TPTP Problem File: SWW476_1.p
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%------------------------------------------------------------------------------
% File : SWW476_1 : TPTP v8.2.0. Released v5.3.0.
% Domain : Software Verification
% Problem : Java type soundness line 197, 100 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : jinja_100_tff_l197 [Bla11]
% Status : CounterSatisfiable
% Rating : 0.33 v8.2.0, 0.67 v7.0.0, 0.33 v6.4.0, 0.67 v6.3.0, 1.00 v5.3.0
% Syntax : Number of formulae : 651 ( 58 unt; 346 typ; 0 def)
% Number of atoms : 734 ( 365 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 526 ( 97 ~; 2 |; 12 &)
% ( 40 <=>; 375 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 142 ( 141 usr)
% Number of type conns : 332 ( 189 >; 143 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 204 ( 204 usr; 16 con; 0-5 aty)
% Number of variables : 1277 (1235 !; 42 ?;1277 :)
% SPC : TF0_CSA_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 15:28:50
%------------------------------------------------------------------------------
%----Should-be-implicit typings (141)
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tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr_,type,
fun_Pr1890037787r_bool: $tType ).
tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_I,type,
fun_Pr693020585l_bool: $tType ).
tff(ty_ty_tc__fun_Itc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
fun_Pr903661919l_bool: $tType ).
tff(ty_ty_tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__prod,type,
produc124828825on_val: $tType ).
tff(ty_ty_tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_Mtc__pro,type,
produc1285161482t_char: $tType ).
tff(ty_ty_tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_Itc__Lis,type,
produc639455274on_val: $tType ).
tff(ty_ty_tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Olist_Itc_,type,
produc220283002t_char: $tType ).
tff(ty_ty_tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__List__Ol,type,
produc662261637t_char: $tType ).
tff(ty_ty_tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List_,type,
produc12694297on_val: $tType ).
tff(ty_ty_tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
produc1102272487on_val: $tType ).
tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_,type,
produc349695911t_char: $tType ).
tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__pro,type,
produc87279271on_val: $tType ).
tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__,type,
produc1406897475t_char: $tType ).
tff(ty_ty_tc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc,type,
produc1826280281t_char: $tType ).
tff(ty_ty_tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_,type,
produc409205479on_val: $tType ).
tff(ty_ty_tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String_,type,
produc231486621on_val: $tType ).
%----Explicit typings (205)
tff(sy_c_BigStep_Oeval,type,
eval: ( list_P1999446415t_char * exp_list_char * produc12694297on_val ) > fun_ex1201926843l_bool ).
tff(sy_c_BigStep_Ofinal_000tc__List__Olist_Itc__String__Ochar_J,type,
final_list_char: exp_list_char > bool ).
tff(sy_c_Conform_Oconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Oc,type,
conf_P373316194t_char: ( list_P1999446415t_char * fun_na939144002on_val ) > fun_val_fun_ty_bool ).
tff(sy_c_Conform_Ohconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
hconf_97414254t_char: ( list_P1999446415t_char * fun_na939144002on_val ) > bool ).
tff(sy_c_Conform_Olconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
lconf_496643946t_char: ( list_P1999446415t_char * fun_na939144002on_val * fun_li1432931796on_val * fun_li688206603ion_ty ) > bool ).
tff(sy_c_Expr_Oexp_OTryCatch_000tc__List__Olist_Itc__String__Ochar_J,type,
tryCatch_list_char: ( exp_list_char * list_char * list_char ) > fun_ex1654222579t_char ).
tff(sy_c_Expr_Oexp_OVal_000tc__List__Olist_Itc__String__Ochar_J,type,
val_list_char: fun_va223928858t_char ).
tff(sy_c_Fun_Ocomp_000tc__List__Olist_Itc__Option__Ooption_Itc__Value__Oval_J_J_000t,type,
comp_l1825390573t_char: ( fun_li1459524056st_val * fun_li1580442732on_val ) > fun_li742655849st_val ).
tff(sy_c_Fun_Ocomp_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__Value__Oval_000t,type,
comp_o1129292306t_char: ( fun_option_val_val * fun_li1432931796on_val ) > fun_list_char_val ).
tff(sy_c_Fun_Ooverride__on_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Oo,type,
overri2012515291on_val: ( fun_li1432931796on_val * fun_li1432931796on_val * fun_list_char_bool ) > fun_li1432931796on_val ).
tff(sy_c_List_Odistinct_000tc__List__Olist_Itc__String__Ochar_J,type,
distinct_list_char: list_list_char > bool ).
tff(sy_c_List_Olist__all2_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_,type,
list_a52822260ion_ty: ( fun_ex1708156690y_bool * list_exp_list_char * list_option_ty ) > bool ).
tff(sy_c_List_Olist__all2_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Oop,type,
list_a1834344429ion_ty: ( fun_li1351943641y_bool * list_list_char * list_option_ty ) > bool ).
tff(sy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Expr__Oexp_,type,
list_a283687028t_char: ( fun_op14579988r_bool * list_option_ty * list_exp_list_char ) > bool ).
tff(sy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist,type,
list_a839443437t_char: ( fun_op668690445r_bool * list_option_ty * list_list_char ) > bool ).
tff(sy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Type__Oty,type,
list_a2039389316_ty_ty: ( fun_op174240306y_bool * list_option_ty * list_ty ) > bool ).
tff(sy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Value__Oval,type,
list_a1073113293ty_val: ( fun_op1696804347l_bool * list_option_ty * list_val ) > bool ).
tff(sy_c_List_Olist__all2_000tc__Type__Oty_000tc__Option__Ooption_Itc__Type__Oty_J,type,
list_a1880637950ion_ty: ( fun_ty1580608948y_bool * list_ty * list_option_ty ) > bool ).
tff(sy_c_List_Olist__all2_000tc__Type__Oty_000tc__Type__Oty,type,
list_all2_ty_ty: ( fun_ty_fun_ty_bool * list_ty * list_ty ) > bool ).
tff(sy_c_List_Olist__all2_000tc__Value__Oval_000tc__Option__Ooption_Itc__Type__Oty_J,type,
list_a1462908359ion_ty: ( fun_va642468779y_bool * list_val * list_option_ty ) > bool ).
tff(sy_c_List_Olist__all2_000tc__Value__Oval_000tc__Type__Oty,type,
list_all2_val_ty: ( fun_val_fun_ty_bool * list_val * list_ty ) > bool ).
tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__,type,
map_ex101166958t_char: fun_ex1654222579t_char > fun_li1279027773t_char ).
tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___024,type,
map_ex2109939687t_char: fun_ex1075505132t_char > fun_li218321462t_char ).
tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___025,type,
map_ex1548475405ion_ty: fun_ex12316946ion_ty > fun_li241576028ion_ty ).
tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___026,type,
map_ex1598883030on_val: fun_ex1158871131on_val > fun_li690207653on_val ).
tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___027,type,
map_exp_list_char_ty: fun_exp_list_char_ty > fun_li1055333287ist_ty ).
tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___028,type,
map_ex740158547ar_val: fun_ex793263652ar_val > fun_li363341936st_val ).
tff(sy_c_List_Omap_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc___029,type,
map_ex840371726on_val: fun_ex1732915347on_val > fun_li1581546589on_val ).
tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__Expr__Oexp_Itc__Li,type,
map_li1249123943t_char: fun_li978641004t_char > fun_li567129860t_char ).
tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__List__Olist_Itc__S,type,
map_li1333403488t_char: fun_li1751394789t_char > fun_li1898638973t_char ).
tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooption_It,type,
map_li771939206ion_ty: fun_li688206603ion_ty > fun_li1921893539ion_ty ).
tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooption_It_030,type,
map_li50976719on_val: fun_li1432931796on_val > fun_li1580442732on_val ).
tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__Type__Oty,type,
map_list_char_ty: fun_list_char_ty > fun_li490940192ist_ty ).
tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
map_list_char_val: fun_list_char_val > fun_li742655849st_val ).
tff(sy_c_List_Omap_000tc__List__Olist_Itc__String__Ochar_J_000tc__prod_Itc__prod_Itc,type,
map_li1100402823on_val: fun_li2145367436on_val > fun_li1867552164on_val ).
tff(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Expr__Oexp_Itc__Li,type,
map_op1779340173t_char: fun_op1508857234t_char > fun_li156600670t_char ).
tff(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist_Itc__S,type,
map_op1924521862t_char: fun_op195029515t_char > fun_li712717783t_char ).
tff(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Option__Ooption_It,type,
map_op1363057580ion_ty: fun_op1279324977ion_ty > fun_li735972349ion_ty ).
tff(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Type__Oty,type,
map_option_ty_ty: fun_option_ty_ty > fun_li202512966ist_ty ).
tff(sy_c_List_Omap_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Value__Oval,type,
map_option_ty_val: fun_option_ty_val > fun_li1333774223st_val ).
tff(sy_c_List_Omap_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__Value__Oval,type,
map_option_val_val: fun_option_val_val > fun_li1459524056st_val ).
tff(sy_c_List_Omap_000tc__Type__Oty_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__,type,
map_ty_exp_list_char: fun_ty_exp_list_char > fun_li1975737011t_char ).
tff(sy_c_List_Omap_000tc__Type__Oty_000tc__List__Olist_Itc__String__Ochar_J,type,
map_ty_list_char: fun_ty_list_char > fun_li2094888364t_char ).
tff(sy_c_List_Omap_000tc__Type__Oty_000tc__Option__Ooption_Itc__Type__Oty_J,type,
map_ty_option_ty: fun_ty_option_ty > fun_li2118142930ion_ty ).
tff(sy_c_List_Omap_000tc__Type__Oty_000tc__Option__Ooption_Itc__Value__Oval_J,type,
map_ty_option_val: fun_ty_option_val > fun_li1110934555on_val ).
tff(sy_c_List_Omap_000tc__Type__Oty_000tc__Type__Oty,type,
map_ty_ty: fun_ty_ty > fun_list_ty_list_ty ).
tff(sy_c_List_Omap_000tc__Type__Oty_000tc__Value__Oval,type,
map_ty_val: fun_ty_val > fun_list_ty_list_val ).
tff(sy_c_List_Omap_000tc__Type__Oty_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List_,type,
map_ty891785382on_val: fun_ty2028523121on_val > fun_li1883640275on_val ).
tff(sy_c_List_Omap_000tc__Value__Oval_000tc__Expr__Oexp_Itc__List__Olist_Itc__String,type,
map_va1934808527t_char: fun_va223928858t_char > fun_li430210730t_char ).
tff(sy_c_List_Omap_000tc__Value__Oval_000tc__List__Olist_Itc__String__Ochar_J,type,
map_val_list_char: fun_val_list_char > fun_li1120813347t_char ).
tff(sy_c_List_Omap_000tc__Value__Oval_000tc__Option__Ooption_Itc__Type__Oty_J,type,
map_val_option_ty: fun_val_option_ty > fun_li1144067913ion_ty ).
tff(sy_c_List_Omap_000tc__Value__Oval_000tc__Option__Ooption_Itc__Value__Oval_J,type,
map_val_option_val: fun_val_option_val > fun_li1091306514on_val ).
tff(sy_c_List_Omap_000tc__Value__Oval_000tc__Type__Oty,type,
map_val_ty: fun_val_ty > fun_list_val_list_ty ).
tff(sy_c_List_Omap_000tc__Value__Oval_000tc__Value__Oval,type,
map_val_val: fun_val_val > fun_li1707879747st_val ).
tff(sy_c_List_Omap_000tc__Value__Oval_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__Lis,type,
map_va527586287on_val: fun_va172965946on_val > fun_li1659202122on_val ).
tff(sy_c_List_Omap_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
map_Pr1655409582on_val: fun_Pr12181427on_val > fun_li1479469629on_val ).
tff(sy_c_List_Oset_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
set_exp_list_char: list_exp_list_char > fun_ex736065929r_bool ).
tff(sy_c_List_Oset_000tc__List__Olist_Itc__String__Ochar_J,type,
set_list_char: list_list_char > fun_list_char_bool ).
tff(sy_c_List_Oset_000tc__Option__Ooption_Itc__Type__Oty_J,type,
set_option_ty: list_option_ty > fun_option_ty_bool ).
tff(sy_c_List_Oset_000tc__Type__Oty,type,
set_ty: list_ty > fun_ty_bool ).
tff(sy_c_List_Oset_000tc__Value__Oval,type,
set_val: list_val > fun_val_bool ).
tff(sy_c_List_Oset_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
set_Pr1921835862on_val: list_P1439941640on_val > fun_Pr691271849l_bool ).
tff(sy_c_Map_Omap__add_000tc__List__Olist_Itc__String__Ochar_J_000tc__Type__Oty,type,
map_add_list_char_ty: ( fun_li688206603ion_ty * fun_li688206603ion_ty ) > fun_li688206603ion_ty ).
tff(sy_c_Map_Omap__add_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
map_ad325961431ar_val: ( fun_li1432931796on_val * fun_li1432931796on_val ) > fun_li1432931796on_val ).
tff(sy_c_Map_Omap__upds_000tc__List__Olist_Itc__String__Ochar_J_000tc__Type__Oty,type,
map_up891053837har_ty: ( fun_li688206603ion_ty * list_list_char * list_ty ) > fun_li688206603ion_ty ).
tff(sy_c_Map_Omap__upds_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
map_up1085636310ar_val: ( fun_li1432931796on_val * list_list_char * list_val ) > fun_li1432931796on_val ).
tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_,type,
size_s1143674878t_char: list_exp_list_char > nat ).
tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__List__Olist_Itc__String__Och,type,
size_s2113983095t_char: list_list_char > nat ).
tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Option__Ooption_Itc__Type__O,type,
size_s1050794909ion_ty: list_option_ty > nat ).
tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Option__Ooption_Itc__Value__,type,
size_s1595297126on_val: list_option_val > nat ).
tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Type__Oty_J,type,
size_size_list_ty: list_ty > nat ).
tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Value__Oval_J,type,
size_size_list_val: list_val > nat ).
tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__prod_Itc__prod_Itc__Expr__Oe,type,
size_s1699857438on_val: list_P1439941640on_val > nat ).
tff(sy_c_Objects_Ohext,type,
hext: ( fun_na939144002on_val * fun_na939144002on_val ) > bool ).
tff(sy_c_Objects_Otypeof__h,type,
typeof_h: fun_na939144002on_val > fun_val_option_ty ).
tff(sy_c_Option_Ooption_OSome_000tc__Type__Oty,type,
some_ty: fun_ty_option_ty ).
tff(sy_c_Option_Ooption_OSome_000tc__Value__Oval,type,
some_val: fun_val_option_val ).
tff(sy_c_Option_Ooption_OSome_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc_,type,
some_P948696889on_val: fun_Pr357631842on_val ).
tff(sy_c_Option_Othe_000tc__Type__Oty,type,
the_ty: fun_option_ty_ty ).
tff(sy_c_Option_Othe_000tc__Value__Oval,type,
the_val: fun_option_val_val ).
tff(sy_c_Option_Othe_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc_,type,
the_Pr431167171on_val: fun_op498348476on_val ).
tff(sy_c_Product__Type_OPair_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J,type,
produc1259058957on_val: ( exp_list_char * produc12694297on_val ) > produc124828825on_val ).
tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_,type,
produc921874948t_char: ( list_list_char * produc220283002t_char ) > produc1285161482t_char ).
tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc_,type,
produc823076510on_val: ( list_char * fun_Pr806764899on_val ) > produc639455274on_val ).
tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Type__Oty_J_000tc__prod_Itc__Li,type,
produc1909267824t_char: ( list_ty * produc662261637t_char ) > produc220283002t_char ).
tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Value__Oval_J_000tc__Expr__Oexp,type,
produc1916172923t_char: ( list_val * exp_list_char ) > produc662261637t_char ).
tff(sy_c_Product__Type_OPair_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pro,type,
produc899768717on_val: ( fun_na939144002on_val * fun_li1432931796on_val ) > produc12694297on_val ).
tff(sy_c_Product__Type_OPair_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Strin,type,
produc1441475159on_val: ( produc124828825on_val * produc124828825on_val ) > produc1102272487on_val ).
tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri,type,
produc24551831t_char: ( produc1285161482t_char * produc1285161482t_char ) > produc349695911t_char ).
tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__,type,
produc499151895on_val: ( produc639455274on_val * produc639455274on_val ) > produc87279271on_val ).
tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod,type,
produc57279289t_char: ( produc220283002t_char * produc220283002t_char ) > produc1406897475t_char ).
tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Ex,type,
produc1299387215t_char: ( produc662261637t_char * produc662261637t_char ) > produc1826280281t_char ).
tff(sy_c_Product__Type_OPair_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooptio,type,
produc870913623on_val: ( produc12694297on_val * produc12694297on_val ) > produc409205479on_val ).
tff(sy_c_Product__Type_OPair_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_,type,
produc1564932627on_val: ( produc1102272487on_val * produc1102272487on_val ) > produc231486621on_val ).
tff(sy_c_Product__Type_Ocurry_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_,type,
produc1911975310l_bool: fun_Pr680585871l_bool > fun_ex1201926843l_bool ).
tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar,type,
produc1574020101r_bool: fun_Pr227936640r_bool > fun_li1024794712r_bool ).
tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc,type,
produc481748255l_bool: fun_Pr315804320l_bool > fun_li823162622l_bool ).
tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Type__Oty_J_000tc__prod_Itc__L,type,
produc156891095r_bool: fun_Pr46158268r_bool > fun_li887890578r_bool ).
tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Value__Oval_J_000tc__Expr__Oex,type,
produc550034914r_bool: fun_Pr827765831r_bool > fun_li826105035r_bool ).
tff(sy_c_Product__Type_Ocurry_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__pr,type,
produc2062775566l_bool: fun_Pr1696029455l_bool > fun_fu100249073l_bool ).
tff(sy_c_Product__Type_Ocurry_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__Stri,type,
produc1159035454l_bool: fun_Pr691271849l_bool > fun_Pr633696065l_bool ).
tff(sy_c_SmallStep_Oblocks,type,
blocks: produc1285161482t_char > exp_list_char ).
tff(sy_c_SmallStep_Ored,type,
red: list_P1999446415t_char > fun_Pr691271849l_bool ).
tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_I,type,
transi2024712006on_val: fun_Pr691271849l_bool > fun_Pr691271849l_bool ).
tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__List__Olist_,type,
transi122195895t_char: fun_Pr1895638121r_bool > fun_Pr1895638121r_bool ).
tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__String__Ocha,type,
transi61620055on_val: fun_Pr235369833l_bool > fun_Pr235369833l_bool ).
tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_,type,
transi1257872013t_char: fun_Pr1728267013r_bool > fun_Pr1728267013r_bool ).
tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__List__Olist_Itc__Value__Oval_,type,
transi1789604888t_char: fun_Pr1890037787r_bool > fun_Pr1890037787r_bool ).
tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Optio,type,
transi921647814on_val: fun_Pr693020585l_bool > fun_Pr693020585l_bool ).
tff(sy_c_Transitive__Closure_Ortrancl_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__Lis,type,
transi910771962on_val: fun_Pr903661919l_bool > fun_Pr903661919l_bool ).
tff(sy_c_TypeRel_Owiden_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O,type,
widen_2090681816t_char: list_P1999446415t_char > fun_ty_fun_ty_bool ).
tff(sy_c_WellTypeRT_OWTrt,type,
wTrt: ( list_P1999446415t_char * fun_na939144002on_val * fun_li688206603ion_ty * exp_list_char * ty ) > bool ).
tff(sy_c_WellTypeRT_OWTrts,type,
wTrts: ( list_P1999446415t_char * fun_na939144002on_val * fun_li688206603ion_ty * list_exp_list_char * list_ty ) > bool ).
tff(sy_c_fequal_000tc__Type__Oty,type,
fequal_ty: fun_ty_fun_ty_bool ).
tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__Expr_,type,
hAPP_e1353749905t_char: ( fun_ex1654222579t_char * exp_list_char ) > exp_list_char ).
tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__HOL__,type,
hAPP_e544220455r_bool: ( fun_ex736065929r_bool * exp_list_char ) > bool ).
tff(sy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_I,type,
hAPP_e1833980889l_bool: ( fun_ex1201926843l_bool * exp_list_char ) > fun_Pr1696029455l_bool ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar,type,
hAPP_l2011456725t_char: ( fun_li1279027773t_char * list_exp_list_char ) > list_exp_list_char ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_031,type,
hAPP_l2065413838t_char: ( fun_li218321462t_char * list_exp_list_char ) > list_list_char ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_032,type,
hAPP_l1002225652ion_ty: ( fun_li241576028ion_ty * list_exp_list_char ) > list_option_ty ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_033,type,
hAPP_l1607890493on_val: ( fun_li690207653on_val * list_exp_list_char ) > list_option_val ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_034,type,
hAPP_l110066169ist_ty: ( fun_li1055333287ist_ty * list_exp_list_char ) > list_ty ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_035,type,
hAPP_l1539861698st_val: ( fun_li363341936st_val * list_exp_list_char ) > list_val ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_036,type,
hAPP_l1557845365on_val: ( fun_li1581546589on_val * list_exp_list_char ) > list_P1439941640on_val ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List,type,
hAPP_l740678812t_char: ( fun_li567129860t_char * list_list_char ) > list_exp_list_char ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_037,type,
hAPP_l407174677t_char: ( fun_li1898638973t_char * list_list_char ) > list_list_char ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_038,type,
hAPP_l1491470139ion_ty: ( fun_li1921893539ion_ty * list_list_char ) > list_option_ty ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_039,type,
hAPP_l297961988on_val: ( fun_li1580442732on_val * list_list_char ) > list_option_val ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_040,type,
hAPP_l1871878770ist_ty: ( fun_li490940192ist_ty * list_list_char ) > list_ty ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_041,type,
hAPP_l1892737211st_val: ( fun_li742655849st_val * list_list_char ) > list_val ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__List_042,type,
hAPP_l418486716on_val: ( fun_li1867552164on_val * list_list_char ) > list_P1439941640on_val ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__fun_,type,
hAPP_l217977712r_bool: ( fun_li1024794712r_bool * list_list_char ) > fun_Pr46158268r_bool ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Option__Ooption_Itc__Type__Oty_J_J_000tc__List,type,
hAPP_l330149622t_char: ( fun_li156600670t_char * list_option_ty ) > list_exp_list_char ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Option__Ooption_Itc__Type__Oty_J_J_000tc__List_043,type,
hAPP_l1368737135t_char: ( fun_li712717783t_char * list_option_ty ) > list_list_char ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Option__Ooption_Itc__Type__Oty_J_J_000tc__List_044,type,
hAPP_l305548949ion_ty: ( fun_li735972349ion_ty * list_option_ty ) > list_option_ty ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Option__Ooption_Itc__Type__Oty_J_J_000tc__List_045,type,
hAPP_l1583451544ist_ty: ( fun_li202512966ist_ty * list_option_ty ) > list_ty ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Option__Ooption_Itc__Type__Oty_J_J_000tc__List_046,type,
hAPP_l336371937st_val: ( fun_li1333774223st_val * list_option_ty ) > list_val ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Option__Ooption_Itc__Value__Oval_J_J_000tc__Li,type,
hAPP_l228474410st_val: ( fun_li1459524056st_val * list_option_val ) > list_val ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__List__Olist_Itc__String,type,
hAPP_l1074208899t_char: ( fun_li1751394789t_char * list_char ) > list_char ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooption_Itc__Ty,type,
hAPP_l512744617ion_ty: ( fun_li688206603ion_ty * list_char ) > option_ty ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Ooption_Itc__Va,type,
hAPP_l207779698on_val: ( fun_li1432931796on_val * list_char ) > option_val ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__Value__Oval,type,
hAPP_list_char_val: ( fun_list_char_val * list_char ) > val ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__fun_Itc__prod_,type,
hAPP_l465799708l_bool: ( fun_li823162622l_bool * list_char ) > fun_fu177229913l_bool ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__Expr__Oexp,type,
hAPP_l578807295t_char: ( fun_li1975737011t_char * list_ty ) > list_exp_list_char ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__List__Olis,type,
hAPP_l402740472t_char: ( fun_li2094888364t_char * list_ty ) > list_list_char ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__Option__Oo,type,
hAPP_l1487035934ion_ty: ( fun_li2118142930ion_ty * list_ty ) > list_option_ty ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__Option__Oo_047,type,
hAPP_l1014734695on_val: ( fun_li1110934555on_val * list_ty ) > list_option_val ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__Type__Oty_,type,
hAPP_list_ty_list_ty: ( fun_list_ty_list_ty * list_ty ) > list_ty ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__Value__Ova,type,
hAPP_l1530663448st_val: ( fun_list_ty_list_val * list_ty ) > list_val ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__List__Olist_Itc__prod_Itc__,type,
hAPP_l1634001311on_val: ( fun_li1883640275on_val * list_ty ) > list_P1439941640on_val ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Type__Oty_J_000tc__fun_Itc__prod_Itc__List__Ol,type,
hAPP_l1987619678r_bool: ( fun_li887890578r_bool * list_ty ) > fun_Pr827765831r_bool ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__Expr__Oe,type,
hAPP_l732421366t_char: ( fun_li430210730t_char * list_val ) > list_exp_list_char ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__List__Ol,type,
hAPP_l922645359t_char: ( fun_li1120813347t_char * list_val ) > list_list_char ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__Option__,type,
hAPP_l2006940821ion_ty: ( fun_li1144067913ion_ty * list_val ) > list_option_ty ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__Option___048,type,
hAPP_l761459294on_val: ( fun_li1091306514on_val * list_val ) > list_option_val ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__Type__Ot,type,
hAPP_l1085267864ist_ty: ( fun_list_val_list_ty * list_val ) > list_ty ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__Value__O,type,
hAPP_l273806049st_val: ( fun_li1707879747st_val * list_val ) > list_val ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__List__Olist_Itc__prod_Itc,type,
hAPP_l382831894on_val: ( fun_li1659202122on_val * list_val ) > list_P1439941640on_val ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__Value__Oval_J_000tc__fun_Itc__Expr__Oexp_Itc__,type,
hAPP_l1062423959r_bool: ( fun_li826105035r_bool * list_val ) > fun_ex736065929r_bool ).
tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olis,type,
hAPP_l1695428693on_val: ( fun_li1479469629on_val * list_P1439941640on_val ) > list_P1439941640on_val ).
tff(sy_c_hAPP_000tc__Nat__Onat_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc,type,
hAPP_n546249108on_val: ( fun_na939144002on_val * nat ) > option1479284511on_val ).
tff(sy_c_hAPP_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Type__Oty,type,
hAPP_option_ty_ty: ( fun_option_ty_ty * option_ty ) > ty ).
tff(sy_c_hAPP_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__Value__Oval,type,
hAPP_option_val_val: ( fun_option_val_val * option_val ) > val ).
tff(sy_c_hAPP_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J,type,
hAPP_o1977518472on_val: ( fun_op498348476on_val * option1479284511on_val ) > produc639455274on_val ).
tff(sy_c_hAPP_000tc__Type__Oty_000tc__HOL__Obool,type,
hAPP_ty_bool: ( fun_ty_bool * ty ) > bool ).
tff(sy_c_hAPP_000tc__Type__Oty_000tc__Option__Ooption_Itc__Type__Oty_J,type,
hAPP_ty_option_ty: ( fun_ty_option_ty * ty ) > option_ty ).
tff(sy_c_hAPP_000tc__Type__Oty_000tc__fun_Itc__Type__Oty_Mtc__HOL__Obool_J,type,
hAPP_ty_fun_ty_bool: ( fun_ty_fun_ty_bool * ty ) > fun_ty_bool ).
tff(sy_c_hAPP_000tc__Value__Oval_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Och,type,
hAPP_v834067052t_char: ( fun_va223928858t_char * val ) > exp_list_char ).
tff(sy_c_hAPP_000tc__Value__Oval_000tc__Option__Ooption_Itc__Type__Oty_J,type,
hAPP_val_option_ty: ( fun_val_option_ty * val ) > option_ty ).
tff(sy_c_hAPP_000tc__Value__Oval_000tc__Option__Ooption_Itc__Value__Oval_J,type,
hAPP_val_option_val: ( fun_val_option_val * val ) > option_val ).
tff(sy_c_hAPP_000tc__Value__Oval_000tc__fun_Itc__Type__Oty_Mtc__HOL__Obool_J,type,
hAPP_val_fun_ty_bool: ( fun_val_fun_ty_bool * val ) > fun_ty_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption_,type,
hAPP_f1033709212l_bool: ( fun_fu1693644106l_bool * fun_li1432931796on_val ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__Ol,type,
hAPP_f1175813647l_bool: ( fun_fu100249073l_bool * fun_na939144002on_val ) > fun_fu1693644106l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__,type,
hAPP_f1715346603l_bool: ( fun_fu177229913l_bool * fun_Pr806764899on_val ) > bool ).
tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt,type,
hAPP_P1708370145l_bool: ( fun_Pr680585871l_bool * produc124828825on_val ) > bool ).
tff(sy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt_049,type,
hAPP_P1116729363l_bool: ( fun_Pr633696065l_bool * produc124828825on_val ) > fun_Pr680585871l_bool ).
tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M,type,
hAPP_P92196306r_bool: ( fun_Pr227936640r_bool * produc1285161482t_char ) > bool ).
tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I,type,
hAPP_P1235399154l_bool: ( fun_Pr315804320l_bool * produc639455274on_val ) > bool ).
tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I_050,type,
hAPP_P1510515380on_val: ( fun_Pr357631842on_val * produc639455274on_val ) > option1479284511on_val ).
tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Oli,type,
hAPP_P1907982426r_bool: ( fun_Pr46158268r_bool * produc220283002t_char ) > bool ).
tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__L,type,
hAPP_P2118621157r_bool: ( fun_Pr827765831r_bool * produc662261637t_char ) > bool ).
tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc,type,
hAPP_P159683425l_bool: ( fun_Pr1696029455l_bool * produc12694297on_val ) > bool ).
tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc,type,
hAPP_P282169671l_bool: ( fun_Pr691271849l_bool * produc1102272487on_val ) > bool ).
tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_051,type,
hAPP_P918220497on_val: ( fun_Pr12181427on_val * produc1102272487on_val ) > produc1102272487on_val ).
tff(sy_c_hBOOL,type,
hBOOL: bool > $o ).
tff(sy_c_member_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J,type,
member_exp_list_char: ( exp_list_char * fun_ex736065929r_bool ) > bool ).
tff(sy_c_member_000tc__List__Olist_Itc__String__Ochar_J,type,
member_list_char: ( list_char * fun_list_char_bool ) > bool ).
tff(sy_c_member_000tc__Option__Ooption_Itc__Type__Oty_J,type,
member_option_ty: ( option_ty * fun_option_ty_bool ) > bool ).
tff(sy_c_member_000tc__Type__Oty,type,
member_ty: ( ty * fun_ty_bool ) > bool ).
tff(sy_c_member_000tc__Value__Oval,type,
member_val: ( val * fun_val_bool ) > bool ).
tff(sy_c_member_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__,type,
member773094996on_val: ( produc1102272487on_val * fun_Pr691271849l_bool ) > bool ).
tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String_,type,
member1420286996t_char: ( produc349695911t_char * fun_Pr1895638121r_bool ) > bool ).
tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun,type,
member1322055188on_val: ( produc87279271on_val * fun_Pr235369833l_bool ) > bool ).
tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_It,type,
member125098544t_char: ( produc1406897475t_char * fun_Pr1728267013r_bool ) > bool ).
tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr_,type,
member1161907014t_char: ( produc1826280281t_char * fun_Pr1890037787r_bool ) > bool ).
tff(sy_c_member_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_I,type,
member563141460on_val: ( produc409205479on_val * fun_Pr693020585l_bool ) > bool ).
tff(sy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc,type,
member808015754on_val: ( produc231486621on_val * fun_Pr903661919l_bool ) > bool ).
tff(sy_v_E,type,
e_1: fun_li688206603ion_ty ).
tff(sy_v_P,type,
p: list_P1999446415t_char ).
tff(sy_v_T,type,
t: ty ).
tff(sy_v_Ts,type,
ts: list_ty ).
tff(sy_v_Vs,type,
vs_1: list_list_char ).
tff(sy_v_e,type,
e: exp_list_char ).
tff(sy_v_h,type,
h: fun_na939144002on_val ).
tff(sy_v_vs,type,
vs: list_val ).
%----Relevant facts (300)
tff(fact_0_widens__refl,axiom,
! [Pa: list_P1999446415t_char,Xs: list_ty] : hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Xs,Xs)) ).
tff(fact_1_widen__refl,axiom,
! [P_3: list_P1999446415t_char,T_4: ty] : hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_3),T_4),T_4)) ).
tff(fact_2_widens__trans,axiom,
! [Us: list_ty,Pa: list_P1999446415t_char,Ss: list_ty,Tsa: list_ty] :
( hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ss,Tsa))
=> ( hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Tsa,Us))
=> hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ss,Us)) ) ) ).
tff(fact_3_list__all2__lengthD,axiom,
! [Pa: fun_val_fun_ty_bool,Xs: list_val,Ys: list_ty] :
( hBOOL(list_all2_val_ty(Pa,Xs,Ys))
=> ( size_size_list_val(Xs) = size_size_list_ty(Ys) ) ) ).
tff(fact_4_list__all2__lengthD,axiom,
! [Pa: fun_ty_fun_ty_bool,Xs: list_ty,Ys: list_ty] :
( hBOOL(list_all2_ty_ty(Pa,Xs,Ys))
=> ( size_size_list_ty(Xs) = size_size_list_ty(Ys) ) ) ).
tff(fact_5_list__all2__lengthD,axiom,
! [Pa: fun_op14579988r_bool,Xs: list_option_ty,Ys: list_exp_list_char] :
( hBOOL(list_a283687028t_char(Pa,Xs,Ys))
=> ( size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys) ) ) ).
tff(fact_6_list__all2__lengthD,axiom,
! [Pa: fun_op1696804347l_bool,Xs: list_option_ty,Ys: list_val] :
( hBOOL(list_a1073113293ty_val(Pa,Xs,Ys))
=> ( size_s1050794909ion_ty(Xs) = size_size_list_val(Ys) ) ) ).
tff(fact_7_list__all2__lengthD,axiom,
! [Pa: fun_op174240306y_bool,Xs: list_option_ty,Ys: list_ty] :
( hBOOL(list_a2039389316_ty_ty(Pa,Xs,Ys))
=> ( size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys) ) ) ).
tff(fact_8_list__all2__lengthD,axiom,
! [Pa: fun_op668690445r_bool,Xs: list_option_ty,Ys: list_list_char] :
( hBOOL(list_a839443437t_char(Pa,Xs,Ys))
=> ( size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_9_list__all2__lengthD,axiom,
! [Pa: fun_ex1708156690y_bool,Xs: list_exp_list_char,Ys: list_option_ty] :
( hBOOL(list_a52822260ion_ty(Pa,Xs,Ys))
=> ( size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_10_list__all2__lengthD,axiom,
! [Pa: fun_va642468779y_bool,Xs: list_val,Ys: list_option_ty] :
( hBOOL(list_a1462908359ion_ty(Pa,Xs,Ys))
=> ( size_size_list_val(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_11_list__all2__lengthD,axiom,
! [Pa: fun_ty1580608948y_bool,Xs: list_ty,Ys: list_option_ty] :
( hBOOL(list_a1880637950ion_ty(Pa,Xs,Ys))
=> ( size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_12_list__all2__lengthD,axiom,
! [Pa: fun_li1351943641y_bool,Xs: list_list_char,Ys: list_option_ty] :
( hBOOL(list_a1834344429ion_ty(Pa,Xs,Ys))
=> ( size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_13_length__map,axiom,
! [F: fun_list_char_val,Xs: list_list_char] : size_size_list_val(hAPP_l1892737211st_val(map_list_char_val(F),Xs)) = size_s2113983095t_char(Xs) ).
tff(fact_14_length__map,axiom,
! [F: fun_va223928858t_char,Xs: list_val] : size_s1143674878t_char(hAPP_l732421366t_char(map_va1934808527t_char(F),Xs)) = size_size_list_val(Xs) ).
