ty] :
( ( list_all2_ty_ty @ ( widen_2090681816t_char @ P_27 ) @ Ss @ Ts_8 )
=> ( ( list_all2_ty_ty @ ( widen_2090681816t_char @ P_27 ) @ Ts_8 @ Us )
=> ( list_all2_ty_ty @ ( widen_2090681816t_char @ P_27 ) @ Ss @ Us ) ) ) ).
thf(fact_3_list__all2__lengthD,axiom,
! [P_26: list_char > option_ty > $o,Xs_15: list_list_char,Ys_10: list_option_ty] :
( ( list_a1834344429ion_ty @ P_26 @ Xs_15 @ Ys_10 )
=> ( ( size_s2113983095t_char @ Xs_15 )
= ( size_s1050794909ion_ty @ Ys_10 ) ) ) ).
thf(fact_4_list__all2__lengthD,axiom,
! [P_26: ty > option_ty > $o,Xs_15: list_ty,Ys_10: list_option_ty] :
( ( list_a1880637950ion_ty @ P_26 @ Xs_15 @ Ys_10 )
=> ( ( size_size_list_ty @ Xs_15 )
= ( size_s1050794909ion_ty @ Ys_10 ) ) ) ).
thf(fact_5_list__all2__lengthD,axiom,
! [P_26: val > option_ty > $o,Xs_15: list_val,Ys_10: list_option_ty] :
( ( list_a1462908359ion_ty @ P_26 @ Xs_15 @ Ys_10 )
=> ( ( size_size_list_val @ Xs_15 )
= ( size_s1050794909ion_ty @ Ys_10 ) ) ) ).
thf(fact_6_list__all2__lengthD,axiom,
! [P_26: exp_list_char > option_ty > $o,Xs_15: list_exp_list_char,Ys_10: list_option_ty] :
( ( list_a52822260ion_ty @ P_26 @ Xs_15 @ Ys_10 )
=> ( ( size_s1143674878t_char @ Xs_15 )
= ( size_s1050794909ion_ty @ Ys_10 ) ) ) ).
thf(fact_7_list__all2__lengthD,axiom,
! [P_26: option_ty > list_char > $o,Xs_15: list_option_ty,Ys_10: list_list_char] :
( ( list_a839443437t_char @ P_26 @ Xs_15 @ Ys_10 )
=> ( ( size_s1050794909ion_ty @ Xs_15 )
= ( size_s2113983095t_char @ Ys_10 ) ) ) ).
thf(fact_8_list__all2__lengthD,axiom,
! [P_26: option_ty > ty > $o,Xs_15: list_option_ty,Ys_10: list_ty] :
( ( list_a2039389316_ty_ty @ P_26 @ Xs_15 @ Ys_10 )
=> ( ( size_s1050794909ion_ty @ Xs_15 )
= ( size_size_list_ty @ Ys_10 ) ) ) ).
thf(fact_9_list__all2__lengthD,axiom,
! [P_26: option_ty > val > $o,Xs_15: list_option_ty,Ys_10: list_val] :
( ( list_a1073113293ty_val @ P_26 @ Xs_15 @ Ys_10 )
=> ( ( size_s1050794909ion_ty @ Xs_15 )
= ( size_size_list_val @ Ys_10 ) ) ) ).
thf(fact_10_list__all2__lengthD,axiom,
! [P_26: option_ty > exp_list_char > $o,Xs_15: list_option_ty,Ys_10: list_exp_list_char] :
( ( list_a283687028t_char @ P_26 @ Xs_15 @ Ys_10 )
=> ( ( size_s1050794909ion_ty @ Xs_15 )
= ( size_s1143674878t_char @ Ys_10 ) ) ) ).
thf(fact_11_list__all2__lengthD,axiom,
! [P_26: ty > ty > $o,Xs_15: list_ty,Ys_10: list_ty] :
( ( list_all2_ty_ty @ P_26 @ Xs_15 @ Ys_10 )
=> ( ( size_size_list_ty @ Xs_15 )
= ( size_size_list_ty @ Ys_10 ) ) ) ).
thf(fact_12_list__all2__lengthD,axiom,
! [P_26: val > ty > $o,Xs_15: list_val,Ys_10: list_ty] :
( ( list_all2_val_ty @ P_26 @ Xs_15 @ Ys_10 )
=> ( ( size_size_list_val @ Xs_15 )
= ( size_size_list_ty @ Ys_10 ) ) ) ).
thf(fact_13_length__map,axiom,
! [F_15: produc1278157519t_char > produc1278157519t_char,Xs_14: list_P1916372464t_char] :
( ( size_s1010401542t_char @ ( map_Pr361633150t_char @ F_15 @ Xs_14 ) )
= ( size_s1010401542t_char @ Xs_14 ) ) ).
thf(fact_14_length__map,axiom,
! [F_15: produc618524391on_val > produc618524391on_val,Xs_14: list_P1314671880on_val] :
( ( size_s658972446on_val @ ( map_Pr1978321326on_val @ F_15 @ Xs_14 ) )
= ( size_s658972446on_val @ Xs_14 ) ) ).
thf(fact_15_length__map,axiom,
! [F_15: produc1746408499on_val > produc1746408499on_val,Xs_14: list_P1964248404on_val] :
( ( size_s350851178on_val @ ( map_Pr816758342on_val @ F_15 @ Xs_14 ) )
= ( size_s350851178on_val @ Xs_14 ) ) ).
thf(fact_16_length__map,axiom,
! [F_15: option_ty > list_char,Xs_14: list_option_ty] :
( ( size_s2113983095t_char @ ( map_op1924521862t_char @ F_15 @ Xs_14 ) )
= ( size_s1050794909ion_ty @ Xs_14 ) ) ).
thf(fact_17_length__map,axiom,
! [F_15: option_ty > ty,Xs_14: list_option_ty] :
( ( size_size_list_ty @ ( map_option_ty_ty @ F_15 @ Xs_14 ) )
= ( size_s1050794909ion_ty @ Xs_14 ) ) ).
thf(fact_18_length__map,axiom,
! [F_15: option_val > val,Xs_14: list_option_val] :
( ( size_size_list_val @ ( map_option_val_val @ F_15 @ Xs_14 ) )
= ( size_s1595297126on_val @ Xs_14 ) ) ).
thf(fact_19_length__map,axiom,
! [F_15: option_ty > val,Xs_14: list_option_ty] :
( ( size_size_list_val @ ( map_option_ty_val @ F_15 @ Xs_14 ) )
= ( size_s1050794909ion_ty @ Xs_14 ) ) ).
thf(fact_20_length__map,axiom,
! [F_15: option_ty > exp_list_char,Xs_14: list_option_ty] :
( ( size_s1143674878t_char @ ( map_op1779340173t_char @ F_15 @ Xs_14 ) )
= ( size_s1050794909ion_ty @ Xs_14 ) ) ).
thf(fact_21_length__map,axiom,
! [F_15: list_char > option_val,Xs_14: list_list_char] :
( ( size_s1595297126on_val @ ( map_li50976719on_val @ F_15 @ Xs_14 ) )
= ( size_s2113983095t_char @ Xs_14 ) ) ).
thf(fact_22_length__map,axiom,
! [F_15: list_char > list_char,Xs_14: list_list_char] :
( ( size_s2113983095t_char @ ( map_li1333403488t_char @ F_15 @ Xs_14 ) )
= ( size_s2113983095t_char @ Xs_14 ) ) ).
thf(fact_23_length__map,axiom,
! [F_15: list_char > option_ty,Xs_14: list_list_char] :
( ( size_s1050794909ion_ty @ ( map_li771939206ion_ty @ F_15 @ Xs_14 ) )
= ( size_s2113983095t_char @ Xs_14 ) ) ).
thf(fact_24_length__map,axiom,
! [F_15: exp_list_char > option_ty,Xs_14: list_exp_list_char] :
( ( size_s1050794909ion_ty @ ( map_ex1548475405ion_ty @ F_15 @ Xs_14 ) )
= ( size_s1143674878t_char @ Xs_14 ) ) ).
thf(fact_25_length__map,axiom,
! [F_15: val > option_ty,Xs_14: list_val] :
( ( size_s1050794909ion_ty @ ( map_val_option_ty @ F_15 @ Xs_14 ) )
= ( size_size_list_val @ Xs_14 ) ) ).
thf(fact_26_length__map,axiom,
! [F_15: ty > option_ty,Xs_14: list_ty] :
( ( size_s1050794909ion_ty @ ( map_ty_option_ty @ F_15 @ Xs_14 ) )
= ( size_size_list_ty @ Xs_14 ) ) ).
thf(fact_27_length__map,axiom,
! [F_15: val > exp_list_char,Xs_14: list_val] :
( ( size_s1143674878t_char @ ( map_va1934808527t_char @ F_15 @ Xs_14 ) )
= ( size_size_list_val @ Xs_14 ) ) ).
thf(fact_28_length__map,axiom,
! [F_15: list_char > val,Xs_14: list_list_char] :
( ( size_size_list_val @ ( map_list_char_val @ F_15 @ Xs_14 ) )
= ( size_s2113983095t_char @ Xs_14 ) ) ).
thf(fact_29_map__eq__imp__length__eq,axiom,
! [F_14: list_char > produc1278157519t_char,Xs_13: list_list_char,G_7: produc1278157519t_char > produc1278157519t_char,Ys_9: list_P1916372464t_char] :
( ( ( map_li239070063t_char @ F_14 @ Xs_13 )
= ( map_Pr361633150t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s1010401542t_char @ Ys_9 ) ) ) ).
thf(fact_30_map__eq__imp__length__eq,axiom,
! [F_14: list_char > produc618524391on_val,Xs_13: list_list_char,G_7: produc618524391on_val > produc618524391on_val,Ys_9: list_P1314671880on_val] :
( ( ( map_li1565673351on_val @ F_14 @ Xs_13 )
= ( map_Pr1978321326on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s658972446on_val @ Ys_9 ) ) ) ).
thf(fact_31_map__eq__imp__length__eq,axiom,
! [F_14: list_char > produc1746408499on_val,Xs_13: list_list_char,G_7: produc1746408499on_val > produc1746408499on_val,Ys_9: list_P1964248404on_val] :
( ( ( map_li772299987on_val @ F_14 @ Xs_13 )
= ( map_Pr816758342on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s350851178on_val @ Ys_9 ) ) ) ).
thf(fact_32_map__eq__imp__length__eq,axiom,
! [F_14: ty > val,Xs_13: list_ty,G_7: option_val > val,Ys_9: list_option_val] :
( ( ( map_ty_val @ F_14 @ Xs_13 )
= ( map_option_val_val @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_ty @ Xs_13 )
= ( size_s1595297126on_val @ Ys_9 ) ) ) ).
thf(fact_33_map__eq__imp__length__eq,axiom,
! [F_14: ty > option_val,Xs_13: list_ty,G_7: list_char > option_val,Ys_9: list_list_char] :
( ( ( map_ty_option_val @ F_14 @ Xs_13 )
= ( map_li50976719on_val @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_ty @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_34_map__eq__imp__length__eq,axiom,
! [F_14: ty > list_char,Xs_13: list_ty,G_7: list_char > list_char,Ys_9: list_list_char] :
( ( ( map_ty_list_char @ F_14 @ Xs_13 )
= ( map_li1333403488t_char @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_ty @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_35_map__eq__imp__length__eq,axiom,
! [F_14: ty > produc1278157519t_char,Xs_13: list_ty,G_7: produc1278157519t_char > produc1278157519t_char,Ys_9: list_P1916372464t_char] :
( ( ( map_ty1751634702t_char @ F_14 @ Xs_13 )
= ( map_Pr361633150t_char @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_ty @ Xs_13 )
= ( size_s1010401542t_char @ Ys_9 ) ) ) ).
thf(fact_36_map__eq__imp__length__eq,axiom,
! [F_14: ty > produc618524391on_val,Xs_13: list_ty,G_7: produc618524391on_val > produc618524391on_val,Ys_9: list_P1314671880on_val] :
( ( ( map_ty804687014on_val @ F_14 @ Xs_13 )
= ( map_Pr1978321326on_val @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_ty @ Xs_13 )
= ( size_s658972446on_val @ Ys_9 ) ) ) ).
thf(fact_37_map__eq__imp__length__eq,axiom,
! [F_14: ty > produc1746408499on_val,Xs_13: list_ty,G_7: produc1746408499on_val > produc1746408499on_val,Ys_9: list_P1964248404on_val] :
( ( ( map_ty908261490on_val @ F_14 @ Xs_13 )
= ( map_Pr816758342on_val @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_ty @ Xs_13 )
= ( size_s350851178on_val @ Ys_9 ) ) ) ).
thf(fact_38_map__eq__imp__length__eq,axiom,
! [F_14: val > val,Xs_13: list_val,G_7: option_val > val,Ys_9: list_option_val] :
( ( ( map_val_val @ F_14 @ Xs_13 )
= ( map_option_val_val @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s1595297126on_val @ Ys_9 ) ) ) ).
thf(fact_39_map__eq__imp__length__eq,axiom,
! [F_14: val > option_val,Xs_13: list_val,G_7: list_char > option_val,Ys_9: list_list_char] :
( ( ( map_val_option_val @ F_14 @ Xs_13 )
= ( map_li50976719on_val @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_40_map__eq__imp__length__eq,axiom,
! [F_14: val > list_char,Xs_13: list_val,G_7: list_char > list_char,Ys_9: list_list_char] :
( ( ( map_val_list_char @ F_14 @ Xs_13 )
= ( map_li1333403488t_char @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_41_map__eq__imp__length__eq,axiom,
! [F_14: val > produc1278157519t_char,Xs_13: list_val,G_7: produc1278157519t_char > produc1278157519t_char,Ys_9: list_P1916372464t_char] :
( ( ( map_va234578647t_char @ F_14 @ Xs_13 )
= ( map_Pr361633150t_char @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s1010401542t_char @ Ys_9 ) ) ) ).
thf(fact_42_map__eq__imp__length__eq,axiom,
! [F_14: val > produc618524391on_val,Xs_13: list_val,G_7: produc618524391on_val > produc618524391on_val,Ys_9: list_P1314671880on_val] :
( ( ( map_va426754799on_val @ F_14 @ Xs_13 )
= ( map_Pr1978321326on_val @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s658972446on_val @ Ys_9 ) ) ) ).
thf(fact_43_map__eq__imp__length__eq,axiom,
! [F_14: val > produc1746408499on_val,Xs_13: list_val,G_7: produc1746408499on_val > produc1746408499on_val,Ys_9: list_P1964248404on_val] :
( ( ( map_va32158779on_val @ F_14 @ Xs_13 )
= ( map_Pr816758342on_val @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s350851178on_val @ Ys_9 ) ) ) ).
thf(fact_44_map__eq__imp__length__eq,axiom,
! [F_14: exp_list_char > val,Xs_13: list_exp_list_char,G_7: option_val > val,Ys_9: list_option_val] :
( ( ( map_ex740158547ar_val @ F_14 @ Xs_13 )
= ( map_option_val_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_s1595297126on_val @ Ys_9 ) ) ) ).
thf(fact_45_map__eq__imp__length__eq,axiom,
! [F_14: exp_list_char > option_val,Xs_13: list_exp_list_char,G_7: list_char > option_val,Ys_9: list_list_char] :
( ( ( map_ex1598883030on_val @ F_14 @ Xs_13 )
= ( map_li50976719on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_46_map__eq__imp__length__eq,axiom,
! [F_14: exp_list_char > list_char,Xs_13: list_exp_list_char,G_7: list_char > list_char,Ys_9: list_list_char] :
( ( ( map_ex2109939687t_char @ F_14 @ Xs_13 )
= ( map_li1333403488t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_47_map__eq__imp__length__eq,axiom,
! [F_14: exp_list_char > produc1278157519t_char,Xs_13: list_exp_list_char,G_7: produc1278157519t_char > produc1278157519t_char,Ys_9: list_P1916372464t_char] :
( ( ( map_ex230966390t_char @ F_14 @ Xs_13 )
= ( map_Pr361633150t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_s1010401542t_char @ Ys_9 ) ) ) ).
thf(fact_48_map__eq__imp__length__eq,axiom,
! [F_14: exp_list_char > produc618524391on_val,Xs_13: list_exp_list_char,G_7: produc618524391on_val > produc618524391on_val,Ys_9: list_P1314671880on_val] :
( ( ( map_ex939917838on_val @ F_14 @ Xs_13 )
= ( map_Pr1978321326on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_s658972446on_val @ Ys_9 ) ) ) ).
thf(fact_49_map__eq__imp__length__eq,axiom,
! [F_14: exp_list_char > produc1746408499on_val,Xs_13: list_exp_list_char,G_7: produc1746408499on_val > produc1746408499on_val,Ys_9: list_P1964248404on_val] :
( ( ( map_ex920537562on_val @ F_14 @ Xs_13 )
= ( map_Pr816758342on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1143674878t_char @ Xs_13 )
= ( size_s350851178on_val @ Ys_9 ) ) ) ).
thf(fact_50_map__eq__imp__length__eq,axiom,
! [F_14: list_char > option_val,Xs_13: list_list_char,G_7: list_char > option_val,Ys_9: list_list_char] :
( ( ( map_li50976719on_val @ F_14 @ Xs_13 )
= ( map_li50976719on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_51_map__eq__imp__length__eq,axiom,
! [F_14: list_char > list_char,Xs_13: list_list_char,G_7: list_char > list_char,Ys_9: list_list_char] :
( ( ( map_li1333403488t_char @ F_14 @ Xs_13 )
= ( map_li1333403488t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_52_map__eq__imp__length__eq,axiom,
! [F_14: produc1278157519t_char > produc1278157519t_char,Xs_13: list_P1916372464t_char,G_7: list_char > produc1278157519t_char,Ys_9: list_list_char] :
( ( ( map_Pr361633150t_char @ F_14 @ Xs_13 )
= ( map_li239070063t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s1010401542t_char @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_53_map__eq__imp__length__eq,axiom,
! [F_14: produc618524391on_val > produc618524391on_val,Xs_13: list_P1314671880on_val,G_7: list_char > produc618524391on_val,Ys_9: list_list_char] :
( ( ( map_Pr1978321326on_val @ F_14 @ Xs_13 )
= ( map_li1565673351on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s658972446on_val @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_54_map__eq__imp__length__eq,axiom,
! [F_14: produc1746408499on_val > produc1746408499on_val,Xs_13: list_P1964248404on_val,G_7: list_char > produc1746408499on_val,Ys_9: list_list_char] :
( ( ( map_Pr816758342on_val @ F_14 @ Xs_13 )
= ( map_li772299987on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s350851178on_val @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_55_map__eq__imp__length__eq,axiom,
! [F_14: option_val > val,Xs_13: list_option_val,G_7: ty > val,Ys_9: list_ty] :
( ( ( map_option_val_val @ F_14 @ Xs_13 )
= ( map_ty_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1595297126on_val @ Xs_13 )
= ( size_size_list_ty @ Ys_9 ) ) ) ).
thf(fact_56_map__eq__imp__length__eq,axiom,
! [F_14: list_char > option_val,Xs_13: list_list_char,G_7: ty > option_val,Ys_9: list_ty] :
( ( ( map_li50976719on_val @ F_14 @ Xs_13 )
= ( map_ty_option_val @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_size_list_ty @ Ys_9 ) ) ) ).
thf(fact_57_map__eq__imp__length__eq,axiom,
! [F_14: list_char > list_char,Xs_13: list_list_char,G_7: ty > list_char,Ys_9: list_ty] :
( ( ( map_li1333403488t_char @ F_14 @ Xs_13 )
= ( map_ty_list_char @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_size_list_ty @ Ys_9 ) ) ) ).
thf(fact_58_map__eq__imp__length__eq,axiom,
! [F_14: produc1278157519t_char > produc1278157519t_char,Xs_13: list_P1916372464t_char,G_7: ty > produc1278157519t_char,Ys_9: list_ty] :
( ( ( map_Pr361633150t_char @ F_14 @ Xs_13 )
= ( map_ty1751634702t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s1010401542t_char @ Xs_13 )
= ( size_size_list_ty @ Ys_9 ) ) ) ).
thf(fact_59_map__eq__imp__length__eq,axiom,
! [F_14: produc618524391on_val > produc618524391on_val,Xs_13: list_P1314671880on_val,G_7: ty > produc618524391on_val,Ys_9: list_ty] :
( ( ( map_Pr1978321326on_val @ F_14 @ Xs_13 )
= ( map_ty804687014on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s658972446on_val @ Xs_13 )
= ( size_size_list_ty @ Ys_9 ) ) ) ).
thf(fact_60_map__eq__imp__length__eq,axiom,
! [F_14: produc1746408499on_val > produc1746408499on_val,Xs_13: list_P1964248404on_val,G_7: ty > produc1746408499on_val,Ys_9: list_ty] :
( ( ( map_Pr816758342on_val @ F_14 @ Xs_13 )
= ( map_ty908261490on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s350851178on_val @ Xs_13 )
= ( size_size_list_ty @ Ys_9 ) ) ) ).
thf(fact_61_map__eq__imp__length__eq,axiom,
! [F_14: option_val > val,Xs_13: list_option_val,G_7: val > val,Ys_9: list_val] :
( ( ( map_option_val_val @ F_14 @ Xs_13 )
= ( map_val_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1595297126on_val @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_62_map__eq__imp__length__eq,axiom,
! [F_14: list_char > option_val,Xs_13: list_list_char,G_7: val > option_val,Ys_9: list_val] :
( ( ( map_li50976719on_val @ F_14 @ Xs_13 )
= ( map_val_option_val @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_63_map__eq__imp__length__eq,axiom,
! [F_14: list_char > list_char,Xs_13: list_list_char,G_7: val > list_char,Ys_9: list_val] :
( ( ( map_li1333403488t_char @ F_14 @ Xs_13 )
= ( map_val_list_char @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_64_map__eq__imp__length__eq,axiom,
! [F_14: produc1278157519t_char > produc1278157519t_char,Xs_13: list_P1916372464t_char,G_7: val > produc1278157519t_char,Ys_9: list_val] :
( ( ( map_Pr361633150t_char @ F_14 @ Xs_13 )
= ( map_va234578647t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s1010401542t_char @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_65_map__eq__imp__length__eq,axiom,
! [F_14: produc618524391on_val > produc618524391on_val,Xs_13: list_P1314671880on_val,G_7: val > produc618524391on_val,Ys_9: list_val] :
( ( ( map_Pr1978321326on_val @ F_14 @ Xs_13 )
= ( map_va426754799on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s658972446on_val @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_66_map__eq__imp__length__eq,axiom,
! [F_14: produc1746408499on_val > produc1746408499on_val,Xs_13: list_P1964248404on_val,G_7: val > produc1746408499on_val,Ys_9: list_val] :
( ( ( map_Pr816758342on_val @ F_14 @ Xs_13 )
= ( map_va32158779on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s350851178on_val @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_67_map__eq__imp__length__eq,axiom,
! [F_14: option_val > val,Xs_13: list_option_val,G_7: exp_list_char > val,Ys_9: list_exp_list_char] :
( ( ( map_option_val_val @ F_14 @ Xs_13 )
= ( map_ex740158547ar_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1595297126on_val @ Xs_13 )
= ( size_s1143674878t_char @ Ys_9 ) ) ) ).
thf(fact_68_map__eq__imp__length__eq,axiom,
! [F_14: list_char > option_val,Xs_13: list_list_char,G_7: exp_list_char > option_val,Ys_9: list_exp_list_char] :
( ( ( map_li50976719on_val @ F_14 @ Xs_13 )
= ( map_ex1598883030on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s1143674878t_char @ Ys_9 ) ) ) ).
thf(fact_69_map__eq__imp__length__eq,axiom,
! [F_14: list_char > list_char,Xs_13: list_list_char,G_7: exp_list_char > list_char,Ys_9: list_exp_list_char] :
( ( ( map_li1333403488t_char @ F_14 @ Xs_13 )
= ( map_ex2109939687t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s1143674878t_char @ Ys_9 ) ) ) ).
thf(fact_70_map__eq__imp__length__eq,axiom,
! [F_14: produc1278157519t_char > produc1278157519t_char,Xs_13: list_P1916372464t_char,G_7: exp_list_char > produc1278157519t_char,Ys_9: list_exp_list_char] :
( ( ( map_Pr361633150t_char @ F_14 @ Xs_13 )
= ( map_ex230966390t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s1010401542t_char @ Xs_13 )
= ( size_s1143674878t_char @ Ys_9 ) ) ) ).
thf(fact_71_map__eq__imp__length__eq,axiom,
! [F_14: produc618524391on_val > produc618524391on_val,Xs_13: list_P1314671880on_val,G_7: exp_list_char > produc618524391on_val,Ys_9: list_exp_list_char] :
( ( ( map_Pr1978321326on_val @ F_14 @ Xs_13 )
= ( map_ex939917838on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s658972446on_val @ Xs_13 )
= ( size_s1143674878t_char @ Ys_9 ) ) ) ).
thf(fact_72_map__eq__imp__length__eq,axiom,
! [F_14: produc1746408499on_val > produc1746408499on_val,Xs_13: list_P1964248404on_val,G_7: exp_list_char > produc1746408499on_val,Ys_9: list_exp_list_char] :
( ( ( map_Pr816758342on_val @ F_14 @ Xs_13 )
= ( map_ex920537562on_val @ G_7 @ Ys_9 ) )
=> ( ( size_s350851178on_val @ Xs_13 )
= ( size_s1143674878t_char @ Ys_9 ) ) ) ).
thf(fact_73_map__eq__imp__length__eq,axiom,
! [F_14: val > option_ty,Xs_13: list_val,G_7: option_ty > option_ty,Ys_9: list_option_ty] :
( ( ( map_val_option_ty @ F_14 @ Xs_13 )
= ( map_op1363057580ion_ty @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_74_map__eq__imp__length__eq,axiom,
! [F_14: ty > option_ty,Xs_13: list_ty,G_7: option_ty > option_ty,Ys_9: list_option_ty] :
( ( ( map_ty_option_ty @ F_14 @ Xs_13 )
= ( map_op1363057580ion_ty @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_ty @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_75_map__eq__imp__length__eq,axiom,
! [F_14: val > exp_list_char,Xs_13: list_val,G_7: option_ty > exp_list_char,Ys_9: list_option_ty] :
( ( ( map_va1934808527t_char @ F_14 @ Xs_13 )
= ( map_op1779340173t_char @ G_7 @ Ys_9 ) )
=> ( ( size_size_list_val @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_76_map__eq__imp__length__eq,axiom,
! [F_14: list_char > val,Xs_13: list_list_char,G_7: option_val > val,Ys_9: list_option_val] :
( ( ( map_list_char_val @ F_14 @ Xs_13 )
= ( map_option_val_val @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s1595297126on_val @ Ys_9 ) ) ) ).
thf(fact_77_map__eq__imp__length__eq,axiom,
! [F_14: list_char > val,Xs_13: list_list_char,G_7: option_ty > val,Ys_9: list_option_ty] :
( ( ( map_list_char_val @ F_14 @ Xs_13 )
= ( map_option_ty_val @ G_7 @ Ys_9 ) )
=> ( ( size_s2113983095t_char @ Xs_13 )
= ( size_s1050794909ion_ty @ Ys_9 ) ) ) ).
thf(fact_78_map__eq__imp__length__eq,axiom,
! [F_14: option_ty > option_ty,Xs_13: list_option_ty,G_7: val > option_ty,Ys_9: list_val] :
( ( ( map_op1363057580ion_ty @ F_14 @ Xs_13 )
= ( map_val_option_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_79_map__eq__imp__length__eq,axiom,
! [F_14: option_ty > option_ty,Xs_13: list_option_ty,G_7: ty > option_ty,Ys_9: list_ty] :
( ( ( map_op1363057580ion_ty @ F_14 @ Xs_13 )
= ( map_ty_option_ty @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_size_list_ty @ Ys_9 ) ) ) ).
thf(fact_80_map__eq__imp__length__eq,axiom,
! [F_14: option_ty > exp_list_char,Xs_13: list_option_ty,G_7: val > exp_list_char,Ys_9: list_val] :
( ( ( map_op1779340173t_char @ F_14 @ Xs_13 )
= ( map_va1934808527t_char @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_size_list_val @ Ys_9 ) ) ) ).
thf(fact_81_map__eq__imp__length__eq,axiom,
! [F_14: option_val > val,Xs_13: list_option_val,G_7: list_char > val,Ys_9: list_list_char] :
( ( ( map_option_val_val @ F_14 @ Xs_13 )
= ( map_list_char_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1595297126on_val @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_82_map__eq__imp__length__eq,axiom,
! [F_14: option_ty > val,Xs_13: list_option_ty,G_7: list_char > val,Ys_9: list_list_char] :
( ( ( map_option_ty_val @ F_14 @ Xs_13 )
= ( map_list_char_val @ G_7 @ Ys_9 ) )
=> ( ( size_s1050794909ion_ty @ Xs_13 )
= ( size_s2113983095t_char @ Ys_9 ) ) ) ).
thf(fact_83_prod__induct5,axiom,
! [X_8: produc349695911t_char,P_25: produc349695911t_char > $o] :
( ! [A_1: produc1285161482t_char,B_4: list_list_char,C_6: list_ty,D_1: list_val,E_4: exp_list_char] : ( P_25 @ ( produc24551831t_char @ A_1 @ ( produc921874948t_char @ B_4 @ ( produc1909267824t_char @ C_6 @ ( produc1916172923t_char @ D_1 @ E_4 ) ) ) ) )
=> ( P_25 @ X_8 ) ) ).
thf(fact_84_prod__induct5,axiom,
! [X_8: produc1250491293on_val,P_25: produc1250491293on_val > $o] :
( ! [A_1: produc618524391on_val,B_4: produc1180562163on_val,C_6: list_exp_list_char,D_1: nat > option1728594148on_val,E_4: list_char > option_val] : ( P_25 @ ( produc1347028499on_val @ A_1 @ ( produc747700183on_val @ B_4 @ ( produc1302104557on_val @ C_6 @ ( produc755559506on_val @ D_1 @ E_4 ) ) ) ) )
=> ( P_25 @ X_8 ) ) ).
thf(fact_85_prod__induct5,axiom,
! [X_8: produc652964533on_val,P_25: produc652964533on_val > $o] :
( ! [A_1: produc1746408499on_val,B_4: produc1282892786on_val,C_6: exp_list_char,D_1: nat > option1728594148on_val,E_4: list_char > option_val] : ( P_25 @ ( produc345758123on_val @ A_1 @ ( produc833389609on_val @ B_4 @ ( produc235638504on_val @ C_6 @ ( produc755559506on_val @ D_1 @ E_4 ) ) ) ) )
=> ( P_25 @ X_8 ) ) ).
thf(fact_86_prod__cases5,axiom,
! [Y_5: produc349695911t_char] :
~ ! [A_1: produc1285161482t_char,B_4: list_list_char,C_6: list_ty,D_1: list_val,E_4: exp_list_char] :
( Y_5
!= ( produc24551831t_char @ A_1 @ ( produc921874948t_char @ B_4 @ ( produc1909267824t_char @ C_6 @ ( produc1916172923t_char @ D_1 @ E_4 ) ) ) ) ) ).
thf(fact_87_prod__cases5,axiom,
! [Y_5: produc1250491293on_val] :
~ ! [A_1: produc618524391on_val,B_4: produc1180562163on_val,C_6: list_exp_list_char,D_1: nat > option1728594148on_val,E_4: list_char > option_val] :
( Y_5
!= ( produc1347028499on_val @ A_1 @ ( produc747700183on_val @ B_4 @ ( produc1302104557on_val @ C_6 @ ( produc755559506on_val @ D_1 @ E_4 ) ) ) ) ) ).
thf(fact_88_prod__cases5,axiom,
! [Y_5: produc652964533on_val] :
~ ! [A_1: produc1746408499on_val,B_4: produc1282892786on_val,C_6: exp_list_char,D_1: nat > option1728594148on_val,E_4: list_char > option_val] :
( Y_5
!= ( produc345758123on_val @ A_1 @ ( produc833389609on_val @ B_4 @ ( produc235638504on_val @ C_6 @ ( produc755559506on_val @ D_1 @ E_4 ) ) ) ) ) ).
