%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP196^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:56:20 AM UTC 2026
% Result : Theorem 3.14s 1.71s
% Output : Refutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 12 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 32 ( 15 ~; 2 |; 0 &; 12 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 28 ( 27 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 157 ( 154 usr; 13 con; 0-3 aty)
% Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_list_poly_real: $tType ).
thf(type_def_6,type,
poly_real: $tType ).
thf(type_def_8,type,
list_poly_real: $tType ).
thf(type_def_9,type,
set_poly_real: $tType ).
thf(type_def_10,type,
nat: $tType ).
thf(type_def_11,type,
list_list_poly_real: $tType ).
thf(type_def_12,type,
list_P736648811y_real: $tType ).
thf(type_def_13,type,
list_P693436111y_real: $tType ).
thf(type_def_14,type,
produc321349221y_real: $tType ).
thf(type_def_15,type,
produc461822025y_real: $tType ).
thf(type_def_16,type,
list_P1001591419y_real: $tType ).
thf(type_def_17,type,
list_P991700890y_real: $tType ).
thf(type_def_18,type,
list_P657095678y_real: $tType ).
thf(type_def_19,type,
set_Pr483210409y_real: $tType ).
thf(type_def_20,type,
set_Pr1405268809y_real: $tType ).
thf(type_def_21,type,
list_l1245274212y_real: $tType ).
thf(type_def_22,type,
list_l6097393y_real: $tType ).
thf(type_def_23,type,
list_l343759061y_real: $tType ).
thf(type_def_24,type,
list_nat: $tType ).
thf(type_def_25,type,
option1330723604y_real: $tType ).
thf(type_def_26,type,
option_poly_real: $tType ).
thf(type_def_27,type,
option988260395y_real: $tType ).
thf(type_def_28,type,
option293660815y_real: $tType ).
thf(type_def_29,type,
produc1456530199y_real: $tType ).
thf(type_def_30,type,
produc1060019729y_real: $tType ).
thf(type_def_31,type,
produc1426596841y_real: $tType ).
thf(type_def_32,type,
produc796638169y_real: $tType ).
thf(func_def_0,type,
produc1456530199y_real: $tType ).
thf(func_def_1,type,
produc1060019729y_real: $tType ).
thf(func_def_2,type,
list_P657095678y_real: $tType ).
thf(func_def_3,type,
set_Pr1405268809y_real: $tType ).
thf(func_def_4,type,
produc1426596841y_real: $tType ).
thf(func_def_5,type,
list_l343759061y_real: $tType ).
thf(func_def_6,type,
list_P991700890y_real: $tType ).
thf(func_def_7,type,
option293660815y_real: $tType ).
thf(func_def_8,type,
produc796638169y_real: $tType ).
thf(func_def_9,type,
list_P693436111y_real: $tType ).
thf(func_def_10,type,
set_Pr483210409y_real: $tType ).
thf(func_def_11,type,
list_P1001591419y_real: $tType ).
thf(func_def_12,type,
list_l6097393y_real: $tType ).
thf(func_def_13,type,
produc461822025y_real: $tType ).
thf(func_def_14,type,
option988260395y_real: $tType ).
thf(func_def_15,type,
list_P736648811y_real: $tType ).
thf(func_def_16,type,
list_l1245274212y_real: $tType ).
thf(func_def_17,type,
produc321349221y_real: $tType ).
thf(func_def_18,type,
option1330723604y_real: $tType ).
thf(func_def_19,type,
list_list_poly_real: $tType ).
thf(func_def_20,type,
set_list_poly_real: $tType ).
thf(func_def_21,type,
option_poly_real: $tType ).
thf(func_def_22,type,
list_poly_real: $tType ).
thf(func_def_23,type,
set_poly_real: $tType ).
thf(func_def_24,type,
poly_real: $tType ).
thf(func_def_25,type,
list_nat: $tType ).
thf(func_def_26,type,
nat: $tType ).
thf(func_def_27,type,
bNF_Gr851617109y_real: set_list_poly_real > poly_real > set_list_poly_real ).
thf(func_def_28,type,
bNF_Gr1644259033y_real: set_list_poly_real > list_poly_real > set_poly_real ).
thf(func_def_29,type,
times_times_nat: nat > nat > nat ).
thf(func_def_30,type,
append527544425y_real: list_list_poly_real > list_list_poly_real > list_list_poly_real ).
thf(func_def_31,type,
append_poly_real: list_poly_real > list_poly_real > list_poly_real ).
thf(func_def_32,type,
bind_l1810664209y_real: list_list_poly_real > ( list_poly_real > list_list_poly_real ) > list_list_poly_real ).
thf(func_def_33,type,
bind_l146959617y_real: list_list_poly_real > ( list_poly_real > list_poly_real ) > list_poly_real ).
thf(func_def_34,type,
bind_l429098840y_real: list_list_poly_real > ( list_poly_real > list_P736648811y_real ) > list_P736648811y_real ).
thf(func_def_35,type,
bind_p1226679937y_real: list_poly_real > ( poly_real > list_list_poly_real ) > list_list_poly_real ).
thf(func_def_36,type,
bind_p420216945y_real: list_poly_real > ( poly_real > list_poly_real ) > list_poly_real ).
thf(func_def_37,type,
bind_p600434664y_real: list_poly_real > ( poly_real > list_P736648811y_real ) > list_P736648811y_real ).
thf(func_def_38,type,
bind_p988182092y_real: list_poly_real > ( poly_real > list_P693436111y_real ) > list_P693436111y_real ).
thf(func_def_39,type,
bind_P1861132770y_real: list_P736648811y_real > ( produc321349221y_real > list_list_poly_real ) > list_list_poly_real ).
thf(func_def_40,type,
bind_P755425362y_real: list_P736648811y_real > ( produc321349221y_real > list_poly_real ) > list_poly_real ).
thf(func_def_41,type,
bind_P120560694y_real: list_P693436111y_real > ( produc461822025y_real > list_poly_real ) > list_poly_real ).
thf(func_def_42,type,
butlast_poly_real: list_poly_real > list_poly_real ).
thf(func_def_43,type,
concat_poly_real: list_list_poly_real > list_poly_real ).
thf(func_def_44,type,
enumer1433313439y_real: nat > list_list_poly_real > list_P1001591419y_real ).
thf(func_def_45,type,
enumerate_poly_real: nat > list_poly_real > list_P736648811y_real ).
thf(func_def_46,type,
enumer1123002698y_real: nat > list_P736648811y_real > list_P991700890y_real ).
thf(func_def_47,type,
enumer1015405230y_real: nat > list_P693436111y_real > list_P657095678y_real ).
thf(func_def_48,type,
foldr_2117681201y_real: ( list_poly_real > list_poly_real > list_poly_real ) > list_list_poly_real > list_poly_real > list_poly_real ).
thf(func_def_49,type,
gen_le1160603377y_real: nat > list_list_poly_real > nat ).
thf(func_def_50,type,
gen_length_poly_real: nat > list_poly_real > nat ).
thf(func_def_51,type,
gen_le904455032y_real: nat > list_P736648811y_real > nat ).
thf(func_def_52,type,
gen_le1524582876y_real: nat > list_P693436111y_real > nat ).
thf(func_def_53,type,
insert_poly_real: poly_real > list_poly_real > list_poly_real ).
thf(func_def_54,type,
last_poly_real: list_poly_real > poly_real ).
thf(func_def_55,type,
last_P21901160y_real: list_P693436111y_real > produc461822025y_real ).
thf(func_def_56,type,
lenlex_poly_real: set_Pr483210409y_real > set_Pr1405268809y_real ).
thf(func_def_57,type,
lex_poly_real: set_Pr483210409y_real > set_Pr1405268809y_real ).
thf(func_def_58,type,
lexord_poly_real: set_Pr483210409y_real > set_Pr1405268809y_real ).
thf(func_def_59,type,
cons_l2022919326y_real: list_list_poly_real > list_l1245274212y_real > list_l1245274212y_real ).
thf(func_def_60,type,
cons_list_poly_real: list_poly_real > list_list_poly_real > list_list_poly_real ).
thf(func_def_61,type,
cons_l730969377y_real: list_P736648811y_real > list_l6097393y_real > list_l6097393y_real ).
thf(func_def_62,type,
cons_l677353093y_real: list_P693436111y_real > list_l343759061y_real > list_l343759061y_real ).
thf(func_def_63,type,
cons_poly_real: poly_real > list_poly_real > list_poly_real ).
thf(func_def_64,type,
cons_P1027346459y_real: produc321349221y_real > list_P736648811y_real > list_P736648811y_real ).
thf(func_def_65,type,
cons_P1129399039y_real: produc461822025y_real > list_P693436111y_real > list_P693436111y_real ).
thf(func_def_66,type,
nil_li2088348750y_real: list_l1245274212y_real ).
thf(func_def_67,type,
nil_list_poly_real: list_list_poly_real ).
thf(func_def_68,type,
nil_li579690865y_real: list_l6097393y_real ).
thf(func_def_69,type,
nil_li1299462869y_real: list_l343759061y_real ).
thf(func_def_70,type,
nil_nat: list_nat ).
thf(func_def_71,type,
nil_poly_real: list_poly_real ).
thf(func_def_72,type,
nil_Pr1161137915y_real: list_P1001591419y_real ).
thf(func_def_73,type,
nil_Pr1492526187y_real: list_P736648811y_real ).
thf(func_def_74,type,
nil_Pr570652676y_real: list_P991700890y_real ).
thf(func_def_75,type,
nil_Pr2056488424y_real: list_P657095678y_real ).
thf(func_def_76,type,
nil_Pr1207979855y_real: list_P693436111y_real ).
thf(func_def_77,type,
map_po2132607150y_real: ( poly_real > poly_real ) > list_poly_real > list_poly_real ).
thf(func_def_78,type,
list_e367462459y_real: ( list_poly_real > $o ) > list_list_poly_real > $o ).
thf(func_def_79,type,
list_ex1_poly_real: ( poly_real > $o ) > list_poly_real > $o ).
thf(func_def_80,type,
list_e1892536494y_real: ( produc321349221y_real > $o ) > list_P736648811y_real > $o ).
thf(func_def_81,type,
list_e1507538962y_real: ( produc461822025y_real > $o ) > list_P693436111y_real > $o ).
thf(func_def_82,type,
list_e809719936y_real: ( list_poly_real > $o ) > list_list_poly_real > $o ).
thf(func_def_83,type,
list_ex_poly_real: ( poly_real > $o ) > list_poly_real > $o ).
thf(func_def_84,type,
list_e2093379497y_real: ( produc321349221y_real > $o ) > list_P736648811y_real > $o ).
thf(func_def_85,type,
list_e1312221069y_real: ( produc461822025y_real > $o ) > list_P693436111y_real > $o ).
thf(func_def_86,type,
listrel1_poly_real: set_Pr483210409y_real > set_Pr1405268809y_real ).
thf(func_def_87,type,
listre572247515y_real: set_Pr483210409y_real > set_Pr1405268809y_real ).
thf(func_def_88,type,
listre1763068361y_real: ( list_poly_real > list_poly_real > $o ) > list_list_poly_real > list_list_poly_real > $o ).
thf(func_def_89,type,
listre713353145y_real: ( list_poly_real > poly_real > $o ) > list_list_poly_real > list_poly_real > $o ).
thf(func_def_90,type,
listre1037026976y_real: ( list_poly_real > produc321349221y_real > $o ) > list_list_poly_real > list_P736648811y_real > $o ).
thf(func_def_91,type,
listre1793073465y_real: ( poly_real > list_poly_real > $o ) > list_poly_real > list_list_poly_real > $o ).
thf(func_def_92,type,
listre1609905961y_real: ( poly_real > poly_real > $o ) > list_poly_real > list_poly_real > $o ).
thf(func_def_93,type,
listre889482032y_real: ( poly_real > produc321349221y_real > $o ) > list_poly_real > list_P736648811y_real > $o ).
thf(func_def_94,type,
listre471999892y_real: ( poly_real > produc461822025y_real > $o ) > list_poly_real > list_P693436111y_real > $o ).
thf(func_def_95,type,
listre321577258y_real: ( produc321349221y_real > list_poly_real > $o ) > list_P736648811y_real > list_list_poly_real > $o ).
thf(func_def_96,type,
listre1044472730y_real: ( produc321349221y_real > poly_real > $o ) > list_P736648811y_real > list_poly_real > $o ).
thf(func_def_97,type,
listre1751862142y_real: ( produc461822025y_real > poly_real > $o ) > list_P693436111y_real > list_poly_real > $o ).
thf(func_def_98,type,
map_fi357666132y_real: ( list_poly_real > option1330723604y_real ) > list_list_poly_real > list_list_poly_real ).
thf(func_def_99,type,
map_fi1988340932y_real: ( list_poly_real > option_poly_real ) > list_list_poly_real > list_poly_real ).
thf(func_def_100,type,
map_fi2104453077y_real: ( list_poly_real > option988260395y_real ) > list_list_poly_real > list_P736648811y_real ).
thf(func_def_101,type,
map_fi920577604y_real: ( poly_real > option1330723604y_real ) > list_poly_real > list_list_poly_real ).
thf(func_def_102,type,
map_fi1183202740y_real: ( poly_real > option_poly_real ) > list_poly_real > list_poly_real ).
thf(func_def_103,type,
map_fi740944613y_real: ( poly_real > option988260395y_real ) > list_poly_real > list_P736648811y_real ).
thf(func_def_104,type,
map_fi1117002953y_real: ( poly_real > option293660815y_real ) > list_poly_real > list_P693436111y_real ).
thf(func_def_105,type,
map_fi1389003359y_real: ( produc321349221y_real > option1330723604y_real ) > list_P736648811y_real > list_list_poly_real ).
thf(func_def_106,type,
map_fi895935311y_real: ( produc321349221y_real > option_poly_real ) > list_P736648811y_real > list_poly_real ).
thf(func_def_107,type,
map_fi249381555y_real: ( produc461822025y_real > option_poly_real ) > list_P693436111y_real > list_poly_real ).
thf(func_def_108,type,
map_ta316995199y_real: ( list_poly_real > list_poly_real ) > list_list_poly_real > list_list_poly_real > list_list_poly_real ).
thf(func_def_109,type,
map_ta434235247y_real: ( list_poly_real > poly_real ) > list_list_poly_real > list_poly_real > list_poly_real ).
thf(func_def_110,type,
map_ta1674185578y_real: ( list_poly_real > produc321349221y_real ) > list_list_poly_real > list_P736648811y_real > list_P736648811y_real ).
thf(func_def_111,type,
map_ta1513955567y_real: ( poly_real > list_poly_real ) > list_poly_real > list_list_poly_real > list_list_poly_real ).
thf(func_def_112,type,
map_ta1919289823y_real: ( poly_real > poly_real ) > list_poly_real > list_poly_real > list_poly_real ).
thf(func_def_113,type,
map_ta632757498y_real: ( poly_real > produc321349221y_real ) > list_poly_real > list_P736648811y_real > list_P736648811y_real ).
thf(func_def_114,type,
map_ta920933982y_real: ( poly_real > produc461822025y_real ) > list_poly_real > list_P693436111y_real > list_P693436111y_real ).
thf(func_def_115,type,
map_ta958735860y_real: ( produc321349221y_real > list_poly_real ) > list_P736648811y_real > list_list_poly_real > list_list_poly_real ).
thf(func_def_116,type,
map_ta787748196y_real: ( produc321349221y_real > poly_real ) > list_P736648811y_real > list_poly_real > list_poly_real ).
thf(func_def_117,type,
map_ta53312584y_real: ( produc461822025y_real > poly_real ) > list_P693436111y_real > list_poly_real > list_poly_real ).
thf(func_def_118,type,
map_ta954657966y_real: produc1456530199y_real > produc1456530199y_real > $o ).
thf(func_def_119,type,
maps_l502643659y_real: ( list_poly_real > list_list_poly_real ) > list_list_poly_real > list_list_poly_real ).
thf(func_def_120,type,
maps_l337560251y_real: ( list_poly_real > list_poly_real ) > list_list_poly_real > list_poly_real ).
thf(func_def_121,type,
maps_l770007326y_real: ( list_poly_real > list_P736648811y_real ) > list_list_poly_real > list_P736648811y_real ).
thf(func_def_122,type,
maps_p1417280571y_real: ( poly_real > list_list_poly_real ) > list_poly_real > list_list_poly_real ).
thf(func_def_123,type,
maps_p961674027y_real: ( poly_real > list_poly_real ) > list_poly_real > list_poly_real ).
thf(func_def_124,type,
maps_p2108677294y_real: ( poly_real > list_P736648811y_real ) > list_poly_real > list_P736648811y_real ).
thf(func_def_125,type,
maps_p86983698y_real: ( poly_real > list_P693436111y_real ) > list_poly_real > list_P693436111y_real ).
thf(func_def_126,type,
maps_P54557608y_real: ( produc321349221y_real > list_list_poly_real ) > list_P736648811y_real > list_list_poly_real ).
thf(func_def_127,type,
maps_P116184344y_real: ( produc321349221y_real > list_poly_real ) > list_P736648811y_real > list_poly_real ).
thf(func_def_128,type,
maps_P1366845948y_real: ( produc461822025y_real > list_poly_real ) > list_P693436111y_real > list_poly_real ).
thf(func_def_129,type,
member1829603177y_real: list_list_poly_real > list_poly_real > $o ).
thf(func_def_130,type,
member_poly_real: list_poly_real > poly_real > $o ).
thf(func_def_131,type,
member1782690048y_real: list_P736648811y_real > produc321349221y_real > $o ).
thf(func_def_132,type,
member202023780y_real: list_P693436111y_real > produc461822025y_real > $o ).
thf(func_def_133,type,
null_list_poly_real: list_list_poly_real > $o ).
thf(func_def_134,type,
null_poly_real: list_poly_real > $o ).
thf(func_def_135,type,
null_P89569907y_real: list_P736648811y_real > $o ).
thf(func_def_136,type,
null_P1782853975y_real: list_P693436111y_real > $o ).
thf(func_def_137,type,
lexord1324236152y_real: ( list_poly_real > list_poly_real > $o ) > list_list_poly_real > list_list_poly_real > $o ).
thf(func_def_138,type,
lexordp_eq_poly_real: ( poly_real > poly_real > $o ) > list_poly_real > list_poly_real > $o ).
thf(func_def_139,type,
lexord834705585y_real: ( produc321349221y_real > produc321349221y_real > $o ) > list_P736648811y_real > list_P736648811y_real > $o ).
thf(func_def_140,type,
lexord1053351061y_real: ( produc461822025y_real > produc461822025y_real > $o ) > list_P693436111y_real > list_P693436111y_real > $o ).
thf(func_def_141,type,
ord_le1233681790y_real: list_poly_real > list_poly_real > $o ).
thf(func_def_142,type,
produc1360353227y_real: list_nat > list_poly_real > list_P736648811y_real ).
thf(func_def_143,type,
produc1733309743y_real: list_poly_real > list_poly_real > list_P693436111y_real ).
thf(func_def_144,type,
produc523415045y_real: list_list_poly_real > list_list_poly_real ).
thf(func_def_145,type,
rotate717473073y_real: list_list_poly_real > list_list_poly_real ).
thf(func_def_146,type,
rotate1_poly_real: list_poly_real > list_poly_real ).
thf(func_def_147,type,
rotate623875384y_real: list_P736648811y_real > list_P736648811y_real ).
thf(func_def_148,type,
rotate867081116y_real: list_P693436111y_real > list_P693436111y_real ).
thf(func_def_149,type,
rotate_poly_real: nat > list_poly_real > list_poly_real ).
thf(func_def_150,type,
splice2080530731y_real: list_list_poly_real > list_list_poly_real > list_list_poly_real ).
thf(func_def_151,type,
splice_poly_real: list_poly_real > list_poly_real > list_poly_real ).
thf(func_def_152,type,
splice1383748542y_real: list_P736648811y_real > list_P736648811y_real > list_P736648811y_real ).
thf(func_def_153,type,
splice1321784098y_real: list_P693436111y_real > list_P693436111y_real > list_P693436111y_real ).
thf(func_def_154,type,
subseqs_poly_real: list_poly_real > list_list_poly_real ).
thf(func_def_155,type,
zip_nat_poly_real: list_nat > list_poly_real > list_P736648811y_real ).
thf(func_def_156,type,
zip_po657915297y_real: list_poly_real > list_poly_real > list_P693436111y_real ).
thf(func_def_157,type,
suc: nat > nat ).
thf(func_def_158,type,
size_s259235672y_real: list_poly_real > nat ).
thf(func_def_159,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_160,type,
plus_c288199817y_real: list_poly_real > list_poly_real > list_poly_real ).
thf(func_def_161,type,
produc1345584779y_real: ( poly_real > poly_real > $o ) > list_poly_real > produc1060019729y_real ).
thf(func_def_162,type,
produc2087464649y_real: ( poly_real > poly_real ) > produc1426596841y_real > produc1456530199y_real ).
thf(func_def_163,type,
produc1000427809y_real: list_poly_real > list_poly_real > produc1426596841y_real ).
thf(func_def_164,type,
produc404352541y_real: nat > poly_real > produc321349221y_real ).
thf(func_def_165,type,
produc490255505y_real: poly_real > list_poly_real > produc796638169y_real ).
thf(func_def_166,type,
produc1867601537y_real: poly_real > poly_real > produc461822025y_real ).
thf(func_def_167,type,
collec1537941401y_real: ( list_poly_real > $o ) > set_list_poly_real ).
thf(func_def_168,type,
collect_poly_real: ( poly_real > $o ) > set_poly_real ).
thf(func_def_169,type,
collec1459394516y_real: ( produc1426596841y_real > $o ) > set_Pr1405268809y_real ).
thf(func_def_170,type,
collec329281332y_real: ( produc461822025y_real > $o ) > set_Pr483210409y_real ).
thf(func_def_171,type,
sturm_891428828rm_seq: list_poly_real > $o ).
thf(func_def_172,type,
sturm_1664866327rm_seq: list_poly_real > poly_real > $o ).
thf(func_def_173,type,
sturm_1683633594axioms: list_poly_real > poly_real > $o ).
thf(func_def_174,type,
accp_P948088014y_real: ( produc1456530199y_real > produc1456530199y_real > $o ) > produc1456530199y_real > $o ).
thf(func_def_175,type,
member708095579y_real: list_poly_real > set_list_poly_real > $o ).
thf(func_def_176,type,
member_poly_real2: poly_real > set_poly_real > $o ).
thf(func_def_177,type,
member403334290y_real: produc1426596841y_real > set_Pr1405268809y_real > $o ).
thf(func_def_178,type,
member1784523250y_real: produc461822025y_real > set_Pr483210409y_real > $o ).
thf(func_def_195,type,
sK0: list_poly_real > poly_real > poly_real ).
thf(func_def_196,type,
sK1: list_poly_real > poly_real > list_poly_real ).
thf(f786,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f784,f785]) ).
thf(f785,plain,
( ( sturm_891428828rm_seq @ nil_poly_real )
!= $true ),
inference(equality_resolution,[status(thm)],[f782]) ).
thf(f782,plain,
! [X0: list_poly_real] :
( ( ( sturm_891428828rm_seq @ X0 )
!= $true )
| ( nil_poly_real != X0 ) ),
inference(cnf_transformation,[status(thm)],[f777]) ).
thf(f777,plain,
! [X0: list_poly_real] :
( ( ( sturm_891428828rm_seq @ X0 )
!= $true )
| ( nil_poly_real != X0 ) ),
inference(ennf_transformation,[status(thm)],[f636]) ).
thf(f636,plain,
! [X0: list_poly_real] :
( ( ( sturm_891428828rm_seq @ X0 )
= $true )
=> ( nil_poly_real != X0 ) ),
inference(fool_elimination,[status(thm)],[f635]) ).
thf(f635,plain,
! [X0: list_poly_real] :
( ( sturm_891428828rm_seq @ X0 )
=> ( nil_poly_real != X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: list_poly_real] :
( ( sturm_891428828rm_seq @ X0 )
=> ( nil_poly_real != X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.MilWfgdHi9/DTF2THF_23528.p',fact_0_quasi__sturm__seq_Ops__not__Nil) ).
thf(f784,plain,
( ( sturm_891428828rm_seq @ nil_poly_real )
= $true ),
inference(cnf_transformation,[status(thm)],[f775]) ).
thf(f775,plain,
( ( sturm_891428828rm_seq @ nil_poly_real )
= $true ),
inference(flattening,[status(thm)],[f428]) ).
thf(f428,plain,
~ ( ( ( sturm_891428828rm_seq @ nil_poly_real )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f427]) ).
thf(f427,plain,
~ ~ ( sturm_891428828rm_seq @ nil_poly_real ),
inference(rectify,[status(thm)],[f351]) ).
thf(f351,negated_conjecture,
~ ~ ( sturm_891428828rm_seq @ nil_poly_real ),
inference(negated_conjecture,[status(cth)],[f350]) ).
thf(f350,conjecture,
~ ( sturm_891428828rm_seq @ nil_poly_real ),
file('/export/starexec/sandbox/tmp/tmp.MilWfgdHi9/DTF2THF_23528.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP196^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n017.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:28:11 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : ITP196^1 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.47 % Domain : Interactive Theorem Proving
% 0.30/0.47 % Problem : Sledgehammer Sturm_Theorem problem prob_153__5878286_1
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.47 % Source : [Des21]
% 0.30/0.47 % Names : Sturm_Theorem/prob_153__5878286_1 [Des21]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.30/0.47 % Syntax : Number of formulae : 529 ( 226 unt; 179 typ; 0 def)
% 0.30/0.47 % Number of atoms : 889 ( 625 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 11 ( 2 avg)
% 0.30/0.47 % Number of connectives : 3412 ( 249 ~; 39 |; 117 &;2544 @)
% 0.30/0.47 % ( 0 <=>; 463 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 29 ( 7 avg)
% 0.30/0.47 % Number of types : 28 ( 27 usr)
% 0.30/0.47 % Number of type conns : 702 ( 702 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 153 ( 152 usr; 11 con; 0-3 aty)
% 0.30/0.47 % Number of variables : 1259 ( 49 ^;1098 !; 112 ?;1259 :)
% 0.30/0.47 % SPC : TH0_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:40:52.335
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % Could-be-implicit typings (27)
% 0.30/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_Mt__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_J_J,type,
% 0.30/0.47 produc1456530199y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_It__Polynomial__Opoly_It__Real__Oreal_J_M_062_It__Polynomial__Opoly_It__Real__Oreal_J_M_Eo_J_J_Mt__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.30/0.47 produc1060019729y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J_J_J,type,
% 0.30/0.47 list_P657095678y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_Mt__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_J_J,type,
% 0.30/0.47 set_Pr1405268809y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_Mt__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.30/0.47 produc1426596841y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J_J_J,type,
% 0.30/0.47 list_l343759061y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Polynomial__Opoly_It__Real__Oreal_J_J_J_J,type,
% 0.30/0.47 list_P991700890y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.30/0.47 option293660815y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Product____Type__Oprod_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.30/0.47 produc796638169y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.30/0.47 list_P693436111y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.30/0.47 set_Pr483210409y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_J_J,type,
% 0.30/0.47 list_P1001591419y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Polynomial__Opoly_It__Real__Oreal_J_J_J_J,type,
% 0.30/0.47 list_l6097393y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Product____Type__Oprod_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.30/0.47 produc461822025y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.30/0.47 option988260395y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.30/0.47 list_P736648811y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_J_J,type,
% 0.30/0.47 list_l1245274212y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.30/0.47 produc321349221y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Option__Ooption_It__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.30/0.47 option1330723604y_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__List__Olist_It__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.30/0.47 list_list_poly_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.30/0.47 set_list_poly_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Option__Ooption_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.30/0.47 option_poly_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.30/0.47 list_poly_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Set__Oset_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.30/0.47 set_poly_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.30/0.47 poly_real: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 0.30/0.47 list_nat: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(ty_n_t__Nat__Onat,type,
% 0.30/0.47 nat: $tType ).
% 0.30/0.47
% 0.30/0.47 % Explicit typings (152)
% 0.30/0.47 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.30/0.47 bNF_Gr851617109y_real: set_list_poly_real > poly_real > set_list_poly_real ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.30/0.47 bNF_Gr1644259033y_real: set_list_poly_real > list_poly_real > set_poly_real ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
% 0.30/0.47 times_times_nat: nat > nat > nat ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_List_Oappend_001t__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.30/0.47 append527544425y_real: list_list_poly_real > list_list_poly_real > list_list_poly_real ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_List_Oappend_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.30/0.47 append_poly_real: list_poly_real > list_poly_real > list_poly_real ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_List_Obind_001t__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_001t__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.30/0.47 bind_l1810664209y_real: list_list_poly_real > ( list_poly_real > list_list_poly_real ) > list_list_poly_real ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_List_Obind_001t__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.30/0.47 bind_l146959617y_real: list_list_poly_real > ( list_poly_real > list_poly_real ) > list_poly_real ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_List_Obind_001t__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.30/0.47 bind_l429098840y_real: list_list_poly_real > ( list_poly_real > list_P736648811y_real ) > list_P736648811y_real ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_List_Obind_001t__Polynomial__Opoly_It__Real__Oreal_J_001t__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.30/0.47 bind_p1226679937y_real: list_poly_real > ( poly_real > list_list_poly_real ) > list_list_poly_real ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_List_Obind_001t__Polynomial__Opoly_It__Real__Oreal_J_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.30/0.47 bind_p420216945y_real: list_poly_real > ( poly_real > list_poly_real ) > list_poly_real ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_List_Obind_001t__Polynomial__Opoly_It__Real__Oreal_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.30/0.47 bind_p600434664y_real: list_poly_real > ( poly_real > list_P736648811y_real ) > list_P736648811y_real ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_List_Obind_001t__Polynomial__Opoly_It__Real__Oreal_J_001t__Product____Type__Oprod_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.30/0.47 bind_p988182092y_real: list_poly_real > ( poly_real > list_P693436111y_real ) > list_P693436111y_real ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_List_Obind_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Polynomial__Opoly_It__Real__Oreal_J_J_001t__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.30/0.47 bind_P1861132770y_real: list_P736648811y_real > ( produc321349221y_real > list_list_poly_real ) > list_list_poly_real ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_List_Obind_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Polynomial__Opoly_It__Real__Oreal_J_J_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.30/0.47 bind_P755425362y_real: list_P736648811y_real > ( produc321349221y_real > list_poly_real ) > list_poly_real ).
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% 0.30/0.47
% 0.30/0.47 thf(sy_c_Sturm__Theorem__Mirabelle__ubahemswrm_Osturm__seq__axioms,type,
% 0.30/0.47 sturm_1683633594axioms: list_poly_real > poly_real > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_Mt__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_J_J,type,
% 0.30/0.47 accp_P948088014y_real: ( produc1456530199y_real > produc1456530199y_real > $o ) > produc1456530199y_real > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_member_001t__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.30/0.47 member708095579y_real: list_poly_real > set_list_poly_real > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_member_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.30/0.47 member_poly_real2: poly_real > set_poly_real > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_Mt__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.30/0.47 member403334290y_real: produc1426596841y_real > set_Pr1405268809y_real > $o ).
% 0.30/0.47
% 0.30/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.30/0.47 member1784523250y_real: produc461822025y_real > set_Pr483210409y_real > $o ).
% 0.30/0.47
% 0.30/0.47 % Relevant facts (349)
% 0.30/0.47 thf(fact_0_quasi__sturm__seq_Ops__not__Nil,axiom,
% 0.30/0.47 ! [Ps: list_poly_real] :
% 0.30/0.47 ( ( sturm_891428828rm_seq @ Ps )
% 0.30/0.47 => ( Ps != nil_poly_real ) ) ).
% 0.30/0.47
% 0.30/0.47 % quasi_sturm_seq.ps_not_Nil
% 0.30/0.47 thf(fact_1_sturm__seq_Oquasi__sturm__seq,axiom,
% 0.30/0.47 ! [Ps: list_poly_real,P: poly_real] :
% 0.30/0.47 ( ( sturm_1664866327rm_seq @ Ps @ P )
% 0.30/0.47 => ( sturm_891428828rm_seq @ Ps ) ) ).
% 0.30/0.47
% 0.30/0.47 % sturm_seq.quasi_sturm_seq
% 0.30/0.47 thf(fact_2_sturm__seq__def,axiom,
% 0.30/0.47 ( sturm_1664866327rm_seq
% 0.30/0.47 = ( ^ [Ps2: list_poly_real,P2: poly_real] :
% 0.30/0.47 ( ( sturm_891428828rm_seq @ Ps2 )
% 0.30/0.47 & ( sturm_1683633594axioms @ Ps2 @ P2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sturm_seq_def
% 0.30/0.47 thf(fact_3_sturm__seq_Ointro,axiom,
% 0.30/0.47 ! [Ps: list_poly_real,P: poly_real] :
% 0.30/0.47 ( ( sturm_891428828rm_seq @ Ps )
% 0.30/0.47 => ( ( sturm_1683633594axioms @ Ps @ P )
% 0.30/0.47 => ( sturm_1664866327rm_seq @ Ps @ P ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % sturm_seq.intro
% 0.30/0.47 thf(fact_4_list__ex1__simps_I1_J,axiom,
% 0.30/0.47 ! [P3: produc321349221y_real > $o] :
% 0.30/0.47 ~ ( list_e1892536494y_real @ P3 @ nil_Pr1492526187y_real ) ).
% 0.30/0.47
% 0.30/0.47 % list_ex1_simps(1)
% 0.30/0.47 thf(fact_5_list__ex1__simps_I1_J,axiom,
% 0.30/0.47 ! [P3: list_poly_real > $o] :
% 0.30/0.47 ~ ( list_e367462459y_real @ P3 @ nil_list_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % list_ex1_simps(1)
% 0.30/0.47 thf(fact_6_list__ex1__simps_I1_J,axiom,
% 0.30/0.47 ! [P3: produc461822025y_real > $o] :
% 0.30/0.47 ~ ( list_e1507538962y_real @ P3 @ nil_Pr1207979855y_real ) ).
% 0.30/0.47
% 0.30/0.47 % list_ex1_simps(1)
% 0.30/0.47 thf(fact_7_list__ex1__simps_I1_J,axiom,
% 0.30/0.47 ! [P3: poly_real > $o] :
% 0.30/0.47 ~ ( list_ex1_poly_real @ P3 @ nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % list_ex1_simps(1)
% 0.30/0.47 thf(fact_8_bind__simps_I1_J,axiom,
% 0.30/0.47 ! [F: poly_real > list_poly_real] :
% 0.30/0.47 ( ( bind_p420216945y_real @ nil_poly_real @ F )
% 0.30/0.47 = nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % bind_simps(1)
% 0.30/0.47 thf(fact_9_bind__simps_I1_J,axiom,
% 0.30/0.47 ! [F: poly_real > list_list_poly_real] :
% 0.30/0.47 ( ( bind_p1226679937y_real @ nil_poly_real @ F )
% 0.30/0.47 = nil_list_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % bind_simps(1)
% 0.30/0.47 thf(fact_10_bind__simps_I1_J,axiom,
% 0.30/0.47 ! [F: list_poly_real > list_poly_real] :
% 0.30/0.47 ( ( bind_l146959617y_real @ nil_list_poly_real @ F )
% 0.30/0.47 = nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % bind_simps(1)
% 0.30/0.47 thf(fact_11_bind__simps_I1_J,axiom,
% 0.30/0.47 ! [F: poly_real > list_P736648811y_real] :
% 0.30/0.47 ( ( bind_p600434664y_real @ nil_poly_real @ F )
% 0.30/0.47 = nil_Pr1492526187y_real ) ).
% 0.30/0.47
% 0.30/0.47 % bind_simps(1)
% 0.30/0.47 thf(fact_12_bind__simps_I1_J,axiom,
% 0.30/0.47 ! [F: produc321349221y_real > list_poly_real] :
% 0.30/0.47 ( ( bind_P755425362y_real @ nil_Pr1492526187y_real @ F )
% 0.30/0.47 = nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % bind_simps(1)
% 0.30/0.47 thf(fact_13_bind__simps_I1_J,axiom,
% 0.30/0.47 ! [F: list_poly_real > list_list_poly_real] :
% 0.30/0.47 ( ( bind_l1810664209y_real @ nil_list_poly_real @ F )
% 0.30/0.47 = nil_list_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % bind_simps(1)
% 0.30/0.47 thf(fact_14_bind__simps_I1_J,axiom,
% 0.30/0.47 ! [F: poly_real > list_P693436111y_real] :
% 0.30/0.47 ( ( bind_p988182092y_real @ nil_poly_real @ F )
% 0.30/0.47 = nil_Pr1207979855y_real ) ).
% 0.30/0.47
% 0.30/0.47 % bind_simps(1)
% 0.30/0.47 thf(fact_15_bind__simps_I1_J,axiom,
% 0.30/0.47 ! [F: produc321349221y_real > list_list_poly_real] :
% 0.30/0.47 ( ( bind_P1861132770y_real @ nil_Pr1492526187y_real @ F )
% 0.30/0.47 = nil_list_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % bind_simps(1)
% 0.30/0.47 thf(fact_16_bind__simps_I1_J,axiom,
% 0.30/0.47 ! [F: list_poly_real > list_P736648811y_real] :
% 0.30/0.47 ( ( bind_l429098840y_real @ nil_list_poly_real @ F )
% 0.30/0.47 = nil_Pr1492526187y_real ) ).
% 0.30/0.47
% 0.30/0.47 % bind_simps(1)
% 0.30/0.47 thf(fact_17_bind__simps_I1_J,axiom,
% 0.30/0.47 ! [F: produc461822025y_real > list_poly_real] :
% 0.30/0.47 ( ( bind_P120560694y_real @ nil_Pr1207979855y_real @ F )
% 0.30/0.47 = nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % bind_simps(1)
% 0.30/0.47 thf(fact_18_member__rec_I2_J,axiom,
% 0.30/0.47 ! [Y: produc321349221y_real] :
% 0.30/0.47 ~ ( member1782690048y_real @ nil_Pr1492526187y_real @ Y ) ).
% 0.30/0.47
% 0.30/0.47 % member_rec(2)
% 0.30/0.47 thf(fact_19_member__rec_I2_J,axiom,
% 0.30/0.47 ! [Y: list_poly_real] :
% 0.30/0.47 ~ ( member1829603177y_real @ nil_list_poly_real @ Y ) ).
% 0.30/0.47
% 0.30/0.47 % member_rec(2)
% 0.30/0.47 thf(fact_20_member__rec_I2_J,axiom,
% 0.30/0.47 ! [Y: produc461822025y_real] :
% 0.30/0.47 ~ ( member202023780y_real @ nil_Pr1207979855y_real @ Y ) ).
% 0.30/0.47
% 0.30/0.47 % member_rec(2)
% 0.30/0.47 thf(fact_21_member__rec_I2_J,axiom,
% 0.30/0.47 ! [Y: poly_real] :
% 0.30/0.47 ~ ( member_poly_real @ nil_poly_real @ Y ) ).
% 0.30/0.47
% 0.30/0.47 % member_rec(2)
% 0.30/0.47 thf(fact_22_gen__length__code_I1_J,axiom,
% 0.30/0.47 ! [N: nat] :
% 0.30/0.47 ( ( gen_le904455032y_real @ N @ nil_Pr1492526187y_real )
% 0.30/0.47 = N ) ).
% 0.30/0.47
% 0.30/0.47 % gen_length_code(1)
% 0.30/0.47 thf(fact_23_gen__length__code_I1_J,axiom,
% 0.30/0.47 ! [N: nat] :
% 0.30/0.47 ( ( gen_le1160603377y_real @ N @ nil_list_poly_real )
% 0.30/0.47 = N ) ).
% 0.30/0.47
% 0.30/0.47 % gen_length_code(1)
% 0.30/0.47 thf(fact_24_gen__length__code_I1_J,axiom,
% 0.30/0.47 ! [N: nat] :
% 0.30/0.47 ( ( gen_le1524582876y_real @ N @ nil_Pr1207979855y_real )
% 0.30/0.47 = N ) ).
% 0.30/0.47
% 0.30/0.47 % gen_length_code(1)
% 0.30/0.47 thf(fact_25_gen__length__code_I1_J,axiom,
% 0.30/0.47 ! [N: nat] :
% 0.30/0.47 ( ( gen_length_poly_real @ N @ nil_poly_real )
% 0.30/0.47 = N ) ).
% 0.30/0.47
% 0.30/0.47 % gen_length_code(1)
% 0.30/0.47 thf(fact_26_maps__simps_I2_J,axiom,
% 0.30/0.47 ! [F: poly_real > list_poly_real] :
% 0.30/0.47 ( ( maps_p961674027y_real @ F @ nil_poly_real )
% 0.30/0.47 = nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % maps_simps(2)
% 0.30/0.47 thf(fact_27_maps__simps_I2_J,axiom,
% 0.30/0.47 ! [F: poly_real > list_list_poly_real] :
% 0.30/0.47 ( ( maps_p1417280571y_real @ F @ nil_poly_real )
% 0.30/0.47 = nil_list_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % maps_simps(2)
% 0.30/0.47 thf(fact_28_maps__simps_I2_J,axiom,
% 0.30/0.47 ! [F: list_poly_real > list_poly_real] :
% 0.30/0.47 ( ( maps_l337560251y_real @ F @ nil_list_poly_real )
% 0.30/0.47 = nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % maps_simps(2)
% 0.30/0.47 thf(fact_29_maps__simps_I2_J,axiom,
% 0.30/0.47 ! [F: poly_real > list_P736648811y_real] :
% 0.30/0.47 ( ( maps_p2108677294y_real @ F @ nil_poly_real )
% 0.30/0.47 = nil_Pr1492526187y_real ) ).
% 0.30/0.47
% 0.30/0.47 % maps_simps(2)
% 0.30/0.47 thf(fact_30_maps__simps_I2_J,axiom,
% 0.30/0.47 ! [F: produc321349221y_real > list_poly_real] :
% 0.30/0.47 ( ( maps_P116184344y_real @ F @ nil_Pr1492526187y_real )
% 0.30/0.47 = nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % maps_simps(2)
% 0.30/0.47 thf(fact_31_maps__simps_I2_J,axiom,
% 0.30/0.47 ! [F: list_poly_real > list_list_poly_real] :
% 0.30/0.47 ( ( maps_l502643659y_real @ F @ nil_list_poly_real )
% 0.30/0.47 = nil_list_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % maps_simps(2)
% 0.30/0.47 thf(fact_32_maps__simps_I2_J,axiom,
% 0.30/0.47 ! [F: poly_real > list_P693436111y_real] :
% 0.30/0.47 ( ( maps_p86983698y_real @ F @ nil_poly_real )
% 0.30/0.47 = nil_Pr1207979855y_real ) ).