tff(fact_15_length__map,axiom,
! [F: fun_ty_option_ty,Xs: list_ty] : size_s1050794909ion_ty(hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs)) = size_size_list_ty(Xs) ).
tff(fact_16_length__map,axiom,
! [F: fun_val_option_ty,Xs: list_val] : size_s1050794909ion_ty(hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs)) = size_size_list_val(Xs) ).
tff(fact_17_length__map,axiom,
! [F: fun_ex12316946ion_ty,Xs: list_exp_list_char] : size_s1050794909ion_ty(hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F),Xs)) = size_s1143674878t_char(Xs) ).
tff(fact_18_length__map,axiom,
! [F: fun_li688206603ion_ty,Xs: list_list_char] : size_s1050794909ion_ty(hAPP_l1491470139ion_ty(map_li771939206ion_ty(F),Xs)) = size_s2113983095t_char(Xs) ).
tff(fact_19_length__map,axiom,
! [F: fun_op1508857234t_char,Xs: list_option_ty] : size_s1143674878t_char(hAPP_l330149622t_char(map_op1779340173t_char(F),Xs)) = size_s1050794909ion_ty(Xs) ).
tff(fact_20_length__map,axiom,
! [F: fun_option_ty_val,Xs: list_option_ty] : size_size_list_val(hAPP_l336371937st_val(map_option_ty_val(F),Xs)) = size_s1050794909ion_ty(Xs) ).
tff(fact_21_length__map,axiom,
! [F: fun_option_ty_ty,Xs: list_option_ty] : size_size_list_ty(hAPP_l1583451544ist_ty(map_option_ty_ty(F),Xs)) = size_s1050794909ion_ty(Xs) ).
tff(fact_22_length__map,axiom,
! [F: fun_op195029515t_char,Xs: list_option_ty] : size_s2113983095t_char(hAPP_l1368737135t_char(map_op1924521862t_char(F),Xs)) = size_s1050794909ion_ty(Xs) ).
tff(fact_23_length__map,axiom,
! [F: fun_li1751394789t_char,Xs: list_list_char] : size_s2113983095t_char(hAPP_l407174677t_char(map_li1333403488t_char(F),Xs)) = size_s2113983095t_char(Xs) ).
tff(fact_24_length__map,axiom,
! [F: fun_Pr12181427on_val,Xs: list_P1439941640on_val] : size_s1699857438on_val(hAPP_l1695428693on_val(map_Pr1655409582on_val(F),Xs)) = size_s1699857438on_val(Xs) ).
tff(fact_25_length__map,axiom,
! [F: fun_option_val_val,Xs: list_option_val] : size_size_list_val(hAPP_l228474410st_val(map_option_val_val(F),Xs)) = size_s1595297126on_val(Xs) ).
tff(fact_26_length__map,axiom,
! [F: fun_li1432931796on_val,Xs: list_list_char] : size_s1595297126on_val(hAPP_l297961988on_val(map_li50976719on_val(F),Xs)) = size_s2113983095t_char(Xs) ).
tff(fact_27_length__map,axiom,
! [F: fun_op1279324977ion_ty,Xs: list_option_ty] : size_s1050794909ion_ty(hAPP_l305548949ion_ty(map_op1363057580ion_ty(F),Xs)) = size_s1050794909ion_ty(Xs) ).
tff(fact_28_map__eq__imp__length__eq,axiom,
! [F: fun_val_option_ty,Xs: list_val,G: fun_op1279324977ion_ty,Ys: list_option_ty] :
( ( hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs) = hAPP_l305548949ion_ty(map_op1363057580ion_ty(G),Ys) )
=> ( size_size_list_val(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_29_map__eq__imp__length__eq,axiom,
! [F: fun_ty_option_ty,Xs: list_ty,G: fun_op1279324977ion_ty,Ys: list_option_ty] :
( ( hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs) = hAPP_l305548949ion_ty(map_op1363057580ion_ty(G),Ys) )
=> ( size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_30_map__eq__imp__length__eq,axiom,
! [F: fun_va223928858t_char,Xs: list_val,G: fun_op1508857234t_char,Ys: list_option_ty] :
( ( hAPP_l732421366t_char(map_va1934808527t_char(F),Xs) = hAPP_l330149622t_char(map_op1779340173t_char(G),Ys) )
=> ( size_size_list_val(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_31_map__eq__imp__length__eq,axiom,
! [F: fun_list_char_val,Xs: list_list_char,G: fun_option_ty_val,Ys: list_option_ty] :
( ( hAPP_l1892737211st_val(map_list_char_val(F),Xs) = hAPP_l336371937st_val(map_option_ty_val(G),Ys) )
=> ( size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_32_map__eq__imp__length__eq,axiom,
! [F: fun_op1279324977ion_ty,Xs: list_option_ty,G: fun_val_option_ty,Ys: list_val] :
( ( hAPP_l305548949ion_ty(map_op1363057580ion_ty(F),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_size_list_val(Ys) ) ) ).
tff(fact_33_map__eq__imp__length__eq,axiom,
! [F: fun_op1279324977ion_ty,Xs: list_option_ty,G: fun_ty_option_ty,Ys: list_ty] :
( ( hAPP_l305548949ion_ty(map_op1363057580ion_ty(F),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys) ) ) ).
tff(fact_34_map__eq__imp__length__eq,axiom,
! [F: fun_op1508857234t_char,Xs: list_option_ty,G: fun_va223928858t_char,Ys: list_val] :
( ( hAPP_l330149622t_char(map_op1779340173t_char(F),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_size_list_val(Ys) ) ) ).
tff(fact_35_map__eq__imp__length__eq,axiom,
! [F: fun_option_ty_val,Xs: list_option_ty,G: fun_list_char_val,Ys: list_list_char] :
( ( hAPP_l336371937st_val(map_option_ty_val(F),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_36_map__eq__imp__length__eq,axiom,
! [F: fun_li1432931796on_val,Xs: list_list_char,G: fun_ex1158871131on_val,Ys: list_exp_list_char] :
( ( hAPP_l297961988on_val(map_li50976719on_val(F),Xs) = hAPP_l1607890493on_val(map_ex1598883030on_val(G),Ys) )
=> ( size_s2113983095t_char(Xs) = size_s1143674878t_char(Ys) ) ) ).
tff(fact_37_map__eq__imp__length__eq,axiom,
! [F: fun_op1279324977ion_ty,Xs: list_option_ty,G: fun_ex12316946ion_ty,Ys: list_exp_list_char] :
( ( hAPP_l305548949ion_ty(map_op1363057580ion_ty(F),Xs) = hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys) ) ) ).
tff(fact_38_map__eq__imp__length__eq,axiom,
! [F: fun_op1508857234t_char,Xs: list_option_ty,G: fun_ex1654222579t_char,Ys: list_exp_list_char] :
( ( hAPP_l330149622t_char(map_op1779340173t_char(F),Xs) = hAPP_l2011456725t_char(map_ex101166958t_char(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys) ) ) ).
tff(fact_39_map__eq__imp__length__eq,axiom,
! [F: fun_option_ty_val,Xs: list_option_ty,G: fun_ex793263652ar_val,Ys: list_exp_list_char] :
( ( hAPP_l336371937st_val(map_option_ty_val(F),Xs) = hAPP_l1539861698st_val(map_ex740158547ar_val(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys) ) ) ).
tff(fact_40_map__eq__imp__length__eq,axiom,
! [F: fun_op195029515t_char,Xs: list_option_ty,G: fun_ex1075505132t_char,Ys: list_exp_list_char] :
( ( hAPP_l1368737135t_char(map_op1924521862t_char(F),Xs) = hAPP_l2065413838t_char(map_ex2109939687t_char(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys) ) ) ).
tff(fact_41_map__eq__imp__length__eq,axiom,
! [F: fun_option_ty_ty,Xs: list_option_ty,G: fun_exp_list_char_ty,Ys: list_exp_list_char] :
( ( hAPP_l1583451544ist_ty(map_option_ty_ty(F),Xs) = hAPP_l110066169ist_ty(map_exp_list_char_ty(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys) ) ) ).
tff(fact_42_map__eq__imp__length__eq,axiom,
! [F: fun_li1751394789t_char,Xs: list_list_char,G: fun_val_list_char,Ys: list_val] :
( ( hAPP_l407174677t_char(map_li1333403488t_char(F),Xs) = hAPP_l922645359t_char(map_val_list_char(G),Ys) )
=> ( size_s2113983095t_char(Xs) = size_size_list_val(Ys) ) ) ).
tff(fact_43_map__eq__imp__length__eq,axiom,
! [F: fun_Pr12181427on_val,Xs: list_P1439941640on_val,G: fun_va172965946on_val,Ys: list_val] :
( ( hAPP_l1695428693on_val(map_Pr1655409582on_val(F),Xs) = hAPP_l382831894on_val(map_va527586287on_val(G),Ys) )
=> ( size_s1699857438on_val(Xs) = size_size_list_val(Ys) ) ) ).
tff(fact_44_map__eq__imp__length__eq,axiom,
! [F: fun_option_val_val,Xs: list_option_val,G: fun_val_val,Ys: list_val] :
( ( hAPP_l228474410st_val(map_option_val_val(F),Xs) = hAPP_l273806049st_val(map_val_val(G),Ys) )
=> ( size_s1595297126on_val(Xs) = size_size_list_val(Ys) ) ) ).
tff(fact_45_map__eq__imp__length__eq,axiom,
! [F: fun_li1432931796on_val,Xs: list_list_char,G: fun_val_option_val,Ys: list_val] :
( ( hAPP_l297961988on_val(map_li50976719on_val(F),Xs) = hAPP_l761459294on_val(map_val_option_val(G),Ys) )
=> ( size_s2113983095t_char(Xs) = size_size_list_val(Ys) ) ) ).
tff(fact_46_map__eq__imp__length__eq,axiom,
! [F: fun_option_ty_val,Xs: list_option_ty,G: fun_val_val,Ys: list_val] :
( ( hAPP_l336371937st_val(map_option_ty_val(F),Xs) = hAPP_l273806049st_val(map_val_val(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_size_list_val(Ys) ) ) ).
tff(fact_47_map__eq__imp__length__eq,axiom,
! [F: fun_op195029515t_char,Xs: list_option_ty,G: fun_val_list_char,Ys: list_val] :
( ( hAPP_l1368737135t_char(map_op1924521862t_char(F),Xs) = hAPP_l922645359t_char(map_val_list_char(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_size_list_val(Ys) ) ) ).
tff(fact_48_map__eq__imp__length__eq,axiom,
! [F: fun_option_ty_ty,Xs: list_option_ty,G: fun_val_ty,Ys: list_val] :
( ( hAPP_l1583451544ist_ty(map_option_ty_ty(F),Xs) = hAPP_l1085267864ist_ty(map_val_ty(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_size_list_val(Ys) ) ) ).
tff(fact_49_map__eq__imp__length__eq,axiom,
! [F: fun_li688206603ion_ty,Xs: list_list_char,G: fun_val_option_ty,Ys: list_val] :
( ( hAPP_l1491470139ion_ty(map_li771939206ion_ty(F),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys) )
=> ( size_s2113983095t_char(Xs) = size_size_list_val(Ys) ) ) ).
tff(fact_50_map__eq__imp__length__eq,axiom,
! [F: fun_ex12316946ion_ty,Xs: list_exp_list_char,G: fun_val_option_ty,Ys: list_val] :
( ( hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys) )
=> ( size_s1143674878t_char(Xs) = size_size_list_val(Ys) ) ) ).
tff(fact_51_map__eq__imp__length__eq,axiom,
! [F: fun_li1751394789t_char,Xs: list_list_char,G: fun_ty_list_char,Ys: list_ty] :
( ( hAPP_l407174677t_char(map_li1333403488t_char(F),Xs) = hAPP_l402740472t_char(map_ty_list_char(G),Ys) )
=> ( size_s2113983095t_char(Xs) = size_size_list_ty(Ys) ) ) ).
tff(fact_52_map__eq__imp__length__eq,axiom,
! [F: fun_Pr12181427on_val,Xs: list_P1439941640on_val,G: fun_ty2028523121on_val,Ys: list_ty] :
( ( hAPP_l1695428693on_val(map_Pr1655409582on_val(F),Xs) = hAPP_l1634001311on_val(map_ty891785382on_val(G),Ys) )
=> ( size_s1699857438on_val(Xs) = size_size_list_ty(Ys) ) ) ).
tff(fact_53_map__eq__imp__length__eq,axiom,
! [F: fun_option_val_val,Xs: list_option_val,G: fun_ty_val,Ys: list_ty] :
( ( hAPP_l228474410st_val(map_option_val_val(F),Xs) = hAPP_l1530663448st_val(map_ty_val(G),Ys) )
=> ( size_s1595297126on_val(Xs) = size_size_list_ty(Ys) ) ) ).
tff(fact_54_map__eq__imp__length__eq,axiom,
! [F: fun_li1432931796on_val,Xs: list_list_char,G: fun_ty_option_val,Ys: list_ty] :
( ( hAPP_l297961988on_val(map_li50976719on_val(F),Xs) = hAPP_l1014734695on_val(map_ty_option_val(G),Ys) )
=> ( size_s2113983095t_char(Xs) = size_size_list_ty(Ys) ) ) ).
tff(fact_55_map__eq__imp__length__eq,axiom,
! [F: fun_op1508857234t_char,Xs: list_option_ty,G: fun_ty_exp_list_char,Ys: list_ty] :
( ( hAPP_l330149622t_char(map_op1779340173t_char(F),Xs) = hAPP_l578807295t_char(map_ty_exp_list_char(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys) ) ) ).
tff(fact_56_map__eq__imp__length__eq,axiom,
! [F: fun_option_ty_val,Xs: list_option_ty,G: fun_ty_val,Ys: list_ty] :
( ( hAPP_l336371937st_val(map_option_ty_val(F),Xs) = hAPP_l1530663448st_val(map_ty_val(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys) ) ) ).
tff(fact_57_map__eq__imp__length__eq,axiom,
! [F: fun_op195029515t_char,Xs: list_option_ty,G: fun_ty_list_char,Ys: list_ty] :
( ( hAPP_l1368737135t_char(map_op1924521862t_char(F),Xs) = hAPP_l402740472t_char(map_ty_list_char(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys) ) ) ).
tff(fact_58_map__eq__imp__length__eq,axiom,
! [F: fun_option_ty_ty,Xs: list_option_ty,G: fun_ty_ty,Ys: list_ty] :
( ( hAPP_l1583451544ist_ty(map_option_ty_ty(F),Xs) = hAPP_list_ty_list_ty(map_ty_ty(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys) ) ) ).
tff(fact_59_map__eq__imp__length__eq,axiom,
! [F: fun_li688206603ion_ty,Xs: list_list_char,G: fun_ty_option_ty,Ys: list_ty] :
( ( hAPP_l1491470139ion_ty(map_li771939206ion_ty(F),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys) )
=> ( size_s2113983095t_char(Xs) = size_size_list_ty(Ys) ) ) ).
tff(fact_60_map__eq__imp__length__eq,axiom,
! [F: fun_ex12316946ion_ty,Xs: list_exp_list_char,G: fun_ty_option_ty,Ys: list_ty] :
( ( hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys) )
=> ( size_s1143674878t_char(Xs) = size_size_list_ty(Ys) ) ) ).
tff(fact_61_map__eq__imp__length__eq,axiom,
! [F: fun_Pr12181427on_val,Xs: list_P1439941640on_val,G: fun_li2145367436on_val,Ys: list_list_char] :
( ( hAPP_l1695428693on_val(map_Pr1655409582on_val(F),Xs) = hAPP_l418486716on_val(map_li1100402823on_val(G),Ys) )
=> ( size_s1699857438on_val(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_62_map__eq__imp__length__eq,axiom,
! [F: fun_option_val_val,Xs: list_option_val,G: fun_list_char_val,Ys: list_list_char] :
( ( hAPP_l228474410st_val(map_option_val_val(F),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Ys) )
=> ( size_s1595297126on_val(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_63_map__eq__imp__length__eq,axiom,
! [F: fun_op1279324977ion_ty,Xs: list_option_ty,G: fun_li688206603ion_ty,Ys: list_list_char] :
( ( hAPP_l305548949ion_ty(map_op1363057580ion_ty(F),Xs) = hAPP_l1491470139ion_ty(map_li771939206ion_ty(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_64_map__eq__imp__length__eq,axiom,
! [F: fun_op1508857234t_char,Xs: list_option_ty,G: fun_li978641004t_char,Ys: list_list_char] :
( ( hAPP_l330149622t_char(map_op1779340173t_char(F),Xs) = hAPP_l740678812t_char(map_li1249123943t_char(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_65_map__eq__imp__length__eq,axiom,
! [F: fun_op195029515t_char,Xs: list_option_ty,G: fun_li1751394789t_char,Ys: list_list_char] :
( ( hAPP_l1368737135t_char(map_op1924521862t_char(F),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_66_map__eq__imp__length__eq,axiom,
! [F: fun_option_ty_ty,Xs: list_option_ty,G: fun_list_char_ty,Ys: list_list_char] :
( ( hAPP_l1583451544ist_ty(map_option_ty_ty(F),Xs) = hAPP_l1871878770ist_ty(map_list_char_ty(G),Ys) )
=> ( size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_67_map__eq__imp__length__eq,axiom,
! [F: fun_ex1075505132t_char,Xs: list_exp_list_char,G: fun_li1751394789t_char,Ys: list_list_char] :
( ( hAPP_l2065413838t_char(map_ex2109939687t_char(F),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys) )
=> ( size_s1143674878t_char(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_68_map__eq__imp__length__eq,axiom,
! [F: fun_ex1732915347on_val,Xs: list_exp_list_char,G: fun_Pr12181427on_val,Ys: list_P1439941640on_val] :
( ( hAPP_l1557845365on_val(map_ex840371726on_val(F),Xs) = hAPP_l1695428693on_val(map_Pr1655409582on_val(G),Ys) )
=> ( size_s1143674878t_char(Xs) = size_s1699857438on_val(Ys) ) ) ).