thf(fact_89_prod__induct4,axiom,
! [X_7: produc1285161482t_char,P_24: produc1285161482t_char > $o] :
( ! [A_1: list_list_char,B_4: list_ty,C_6: list_val,D_1: exp_list_char] : ( P_24 @ ( produc921874948t_char @ A_1 @ ( produc1909267824t_char @ B_4 @ ( produc1916172923t_char @ C_6 @ D_1 ) ) ) )
=> ( P_24 @ X_7 ) ) ).
thf(fact_90_prod__induct4,axiom,
! [X_7: produc1746408499on_val,P_24: produc1746408499on_val > $o] :
( ! [A_1: produc1282892786on_val,B_4: exp_list_char,C_6: nat > option1728594148on_val,D_1: list_char > option_val] : ( P_24 @ ( produc833389609on_val @ A_1 @ ( produc235638504on_val @ B_4 @ ( produc755559506on_val @ C_6 @ D_1 ) ) ) )
=> ( P_24 @ X_7 ) ) ).
thf(fact_91_prod__induct4,axiom,
! [X_7: produc618524391on_val,P_24: produc618524391on_val > $o] :
( ! [A_1: produc1180562163on_val,B_4: list_exp_list_char,C_6: nat > option1728594148on_val,D_1: list_char > option_val] : ( P_24 @ ( produc747700183on_val @ A_1 @ ( produc1302104557on_val @ B_4 @ ( produc755559506on_val @ C_6 @ D_1 ) ) ) )
=> ( P_24 @ X_7 ) ) ).
thf(fact_92_prod__induct4,axiom,
! [X_7: produc349695911t_char,P_24: produc349695911t_char > $o] :
( ! [A_1: produc1285161482t_char,B_4: list_list_char,C_6: list_ty,D_1: produc662261637t_char] : ( P_24 @ ( produc24551831t_char @ A_1 @ ( produc921874948t_char @ B_4 @ ( produc1909267824t_char @ C_6 @ D_1 ) ) ) )
=> ( P_24 @ X_7 ) ) ).
thf(fact_93_prod__induct4,axiom,
! [X_7: produc1406897475t_char,P_24: produc1406897475t_char > $o] :
( ! [A_1: produc220283002t_char,B_4: list_ty,C_6: list_val,D_1: exp_list_char] : ( P_24 @ ( produc57279289t_char @ A_1 @ ( produc1909267824t_char @ B_4 @ ( produc1916172923t_char @ C_6 @ D_1 ) ) ) )
=> ( P_24 @ X_7 ) ) ).
thf(fact_94_prod__induct4,axiom,
! [X_7: produc652964533on_val,P_24: produc652964533on_val > $o] :
( ! [A_1: produc1746408499on_val,B_4: produc1282892786on_val,C_6: exp_list_char,D_1: produc2090907612on_val] : ( P_24 @ ( produc345758123on_val @ A_1 @ ( produc833389609on_val @ B_4 @ ( produc235638504on_val @ C_6 @ D_1 ) ) ) )
=> ( P_24 @ X_7 ) ) ).
thf(fact_95_prod__induct4,axiom,
! [X_7: produc1250491293on_val,P_24: produc1250491293on_val > $o] :
( ! [A_1: produc618524391on_val,B_4: produc1180562163on_val,C_6: list_exp_list_char,D_1: produc2090907612on_val] : ( P_24 @ ( produc1347028499on_val @ A_1 @ ( produc747700183on_val @ B_4 @ ( produc1302104557on_val @ C_6 @ D_1 ) ) ) )
=> ( P_24 @ X_7 ) ) ).
thf(fact_96_prod__induct4,axiom,
! [X_7: produc630464863al_val,P_24: produc630464863al_val > $o] :
( ! [A_1: produc1645268488al_val,B_4: bop,C_6: val,D_1: val] : ( P_24 @ ( produc1924279125al_val @ A_1 @ ( produc621191550al_val @ B_4 @ ( product_Pair_val_val @ C_6 @ D_1 ) ) ) )
=> ( P_24 @ X_7 ) ) ).
thf(fact_97_prod__cases4,axiom,
! [Y_4: produc1285161482t_char] :
~ ! [A_1: list_list_char,B_4: list_ty,C_6: list_val,D_1: exp_list_char] :
( Y_4
!= ( produc921874948t_char @ A_1 @ ( produc1909267824t_char @ B_4 @ ( produc1916172923t_char @ C_6 @ D_1 ) ) ) ) ).
thf(fact_98_prod__cases4,axiom,
! [Y_4: produc1746408499on_val] :
~ ! [A_1: produc1282892786on_val,B_4: exp_list_char,C_6: nat > option1728594148on_val,D_1: list_char > option_val] :
( Y_4
!= ( produc833389609on_val @ A_1 @ ( produc235638504on_val @ B_4 @ ( produc755559506on_val @ C_6 @ D_1 ) ) ) ) ).
thf(fact_99_prod__cases4,axiom,
! [Y_4: produc618524391on_val] :
~ ! [A_1: produc1180562163on_val,B_4: list_exp_list_char,C_6: nat > option1728594148on_val,D_1: list_char > option_val] :
( Y_4
!= ( produc747700183on_val @ A_1 @ ( produc1302104557on_val @ B_4 @ ( produc755559506on_val @ C_6 @ D_1 ) ) ) ) ).
thf(fact_100_prod__cases4,axiom,
! [Y_4: produc349695911t_char] :
~ ! [A_1: produc1285161482t_char,B_4: list_list_char,C_6: list_ty,D_1: produc662261637t_char] :
( Y_4
!= ( produc24551831t_char @ A_1 @ ( produc921874948t_char @ B_4 @ ( produc1909267824t_char @ C_6 @ D_1 ) ) ) ) ).
thf(fact_101_prod__cases4,axiom,
! [Y_4: produc1406897475t_char] :
~ ! [A_1: produc220283002t_char,B_4: list_ty,C_6: list_val,D_1: exp_list_char] :
( Y_4
!= ( produc57279289t_char @ A_1 @ ( produc1909267824t_char @ B_4 @ ( produc1916172923t_char @ C_6 @ D_1 ) ) ) ) ).
thf(fact_102_prod__cases4,axiom,
! [Y_4: produc652964533on_val] :
~ ! [A_1: produc1746408499on_val,B_4: produc1282892786on_val,C_6: exp_list_char,D_1: produc2090907612on_val] :
( Y_4
!= ( produc345758123on_val @ A_1 @ ( produc833389609on_val @ B_4 @ ( produc235638504on_val @ C_6 @ D_1 ) ) ) ) ).
thf(fact_103_prod__cases4,axiom,
! [Y_4: produc1250491293on_val] :
~ ! [A_1: produc618524391on_val,B_4: produc1180562163on_val,C_6: list_exp_list_char,D_1: produc2090907612on_val] :
( Y_4
!= ( produc1347028499on_val @ A_1 @ ( produc747700183on_val @ B_4 @ ( produc1302104557on_val @ C_6 @ D_1 ) ) ) ) ).
thf(fact_104_prod__cases4,axiom,
! [Y_4: produc630464863al_val] :
~ ! [A_1: produc1645268488al_val,B_4: bop,C_6: val,D_1: val] :
( Y_4
!= ( produc1924279125al_val @ A_1 @ ( produc621191550al_val @ B_4 @ ( product_Pair_val_val @ C_6 @ D_1 ) ) ) ) ).
thf(fact_105_Pair__inject,axiom,
! [A_18: produc809539159t_char,B_14: produc809539159t_char,A_17: produc809539159t_char,B_13: produc809539159t_char] :
( ( ( produc1897818327t_char @ A_18 @ B_14 )
= ( produc1897818327t_char @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_106_Pair__inject,axiom,
! [A_18: produc1278157519t_char,B_14: produc1278157519t_char,A_17: produc1278157519t_char,B_13: produc1278157519t_char] :
( ( ( produc2080520419t_char @ A_18 @ B_14 )
= ( produc2080520419t_char @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_107_Pair__inject,axiom,
! [A_18: product_prod_val_val,B_14: product_prod_val_val,A_17: product_prod_val_val,B_13: product_prod_val_val] :
( ( ( produc1244920211al_val @ A_18 @ B_14 )
= ( produc1244920211al_val @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_108_Pair__inject,axiom,
! [A_18: produc1645268488al_val,B_14: produc1645268488al_val,A_17: produc1645268488al_val,B_13: produc1645268488al_val] :
( ( ( produc1924279125al_val @ A_18 @ B_14 )
= ( produc1924279125al_val @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_109_Pair__inject,axiom,
! [A_18: produc618524391on_val,B_14: produc618524391on_val,A_17: produc618524391on_val,B_13: produc618524391on_val] :
( ( ( produc1347028499on_val @ A_18 @ B_14 )
= ( produc1347028499on_val @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_110_Pair__inject,axiom,
! [A_18: produc2088785539on_val,B_14: produc2088785539on_val,A_17: produc2088785539on_val,B_13: produc2088785539on_val] :
( ( ( produc1773146955on_val @ A_18 @ B_14 )
= ( produc1773146955on_val @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_111_Pair__inject,axiom,
! [A_18: produc1746408499on_val,B_14: produc1746408499on_val,A_17: produc1746408499on_val,B_13: produc1746408499on_val] :
( ( ( produc345758123on_val @ A_18 @ B_14 )
= ( produc345758123on_val @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_112_Pair__inject,axiom,
! [A_18: produc2090907612on_val,B_14: produc2090907612on_val,A_17: produc2090907612on_val,B_13: produc2090907612on_val] :
( ( ( produc259392253on_val @ A_18 @ B_14 )
= ( produc259392253on_val @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_113_Pair__inject,axiom,
! [A_18: produc662261637t_char,B_14: produc662261637t_char,A_17: produc662261637t_char,B_13: produc662261637t_char] :
( ( ( produc1299387215t_char @ A_18 @ B_14 )
= ( produc1299387215t_char @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_114_Pair__inject,axiom,
! [A_18: produc220283002t_char,B_14: produc220283002t_char,A_17: produc220283002t_char,B_13: produc220283002t_char] :
( ( ( produc57279289t_char @ A_18 @ B_14 )
= ( produc57279289t_char @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_115_Pair__inject,axiom,
! [A_18: produc1285161482t_char,B_14: produc1285161482t_char,A_17: produc1285161482t_char,B_13: produc1285161482t_char] :
( ( ( produc24551831t_char @ A_18 @ B_14 )
= ( produc24551831t_char @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_116_Pair__inject,axiom,
! [A_18: list_list_char,B_14: produc220283002t_char,A_17: list_list_char,B_13: produc220283002t_char] :
( ( ( produc921874948t_char @ A_18 @ B_14 )
= ( produc921874948t_char @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_117_Pair__inject,axiom,
! [A_18: list_ty,B_14: produc662261637t_char,A_17: list_ty,B_13: produc662261637t_char] :
( ( ( produc1909267824t_char @ A_18 @ B_14 )
= ( produc1909267824t_char @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_118_Pair__inject,axiom,
! [A_18: list_val,B_14: exp_list_char,A_17: list_val,B_13: exp_list_char] :
( ( ( produc1916172923t_char @ A_18 @ B_14 )
= ( produc1916172923t_char @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_119_Pair__inject,axiom,
! [A_18: nat > option1728594148on_val,B_14: list_char > option_val,A_17: nat > option1728594148on_val,B_13: list_char > option_val] :
( ( ( produc755559506on_val @ A_18 @ B_14 )
= ( produc755559506on_val @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_120_Pair__inject,axiom,
! [A_18: produc1282892786on_val,B_14: produc1282892786on_val,A_17: produc1282892786on_val,B_13: produc1282892786on_val] :
( ( ( produc833389609on_val @ A_18 @ B_14 )
= ( produc833389609on_val @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_121_Pair__inject,axiom,
! [A_18: exp_list_char,B_14: produc2090907612on_val,A_17: exp_list_char,B_13: produc2090907612on_val] :
( ( ( produc235638504on_val @ A_18 @ B_14 )
= ( produc235638504on_val @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_122_Pair__inject,axiom,
! [A_18: list_char,B_14: produc1278157519t_char > option_val,A_17: list_char,B_13: produc1278157519t_char > option_val] :
( ( ( produc926070009on_val @ A_18 @ B_14 )
= ( produc926070009on_val @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_123_Pair__inject,axiom,
! [A_18: produc1180562163on_val,B_14: produc1180562163on_val,A_17: produc1180562163on_val,B_13: produc1180562163on_val] :
( ( ( produc747700183on_val @ A_18 @ B_14 )
= ( produc747700183on_val @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_124_Pair__inject,axiom,
! [A_18: list_exp_list_char,B_14: produc2090907612on_val,A_17: list_exp_list_char,B_13: produc2090907612on_val] :
( ( ( produc1302104557on_val @ A_18 @ B_14 )
= ( produc1302104557on_val @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_125_Pair__inject,axiom,
! [A_18: bop,B_14: product_prod_val_val,A_17: bop,B_13: product_prod_val_val] :
( ( ( produc621191550al_val @ A_18 @ B_14 )
= ( produc621191550al_val @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_126_Pair__inject,axiom,
! [A_18: val,B_14: val,A_17: val,B_13: val] :
( ( ( product_Pair_val_val @ A_18 @ B_14 )
= ( product_Pair_val_val @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_127_Pair__inject,axiom,
! [A_18: list_char,B_14: list_char,A_17: list_char,B_13: list_char] :
( ( ( produc5062597t_char @ A_18 @ B_14 )
= ( produc5062597t_char @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_128_Pair__inject,axiom,
! [A_18: list_list_char,B_14: exp_list_char,A_17: list_list_char,B_13: exp_list_char] :
( ( ( produc1147572817t_char @ A_18 @ B_14 )
= ( produc1147572817t_char @ A_17 @ B_13 ) )
=> ~ ( ( A_18 = A_17 )
=> ( B_14 != B_13 ) ) ) ).
thf(fact_129_Pair__eq,axiom,
! [A_16: produc809539159t_char,B_12: produc809539159t_char,A_15: produc809539159t_char,B_11: produc809539159t_char] :
( ( ( produc1897818327t_char @ A_16 @ B_12 )
= ( produc1897818327t_char @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_130_Pair__eq,axiom,
! [A_16: produc1278157519t_char,B_12: produc1278157519t_char,A_15: produc1278157519t_char,B_11: produc1278157519t_char] :
( ( ( produc2080520419t_char @ A_16 @ B_12 )
= ( produc2080520419t_char @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_131_Pair__eq,axiom,
! [A_16: product_prod_val_val,B_12: product_prod_val_val,A_15: product_prod_val_val,B_11: product_prod_val_val] :
( ( ( produc1244920211al_val @ A_16 @ B_12 )
= ( produc1244920211al_val @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_132_Pair__eq,axiom,
! [A_16: produc1645268488al_val,B_12: produc1645268488al_val,A_15: produc1645268488al_val,B_11: produc1645268488al_val] :
( ( ( produc1924279125al_val @ A_16 @ B_12 )
= ( produc1924279125al_val @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_133_Pair__eq,axiom,
! [A_16: produc618524391on_val,B_12: produc618524391on_val,A_15: produc618524391on_val,B_11: produc618524391on_val] :
( ( ( produc1347028499on_val @ A_16 @ B_12 )
= ( produc1347028499on_val @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_134_Pair__eq,axiom,
! [A_16: produc2088785539on_val,B_12: produc2088785539on_val,A_15: produc2088785539on_val,B_11: produc2088785539on_val] :
( ( ( produc1773146955on_val @ A_16 @ B_12 )
= ( produc1773146955on_val @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_135_Pair__eq,axiom,
! [A_16: produc1746408499on_val,B_12: produc1746408499on_val,A_15: produc1746408499on_val,B_11: produc1746408499on_val] :
( ( ( produc345758123on_val @ A_16 @ B_12 )
= ( produc345758123on_val @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_136_Pair__eq,axiom,
! [A_16: produc2090907612on_val,B_12: produc2090907612on_val,A_15: produc2090907612on_val,B_11: produc2090907612on_val] :
( ( ( produc259392253on_val @ A_16 @ B_12 )
= ( produc259392253on_val @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_137_Pair__eq,axiom,
! [A_16: produc662261637t_char,B_12: produc662261637t_char,A_15: produc662261637t_char,B_11: produc662261637t_char] :
( ( ( produc1299387215t_char @ A_16 @ B_12 )
= ( produc1299387215t_char @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_138_Pair__eq,axiom,
! [A_16: produc220283002t_char,B_12: produc220283002t_char,A_15: produc220283002t_char,B_11: produc220283002t_char] :
( ( ( produc57279289t_char @ A_16 @ B_12 )
= ( produc57279289t_char @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_139_Pair__eq,axiom,
! [A_16: produc1285161482t_char,B_12: produc1285161482t_char,A_15: produc1285161482t_char,B_11: produc1285161482t_char] :
( ( ( produc24551831t_char @ A_16 @ B_12 )
= ( produc24551831t_char @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_140_Pair__eq,axiom,
! [A_16: list_list_char,B_12: produc220283002t_char,A_15: list_list_char,B_11: produc220283002t_char] :
( ( ( produc921874948t_char @ A_16 @ B_12 )
= ( produc921874948t_char @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_141_Pair__eq,axiom,
! [A_16: list_ty,B_12: produc662261637t_char,A_15: list_ty,B_11: produc662261637t_char] :
( ( ( produc1909267824t_char @ A_16 @ B_12 )
= ( produc1909267824t_char @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_142_Pair__eq,axiom,
! [A_16: list_val,B_12: exp_list_char,A_15: list_val,B_11: exp_list_char] :
( ( ( produc1916172923t_char @ A_16 @ B_12 )
= ( produc1916172923t_char @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_143_Pair__eq,axiom,
! [A_16: nat > option1728594148on_val,B_12: list_char > option_val,A_15: nat > option1728594148on_val,B_11: list_char > option_val] :
( ( ( produc755559506on_val @ A_16 @ B_12 )
= ( produc755559506on_val @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_144_Pair__eq,axiom,
! [A_16: produc1282892786on_val,B_12: produc1282892786on_val,A_15: produc1282892786on_val,B_11: produc1282892786on_val] :
( ( ( produc833389609on_val @ A_16 @ B_12 )
= ( produc833389609on_val @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_145_Pair__eq,axiom,
! [A_16: exp_list_char,B_12: produc2090907612on_val,A_15: exp_list_char,B_11: produc2090907612on_val] :
( ( ( produc235638504on_val @ A_16 @ B_12 )
= ( produc235638504on_val @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_146_Pair__eq,axiom,
! [A_16: list_char,B_12: produc1278157519t_char > option_val,A_15: list_char,B_11: produc1278157519t_char > option_val] :
( ( ( produc926070009on_val @ A_16 @ B_12 )
= ( produc926070009on_val @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_147_Pair__eq,axiom,
! [A_16: produc1180562163on_val,B_12: produc1180562163on_val,A_15: produc1180562163on_val,B_11: produc1180562163on_val] :
( ( ( produc747700183on_val @ A_16 @ B_12 )
= ( produc747700183on_val @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_148_Pair__eq,axiom,
! [A_16: list_exp_list_char,B_12: produc2090907612on_val,A_15: list_exp_list_char,B_11: produc2090907612on_val] :
( ( ( produc1302104557on_val @ A_16 @ B_12 )
= ( produc1302104557on_val @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_149_Pair__eq,axiom,
! [A_16: bop,B_12: product_prod_val_val,A_15: bop,B_11: product_prod_val_val] :
( ( ( produc621191550al_val @ A_16 @ B_12 )
= ( produc621191550al_val @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_150_Pair__eq,axiom,
! [A_16: val,B_12: val,A_15: val,B_11: val] :
( ( ( product_Pair_val_val @ A_16 @ B_12 )
= ( product_Pair_val_val @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_151_Pair__eq,axiom,
! [A_16: list_char,B_12: list_char,A_15: list_char,B_11: list_char] :
( ( ( produc5062597t_char @ A_16 @ B_12 )
= ( produc5062597t_char @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_152_Pair__eq,axiom,
! [A_16: list_list_char,B_12: exp_list_char,A_15: list_list_char,B_11: exp_list_char] :
( ( ( produc1147572817t_char @ A_16 @ B_12 )
= ( produc1147572817t_char @ A_15 @ B_11 ) )
<=> ( ( A_16 = A_15 )
& ( B_12 = B_11 ) ) ) ).
thf(fact_153_split__paired__All,axiom,
! [P_23: produc1534059751t_char > $o] :
( ( !! @ produc1534059751t_char @ P_23 )
<=> ! [A_1: produc809539159t_char,B_4: produc809539159t_char] : ( P_23 @ ( produc1897818327t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_154_split__paired__All,axiom,
! [P_23: produc1350825965t_char > $o] :
( ( !! @ produc1350825965t_char @ P_23 )
<=> ! [A_1: produc1278157519t_char,B_4: produc1278157519t_char] : ( P_23 @ ( produc2080520419t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_155_split__paired__All,axiom,
! [P_23: produc800118557al_val > $o] :
( ( !! @ produc800118557al_val @ P_23 )
<=> ! [A_1: product_prod_val_val,B_4: product_prod_val_val] : ( P_23 @ ( produc1244920211al_val @ A_1 @ B_4 ) ) ) ).
thf(fact_156_split__paired__All,axiom,
! [P_23: produc630464863al_val > $o] :
( ( !! @ produc630464863al_val @ P_23 )
<=> ! [A_1: produc1645268488al_val,B_4: produc1645268488al_val] : ( P_23 @ ( produc1924279125al_val @ A_1 @ B_4 ) ) ) ).
thf(fact_157_split__paired__All,axiom,
! [P_23: produc1250491293on_val > $o] :
( ( !! @ produc1250491293on_val @ P_23 )
<=> ! [A_1: produc618524391on_val,B_4: produc618524391on_val] : ( P_23 @ ( produc1347028499on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_158_split__paired__All,axiom,
! [P_23: produc1368416213on_val > $o] :
( ( !! @ produc1368416213on_val @ P_23 )
<=> ! [A_1: produc2088785539on_val,B_4: produc2088785539on_val] : ( P_23 @ ( produc1773146955on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_159_split__paired__All,axiom,
! [P_23: produc652964533on_val > $o] :
( ( !! @ produc652964533on_val @ P_23 )
<=> ! [A_1: produc1746408499on_val,B_4: produc1746408499on_val] : ( P_23 @ ( produc345758123on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_160_split__paired__All,axiom,
! [P_23: produc1581780743on_val > $o] :
( ( !! @ produc1581780743on_val @ P_23 )
<=> ! [A_1: produc2090907612on_val,B_4: produc2090907612on_val] : ( P_23 @ ( produc259392253on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_161_split__paired__All,axiom,
! [P_23: produc1826280281t_char > $o] :
( ( !! @ produc1826280281t_char @ P_23 )
<=> ! [A_1: produc662261637t_char,B_4: produc662261637t_char] : ( P_23 @ ( produc1299387215t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_162_split__paired__All,axiom,
! [P_23: produc1406897475t_char > $o] :
( ( !! @ produc1406897475t_char @ P_23 )
<=> ! [A_1: produc220283002t_char,B_4: produc220283002t_char] : ( P_23 @ ( produc57279289t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_163_split__paired__All,axiom,
! [P_23: produc349695911t_char > $o] :
( ( !! @ produc349695911t_char @ P_23 )
<=> ! [A_1: produc1285161482t_char,B_4: produc1285161482t_char] : ( P_23 @ ( produc24551831t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_164_split__paired__All,axiom,
! [P_23: produc1285161482t_char > $o] :
( ( !! @ produc1285161482t_char @ P_23 )
<=> ! [A_1: list_list_char,B_4: produc220283002t_char] : ( P_23 @ ( produc921874948t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_165_split__paired__All,axiom,
! [P_23: produc220283002t_char > $o] :
( ( !! @ produc220283002t_char @ P_23 )
<=> ! [A_1: list_ty,B_4: produc662261637t_char] : ( P_23 @ ( produc1909267824t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_166_split__paired__All,axiom,
! [P_23: produc662261637t_char > $o] :
( ( !! @ produc662261637t_char @ P_23 )
<=> ! [A_1: list_val,B_4: exp_list_char] : ( P_23 @ ( produc1916172923t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_167_split__paired__All,axiom,
! [P_23: produc2090907612on_val > $o] :
( ( !! @ produc2090907612on_val @ P_23 )
<=> ! [A_1: nat > option1728594148on_val,B_4: list_char > option_val] : ( P_23 @ ( produc755559506on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_168_split__paired__All,axiom,
! [P_23: produc1746408499on_val > $o] :
( ( !! @ produc1746408499on_val @ P_23 )
<=> ! [A_1: produc1282892786on_val,B_4: produc1282892786on_val] : ( P_23 @ ( produc833389609on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_169_split__paired__All,axiom,
! [P_23: produc1282892786on_val > $o] :
( ( !! @ produc1282892786on_val @ P_23 )
<=> ! [A_1: exp_list_char,B_4: produc2090907612on_val] : ( P_23 @ ( produc235638504on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_170_split__paired__All,axiom,
! [P_23: produc2088785539on_val > $o] :
( ( !! @ produc2088785539on_val @ P_23 )
<=> ! [A_1: list_char,B_4: produc1278157519t_char > option_val] : ( P_23 @ ( produc926070009on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_171_split__paired__All,axiom,
! [P_23: produc618524391on_val > $o] :
( ( !! @ produc618524391on_val @ P_23 )
<=> ! [A_1: produc1180562163on_val,B_4: produc1180562163on_val] : ( P_23 @ ( produc747700183on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_172_split__paired__All,axiom,
! [P_23: produc1180562163on_val > $o] :
( ( !! @ produc1180562163on_val @ P_23 )
<=> ! [A_1: list_exp_list_char,B_4: produc2090907612on_val] : ( P_23 @ ( produc1302104557on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_173_split__paired__All,axiom,
! [P_23: produc1645268488al_val > $o] :
( ( !! @ produc1645268488al_val @ P_23 )
<=> ! [A_1: bop,B_4: product_prod_val_val] : ( P_23 @ ( produc621191550al_val @ A_1 @ B_4 ) ) ) ).
thf(fact_174_split__paired__All,axiom,
! [P_23: product_prod_val_val > $o] :
( ( !! @ product_prod_val_val @ P_23 )
<=> ! [A_1: val,B_4: val] : ( P_23 @ ( product_Pair_val_val @ A_1 @ B_4 ) ) ) ).
thf(fact_175_split__paired__All,axiom,
! [P_23: produc1278157519t_char > $o] :
( ( !! @ produc1278157519t_char @ P_23 )
<=> ! [A_1: list_char,B_4: list_char] : ( P_23 @ ( produc5062597t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_176_split__paired__All,axiom,
! [P_23: produc809539159t_char > $o] :
( ( !! @ produc809539159t_char @ P_23 )
<=> ! [A_1: list_list_char,B_4: exp_list_char] : ( P_23 @ ( produc1147572817t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_177_neq__if__length__neq,axiom,
! [Xs_12: list_option_ty,Ys_8: list_option_ty] :
( ( ( size_s1050794909ion_ty @ Xs_12 )
!= ( size_s1050794909ion_ty @ Ys_8 ) )
=> ( Xs_12 != Ys_8 ) ) ).
thf(fact_178_neq__if__length__neq,axiom,
! [Xs_12: list_list_char,Ys_8: list_list_char] :
( ( ( size_s2113983095t_char @ Xs_12 )
!= ( size_s2113983095t_char @ Ys_8 ) )
=> ( Xs_12 != Ys_8 ) ) ).
thf(fact_179_neq__if__length__neq,axiom,
! [Xs_12: list_ty,Ys_8: list_ty] :
( ( ( size_size_list_ty @ Xs_12 )
!= ( size_size_list_ty @ Ys_8 ) )
=> ( Xs_12 != Ys_8 ) ) ).
thf(fact_180_neq__if__length__neq,axiom,
! [Xs_12: list_val,Ys_8: list_val] :
( ( ( size_size_list_val @ Xs_12 )
!= ( size_size_list_val @ Ys_8 ) )
=> ( Xs_12 != Ys_8 ) ) ).
thf(fact_181_neq__if__length__neq,axiom,
! [Xs_12: list_exp_list_char,Ys_8: list_exp_list_char] :
( ( ( size_s1143674878t_char @ Xs_12 )
!= ( size_s1143674878t_char @ Ys_8 ) )
=> ( Xs_12 != Ys_8 ) ) ).
thf(fact_182_list__all2__eq,axiom,
! [Xs_11: list_ty,Ys_7: list_ty] :
( ( Xs_11 = Ys_7 )
<=> ( list_all2_ty_ty @ fequal_ty @ Xs_11 @ Ys_7 ) ) ).
thf(fact_183_widen__trans,axiom,
! [T_11: ty,P_22: list_P1999446415t_char,S_4: ty,U_1: ty] :
( ( widen_2090681816t_char @ P_22 @ S_4 @ U_1 )
=> ( ( widen_2090681816t_char @ P_22 @ U_1 @ T_11 )
=> ( widen_2090681816t_char @ P_22 @ S_4 @ T_11 ) ) ) ).
thf(fact_184_prod__cases3,axiom,
! [Y_3: produc1285161482t_char] :
~ ! [A_1: list_list_char,B_4: list_ty,C_6: produc662261637t_char] :
( Y_3
!= ( produc921874948t_char @ A_1 @ ( produc1909267824t_char @ B_4 @ C_6 ) ) ) ).
thf(fact_185_prod__cases3,axiom,
! [Y_3: produc220283002t_char] :
~ ! [A_1: list_ty,B_4: list_val,C_6: exp_list_char] :
( Y_3
!= ( produc1909267824t_char @ A_1 @ ( produc1916172923t_char @ B_4 @ C_6 ) ) ) ).
thf(fact_186_prod__cases3,axiom,
! [Y_3: produc1746408499on_val] :
~ ! [A_1: produc1282892786on_val,B_4: exp_list_char,C_6: produc2090907612on_val] :
( Y_3
!= ( produc833389609on_val @ A_1 @ ( produc235638504on_val @ B_4 @ C_6 ) ) ) ).
thf(fact_187_prod__cases3,axiom,
! [Y_3: produc1282892786on_val] :
~ ! [A_1: exp_list_char,B_4: nat > option1728594148on_val,C_6: list_char > option_val] :
( Y_3
!= ( produc235638504on_val @ A_1 @ ( produc755559506on_val @ B_4 @ C_6 ) ) ) ).
thf(fact_188_prod__cases3,axiom,
! [Y_3: produc618524391on_val] :
~ ! [A_1: produc1180562163on_val,B_4: list_exp_list_char,C_6: produc2090907612on_val] :
( Y_3
!= ( produc747700183on_val @ A_1 @ ( produc1302104557on_val @ B_4 @ C_6 ) ) ) ).
thf(fact_189_prod__cases3,axiom,
! [Y_3: produc1180562163on_val] :
~ ! [A_1: list_exp_list_char,B_4: nat > option1728594148on_val,C_6: list_char > option_val] :
( Y_3
!= ( produc1302104557on_val @ A_1 @ ( produc755559506on_val @ B_4 @ C_6 ) ) ) ).
thf(fact_190_prod__cases3,axiom,
! [Y_3: produc1645268488al_val] :
~ ! [A_1: bop,B_4: val,C_6: val] :
( Y_3
!= ( produc621191550al_val @ A_1 @ ( product_Pair_val_val @ B_4 @ C_6 ) ) ) ).
thf(fact_191_prod__cases3,axiom,
! [Y_3: produc349695911t_char] :
~ ! [A_1: produc1285161482t_char,B_4: list_list_char,C_6: produc220283002t_char] :
( Y_3
!= ( produc24551831t_char @ A_1 @ ( produc921874948t_char @ B_4 @ C_6 ) ) ) ).
thf(fact_192_prod__cases3,axiom,
! [Y_3: produc1406897475t_char] :
~ ! [A_1: produc220283002t_char,B_4: list_ty,C_6: produc662261637t_char] :
( Y_3
!= ( produc57279289t_char @ A_1 @ ( produc1909267824t_char @ B_4 @ C_6 ) ) ) ).
thf(fact_193_prod__cases3,axiom,
! [Y_3: produc1826280281t_char] :
~ ! [A_1: produc662261637t_char,B_4: list_val,C_6: exp_list_char] :
( Y_3
!= ( produc1299387215t_char @ A_1 @ ( produc1916172923t_char @ B_4 @ C_6 ) ) ) ).