% 0.30/0.47
% 0.30/0.47 % maps_simps(2)
% 0.30/0.47 thf(fact_33_maps__simps_I2_J,axiom,
% 0.30/0.47 ! [F: produc321349221y_real > list_list_poly_real] :
% 0.30/0.47 ( ( maps_P54557608y_real @ F @ nil_Pr1492526187y_real )
% 0.30/0.47 = nil_list_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % maps_simps(2)
% 0.30/0.47 thf(fact_34_maps__simps_I2_J,axiom,
% 0.30/0.47 ! [F: list_poly_real > list_P736648811y_real] :
% 0.30/0.47 ( ( maps_l770007326y_real @ F @ nil_list_poly_real )
% 0.30/0.47 = nil_Pr1492526187y_real ) ).
% 0.30/0.47
% 0.30/0.47 % maps_simps(2)
% 0.30/0.47 thf(fact_35_maps__simps_I2_J,axiom,
% 0.30/0.47 ! [F: produc461822025y_real > list_poly_real] :
% 0.30/0.47 ( ( maps_P1366845948y_real @ F @ nil_Pr1207979855y_real )
% 0.30/0.47 = nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % maps_simps(2)
% 0.30/0.47 thf(fact_36_map__filter__simps_I2_J,axiom,
% 0.30/0.47 ! [F: poly_real > option_poly_real] :
% 0.30/0.47 ( ( map_fi1183202740y_real @ F @ nil_poly_real )
% 0.30/0.47 = nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % map_filter_simps(2)
% 0.30/0.47 thf(fact_37_map__filter__simps_I2_J,axiom,
% 0.30/0.47 ! [F: poly_real > option1330723604y_real] :
% 0.30/0.47 ( ( map_fi920577604y_real @ F @ nil_poly_real )
% 0.30/0.47 = nil_list_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % map_filter_simps(2)
% 0.30/0.47 thf(fact_38_map__filter__simps_I2_J,axiom,
% 0.30/0.47 ! [F: list_poly_real > option_poly_real] :
% 0.30/0.47 ( ( map_fi1988340932y_real @ F @ nil_list_poly_real )
% 0.30/0.47 = nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % map_filter_simps(2)
% 0.30/0.47 thf(fact_39_map__filter__simps_I2_J,axiom,
% 0.30/0.47 ! [F: poly_real > option988260395y_real] :
% 0.30/0.47 ( ( map_fi740944613y_real @ F @ nil_poly_real )
% 0.30/0.47 = nil_Pr1492526187y_real ) ).
% 0.30/0.47
% 0.30/0.47 % map_filter_simps(2)
% 0.30/0.47 thf(fact_40_map__filter__simps_I2_J,axiom,
% 0.30/0.47 ! [F: produc321349221y_real > option_poly_real] :
% 0.30/0.47 ( ( map_fi895935311y_real @ F @ nil_Pr1492526187y_real )
% 0.30/0.47 = nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % map_filter_simps(2)
% 0.30/0.47 thf(fact_41_map__filter__simps_I2_J,axiom,
% 0.30/0.47 ! [F: list_poly_real > option1330723604y_real] :
% 0.30/0.47 ( ( map_fi357666132y_real @ F @ nil_list_poly_real )
% 0.30/0.47 = nil_list_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % map_filter_simps(2)
% 0.30/0.47 thf(fact_42_map__filter__simps_I2_J,axiom,
% 0.30/0.47 ! [F: poly_real > option293660815y_real] :
% 0.30/0.47 ( ( map_fi1117002953y_real @ F @ nil_poly_real )
% 0.30/0.47 = nil_Pr1207979855y_real ) ).
% 0.30/0.47
% 0.30/0.47 % map_filter_simps(2)
% 0.30/0.47 thf(fact_43_map__filter__simps_I2_J,axiom,
% 0.30/0.47 ! [F: produc321349221y_real > option1330723604y_real] :
% 0.30/0.47 ( ( map_fi1389003359y_real @ F @ nil_Pr1492526187y_real )
% 0.30/0.47 = nil_list_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % map_filter_simps(2)
% 0.30/0.47 thf(fact_44_map__filter__simps_I2_J,axiom,
% 0.30/0.47 ! [F: list_poly_real > option988260395y_real] :
% 0.30/0.47 ( ( map_fi2104453077y_real @ F @ nil_list_poly_real )
% 0.30/0.47 = nil_Pr1492526187y_real ) ).
% 0.30/0.47
% 0.30/0.47 % map_filter_simps(2)
% 0.30/0.47 thf(fact_45_map__filter__simps_I2_J,axiom,
% 0.30/0.47 ! [F: produc461822025y_real > option_poly_real] :
% 0.30/0.47 ( ( map_fi249381555y_real @ F @ nil_Pr1207979855y_real )
% 0.30/0.47 = nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % map_filter_simps(2)
% 0.30/0.47 thf(fact_46_null__rec_I2_J,axiom,
% 0.30/0.47 null_P89569907y_real @ nil_Pr1492526187y_real ).
% 0.30/0.47
% 0.30/0.47 % null_rec(2)
% 0.30/0.47 thf(fact_47_null__rec_I2_J,axiom,
% 0.30/0.47 null_list_poly_real @ nil_list_poly_real ).
% 0.30/0.47
% 0.30/0.47 % null_rec(2)
% 0.30/0.47 thf(fact_48_null__rec_I2_J,axiom,
% 0.30/0.47 null_P1782853975y_real @ nil_Pr1207979855y_real ).
% 0.30/0.47
% 0.30/0.47 % null_rec(2)
% 0.30/0.47 thf(fact_49_null__rec_I2_J,axiom,
% 0.30/0.47 null_poly_real @ nil_poly_real ).
% 0.30/0.47
% 0.30/0.47 % null_rec(2)
% 0.30/0.47 thf(fact_50_eq__Nil__null,axiom,
% 0.30/0.47 ! [Xs: list_P736648811y_real] :
% 0.30/0.47 ( ( Xs = nil_Pr1492526187y_real )
% 0.30/0.47 = ( null_P89569907y_real @ Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % eq_Nil_null
% 0.30/0.47 thf(fact_51_eq__Nil__null,axiom,
% 0.30/0.47 ! [Xs: list_list_poly_real] :
% 0.30/0.47 ( ( Xs = nil_list_poly_real )
% 0.30/0.47 = ( null_list_poly_real @ Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % eq_Nil_null
% 0.30/0.47 thf(fact_52_eq__Nil__null,axiom,
% 0.30/0.47 ! [Xs: list_P693436111y_real] :
% 0.30/0.47 ( ( Xs = nil_Pr1207979855y_real )
% 0.30/0.47 = ( null_P1782853975y_real @ Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % eq_Nil_null
% 0.30/0.47 thf(fact_53_eq__Nil__null,axiom,
% 0.30/0.47 ! [Xs: list_poly_real] :
% 0.30/0.47 ( ( Xs = nil_poly_real )
% 0.30/0.47 = ( null_poly_real @ Xs ) ) ).
% 0.30/0.47
% 0.30/0.47 % eq_Nil_null
% 0.30/0.47 thf(fact_54_sturm__seq_Oaxioms_I2_J,axiom,
% 0.30/0.47 ! [Ps: list_poly_real,P: poly_real] :
% 0.30/0.47 ( ( sturm_1664866327rm_seq @ Ps @ P )
% 0.30/0.47 => ( sturm_1683633594axioms @ Ps @ P ) ) ).
% 0.30/0.47
% 0.30/0.47 % sturm_seq.axioms(2)
% 0.30/0.47 thf(fact_55_list__ex__simps_I2_J,axiom,
% 0.30/0.47 ! [P3: produc321349221y_real > $o] :
% 0.30/0.47 ~ ( list_e2093379497y_real @ P3 @ nil_Pr1492526187y_real ) ).
% 0.30/0.47
% 0.30/0.47 % list_ex_simps(2)
% 0.30/0.47 thf(fact_56_list__ex__simps_I2_J,axiom,
% 0.30/0.47 ! [P3: list_poly_real > $o] :
% 0.30/0.47 ~ ( list_e809719936y_real @ P3 @ nil_list_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % list_ex_simps(2)
% 0.30/0.47 thf(fact_57_list__ex__simps_I2_J,axiom,
% 0.30/0.47 ! [P3: produc461822025y_real > $o] :
% 0.30/0.47 ~ ( list_e1312221069y_real @ P3 @ nil_Pr1207979855y_real ) ).
% 0.30/0.47
% 0.30/0.47 % list_ex_simps(2)
% 0.30/0.47 thf(fact_58_list__ex__simps_I2_J,axiom,
% 0.30/0.47 ! [P3: poly_real > $o] :
% 0.30/0.47 ~ ( list_ex_poly_real @ P3 @ nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % list_ex_simps(2)
% 0.30/0.47 thf(fact_59_rotate1__is__Nil__conv,axiom,
% 0.30/0.47 ! [Xs: list_P736648811y_real] :
% 0.30/0.47 ( ( ( rotate623875384y_real @ Xs )
% 0.30/0.47 = nil_Pr1492526187y_real )
% 0.30/0.47 = ( Xs = nil_Pr1492526187y_real ) ) ).
% 0.30/0.47
% 0.30/0.47 % rotate1_is_Nil_conv
% 0.30/0.47 thf(fact_60_rotate1__is__Nil__conv,axiom,
% 0.30/0.47 ! [Xs: list_list_poly_real] :
% 0.30/0.47 ( ( ( rotate717473073y_real @ Xs )
% 0.30/0.47 = nil_list_poly_real )
% 0.30/0.47 = ( Xs = nil_list_poly_real ) ) ).
% 0.30/0.47
% 0.30/0.47 % rotate1_is_Nil_conv
% 0.30/0.47 thf(fact_61_rotate1__is__Nil__conv,axiom,
% 0.30/0.47 ! [Xs: list_P693436111y_real] :
% 0.30/0.47 ( ( ( rotate867081116y_real @ Xs )
% 0.30/0.47 = nil_Pr1207979855y_real )
% 0.30/0.47 = ( Xs = nil_Pr1207979855y_real ) ) ).
% 0.30/0.47
% 0.30/0.47 % rotate1_is_Nil_conv
% 0.30/0.47 thf(fact_62_rotate1__is__Nil__conv,axiom,
% 0.30/0.47 ! [Xs: list_poly_real] :
% 0.30/0.47 ( ( ( rotate1_poly_real @ Xs )
% 0.30/0.47 = nil_poly_real )
% 0.30/0.47 = ( Xs = nil_poly_real ) ) ).
% 0.30/0.47
% 0.30/0.47 % rotate1_is_Nil_conv
% 0.30/0.47 thf(fact_63_split__Nil__iff,axiom,
% 0.30/0.47 ! [Xs: list_P736648811y_real,Ys: list_P736648811y_real] :
% 0.30/0.47 ( ( ( splice1383748542y_real @ Xs @ Ys )
% 0.30/0.47 = nil_Pr1492526187y_real )
% 0.30/0.47 = ( ( Xs = nil_Pr1492526187y_real )
% 0.30/0.47 & ( Ys = nil_Pr1492526187y_real ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % split_Nil_iff
% 0.30/0.47 thf(fact_64_split__Nil__iff,axiom,
% 0.30/0.47 ! [Xs: list_list_poly_real,Ys: list_list_poly_real] :
% 0.30/0.47 ( ( ( splice2080530731y_real @ Xs @ Ys )
% 0.30/0.47 = nil_list_poly_real )
% 0.30/0.47 = ( ( Xs = nil_list_poly_real )
% 0.30/0.47 & ( Ys = nil_list_poly_real ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % split_Nil_iff
% 0.30/0.47 thf(fact_65_split__Nil__iff,axiom,
% 0.30/0.47 ! [Xs: list_P693436111y_real,Ys: list_P693436111y_real] :
% 0.30/0.47 ( ( ( splice1321784098y_real @ Xs @ Ys )
% 0.30/0.47 = nil_Pr1207979855y_real )
% 0.30/0.47 = ( ( Xs = nil_Pr1207979855y_real )
% 0.30/0.47 & ( Ys = nil_Pr1207979855y_real ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % split_Nil_iff
% 0.30/0.47 thf(fact_66_split__Nil__iff,axiom,
% 0.30/0.47 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 0.30/0.47 ( ( ( splice_poly_real @ Xs @ Ys )
% 0.30/0.47 = nil_poly_real )
% 0.30/0.47 = ( ( Xs = nil_poly_real )
% 0.30/0.47 & ( Ys = nil_poly_real ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % split_Nil_iff
% 0.30/0.47 thf(fact_67_splice__Nil2,axiom,
% 0.30/0.47 ! [Xs: list_P736648811y_real] :
% 0.30/0.47 ( ( splice1383748542y_real @ Xs @ nil_Pr1492526187y_real )
% 0.30/0.47 = Xs ) ).
% 0.30/0.47
% 0.30/0.47 % splice_Nil2
% 0.30/0.47 thf(fact_68_splice__Nil2,axiom,
% 0.30/0.47 ! [Xs: list_list_poly_real] :
% 0.30/0.47 ( ( splice2080530731y_real @ Xs @ nil_list_poly_real )
% 0.30/0.47 = Xs ) ).
% 0.30/0.47
% 0.30/0.47 % splice_Nil2
% 0.30/0.47 thf(fact_69_splice__Nil2,axiom,
% 0.30/0.47 ! [Xs: list_P693436111y_real] :
% 0.30/0.47 ( ( splice1321784098y_real @ Xs @ nil_Pr1207979855y_real )
% 0.30/0.47 = Xs ) ).
% 0.30/0.47
% 0.30/0.47 % splice_Nil2
% 0.30/0.47 thf(fact_70_splice__Nil2,axiom,
% 0.30/0.47 ! [Xs: list_poly_real] :
% 0.30/0.47 ( ( splice_poly_real @ Xs @ nil_poly_real )
% 0.30/0.47 = Xs ) ).
% 0.30/0.47
% 0.30/0.47 % splice_Nil2
% 0.30/0.47 thf(fact_71_enumerate__simps_I1_J,axiom,
% 0.30/0.47 ! [N: nat] :
% 0.30/0.47 ( ( enumer1123002698y_real @ N @ nil_Pr1492526187y_real )
% 0.30/0.47 = nil_Pr570652676y_real ) ).
% 0.30/0.47
% 0.30/0.47 % enumerate_simps(1)
% 0.30/0.47 thf(fact_72_enumerate__simps_I1_J,axiom,
% 0.30/0.47 ! [N: nat] :
% 0.30/0.47 ( ( enumer1433313439y_real @ N @ nil_list_poly_real )
% 0.30/0.47 = nil_Pr1161137915y_real ) ).
% 0.30/0.47
% 0.30/0.47 % enumerate_simps(1)
% 0.30/0.47 thf(fact_73_enumerate__simps_I1_J,axiom,
% 0.30/0.47 ! [N: nat] :
% 0.30/0.47 ( ( enumer1015405230y_real @ N @ nil_Pr1207979855y_real )
% 0.30/0.47 = nil_Pr2056488424y_real ) ).
% 0.30/0.47
% 0.30/0.47 % enumerate_simps(1)
% 0.30/0.47 thf(fact_74_enumerate__simps_I1_J,axiom,
% 0.30/0.47 ! [N: nat] :
% 0.30/0.47 ( ( enumerate_poly_real @ N @ nil_poly_real )
% 0.30/0.47 = nil_Pr1492526187y_real ) ).
% 0.30/0.47
% 0.30/0.47 % enumerate_simps(1)
% 0.30/0.47 thf(fact_75_product_Osimps_I1_J,axiom,
% 0.30/0.47 ! [Uu: list_poly_real] :
% 0.30/0.47 ( ( produc1360353227y_real @ nil_nat @ Uu )
% 0.30/0.47 = nil_Pr1492526187y_real ) ).
% 0.30/0.47
% 0.30/0.47 % product.simps(1)
% 0.30/0.47 thf(fact_76_product_Osimps_I1_J,axiom,
% 0.30/0.47 ! [Uu: list_poly_real] :
% 0.30/0.47 ( ( produc1733309743y_real @ nil_poly_real @ Uu )
% 0.30/0.47 = nil_Pr1207979855y_real ) ).
% 0.30/0.47
% 0.30/0.47 % product.simps(1)
% 0.30/0.47 thf(fact_77_map__tailrec__rev_Osimps_I1_J,axiom,
% 0.30/0.47 ! [F: poly_real > poly_real,Bs: list_poly_real] :
% 0.30/0.47 ( ( map_ta1919289823y_real @ F @ nil_poly_real @ Bs )
% 0.30/0.47 = Bs ) ).
% 0.30/0.47
% 0.30/0.47 % map_tailrec_rev.simps(1)
% 0.30/0.47 thf(fact_78_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.30/0.47 ! [Less: produc321349221y_real > produc321349221y_real > $o,Ys: list_P736648811y_real] : ( lexord834705585y_real @ Less @ nil_Pr1492526187y_real @ Ys ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq_simps(1)
% 0.30/0.47 thf(fact_79_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.30/0.47 ! [Less: list_poly_real > list_poly_real > $o,Ys: list_list_poly_real] : ( lexord1324236152y_real @ Less @ nil_list_poly_real @ Ys ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq_simps(1)
% 0.30/0.47 thf(fact_80_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.30/0.47 ! [Less: produc461822025y_real > produc461822025y_real > $o,Ys: list_P693436111y_real] : ( lexord1053351061y_real @ Less @ nil_Pr1207979855y_real @ Ys ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq_simps(1)
% 0.30/0.47 thf(fact_81_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.30/0.47 ! [Less: poly_real > poly_real > $o,Ys: list_poly_real] : ( lexordp_eq_poly_real @ Less @ nil_poly_real @ Ys ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq_simps(1)
% 0.30/0.47 thf(fact_82_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.30/0.47 ! [Less: produc321349221y_real > produc321349221y_real > $o,Xs: list_P736648811y_real] :
% 0.30/0.47 ( ( lexord834705585y_real @ Less @ Xs @ nil_Pr1492526187y_real )
% 0.30/0.47 = ( Xs = nil_Pr1492526187y_real ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq_simps(2)
% 0.30/0.47 thf(fact_83_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.30/0.47 ! [Less: list_poly_real > list_poly_real > $o,Xs: list_list_poly_real] :
% 0.30/0.47 ( ( lexord1324236152y_real @ Less @ Xs @ nil_list_poly_real )
% 0.30/0.47 = ( Xs = nil_list_poly_real ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq_simps(2)
% 0.30/0.47 thf(fact_84_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.30/0.47 ! [Less: produc461822025y_real > produc461822025y_real > $o,Xs: list_P693436111y_real] :
% 0.30/0.47 ( ( lexord1053351061y_real @ Less @ Xs @ nil_Pr1207979855y_real )
% 0.30/0.47 = ( Xs = nil_Pr1207979855y_real ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq_simps(2)
% 0.30/0.47 thf(fact_85_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.30/0.47 ! [Less: poly_real > poly_real > $o,Xs: list_poly_real] :
% 0.30/0.47 ( ( lexordp_eq_poly_real @ Less @ Xs @ nil_poly_real )
% 0.30/0.47 = ( Xs = nil_poly_real ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq_simps(2)
% 0.30/0.47 thf(fact_86_listrelp_ONil,axiom,
% 0.30/0.47 ! [R: poly_real > poly_real > $o] : ( listre1609905961y_real @ R @ nil_poly_real @ nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.Nil
% 0.30/0.47 thf(fact_87_listrelp_ONil,axiom,
% 0.30/0.47 ! [R: poly_real > list_poly_real > $o] : ( listre1793073465y_real @ R @ nil_poly_real @ nil_list_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.Nil
% 0.30/0.47 thf(fact_88_listrelp_ONil,axiom,
% 0.30/0.47 ! [R: list_poly_real > poly_real > $o] : ( listre713353145y_real @ R @ nil_list_poly_real @ nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.Nil
% 0.30/0.47 thf(fact_89_listrelp_ONil,axiom,
% 0.30/0.47 ! [R: poly_real > produc321349221y_real > $o] : ( listre889482032y_real @ R @ nil_poly_real @ nil_Pr1492526187y_real ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.Nil
% 0.30/0.47 thf(fact_90_listrelp_ONil,axiom,
% 0.30/0.47 ! [R: produc321349221y_real > poly_real > $o] : ( listre1044472730y_real @ R @ nil_Pr1492526187y_real @ nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.Nil
% 0.30/0.47 thf(fact_91_listrelp_ONil,axiom,
% 0.30/0.47 ! [R: list_poly_real > list_poly_real > $o] : ( listre1763068361y_real @ R @ nil_list_poly_real @ nil_list_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.Nil
% 0.30/0.47 thf(fact_92_listrelp_ONil,axiom,
% 0.30/0.47 ! [R: poly_real > produc461822025y_real > $o] : ( listre471999892y_real @ R @ nil_poly_real @ nil_Pr1207979855y_real ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.Nil
% 0.30/0.47 thf(fact_93_listrelp_ONil,axiom,
% 0.30/0.47 ! [R: produc321349221y_real > list_poly_real > $o] : ( listre321577258y_real @ R @ nil_Pr1492526187y_real @ nil_list_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.Nil
% 0.30/0.47 thf(fact_94_listrelp_ONil,axiom,
% 0.30/0.47 ! [R: list_poly_real > produc321349221y_real > $o] : ( listre1037026976y_real @ R @ nil_list_poly_real @ nil_Pr1492526187y_real ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.Nil
% 0.30/0.47 thf(fact_95_listrelp_ONil,axiom,
% 0.30/0.47 ! [R: produc461822025y_real > poly_real > $o] : ( listre1751862142y_real @ R @ nil_Pr1207979855y_real @ nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.Nil
% 0.30/0.47 thf(fact_96_ord_Olexordp__eq_Ocong,axiom,
% 0.30/0.47 lexordp_eq_poly_real = lexordp_eq_poly_real ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq.cong
% 0.30/0.47 thf(fact_97_ord_Olexordp__eq__refl,axiom,
% 0.30/0.47 ! [Less: poly_real > poly_real > $o,Xs: list_poly_real] : ( lexordp_eq_poly_real @ Less @ Xs @ Xs ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq_refl
% 0.30/0.47 thf(fact_98_ord_Olexordp__eq_ONil,axiom,
% 0.30/0.47 ! [Less: produc321349221y_real > produc321349221y_real > $o,Ys: list_P736648811y_real] : ( lexord834705585y_real @ Less @ nil_Pr1492526187y_real @ Ys ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq.Nil
% 0.30/0.47 thf(fact_99_ord_Olexordp__eq_ONil,axiom,
% 0.30/0.47 ! [Less: list_poly_real > list_poly_real > $o,Ys: list_list_poly_real] : ( lexord1324236152y_real @ Less @ nil_list_poly_real @ Ys ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq.Nil
% 0.30/0.47 thf(fact_100_ord_Olexordp__eq_ONil,axiom,
% 0.30/0.47 ! [Less: produc461822025y_real > produc461822025y_real > $o,Ys: list_P693436111y_real] : ( lexord1053351061y_real @ Less @ nil_Pr1207979855y_real @ Ys ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq.Nil
% 0.30/0.47 thf(fact_101_ord_Olexordp__eq_ONil,axiom,
% 0.30/0.47 ! [Less: poly_real > poly_real > $o,Ys: list_poly_real] : ( lexordp_eq_poly_real @ Less @ nil_poly_real @ Ys ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq.Nil
% 0.30/0.47 thf(fact_102_splice_Osimps_I1_J,axiom,
% 0.30/0.47 ! [Ys: list_P736648811y_real] :
% 0.30/0.47 ( ( splice1383748542y_real @ nil_Pr1492526187y_real @ Ys )
% 0.30/0.47 = Ys ) ).
% 0.30/0.47
% 0.30/0.47 % splice.simps(1)
% 0.30/0.47 thf(fact_103_splice_Osimps_I1_J,axiom,
% 0.30/0.47 ! [Ys: list_list_poly_real] :
% 0.30/0.47 ( ( splice2080530731y_real @ nil_list_poly_real @ Ys )
% 0.30/0.47 = Ys ) ).
% 0.30/0.47
% 0.30/0.47 % splice.simps(1)
% 0.30/0.47 thf(fact_104_splice_Osimps_I1_J,axiom,
% 0.30/0.47 ! [Ys: list_P693436111y_real] :
% 0.30/0.47 ( ( splice1321784098y_real @ nil_Pr1207979855y_real @ Ys )
% 0.30/0.47 = Ys ) ).
% 0.30/0.47
% 0.30/0.47 % splice.simps(1)
% 0.30/0.47 thf(fact_105_splice_Osimps_I1_J,axiom,
% 0.30/0.47 ! [Ys: list_poly_real] :
% 0.30/0.47 ( ( splice_poly_real @ nil_poly_real @ Ys )
% 0.30/0.47 = Ys ) ).
% 0.30/0.47
% 0.30/0.47 % splice.simps(1)
% 0.30/0.47 thf(fact_106_rotate1_Osimps_I1_J,axiom,
% 0.30/0.47 ( ( rotate623875384y_real @ nil_Pr1492526187y_real )
% 0.30/0.47 = nil_Pr1492526187y_real ) ).
% 0.30/0.47
% 0.30/0.47 % rotate1.simps(1)
% 0.30/0.47 thf(fact_107_rotate1_Osimps_I1_J,axiom,
% 0.30/0.47 ( ( rotate717473073y_real @ nil_list_poly_real )
% 0.30/0.47 = nil_list_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % rotate1.simps(1)
% 0.30/0.47 thf(fact_108_rotate1_Osimps_I1_J,axiom,
% 0.30/0.47 ( ( rotate867081116y_real @ nil_Pr1207979855y_real )
% 0.30/0.47 = nil_Pr1207979855y_real ) ).
% 0.30/0.47
% 0.30/0.47 % rotate1.simps(1)
% 0.30/0.47 thf(fact_109_rotate1_Osimps_I1_J,axiom,
% 0.30/0.47 ( ( rotate1_poly_real @ nil_poly_real )
% 0.30/0.47 = nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % rotate1.simps(1)
% 0.30/0.47 thf(fact_110_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.30/0.47 ! [Less: list_poly_real > list_poly_real > $o,X: list_poly_real,Xs: list_list_poly_real] :
% 0.30/0.47 ~ ( lexord1324236152y_real @ Less @ ( cons_list_poly_real @ X @ Xs ) @ nil_list_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq_simps(3)
% 0.30/0.47 thf(fact_111_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.30/0.47 ! [Less: produc321349221y_real > produc321349221y_real > $o,X: produc321349221y_real,Xs: list_P736648811y_real] :
% 0.30/0.47 ~ ( lexord834705585y_real @ Less @ ( cons_P1027346459y_real @ X @ Xs ) @ nil_Pr1492526187y_real ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq_simps(3)
% 0.30/0.47 thf(fact_112_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.30/0.47 ! [Less: produc461822025y_real > produc461822025y_real > $o,X: produc461822025y_real,Xs: list_P693436111y_real] :
% 0.30/0.47 ~ ( lexord1053351061y_real @ Less @ ( cons_P1129399039y_real @ X @ Xs ) @ nil_Pr1207979855y_real ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq_simps(3)
% 0.30/0.47 thf(fact_113_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.30/0.47 ! [Less: poly_real > poly_real > $o,X: poly_real,Xs: list_poly_real] :
% 0.30/0.47 ~ ( lexordp_eq_poly_real @ Less @ ( cons_poly_real @ X @ Xs ) @ nil_poly_real ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq_simps(3)
% 0.30/0.47 thf(fact_114_zip__Nil,axiom,
% 0.30/0.47 ! [Ys: list_poly_real] :
% 0.30/0.47 ( ( zip_nat_poly_real @ nil_nat @ Ys )
% 0.30/0.47 = nil_Pr1492526187y_real ) ).
% 0.30/0.47
% 0.30/0.47 % zip_Nil
% 0.30/0.47 thf(fact_115_zip__Nil,axiom,
% 0.30/0.47 ! [Ys: list_poly_real] :
% 0.30/0.47 ( ( zip_po657915297y_real @ nil_poly_real @ Ys )
% 0.30/0.47 = nil_Pr1207979855y_real ) ).
% 0.30/0.47
% 0.30/0.47 % zip_Nil
% 0.30/0.47 thf(fact_116_map__tailrec__rev_Oelims,axiom,
% 0.30/0.47 ! [X: poly_real > poly_real,Xa: list_poly_real,Xb: list_poly_real,Y: list_poly_real] :
% 0.30/0.47 ( ( ( map_ta1919289823y_real @ X @ Xa @ Xb )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( ( Xa = nil_poly_real )
% 0.30/0.47 => ( Y != Xb ) )
% 0.30/0.47 => ~ ! [A: poly_real,As: list_poly_real] :
% 0.30/0.47 ( ( Xa
% 0.30/0.47 = ( cons_poly_real @ A @ As ) )
% 0.30/0.47 => ( Y
% 0.30/0.47 != ( map_ta1919289823y_real @ X @ As @ ( cons_poly_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_tailrec_rev.elims
% 0.30/0.47 thf(fact_117_map__tailrec__rev_Oelims,axiom,
% 0.30/0.47 ! [X: poly_real > list_poly_real,Xa: list_poly_real,Xb: list_list_poly_real,Y: list_list_poly_real] :
% 0.30/0.47 ( ( ( map_ta1513955567y_real @ X @ Xa @ Xb )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( ( Xa = nil_poly_real )
% 0.30/0.47 => ( Y != Xb ) )
% 0.30/0.47 => ~ ! [A: poly_real,As: list_poly_real] :
% 0.30/0.47 ( ( Xa
% 0.30/0.47 = ( cons_poly_real @ A @ As ) )
% 0.30/0.47 => ( Y
% 0.30/0.47 != ( map_ta1513955567y_real @ X @ As @ ( cons_list_poly_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_tailrec_rev.elims
% 0.30/0.47 thf(fact_118_map__tailrec__rev_Oelims,axiom,
% 0.30/0.47 ! [X: list_poly_real > poly_real,Xa: list_list_poly_real,Xb: list_poly_real,Y: list_poly_real] :
% 0.30/0.47 ( ( ( map_ta434235247y_real @ X @ Xa @ Xb )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( ( Xa = nil_list_poly_real )
% 0.30/0.47 => ( Y != Xb ) )
% 0.30/0.47 => ~ ! [A: list_poly_real,As: list_list_poly_real] :
% 0.30/0.47 ( ( Xa
% 0.30/0.47 = ( cons_list_poly_real @ A @ As ) )
% 0.30/0.47 => ( Y
% 0.30/0.47 != ( map_ta434235247y_real @ X @ As @ ( cons_poly_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_tailrec_rev.elims
% 0.30/0.47 thf(fact_119_map__tailrec__rev_Oelims,axiom,
% 0.30/0.47 ! [X: poly_real > produc321349221y_real,Xa: list_poly_real,Xb: list_P736648811y_real,Y: list_P736648811y_real] :
% 0.30/0.47 ( ( ( map_ta632757498y_real @ X @ Xa @ Xb )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( ( Xa = nil_poly_real )
% 0.30/0.47 => ( Y != Xb ) )
% 0.30/0.47 => ~ ! [A: poly_real,As: list_poly_real] :
% 0.30/0.47 ( ( Xa
% 0.30/0.47 = ( cons_poly_real @ A @ As ) )
% 0.30/0.47 => ( Y
% 0.30/0.47 != ( map_ta632757498y_real @ X @ As @ ( cons_P1027346459y_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_tailrec_rev.elims
% 0.30/0.47 thf(fact_120_map__tailrec__rev_Oelims,axiom,
% 0.30/0.47 ! [X: list_poly_real > list_poly_real,Xa: list_list_poly_real,Xb: list_list_poly_real,Y: list_list_poly_real] :
% 0.30/0.47 ( ( ( map_ta316995199y_real @ X @ Xa @ Xb )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( ( Xa = nil_list_poly_real )
% 0.30/0.47 => ( Y != Xb ) )
% 0.30/0.47 => ~ ! [A: list_poly_real,As: list_list_poly_real] :
% 0.30/0.47 ( ( Xa
% 0.30/0.47 = ( cons_list_poly_real @ A @ As ) )
% 0.30/0.47 => ( Y
% 0.30/0.47 != ( map_ta316995199y_real @ X @ As @ ( cons_list_poly_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_tailrec_rev.elims
% 0.30/0.47 thf(fact_121_map__tailrec__rev_Oelims,axiom,
% 0.30/0.47 ! [X: produc321349221y_real > poly_real,Xa: list_P736648811y_real,Xb: list_poly_real,Y: list_poly_real] :
% 0.30/0.47 ( ( ( map_ta787748196y_real @ X @ Xa @ Xb )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( ( Xa = nil_Pr1492526187y_real )
% 0.30/0.47 => ( Y != Xb ) )
% 0.30/0.47 => ~ ! [A: produc321349221y_real,As: list_P736648811y_real] :
% 0.30/0.47 ( ( Xa
% 0.30/0.47 = ( cons_P1027346459y_real @ A @ As ) )
% 0.30/0.47 => ( Y
% 0.30/0.47 != ( map_ta787748196y_real @ X @ As @ ( cons_poly_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_tailrec_rev.elims
% 0.30/0.47 thf(fact_122_map__tailrec__rev_Oelims,axiom,
% 0.30/0.47 ! [X: poly_real > produc461822025y_real,Xa: list_poly_real,Xb: list_P693436111y_real,Y: list_P693436111y_real] :
% 0.30/0.47 ( ( ( map_ta920933982y_real @ X @ Xa @ Xb )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( ( Xa = nil_poly_real )
% 0.30/0.47 => ( Y != Xb ) )
% 0.30/0.47 => ~ ! [A: poly_real,As: list_poly_real] :
% 0.30/0.47 ( ( Xa
% 0.30/0.47 = ( cons_poly_real @ A @ As ) )
% 0.30/0.47 => ( Y
% 0.30/0.47 != ( map_ta920933982y_real @ X @ As @ ( cons_P1129399039y_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_tailrec_rev.elims
% 0.30/0.47 thf(fact_123_map__tailrec__rev_Oelims,axiom,
% 0.30/0.47 ! [X: list_poly_real > produc321349221y_real,Xa: list_list_poly_real,Xb: list_P736648811y_real,Y: list_P736648811y_real] :
% 0.30/0.47 ( ( ( map_ta1674185578y_real @ X @ Xa @ Xb )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( ( Xa = nil_list_poly_real )
% 0.30/0.47 => ( Y != Xb ) )
% 0.30/0.47 => ~ ! [A: list_poly_real,As: list_list_poly_real] :
% 0.30/0.47 ( ( Xa
% 0.30/0.47 = ( cons_list_poly_real @ A @ As ) )
% 0.30/0.47 => ( Y
% 0.30/0.47 != ( map_ta1674185578y_real @ X @ As @ ( cons_P1027346459y_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_tailrec_rev.elims
% 0.30/0.47 thf(fact_124_map__tailrec__rev_Oelims,axiom,
% 0.30/0.47 ! [X: produc321349221y_real > list_poly_real,Xa: list_P736648811y_real,Xb: list_list_poly_real,Y: list_list_poly_real] :
% 0.30/0.47 ( ( ( map_ta958735860y_real @ X @ Xa @ Xb )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( ( Xa = nil_Pr1492526187y_real )
% 0.30/0.47 => ( Y != Xb ) )
% 0.30/0.47 => ~ ! [A: produc321349221y_real,As: list_P736648811y_real] :
% 0.30/0.47 ( ( Xa
% 0.30/0.47 = ( cons_P1027346459y_real @ A @ As ) )
% 0.30/0.47 => ( Y
% 0.30/0.47 != ( map_ta958735860y_real @ X @ As @ ( cons_list_poly_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_tailrec_rev.elims
% 0.30/0.47 thf(fact_125_map__tailrec__rev_Oelims,axiom,
% 0.30/0.47 ! [X: produc461822025y_real > poly_real,Xa: list_P693436111y_real,Xb: list_poly_real,Y: list_poly_real] :
% 0.30/0.47 ( ( ( map_ta53312584y_real @ X @ Xa @ Xb )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( ( Xa = nil_Pr1207979855y_real )
% 0.30/0.47 => ( Y != Xb ) )
% 0.30/0.47 => ~ ! [A: produc461822025y_real,As: list_P693436111y_real] :
% 0.30/0.47 ( ( Xa
% 0.30/0.47 = ( cons_P1129399039y_real @ A @ As ) )
% 0.30/0.47 => ( Y
% 0.30/0.47 != ( map_ta53312584y_real @ X @ As @ ( cons_poly_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % map_tailrec_rev.elims
% 0.30/0.47 thf(fact_126_listrelp_Oinducts,axiom,
% 0.30/0.47 ! [R: poly_real > poly_real > $o,X1: list_poly_real,X2: list_poly_real,P3: list_poly_real > list_poly_real > $o] :
% 0.30/0.47 ( ( listre1609905961y_real @ R @ X1 @ X2 )
% 0.30/0.47 => ( ( P3 @ nil_poly_real @ nil_poly_real )
% 0.30/0.47 => ( ! [X3: poly_real,Y2: poly_real,Xs2: list_poly_real,Ys2: list_poly_real] :
% 0.30/0.47 ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ( ( listre1609905961y_real @ R @ Xs2 @ Ys2 )
% 0.30/0.47 => ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.47 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) ) )
% 0.30/0.47 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.inducts
% 0.30/0.47 thf(fact_127_listrelp_Oinducts,axiom,
% 0.30/0.47 ! [R: poly_real > list_poly_real > $o,X1: list_poly_real,X2: list_list_poly_real,P3: list_poly_real > list_list_poly_real > $o] :
% 0.30/0.47 ( ( listre1793073465y_real @ R @ X1 @ X2 )
% 0.30/0.47 => ( ( P3 @ nil_poly_real @ nil_list_poly_real )
% 0.30/0.47 => ( ! [X3: poly_real,Y2: list_poly_real,Xs2: list_poly_real,Ys2: list_list_poly_real] :
% 0.30/0.47 ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ( ( listre1793073465y_real @ R @ Xs2 @ Ys2 )
% 0.30/0.47 => ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.47 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_list_poly_real @ Y2 @ Ys2 ) ) ) ) )
% 0.30/0.47 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.inducts
% 0.30/0.47 thf(fact_128_listrelp_Oinducts,axiom,
% 0.30/0.47 ! [R: list_poly_real > poly_real > $o,X1: list_list_poly_real,X2: list_poly_real,P3: list_list_poly_real > list_poly_real > $o] :
% 0.30/0.47 ( ( listre713353145y_real @ R @ X1 @ X2 )
% 0.30/0.47 => ( ( P3 @ nil_list_poly_real @ nil_poly_real )
% 0.30/0.47 => ( ! [X3: list_poly_real,Y2: poly_real,Xs2: list_list_poly_real,Ys2: list_poly_real] :
% 0.30/0.47 ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ( ( listre713353145y_real @ R @ Xs2 @ Ys2 )
% 0.30/0.47 => ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.47 => ( P3 @ ( cons_list_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) ) )
% 0.30/0.47 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.inducts
% 0.30/0.47 thf(fact_129_listrelp_Oinducts,axiom,
% 0.30/0.47 ! [R: poly_real > produc321349221y_real > $o,X1: list_poly_real,X2: list_P736648811y_real,P3: list_poly_real > list_P736648811y_real > $o] :
% 0.30/0.47 ( ( listre889482032y_real @ R @ X1 @ X2 )
% 0.30/0.47 => ( ( P3 @ nil_poly_real @ nil_Pr1492526187y_real )
% 0.30/0.47 => ( ! [X3: poly_real,Y2: produc321349221y_real,Xs2: list_poly_real,Ys2: list_P736648811y_real] :
% 0.30/0.47 ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ( ( listre889482032y_real @ R @ Xs2 @ Ys2 )
% 0.30/0.47 => ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.47 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_P1027346459y_real @ Y2 @ Ys2 ) ) ) ) )
% 0.30/0.47 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.inducts
% 0.30/0.47 thf(fact_130_listrelp_Oinducts,axiom,
% 0.30/0.47 ! [R: list_poly_real > list_poly_real > $o,X1: list_list_poly_real,X2: list_list_poly_real,P3: list_list_poly_real > list_list_poly_real > $o] :
% 0.30/0.47 ( ( listre1763068361y_real @ R @ X1 @ X2 )
% 0.30/0.47 => ( ( P3 @ nil_list_poly_real @ nil_list_poly_real )
% 0.30/0.47 => ( ! [X3: list_poly_real,Y2: list_poly_real,Xs2: list_list_poly_real,Ys2: list_list_poly_real] :
% 0.30/0.47 ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ( ( listre1763068361y_real @ R @ Xs2 @ Ys2 )
% 0.30/0.47 => ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.47 => ( P3 @ ( cons_list_poly_real @ X3 @ Xs2 ) @ ( cons_list_poly_real @ Y2 @ Ys2 ) ) ) ) )
% 0.30/0.47 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.inducts
% 0.30/0.47 thf(fact_131_listrelp_Oinducts,axiom,
% 0.30/0.47 ! [R: produc321349221y_real > poly_real > $o,X1: list_P736648811y_real,X2: list_poly_real,P3: list_P736648811y_real > list_poly_real > $o] :
% 0.30/0.47 ( ( listre1044472730y_real @ R @ X1 @ X2 )
% 0.30/0.47 => ( ( P3 @ nil_Pr1492526187y_real @ nil_poly_real )
% 0.30/0.47 => ( ! [X3: produc321349221y_real,Y2: poly_real,Xs2: list_P736648811y_real,Ys2: list_poly_real] :
% 0.30/0.47 ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ( ( listre1044472730y_real @ R @ Xs2 @ Ys2 )
% 0.30/0.47 => ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.47 => ( P3 @ ( cons_P1027346459y_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) ) )
% 0.30/0.47 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.inducts
% 0.30/0.47 thf(fact_132_listrelp_Oinducts,axiom,
% 0.30/0.47 ! [R: poly_real > produc461822025y_real > $o,X1: list_poly_real,X2: list_P693436111y_real,P3: list_poly_real > list_P693436111y_real > $o] :
% 0.30/0.47 ( ( listre471999892y_real @ R @ X1 @ X2 )
% 0.30/0.47 => ( ( P3 @ nil_poly_real @ nil_Pr1207979855y_real )
% 0.30/0.47 => ( ! [X3: poly_real,Y2: produc461822025y_real,Xs2: list_poly_real,Ys2: list_P693436111y_real] :
% 0.30/0.47 ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ( ( listre471999892y_real @ R @ Xs2 @ Ys2 )
% 0.30/0.47 => ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.47 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_P1129399039y_real @ Y2 @ Ys2 ) ) ) ) )
% 0.30/0.47 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.inducts
% 0.30/0.47 thf(fact_133_listrelp_Oinducts,axiom,
% 0.30/0.47 ! [R: list_poly_real > produc321349221y_real > $o,X1: list_list_poly_real,X2: list_P736648811y_real,P3: list_list_poly_real > list_P736648811y_real > $o] :
% 0.30/0.47 ( ( listre1037026976y_real @ R @ X1 @ X2 )
% 0.30/0.47 => ( ( P3 @ nil_list_poly_real @ nil_Pr1492526187y_real )
% 0.30/0.47 => ( ! [X3: list_poly_real,Y2: produc321349221y_real,Xs2: list_list_poly_real,Ys2: list_P736648811y_real] :
% 0.30/0.47 ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ( ( listre1037026976y_real @ R @ Xs2 @ Ys2 )
% 0.30/0.47 => ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.47 => ( P3 @ ( cons_list_poly_real @ X3 @ Xs2 ) @ ( cons_P1027346459y_real @ Y2 @ Ys2 ) ) ) ) )
% 0.30/0.47 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.inducts
% 0.30/0.47 thf(fact_134_listrelp_Oinducts,axiom,
% 0.30/0.47 ! [R: produc321349221y_real > list_poly_real > $o,X1: list_P736648811y_real,X2: list_list_poly_real,P3: list_P736648811y_real > list_list_poly_real > $o] :
% 0.30/0.47 ( ( listre321577258y_real @ R @ X1 @ X2 )
% 0.30/0.47 => ( ( P3 @ nil_Pr1492526187y_real @ nil_list_poly_real )
% 0.30/0.47 => ( ! [X3: produc321349221y_real,Y2: list_poly_real,Xs2: list_P736648811y_real,Ys2: list_list_poly_real] :
% 0.30/0.47 ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ( ( listre321577258y_real @ R @ Xs2 @ Ys2 )
% 0.30/0.47 => ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.47 => ( P3 @ ( cons_P1027346459y_real @ X3 @ Xs2 ) @ ( cons_list_poly_real @ Y2 @ Ys2 ) ) ) ) )
% 0.30/0.47 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.inducts
% 0.30/0.47 thf(fact_135_listrelp_Oinducts,axiom,
% 0.30/0.47 ! [R: produc461822025y_real > poly_real > $o,X1: list_P693436111y_real,X2: list_poly_real,P3: list_P693436111y_real > list_poly_real > $o] :
% 0.30/0.47 ( ( listre1751862142y_real @ R @ X1 @ X2 )
% 0.30/0.47 => ( ( P3 @ nil_Pr1207979855y_real @ nil_poly_real )
% 0.30/0.47 => ( ! [X3: produc461822025y_real,Y2: poly_real,Xs2: list_P693436111y_real,Ys2: list_poly_real] :
% 0.30/0.47 ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ( ( listre1751862142y_real @ R @ Xs2 @ Ys2 )
% 0.30/0.47 => ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.47 => ( P3 @ ( cons_P1129399039y_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) ) )
% 0.30/0.47 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.inducts
% 0.30/0.47 thf(fact_136_listrelp_Osimps,axiom,
% 0.30/0.47 ( listre1609905961y_real
% 0.30/0.47 = ( ^ [R2: poly_real > poly_real > $o,A1: list_poly_real,A2: list_poly_real] :
% 0.30/0.47 ( ( ( A1 = nil_poly_real )
% 0.30/0.47 & ( A2 = nil_poly_real ) )
% 0.30/0.47 | ? [X4: poly_real,Y3: poly_real,Xs3: list_poly_real,Ys3: list_poly_real] :
% 0.30/0.47 ( ( A1
% 0.30/0.47 = ( cons_poly_real @ X4 @ Xs3 ) )
% 0.30/0.47 & ( A2
% 0.30/0.47 = ( cons_poly_real @ Y3 @ Ys3 ) )
% 0.30/0.47 & ( R2 @ X4 @ Y3 )
% 0.30/0.47 & ( listre1609905961y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.simps
% 0.30/0.47 thf(fact_137_listrelp_Osimps,axiom,
% 0.30/0.47 ( listre1793073465y_real
% 0.30/0.47 = ( ^ [R2: poly_real > list_poly_real > $o,A1: list_poly_real,A2: list_list_poly_real] :
% 0.30/0.47 ( ( ( A1 = nil_poly_real )
% 0.30/0.47 & ( A2 = nil_list_poly_real ) )
% 0.30/0.47 | ? [X4: poly_real,Y3: list_poly_real,Xs3: list_poly_real,Ys3: list_list_poly_real] :
% 0.30/0.47 ( ( A1
% 0.30/0.47 = ( cons_poly_real @ X4 @ Xs3 ) )
% 0.30/0.47 & ( A2