tff(fact_69_map__eq__imp__length__eq,axiom,
! [F: fun_ex793263652ar_val,Xs: list_exp_list_char,G: fun_option_val_val,Ys: list_option_val] :
( ( hAPP_l1539861698st_val(map_ex740158547ar_val(F),Xs) = hAPP_l228474410st_val(map_option_val_val(G),Ys) )
=> ( size_s1143674878t_char(Xs) = size_s1595297126on_val(Ys) ) ) ).
tff(fact_70_map__eq__imp__length__eq,axiom,
! [F: fun_ex1158871131on_val,Xs: list_exp_list_char,G: fun_li1432931796on_val,Ys: list_list_char] :
( ( hAPP_l1607890493on_val(map_ex1598883030on_val(F),Xs) = hAPP_l297961988on_val(map_li50976719on_val(G),Ys) )
=> ( size_s1143674878t_char(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_71_map__eq__imp__length__eq,axiom,
! [F: fun_ex12316946ion_ty,Xs: list_exp_list_char,G: fun_li688206603ion_ty,Ys: list_list_char] :
( ( hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F),Xs) = hAPP_l1491470139ion_ty(map_li771939206ion_ty(G),Ys) )
=> ( size_s1143674878t_char(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_72_map__eq__imp__length__eq,axiom,
! [F: fun_ex12316946ion_ty,Xs: list_exp_list_char,G: fun_ex12316946ion_ty,Ys: list_exp_list_char] :
( ( hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F),Xs) = hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(G),Ys) )
=> ( size_s1143674878t_char(Xs) = size_s1143674878t_char(Ys) ) ) ).
tff(fact_73_map__eq__imp__length__eq,axiom,
! [F: fun_ex12316946ion_ty,Xs: list_exp_list_char,G: fun_op1279324977ion_ty,Ys: list_option_ty] :
( ( hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F),Xs) = hAPP_l305548949ion_ty(map_op1363057580ion_ty(G),Ys) )
=> ( size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_74_map__eq__imp__length__eq,axiom,
! [F: fun_ex1654222579t_char,Xs: list_exp_list_char,G: fun_op1508857234t_char,Ys: list_option_ty] :
( ( hAPP_l2011456725t_char(map_ex101166958t_char(F),Xs) = hAPP_l330149622t_char(map_op1779340173t_char(G),Ys) )
=> ( size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_75_map__eq__imp__length__eq,axiom,
! [F: fun_ex793263652ar_val,Xs: list_exp_list_char,G: fun_option_ty_val,Ys: list_option_ty] :
( ( hAPP_l1539861698st_val(map_ex740158547ar_val(F),Xs) = hAPP_l336371937st_val(map_option_ty_val(G),Ys) )
=> ( size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_76_map__eq__imp__length__eq,axiom,
! [F: fun_ex1075505132t_char,Xs: list_exp_list_char,G: fun_op195029515t_char,Ys: list_option_ty] :
( ( hAPP_l2065413838t_char(map_ex2109939687t_char(F),Xs) = hAPP_l1368737135t_char(map_op1924521862t_char(G),Ys) )
=> ( size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_77_map__eq__imp__length__eq,axiom,
! [F: fun_exp_list_char_ty,Xs: list_exp_list_char,G: fun_option_ty_ty,Ys: list_option_ty] :
( ( hAPP_l110066169ist_ty(map_exp_list_char_ty(F),Xs) = hAPP_l1583451544ist_ty(map_option_ty_ty(G),Ys) )
=> ( size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_78_map__eq__imp__length__eq,axiom,
! [F: fun_val_list_char,Xs: list_val,G: fun_li1751394789t_char,Ys: list_list_char] :
( ( hAPP_l922645359t_char(map_val_list_char(F),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys) )
=> ( size_size_list_val(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_79_map__eq__imp__length__eq,axiom,
! [F: fun_va172965946on_val,Xs: list_val,G: fun_Pr12181427on_val,Ys: list_P1439941640on_val] :
( ( hAPP_l382831894on_val(map_va527586287on_val(F),Xs) = hAPP_l1695428693on_val(map_Pr1655409582on_val(G),Ys) )
=> ( size_size_list_val(Xs) = size_s1699857438on_val(Ys) ) ) ).
tff(fact_80_map__eq__imp__length__eq,axiom,
! [F: fun_val_val,Xs: list_val,G: fun_option_val_val,Ys: list_option_val] :
( ( hAPP_l273806049st_val(map_val_val(F),Xs) = hAPP_l228474410st_val(map_option_val_val(G),Ys) )
=> ( size_size_list_val(Xs) = size_s1595297126on_val(Ys) ) ) ).
tff(fact_81_map__eq__imp__length__eq,axiom,
! [F: fun_val_option_val,Xs: list_val,G: fun_li1432931796on_val,Ys: list_list_char] :
( ( hAPP_l761459294on_val(map_val_option_val(F),Xs) = hAPP_l297961988on_val(map_li50976719on_val(G),Ys) )
=> ( size_size_list_val(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_82_map__eq__imp__length__eq,axiom,
! [F: fun_val_val,Xs: list_val,G: fun_option_ty_val,Ys: list_option_ty] :
( ( hAPP_l273806049st_val(map_val_val(F),Xs) = hAPP_l336371937st_val(map_option_ty_val(G),Ys) )
=> ( size_size_list_val(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_83_map__eq__imp__length__eq,axiom,
! [F: fun_val_list_char,Xs: list_val,G: fun_op195029515t_char,Ys: list_option_ty] :
( ( hAPP_l922645359t_char(map_val_list_char(F),Xs) = hAPP_l1368737135t_char(map_op1924521862t_char(G),Ys) )
=> ( size_size_list_val(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_84_map__eq__imp__length__eq,axiom,
! [F: fun_val_ty,Xs: list_val,G: fun_option_ty_ty,Ys: list_option_ty] :
( ( hAPP_l1085267864ist_ty(map_val_ty(F),Xs) = hAPP_l1583451544ist_ty(map_option_ty_ty(G),Ys) )
=> ( size_size_list_val(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_85_map__eq__imp__length__eq,axiom,
! [F: fun_val_option_ty,Xs: list_val,G: fun_li688206603ion_ty,Ys: list_list_char] :
( ( hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs) = hAPP_l1491470139ion_ty(map_li771939206ion_ty(G),Ys) )
=> ( size_size_list_val(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_86_map__eq__imp__length__eq,axiom,
! [F: fun_val_option_ty,Xs: list_val,G: fun_ex12316946ion_ty,Ys: list_exp_list_char] :
( ( hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs) = hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(G),Ys) )
=> ( size_size_list_val(Xs) = size_s1143674878t_char(Ys) ) ) ).
tff(fact_87_map__eq__imp__length__eq,axiom,
! [F: fun_ty_list_char,Xs: list_ty,G: fun_li1751394789t_char,Ys: list_list_char] :
( ( hAPP_l402740472t_char(map_ty_list_char(F),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys) )
=> ( size_size_list_ty(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_88_map__eq__imp__length__eq,axiom,
! [F: fun_ty2028523121on_val,Xs: list_ty,G: fun_Pr12181427on_val,Ys: list_P1439941640on_val] :
( ( hAPP_l1634001311on_val(map_ty891785382on_val(F),Xs) = hAPP_l1695428693on_val(map_Pr1655409582on_val(G),Ys) )
=> ( size_size_list_ty(Xs) = size_s1699857438on_val(Ys) ) ) ).
tff(fact_89_map__eq__imp__length__eq,axiom,
! [F: fun_ty_val,Xs: list_ty,G: fun_option_val_val,Ys: list_option_val] :
( ( hAPP_l1530663448st_val(map_ty_val(F),Xs) = hAPP_l228474410st_val(map_option_val_val(G),Ys) )
=> ( size_size_list_ty(Xs) = size_s1595297126on_val(Ys) ) ) ).
tff(fact_90_map__eq__imp__length__eq,axiom,
! [F: fun_ty_option_val,Xs: list_ty,G: fun_li1432931796on_val,Ys: list_list_char] :
( ( hAPP_l1014734695on_val(map_ty_option_val(F),Xs) = hAPP_l297961988on_val(map_li50976719on_val(G),Ys) )
=> ( size_size_list_ty(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_91_map__eq__imp__length__eq,axiom,
! [F: fun_ty_exp_list_char,Xs: list_ty,G: fun_op1508857234t_char,Ys: list_option_ty] :
( ( hAPP_l578807295t_char(map_ty_exp_list_char(F),Xs) = hAPP_l330149622t_char(map_op1779340173t_char(G),Ys) )
=> ( size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_92_map__eq__imp__length__eq,axiom,
! [F: fun_ty_val,Xs: list_ty,G: fun_option_ty_val,Ys: list_option_ty] :
( ( hAPP_l1530663448st_val(map_ty_val(F),Xs) = hAPP_l336371937st_val(map_option_ty_val(G),Ys) )
=> ( size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_93_map__eq__imp__length__eq,axiom,
! [F: fun_ty_list_char,Xs: list_ty,G: fun_op195029515t_char,Ys: list_option_ty] :
( ( hAPP_l402740472t_char(map_ty_list_char(F),Xs) = hAPP_l1368737135t_char(map_op1924521862t_char(G),Ys) )
=> ( size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_94_map__eq__imp__length__eq,axiom,
! [F: fun_ty_ty,Xs: list_ty,G: fun_option_ty_ty,Ys: list_option_ty] :
( ( hAPP_list_ty_list_ty(map_ty_ty(F),Xs) = hAPP_l1583451544ist_ty(map_option_ty_ty(G),Ys) )
=> ( size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_95_map__eq__imp__length__eq,axiom,
! [F: fun_ty_option_ty,Xs: list_ty,G: fun_li688206603ion_ty,Ys: list_list_char] :
( ( hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs) = hAPP_l1491470139ion_ty(map_li771939206ion_ty(G),Ys) )
=> ( size_size_list_ty(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_96_map__eq__imp__length__eq,axiom,
! [F: fun_ty_option_ty,Xs: list_ty,G: fun_ex12316946ion_ty,Ys: list_exp_list_char] :
( ( hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs) = hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(G),Ys) )
=> ( size_size_list_ty(Xs) = size_s1143674878t_char(Ys) ) ) ).
tff(fact_97_map__eq__imp__length__eq,axiom,
! [F: fun_li1751394789t_char,Xs: list_list_char,G: fun_li1751394789t_char,Ys: list_list_char] :
( ( hAPP_l407174677t_char(map_li1333403488t_char(F),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys) )
=> ( size_s2113983095t_char(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_98_map__eq__imp__length__eq,axiom,
! [F: fun_li2145367436on_val,Xs: list_list_char,G: fun_Pr12181427on_val,Ys: list_P1439941640on_val] :
( ( hAPP_l418486716on_val(map_li1100402823on_val(F),Xs) = hAPP_l1695428693on_val(map_Pr1655409582on_val(G),Ys) )
=> ( size_s2113983095t_char(Xs) = size_s1699857438on_val(Ys) ) ) ).
tff(fact_99_map__eq__imp__length__eq,axiom,
! [F: fun_list_char_val,Xs: list_list_char,G: fun_option_val_val,Ys: list_option_val] :
( ( hAPP_l1892737211st_val(map_list_char_val(F),Xs) = hAPP_l228474410st_val(map_option_val_val(G),Ys) )
=> ( size_s2113983095t_char(Xs) = size_s1595297126on_val(Ys) ) ) ).
tff(fact_100_map__eq__imp__length__eq,axiom,
! [F: fun_li1432931796on_val,Xs: list_list_char,G: fun_li1432931796on_val,Ys: list_list_char] :
( ( hAPP_l297961988on_val(map_li50976719on_val(F),Xs) = hAPP_l297961988on_val(map_li50976719on_val(G),Ys) )
=> ( size_s2113983095t_char(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_101_map__eq__imp__length__eq,axiom,
! [F: fun_li688206603ion_ty,Xs: list_list_char,G: fun_op1279324977ion_ty,Ys: list_option_ty] :
( ( hAPP_l1491470139ion_ty(map_li771939206ion_ty(F),Xs) = hAPP_l305548949ion_ty(map_op1363057580ion_ty(G),Ys) )
=> ( size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_102_map__eq__imp__length__eq,axiom,
! [F: fun_li978641004t_char,Xs: list_list_char,G: fun_op1508857234t_char,Ys: list_option_ty] :
( ( hAPP_l740678812t_char(map_li1249123943t_char(F),Xs) = hAPP_l330149622t_char(map_op1779340173t_char(G),Ys) )
=> ( size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_103_map__eq__imp__length__eq,axiom,
! [F: fun_li1751394789t_char,Xs: list_list_char,G: fun_op195029515t_char,Ys: list_option_ty] :
( ( hAPP_l407174677t_char(map_li1333403488t_char(F),Xs) = hAPP_l1368737135t_char(map_op1924521862t_char(G),Ys) )
=> ( size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_104_map__eq__imp__length__eq,axiom,
! [F: fun_list_char_ty,Xs: list_list_char,G: fun_option_ty_ty,Ys: list_option_ty] :
( ( hAPP_l1871878770ist_ty(map_list_char_ty(F),Xs) = hAPP_l1583451544ist_ty(map_option_ty_ty(G),Ys) )
=> ( size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys) ) ) ).
tff(fact_105_map__eq__imp__length__eq,axiom,
! [F: fun_li688206603ion_ty,Xs: list_list_char,G: fun_li688206603ion_ty,Ys: list_list_char] :
( ( hAPP_l1491470139ion_ty(map_li771939206ion_ty(F),Xs) = hAPP_l1491470139ion_ty(map_li771939206ion_ty(G),Ys) )
=> ( size_s2113983095t_char(Xs) = size_s2113983095t_char(Ys) ) ) ).
tff(fact_106_map__eq__imp__length__eq,axiom,
! [F: fun_li688206603ion_ty,Xs: list_list_char,G: fun_ex12316946ion_ty,Ys: list_exp_list_char] :
( ( hAPP_l1491470139ion_ty(map_li771939206ion_ty(F),Xs) = hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(G),Ys) )
=> ( size_s2113983095t_char(Xs) = size_s1143674878t_char(Ys) ) ) ).
tff(fact_107_prod__induct4,axiom,
! [X_1: produc1285161482t_char,Pa: fun_Pr227936640r_bool] :
( ! [A: list_list_char,B_1: list_ty,C_3: list_val,D: exp_list_char] : hBOOL(hAPP_P92196306r_bool(Pa,produc921874948t_char(A,produc1909267824t_char(B_1,produc1916172923t_char(C_3,D)))))
=> hBOOL(hAPP_P92196306r_bool(Pa,X_1)) ) ).
tff(fact_108_prod__induct4,axiom,
! [X_1: produc1102272487on_val,Pa: fun_Pr691271849l_bool] :
( ! [A: produc124828825on_val,B_1: exp_list_char,C_3: fun_na939144002on_val,D: fun_li1432931796on_val] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A,produc1259058957on_val(B_1,produc899768717on_val(C_3,D)))))
=> hBOOL(hAPP_P282169671l_bool(Pa,X_1)) ) ).
tff(fact_109_prod__cases4,axiom,
! [Y_5: produc1285161482t_char] :
~ ! [A: list_list_char,B_1: list_ty,C_3: list_val,D: exp_list_char] : Y_5 != produc921874948t_char(A,produc1909267824t_char(B_1,produc1916172923t_char(C_3,D))) ).
tff(fact_110_prod__cases4,axiom,
! [Y_3: produc1102272487on_val] :
~ ! [A: produc124828825on_val,B_1: exp_list_char,C_3: fun_na939144002on_val,D: fun_li1432931796on_val] : Y_3 != produc1441475159on_val(A,produc1259058957on_val(B_1,produc899768717on_val(C_3,D))) ).
tff(fact_111_Pair__inject,axiom,
! [A_5: list_list_char,B_4: produc220283002t_char,A_4: list_list_char,B_3: produc220283002t_char] :
( ( produc921874948t_char(A_5,B_4) = produc921874948t_char(A_4,B_3) )
=> ~ ( ( A_5 = A_4 )
=> ( B_4 != B_3 ) ) ) ).
tff(fact_112_Pair__inject,axiom,
! [A_5: list_ty,B_4: produc662261637t_char,A_4: list_ty,B_3: produc662261637t_char] :
( ( produc1909267824t_char(A_5,B_4) = produc1909267824t_char(A_4,B_3) )
=> ~ ( ( A_5 = A_4 )
=> ( B_4 != B_3 ) ) ) ).
tff(fact_113_Pair__inject,axiom,
! [A_5: list_val,B_4: exp_list_char,A_4: list_val,B_3: exp_list_char] :
( ( produc1916172923t_char(A_5,B_4) = produc1916172923t_char(A_4,B_3) )
=> ~ ( ( A_5 = A_4 )
=> ( B_4 != B_3 ) ) ) ).
tff(fact_114_Pair__inject,axiom,
! [A_1: fun_na939144002on_val,B: fun_li1432931796on_val,A_3: fun_na939144002on_val,B_2: fun_li1432931796on_val] :
( ( produc899768717on_val(A_1,B) = produc899768717on_val(A_3,B_2) )
=> ~ ( ( A_1 = A_3 )
=> ( B != B_2 ) ) ) ).
tff(fact_115_Pair__inject,axiom,
! [A_1: produc124828825on_val,B: produc124828825on_val,A_3: produc124828825on_val,B_2: produc124828825on_val] :
( ( produc1441475159on_val(A_1,B) = produc1441475159on_val(A_3,B_2) )
=> ~ ( ( A_1 = A_3 )
=> ( B != B_2 ) ) ) ).
tff(fact_116_Pair__inject,axiom,
! [A_1: exp_list_char,B: produc12694297on_val,A_3: exp_list_char,B_2: produc12694297on_val] :
( ( produc1259058957on_val(A_1,B) = produc1259058957on_val(A_3,B_2) )
=> ~ ( ( A_1 = A_3 )
=> ( B != B_2 ) ) ) ).
tff(fact_117_Pair__inject,axiom,
! [A_1: list_char,B: fun_Pr806764899on_val,A_3: list_char,B_2: fun_Pr806764899on_val] :
( ( produc823076510on_val(A_1,B) = produc823076510on_val(A_3,B_2) )
=> ~ ( ( A_1 = A_3 )
=> ( B != B_2 ) ) ) ).