thf(fact_194_prod__cases3,axiom,
! [Y_3: produc1581780743on_val] :
~ ! [A_1: produc2090907612on_val,B_4: nat > option1728594148on_val,C_6: list_char > option_val] :
( Y_3
!= ( produc259392253on_val @ A_1 @ ( produc755559506on_val @ B_4 @ C_6 ) ) ) ).
thf(fact_195_prod__cases3,axiom,
! [Y_3: produc652964533on_val] :
~ ! [A_1: produc1746408499on_val,B_4: produc1282892786on_val,C_6: produc1282892786on_val] :
( Y_3
!= ( produc345758123on_val @ A_1 @ ( produc833389609on_val @ B_4 @ C_6 ) ) ) ).
thf(fact_196_prod__cases3,axiom,
! [Y_3: produc1368416213on_val] :
~ ! [A_1: produc2088785539on_val,B_4: list_char,C_6: produc1278157519t_char > option_val] :
( Y_3
!= ( produc1773146955on_val @ A_1 @ ( produc926070009on_val @ B_4 @ C_6 ) ) ) ).
thf(fact_197_prod__cases3,axiom,
! [Y_3: produc1250491293on_val] :
~ ! [A_1: produc618524391on_val,B_4: produc1180562163on_val,C_6: produc1180562163on_val] :
( Y_3
!= ( produc1347028499on_val @ A_1 @ ( produc747700183on_val @ B_4 @ C_6 ) ) ) ).
thf(fact_198_prod__cases3,axiom,
! [Y_3: produc630464863al_val] :
~ ! [A_1: produc1645268488al_val,B_4: bop,C_6: product_prod_val_val] :
( Y_3
!= ( produc1924279125al_val @ A_1 @ ( produc621191550al_val @ B_4 @ C_6 ) ) ) ).
thf(fact_199_prod__cases3,axiom,
! [Y_3: produc800118557al_val] :
~ ! [A_1: product_prod_val_val,B_4: val,C_6: val] :
( Y_3
!= ( produc1244920211al_val @ A_1 @ ( product_Pair_val_val @ B_4 @ C_6 ) ) ) ).
thf(fact_200_prod__cases3,axiom,
! [Y_3: produc1350825965t_char] :
~ ! [A_1: produc1278157519t_char,B_4: list_char,C_6: list_char] :
( Y_3
!= ( produc2080520419t_char @ A_1 @ ( produc5062597t_char @ B_4 @ C_6 ) ) ) ).
thf(fact_201_prod__cases3,axiom,
! [Y_3: produc1534059751t_char] :
~ ! [A_1: produc809539159t_char,B_4: list_list_char,C_6: exp_list_char] :
( Y_3
!= ( produc1897818327t_char @ A_1 @ ( produc1147572817t_char @ B_4 @ C_6 ) ) ) ).
thf(fact_202_prod__induct3,axiom,
! [X_6: produc1285161482t_char,P_21: produc1285161482t_char > $o] :
( ! [A_1: list_list_char,B_4: list_ty,C_6: produc662261637t_char] : ( P_21 @ ( produc921874948t_char @ A_1 @ ( produc1909267824t_char @ B_4 @ C_6 ) ) )
=> ( P_21 @ X_6 ) ) ).
thf(fact_203_prod__induct3,axiom,
! [X_6: produc220283002t_char,P_21: produc220283002t_char > $o] :
( ! [A_1: list_ty,B_4: list_val,C_6: exp_list_char] : ( P_21 @ ( produc1909267824t_char @ A_1 @ ( produc1916172923t_char @ B_4 @ C_6 ) ) )
=> ( P_21 @ X_6 ) ) ).
thf(fact_204_prod__induct3,axiom,
! [X_6: produc1746408499on_val,P_21: produc1746408499on_val > $o] :
( ! [A_1: produc1282892786on_val,B_4: exp_list_char,C_6: produc2090907612on_val] : ( P_21 @ ( produc833389609on_val @ A_1 @ ( produc235638504on_val @ B_4 @ C_6 ) ) )
=> ( P_21 @ X_6 ) ) ).
thf(fact_205_prod__induct3,axiom,
! [X_6: produc1282892786on_val,P_21: produc1282892786on_val > $o] :
( ! [A_1: exp_list_char,B_4: nat > option1728594148on_val,C_6: list_char > option_val] : ( P_21 @ ( produc235638504on_val @ A_1 @ ( produc755559506on_val @ B_4 @ C_6 ) ) )
=> ( P_21 @ X_6 ) ) ).
thf(fact_206_prod__induct3,axiom,
! [X_6: produc618524391on_val,P_21: produc618524391on_val > $o] :
( ! [A_1: produc1180562163on_val,B_4: list_exp_list_char,C_6: produc2090907612on_val] : ( P_21 @ ( produc747700183on_val @ A_1 @ ( produc1302104557on_val @ B_4 @ C_6 ) ) )
=> ( P_21 @ X_6 ) ) ).
thf(fact_207_prod__induct3,axiom,
! [X_6: produc1180562163on_val,P_21: produc1180562163on_val > $o] :
( ! [A_1: list_exp_list_char,B_4: nat > option1728594148on_val,C_6: list_char > option_val] : ( P_21 @ ( produc1302104557on_val @ A_1 @ ( produc755559506on_val @ B_4 @ C_6 ) ) )
=> ( P_21 @ X_6 ) ) ).
thf(fact_208_prod__induct3,axiom,
! [X_6: produc1645268488al_val,P_21: produc1645268488al_val > $o] :
( ! [A_1: bop,B_4: val,C_6: val] : ( P_21 @ ( produc621191550al_val @ A_1 @ ( product_Pair_val_val @ B_4 @ C_6 ) ) )
=> ( P_21 @ X_6 ) ) ).
thf(fact_209_prod__induct3,axiom,
! [X_6: produc349695911t_char,P_21: produc349695911t_char > $o] :
( ! [A_1: produc1285161482t_char,B_4: list_list_char,C_6: produc220283002t_char] : ( P_21 @ ( produc24551831t_char @ A_1 @ ( produc921874948t_char @ B_4 @ C_6 ) ) )
=> ( P_21 @ X_6 ) ) ).
thf(fact_210_prod__induct3,axiom,
! [X_6: produc1406897475t_char,P_21: produc1406897475t_char > $o] :
( ! [A_1: produc220283002t_char,B_4: list_ty,C_6: produc662261637t_char] : ( P_21 @ ( produc57279289t_char @ A_1 @ ( produc1909267824t_char @ B_4 @ C_6 ) ) )
=> ( P_21 @ X_6 ) ) ).
thf(fact_211_prod__induct3,axiom,
! [X_6: produc1826280281t_char,P_21: produc1826280281t_char > $o] :
( ! [A_1: produc662261637t_char,B_4: list_val,C_6: exp_list_char] : ( P_21 @ ( produc1299387215t_char @ A_1 @ ( produc1916172923t_char @ B_4 @ C_6 ) ) )
=> ( P_21 @ X_6 ) ) ).
thf(fact_212_prod__induct3,axiom,
! [X_6: produc1581780743on_val,P_21: produc1581780743on_val > $o] :
( ! [A_1: produc2090907612on_val,B_4: nat > option1728594148on_val,C_6: list_char > option_val] : ( P_21 @ ( produc259392253on_val @ A_1 @ ( produc755559506on_val @ B_4 @ C_6 ) ) )
=> ( P_21 @ X_6 ) ) ).
thf(fact_213_prod__induct3,axiom,
! [X_6: produc652964533on_val,P_21: produc652964533on_val > $o] :
( ! [A_1: produc1746408499on_val,B_4: produc1282892786on_val,C_6: produc1282892786on_val] : ( P_21 @ ( produc345758123on_val @ A_1 @ ( produc833389609on_val @ B_4 @ C_6 ) ) )
=> ( P_21 @ X_6 ) ) ).
thf(fact_214_prod__induct3,axiom,
! [X_6: produc1368416213on_val,P_21: produc1368416213on_val > $o] :
( ! [A_1: produc2088785539on_val,B_4: list_char,C_6: produc1278157519t_char > option_val] : ( P_21 @ ( produc1773146955on_val @ A_1 @ ( produc926070009on_val @ B_4 @ C_6 ) ) )
=> ( P_21 @ X_6 ) ) ).
thf(fact_215_prod__induct3,axiom,
! [X_6: produc1250491293on_val,P_21: produc1250491293on_val > $o] :
( ! [A_1: produc618524391on_val,B_4: produc1180562163on_val,C_6: produc1180562163on_val] : ( P_21 @ ( produc1347028499on_val @ A_1 @ ( produc747700183on_val @ B_4 @ C_6 ) ) )
=> ( P_21 @ X_6 ) ) ).
thf(fact_216_prod__induct3,axiom,
! [X_6: produc630464863al_val,P_21: produc630464863al_val > $o] :
( ! [A_1: produc1645268488al_val,B_4: bop,C_6: product_prod_val_val] : ( P_21 @ ( produc1924279125al_val @ A_1 @ ( produc621191550al_val @ B_4 @ C_6 ) ) )
=> ( P_21 @ X_6 ) ) ).
thf(fact_217_prod__induct3,axiom,
! [X_6: produc800118557al_val,P_21: produc800118557al_val > $o] :
( ! [A_1: product_prod_val_val,B_4: val,C_6: val] : ( P_21 @ ( produc1244920211al_val @ A_1 @ ( product_Pair_val_val @ B_4 @ C_6 ) ) )
=> ( P_21 @ X_6 ) ) ).
thf(fact_218_prod__induct3,axiom,
! [X_6: produc1350825965t_char,P_21: produc1350825965t_char > $o] :
( ! [A_1: produc1278157519t_char,B_4: list_char,C_6: list_char] : ( P_21 @ ( produc2080520419t_char @ A_1 @ ( produc5062597t_char @ B_4 @ C_6 ) ) )
=> ( P_21 @ X_6 ) ) ).
thf(fact_219_prod__induct3,axiom,
! [X_6: produc1534059751t_char,P_21: produc1534059751t_char > $o] :
( ! [A_1: produc809539159t_char,B_4: list_list_char,C_6: exp_list_char] : ( P_21 @ ( produc1897818327t_char @ A_1 @ ( produc1147572817t_char @ B_4 @ C_6 ) ) )
=> ( P_21 @ X_6 ) ) ).
thf(fact_220_confs__conv__map,axiom,
! [P_20: list_P1999446415t_char,H_16: nat > option1728594148on_val,Vs_5: list_val,Ts_6: list_ty] :
( ( list_all2_val_ty @ ( conf_P373316194t_char @ P_20 @ H_16 ) @ Vs_5 @ Ts_6 )
<=> ? [Ts_7: list_ty] :
( ( ( map_val_option_ty @ ( typeof_h @ H_16 ) @ Vs_5 )
= ( map_ty_option_ty @ some_ty @ Ts_7 ) )
& ( list_all2_ty_ty @ ( widen_2090681816t_char @ P_20 ) @ Ts_7 @ Ts_6 ) ) ) ).
thf(fact_221_list__all2__mono,axiom,
! [Q_1: ty > ty > $o,P_19: ty > ty > $o,Xs_10: list_ty,Ys_5: list_ty] :
( ( list_all2_ty_ty @ P_19 @ Xs_10 @ Ys_5 )
=> ( ! [Xs_3: ty,Ys_6: ty] :
( ( P_19 @ Xs_3 @ Ys_6 )
=> ( Q_1 @ Xs_3 @ Ys_6 ) )
=> ( list_all2_ty_ty @ Q_1 @ Xs_10 @ Ys_5 ) ) ) ).
thf(fact_222_list__all2__mono,axiom,
! [Q_1: val > ty > $o,P_19: val > ty > $o,Xs_10: list_val,Ys_5: list_ty] :
( ( list_all2_val_ty @ P_19 @ Xs_10 @ Ys_5 )
=> ( ! [Xs_3: val,Ys_6: ty] :
( ( P_19 @ Xs_3 @ Ys_6 )
=> ( Q_1 @ Xs_3 @ Ys_6 ) )
=> ( list_all2_val_ty @ Q_1 @ Xs_10 @ Ys_5 ) ) ) ).
thf(fact_223_list__all2__refl,axiom,
! [Xs_9: list_ty,P_18: ty > ty > $o] :
( ! [X_3: ty] : ( P_18 @ X_3 @ X_3 )
=> ( list_all2_ty_ty @ P_18 @ Xs_9 @ Xs_9 ) ) ).
thf(fact_224_list__all2__antisym,axiom,
! [Xs_8: list_ty,Ys_4: list_ty,Q: ty > ty > $o,P_17: ty > ty > $o] :
( ! [X_3: ty,Y_1: ty] :
( ( P_17 @ X_3 @ Y_1 )
=> ( ( Q @ Y_1 @ X_3 )
=> ( X_3 = Y_1 ) ) )
=> ( ( list_all2_ty_ty @ P_17 @ Xs_8 @ Ys_4 )
=> ( ( list_all2_ty_ty @ Q @ Ys_4 @ Xs_8 )
=> ( Xs_8 = Ys_4 ) ) ) ) ).
thf(fact_225_Ex__list__of__length,axiom,
! [N_1: nat] :
? [Xs_3: list_option_ty] :
( ( size_s1050794909ion_ty @ Xs_3 )
= N_1 ) ).
thf(fact_226_Ex__list__of__length,axiom,
! [N_1: nat] :
? [Xs_3: list_list_char] :
( ( size_s2113983095t_char @ Xs_3 )
= N_1 ) ).
thf(fact_227_Ex__list__of__length,axiom,
! [N_1: nat] :
? [Xs_3: list_ty] :
( ( size_size_list_ty @ Xs_3 )
= N_1 ) ).
thf(fact_228_Ex__list__of__length,axiom,
! [N_1: nat] :
? [Xs_3: list_val] :
( ( size_size_list_val @ Xs_3 )
= N_1 ) ).
thf(fact_229_Ex__list__of__length,axiom,
! [N_1: nat] :
? [Xs_3: list_exp_list_char] :
( ( size_s1143674878t_char @ Xs_3 )
= N_1 ) ).
thf(fact_230_prod_Oexhaust,axiom,
! [Y_2: produc1534059751t_char] :
~ ! [A_1: produc809539159t_char,B_4: produc809539159t_char] :
( Y_2
!= ( produc1897818327t_char @ A_1 @ B_4 ) ) ).
thf(fact_231_prod_Oexhaust,axiom,
! [Y_2: produc1350825965t_char] :
~ ! [A_1: produc1278157519t_char,B_4: produc1278157519t_char] :
( Y_2
!= ( produc2080520419t_char @ A_1 @ B_4 ) ) ).
thf(fact_232_prod_Oexhaust,axiom,
! [Y_2: produc800118557al_val] :
~ ! [A_1: product_prod_val_val,B_4: product_prod_val_val] :
( Y_2
!= ( produc1244920211al_val @ A_1 @ B_4 ) ) ).
thf(fact_233_prod_Oexhaust,axiom,
! [Y_2: produc630464863al_val] :
~ ! [A_1: produc1645268488al_val,B_4: produc1645268488al_val] :
( Y_2
!= ( produc1924279125al_val @ A_1 @ B_4 ) ) ).
thf(fact_234_prod_Oexhaust,axiom,
! [Y_2: produc1250491293on_val] :
~ ! [A_1: produc618524391on_val,B_4: produc618524391on_val] :
( Y_2
!= ( produc1347028499on_val @ A_1 @ B_4 ) ) ).
thf(fact_235_prod_Oexhaust,axiom,
! [Y_2: produc1368416213on_val] :
~ ! [A_1: produc2088785539on_val,B_4: produc2088785539on_val] :
( Y_2
!= ( produc1773146955on_val @ A_1 @ B_4 ) ) ).
thf(fact_236_prod_Oexhaust,axiom,
! [Y_2: produc652964533on_val] :
~ ! [A_1: produc1746408499on_val,B_4: produc1746408499on_val] :
( Y_2
!= ( produc345758123on_val @ A_1 @ B_4 ) ) ).
thf(fact_237_prod_Oexhaust,axiom,
! [Y_2: produc1581780743on_val] :
~ ! [A_1: produc2090907612on_val,B_4: produc2090907612on_val] :
( Y_2
!= ( produc259392253on_val @ A_1 @ B_4 ) ) ).
thf(fact_238_prod_Oexhaust,axiom,
! [Y_2: produc1826280281t_char] :
~ ! [A_1: produc662261637t_char,B_4: produc662261637t_char] :
( Y_2
!= ( produc1299387215t_char @ A_1 @ B_4 ) ) ).
thf(fact_239_prod_Oexhaust,axiom,
! [Y_2: produc1406897475t_char] :
~ ! [A_1: produc220283002t_char,B_4: produc220283002t_char] :
( Y_2
!= ( produc57279289t_char @ A_1 @ B_4 ) ) ).
thf(fact_240_prod_Oexhaust,axiom,
! [Y_2: produc349695911t_char] :
~ ! [A_1: produc1285161482t_char,B_4: produc1285161482t_char] :
( Y_2
!= ( produc24551831t_char @ A_1 @ B_4 ) ) ).
thf(fact_241_prod_Oexhaust,axiom,
! [Y_2: produc1285161482t_char] :
~ ! [A_1: list_list_char,B_4: produc220283002t_char] :
( Y_2
!= ( produc921874948t_char @ A_1 @ B_4 ) ) ).
thf(fact_242_prod_Oexhaust,axiom,
! [Y_2: produc220283002t_char] :
~ ! [A_1: list_ty,B_4: produc662261637t_char] :
( Y_2
!= ( produc1909267824t_char @ A_1 @ B_4 ) ) ).
thf(fact_243_prod_Oexhaust,axiom,
! [Y_2: produc662261637t_char] :
~ ! [A_1: list_val,B_4: exp_list_char] :
( Y_2
!= ( produc1916172923t_char @ A_1 @ B_4 ) ) ).
thf(fact_244_prod_Oexhaust,axiom,
! [Y_2: produc2090907612on_val] :
~ ! [A_1: nat > option1728594148on_val,B_4: list_char > option_val] :
( Y_2
!= ( produc755559506on_val @ A_1 @ B_4 ) ) ).
thf(fact_245_prod_Oexhaust,axiom,
! [Y_2: produc1746408499on_val] :
~ ! [A_1: produc1282892786on_val,B_4: produc1282892786on_val] :
( Y_2
!= ( produc833389609on_val @ A_1 @ B_4 ) ) ).
thf(fact_246_prod_Oexhaust,axiom,
! [Y_2: produc1282892786on_val] :
~ ! [A_1: exp_list_char,B_4: produc2090907612on_val] :
( Y_2
!= ( produc235638504on_val @ A_1 @ B_4 ) ) ).
thf(fact_247_prod_Oexhaust,axiom,
! [Y_2: produc2088785539on_val] :
~ ! [A_1: list_char,B_4: produc1278157519t_char > option_val] :
( Y_2
!= ( produc926070009on_val @ A_1 @ B_4 ) ) ).
thf(fact_248_prod_Oexhaust,axiom,
! [Y_2: produc618524391on_val] :
~ ! [A_1: produc1180562163on_val,B_4: produc1180562163on_val] :
( Y_2
!= ( produc747700183on_val @ A_1 @ B_4 ) ) ).
thf(fact_249_prod_Oexhaust,axiom,
! [Y_2: produc1180562163on_val] :
~ ! [A_1: list_exp_list_char,B_4: produc2090907612on_val] :
( Y_2
!= ( produc1302104557on_val @ A_1 @ B_4 ) ) ).
thf(fact_250_prod_Oexhaust,axiom,
! [Y_2: produc1645268488al_val] :
~ ! [A_1: bop,B_4: product_prod_val_val] :
( Y_2
!= ( produc621191550al_val @ A_1 @ B_4 ) ) ).
thf(fact_251_prod_Oexhaust,axiom,
! [Y_2: product_prod_val_val] :
~ ! [A_1: val,B_4: val] :
( Y_2
!= ( product_Pair_val_val @ A_1 @ B_4 ) ) ).
thf(fact_252_prod_Oexhaust,axiom,
! [Y_2: produc1278157519t_char] :
~ ! [A_1: list_char,B_4: list_char] :
( Y_2
!= ( produc5062597t_char @ A_1 @ B_4 ) ) ).
thf(fact_253_prod_Oexhaust,axiom,
! [Y_2: produc809539159t_char] :
~ ! [A_1: list_list_char,B_4: exp_list_char] :
( Y_2
!= ( produc1147572817t_char @ A_1 @ B_4 ) ) ).
thf(fact_254_PairE,axiom,
! [P_16: produc1534059751t_char] :
~ ! [X_3: produc809539159t_char,Y_1: produc809539159t_char] :
( P_16
!= ( produc1897818327t_char @ X_3 @ Y_1 ) ) ).
thf(fact_255_PairE,axiom,
! [P_16: produc1350825965t_char] :
~ ! [X_3: produc1278157519t_char,Y_1: produc1278157519t_char] :
( P_16
!= ( produc2080520419t_char @ X_3 @ Y_1 ) ) ).
thf(fact_256_PairE,axiom,
! [P_16: produc800118557al_val] :
~ ! [X_3: product_prod_val_val,Y_1: product_prod_val_val] :
( P_16
!= ( produc1244920211al_val @ X_3 @ Y_1 ) ) ).
thf(fact_257_PairE,axiom,
! [P_16: produc630464863al_val] :
~ ! [X_3: produc1645268488al_val,Y_1: produc1645268488al_val] :
( P_16
!= ( produc1924279125al_val @ X_3 @ Y_1 ) ) ).
thf(fact_258_PairE,axiom,
! [P_16: produc1250491293on_val] :
~ ! [X_3: produc618524391on_val,Y_1: produc618524391on_val] :
( P_16
!= ( produc1347028499on_val @ X_3 @ Y_1 ) ) ).
thf(fact_259_PairE,axiom,
! [P_16: produc1368416213on_val] :
~ ! [X_3: produc2088785539on_val,Y_1: produc2088785539on_val] :
( P_16
!= ( produc1773146955on_val @ X_3 @ Y_1 ) ) ).
thf(fact_260_PairE,axiom,
! [P_16: produc652964533on_val] :
~ ! [X_3: produc1746408499on_val,Y_1: produc1746408499on_val] :
( P_16
!= ( produc345758123on_val @ X_3 @ Y_1 ) ) ).
thf(fact_261_PairE,axiom,
! [P_16: produc1581780743on_val] :
~ ! [X_3: produc2090907612on_val,Y_1: produc2090907612on_val] :
( P_16
!= ( produc259392253on_val @ X_3 @ Y_1 ) ) ).
thf(fact_262_PairE,axiom,
! [P_16: produc1826280281t_char] :
~ ! [X_3: produc662261637t_char,Y_1: produc662261637t_char] :
( P_16
!= ( produc1299387215t_char @ X_3 @ Y_1 ) ) ).
thf(fact_263_PairE,axiom,
! [P_16: produc1406897475t_char] :
~ ! [X_3: produc220283002t_char,Y_1: produc220283002t_char] :
( P_16
!= ( produc57279289t_char @ X_3 @ Y_1 ) ) ).
thf(fact_264_PairE,axiom,
! [P_16: produc349695911t_char] :
~ ! [X_3: produc1285161482t_char,Y_1: produc1285161482t_char] :
( P_16
!= ( produc24551831t_char @ X_3 @ Y_1 ) ) ).
thf(fact_265_PairE,axiom,
! [P_16: produc1285161482t_char] :
~ ! [X_3: list_list_char,Y_1: produc220283002t_char] :
( P_16
!= ( produc921874948t_char @ X_3 @ Y_1 ) ) ).
thf(fact_266_PairE,axiom,
! [P_16: produc220283002t_char] :
~ ! [X_3: list_ty,Y_1: produc662261637t_char] :
( P_16
!= ( produc1909267824t_char @ X_3 @ Y_1 ) ) ).
thf(fact_267_PairE,axiom,
! [P_16: produc662261637t_char] :
~ ! [X_3: list_val,Y_1: exp_list_char] :
( P_16
!= ( produc1916172923t_char @ X_3 @ Y_1 ) ) ).
thf(fact_268_PairE,axiom,
! [P_16: produc2090907612on_val] :
~ ! [X_3: nat > option1728594148on_val,Y_1: list_char > option_val] :
( P_16
!= ( produc755559506on_val @ X_3 @ Y_1 ) ) ).
thf(fact_269_PairE,axiom,
! [P_16: produc1746408499on_val] :
~ ! [X_3: produc1282892786on_val,Y_1: produc1282892786on_val] :
( P_16
!= ( produc833389609on_val @ X_3 @ Y_1 ) ) ).
thf(fact_270_PairE,axiom,
! [P_16: produc1282892786on_val] :
~ ! [X_3: exp_list_char,Y_1: produc2090907612on_val] :
( P_16
!= ( produc235638504on_val @ X_3 @ Y_1 ) ) ).
thf(fact_271_PairE,axiom,
! [P_16: produc2088785539on_val] :
~ ! [X_3: list_char,Y_1: produc1278157519t_char > option_val] :
( P_16
!= ( produc926070009on_val @ X_3 @ Y_1 ) ) ).
thf(fact_272_PairE,axiom,
! [P_16: produc618524391on_val] :
~ ! [X_3: produc1180562163on_val,Y_1: produc1180562163on_val] :
( P_16
!= ( produc747700183on_val @ X_3 @ Y_1 ) ) ).
thf(fact_273_PairE,axiom,
! [P_16: produc1180562163on_val] :
~ ! [X_3: list_exp_list_char,Y_1: produc2090907612on_val] :
( P_16
!= ( produc1302104557on_val @ X_3 @ Y_1 ) ) ).
thf(fact_274_PairE,axiom,
! [P_16: produc1645268488al_val] :
~ ! [X_3: bop,Y_1: product_prod_val_val] :
( P_16
!= ( produc621191550al_val @ X_3 @ Y_1 ) ) ).
thf(fact_275_PairE,axiom,
! [P_16: product_prod_val_val] :
~ ! [X_3: val,Y_1: val] :
( P_16
!= ( product_Pair_val_val @ X_3 @ Y_1 ) ) ).
thf(fact_276_PairE,axiom,
! [P_16: produc1278157519t_char] :
~ ! [X_3: list_char,Y_1: list_char] :
( P_16
!= ( produc5062597t_char @ X_3 @ Y_1 ) ) ).
thf(fact_277_PairE,axiom,
! [P_16: produc809539159t_char] :
~ ! [X_3: list_list_char,Y_1: exp_list_char] :
( P_16
!= ( produc1147572817t_char @ X_3 @ Y_1 ) ) ).
thf(fact_278_conf__widen,axiom,
! [T_10: ty,P_15: list_P1999446415t_char,H_15: nat > option1728594148on_val,V_7: val,T_9: ty] :
( ( conf_P373316194t_char @ P_15 @ H_15 @ V_7 @ T_9 )
=> ( ( widen_2090681816t_char @ P_15 @ T_9 @ T_10 )
=> ( conf_P373316194t_char @ P_15 @ H_15 @ V_7 @ T_10 ) ) ) ).
thf(fact_279_typeof__conf,axiom,
! [P_14: list_P1999446415t_char,H_14: nat > option1728594148on_val,V_6: val,T_8: ty] :
( ( ( typeof_h @ H_14 @ V_6 )
= ( some_ty @ T_8 ) )
=> ( conf_P373316194t_char @ P_14 @ H_14 @ V_6 @ T_8 ) ) ).
thf(fact_280_confs__widens,axiom,
! [Ts_5: list_ty,P_13: list_P1999446415t_char,H_13: nat > option1728594148on_val,Vs_4: list_val,Ts_4: list_ty] :
( ( list_all2_val_ty @ ( conf_P373316194t_char @ P_13 @ H_13 ) @ Vs_4 @ Ts_4 )
=> ( ( list_all2_ty_ty @ ( widen_2090681816t_char @ P_13 ) @ Ts_4 @ Ts_5 )
=> ( list_all2_val_ty @ ( conf_P373316194t_char @ P_13 @ H_13 ) @ Vs_4 @ Ts_5 ) ) ) ).
thf(fact_281_conf__def,axiom,
! [P_12: list_P1999446415t_char,H_12: nat > option1728594148on_val,V_5: val,T_6: ty] :
( ( conf_P373316194t_char @ P_12 @ H_12 @ V_5 @ T_6 )
<=> ? [T_7: ty] :
( ( ( typeof_h @ H_12 @ V_5 )
= ( some_ty @ T_7 ) )
& ( widen_2090681816t_char @ P_12 @ T_7 @ T_6 ) ) ) ).
thf(fact_282_split__paired__Ex,axiom,
! [P_11: produc1534059751t_char > $o] :
( ( ?? @ produc1534059751t_char @ P_11 )
<=> ? [A_1: produc809539159t_char,B_4: produc809539159t_char] : ( P_11 @ ( produc1897818327t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_283_split__paired__Ex,axiom,
! [P_11: produc1350825965t_char > $o] :
( ( ?? @ produc1350825965t_char @ P_11 )
<=> ? [A_1: produc1278157519t_char,B_4: produc1278157519t_char] : ( P_11 @ ( produc2080520419t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_284_split__paired__Ex,axiom,
! [P_11: produc800118557al_val > $o] :
( ( ?? @ produc800118557al_val @ P_11 )
<=> ? [A_1: product_prod_val_val,B_4: product_prod_val_val] : ( P_11 @ ( produc1244920211al_val @ A_1 @ B_4 ) ) ) ).
thf(fact_285_split__paired__Ex,axiom,
! [P_11: produc630464863al_val > $o] :
( ( ?? @ produc630464863al_val @ P_11 )
<=> ? [A_1: produc1645268488al_val,B_4: produc1645268488al_val] : ( P_11 @ ( produc1924279125al_val @ A_1 @ B_4 ) ) ) ).
thf(fact_286_split__paired__Ex,axiom,
! [P_11: produc1250491293on_val > $o] :
( ( ?? @ produc1250491293on_val @ P_11 )
<=> ? [A_1: produc618524391on_val,B_4: produc618524391on_val] : ( P_11 @ ( produc1347028499on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_287_split__paired__Ex,axiom,
! [P_11: produc1368416213on_val > $o] :
( ( ?? @ produc1368416213on_val @ P_11 )
<=> ? [A_1: produc2088785539on_val,B_4: produc2088785539on_val] : ( P_11 @ ( produc1773146955on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_288_split__paired__Ex,axiom,
! [P_11: produc652964533on_val > $o] :
( ( ?? @ produc652964533on_val @ P_11 )
<=> ? [A_1: produc1746408499on_val,B_4: produc1746408499on_val] : ( P_11 @ ( produc345758123on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_289_split__paired__Ex,axiom,
! [P_11: produc1581780743on_val > $o] :
( ( ?? @ produc1581780743on_val @ P_11 )
<=> ? [A_1: produc2090907612on_val,B_4: produc2090907612on_val] : ( P_11 @ ( produc259392253on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_290_split__paired__Ex,axiom,
! [P_11: produc1826280281t_char > $o] :
( ( ?? @ produc1826280281t_char @ P_11 )
<=> ? [A_1: produc662261637t_char,B_4: produc662261637t_char] : ( P_11 @ ( produc1299387215t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_291_split__paired__Ex,axiom,
! [P_11: produc1406897475t_char > $o] :
( ( ?? @ produc1406897475t_char @ P_11 )
<=> ? [A_1: produc220283002t_char,B_4: produc220283002t_char] : ( P_11 @ ( produc57279289t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_292_split__paired__Ex,axiom,
! [P_11: produc349695911t_char > $o] :
( ( ?? @ produc349695911t_char @ P_11 )
<=> ? [A_1: produc1285161482t_char,B_4: produc1285161482t_char] : ( P_11 @ ( produc24551831t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_293_split__paired__Ex,axiom,
! [P_11: produc1285161482t_char > $o] :
( ( ?? @ produc1285161482t_char @ P_11 )
<=> ? [A_1: list_list_char,B_4: produc220283002t_char] : ( P_11 @ ( produc921874948t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_294_split__paired__Ex,axiom,
! [P_11: produc220283002t_char > $o] :
( ( ?? @ produc220283002t_char @ P_11 )
<=> ? [A_1: list_ty,B_4: produc662261637t_char] : ( P_11 @ ( produc1909267824t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_295_split__paired__Ex,axiom,
! [P_11: produc662261637t_char > $o] :
( ( ?? @ produc662261637t_char @ P_11 )
<=> ? [A_1: list_val,B_4: exp_list_char] : ( P_11 @ ( produc1916172923t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_296_split__paired__Ex,axiom,
! [P_11: produc2090907612on_val > $o] :
( ( ?? @ produc2090907612on_val @ P_11 )
<=> ? [A_1: nat > option1728594148on_val,B_4: list_char > option_val] : ( P_11 @ ( produc755559506on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_297_split__paired__Ex,axiom,
! [P_11: produc1746408499on_val > $o] :
( ( ?? @ produc1746408499on_val @ P_11 )
<=> ? [A_1: produc1282892786on_val,B_4: produc1282892786on_val] : ( P_11 @ ( produc833389609on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_298_split__paired__Ex,axiom,
! [P_11: produc1282892786on_val > $o] :
( ( ?? @ produc1282892786on_val @ P_11 )
<=> ? [A_1: exp_list_char,B_4: produc2090907612on_val] : ( P_11 @ ( produc235638504on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_299_split__paired__Ex,axiom,
! [P_11: produc2088785539on_val > $o] :
( ( ?? @ produc2088785539on_val @ P_11 )
<=> ? [A_1: list_char,B_4: produc1278157519t_char > option_val] : ( P_11 @ ( produc926070009on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_300_split__paired__Ex,axiom,
! [P_11: produc618524391on_val > $o] :
( ( ?? @ produc618524391on_val @ P_11 )
<=> ? [A_1: produc1180562163on_val,B_4: produc1180562163on_val] : ( P_11 @ ( produc747700183on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_301_split__paired__Ex,axiom,
! [P_11: produc1180562163on_val > $o] :
( ( ?? @ produc1180562163on_val @ P_11 )
<=> ? [A_1: list_exp_list_char,B_4: produc2090907612on_val] : ( P_11 @ ( produc1302104557on_val @ A_1 @ B_4 ) ) ) ).