% 0.30/0.47 = ( cons_list_poly_real @ Y3 @ Ys3 ) )
% 0.30/0.47 & ( R2 @ X4 @ Y3 )
% 0.30/0.47 & ( listre1793073465y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.simps
% 0.30/0.47 thf(fact_138_listrelp_Osimps,axiom,
% 0.30/0.47 ( listre713353145y_real
% 0.30/0.47 = ( ^ [R2: list_poly_real > poly_real > $o,A1: list_list_poly_real,A2: list_poly_real] :
% 0.30/0.47 ( ( ( A1 = nil_list_poly_real )
% 0.30/0.47 & ( A2 = nil_poly_real ) )
% 0.30/0.47 | ? [X4: list_poly_real,Y3: poly_real,Xs3: list_list_poly_real,Ys3: list_poly_real] :
% 0.30/0.47 ( ( A1
% 0.30/0.47 = ( cons_list_poly_real @ X4 @ Xs3 ) )
% 0.30/0.47 & ( A2
% 0.30/0.47 = ( cons_poly_real @ Y3 @ Ys3 ) )
% 0.30/0.47 & ( R2 @ X4 @ Y3 )
% 0.30/0.47 & ( listre713353145y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.simps
% 0.30/0.47 thf(fact_139_listrelp_Osimps,axiom,
% 0.30/0.47 ( listre889482032y_real
% 0.30/0.47 = ( ^ [R2: poly_real > produc321349221y_real > $o,A1: list_poly_real,A2: list_P736648811y_real] :
% 0.30/0.47 ( ( ( A1 = nil_poly_real )
% 0.30/0.47 & ( A2 = nil_Pr1492526187y_real ) )
% 0.30/0.47 | ? [X4: poly_real,Y3: produc321349221y_real,Xs3: list_poly_real,Ys3: list_P736648811y_real] :
% 0.30/0.47 ( ( A1
% 0.30/0.47 = ( cons_poly_real @ X4 @ Xs3 ) )
% 0.30/0.47 & ( A2
% 0.30/0.47 = ( cons_P1027346459y_real @ Y3 @ Ys3 ) )
% 0.30/0.47 & ( R2 @ X4 @ Y3 )
% 0.30/0.47 & ( listre889482032y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.simps
% 0.30/0.47 thf(fact_140_listrelp_Osimps,axiom,
% 0.30/0.47 ( listre1763068361y_real
% 0.30/0.47 = ( ^ [R2: list_poly_real > list_poly_real > $o,A1: list_list_poly_real,A2: list_list_poly_real] :
% 0.30/0.47 ( ( ( A1 = nil_list_poly_real )
% 0.30/0.47 & ( A2 = nil_list_poly_real ) )
% 0.30/0.47 | ? [X4: list_poly_real,Y3: list_poly_real,Xs3: list_list_poly_real,Ys3: list_list_poly_real] :
% 0.30/0.47 ( ( A1
% 0.30/0.47 = ( cons_list_poly_real @ X4 @ Xs3 ) )
% 0.30/0.47 & ( A2
% 0.30/0.47 = ( cons_list_poly_real @ Y3 @ Ys3 ) )
% 0.30/0.47 & ( R2 @ X4 @ Y3 )
% 0.30/0.47 & ( listre1763068361y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.simps
% 0.30/0.47 thf(fact_141_listrelp_Osimps,axiom,
% 0.30/0.47 ( listre1044472730y_real
% 0.30/0.47 = ( ^ [R2: produc321349221y_real > poly_real > $o,A1: list_P736648811y_real,A2: list_poly_real] :
% 0.30/0.47 ( ( ( A1 = nil_Pr1492526187y_real )
% 0.30/0.47 & ( A2 = nil_poly_real ) )
% 0.30/0.47 | ? [X4: produc321349221y_real,Y3: poly_real,Xs3: list_P736648811y_real,Ys3: list_poly_real] :
% 0.30/0.47 ( ( A1
% 0.30/0.47 = ( cons_P1027346459y_real @ X4 @ Xs3 ) )
% 0.30/0.47 & ( A2
% 0.30/0.47 = ( cons_poly_real @ Y3 @ Ys3 ) )
% 0.30/0.47 & ( R2 @ X4 @ Y3 )
% 0.30/0.47 & ( listre1044472730y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.simps
% 0.30/0.47 thf(fact_142_listrelp_Osimps,axiom,
% 0.30/0.47 ( listre471999892y_real
% 0.30/0.47 = ( ^ [R2: poly_real > produc461822025y_real > $o,A1: list_poly_real,A2: list_P693436111y_real] :
% 0.30/0.47 ( ( ( A1 = nil_poly_real )
% 0.30/0.47 & ( A2 = nil_Pr1207979855y_real ) )
% 0.30/0.47 | ? [X4: poly_real,Y3: produc461822025y_real,Xs3: list_poly_real,Ys3: list_P693436111y_real] :
% 0.30/0.47 ( ( A1
% 0.30/0.47 = ( cons_poly_real @ X4 @ Xs3 ) )
% 0.30/0.47 & ( A2
% 0.30/0.47 = ( cons_P1129399039y_real @ Y3 @ Ys3 ) )
% 0.30/0.47 & ( R2 @ X4 @ Y3 )
% 0.30/0.47 & ( listre471999892y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.simps
% 0.30/0.47 thf(fact_143_listrelp_Osimps,axiom,
% 0.30/0.47 ( listre1037026976y_real
% 0.30/0.47 = ( ^ [R2: list_poly_real > produc321349221y_real > $o,A1: list_list_poly_real,A2: list_P736648811y_real] :
% 0.30/0.47 ( ( ( A1 = nil_list_poly_real )
% 0.30/0.47 & ( A2 = nil_Pr1492526187y_real ) )
% 0.30/0.47 | ? [X4: list_poly_real,Y3: produc321349221y_real,Xs3: list_list_poly_real,Ys3: list_P736648811y_real] :
% 0.30/0.47 ( ( A1
% 0.30/0.47 = ( cons_list_poly_real @ X4 @ Xs3 ) )
% 0.30/0.47 & ( A2
% 0.30/0.47 = ( cons_P1027346459y_real @ Y3 @ Ys3 ) )
% 0.30/0.47 & ( R2 @ X4 @ Y3 )
% 0.30/0.47 & ( listre1037026976y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.simps
% 0.30/0.47 thf(fact_144_listrelp_Osimps,axiom,
% 0.30/0.47 ( listre321577258y_real
% 0.30/0.47 = ( ^ [R2: produc321349221y_real > list_poly_real > $o,A1: list_P736648811y_real,A2: list_list_poly_real] :
% 0.30/0.47 ( ( ( A1 = nil_Pr1492526187y_real )
% 0.30/0.47 & ( A2 = nil_list_poly_real ) )
% 0.30/0.47 | ? [X4: produc321349221y_real,Y3: list_poly_real,Xs3: list_P736648811y_real,Ys3: list_list_poly_real] :
% 0.30/0.47 ( ( A1
% 0.30/0.47 = ( cons_P1027346459y_real @ X4 @ Xs3 ) )
% 0.30/0.47 & ( A2
% 0.30/0.47 = ( cons_list_poly_real @ Y3 @ Ys3 ) )
% 0.30/0.47 & ( R2 @ X4 @ Y3 )
% 0.30/0.47 & ( listre321577258y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.simps
% 0.30/0.47 thf(fact_145_listrelp_Osimps,axiom,
% 0.30/0.47 ( listre1751862142y_real
% 0.30/0.47 = ( ^ [R2: produc461822025y_real > poly_real > $o,A1: list_P693436111y_real,A2: list_poly_real] :
% 0.30/0.47 ( ( ( A1 = nil_Pr1207979855y_real )
% 0.30/0.47 & ( A2 = nil_poly_real ) )
% 0.30/0.47 | ? [X4: produc461822025y_real,Y3: poly_real,Xs3: list_P693436111y_real,Ys3: list_poly_real] :
% 0.30/0.47 ( ( A1
% 0.30/0.47 = ( cons_P1129399039y_real @ X4 @ Xs3 ) )
% 0.30/0.47 & ( A2
% 0.30/0.47 = ( cons_poly_real @ Y3 @ Ys3 ) )
% 0.30/0.47 & ( R2 @ X4 @ Y3 )
% 0.30/0.47 & ( listre1751862142y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.simps
% 0.30/0.47 thf(fact_146_listrelp_Ocases,axiom,
% 0.30/0.47 ! [R: poly_real > poly_real > $o,A12: list_poly_real,A22: list_poly_real] :
% 0.30/0.47 ( ( listre1609905961y_real @ R @ A12 @ A22 )
% 0.30/0.47 => ( ( ( A12 = nil_poly_real )
% 0.30/0.47 => ( A22 != nil_poly_real ) )
% 0.30/0.47 => ~ ! [X3: poly_real,Y2: poly_real,Xs2: list_poly_real] :
% 0.30/0.47 ( ( A12
% 0.30/0.47 = ( cons_poly_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ! [Ys2: list_poly_real] :
% 0.30/0.47 ( ( A22
% 0.30/0.47 = ( cons_poly_real @ Y2 @ Ys2 ) )
% 0.30/0.47 => ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ~ ( listre1609905961y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.cases
% 0.30/0.47 thf(fact_147_listrelp_Ocases,axiom,
% 0.30/0.47 ! [R: poly_real > list_poly_real > $o,A12: list_poly_real,A22: list_list_poly_real] :
% 0.30/0.47 ( ( listre1793073465y_real @ R @ A12 @ A22 )
% 0.30/0.47 => ( ( ( A12 = nil_poly_real )
% 0.30/0.47 => ( A22 != nil_list_poly_real ) )
% 0.30/0.47 => ~ ! [X3: poly_real,Y2: list_poly_real,Xs2: list_poly_real] :
% 0.30/0.47 ( ( A12
% 0.30/0.47 = ( cons_poly_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ! [Ys2: list_list_poly_real] :
% 0.30/0.47 ( ( A22
% 0.30/0.47 = ( cons_list_poly_real @ Y2 @ Ys2 ) )
% 0.30/0.47 => ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ~ ( listre1793073465y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.cases
% 0.30/0.47 thf(fact_148_listrelp_Ocases,axiom,
% 0.30/0.47 ! [R: list_poly_real > poly_real > $o,A12: list_list_poly_real,A22: list_poly_real] :
% 0.30/0.47 ( ( listre713353145y_real @ R @ A12 @ A22 )
% 0.30/0.47 => ( ( ( A12 = nil_list_poly_real )
% 0.30/0.47 => ( A22 != nil_poly_real ) )
% 0.30/0.47 => ~ ! [X3: list_poly_real,Y2: poly_real,Xs2: list_list_poly_real] :
% 0.30/0.47 ( ( A12
% 0.30/0.47 = ( cons_list_poly_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ! [Ys2: list_poly_real] :
% 0.30/0.47 ( ( A22
% 0.30/0.47 = ( cons_poly_real @ Y2 @ Ys2 ) )
% 0.30/0.47 => ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ~ ( listre713353145y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.cases
% 0.30/0.47 thf(fact_149_listrelp_Ocases,axiom,
% 0.30/0.47 ! [R: poly_real > produc321349221y_real > $o,A12: list_poly_real,A22: list_P736648811y_real] :
% 0.30/0.47 ( ( listre889482032y_real @ R @ A12 @ A22 )
% 0.30/0.47 => ( ( ( A12 = nil_poly_real )
% 0.30/0.47 => ( A22 != nil_Pr1492526187y_real ) )
% 0.30/0.47 => ~ ! [X3: poly_real,Y2: produc321349221y_real,Xs2: list_poly_real] :
% 0.30/0.47 ( ( A12
% 0.30/0.47 = ( cons_poly_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ! [Ys2: list_P736648811y_real] :
% 0.30/0.47 ( ( A22
% 0.30/0.47 = ( cons_P1027346459y_real @ Y2 @ Ys2 ) )
% 0.30/0.47 => ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ~ ( listre889482032y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.cases
% 0.30/0.47 thf(fact_150_listrelp_Ocases,axiom,
% 0.30/0.47 ! [R: list_poly_real > list_poly_real > $o,A12: list_list_poly_real,A22: list_list_poly_real] :
% 0.30/0.47 ( ( listre1763068361y_real @ R @ A12 @ A22 )
% 0.30/0.47 => ( ( ( A12 = nil_list_poly_real )
% 0.30/0.47 => ( A22 != nil_list_poly_real ) )
% 0.30/0.47 => ~ ! [X3: list_poly_real,Y2: list_poly_real,Xs2: list_list_poly_real] :
% 0.30/0.47 ( ( A12
% 0.30/0.47 = ( cons_list_poly_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ! [Ys2: list_list_poly_real] :
% 0.30/0.47 ( ( A22
% 0.30/0.47 = ( cons_list_poly_real @ Y2 @ Ys2 ) )
% 0.30/0.47 => ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ~ ( listre1763068361y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.cases
% 0.30/0.47 thf(fact_151_listrelp_Ocases,axiom,
% 0.30/0.47 ! [R: produc321349221y_real > poly_real > $o,A12: list_P736648811y_real,A22: list_poly_real] :
% 0.30/0.47 ( ( listre1044472730y_real @ R @ A12 @ A22 )
% 0.30/0.47 => ( ( ( A12 = nil_Pr1492526187y_real )
% 0.30/0.47 => ( A22 != nil_poly_real ) )
% 0.30/0.47 => ~ ! [X3: produc321349221y_real,Y2: poly_real,Xs2: list_P736648811y_real] :
% 0.30/0.47 ( ( A12
% 0.30/0.47 = ( cons_P1027346459y_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ! [Ys2: list_poly_real] :
% 0.30/0.47 ( ( A22
% 0.30/0.47 = ( cons_poly_real @ Y2 @ Ys2 ) )
% 0.30/0.47 => ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ~ ( listre1044472730y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.cases
% 0.30/0.47 thf(fact_152_listrelp_Ocases,axiom,
% 0.30/0.47 ! [R: poly_real > produc461822025y_real > $o,A12: list_poly_real,A22: list_P693436111y_real] :
% 0.30/0.47 ( ( listre471999892y_real @ R @ A12 @ A22 )
% 0.30/0.47 => ( ( ( A12 = nil_poly_real )
% 0.30/0.47 => ( A22 != nil_Pr1207979855y_real ) )
% 0.30/0.47 => ~ ! [X3: poly_real,Y2: produc461822025y_real,Xs2: list_poly_real] :
% 0.30/0.47 ( ( A12
% 0.30/0.47 = ( cons_poly_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ! [Ys2: list_P693436111y_real] :
% 0.30/0.47 ( ( A22
% 0.30/0.47 = ( cons_P1129399039y_real @ Y2 @ Ys2 ) )
% 0.30/0.47 => ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ~ ( listre471999892y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.cases
% 0.30/0.47 thf(fact_153_listrelp_Ocases,axiom,
% 0.30/0.47 ! [R: list_poly_real > produc321349221y_real > $o,A12: list_list_poly_real,A22: list_P736648811y_real] :
% 0.30/0.47 ( ( listre1037026976y_real @ R @ A12 @ A22 )
% 0.30/0.47 => ( ( ( A12 = nil_list_poly_real )
% 0.30/0.47 => ( A22 != nil_Pr1492526187y_real ) )
% 0.30/0.47 => ~ ! [X3: list_poly_real,Y2: produc321349221y_real,Xs2: list_list_poly_real] :
% 0.30/0.47 ( ( A12
% 0.30/0.47 = ( cons_list_poly_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ! [Ys2: list_P736648811y_real] :
% 0.30/0.47 ( ( A22
% 0.30/0.47 = ( cons_P1027346459y_real @ Y2 @ Ys2 ) )
% 0.30/0.47 => ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ~ ( listre1037026976y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.cases
% 0.30/0.47 thf(fact_154_listrelp_Ocases,axiom,
% 0.30/0.47 ! [R: produc321349221y_real > list_poly_real > $o,A12: list_P736648811y_real,A22: list_list_poly_real] :
% 0.30/0.47 ( ( listre321577258y_real @ R @ A12 @ A22 )
% 0.30/0.47 => ( ( ( A12 = nil_Pr1492526187y_real )
% 0.30/0.47 => ( A22 != nil_list_poly_real ) )
% 0.30/0.47 => ~ ! [X3: produc321349221y_real,Y2: list_poly_real,Xs2: list_P736648811y_real] :
% 0.30/0.47 ( ( A12
% 0.30/0.47 = ( cons_P1027346459y_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ! [Ys2: list_list_poly_real] :
% 0.30/0.47 ( ( A22
% 0.30/0.47 = ( cons_list_poly_real @ Y2 @ Ys2 ) )
% 0.30/0.47 => ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ~ ( listre321577258y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.cases
% 0.30/0.47 thf(fact_155_listrelp_Ocases,axiom,
% 0.30/0.47 ! [R: produc461822025y_real > poly_real > $o,A12: list_P693436111y_real,A22: list_poly_real] :
% 0.30/0.47 ( ( listre1751862142y_real @ R @ A12 @ A22 )
% 0.30/0.47 => ( ( ( A12 = nil_Pr1207979855y_real )
% 0.30/0.47 => ( A22 != nil_poly_real ) )
% 0.30/0.47 => ~ ! [X3: produc461822025y_real,Y2: poly_real,Xs2: list_P693436111y_real] :
% 0.30/0.47 ( ( A12
% 0.30/0.47 = ( cons_P1129399039y_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ! [Ys2: list_poly_real] :
% 0.30/0.47 ( ( A22
% 0.30/0.47 = ( cons_poly_real @ Y2 @ Ys2 ) )
% 0.30/0.47 => ( ( R @ X3 @ Y2 )
% 0.30/0.47 => ~ ( listre1751862142y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % listrelp.cases
% 0.30/0.47 thf(fact_156_splice_Oelims,axiom,
% 0.30/0.47 ! [X: list_list_poly_real,Xa: list_list_poly_real,Y: list_list_poly_real] :
% 0.30/0.47 ( ( ( splice2080530731y_real @ X @ Xa )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( ( X = nil_list_poly_real )
% 0.30/0.47 => ( Y != Xa ) )
% 0.30/0.47 => ~ ! [X3: list_poly_real,Xs2: list_list_poly_real] :
% 0.30/0.47 ( ( X
% 0.30/0.47 = ( cons_list_poly_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ( Y
% 0.30/0.47 != ( cons_list_poly_real @ X3 @ ( splice2080530731y_real @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % splice.elims
% 0.30/0.47 thf(fact_157_splice_Oelims,axiom,
% 0.30/0.47 ! [X: list_P736648811y_real,Xa: list_P736648811y_real,Y: list_P736648811y_real] :
% 0.30/0.47 ( ( ( splice1383748542y_real @ X @ Xa )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( ( X = nil_Pr1492526187y_real )
% 0.30/0.47 => ( Y != Xa ) )
% 0.30/0.47 => ~ ! [X3: produc321349221y_real,Xs2: list_P736648811y_real] :
% 0.30/0.47 ( ( X
% 0.30/0.47 = ( cons_P1027346459y_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ( Y
% 0.30/0.47 != ( cons_P1027346459y_real @ X3 @ ( splice1383748542y_real @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % splice.elims
% 0.30/0.47 thf(fact_158_splice_Oelims,axiom,
% 0.30/0.47 ! [X: list_P693436111y_real,Xa: list_P693436111y_real,Y: list_P693436111y_real] :
% 0.30/0.47 ( ( ( splice1321784098y_real @ X @ Xa )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( ( X = nil_Pr1207979855y_real )
% 0.30/0.47 => ( Y != Xa ) )
% 0.30/0.47 => ~ ! [X3: produc461822025y_real,Xs2: list_P693436111y_real] :
% 0.30/0.47 ( ( X
% 0.30/0.47 = ( cons_P1129399039y_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ( Y
% 0.30/0.47 != ( cons_P1129399039y_real @ X3 @ ( splice1321784098y_real @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % splice.elims
% 0.30/0.47 thf(fact_159_splice_Oelims,axiom,
% 0.30/0.47 ! [X: list_poly_real,Xa: list_poly_real,Y: list_poly_real] :
% 0.30/0.47 ( ( ( splice_poly_real @ X @ Xa )
% 0.30/0.47 = Y )
% 0.30/0.47 => ( ( ( X = nil_poly_real )
% 0.30/0.47 => ( Y != Xa ) )
% 0.30/0.47 => ~ ! [X3: poly_real,Xs2: list_poly_real] :
% 0.30/0.47 ( ( X
% 0.30/0.47 = ( cons_poly_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ( Y
% 0.30/0.47 != ( cons_poly_real @ X3 @ ( splice_poly_real @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % splice.elims
% 0.30/0.47 thf(fact_160_ord_Olexordp__eq_Oinducts,axiom,
% 0.30/0.47 ! [Less: list_poly_real > list_poly_real > $o,X1: list_list_poly_real,X2: list_list_poly_real,P3: list_list_poly_real > list_list_poly_real > $o] :
% 0.30/0.47 ( ( lexord1324236152y_real @ Less @ X1 @ X2 )
% 0.30/0.47 => ( ! [X_1: list_list_poly_real] : ( P3 @ nil_list_poly_real @ X_1 )
% 0.30/0.47 => ( ! [X3: list_poly_real,Y2: list_poly_real,Xs2: list_list_poly_real,Ys2: list_list_poly_real] :
% 0.30/0.47 ( ( Less @ X3 @ Y2 )
% 0.30/0.47 => ( P3 @ ( cons_list_poly_real @ X3 @ Xs2 ) @ ( cons_list_poly_real @ Y2 @ Ys2 ) ) )
% 0.30/0.47 => ( ! [X3: list_poly_real,Y2: list_poly_real,Xs2: list_list_poly_real,Ys2: list_list_poly_real] :
% 0.30/0.47 ( ~ ( Less @ X3 @ Y2 )
% 0.30/0.47 => ( ~ ( Less @ Y2 @ X3 )
% 0.30/0.47 => ( ( lexord1324236152y_real @ Less @ Xs2 @ Ys2 )
% 0.30/0.47 => ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.47 => ( P3 @ ( cons_list_poly_real @ X3 @ Xs2 ) @ ( cons_list_poly_real @ Y2 @ Ys2 ) ) ) ) ) )
% 0.30/0.47 => ( P3 @ X1 @ X2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq.inducts
% 0.30/0.47 thf(fact_161_ord_Olexordp__eq_Oinducts,axiom,
% 0.30/0.47 ! [Less: produc321349221y_real > produc321349221y_real > $o,X1: list_P736648811y_real,X2: list_P736648811y_real,P3: list_P736648811y_real > list_P736648811y_real > $o] :
% 0.30/0.47 ( ( lexord834705585y_real @ Less @ X1 @ X2 )
% 0.30/0.47 => ( ! [X_1: list_P736648811y_real] : ( P3 @ nil_Pr1492526187y_real @ X_1 )
% 0.30/0.47 => ( ! [X3: produc321349221y_real,Y2: produc321349221y_real,Xs2: list_P736648811y_real,Ys2: list_P736648811y_real] :
% 0.30/0.47 ( ( Less @ X3 @ Y2 )
% 0.30/0.47 => ( P3 @ ( cons_P1027346459y_real @ X3 @ Xs2 ) @ ( cons_P1027346459y_real @ Y2 @ Ys2 ) ) )
% 0.30/0.47 => ( ! [X3: produc321349221y_real,Y2: produc321349221y_real,Xs2: list_P736648811y_real,Ys2: list_P736648811y_real] :
% 0.30/0.47 ( ~ ( Less @ X3 @ Y2 )
% 0.30/0.47 => ( ~ ( Less @ Y2 @ X3 )
% 0.30/0.47 => ( ( lexord834705585y_real @ Less @ Xs2 @ Ys2 )
% 0.30/0.47 => ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.47 => ( P3 @ ( cons_P1027346459y_real @ X3 @ Xs2 ) @ ( cons_P1027346459y_real @ Y2 @ Ys2 ) ) ) ) ) )
% 0.30/0.47 => ( P3 @ X1 @ X2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq.inducts
% 0.30/0.47 thf(fact_162_ord_Olexordp__eq_Oinducts,axiom,
% 0.30/0.47 ! [Less: produc461822025y_real > produc461822025y_real > $o,X1: list_P693436111y_real,X2: list_P693436111y_real,P3: list_P693436111y_real > list_P693436111y_real > $o] :
% 0.30/0.47 ( ( lexord1053351061y_real @ Less @ X1 @ X2 )
% 0.30/0.47 => ( ! [X_1: list_P693436111y_real] : ( P3 @ nil_Pr1207979855y_real @ X_1 )
% 0.30/0.47 => ( ! [X3: produc461822025y_real,Y2: produc461822025y_real,Xs2: list_P693436111y_real,Ys2: list_P693436111y_real] :
% 0.30/0.47 ( ( Less @ X3 @ Y2 )
% 0.30/0.47 => ( P3 @ ( cons_P1129399039y_real @ X3 @ Xs2 ) @ ( cons_P1129399039y_real @ Y2 @ Ys2 ) ) )
% 0.30/0.47 => ( ! [X3: produc461822025y_real,Y2: produc461822025y_real,Xs2: list_P693436111y_real,Ys2: list_P693436111y_real] :
% 0.30/0.47 ( ~ ( Less @ X3 @ Y2 )
% 0.30/0.47 => ( ~ ( Less @ Y2 @ X3 )
% 0.30/0.47 => ( ( lexord1053351061y_real @ Less @ Xs2 @ Ys2 )
% 0.30/0.47 => ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.47 => ( P3 @ ( cons_P1129399039y_real @ X3 @ Xs2 ) @ ( cons_P1129399039y_real @ Y2 @ Ys2 ) ) ) ) ) )
% 0.30/0.47 => ( P3 @ X1 @ X2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq.inducts
% 0.30/0.47 thf(fact_163_ord_Olexordp__eq_Oinducts,axiom,
% 0.30/0.47 ! [Less: poly_real > poly_real > $o,X1: list_poly_real,X2: list_poly_real,P3: list_poly_real > list_poly_real > $o] :
% 0.30/0.47 ( ( lexordp_eq_poly_real @ Less @ X1 @ X2 )
% 0.30/0.47 => ( ! [X_1: list_poly_real] : ( P3 @ nil_poly_real @ X_1 )
% 0.30/0.47 => ( ! [X3: poly_real,Y2: poly_real,Xs2: list_poly_real,Ys2: list_poly_real] :
% 0.30/0.47 ( ( Less @ X3 @ Y2 )
% 0.30/0.47 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) )
% 0.30/0.47 => ( ! [X3: poly_real,Y2: poly_real,Xs2: list_poly_real,Ys2: list_poly_real] :
% 0.30/0.47 ( ~ ( Less @ X3 @ Y2 )
% 0.30/0.47 => ( ~ ( Less @ Y2 @ X3 )
% 0.30/0.47 => ( ( lexordp_eq_poly_real @ Less @ Xs2 @ Ys2 )
% 0.30/0.47 => ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.47 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) ) ) )
% 0.30/0.47 => ( P3 @ X1 @ X2 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq.inducts
% 0.30/0.47 thf(fact_164_ord_Olexordp__eq_Osimps,axiom,
% 0.30/0.47 ( lexord1324236152y_real
% 0.30/0.47 = ( ^ [Less2: list_poly_real > list_poly_real > $o,A1: list_list_poly_real,A2: list_list_poly_real] :
% 0.30/0.47 ( ? [Ys3: list_list_poly_real] :
% 0.30/0.47 ( ( A1 = nil_list_poly_real )
% 0.30/0.47 & ( A2 = Ys3 ) )
% 0.30/0.47 | ? [X4: list_poly_real,Y3: list_poly_real,Xs3: list_list_poly_real,Ys3: list_list_poly_real] :
% 0.30/0.47 ( ( A1
% 0.30/0.47 = ( cons_list_poly_real @ X4 @ Xs3 ) )
% 0.30/0.47 & ( A2
% 0.30/0.47 = ( cons_list_poly_real @ Y3 @ Ys3 ) )
% 0.30/0.47 & ( Less2 @ X4 @ Y3 ) )
% 0.30/0.47 | ? [X4: list_poly_real,Y3: list_poly_real,Xs3: list_list_poly_real,Ys3: list_list_poly_real] :
% 0.30/0.47 ( ( A1
% 0.30/0.47 = ( cons_list_poly_real @ X4 @ Xs3 ) )
% 0.30/0.47 & ( A2
% 0.30/0.47 = ( cons_list_poly_real @ Y3 @ Ys3 ) )
% 0.30/0.47 & ~ ( Less2 @ X4 @ Y3 )
% 0.30/0.47 & ~ ( Less2 @ Y3 @ X4 )
% 0.30/0.47 & ( lexord1324236152y_real @ Less2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq.simps
% 0.30/0.47 thf(fact_165_ord_Olexordp__eq_Osimps,axiom,
% 0.30/0.47 ( lexord834705585y_real
% 0.30/0.47 = ( ^ [Less2: produc321349221y_real > produc321349221y_real > $o,A1: list_P736648811y_real,A2: list_P736648811y_real] :
% 0.30/0.47 ( ? [Ys3: list_P736648811y_real] :
% 0.30/0.47 ( ( A1 = nil_Pr1492526187y_real )
% 0.30/0.47 & ( A2 = Ys3 ) )
% 0.30/0.47 | ? [X4: produc321349221y_real,Y3: produc321349221y_real,Xs3: list_P736648811y_real,Ys3: list_P736648811y_real] :
% 0.30/0.47 ( ( A1
% 0.30/0.47 = ( cons_P1027346459y_real @ X4 @ Xs3 ) )
% 0.30/0.47 & ( A2
% 0.30/0.47 = ( cons_P1027346459y_real @ Y3 @ Ys3 ) )
% 0.30/0.47 & ( Less2 @ X4 @ Y3 ) )
% 0.30/0.47 | ? [X4: produc321349221y_real,Y3: produc321349221y_real,Xs3: list_P736648811y_real,Ys3: list_P736648811y_real] :
% 0.30/0.47 ( ( A1
% 0.30/0.47 = ( cons_P1027346459y_real @ X4 @ Xs3 ) )
% 0.30/0.47 & ( A2
% 0.30/0.47 = ( cons_P1027346459y_real @ Y3 @ Ys3 ) )
% 0.30/0.47 & ~ ( Less2 @ X4 @ Y3 )
% 0.30/0.47 & ~ ( Less2 @ Y3 @ X4 )
% 0.30/0.47 & ( lexord834705585y_real @ Less2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq.simps
% 0.30/0.47 thf(fact_166_ord_Olexordp__eq_Osimps,axiom,
% 0.30/0.47 ( lexord1053351061y_real
% 0.30/0.47 = ( ^ [Less2: produc461822025y_real > produc461822025y_real > $o,A1: list_P693436111y_real,A2: list_P693436111y_real] :
% 0.30/0.47 ( ? [Ys3: list_P693436111y_real] :
% 0.30/0.47 ( ( A1 = nil_Pr1207979855y_real )
% 0.30/0.47 & ( A2 = Ys3 ) )
% 0.30/0.47 | ? [X4: produc461822025y_real,Y3: produc461822025y_real,Xs3: list_P693436111y_real,Ys3: list_P693436111y_real] :
% 0.30/0.47 ( ( A1
% 0.30/0.47 = ( cons_P1129399039y_real @ X4 @ Xs3 ) )
% 0.30/0.47 & ( A2
% 0.30/0.47 = ( cons_P1129399039y_real @ Y3 @ Ys3 ) )
% 0.30/0.47 & ( Less2 @ X4 @ Y3 ) )
% 0.30/0.47 | ? [X4: produc461822025y_real,Y3: produc461822025y_real,Xs3: list_P693436111y_real,Ys3: list_P693436111y_real] :
% 0.30/0.47 ( ( A1
% 0.30/0.47 = ( cons_P1129399039y_real @ X4 @ Xs3 ) )
% 0.30/0.47 & ( A2
% 0.30/0.47 = ( cons_P1129399039y_real @ Y3 @ Ys3 ) )
% 0.30/0.47 & ~ ( Less2 @ X4 @ Y3 )
% 0.30/0.47 & ~ ( Less2 @ Y3 @ X4 )
% 0.30/0.47 & ( lexord1053351061y_real @ Less2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq.simps
% 0.30/0.47 thf(fact_167_ord_Olexordp__eq_Osimps,axiom,
% 0.30/0.47 ( lexordp_eq_poly_real
% 0.30/0.47 = ( ^ [Less2: poly_real > poly_real > $o,A1: list_poly_real,A2: list_poly_real] :
% 0.30/0.47 ( ? [Ys3: list_poly_real] :
% 0.30/0.47 ( ( A1 = nil_poly_real )
% 0.30/0.47 & ( A2 = Ys3 ) )
% 0.30/0.47 | ? [X4: poly_real,Y3: poly_real,Xs3: list_poly_real,Ys3: list_poly_real] :
% 0.30/0.47 ( ( A1
% 0.30/0.47 = ( cons_poly_real @ X4 @ Xs3 ) )
% 0.30/0.47 & ( A2
% 0.30/0.47 = ( cons_poly_real @ Y3 @ Ys3 ) )
% 0.30/0.47 & ( Less2 @ X4 @ Y3 ) )
% 0.30/0.47 | ? [X4: poly_real,Y3: poly_real,Xs3: list_poly_real,Ys3: list_poly_real] :
% 0.30/0.47 ( ( A1
% 0.30/0.47 = ( cons_poly_real @ X4 @ Xs3 ) )
% 0.30/0.47 & ( A2
% 0.30/0.47 = ( cons_poly_real @ Y3 @ Ys3 ) )
% 0.30/0.47 & ~ ( Less2 @ X4 @ Y3 )
% 0.30/0.47 & ~ ( Less2 @ Y3 @ X4 )
% 0.30/0.47 & ( lexordp_eq_poly_real @ Less2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq.simps
% 0.30/0.47 thf(fact_168_ord_Olexordp__eq_Ocases,axiom,
% 0.30/0.47 ! [Less: list_poly_real > list_poly_real > $o,A12: list_list_poly_real,A22: list_list_poly_real] :
% 0.30/0.47 ( ( lexord1324236152y_real @ Less @ A12 @ A22 )
% 0.30/0.47 => ( ( A12 != nil_list_poly_real )
% 0.30/0.47 => ( ! [X3: list_poly_real] :
% 0.30/0.47 ( ? [Xs2: list_list_poly_real] :
% 0.30/0.47 ( A12
% 0.30/0.47 = ( cons_list_poly_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ! [Y2: list_poly_real] :
% 0.30/0.47 ( ? [Ys2: list_list_poly_real] :
% 0.30/0.47 ( A22
% 0.30/0.47 = ( cons_list_poly_real @ Y2 @ Ys2 ) )
% 0.30/0.47 => ~ ( Less @ X3 @ Y2 ) ) )
% 0.30/0.47 => ~ ! [X3: list_poly_real,Y2: list_poly_real,Xs2: list_list_poly_real] :
% 0.30/0.47 ( ( A12
% 0.30/0.47 = ( cons_list_poly_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ! [Ys2: list_list_poly_real] :
% 0.30/0.47 ( ( A22
% 0.30/0.47 = ( cons_list_poly_real @ Y2 @ Ys2 ) )
% 0.30/0.47 => ( ~ ( Less @ X3 @ Y2 )
% 0.30/0.47 => ( ~ ( Less @ Y2 @ X3 )
% 0.30/0.47 => ~ ( lexord1324236152y_real @ Less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq.cases
% 0.30/0.47 thf(fact_169_ord_Olexordp__eq_Ocases,axiom,
% 0.30/0.47 ! [Less: produc321349221y_real > produc321349221y_real > $o,A12: list_P736648811y_real,A22: list_P736648811y_real] :
% 0.30/0.47 ( ( lexord834705585y_real @ Less @ A12 @ A22 )
% 0.30/0.47 => ( ( A12 != nil_Pr1492526187y_real )
% 0.30/0.47 => ( ! [X3: produc321349221y_real] :
% 0.30/0.47 ( ? [Xs2: list_P736648811y_real] :
% 0.30/0.47 ( A12
% 0.30/0.47 = ( cons_P1027346459y_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ! [Y2: produc321349221y_real] :
% 0.30/0.47 ( ? [Ys2: list_P736648811y_real] :
% 0.30/0.47 ( A22
% 0.30/0.47 = ( cons_P1027346459y_real @ Y2 @ Ys2 ) )
% 0.30/0.47 => ~ ( Less @ X3 @ Y2 ) ) )
% 0.30/0.47 => ~ ! [X3: produc321349221y_real,Y2: produc321349221y_real,Xs2: list_P736648811y_real] :
% 0.30/0.47 ( ( A12
% 0.30/0.47 = ( cons_P1027346459y_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ! [Ys2: list_P736648811y_real] :
% 0.30/0.47 ( ( A22
% 0.30/0.47 = ( cons_P1027346459y_real @ Y2 @ Ys2 ) )
% 0.30/0.47 => ( ~ ( Less @ X3 @ Y2 )
% 0.30/0.47 => ( ~ ( Less @ Y2 @ X3 )
% 0.30/0.47 => ~ ( lexord834705585y_real @ Less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq.cases
% 0.30/0.47 thf(fact_170_ord_Olexordp__eq_Ocases,axiom,
% 0.30/0.47 ! [Less: produc461822025y_real > produc461822025y_real > $o,A12: list_P693436111y_real,A22: list_P693436111y_real] :
% 0.30/0.47 ( ( lexord1053351061y_real @ Less @ A12 @ A22 )
% 0.30/0.47 => ( ( A12 != nil_Pr1207979855y_real )
% 0.30/0.47 => ( ! [X3: produc461822025y_real] :
% 0.30/0.47 ( ? [Xs2: list_P693436111y_real] :
% 0.30/0.47 ( A12
% 0.30/0.47 = ( cons_P1129399039y_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ! [Y2: produc461822025y_real] :
% 0.30/0.47 ( ? [Ys2: list_P693436111y_real] :
% 0.30/0.47 ( A22
% 0.30/0.47 = ( cons_P1129399039y_real @ Y2 @ Ys2 ) )
% 0.30/0.47 => ~ ( Less @ X3 @ Y2 ) ) )
% 0.30/0.47 => ~ ! [X3: produc461822025y_real,Y2: produc461822025y_real,Xs2: list_P693436111y_real] :
% 0.30/0.47 ( ( A12
% 0.30/0.47 = ( cons_P1129399039y_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ! [Ys2: list_P693436111y_real] :
% 0.30/0.47 ( ( A22
% 0.30/0.47 = ( cons_P1129399039y_real @ Y2 @ Ys2 ) )
% 0.30/0.47 => ( ~ ( Less @ X3 @ Y2 )
% 0.30/0.47 => ( ~ ( Less @ Y2 @ X3 )
% 0.30/0.47 => ~ ( lexord1053351061y_real @ Less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq.cases
% 0.30/0.47 thf(fact_171_ord_Olexordp__eq_Ocases,axiom,
% 0.30/0.47 ! [Less: poly_real > poly_real > $o,A12: list_poly_real,A22: list_poly_real] :
% 0.30/0.47 ( ( lexordp_eq_poly_real @ Less @ A12 @ A22 )
% 0.30/0.47 => ( ( A12 != nil_poly_real )
% 0.30/0.47 => ( ! [X3: poly_real] :
% 0.30/0.47 ( ? [Xs2: list_poly_real] :
% 0.30/0.47 ( A12
% 0.30/0.47 = ( cons_poly_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ! [Y2: poly_real] :
% 0.30/0.47 ( ? [Ys2: list_poly_real] :
% 0.30/0.47 ( A22
% 0.30/0.47 = ( cons_poly_real @ Y2 @ Ys2 ) )
% 0.30/0.47 => ~ ( Less @ X3 @ Y2 ) ) )
% 0.30/0.47 => ~ ! [X3: poly_real,Y2: poly_real,Xs2: list_poly_real] :
% 0.30/0.47 ( ( A12
% 0.30/0.47 = ( cons_poly_real @ X3 @ Xs2 ) )
% 0.30/0.47 => ! [Ys2: list_poly_real] :
% 0.30/0.47 ( ( A22
% 0.30/0.47 = ( cons_poly_real @ Y2 @ Ys2 ) )
% 0.30/0.47 => ( ~ ( Less @ X3 @ Y2 )
% 0.30/0.47 => ( ~ ( Less @ Y2 @ X3 )
% 0.30/0.47 => ~ ( lexordp_eq_poly_real @ Less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq.cases
% 0.30/0.47 thf(fact_172_list_Oinject,axiom,
% 0.30/0.47 ! [X21: list_poly_real,X22: list_list_poly_real,Y21: list_poly_real,Y22: list_list_poly_real] :
% 0.30/0.47 ( ( ( cons_list_poly_real @ X21 @ X22 )
% 0.30/0.47 = ( cons_list_poly_real @ Y21 @ Y22 ) )
% 0.30/0.47 = ( ( X21 = Y21 )
% 0.30/0.47 & ( X22 = Y22 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list.inject
% 0.30/0.47 thf(fact_173_list_Oinject,axiom,
% 0.30/0.47 ! [X21: produc321349221y_real,X22: list_P736648811y_real,Y21: produc321349221y_real,Y22: list_P736648811y_real] :
% 0.30/0.47 ( ( ( cons_P1027346459y_real @ X21 @ X22 )
% 0.30/0.47 = ( cons_P1027346459y_real @ Y21 @ Y22 ) )
% 0.30/0.47 = ( ( X21 = Y21 )
% 0.30/0.47 & ( X22 = Y22 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list.inject
% 0.30/0.47 thf(fact_174_list_Oinject,axiom,
% 0.30/0.47 ! [X21: produc461822025y_real,X22: list_P693436111y_real,Y21: produc461822025y_real,Y22: list_P693436111y_real] :
% 0.30/0.47 ( ( ( cons_P1129399039y_real @ X21 @ X22 )
% 0.30/0.47 = ( cons_P1129399039y_real @ Y21 @ Y22 ) )
% 0.30/0.47 = ( ( X21 = Y21 )
% 0.30/0.47 & ( X22 = Y22 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list.inject
% 0.30/0.47 thf(fact_175_list_Oinject,axiom,
% 0.30/0.47 ! [X21: poly_real,X22: list_poly_real,Y21: poly_real,Y22: list_poly_real] :
% 0.30/0.47 ( ( ( cons_poly_real @ X21 @ X22 )
% 0.30/0.47 = ( cons_poly_real @ Y21 @ Y22 ) )
% 0.30/0.47 = ( ( X21 = Y21 )
% 0.30/0.47 & ( X22 = Y22 ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % list.inject
% 0.30/0.47 thf(fact_176_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.30/0.47 ! [Less: list_poly_real > list_poly_real > $o,X: list_poly_real,Xs: list_list_poly_real,Y: list_poly_real,Ys: list_list_poly_real] :
% 0.30/0.47 ( ( lexord1324236152y_real @ Less @ ( cons_list_poly_real @ X @ Xs ) @ ( cons_list_poly_real @ Y @ Ys ) )
% 0.30/0.47 = ( ( Less @ X @ Y )
% 0.30/0.47 | ( ~ ( Less @ Y @ X )
% 0.30/0.47 & ( lexord1324236152y_real @ Less @ Xs @ Ys ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 % ord.lexordp_eq_simps(4)
% 0.30/0.47 thf(fact_177_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.30/0.47 ! [Less: produc321349221y_real > produc321349221y_real > $o,X: produc321349221y_real,Xs: list_P736648811y_real,Y: produc321349221y_real,Ys: list_P736648811y_real] :
% 0.30/0.48 ( ( lexord834705585y_real @ Less @ ( cons_P1027346459y_real @ X @ Xs ) @ ( cons_P1027346459y_real @ Y @ Ys ) )
% 0.30/0.48 = ( ( Less @ X @ Y )
% 0.30/0.48 | ( ~ ( Less @ Y @ X )
% 0.30/0.48 & ( lexord834705585y_real @ Less @ Xs @ Ys ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ord.lexordp_eq_simps(4)
% 0.30/0.48 thf(fact_178_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.30/0.48 ! [Less: produc461822025y_real > produc461822025y_real > $o,X: produc461822025y_real,Xs: list_P693436111y_real,Y: produc461822025y_real,Ys: list_P693436111y_real] :
% 0.30/0.48 ( ( lexord1053351061y_real @ Less @ ( cons_P1129399039y_real @ X @ Xs ) @ ( cons_P1129399039y_real @ Y @ Ys ) )
% 0.30/0.48 = ( ( Less @ X @ Y )
% 0.30/0.48 | ( ~ ( Less @ Y @ X )
% 0.30/0.48 & ( lexord1053351061y_real @ Less @ Xs @ Ys ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ord.lexordp_eq_simps(4)
% 0.30/0.48 thf(fact_179_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.30/0.48 ! [Less: poly_real > poly_real > $o,X: poly_real,Xs: list_poly_real,Y: poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( lexordp_eq_poly_real @ Less @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ Y @ Ys ) )
% 0.30/0.48 = ( ( Less @ X @ Y )
% 0.30/0.48 | ( ~ ( Less @ Y @ X )
% 0.30/0.48 & ( lexordp_eq_poly_real @ Less @ Xs @ Ys ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ord.lexordp_eq_simps(4)
% 0.30/0.48 thf(fact_180_list__ex__simps_I1_J,axiom,
% 0.30/0.48 ! [P3: list_poly_real > $o,X: list_poly_real,Xs: list_list_poly_real] :
% 0.30/0.48 ( ( list_e809719936y_real @ P3 @ ( cons_list_poly_real @ X @ Xs ) )
% 0.30/0.48 = ( ( P3 @ X )
% 0.30/0.48 | ( list_e809719936y_real @ P3 @ Xs ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % list_ex_simps(1)
% 0.30/0.48 thf(fact_181_list__ex__simps_I1_J,axiom,
% 0.30/0.48 ! [P3: produc321349221y_real > $o,X: produc321349221y_real,Xs: list_P736648811y_real] :
% 0.30/0.48 ( ( list_e2093379497y_real @ P3 @ ( cons_P1027346459y_real @ X @ Xs ) )
% 0.30/0.48 = ( ( P3 @ X )
% 0.30/0.48 | ( list_e2093379497y_real @ P3 @ Xs ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % list_ex_simps(1)
% 0.30/0.48 thf(fact_182_list__ex__simps_I1_J,axiom,
% 0.30/0.48 ! [P3: produc461822025y_real > $o,X: produc461822025y_real,Xs: list_P693436111y_real] :
% 0.30/0.48 ( ( list_e1312221069y_real @ P3 @ ( cons_P1129399039y_real @ X @ Xs ) )
% 0.30/0.48 = ( ( P3 @ X )
% 0.30/0.48 | ( list_e1312221069y_real @ P3 @ Xs ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % list_ex_simps(1)
% 0.30/0.48 thf(fact_183_list__ex__simps_I1_J,axiom,
% 0.30/0.48 ! [P3: poly_real > $o,X: poly_real,Xs: list_poly_real] :
% 0.30/0.48 ( ( list_ex_poly_real @ P3 @ ( cons_poly_real @ X @ Xs ) )
% 0.30/0.48 = ( ( P3 @ X )
% 0.30/0.48 | ( list_ex_poly_real @ P3 @ Xs ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % list_ex_simps(1)
% 0.30/0.48 thf(fact_184_transpose_Ocases,axiom,
% 0.30/0.48 ! [X: list_l1245274212y_real] :
% 0.30/0.48 ( ( X != nil_li2088348750y_real )
% 0.30/0.48 => ( ! [Xss: list_l1245274212y_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( cons_l2022919326y_real @ nil_list_poly_real @ Xss ) )
% 0.30/0.48 => ~ ! [X3: list_poly_real,Xs2: list_list_poly_real,Xss: list_l1245274212y_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( cons_l2022919326y_real @ ( cons_list_poly_real @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % transpose.cases
% 0.30/0.48 thf(fact_185_transpose_Ocases,axiom,
% 0.30/0.48 ! [X: list_l6097393y_real] :
% 0.30/0.48 ( ( X != nil_li579690865y_real )
% 0.30/0.48 => ( ! [Xss: list_l6097393y_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( cons_l730969377y_real @ nil_Pr1492526187y_real @ Xss ) )
% 0.30/0.48 => ~ ! [X3: produc321349221y_real,Xs2: list_P736648811y_real,Xss: list_l6097393y_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( cons_l730969377y_real @ ( cons_P1027346459y_real @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % transpose.cases
% 0.30/0.48 thf(fact_186_transpose_Ocases,axiom,
% 0.30/0.48 ! [X: list_l343759061y_real] :
% 0.30/0.48 ( ( X != nil_li1299462869y_real )
% 0.30/0.48 => ( ! [Xss: list_l343759061y_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( cons_l677353093y_real @ nil_Pr1207979855y_real @ Xss ) )
% 0.30/0.48 => ~ ! [X3: produc461822025y_real,Xs2: list_P693436111y_real,Xss: list_l343759061y_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( cons_l677353093y_real @ ( cons_P1129399039y_real @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % transpose.cases
% 0.30/0.48 thf(fact_187_transpose_Ocases,axiom,
% 0.30/0.48 ! [X: list_list_poly_real] :
% 0.30/0.48 ( ( X != nil_list_poly_real )
% 0.30/0.48 => ( ! [Xss: list_list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( cons_list_poly_real @ nil_poly_real @ Xss ) )
% 0.30/0.48 => ~ ! [X3: poly_real,Xs2: list_poly_real,Xss: list_list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( cons_list_poly_real @ ( cons_poly_real @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % transpose.cases
% 0.30/0.48 thf(fact_188_not__Cons__self2,axiom,
% 0.30/0.48 ! [X: list_poly_real,Xs: list_list_poly_real] :
% 0.30/0.48 ( ( cons_list_poly_real @ X @ Xs )
% 0.30/0.48 != Xs ) ).