tff(fact_118_Pair__eq,axiom,
! [A_1: list_list_char,B: produc220283002t_char,A_3: list_list_char,B_2: produc220283002t_char] :
( ( produc921874948t_char(A_1,B) = produc921874948t_char(A_3,B_2) )
<=> ( ( A_1 = A_3 )
& ( B = B_2 ) ) ) ).
tff(fact_119_Pair__eq,axiom,
! [A_1: list_ty,B: produc662261637t_char,A_3: list_ty,B_2: produc662261637t_char] :
( ( produc1909267824t_char(A_1,B) = produc1909267824t_char(A_3,B_2) )
<=> ( ( A_1 = A_3 )
& ( B = B_2 ) ) ) ).
tff(fact_120_Pair__eq,axiom,
! [A_1: list_val,B: exp_list_char,A_3: list_val,B_2: exp_list_char] :
( ( produc1916172923t_char(A_1,B) = produc1916172923t_char(A_3,B_2) )
<=> ( ( A_1 = A_3 )
& ( B = B_2 ) ) ) ).
tff(fact_121_Pair__eq,axiom,
! [A_1: fun_na939144002on_val,B: fun_li1432931796on_val,A_3: fun_na939144002on_val,B_2: fun_li1432931796on_val] :
( ( produc899768717on_val(A_1,B) = produc899768717on_val(A_3,B_2) )
<=> ( ( A_1 = A_3 )
& ( B = B_2 ) ) ) ).
tff(fact_122_Pair__eq,axiom,
! [A_1: produc124828825on_val,B: produc124828825on_val,A_3: produc124828825on_val,B_2: produc124828825on_val] :
( ( produc1441475159on_val(A_1,B) = produc1441475159on_val(A_3,B_2) )
<=> ( ( A_1 = A_3 )
& ( B = B_2 ) ) ) ).
tff(fact_123_Pair__eq,axiom,
! [A_1: exp_list_char,B: produc12694297on_val,A_3: exp_list_char,B_2: produc12694297on_val] :
( ( produc1259058957on_val(A_1,B) = produc1259058957on_val(A_3,B_2) )
<=> ( ( A_1 = A_3 )
& ( B = B_2 ) ) ) ).
tff(fact_124_Pair__eq,axiom,
! [A_1: list_char,B: fun_Pr806764899on_val,A_3: list_char,B_2: fun_Pr806764899on_val] :
( ( produc823076510on_val(A_1,B) = produc823076510on_val(A_3,B_2) )
<=> ( ( A_1 = A_3 )
& ( B = B_2 ) ) ) ).
tff(fact_125_split__paired__All,axiom,
! [Pa: fun_Pr227936640r_bool] :
( ! [X1: produc1285161482t_char] : hBOOL(hAPP_P92196306r_bool(Pa,X1))
<=> ! [A: list_list_char,B_1: produc220283002t_char] : hBOOL(hAPP_P92196306r_bool(Pa,produc921874948t_char(A,B_1))) ) ).
tff(fact_126_split__paired__All,axiom,
! [Pa: fun_Pr46158268r_bool] :
( ! [X1: produc220283002t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,X1))
<=> ! [A: list_ty,B_1: produc662261637t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,produc1909267824t_char(A,B_1))) ) ).
tff(fact_127_split__paired__All,axiom,
! [Pa: fun_Pr827765831r_bool] :
( ! [X1: produc662261637t_char] : hBOOL(hAPP_P2118621157r_bool(Pa,X1))
<=> ! [A: list_val,B_1: exp_list_char] : hBOOL(hAPP_P2118621157r_bool(Pa,produc1916172923t_char(A,B_1))) ) ).
tff(fact_128_split__paired__All,axiom,
! [Pa: fun_Pr1696029455l_bool] :
( ! [X1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
<=> ! [A: fun_na939144002on_val,B_1: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(Pa,produc899768717on_val(A,B_1))) ) ).
tff(fact_129_split__paired__All,axiom,
! [Pa: fun_Pr691271849l_bool] :
( ! [X1: produc1102272487on_val] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
<=> ! [A: produc124828825on_val,B_1: produc124828825on_val] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A,B_1))) ) ).
tff(fact_130_split__paired__All,axiom,
! [Pa: fun_Pr680585871l_bool] :
( ! [X1: produc124828825on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
<=> ! [A: exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A,B_1))) ) ).
tff(fact_131_split__paired__All,axiom,
! [Pa: fun_Pr315804320l_bool] :
( ! [X1: produc639455274on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,X1))
<=> ! [A: list_char,B_1: fun_Pr806764899on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,produc823076510on_val(A,B_1))) ) ).
tff(fact_132_neq__if__length__neq,axiom,
! [Xs_2: list_option_ty,Ys_2: list_option_ty] :
( ( size_s1050794909ion_ty(Xs_2) != size_s1050794909ion_ty(Ys_2) )
=> ( Xs_2 != Ys_2 ) ) ).
tff(fact_133_neq__if__length__neq,axiom,
! [Xs_2: list_list_char,Ys_2: list_list_char] :
( ( size_s2113983095t_char(Xs_2) != size_s2113983095t_char(Ys_2) )
=> ( Xs_2 != Ys_2 ) ) ).
tff(fact_134_neq__if__length__neq,axiom,
! [Xs_2: list_ty,Ys_2: list_ty] :
( ( size_size_list_ty(Xs_2) != size_size_list_ty(Ys_2) )
=> ( Xs_2 != Ys_2 ) ) ).
tff(fact_135_neq__if__length__neq,axiom,
! [Xs_2: list_val,Ys_2: list_val] :
( ( size_size_list_val(Xs_2) != size_size_list_val(Ys_2) )
=> ( Xs_2 != Ys_2 ) ) ).
tff(fact_136_neq__if__length__neq,axiom,
! [Xs_2: list_exp_list_char,Ys_2: list_exp_list_char] :
( ( size_s1143674878t_char(Xs_2) != size_s1143674878t_char(Ys_2) )
=> ( Xs_2 != Ys_2 ) ) ).
tff(fact_137_list__all2__eq,axiom,
! [Xs: list_ty,Ys: list_ty] :
( ( Xs = Ys )
<=> hBOOL(list_all2_ty_ty(fequal_ty,Xs,Ys)) ) ).
tff(fact_138_widen__trans,axiom,
! [T_3: ty,P_2: list_P1999446415t_char,S_2: ty,U: ty] :
( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_2),S_2),U))
=> ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_2),U),T_3))
=> hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_2),S_2),T_3)) ) ) ).
tff(fact_139_prod__cases3,axiom,
! [Y_4: produc1285161482t_char] :
~ ! [A: list_list_char,B_1: list_ty,C_3: produc662261637t_char] : Y_4 != produc921874948t_char(A,produc1909267824t_char(B_1,C_3)) ).
tff(fact_140_prod__cases3,axiom,
! [Y_4: produc220283002t_char] :
~ ! [A: list_ty,B_1: list_val,C_3: exp_list_char] : Y_4 != produc1909267824t_char(A,produc1916172923t_char(B_1,C_3)) ).
tff(fact_141_prod__cases3,axiom,
! [Y_3: produc1102272487on_val] :
~ ! [A: produc124828825on_val,B_1: exp_list_char,C_3: produc12694297on_val] : Y_3 != produc1441475159on_val(A,produc1259058957on_val(B_1,C_3)) ).
tff(fact_142_prod__cases3,axiom,
! [Y_3: produc124828825on_val] :
~ ! [A: exp_list_char,B_1: fun_na939144002on_val,C_3: fun_li1432931796on_val] : Y_3 != produc1259058957on_val(A,produc899768717on_val(B_1,C_3)) ).
tff(fact_143_prod__induct3,axiom,
! [X_1: produc1285161482t_char,Pa: fun_Pr227936640r_bool] :
( ! [A: list_list_char,B_1: list_ty,C_3: produc662261637t_char] : hBOOL(hAPP_P92196306r_bool(Pa,produc921874948t_char(A,produc1909267824t_char(B_1,C_3))))
=> hBOOL(hAPP_P92196306r_bool(Pa,X_1)) ) ).
tff(fact_144_prod__induct3,axiom,
! [X_1: produc220283002t_char,Pa: fun_Pr46158268r_bool] :
( ! [A: list_ty,B_1: list_val,C_3: exp_list_char] : hBOOL(hAPP_P1907982426r_bool(Pa,produc1909267824t_char(A,produc1916172923t_char(B_1,C_3))))
=> hBOOL(hAPP_P1907982426r_bool(Pa,X_1)) ) ).
tff(fact_145_prod__induct3,axiom,
! [X_1: produc1102272487on_val,Pa: fun_Pr691271849l_bool] :
( ! [A: produc124828825on_val,B_1: exp_list_char,C_3: produc12694297on_val] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A,produc1259058957on_val(B_1,C_3))))
=> hBOOL(hAPP_P282169671l_bool(Pa,X_1)) ) ).
tff(fact_146_prod__induct3,axiom,
! [X_1: produc124828825on_val,Pa: fun_Pr680585871l_bool] :
( ! [A: exp_list_char,B_1: fun_na939144002on_val,C_3: fun_li1432931796on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A,produc899768717on_val(B_1,C_3))))
=> hBOOL(hAPP_P1708370145l_bool(Pa,X_1)) ) ).
tff(fact_147_confs__conv__map,axiom,
! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,Vsa_1: list_val,Ts_1: list_ty] :
( hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa_1,Ts_1))
<=> ? [Ts_2: list_ty] :
( ( hAPP_l2006940821ion_ty(map_val_option_ty(typeof_h(Ha)),Vsa_1) = hAPP_l1487035934ion_ty(map_ty_option_ty(some_ty),Ts_2) )
& hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_2,Ts_1)) ) ) ).
tff(fact_148_list__all2__mono,axiom,
! [Q: fun_ty_fun_ty_bool,Pa: fun_ty_fun_ty_bool,Xs: list_ty,Ys: list_ty] :
( hBOOL(list_all2_ty_ty(Pa,Xs,Ys))
=> ( ! [Xs_1: ty,Ys_1: ty] :
( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Pa,Xs_1),Ys_1))
=> hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Q,Xs_1),Ys_1)) )
=> hBOOL(list_all2_ty_ty(Q,Xs,Ys)) ) ) ).
tff(fact_149_list__all2__mono,axiom,
! [Q: fun_val_fun_ty_bool,Pa: fun_val_fun_ty_bool,Xs: list_val,Ys: list_ty] :
( hBOOL(list_all2_val_ty(Pa,Xs,Ys))
=> ( ! [Xs_1: val,Ys_1: ty] :
( hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(Pa,Xs_1),Ys_1))
=> hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(Q,Xs_1),Ys_1)) )
=> hBOOL(list_all2_val_ty(Q,Xs,Ys)) ) ) ).
tff(fact_150_list__all2__refl,axiom,
! [Xs: list_ty,Pa: fun_ty_fun_ty_bool] :
( ! [X_2: ty] : hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Pa,X_2),X_2))
=> hBOOL(list_all2_ty_ty(Pa,Xs,Xs)) ) ).
tff(fact_151_list__all2__antisym,axiom,
! [Xs: list_ty,Ys: list_ty,Q: fun_ty_fun_ty_bool,Pa: fun_ty_fun_ty_bool] :
( ! [X_2: ty,Y_1: ty] :
( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Pa,X_2),Y_1))
=> ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Q,Y_1),X_2))
=> ( X_2 = Y_1 ) ) )
=> ( hBOOL(list_all2_ty_ty(Pa,Xs,Ys))
=> ( hBOOL(list_all2_ty_ty(Q,Ys,Xs))
=> ( Xs = Ys ) ) ) ) ).
tff(fact_152_Ex__list__of__length,axiom,
! [N_1: nat] :
? [Xs_1: list_option_ty] : size_s1050794909ion_ty(Xs_1) = N_1 ).
tff(fact_153_Ex__list__of__length,axiom,
! [N_1: nat] :
? [Xs_1: list_exp_list_char] : size_s1143674878t_char(Xs_1) = N_1 ).
tff(fact_154_Ex__list__of__length,axiom,
! [N_1: nat] :
? [Xs_1: list_val] : size_size_list_val(Xs_1) = N_1 ).
tff(fact_155_Ex__list__of__length,axiom,
! [N_1: nat] :
? [Xs_1: list_ty] : size_size_list_ty(Xs_1) = N_1 ).
tff(fact_156_Ex__list__of__length,axiom,
! [N_1: nat] :
? [Xs_1: list_list_char] : size_s2113983095t_char(Xs_1) = N_1 ).
tff(fact_157_conf__widen,axiom,
! [T_2: ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,V_1: val,Ta: ty] :
( hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_1),Ta))
=> ( hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),Ta),T_2))
=> hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_1),T_2)) ) ) ).
tff(fact_158_typeof__conf,axiom,
! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,V_1: val,Ta: ty] :
( ( hAPP_val_option_ty(typeof_h(Ha),V_1) = hAPP_ty_option_ty(some_ty,Ta) )
=> hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_1),Ta)) ) ).
tff(fact_159_confs__widens,axiom,
! [Ts_1: list_ty,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,Vsa_1: list_val,Tsa: list_ty] :
( hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa_1,Tsa))
=> ( hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Tsa,Ts_1))
=> hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa_1,Ts_1)) ) ) ).
tff(fact_160_conf__def,axiom,
! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,V_1: val,Ta: ty] :
( hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_1),Ta))
<=> ? [T_1: ty] :
( ( hAPP_val_option_ty(typeof_h(Ha),V_1) = hAPP_ty_option_ty(some_ty,T_1) )
& hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1),Ta)) ) ) ).
tff(fact_161_split__paired__Ex,axiom,
! [Pa: fun_Pr315804320l_bool] :
( ? [X1: produc639455274on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,X1))
<=> ? [A: list_char,B_1: fun_Pr806764899on_val] : hBOOL(hAPP_P1235399154l_bool(Pa,produc823076510on_val(A,B_1))) ) ).
tff(fact_162_split__paired__Ex,axiom,
! [Pa: fun_Pr680585871l_bool] :
( ? [X1: produc124828825on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,X1))
<=> ? [A: exp_list_char,B_1: produc12694297on_val] : hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A,B_1))) ) ).
tff(fact_163_split__paired__Ex,axiom,
! [Pa: fun_Pr691271849l_bool] :
( ? [X1: produc1102272487on_val] : hBOOL(hAPP_P282169671l_bool(Pa,X1))
<=> ? [A: produc124828825on_val,B_1: produc124828825on_val] : hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A,B_1))) ) ).
tff(fact_164_split__paired__Ex,axiom,
! [Pa: fun_Pr1696029455l_bool] :
( ? [X1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(Pa,X1))
<=> ? [A: fun_na939144002on_val,B_1: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(Pa,produc899768717on_val(A,B_1))) ) ).
tff(fact_165_split__paired__Ex,axiom,
! [Pa: fun_Pr827765831r_bool] :
( ? [X1: produc662261637t_char] : hBOOL(hAPP_P2118621157r_bool(Pa,X1))
<=> ? [A: list_val,B_1: exp_list_char] : hBOOL(hAPP_P2118621157r_bool(Pa,produc1916172923t_char(A,B_1))) ) ).
tff(fact_166_split__paired__Ex,axiom,
! [Pa: fun_Pr46158268r_bool] :
( ? [X1: produc220283002t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,X1))
<=> ? [A: list_ty,B_1: produc662261637t_char] : hBOOL(hAPP_P1907982426r_bool(Pa,produc1909267824t_char(A,B_1))) ) ).
tff(fact_167_split__paired__Ex,axiom,
! [Pa: fun_Pr227936640r_bool] :
( ? [X1: produc1285161482t_char] : hBOOL(hAPP_P92196306r_bool(Pa,X1))
<=> ? [A: list_list_char,B_1: produc220283002t_char] : hBOOL(hAPP_P92196306r_bool(Pa,produc921874948t_char(A,B_1))) ) ).
tff(fact_168_PairE,axiom,
! [P: produc639455274on_val] :
~ ! [X_2: list_char,Y_1: fun_Pr806764899on_val] : P != produc823076510on_val(X_2,Y_1) ).
tff(fact_169_PairE,axiom,
! [P: produc124828825on_val] :
~ ! [X_2: exp_list_char,Y_1: produc12694297on_val] : P != produc1259058957on_val(X_2,Y_1) ).
tff(fact_170_PairE,axiom,
! [P: produc1102272487on_val] :
~ ! [X_2: produc124828825on_val,Y_1: produc124828825on_val] : P != produc1441475159on_val(X_2,Y_1) ).
tff(fact_171_PairE,axiom,
! [P: produc12694297on_val] :
~ ! [X_2: fun_na939144002on_val,Y_1: fun_li1432931796on_val] : P != produc899768717on_val(X_2,Y_1) ).
tff(fact_172_PairE,axiom,
! [P_1: produc662261637t_char] :
~ ! [X_2: list_val,Y_1: exp_list_char] : P_1 != produc1916172923t_char(X_2,Y_1) ).
tff(fact_173_PairE,axiom,
! [P_1: produc220283002t_char] :
~ ! [X_2: list_ty,Y_1: produc662261637t_char] : P_1 != produc1909267824t_char(X_2,Y_1) ).
tff(fact_174_PairE,axiom,
! [P_1: produc1285161482t_char] :
~ ! [X_2: list_list_char,Y_1: produc220283002t_char] : P_1 != produc921874948t_char(X_2,Y_1) ).
tff(fact_175_prod_Oexhaust,axiom,
! [Y_3: produc639455274on_val] :
~ ! [A: list_char,B_1: fun_Pr806764899on_val] : Y_3 != produc823076510on_val(A,B_1) ).
tff(fact_176_prod_Oexhaust,axiom,
! [Y_3: produc124828825on_val] :
~ ! [A: exp_list_char,B_1: produc12694297on_val] : Y_3 != produc1259058957on_val(A,B_1) ).
tff(fact_177_prod_Oexhaust,axiom,
! [Y_3: produc1102272487on_val] :
~ ! [A: produc124828825on_val,B_1: produc124828825on_val] : Y_3 != produc1441475159on_val(A,B_1) ).