thf(fact_302_split__paired__Ex,axiom,
! [P_11: produc1645268488al_val > $o] :
( ( ?? @ produc1645268488al_val @ P_11 )
<=> ? [A_1: bop,B_4: product_prod_val_val] : ( P_11 @ ( produc621191550al_val @ A_1 @ B_4 ) ) ) ).
thf(fact_303_split__paired__Ex,axiom,
! [P_11: product_prod_val_val > $o] :
( ( ?? @ product_prod_val_val @ P_11 )
<=> ? [A_1: val,B_4: val] : ( P_11 @ ( product_Pair_val_val @ A_1 @ B_4 ) ) ) ).
thf(fact_304_split__paired__Ex,axiom,
! [P_11: produc1278157519t_char > $o] :
( ( ?? @ produc1278157519t_char @ P_11 )
<=> ? [A_1: list_char,B_4: list_char] : ( P_11 @ ( produc5062597t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_305_split__paired__Ex,axiom,
! [P_11: produc809539159t_char > $o] :
( ( ?? @ produc809539159t_char @ P_11 )
<=> ? [A_1: list_list_char,B_4: exp_list_char] : ( P_11 @ ( produc1147572817t_char @ A_1 @ B_4 ) ) ) ).
thf(fact_306_confs__hext,axiom,
! [H_11: nat > option1728594148on_val,P_10: list_P1999446415t_char,H_10: nat > option1728594148on_val,Vs_3: list_val,Ts_3: list_ty] :
( ( list_all2_val_ty @ ( conf_P373316194t_char @ P_10 @ H_10 ) @ Vs_3 @ Ts_3 )
=> ( ( hext @ H_10 @ H_11 )
=> ( list_all2_val_ty @ ( conf_P373316194t_char @ P_10 @ H_11 ) @ Vs_3 @ Ts_3 ) ) ) ).
thf(fact_307_blocksEval,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,E_2: exp_list_char,H_2: nat > option1728594148on_val,L_2: list_char > option_val,Vs: list_val,Ps: list_list_char,Ts_1: list_ty] :
( ( ( size_s2113983095t_char @ Ps )
= ( size_size_list_ty @ Ts_1 ) )
=> ( ( ( size_s2113983095t_char @ Ps )
= ( size_size_list_val @ Vs ) )
=> ( ( eval @ P @ ( blocks @ ( produc921874948t_char @ Ps @ ( produc1909267824t_char @ Ts_1 @ ( produc1916172923t_char @ Vs @ E ) ) ) ) @ ( produc755559506on_val @ H @ L_1 ) @ E_2 @ ( produc755559506on_val @ H_2 @ L_2 ) )
=> ? [L_6: list_char > option_val] : ( eval @ P @ E @ ( produc755559506on_val @ H @ ( map_up1085636310ar_val @ L_1 @ Ps @ Vs ) ) @ E_2 @ ( produc755559506on_val @ H_2 @ L_6 ) ) ) ) ) ).
thf(fact_308_option_Oinject,axiom,
! [A_14: ty,A_13: ty] :
( ( ( some_ty @ A_14 )
= ( some_ty @ A_13 ) )
<=> ( A_14 = A_13 ) ) ).
thf(fact_309_option_Oinject,axiom,
! [A_14: produc2088785539on_val,A_13: produc2088785539on_val] :
( ( ( some_P451527732on_val @ A_14 )
= ( some_P451527732on_val @ A_13 ) )
<=> ( A_14 = A_13 ) ) ).
thf(fact_310_option_Oinject,axiom,
! [A_14: val,A_13: val] :
( ( ( some_val @ A_14 )
= ( some_val @ A_13 ) )
<=> ( A_14 = A_13 ) ) ).
thf(fact_311_curryI,axiom,
! [F_13: produc1534059751t_char > $o,A_12: produc809539159t_char,B_10: produc809539159t_char] :
( ( F_13 @ ( produc1897818327t_char @ A_12 @ B_10 ) )
=> ( produc810272782char_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_312_curryI,axiom,
! [F_13: produc1350825965t_char > $o,A_12: produc1278157519t_char,B_10: produc1278157519t_char] :
( ( F_13 @ ( produc2080520419t_char @ A_12 @ B_10 ) )
=> ( produc1255505282char_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_313_curryI,axiom,
! [F_13: produc800118557al_val > $o,A_12: product_prod_val_val,B_10: product_prod_val_val] :
( ( F_13 @ ( produc1244920211al_val @ A_12 @ B_10 ) )
=> ( produc1669808594_val_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_314_curryI,axiom,
! [F_13: produc630464863al_val > $o,A_12: produc1645268488al_val,B_10: produc1645268488al_val] :
( ( F_13 @ ( produc1924279125al_val @ A_12 @ B_10 ) )
=> ( produc1498697104_val_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_315_curryI,axiom,
! [F_13: produc1250491293on_val > $o,A_12: produc618524391on_val,B_10: produc618524391on_val] :
( ( F_13 @ ( produc1347028499on_val @ A_12 @ B_10 ) )
=> ( produc317637970_val_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_316_curryI,axiom,
! [F_13: produc1368416213on_val > $o,A_12: produc2088785539on_val,B_10: produc2088785539on_val] :
( ( F_13 @ ( produc1773146955on_val @ A_12 @ B_10 ) )
=> ( produc1333173274_val_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_317_curryI,axiom,
! [F_13: produc652964533on_val > $o,A_12: produc1746408499on_val,B_10: produc1746408499on_val] :
( ( F_13 @ ( produc345758123on_val @ A_12 @ B_10 ) )
=> ( produc1882616506_val_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_318_curryI,axiom,
! [F_13: produc1581780743on_val > $o,A_12: produc2090907612on_val,B_10: produc2090907612on_val] :
( ( F_13 @ ( produc259392253on_val @ A_12 @ B_10 ) )
=> ( produc1959713768_val_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_319_curryI,axiom,
! [F_13: produc1826280281t_char > $o,A_12: produc662261637t_char,B_10: produc662261637t_char] :
( ( F_13 @ ( produc1299387215t_char @ A_12 @ B_10 ) )
=> ( produc1625470998char_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_320_curryI,axiom,
! [F_13: produc1406897475t_char > $o,A_12: produc220283002t_char,B_10: produc220283002t_char] :
( ( F_13 @ ( produc57279289t_char @ A_12 @ B_10 ) )
=> ( produc1560057516char_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_321_curryI,axiom,
! [F_13: produc349695911t_char > $o,A_12: produc1285161482t_char,B_10: produc1285161482t_char] :
( ( F_13 @ ( produc24551831t_char @ A_12 @ B_10 ) )
=> ( produc261176398char_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_322_curryI,axiom,
! [F_13: produc1285161482t_char > $o,A_12: list_list_char,B_10: produc220283002t_char] :
( ( F_13 @ ( produc921874948t_char @ A_12 @ B_10 ) )
=> ( produc193646727char_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_323_curryI,axiom,
! [F_13: produc220283002t_char > $o,A_12: list_ty,B_10: produc662261637t_char] :
( ( F_13 @ ( produc1909267824t_char @ A_12 @ B_10 ) )
=> ( produc786676533char_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_324_curryI,axiom,
! [F_13: produc662261637t_char > $o,A_12: list_val,B_10: exp_list_char] :
( ( F_13 @ ( produc1916172923t_char @ A_12 @ B_10 ) )
=> ( produc1072551658char_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_325_curryI,axiom,
! [F_13: produc2090907612on_val > $o,A_12: nat > option1728594148on_val,B_10: list_char > option_val] :
( ( F_13 @ ( produc755559506on_val @ A_12 @ B_10 ) )
=> ( produc1402621651_val_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_326_curryI,axiom,
! [F_13: produc1746408499on_val > $o,A_12: produc1282892786on_val,B_10: produc1282892786on_val] :
( ( F_13 @ ( produc833389609on_val @ A_12 @ B_10 ) )
=> ( produc803302844_val_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_327_curryI,axiom,
! [F_13: produc1282892786on_val > $o,A_12: exp_list_char,B_10: produc2090907612on_val] :
( ( F_13 @ ( produc235638504on_val @ A_12 @ B_10 ) )
=> ( produc1287763389_val_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_328_curryI,axiom,
! [F_13: produc2088785539on_val > $o,A_12: list_char,B_10: produc1278157519t_char > option_val] :
( ( F_13 @ ( produc926070009on_val @ A_12 @ B_10 ) )
=> ( produc1177570924_val_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_329_curryI,axiom,
! [F_13: produc618524391on_val > $o,A_12: produc1180562163on_val,B_10: produc1180562163on_val] :
( ( F_13 @ ( produc747700183on_val @ A_12 @ B_10 ) )
=> ( produc551782158_val_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_330_curryI,axiom,
! [F_13: produc1180562163on_val > $o,A_12: list_exp_list_char,B_10: produc2090907612on_val] :
( ( F_13 @ ( produc1302104557on_val @ A_12 @ B_10 ) )
=> ( produc618849246_val_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_331_curryI,axiom,
! [F_13: produc1645268488al_val > $o,A_12: bop,B_10: product_prod_val_val] :
( ( F_13 @ ( produc621191550al_val @ A_12 @ B_10 ) )
=> ( produc275195559_val_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_332_curryI,axiom,
! [F_13: product_prod_val_val > $o,A_12: val,B_10: val] :
( ( F_13 @ ( product_Pair_val_val @ A_12 @ B_10 ) )
=> ( produc575837646_val_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_333_curryI,axiom,
! [F_13: produc1278157519t_char > $o,A_12: list_char,B_10: list_char] :
( ( F_13 @ ( produc5062597t_char @ A_12 @ B_10 ) )
=> ( produc1709467424char_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_334_curryI,axiom,
! [F_13: produc809539159t_char > $o,A_12: list_list_char,B_10: exp_list_char] :
( ( F_13 @ ( produc1147572817t_char @ A_12 @ B_10 ) )
=> ( produc1404278138char_o @ F_13 @ A_12 @ B_10 ) ) ).
thf(fact_335_WTrts__Val,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,Vs: list_val,Ts_1: list_ty] :
( ( wTrts @ P @ H @ E_1 @ ( map_va1934808527t_char @ val_list_char @ Vs ) @ Ts_1 )
<=> ( ( map_val_option_ty @ ( typeof_h @ H ) @ Vs )
= ( map_ty_option_ty @ some_ty @ Ts_1 ) ) ) ).
thf(fact_336_defval__conf,axiom,
! [P_9: list_P1999446415t_char,H_9: nat > option1728594148on_val,T_5: ty] : ( conf_P373316194t_char @ P_9 @ H_9 @ ( default_val @ T_5 ) @ T_5 ) ).
thf(fact_337_blocksFinal,axiom,
! [H: nat > option1728594148on_val,L_1: list_char > option_val,P: list_P1999446415t_char,E: exp_list_char,Vs: list_val,Vs_2: list_list_char,Ts_1: list_ty] :
( ( ( size_s2113983095t_char @ Vs_2 )
= ( size_size_list_ty @ Ts_1 ) )
=> ( ( ( size_size_list_val @ Vs )
= ( size_size_list_ty @ Ts_1 ) )
=> ( ( final_list_char @ E )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( blocks @ ( produc921874948t_char @ Vs_2 @ ( produc1909267824t_char @ Ts_1 @ ( produc1916172923t_char @ Vs @ E ) ) ) ) @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L_1 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_338_WTrtVal,axiom,
! [P: list_P1999446415t_char,E_1: list_char > option_ty,H: nat > option1728594148on_val,V_2: val,T: ty] :
( ( ( typeof_h @ H @ V_2 )
= ( some_ty @ T ) )
=> ( wTrt @ P @ H @ E_1 @ ( val_list_char @ V_2 ) @ T ) ) ).
thf(fact_339_WTrts__hext__mono,axiom,
! [H_2: nat > option1728594148on_val,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,Es: list_exp_list_char,Ts_1: list_ty] :
( ( wTrts @ P @ H @ E_1 @ Es @ Ts_1 )
=> ( ( hext @ H @ H_2 )
=> ( wTrts @ P @ H_2 @ E_1 @ Es @ Ts_1 ) ) ) ).
thf(fact_340_WTrt__hext__mono,axiom,
! [H_2: nat > option1728594148on_val,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_1 @ E @ T )
=> ( ( hext @ H @ H_2 )
=> ( wTrt @ P @ H_2 @ E_1 @ E @ T ) ) ) ).
thf(fact_341_WTrts__same__length,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,Es: list_exp_list_char,Ts_1: list_ty] :
( ( wTrts @ P @ H @ E_1 @ Es @ Ts_1 )
=> ( ( size_s1143674878t_char @ Es )
= ( size_size_list_ty @ Ts_1 ) ) ) ).
thf(fact_342_conf__hext,axiom,
! [P_8: list_P1999446415t_char,V_4: val,T_4: ty,H_8: nat > option1728594148on_val,H_7: nat > option1728594148on_val] :
( ( hext @ H_8 @ H_7 )
=> ( ( conf_P373316194t_char @ P_8 @ H_8 @ V_4 @ T_4 )
=> ( conf_P373316194t_char @ P_8 @ H_7 @ V_4 @ T_4 ) ) ) ).
thf(fact_343_curryE,axiom,
! [F_12: produc809539159t_char > $o,A_11: list_list_char,B_9: exp_list_char] :
( ( produc1404278138char_o @ F_12 @ A_11 @ B_9 )
=> ( F_12 @ ( produc1147572817t_char @ A_11 @ B_9 ) ) ) ).
thf(fact_344_curryE,axiom,
! [F_12: produc1278157519t_char > $o,A_11: list_char,B_9: list_char] :
( ( produc1709467424char_o @ F_12 @ A_11 @ B_9 )
=> ( F_12 @ ( produc5062597t_char @ A_11 @ B_9 ) ) ) ).
thf(fact_345_curryE,axiom,
! [F_12: product_prod_val_val > $o,A_11: val,B_9: val] :
( ( produc575837646_val_o @ F_12 @ A_11 @ B_9 )
=> ( F_12 @ ( product_Pair_val_val @ A_11 @ B_9 ) ) ) ).
thf(fact_346_curryE,axiom,
! [F_12: produc1645268488al_val > $o,A_11: bop,B_9: product_prod_val_val] :
( ( produc275195559_val_o @ F_12 @ A_11 @ B_9 )
=> ( F_12 @ ( produc621191550al_val @ A_11 @ B_9 ) ) ) ).
thf(fact_347_curryE,axiom,
! [F_12: produc1180562163on_val > $o,A_11: list_exp_list_char,B_9: produc2090907612on_val] :
( ( produc618849246_val_o @ F_12 @ A_11 @ B_9 )
=> ( F_12 @ ( produc1302104557on_val @ A_11 @ B_9 ) ) ) ).
thf(fact_348_curryE,axiom,
! [F_12: produc618524391on_val > $o,A_11: produc1180562163on_val,B_9: produc1180562163on_val] :
( ( produc551782158_val_o @ F_12 @ A_11 @ B_9 )
=> ( F_12 @ ( produc747700183on_val @ A_11 @ B_9 ) ) ) ).
thf(fact_349_curryE,axiom,
! [F_12: produc2088785539on_val > $o,A_11: list_char,B_9: produc1278157519t_char > option_val] :
( ( produc1177570924_val_o @ F_12 @ A_11 @ B_9 )
=> ( F_12 @ ( produc926070009on_val @ A_11 @ B_9 ) ) ) ).
thf(fact_350_curryE,axiom,
! [F_12: produc1282892786on_val > $o,A_11: exp_list_char,B_9: produc2090907612on_val] :
( ( produc1287763389_val_o @ F_12 @ A_11 @ B_9 )
=> ( F_12 @ ( produc235638504on_val @ A_11 @ B_9 ) ) ) ).
thf(fact_351_curryE,axiom,
! [F_12: produc1746408499on_val > $o,A_11: produc1282892786on_val,B_9: produc1282892786on_val] :
( ( produc803302844_val_o @ F_12 @ A_11 @ B_9 )
=> ( F_12 @ ( produc833389609on_val @ A_11 @ B_9 ) ) ) ).
thf(fact_352_curryE,axiom,
! [F_12: produc2090907612on_val > $o,A_11: nat > option1728594148on_val,B_9: list_char > option_val] :
( ( produc1402621651_val_o @ F_12 @ A_11 @ B_9 )
=> ( F_12 @ ( produc755559506on_val @ A_11 @ B_9 ) ) ) ).
thf(fact_353_curryE,axiom,
! [F_12: produc662261637t_char > $o,A_11: list_val,B_9: exp_list_char] :
( ( produc1072551658char_o @ F_12 @ A_11 @ B_9 )
=> ( F_12 @ ( produc1916172923t_char @ A_11 @ B_9 ) ) ) ).
thf(fact_354_curryE,axiom,
! [F_12: produc220283002t_char > $o,A_11: list_ty,B_9: produc662261637t_char] :
( ( produc786676533char_o @ F_12 @ A_11 @ B_9 )
=> ( F_12 @ ( produc1909267824t_char @ A_11 @ B_9 ) ) ) ).
thf(fact_355_curryE,axiom,
! [F_12: produc1285161482t_char > $o,A_11: list_list_char,B_9: produc220283002t_char] :
( ( produc193646727char_o @ F_12 @ A_11 @ B_9 )
=> ( F_12 @ ( produc921874948t_char @ A_11 @ B_9 ) ) ) ).
thf(fact_356_curryD,axiom,
! [F_11: produc809539159t_char > $o,A_10: list_list_char,B_8: exp_list_char] :
( ( produc1404278138char_o @ F_11 @ A_10 @ B_8 )
=> ( F_11 @ ( produc1147572817t_char @ A_10 @ B_8 ) ) ) ).
thf(fact_357_curryD,axiom,
! [F_11: produc1278157519t_char > $o,A_10: list_char,B_8: list_char] :
( ( produc1709467424char_o @ F_11 @ A_10 @ B_8 )
=> ( F_11 @ ( produc5062597t_char @ A_10 @ B_8 ) ) ) ).
thf(fact_358_curryD,axiom,
! [F_11: product_prod_val_val > $o,A_10: val,B_8: val] :
( ( produc575837646_val_o @ F_11 @ A_10 @ B_8 )
=> ( F_11 @ ( product_Pair_val_val @ A_10 @ B_8 ) ) ) ).
thf(fact_359_curryD,axiom,
! [F_11: produc1645268488al_val > $o,A_10: bop,B_8: product_prod_val_val] :
( ( produc275195559_val_o @ F_11 @ A_10 @ B_8 )
=> ( F_11 @ ( produc621191550al_val @ A_10 @ B_8 ) ) ) ).
thf(fact_360_curryD,axiom,
! [F_11: produc1180562163on_val > $o,A_10: list_exp_list_char,B_8: produc2090907612on_val] :
( ( produc618849246_val_o @ F_11 @ A_10 @ B_8 )
=> ( F_11 @ ( produc1302104557on_val @ A_10 @ B_8 ) ) ) ).
thf(fact_361_curryD,axiom,
! [F_11: produc618524391on_val > $o,A_10: produc1180562163on_val,B_8: produc1180562163on_val] :
( ( produc551782158_val_o @ F_11 @ A_10 @ B_8 )
=> ( F_11 @ ( produc747700183on_val @ A_10 @ B_8 ) ) ) ).
thf(fact_362_curryD,axiom,
! [F_11: produc2088785539on_val > $o,A_10: list_char,B_8: produc1278157519t_char > option_val] :
( ( produc1177570924_val_o @ F_11 @ A_10 @ B_8 )
=> ( F_11 @ ( produc926070009on_val @ A_10 @ B_8 ) ) ) ).
thf(fact_363_curryD,axiom,
! [F_11: produc1282892786on_val > $o,A_10: exp_list_char,B_8: produc2090907612on_val] :
( ( produc1287763389_val_o @ F_11 @ A_10 @ B_8 )
=> ( F_11 @ ( produc235638504on_val @ A_10 @ B_8 ) ) ) ).
thf(fact_364_curryD,axiom,
! [F_11: produc1746408499on_val > $o,A_10: produc1282892786on_val,B_8: produc1282892786on_val] :
( ( produc803302844_val_o @ F_11 @ A_10 @ B_8 )
=> ( F_11 @ ( produc833389609on_val @ A_10 @ B_8 ) ) ) ).
thf(fact_365_curryD,axiom,
! [F_11: produc2090907612on_val > $o,A_10: nat > option1728594148on_val,B_8: list_char > option_val] :
( ( produc1402621651_val_o @ F_11 @ A_10 @ B_8 )
=> ( F_11 @ ( produc755559506on_val @ A_10 @ B_8 ) ) ) ).
thf(fact_366_curryD,axiom,
! [F_11: produc662261637t_char > $o,A_10: list_val,B_8: exp_list_char] :
( ( produc1072551658char_o @ F_11 @ A_10 @ B_8 )
=> ( F_11 @ ( produc1916172923t_char @ A_10 @ B_8 ) ) ) ).
thf(fact_367_curryD,axiom,
! [F_11: produc220283002t_char > $o,A_10: list_ty,B_8: produc662261637t_char] :
( ( produc786676533char_o @ F_11 @ A_10 @ B_8 )
=> ( F_11 @ ( produc1909267824t_char @ A_10 @ B_8 ) ) ) ).
thf(fact_368_curryD,axiom,
! [F_11: produc1285161482t_char > $o,A_10: list_list_char,B_8: produc220283002t_char] :
( ( produc193646727char_o @ F_11 @ A_10 @ B_8 )
=> ( F_11 @ ( produc921874948t_char @ A_10 @ B_8 ) ) ) ).
thf(fact_369_red__hext__incr,axiom,
! [E: exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,E_2: exp_list_char,H_2: nat > option1728594148on_val,L_2: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_2 @ L_2 ) ) ) @ ( red @ P ) )
=> ( hext @ H @ H_2 ) ) ).
thf(fact_370_rtrancl_Ortrancl__refl,axiom,
! [A_9: list_char,R_12: produc1278157519t_char > $o] : ( member1251428284t_char @ ( produc5062597t_char @ A_9 @ A_9 ) @ ( transi1395422419t_char @ R_12 ) ) ).
thf(fact_371_rtrancl_Ortrancl__refl,axiom,
! [A_9: produc1180562163on_val,R_12: produc618524391on_val > $o] : ( member2042188884on_val @ ( produc747700183on_val @ A_9 @ A_9 ) @ ( transi808828192on_val @ R_12 ) ) ).
thf(fact_372_rtrancl_Ortrancl__refl,axiom,
! [A_9: produc1282892786on_val,R_12: produc1746408499on_val > $o] : ( member1913460000on_val @ ( produc833389609on_val @ A_9 @ A_9 ) @ ( transi2118771717on_val @ R_12 ) ) ).
thf(fact_373_rtrancl_Ortrancl__refl,axiom,
! [A_9: val,R_12: product_prod_val_val > $o] : ( member649088532al_val @ ( product_Pair_val_val @ A_9 @ A_9 ) @ ( transi935034983cl_val @ R_12 ) ) ).
thf(fact_374_hext__typeof__mono,axiom,
! [V_2: val,T: ty,H: nat > option1728594148on_val,H_2: nat > option1728594148on_val] :
( ( hext @ H @ H_2 )
=> ( ( ( typeof_h @ H @ V_2 )
= ( some_ty @ T ) )
=> ( ( typeof_h @ H_2 @ V_2 )
= ( some_ty @ T ) ) ) ) ).
thf(fact_375_eval__hext,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,E_2: exp_list_char,H_2: nat > option1728594148on_val,L_2: list_char > option_val] :
( ( eval @ P @ E @ ( produc755559506on_val @ H @ L_1 ) @ E_2 @ ( produc755559506on_val @ H_2 @ L_2 ) )
=> ( hext @ H @ H_2 ) ) ).
thf(fact_376_hext__refl,axiom,
! [H: nat > option1728594148on_val] : ( hext @ H @ H ) ).
thf(fact_377_r__into__rtrancl,axiom,
! [P_7: produc1278157519t_char,R_11: produc1278157519t_char > $o] :
( ( member1251428284t_char @ P_7 @ R_11 )
=> ( member1251428284t_char @ P_7 @ ( transi1395422419t_char @ R_11 ) ) ) ).
thf(fact_378_r__into__rtrancl,axiom,
! [P_7: produc618524391on_val,R_11: produc618524391on_val > $o] :
( ( member2042188884on_val @ P_7 @ R_11 )
=> ( member2042188884on_val @ P_7 @ ( transi808828192on_val @ R_11 ) ) ) ).
thf(fact_379_r__into__rtrancl,axiom,
! [P_7: produc1746408499on_val,R_11: produc1746408499on_val > $o] :
( ( member1913460000on_val @ P_7 @ R_11 )
=> ( member1913460000on_val @ P_7 @ ( transi2118771717on_val @ R_11 ) ) ) ).
thf(fact_380_red__preserves__hconf,axiom,
! [E_1: list_char > option_ty,T: ty,E: exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,E_2: exp_list_char,H_2: nat > option1728594148on_val,L_2: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_2 @ L_2 ) ) ) @ ( red @ P ) )
=> ( ( wTrt @ P @ H @ E_1 @ E @ T )
=> ( ( hconf_97414254t_char @ P @ H )
=> ( hconf_97414254t_char @ P @ H_2 ) ) ) ) ).
thf(fact_381_eval__finalId,axiom,
! [P: list_P1999446415t_char,S: produc2090907612on_val,E: exp_list_char] :
( ( final_list_char @ E )
=> ( eval @ P @ E @ S @ E @ S ) ) ).
thf(fact_382_eval__final,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ E @ S @ E_2 @ S_1 )
=> ( final_list_char @ E_2 ) ) ).
thf(fact_383_red__preserves__lconf,axiom,
! [E_1: list_char > option_ty,T: ty,E: exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,E_2: exp_list_char,H_2: nat > option1728594148on_val,L_2: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_2 @ L_2 ) ) ) @ ( red @ P ) )
=> ( ( wTrt @ P @ H @ E_1 @ E @ T )
=> ( ( lconf_496643946t_char @ P @ H @ L_1 @ E_1 )
=> ( lconf_496643946t_char @ P @ H_2 @ L_2 @ E_1 ) ) ) ) ).
thf(fact_384_lconf__hext,axiom,
! [H_6: nat > option1728594148on_val,P_6: list_P1999446415t_char,H_5: nat > option1728594148on_val,L_5: list_char > option_val,E_6: list_char > option_ty] :
( ( lconf_496643946t_char @ P_6 @ H_5 @ L_5 @ E_6 )
=> ( ( hext @ H_5 @ H_6 )
=> ( lconf_496643946t_char @ P_6 @ H_6 @ L_5 @ E_6 ) ) ) ).
thf(fact_385_rtrancl__idemp,axiom,
! [R_10: produc1278157519t_char > $o] :
( ( transi1395422419t_char @ ( transi1395422419t_char @ R_10 ) )
= ( transi1395422419t_char @ R_10 ) ) ).
thf(fact_386_rtrancl__idemp,axiom,
! [R_10: produc618524391on_val > $o] :
( ( transi808828192on_val @ ( transi808828192on_val @ R_10 ) )
= ( transi808828192on_val @ R_10 ) ) ).
thf(fact_387_rtrancl__idemp,axiom,
! [R_10: produc1746408499on_val > $o] :
( ( transi2118771717on_val @ ( transi2118771717on_val @ R_10 ) )
= ( transi2118771717on_val @ R_10 ) ) ).
thf(fact_388_hext__trans,axiom,
! [H_4: nat > option1728594148on_val,H: nat > option1728594148on_val,H_2: nat > option1728594148on_val] :
( ( hext @ H @ H_2 )
=> ( ( hext @ H_2 @ H_4 )
=> ( hext @ H @ H_4 ) ) ) ).
thf(fact_389_converse__rtrancl__into__rtrancl,axiom,
! [C_5: list_char,A_8: list_char,B_7: list_char,R_9: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_8 @ B_7 ) @ R_9 )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ B_7 @ C_5 ) @ ( transi1395422419t_char @ R_9 ) )
=> ( member1251428284t_char @ ( produc5062597t_char @ A_8 @ C_5 ) @ ( transi1395422419t_char @ R_9 ) ) ) ) ).
thf(fact_390_converse__rtrancl__into__rtrancl,axiom,
! [C_5: produc1180562163on_val,A_8: produc1180562163on_val,B_7: produc1180562163on_val,R_9: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_8 @ B_7 ) @ R_9 )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ B_7 @ C_5 ) @ ( transi808828192on_val @ R_9 ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ A_8 @ C_5 ) @ ( transi808828192on_val @ R_9 ) ) ) ) ).
thf(fact_391_converse__rtrancl__into__rtrancl,axiom,
! [C_5: produc1282892786on_val,A_8: produc1282892786on_val,B_7: produc1282892786on_val,R_9: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_8 @ B_7 ) @ R_9 )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ B_7 @ C_5 ) @ ( transi2118771717on_val @ R_9 ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ A_8 @ C_5 ) @ ( transi2118771717on_val @ R_9 ) ) ) ) ).
thf(fact_392_converse__rtrancl__into__rtrancl,axiom,
! [C_5: val,A_8: val,B_7: val,R_9: product_prod_val_val > $o] :
( ( member649088532al_val @ ( product_Pair_val_val @ A_8 @ B_7 ) @ R_9 )
=> ( ( member649088532al_val @ ( product_Pair_val_val @ B_7 @ C_5 ) @ ( transi935034983cl_val @ R_9 ) )
=> ( member649088532al_val @ ( product_Pair_val_val @ A_8 @ C_5 ) @ ( transi935034983cl_val @ R_9 ) ) ) ) ).
thf(fact_393_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_4: list_char,A_7: list_char,B_6: list_char,R_8: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_7 @ B_6 ) @ ( transi1395422419t_char @ R_8 ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ B_6 @ C_4 ) @ R_8 )
=> ( member1251428284t_char @ ( produc5062597t_char @ A_7 @ C_4 ) @ ( transi1395422419t_char @ R_8 ) ) ) ) ).