% 0.30/0.48
% 0.30/0.48 % not_Cons_self2
% 0.30/0.48 thf(fact_189_not__Cons__self2,axiom,
% 0.30/0.48 ! [X: produc321349221y_real,Xs: list_P736648811y_real] :
% 0.30/0.48 ( ( cons_P1027346459y_real @ X @ Xs )
% 0.30/0.48 != Xs ) ).
% 0.30/0.48
% 0.30/0.48 % not_Cons_self2
% 0.30/0.48 thf(fact_190_not__Cons__self2,axiom,
% 0.30/0.48 ! [X: produc461822025y_real,Xs: list_P693436111y_real] :
% 0.30/0.48 ( ( cons_P1129399039y_real @ X @ Xs )
% 0.30/0.48 != Xs ) ).
% 0.30/0.48
% 0.30/0.48 % not_Cons_self2
% 0.30/0.48 thf(fact_191_not__Cons__self2,axiom,
% 0.30/0.48 ! [X: poly_real,Xs: list_poly_real] :
% 0.30/0.48 ( ( cons_poly_real @ X @ Xs )
% 0.30/0.48 != Xs ) ).
% 0.30/0.48
% 0.30/0.48 % not_Cons_self2
% 0.30/0.48 thf(fact_192_mem__Collect__eq,axiom,
% 0.30/0.48 ! [A3: produc1426596841y_real,P3: produc1426596841y_real > $o] :
% 0.30/0.48 ( ( member403334290y_real @ A3 @ ( collec1459394516y_real @ P3 ) )
% 0.30/0.48 = ( P3 @ A3 ) ) ).
% 0.30/0.48
% 0.30/0.48 % mem_Collect_eq
% 0.30/0.48 thf(fact_193_mem__Collect__eq,axiom,
% 0.30/0.48 ! [A3: produc461822025y_real,P3: produc461822025y_real > $o] :
% 0.30/0.48 ( ( member1784523250y_real @ A3 @ ( collec329281332y_real @ P3 ) )
% 0.30/0.48 = ( P3 @ A3 ) ) ).
% 0.30/0.48
% 0.30/0.48 % mem_Collect_eq
% 0.30/0.48 thf(fact_194_mem__Collect__eq,axiom,
% 0.30/0.48 ! [A3: poly_real,P3: poly_real > $o] :
% 0.30/0.48 ( ( member_poly_real2 @ A3 @ ( collect_poly_real @ P3 ) )
% 0.30/0.48 = ( P3 @ A3 ) ) ).
% 0.30/0.48
% 0.30/0.48 % mem_Collect_eq
% 0.30/0.48 thf(fact_195_mem__Collect__eq,axiom,
% 0.30/0.48 ! [A3: list_poly_real,P3: list_poly_real > $o] :
% 0.30/0.48 ( ( member708095579y_real @ A3 @ ( collec1537941401y_real @ P3 ) )
% 0.30/0.48 = ( P3 @ A3 ) ) ).
% 0.30/0.48
% 0.30/0.48 % mem_Collect_eq
% 0.30/0.48 thf(fact_196_Collect__mem__eq,axiom,
% 0.30/0.48 ! [A4: set_Pr1405268809y_real] :
% 0.30/0.48 ( ( collec1459394516y_real
% 0.30/0.48 @ ^ [X4: produc1426596841y_real] : ( member403334290y_real @ X4 @ A4 ) )
% 0.30/0.48 = A4 ) ).
% 0.30/0.48
% 0.30/0.48 % Collect_mem_eq
% 0.30/0.48 thf(fact_197_Collect__mem__eq,axiom,
% 0.30/0.48 ! [A4: set_Pr483210409y_real] :
% 0.30/0.48 ( ( collec329281332y_real
% 0.30/0.48 @ ^ [X4: produc461822025y_real] : ( member1784523250y_real @ X4 @ A4 ) )
% 0.30/0.48 = A4 ) ).
% 0.30/0.48
% 0.30/0.48 % Collect_mem_eq
% 0.30/0.48 thf(fact_198_Collect__mem__eq,axiom,
% 0.30/0.48 ! [A4: set_poly_real] :
% 0.30/0.48 ( ( collect_poly_real
% 0.30/0.48 @ ^ [X4: poly_real] : ( member_poly_real2 @ X4 @ A4 ) )
% 0.30/0.48 = A4 ) ).
% 0.30/0.48
% 0.30/0.48 % Collect_mem_eq
% 0.30/0.48 thf(fact_199_Collect__mem__eq,axiom,
% 0.30/0.48 ! [A4: set_list_poly_real] :
% 0.30/0.48 ( ( collec1537941401y_real
% 0.30/0.48 @ ^ [X4: list_poly_real] : ( member708095579y_real @ X4 @ A4 ) )
% 0.30/0.48 = A4 ) ).
% 0.30/0.48
% 0.30/0.48 % Collect_mem_eq
% 0.30/0.48 thf(fact_200_strict__sorted_Oinduct,axiom,
% 0.30/0.48 ! [P3: list_poly_real > $o,A0: list_poly_real] :
% 0.30/0.48 ( ( P3 @ nil_poly_real )
% 0.30/0.48 => ( ! [X3: poly_real,Ys2: list_poly_real] :
% 0.30/0.48 ( ( P3 @ Ys2 )
% 0.30/0.48 => ( P3 @ ( cons_poly_real @ X3 @ Ys2 ) ) )
% 0.30/0.48 => ( P3 @ A0 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_sorted.induct
% 0.30/0.48 thf(fact_201_strict__sorted_Ocases,axiom,
% 0.30/0.48 ! [X: list_poly_real] :
% 0.30/0.48 ( ( X != nil_poly_real )
% 0.30/0.48 => ~ ! [X3: poly_real,Ys2: list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( cons_poly_real @ X3 @ Ys2 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % strict_sorted.cases
% 0.30/0.48 thf(fact_202_map__tailrec__rev_Oinduct,axiom,
% 0.30/0.48 ! [P3: ( list_poly_real > produc461822025y_real ) > list_list_poly_real > list_P693436111y_real > $o,A0: list_poly_real > produc461822025y_real,A12: list_list_poly_real,A22: list_P693436111y_real] :
% 0.30/0.48 ( ! [F2: list_poly_real > produc461822025y_real,X_1: list_P693436111y_real] : ( P3 @ F2 @ nil_list_poly_real @ X_1 )
% 0.30/0.48 => ( ! [F2: list_poly_real > produc461822025y_real,A: list_poly_real,As: list_list_poly_real,Bs2: list_P693436111y_real] :
% 0.30/0.48 ( ( P3 @ F2 @ As @ ( cons_P1129399039y_real @ ( F2 @ A ) @ Bs2 ) )
% 0.30/0.48 => ( P3 @ F2 @ ( cons_list_poly_real @ A @ As ) @ Bs2 ) )
% 0.30/0.48 => ( P3 @ A0 @ A12 @ A22 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % map_tailrec_rev.induct
% 0.30/0.48 thf(fact_203_map__tailrec__rev_Oinduct,axiom,
% 0.30/0.48 ! [P3: ( produc321349221y_real > produc461822025y_real ) > list_P736648811y_real > list_P693436111y_real > $o,A0: produc321349221y_real > produc461822025y_real,A12: list_P736648811y_real,A22: list_P693436111y_real] :
% 0.30/0.48 ( ! [F2: produc321349221y_real > produc461822025y_real,X_1: list_P693436111y_real] : ( P3 @ F2 @ nil_Pr1492526187y_real @ X_1 )
% 0.30/0.48 => ( ! [F2: produc321349221y_real > produc461822025y_real,A: produc321349221y_real,As: list_P736648811y_real,Bs2: list_P693436111y_real] :
% 0.30/0.48 ( ( P3 @ F2 @ As @ ( cons_P1129399039y_real @ ( F2 @ A ) @ Bs2 ) )
% 0.30/0.48 => ( P3 @ F2 @ ( cons_P1027346459y_real @ A @ As ) @ Bs2 ) )
% 0.30/0.48 => ( P3 @ A0 @ A12 @ A22 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % map_tailrec_rev.induct
% 0.30/0.48 thf(fact_204_map__tailrec__rev_Oinduct,axiom,
% 0.30/0.48 ! [P3: ( produc461822025y_real > produc461822025y_real ) > list_P693436111y_real > list_P693436111y_real > $o,A0: produc461822025y_real > produc461822025y_real,A12: list_P693436111y_real,A22: list_P693436111y_real] :
% 0.30/0.48 ( ! [F2: produc461822025y_real > produc461822025y_real,X_1: list_P693436111y_real] : ( P3 @ F2 @ nil_Pr1207979855y_real @ X_1 )
% 0.30/0.48 => ( ! [F2: produc461822025y_real > produc461822025y_real,A: produc461822025y_real,As: list_P693436111y_real,Bs2: list_P693436111y_real] :
% 0.30/0.48 ( ( P3 @ F2 @ As @ ( cons_P1129399039y_real @ ( F2 @ A ) @ Bs2 ) )
% 0.30/0.48 => ( P3 @ F2 @ ( cons_P1129399039y_real @ A @ As ) @ Bs2 ) )
% 0.30/0.48 => ( P3 @ A0 @ A12 @ A22 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % map_tailrec_rev.induct
% 0.30/0.48 thf(fact_205_map__tailrec__rev_Oinduct,axiom,
% 0.30/0.48 ! [P3: ( poly_real > poly_real ) > list_poly_real > list_poly_real > $o,A0: poly_real > poly_real,A12: list_poly_real,A22: list_poly_real] :
% 0.30/0.48 ( ! [F2: poly_real > poly_real,X_1: list_poly_real] : ( P3 @ F2 @ nil_poly_real @ X_1 )
% 0.30/0.48 => ( ! [F2: poly_real > poly_real,A: poly_real,As: list_poly_real,Bs2: list_poly_real] :
% 0.30/0.48 ( ( P3 @ F2 @ As @ ( cons_poly_real @ ( F2 @ A ) @ Bs2 ) )
% 0.30/0.48 => ( P3 @ F2 @ ( cons_poly_real @ A @ As ) @ Bs2 ) )
% 0.30/0.48 => ( P3 @ A0 @ A12 @ A22 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % map_tailrec_rev.induct
% 0.30/0.48 thf(fact_206_list__nonempty__induct,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,P3: list_poly_real > $o] :
% 0.30/0.48 ( ( Xs != nil_poly_real )
% 0.30/0.48 => ( ! [X3: poly_real] : ( P3 @ ( cons_poly_real @ X3 @ nil_poly_real ) )
% 0.30/0.48 => ( ! [X3: poly_real,Xs2: list_poly_real] :
% 0.30/0.48 ( ( Xs2 != nil_poly_real )
% 0.30/0.48 => ( ( P3 @ Xs2 )
% 0.30/0.48 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) ) ) )
% 0.30/0.48 => ( P3 @ Xs ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % list_nonempty_induct
% 0.30/0.48 thf(fact_207_successively_Oinduct,axiom,
% 0.30/0.48 ! [P3: ( poly_real > poly_real > $o ) > list_poly_real > $o,A0: poly_real > poly_real > $o,A12: list_poly_real] :
% 0.30/0.48 ( ! [P4: poly_real > poly_real > $o] : ( P3 @ P4 @ nil_poly_real )
% 0.30/0.48 => ( ! [P4: poly_real > poly_real > $o,X3: poly_real] : ( P3 @ P4 @ ( cons_poly_real @ X3 @ nil_poly_real ) )
% 0.30/0.48 => ( ! [P4: poly_real > poly_real > $o,X3: poly_real,Y2: poly_real,Xs2: list_poly_real] :
% 0.30/0.48 ( ( P3 @ P4 @ ( cons_poly_real @ Y2 @ Xs2 ) )
% 0.30/0.48 => ( P3 @ P4 @ ( cons_poly_real @ X3 @ ( cons_poly_real @ Y2 @ Xs2 ) ) ) )
% 0.30/0.48 => ( P3 @ A0 @ A12 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % successively.induct
% 0.30/0.48 thf(fact_208_remdups__adj_Oinduct,axiom,
% 0.30/0.48 ! [P3: list_poly_real > $o,A0: list_poly_real] :
% 0.30/0.48 ( ( P3 @ nil_poly_real )
% 0.30/0.48 => ( ! [X3: poly_real] : ( P3 @ ( cons_poly_real @ X3 @ nil_poly_real ) )
% 0.30/0.48 => ( ! [X3: poly_real,Y2: poly_real,Xs2: list_poly_real] :
% 0.30/0.48 ( ( ( X3 = Y2 )
% 0.30/0.48 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) ) )
% 0.30/0.48 => ( ( ( X3 != Y2 )
% 0.30/0.48 => ( P3 @ ( cons_poly_real @ Y2 @ Xs2 ) ) )
% 0.30/0.48 => ( P3 @ ( cons_poly_real @ X3 @ ( cons_poly_real @ Y2 @ Xs2 ) ) ) ) )
% 0.30/0.48 => ( P3 @ A0 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % remdups_adj.induct
% 0.30/0.48 thf(fact_209_sorted__wrt_Oinduct,axiom,
% 0.30/0.48 ! [P3: ( poly_real > poly_real > $o ) > list_poly_real > $o,A0: poly_real > poly_real > $o,A12: list_poly_real] :
% 0.30/0.48 ( ! [P4: poly_real > poly_real > $o] : ( P3 @ P4 @ nil_poly_real )
% 0.30/0.48 => ( ! [P4: poly_real > poly_real > $o,X3: poly_real,Ys2: list_poly_real] :
% 0.30/0.48 ( ( P3 @ P4 @ Ys2 )
% 0.30/0.48 => ( P3 @ P4 @ ( cons_poly_real @ X3 @ Ys2 ) ) )
% 0.30/0.48 => ( P3 @ A0 @ A12 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % sorted_wrt.induct
% 0.30/0.48 thf(fact_210_remdups__adj_Ocases,axiom,
% 0.30/0.48 ! [X: list_poly_real] :
% 0.30/0.48 ( ( X != nil_poly_real )
% 0.30/0.48 => ( ! [X3: poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( cons_poly_real @ X3 @ nil_poly_real ) )
% 0.30/0.48 => ~ ! [X3: poly_real,Y2: poly_real,Xs2: list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( cons_poly_real @ X3 @ ( cons_poly_real @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % remdups_adj.cases
% 0.30/0.48 thf(fact_211_shuffles_Oinduct,axiom,
% 0.30/0.48 ! [P3: list_poly_real > list_poly_real > $o,A0: list_poly_real,A12: list_poly_real] :
% 0.30/0.48 ( ! [X_1: list_poly_real] : ( P3 @ nil_poly_real @ X_1 )
% 0.30/0.48 => ( ! [Xs2: list_poly_real] : ( P3 @ Xs2 @ nil_poly_real )
% 0.30/0.48 => ( ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real] :
% 0.30/0.48 ( ( P3 @ Xs2 @ ( cons_poly_real @ Y2 @ Ys2 ) )
% 0.30/0.48 => ( ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ Ys2 )
% 0.30/0.48 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) )
% 0.30/0.48 => ( P3 @ A0 @ A12 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % shuffles.induct
% 0.30/0.48 thf(fact_212_min__list_Oinduct,axiom,
% 0.30/0.48 ! [P3: list_poly_real > $o,A0: list_poly_real] :
% 0.30/0.48 ( ! [X3: poly_real,Xs2: list_poly_real] :
% 0.30/0.48 ( ! [X212: poly_real,X222: list_poly_real] :
% 0.30/0.48 ( ( Xs2
% 0.30/0.48 = ( cons_poly_real @ X212 @ X222 ) )
% 0.30/0.48 => ( P3 @ Xs2 ) )
% 0.30/0.48 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) ) )
% 0.30/0.48 => ( ( P3 @ nil_poly_real )
% 0.30/0.48 => ( P3 @ A0 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % min_list.induct
% 0.30/0.48 thf(fact_213_min__list_Ocases,axiom,
% 0.30/0.48 ! [X: list_poly_real] :
% 0.30/0.48 ( ! [X3: poly_real,Xs2: list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( cons_poly_real @ X3 @ Xs2 ) )
% 0.30/0.48 => ( X = nil_poly_real ) ) ).
% 0.30/0.48
% 0.30/0.48 % min_list.cases
% 0.30/0.48 thf(fact_214_induct__list012,axiom,
% 0.30/0.48 ! [P3: list_poly_real > $o,Xs: list_poly_real] :
% 0.30/0.48 ( ( P3 @ nil_poly_real )
% 0.30/0.48 => ( ! [X3: poly_real] : ( P3 @ ( cons_poly_real @ X3 @ nil_poly_real ) )
% 0.30/0.48 => ( ! [X3: poly_real,Y2: poly_real,Zs: list_poly_real] :
% 0.30/0.48 ( ( P3 @ Zs )
% 0.30/0.48 => ( ( P3 @ ( cons_poly_real @ Y2 @ Zs ) )
% 0.30/0.48 => ( P3 @ ( cons_poly_real @ X3 @ ( cons_poly_real @ Y2 @ Zs ) ) ) ) )
% 0.30/0.48 => ( P3 @ Xs ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % induct_list012
% 0.30/0.48 thf(fact_215_splice_Oinduct,axiom,
% 0.30/0.48 ! [P3: list_poly_real > list_poly_real > $o,A0: list_poly_real,A12: list_poly_real] :
% 0.30/0.48 ( ! [X_1: list_poly_real] : ( P3 @ nil_poly_real @ X_1 )
% 0.30/0.48 => ( ! [X3: poly_real,Xs2: list_poly_real,Ys2: list_poly_real] :
% 0.30/0.48 ( ( P3 @ Ys2 @ Xs2 )
% 0.30/0.48 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ Ys2 ) )
% 0.30/0.48 => ( P3 @ A0 @ A12 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % splice.induct
% 0.30/0.48 thf(fact_216_list__induct2_H,axiom,
% 0.30/0.48 ! [P3: list_poly_real > list_poly_real > $o,Xs: list_poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( P3 @ nil_poly_real @ nil_poly_real )
% 0.30/0.48 => ( ! [X3: poly_real,Xs2: list_poly_real] : ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ nil_poly_real )
% 0.30/0.48 => ( ! [Y2: poly_real,Ys2: list_poly_real] : ( P3 @ nil_poly_real @ ( cons_poly_real @ Y2 @ Ys2 ) )
% 0.30/0.48 => ( ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real] :
% 0.30/0.48 ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.48 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) )
% 0.30/0.48 => ( P3 @ Xs @ Ys ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % list_induct2'
% 0.30/0.48 thf(fact_217_neq__Nil__conv,axiom,
% 0.30/0.48 ! [Xs: list_poly_real] :
% 0.30/0.48 ( ( Xs != nil_poly_real )
% 0.30/0.48 = ( ? [Y3: poly_real,Ys3: list_poly_real] :
% 0.30/0.48 ( Xs
% 0.30/0.48 = ( cons_poly_real @ Y3 @ Ys3 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % neq_Nil_conv
% 0.30/0.48 thf(fact_218_list_Oinducts,axiom,
% 0.30/0.48 ! [P3: list_poly_real > $o,List: list_poly_real] :
% 0.30/0.48 ( ( P3 @ nil_poly_real )
% 0.30/0.48 => ( ! [X12: poly_real,X23: list_poly_real] :
% 0.30/0.48 ( ( P3 @ X23 )
% 0.30/0.48 => ( P3 @ ( cons_poly_real @ X12 @ X23 ) ) )
% 0.30/0.48 => ( P3 @ List ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % list.inducts
% 0.30/0.48 thf(fact_219_list_Oexhaust,axiom,
% 0.30/0.48 ! [Y: list_poly_real] :
% 0.30/0.48 ( ( Y != nil_poly_real )
% 0.30/0.48 => ~ ! [X213: poly_real,X223: list_poly_real] :
% 0.30/0.48 ( Y
% 0.30/0.48 != ( cons_poly_real @ X213 @ X223 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % list.exhaust
% 0.30/0.48 thf(fact_220_list_OdiscI,axiom,
% 0.30/0.48 ! [List: list_poly_real,X21: poly_real,X22: list_poly_real] :
% 0.30/0.48 ( ( List
% 0.30/0.48 = ( cons_poly_real @ X21 @ X22 ) )
% 0.30/0.48 => ( List != nil_poly_real ) ) ).
% 0.30/0.48
% 0.30/0.48 % list.discI
% 0.30/0.48 thf(fact_221_list_Odistinct_I1_J,axiom,
% 0.30/0.48 ! [X21: poly_real,X22: list_poly_real] :
% 0.30/0.48 ( nil_poly_real
% 0.30/0.48 != ( cons_poly_real @ X21 @ X22 ) ) ).
% 0.30/0.48
% 0.30/0.48 % list.distinct(1)
% 0.30/0.48 thf(fact_222_ord_Olexordp__eq_OCons__eq,axiom,
% 0.30/0.48 ! [Less: poly_real > poly_real > $o,X: poly_real,Y: poly_real,Xs: list_poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ~ ( Less @ X @ Y )
% 0.30/0.48 => ( ~ ( Less @ Y @ X )
% 0.30/0.48 => ( ( lexordp_eq_poly_real @ Less @ Xs @ Ys )
% 0.30/0.48 => ( lexordp_eq_poly_real @ Less @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ Y @ Ys ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ord.lexordp_eq.Cons_eq
% 0.30/0.48 thf(fact_223_ord_Olexordp__eq_OCons,axiom,
% 0.30/0.48 ! [Less: poly_real > poly_real > $o,X: poly_real,Y: poly_real,Xs: list_poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( Less @ X @ Y )
% 0.30/0.48 => ( lexordp_eq_poly_real @ Less @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ Y @ Ys ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % ord.lexordp_eq.Cons
% 0.30/0.48 thf(fact_224_splice_Osimps_I2_J,axiom,
% 0.30/0.48 ! [X: poly_real,Xs: list_poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( splice_poly_real @ ( cons_poly_real @ X @ Xs ) @ Ys )
% 0.30/0.48 = ( cons_poly_real @ X @ ( splice_poly_real @ Ys @ Xs ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % splice.simps(2)
% 0.30/0.48 thf(fact_225_listrelp_OCons,axiom,
% 0.30/0.48 ! [R: poly_real > poly_real > $o,X: poly_real,Y: poly_real,Xs: list_poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( R @ X @ Y )
% 0.30/0.48 => ( ( listre1609905961y_real @ R @ Xs @ Ys )
% 0.30/0.48 => ( listre1609905961y_real @ R @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ Y @ Ys ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % listrelp.Cons
% 0.30/0.48 thf(fact_226_sturm__seq_Ops__first__two,axiom,
% 0.30/0.48 ! [Ps: list_poly_real,P: poly_real] :
% 0.30/0.48 ( ( sturm_1664866327rm_seq @ Ps @ P )
% 0.30/0.48 => ~ ! [Q: poly_real,Ps3: list_poly_real] :
% 0.30/0.48 ( Ps
% 0.30/0.48 != ( cons_poly_real @ P @ ( cons_poly_real @ Q @ Ps3 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % sturm_seq.ps_first_two
% 0.30/0.48 thf(fact_227_map__tailrec__rev_Osimps_I2_J,axiom,
% 0.30/0.48 ! [F: poly_real > poly_real,A3: poly_real,As2: list_poly_real,Bs: list_poly_real] :
% 0.30/0.48 ( ( map_ta1919289823y_real @ F @ ( cons_poly_real @ A3 @ As2 ) @ Bs )
% 0.30/0.48 = ( map_ta1919289823y_real @ F @ As2 @ ( cons_poly_real @ ( F @ A3 ) @ Bs ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % map_tailrec_rev.simps(2)
% 0.30/0.48 thf(fact_228_null__rec_I1_J,axiom,
% 0.30/0.48 ! [X: poly_real,Xs: list_poly_real] :
% 0.30/0.48 ~ ( null_poly_real @ ( cons_poly_real @ X @ Xs ) ) ).
% 0.30/0.48
% 0.30/0.48 % null_rec(1)
% 0.30/0.48 thf(fact_229_member__rec_I1_J,axiom,
% 0.30/0.48 ! [X: poly_real,Xs: list_poly_real,Y: poly_real] :
% 0.30/0.48 ( ( member_poly_real @ ( cons_poly_real @ X @ Xs ) @ Y )
% 0.30/0.48 = ( ( X = Y )
% 0.30/0.48 | ( member_poly_real @ Xs @ Y ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % member_rec(1)
% 0.30/0.48 thf(fact_230_zip__eq__Nil__iff,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( ( zip_po657915297y_real @ Xs @ Ys )
% 0.30/0.48 = nil_Pr1207979855y_real )
% 0.30/0.48 = ( ( Xs = nil_poly_real )
% 0.30/0.48 | ( Ys = nil_poly_real ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % zip_eq_Nil_iff
% 0.30/0.48 thf(fact_231_minus__poly__rev__list_Oinduct,axiom,
% 0.30/0.48 ! [P3: list_poly_real > list_poly_real > $o,A0: list_poly_real,A12: list_poly_real] :
% 0.30/0.48 ( ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real] :
% 0.30/0.48 ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.48 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) )
% 0.30/0.48 => ( ! [Xs2: list_poly_real] : ( P3 @ Xs2 @ nil_poly_real )
% 0.30/0.48 => ( ! [Y2: poly_real,Ys2: list_poly_real] : ( P3 @ nil_poly_real @ ( cons_poly_real @ Y2 @ Ys2 ) )
% 0.30/0.48 => ( P3 @ A0 @ A12 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % minus_poly_rev_list.induct
% 0.30/0.48 thf(fact_232_plus__coeffs_Oinduct,axiom,
% 0.30/0.48 ! [P3: list_poly_real > list_poly_real > $o,A0: list_poly_real,A12: list_poly_real] :
% 0.30/0.48 ( ! [Xs2: list_poly_real] : ( P3 @ Xs2 @ nil_poly_real )
% 0.30/0.48 => ( ! [V: poly_real,Va: list_poly_real] : ( P3 @ nil_poly_real @ ( cons_poly_real @ V @ Va ) )
% 0.30/0.48 => ( ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real] :
% 0.30/0.48 ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.48 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) )
% 0.30/0.48 => ( P3 @ A0 @ A12 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % plus_coeffs.induct
% 0.30/0.48 thf(fact_233_insert__Nil,axiom,
% 0.30/0.48 ! [X: poly_real] :
% 0.30/0.48 ( ( insert_poly_real @ X @ nil_poly_real )
% 0.30/0.48 = ( cons_poly_real @ X @ nil_poly_real ) ) ).
% 0.30/0.48
% 0.30/0.48 % insert_Nil
% 0.30/0.48 thf(fact_234_lexordp__eq__simps_I3_J,axiom,
% 0.30/0.48 ! [X: poly_real,Xs: list_poly_real] :
% 0.30/0.48 ~ ( ord_le1233681790y_real @ ( cons_poly_real @ X @ Xs ) @ nil_poly_real ) ).
% 0.30/0.48
% 0.30/0.48 % lexordp_eq_simps(3)
% 0.30/0.48 thf(fact_235_rotate1_Osimps_I2_J,axiom,
% 0.30/0.48 ! [X: poly_real,Xs: list_poly_real] :
% 0.30/0.48 ( ( rotate1_poly_real @ ( cons_poly_real @ X @ Xs ) )
% 0.30/0.48 = ( append_poly_real @ Xs @ ( cons_poly_real @ X @ nil_poly_real ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % rotate1.simps(2)
% 0.30/0.48 thf(fact_236_bind__simps_I2_J,axiom,
% 0.30/0.48 ! [X: poly_real,Xs: list_poly_real,F: poly_real > list_poly_real] :
% 0.30/0.48 ( ( bind_p420216945y_real @ ( cons_poly_real @ X @ Xs ) @ F )
% 0.30/0.48 = ( append_poly_real @ ( F @ X ) @ ( bind_p420216945y_real @ Xs @ F ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % bind_simps(2)
% 0.30/0.48 thf(fact_237_gen__length__code_I2_J,axiom,
% 0.30/0.48 ! [N: nat,X: poly_real,Xs: list_poly_real] :
% 0.30/0.48 ( ( gen_length_poly_real @ N @ ( cons_poly_real @ X @ Xs ) )
% 0.30/0.48 = ( gen_length_poly_real @ ( suc @ N ) @ Xs ) ) ).
% 0.30/0.48
% 0.30/0.48 % gen_length_code(2)
% 0.30/0.48 thf(fact_238_append__Nil2,axiom,
% 0.30/0.48 ! [Xs: list_poly_real] :
% 0.30/0.48 ( ( append_poly_real @ Xs @ nil_poly_real )
% 0.30/0.48 = Xs ) ).
% 0.30/0.48
% 0.30/0.48 % append_Nil2
% 0.30/0.48 thf(fact_239_append__self__conv,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( ( append_poly_real @ Xs @ Ys )
% 0.30/0.48 = Xs )
% 0.30/0.48 = ( Ys = nil_poly_real ) ) ).
% 0.30/0.48
% 0.30/0.48 % append_self_conv
% 0.30/0.48 thf(fact_240_self__append__conv,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( Xs
% 0.30/0.48 = ( append_poly_real @ Xs @ Ys ) )
% 0.30/0.48 = ( Ys = nil_poly_real ) ) ).
% 0.30/0.48
% 0.30/0.48 % self_append_conv
% 0.30/0.48 thf(fact_241_append__self__conv2,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( ( append_poly_real @ Xs @ Ys )
% 0.30/0.48 = Ys )
% 0.30/0.48 = ( Xs = nil_poly_real ) ) ).
% 0.30/0.48
% 0.30/0.48 % append_self_conv2
% 0.30/0.48 thf(fact_242_self__append__conv2,axiom,
% 0.30/0.48 ! [Ys: list_poly_real,Xs: list_poly_real] :
% 0.30/0.48 ( ( Ys
% 0.30/0.48 = ( append_poly_real @ Xs @ Ys ) )
% 0.30/0.48 = ( Xs = nil_poly_real ) ) ).
% 0.30/0.48
% 0.30/0.48 % self_append_conv2
% 0.30/0.48 thf(fact_243_Nil__is__append__conv,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( nil_poly_real
% 0.30/0.48 = ( append_poly_real @ Xs @ Ys ) )
% 0.30/0.48 = ( ( Xs = nil_poly_real )
% 0.30/0.48 & ( Ys = nil_poly_real ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Nil_is_append_conv
% 0.30/0.48 thf(fact_244_append__is__Nil__conv,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( ( append_poly_real @ Xs @ Ys )
% 0.30/0.48 = nil_poly_real )
% 0.30/0.48 = ( ( Xs = nil_poly_real )
% 0.30/0.48 & ( Ys = nil_poly_real ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % append_is_Nil_conv
% 0.30/0.48 thf(fact_245_append_Oright__neutral,axiom,
% 0.30/0.48 ! [A3: list_poly_real] :
% 0.30/0.48 ( ( append_poly_real @ A3 @ nil_poly_real )
% 0.30/0.48 = A3 ) ).