tff(fact_178_prod_Oexhaust,axiom,
! [Y_3: produc12694297on_val] :
~ ! [A: fun_na939144002on_val,B_1: fun_li1432931796on_val] : Y_3 != produc899768717on_val(A,B_1) ).
tff(fact_179_prod_Oexhaust,axiom,
! [Y_2: produc662261637t_char] :
~ ! [A: list_val,B_1: exp_list_char] : Y_2 != produc1916172923t_char(A,B_1) ).
tff(fact_180_prod_Oexhaust,axiom,
! [Y_2: produc220283002t_char] :
~ ! [A: list_ty,B_1: produc662261637t_char] : Y_2 != produc1909267824t_char(A,B_1) ).
tff(fact_181_prod_Oexhaust,axiom,
! [Y_2: produc1285161482t_char] :
~ ! [A: list_list_char,B_1: produc220283002t_char] : Y_2 != produc921874948t_char(A,B_1) ).
tff(fact_182_confs__hext,axiom,
! [H: fun_na939144002on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,Vsa_1: list_val,Tsa: list_ty] :
( hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa_1,Tsa))
=> ( hBOOL(hext(Ha,H))
=> hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,H),Vsa_1,Tsa)) ) ) ).
tff(fact_183_blocksEval,axiom,
! [Pa: list_P1999446415t_char,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Vsa_1: list_val,Ps: list_list_char,Tsa: list_ty] :
( ( size_s2113983095t_char(Ps) = size_size_list_ty(Tsa) )
=> ( ( size_s2113983095t_char(Ps) = size_size_list_val(Vsa_1) )
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,blocks(produc921874948t_char(Ps,produc1909267824t_char(Tsa,produc1916172923t_char(Vsa_1,Ea)))),produc899768717on_val(Ha,L_1)),E),produc899768717on_val(H,L)))
=> ? [L_3: fun_li1432931796on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,produc899768717on_val(Ha,map_up1085636310ar_val(L_1,Ps,Vsa_1))),E),produc899768717on_val(H,L_3))) ) ) ) ).
tff(fact_184_conf__hext,axiom,
! [Pa: list_P1999446415t_char,V_1: val,Ta: ty,Ha: fun_na939144002on_val,H: fun_na939144002on_val] :
( hBOOL(hext(Ha,H))
=> ( hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_1),Ta))
=> hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,H),V_1),Ta)) ) ) ).
tff(fact_185_hext__typeof__mono,axiom,
! [V_1: val,Ta: ty,Ha: fun_na939144002on_val,H: fun_na939144002on_val] :
( hBOOL(hext(Ha,H))
=> ( ( hAPP_val_option_ty(typeof_h(Ha),V_1) = hAPP_ty_option_ty(some_ty,Ta) )
=> ( hAPP_val_option_ty(typeof_h(H),V_1) = hAPP_ty_option_ty(some_ty,Ta) ) ) ) ).
tff(fact_186_eval__hext,axiom,
! [Pa: list_P1999446415t_char,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,produc899768717on_val(Ha,L_1)),E),produc899768717on_val(H,L)))
=> hBOOL(hext(Ha,H)) ) ).
tff(fact_187_hext__refl,axiom,
! [Ha: fun_na939144002on_val] : hBOOL(hext(Ha,Ha)) ).
tff(fact_188_WTrt__hext__mono,axiom,
! [H: fun_na939144002on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Ea: exp_list_char,Ta: ty] :
( hBOOL(wTrt(Pa,Ha,E_1,Ea,Ta))
=> ( hBOOL(hext(Ha,H))
=> hBOOL(wTrt(Pa,H,E_1,Ea,Ta)) ) ) ).
tff(fact_189_hext__trans,axiom,
! [H_1: fun_na939144002on_val,Ha: fun_na939144002on_val,H: fun_na939144002on_val] :
( hBOOL(hext(Ha,H))
=> ( hBOOL(hext(H,H_1))
=> hBOOL(hext(Ha,H_1)) ) ) ).
tff(fact_190_WTrtVal,axiom,
! [Pa: list_P1999446415t_char,E_1: fun_li688206603ion_ty,Ha: fun_na939144002on_val,V_1: val,Ta: ty] :
( ( hAPP_val_option_ty(typeof_h(Ha),V_1) = hAPP_ty_option_ty(some_ty,Ta) )
=> hBOOL(wTrt(Pa,Ha,E_1,hAPP_v834067052t_char(val_list_char,V_1),Ta)) ) ).
tff(fact_191_blocksFinal,axiom,
! [Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,Pa: list_P1999446415t_char,Ea: exp_list_char,Vsa_1: list_val,Vsa: list_list_char,Tsa: list_ty] :
( ( size_s2113983095t_char(Vsa) = size_size_list_ty(Tsa) )
=> ( ( size_size_list_val(Vsa_1) = size_size_list_ty(Tsa) )
=> ( hBOOL(final_list_char(Ea))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(blocks(produc921874948t_char(Vsa,produc1909267824t_char(Tsa,produc1916172923t_char(Vsa_1,Ea)))),produc899768717on_val(Ha,L_1)),produc1259058957on_val(Ea,produc899768717on_val(Ha,L_1))),transi2024712006on_val(red(Pa)))) ) ) ) ).
tff(fact_192_WTrts__Val,axiom,
! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Vsa_1: list_val,Tsa: list_ty] :
( hBOOL(wTrts(Pa,Ha,E_1,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa_1),Tsa))
<=> ( hAPP_l2006940821ion_ty(map_val_option_ty(typeof_h(Ha)),Vsa_1) = hAPP_l1487035934ion_ty(map_ty_option_ty(some_ty),Tsa) ) ) ).
tff(fact_193_option_Oinject,axiom,
! [A_1: val,A_3: val] :
( ( hAPP_val_option_val(some_val,A_1) = hAPP_val_option_val(some_val,A_3) )
<=> ( A_1 = A_3 ) ) ).
tff(fact_194_option_Oinject,axiom,
! [A_1: produc639455274on_val,A_3: produc639455274on_val] :
( ( hAPP_P1510515380on_val(some_P948696889on_val,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,A_3) )
<=> ( A_1 = A_3 ) ) ).
tff(fact_195_option_Oinject,axiom,
! [A_1: ty,A_3: ty] :
( ( hAPP_ty_option_ty(some_ty,A_1) = hAPP_ty_option_ty(some_ty,A_3) )
<=> ( A_1 = A_3 ) ) ).
tff(fact_196_curryI,axiom,
! [F: fun_Pr315804320l_bool,A_1: list_char,B: fun_Pr806764899on_val] :
( hBOOL(hAPP_P1235399154l_bool(F,produc823076510on_val(A_1,B)))
=> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F),A_1),B)) ) ).
tff(fact_197_curryI,axiom,
! [F: fun_Pr680585871l_bool,A_1: exp_list_char,B: produc12694297on_val] :
( hBOOL(hAPP_P1708370145l_bool(F,produc1259058957on_val(A_1,B)))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F),A_1),B)) ) ).
tff(fact_198_curryI,axiom,
! [F: fun_Pr691271849l_bool,A_1: produc124828825on_val,B: produc124828825on_val] :
( hBOOL(hAPP_P282169671l_bool(F,produc1441475159on_val(A_1,B)))
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F),A_1),B)) ) ).
tff(fact_199_curryI,axiom,
! [F: fun_Pr1696029455l_bool,A_1: fun_na939144002on_val,B: fun_li1432931796on_val] :
( hBOOL(hAPP_P159683425l_bool(F,produc899768717on_val(A_1,B)))
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F),A_1),B)) ) ).
tff(fact_200_curryI,axiom,
! [F: fun_Pr827765831r_bool,A_1: list_val,B: exp_list_char] :
( hBOOL(hAPP_P2118621157r_bool(F,produc1916172923t_char(A_1,B)))
=> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F),A_1),B)) ) ).
tff(fact_201_curryI,axiom,
! [F: fun_Pr46158268r_bool,A_1: list_ty,B: produc662261637t_char] :
( hBOOL(hAPP_P1907982426r_bool(F,produc1909267824t_char(A_1,B)))
=> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F),A_1),B)) ) ).
tff(fact_202_curryI,axiom,
! [F: fun_Pr227936640r_bool,A_1: list_list_char,B: produc220283002t_char] :
( hBOOL(hAPP_P92196306r_bool(F,produc921874948t_char(A_1,B)))
=> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F),A_1),B)) ) ).
tff(fact_203_Val,axiom,
! [Pa: list_P1999446415t_char,V_1: val,S_1: produc12694297on_val] : hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,hAPP_v834067052t_char(val_list_char,V_1),S_1),hAPP_v834067052t_char(val_list_char,V_1)),S_1)) ).
tff(fact_204_eval__cases_I2_J,axiom,
! [Pa: list_P1999446415t_char,V_1: val,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,hAPP_v834067052t_char(val_list_char,V_1),S_1),E),S))
=> ~ ( ( E = hAPP_v834067052t_char(val_list_char,V_1) )
=> ( S != S_1 ) ) ) ).
tff(fact_205_WTrts__hext__mono,axiom,
! [H: fun_na939144002on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Es: list_exp_list_char,Tsa: list_ty] :
( hBOOL(wTrts(Pa,Ha,E_1,Es,Tsa))
=> ( hBOOL(hext(Ha,H))
=> hBOOL(wTrts(Pa,H,E_1,Es,Tsa)) ) ) ).
tff(fact_206_WTrts__same__length,axiom,
! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,E_1: fun_li688206603ion_ty,Es: list_exp_list_char,Tsa: list_ty] :
( hBOOL(wTrts(Pa,Ha,E_1,Es,Tsa))
=> ( size_s1143674878t_char(Es) = size_size_list_ty(Tsa) ) ) ).
tff(fact_207_eval__final,axiom,
! [Pa: list_P1999446415t_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),E),S))
=> hBOOL(final_list_char(E)) ) ).
tff(fact_208_eval__finalId,axiom,
! [Pa: list_P1999446415t_char,S_1: produc12694297on_val,Ea: exp_list_char] :
( hBOOL(final_list_char(Ea))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),Ea),S_1)) ) ).
tff(fact_209_curryE,axiom,
! [F: fun_Pr315804320l_bool,A_1: list_char,B: fun_Pr806764899on_val] :
( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F),A_1),B))
=> hBOOL(hAPP_P1235399154l_bool(F,produc823076510on_val(A_1,B))) ) ).
tff(fact_210_curryE,axiom,
! [F: fun_Pr680585871l_bool,A_1: exp_list_char,B: produc12694297on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F),A_1),B))
=> hBOOL(hAPP_P1708370145l_bool(F,produc1259058957on_val(A_1,B))) ) ).
tff(fact_211_curryE,axiom,
! [F: fun_Pr691271849l_bool,A_1: produc124828825on_val,B: produc124828825on_val] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F),A_1),B))
=> hBOOL(hAPP_P282169671l_bool(F,produc1441475159on_val(A_1,B))) ) ).
tff(fact_212_curryE,axiom,
! [F: fun_Pr1696029455l_bool,A_1: fun_na939144002on_val,B: fun_li1432931796on_val] :
( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F),A_1),B))
=> hBOOL(hAPP_P159683425l_bool(F,produc899768717on_val(A_1,B))) ) ).
tff(fact_213_curryE,axiom,
! [F: fun_Pr827765831r_bool,A_1: list_val,B: exp_list_char] :
( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F),A_1),B))
=> hBOOL(hAPP_P2118621157r_bool(F,produc1916172923t_char(A_1,B))) ) ).
tff(fact_214_curryE,axiom,
! [F: fun_Pr46158268r_bool,A_1: list_ty,B: produc662261637t_char] :
( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F),A_1),B))
=> hBOOL(hAPP_P1907982426r_bool(F,produc1909267824t_char(A_1,B))) ) ).
tff(fact_215_curryE,axiom,
! [F: fun_Pr227936640r_bool,A_1: list_list_char,B: produc220283002t_char] :
( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F),A_1),B))
=> hBOOL(hAPP_P92196306r_bool(F,produc921874948t_char(A_1,B))) ) ).
tff(fact_216_curryD,axiom,
! [F: fun_Pr315804320l_bool,A_1: list_char,B: fun_Pr806764899on_val] :
( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F),A_1),B))
=> hBOOL(hAPP_P1235399154l_bool(F,produc823076510on_val(A_1,B))) ) ).
tff(fact_217_curryD,axiom,
! [F: fun_Pr680585871l_bool,A_1: exp_list_char,B: produc12694297on_val] :
( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F),A_1),B))
=> hBOOL(hAPP_P1708370145l_bool(F,produc1259058957on_val(A_1,B))) ) ).
tff(fact_218_curryD,axiom,
! [F: fun_Pr691271849l_bool,A_1: produc124828825on_val,B: produc124828825on_val] :
( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F),A_1),B))
=> hBOOL(hAPP_P282169671l_bool(F,produc1441475159on_val(A_1,B))) ) ).
tff(fact_219_curryD,axiom,
! [F: fun_Pr1696029455l_bool,A_1: fun_na939144002on_val,B: fun_li1432931796on_val] :
( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F),A_1),B))
=> hBOOL(hAPP_P159683425l_bool(F,produc899768717on_val(A_1,B))) ) ).
tff(fact_220_curryD,axiom,
! [F: fun_Pr827765831r_bool,A_1: list_val,B: exp_list_char] :
( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F),A_1),B))
=> hBOOL(hAPP_P2118621157r_bool(F,produc1916172923t_char(A_1,B))) ) ).
tff(fact_221_curryD,axiom,
! [F: fun_Pr46158268r_bool,A_1: list_ty,B: produc662261637t_char] :
( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F),A_1),B))
=> hBOOL(hAPP_P1907982426r_bool(F,produc1909267824t_char(A_1,B))) ) ).
tff(fact_222_curryD,axiom,
! [F: fun_Pr227936640r_bool,A_1: list_list_char,B: produc220283002t_char] :
( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F),A_1),B))
=> hBOOL(hAPP_P92196306r_bool(F,produc921874948t_char(A_1,B))) ) ).
tff(fact_223_red__hext__incr,axiom,
! [Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,L_1)),produc1259058957on_val(E,produc899768717on_val(H,L))),red(Pa)))
=> hBOOL(hext(Ha,H)) ) ).
tff(fact_224_rtrancl_Ortrancl__refl,axiom,
! [A_1: produc124828825on_val,R: fun_Pr691271849l_bool] : hBOOL(member773094996on_val(produc1441475159on_val(A_1,A_1),transi2024712006on_val(R))) ).
tff(fact_225_r__into__rtrancl,axiom,
! [P: produc1102272487on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(P,R))
=> hBOOL(member773094996on_val(P,transi2024712006on_val(R))) ) ).
tff(fact_226_red__preserves__hconf,axiom,
! [E_1: fun_li688206603ion_ty,Ta: ty,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,L_1)),produc1259058957on_val(E,produc899768717on_val(H,L))),red(Pa)))
=> ( hBOOL(wTrt(Pa,Ha,E_1,Ea,Ta))
=> ( hBOOL(hconf_97414254t_char(Pa,Ha))
=> hBOOL(hconf_97414254t_char(Pa,H)) ) ) ) ).
tff(fact_227_rtrancl__idemp,axiom,
! [R: fun_Pr691271849l_bool] : transi2024712006on_val(transi2024712006on_val(R)) = transi2024712006on_val(R) ).
tff(fact_228_converse__rtrancl__into__rtrancl,axiom,
! [C_2: produc124828825on_val,A_1: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_1,B),R))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(B,C_2),transi2024712006on_val(R)))
=> hBOOL(member773094996on_val(produc1441475159on_val(A_1,C_2),transi2024712006on_val(R))) ) ) ).
tff(fact_229_rtrancl_Ortrancl__into__rtrancl,axiom,
! [C_2: produc124828825on_val,A_1: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_1,B),transi2024712006on_val(R)))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(B,C_2),R))
=> hBOOL(member773094996on_val(produc1441475159on_val(A_1,C_2),transi2024712006on_val(R))) ) ) ).
tff(fact_230_rtrancl__trans,axiom,
! [C_2: produc124828825on_val,A_1: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_1,B),transi2024712006on_val(R)))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(B,C_2),transi2024712006on_val(R)))
=> hBOOL(member773094996on_val(produc1441475159on_val(A_1,C_2),transi2024712006on_val(R))) ) ) ).
tff(fact_231_rtrancl__induct2,axiom,
! [Pa: fun_ex1201926843l_bool,Ax: exp_list_char,Ay: produc12694297on_val,Bx: exp_list_char,By: produc12694297on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(Bx,By)),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay))
=> ( ! [A: exp_list_char,B_1: produc12694297on_val,Aa: exp_list_char,Ba: produc12694297on_val] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(A,B_1)),transi2024712006on_val(R)))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A,B_1),produc1259058957on_val(Aa,Ba)),R))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A),B_1))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By)) ) ) ) ).
tff(fact_232_rtrancl__induct2,axiom,
! [Pa: fun_li823162622l_bool,Ax: list_char,Ay: fun_Pr806764899on_val,Bx: list_char,By: fun_Pr806764899on_val,R: fun_Pr235369833l_bool] :
( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Ax,Ay),produc823076510on_val(Bx,By)),transi61620055on_val(R)))
=> ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Ax),Ay))
=> ( ! [A: list_char,B_1: fun_Pr806764899on_val,Aa: list_char,Ba: fun_Pr806764899on_val] :
( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Ax,Ay),produc823076510on_val(A,B_1)),transi61620055on_val(R)))
=> ( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(A,B_1),produc823076510on_val(Aa,Ba)),R))
=> ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,A),B_1))
=> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Bx),By)) ) ) ) ).
tff(fact_233_rtrancl__induct2,axiom,
! [Pa: fun_Pr633696065l_bool,Ax: produc124828825on_val,Ay: produc124828825on_val,Bx: produc124828825on_val,By: produc124828825on_val,R: fun_Pr903661919l_bool] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(Bx,By)),transi910771962on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay))
=> ( ! [A: produc124828825on_val,B_1: produc124828825on_val,Aa: produc124828825on_val,Ba: produc124828825on_val] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(A,B_1)),transi910771962on_val(R)))
=> ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A,B_1),produc1441475159on_val(Aa,Ba)),R))
=> ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A),B_1))
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By)) ) ) ) ).