thf(fact_394_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_4: produc1180562163on_val,A_7: produc1180562163on_val,B_6: produc1180562163on_val,R_8: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_7 @ B_6 ) @ ( transi808828192on_val @ R_8 ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ B_6 @ C_4 ) @ R_8 )
=> ( member2042188884on_val @ ( produc747700183on_val @ A_7 @ C_4 ) @ ( transi808828192on_val @ R_8 ) ) ) ) ).
thf(fact_395_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_4: produc1282892786on_val,A_7: produc1282892786on_val,B_6: produc1282892786on_val,R_8: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_7 @ B_6 ) @ ( transi2118771717on_val @ R_8 ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ B_6 @ C_4 ) @ R_8 )
=> ( member1913460000on_val @ ( produc833389609on_val @ A_7 @ C_4 ) @ ( transi2118771717on_val @ R_8 ) ) ) ) ).
thf(fact_396_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_4: val,A_7: val,B_6: val,R_8: product_prod_val_val > $o] :
( ( member649088532al_val @ ( product_Pair_val_val @ A_7 @ B_6 ) @ ( transi935034983cl_val @ R_8 ) )
=> ( ( member649088532al_val @ ( product_Pair_val_val @ B_6 @ C_4 ) @ R_8 )
=> ( member649088532al_val @ ( product_Pair_val_val @ A_7 @ C_4 ) @ ( transi935034983cl_val @ R_8 ) ) ) ) ).
thf(fact_397_rtrancl__trans,axiom,
! [C_3: list_char,A_6: list_char,B_5: list_char,R_7: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_6 @ B_5 ) @ ( transi1395422419t_char @ R_7 ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ B_5 @ C_3 ) @ ( transi1395422419t_char @ R_7 ) )
=> ( member1251428284t_char @ ( produc5062597t_char @ A_6 @ C_3 ) @ ( transi1395422419t_char @ R_7 ) ) ) ) ).
thf(fact_398_rtrancl__trans,axiom,
! [C_3: produc1180562163on_val,A_6: produc1180562163on_val,B_5: produc1180562163on_val,R_7: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_6 @ B_5 ) @ ( transi808828192on_val @ R_7 ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ B_5 @ C_3 ) @ ( transi808828192on_val @ R_7 ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ A_6 @ C_3 ) @ ( transi808828192on_val @ R_7 ) ) ) ) ).
thf(fact_399_rtrancl__trans,axiom,
! [C_3: produc1282892786on_val,A_6: produc1282892786on_val,B_5: produc1282892786on_val,R_7: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_6 @ B_5 ) @ ( transi2118771717on_val @ R_7 ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ B_5 @ C_3 ) @ ( transi2118771717on_val @ R_7 ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ A_6 @ C_3 ) @ ( transi2118771717on_val @ R_7 ) ) ) ) ).
thf(fact_400_rtrancl__trans,axiom,
! [C_3: val,A_6: val,B_5: val,R_7: product_prod_val_val > $o] :
( ( member649088532al_val @ ( product_Pair_val_val @ A_6 @ B_5 ) @ ( transi935034983cl_val @ R_7 ) )
=> ( ( member649088532al_val @ ( product_Pair_val_val @ B_5 @ C_3 ) @ ( transi935034983cl_val @ R_7 ) )
=> ( member649088532al_val @ ( product_Pair_val_val @ A_6 @ C_3 ) @ ( transi935034983cl_val @ R_7 ) ) ) ) ).
thf(fact_401_eval__cases_I2_J,axiom,
! [P: list_P1999446415t_char,V_2: val,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ ( val_list_char @ V_2 ) @ S @ E_2 @ S_1 )
=> ~ ( ( E_2
= ( val_list_char @ V_2 ) )
=> ( S_1 != S ) ) ) ).
thf(fact_402_Val,axiom,
! [P: list_P1999446415t_char,V_2: val,S: produc2090907612on_val] : ( eval @ P @ ( val_list_char @ V_2 ) @ S @ ( val_list_char @ V_2 ) @ S ) ).
thf(fact_403_lconf__def,axiom,
! [P_5: list_P1999446415t_char,H_3: nat > option1728594148on_val,L_4: list_char > option_val,E_5: list_char > option_ty] :
( ( lconf_496643946t_char @ P_5 @ H_3 @ L_4 @ E_5 )
<=> ! [V_3: list_char,V_1: val] :
( ( ( L_4 @ V_3 )
= ( some_val @ V_1 ) )
=> ? [T_3: ty] :
( ( ( E_5 @ V_3 )
= ( some_ty @ T_3 ) )
& ( conf_P373316194t_char @ P_5 @ H_3 @ V_1 @ T_3 ) ) ) ) ).
thf(fact_404_converse__rtranclE2,axiom,
! [Xa_1: list_exp_list_char,Xb: produc2090907612on_val,Za: list_exp_list_char,Zb: produc2090907612on_val,R_6: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Xa_1 @ Xb ) @ ( produc1302104557on_val @ Za @ Zb ) ) @ ( transi808828192on_val @ R_6 ) )
=> ( ( ( produc1302104557on_val @ Xa_1 @ Xb )
!= ( produc1302104557on_val @ Za @ Zb ) )
=> ~ ! [A_1: list_exp_list_char,B_4: produc2090907612on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Xa_1 @ Xb ) @ ( produc1302104557on_val @ A_1 @ B_4 ) ) @ R_6 )
=> ~ ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ A_1 @ B_4 ) @ ( produc1302104557on_val @ Za @ Zb ) ) @ ( transi808828192on_val @ R_6 ) ) ) ) ) ).
thf(fact_405_converse__rtranclE2,axiom,
! [Xa_1: exp_list_char,Xb: produc2090907612on_val,Za: exp_list_char,Zb: produc2090907612on_val,R_6: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Xa_1 @ Xb ) @ ( produc235638504on_val @ Za @ Zb ) ) @ ( transi2118771717on_val @ R_6 ) )
=> ( ( ( produc235638504on_val @ Xa_1 @ Xb )
!= ( produc235638504on_val @ Za @ Zb ) )
=> ~ ! [A_1: exp_list_char,B_4: produc2090907612on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Xa_1 @ Xb ) @ ( produc235638504on_val @ A_1 @ B_4 ) ) @ R_6 )
=> ~ ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ A_1 @ B_4 ) @ ( produc235638504on_val @ Za @ Zb ) ) @ ( transi2118771717on_val @ R_6 ) ) ) ) ) ).
thf(fact_406_converse__rtranclE2,axiom,
! [Xa_1: list_list_char,Xb: exp_list_char,Za: list_list_char,Zb: exp_list_char,R_6: produc1534059751t_char > $o] :
( ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ Xa_1 @ Xb ) @ ( produc1147572817t_char @ Za @ Zb ) ) @ ( transi198989188t_char @ R_6 ) )
=> ( ( ( produc1147572817t_char @ Xa_1 @ Xb )
!= ( produc1147572817t_char @ Za @ Zb ) )
=> ~ ! [A_1: list_list_char,B_4: exp_list_char] :
( ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ Xa_1 @ Xb ) @ ( produc1147572817t_char @ A_1 @ B_4 ) ) @ R_6 )
=> ~ ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ A_1 @ B_4 ) @ ( produc1147572817t_char @ Za @ Zb ) ) @ ( transi198989188t_char @ R_6 ) ) ) ) ) ).
thf(fact_407_converse__rtranclE2,axiom,
! [Xa_1: list_char,Xb: list_char,Za: list_char,Zb: list_char,R_6: produc1350825965t_char > $o] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ Xa_1 @ Xb ) @ ( produc5062597t_char @ Za @ Zb ) ) @ ( transi1095029602t_char @ R_6 ) )
=> ( ( ( produc5062597t_char @ Xa_1 @ Xb )
!= ( produc5062597t_char @ Za @ Zb ) )
=> ~ ! [A_1: list_char,B_4: list_char] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ Xa_1 @ Xb ) @ ( produc5062597t_char @ A_1 @ B_4 ) ) @ R_6 )
=> ~ ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ A_1 @ B_4 ) @ ( produc5062597t_char @ Za @ Zb ) ) @ ( transi1095029602t_char @ R_6 ) ) ) ) ) ).
thf(fact_408_converse__rtranclE2,axiom,
! [Xa_1: val,Xb: val,Za: val,Zb: val,R_6: produc800118557al_val > $o] :
( ( member837208074al_val @ ( produc1244920211al_val @ ( product_Pair_val_val @ Xa_1 @ Xb ) @ ( product_Pair_val_val @ Za @ Zb ) ) @ ( transi1423755450al_val @ R_6 ) )
=> ( ( ( product_Pair_val_val @ Xa_1 @ Xb )
!= ( product_Pair_val_val @ Za @ Zb ) )
=> ~ ! [A_1: val,B_4: val] :
( ( member837208074al_val @ ( produc1244920211al_val @ ( product_Pair_val_val @ Xa_1 @ Xb ) @ ( product_Pair_val_val @ A_1 @ B_4 ) ) @ R_6 )
=> ~ ( member837208074al_val @ ( produc1244920211al_val @ ( product_Pair_val_val @ A_1 @ B_4 ) @ ( product_Pair_val_val @ Za @ Zb ) ) @ ( transi1423755450al_val @ R_6 ) ) ) ) ) ).
thf(fact_409_converse__rtranclE2,axiom,
! [Xa_1: bop,Xb: product_prod_val_val,Za: bop,Zb: product_prod_val_val,R_6: produc630464863al_val > $o] :
( ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ Xa_1 @ Xb ) @ ( produc621191550al_val @ Za @ Zb ) ) @ ( transi1906258203al_val @ R_6 ) )
=> ( ( ( produc621191550al_val @ Xa_1 @ Xb )
!= ( produc621191550al_val @ Za @ Zb ) )
=> ~ ! [A_1: bop,B_4: product_prod_val_val] :
( ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ Xa_1 @ Xb ) @ ( produc621191550al_val @ A_1 @ B_4 ) ) @ R_6 )
=> ~ ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ A_1 @ B_4 ) @ ( produc621191550al_val @ Za @ Zb ) ) @ ( transi1906258203al_val @ R_6 ) ) ) ) ) ).
thf(fact_410_converse__rtranclE2,axiom,
! [Xa_1: produc1180562163on_val,Xb: produc1180562163on_val,Za: produc1180562163on_val,Zb: produc1180562163on_val,R_6: produc1250491293on_val > $o] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ Xa_1 @ Xb ) @ ( produc747700183on_val @ Za @ Zb ) ) @ ( transi1457397498on_val @ R_6 ) )
=> ( ( ( produc747700183on_val @ Xa_1 @ Xb )
!= ( produc747700183on_val @ Za @ Zb ) )
=> ~ ! [A_1: produc1180562163on_val,B_4: produc1180562163on_val] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ Xa_1 @ Xb ) @ ( produc747700183on_val @ A_1 @ B_4 ) ) @ R_6 )
=> ~ ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ A_1 @ B_4 ) @ ( produc747700183on_val @ Za @ Zb ) ) @ ( transi1457397498on_val @ R_6 ) ) ) ) ) ).
thf(fact_411_converse__rtranclE2,axiom,
! [Xa_1: list_char,Xb: produc1278157519t_char > option_val,Za: list_char,Zb: produc1278157519t_char > option_val,R_6: produc1368416213on_val > $o] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Xa_1 @ Xb ) @ ( produc926070009on_val @ Za @ Zb ) ) @ ( transi1669211542on_val @ R_6 ) )
=> ( ( ( produc926070009on_val @ Xa_1 @ Xb )
!= ( produc926070009on_val @ Za @ Zb ) )
=> ~ ! [A_1: list_char,B_4: produc1278157519t_char > option_val] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Xa_1 @ Xb ) @ ( produc926070009on_val @ A_1 @ B_4 ) ) @ R_6 )
=> ~ ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ A_1 @ B_4 ) @ ( produc926070009on_val @ Za @ Zb ) ) @ ( transi1669211542on_val @ R_6 ) ) ) ) ) ).
thf(fact_412_converse__rtranclE2,axiom,
! [Xa_1: produc1282892786on_val,Xb: produc1282892786on_val,Za: produc1282892786on_val,Zb: produc1282892786on_val,R_6: produc652964533on_val > $o] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Xa_1 @ Xb ) @ ( produc833389609on_val @ Za @ Zb ) ) @ ( transi130214086on_val @ R_6 ) )
=> ( ( ( produc833389609on_val @ Xa_1 @ Xb )
!= ( produc833389609on_val @ Za @ Zb ) )
=> ~ ! [A_1: produc1282892786on_val,B_4: produc1282892786on_val] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Xa_1 @ Xb ) @ ( produc833389609on_val @ A_1 @ B_4 ) ) @ R_6 )
=> ~ ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ A_1 @ B_4 ) @ ( produc833389609on_val @ Za @ Zb ) ) @ ( transi130214086on_val @ R_6 ) ) ) ) ) ).
thf(fact_413_converse__rtranclE2,axiom,
! [Xa_1: nat > option1728594148on_val,Xb: list_char > option_val,Za: nat > option1728594148on_val,Zb: list_char > option_val,R_6: produc1581780743on_val > $o] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Xa_1 @ Xb ) @ ( produc755559506on_val @ Za @ Zb ) ) @ ( transi466770671on_val @ R_6 ) )
=> ( ( ( produc755559506on_val @ Xa_1 @ Xb )
!= ( produc755559506on_val @ Za @ Zb ) )
=> ~ ! [A_1: nat > option1728594148on_val,B_4: list_char > option_val] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Xa_1 @ Xb ) @ ( produc755559506on_val @ A_1 @ B_4 ) ) @ R_6 )
=> ~ ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ A_1 @ B_4 ) @ ( produc755559506on_val @ Za @ Zb ) ) @ ( transi466770671on_val @ R_6 ) ) ) ) ) ).
thf(fact_414_converse__rtranclE2,axiom,
! [Xa_1: list_val,Xb: exp_list_char,Za: list_val,Zb: exp_list_char,R_6: produc1826280281t_char > $o] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Xa_1 @ Xb ) @ ( produc1916172923t_char @ Za @ Zb ) ) @ ( transi1789604888t_char @ R_6 ) )
=> ( ( ( produc1916172923t_char @ Xa_1 @ Xb )
!= ( produc1916172923t_char @ Za @ Zb ) )
=> ~ ! [A_1: list_val,B_4: exp_list_char] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Xa_1 @ Xb ) @ ( produc1916172923t_char @ A_1 @ B_4 ) ) @ R_6 )
=> ~ ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ A_1 @ B_4 ) @ ( produc1916172923t_char @ Za @ Zb ) ) @ ( transi1789604888t_char @ R_6 ) ) ) ) ) ).
thf(fact_415_converse__rtranclE2,axiom,
! [Xa_1: list_ty,Xb: produc662261637t_char,Za: list_ty,Zb: produc662261637t_char,R_6: produc1406897475t_char > $o] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Xa_1 @ Xb ) @ ( produc1909267824t_char @ Za @ Zb ) ) @ ( transi1257872013t_char @ R_6 ) )
=> ( ( ( produc1909267824t_char @ Xa_1 @ Xb )
!= ( produc1909267824t_char @ Za @ Zb ) )
=> ~ ! [A_1: list_ty,B_4: produc662261637t_char] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Xa_1 @ Xb ) @ ( produc1909267824t_char @ A_1 @ B_4 ) ) @ R_6 )
=> ~ ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ A_1 @ B_4 ) @ ( produc1909267824t_char @ Za @ Zb ) ) @ ( transi1257872013t_char @ R_6 ) ) ) ) ) ).
thf(fact_416_converse__rtranclE2,axiom,
! [Xa_1: list_list_char,Xb: produc220283002t_char,Za: list_list_char,Zb: produc220283002t_char,R_6: produc349695911t_char > $o] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Xa_1 @ Xb ) @ ( produc921874948t_char @ Za @ Zb ) ) @ ( transi122195895t_char @ R_6 ) )
=> ( ( ( produc921874948t_char @ Xa_1 @ Xb )
!= ( produc921874948t_char @ Za @ Zb ) )
=> ~ ! [A_1: list_list_char,B_4: produc220283002t_char] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Xa_1 @ Xb ) @ ( produc921874948t_char @ A_1 @ B_4 ) ) @ R_6 )
=> ~ ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ A_1 @ B_4 ) @ ( produc921874948t_char @ Za @ Zb ) ) @ ( transi122195895t_char @ R_6 ) ) ) ) ) ).
thf(fact_417_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_5: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Ax_1 @ Ay_1 ) @ ( produc1302104557on_val @ Bx_1 @ By_1 ) ) @ ( transi808828192on_val @ R_5 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: list_exp_list_char,B_4: produc2090907612on_val,Aa: list_exp_list_char,Ba: produc2090907612on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ A_1 @ B_4 ) @ ( produc1302104557on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Aa @ Ba ) @ ( produc1302104557on_val @ Bx_1 @ By_1 ) ) @ ( transi808828192on_val @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_418_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_5: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Ax_1 @ Ay_1 ) @ ( produc235638504on_val @ Bx_1 @ By_1 ) ) @ ( transi2118771717on_val @ R_5 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: exp_list_char,B_4: produc2090907612on_val,Aa: exp_list_char,Ba: produc2090907612on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ A_1 @ B_4 ) @ ( produc235638504on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Aa @ Ba ) @ ( produc235638504on_val @ Bx_1 @ By_1 ) ) @ ( transi2118771717on_val @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_419_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_5: produc1534059751t_char > $o] :
( ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ Ax_1 @ Ay_1 ) @ ( produc1147572817t_char @ Bx_1 @ By_1 ) ) @ ( transi198989188t_char @ R_5 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: list_list_char,B_4: exp_list_char,Aa: list_list_char,Ba: exp_list_char] :
( ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ A_1 @ B_4 ) @ ( produc1147572817t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ Aa @ Ba ) @ ( produc1147572817t_char @ Bx_1 @ By_1 ) ) @ ( transi198989188t_char @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_420_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_5: produc1350825965t_char > $o] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ Ax_1 @ Ay_1 ) @ ( produc5062597t_char @ Bx_1 @ By_1 ) ) @ ( transi1095029602t_char @ R_5 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: list_char,B_4: list_char,Aa: list_char,Ba: list_char] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ A_1 @ B_4 ) @ ( produc5062597t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ Aa @ Ba ) @ ( produc5062597t_char @ Bx_1 @ By_1 ) ) @ ( transi1095029602t_char @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_421_converse__rtrancl__induct2,axiom,
! [P_4: val > val > $o,Ax_1: val,Ay_1: val,Bx_1: val,By_1: val,R_5: 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_5 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: val,B_4: val,Aa: val,Ba: val] :
( ( member837208074al_val @ ( produc1244920211al_val @ ( product_Pair_val_val @ A_1 @ B_4 ) @ ( product_Pair_val_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( member837208074al_val @ ( produc1244920211al_val @ ( product_Pair_val_val @ Aa @ Ba ) @ ( product_Pair_val_val @ Bx_1 @ By_1 ) ) @ ( transi1423755450al_val @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_422_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_5: produc630464863al_val > $o] :
( ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ Ax_1 @ Ay_1 ) @ ( produc621191550al_val @ Bx_1 @ By_1 ) ) @ ( transi1906258203al_val @ R_5 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: bop,B_4: product_prod_val_val,Aa: bop,Ba: product_prod_val_val] :
( ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ A_1 @ B_4 ) @ ( produc621191550al_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ Aa @ Ba ) @ ( produc621191550al_val @ Bx_1 @ By_1 ) ) @ ( transi1906258203al_val @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_423_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_5: produc1250491293on_val > $o] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ Ax_1 @ Ay_1 ) @ ( produc747700183on_val @ Bx_1 @ By_1 ) ) @ ( transi1457397498on_val @ R_5 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: produc1180562163on_val,B_4: produc1180562163on_val,Aa: produc1180562163on_val,Ba: produc1180562163on_val] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ A_1 @ B_4 ) @ ( produc747700183on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ Aa @ Ba ) @ ( produc747700183on_val @ Bx_1 @ By_1 ) ) @ ( transi1457397498on_val @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_424_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_5: produc1368416213on_val > $o] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Ax_1 @ Ay_1 ) @ ( produc926070009on_val @ Bx_1 @ By_1 ) ) @ ( transi1669211542on_val @ R_5 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: list_char,B_4: produc1278157519t_char > option_val,Aa: list_char,Ba: produc1278157519t_char > option_val] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ A_1 @ B_4 ) @ ( produc926070009on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Aa @ Ba ) @ ( produc926070009on_val @ Bx_1 @ By_1 ) ) @ ( transi1669211542on_val @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_425_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_5: produc652964533on_val > $o] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Ax_1 @ Ay_1 ) @ ( produc833389609on_val @ Bx_1 @ By_1 ) ) @ ( transi130214086on_val @ R_5 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: produc1282892786on_val,B_4: produc1282892786on_val,Aa: produc1282892786on_val,Ba: produc1282892786on_val] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ A_1 @ B_4 ) @ ( produc833389609on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Aa @ Ba ) @ ( produc833389609on_val @ Bx_1 @ By_1 ) ) @ ( transi130214086on_val @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_426_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_5: produc1581780743on_val > $o] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Ax_1 @ Ay_1 ) @ ( produc755559506on_val @ Bx_1 @ By_1 ) ) @ ( transi466770671on_val @ R_5 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: nat > option1728594148on_val,B_4: list_char > option_val,Aa: nat > option1728594148on_val,Ba: list_char > option_val] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ A_1 @ B_4 ) @ ( produc755559506on_val @ Aa @ Ba ) ) @ R_5 )
=> ( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Aa @ Ba ) @ ( produc755559506on_val @ Bx_1 @ By_1 ) ) @ ( transi466770671on_val @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_427_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_5: produc1826280281t_char > $o] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Ax_1 @ Ay_1 ) @ ( produc1916172923t_char @ Bx_1 @ By_1 ) ) @ ( transi1789604888t_char @ R_5 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: list_val,B_4: exp_list_char,Aa: list_val,Ba: exp_list_char] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ A_1 @ B_4 ) @ ( produc1916172923t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Aa @ Ba ) @ ( produc1916172923t_char @ Bx_1 @ By_1 ) ) @ ( transi1789604888t_char @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_428_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_5: produc1406897475t_char > $o] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Ax_1 @ Ay_1 ) @ ( produc1909267824t_char @ Bx_1 @ By_1 ) ) @ ( transi1257872013t_char @ R_5 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: list_ty,B_4: produc662261637t_char,Aa: list_ty,Ba: produc662261637t_char] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ A_1 @ B_4 ) @ ( produc1909267824t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Aa @ Ba ) @ ( produc1909267824t_char @ Bx_1 @ By_1 ) ) @ ( transi1257872013t_char @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_429_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_5: produc349695911t_char > $o] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Ax_1 @ Ay_1 ) @ ( produc921874948t_char @ Bx_1 @ By_1 ) ) @ ( transi122195895t_char @ R_5 ) )
=> ( ( P_4 @ Bx_1 @ By_1 )
=> ( ! [A_1: list_list_char,B_4: produc220283002t_char,Aa: list_list_char,Ba: produc220283002t_char] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ A_1 @ B_4 ) @ ( produc921874948t_char @ Aa @ Ba ) ) @ R_5 )
=> ( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Aa @ Ba ) @ ( produc921874948t_char @ Bx_1 @ By_1 ) ) @ ( transi122195895t_char @ R_5 ) )
=> ( ( P_4 @ Aa @ Ba )
=> ( P_4 @ A_1 @ B_4 ) ) ) )
=> ( P_4 @ Ax_1 @ Ay_1 ) ) ) ) ).
thf(fact_430_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_4: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Ax @ Ay ) @ ( produc1302104557on_val @ Bx @ By ) ) @ ( transi808828192on_val @ R_4 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: list_exp_list_char,B_4: produc2090907612on_val,Aa: list_exp_list_char,Ba: produc2090907612on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Ax @ Ay ) @ ( produc1302104557on_val @ A_1 @ B_4 ) ) @ ( transi808828192on_val @ R_4 ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ A_1 @ B_4 ) @ ( produc1302104557on_val @ Aa @ Ba ) ) @ R_4 )
=> ( ( P_3 @ A_1 @ B_4 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_431_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_4: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Ax @ Ay ) @ ( produc235638504on_val @ Bx @ By ) ) @ ( transi2118771717on_val @ R_4 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: exp_list_char,B_4: produc2090907612on_val,Aa: exp_list_char,Ba: produc2090907612on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ Ax @ Ay ) @ ( produc235638504on_val @ A_1 @ B_4 ) ) @ ( transi2118771717on_val @ R_4 ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ A_1 @ B_4 ) @ ( produc235638504on_val @ Aa @ Ba ) ) @ R_4 )
=> ( ( P_3 @ A_1 @ B_4 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_432_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_4: produc1534059751t_char > $o] :
( ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ Ax @ Ay ) @ ( produc1147572817t_char @ Bx @ By ) ) @ ( transi198989188t_char @ R_4 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: list_list_char,B_4: exp_list_char,Aa: list_list_char,Ba: exp_list_char] :
( ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ Ax @ Ay ) @ ( produc1147572817t_char @ A_1 @ B_4 ) ) @ ( transi198989188t_char @ R_4 ) )
=> ( ( member1999287380t_char @ ( produc1897818327t_char @ ( produc1147572817t_char @ A_1 @ B_4 ) @ ( produc1147572817t_char @ Aa @ Ba ) ) @ R_4 )
=> ( ( P_3 @ A_1 @ B_4 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_433_rtrancl__induct2,axiom,
! [P_3: list_char > list_char > $o,Ax: list_char,Ay: list_char,Bx: list_char,By: list_char,R_4: produc1350825965t_char > $o] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ Ax @ Ay ) @ ( produc5062597t_char @ Bx @ By ) ) @ ( transi1095029602t_char @ R_4 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: list_char,B_4: list_char,Aa: list_char,Ba: list_char] :
( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ Ax @ Ay ) @ ( produc5062597t_char @ A_1 @ B_4 ) ) @ ( transi1095029602t_char @ R_4 ) )
=> ( ( member794220506t_char @ ( produc2080520419t_char @ ( produc5062597t_char @ A_1 @ B_4 ) @ ( produc5062597t_char @ Aa @ Ba ) ) @ R_4 )
=> ( ( P_3 @ A_1 @ B_4 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_434_rtrancl__induct2,axiom,
! [P_3: val > val > $o,Ax: val,Ay: val,Bx: val,By: val,R_4: produc800118557al_val > $o] :
( ( member837208074al_val @ ( produc1244920211al_val @ ( product_Pair_val_val @ Ax @ Ay ) @ ( product_Pair_val_val @ Bx @ By ) ) @ ( transi1423755450al_val @ R_4 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: val,B_4: val,Aa: val,Ba: val] :
( ( member837208074al_val @ ( produc1244920211al_val @ ( product_Pair_val_val @ Ax @ Ay ) @ ( product_Pair_val_val @ A_1 @ B_4 ) ) @ ( transi1423755450al_val @ R_4 ) )
=> ( ( member837208074al_val @ ( produc1244920211al_val @ ( product_Pair_val_val @ A_1 @ B_4 ) @ ( product_Pair_val_val @ Aa @ Ba ) ) @ R_4 )
=> ( ( P_3 @ A_1 @ B_4 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_435_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_4: produc630464863al_val > $o] :
( ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ Ax @ Ay ) @ ( produc621191550al_val @ Bx @ By ) ) @ ( transi1906258203al_val @ R_4 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: bop,B_4: product_prod_val_val,Aa: bop,Ba: product_prod_val_val] :
( ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ Ax @ Ay ) @ ( produc621191550al_val @ A_1 @ B_4 ) ) @ ( transi1906258203al_val @ R_4 ) )
=> ( ( member1732271180al_val @ ( produc1924279125al_val @ ( produc621191550al_val @ A_1 @ B_4 ) @ ( produc621191550al_val @ Aa @ Ba ) ) @ R_4 )
=> ( ( P_3 @ A_1 @ B_4 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_436_rtrancl__induct2,axiom,
! [P_3: produc1180562163on_val > produc1180562163on_val > $o,Ax: produc1180562163on_val,Ay: produc1180562163on_val,Bx: produc1180562163on_val,By: produc1180562163on_val,R_4: produc1250491293on_val > $o] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ Ax @ Ay ) @ ( produc747700183on_val @ Bx @ By ) ) @ ( transi1457397498on_val @ R_4 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: produc1180562163on_val,B_4: produc1180562163on_val,Aa: produc1180562163on_val,Ba: produc1180562163on_val] :
( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ Ax @ Ay ) @ ( produc747700183on_val @ A_1 @ B_4 ) ) @ ( transi1457397498on_val @ R_4 ) )
=> ( ( member1145216138on_val @ ( produc1347028499on_val @ ( produc747700183on_val @ A_1 @ B_4 ) @ ( produc747700183on_val @ Aa @ Ba ) ) @ R_4 )
=> ( ( P_3 @ A_1 @ B_4 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_437_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_4: produc1368416213on_val > $o] :
( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ Ax @ Ay ) @ ( produc926070009on_val @ Bx @ By ) ) @ ( transi1669211542on_val @ R_4 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: list_char,B_4: 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_4 ) ) @ ( transi1669211542on_val @ R_4 ) )
=> ( ( member1235075778on_val @ ( produc1773146955on_val @ ( produc926070009on_val @ A_1 @ B_4 ) @ ( produc926070009on_val @ Aa @ Ba ) ) @ R_4 )
=> ( ( P_3 @ A_1 @ B_4 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_438_rtrancl__induct2,axiom,
! [P_3: produc1282892786on_val > produc1282892786on_val > $o,Ax: produc1282892786on_val,Ay: produc1282892786on_val,Bx: produc1282892786on_val,By: produc1282892786on_val,R_4: produc652964533on_val > $o] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Ax @ Ay ) @ ( produc833389609on_val @ Bx @ By ) ) @ ( transi130214086on_val @ R_4 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: produc1282892786on_val,B_4: produc1282892786on_val,Aa: produc1282892786on_val,Ba: produc1282892786on_val] :
( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ Ax @ Ay ) @ ( produc833389609on_val @ A_1 @ B_4 ) ) @ ( transi130214086on_val @ R_4 ) )
=> ( ( member1714424482on_val @ ( produc345758123on_val @ ( produc833389609on_val @ A_1 @ B_4 ) @ ( produc833389609on_val @ Aa @ Ba ) ) @ R_4 )
=> ( ( P_3 @ A_1 @ B_4 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_439_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_4: produc1581780743on_val > $o] :
( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ Ax @ Ay ) @ ( produc755559506on_val @ Bx @ By ) ) @ ( transi466770671on_val @ R_4 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: nat > option1728594148on_val,B_4: 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_4 ) ) @ ( transi466770671on_val @ R_4 ) )
=> ( ( member565037556on_val @ ( produc259392253on_val @ ( produc755559506on_val @ A_1 @ B_4 ) @ ( produc755559506on_val @ Aa @ Ba ) ) @ R_4 )
=> ( ( P_3 @ A_1 @ B_4 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_440_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_4: produc1826280281t_char > $o] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Ax @ Ay ) @ ( produc1916172923t_char @ Bx @ By ) ) @ ( transi1789604888t_char @ R_4 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: list_val,B_4: exp_list_char,Aa: list_val,Ba: exp_list_char] :
( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ Ax @ Ay ) @ ( produc1916172923t_char @ A_1 @ B_4 ) ) @ ( transi1789604888t_char @ R_4 ) )
=> ( ( member1161907014t_char @ ( produc1299387215t_char @ ( produc1916172923t_char @ A_1 @ B_4 ) @ ( produc1916172923t_char @ Aa @ Ba ) ) @ R_4 )
=> ( ( P_3 @ A_1 @ B_4 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_441_rtrancl__induct2,axiom,
! [P_3: list_ty > produc662261637t_char > $o,Ax: list_ty,Ay: produc662261637t_char,Bx: list_ty,By: produc662261637t_char,R_4: produc1406897475t_char > $o] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Ax @ Ay ) @ ( produc1909267824t_char @ Bx @ By ) ) @ ( transi1257872013t_char @ R_4 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: list_ty,B_4: produc662261637t_char,Aa: list_ty,Ba: produc662261637t_char] :
( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ Ax @ Ay ) @ ( produc1909267824t_char @ A_1 @ B_4 ) ) @ ( transi1257872013t_char @ R_4 ) )
=> ( ( member125098544t_char @ ( produc57279289t_char @ ( produc1909267824t_char @ A_1 @ B_4 ) @ ( produc1909267824t_char @ Aa @ Ba ) ) @ R_4 )
=> ( ( P_3 @ A_1 @ B_4 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_442_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_4: produc349695911t_char > $o] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Ax @ Ay ) @ ( produc921874948t_char @ Bx @ By ) ) @ ( transi122195895t_char @ R_4 ) )
=> ( ( P_3 @ Ax @ Ay )
=> ( ! [A_1: list_list_char,B_4: produc220283002t_char,Aa: list_list_char,Ba: produc220283002t_char] :
( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ Ax @ Ay ) @ ( produc921874948t_char @ A_1 @ B_4 ) ) @ ( transi122195895t_char @ R_4 ) )
=> ( ( member1420286996t_char @ ( produc24551831t_char @ ( produc921874948t_char @ A_1 @ B_4 ) @ ( produc921874948t_char @ Aa @ Ba ) ) @ R_4 )
=> ( ( P_3 @ A_1 @ B_4 )
=> ( P_3 @ Aa @ Ba ) ) ) )
=> ( P_3 @ Bx @ By ) ) ) ) ).