% 0.30/0.48
% 0.30/0.48 % append.right_neutral
% 0.30/0.48 thf(fact_246_lexordp__eq__simps_I2_J,axiom,
% 0.30/0.48 ! [Xs: list_poly_real] :
% 0.30/0.48 ( ( ord_le1233681790y_real @ Xs @ nil_poly_real )
% 0.30/0.48 = ( Xs = nil_poly_real ) ) ).
% 0.30/0.48
% 0.30/0.48 % lexordp_eq_simps(2)
% 0.30/0.48 thf(fact_247_lexordp__eq__simps_I1_J,axiom,
% 0.30/0.48 ! [Ys: list_poly_real] : ( ord_le1233681790y_real @ nil_poly_real @ Ys ) ).
% 0.30/0.48
% 0.30/0.48 % lexordp_eq_simps(1)
% 0.30/0.48 thf(fact_248_append1__eq__conv,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,X: poly_real,Ys: list_poly_real,Y: poly_real] :
% 0.30/0.48 ( ( ( append_poly_real @ Xs @ ( cons_poly_real @ X @ nil_poly_real ) )
% 0.30/0.48 = ( append_poly_real @ Ys @ ( cons_poly_real @ Y @ nil_poly_real ) ) )
% 0.30/0.48 = ( ( Xs = Ys )
% 0.30/0.48 & ( X = Y ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % append1_eq_conv
% 0.30/0.48 thf(fact_249_Cons__eq__appendI,axiom,
% 0.30/0.48 ! [X: poly_real,Xs1: list_poly_real,Ys: list_poly_real,Xs: list_poly_real,Zs2: list_poly_real] :
% 0.30/0.48 ( ( ( cons_poly_real @ X @ Xs1 )
% 0.30/0.48 = Ys )
% 0.30/0.48 => ( ( Xs
% 0.30/0.48 = ( append_poly_real @ Xs1 @ Zs2 ) )
% 0.30/0.48 => ( ( cons_poly_real @ X @ Xs )
% 0.30/0.48 = ( append_poly_real @ Ys @ Zs2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Cons_eq_appendI
% 0.30/0.48 thf(fact_250_append__Cons,axiom,
% 0.30/0.48 ! [X: poly_real,Xs: list_poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( append_poly_real @ ( cons_poly_real @ X @ Xs ) @ Ys )
% 0.30/0.48 = ( cons_poly_real @ X @ ( append_poly_real @ Xs @ Ys ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % append_Cons
% 0.30/0.48 thf(fact_251_eq__Nil__appendI,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( Xs = Ys )
% 0.30/0.48 => ( Xs
% 0.30/0.48 = ( append_poly_real @ nil_poly_real @ Ys ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % eq_Nil_appendI
% 0.30/0.48 thf(fact_252_append__Nil,axiom,
% 0.30/0.48 ! [Ys: list_poly_real] :
% 0.30/0.48 ( ( append_poly_real @ nil_poly_real @ Ys )
% 0.30/0.48 = Ys ) ).
% 0.30/0.48
% 0.30/0.48 % append_Nil
% 0.30/0.48 thf(fact_253_append_Oleft__neutral,axiom,
% 0.30/0.48 ! [A3: list_poly_real] :
% 0.30/0.48 ( ( append_poly_real @ nil_poly_real @ A3 )
% 0.30/0.48 = A3 ) ).
% 0.30/0.48
% 0.30/0.48 % append.left_neutral
% 0.30/0.48 thf(fact_254_lexordp__eq_ONil,axiom,
% 0.30/0.48 ! [Ys: list_poly_real] : ( ord_le1233681790y_real @ nil_poly_real @ Ys ) ).
% 0.30/0.48
% 0.30/0.48 % lexordp_eq.Nil
% 0.30/0.48 thf(fact_255_rev__induct,axiom,
% 0.30/0.48 ! [P3: list_poly_real > $o,Xs: list_poly_real] :
% 0.30/0.48 ( ( P3 @ nil_poly_real )
% 0.30/0.48 => ( ! [X3: poly_real,Xs2: list_poly_real] :
% 0.30/0.48 ( ( P3 @ Xs2 )
% 0.30/0.48 => ( P3 @ ( append_poly_real @ Xs2 @ ( cons_poly_real @ X3 @ nil_poly_real ) ) ) )
% 0.30/0.48 => ( P3 @ Xs ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % rev_induct
% 0.30/0.48 thf(fact_256_rev__exhaust,axiom,
% 0.30/0.48 ! [Xs: list_poly_real] :
% 0.30/0.48 ( ( Xs != nil_poly_real )
% 0.30/0.48 => ~ ! [Ys2: list_poly_real,Y2: poly_real] :
% 0.30/0.48 ( Xs
% 0.30/0.48 != ( append_poly_real @ Ys2 @ ( cons_poly_real @ Y2 @ nil_poly_real ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % rev_exhaust
% 0.30/0.48 thf(fact_257_Cons__eq__append__conv,axiom,
% 0.30/0.48 ! [X: poly_real,Xs: list_poly_real,Ys: list_poly_real,Zs2: list_poly_real] :
% 0.30/0.48 ( ( ( cons_poly_real @ X @ Xs )
% 0.30/0.48 = ( append_poly_real @ Ys @ Zs2 ) )
% 0.30/0.48 = ( ( ( Ys = nil_poly_real )
% 0.30/0.48 & ( ( cons_poly_real @ X @ Xs )
% 0.30/0.48 = Zs2 ) )
% 0.30/0.48 | ? [Ys4: list_poly_real] :
% 0.30/0.48 ( ( ( cons_poly_real @ X @ Ys4 )
% 0.30/0.48 = Ys )
% 0.30/0.48 & ( Xs
% 0.30/0.48 = ( append_poly_real @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Cons_eq_append_conv
% 0.30/0.48 thf(fact_258_append__eq__Cons__conv,axiom,
% 0.30/0.48 ! [Ys: list_poly_real,Zs2: list_poly_real,X: poly_real,Xs: list_poly_real] :
% 0.30/0.48 ( ( ( append_poly_real @ Ys @ Zs2 )
% 0.30/0.48 = ( cons_poly_real @ X @ Xs ) )
% 0.30/0.48 = ( ( ( Ys = nil_poly_real )
% 0.30/0.48 & ( Zs2
% 0.30/0.48 = ( cons_poly_real @ X @ Xs ) ) )
% 0.30/0.48 | ? [Ys4: list_poly_real] :
% 0.30/0.48 ( ( Ys
% 0.30/0.48 = ( cons_poly_real @ X @ Ys4 ) )
% 0.30/0.48 & ( ( append_poly_real @ Ys4 @ Zs2 )
% 0.30/0.48 = Xs ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % append_eq_Cons_conv
% 0.30/0.48 thf(fact_259_rev__nonempty__induct,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,P3: list_poly_real > $o] :
% 0.30/0.48 ( ( Xs != nil_poly_real )
% 0.30/0.48 => ( ! [X3: poly_real] : ( P3 @ ( cons_poly_real @ X3 @ nil_poly_real ) )
% 0.30/0.48 => ( ! [X3: poly_real,Xs2: list_poly_real] :
% 0.30/0.48 ( ( Xs2 != nil_poly_real )
% 0.30/0.48 => ( ( P3 @ Xs2 )
% 0.30/0.48 => ( P3 @ ( append_poly_real @ Xs2 @ ( cons_poly_real @ X3 @ nil_poly_real ) ) ) ) )
% 0.30/0.48 => ( P3 @ Xs ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % rev_nonempty_induct
% 0.30/0.48 thf(fact_260_maps__simps_I1_J,axiom,
% 0.30/0.48 ! [F: poly_real > list_poly_real,X: poly_real,Xs: list_poly_real] :
% 0.30/0.48 ( ( maps_p961674027y_real @ F @ ( cons_poly_real @ X @ Xs ) )
% 0.30/0.48 = ( append_poly_real @ ( F @ X ) @ ( maps_p961674027y_real @ F @ Xs ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % maps_simps(1)
% 0.30/0.48 thf(fact_261_old_Onat_Oinject,axiom,
% 0.30/0.48 ! [Nat: nat,Nat2: nat] :
% 0.30/0.48 ( ( ( suc @ Nat )
% 0.30/0.48 = ( suc @ Nat2 ) )
% 0.30/0.48 = ( Nat = Nat2 ) ) ).
% 0.30/0.48
% 0.30/0.48 % old.nat.inject
% 0.30/0.48 thf(fact_262_nat_Oinject,axiom,
% 0.30/0.48 ! [X2: nat,Y23: nat] :
% 0.30/0.48 ( ( ( suc @ X2 )
% 0.30/0.48 = ( suc @ Y23 ) )
% 0.30/0.48 = ( X2 = Y23 ) ) ).
% 0.30/0.48
% 0.30/0.48 % nat.inject
% 0.30/0.48 thf(fact_263_product__lists_Osimps_I1_J,axiom,
% 0.30/0.48 ( ( produc523415045y_real @ nil_list_poly_real )
% 0.30/0.48 = ( cons_list_poly_real @ nil_poly_real @ nil_list_poly_real ) ) ).
% 0.30/0.48
% 0.30/0.48 % product_lists.simps(1)
% 0.30/0.48 thf(fact_264_subseqs_Osimps_I1_J,axiom,
% 0.30/0.48 ( ( subseqs_poly_real @ nil_poly_real )
% 0.30/0.48 = ( cons_list_poly_real @ nil_poly_real @ nil_list_poly_real ) ) ).
% 0.30/0.48
% 0.30/0.48 % subseqs.simps(1)
% 0.30/0.48 thf(fact_265_concat__eq__append__conv,axiom,
% 0.30/0.48 ! [Xss2: list_list_poly_real,Ys: list_poly_real,Zs2: list_poly_real] :
% 0.30/0.48 ( ( ( concat_poly_real @ Xss2 )
% 0.30/0.48 = ( append_poly_real @ Ys @ Zs2 ) )
% 0.30/0.48 = ( ( ( Xss2 = nil_list_poly_real )
% 0.30/0.48 => ( ( Ys = nil_poly_real )
% 0.30/0.48 & ( Zs2 = nil_poly_real ) ) )
% 0.30/0.48 & ( ( Xss2 != nil_list_poly_real )
% 0.30/0.48 => ? [Xss1: list_list_poly_real,Xs3: list_poly_real,Xs4: list_poly_real,Xss22: list_list_poly_real] :
% 0.30/0.48 ( ( Xss2
% 0.30/0.48 = ( append527544425y_real @ Xss1 @ ( cons_list_poly_real @ ( append_poly_real @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 0.30/0.48 & ( Ys
% 0.30/0.48 = ( append_poly_real @ ( concat_poly_real @ Xss1 ) @ Xs3 ) )
% 0.30/0.48 & ( Zs2
% 0.30/0.48 = ( append_poly_real @ Xs4 @ ( concat_poly_real @ Xss22 ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % concat_eq_append_conv
% 0.30/0.48 thf(fact_266_concat_Osimps_I1_J,axiom,
% 0.30/0.48 ( ( concat_poly_real @ nil_list_poly_real )
% 0.30/0.48 = nil_poly_real ) ).
% 0.30/0.48
% 0.30/0.48 % concat.simps(1)
% 0.30/0.48 thf(fact_267_Suc__inject,axiom,
% 0.30/0.48 ! [X: nat,Y: nat] :
% 0.30/0.48 ( ( ( suc @ X )
% 0.30/0.48 = ( suc @ Y ) )
% 0.30/0.48 => ( X = Y ) ) ).
% 0.30/0.48
% 0.30/0.48 % Suc_inject
% 0.30/0.48 thf(fact_268_n__not__Suc__n,axiom,
% 0.30/0.48 ! [N: nat] :
% 0.30/0.48 ( N
% 0.30/0.48 != ( suc @ N ) ) ).
% 0.30/0.48
% 0.30/0.48 % n_not_Suc_n
% 0.30/0.48 thf(fact_269_butlast__snoc,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,X: poly_real] :
% 0.30/0.48 ( ( butlast_poly_real @ ( append_poly_real @ Xs @ ( cons_poly_real @ X @ nil_poly_real ) ) )
% 0.30/0.48 = Xs ) ).
% 0.30/0.48
% 0.30/0.48 % butlast_snoc
% 0.30/0.48 thf(fact_270_enumerate__simps_I2_J,axiom,
% 0.30/0.48 ! [N: nat,X: poly_real,Xs: list_poly_real] :
% 0.30/0.48 ( ( enumerate_poly_real @ N @ ( cons_poly_real @ X @ Xs ) )
% 0.30/0.48 = ( cons_P1027346459y_real @ ( produc404352541y_real @ N @ X ) @ ( enumerate_poly_real @ ( suc @ N ) @ Xs ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % enumerate_simps(2)
% 0.30/0.48 thf(fact_271_last__snoc,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,X: poly_real] :
% 0.30/0.48 ( ( last_poly_real @ ( append_poly_real @ Xs @ ( cons_poly_real @ X @ nil_poly_real ) ) )
% 0.30/0.48 = X ) ).
% 0.30/0.48
% 0.30/0.48 % last_snoc
% 0.30/0.48 thf(fact_272_plus__coeffs_Osimps_I2_J,axiom,
% 0.30/0.48 ! [V2: poly_real,Va2: list_poly_real] :
% 0.30/0.48 ( ( plus_c288199817y_real @ nil_poly_real @ ( cons_poly_real @ V2 @ Va2 ) )
% 0.30/0.48 = ( cons_poly_real @ V2 @ Va2 ) ) ).
% 0.30/0.48
% 0.30/0.48 % plus_coeffs.simps(2)
% 0.30/0.48 thf(fact_273_last__appendL,axiom,
% 0.30/0.48 ! [Ys: list_poly_real,Xs: list_poly_real] :
% 0.30/0.48 ( ( Ys = nil_poly_real )
% 0.30/0.48 => ( ( last_poly_real @ ( append_poly_real @ Xs @ Ys ) )
% 0.30/0.48 = ( last_poly_real @ Xs ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % last_appendL
% 0.30/0.48 thf(fact_274_last__appendR,axiom,
% 0.30/0.48 ! [Ys: list_poly_real,Xs: list_poly_real] :
% 0.30/0.48 ( ( Ys != nil_poly_real )
% 0.30/0.48 => ( ( last_poly_real @ ( append_poly_real @ Xs @ Ys ) )
% 0.30/0.48 = ( last_poly_real @ Ys ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % last_appendR
% 0.30/0.48 thf(fact_275_zip__Cons__Cons,axiom,
% 0.30/0.48 ! [X: poly_real,Xs: list_poly_real,Y: poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( zip_po657915297y_real @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ Y @ Ys ) )
% 0.30/0.48 = ( cons_P1129399039y_real @ ( produc1867601537y_real @ X @ Y ) @ ( zip_po657915297y_real @ Xs @ Ys ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % zip_Cons_Cons
% 0.30/0.48 thf(fact_276_append__butlast__last__id,axiom,
% 0.30/0.48 ! [Xs: list_poly_real] :
% 0.30/0.48 ( ( Xs != nil_poly_real )
% 0.30/0.48 => ( ( append_poly_real @ ( butlast_poly_real @ Xs ) @ ( cons_poly_real @ ( last_poly_real @ Xs ) @ nil_poly_real ) )
% 0.30/0.48 = Xs ) ) ).
% 0.30/0.48
% 0.30/0.48 % append_butlast_last_id
% 0.30/0.48 thf(fact_277_butlast_Osimps_I1_J,axiom,
% 0.30/0.48 ( ( butlast_poly_real @ nil_poly_real )
% 0.30/0.48 = nil_poly_real ) ).
% 0.30/0.48
% 0.30/0.48 % butlast.simps(1)
% 0.30/0.48 thf(fact_278_snoc__eq__iff__butlast,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,X: poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( ( append_poly_real @ Xs @ ( cons_poly_real @ X @ nil_poly_real ) )
% 0.30/0.48 = Ys )
% 0.30/0.48 = ( ( Ys != nil_poly_real )
% 0.30/0.48 & ( ( butlast_poly_real @ Ys )
% 0.30/0.48 = Xs )
% 0.30/0.48 & ( ( last_poly_real @ Ys )
% 0.30/0.48 = X ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % snoc_eq_iff_butlast
% 0.30/0.48 thf(fact_279_last_Osimps,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,X: poly_real] :
% 0.30/0.48 ( ( ( Xs = nil_poly_real )
% 0.30/0.48 => ( ( last_poly_real @ ( cons_poly_real @ X @ Xs ) )
% 0.30/0.48 = X ) )
% 0.30/0.48 & ( ( Xs != nil_poly_real )
% 0.30/0.48 => ( ( last_poly_real @ ( cons_poly_real @ X @ Xs ) )
% 0.30/0.48 = ( last_poly_real @ Xs ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % last.simps
% 0.30/0.48 thf(fact_280_last__ConsL,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,X: poly_real] :
% 0.30/0.48 ( ( Xs = nil_poly_real )
% 0.30/0.48 => ( ( last_poly_real @ ( cons_poly_real @ X @ Xs ) )
% 0.30/0.48 = X ) ) ).
% 0.30/0.48
% 0.30/0.48 % last_ConsL
% 0.30/0.48 thf(fact_281_last__ConsR,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,X: poly_real] :
% 0.30/0.48 ( ( Xs != nil_poly_real )
% 0.30/0.48 => ( ( last_poly_real @ ( cons_poly_real @ X @ Xs ) )
% 0.30/0.48 = ( last_poly_real @ Xs ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % last_ConsR
% 0.30/0.48 thf(fact_282_zip__eq__ConsE,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,Ys: list_poly_real,Xy: produc461822025y_real,Xys: list_P693436111y_real] :
% 0.30/0.48 ( ( ( zip_po657915297y_real @ Xs @ Ys )
% 0.30/0.48 = ( cons_P1129399039y_real @ Xy @ Xys ) )
% 0.30/0.48 => ~ ! [X3: poly_real,Xs5: list_poly_real] :
% 0.30/0.48 ( ( Xs
% 0.30/0.48 = ( cons_poly_real @ X3 @ Xs5 ) )
% 0.30/0.48 => ! [Y2: poly_real,Ys5: list_poly_real] :
% 0.30/0.48 ( ( Ys
% 0.30/0.48 = ( cons_poly_real @ Y2 @ Ys5 ) )
% 0.30/0.48 => ( ( Xy
% 0.30/0.48 = ( produc1867601537y_real @ X3 @ Y2 ) )
% 0.30/0.48 => ( Xys
% 0.30/0.48 != ( zip_po657915297y_real @ Xs5 @ Ys5 ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % zip_eq_ConsE
% 0.30/0.48 thf(fact_283_plus__coeffs_Osimps_I1_J,axiom,
% 0.30/0.48 ! [Xs: list_poly_real] :
% 0.30/0.48 ( ( plus_c288199817y_real @ Xs @ nil_poly_real )
% 0.30/0.48 = Xs ) ).
% 0.30/0.48
% 0.30/0.48 % plus_coeffs.simps(1)
% 0.30/0.48 thf(fact_284_last__append,axiom,
% 0.30/0.48 ! [Ys: list_poly_real,Xs: list_poly_real] :
% 0.30/0.48 ( ( ( Ys = nil_poly_real )
% 0.30/0.48 => ( ( last_poly_real @ ( append_poly_real @ Xs @ Ys ) )
% 0.30/0.48 = ( last_poly_real @ Xs ) ) )
% 0.30/0.48 & ( ( Ys != nil_poly_real )
% 0.30/0.48 => ( ( last_poly_real @ ( append_poly_real @ Xs @ Ys ) )
% 0.30/0.48 = ( last_poly_real @ Ys ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % last_append
% 0.30/0.48 thf(fact_285_longest__common__suffix,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 0.30/0.48 ? [Ss: list_poly_real,Xs5: list_poly_real,Ys5: list_poly_real] :
% 0.30/0.48 ( ( Xs
% 0.30/0.48 = ( append_poly_real @ Xs5 @ Ss ) )
% 0.30/0.48 & ( Ys
% 0.30/0.48 = ( append_poly_real @ Ys5 @ Ss ) )
% 0.30/0.48 & ( ( Xs5 = nil_poly_real )
% 0.30/0.48 | ( Ys5 = nil_poly_real )
% 0.30/0.48 | ( ( last_poly_real @ Xs5 )
% 0.30/0.48 != ( last_poly_real @ Ys5 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % longest_common_suffix
% 0.30/0.48 thf(fact_286_butlast_Osimps_I2_J,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,X: poly_real] :
% 0.30/0.48 ( ( ( Xs = nil_poly_real )
% 0.30/0.48 => ( ( butlast_poly_real @ ( cons_poly_real @ X @ Xs ) )
% 0.30/0.48 = nil_poly_real ) )
% 0.30/0.48 & ( ( Xs != nil_poly_real )
% 0.30/0.48 => ( ( butlast_poly_real @ ( cons_poly_real @ X @ Xs ) )
% 0.30/0.48 = ( cons_poly_real @ X @ ( butlast_poly_real @ Xs ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % butlast.simps(2)
% 0.30/0.48 thf(fact_287_butlast__append,axiom,
% 0.30/0.48 ! [Ys: list_poly_real,Xs: list_poly_real] :
% 0.30/0.48 ( ( ( Ys = nil_poly_real )
% 0.30/0.48 => ( ( butlast_poly_real @ ( append_poly_real @ Xs @ Ys ) )
% 0.30/0.48 = ( butlast_poly_real @ Xs ) ) )
% 0.30/0.48 & ( ( Ys != nil_poly_real )
% 0.30/0.48 => ( ( butlast_poly_real @ ( append_poly_real @ Xs @ Ys ) )
% 0.30/0.48 = ( append_poly_real @ Xs @ ( butlast_poly_real @ Ys ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % butlast_append
% 0.30/0.48 thf(fact_288_snoc__listrel1__snoc__iff,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,X: poly_real,Ys: list_poly_real,Y: poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ( ( member403334290y_real @ ( produc1000427809y_real @ ( append_poly_real @ Xs @ ( cons_poly_real @ X @ nil_poly_real ) ) @ ( append_poly_real @ Ys @ ( cons_poly_real @ Y @ nil_poly_real ) ) ) @ ( listrel1_poly_real @ R ) )
% 0.30/0.48 = ( ( ( member403334290y_real @ ( produc1000427809y_real @ Xs @ Ys ) @ ( listrel1_poly_real @ R ) )
% 0.30/0.48 & ( X = Y ) )
% 0.30/0.48 | ( ( Xs = Ys )
% 0.30/0.48 & ( member1784523250y_real @ ( produc1867601537y_real @ X @ Y ) @ R ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % snoc_listrel1_snoc_iff
% 0.30/0.48 thf(fact_289_last__zip,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( Xs != nil_poly_real )
% 0.30/0.48 => ( ( Ys != nil_poly_real )
% 0.30/0.48 => ( ( ( size_s259235672y_real @ Xs )
% 0.30/0.48 = ( size_s259235672y_real @ Ys ) )
% 0.30/0.48 => ( ( last_P21901160y_real @ ( zip_po657915297y_real @ Xs @ Ys ) )
% 0.30/0.48 = ( produc1867601537y_real @ ( last_poly_real @ Xs ) @ ( last_poly_real @ Ys ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % last_zip
% 0.30/0.48 thf(fact_290_concat__conv__foldr,axiom,
% 0.30/0.48 ( concat_poly_real
% 0.30/0.48 = ( ^ [Xss3: list_list_poly_real] : ( foldr_2117681201y_real @ append_poly_real @ Xss3 @ nil_poly_real ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % concat_conv_foldr
% 0.30/0.48 thf(fact_291_rotate__is__Nil__conv,axiom,
% 0.30/0.48 ! [N: nat,Xs: list_poly_real] :
% 0.30/0.48 ( ( ( rotate_poly_real @ N @ Xs )
% 0.30/0.48 = nil_poly_real )
% 0.30/0.48 = ( Xs = nil_poly_real ) ) ).
% 0.30/0.48
% 0.30/0.48 % rotate_is_Nil_conv
% 0.30/0.48 thf(fact_292_Cons__listrel1__Cons,axiom,
% 0.30/0.48 ! [X: poly_real,Xs: list_poly_real,Y: poly_real,Ys: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ( ( member403334290y_real @ ( produc1000427809y_real @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ Y @ Ys ) ) @ ( listrel1_poly_real @ R ) )
% 0.30/0.48 = ( ( ( member1784523250y_real @ ( produc1867601537y_real @ X @ Y ) @ R )
% 0.30/0.48 & ( Xs = Ys ) )
% 0.30/0.48 | ( ( X = Y )
% 0.30/0.48 & ( member403334290y_real @ ( produc1000427809y_real @ Xs @ Ys ) @ ( listrel1_poly_real @ R ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Cons_listrel1_Cons
% 0.30/0.48 thf(fact_293_not__listrel1__Nil,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ~ ( member403334290y_real @ ( produc1000427809y_real @ Xs @ nil_poly_real ) @ ( listrel1_poly_real @ R ) ) ).
% 0.30/0.48
% 0.30/0.48 % not_listrel1_Nil
% 0.30/0.48 thf(fact_294_not__Nil__listrel1,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ~ ( member403334290y_real @ ( produc1000427809y_real @ nil_poly_real @ Xs ) @ ( listrel1_poly_real @ R ) ) ).
% 0.30/0.48
% 0.30/0.48 % not_Nil_listrel1
% 0.30/0.48 thf(fact_295_listrel1I2,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,Ys: list_poly_real,R: set_Pr483210409y_real,X: poly_real] :
% 0.30/0.48 ( ( member403334290y_real @ ( produc1000427809y_real @ Xs @ Ys ) @ ( listrel1_poly_real @ R ) )
% 0.30/0.48 => ( member403334290y_real @ ( produc1000427809y_real @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ X @ Ys ) ) @ ( listrel1_poly_real @ R ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % listrel1I2
% 0.30/0.48 thf(fact_296_successively_Ocases,axiom,
% 0.30/0.48 ! [X: produc1060019729y_real] :
% 0.30/0.48 ( ! [P4: poly_real > poly_real > $o] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( produc1345584779y_real @ P4 @ nil_poly_real ) )
% 0.30/0.48 => ( ! [P4: poly_real > poly_real > $o,X3: poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( produc1345584779y_real @ P4 @ ( cons_poly_real @ X3 @ nil_poly_real ) ) )
% 0.30/0.48 => ~ ! [P4: poly_real > poly_real > $o,X3: poly_real,Y2: poly_real,Xs2: list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( produc1345584779y_real @ P4 @ ( cons_poly_real @ X3 @ ( cons_poly_real @ Y2 @ Xs2 ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % successively.cases
% 0.30/0.48 thf(fact_297_sorted__wrt_Ocases,axiom,
% 0.30/0.48 ! [X: produc1060019729y_real] :
% 0.30/0.48 ( ! [P4: poly_real > poly_real > $o] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( produc1345584779y_real @ P4 @ nil_poly_real ) )
% 0.30/0.48 => ~ ! [P4: poly_real > poly_real > $o,X3: poly_real,Ys2: list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( produc1345584779y_real @ P4 @ ( cons_poly_real @ X3 @ Ys2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % sorted_wrt.cases
% 0.30/0.48 thf(fact_298_Suc__length__conv,axiom,
% 0.30/0.48 ! [N: nat,Xs: list_poly_real] :
% 0.30/0.48 ( ( ( suc @ N )
% 0.30/0.48 = ( size_s259235672y_real @ Xs ) )
% 0.30/0.48 = ( ? [Y3: poly_real,Ys3: list_poly_real] :
% 0.30/0.48 ( ( Xs
% 0.30/0.48 = ( cons_poly_real @ Y3 @ Ys3 ) )
% 0.30/0.48 & ( ( size_s259235672y_real @ Ys3 )
% 0.30/0.48 = N ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Suc_length_conv
% 0.30/0.48 thf(fact_299_length__Suc__conv,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,N: nat] :
% 0.30/0.48 ( ( ( size_s259235672y_real @ Xs )
% 0.30/0.48 = ( suc @ N ) )
% 0.30/0.48 = ( ? [Y3: poly_real,Ys3: list_poly_real] :
% 0.30/0.48 ( ( Xs
% 0.30/0.48 = ( cons_poly_real @ Y3 @ Ys3 ) )
% 0.30/0.48 & ( ( size_s259235672y_real @ Ys3 )
% 0.30/0.48 = N ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % length_Suc_conv
% 0.30/0.48 thf(fact_300_list__induct4,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,Ys: list_poly_real,Zs2: list_poly_real,Ws: list_poly_real,P3: list_poly_real > list_poly_real > list_poly_real > list_poly_real > $o] :
% 0.30/0.48 ( ( ( size_s259235672y_real @ Xs )
% 0.30/0.48 = ( size_s259235672y_real @ Ys ) )
% 0.30/0.48 => ( ( ( size_s259235672y_real @ Ys )
% 0.30/0.48 = ( size_s259235672y_real @ Zs2 ) )
% 0.30/0.48 => ( ( ( size_s259235672y_real @ Zs2 )
% 0.30/0.48 = ( size_s259235672y_real @ Ws ) )
% 0.30/0.48 => ( ( P3 @ nil_poly_real @ nil_poly_real @ nil_poly_real @ nil_poly_real )
% 0.30/0.48 => ( ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real,Z: poly_real,Zs: list_poly_real,W: poly_real,Ws2: list_poly_real] :
% 0.30/0.48 ( ( ( size_s259235672y_real @ Xs2 )
% 0.30/0.48 = ( size_s259235672y_real @ Ys2 ) )
% 0.30/0.48 => ( ( ( size_s259235672y_real @ Ys2 )
% 0.30/0.48 = ( size_s259235672y_real @ Zs ) )
% 0.30/0.48 => ( ( ( size_s259235672y_real @ Zs )
% 0.30/0.48 = ( size_s259235672y_real @ Ws2 ) )
% 0.30/0.48 => ( ( P3 @ Xs2 @ Ys2 @ Zs @ Ws2 )
% 0.30/0.48 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) @ ( cons_poly_real @ Z @ Zs ) @ ( cons_poly_real @ W @ Ws2 ) ) ) ) ) )
% 0.30/0.48 => ( P3 @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % list_induct4
% 0.30/0.48 thf(fact_301_list__induct3,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,Ys: list_poly_real,Zs2: list_poly_real,P3: list_poly_real > list_poly_real > list_poly_real > $o] :
% 0.30/0.48 ( ( ( size_s259235672y_real @ Xs )
% 0.30/0.48 = ( size_s259235672y_real @ Ys ) )
% 0.30/0.48 => ( ( ( size_s259235672y_real @ Ys )
% 0.30/0.48 = ( size_s259235672y_real @ Zs2 ) )
% 0.30/0.48 => ( ( P3 @ nil_poly_real @ nil_poly_real @ nil_poly_real )
% 0.30/0.48 => ( ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real,Z: poly_real,Zs: list_poly_real] :
% 0.30/0.48 ( ( ( size_s259235672y_real @ Xs2 )
% 0.30/0.48 = ( size_s259235672y_real @ Ys2 ) )
% 0.30/0.48 => ( ( ( size_s259235672y_real @ Ys2 )
% 0.30/0.48 = ( size_s259235672y_real @ Zs ) )
% 0.30/0.48 => ( ( P3 @ Xs2 @ Ys2 @ Zs )
% 0.30/0.48 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) @ ( cons_poly_real @ Z @ Zs ) ) ) ) )
% 0.30/0.48 => ( P3 @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % list_induct3
% 0.30/0.48 thf(fact_302_list__induct2,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,Ys: list_poly_real,P3: list_poly_real > list_poly_real > $o] :
% 0.30/0.48 ( ( ( size_s259235672y_real @ Xs )
% 0.30/0.48 = ( size_s259235672y_real @ Ys ) )
% 0.30/0.48 => ( ( P3 @ nil_poly_real @ nil_poly_real )
% 0.30/0.48 => ( ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real] :
% 0.30/0.48 ( ( ( size_s259235672y_real @ Xs2 )
% 0.30/0.48 = ( size_s259235672y_real @ Ys2 ) )
% 0.30/0.48 => ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.48 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) )
% 0.30/0.48 => ( P3 @ Xs @ Ys ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % list_induct2
% 0.30/0.48 thf(fact_303_pderiv__coeffs__code_Ocases,axiom,
% 0.30/0.48 ! [X: produc796638169y_real] :
% 0.30/0.48 ( ! [F2: poly_real,X3: poly_real,Xs2: list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( produc490255505y_real @ F2 @ ( cons_poly_real @ X3 @ Xs2 ) ) )
% 0.30/0.48 => ~ ! [F2: poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( produc490255505y_real @ F2 @ nil_poly_real ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % pderiv_coeffs_code.cases
% 0.30/0.48 thf(fact_304_shuffles_Ocases,axiom,
% 0.30/0.48 ! [X: produc1426596841y_real] :
% 0.30/0.48 ( ! [Ys2: list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( produc1000427809y_real @ nil_poly_real @ Ys2 ) )
% 0.30/0.48 => ( ! [Xs2: list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( produc1000427809y_real @ Xs2 @ nil_poly_real ) )
% 0.30/0.48 => ~ ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( produc1000427809y_real @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % shuffles.cases
% 0.30/0.48 thf(fact_305_plus__coeffs_Ocases,axiom,
% 0.30/0.48 ! [X: produc1426596841y_real] :
% 0.30/0.48 ( ! [Xs2: list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( produc1000427809y_real @ Xs2 @ nil_poly_real ) )
% 0.30/0.48 => ( ! [V: poly_real,Va: list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( produc1000427809y_real @ nil_poly_real @ ( cons_poly_real @ V @ Va ) ) )
% 0.30/0.48 => ~ ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( produc1000427809y_real @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % plus_coeffs.cases
% 0.30/0.48 thf(fact_306_minus__poly__rev__list_Ocases,axiom,
% 0.30/0.48 ! [X: produc1426596841y_real] :
% 0.30/0.48 ( ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( produc1000427809y_real @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) )
% 0.30/0.48 => ( ! [Xs2: list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( produc1000427809y_real @ Xs2 @ nil_poly_real ) )
% 0.30/0.48 => ~ ! [Y2: poly_real,Ys2: list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( produc1000427809y_real @ nil_poly_real @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % minus_poly_rev_list.cases
% 0.30/0.48 thf(fact_307_Cons__listrel1E2,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,Y: poly_real,Ys: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ( ( member403334290y_real @ ( produc1000427809y_real @ Xs @ ( cons_poly_real @ Y @ Ys ) ) @ ( listrel1_poly_real @ R ) )
% 0.30/0.48 => ( ! [X3: poly_real] :
% 0.30/0.48 ( ( Xs
% 0.30/0.48 = ( cons_poly_real @ X3 @ Ys ) )
% 0.30/0.48 => ~ ( member1784523250y_real @ ( produc1867601537y_real @ X3 @ Y ) @ R ) )
% 0.30/0.48 => ~ ! [Zs: list_poly_real] :
% 0.30/0.48 ( ( Xs
% 0.30/0.48 = ( cons_poly_real @ Y @ Zs ) )
% 0.30/0.48 => ~ ( member403334290y_real @ ( produc1000427809y_real @ Zs @ Ys ) @ ( listrel1_poly_real @ R ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Cons_listrel1E2
% 0.30/0.48 thf(fact_308_Cons__listrel1E1,axiom,
% 0.30/0.48 ! [X: poly_real,Xs: list_poly_real,Ys: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ( ( member403334290y_real @ ( produc1000427809y_real @ ( cons_poly_real @ X @ Xs ) @ Ys ) @ ( listrel1_poly_real @ R ) )
% 0.30/0.48 => ( ! [Y2: poly_real] :
% 0.30/0.48 ( ( Ys
% 0.30/0.48 = ( cons_poly_real @ Y2 @ Xs ) )
% 0.30/0.48 => ~ ( member1784523250y_real @ ( produc1867601537y_real @ X @ Y2 ) @ R ) )
% 0.30/0.48 => ~ ! [Zs: list_poly_real] :
% 0.30/0.48 ( ( Ys
% 0.30/0.48 = ( cons_poly_real @ X @ Zs ) )
% 0.30/0.48 => ~ ( member403334290y_real @ ( produc1000427809y_real @ Xs @ Zs ) @ ( listrel1_poly_real @ R ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Cons_listrel1E1
% 0.30/0.48 thf(fact_309_listrel1I1,axiom,
% 0.30/0.48 ! [X: poly_real,Y: poly_real,R: set_Pr483210409y_real,Xs: list_poly_real] :
% 0.30/0.48 ( ( member1784523250y_real @ ( produc1867601537y_real @ X @ Y ) @ R )
% 0.30/0.48 => ( member403334290y_real @ ( produc1000427809y_real @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ Y @ Xs ) ) @ ( listrel1_poly_real @ R ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % listrel1I1
% 0.30/0.48 thf(fact_310_same__length__different,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( Xs != Ys )
% 0.30/0.48 => ( ( ( size_s259235672y_real @ Xs )
% 0.30/0.48 = ( size_s259235672y_real @ Ys ) )
% 0.30/0.48 => ? [Pre: list_poly_real,X3: poly_real,Xs5: list_poly_real,Y2: poly_real,Ys5: list_poly_real] :
% 0.30/0.48 ( ( X3 != Y2 )
% 0.30/0.48 & ( Xs
% 0.30/0.48 = ( append_poly_real @ Pre @ ( append_poly_real @ ( cons_poly_real @ X3 @ nil_poly_real ) @ Xs5 ) ) )
% 0.30/0.48 & ( Ys
% 0.30/0.48 = ( append_poly_real @ Pre @ ( append_poly_real @ ( cons_poly_real @ Y2 @ nil_poly_real ) @ Ys5 ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % same_length_different
% 0.30/0.48 thf(fact_311_listrel1E,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,Ys: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ( ( member403334290y_real @ ( produc1000427809y_real @ Xs @ Ys ) @ ( listrel1_poly_real @ R ) )
% 0.30/0.48 => ~ ! [X3: poly_real,Y2: poly_real] :
% 0.30/0.48 ( ( member1784523250y_real @ ( produc1867601537y_real @ X3 @ Y2 ) @ R )
% 0.30/0.48 => ! [Us: list_poly_real,Vs: list_poly_real] :
% 0.30/0.48 ( ( Xs
% 0.30/0.48 = ( append_poly_real @ Us @ ( cons_poly_real @ X3 @ Vs ) ) )
% 0.30/0.48 => ( Ys
% 0.30/0.48 != ( append_poly_real @ Us @ ( cons_poly_real @ Y2 @ Vs ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % listrel1E
% 0.30/0.48 thf(fact_312_listrel1I,axiom,
% 0.30/0.48 ! [X: poly_real,Y: poly_real,R: set_Pr483210409y_real,Xs: list_poly_real,Us2: list_poly_real,Vs2: list_poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( member1784523250y_real @ ( produc1867601537y_real @ X @ Y ) @ R )
% 0.30/0.48 => ( ( Xs
% 0.30/0.48 = ( append_poly_real @ Us2 @ ( cons_poly_real @ X @ Vs2 ) ) )
% 0.30/0.48 => ( ( Ys
% 0.30/0.48 = ( append_poly_real @ Us2 @ ( cons_poly_real @ Y @ Vs2 ) ) )
% 0.30/0.48 => ( member403334290y_real @ ( produc1000427809y_real @ Xs @ Ys ) @ ( listrel1_poly_real @ R ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % listrel1I
% 0.30/0.48 thf(fact_313_length__append__singleton,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,X: poly_real] :
% 0.30/0.48 ( ( size_s259235672y_real @ ( append_poly_real @ Xs @ ( cons_poly_real @ X @ nil_poly_real ) ) )
% 0.30/0.48 = ( suc @ ( size_s259235672y_real @ Xs ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % length_append_singleton
% 0.30/0.48 thf(fact_314_subset__eq__mset__impl_Ocases,axiom,
% 0.30/0.48 ! [X: produc1426596841y_real] :
% 0.30/0.48 ( ! [Ys2: list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( produc1000427809y_real @ nil_poly_real @ Ys2 ) )
% 0.30/0.48 => ~ ! [X3: poly_real,Xs2: list_poly_real,Ys2: list_poly_real] :
% 0.30/0.48 ( X
% 0.30/0.48 != ( produc1000427809y_real @ ( cons_poly_real @ X3 @ Xs2 ) @ Ys2 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % subset_eq_mset_impl.cases
% 0.30/0.48 thf(fact_315_length__Cons,axiom,
% 0.30/0.48 ! [X: poly_real,Xs: list_poly_real] :
% 0.30/0.48 ( ( size_s259235672y_real @ ( cons_poly_real @ X @ Xs ) )
% 0.30/0.48 = ( suc @ ( size_s259235672y_real @ Xs ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % length_Cons
% 0.30/0.48 thf(fact_316_Cons__in__lex,axiom,
% 0.30/0.48 ! [X: poly_real,Xs: list_poly_real,Y: poly_real,Ys: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ( ( member403334290y_real @ ( produc1000427809y_real @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ Y @ Ys ) ) @ ( lex_poly_real @ R ) )
% 0.30/0.48 = ( ( ( member1784523250y_real @ ( produc1867601537y_real @ X @ Y ) @ R )
% 0.30/0.48 & ( ( size_s259235672y_real @ Xs )
% 0.30/0.48 = ( size_s259235672y_real @ Ys ) ) )
% 0.30/0.48 | ( ( X = Y )
% 0.30/0.48 & ( member403334290y_real @ ( produc1000427809y_real @ Xs @ Ys ) @ ( lex_poly_real @ R ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Cons_in_lex
% 0.30/0.48 thf(fact_317_Nil2__notin__lex,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ~ ( member403334290y_real @ ( produc1000427809y_real @ Xs @ nil_poly_real ) @ ( lex_poly_real @ R ) ) ).
% 0.30/0.48
% 0.30/0.48 % Nil2_notin_lex
% 0.30/0.48 thf(fact_318_Nil__notin__lex,axiom,
% 0.30/0.48 ! [Ys: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ~ ( member403334290y_real @ ( produc1000427809y_real @ nil_poly_real @ Ys ) @ ( lex_poly_real @ R ) ) ).
% 0.30/0.48
% 0.30/0.48 % Nil_notin_lex
% 0.30/0.48 thf(fact_319_SuccD,axiom,
% 0.30/0.48 ! [K: poly_real,Kl: set_list_poly_real,Kl2: list_poly_real] :
% 0.30/0.48 ( ( member_poly_real2 @ K @ ( bNF_Gr1644259033y_real @ Kl @ Kl2 ) )
% 0.30/0.48 => ( member708095579y_real @ ( append_poly_real @ Kl2 @ ( cons_poly_real @ K @ nil_poly_real ) ) @ Kl ) ) ).