tff(fact_234_rtrancl__induct2,axiom,
! [Pa: fun_fu100249073l_bool,Ax: fun_na939144002on_val,Ay: fun_li1432931796on_val,Bx: fun_na939144002on_val,By: fun_li1432931796on_val,R: fun_Pr693020585l_bool] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(Bx,By)),transi921647814on_val(R)))
=> ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay))
=> ( ! [A: fun_na939144002on_val,B_1: fun_li1432931796on_val,Aa: fun_na939144002on_val,Ba: fun_li1432931796on_val] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(A,B_1)),transi921647814on_val(R)))
=> ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A,B_1),produc899768717on_val(Aa,Ba)),R))
=> ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A),B_1))
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By)) ) ) ) ).
tff(fact_235_rtrancl__induct2,axiom,
! [Pa: fun_li826105035r_bool,Ax: list_val,Ay: exp_list_char,Bx: list_val,By: exp_list_char,R: fun_Pr1890037787r_bool] :
( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Ax,Ay),produc1916172923t_char(Bx,By)),transi1789604888t_char(R)))
=> ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Ax),Ay))
=> ( ! [A: list_val,B_1: exp_list_char,Aa: list_val,Ba: exp_list_char] :
( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Ax,Ay),produc1916172923t_char(A,B_1)),transi1789604888t_char(R)))
=> ( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(A,B_1),produc1916172923t_char(Aa,Ba)),R))
=> ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,A),B_1))
=> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Bx),By)) ) ) ) ).
tff(fact_236_rtrancl__induct2,axiom,
! [Pa: fun_li887890578r_bool,Ax: list_ty,Ay: produc662261637t_char,Bx: list_ty,By: produc662261637t_char,R: fun_Pr1728267013r_bool] :
( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Ax,Ay),produc1909267824t_char(Bx,By)),transi1257872013t_char(R)))
=> ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Ax),Ay))
=> ( ! [A: list_ty,B_1: produc662261637t_char,Aa: list_ty,Ba: produc662261637t_char] :
( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Ax,Ay),produc1909267824t_char(A,B_1)),transi1257872013t_char(R)))
=> ( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(A,B_1),produc1909267824t_char(Aa,Ba)),R))
=> ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,A),B_1))
=> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Bx),By)) ) ) ) ).
tff(fact_237_rtrancl__induct2,axiom,
! [Pa: fun_li1024794712r_bool,Ax: list_list_char,Ay: produc220283002t_char,Bx: list_list_char,By: produc220283002t_char,R: fun_Pr1895638121r_bool] :
( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Ax,Ay),produc921874948t_char(Bx,By)),transi122195895t_char(R)))
=> ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Ax),Ay))
=> ( ! [A: list_list_char,B_1: produc220283002t_char,Aa: list_list_char,Ba: produc220283002t_char] :
( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Ax,Ay),produc921874948t_char(A,B_1)),transi122195895t_char(R)))
=> ( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(A,B_1),produc921874948t_char(Aa,Ba)),R))
=> ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,A),B_1))
=> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Aa),Ba)) ) ) )
=> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Bx),By)) ) ) ) ).
tff(fact_238_converse__rtrancl__induct2,axiom,
! [Pa: fun_ex1201926843l_bool,Ax: exp_list_char,Ay: produc12694297on_val,Bx: exp_list_char,By: produc12694297on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(Bx,By)),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By))
=> ( ! [A: exp_list_char,B_1: produc12694297on_val,Aa: exp_list_char,Ba: produc12694297on_val] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A,B_1),produc1259058957on_val(Aa,Ba)),R))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Aa,Ba),produc1259058957on_val(Bx,By)),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A),B_1)) ) ) )
=> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay)) ) ) ) ).
tff(fact_239_converse__rtrancl__induct2,axiom,
! [Pa: fun_li823162622l_bool,Ax: list_char,Ay: fun_Pr806764899on_val,Bx: list_char,By: fun_Pr806764899on_val,R: fun_Pr235369833l_bool] :
( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Ax,Ay),produc823076510on_val(Bx,By)),transi61620055on_val(R)))
=> ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Bx),By))
=> ( ! [A: list_char,B_1: fun_Pr806764899on_val,Aa: list_char,Ba: fun_Pr806764899on_val] :
( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(A,B_1),produc823076510on_val(Aa,Ba)),R))
=> ( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Aa,Ba),produc823076510on_val(Bx,By)),transi61620055on_val(R)))
=> ( hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,A),B_1)) ) ) )
=> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Ax),Ay)) ) ) ) ).
tff(fact_240_converse__rtrancl__induct2,axiom,
! [Pa: fun_Pr633696065l_bool,Ax: produc124828825on_val,Ay: produc124828825on_val,Bx: produc124828825on_val,By: produc124828825on_val,R: fun_Pr903661919l_bool] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(Bx,By)),transi910771962on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By))
=> ( ! [A: produc124828825on_val,B_1: produc124828825on_val,Aa: produc124828825on_val,Ba: produc124828825on_val] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A,B_1),produc1441475159on_val(Aa,Ba)),R))
=> ( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Aa,Ba),produc1441475159on_val(Bx,By)),transi910771962on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A),B_1)) ) ) )
=> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay)) ) ) ) ).
tff(fact_241_converse__rtrancl__induct2,axiom,
! [Pa: fun_fu100249073l_bool,Ax: fun_na939144002on_val,Ay: fun_li1432931796on_val,Bx: fun_na939144002on_val,By: fun_li1432931796on_val,R: fun_Pr693020585l_bool] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(Bx,By)),transi921647814on_val(R)))
=> ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By))
=> ( ! [A: fun_na939144002on_val,B_1: fun_li1432931796on_val,Aa: fun_na939144002on_val,Ba: fun_li1432931796on_val] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A,B_1),produc899768717on_val(Aa,Ba)),R))
=> ( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Aa,Ba),produc899768717on_val(Bx,By)),transi921647814on_val(R)))
=> ( hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A),B_1)) ) ) )
=> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay)) ) ) ) ).
tff(fact_242_converse__rtrancl__induct2,axiom,
! [Pa: fun_li826105035r_bool,Ax: list_val,Ay: exp_list_char,Bx: list_val,By: exp_list_char,R: fun_Pr1890037787r_bool] :
( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Ax,Ay),produc1916172923t_char(Bx,By)),transi1789604888t_char(R)))
=> ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Bx),By))
=> ( ! [A: list_val,B_1: exp_list_char,Aa: list_val,Ba: exp_list_char] :
( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(A,B_1),produc1916172923t_char(Aa,Ba)),R))
=> ( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Aa,Ba),produc1916172923t_char(Bx,By)),transi1789604888t_char(R)))
=> ( hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,A),B_1)) ) ) )
=> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Ax),Ay)) ) ) ) ).
tff(fact_243_converse__rtrancl__induct2,axiom,
! [Pa: fun_li887890578r_bool,Ax: list_ty,Ay: produc662261637t_char,Bx: list_ty,By: produc662261637t_char,R: fun_Pr1728267013r_bool] :
( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Ax,Ay),produc1909267824t_char(Bx,By)),transi1257872013t_char(R)))
=> ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Bx),By))
=> ( ! [A: list_ty,B_1: produc662261637t_char,Aa: list_ty,Ba: produc662261637t_char] :
( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(A,B_1),produc1909267824t_char(Aa,Ba)),R))
=> ( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Aa,Ba),produc1909267824t_char(Bx,By)),transi1257872013t_char(R)))
=> ( hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,A),B_1)) ) ) )
=> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Ax),Ay)) ) ) ) ).
tff(fact_244_converse__rtrancl__induct2,axiom,
! [Pa: fun_li1024794712r_bool,Ax: list_list_char,Ay: produc220283002t_char,Bx: list_list_char,By: produc220283002t_char,R: fun_Pr1895638121r_bool] :
( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Ax,Ay),produc921874948t_char(Bx,By)),transi122195895t_char(R)))
=> ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Bx),By))
=> ( ! [A: list_list_char,B_1: produc220283002t_char,Aa: list_list_char,Ba: produc220283002t_char] :
( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(A,B_1),produc921874948t_char(Aa,Ba)),R))
=> ( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Aa,Ba),produc921874948t_char(Bx,By)),transi122195895t_char(R)))
=> ( hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Aa),Ba))
=> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,A),B_1)) ) ) )
=> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Ax),Ay)) ) ) ) ).
tff(fact_245_converse__rtranclE2,axiom,
! [Xa_1: exp_list_char,Xb: produc12694297on_val,Za: exp_list_char,Zb: produc12694297on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Xa_1,Xb),produc1259058957on_val(Za,Zb)),transi2024712006on_val(R)))
=> ( ( produc1259058957on_val(Xa_1,Xb) != produc1259058957on_val(Za,Zb) )
=> ~ ! [A: exp_list_char,B_1: produc12694297on_val] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Xa_1,Xb),produc1259058957on_val(A,B_1)),R))
=> ~ hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A,B_1),produc1259058957on_val(Za,Zb)),transi2024712006on_val(R))) ) ) ) ).
tff(fact_246_converse__rtranclE2,axiom,
! [Xa_1: list_char,Xb: fun_Pr806764899on_val,Za: list_char,Zb: fun_Pr806764899on_val,R: fun_Pr235369833l_bool] :
( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Xa_1,Xb),produc823076510on_val(Za,Zb)),transi61620055on_val(R)))
=> ( ( produc823076510on_val(Xa_1,Xb) != produc823076510on_val(Za,Zb) )
=> ~ ! [A: list_char,B_1: fun_Pr806764899on_val] :
( hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Xa_1,Xb),produc823076510on_val(A,B_1)),R))
=> ~ hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(A,B_1),produc823076510on_val(Za,Zb)),transi61620055on_val(R))) ) ) ) ).
tff(fact_247_converse__rtranclE2,axiom,
! [Xa_1: produc124828825on_val,Xb: produc124828825on_val,Za: produc124828825on_val,Zb: produc124828825on_val,R: fun_Pr903661919l_bool] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Xa_1,Xb),produc1441475159on_val(Za,Zb)),transi910771962on_val(R)))
=> ( ( produc1441475159on_val(Xa_1,Xb) != produc1441475159on_val(Za,Zb) )
=> ~ ! [A: produc124828825on_val,B_1: produc124828825on_val] :
( hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Xa_1,Xb),produc1441475159on_val(A,B_1)),R))
=> ~ hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A,B_1),produc1441475159on_val(Za,Zb)),transi910771962on_val(R))) ) ) ) ).
tff(fact_248_converse__rtranclE2,axiom,
! [Xa_1: fun_na939144002on_val,Xb: fun_li1432931796on_val,Za: fun_na939144002on_val,Zb: fun_li1432931796on_val,R: fun_Pr693020585l_bool] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Xa_1,Xb),produc899768717on_val(Za,Zb)),transi921647814on_val(R)))
=> ( ( produc899768717on_val(Xa_1,Xb) != produc899768717on_val(Za,Zb) )
=> ~ ! [A: fun_na939144002on_val,B_1: fun_li1432931796on_val] :
( hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Xa_1,Xb),produc899768717on_val(A,B_1)),R))
=> ~ hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A,B_1),produc899768717on_val(Za,Zb)),transi921647814on_val(R))) ) ) ) ).
tff(fact_249_converse__rtranclE2,axiom,
! [Xa_1: list_val,Xb: exp_list_char,Za: list_val,Zb: exp_list_char,R: fun_Pr1890037787r_bool] :
( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Xa_1,Xb),produc1916172923t_char(Za,Zb)),transi1789604888t_char(R)))
=> ( ( produc1916172923t_char(Xa_1,Xb) != produc1916172923t_char(Za,Zb) )
=> ~ ! [A: list_val,B_1: exp_list_char] :
( hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Xa_1,Xb),produc1916172923t_char(A,B_1)),R))
=> ~ hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(A,B_1),produc1916172923t_char(Za,Zb)),transi1789604888t_char(R))) ) ) ) ).
tff(fact_250_converse__rtranclE2,axiom,
! [Xa_1: list_ty,Xb: produc662261637t_char,Za: list_ty,Zb: produc662261637t_char,R: fun_Pr1728267013r_bool] :
( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Xa_1,Xb),produc1909267824t_char(Za,Zb)),transi1257872013t_char(R)))
=> ( ( produc1909267824t_char(Xa_1,Xb) != produc1909267824t_char(Za,Zb) )
=> ~ ! [A: list_ty,B_1: produc662261637t_char] :
( hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Xa_1,Xb),produc1909267824t_char(A,B_1)),R))
=> ~ hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(A,B_1),produc1909267824t_char(Za,Zb)),transi1257872013t_char(R))) ) ) ) ).
tff(fact_251_converse__rtranclE2,axiom,
! [Xa_1: list_list_char,Xb: produc220283002t_char,Za: list_list_char,Zb: produc220283002t_char,R: fun_Pr1895638121r_bool] :
( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Xa_1,Xb),produc921874948t_char(Za,Zb)),transi122195895t_char(R)))
=> ( ( produc921874948t_char(Xa_1,Xb) != produc921874948t_char(Za,Zb) )
=> ~ ! [A: list_list_char,B_1: produc220283002t_char] :
( hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Xa_1,Xb),produc921874948t_char(A,B_1)),R))
=> ~ hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(A,B_1),produc921874948t_char(Za,Zb)),transi122195895t_char(R))) ) ) ) ).
tff(fact_252_rtranclE,axiom,
! [A_1: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_1,B),transi2024712006on_val(R)))
=> ( ( A_1 != B )
=> ~ ! [Y_1: produc124828825on_val] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_1,Y_1),transi2024712006on_val(R)))
=> ~ hBOOL(member773094996on_val(produc1441475159on_val(Y_1,B),R)) ) ) ) ).
tff(fact_253_converse__rtranclE,axiom,
! [X_1: produc124828825on_val,Z_1: produc124828825on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(X_1,Z_1),transi2024712006on_val(R)))
=> ( ( X_1 != Z_1 )
=> ~ ! [Y_1: produc124828825on_val] :
( hBOOL(member773094996on_val(produc1441475159on_val(X_1,Y_1),R))
=> ~ hBOOL(member773094996on_val(produc1441475159on_val(Y_1,Z_1),transi2024712006on_val(R))) ) ) ) ).
tff(fact_254_converse__rtrancl__induct,axiom,
! [Pa: fun_Pr680585871l_bool,A_1: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_1,B),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(Pa,B))
=> ( ! [Y_1: produc124828825on_val,Z: produc124828825on_val] :
( hBOOL(member773094996on_val(produc1441475159on_val(Y_1,Z),R))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(Z,B),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(Pa,Z))
=> hBOOL(hAPP_P1708370145l_bool(Pa,Y_1)) ) ) )
=> hBOOL(hAPP_P1708370145l_bool(Pa,A_1)) ) ) ) ).
tff(fact_255_rtrancl__induct,axiom,
! [Pa: fun_Pr680585871l_bool,A_1: produc124828825on_val,B: produc124828825on_val,R: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_1,B),transi2024712006on_val(R)))
=> ( hBOOL(hAPP_P1708370145l_bool(Pa,A_1))
=> ( ! [Y_1: produc124828825on_val,Z: produc124828825on_val] :
( hBOOL(member773094996on_val(produc1441475159on_val(A_1,Y_1),transi2024712006on_val(R)))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(Y_1,Z),R))
=> ( hBOOL(hAPP_P1708370145l_bool(Pa,Y_1))
=> hBOOL(hAPP_P1708370145l_bool(Pa,Z)) ) ) )
=> hBOOL(hAPP_P1708370145l_bool(Pa,B)) ) ) ) ).
tff(fact_256_red__preserves__lconf,axiom,
! [E_1: fun_li688206603ion_ty,Ta: ty,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,L_1)),produc1259058957on_val(E,produc899768717on_val(H,L))),red(Pa)))
=> ( hBOOL(wTrt(Pa,Ha,E_1,Ea,Ta))
=> ( hBOOL(lconf_496643946t_char(Pa,Ha,L_1,E_1))
=> hBOOL(lconf_496643946t_char(Pa,H,L,E_1)) ) ) ) ).
tff(fact_257_blocksRedsFinal,axiom,
! [L_2: fun_li1432931796on_val,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char,Vsa_1: list_val,Vsa: list_list_char,Tsa: list_ty] :
( ( size_s2113983095t_char(Vsa) = size_size_list_ty(Tsa) )
=> ( ( size_size_list_val(Vsa_1) = size_size_list_ty(Tsa) )
=> ( hBOOL(distinct_list_char(Vsa))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,map_up1085636310ar_val(L_1,Vsa,Vsa_1))),produc1259058957on_val(E,produc899768717on_val(H,L))),transi2024712006on_val(red(Pa))))
=> ( hBOOL(final_list_char(E))
=> ( ( L_2 = overri2012515291on_val(L,L_1,set_list_char(Vsa)) )
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(blocks(produc921874948t_char(Vsa,produc1909267824t_char(Tsa,produc1916172923t_char(Vsa_1,Ea)))),produc899768717on_val(Ha,L_1)),produc1259058957on_val(E,produc899768717on_val(H,L_2))),transi2024712006on_val(red(Pa)))) ) ) ) ) ) ) ).
tff(fact_258_map__eq__conv,axiom,
! [F: fun_list_char_val,Xs: list_list_char,G: fun_list_char_val] :
( ( hAPP_l1892737211st_val(map_list_char_val(F),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Xs) )
<=> ! [X_2: list_char] :
( hBOOL(member_list_char(X_2,set_list_char(Xs)))
=> ( hAPP_list_char_val(F,X_2) = hAPP_list_char_val(G,X_2) ) ) ) ).
tff(fact_259_map__eq__conv,axiom,
! [F: fun_va223928858t_char,Xs: list_val,G: fun_va223928858t_char] :
( ( hAPP_l732421366t_char(map_va1934808527t_char(F),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Xs) )
<=> ! [X_2: val] :
( hBOOL(member_val(X_2,set_val(Xs)))
=> ( hAPP_v834067052t_char(F,X_2) = hAPP_v834067052t_char(G,X_2) ) ) ) ).