thf(fact_443_rtranclE,axiom,
! [A_5: list_char,B_3: list_char,R_3: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_5 @ B_3 ) @ ( transi1395422419t_char @ R_3 ) )
=> ( ( A_5 != B_3 )
=> ~ ! [Y_1: list_char] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_5 @ Y_1 ) @ ( transi1395422419t_char @ R_3 ) )
=> ~ ( member1251428284t_char @ ( produc5062597t_char @ Y_1 @ B_3 ) @ R_3 ) ) ) ) ).
thf(fact_444_rtranclE,axiom,
! [A_5: produc1180562163on_val,B_3: produc1180562163on_val,R_3: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_5 @ B_3 ) @ ( transi808828192on_val @ R_3 ) )
=> ( ( A_5 != B_3 )
=> ~ ! [Y_1: produc1180562163on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_5 @ Y_1 ) @ ( transi808828192on_val @ R_3 ) )
=> ~ ( member2042188884on_val @ ( produc747700183on_val @ Y_1 @ B_3 ) @ R_3 ) ) ) ) ).
thf(fact_445_rtranclE,axiom,
! [A_5: produc1282892786on_val,B_3: produc1282892786on_val,R_3: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_5 @ B_3 ) @ ( transi2118771717on_val @ R_3 ) )
=> ( ( A_5 != B_3 )
=> ~ ! [Y_1: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_5 @ Y_1 ) @ ( transi2118771717on_val @ R_3 ) )
=> ~ ( member1913460000on_val @ ( produc833389609on_val @ Y_1 @ B_3 ) @ R_3 ) ) ) ) ).
thf(fact_446_rtranclE,axiom,
! [A_5: val,B_3: val,R_3: product_prod_val_val > $o] :
( ( member649088532al_val @ ( product_Pair_val_val @ A_5 @ B_3 ) @ ( transi935034983cl_val @ R_3 ) )
=> ( ( A_5 != B_3 )
=> ~ ! [Y_1: val] :
( ( member649088532al_val @ ( product_Pair_val_val @ A_5 @ Y_1 ) @ ( transi935034983cl_val @ R_3 ) )
=> ~ ( member649088532al_val @ ( product_Pair_val_val @ Y_1 @ B_3 ) @ R_3 ) ) ) ) ).
thf(fact_447_converse__rtranclE,axiom,
! [X_5: list_char,Z_1: list_char,R_2: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ X_5 @ Z_1 ) @ ( transi1395422419t_char @ R_2 ) )
=> ( ( X_5 != Z_1 )
=> ~ ! [Y_1: list_char] :
( ( member1251428284t_char @ ( produc5062597t_char @ X_5 @ Y_1 ) @ R_2 )
=> ~ ( member1251428284t_char @ ( produc5062597t_char @ Y_1 @ Z_1 ) @ ( transi1395422419t_char @ R_2 ) ) ) ) ) ).
thf(fact_448_converse__rtranclE,axiom,
! [X_5: produc1180562163on_val,Z_1: produc1180562163on_val,R_2: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ X_5 @ Z_1 ) @ ( transi808828192on_val @ R_2 ) )
=> ( ( X_5 != Z_1 )
=> ~ ! [Y_1: produc1180562163on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ X_5 @ Y_1 ) @ R_2 )
=> ~ ( member2042188884on_val @ ( produc747700183on_val @ Y_1 @ Z_1 ) @ ( transi808828192on_val @ R_2 ) ) ) ) ) ).
thf(fact_449_converse__rtranclE,axiom,
! [X_5: produc1282892786on_val,Z_1: produc1282892786on_val,R_2: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ X_5 @ Z_1 ) @ ( transi2118771717on_val @ R_2 ) )
=> ( ( X_5 != Z_1 )
=> ~ ! [Y_1: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ X_5 @ Y_1 ) @ R_2 )
=> ~ ( member1913460000on_val @ ( produc833389609on_val @ Y_1 @ Z_1 ) @ ( transi2118771717on_val @ R_2 ) ) ) ) ) ).
thf(fact_450_converse__rtranclE,axiom,
! [X_5: val,Z_1: val,R_2: product_prod_val_val > $o] :
( ( member649088532al_val @ ( product_Pair_val_val @ X_5 @ Z_1 ) @ ( transi935034983cl_val @ R_2 ) )
=> ( ( X_5 != Z_1 )
=> ~ ! [Y_1: val] :
( ( member649088532al_val @ ( product_Pair_val_val @ X_5 @ Y_1 ) @ R_2 )
=> ~ ( member649088532al_val @ ( product_Pair_val_val @ Y_1 @ Z_1 ) @ ( transi935034983cl_val @ R_2 ) ) ) ) ) ).
thf(fact_451_converse__rtrancl__induct,axiom,
! [P_2: list_char > $o,A_4: list_char,B_2: list_char,R_1: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_4 @ B_2 ) @ ( transi1395422419t_char @ R_1 ) )
=> ( ( P_2 @ B_2 )
=> ( ! [Y_1: list_char,Z: list_char] :
( ( member1251428284t_char @ ( produc5062597t_char @ Y_1 @ Z ) @ R_1 )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ Z @ B_2 ) @ ( transi1395422419t_char @ R_1 ) )
=> ( ( P_2 @ Z )
=> ( P_2 @ Y_1 ) ) ) )
=> ( P_2 @ A_4 ) ) ) ) ).
thf(fact_452_converse__rtrancl__induct,axiom,
! [P_2: produc1180562163on_val > $o,A_4: produc1180562163on_val,B_2: produc1180562163on_val,R_1: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_4 @ B_2 ) @ ( transi808828192on_val @ R_1 ) )
=> ( ( P_2 @ B_2 )
=> ( ! [Y_1: produc1180562163on_val,Z: produc1180562163on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ Y_1 @ Z ) @ R_1 )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ Z @ B_2 ) @ ( transi808828192on_val @ R_1 ) )
=> ( ( P_2 @ Z )
=> ( P_2 @ Y_1 ) ) ) )
=> ( P_2 @ A_4 ) ) ) ) ).
thf(fact_453_converse__rtrancl__induct,axiom,
! [P_2: produc1282892786on_val > $o,A_4: produc1282892786on_val,B_2: produc1282892786on_val,R_1: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_4 @ B_2 ) @ ( transi2118771717on_val @ R_1 ) )
=> ( ( P_2 @ B_2 )
=> ( ! [Y_1: produc1282892786on_val,Z: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ Y_1 @ Z ) @ R_1 )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ Z @ B_2 ) @ ( transi2118771717on_val @ R_1 ) )
=> ( ( P_2 @ Z )
=> ( P_2 @ Y_1 ) ) ) )
=> ( P_2 @ A_4 ) ) ) ) ).
thf(fact_454_converse__rtrancl__induct,axiom,
! [P_2: val > $o,A_4: val,B_2: val,R_1: product_prod_val_val > $o] :
( ( member649088532al_val @ ( product_Pair_val_val @ A_4 @ B_2 ) @ ( transi935034983cl_val @ R_1 ) )
=> ( ( P_2 @ B_2 )
=> ( ! [Y_1: val,Z: val] :
( ( member649088532al_val @ ( product_Pair_val_val @ Y_1 @ Z ) @ R_1 )
=> ( ( member649088532al_val @ ( product_Pair_val_val @ Z @ B_2 ) @ ( transi935034983cl_val @ R_1 ) )
=> ( ( P_2 @ Z )
=> ( P_2 @ Y_1 ) ) ) )
=> ( P_2 @ A_4 ) ) ) ) ).
thf(fact_455_mem__def,axiom,
! [X_4: produc1278157519t_char,A_3: produc1278157519t_char > $o] :
( ( member1251428284t_char @ X_4 @ A_3 )
<=> ( A_3 @ X_4 ) ) ).
thf(fact_456_mem__def,axiom,
! [X_4: produc618524391on_val,A_3: produc618524391on_val > $o] :
( ( member2042188884on_val @ X_4 @ A_3 )
<=> ( A_3 @ X_4 ) ) ).
thf(fact_457_mem__def,axiom,
! [X_4: produc1746408499on_val,A_3: produc1746408499on_val > $o] :
( ( member1913460000on_val @ X_4 @ A_3 )
<=> ( A_3 @ X_4 ) ) ).
thf(fact_458_rtrancl__induct,axiom,
! [P_1: list_char > $o,A_2: list_char,B_1: list_char,R: produc1278157519t_char > $o] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_2 @ B_1 ) @ ( transi1395422419t_char @ R ) )
=> ( ( P_1 @ A_2 )
=> ( ! [Y_1: list_char,Z: list_char] :
( ( member1251428284t_char @ ( produc5062597t_char @ A_2 @ Y_1 ) @ ( transi1395422419t_char @ R ) )
=> ( ( member1251428284t_char @ ( produc5062597t_char @ Y_1 @ Z ) @ R )
=> ( ( P_1 @ Y_1 )
=> ( P_1 @ Z ) ) ) )
=> ( P_1 @ B_1 ) ) ) ) ).
thf(fact_459_rtrancl__induct,axiom,
! [P_1: produc1180562163on_val > $o,A_2: produc1180562163on_val,B_1: produc1180562163on_val,R: produc618524391on_val > $o] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_2 @ B_1 ) @ ( transi808828192on_val @ R ) )
=> ( ( P_1 @ A_2 )
=> ( ! [Y_1: produc1180562163on_val,Z: produc1180562163on_val] :
( ( member2042188884on_val @ ( produc747700183on_val @ A_2 @ Y_1 ) @ ( transi808828192on_val @ R ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ Y_1 @ Z ) @ R )
=> ( ( P_1 @ Y_1 )
=> ( P_1 @ Z ) ) ) )
=> ( P_1 @ B_1 ) ) ) ) ).
thf(fact_460_rtrancl__induct,axiom,
! [P_1: produc1282892786on_val > $o,A_2: produc1282892786on_val,B_1: produc1282892786on_val,R: produc1746408499on_val > $o] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_2 @ B_1 ) @ ( transi2118771717on_val @ R ) )
=> ( ( P_1 @ A_2 )
=> ( ! [Y_1: produc1282892786on_val,Z: produc1282892786on_val] :
( ( member1913460000on_val @ ( produc833389609on_val @ A_2 @ Y_1 ) @ ( transi2118771717on_val @ R ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ Y_1 @ Z ) @ R )
=> ( ( P_1 @ Y_1 )
=> ( P_1 @ Z ) ) ) )
=> ( P_1 @ B_1 ) ) ) ) ).
thf(fact_461_rtrancl__induct,axiom,
! [P_1: val > $o,A_2: val,B_1: val,R: product_prod_val_val > $o] :
( ( member649088532al_val @ ( product_Pair_val_val @ A_2 @ B_1 ) @ ( transi935034983cl_val @ R ) )
=> ( ( P_1 @ A_2 )
=> ( ! [Y_1: val,Z: val] :
( ( member649088532al_val @ ( product_Pair_val_val @ A_2 @ Y_1 ) @ ( transi935034983cl_val @ R ) )
=> ( ( member649088532al_val @ ( product_Pair_val_val @ Y_1 @ Z ) @ R )
=> ( ( P_1 @ Y_1 )
=> ( P_1 @ Z ) ) ) )
=> ( P_1 @ B_1 ) ) ) ) ).
thf(fact_462_blocksRedsFinal,axiom,
! [L_3: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,E_2: exp_list_char,H_2: nat > option1728594148on_val,L_2: list_char > option_val,P: list_P1999446415t_char,Vs: list_val,Vs_2: list_list_char,Ts_1: list_ty] :
( ( ( size_s2113983095t_char @ Vs_2 )
= ( size_size_list_ty @ Ts_1 ) )
=> ( ( ( size_size_list_val @ Vs )
= ( size_size_list_ty @ Ts_1 ) )
=> ( ( distinct_list_char @ Vs_2 )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ ( map_up1085636310ar_val @ L_1 @ Vs_2 @ Vs ) ) ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_2 @ L_2 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( final_list_char @ E_2 )
=> ( ( L_3
= ( overri2012515291on_val @ L_2 @ L_1 @ ( set_list_char @ Vs_2 ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( blocks @ ( produc921874948t_char @ Vs_2 @ ( produc1909267824t_char @ Ts_1 @ ( produc1916172923t_char @ Vs @ E ) ) ) ) @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_2 @ L_3 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ) ) ) ).
thf(fact_463_map__eq__conv,axiom,
! [F_10: list_char > val,Xs_7: list_list_char,G_6: list_char > val] :
( ( ( map_list_char_val @ F_10 @ Xs_7 )
= ( map_list_char_val @ G_6 @ Xs_7 ) )
<=> ! [X_3: list_char] :
( ( member_list_char @ X_3 @ ( set_list_char @ Xs_7 ) )
=> ( ( F_10 @ X_3 )
= ( G_6 @ X_3 ) ) ) ) ).
thf(fact_464_map__eq__conv,axiom,
! [F_10: val > exp_list_char,Xs_7: list_val,G_6: val > exp_list_char] :
( ( ( map_va1934808527t_char @ F_10 @ Xs_7 )
= ( map_va1934808527t_char @ G_6 @ Xs_7 ) )
<=> ! [X_3: val] :
( ( member_val @ X_3 @ ( set_val @ Xs_7 ) )
=> ( ( F_10 @ X_3 )
= ( G_6 @ X_3 ) ) ) ) ).
thf(fact_465_map__eq__conv,axiom,
! [F_10: ty > option_ty,Xs_7: list_ty,G_6: ty > option_ty] :
( ( ( map_ty_option_ty @ F_10 @ Xs_7 )
= ( map_ty_option_ty @ G_6 @ Xs_7 ) )
<=> ! [X_3: ty] :
( ( member_ty @ X_3 @ ( set_ty @ Xs_7 ) )
=> ( ( F_10 @ X_3 )
= ( G_6 @ X_3 ) ) ) ) ).
thf(fact_466_map__eq__conv,axiom,
! [F_10: val > option_ty,Xs_7: list_val,G_6: val > option_ty] :
( ( ( map_val_option_ty @ F_10 @ Xs_7 )
= ( map_val_option_ty @ G_6 @ Xs_7 ) )
<=> ! [X_3: val] :
( ( member_val @ X_3 @ ( set_val @ Xs_7 ) )
=> ( ( F_10 @ X_3 )
= ( G_6 @ X_3 ) ) ) ) ).
thf(fact_467_blocksReds,axiom,
! [E: exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,E_2: exp_list_char,H_2: nat > option1728594148on_val,L_2: list_char > option_val,P: list_P1999446415t_char,Vs: list_val,Vs_2: list_list_char,Ts_1: list_ty] :
( ( ( size_s2113983095t_char @ Vs_2 )
= ( size_size_list_ty @ Ts_1 ) )
=> ( ( ( size_size_list_val @ Vs )
= ( size_size_list_ty @ Ts_1 ) )
=> ( ( distinct_list_char @ Vs_2 )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ ( map_up1085636310ar_val @ L_1 @ Vs_2 @ Vs ) ) ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_2 @ L_2 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( blocks @ ( produc921874948t_char @ Vs_2 @ ( produc1909267824t_char @ Ts_1 @ ( produc1916172923t_char @ Vs @ E ) ) ) ) @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc235638504on_val @ ( blocks @ ( produc921874948t_char @ Vs_2 @ ( produc1909267824t_char @ Ts_1 @ ( produc1916172923t_char @ ( map_list_char_val @ ( comp_o1129292306t_char @ the_val @ L_2 ) @ Vs_2 ) @ E_2 ) ) ) ) @ ( produc755559506on_val @ H_2 @ ( overri2012515291on_val @ L_2 @ L_1 @ ( set_list_char @ Vs_2 ) ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ) ).
thf(fact_468_map__cong,axiom,
! [F_9: list_char > val,G_5: list_char > val,Xs_6: list_list_char,Ys_3: list_list_char] :
( ( Xs_6 = Ys_3 )
=> ( ! [X_3: list_char] :
( ( member_list_char @ X_3 @ ( set_list_char @ Ys_3 ) )
=> ( ( F_9 @ X_3 )
= ( G_5 @ X_3 ) ) )
=> ( ( map_list_char_val @ F_9 @ Xs_6 )
= ( map_list_char_val @ G_5 @ Ys_3 ) ) ) ) ).
thf(fact_469_map__cong,axiom,
! [F_9: val > exp_list_char,G_5: val > exp_list_char,Xs_6: list_val,Ys_3: list_val] :
( ( Xs_6 = Ys_3 )
=> ( ! [X_3: val] :
( ( member_val @ X_3 @ ( set_val @ Ys_3 ) )
=> ( ( F_9 @ X_3 )
= ( G_5 @ X_3 ) ) )
=> ( ( map_va1934808527t_char @ F_9 @ Xs_6 )
= ( map_va1934808527t_char @ G_5 @ Ys_3 ) ) ) ) ).
thf(fact_470_map__cong,axiom,
! [F_9: ty > option_ty,G_5: ty > option_ty,Xs_6: list_ty,Ys_3: list_ty] :
( ( Xs_6 = Ys_3 )
=> ( ! [X_3: ty] :
( ( member_ty @ X_3 @ ( set_ty @ Ys_3 ) )
=> ( ( F_9 @ X_3 )
= ( G_5 @ X_3 ) ) )
=> ( ( map_ty_option_ty @ F_9 @ Xs_6 )
= ( map_ty_option_ty @ G_5 @ Ys_3 ) ) ) ) ).
thf(fact_471_map__cong,axiom,
! [F_9: val > option_ty,G_5: val > option_ty,Xs_6: list_val,Ys_3: list_val] :
( ( Xs_6 = Ys_3 )
=> ( ! [X_3: val] :
( ( member_val @ X_3 @ ( set_val @ Ys_3 ) )
=> ( ( F_9 @ X_3 )
= ( G_5 @ X_3 ) ) )
=> ( ( map_val_option_ty @ F_9 @ Xs_6 )
= ( map_val_option_ty @ G_5 @ Ys_3 ) ) ) ) ).
thf(fact_472_map__idI,axiom,
! [F_8: list_char > list_char,Xs_5: list_list_char] :
( ! [X_3: list_char] :
( ( member_list_char @ X_3 @ ( set_list_char @ Xs_5 ) )
=> ( ( F_8 @ X_3 )
= X_3 ) )
=> ( ( map_li1333403488t_char @ F_8 @ Xs_5 )
= Xs_5 ) ) ).
thf(fact_473_map__idI,axiom,
! [F_8: produc1278157519t_char > produc1278157519t_char,Xs_5: list_P1916372464t_char] :
( ! [X_3: produc1278157519t_char] :
( ( member1251428284t_char @ X_3 @ ( set_Pr550895038t_char @ Xs_5 ) )
=> ( ( F_8 @ X_3 )
= X_3 ) )
=> ( ( map_Pr361633150t_char @ F_8 @ Xs_5 )
= Xs_5 ) ) ).
thf(fact_474_map__idI,axiom,
! [F_8: produc618524391on_val > produc618524391on_val,Xs_5: list_P1314671880on_val] :
( ! [X_3: produc618524391on_val] :
( ( member2042188884on_val @ X_3 @ ( set_Pr333999958on_val @ Xs_5 ) )
=> ( ( F_8 @ X_3 )
= X_3 ) )
=> ( ( map_Pr1978321326on_val @ F_8 @ Xs_5 )
= Xs_5 ) ) ).
thf(fact_475_map__idI,axiom,
! [F_8: produc1746408499on_val > produc1746408499on_val,Xs_5: list_P1964248404on_val] :
( ! [X_3: produc1746408499on_val] :
( ( member1913460000on_val @ X_3 @ ( set_Pr1184195362on_val @ Xs_5 ) )
=> ( ( F_8 @ X_3 )
= X_3 ) )
=> ( ( map_Pr816758342on_val @ F_8 @ Xs_5 )
= Xs_5 ) ) ).
thf(fact_476_map__ext,axiom,
! [F_7: list_char > val,G_4: list_char > val,Xs_4: list_list_char] :
( ! [X_3: list_char] :
( ( member_list_char @ X_3 @ ( set_list_char @ Xs_4 ) )
=> ( ( F_7 @ X_3 )
= ( G_4 @ X_3 ) ) )
=> ( ( map_list_char_val @ F_7 @ Xs_4 )
= ( map_list_char_val @ G_4 @ Xs_4 ) ) ) ).
thf(fact_477_map__ext,axiom,
! [F_7: val > exp_list_char,G_4: val > exp_list_char,Xs_4: list_val] :
( ! [X_3: val] :
( ( member_val @ X_3 @ ( set_val @ Xs_4 ) )
=> ( ( F_7 @ X_3 )
= ( G_4 @ X_3 ) ) )
=> ( ( map_va1934808527t_char @ F_7 @ Xs_4 )
= ( map_va1934808527t_char @ G_4 @ Xs_4 ) ) ) ).
thf(fact_478_map__ext,axiom,
! [F_7: ty > option_ty,G_4: ty > option_ty,Xs_4: list_ty] :
( ! [X_3: ty] :
( ( member_ty @ X_3 @ ( set_ty @ Xs_4 ) )
=> ( ( F_7 @ X_3 )
= ( G_4 @ X_3 ) ) )
=> ( ( map_ty_option_ty @ F_7 @ Xs_4 )
= ( map_ty_option_ty @ G_4 @ Xs_4 ) ) ) ).
thf(fact_479_map__ext,axiom,
! [F_7: val > option_ty,G_4: val > option_ty,Xs_4: list_val] :
( ! [X_3: val] :
( ( member_val @ X_3 @ ( set_val @ Xs_4 ) )
=> ( ( F_7 @ X_3 )
= ( G_4 @ X_3 ) ) )
=> ( ( map_val_option_ty @ F_7 @ Xs_4 )
= ( map_val_option_ty @ G_4 @ Xs_4 ) ) ) ).
thf(fact_480_ex__map__conv,axiom,
! [Ys_2: list_val,F_6: list_char > val] :
( ? [Xs_3: list_list_char] :
( Ys_2
= ( map_list_char_val @ F_6 @ Xs_3 ) )
<=> ! [X_3: val] :
( ( member_val @ X_3 @ ( set_val @ Ys_2 ) )
=> ? [Xa: list_char] :
( X_3
= ( F_6 @ Xa ) ) ) ) ).
thf(fact_481_ex__map__conv,axiom,
! [Ys_2: list_exp_list_char,F_6: val > exp_list_char] :
( ? [Xs_3: list_val] :
( Ys_2
= ( map_va1934808527t_char @ F_6 @ Xs_3 ) )
<=> ! [X_3: exp_list_char] :
( ( member_exp_list_char @ X_3 @ ( set_exp_list_char @ Ys_2 ) )
=> ? [Xa: val] :
( X_3
= ( F_6 @ Xa ) ) ) ) ).
thf(fact_482_ex__map__conv,axiom,
! [Ys_2: list_option_ty,F_6: ty > option_ty] :
( ? [Xs_3: list_ty] :
( Ys_2
= ( map_ty_option_ty @ F_6 @ Xs_3 ) )
<=> ! [X_3: option_ty] :
( ( member_option_ty @ X_3 @ ( set_option_ty @ Ys_2 ) )
=> ? [Xa: ty] :
( X_3
= ( F_6 @ Xa ) ) ) ) ).
thf(fact_483_ex__map__conv,axiom,
! [Ys_2: list_option_ty,F_6: val > option_ty] :
( ? [Xs_3: list_val] :
( Ys_2
= ( map_val_option_ty @ F_6 @ Xs_3 ) )
<=> ! [X_3: option_ty] :
( ( member_option_ty @ X_3 @ ( set_option_ty @ Ys_2 ) )
=> ? [Xa: val] :
( X_3
= ( F_6 @ Xa ) ) ) ) ).
thf(fact_484_map__upds__apply__nontin,axiom,
! [F_5: list_char > option_val,Ys_1: list_val,X_2: list_char,Xs_2: list_list_char] :
( ~ ( member_list_char @ X_2 @ ( set_list_char @ Xs_2 ) )
=> ( ( map_up1085636310ar_val @ F_5 @ Xs_2 @ Ys_1 @ X_2 )
= ( F_5 @ X_2 ) ) ) ).
thf(fact_485_map__upds__apply__nontin,axiom,
! [F_5: list_char > option_ty,Ys_1: list_ty,X_2: list_char,Xs_2: list_list_char] :
( ~ ( member_list_char @ X_2 @ ( set_list_char @ Xs_2 ) )
=> ( ( map_up891053837har_ty @ F_5 @ Xs_2 @ Ys_1 @ X_2 )
= ( F_5 @ X_2 ) ) ) ).
thf(fact_486_Red__lcl__add,axiom,
! [L_0: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,E_2: exp_list_char,H_2: nat > option1728594148on_val,L_2: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_2 @ L_2 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ ( map_ad325961431ar_val @ L_0 @ L_1 ) ) ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_2 @ ( map_ad325961431ar_val @ L_0 @ L_2 ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_487_hext__def,axiom,
! [H: nat > option1728594148on_val,H_2: nat > option1728594148on_val] :
( ( hext @ H @ H_2 )
<=> ! [A_1: nat,C_1: list_char,Fs_2: produc1278157519t_char > option_val] :
( ( ( H @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs_2 ) ) )
=> ? [Fs_3: produc1278157519t_char > option_val] :
( ( H_2 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs_3 ) ) ) ) ) ).
thf(fact_488_List_Omap_Ocomp,axiom,
! [F_4: option_val > val,G_3: list_char > option_val] :
( ( comp_l1825390573t_char @ ( map_option_val_val @ F_4 ) @ ( map_li50976719on_val @ G_3 ) )
= ( map_list_char_val @ ( comp_o1129292306t_char @ F_4 @ G_3 ) ) ) ).
thf(fact_489_map__comp__map,axiom,
! [F_3: option_val > val,G_2: list_char > option_val] :
( ( comp_l1825390573t_char @ ( map_option_val_val @ F_3 ) @ ( map_li50976719on_val @ G_2 ) )
= ( map_list_char_val @ ( comp_o1129292306t_char @ F_3 @ G_2 ) ) ) ).
thf(fact_490_map__add__assoc,axiom,
! [M1_1: list_char > option_val,M2_1: list_char > option_val,M3: list_char > option_val] :
( ( map_ad325961431ar_val @ M1_1 @ ( map_ad325961431ar_val @ M2_1 @ M3 ) )
= ( map_ad325961431ar_val @ ( map_ad325961431ar_val @ M1_1 @ M2_1 ) @ M3 ) ) ).
thf(fact_491_map__add__find__right,axiom,
! [M_1: list_char > option_val,N: list_char > option_val,K: list_char,Xx: val] :
( ( ( N @ K )
= ( some_val @ Xx ) )
=> ( ( map_ad325961431ar_val @ M_1 @ N @ K )
= ( some_val @ Xx ) ) ) ).
thf(fact_492_map__add__upds,axiom,
! [M1: list_char > option_val,M2: list_char > option_val,Xs_1: list_list_char,Ys: list_val] :
( ( map_ad325961431ar_val @ M1 @ ( map_up1085636310ar_val @ M2 @ Xs_1 @ Ys ) )
= ( map_up1085636310ar_val @ ( map_ad325961431ar_val @ M1 @ M2 ) @ Xs_1 @ Ys ) ) ).
thf(fact_493_map__add__upds,axiom,
! [M1: list_char > option_ty,M2: list_char > option_ty,Xs_1: list_list_char,Ys: list_ty] :
( ( map_add_list_char_ty @ M1 @ ( map_up891053837har_ty @ M2 @ Xs_1 @ Ys ) )
= ( map_up891053837har_ty @ ( map_add_list_char_ty @ M1 @ M2 ) @ Xs_1 @ Ys ) ) ).
thf(fact_494_map__map,axiom,
! [F_2: option_val > val,G_1: list_char > option_val,Xs: list_list_char] :
( ( map_option_val_val @ F_2 @ ( map_li50976719on_val @ G_1 @ Xs ) )
= ( map_list_char_val @ ( comp_o1129292306t_char @ F_2 @ G_1 ) @ Xs ) ) ).
thf(fact_495_List_Omap_Ocompositionality,axiom,
! [F_1: option_val > val,G: list_char > option_val,List: list_list_char] :
( ( map_option_val_val @ F_1 @ ( map_li50976719on_val @ G @ List ) )
= ( map_list_char_val @ ( comp_o1129292306t_char @ F_1 @ G ) @ List ) ) ).
thf(fact_496_the_Osimps,axiom,
! [X_1: val] :
( ( the_val @ ( some_val @ X_1 ) )
= X_1 ) ).
thf(fact_497_the_Osimps,axiom,
! [X_1: produc2088785539on_val] :
( ( the_Pr1885945130on_val @ ( some_P451527732on_val @ X_1 ) )
= X_1 ) ).
thf(fact_498_the_Osimps,axiom,
! [X_1: ty] :
( ( the_ty @ ( some_ty @ X_1 ) )
= X_1 ) ).
thf(fact_499_red__lcl__add,axiom,
! [L_0: list_char > option_val,E: exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,E_2: exp_list_char,H_2: nat > option1728594148on_val,L_2: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_2 @ L_2 ) ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ ( produc755559506on_val @ H @ ( map_ad325961431ar_val @ L_0 @ L_1 ) ) ) @ ( produc235638504on_val @ E_2 @ ( produc755559506on_val @ H_2 @ ( map_ad325961431ar_val @ L_0 @ L_2 ) ) ) ) @ ( red @ P ) ) ) ).
thf(fact_500_hext__objD,axiom,
! [A: nat,C: list_char,Fs: produc1278157519t_char > option_val,H: nat > option1728594148on_val,H_2: nat > option1728594148on_val] :
( ( hext @ H @ H_2 )
=> ( ( ( H @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ? [Fs_3: produc1278157519t_char > option_val] :
( ( H_2 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs_3 ) ) ) ) ) ).
thf(fact_501_hextI,axiom,
! [H_2: nat > option1728594148on_val,H: nat > option1728594148on_val] :
( ! [A_1: nat,C_1: list_char,Fs_2: produc1278157519t_char > option_val] :
( ( ( H @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs_2 ) ) )
=> ? [Fs_3: produc1278157519t_char > option_val] :
( ( H_2 @ A_1 )
= ( some_P451527732on_val @ ( produc926070009on_val @ C_1 @ Fs_3 ) ) ) )
=> ( hext @ H @ H_2 ) ) ).
thf(fact_502_TryRedsVal,axiom,
! [C: list_char,V: list_char,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,V_2: val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( val_list_char @ V_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ E @ C @ V @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ V_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_503_reds__preserves__lconf,axiom,
! [E_1: list_char > option_ty,Ts_1: list_ty,Es: list_exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,Es_1: list_exp_list_char,H_2: nat > option1728594148on_val,L_2: list_char > option_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc1302104557on_val @ Es_1 @ ( produc755559506on_val @ H_2 @ L_2 ) ) ) @ ( reds @ P ) )
=> ( ( wTrts @ P @ H @ E_1 @ Es @ Ts_1 )
=> ( ( lconf_496643946t_char @ P @ H @ L_1 @ E_1 )
=> ( lconf_496643946t_char @ P @ H_2 @ L_2 @ E_1 ) ) ) ) ).