% 0.30/0.48
% 0.30/0.48 % SuccD
% 0.30/0.48 thf(fact_320_SuccI,axiom,
% 0.30/0.48 ! [Kl2: list_poly_real,K: poly_real,Kl: set_list_poly_real] :
% 0.30/0.48 ( ( member708095579y_real @ ( append_poly_real @ Kl2 @ ( cons_poly_real @ K @ nil_poly_real ) ) @ Kl )
% 0.30/0.48 => ( member_poly_real2 @ K @ ( bNF_Gr1644259033y_real @ Kl @ Kl2 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % SuccI
% 0.30/0.48 thf(fact_321_empty__Shift,axiom,
% 0.30/0.48 ! [Kl: set_list_poly_real,K: poly_real] :
% 0.30/0.48 ( ( member708095579y_real @ nil_poly_real @ Kl )
% 0.30/0.48 => ( ( member_poly_real2 @ K @ ( bNF_Gr1644259033y_real @ Kl @ nil_poly_real ) )
% 0.30/0.48 => ( member708095579y_real @ nil_poly_real @ ( bNF_Gr851617109y_real @ Kl @ K ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % empty_Shift
% 0.30/0.48 thf(fact_322_Succ__Shift,axiom,
% 0.30/0.48 ! [Kl: set_list_poly_real,K: poly_real,Kl2: list_poly_real] :
% 0.30/0.48 ( ( bNF_Gr1644259033y_real @ ( bNF_Gr851617109y_real @ Kl @ K ) @ Kl2 )
% 0.30/0.48 = ( bNF_Gr1644259033y_real @ Kl @ ( cons_poly_real @ K @ Kl2 ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Succ_Shift
% 0.30/0.48 thf(fact_323_ShiftD,axiom,
% 0.30/0.48 ! [Kl2: list_poly_real,Kl: set_list_poly_real,K: poly_real] :
% 0.30/0.48 ( ( member708095579y_real @ Kl2 @ ( bNF_Gr851617109y_real @ Kl @ K ) )
% 0.30/0.48 => ( member708095579y_real @ ( cons_poly_real @ K @ Kl2 ) @ Kl ) ) ).
% 0.30/0.48
% 0.30/0.48 % ShiftD
% 0.30/0.48 thf(fact_324_Suc__mult__cancel1,axiom,
% 0.30/0.48 ! [K: nat,M: nat,N: nat] :
% 0.30/0.48 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 0.30/0.48 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.30/0.48 = ( M = N ) ) ).
% 0.30/0.48
% 0.30/0.48 % Suc_mult_cancel1
% 0.30/0.48 thf(fact_325_lexord__append__left__rightI,axiom,
% 0.30/0.48 ! [A3: poly_real,B: poly_real,R: set_Pr483210409y_real,U: list_poly_real,X: list_poly_real,Y: list_poly_real] :
% 0.30/0.48 ( ( member1784523250y_real @ ( produc1867601537y_real @ A3 @ B ) @ R )
% 0.30/0.48 => ( member403334290y_real @ ( produc1000427809y_real @ ( append_poly_real @ U @ ( cons_poly_real @ A3 @ X ) ) @ ( append_poly_real @ U @ ( cons_poly_real @ B @ Y ) ) ) @ ( lexord_poly_real @ R ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % lexord_append_left_rightI
% 0.30/0.48 thf(fact_326_listrel_Oinducts,axiom,
% 0.30/0.48 ! [X1: list_poly_real,X2: list_poly_real,R: set_Pr483210409y_real,P3: list_poly_real > list_poly_real > $o] :
% 0.30/0.48 ( ( member403334290y_real @ ( produc1000427809y_real @ X1 @ X2 ) @ ( listre572247515y_real @ R ) )
% 0.30/0.48 => ( ( P3 @ nil_poly_real @ nil_poly_real )
% 0.30/0.48 => ( ! [X3: poly_real,Y2: poly_real,Xs2: list_poly_real,Ys2: list_poly_real] :
% 0.30/0.48 ( ( member1784523250y_real @ ( produc1867601537y_real @ X3 @ Y2 ) @ R )
% 0.30/0.48 => ( ( member403334290y_real @ ( produc1000427809y_real @ Xs2 @ Ys2 ) @ ( listre572247515y_real @ R ) )
% 0.30/0.48 => ( ( P3 @ Xs2 @ Ys2 )
% 0.30/0.48 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) ) )
% 0.30/0.48 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % listrel.inducts
% 0.30/0.48 thf(fact_327_lexord__cons__cons,axiom,
% 0.30/0.48 ! [A3: poly_real,X: list_poly_real,B: poly_real,Y: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ( ( member403334290y_real @ ( produc1000427809y_real @ ( cons_poly_real @ A3 @ X ) @ ( cons_poly_real @ B @ Y ) ) @ ( lexord_poly_real @ R ) )
% 0.30/0.48 = ( ( member1784523250y_real @ ( produc1867601537y_real @ A3 @ B ) @ R )
% 0.30/0.48 | ( ( A3 = B )
% 0.30/0.48 & ( member403334290y_real @ ( produc1000427809y_real @ X @ Y ) @ ( lexord_poly_real @ R ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % lexord_cons_cons
% 0.30/0.48 thf(fact_328_lexord__Nil__left,axiom,
% 0.30/0.48 ! [Y: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ( ( member403334290y_real @ ( produc1000427809y_real @ nil_poly_real @ Y ) @ ( lexord_poly_real @ R ) )
% 0.30/0.48 = ( ? [A5: poly_real,X4: list_poly_real] :
% 0.30/0.48 ( Y
% 0.30/0.48 = ( cons_poly_real @ A5 @ X4 ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % lexord_Nil_left
% 0.30/0.48 thf(fact_329_lexord__Nil__right,axiom,
% 0.30/0.48 ! [X: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ~ ( member403334290y_real @ ( produc1000427809y_real @ X @ nil_poly_real ) @ ( lexord_poly_real @ R ) ) ).
% 0.30/0.48
% 0.30/0.48 % lexord_Nil_right
% 0.30/0.48 thf(fact_330_listrel__Nil2,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ( ( member403334290y_real @ ( produc1000427809y_real @ Xs @ nil_poly_real ) @ ( listre572247515y_real @ R ) )
% 0.30/0.48 => ( Xs = nil_poly_real ) ) ).
% 0.30/0.48
% 0.30/0.48 % listrel_Nil2
% 0.30/0.48 thf(fact_331_listrel__Nil1,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ( ( member403334290y_real @ ( produc1000427809y_real @ nil_poly_real @ Xs ) @ ( listre572247515y_real @ R ) )
% 0.30/0.48 => ( Xs = nil_poly_real ) ) ).
% 0.30/0.48
% 0.30/0.48 % listrel_Nil1
% 0.30/0.48 thf(fact_332_listrel_ONil,axiom,
% 0.30/0.48 ! [R: set_Pr483210409y_real] : ( member403334290y_real @ ( produc1000427809y_real @ nil_poly_real @ nil_poly_real ) @ ( listre572247515y_real @ R ) ) ).
% 0.30/0.48
% 0.30/0.48 % listrel.Nil
% 0.30/0.48 thf(fact_333_listrel__Cons2,axiom,
% 0.30/0.48 ! [Xs: list_poly_real,Y: poly_real,Ys: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ( ( member403334290y_real @ ( produc1000427809y_real @ Xs @ ( cons_poly_real @ Y @ Ys ) ) @ ( listre572247515y_real @ R ) )
% 0.30/0.48 => ~ ! [X3: poly_real,Xs2: list_poly_real] :
% 0.30/0.48 ( ( Xs
% 0.30/0.48 = ( cons_poly_real @ X3 @ Xs2 ) )
% 0.30/0.48 => ( ( member1784523250y_real @ ( produc1867601537y_real @ X3 @ Y ) @ R )
% 0.30/0.48 => ~ ( member403334290y_real @ ( produc1000427809y_real @ Xs2 @ Ys ) @ ( listre572247515y_real @ R ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % listrel_Cons2
% 0.30/0.48 thf(fact_334_listrel__Cons1,axiom,
% 0.30/0.48 ! [Y: poly_real,Ys: list_poly_real,Xs: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ( ( member403334290y_real @ ( produc1000427809y_real @ ( cons_poly_real @ Y @ Ys ) @ Xs ) @ ( listre572247515y_real @ R ) )
% 0.30/0.48 => ~ ! [Y2: poly_real,Ys2: list_poly_real] :
% 0.30/0.48 ( ( Xs
% 0.30/0.48 = ( cons_poly_real @ Y2 @ Ys2 ) )
% 0.30/0.48 => ( ( member1784523250y_real @ ( produc1867601537y_real @ Y @ Y2 ) @ R )
% 0.30/0.48 => ~ ( member403334290y_real @ ( produc1000427809y_real @ Ys @ Ys2 ) @ ( listre572247515y_real @ R ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % listrel_Cons1
% 0.30/0.48 thf(fact_335_listrel_OCons,axiom,
% 0.30/0.48 ! [X: poly_real,Y: poly_real,R: set_Pr483210409y_real,Xs: list_poly_real,Ys: list_poly_real] :
% 0.30/0.48 ( ( member1784523250y_real @ ( produc1867601537y_real @ X @ Y ) @ R )
% 0.30/0.48 => ( ( member403334290y_real @ ( produc1000427809y_real @ Xs @ Ys ) @ ( listre572247515y_real @ R ) )
% 0.30/0.48 => ( member403334290y_real @ ( produc1000427809y_real @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ Y @ Ys ) ) @ ( listre572247515y_real @ R ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % listrel.Cons
% 0.30/0.48 thf(fact_336_lexord__append__rightI,axiom,
% 0.30/0.48 ! [Y: list_poly_real,X: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ( ? [B2: poly_real,Z2: list_poly_real] :
% 0.30/0.48 ( Y
% 0.30/0.48 = ( cons_poly_real @ B2 @ Z2 ) )
% 0.30/0.48 => ( member403334290y_real @ ( produc1000427809y_real @ X @ ( append_poly_real @ X @ Y ) ) @ ( lexord_poly_real @ R ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % lexord_append_rightI
% 0.30/0.48 thf(fact_337_listrel_Ocases,axiom,
% 0.30/0.48 ! [A12: list_poly_real,A22: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ( ( member403334290y_real @ ( produc1000427809y_real @ A12 @ A22 ) @ ( listre572247515y_real @ R ) )
% 0.30/0.48 => ( ( ( A12 = nil_poly_real )
% 0.30/0.48 => ( A22 != nil_poly_real ) )
% 0.30/0.48 => ~ ! [X3: poly_real,Y2: poly_real,Xs2: list_poly_real] :
% 0.30/0.48 ( ( A12
% 0.30/0.48 = ( cons_poly_real @ X3 @ Xs2 ) )
% 0.30/0.48 => ! [Ys2: list_poly_real] :
% 0.30/0.48 ( ( A22
% 0.30/0.48 = ( cons_poly_real @ Y2 @ Ys2 ) )
% 0.30/0.48 => ( ( member1784523250y_real @ ( produc1867601537y_real @ X3 @ Y2 ) @ R )
% 0.30/0.48 => ~ ( member403334290y_real @ ( produc1000427809y_real @ Xs2 @ Ys2 ) @ ( listre572247515y_real @ R ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % listrel.cases
% 0.30/0.48 thf(fact_338_listrel_Osimps,axiom,
% 0.30/0.48 ! [A12: list_poly_real,A22: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ( ( member403334290y_real @ ( produc1000427809y_real @ A12 @ A22 ) @ ( listre572247515y_real @ R ) )
% 0.30/0.48 = ( ( ( A12 = nil_poly_real )
% 0.30/0.48 & ( A22 = nil_poly_real ) )
% 0.30/0.48 | ? [X4: poly_real,Y3: poly_real,Xs3: list_poly_real,Ys3: list_poly_real] :
% 0.30/0.48 ( ( A12
% 0.30/0.48 = ( cons_poly_real @ X4 @ Xs3 ) )
% 0.30/0.48 & ( A22
% 0.30/0.48 = ( cons_poly_real @ Y3 @ Ys3 ) )
% 0.30/0.48 & ( member1784523250y_real @ ( produc1867601537y_real @ X4 @ Y3 ) @ R )
% 0.30/0.48 & ( member403334290y_real @ ( produc1000427809y_real @ Xs3 @ Ys3 ) @ ( listre572247515y_real @ R ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % listrel.simps
% 0.30/0.48 thf(fact_339_map__tailrec__rev_Opelims,axiom,
% 0.30/0.48 ! [X: poly_real > poly_real,Xa: list_poly_real,Xb: list_poly_real,Y: list_poly_real] :
% 0.30/0.48 ( ( ( map_ta1919289823y_real @ X @ Xa @ Xb )
% 0.30/0.48 = Y )
% 0.30/0.48 => ( ( accp_P948088014y_real @ map_ta954657966y_real @ ( produc2087464649y_real @ X @ ( produc1000427809y_real @ Xa @ Xb ) ) )
% 0.30/0.48 => ( ( ( Xa = nil_poly_real )
% 0.30/0.48 => ( ( Y = Xb )
% 0.30/0.48 => ~ ( accp_P948088014y_real @ map_ta954657966y_real @ ( produc2087464649y_real @ X @ ( produc1000427809y_real @ nil_poly_real @ Xb ) ) ) ) )
% 0.30/0.48 => ~ ! [A: poly_real,As: list_poly_real] :
% 0.30/0.48 ( ( Xa
% 0.30/0.48 = ( cons_poly_real @ A @ As ) )
% 0.30/0.48 => ( ( Y
% 0.30/0.48 = ( map_ta1919289823y_real @ X @ As @ ( cons_poly_real @ ( X @ A ) @ Xb ) ) )
% 0.30/0.48 => ~ ( accp_P948088014y_real @ map_ta954657966y_real @ ( produc2087464649y_real @ X @ ( produc1000427809y_real @ ( cons_poly_real @ A @ As ) @ Xb ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % map_tailrec_rev.pelims
% 0.30/0.48 thf(fact_340_Nil__lenlex__iff1,axiom,
% 0.30/0.48 ! [Ns: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ( ( member403334290y_real @ ( produc1000427809y_real @ nil_poly_real @ Ns ) @ ( lenlex_poly_real @ R ) )
% 0.30/0.48 = ( Ns != nil_poly_real ) ) ).
% 0.30/0.48
% 0.30/0.48 % Nil_lenlex_iff1
% 0.30/0.48 thf(fact_341_Nil__lenlex__iff2,axiom,
% 0.30/0.48 ! [Ns: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ~ ( member403334290y_real @ ( produc1000427809y_real @ Ns @ nil_poly_real ) @ ( lenlex_poly_real @ R ) ) ).
% 0.30/0.48
% 0.30/0.48 % Nil_lenlex_iff2
% 0.30/0.48 thf(fact_342_Cons__lenlex__iff,axiom,
% 0.30/0.48 ! [M: poly_real,Ms: list_poly_real,N: poly_real,Ns: list_poly_real,R: set_Pr483210409y_real] :
% 0.30/0.48 ( ( member403334290y_real @ ( produc1000427809y_real @ ( cons_poly_real @ M @ Ms ) @ ( cons_poly_real @ N @ Ns ) ) @ ( lenlex_poly_real @ R ) )
% 0.30/0.48 = ( ( ord_less_nat @ ( size_s259235672y_real @ Ms ) @ ( size_s259235672y_real @ Ns ) )
% 0.30/0.48 | ( ( ( size_s259235672y_real @ Ms )
% 0.30/0.48 = ( size_s259235672y_real @ Ns ) )
% 0.30/0.48 & ( member1784523250y_real @ ( produc1867601537y_real @ M @ N ) @ R ) )
% 0.30/0.48 | ( ( M = N )
% 0.30/0.48 & ( member403334290y_real @ ( produc1000427809y_real @ Ms @ Ns ) @ ( lenlex_poly_real @ R ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Cons_lenlex_iff
% 0.30/0.48 thf(fact_343_Suc__less__eq,axiom,
% 0.30/0.48 ! [M: nat,N: nat] :
% 0.30/0.48 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.30/0.48 = ( ord_less_nat @ M @ N ) ) ).
% 0.30/0.48
% 0.30/0.48 % Suc_less_eq
% 0.30/0.48 thf(fact_344_Suc__mono,axiom,
% 0.30/0.48 ! [M: nat,N: nat] :
% 0.30/0.48 ( ( ord_less_nat @ M @ N )
% 0.30/0.48 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.30/0.48
% 0.30/0.48 % Suc_mono
% 0.30/0.48 thf(fact_345_lessI,axiom,
% 0.30/0.48 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 0.30/0.48
% 0.30/0.48 % lessI
% 0.30/0.48 thf(fact_346_list_Omap__disc__iff,axiom,
% 0.30/0.48 ! [F: poly_real > poly_real,A3: list_poly_real] :
% 0.30/0.48 ( ( ( map_po2132607150y_real @ F @ A3 )
% 0.30/0.48 = nil_poly_real )
% 0.30/0.48 = ( A3 = nil_poly_real ) ) ).
% 0.30/0.48
% 0.30/0.48 % list.map_disc_iff
% 0.30/0.48 thf(fact_347_map__is__Nil__conv,axiom,
% 0.30/0.48 ! [F: poly_real > poly_real,Xs: list_poly_real] :
% 0.30/0.48 ( ( ( map_po2132607150y_real @ F @ Xs )
% 0.30/0.48 = nil_poly_real )
% 0.30/0.48 = ( Xs = nil_poly_real ) ) ).
% 0.30/0.48
% 0.30/0.48 % map_is_Nil_conv
% 0.30/0.48 thf(fact_348_Nil__is__map__conv,axiom,
% 0.30/0.48 ! [F: poly_real > poly_real,Xs: list_poly_real] :
% 0.30/0.48 ( ( nil_poly_real
% 0.30/0.48 = ( map_po2132607150y_real @ F @ Xs ) )
% 0.30/0.48 = ( Xs = nil_poly_real ) ) ).
% 0.30/0.48
% 0.30/0.48 % Nil_is_map_conv
% 0.30/0.48
% 0.30/0.48 % Conjectures (1)
% 0.30/0.48 thf(conj_0,conjecture,
% 0.30/0.48 ~ ( sturm_891428828rm_seq @ nil_poly_real ) ).
% 0.30/0.48
% 0.30/0.48 %------------------------------------------------------------------------------
% 0.30/0.48 ------------------------
% 2.91/1.57 ---- Embedded in THF ---
% 2.91/1.57 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.91/1.57 %%% Generated on Tue Feb 24 08:28:12 EST 2026
% 2.91/1.57 %%% using '$$dhol' embedding, version 1.3.0.
% 2.91/1.57 %%% Logic specification used:
% 2.91/1.57 %%% thf(spec, logic, $$dhol).
% 2.91/1.57
% 2.91/1.57 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.MilWfgdHi9/DTF2DTF23528.p
% See solution above
% 2.91/1.57 ------------------------
% 3.10/1.61 ---- Cleaned THF ---
% 3.10/1.62 thf(ty_n_t__Product____Type__Oprod_I_062_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_Mt__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_J_J,type,
% 3.10/1.62 produc1456530199y_real: $tType ).
% 3.10/1.62
% 3.10/1.62 thf(ty_n_t__Product____Type__Oprod_I_062_It__Polynomial__Opoly_It__Real__Oreal_J_M_062_It__Polynomial__Opoly_It__Real__Oreal_J_M_Eo_J_J_Mt__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 3.10/1.62 produc1060019729y_real: $tType ).
% 3.10/1.62
% 3.10/1.62 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J_J_J,type,
% 3.10/1.62 list_P657095678y_real: $tType ).
% 3.10/1.62
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% 3.10/1.62 lexord1324236152y_real: ( list_poly_real > list_poly_real > $o ) > list_list_poly_real > list_list_poly_real > $o ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Oord_Olexordp__eq_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.10/1.62 lexordp_eq_poly_real: ( poly_real > poly_real > $o ) > list_poly_real > list_poly_real > $o ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Oord_Olexordp__eq_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.10/1.62 lexord834705585y_real: ( produc321349221y_real > produc321349221y_real > $o ) > list_P736648811y_real > list_P736648811y_real > $o ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Oord_Olexordp__eq_001t__Product____Type__Oprod_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.10/1.62 lexord1053351061y_real: ( produc461822025y_real > produc461822025y_real > $o ) > list_P693436111y_real > list_P693436111y_real > $o ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Oord__class_Olexordp__eq_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.10/1.62 ord_le1233681790y_real: list_poly_real > list_poly_real > $o ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.10/1.62 produc1360353227y_real: list_nat > list_poly_real > list_P736648811y_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Oproduct_001t__Polynomial__Opoly_It__Real__Oreal_J_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.10/1.62 produc1733309743y_real: list_poly_real > list_poly_real > list_P693436111y_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Oproduct__lists_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.10/1.62 produc523415045y_real: list_list_poly_real > list_list_poly_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Orotate1_001t__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.10/1.62 rotate717473073y_real: list_list_poly_real > list_list_poly_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Orotate1_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.10/1.62 rotate1_poly_real: list_poly_real > list_poly_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Orotate1_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.10/1.62 rotate623875384y_real: list_P736648811y_real > list_P736648811y_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Orotate1_001t__Product____Type__Oprod_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.10/1.62 rotate867081116y_real: list_P693436111y_real > list_P693436111y_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Orotate_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.10/1.62 rotate_poly_real: nat > list_poly_real > list_poly_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Osplice_001t__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.10/1.62 splice2080530731y_real: list_list_poly_real > list_list_poly_real > list_list_poly_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Osplice_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.10/1.62 splice_poly_real: list_poly_real > list_poly_real > list_poly_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Osplice_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.10/1.62 splice1383748542y_real: list_P736648811y_real > list_P736648811y_real > list_P736648811y_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Osplice_001t__Product____Type__Oprod_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.10/1.62 splice1321784098y_real: list_P693436111y_real > list_P693436111y_real > list_P693436111y_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Osubseqs_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.10/1.62 subseqs_poly_real: list_poly_real > list_list_poly_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.10/1.62 zip_nat_poly_real: list_nat > list_poly_real > list_P736648811y_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_List_Ozip_001t__Polynomial__Opoly_It__Real__Oreal_J_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.10/1.62 zip_po657915297y_real: list_poly_real > list_poly_real > list_P693436111y_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_Nat_OSuc,type,
% 3.10/1.62 suc: nat > nat ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.10/1.62 size_s259235672y_real: list_poly_real > nat ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 3.10/1.62 ord_less_nat: nat > nat > $o ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_Polynomial_Oplus__coeffs_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.10/1.62 plus_c288199817y_real: list_poly_real > list_poly_real > list_poly_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_Product__Type_OPair_001_062_It__Polynomial__Opoly_It__Real__Oreal_J_M_062_It__Polynomial__Opoly_It__Real__Oreal_J_M_Eo_J_J_001t__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.10/1.62 produc1345584779y_real: ( poly_real > poly_real > $o ) > list_poly_real > produc1060019729y_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_Product__Type_OPair_001_062_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_Mt__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 3.10/1.62 produc2087464649y_real: ( poly_real > poly_real ) > produc1426596841y_real > produc1456530199y_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_001t__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.10/1.62 produc1000427809y_real: list_poly_real > list_poly_real > produc1426596841y_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.10/1.62 produc404352541y_real: nat > poly_real > produc321349221y_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_Product__Type_OPair_001t__Polynomial__Opoly_It__Real__Oreal_J_001t__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.10/1.62 produc490255505y_real: poly_real > list_poly_real > produc796638169y_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_Product__Type_OPair_001t__Polynomial__Opoly_It__Real__Oreal_J_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.10/1.62 produc1867601537y_real: poly_real > poly_real > produc461822025y_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_Set_OCollect_001t__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.10/1.62 collec1537941401y_real: ( list_poly_real > $o ) > set_list_poly_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_Set_OCollect_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.10/1.62 collect_poly_real: ( poly_real > $o ) > set_poly_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_Mt__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 3.10/1.62 collec1459394516y_real: ( produc1426596841y_real > $o ) > set_Pr1405268809y_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.10/1.62 collec329281332y_real: ( produc461822025y_real > $o ) > set_Pr483210409y_real ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_Sturm__Theorem__Mirabelle__ubahemswrm_Oquasi__sturm__seq,type,
% 3.10/1.62 sturm_891428828rm_seq: list_poly_real > $o ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_Sturm__Theorem__Mirabelle__ubahemswrm_Osturm__seq,type,
% 3.10/1.62 sturm_1664866327rm_seq: list_poly_real > poly_real > $o ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_Sturm__Theorem__Mirabelle__ubahemswrm_Osturm__seq__axioms,type,
% 3.10/1.62 sturm_1683633594axioms: list_poly_real > poly_real > $o ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J_Mt__Product____Type__Oprod_It__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_Mt__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_J_J,type,
% 3.10/1.62 accp_P948088014y_real: ( produc1456530199y_real > produc1456530199y_real > $o ) > produc1456530199y_real > $o ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_member_001t__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.10/1.62 member708095579y_real: list_poly_real > set_list_poly_real > $o ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_member_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.10/1.62 member_poly_real2: poly_real > set_poly_real > $o ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_Mt__List__Olist_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 3.10/1.62 member403334290y_real: produc1426596841y_real > set_Pr1405268809y_real > $o ).
% 3.10/1.62
% 3.10/1.62 thf(sy_c_member_001t__Product____Type__Oprod_It__Polynomial__Opoly_It__Real__Oreal_J_Mt__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.10/1.62 member1784523250y_real: produc461822025y_real > set_Pr483210409y_real > $o ).
% 3.10/1.62
% 3.10/1.62 thf(fact_0_quasi__sturm__seq_Ops__not__Nil,axiom,
% 3.10/1.62 ! [Ps: list_poly_real] :
% 3.10/1.62 ( ( sturm_891428828rm_seq @ Ps )
% 3.10/1.62 => ( Ps != nil_poly_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_1_sturm__seq_Oquasi__sturm__seq,axiom,
% 3.10/1.62 ! [Ps: list_poly_real,P: poly_real] :
% 3.10/1.62 ( ( sturm_1664866327rm_seq @ Ps @ P )
% 3.10/1.62 => ( sturm_891428828rm_seq @ Ps ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_2_sturm__seq__def,axiom,
% 3.10/1.62 ( sturm_1664866327rm_seq
% 3.10/1.62 = ( ^ [Ps2: list_poly_real,P2: poly_real] :
% 3.10/1.62 ( ( sturm_891428828rm_seq @ Ps2 )
% 3.10/1.62 & ( sturm_1683633594axioms @ Ps2 @ P2 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_3_sturm__seq_Ointro,axiom,
% 3.10/1.62 ! [Ps: list_poly_real,P: poly_real] :
% 3.10/1.62 ( ( sturm_891428828rm_seq @ Ps )
% 3.10/1.62 => ( ( sturm_1683633594axioms @ Ps @ P )
% 3.10/1.62 => ( sturm_1664866327rm_seq @ Ps @ P ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_4_list__ex1__simps_I1_J,axiom,
% 3.10/1.62 ! [P3: produc321349221y_real > $o] :
% 3.10/1.62 ~ ( list_e1892536494y_real @ P3 @ nil_Pr1492526187y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_5_list__ex1__simps_I1_J,axiom,
% 3.10/1.62 ! [P3: list_poly_real > $o] :
% 3.10/1.62 ~ ( list_e367462459y_real @ P3 @ nil_list_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_6_list__ex1__simps_I1_J,axiom,
% 3.10/1.62 ! [P3: produc461822025y_real > $o] :
% 3.10/1.62 ~ ( list_e1507538962y_real @ P3 @ nil_Pr1207979855y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_7_list__ex1__simps_I1_J,axiom,
% 3.10/1.62 ! [P3: poly_real > $o] :
% 3.10/1.62 ~ ( list_ex1_poly_real @ P3 @ nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_8_bind__simps_I1_J,axiom,
% 3.10/1.62 ! [F: poly_real > list_poly_real] :
% 3.10/1.62 ( ( bind_p420216945y_real @ nil_poly_real @ F )
% 3.10/1.62 = nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_9_bind__simps_I1_J,axiom,
% 3.10/1.62 ! [F: poly_real > list_list_poly_real] :
% 3.10/1.62 ( ( bind_p1226679937y_real @ nil_poly_real @ F )
% 3.10/1.62 = nil_list_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_10_bind__simps_I1_J,axiom,
% 3.10/1.62 ! [F: list_poly_real > list_poly_real] :
% 3.10/1.62 ( ( bind_l146959617y_real @ nil_list_poly_real @ F )
% 3.10/1.62 = nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_11_bind__simps_I1_J,axiom,
% 3.10/1.62 ! [F: poly_real > list_P736648811y_real] :
% 3.10/1.62 ( ( bind_p600434664y_real @ nil_poly_real @ F )
% 3.10/1.62 = nil_Pr1492526187y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_12_bind__simps_I1_J,axiom,
% 3.10/1.62 ! [F: produc321349221y_real > list_poly_real] :
% 3.10/1.62 ( ( bind_P755425362y_real @ nil_Pr1492526187y_real @ F )
% 3.10/1.62 = nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_13_bind__simps_I1_J,axiom,
% 3.10/1.62 ! [F: list_poly_real > list_list_poly_real] :
% 3.10/1.62 ( ( bind_l1810664209y_real @ nil_list_poly_real @ F )
% 3.10/1.62 = nil_list_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_14_bind__simps_I1_J,axiom,
% 3.10/1.62 ! [F: poly_real > list_P693436111y_real] :
% 3.10/1.62 ( ( bind_p988182092y_real @ nil_poly_real @ F )
% 3.10/1.62 = nil_Pr1207979855y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_15_bind__simps_I1_J,axiom,
% 3.10/1.62 ! [F: produc321349221y_real > list_list_poly_real] :
% 3.10/1.62 ( ( bind_P1861132770y_real @ nil_Pr1492526187y_real @ F )
% 3.10/1.62 = nil_list_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_16_bind__simps_I1_J,axiom,
% 3.10/1.62 ! [F: list_poly_real > list_P736648811y_real] :
% 3.10/1.62 ( ( bind_l429098840y_real @ nil_list_poly_real @ F )
% 3.10/1.62 = nil_Pr1492526187y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_17_bind__simps_I1_J,axiom,
% 3.10/1.62 ! [F: produc461822025y_real > list_poly_real] :
% 3.10/1.62 ( ( bind_P120560694y_real @ nil_Pr1207979855y_real @ F )
% 3.10/1.62 = nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_18_member__rec_I2_J,axiom,
% 3.10/1.62 ! [Y: produc321349221y_real] :
% 3.10/1.62 ~ ( member1782690048y_real @ nil_Pr1492526187y_real @ Y ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_19_member__rec_I2_J,axiom,
% 3.10/1.62 ! [Y: list_poly_real] :
% 3.10/1.62 ~ ( member1829603177y_real @ nil_list_poly_real @ Y ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_20_member__rec_I2_J,axiom,
% 3.10/1.62 ! [Y: produc461822025y_real] :
% 3.10/1.62 ~ ( member202023780y_real @ nil_Pr1207979855y_real @ Y ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_21_member__rec_I2_J,axiom,
% 3.10/1.62 ! [Y: poly_real] :
% 3.10/1.62 ~ ( member_poly_real @ nil_poly_real @ Y ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_22_gen__length__code_I1_J,axiom,
% 3.10/1.62 ! [N: nat] :
% 3.10/1.62 ( ( gen_le904455032y_real @ N @ nil_Pr1492526187y_real )
% 3.10/1.62 = N ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_23_gen__length__code_I1_J,axiom,
% 3.10/1.62 ! [N: nat] :
% 3.10/1.62 ( ( gen_le1160603377y_real @ N @ nil_list_poly_real )
% 3.10/1.62 = N ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_24_gen__length__code_I1_J,axiom,
% 3.10/1.62 ! [N: nat] :
% 3.10/1.62 ( ( gen_le1524582876y_real @ N @ nil_Pr1207979855y_real )
% 3.10/1.62 = N ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_25_gen__length__code_I1_J,axiom,
% 3.10/1.62 ! [N: nat] :
% 3.10/1.62 ( ( gen_length_poly_real @ N @ nil_poly_real )
% 3.10/1.62 = N ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_26_maps__simps_I2_J,axiom,
% 3.10/1.62 ! [F: poly_real > list_poly_real] :
% 3.10/1.62 ( ( maps_p961674027y_real @ F @ nil_poly_real )
% 3.10/1.62 = nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_27_maps__simps_I2_J,axiom,
% 3.10/1.62 ! [F: poly_real > list_list_poly_real] :
% 3.10/1.62 ( ( maps_p1417280571y_real @ F @ nil_poly_real )
% 3.10/1.62 = nil_list_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_28_maps__simps_I2_J,axiom,
% 3.10/1.62 ! [F: list_poly_real > list_poly_real] :
% 3.10/1.62 ( ( maps_l337560251y_real @ F @ nil_list_poly_real )
% 3.10/1.62 = nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_29_maps__simps_I2_J,axiom,
% 3.10/1.62 ! [F: poly_real > list_P736648811y_real] :
% 3.10/1.62 ( ( maps_p2108677294y_real @ F @ nil_poly_real )
% 3.10/1.62 = nil_Pr1492526187y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_30_maps__simps_I2_J,axiom,
% 3.10/1.62 ! [F: produc321349221y_real > list_poly_real] :
% 3.10/1.62 ( ( maps_P116184344y_real @ F @ nil_Pr1492526187y_real )
% 3.10/1.62 = nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_31_maps__simps_I2_J,axiom,
% 3.10/1.62 ! [F: list_poly_real > list_list_poly_real] :
% 3.10/1.62 ( ( maps_l502643659y_real @ F @ nil_list_poly_real )
% 3.10/1.62 = nil_list_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_32_maps__simps_I2_J,axiom,
% 3.10/1.62 ! [F: poly_real > list_P693436111y_real] :
% 3.10/1.62 ( ( maps_p86983698y_real @ F @ nil_poly_real )
% 3.10/1.62 = nil_Pr1207979855y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_33_maps__simps_I2_J,axiom,
% 3.10/1.62 ! [F: produc321349221y_real > list_list_poly_real] :
% 3.10/1.62 ( ( maps_P54557608y_real @ F @ nil_Pr1492526187y_real )
% 3.10/1.62 = nil_list_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_34_maps__simps_I2_J,axiom,
% 3.10/1.62 ! [F: list_poly_real > list_P736648811y_real] :
% 3.10/1.62 ( ( maps_l770007326y_real @ F @ nil_list_poly_real )
% 3.10/1.62 = nil_Pr1492526187y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_35_maps__simps_I2_J,axiom,
% 3.10/1.62 ! [F: produc461822025y_real > list_poly_real] :
% 3.10/1.62 ( ( maps_P1366845948y_real @ F @ nil_Pr1207979855y_real )
% 3.10/1.62 = nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_36_map__filter__simps_I2_J,axiom,
% 3.10/1.62 ! [F: poly_real > option_poly_real] :
% 3.10/1.62 ( ( map_fi1183202740y_real @ F @ nil_poly_real )
% 3.10/1.62 = nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_37_map__filter__simps_I2_J,axiom,
% 3.10/1.62 ! [F: poly_real > option1330723604y_real] :
% 3.10/1.62 ( ( map_fi920577604y_real @ F @ nil_poly_real )
% 3.10/1.62 = nil_list_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_38_map__filter__simps_I2_J,axiom,
% 3.10/1.62 ! [F: list_poly_real > option_poly_real] :
% 3.10/1.62 ( ( map_fi1988340932y_real @ F @ nil_list_poly_real )
% 3.10/1.62 = nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_39_map__filter__simps_I2_J,axiom,
% 3.10/1.62 ! [F: poly_real > option988260395y_real] :
% 3.10/1.62 ( ( map_fi740944613y_real @ F @ nil_poly_real )
% 3.10/1.62 = nil_Pr1492526187y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_40_map__filter__simps_I2_J,axiom,
% 3.10/1.62 ! [F: produc321349221y_real > option_poly_real] :
% 3.10/1.62 ( ( map_fi895935311y_real @ F @ nil_Pr1492526187y_real )
% 3.10/1.62 = nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_41_map__filter__simps_I2_J,axiom,
% 3.10/1.62 ! [F: list_poly_real > option1330723604y_real] :
% 3.10/1.62 ( ( map_fi357666132y_real @ F @ nil_list_poly_real )
% 3.10/1.62 = nil_list_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_42_map__filter__simps_I2_J,axiom,
% 3.10/1.62 ! [F: poly_real > option293660815y_real] :
% 3.10/1.62 ( ( map_fi1117002953y_real @ F @ nil_poly_real )
% 3.10/1.62 = nil_Pr1207979855y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_43_map__filter__simps_I2_J,axiom,
% 3.10/1.62 ! [F: produc321349221y_real > option1330723604y_real] :
% 3.10/1.62 ( ( map_fi1389003359y_real @ F @ nil_Pr1492526187y_real )
% 3.10/1.62 = nil_list_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_44_map__filter__simps_I2_J,axiom,
% 3.10/1.62 ! [F: list_poly_real > option988260395y_real] :
% 3.10/1.62 ( ( map_fi2104453077y_real @ F @ nil_list_poly_real )
% 3.10/1.62 = nil_Pr1492526187y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_45_map__filter__simps_I2_J,axiom,
% 3.10/1.62 ! [F: produc461822025y_real > option_poly_real] :
% 3.10/1.62 ( ( map_fi249381555y_real @ F @ nil_Pr1207979855y_real )
% 3.10/1.62 = nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_46_null__rec_I2_J,axiom,
% 3.10/1.62 null_P89569907y_real @ nil_Pr1492526187y_real ).
% 3.10/1.62
% 3.10/1.62 thf(fact_47_null__rec_I2_J,axiom,
% 3.10/1.62 null_list_poly_real @ nil_list_poly_real ).
% 3.10/1.62
% 3.10/1.62 thf(fact_48_null__rec_I2_J,axiom,
% 3.10/1.62 null_P1782853975y_real @ nil_Pr1207979855y_real ).
% 3.10/1.62
% 3.10/1.62 thf(fact_49_null__rec_I2_J,axiom,
% 3.10/1.62 null_poly_real @ nil_poly_real ).