tff(fact_260_map__eq__conv,axiom,
! [F: fun_ty_option_ty,Xs: list_ty,G: fun_ty_option_ty] :
( ( hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Xs) )
<=> ! [X_2: ty] :
( hBOOL(member_ty(X_2,set_ty(Xs)))
=> ( hAPP_ty_option_ty(F,X_2) = hAPP_ty_option_ty(G,X_2) ) ) ) ).
tff(fact_261_map__eq__conv,axiom,
! [F: fun_val_option_ty,Xs: list_val,G: fun_val_option_ty] :
( ( hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Xs) )
<=> ! [X_2: val] :
( hBOOL(member_val(X_2,set_val(Xs)))
=> ( hAPP_val_option_ty(F,X_2) = hAPP_val_option_ty(G,X_2) ) ) ) ).
tff(fact_262_mem__def,axiom,
! [X_1: produc1102272487on_val,A_2: fun_Pr691271849l_bool] :
( hBOOL(member773094996on_val(X_1,A_2))
<=> hBOOL(hAPP_P282169671l_bool(A_2,X_1)) ) ).
tff(fact_263_lconf__hext,axiom,
! [H: fun_na939144002on_val,Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E_1: fun_li688206603ion_ty] :
( hBOOL(lconf_496643946t_char(Pa,Ha,L_1,E_1))
=> ( hBOOL(hext(Ha,H))
=> hBOOL(lconf_496643946t_char(Pa,H,L_1,E_1)) ) ) ).
tff(fact_264_lconf__def,axiom,
! [Pa: list_P1999446415t_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E_1: fun_li688206603ion_ty] :
( hBOOL(lconf_496643946t_char(Pa,Ha,L_1,E_1))
<=> ! [V_3: list_char,V_2: val] :
( ( hAPP_l207779698on_val(L_1,V_3) = hAPP_val_option_val(some_val,V_2) )
=> ? [T: ty] :
( ( hAPP_l512744617ion_ty(E_1,V_3) = hAPP_ty_option_ty(some_ty,T) )
& hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_2),T)) ) ) ) ).
tff(fact_265_blocksReds,axiom,
! [Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char,Vsa_1: list_val,Vsa: list_list_char,Tsa: list_ty] :
( ( size_s2113983095t_char(Vsa) = size_size_list_ty(Tsa) )
=> ( ( size_size_list_val(Vsa_1) = size_size_list_ty(Tsa) )
=> ( hBOOL(distinct_list_char(Vsa))
=> ( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,map_up1085636310ar_val(L_1,Vsa,Vsa_1))),produc1259058957on_val(E,produc899768717on_val(H,L))),transi2024712006on_val(red(Pa))))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(blocks(produc921874948t_char(Vsa,produc1909267824t_char(Tsa,produc1916172923t_char(Vsa_1,Ea)))),produc899768717on_val(Ha,L_1)),produc1259058957on_val(blocks(produc921874948t_char(Vsa,produc1909267824t_char(Tsa,produc1916172923t_char(hAPP_l1892737211st_val(map_list_char_val(comp_o1129292306t_char(the_val,L)),Vsa),E)))),produc899768717on_val(H,overri2012515291on_val(L,L_1,set_list_char(Vsa))))),transi2024712006on_val(red(Pa)))) ) ) ) ) ).
tff(fact_266_List_Omap_Ocomp,axiom,
! [F: fun_option_val_val,G: fun_li1432931796on_val] : comp_l1825390573t_char(map_option_val_val(F),map_li50976719on_val(G)) = map_list_char_val(comp_o1129292306t_char(F,G)) ).
tff(fact_267_map__comp__map,axiom,
! [F: fun_option_val_val,G: fun_li1432931796on_val] : comp_l1825390573t_char(map_option_val_val(F),map_li50976719on_val(G)) = map_list_char_val(comp_o1129292306t_char(F,G)) ).
tff(fact_268_map__map,axiom,
! [F: fun_option_val_val,G: fun_li1432931796on_val,Xs: list_list_char] : hAPP_l228474410st_val(map_option_val_val(F),hAPP_l297961988on_val(map_li50976719on_val(G),Xs)) = hAPP_l1892737211st_val(map_list_char_val(comp_o1129292306t_char(F,G)),Xs) ).
tff(fact_269_List_Omap_Ocompositionality,axiom,
! [F: fun_option_val_val,G: fun_li1432931796on_val,List: list_list_char] : hAPP_l228474410st_val(map_option_val_val(F),hAPP_l297961988on_val(map_li50976719on_val(G),List)) = hAPP_l1892737211st_val(map_list_char_val(comp_o1129292306t_char(F,G)),List) ).
tff(fact_270_the_Osimps,axiom,
! [X_3: val] : hAPP_option_val_val(the_val,hAPP_val_option_val(some_val,X_3)) = X_3 ).
tff(fact_271_the_Osimps,axiom,
! [X_1: produc639455274on_val] : hAPP_o1977518472on_val(the_Pr431167171on_val,hAPP_P1510515380on_val(some_P948696889on_val,X_1)) = X_1 ).
tff(fact_272_the_Osimps,axiom,
! [X_3: ty] : hAPP_option_ty_ty(the_ty,hAPP_ty_option_ty(some_ty,X_3)) = X_3 ).
tff(fact_273_ex__map__conv,axiom,
! [Ys: list_val,F: fun_list_char_val] :
( ? [Xs_1: list_list_char] : Ys = hAPP_l1892737211st_val(map_list_char_val(F),Xs_1)
<=> ! [X_2: val] :
( hBOOL(member_val(X_2,set_val(Ys)))
=> ? [Xa: list_char] : X_2 = hAPP_list_char_val(F,Xa) ) ) ).
tff(fact_274_ex__map__conv,axiom,
! [Ys: list_exp_list_char,F: fun_va223928858t_char] :
( ? [Xs_1: list_val] : Ys = hAPP_l732421366t_char(map_va1934808527t_char(F),Xs_1)
<=> ! [X_2: exp_list_char] :
( hBOOL(member_exp_list_char(X_2,set_exp_list_char(Ys)))
=> ? [Xa: val] : X_2 = hAPP_v834067052t_char(F,Xa) ) ) ).
tff(fact_275_ex__map__conv,axiom,
! [Ys: list_option_ty,F: fun_ty_option_ty] :
( ? [Xs_1: list_ty] : Ys = hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs_1)
<=> ! [X_2: option_ty] :
( hBOOL(member_option_ty(X_2,set_option_ty(Ys)))
=> ? [Xa: ty] : X_2 = hAPP_ty_option_ty(F,Xa) ) ) ).
tff(fact_276_ex__map__conv,axiom,
! [Ys: list_option_ty,F: fun_val_option_ty] :
( ? [Xs_1: list_val] : Ys = hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs_1)
<=> ! [X_2: option_ty] :
( hBOOL(member_option_ty(X_2,set_option_ty(Ys)))
=> ? [Xa: val] : X_2 = hAPP_val_option_ty(F,Xa) ) ) ).
tff(fact_277_map__ext,axiom,
! [F: fun_list_char_val,G: fun_list_char_val,Xs: list_list_char] :
( ! [X_2: list_char] :
( hBOOL(member_list_char(X_2,set_list_char(Xs)))
=> ( hAPP_list_char_val(F,X_2) = hAPP_list_char_val(G,X_2) ) )
=> ( hAPP_l1892737211st_val(map_list_char_val(F),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Xs) ) ) ).
tff(fact_278_map__ext,axiom,
! [F: fun_va223928858t_char,G: fun_va223928858t_char,Xs: list_val] :
( ! [X_2: val] :
( hBOOL(member_val(X_2,set_val(Xs)))
=> ( hAPP_v834067052t_char(F,X_2) = hAPP_v834067052t_char(G,X_2) ) )
=> ( hAPP_l732421366t_char(map_va1934808527t_char(F),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Xs) ) ) ).
tff(fact_279_map__ext,axiom,
! [F: fun_ty_option_ty,G: fun_ty_option_ty,Xs: list_ty] :
( ! [X_2: ty] :
( hBOOL(member_ty(X_2,set_ty(Xs)))
=> ( hAPP_ty_option_ty(F,X_2) = hAPP_ty_option_ty(G,X_2) ) )
=> ( hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Xs) ) ) ).
tff(fact_280_map__ext,axiom,
! [F: fun_val_option_ty,G: fun_val_option_ty,Xs: list_val] :
( ! [X_2: val] :
( hBOOL(member_val(X_2,set_val(Xs)))
=> ( hAPP_val_option_ty(F,X_2) = hAPP_val_option_ty(G,X_2) ) )
=> ( hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Xs) ) ) ).
tff(fact_281_map__cong,axiom,
! [F: fun_list_char_val,G: fun_list_char_val,Xs: list_list_char,Ys: list_list_char] :
( ( Xs = Ys )
=> ( ! [X_2: list_char] :
( hBOOL(member_list_char(X_2,set_list_char(Ys)))
=> ( hAPP_list_char_val(F,X_2) = hAPP_list_char_val(G,X_2) ) )
=> ( hAPP_l1892737211st_val(map_list_char_val(F),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Ys) ) ) ) ).
tff(fact_282_map__cong,axiom,
! [F: fun_va223928858t_char,G: fun_va223928858t_char,Xs: list_val,Ys: list_val] :
( ( Xs = Ys )
=> ( ! [X_2: val] :
( hBOOL(member_val(X_2,set_val(Ys)))
=> ( hAPP_v834067052t_char(F,X_2) = hAPP_v834067052t_char(G,X_2) ) )
=> ( hAPP_l732421366t_char(map_va1934808527t_char(F),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Ys) ) ) ) ).
tff(fact_283_map__cong,axiom,
! [F: fun_ty_option_ty,G: fun_ty_option_ty,Xs: list_ty,Ys: list_ty] :
( ( Xs = Ys )
=> ( ! [X_2: ty] :
( hBOOL(member_ty(X_2,set_ty(Ys)))
=> ( hAPP_ty_option_ty(F,X_2) = hAPP_ty_option_ty(G,X_2) ) )
=> ( hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys) ) ) ) ).
tff(fact_284_map__cong,axiom,
! [F: fun_val_option_ty,G: fun_val_option_ty,Xs: list_val,Ys: list_val] :
( ( Xs = Ys )
=> ( ! [X_2: val] :
( hBOOL(member_val(X_2,set_val(Ys)))
=> ( hAPP_val_option_ty(F,X_2) = hAPP_val_option_ty(G,X_2) ) )
=> ( hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys) ) ) ) ).
tff(fact_285_map__idI,axiom,
! [F: fun_li1751394789t_char,Xs: list_list_char] :
( ! [X_2: list_char] :
( hBOOL(member_list_char(X_2,set_list_char(Xs)))
=> ( hAPP_l1074208899t_char(F,X_2) = X_2 ) )
=> ( hAPP_l407174677t_char(map_li1333403488t_char(F),Xs) = Xs ) ) ).
tff(fact_286_map__idI,axiom,
! [F: fun_Pr12181427on_val,Xs: list_P1439941640on_val] :
( ! [X_2: produc1102272487on_val] :
( hBOOL(member773094996on_val(X_2,set_Pr1921835862on_val(Xs)))
=> ( hAPP_P918220497on_val(F,X_2) = X_2 ) )
=> ( hAPP_l1695428693on_val(map_Pr1655409582on_val(F),Xs) = Xs ) ) ).
tff(fact_287_map__upds__apply__nontin,axiom,
! [F: fun_li1432931796on_val,Ys: list_val,X_1: list_char,Xs: list_list_char] :
( ~ hBOOL(member_list_char(X_1,set_list_char(Xs)))
=> ( hAPP_l207779698on_val(map_up1085636310ar_val(F,Xs,Ys),X_1) = hAPP_l207779698on_val(F,X_1) ) ) ).
tff(fact_288_map__upds__apply__nontin,axiom,
! [F: fun_li688206603ion_ty,Ys: list_ty,X_1: list_char,Xs: list_list_char] :
( ~ hBOOL(member_list_char(X_1,set_list_char(Xs)))
=> ( hAPP_l512744617ion_ty(map_up891053837har_ty(F,Xs,Ys),X_1) = hAPP_l512744617ion_ty(F,X_1) ) ) ).
tff(fact_289_Red__lcl__add,axiom,
! [L_0: fun_li1432931796on_val,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,L_1)),produc1259058957on_val(E,produc899768717on_val(H,L))),transi2024712006on_val(red(Pa))))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,map_ad325961431ar_val(L_0,L_1))),produc1259058957on_val(E,produc899768717on_val(H,map_ad325961431ar_val(L_0,L)))),transi2024712006on_val(red(Pa)))) ) ).
tff(fact_290_map__add__find__right,axiom,
! [M: fun_li1432931796on_val,N: fun_li1432931796on_val,K: list_char,Xx: val] :
( ( hAPP_l207779698on_val(N,K) = hAPP_val_option_val(some_val,Xx) )
=> ( hAPP_l207779698on_val(map_ad325961431ar_val(M,N),K) = hAPP_val_option_val(some_val,Xx) ) ) ).
tff(fact_291_map__add__assoc,axiom,
! [M1: fun_li1432931796on_val,M2: fun_li1432931796on_val,M3: fun_li1432931796on_val] : map_ad325961431ar_val(M1,map_ad325961431ar_val(M2,M3)) = map_ad325961431ar_val(map_ad325961431ar_val(M1,M2),M3) ).
tff(fact_292_map__add__upds,axiom,
! [M1: fun_li1432931796on_val,M2: fun_li1432931796on_val,Xs: list_list_char,Ys: list_val] : map_ad325961431ar_val(M1,map_up1085636310ar_val(M2,Xs,Ys)) = map_up1085636310ar_val(map_ad325961431ar_val(M1,M2),Xs,Ys) ).
tff(fact_293_map__add__upds,axiom,
! [M1: fun_li688206603ion_ty,M2: fun_li688206603ion_ty,Xs: list_list_char,Ys: list_ty] : map_add_list_char_ty(M1,map_up891053837har_ty(M2,Xs,Ys)) = map_up891053837har_ty(map_add_list_char_ty(M1,M2),Xs,Ys) ).
tff(fact_294_red__lcl__add,axiom,
! [L_0: fun_li1432931796on_val,Ea: exp_list_char,Ha: fun_na939144002on_val,L_1: fun_li1432931796on_val,E: exp_list_char,H: fun_na939144002on_val,L: fun_li1432931796on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,L_1)),produc1259058957on_val(E,produc899768717on_val(H,L))),red(Pa)))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,map_ad325961431ar_val(L_0,L_1))),produc1259058957on_val(E,produc899768717on_val(H,map_ad325961431ar_val(L_0,L)))),red(Pa))) ) ).
tff(fact_295_hext__def,axiom,
! [Ha: fun_na939144002on_val,H: fun_na939144002on_val] :
( hBOOL(hext(Ha,H))
<=> ! [A: nat,C_1: list_char,Fs: fun_Pr806764899on_val] :
( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C_1,Fs)) )
=> ? [Fs_1: fun_Pr806764899on_val] : hAPP_n546249108on_val(H,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C_1,Fs_1)) ) ) ).
tff(fact_296_hext__objD,axiom,
! [A_1: nat,C: list_char,Fs_2: fun_Pr806764899on_val,Ha: fun_na939144002on_val,H: fun_na939144002on_val] :
( hBOOL(hext(Ha,H))
=> ( ( hAPP_n546249108on_val(Ha,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs_2)) )
=> ? [Fs_1: fun_Pr806764899on_val] : hAPP_n546249108on_val(H,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs_1)) ) ) ).
tff(fact_297_hextI,axiom,
! [H: fun_na939144002on_val,Ha: fun_na939144002on_val] :
( ! [A: nat,C_1: list_char,Fs: fun_Pr806764899on_val] :
( ( hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C_1,Fs)) )
=> ? [Fs_1: fun_Pr806764899on_val] : hAPP_n546249108on_val(H,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C_1,Fs_1)) )
=> hBOOL(hext(Ha,H)) ) ).
tff(fact_298_TryRedsVal,axiom,
! [C: list_char,V: list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,V_1: val,S: produc12694297on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),S)),transi2024712006on_val(red(Pa))))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(hAPP_e1353749905t_char(tryCatch_list_char(Ea,C,V),E_2),S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),S)),transi2024712006on_val(red(Pa)))) ) ).
tff(fact_299_red__reds_OTryRed,axiom,
! [C: list_char,V: list_char,E_2: exp_list_char,Ea: exp_list_char,S_1: produc12694297on_val,E: exp_list_char,S: produc12694297on_val,Pa: list_P1999446415t_char] :
( hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E,S)),red(Pa)))
=> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(hAPP_e1353749905t_char(tryCatch_list_char(Ea,C,V),E_2),S_1),produc1259058957on_val(hAPP_e1353749905t_char(tryCatch_list_char(E,C,V),E_2),S)),red(Pa))) ) ).
%----Helper facts (2)
tff(help_fequal_1_1_fequal_000tc__Type__Oty_T,axiom,
! [X: ty,Y: ty] :
( ~ hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(fequal_ty,X),Y))
| ( X = Y ) ) ).
tff(help_fequal_2_1_fequal_000tc__Type__Oty_T,axiom,
! [X: ty,Y: ty] :
( ( X != Y )
| hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(fequal_ty,X),Y)) ) ).
%----Conjectures (3)
tff(conj_0,hypothesis,
size_s2113983095t_char(vs_1) = size_size_list_ty(ts) ).
tff(conj_1,hypothesis,
size_size_list_val(vs) = size_size_list_ty(ts) ).
tff(conj_2,conjecture,
( hBOOL(wTrt(p,h,e_1,blocks(produc921874948t_char(vs_1,produc1909267824t_char(ts,produc1916172923t_char(vs,e)))),t))
<=> ( hBOOL(wTrt(p,h,map_up891053837har_ty(e_1,vs_1,ts),e,t))
& ? [Ts: list_ty] :
( ( hAPP_l2006940821ion_ty(map_val_option_ty(typeof_h(h)),vs) = hAPP_l1487035934ion_ty(map_ty_option_ty(some_ty),Ts) )
& hBOOL(list_all2_ty_ty(widen_2090681816t_char(p),Ts,ts)) ) ) ) ).
%------------------------------------------------------------------------------