thf(fact_504_reds__preserves__hconf,axiom,
! [E_1: list_char > option_ty,Ts_1: list_ty,Es: list_exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,Es_1: list_exp_list_char,H_2: nat > option1728594148on_val,L_2: list_char > option_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc1302104557on_val @ Es_1 @ ( produc755559506on_val @ H_2 @ L_2 ) ) ) @ ( reds @ P ) )
=> ( ( wTrts @ P @ H @ E_1 @ Es @ Ts_1 )
=> ( ( hconf_97414254t_char @ P @ H )
=> ( hconf_97414254t_char @ P @ H_2 ) ) ) ) ).
thf(fact_505_BinOp2Reds,axiom,
! [V_2: val,Bop: bop,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V_2 ) @ Bop @ E ) @ S ) @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V_2 ) @ Bop @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_506_FAssReds2,axiom,
! [V_2: val,F: list_char,D: list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V_2 ) @ F @ D @ E ) @ S ) @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V_2 ) @ F @ D @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_507_SeqReds2,axiom,
! [E_2_1: exp_list_char,E_2_2: exp_list_char,S_2: produc2090907612on_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1_1: val,S_1_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_1 ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2_1 @ S_1_1 ) @ ( produc235638504on_val @ E_2_2 @ S_2 ) ) @ ( 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 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_508_WTrtSeq,axiom,
! [E_2_1: exp_list_char,T_2: ty,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E_1_1: exp_list_char,T_1_2: ty] :
( ( wTrt @ P @ H @ E_1 @ E_1_1 @ T_1_2 )
=> ( ( wTrt @ P @ H @ E_1 @ E_2_1 @ T_2 )
=> ( wTrt @ P @ H @ E_1 @ ( seq_list_char @ E_1_1 @ E_2_1 ) @ T_2 ) ) ) ).
thf(fact_509_Seq,axiom,
! [E_1_1: exp_list_char,E_2_1: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char,E_0: exp_list_char,S_0: produc2090907612on_val,V_2: val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_0 @ S_0 @ ( val_list_char @ V_2 ) @ S_1_1 )
=> ( ( eval @ P @ E_1_1 @ S_1_1 @ E_2_1 @ S_2 )
=> ( eval @ P @ ( seq_list_char @ E_0 @ E_1_1 ) @ S_0 @ E_2_1 @ S_2 ) ) ) ).
thf(fact_510_Try,axiom,
! [C: list_char,V: list_char,E_2_1: exp_list_char,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1_1: val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ V_1_1 ) @ S_1_1 )
=> ( eval @ P @ ( tryCatch_list_char @ E_1_1 @ C @ V @ E_2_1 ) @ S_0 @ ( val_list_char @ V_1_1 ) @ S_1_1 ) ) ).
thf(fact_511_red__reds_OSeqRed,axiom,
! [E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ E @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( seq_list_char @ E_2 @ E_2_1 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_512_red__reds_OFAssRed1,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ E @ F @ D @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( fAss_list_char @ E_2 @ F @ D @ E_2_1 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_513_red__reds_OBinOpRed1,axiom,
! [Bop: bop,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ E @ Bop @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( binOp_list_char @ E_2 @ Bop @ E_2_1 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_514_reds__hext__incr,axiom,
! [Es: list_exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,Es_1: list_exp_list_char,H_2: nat > option1728594148on_val,L_2: list_char > option_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc1302104557on_val @ Es_1 @ ( produc755559506on_val @ H_2 @ L_2 ) ) ) @ ( reds @ P ) )
=> ( hext @ H @ H_2 ) ) ).
thf(fact_515_red__reds_OTryRed,axiom,
! [C: list_char,V: list_char,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ E @ C @ V @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( tryCatch_list_char @ E_2 @ C @ V @ E_2_1 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_516_red__reds_ORedSeq,axiom,
! [V_2: 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_2 ) @ E_2_1 ) @ S ) @ ( produc235638504on_val @ E_2_1 @ S ) ) @ ( red @ P ) ) ).
thf(fact_517_SeqReds,axiom,
! [E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ E @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( seq_list_char @ E_2 @ E_2_1 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_518_red__reds_OFAssRed2,axiom,
! [V_2: val,F: list_char,D: list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V_2 ) @ F @ D @ E ) @ S ) @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V_2 ) @ F @ D @ E_2 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_519_red__reds_OBinOpRed2,axiom,
! [V_1_1: val,Bop: bop,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V_1_1 ) @ Bop @ E ) @ S ) @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V_1_1 ) @ Bop @ E_2 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_520_FAssReds1,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ E @ F @ D @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( fAss_list_char @ E_2 @ F @ D @ E_2_1 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_521_BinOp1Reds,axiom,
! [Bop: bop,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ E @ Bop @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( binOp_list_char @ E_2 @ Bop @ E_2_1 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_522_red__reds_ORedTry,axiom,
! [V_2: val,C: list_char,V: 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_2 ) @ C @ V @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ V_2 ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_523_TryReds,axiom,
! [C: list_char,V: list_char,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( tryCatch_list_char @ E @ C @ V @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( tryCatch_list_char @ E_2 @ C @ V @ E_2_1 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_524_BinOpRedsVal,axiom,
! [Bop: bop,V_2: val,E_2_1: exp_list_char,V_2_1: val,S_2: produc2090907612on_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1_1: val,S_1_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_1 ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2_1 @ S_1_1 ) @ ( produc235638504on_val @ ( val_list_char @ V_2_1 ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( binop @ ( produc621191550al_val @ Bop @ ( product_Pair_val_val @ V_1_1 @ V_2_1 ) ) )
= ( some_val @ V_2 ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ E_1_1 @ Bop @ E_2_1 ) @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ V_2 ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_525_red__reds_ORedBinOp,axiom,
! [S: produc2090907612on_val,P: list_P1999446415t_char,Bop: bop,V_1_1: val,V_2_1: val,V_2: val] :
( ( ( binop @ ( produc621191550al_val @ Bop @ ( product_Pair_val_val @ V_1_1 @ V_2_1 ) ) )
= ( some_val @ V_2 ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V_1_1 ) @ Bop @ ( val_list_char @ V_2_1 ) ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ V_2 ) @ S ) ) @ ( red @ P ) ) ) ).
thf(fact_526_CallRedsParams,axiom,
! [V_2: val,M: list_char,Es: list_exp_list_char,S: produc2090907612on_val,Es_1: list_exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_1 @ S_1 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ ( val_list_char @ V_2 ) @ M @ Es ) @ S ) @ ( produc235638504on_val @ ( call_list_char @ ( val_list_char @ V_2 ) @ M @ Es_1 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_527_ListRedsVal,axiom,
! [Es: list_exp_list_char,Es_1: list_exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S_0: produc2090907612on_val,V_2: val,S_1_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ V_2 ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S_1_1 ) @ ( produc1302104557on_val @ Es_1 @ S_2 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ ( cons_exp_list_char @ E @ Es ) @ S_0 ) @ ( produc1302104557on_val @ ( cons_exp_list_char @ ( val_list_char @ V_2 ) @ Es_1 ) @ S_2 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) ) ) ) ).
thf(fact_528_red__reds_OCallObj,axiom,
! [M: list_char,Es: list_exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ E @ M @ Es ) @ S ) @ ( produc235638504on_val @ ( call_list_char @ E_2 @ M @ Es ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_529_CallRedsObj,axiom,
! [M: list_char,Es: list_exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ E @ M @ Es ) @ S ) @ ( produc235638504on_val @ ( call_list_char @ E_2 @ M @ Es ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_530_ListReds2,axiom,
! [V_2: val,Es: list_exp_list_char,S: produc2090907612on_val,Es_1: list_exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_1 @ S_1 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ ( cons_exp_list_char @ ( val_list_char @ V_2 ) @ Es ) @ S ) @ ( produc1302104557on_val @ ( cons_exp_list_char @ ( val_list_char @ V_2 ) @ Es_1 ) @ S_1 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) ) ) ).
thf(fact_531_red__reds_OListRed2,axiom,
! [V_2: val,Es: list_exp_list_char,S: produc2090907612on_val,Es_1: list_exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_1 @ S_1 ) ) @ ( reds @ P ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ ( cons_exp_list_char @ ( val_list_char @ V_2 ) @ Es ) @ S ) @ ( produc1302104557on_val @ ( cons_exp_list_char @ ( val_list_char @ V_2 ) @ Es_1 ) @ S_1 ) ) @ ( reds @ P ) ) ) ).
thf(fact_532_red__reds_OListRed1,axiom,
! [Es: list_exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ ( cons_exp_list_char @ E @ Es ) @ S ) @ ( produc1302104557on_val @ ( cons_exp_list_char @ E_2 @ Es ) @ S_1 ) ) @ ( reds @ P ) ) ) ).
thf(fact_533_BinOp,axiom,
! [Bop: bop,V_2: val,E_2_1: exp_list_char,V_2_1: val,S_2: produc2090907612on_val,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1_1: val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ V_1_1 ) @ S_1_1 )
=> ( ( eval @ P @ E_2_1 @ S_1_1 @ ( val_list_char @ V_2_1 ) @ S_2 )
=> ( ( ( binop @ ( produc621191550al_val @ Bop @ ( product_Pair_val_val @ V_1_1 @ V_2_1 ) ) )
= ( some_val @ V_2 ) )
=> ( eval @ P @ ( binOp_list_char @ E_1_1 @ Bop @ E_2_1 ) @ S_0 @ ( val_list_char @ V_2 ) @ S_2 ) ) ) ) ).
thf(fact_534_red__reds_OCallParams,axiom,
! [V_2: val,M: list_char,Es: list_exp_list_char,S: produc2090907612on_val,Es_1: list_exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_1 @ S_1 ) ) @ ( reds @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ ( val_list_char @ V_2 ) @ M @ Es ) @ S ) @ ( produc235638504on_val @ ( call_list_char @ ( val_list_char @ V_2 ) @ M @ Es_1 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_535_ListReds1,axiom,
! [Es: list_exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ ( cons_exp_list_char @ E @ Es ) @ S ) @ ( produc1302104557on_val @ ( cons_exp_list_char @ E_2 @ Es ) @ S_1 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) ) ) ).
thf(fact_536_redp__redsp_ORedBinOp,axiom,
! [P: list_P1999446415t_char,S: produc2090907612on_val,Bop: bop,V_1_1: val,V_2_1: val,V_2: val] :
( ( ( binop @ ( produc621191550al_val @ Bop @ ( product_Pair_val_val @ V_1_1 @ V_2_1 ) ) )
= ( some_val @ V_2 ) )
=> ( redp @ P @ ( binOp_list_char @ ( val_list_char @ V_1_1 ) @ Bop @ ( val_list_char @ V_2_1 ) ) @ S @ ( val_list_char @ V_2 ) @ S ) ) ).
thf(fact_537_CallRedsThrowParams,axiom,
! [M: list_char,Es: list_exp_list_char,Vs_1: list_val,A: exp_list_char,Es_2_1: list_exp_list_char,S_2: produc2090907612on_val,E: exp_list_char,S0: produc2090907612on_val,V_2: val,S_1_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S0 ) @ ( produc235638504on_val @ ( val_list_char @ V_2 ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S_1_1 ) @ ( produc1302104557on_val @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ Vs_1 ) @ ( cons_exp_list_char @ ( throw_list_char @ A ) @ Es_2_1 ) ) @ S_2 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ E @ M @ Es ) @ S0 ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_538_WTrtCons,axiom,
! [Es: list_exp_list_char,Ts_1: list_ty,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_1 @ E @ T )
=> ( ( wTrts @ P @ H @ E_1 @ Es @ Ts_1 )
=> ( wTrts @ P @ H @ E_1 @ ( cons_exp_list_char @ E @ Es ) @ ( cons_ty @ T @ Ts_1 ) ) ) ) ).
thf(fact_539_redp__redsp_OFAssThrow1,axiom,
! [P: list_P1999446415t_char,E: 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 ) @ F @ D @ E_2_1 ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_540_redp__redsp_OBinOpThrow1,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,Bop: bop,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( binOp_list_char @ ( throw_list_char @ E ) @ Bop @ E_2_1 ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_541_redp__redsp_OCallThrowObj,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,M: list_char,Es: list_exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( call_list_char @ ( throw_list_char @ E ) @ M @ Es ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_542_redp__redsp_OThrowRed,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( throw_list_char @ E ) @ S @ ( throw_list_char @ E_2 ) @ S_1 ) ) ).
thf(fact_543_redp__redsp_OThrowThrow,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( throw_list_char @ ( throw_list_char @ E ) ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_544_redp__redsp_OSeqThrow,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( seq_list_char @ ( throw_list_char @ E ) @ E_2_1 ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_545_redp__redsp_OFAssThrow2,axiom,
! [P: list_P1999446415t_char,V_2: val,F: list_char,D: list_char,E: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( fAss_list_char @ ( val_list_char @ V_2 ) @ F @ D @ ( throw_list_char @ E ) ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_546_redp__redsp_OBinOpThrow2,axiom,
! [P: list_P1999446415t_char,V_1_1: val,Bop: bop,E: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( binOp_list_char @ ( val_list_char @ V_1_1 ) @ Bop @ ( throw_list_char @ E ) ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_547_eval__evals_OThrowThrow,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,E_2: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 )
=> ( eval @ P @ ( throw_list_char @ E ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 ) ) ).
thf(fact_548_redp__redsp_OSeqRed,axiom,
! [E_2_1: exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( seq_list_char @ E @ E_2_1 ) @ S @ ( seq_list_char @ E_2 @ E_2_1 ) @ S_1 ) ) ).
thf(fact_549_redp__redsp_OFAssRed1,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( fAss_list_char @ E @ F @ D @ E_2_1 ) @ S @ ( fAss_list_char @ E_2 @ F @ D @ E_2_1 ) @ S_1 ) ) ).
thf(fact_550_redp__redsp_OCallObj,axiom,
! [M: list_char,Es: list_exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( call_list_char @ E @ M @ Es ) @ S @ ( call_list_char @ E_2 @ M @ Es ) @ S_1 ) ) ).
thf(fact_551_redp__redsp_OBinOpRed1,axiom,
! [Bop: bop,E_2_1: exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( binOp_list_char @ E @ Bop @ E_2_1 ) @ S @ ( binOp_list_char @ E_2 @ Bop @ E_2_1 ) @ S_1 ) ) ).
thf(fact_552_redp__redsp_OTryRed,axiom,
! [C: list_char,V: list_char,E_2_1: exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( tryCatch_list_char @ E @ C @ V @ E_2_1 ) @ S @ ( tryCatch_list_char @ E_2 @ C @ V @ E_2_1 ) @ S_1 ) ) ).
thf(fact_553_redp__redsp_OCallThrowParams,axiom,
! [P: list_P1999446415t_char,V_2: val,M: list_char,S: produc2090907612on_val,Es: list_exp_list_char,Vs: list_val,E: exp_list_char,Es_1: list_exp_list_char] :
( ( Es
= ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ Vs ) @ ( cons_exp_list_char @ ( throw_list_char @ E ) @ Es_1 ) ) )
=> ( redp @ P @ ( call_list_char @ ( val_list_char @ V_2 ) @ M @ Es ) @ S @ ( throw_list_char @ E ) @ S ) ) ).
thf(fact_554_redp__redsp_ORedSeq,axiom,
! [P: list_P1999446415t_char,V_2: val,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( seq_list_char @ ( val_list_char @ V_2 ) @ E_2_1 ) @ S @ E_2_1 @ S ) ).
thf(fact_555_redp__redsp_OFAssRed2,axiom,
! [V_2: val,F: list_char,D: list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( fAss_list_char @ ( val_list_char @ V_2 ) @ F @ D @ E ) @ S @ ( fAss_list_char @ ( val_list_char @ V_2 ) @ F @ D @ E_2 ) @ S_1 ) ) ).
thf(fact_556_redp__redsp_OBinOpRed2,axiom,
! [V_1_1: val,Bop: bop,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( binOp_list_char @ ( val_list_char @ V_1_1 ) @ Bop @ E ) @ S @ ( binOp_list_char @ ( val_list_char @ V_1_1 ) @ Bop @ E_2 ) @ S_1 ) ) ).
thf(fact_557_redp__redsp_ORedTry,axiom,
! [P: list_P1999446415t_char,V_2: val,C: list_char,V: list_char,E_2_1: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( tryCatch_list_char @ ( val_list_char @ V_2 ) @ C @ V @ E_2_1 ) @ S @ ( val_list_char @ V_2 ) @ S ) ).
thf(fact_558_eval__evals_OSeqThrow,axiom,
! [E_1_1: exp_list_char,P: list_P1999446415t_char,E_0: exp_list_char,S_0: produc2090907612on_val,E: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_0 @ S_0 @ ( throw_list_char @ E ) @ S_1_1 )
=> ( eval @ P @ ( seq_list_char @ E_0 @ E_1_1 ) @ S_0 @ ( throw_list_char @ E ) @ S_1_1 ) ) ).
thf(fact_559_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_2: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 )
=> ( eval @ P @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2_1 ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 ) ) ).
thf(fact_560_CallObjThrow,axiom,
! [M: list_char,Ps: list_exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,E_2: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 )
=> ( eval @ P @ ( call_list_char @ E @ M @ Ps ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 ) ) ).
thf(fact_561_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: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( throw_list_char @ E ) @ S_1_1 )
=> ( eval @ P @ ( binOp_list_char @ E_1_1 @ Bop @ E_2_1 ) @ S_0 @ ( throw_list_char @ E ) @ S_1_1 ) ) ).
thf(fact_562_red__reds_OThrowRed,axiom,
! [E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_2 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_563_red__reds_OThrowThrow,axiom,
! [E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ ( throw_list_char @ E ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_564_eval__evals_OFAssThrow2,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,E_2: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_2: val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ V_2 ) @ S_1_1 )
=> ( ( eval @ P @ E_2_1 @ S_1_1 @ ( throw_list_char @ E_2 ) @ S_2 )
=> ( eval @ P @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2_1 ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_2 ) ) ) ).
thf(fact_565_eval__evals_OBinOpThrow2,axiom,
! [Bop: bop,E_2_1: exp_list_char,E: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1_1: val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ V_1_1 ) @ S_1_1 )
=> ( ( eval @ P @ E_2_1 @ S_1_1 @ ( throw_list_char @ E ) @ S_2 )
=> ( eval @ P @ ( binOp_list_char @ E_1_1 @ Bop @ E_2_1 ) @ S_0 @ ( throw_list_char @ E ) @ S_2 ) ) ) ).
thf(fact_566_red__reds_OCallThrowParams,axiom,
! [V_2: val,M: list_char,S: produc2090907612on_val,P: list_P1999446415t_char,Es: list_exp_list_char,Vs: list_val,E: exp_list_char,Es_1: list_exp_list_char] :
( ( Es
= ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ Vs ) @ ( cons_exp_list_char @ ( throw_list_char @ E ) @ Es_1 ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ ( val_list_char @ V_2 ) @ M @ Es ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ) ).
thf(fact_567_ThrowRedsThrow,axiom,
! [E: exp_list_char,S: produc2090907612on_val,A: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_568_ThrowReds,axiom,
! [E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_569_red__reds_OSeqThrow,axiom,
! [E: 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 ) @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_570_red__reds_OFAssThrow1,axiom,
! [E: 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 ) @ F @ D @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_571_red__reds_OCallThrowObj,axiom,
! [E: 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 ) @ M @ Es ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_572_red__reds_OBinOpThrow1,axiom,
! [E: 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 ) @ Bop @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_573_red__reds_OFAssThrow2,axiom,
! [V_2: val,F: list_char,D: list_char,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ ( val_list_char @ V_2 ) @ F @ D @ ( throw_list_char @ E ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_574_red__reds_OBinOpThrow2,axiom,
! [V_1_1: val,Bop: bop,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ ( val_list_char @ V_1_1 ) @ Bop @ ( throw_list_char @ E ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_575_SeqRedsThrow,axiom,
! [E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( seq_list_char @ E @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_576_FAssRedsThrow1,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAss_list_char @ E @ F @ D @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_577_CallRedsThrowObj,axiom,
! [M: list_char,Es: list_exp_list_char,E: exp_list_char,S0: produc2090907612on_val,A: exp_list_char,S_1_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S0 ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ E @ M @ Es ) @ S0 ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_578_BinOpRedsThrow1,axiom,
! [Bop: bop,E_2_1: exp_list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( binOp_list_char @ E @ Bop @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_579_FAssRedsThrow2,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,E: exp_list_char,S_2: produc2090907612on_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_2: val,S_1_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_1_1 @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ V_2 ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2_1 @ S_1_1 ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_2 ) ) @ ( 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 ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_580_BinOpRedsThrow2,axiom,
! [Bop: bop,E_2_1: exp_list_char,E: exp_list_char,S_2: produc2090907612on_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,V_1_1: val,S_1_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_1 ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2_1 @ S_1_1 ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_2 ) ) @ ( 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 ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_581_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_2: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ ( binOp_list_char @ E_1_1 @ Bop @ E_2_1 ) @ S @ E_2 @ S_1 )
=> ( ! [V_1_2: val,S_1_2: produc2090907612on_val,V_2_2: val,V_1: val] :
( ( E_2
= ( val_list_char @ V_1 ) )
=> ( ( eval @ P @ E_1_1 @ S @ ( val_list_char @ V_1_2 ) @ S_1_2 )
=> ( ( eval @ P @ E_2_1 @ S_1_2 @ ( val_list_char @ V_2_2 ) @ S_1 )
=> ( ( binop @ ( produc621191550al_val @ Bop @ ( product_Pair_val_val @ V_1_2 @ V_2_2 ) ) )
!= ( some_val @ V_1 ) ) ) ) )
=> ( ! [E_4: exp_list_char] :
( ( E_2
= ( throw_list_char @ E_4 ) )
=> ~ ( eval @ P @ E_1_1 @ S @ ( throw_list_char @ E_4 ) @ S_1 ) )
=> ~ ! [V_1_2: val,S_1_2: produc2090907612on_val,E_4: exp_list_char] :
( ( E_2
= ( throw_list_char @ E_4 ) )
=> ( ( eval @ P @ E_1_1 @ S @ ( val_list_char @ V_1_2 ) @ S_1_2 )
=> ~ ( eval @ P @ E_2_1 @ S_1_2 @ ( throw_list_char @ E_4 ) @ S_1 ) ) ) ) ) ) ).
thf(fact_582_CallParamsThrow,axiom,
! [M: list_char,Es: list_exp_list_char,Vs: list_val,Ex: exp_list_char,Es_1: list_exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,V_2: val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ V_2 ) @ S_1_1 )
=> ( ( evals @ P @ Es @ S_1_1 @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ Vs ) @ ( cons_exp_list_char @ ( throw_list_char @ Ex ) @ Es_1 ) ) @ S_2 )
=> ( eval @ P @ ( call_list_char @ E @ M @ Es ) @ S_0 @ ( throw_list_char @ Ex ) @ S_2 ) ) ) ).
thf(fact_583_list__eval__Throw,axiom,
! [Vs: list_val,Es_1: list_exp_list_char,P: list_P1999446415t_char,X: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ ( throw_list_char @ X ) @ S @ E_2 @ S_1 )
=> ( evals @ P @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ Vs ) @ ( cons_exp_list_char @ ( throw_list_char @ X ) @ Es_1 ) ) @ S @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ Vs ) @ ( cons_exp_list_char @ E_2 @ Es_1 ) ) @ S_1 ) ) ).
thf(fact_584_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_2: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ ( seq_list_char @ E_1_1 @ E_2_1 ) @ S @ E_2 @ S_1 )
=> ( ! [V_1: val,S_1_2: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S @ ( val_list_char @ V_1 ) @ S_1_2 )
=> ~ ( eval @ P @ E_2_1 @ S_1_2 @ E_2 @ S_1 ) )
=> ~ ! [E_4: exp_list_char] :
( ( E_2
= ( throw_list_char @ E_4 ) )
=> ~ ( eval @ P @ E_1_1 @ S @ ( throw_list_char @ E_4 ) @ S_1 ) ) ) ) ).
thf(fact_585_redp__redsp_OCallParams,axiom,
! [V_2: val,M: list_char,P: list_P1999446415t_char,Es: list_exp_list_char,S: produc2090907612on_val,Es_1: list_exp_list_char,S_1: produc2090907612on_val] :
( ( redsp @ P @ Es @ S @ Es_1 @ S_1 )
=> ( redp @ P @ ( call_list_char @ ( val_list_char @ V_2 ) @ M @ Es ) @ S @ ( call_list_char @ ( val_list_char @ V_2 ) @ M @ Es_1 ) @ S_1 ) ) ).
thf(fact_586_evals__final,axiom,
! [P: list_P1999446415t_char,Es: list_exp_list_char,S: produc2090907612on_val,Es_1: list_exp_list_char,S_1: produc2090907612on_val] :
( ( evals @ P @ Es @ S @ Es_1 @ S_1 )
=> ( finals_list_char @ Es_1 ) ) ).
thf(fact_587_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_588_evals__hext,axiom,
! [P: list_P1999446415t_char,Es: list_exp_list_char,H: nat > option1728594148on_val,L_1: list_char > option_val,Es_1: list_exp_list_char,H_2: nat > option1728594148on_val,L_2: list_char > option_val] :
( ( evals @ P @ Es @ ( produc755559506on_val @ H @ L_1 ) @ Es_1 @ ( produc755559506on_val @ H_2 @ L_2 ) )
=> ( hext @ H @ H_2 ) ) ).
thf(fact_589_redp__redsp_OListRed2,axiom,
! [V_2: val,P: list_P1999446415t_char,Es: list_exp_list_char,S: produc2090907612on_val,Es_1: list_exp_list_char,S_1: produc2090907612on_val] :
( ( redsp @ P @ Es @ S @ Es_1 @ S_1 )
=> ( redsp @ P @ ( cons_exp_list_char @ ( val_list_char @ V_2 ) @ Es ) @ S @ ( cons_exp_list_char @ ( val_list_char @ V_2 ) @ Es_1 ) @ S_1 ) ) ).
thf(fact_590_eval__evals_OCons,axiom,
! [Es: list_exp_list_char,Es_1: list_exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,V_2: val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ V_2 ) @ S_1_1 )
=> ( ( evals @ P @ Es @ S_1_1 @ Es_1 @ S_2 )
=> ( evals @ P @ ( cons_exp_list_char @ E @ Es ) @ S_0 @ ( cons_exp_list_char @ ( val_list_char @ V_2 ) @ Es_1 ) @ S_2 ) ) ) ).
thf(fact_591_ConsThrow,axiom,
! [Es: list_exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,E_2: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 )
=> ( evals @ P @ ( cons_exp_list_char @ E @ Es ) @ S_0 @ ( cons_exp_list_char @ ( throw_list_char @ E_2 ) @ Es ) @ S_1_1 ) ) ).
thf(fact_592_redp__redsp_OListRed1,axiom,
! [Es: list_exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redsp @ P @ ( cons_exp_list_char @ E @ Es ) @ S @ ( cons_exp_list_char @ E_2 @ Es ) @ S_1 ) ) ).
thf(fact_593_evals__cases_I2_J,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,Es: list_exp_list_char,S: produc2090907612on_val,E_2: list_exp_list_char,S_1: produc2090907612on_val] :
( ( evals @ P @ ( cons_exp_list_char @ E @ Es ) @ S @ E_2 @ S_1 )
=> ( ! [V_1: val,S_1_2: produc2090907612on_val,Es_2: list_exp_list_char] :
( ( E_2
= ( cons_exp_list_char @ ( val_list_char @ V_1 ) @ Es_2 ) )
=> ( ( eval @ P @ E @ S @ ( val_list_char @ V_1 ) @ S_1_2 )
=> ~ ( evals @ P @ Es @ S_1_2 @ Es_2 @ S_1 ) ) )
=> ~ ! [E_3: exp_list_char] :
( ( E_2
= ( cons_exp_list_char @ ( throw_list_char @ E_3 ) @ Es ) )
=> ~ ( eval @ P @ E @ S @ ( throw_list_char @ E_3 ) @ S_1 ) ) ) ) ).
thf(fact_594_WTrtThrow,axiom,
! [T: ty,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E: exp_list_char,T_r_1: ty] :
( ( wTrt @ P @ H @ E_1 @ E @ T_r_1 )
=> ( ( is_refT @ T_r_1 )
=> ( wTrt @ P @ H @ E_1 @ ( throw_list_char @ E ) @ T ) ) ) ).
thf(fact_595_WTrt__elim__cases_I4_J,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_1 @ ( throw_list_char @ E ) @ T )
=> ~ ! [T_r: ty] :
( ( wTrt @ P @ H @ E_1 @ E @ T_r )
=> ~ ( is_refT @ T_r ) ) ) ).
thf(fact_596_WhileRedsThrow,axiom,
! [C_2: exp_list_char,B: exp_list_char,S: produc2090907612on_val,E: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ B @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( while_list_char @ B @ C_2 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_597_FAccRedsThrow,axiom,
! [F: list_char,D: list_char,E: exp_list_char,S: produc2090907612on_val,A: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E @ F @ D ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_598_redp__redsp_OFAccRed,axiom,
! [F: list_char,D: list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( fAcc_list_char @ E @ F @ D ) @ S @ ( fAcc_list_char @ E_2 @ F @ D ) @ S_1 ) ) ).
thf(fact_599_eval__evals_OFAccThrow,axiom,
! [F: list_char,D: list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,E_2: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 )
=> ( eval @ P @ ( fAcc_list_char @ E @ F @ D ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 ) ) ).
thf(fact_600_WhileCondThrow,axiom,
! [C_2: exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,E_2: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 )
=> ( eval @ P @ ( while_list_char @ E @ C_2 ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 ) ) ).
thf(fact_601_redp__redsp_OFAccThrow,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,F: list_char,D: list_char,S: produc2090907612on_val] : ( redp @ P @ ( fAcc_list_char @ ( throw_list_char @ E ) @ F @ D ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_602_red__reds_OFAccRed,axiom,
! [F: list_char,D: list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E @ F @ D ) @ S ) @ ( produc235638504on_val @ ( fAcc_list_char @ E_2 @ F @ D ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_603_red__reds_OFAccThrow,axiom,
! [E: 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 ) @ F @ D ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_604_FAccReds,axiom,
! [F: list_char,D: list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E @ F @ D ) @ S ) @ ( produc235638504on_val @ ( fAcc_list_char @ E_2 @ F @ D ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_605_WhileTRedsThrow,axiom,
! [C_2: exp_list_char,E: exp_list_char,S_2: produc2090907612on_val,B: exp_list_char,S_0: produc2090907612on_val,S_1_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_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ C_2 @ S_1_1 ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( while_list_char @ B @ C_2 ) @ S_0 ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_606_WhileT,axiom,
! [E_3_1: exp_list_char,S_3: produc2090907612on_val,C_2: exp_list_char,V_1_1: val,S_2: produc2090907612on_val,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ ( bool @ $true ) ) @ S_1_1 )
=> ( ( eval @ P @ C_2 @ S_1_1 @ ( val_list_char @ V_1_1 ) @ S_2 )
=> ( ( eval @ P @ ( while_list_char @ E @ C_2 ) @ S_2 @ E_3_1 @ S_3 )
=> ( eval @ P @ ( while_list_char @ E @ C_2 ) @ S_0 @ E_3_1 @ S_3 ) ) ) ) ).
thf(fact_607_WhileBodyThrow,axiom,
! [C_2: exp_list_char,E_2: exp_list_char,S_2: produc2090907612on_val,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ ( bool @ $true ) ) @ S_1_1 )
=> ( ( eval @ P @ C_2 @ S_1_1 @ ( throw_list_char @ E_2 ) @ S_2 )
=> ( eval @ P @ ( while_list_char @ E @ C_2 ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_2 ) ) ) ).
thf(fact_608_WhileTReds,axiom,
! [E: exp_list_char,S_3: produc2090907612on_val,C_2: exp_list_char,V_1_1: val,S_2: produc2090907612on_val,B: exp_list_char,S_0: produc2090907612on_val,S_1_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_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ C_2 @ S_1_1 ) @ ( produc235638504on_val @ ( val_list_char @ V_1_1 ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( while_list_char @ B @ C_2 ) @ S_2 ) @ ( produc235638504on_val @ E @ S_3 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( while_list_char @ B @ C_2 ) @ S_0 ) @ ( produc235638504on_val @ E @ S_3 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_609_binop_Osimps_I1_J,axiom,
! [V_1_1: val,V_2_1: val] :
( ( binop @ ( produc621191550al_val @ c_Expr_Obop_OEq @ ( product_Pair_val_val @ V_1_1 @ V_2_1 ) ) )
= ( some_val @ ( bool @ ( V_1_1 = V_2_1 ) ) ) ) ).