% 3.10/1.62
% 3.10/1.62 thf(fact_50_eq__Nil__null,axiom,
% 3.10/1.62 ! [Xs: list_P736648811y_real] :
% 3.10/1.62 ( ( Xs = nil_Pr1492526187y_real )
% 3.10/1.62 = ( null_P89569907y_real @ Xs ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_51_eq__Nil__null,axiom,
% 3.10/1.62 ! [Xs: list_list_poly_real] :
% 3.10/1.62 ( ( Xs = nil_list_poly_real )
% 3.10/1.62 = ( null_list_poly_real @ Xs ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_52_eq__Nil__null,axiom,
% 3.10/1.62 ! [Xs: list_P693436111y_real] :
% 3.10/1.62 ( ( Xs = nil_Pr1207979855y_real )
% 3.10/1.62 = ( null_P1782853975y_real @ Xs ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_53_eq__Nil__null,axiom,
% 3.10/1.62 ! [Xs: list_poly_real] :
% 3.10/1.62 ( ( Xs = nil_poly_real )
% 3.10/1.62 = ( null_poly_real @ Xs ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_54_sturm__seq_Oaxioms_I2_J,axiom,
% 3.10/1.62 ! [Ps: list_poly_real,P: poly_real] :
% 3.10/1.62 ( ( sturm_1664866327rm_seq @ Ps @ P )
% 3.10/1.62 => ( sturm_1683633594axioms @ Ps @ P ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_55_list__ex__simps_I2_J,axiom,
% 3.10/1.62 ! [P3: produc321349221y_real > $o] :
% 3.10/1.62 ~ ( list_e2093379497y_real @ P3 @ nil_Pr1492526187y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_56_list__ex__simps_I2_J,axiom,
% 3.10/1.62 ! [P3: list_poly_real > $o] :
% 3.10/1.62 ~ ( list_e809719936y_real @ P3 @ nil_list_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_57_list__ex__simps_I2_J,axiom,
% 3.10/1.62 ! [P3: produc461822025y_real > $o] :
% 3.10/1.62 ~ ( list_e1312221069y_real @ P3 @ nil_Pr1207979855y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_58_list__ex__simps_I2_J,axiom,
% 3.10/1.62 ! [P3: poly_real > $o] :
% 3.10/1.62 ~ ( list_ex_poly_real @ P3 @ nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_59_rotate1__is__Nil__conv,axiom,
% 3.10/1.62 ! [Xs: list_P736648811y_real] :
% 3.10/1.62 ( ( ( rotate623875384y_real @ Xs )
% 3.10/1.62 = nil_Pr1492526187y_real )
% 3.10/1.62 = ( Xs = nil_Pr1492526187y_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_60_rotate1__is__Nil__conv,axiom,
% 3.10/1.62 ! [Xs: list_list_poly_real] :
% 3.10/1.62 ( ( ( rotate717473073y_real @ Xs )
% 3.10/1.62 = nil_list_poly_real )
% 3.10/1.62 = ( Xs = nil_list_poly_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_61_rotate1__is__Nil__conv,axiom,
% 3.10/1.62 ! [Xs: list_P693436111y_real] :
% 3.10/1.62 ( ( ( rotate867081116y_real @ Xs )
% 3.10/1.62 = nil_Pr1207979855y_real )
% 3.10/1.62 = ( Xs = nil_Pr1207979855y_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_62_rotate1__is__Nil__conv,axiom,
% 3.10/1.62 ! [Xs: list_poly_real] :
% 3.10/1.62 ( ( ( rotate1_poly_real @ Xs )
% 3.10/1.62 = nil_poly_real )
% 3.10/1.62 = ( Xs = nil_poly_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_63_split__Nil__iff,axiom,
% 3.10/1.62 ! [Xs: list_P736648811y_real,Ys: list_P736648811y_real] :
% 3.10/1.62 ( ( ( splice1383748542y_real @ Xs @ Ys )
% 3.10/1.62 = nil_Pr1492526187y_real )
% 3.10/1.62 = ( ( Xs = nil_Pr1492526187y_real )
% 3.10/1.62 & ( Ys = nil_Pr1492526187y_real ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_64_split__Nil__iff,axiom,
% 3.10/1.62 ! [Xs: list_list_poly_real,Ys: list_list_poly_real] :
% 3.10/1.62 ( ( ( splice2080530731y_real @ Xs @ Ys )
% 3.10/1.62 = nil_list_poly_real )
% 3.10/1.62 = ( ( Xs = nil_list_poly_real )
% 3.10/1.62 & ( Ys = nil_list_poly_real ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_65_split__Nil__iff,axiom,
% 3.10/1.62 ! [Xs: list_P693436111y_real,Ys: list_P693436111y_real] :
% 3.10/1.62 ( ( ( splice1321784098y_real @ Xs @ Ys )
% 3.10/1.62 = nil_Pr1207979855y_real )
% 3.10/1.62 = ( ( Xs = nil_Pr1207979855y_real )
% 3.10/1.62 & ( Ys = nil_Pr1207979855y_real ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_66_split__Nil__iff,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 3.10/1.62 ( ( ( splice_poly_real @ Xs @ Ys )
% 3.10/1.62 = nil_poly_real )
% 3.10/1.62 = ( ( Xs = nil_poly_real )
% 3.10/1.62 & ( Ys = nil_poly_real ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_67_splice__Nil2,axiom,
% 3.10/1.62 ! [Xs: list_P736648811y_real] :
% 3.10/1.62 ( ( splice1383748542y_real @ Xs @ nil_Pr1492526187y_real )
% 3.10/1.62 = Xs ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_68_splice__Nil2,axiom,
% 3.10/1.62 ! [Xs: list_list_poly_real] :
% 3.10/1.62 ( ( splice2080530731y_real @ Xs @ nil_list_poly_real )
% 3.10/1.62 = Xs ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_69_splice__Nil2,axiom,
% 3.10/1.62 ! [Xs: list_P693436111y_real] :
% 3.10/1.62 ( ( splice1321784098y_real @ Xs @ nil_Pr1207979855y_real )
% 3.10/1.62 = Xs ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_70_splice__Nil2,axiom,
% 3.10/1.62 ! [Xs: list_poly_real] :
% 3.10/1.62 ( ( splice_poly_real @ Xs @ nil_poly_real )
% 3.10/1.62 = Xs ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_71_enumerate__simps_I1_J,axiom,
% 3.10/1.62 ! [N: nat] :
% 3.10/1.62 ( ( enumer1123002698y_real @ N @ nil_Pr1492526187y_real )
% 3.10/1.62 = nil_Pr570652676y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_72_enumerate__simps_I1_J,axiom,
% 3.10/1.62 ! [N: nat] :
% 3.10/1.62 ( ( enumer1433313439y_real @ N @ nil_list_poly_real )
% 3.10/1.62 = nil_Pr1161137915y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_73_enumerate__simps_I1_J,axiom,
% 3.10/1.62 ! [N: nat] :
% 3.10/1.62 ( ( enumer1015405230y_real @ N @ nil_Pr1207979855y_real )
% 3.10/1.62 = nil_Pr2056488424y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_74_enumerate__simps_I1_J,axiom,
% 3.10/1.62 ! [N: nat] :
% 3.10/1.62 ( ( enumerate_poly_real @ N @ nil_poly_real )
% 3.10/1.62 = nil_Pr1492526187y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_75_product_Osimps_I1_J,axiom,
% 3.10/1.62 ! [Uu: list_poly_real] :
% 3.10/1.62 ( ( produc1360353227y_real @ nil_nat @ Uu )
% 3.10/1.62 = nil_Pr1492526187y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_76_product_Osimps_I1_J,axiom,
% 3.10/1.62 ! [Uu: list_poly_real] :
% 3.10/1.62 ( ( produc1733309743y_real @ nil_poly_real @ Uu )
% 3.10/1.62 = nil_Pr1207979855y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_77_map__tailrec__rev_Osimps_I1_J,axiom,
% 3.10/1.62 ! [F: poly_real > poly_real,Bs: list_poly_real] :
% 3.10/1.62 ( ( map_ta1919289823y_real @ F @ nil_poly_real @ Bs )
% 3.10/1.62 = Bs ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_78_ord_Olexordp__eq__simps_I1_J,axiom,
% 3.10/1.62 ! [Less: produc321349221y_real > produc321349221y_real > $o,Ys: list_P736648811y_real] : ( lexord834705585y_real @ Less @ nil_Pr1492526187y_real @ Ys ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_79_ord_Olexordp__eq__simps_I1_J,axiom,
% 3.10/1.62 ! [Less: list_poly_real > list_poly_real > $o,Ys: list_list_poly_real] : ( lexord1324236152y_real @ Less @ nil_list_poly_real @ Ys ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_80_ord_Olexordp__eq__simps_I1_J,axiom,
% 3.10/1.62 ! [Less: produc461822025y_real > produc461822025y_real > $o,Ys: list_P693436111y_real] : ( lexord1053351061y_real @ Less @ nil_Pr1207979855y_real @ Ys ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_81_ord_Olexordp__eq__simps_I1_J,axiom,
% 3.10/1.62 ! [Less: poly_real > poly_real > $o,Ys: list_poly_real] : ( lexordp_eq_poly_real @ Less @ nil_poly_real @ Ys ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_82_ord_Olexordp__eq__simps_I2_J,axiom,
% 3.10/1.62 ! [Less: produc321349221y_real > produc321349221y_real > $o,Xs: list_P736648811y_real] :
% 3.10/1.62 ( ( lexord834705585y_real @ Less @ Xs @ nil_Pr1492526187y_real )
% 3.10/1.62 = ( Xs = nil_Pr1492526187y_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_83_ord_Olexordp__eq__simps_I2_J,axiom,
% 3.10/1.62 ! [Less: list_poly_real > list_poly_real > $o,Xs: list_list_poly_real] :
% 3.10/1.62 ( ( lexord1324236152y_real @ Less @ Xs @ nil_list_poly_real )
% 3.10/1.62 = ( Xs = nil_list_poly_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_84_ord_Olexordp__eq__simps_I2_J,axiom,
% 3.10/1.62 ! [Less: produc461822025y_real > produc461822025y_real > $o,Xs: list_P693436111y_real] :
% 3.10/1.62 ( ( lexord1053351061y_real @ Less @ Xs @ nil_Pr1207979855y_real )
% 3.10/1.62 = ( Xs = nil_Pr1207979855y_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_85_ord_Olexordp__eq__simps_I2_J,axiom,
% 3.10/1.62 ! [Less: poly_real > poly_real > $o,Xs: list_poly_real] :
% 3.10/1.62 ( ( lexordp_eq_poly_real @ Less @ Xs @ nil_poly_real )
% 3.10/1.62 = ( Xs = nil_poly_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_86_listrelp_ONil,axiom,
% 3.10/1.62 ! [R: poly_real > poly_real > $o] : ( listre1609905961y_real @ R @ nil_poly_real @ nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_87_listrelp_ONil,axiom,
% 3.10/1.62 ! [R: poly_real > list_poly_real > $o] : ( listre1793073465y_real @ R @ nil_poly_real @ nil_list_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_88_listrelp_ONil,axiom,
% 3.10/1.62 ! [R: list_poly_real > poly_real > $o] : ( listre713353145y_real @ R @ nil_list_poly_real @ nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_89_listrelp_ONil,axiom,
% 3.10/1.62 ! [R: poly_real > produc321349221y_real > $o] : ( listre889482032y_real @ R @ nil_poly_real @ nil_Pr1492526187y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_90_listrelp_ONil,axiom,
% 3.10/1.62 ! [R: produc321349221y_real > poly_real > $o] : ( listre1044472730y_real @ R @ nil_Pr1492526187y_real @ nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_91_listrelp_ONil,axiom,
% 3.10/1.62 ! [R: list_poly_real > list_poly_real > $o] : ( listre1763068361y_real @ R @ nil_list_poly_real @ nil_list_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_92_listrelp_ONil,axiom,
% 3.10/1.62 ! [R: poly_real > produc461822025y_real > $o] : ( listre471999892y_real @ R @ nil_poly_real @ nil_Pr1207979855y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_93_listrelp_ONil,axiom,
% 3.10/1.62 ! [R: produc321349221y_real > list_poly_real > $o] : ( listre321577258y_real @ R @ nil_Pr1492526187y_real @ nil_list_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_94_listrelp_ONil,axiom,
% 3.10/1.62 ! [R: list_poly_real > produc321349221y_real > $o] : ( listre1037026976y_real @ R @ nil_list_poly_real @ nil_Pr1492526187y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_95_listrelp_ONil,axiom,
% 3.10/1.62 ! [R: produc461822025y_real > poly_real > $o] : ( listre1751862142y_real @ R @ nil_Pr1207979855y_real @ nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_96_ord_Olexordp__eq_Ocong,axiom,
% 3.10/1.62 lexordp_eq_poly_real = lexordp_eq_poly_real ).
% 3.10/1.62
% 3.10/1.62 thf(fact_97_ord_Olexordp__eq__refl,axiom,
% 3.10/1.62 ! [Less: poly_real > poly_real > $o,Xs: list_poly_real] : ( lexordp_eq_poly_real @ Less @ Xs @ Xs ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_98_ord_Olexordp__eq_ONil,axiom,
% 3.10/1.62 ! [Less: produc321349221y_real > produc321349221y_real > $o,Ys: list_P736648811y_real] : ( lexord834705585y_real @ Less @ nil_Pr1492526187y_real @ Ys ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_99_ord_Olexordp__eq_ONil,axiom,
% 3.10/1.62 ! [Less: list_poly_real > list_poly_real > $o,Ys: list_list_poly_real] : ( lexord1324236152y_real @ Less @ nil_list_poly_real @ Ys ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_100_ord_Olexordp__eq_ONil,axiom,
% 3.10/1.62 ! [Less: produc461822025y_real > produc461822025y_real > $o,Ys: list_P693436111y_real] : ( lexord1053351061y_real @ Less @ nil_Pr1207979855y_real @ Ys ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_101_ord_Olexordp__eq_ONil,axiom,
% 3.10/1.62 ! [Less: poly_real > poly_real > $o,Ys: list_poly_real] : ( lexordp_eq_poly_real @ Less @ nil_poly_real @ Ys ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_102_splice_Osimps_I1_J,axiom,
% 3.10/1.62 ! [Ys: list_P736648811y_real] :
% 3.10/1.62 ( ( splice1383748542y_real @ nil_Pr1492526187y_real @ Ys )
% 3.10/1.62 = Ys ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_103_splice_Osimps_I1_J,axiom,
% 3.10/1.62 ! [Ys: list_list_poly_real] :
% 3.10/1.62 ( ( splice2080530731y_real @ nil_list_poly_real @ Ys )
% 3.10/1.62 = Ys ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_104_splice_Osimps_I1_J,axiom,
% 3.10/1.62 ! [Ys: list_P693436111y_real] :
% 3.10/1.62 ( ( splice1321784098y_real @ nil_Pr1207979855y_real @ Ys )
% 3.10/1.62 = Ys ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_105_splice_Osimps_I1_J,axiom,
% 3.10/1.62 ! [Ys: list_poly_real] :
% 3.10/1.62 ( ( splice_poly_real @ nil_poly_real @ Ys )
% 3.10/1.62 = Ys ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_106_rotate1_Osimps_I1_J,axiom,
% 3.10/1.62 ( ( rotate623875384y_real @ nil_Pr1492526187y_real )
% 3.10/1.62 = nil_Pr1492526187y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_107_rotate1_Osimps_I1_J,axiom,
% 3.10/1.62 ( ( rotate717473073y_real @ nil_list_poly_real )
% 3.10/1.62 = nil_list_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_108_rotate1_Osimps_I1_J,axiom,
% 3.10/1.62 ( ( rotate867081116y_real @ nil_Pr1207979855y_real )
% 3.10/1.62 = nil_Pr1207979855y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_109_rotate1_Osimps_I1_J,axiom,
% 3.10/1.62 ( ( rotate1_poly_real @ nil_poly_real )
% 3.10/1.62 = nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_110_ord_Olexordp__eq__simps_I3_J,axiom,
% 3.10/1.62 ! [Less: list_poly_real > list_poly_real > $o,X: list_poly_real,Xs: list_list_poly_real] :
% 3.10/1.62 ~ ( lexord1324236152y_real @ Less @ ( cons_list_poly_real @ X @ Xs ) @ nil_list_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_111_ord_Olexordp__eq__simps_I3_J,axiom,
% 3.10/1.62 ! [Less: produc321349221y_real > produc321349221y_real > $o,X: produc321349221y_real,Xs: list_P736648811y_real] :
% 3.10/1.62 ~ ( lexord834705585y_real @ Less @ ( cons_P1027346459y_real @ X @ Xs ) @ nil_Pr1492526187y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_112_ord_Olexordp__eq__simps_I3_J,axiom,
% 3.10/1.62 ! [Less: produc461822025y_real > produc461822025y_real > $o,X: produc461822025y_real,Xs: list_P693436111y_real] :
% 3.10/1.62 ~ ( lexord1053351061y_real @ Less @ ( cons_P1129399039y_real @ X @ Xs ) @ nil_Pr1207979855y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_113_ord_Olexordp__eq__simps_I3_J,axiom,
% 3.10/1.62 ! [Less: poly_real > poly_real > $o,X: poly_real,Xs: list_poly_real] :
% 3.10/1.62 ~ ( lexordp_eq_poly_real @ Less @ ( cons_poly_real @ X @ Xs ) @ nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_114_zip__Nil,axiom,
% 3.10/1.62 ! [Ys: list_poly_real] :
% 3.10/1.62 ( ( zip_nat_poly_real @ nil_nat @ Ys )
% 3.10/1.62 = nil_Pr1492526187y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_115_zip__Nil,axiom,
% 3.10/1.62 ! [Ys: list_poly_real] :
% 3.10/1.62 ( ( zip_po657915297y_real @ nil_poly_real @ Ys )
% 3.10/1.62 = nil_Pr1207979855y_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_116_map__tailrec__rev_Oelims,axiom,
% 3.10/1.62 ! [X: poly_real > poly_real,Xa: list_poly_real,Xb: list_poly_real,Y: list_poly_real] :
% 3.10/1.62 ( ( ( map_ta1919289823y_real @ X @ Xa @ Xb )
% 3.10/1.62 = Y )
% 3.10/1.62 => ( ( ( Xa = nil_poly_real )
% 3.10/1.62 => ( Y != Xb ) )
% 3.10/1.62 => ~ ! [A: poly_real,As: list_poly_real] :
% 3.10/1.62 ( ( Xa
% 3.10/1.62 = ( cons_poly_real @ A @ As ) )
% 3.10/1.62 => ( Y
% 3.10/1.62 != ( map_ta1919289823y_real @ X @ As @ ( cons_poly_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_117_map__tailrec__rev_Oelims,axiom,
% 3.10/1.62 ! [X: poly_real > list_poly_real,Xa: list_poly_real,Xb: list_list_poly_real,Y: list_list_poly_real] :
% 3.10/1.62 ( ( ( map_ta1513955567y_real @ X @ Xa @ Xb )
% 3.10/1.62 = Y )
% 3.10/1.62 => ( ( ( Xa = nil_poly_real )
% 3.10/1.62 => ( Y != Xb ) )
% 3.10/1.62 => ~ ! [A: poly_real,As: list_poly_real] :
% 3.10/1.62 ( ( Xa
% 3.10/1.62 = ( cons_poly_real @ A @ As ) )
% 3.10/1.62 => ( Y
% 3.10/1.62 != ( map_ta1513955567y_real @ X @ As @ ( cons_list_poly_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_118_map__tailrec__rev_Oelims,axiom,
% 3.10/1.62 ! [X: list_poly_real > poly_real,Xa: list_list_poly_real,Xb: list_poly_real,Y: list_poly_real] :
% 3.10/1.62 ( ( ( map_ta434235247y_real @ X @ Xa @ Xb )
% 3.10/1.62 = Y )
% 3.10/1.62 => ( ( ( Xa = nil_list_poly_real )
% 3.10/1.62 => ( Y != Xb ) )
% 3.10/1.62 => ~ ! [A: list_poly_real,As: list_list_poly_real] :
% 3.10/1.62 ( ( Xa
% 3.10/1.62 = ( cons_list_poly_real @ A @ As ) )
% 3.10/1.62 => ( Y
% 3.10/1.62 != ( map_ta434235247y_real @ X @ As @ ( cons_poly_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_119_map__tailrec__rev_Oelims,axiom,
% 3.10/1.62 ! [X: poly_real > produc321349221y_real,Xa: list_poly_real,Xb: list_P736648811y_real,Y: list_P736648811y_real] :
% 3.10/1.62 ( ( ( map_ta632757498y_real @ X @ Xa @ Xb )
% 3.10/1.62 = Y )
% 3.10/1.62 => ( ( ( Xa = nil_poly_real )
% 3.10/1.62 => ( Y != Xb ) )
% 3.10/1.62 => ~ ! [A: poly_real,As: list_poly_real] :
% 3.10/1.62 ( ( Xa
% 3.10/1.62 = ( cons_poly_real @ A @ As ) )
% 3.10/1.62 => ( Y
% 3.10/1.62 != ( map_ta632757498y_real @ X @ As @ ( cons_P1027346459y_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_120_map__tailrec__rev_Oelims,axiom,
% 3.10/1.62 ! [X: list_poly_real > list_poly_real,Xa: list_list_poly_real,Xb: list_list_poly_real,Y: list_list_poly_real] :
% 3.10/1.62 ( ( ( map_ta316995199y_real @ X @ Xa @ Xb )
% 3.10/1.62 = Y )
% 3.10/1.62 => ( ( ( Xa = nil_list_poly_real )
% 3.10/1.62 => ( Y != Xb ) )
% 3.10/1.62 => ~ ! [A: list_poly_real,As: list_list_poly_real] :
% 3.10/1.62 ( ( Xa
% 3.10/1.62 = ( cons_list_poly_real @ A @ As ) )
% 3.10/1.62 => ( Y
% 3.10/1.62 != ( map_ta316995199y_real @ X @ As @ ( cons_list_poly_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_121_map__tailrec__rev_Oelims,axiom,
% 3.10/1.62 ! [X: produc321349221y_real > poly_real,Xa: list_P736648811y_real,Xb: list_poly_real,Y: list_poly_real] :
% 3.10/1.62 ( ( ( map_ta787748196y_real @ X @ Xa @ Xb )
% 3.10/1.62 = Y )
% 3.10/1.62 => ( ( ( Xa = nil_Pr1492526187y_real )
% 3.10/1.62 => ( Y != Xb ) )
% 3.10/1.62 => ~ ! [A: produc321349221y_real,As: list_P736648811y_real] :
% 3.10/1.62 ( ( Xa
% 3.10/1.62 = ( cons_P1027346459y_real @ A @ As ) )
% 3.10/1.62 => ( Y
% 3.10/1.62 != ( map_ta787748196y_real @ X @ As @ ( cons_poly_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_122_map__tailrec__rev_Oelims,axiom,
% 3.10/1.62 ! [X: poly_real > produc461822025y_real,Xa: list_poly_real,Xb: list_P693436111y_real,Y: list_P693436111y_real] :
% 3.10/1.62 ( ( ( map_ta920933982y_real @ X @ Xa @ Xb )
% 3.10/1.62 = Y )
% 3.10/1.62 => ( ( ( Xa = nil_poly_real )
% 3.10/1.62 => ( Y != Xb ) )
% 3.10/1.62 => ~ ! [A: poly_real,As: list_poly_real] :
% 3.10/1.62 ( ( Xa
% 3.10/1.62 = ( cons_poly_real @ A @ As ) )
% 3.10/1.62 => ( Y
% 3.10/1.62 != ( map_ta920933982y_real @ X @ As @ ( cons_P1129399039y_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_123_map__tailrec__rev_Oelims,axiom,
% 3.10/1.62 ! [X: list_poly_real > produc321349221y_real,Xa: list_list_poly_real,Xb: list_P736648811y_real,Y: list_P736648811y_real] :
% 3.10/1.62 ( ( ( map_ta1674185578y_real @ X @ Xa @ Xb )
% 3.10/1.62 = Y )
% 3.10/1.62 => ( ( ( Xa = nil_list_poly_real )
% 3.10/1.62 => ( Y != Xb ) )
% 3.10/1.62 => ~ ! [A: list_poly_real,As: list_list_poly_real] :
% 3.10/1.62 ( ( Xa
% 3.10/1.62 = ( cons_list_poly_real @ A @ As ) )
% 3.10/1.62 => ( Y
% 3.10/1.62 != ( map_ta1674185578y_real @ X @ As @ ( cons_P1027346459y_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_124_map__tailrec__rev_Oelims,axiom,
% 3.10/1.62 ! [X: produc321349221y_real > list_poly_real,Xa: list_P736648811y_real,Xb: list_list_poly_real,Y: list_list_poly_real] :
% 3.10/1.62 ( ( ( map_ta958735860y_real @ X @ Xa @ Xb )
% 3.10/1.62 = Y )
% 3.10/1.62 => ( ( ( Xa = nil_Pr1492526187y_real )
% 3.10/1.62 => ( Y != Xb ) )
% 3.10/1.62 => ~ ! [A: produc321349221y_real,As: list_P736648811y_real] :
% 3.10/1.62 ( ( Xa
% 3.10/1.62 = ( cons_P1027346459y_real @ A @ As ) )
% 3.10/1.62 => ( Y
% 3.10/1.62 != ( map_ta958735860y_real @ X @ As @ ( cons_list_poly_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_125_map__tailrec__rev_Oelims,axiom,
% 3.10/1.62 ! [X: produc461822025y_real > poly_real,Xa: list_P693436111y_real,Xb: list_poly_real,Y: list_poly_real] :
% 3.10/1.62 ( ( ( map_ta53312584y_real @ X @ Xa @ Xb )
% 3.10/1.62 = Y )
% 3.10/1.62 => ( ( ( Xa = nil_Pr1207979855y_real )
% 3.10/1.62 => ( Y != Xb ) )
% 3.10/1.62 => ~ ! [A: produc461822025y_real,As: list_P693436111y_real] :
% 3.10/1.62 ( ( Xa
% 3.10/1.62 = ( cons_P1129399039y_real @ A @ As ) )
% 3.10/1.62 => ( Y
% 3.10/1.62 != ( map_ta53312584y_real @ X @ As @ ( cons_poly_real @ ( X @ A ) @ Xb ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_126_listrelp_Oinducts,axiom,
% 3.10/1.62 ! [R: poly_real > poly_real > $o,X1: list_poly_real,X2: list_poly_real,P3: list_poly_real > list_poly_real > $o] :
% 3.10/1.62 ( ( listre1609905961y_real @ R @ X1 @ X2 )
% 3.10/1.62 => ( ( P3 @ nil_poly_real @ nil_poly_real )
% 3.10/1.62 => ( ! [X3: poly_real,Y2: poly_real,Xs2: list_poly_real,Ys2: list_poly_real] :
% 3.10/1.62 ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ( ( listre1609905961y_real @ R @ Xs2 @ Ys2 )
% 3.10/1.62 => ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) ) )
% 3.10/1.62 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_127_listrelp_Oinducts,axiom,
% 3.10/1.62 ! [R: poly_real > list_poly_real > $o,X1: list_poly_real,X2: list_list_poly_real,P3: list_poly_real > list_list_poly_real > $o] :
% 3.10/1.62 ( ( listre1793073465y_real @ R @ X1 @ X2 )
% 3.10/1.62 => ( ( P3 @ nil_poly_real @ nil_list_poly_real )
% 3.10/1.62 => ( ! [X3: poly_real,Y2: list_poly_real,Xs2: list_poly_real,Ys2: list_list_poly_real] :
% 3.10/1.62 ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ( ( listre1793073465y_real @ R @ Xs2 @ Ys2 )
% 3.10/1.62 => ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_list_poly_real @ Y2 @ Ys2 ) ) ) ) )
% 3.10/1.62 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_128_listrelp_Oinducts,axiom,
% 3.10/1.62 ! [R: list_poly_real > poly_real > $o,X1: list_list_poly_real,X2: list_poly_real,P3: list_list_poly_real > list_poly_real > $o] :
% 3.10/1.62 ( ( listre713353145y_real @ R @ X1 @ X2 )
% 3.10/1.62 => ( ( P3 @ nil_list_poly_real @ nil_poly_real )
% 3.10/1.62 => ( ! [X3: list_poly_real,Y2: poly_real,Xs2: list_list_poly_real,Ys2: list_poly_real] :
% 3.10/1.62 ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ( ( listre713353145y_real @ R @ Xs2 @ Ys2 )
% 3.10/1.62 => ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_list_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) ) )
% 3.10/1.62 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_129_listrelp_Oinducts,axiom,
% 3.10/1.62 ! [R: poly_real > produc321349221y_real > $o,X1: list_poly_real,X2: list_P736648811y_real,P3: list_poly_real > list_P736648811y_real > $o] :
% 3.10/1.62 ( ( listre889482032y_real @ R @ X1 @ X2 )
% 3.10/1.62 => ( ( P3 @ nil_poly_real @ nil_Pr1492526187y_real )
% 3.10/1.62 => ( ! [X3: poly_real,Y2: produc321349221y_real,Xs2: list_poly_real,Ys2: list_P736648811y_real] :
% 3.10/1.62 ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ( ( listre889482032y_real @ R @ Xs2 @ Ys2 )
% 3.10/1.62 => ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_P1027346459y_real @ Y2 @ Ys2 ) ) ) ) )
% 3.10/1.62 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_130_listrelp_Oinducts,axiom,
% 3.10/1.62 ! [R: list_poly_real > list_poly_real > $o,X1: list_list_poly_real,X2: list_list_poly_real,P3: list_list_poly_real > list_list_poly_real > $o] :
% 3.10/1.62 ( ( listre1763068361y_real @ R @ X1 @ X2 )
% 3.10/1.62 => ( ( P3 @ nil_list_poly_real @ nil_list_poly_real )
% 3.10/1.62 => ( ! [X3: list_poly_real,Y2: list_poly_real,Xs2: list_list_poly_real,Ys2: list_list_poly_real] :
% 3.10/1.62 ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ( ( listre1763068361y_real @ R @ Xs2 @ Ys2 )
% 3.10/1.62 => ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_list_poly_real @ X3 @ Xs2 ) @ ( cons_list_poly_real @ Y2 @ Ys2 ) ) ) ) )
% 3.10/1.62 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_131_listrelp_Oinducts,axiom,
% 3.10/1.62 ! [R: produc321349221y_real > poly_real > $o,X1: list_P736648811y_real,X2: list_poly_real,P3: list_P736648811y_real > list_poly_real > $o] :
% 3.10/1.62 ( ( listre1044472730y_real @ R @ X1 @ X2 )
% 3.10/1.62 => ( ( P3 @ nil_Pr1492526187y_real @ nil_poly_real )
% 3.10/1.62 => ( ! [X3: produc321349221y_real,Y2: poly_real,Xs2: list_P736648811y_real,Ys2: list_poly_real] :
% 3.10/1.62 ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ( ( listre1044472730y_real @ R @ Xs2 @ Ys2 )
% 3.10/1.62 => ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_P1027346459y_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) ) )
% 3.10/1.62 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_132_listrelp_Oinducts,axiom,
% 3.10/1.62 ! [R: poly_real > produc461822025y_real > $o,X1: list_poly_real,X2: list_P693436111y_real,P3: list_poly_real > list_P693436111y_real > $o] :
% 3.10/1.62 ( ( listre471999892y_real @ R @ X1 @ X2 )
% 3.10/1.62 => ( ( P3 @ nil_poly_real @ nil_Pr1207979855y_real )
% 3.10/1.62 => ( ! [X3: poly_real,Y2: produc461822025y_real,Xs2: list_poly_real,Ys2: list_P693436111y_real] :
% 3.10/1.62 ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ( ( listre471999892y_real @ R @ Xs2 @ Ys2 )
% 3.10/1.62 => ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_P1129399039y_real @ Y2 @ Ys2 ) ) ) ) )
% 3.10/1.62 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_133_listrelp_Oinducts,axiom,
% 3.10/1.62 ! [R: list_poly_real > produc321349221y_real > $o,X1: list_list_poly_real,X2: list_P736648811y_real,P3: list_list_poly_real > list_P736648811y_real > $o] :
% 3.10/1.62 ( ( listre1037026976y_real @ R @ X1 @ X2 )
% 3.10/1.62 => ( ( P3 @ nil_list_poly_real @ nil_Pr1492526187y_real )
% 3.10/1.62 => ( ! [X3: list_poly_real,Y2: produc321349221y_real,Xs2: list_list_poly_real,Ys2: list_P736648811y_real] :
% 3.10/1.62 ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ( ( listre1037026976y_real @ R @ Xs2 @ Ys2 )
% 3.10/1.62 => ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_list_poly_real @ X3 @ Xs2 ) @ ( cons_P1027346459y_real @ Y2 @ Ys2 ) ) ) ) )
% 3.10/1.62 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_134_listrelp_Oinducts,axiom,
% 3.10/1.62 ! [R: produc321349221y_real > list_poly_real > $o,X1: list_P736648811y_real,X2: list_list_poly_real,P3: list_P736648811y_real > list_list_poly_real > $o] :
% 3.10/1.62 ( ( listre321577258y_real @ R @ X1 @ X2 )
% 3.10/1.62 => ( ( P3 @ nil_Pr1492526187y_real @ nil_list_poly_real )
% 3.10/1.62 => ( ! [X3: produc321349221y_real,Y2: list_poly_real,Xs2: list_P736648811y_real,Ys2: list_list_poly_real] :
% 3.10/1.62 ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ( ( listre321577258y_real @ R @ Xs2 @ Ys2 )
% 3.10/1.62 => ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_P1027346459y_real @ X3 @ Xs2 ) @ ( cons_list_poly_real @ Y2 @ Ys2 ) ) ) ) )
% 3.10/1.62 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_135_listrelp_Oinducts,axiom,
% 3.10/1.62 ! [R: produc461822025y_real > poly_real > $o,X1: list_P693436111y_real,X2: list_poly_real,P3: list_P693436111y_real > list_poly_real > $o] :
% 3.10/1.62 ( ( listre1751862142y_real @ R @ X1 @ X2 )
% 3.10/1.62 => ( ( P3 @ nil_Pr1207979855y_real @ nil_poly_real )
% 3.10/1.62 => ( ! [X3: produc461822025y_real,Y2: poly_real,Xs2: list_P693436111y_real,Ys2: list_poly_real] :
% 3.10/1.62 ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ( ( listre1751862142y_real @ R @ Xs2 @ Ys2 )
% 3.10/1.62 => ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_P1129399039y_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) ) )
% 3.10/1.62 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_136_listrelp_Osimps,axiom,
% 3.10/1.62 ( listre1609905961y_real
% 3.10/1.62 = ( ^ [R2: poly_real > poly_real > $o,A1: list_poly_real,A2: list_poly_real] :
% 3.10/1.62 ( ( ( A1 = nil_poly_real )
% 3.10/1.62 & ( A2 = nil_poly_real ) )
% 3.10/1.62 | ? [X4: poly_real,Y3: poly_real,Xs3: list_poly_real,Ys3: list_poly_real] :
% 3.10/1.62 ( ( A1
% 3.10/1.62 = ( cons_poly_real @ X4 @ Xs3 ) )
% 3.10/1.62 & ( A2
% 3.10/1.62 = ( cons_poly_real @ Y3 @ Ys3 ) )
% 3.10/1.62 & ( R2 @ X4 @ Y3 )
% 3.10/1.62 & ( listre1609905961y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_137_listrelp_Osimps,axiom,
% 3.10/1.62 ( listre1793073465y_real
% 3.10/1.62 = ( ^ [R2: poly_real > list_poly_real > $o,A1: list_poly_real,A2: list_list_poly_real] :
% 3.10/1.62 ( ( ( A1 = nil_poly_real )
% 3.10/1.62 & ( A2 = nil_list_poly_real ) )
% 3.10/1.62 | ? [X4: poly_real,Y3: list_poly_real,Xs3: list_poly_real,Ys3: list_list_poly_real] :
% 3.10/1.62 ( ( A1
% 3.10/1.62 = ( cons_poly_real @ X4 @ Xs3 ) )
% 3.10/1.62 & ( A2
% 3.10/1.62 = ( cons_list_poly_real @ Y3 @ Ys3 ) )
% 3.10/1.62 & ( R2 @ X4 @ Y3 )
% 3.10/1.62 & ( listre1793073465y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_138_listrelp_Osimps,axiom,
% 3.10/1.62 ( listre713353145y_real
% 3.10/1.62 = ( ^ [R2: list_poly_real > poly_real > $o,A1: list_list_poly_real,A2: list_poly_real] :
% 3.10/1.62 ( ( ( A1 = nil_list_poly_real )
% 3.10/1.62 & ( A2 = nil_poly_real ) )
% 3.10/1.62 | ? [X4: list_poly_real,Y3: poly_real,Xs3: list_list_poly_real,Ys3: list_poly_real] :
% 3.10/1.62 ( ( A1
% 3.10/1.62 = ( cons_list_poly_real @ X4 @ Xs3 ) )
% 3.10/1.62 & ( A2
% 3.10/1.62 = ( cons_poly_real @ Y3 @ Ys3 ) )
% 3.10/1.62 & ( R2 @ X4 @ Y3 )
% 3.10/1.62 & ( listre713353145y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_139_listrelp_Osimps,axiom,
% 3.10/1.62 ( listre889482032y_real
% 3.10/1.62 = ( ^ [R2: poly_real > produc321349221y_real > $o,A1: list_poly_real,A2: list_P736648811y_real] :
% 3.10/1.62 ( ( ( A1 = nil_poly_real )
% 3.10/1.62 & ( A2 = nil_Pr1492526187y_real ) )
% 3.10/1.62 | ? [X4: poly_real,Y3: produc321349221y_real,Xs3: list_poly_real,Ys3: list_P736648811y_real] :
% 3.10/1.62 ( ( A1
% 3.10/1.62 = ( cons_poly_real @ X4 @ Xs3 ) )
% 3.10/1.62 & ( A2
% 3.10/1.62 = ( cons_P1027346459y_real @ Y3 @ Ys3 ) )
% 3.10/1.62 & ( R2 @ X4 @ Y3 )
% 3.10/1.62 & ( listre889482032y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_140_listrelp_Osimps,axiom,
% 3.10/1.62 ( listre1763068361y_real
% 3.10/1.62 = ( ^ [R2: list_poly_real > list_poly_real > $o,A1: list_list_poly_real,A2: list_list_poly_real] :
% 3.10/1.62 ( ( ( A1 = nil_list_poly_real )
% 3.10/1.62 & ( A2 = nil_list_poly_real ) )
% 3.10/1.62 | ? [X4: list_poly_real,Y3: list_poly_real,Xs3: list_list_poly_real,Ys3: list_list_poly_real] :
% 3.10/1.62 ( ( A1
% 3.10/1.62 = ( cons_list_poly_real @ X4 @ Xs3 ) )
% 3.10/1.62 & ( A2
% 3.10/1.62 = ( cons_list_poly_real @ Y3 @ Ys3 ) )
% 3.10/1.62 & ( R2 @ X4 @ Y3 )
% 3.10/1.62 & ( listre1763068361y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_141_listrelp_Osimps,axiom,
% 3.10/1.62 ( listre1044472730y_real
% 3.10/1.62 = ( ^ [R2: produc321349221y_real > poly_real > $o,A1: list_P736648811y_real,A2: list_poly_real] :
% 3.10/1.62 ( ( ( A1 = nil_Pr1492526187y_real )
% 3.10/1.62 & ( A2 = nil_poly_real ) )
% 3.10/1.62 | ? [X4: produc321349221y_real,Y3: poly_real,Xs3: list_P736648811y_real,Ys3: list_poly_real] :
% 3.10/1.62 ( ( A1
% 3.10/1.62 = ( cons_P1027346459y_real @ X4 @ Xs3 ) )
% 3.10/1.62 & ( A2
% 3.10/1.62 = ( cons_poly_real @ Y3 @ Ys3 ) )
% 3.10/1.62 & ( R2 @ X4 @ Y3 )
% 3.10/1.62 & ( listre1044472730y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_142_listrelp_Osimps,axiom,
% 3.10/1.62 ( listre471999892y_real
% 3.10/1.62 = ( ^ [R2: poly_real > produc461822025y_real > $o,A1: list_poly_real,A2: list_P693436111y_real] :
% 3.10/1.62 ( ( ( A1 = nil_poly_real )
% 3.10/1.62 & ( A2 = nil_Pr1207979855y_real ) )
% 3.10/1.62 | ? [X4: poly_real,Y3: produc461822025y_real,Xs3: list_poly_real,Ys3: list_P693436111y_real] :
% 3.10/1.62 ( ( A1
% 3.10/1.62 = ( cons_poly_real @ X4 @ Xs3 ) )
% 3.10/1.62 & ( A2
% 3.10/1.62 = ( cons_P1129399039y_real @ Y3 @ Ys3 ) )
% 3.10/1.62 & ( R2 @ X4 @ Y3 )
% 3.10/1.62 & ( listre471999892y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_143_listrelp_Osimps,axiom,
% 3.10/1.62 ( listre1037026976y_real
% 3.10/1.62 = ( ^ [R2: list_poly_real > produc321349221y_real > $o,A1: list_list_poly_real,A2: list_P736648811y_real] :
% 3.10/1.62 ( ( ( A1 = nil_list_poly_real )
% 3.10/1.62 & ( A2 = nil_Pr1492526187y_real ) )
% 3.10/1.62 | ? [X4: list_poly_real,Y3: produc321349221y_real,Xs3: list_list_poly_real,Ys3: list_P736648811y_real] :
% 3.10/1.62 ( ( A1
% 3.10/1.62 = ( cons_list_poly_real @ X4 @ Xs3 ) )
% 3.10/1.62 & ( A2
% 3.10/1.62 = ( cons_P1027346459y_real @ Y3 @ Ys3 ) )
% 3.10/1.62 & ( R2 @ X4 @ Y3 )
% 3.10/1.62 & ( listre1037026976y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_144_listrelp_Osimps,axiom,
% 3.10/1.62 ( listre321577258y_real
% 3.10/1.62 = ( ^ [R2: produc321349221y_real > list_poly_real > $o,A1: list_P736648811y_real,A2: list_list_poly_real] :
% 3.10/1.62 ( ( ( A1 = nil_Pr1492526187y_real )
% 3.10/1.62 & ( A2 = nil_list_poly_real ) )
% 3.10/1.62 | ? [X4: produc321349221y_real,Y3: list_poly_real,Xs3: list_P736648811y_real,Ys3: list_list_poly_real] :
% 3.10/1.62 ( ( A1
% 3.10/1.62 = ( cons_P1027346459y_real @ X4 @ Xs3 ) )
% 3.10/1.62 & ( A2
% 3.10/1.62 = ( cons_list_poly_real @ Y3 @ Ys3 ) )
% 3.10/1.62 & ( R2 @ X4 @ Y3 )
% 3.10/1.62 & ( listre321577258y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_145_listrelp_Osimps,axiom,
% 3.10/1.62 ( listre1751862142y_real
% 3.10/1.62 = ( ^ [R2: produc461822025y_real > poly_real > $o,A1: list_P693436111y_real,A2: list_poly_real] :
% 3.10/1.62 ( ( ( A1 = nil_Pr1207979855y_real )
% 3.10/1.62 & ( A2 = nil_poly_real ) )
% 3.10/1.62 | ? [X4: produc461822025y_real,Y3: poly_real,Xs3: list_P693436111y_real,Ys3: list_poly_real] :
% 3.10/1.62 ( ( A1
% 3.10/1.62 = ( cons_P1129399039y_real @ X4 @ Xs3 ) )
% 3.10/1.62 & ( A2
% 3.10/1.62 = ( cons_poly_real @ Y3 @ Ys3 ) )
% 3.10/1.62 & ( R2 @ X4 @ Y3 )
% 3.10/1.62 & ( listre1751862142y_real @ R2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_146_listrelp_Ocases,axiom,