thf(fact_610_WhileFReds,axiom,
! [C_2: exp_list_char,B: exp_list_char,S: produc2090907612on_val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ B @ S ) @ ( produc235638504on_val @ ( val_list_char @ ( bool @ $false ) ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( while_list_char @ B @ C_2 ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ unit ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_611_FAcc,axiom,
! [F: list_char,D: list_char,V_2: val,C: list_char,Fs: produc1278157519t_char > option_val,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,A: nat,H: nat > option1728594148on_val,L_1: list_char > option_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ ( addr @ A ) ) @ ( produc755559506on_val @ H @ L_1 ) )
=> ( ( ( H @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( ( ( Fs @ ( produc5062597t_char @ F @ D ) )
= ( some_val @ V_2 ) )
=> ( eval @ P @ ( fAcc_list_char @ E @ F @ D ) @ S_0 @ ( val_list_char @ V_2 ) @ ( produc755559506on_val @ H @ L_1 ) ) ) ) ) ).
thf(fact_612_Throw,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,A: nat,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ ( addr @ A ) ) @ S_1_1 )
=> ( eval @ P @ ( throw_list_char @ E ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ S_1_1 ) ) ).
thf(fact_613_WhileF,axiom,
! [C_2: exp_list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ ( bool @ $false ) ) @ S_1_1 )
=> ( eval @ P @ ( while_list_char @ E @ C_2 ) @ S_0 @ ( val_list_char @ unit ) @ S_1_1 ) ) ).
thf(fact_614_FAccRedsVal,axiom,
! [F: list_char,D: list_char,V_2: val,C: list_char,Fs: produc1278157519t_char > option_val,E: exp_list_char,S: produc2090907612on_val,A: nat,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( val_list_char @ ( addr @ A ) ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( hp @ S_1 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( ( ( Fs @ ( produc5062597t_char @ F @ D ) )
= ( some_val @ V_2 ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E @ F @ D ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ V_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_615_red__reds_ORedFAcc,axiom,
! [P: list_P1999446415t_char,F: list_char,D: list_char,V_2: 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_2 ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ ( val_list_char @ ( addr @ A ) ) @ F @ D ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ V_2 ) @ S ) ) @ ( red @ P ) ) ) ) ).
thf(fact_616_redp__redsp_ORedFAcc,axiom,
! [P: list_P1999446415t_char,F: list_char,D: list_char,V_2: 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_2 ) )
=> ( redp @ P @ ( fAcc_list_char @ ( val_list_char @ ( addr @ A ) ) @ F @ D ) @ S @ ( val_list_char @ V_2 ) @ S ) ) ) ).
thf(fact_617_reds__preserves__sconf,axiom,
! [E_1: list_char > option_ty,Ts_1: list_ty,Es: list_exp_list_char,S: produc2090907612on_val,Es_1: list_exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S ) @ ( produc1302104557on_val @ Es_1 @ S_1 ) ) @ ( reds @ P ) )
=> ( ( wTrts @ P @ ( hp @ S ) @ E_1 @ Es @ Ts_1 )
=> ( ( typeSa1102574168_sconf @ P @ E_1 @ S )
=> ( typeSa1102574168_sconf @ P @ E_1 @ S_1 ) ) ) ) ).
thf(fact_618_TryRedsFail,axiom,
! [V: 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: 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 @ L_1 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( H @ 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 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ ( produc755559506on_val @ H @ L_1 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_619_red__reds_ORedTryFail,axiom,
! [V: 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 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ S ) ) @ ( red @ P ) ) ) ) ).
thf(fact_620_TryThrow,axiom,
! [V: 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 @ E_2_1 ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ A ) ) ) @ ( produc755559506on_val @ H_1_1 @ L_1_1 ) ) ) ) ) ).
thf(fact_621_red__preserves__sconf,axiom,
! [E_1: list_char > option_ty,T: ty,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( ( wTrt @ P @ ( hp @ S ) @ E_1 @ E @ T )
=> ( ( typeSa1102574168_sconf @ P @ E_1 @ S )
=> ( typeSa1102574168_sconf @ P @ E_1 @ S_1 ) ) ) ) ).
thf(fact_622_TryCatchRedsFinal,axiom,
! [E_2_1: exp_list_char,V: list_char,E_2_2: exp_list_char,H_2_1: 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 @ ( some_val @ ( addr @ A ) ) ) ) ) @ ( produc235638504on_val @ E_2_2 @ ( produc755559506on_val @ H_2_1 @ 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 @ E_2_1 ) @ S_0 ) @ ( produc235638504on_val @ E_2_2 @ ( produc755559506on_val @ H_2_1 @ ( fun_up1149430426on_val @ L_2_1 @ V @ ( L_1_1 @ V ) ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ) ) ).
thf(fact_623_CastRedsAddr,axiom,
! [C: list_char,D: list_char,Fs: produc1278157519t_char > option_val,E: exp_list_char,S: produc2090907612on_val,A: nat,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( val_list_char @ ( addr @ A ) ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( hp @ S_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 @ ( cast_list_char @ C @ E ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ ( addr @ A ) ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_624_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_625_redp__redsp_OCastRed,axiom,
! [C: list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( cast_list_char @ C @ E ) @ S @ ( cast_list_char @ C @ E_2 ) @ S_1 ) ) ).
thf(fact_626_eval__evals_OCastThrow,axiom,
! [C: list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,E_2: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 )
=> ( eval @ P @ ( cast_list_char @ C @ E ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 ) ) ).
thf(fact_627_redp__redsp_OCastThrow,axiom,
! [P: list_P1999446415t_char,C: list_char,E: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( cast_list_char @ C @ ( throw_list_char @ E ) ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_628_red__reds_OCastRed,axiom,
! [C: list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ E ) @ S ) @ ( produc235638504on_val @ ( cast_list_char @ C @ E_2 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_629_red__reds_OCastThrow,axiom,
! [C: list_char,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ ( throw_list_char @ E ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_630_CastReds,axiom,
! [C: list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ E ) @ S ) @ ( produc235638504on_val @ ( cast_list_char @ C @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_631_CastRedsThrow,axiom,
! [C: list_char,E: exp_list_char,S: produc2090907612on_val,A: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ E ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_632_Cast,axiom,
! [C: list_char,D: list_char,Fs: produc1278157519t_char > option_val,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,A: nat,H: nat > option1728594148on_val,L_1: list_char > option_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ ( addr @ A ) ) @ ( produc755559506on_val @ H @ L_1 ) )
=> ( ( ( H @ 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 ) @ S_0 @ ( val_list_char @ ( addr @ A ) ) @ ( produc755559506on_val @ H @ L_1 ) ) ) ) ) ).
thf(fact_633_TryCatch,axiom,
! [E_2_1: exp_list_char,V: list_char,E_2_2: exp_list_char,H_2_1: 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 @ ( some_val @ ( addr @ A ) ) ) ) @ E_2_2 @ ( produc755559506on_val @ H_2_1 @ L_2_1 ) )
=> ( eval @ P @ ( tryCatch_list_char @ E_1_1 @ C @ V @ E_2_1 ) @ S_0 @ E_2_2 @ ( produc755559506on_val @ H_2_1 @ ( fun_up1149430426on_val @ L_2_1 @ V @ ( L_1_1 @ V ) ) ) ) ) ) ) ) ).
thf(fact_634_CastRedsFail,axiom,
! [C: list_char,D: list_char,Fs: produc1278157519t_char > option_val,E: exp_list_char,S: produc2090907612on_val,A: nat,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( val_list_char @ ( addr @ A ) ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( hp @ S_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 @ ( cast_list_char @ C @ E ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_635_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_636_red__reds_ORedCall,axiom,
! [Vs: list_val,P: list_P1999446415t_char,M: list_char,Ts_1: 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_1 @ T @ ( produc1147572817t_char @ Pns @ Body ) @ D )
=> ( ( ( size_size_list_val @ Vs )
= ( size_s2113983095t_char @ Pns ) )
=> ( ( ( size_size_list_ty @ Ts_1 )
= ( 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 ) ) @ S ) @ ( produc235638504on_val @ ( blocks @ ( produc921874948t_char @ ( cons_list_char @ this @ Pns ) @ ( produc1909267824t_char @ ( cons_ty @ ( class @ D ) @ Ts_1 ) @ ( produc1916172923t_char @ ( cons_val @ ( addr @ A ) @ Vs ) @ Body ) ) ) ) @ S ) ) @ ( red @ P ) ) ) ) ) ) ).
thf(fact_637_WTrtTry,axiom,
! [V: list_char,C: list_char,E_2_1: exp_list_char,T_2: ty,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E_1_1: exp_list_char,T_1_2: ty] :
( ( wTrt @ P @ H @ E_1 @ E_1_1 @ T_1_2 )
=> ( ( wTrt @ P @ H @ ( fun_up424764369ion_ty @ E_1 @ V @ ( some_ty @ ( class @ C ) ) ) @ E_2_1 @ T_2 )
=> ( ( widen_2090681816t_char @ P @ T_1_2 @ T_2 )
=> ( wTrt @ P @ H @ E_1 @ ( tryCatch_list_char @ E_1_1 @ C @ V @ E_2_1 ) @ T_2 ) ) ) ) ).
thf(fact_638_WTrtCall,axiom,
! [Es: list_exp_list_char,Ts_2: list_ty,M: list_char,Ts_1: list_ty,T: ty,Pns: list_list_char,Body: exp_list_char,D: list_char,P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E: exp_list_char,C: list_char] :
( ( wTrt @ P @ H @ E_1 @ E @ ( class @ C ) )
=> ( ( method1809630380t_char @ P @ C @ M @ Ts_1 @ T @ ( produc1147572817t_char @ Pns @ Body ) @ D )
=> ( ( wTrts @ P @ H @ E_1 @ Es @ Ts_2 )
=> ( ( list_all2_ty_ty @ ( widen_2090681816t_char @ P ) @ Ts_2 @ Ts_1 )
=> ( wTrt @ P @ H @ E_1 @ ( call_list_char @ E @ M @ Es ) @ T ) ) ) ) ) ).
thf(fact_639_hext__upd__obj,axiom,
! [Fs_1: produc1278157519t_char > option_val,H: nat > option1728594148on_val,A: nat,C: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( H @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( hext @ H @ ( fun_up1472480727on_val @ H @ A @ ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs_1 ) ) ) ) ) ).
thf(fact_640_FAss,axiom,
! [H_2_2: nat > option1728594148on_val,Fs_1: 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_2: val,H_2_1: 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_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ ( addr @ A ) ) @ S_1_1 )
=> ( ( eval @ P @ E_2_1 @ S_1_1 @ ( val_list_char @ V_2 ) @ ( produc755559506on_val @ H_2_1 @ L_2_1 ) )
=> ( ( ( H_2_1 @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( ( Fs_1
= ( fun_up204312361on_val @ Fs @ ( produc5062597t_char @ F @ D ) @ ( some_val @ V_2 ) ) )
=> ( ( H_2_2
= ( fun_up1472480727on_val @ H_2_1 @ A @ ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs_1 ) ) ) )
=> ( eval @ P @ ( fAss_list_char @ E_1_1 @ F @ D @ E_2_1 ) @ S_0 @ ( val_list_char @ unit ) @ ( produc755559506on_val @ H_2_2 @ L_2_1 ) ) ) ) ) ) ) ).
thf(fact_641_redp__redsp_ORedFAss,axiom,
! [P: list_P1999446415t_char,F: list_char,D: list_char,V_2: val,L_1: list_char > option_val,H: nat > option1728594148on_val,A: nat,C: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( H @ A )
= ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) ) )
=> ( redp @ P @ ( fAss_list_char @ ( val_list_char @ ( addr @ A ) ) @ F @ D @ ( val_list_char @ V_2 ) ) @ ( produc755559506on_val @ H @ L_1 ) @ ( val_list_char @ unit ) @ ( produc755559506on_val @ ( fun_up1472480727on_val @ H @ A @ ( some_P451527732on_val @ ( produc926070009on_val @ C @ ( fun_up204312361on_val @ Fs @ ( produc5062597t_char @ F @ D ) @ ( some_val @ V_2 ) ) ) ) ) @ L_1 ) ) ) ).
thf(fact_642_red__reds_ORedFAss,axiom,
! [F: list_char,D: list_char,V_2: val,L_1: list_char > option_val,P: list_P1999446415t_char,H: nat > option1728594148on_val,A: nat,C: list_char,Fs: produc1278157519t_char > option_val] :
( ( ( H @ 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_2 ) ) @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc235638504on_val @ ( val_list_char @ unit ) @ ( produc755559506on_val @ ( fun_up1472480727on_val @ H @ A @ ( some_P451527732on_val @ ( produc926070009on_val @ C @ ( fun_up204312361on_val @ Fs @ ( produc5062597t_char @ F @ D ) @ ( some_val @ V_2 ) ) ) ) ) @ L_1 ) ) ) @ ( red @ P ) ) ) ).
thf(fact_643_FAssRedsVal,axiom,
! [F: list_char,D: list_char,C: list_char,Fs: produc1278157519t_char > option_val,E_2_1: exp_list_char,V_2: val,H_2_1: nat > option1728594148on_val,L_2_1: list_char > option_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,A: nat,S_1_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_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2_1 @ S_1_1 ) @ ( produc235638504on_val @ ( val_list_char @ V_2 ) @ ( produc755559506on_val @ H_2_1 @ L_2_1 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( ( some_P451527732on_val @ ( produc926070009on_val @ C @ Fs ) )
= ( H_2_1 @ 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_1 @ A @ ( some_P451527732on_val @ ( produc926070009on_val @ C @ ( fun_up204312361on_val @ Fs @ ( produc5062597t_char @ F @ D ) @ ( some_val @ V_2 ) ) ) ) ) @ L_2_1 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ) ).
thf(fact_644_CastFail,axiom,
! [C: list_char,D: list_char,Fs: produc1278157519t_char > option_val,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,A: nat,H: nat > option1728594148on_val,L_1: list_char > option_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ ( addr @ A ) ) @ ( produc755559506on_val @ H @ L_1 ) )
=> ( ( ( H @ 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 ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) @ ( produc755559506on_val @ H @ L_1 ) ) ) ) ) ).
thf(fact_645_redp__redsp_ORedCall,axiom,
! [Vs: list_val,P: list_P1999446415t_char,M: list_char,Ts_1: 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_1 @ T @ ( produc1147572817t_char @ Pns @ Body ) @ D )
=> ( ( ( size_size_list_val @ Vs )
= ( size_s2113983095t_char @ Pns ) )
=> ( ( ( size_size_list_ty @ Ts_1 )
= ( size_s2113983095t_char @ Pns ) )
=> ( redp @ P @ ( call_list_char @ ( val_list_char @ ( addr @ A ) ) @ M @ ( map_va1934808527t_char @ val_list_char @ Vs ) ) @ S @ ( blocks @ ( produc921874948t_char @ ( cons_list_char @ this @ Pns ) @ ( produc1909267824t_char @ ( cons_ty @ ( class @ D ) @ Ts_1 ) @ ( produc1916172923t_char @ ( cons_val @ ( addr @ A ) @ Vs ) @ Body ) ) ) ) @ S ) ) ) ) ) ).
thf(fact_646_WTrt__elim__cases_I5_J,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E_1_1: exp_list_char,C: list_char,V: list_char,E_2_1: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_1 @ ( tryCatch_list_char @ E_1_1 @ C @ V @ E_2_1 ) @ T )
=> ~ ! [T_1_1: ty] :
( ( wTrt @ P @ H @ E_1 @ E_1_1 @ T_1_1 )
=> ( ( wTrt @ P @ H @ ( fun_up424764369ion_ty @ E_1 @ V @ ( some_ty @ ( class @ C ) ) ) @ E_2_1 @ T )
=> ~ ( widen_2090681816t_char @ P @ T_1_1 @ T ) ) ) ) ).
thf(fact_647_CallRedsNull,axiom,
! [M: list_char,Es: list_exp_list_char,Vs: list_val,S_2: produc2090907612on_val,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S_0 ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S_1_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member2042188884on_val @ ( produc747700183on_val @ ( produc1302104557on_val @ Es @ S_1_1 ) @ ( produc1302104557on_val @ ( map_va1934808527t_char @ val_list_char @ Vs ) @ S_2 ) ) @ ( transi808828192on_val @ ( reds @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( call_list_char @ E @ M @ Es ) @ S_0 ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_2 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_648_ThrowNull,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ null ) @ S_1_1 )
=> ( eval @ P @ ( throw_list_char @ E ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_1_1 ) ) ).
thf(fact_649_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_650_CastNull,axiom,
! [C: list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ null ) @ S_1_1 )
=> ( eval @ P @ ( cast_list_char @ C @ E ) @ S_0 @ ( val_list_char @ null ) @ S_1_1 ) ) ).
thf(fact_651_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_652_FAssNull,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,V_2: val,S_2: produc2090907612on_val,P: list_P1999446415t_char,E_1_1: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E_1_1 @ S_0 @ ( val_list_char @ null ) @ S_1_1 )
=> ( ( eval @ P @ E_2_1 @ S_1_1 @ ( val_list_char @ V_2 ) @ S_2 )
=> ( 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 ) ) ) ).
thf(fact_653_FAccNull,axiom,
! [F: list_char,D: list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ null ) @ S_1_1 )
=> ( eval @ P @ ( fAcc_list_char @ E @ F @ D ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_1_1 ) ) ).
thf(fact_654_redp__redsp_ORedFAssNull,axiom,
! [P: list_P1999446415t_char,F: list_char,D: list_char,V_2: val,S: produc2090907612on_val] : ( redp @ P @ ( fAss_list_char @ ( val_list_char @ null ) @ F @ D @ ( val_list_char @ V_2 ) ) @ S @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ).
thf(fact_655_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_656_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_657_redp__redsp_ORedCallNull,axiom,
! [P: list_P1999446415t_char,M: list_char,Vs: list_val,S: produc2090907612on_val] : ( redp @ P @ ( call_list_char @ ( val_list_char @ null ) @ M @ ( map_va1934808527t_char @ val_list_char @ Vs ) ) @ S @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ).
thf(fact_658_ThrowRedsNull,axiom,
! [E: exp_list_char,S: produc2090907612on_val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_659_red__reds_ORedFAssNull,axiom,
! [F: list_char,D: list_char,V_2: 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_2 ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_660_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_661_CallNull,axiom,
! [M: list_char,Ps: list_exp_list_char,Vs: list_val,S_2: produc2090907612on_val,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ null ) @ S_1_1 )
=> ( ( evals @ P @ Ps @ S_1_1 @ ( map_va1934808527t_char @ val_list_char @ Vs ) @ S_2 )
=> ( eval @ P @ ( call_list_char @ E @ M @ Ps ) @ S_0 @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_2 ) ) ) ).
thf(fact_662_FAssRedsNull,axiom,
! [F: list_char,D: list_char,E_2_1: exp_list_char,V_2: val,S_2: produc2090907612on_val,E_1_1: exp_list_char,S_0: produc2090907612on_val,S_1_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_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E_2_1 @ S_1_1 ) @ ( produc235638504on_val @ ( val_list_char @ V_2 ) @ S_2 ) ) @ ( 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 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ) ).
thf(fact_663_FAccRedsNull,axiom,
! [F: list_char,D: list_char,E: exp_list_char,S: produc2090907612on_val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( fAcc_list_char @ E @ F @ D ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_664_red__reds_ORedCallNull,axiom,
! [M: list_char,Vs: 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 ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_665_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_666_CastRedsNull,axiom,
! [C: list_char,E: exp_list_char,S: produc2090907612on_val,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( cast_list_char @ C @ E ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ null ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_667_eval__cases_I12_J,axiom,
! [P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ ( throw_list_char @ E ) @ S @ E_2 @ S_1 )
=> ( ! [A_1: nat] :
( ( E_2
= ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) )
=> ~ ( eval @ P @ E @ S @ ( val_list_char @ ( addr @ A_1 ) ) @ S_1 ) )
=> ( ( ( E_2
= ( throw_list_char @ ( val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) )
=> ~ ( eval @ P @ E @ S @ ( val_list_char @ null ) @ S_1 ) )
=> ~ ! [E_3: exp_list_char] :
( ( E_2
= ( throw_list_char @ E_3 ) )
=> ~ ( eval @ P @ E @ S @ ( throw_list_char @ E_3 ) @ S_1 ) ) ) ) ) ).
thf(fact_668_default__val_Osimps_I5_J,axiom,
! [C: list_char] :
( ( default_val @ ( class @ C ) )
= null ) ).
thf(fact_669_val_Osimps_I3_J,axiom,
! [Nat_1: nat,Nat: nat] :
( ( ( addr @ Nat_1 )
= ( addr @ Nat ) )
<=> ( Nat_1 = Nat ) ) ).
thf(fact_670_val_Osimps_I1_J,axiom,
! [Bool_1: $o,Bool: $o] :
( ( ( bool @ Bool_1 )
= ( bool @ Bool ) )
<=> ( Bool_1
<=> Bool ) ) ).
thf(fact_671_val_Osimps_I17_J,axiom,
! [Nat: nat] :
( ( addr @ Nat )
!= null ) ).
thf(fact_672_val_Osimps_I16_J,axiom,
! [Nat: nat] :
( null
!= ( addr @ Nat ) ) ).
thf(fact_673_val_Osimps_I20_J,axiom,
! [Bool_1: $o,Nat: nat] :
( ( bool @ Bool_1 )
!= ( addr @ Nat ) ) ).
thf(fact_674_val_Osimps_I21_J,axiom,
! [Nat: nat,Bool_1: $o] :
( ( addr @ Nat )
!= ( bool @ Bool_1 ) ) ).
thf(fact_675_val_Osimps_I10_J,axiom,
! [Nat: nat] :
( unit
!= ( addr @ Nat ) ) ).
thf(fact_676_val_Osimps_I11_J,axiom,
! [Nat: nat] :
( ( addr @ Nat )
!= unit ) ).
thf(fact_677_val_Osimps_I13_J,axiom,
! [Bool: $o] :
( ( bool @ Bool )
!= null ) ).
thf(fact_678_val_Osimps_I12_J,axiom,
! [Bool: $o] :
( null
!= ( bool @ Bool ) ) ).
thf(fact_679_val_Osimps_I4_J,axiom,
unit != null ).
thf(fact_680_val_Osimps_I5_J,axiom,
null != unit ).
thf(fact_681_val_Osimps_I7_J,axiom,
! [Bool: $o] :
( ( bool @ Bool )
!= unit ) ).
thf(fact_682_val_Osimps_I6_J,axiom,
! [Bool: $o] :
( unit
!= ( bool @ Bool ) ) ).
thf(fact_683_finalRefE,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E: exp_list_char,T: ty] :
( ( wTrt @ P @ H @ E_1 @ E @ T )
=> ( ( is_refT @ T )
=> ( ( final_list_char @ E )
=> ( ( E
!= ( val_list_char @ null ) )
=> ( ( ? [A_1: nat] :
( E
= ( val_list_char @ ( addr @ A_1 ) ) )
=> ! [C_1: list_char] :
( T
!= ( class @ C_1 ) ) )
=> ~ ! [A_1: nat] :
( E
!= ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) ) ) ) ) ) ) ).
thf(fact_684_final__addrE,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,E: exp_list_char,C: list_char] :
( ( wTrt @ P @ H @ E_1 @ E @ ( class @ C ) )
=> ( ( final_list_char @ E )
=> ( ! [A_1: nat] :
( E
!= ( val_list_char @ ( addr @ A_1 ) ) )
=> ~ ! [A_1: nat] :
( E
!= ( throw_list_char @ ( val_list_char @ ( addr @ A_1 ) ) ) ) ) ) ) ).
thf(fact_685_LAssRedsVal,axiom,
! [V: list_char,E: exp_list_char,S: produc2090907612on_val,V_2: val,H_2: nat > option1728594148on_val,L_2: list_char > option_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( val_list_char @ V_2 ) @ ( produc755559506on_val @ H_2 @ L_2 ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V @ E ) @ S ) @ ( produc235638504on_val @ ( val_list_char @ unit ) @ ( produc755559506on_val @ H_2 @ ( fun_up1149430426on_val @ L_2 @ V @ ( some_val @ V_2 ) ) ) ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_686_redp__redsp_OLAssRed,axiom,
! [V: list_char,P: list_P1999446415t_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( redp @ P @ E @ S @ E_2 @ S_1 )
=> ( redp @ P @ ( lAss_list_char @ V @ E ) @ S @ ( lAss_list_char @ V @ E_2 ) @ S_1 ) ) ).
thf(fact_687_eval__evals_OLAssThrow,axiom,
! [V: list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,E_2: exp_list_char,S_1_1: produc2090907612on_val] :
( ( eval @ P @ E @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 )
=> ( eval @ P @ ( lAss_list_char @ V @ E ) @ S_0 @ ( throw_list_char @ E_2 ) @ S_1_1 ) ) ).
thf(fact_688_redp__redsp_OLAssThrow,axiom,
! [P: list_P1999446415t_char,V: list_char,E: exp_list_char,S: produc2090907612on_val] : ( redp @ P @ ( lAss_list_char @ V @ ( throw_list_char @ E ) ) @ S @ ( throw_list_char @ E ) @ S ) ).
thf(fact_689_red__reds_OLAssRed,axiom,
! [V: list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( red @ P ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V @ E ) @ S ) @ ( produc235638504on_val @ ( lAss_list_char @ V @ E_2 ) @ S_1 ) ) @ ( red @ P ) ) ) ).
thf(fact_690_red__reds_OLAssThrow,axiom,
! [V: list_char,E: exp_list_char,S: produc2090907612on_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V @ ( throw_list_char @ E ) ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ E ) @ S ) ) @ ( red @ P ) ) ).
thf(fact_691_LAssReds,axiom,
! [V: list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ E_2 @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V @ E ) @ S ) @ ( produc235638504on_val @ ( lAss_list_char @ V @ E_2 ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_692_LAssRedsThrow,axiom,
! [V: list_char,E: exp_list_char,S: produc2090907612on_val,A: exp_list_char,S_1: produc2090907612on_val,P: list_P1999446415t_char] :
( ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ E @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) )
=> ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V @ E ) @ S ) @ ( produc235638504on_val @ ( throw_list_char @ A ) @ S_1 ) ) @ ( transi2118771717on_val @ ( red @ P ) ) ) ) ).
thf(fact_693_LAss,axiom,
! [L_2: list_char > option_val,V: list_char,P: list_P1999446415t_char,E: exp_list_char,S_0: produc2090907612on_val,V_2: val,H: nat > option1728594148on_val,L_1: list_char > option_val] :
( ( eval @ P @ E @ S_0 @ ( val_list_char @ V_2 ) @ ( produc755559506on_val @ H @ L_1 ) )
=> ( ( L_2
= ( fun_up1149430426on_val @ L_1 @ V @ ( some_val @ V_2 ) ) )
=> ( eval @ P @ ( lAss_list_char @ V @ E ) @ S_0 @ ( val_list_char @ unit ) @ ( produc755559506on_val @ H @ L_2 ) ) ) ) ).
thf(fact_694_redp__redsp_ORedLAss,axiom,
! [P: list_P1999446415t_char,V: list_char,V_2: val,H: nat > option1728594148on_val,L_1: list_char > option_val] : ( redp @ P @ ( lAss_list_char @ V @ ( val_list_char @ V_2 ) ) @ ( produc755559506on_val @ H @ L_1 ) @ ( val_list_char @ unit ) @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L_1 @ V @ ( some_val @ V_2 ) ) ) ) ).
thf(fact_695_red__reds_ORedLAss,axiom,
! [V: list_char,V_2: val,H: nat > option1728594148on_val,L_1: list_char > option_val,P: list_P1999446415t_char] : ( member1913460000on_val @ ( produc833389609on_val @ ( produc235638504on_val @ ( lAss_list_char @ V @ ( val_list_char @ V_2 ) ) @ ( produc755559506on_val @ H @ L_1 ) ) @ ( produc235638504on_val @ ( val_list_char @ unit ) @ ( produc755559506on_val @ H @ ( fun_up1149430426on_val @ L_1 @ V @ ( some_val @ V_2 ) ) ) ) ) @ ( red @ P ) ) ).
thf(fact_696_red__reds_ORedTryCatch,axiom,
! [V: 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 @ E_2_1 ) @ S ) @ ( produc235638504on_val @ ( block_list_char @ V @ ( class @ C ) @ ( seq_list_char @ ( lAss_list_char @ V @ ( val_list_char @ ( addr @ A ) ) ) @ E_2_1 ) ) @ S ) ) @ ( red @ P ) ) ) ) ).
thf(fact_697_eval__cases_I4_J,axiom,
! [P: list_P1999446415t_char,V: list_char,E: exp_list_char,S: produc2090907612on_val,E_2: exp_list_char,S_1: produc2090907612on_val] :
( ( eval @ P @ ( lAss_list_char @ V @ E ) @ S @ E_2 @ S_1 )
=> ( ( ( E_2
= ( val_list_char @ unit ) )
=> ! [V_1: val,H_1: nat > option1728594148on_val,L: list_char > option_val] :
( ( S_1
= ( produc755559506on_val @ H_1 @ ( fun_up1149430426on_val @ L @ V @ ( some_val @ V_1 ) ) ) )
=> ~ ( eval @ P @ E @ S @ ( val_list_char @ V_1 ) @ ( produc755559506on_val @ H_1 @ L ) ) ) )
=> ~ ! [E_3: exp_list_char] :
( ( E_2
= ( throw_list_char @ E_3 ) )
=> ~ ( eval @ P @ E @ S @ ( throw_list_char @ E_3 ) @ S_1 ) ) ) ) ).
thf(fact_698_WTrtBlock,axiom,
! [P: list_P1999446415t_char,H: nat > option1728594148on_val,E_1: list_char > option_ty,V: list_char,T: ty,E: exp_list_char,T_1: ty] :
( ( wTrt @ P @ H @ ( fun_up424764369ion_ty @ E_1 @ V @ ( some_ty @ T ) ) @ E @ T_1 )
=> ( wTrt @ P @ H @ E_1 @ ( block_list_char @ V @ T @ E ) @ T_1 ) ) ).
thf(fact_699_redp__redsp_ORedBlock,axiom,
! [P: list_P1999446415t_char,V: list_char,T: ty,U: val,S: produc2090907612on_val] : ( redp @ P @ ( block_list_char @ V @ T @ ( val_list_char @ U ) ) @ S @ ( val_list_char @ U ) @ S ) ).
%----Helper facts (2)
thf(help_fequal_1_1_fequal_000tc__Type__Oty_T,axiom,
! [X: ty,Y: ty] :
( ~ ( fequal_ty @ X @ Y )
| ( X = Y ) ) ).
thf(help_fequal_2_1_fequal_000tc__Type__Oty_T,axiom,
! [X: ty,Y: ty] :
( ( X != Y )
| ( fequal_ty @ X @ Y ) ) ).
%----Conjectures (3)
thf(conj_0,hypothesis,
( ( size_s2113983095t_char @ vs_1 )
= ( size_size_list_ty @ ts ) ) ).
thf(conj_1,hypothesis,
( ( size_size_list_val @ vs )
= ( size_size_list_ty @ ts ) ) ).
thf(conj_2,conjecture,
( ( wTrt @ p @ h @ e_1 @ ( blocks @ ( produc921874948t_char @ vs_1 @ ( produc1909267824t_char @ ts @ ( produc1916172923t_char @ vs @ e ) ) ) ) @ t )
<=> ( ( wTrt @ p @ h @ ( map_up891053837har_ty @ e_1 @ vs_1 @ ts ) @ e @ t )
& ? [Ts: list_ty] :
( ( ( map_val_option_ty @ ( typeof_h @ h ) @ vs )
= ( map_ty_option_ty @ some_ty @ Ts ) )
& ( list_all2_ty_ty @ ( widen_2090681816t_char @ p ) @ Ts @ ts ) ) ) ) ).
%------------------------------------------------------------------------------