% 3.10/1.62 ! [R: poly_real > poly_real > $o,A12: list_poly_real,A22: list_poly_real] :
% 3.10/1.62 ( ( listre1609905961y_real @ R @ A12 @ A22 )
% 3.10/1.62 => ( ( ( A12 = nil_poly_real )
% 3.10/1.62 => ( A22 != nil_poly_real ) )
% 3.10/1.62 => ~ ! [X3: poly_real,Y2: poly_real,Xs2: list_poly_real] :
% 3.10/1.62 ( ( A12
% 3.10/1.62 = ( cons_poly_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ! [Ys2: list_poly_real] :
% 3.10/1.62 ( ( A22
% 3.10/1.62 = ( cons_poly_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ~ ( listre1609905961y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_147_listrelp_Ocases,axiom,
% 3.10/1.62 ! [R: poly_real > list_poly_real > $o,A12: list_poly_real,A22: list_list_poly_real] :
% 3.10/1.62 ( ( listre1793073465y_real @ R @ A12 @ A22 )
% 3.10/1.62 => ( ( ( A12 = nil_poly_real )
% 3.10/1.62 => ( A22 != nil_list_poly_real ) )
% 3.10/1.62 => ~ ! [X3: poly_real,Y2: list_poly_real,Xs2: list_poly_real] :
% 3.10/1.62 ( ( A12
% 3.10/1.62 = ( cons_poly_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ! [Ys2: list_list_poly_real] :
% 3.10/1.62 ( ( A22
% 3.10/1.62 = ( cons_list_poly_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ~ ( listre1793073465y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_148_listrelp_Ocases,axiom,
% 3.10/1.62 ! [R: list_poly_real > poly_real > $o,A12: list_list_poly_real,A22: list_poly_real] :
% 3.10/1.62 ( ( listre713353145y_real @ R @ A12 @ A22 )
% 3.10/1.62 => ( ( ( A12 = nil_list_poly_real )
% 3.10/1.62 => ( A22 != nil_poly_real ) )
% 3.10/1.62 => ~ ! [X3: list_poly_real,Y2: poly_real,Xs2: list_list_poly_real] :
% 3.10/1.62 ( ( A12
% 3.10/1.62 = ( cons_list_poly_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ! [Ys2: list_poly_real] :
% 3.10/1.62 ( ( A22
% 3.10/1.62 = ( cons_poly_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ~ ( listre713353145y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_149_listrelp_Ocases,axiom,
% 3.10/1.62 ! [R: poly_real > produc321349221y_real > $o,A12: list_poly_real,A22: list_P736648811y_real] :
% 3.10/1.62 ( ( listre889482032y_real @ R @ A12 @ A22 )
% 3.10/1.62 => ( ( ( A12 = nil_poly_real )
% 3.10/1.62 => ( A22 != nil_Pr1492526187y_real ) )
% 3.10/1.62 => ~ ! [X3: poly_real,Y2: produc321349221y_real,Xs2: list_poly_real] :
% 3.10/1.62 ( ( A12
% 3.10/1.62 = ( cons_poly_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ! [Ys2: list_P736648811y_real] :
% 3.10/1.62 ( ( A22
% 3.10/1.62 = ( cons_P1027346459y_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ~ ( listre889482032y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_150_listrelp_Ocases,axiom,
% 3.10/1.62 ! [R: list_poly_real > list_poly_real > $o,A12: list_list_poly_real,A22: list_list_poly_real] :
% 3.10/1.62 ( ( listre1763068361y_real @ R @ A12 @ A22 )
% 3.10/1.62 => ( ( ( A12 = nil_list_poly_real )
% 3.10/1.62 => ( A22 != nil_list_poly_real ) )
% 3.10/1.62 => ~ ! [X3: list_poly_real,Y2: list_poly_real,Xs2: list_list_poly_real] :
% 3.10/1.62 ( ( A12
% 3.10/1.62 = ( cons_list_poly_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ! [Ys2: list_list_poly_real] :
% 3.10/1.62 ( ( A22
% 3.10/1.62 = ( cons_list_poly_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ~ ( listre1763068361y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_151_listrelp_Ocases,axiom,
% 3.10/1.62 ! [R: produc321349221y_real > poly_real > $o,A12: list_P736648811y_real,A22: list_poly_real] :
% 3.10/1.62 ( ( listre1044472730y_real @ R @ A12 @ A22 )
% 3.10/1.62 => ( ( ( A12 = nil_Pr1492526187y_real )
% 3.10/1.62 => ( A22 != nil_poly_real ) )
% 3.10/1.62 => ~ ! [X3: produc321349221y_real,Y2: poly_real,Xs2: list_P736648811y_real] :
% 3.10/1.62 ( ( A12
% 3.10/1.62 = ( cons_P1027346459y_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ! [Ys2: list_poly_real] :
% 3.10/1.62 ( ( A22
% 3.10/1.62 = ( cons_poly_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ~ ( listre1044472730y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_152_listrelp_Ocases,axiom,
% 3.10/1.62 ! [R: poly_real > produc461822025y_real > $o,A12: list_poly_real,A22: list_P693436111y_real] :
% 3.10/1.62 ( ( listre471999892y_real @ R @ A12 @ A22 )
% 3.10/1.62 => ( ( ( A12 = nil_poly_real )
% 3.10/1.62 => ( A22 != nil_Pr1207979855y_real ) )
% 3.10/1.62 => ~ ! [X3: poly_real,Y2: produc461822025y_real,Xs2: list_poly_real] :
% 3.10/1.62 ( ( A12
% 3.10/1.62 = ( cons_poly_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ! [Ys2: list_P693436111y_real] :
% 3.10/1.62 ( ( A22
% 3.10/1.62 = ( cons_P1129399039y_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ~ ( listre471999892y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_153_listrelp_Ocases,axiom,
% 3.10/1.62 ! [R: list_poly_real > produc321349221y_real > $o,A12: list_list_poly_real,A22: list_P736648811y_real] :
% 3.10/1.62 ( ( listre1037026976y_real @ R @ A12 @ A22 )
% 3.10/1.62 => ( ( ( A12 = nil_list_poly_real )
% 3.10/1.62 => ( A22 != nil_Pr1492526187y_real ) )
% 3.10/1.62 => ~ ! [X3: list_poly_real,Y2: produc321349221y_real,Xs2: list_list_poly_real] :
% 3.10/1.62 ( ( A12
% 3.10/1.62 = ( cons_list_poly_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ! [Ys2: list_P736648811y_real] :
% 3.10/1.62 ( ( A22
% 3.10/1.62 = ( cons_P1027346459y_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ~ ( listre1037026976y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_154_listrelp_Ocases,axiom,
% 3.10/1.62 ! [R: produc321349221y_real > list_poly_real > $o,A12: list_P736648811y_real,A22: list_list_poly_real] :
% 3.10/1.62 ( ( listre321577258y_real @ R @ A12 @ A22 )
% 3.10/1.62 => ( ( ( A12 = nil_Pr1492526187y_real )
% 3.10/1.62 => ( A22 != nil_list_poly_real ) )
% 3.10/1.62 => ~ ! [X3: produc321349221y_real,Y2: list_poly_real,Xs2: list_P736648811y_real] :
% 3.10/1.62 ( ( A12
% 3.10/1.62 = ( cons_P1027346459y_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ! [Ys2: list_list_poly_real] :
% 3.10/1.62 ( ( A22
% 3.10/1.62 = ( cons_list_poly_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ~ ( listre321577258y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_155_listrelp_Ocases,axiom,
% 3.10/1.62 ! [R: produc461822025y_real > poly_real > $o,A12: list_P693436111y_real,A22: list_poly_real] :
% 3.10/1.62 ( ( listre1751862142y_real @ R @ A12 @ A22 )
% 3.10/1.62 => ( ( ( A12 = nil_Pr1207979855y_real )
% 3.10/1.62 => ( A22 != nil_poly_real ) )
% 3.10/1.62 => ~ ! [X3: produc461822025y_real,Y2: poly_real,Xs2: list_P693436111y_real] :
% 3.10/1.62 ( ( A12
% 3.10/1.62 = ( cons_P1129399039y_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ! [Ys2: list_poly_real] :
% 3.10/1.62 ( ( A22
% 3.10/1.62 = ( cons_poly_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ( ( R @ X3 @ Y2 )
% 3.10/1.62 => ~ ( listre1751862142y_real @ R @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_156_splice_Oelims,axiom,
% 3.10/1.62 ! [X: list_list_poly_real,Xa: list_list_poly_real,Y: list_list_poly_real] :
% 3.10/1.62 ( ( ( splice2080530731y_real @ X @ Xa )
% 3.10/1.62 = Y )
% 3.10/1.62 => ( ( ( X = nil_list_poly_real )
% 3.10/1.62 => ( Y != Xa ) )
% 3.10/1.62 => ~ ! [X3: list_poly_real,Xs2: list_list_poly_real] :
% 3.10/1.62 ( ( X
% 3.10/1.62 = ( cons_list_poly_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ( Y
% 3.10/1.62 != ( cons_list_poly_real @ X3 @ ( splice2080530731y_real @ Xa @ Xs2 ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_157_splice_Oelims,axiom,
% 3.10/1.62 ! [X: list_P736648811y_real,Xa: list_P736648811y_real,Y: list_P736648811y_real] :
% 3.10/1.62 ( ( ( splice1383748542y_real @ X @ Xa )
% 3.10/1.62 = Y )
% 3.10/1.62 => ( ( ( X = nil_Pr1492526187y_real )
% 3.10/1.62 => ( Y != Xa ) )
% 3.10/1.62 => ~ ! [X3: produc321349221y_real,Xs2: list_P736648811y_real] :
% 3.10/1.62 ( ( X
% 3.10/1.62 = ( cons_P1027346459y_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ( Y
% 3.10/1.62 != ( cons_P1027346459y_real @ X3 @ ( splice1383748542y_real @ Xa @ Xs2 ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_158_splice_Oelims,axiom,
% 3.10/1.62 ! [X: list_P693436111y_real,Xa: list_P693436111y_real,Y: list_P693436111y_real] :
% 3.10/1.62 ( ( ( splice1321784098y_real @ X @ Xa )
% 3.10/1.62 = Y )
% 3.10/1.62 => ( ( ( X = nil_Pr1207979855y_real )
% 3.10/1.62 => ( Y != Xa ) )
% 3.10/1.62 => ~ ! [X3: produc461822025y_real,Xs2: list_P693436111y_real] :
% 3.10/1.62 ( ( X
% 3.10/1.62 = ( cons_P1129399039y_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ( Y
% 3.10/1.62 != ( cons_P1129399039y_real @ X3 @ ( splice1321784098y_real @ Xa @ Xs2 ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_159_splice_Oelims,axiom,
% 3.10/1.62 ! [X: list_poly_real,Xa: list_poly_real,Y: list_poly_real] :
% 3.10/1.62 ( ( ( splice_poly_real @ X @ Xa )
% 3.10/1.62 = Y )
% 3.10/1.62 => ( ( ( X = nil_poly_real )
% 3.10/1.62 => ( Y != Xa ) )
% 3.10/1.62 => ~ ! [X3: poly_real,Xs2: list_poly_real] :
% 3.10/1.62 ( ( X
% 3.10/1.62 = ( cons_poly_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ( Y
% 3.10/1.62 != ( cons_poly_real @ X3 @ ( splice_poly_real @ Xa @ Xs2 ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_160_ord_Olexordp__eq_Oinducts,axiom,
% 3.10/1.62 ! [Less: list_poly_real > list_poly_real > $o,X1: list_list_poly_real,X2: list_list_poly_real,P3: list_list_poly_real > list_list_poly_real > $o] :
% 3.10/1.62 ( ( lexord1324236152y_real @ Less @ X1 @ X2 )
% 3.10/1.62 => ( ! [X_1: list_list_poly_real] : ( P3 @ nil_list_poly_real @ X_1 )
% 3.10/1.62 => ( ! [X3: list_poly_real,Y2: list_poly_real,Xs2: list_list_poly_real,Ys2: list_list_poly_real] :
% 3.10/1.62 ( ( Less @ X3 @ Y2 )
% 3.10/1.62 => ( P3 @ ( cons_list_poly_real @ X3 @ Xs2 ) @ ( cons_list_poly_real @ Y2 @ Ys2 ) ) )
% 3.10/1.62 => ( ! [X3: list_poly_real,Y2: list_poly_real,Xs2: list_list_poly_real,Ys2: list_list_poly_real] :
% 3.10/1.62 ( ~ ( Less @ X3 @ Y2 )
% 3.10/1.62 => ( ~ ( Less @ Y2 @ X3 )
% 3.10/1.62 => ( ( lexord1324236152y_real @ Less @ Xs2 @ Ys2 )
% 3.10/1.62 => ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_list_poly_real @ X3 @ Xs2 ) @ ( cons_list_poly_real @ Y2 @ Ys2 ) ) ) ) ) )
% 3.10/1.62 => ( P3 @ X1 @ X2 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_161_ord_Olexordp__eq_Oinducts,axiom,
% 3.10/1.62 ! [Less: produc321349221y_real > produc321349221y_real > $o,X1: list_P736648811y_real,X2: list_P736648811y_real,P3: list_P736648811y_real > list_P736648811y_real > $o] :
% 3.10/1.62 ( ( lexord834705585y_real @ Less @ X1 @ X2 )
% 3.10/1.62 => ( ! [X_1: list_P736648811y_real] : ( P3 @ nil_Pr1492526187y_real @ X_1 )
% 3.10/1.62 => ( ! [X3: produc321349221y_real,Y2: produc321349221y_real,Xs2: list_P736648811y_real,Ys2: list_P736648811y_real] :
% 3.10/1.62 ( ( Less @ X3 @ Y2 )
% 3.10/1.62 => ( P3 @ ( cons_P1027346459y_real @ X3 @ Xs2 ) @ ( cons_P1027346459y_real @ Y2 @ Ys2 ) ) )
% 3.10/1.62 => ( ! [X3: produc321349221y_real,Y2: produc321349221y_real,Xs2: list_P736648811y_real,Ys2: list_P736648811y_real] :
% 3.10/1.62 ( ~ ( Less @ X3 @ Y2 )
% 3.10/1.62 => ( ~ ( Less @ Y2 @ X3 )
% 3.10/1.62 => ( ( lexord834705585y_real @ Less @ Xs2 @ Ys2 )
% 3.10/1.62 => ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_P1027346459y_real @ X3 @ Xs2 ) @ ( cons_P1027346459y_real @ Y2 @ Ys2 ) ) ) ) ) )
% 3.10/1.62 => ( P3 @ X1 @ X2 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_162_ord_Olexordp__eq_Oinducts,axiom,
% 3.10/1.62 ! [Less: produc461822025y_real > produc461822025y_real > $o,X1: list_P693436111y_real,X2: list_P693436111y_real,P3: list_P693436111y_real > list_P693436111y_real > $o] :
% 3.10/1.62 ( ( lexord1053351061y_real @ Less @ X1 @ X2 )
% 3.10/1.62 => ( ! [X_1: list_P693436111y_real] : ( P3 @ nil_Pr1207979855y_real @ X_1 )
% 3.10/1.62 => ( ! [X3: produc461822025y_real,Y2: produc461822025y_real,Xs2: list_P693436111y_real,Ys2: list_P693436111y_real] :
% 3.10/1.62 ( ( Less @ X3 @ Y2 )
% 3.10/1.62 => ( P3 @ ( cons_P1129399039y_real @ X3 @ Xs2 ) @ ( cons_P1129399039y_real @ Y2 @ Ys2 ) ) )
% 3.10/1.62 => ( ! [X3: produc461822025y_real,Y2: produc461822025y_real,Xs2: list_P693436111y_real,Ys2: list_P693436111y_real] :
% 3.10/1.62 ( ~ ( Less @ X3 @ Y2 )
% 3.10/1.62 => ( ~ ( Less @ Y2 @ X3 )
% 3.10/1.62 => ( ( lexord1053351061y_real @ Less @ Xs2 @ Ys2 )
% 3.10/1.62 => ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_P1129399039y_real @ X3 @ Xs2 ) @ ( cons_P1129399039y_real @ Y2 @ Ys2 ) ) ) ) ) )
% 3.10/1.62 => ( P3 @ X1 @ X2 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_163_ord_Olexordp__eq_Oinducts,axiom,
% 3.10/1.62 ! [Less: poly_real > poly_real > $o,X1: list_poly_real,X2: list_poly_real,P3: list_poly_real > list_poly_real > $o] :
% 3.10/1.62 ( ( lexordp_eq_poly_real @ Less @ X1 @ X2 )
% 3.10/1.62 => ( ! [X_1: list_poly_real] : ( P3 @ nil_poly_real @ X_1 )
% 3.10/1.62 => ( ! [X3: poly_real,Y2: poly_real,Xs2: list_poly_real,Ys2: list_poly_real] :
% 3.10/1.62 ( ( Less @ X3 @ Y2 )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) )
% 3.10/1.62 => ( ! [X3: poly_real,Y2: poly_real,Xs2: list_poly_real,Ys2: list_poly_real] :
% 3.10/1.62 ( ~ ( Less @ X3 @ Y2 )
% 3.10/1.62 => ( ~ ( Less @ Y2 @ X3 )
% 3.10/1.62 => ( ( lexordp_eq_poly_real @ Less @ Xs2 @ Ys2 )
% 3.10/1.62 => ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) ) ) )
% 3.10/1.62 => ( P3 @ X1 @ X2 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_164_ord_Olexordp__eq_Osimps,axiom,
% 3.10/1.62 ( lexord1324236152y_real
% 3.10/1.62 = ( ^ [Less2: list_poly_real > list_poly_real > $o,A1: list_list_poly_real,A2: list_list_poly_real] :
% 3.10/1.62 ( ? [Ys3: list_list_poly_real] :
% 3.10/1.62 ( ( A1 = nil_list_poly_real )
% 3.10/1.62 & ( A2 = Ys3 ) )
% 3.10/1.62 | ? [X4: list_poly_real,Y3: list_poly_real,Xs3: list_list_poly_real,Ys3: list_list_poly_real] :
% 3.10/1.62 ( ( A1
% 3.10/1.62 = ( cons_list_poly_real @ X4 @ Xs3 ) )
% 3.10/1.62 & ( A2
% 3.10/1.62 = ( cons_list_poly_real @ Y3 @ Ys3 ) )
% 3.10/1.62 & ( Less2 @ X4 @ Y3 ) )
% 3.10/1.62 | ? [X4: list_poly_real,Y3: list_poly_real,Xs3: list_list_poly_real,Ys3: list_list_poly_real] :
% 3.10/1.62 ( ( A1
% 3.10/1.62 = ( cons_list_poly_real @ X4 @ Xs3 ) )
% 3.10/1.62 & ( A2
% 3.10/1.62 = ( cons_list_poly_real @ Y3 @ Ys3 ) )
% 3.10/1.62 & ~ ( Less2 @ X4 @ Y3 )
% 3.10/1.62 & ~ ( Less2 @ Y3 @ X4 )
% 3.10/1.62 & ( lexord1324236152y_real @ Less2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_165_ord_Olexordp__eq_Osimps,axiom,
% 3.10/1.62 ( lexord834705585y_real
% 3.10/1.62 = ( ^ [Less2: produc321349221y_real > produc321349221y_real > $o,A1: list_P736648811y_real,A2: list_P736648811y_real] :
% 3.10/1.62 ( ? [Ys3: list_P736648811y_real] :
% 3.10/1.62 ( ( A1 = nil_Pr1492526187y_real )
% 3.10/1.62 & ( A2 = Ys3 ) )
% 3.10/1.62 | ? [X4: produc321349221y_real,Y3: produc321349221y_real,Xs3: list_P736648811y_real,Ys3: list_P736648811y_real] :
% 3.10/1.62 ( ( A1
% 3.10/1.62 = ( cons_P1027346459y_real @ X4 @ Xs3 ) )
% 3.10/1.62 & ( A2
% 3.10/1.62 = ( cons_P1027346459y_real @ Y3 @ Ys3 ) )
% 3.10/1.62 & ( Less2 @ X4 @ Y3 ) )
% 3.10/1.62 | ? [X4: produc321349221y_real,Y3: produc321349221y_real,Xs3: list_P736648811y_real,Ys3: list_P736648811y_real] :
% 3.10/1.62 ( ( A1
% 3.10/1.62 = ( cons_P1027346459y_real @ X4 @ Xs3 ) )
% 3.10/1.62 & ( A2
% 3.10/1.62 = ( cons_P1027346459y_real @ Y3 @ Ys3 ) )
% 3.10/1.62 & ~ ( Less2 @ X4 @ Y3 )
% 3.10/1.62 & ~ ( Less2 @ Y3 @ X4 )
% 3.10/1.62 & ( lexord834705585y_real @ Less2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_166_ord_Olexordp__eq_Osimps,axiom,
% 3.10/1.62 ( lexord1053351061y_real
% 3.10/1.62 = ( ^ [Less2: produc461822025y_real > produc461822025y_real > $o,A1: list_P693436111y_real,A2: list_P693436111y_real] :
% 3.10/1.62 ( ? [Ys3: list_P693436111y_real] :
% 3.10/1.62 ( ( A1 = nil_Pr1207979855y_real )
% 3.10/1.62 & ( A2 = Ys3 ) )
% 3.10/1.62 | ? [X4: produc461822025y_real,Y3: produc461822025y_real,Xs3: list_P693436111y_real,Ys3: list_P693436111y_real] :
% 3.10/1.62 ( ( A1
% 3.10/1.62 = ( cons_P1129399039y_real @ X4 @ Xs3 ) )
% 3.10/1.62 & ( A2
% 3.10/1.62 = ( cons_P1129399039y_real @ Y3 @ Ys3 ) )
% 3.10/1.62 & ( Less2 @ X4 @ Y3 ) )
% 3.10/1.62 | ? [X4: produc461822025y_real,Y3: produc461822025y_real,Xs3: list_P693436111y_real,Ys3: list_P693436111y_real] :
% 3.10/1.62 ( ( A1
% 3.10/1.62 = ( cons_P1129399039y_real @ X4 @ Xs3 ) )
% 3.10/1.62 & ( A2
% 3.10/1.62 = ( cons_P1129399039y_real @ Y3 @ Ys3 ) )
% 3.10/1.62 & ~ ( Less2 @ X4 @ Y3 )
% 3.10/1.62 & ~ ( Less2 @ Y3 @ X4 )
% 3.10/1.62 & ( lexord1053351061y_real @ Less2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_167_ord_Olexordp__eq_Osimps,axiom,
% 3.10/1.62 ( lexordp_eq_poly_real
% 3.10/1.62 = ( ^ [Less2: poly_real > poly_real > $o,A1: list_poly_real,A2: list_poly_real] :
% 3.10/1.62 ( ? [Ys3: list_poly_real] :
% 3.10/1.62 ( ( A1 = nil_poly_real )
% 3.10/1.62 & ( A2 = Ys3 ) )
% 3.10/1.62 | ? [X4: poly_real,Y3: poly_real,Xs3: list_poly_real,Ys3: list_poly_real] :
% 3.10/1.62 ( ( A1
% 3.10/1.62 = ( cons_poly_real @ X4 @ Xs3 ) )
% 3.10/1.62 & ( A2
% 3.10/1.62 = ( cons_poly_real @ Y3 @ Ys3 ) )
% 3.10/1.62 & ( Less2 @ X4 @ Y3 ) )
% 3.10/1.62 | ? [X4: poly_real,Y3: poly_real,Xs3: list_poly_real,Ys3: list_poly_real] :
% 3.10/1.62 ( ( A1
% 3.10/1.62 = ( cons_poly_real @ X4 @ Xs3 ) )
% 3.10/1.62 & ( A2
% 3.10/1.62 = ( cons_poly_real @ Y3 @ Ys3 ) )
% 3.10/1.62 & ~ ( Less2 @ X4 @ Y3 )
% 3.10/1.62 & ~ ( Less2 @ Y3 @ X4 )
% 3.10/1.62 & ( lexordp_eq_poly_real @ Less2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_168_ord_Olexordp__eq_Ocases,axiom,
% 3.10/1.62 ! [Less: list_poly_real > list_poly_real > $o,A12: list_list_poly_real,A22: list_list_poly_real] :
% 3.10/1.62 ( ( lexord1324236152y_real @ Less @ A12 @ A22 )
% 3.10/1.62 => ( ( A12 != nil_list_poly_real )
% 3.10/1.62 => ( ! [X3: list_poly_real] :
% 3.10/1.62 ( ? [Xs2: list_list_poly_real] :
% 3.10/1.62 ( A12
% 3.10/1.62 = ( cons_list_poly_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ! [Y2: list_poly_real] :
% 3.10/1.62 ( ? [Ys2: list_list_poly_real] :
% 3.10/1.62 ( A22
% 3.10/1.62 = ( cons_list_poly_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ~ ( Less @ X3 @ Y2 ) ) )
% 3.10/1.62 => ~ ! [X3: list_poly_real,Y2: list_poly_real,Xs2: list_list_poly_real] :
% 3.10/1.62 ( ( A12
% 3.10/1.62 = ( cons_list_poly_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ! [Ys2: list_list_poly_real] :
% 3.10/1.62 ( ( A22
% 3.10/1.62 = ( cons_list_poly_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ( ~ ( Less @ X3 @ Y2 )
% 3.10/1.62 => ( ~ ( Less @ Y2 @ X3 )
% 3.10/1.62 => ~ ( lexord1324236152y_real @ Less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_169_ord_Olexordp__eq_Ocases,axiom,
% 3.10/1.62 ! [Less: produc321349221y_real > produc321349221y_real > $o,A12: list_P736648811y_real,A22: list_P736648811y_real] :
% 3.10/1.62 ( ( lexord834705585y_real @ Less @ A12 @ A22 )
% 3.10/1.62 => ( ( A12 != nil_Pr1492526187y_real )
% 3.10/1.62 => ( ! [X3: produc321349221y_real] :
% 3.10/1.62 ( ? [Xs2: list_P736648811y_real] :
% 3.10/1.62 ( A12
% 3.10/1.62 = ( cons_P1027346459y_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ! [Y2: produc321349221y_real] :
% 3.10/1.62 ( ? [Ys2: list_P736648811y_real] :
% 3.10/1.62 ( A22
% 3.10/1.62 = ( cons_P1027346459y_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ~ ( Less @ X3 @ Y2 ) ) )
% 3.10/1.62 => ~ ! [X3: produc321349221y_real,Y2: produc321349221y_real,Xs2: list_P736648811y_real] :
% 3.10/1.62 ( ( A12
% 3.10/1.62 = ( cons_P1027346459y_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ! [Ys2: list_P736648811y_real] :
% 3.10/1.62 ( ( A22
% 3.10/1.62 = ( cons_P1027346459y_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ( ~ ( Less @ X3 @ Y2 )
% 3.10/1.62 => ( ~ ( Less @ Y2 @ X3 )
% 3.10/1.62 => ~ ( lexord834705585y_real @ Less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_170_ord_Olexordp__eq_Ocases,axiom,
% 3.10/1.62 ! [Less: produc461822025y_real > produc461822025y_real > $o,A12: list_P693436111y_real,A22: list_P693436111y_real] :
% 3.10/1.62 ( ( lexord1053351061y_real @ Less @ A12 @ A22 )
% 3.10/1.62 => ( ( A12 != nil_Pr1207979855y_real )
% 3.10/1.62 => ( ! [X3: produc461822025y_real] :
% 3.10/1.62 ( ? [Xs2: list_P693436111y_real] :
% 3.10/1.62 ( A12
% 3.10/1.62 = ( cons_P1129399039y_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ! [Y2: produc461822025y_real] :
% 3.10/1.62 ( ? [Ys2: list_P693436111y_real] :
% 3.10/1.62 ( A22
% 3.10/1.62 = ( cons_P1129399039y_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ~ ( Less @ X3 @ Y2 ) ) )
% 3.10/1.62 => ~ ! [X3: produc461822025y_real,Y2: produc461822025y_real,Xs2: list_P693436111y_real] :
% 3.10/1.62 ( ( A12
% 3.10/1.62 = ( cons_P1129399039y_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ! [Ys2: list_P693436111y_real] :
% 3.10/1.62 ( ( A22
% 3.10/1.62 = ( cons_P1129399039y_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ( ~ ( Less @ X3 @ Y2 )
% 3.10/1.62 => ( ~ ( Less @ Y2 @ X3 )
% 3.10/1.62 => ~ ( lexord1053351061y_real @ Less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_171_ord_Olexordp__eq_Ocases,axiom,
% 3.10/1.62 ! [Less: poly_real > poly_real > $o,A12: list_poly_real,A22: list_poly_real] :
% 3.10/1.62 ( ( lexordp_eq_poly_real @ Less @ A12 @ A22 )
% 3.10/1.62 => ( ( A12 != nil_poly_real )
% 3.10/1.62 => ( ! [X3: poly_real] :
% 3.10/1.62 ( ? [Xs2: list_poly_real] :
% 3.10/1.62 ( A12
% 3.10/1.62 = ( cons_poly_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ! [Y2: poly_real] :
% 3.10/1.62 ( ? [Ys2: list_poly_real] :
% 3.10/1.62 ( A22
% 3.10/1.62 = ( cons_poly_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ~ ( Less @ X3 @ Y2 ) ) )
% 3.10/1.62 => ~ ! [X3: poly_real,Y2: poly_real,Xs2: list_poly_real] :
% 3.10/1.62 ( ( A12
% 3.10/1.62 = ( cons_poly_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ! [Ys2: list_poly_real] :
% 3.10/1.62 ( ( A22
% 3.10/1.62 = ( cons_poly_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ( ~ ( Less @ X3 @ Y2 )
% 3.10/1.62 => ( ~ ( Less @ Y2 @ X3 )
% 3.10/1.62 => ~ ( lexordp_eq_poly_real @ Less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_172_list_Oinject,axiom,
% 3.10/1.62 ! [X21: list_poly_real,X22: list_list_poly_real,Y21: list_poly_real,Y22: list_list_poly_real] :
% 3.10/1.62 ( ( ( cons_list_poly_real @ X21 @ X22 )
% 3.10/1.62 = ( cons_list_poly_real @ Y21 @ Y22 ) )
% 3.10/1.62 = ( ( X21 = Y21 )
% 3.10/1.62 & ( X22 = Y22 ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_173_list_Oinject,axiom,
% 3.10/1.62 ! [X21: produc321349221y_real,X22: list_P736648811y_real,Y21: produc321349221y_real,Y22: list_P736648811y_real] :
% 3.10/1.62 ( ( ( cons_P1027346459y_real @ X21 @ X22 )
% 3.10/1.62 = ( cons_P1027346459y_real @ Y21 @ Y22 ) )
% 3.10/1.62 = ( ( X21 = Y21 )
% 3.10/1.62 & ( X22 = Y22 ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_174_list_Oinject,axiom,
% 3.10/1.62 ! [X21: produc461822025y_real,X22: list_P693436111y_real,Y21: produc461822025y_real,Y22: list_P693436111y_real] :
% 3.10/1.62 ( ( ( cons_P1129399039y_real @ X21 @ X22 )
% 3.10/1.62 = ( cons_P1129399039y_real @ Y21 @ Y22 ) )
% 3.10/1.62 = ( ( X21 = Y21 )
% 3.10/1.62 & ( X22 = Y22 ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_175_list_Oinject,axiom,
% 3.10/1.62 ! [X21: poly_real,X22: list_poly_real,Y21: poly_real,Y22: list_poly_real] :
% 3.10/1.62 ( ( ( cons_poly_real @ X21 @ X22 )
% 3.10/1.62 = ( cons_poly_real @ Y21 @ Y22 ) )
% 3.10/1.62 = ( ( X21 = Y21 )
% 3.10/1.62 & ( X22 = Y22 ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_176_ord_Olexordp__eq__simps_I4_J,axiom,
% 3.10/1.62 ! [Less: list_poly_real > list_poly_real > $o,X: list_poly_real,Xs: list_list_poly_real,Y: list_poly_real,Ys: list_list_poly_real] :
% 3.10/1.62 ( ( lexord1324236152y_real @ Less @ ( cons_list_poly_real @ X @ Xs ) @ ( cons_list_poly_real @ Y @ Ys ) )
% 3.10/1.62 = ( ( Less @ X @ Y )
% 3.10/1.62 | ( ~ ( Less @ Y @ X )
% 3.10/1.62 & ( lexord1324236152y_real @ Less @ Xs @ Ys ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_177_ord_Olexordp__eq__simps_I4_J,axiom,
% 3.10/1.62 ! [Less: produc321349221y_real > produc321349221y_real > $o,X: produc321349221y_real,Xs: list_P736648811y_real,Y: produc321349221y_real,Ys: list_P736648811y_real] :
% 3.10/1.62 ( ( lexord834705585y_real @ Less @ ( cons_P1027346459y_real @ X @ Xs ) @ ( cons_P1027346459y_real @ Y @ Ys ) )
% 3.10/1.62 = ( ( Less @ X @ Y )
% 3.10/1.62 | ( ~ ( Less @ Y @ X )
% 3.10/1.62 & ( lexord834705585y_real @ Less @ Xs @ Ys ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_178_ord_Olexordp__eq__simps_I4_J,axiom,
% 3.10/1.62 ! [Less: produc461822025y_real > produc461822025y_real > $o,X: produc461822025y_real,Xs: list_P693436111y_real,Y: produc461822025y_real,Ys: list_P693436111y_real] :
% 3.10/1.62 ( ( lexord1053351061y_real @ Less @ ( cons_P1129399039y_real @ X @ Xs ) @ ( cons_P1129399039y_real @ Y @ Ys ) )
% 3.10/1.62 = ( ( Less @ X @ Y )
% 3.10/1.62 | ( ~ ( Less @ Y @ X )
% 3.10/1.62 & ( lexord1053351061y_real @ Less @ Xs @ Ys ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_179_ord_Olexordp__eq__simps_I4_J,axiom,
% 3.10/1.62 ! [Less: poly_real > poly_real > $o,X: poly_real,Xs: list_poly_real,Y: poly_real,Ys: list_poly_real] :
% 3.10/1.62 ( ( lexordp_eq_poly_real @ Less @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ Y @ Ys ) )
% 3.10/1.62 = ( ( Less @ X @ Y )
% 3.10/1.62 | ( ~ ( Less @ Y @ X )
% 3.10/1.62 & ( lexordp_eq_poly_real @ Less @ Xs @ Ys ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_180_list__ex__simps_I1_J,axiom,
% 3.10/1.62 ! [P3: list_poly_real > $o,X: list_poly_real,Xs: list_list_poly_real] :
% 3.10/1.62 ( ( list_e809719936y_real @ P3 @ ( cons_list_poly_real @ X @ Xs ) )
% 3.10/1.62 = ( ( P3 @ X )
% 3.10/1.62 | ( list_e809719936y_real @ P3 @ Xs ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_181_list__ex__simps_I1_J,axiom,
% 3.10/1.62 ! [P3: produc321349221y_real > $o,X: produc321349221y_real,Xs: list_P736648811y_real] :
% 3.10/1.62 ( ( list_e2093379497y_real @ P3 @ ( cons_P1027346459y_real @ X @ Xs ) )
% 3.10/1.62 = ( ( P3 @ X )
% 3.10/1.62 | ( list_e2093379497y_real @ P3 @ Xs ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_182_list__ex__simps_I1_J,axiom,
% 3.10/1.62 ! [P3: produc461822025y_real > $o,X: produc461822025y_real,Xs: list_P693436111y_real] :
% 3.10/1.62 ( ( list_e1312221069y_real @ P3 @ ( cons_P1129399039y_real @ X @ Xs ) )
% 3.10/1.62 = ( ( P3 @ X )
% 3.10/1.62 | ( list_e1312221069y_real @ P3 @ Xs ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_183_list__ex__simps_I1_J,axiom,
% 3.10/1.62 ! [P3: poly_real > $o,X: poly_real,Xs: list_poly_real] :
% 3.10/1.62 ( ( list_ex_poly_real @ P3 @ ( cons_poly_real @ X @ Xs ) )
% 3.10/1.62 = ( ( P3 @ X )
% 3.10/1.62 | ( list_ex_poly_real @ P3 @ Xs ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_184_transpose_Ocases,axiom,
% 3.10/1.62 ! [X: list_l1245274212y_real] :
% 3.10/1.62 ( ( X != nil_li2088348750y_real )
% 3.10/1.62 => ( ! [Xss: list_l1245274212y_real] :
% 3.10/1.62 ( X
% 3.10/1.62 != ( cons_l2022919326y_real @ nil_list_poly_real @ Xss ) )
% 3.10/1.62 => ~ ! [X3: list_poly_real,Xs2: list_list_poly_real,Xss: list_l1245274212y_real] :
% 3.10/1.62 ( X
% 3.10/1.62 != ( cons_l2022919326y_real @ ( cons_list_poly_real @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_185_transpose_Ocases,axiom,
% 3.10/1.62 ! [X: list_l6097393y_real] :
% 3.10/1.62 ( ( X != nil_li579690865y_real )
% 3.10/1.62 => ( ! [Xss: list_l6097393y_real] :
% 3.10/1.62 ( X
% 3.10/1.62 != ( cons_l730969377y_real @ nil_Pr1492526187y_real @ Xss ) )
% 3.10/1.62 => ~ ! [X3: produc321349221y_real,Xs2: list_P736648811y_real,Xss: list_l6097393y_real] :
% 3.10/1.62 ( X
% 3.10/1.62 != ( cons_l730969377y_real @ ( cons_P1027346459y_real @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_186_transpose_Ocases,axiom,
% 3.10/1.62 ! [X: list_l343759061y_real] :
% 3.10/1.62 ( ( X != nil_li1299462869y_real )
% 3.10/1.62 => ( ! [Xss: list_l343759061y_real] :
% 3.10/1.62 ( X
% 3.10/1.62 != ( cons_l677353093y_real @ nil_Pr1207979855y_real @ Xss ) )
% 3.10/1.62 => ~ ! [X3: produc461822025y_real,Xs2: list_P693436111y_real,Xss: list_l343759061y_real] :
% 3.10/1.62 ( X
% 3.10/1.62 != ( cons_l677353093y_real @ ( cons_P1129399039y_real @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_187_transpose_Ocases,axiom,
% 3.10/1.62 ! [X: list_list_poly_real] :
% 3.10/1.62 ( ( X != nil_list_poly_real )
% 3.10/1.62 => ( ! [Xss: list_list_poly_real] :
% 3.10/1.62 ( X
% 3.10/1.62 != ( cons_list_poly_real @ nil_poly_real @ Xss ) )
% 3.10/1.62 => ~ ! [X3: poly_real,Xs2: list_poly_real,Xss: list_list_poly_real] :
% 3.10/1.62 ( X
% 3.10/1.62 != ( cons_list_poly_real @ ( cons_poly_real @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_188_not__Cons__self2,axiom,
% 3.10/1.62 ! [X: list_poly_real,Xs: list_list_poly_real] :
% 3.10/1.62 ( ( cons_list_poly_real @ X @ Xs )
% 3.10/1.62 != Xs ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_189_not__Cons__self2,axiom,
% 3.10/1.62 ! [X: produc321349221y_real,Xs: list_P736648811y_real] :
% 3.10/1.62 ( ( cons_P1027346459y_real @ X @ Xs )
% 3.10/1.62 != Xs ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_190_not__Cons__self2,axiom,
% 3.10/1.62 ! [X: produc461822025y_real,Xs: list_P693436111y_real] :
% 3.10/1.62 ( ( cons_P1129399039y_real @ X @ Xs )
% 3.10/1.62 != Xs ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_191_not__Cons__self2,axiom,
% 3.10/1.62 ! [X: poly_real,Xs: list_poly_real] :
% 3.10/1.62 ( ( cons_poly_real @ X @ Xs )
% 3.10/1.62 != Xs ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_192_mem__Collect__eq,axiom,
% 3.10/1.62 ! [A3: produc1426596841y_real,P3: produc1426596841y_real > $o] :
% 3.10/1.62 ( ( member403334290y_real @ A3 @ ( collec1459394516y_real @ P3 ) )
% 3.10/1.62 = ( P3 @ A3 ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_193_mem__Collect__eq,axiom,
% 3.10/1.62 ! [A3: produc461822025y_real,P3: produc461822025y_real > $o] :
% 3.10/1.62 ( ( member1784523250y_real @ A3 @ ( collec329281332y_real @ P3 ) )
% 3.10/1.62 = ( P3 @ A3 ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_194_mem__Collect__eq,axiom,
% 3.10/1.62 ! [A3: poly_real,P3: poly_real > $o] :
% 3.10/1.62 ( ( member_poly_real2 @ A3 @ ( collect_poly_real @ P3 ) )
% 3.10/1.62 = ( P3 @ A3 ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_195_mem__Collect__eq,axiom,
% 3.10/1.62 ! [A3: list_poly_real,P3: list_poly_real > $o] :
% 3.10/1.62 ( ( member708095579y_real @ A3 @ ( collec1537941401y_real @ P3 ) )
% 3.10/1.62 = ( P3 @ A3 ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_196_Collect__mem__eq,axiom,
% 3.10/1.62 ! [A4: set_Pr1405268809y_real] :
% 3.10/1.62 ( ( collec1459394516y_real
% 3.10/1.62 @ ^ [X4: produc1426596841y_real] : ( member403334290y_real @ X4 @ A4 ) )
% 3.10/1.62 = A4 ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_197_Collect__mem__eq,axiom,
% 3.10/1.62 ! [A4: set_Pr483210409y_real] :
% 3.10/1.62 ( ( collec329281332y_real
% 3.10/1.62 @ ^ [X4: produc461822025y_real] : ( member1784523250y_real @ X4 @ A4 ) )
% 3.10/1.62 = A4 ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_198_Collect__mem__eq,axiom,
% 3.10/1.62 ! [A4: set_poly_real] :
% 3.10/1.62 ( ( collect_poly_real
% 3.10/1.62 @ ^ [X4: poly_real] : ( member_poly_real2 @ X4 @ A4 ) )
% 3.10/1.62 = A4 ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_199_Collect__mem__eq,axiom,
% 3.10/1.62 ! [A4: set_list_poly_real] :
% 3.10/1.62 ( ( collec1537941401y_real
% 3.10/1.62 @ ^ [X4: list_poly_real] : ( member708095579y_real @ X4 @ A4 ) )
% 3.10/1.62 = A4 ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_200_strict__sorted_Oinduct,axiom,
% 3.10/1.62 ! [P3: list_poly_real > $o,A0: list_poly_real] :
% 3.10/1.62 ( ( P3 @ nil_poly_real )
% 3.10/1.62 => ( ! [X3: poly_real,Ys2: list_poly_real] :
% 3.10/1.62 ( ( P3 @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ X3 @ Ys2 ) ) )
% 3.10/1.62 => ( P3 @ A0 ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_201_strict__sorted_Ocases,axiom,
% 3.10/1.62 ! [X: list_poly_real] :
% 3.10/1.62 ( ( X != nil_poly_real )
% 3.10/1.62 => ~ ! [X3: poly_real,Ys2: list_poly_real] :
% 3.10/1.62 ( X
% 3.10/1.62 != ( cons_poly_real @ X3 @ Ys2 ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_202_map__tailrec__rev_Oinduct,axiom,
% 3.10/1.62 ! [P3: ( list_poly_real > produc461822025y_real ) > list_list_poly_real > list_P693436111y_real > $o,A0: list_poly_real > produc461822025y_real,A12: list_list_poly_real,A22: list_P693436111y_real] :
% 3.10/1.62 ( ! [F2: list_poly_real > produc461822025y_real,X_1: list_P693436111y_real] : ( P3 @ F2 @ nil_list_poly_real @ X_1 )
% 3.10/1.62 => ( ! [F2: list_poly_real > produc461822025y_real,A: list_poly_real,As: list_list_poly_real,Bs2: list_P693436111y_real] :
% 3.10/1.62 ( ( P3 @ F2 @ As @ ( cons_P1129399039y_real @ ( F2 @ A ) @ Bs2 ) )
% 3.10/1.62 => ( P3 @ F2 @ ( cons_list_poly_real @ A @ As ) @ Bs2 ) )
% 3.10/1.62 => ( P3 @ A0 @ A12 @ A22 ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_203_map__tailrec__rev_Oinduct,axiom,
% 3.10/1.62 ! [P3: ( produc321349221y_real > produc461822025y_real ) > list_P736648811y_real > list_P693436111y_real > $o,A0: produc321349221y_real > produc461822025y_real,A12: list_P736648811y_real,A22: list_P693436111y_real] :
% 3.10/1.62 ( ! [F2: produc321349221y_real > produc461822025y_real,X_1: list_P693436111y_real] : ( P3 @ F2 @ nil_Pr1492526187y_real @ X_1 )
% 3.10/1.62 => ( ! [F2: produc321349221y_real > produc461822025y_real,A: produc321349221y_real,As: list_P736648811y_real,Bs2: list_P693436111y_real] :
% 3.10/1.62 ( ( P3 @ F2 @ As @ ( cons_P1129399039y_real @ ( F2 @ A ) @ Bs2 ) )
% 3.10/1.62 => ( P3 @ F2 @ ( cons_P1027346459y_real @ A @ As ) @ Bs2 ) )
% 3.10/1.62 => ( P3 @ A0 @ A12 @ A22 ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_204_map__tailrec__rev_Oinduct,axiom,
% 3.10/1.62 ! [P3: ( produc461822025y_real > produc461822025y_real ) > list_P693436111y_real > list_P693436111y_real > $o,A0: produc461822025y_real > produc461822025y_real,A12: list_P693436111y_real,A22: list_P693436111y_real] :
% 3.10/1.62 ( ! [F2: produc461822025y_real > produc461822025y_real,X_1: list_P693436111y_real] : ( P3 @ F2 @ nil_Pr1207979855y_real @ X_1 )
% 3.10/1.62 => ( ! [F2: produc461822025y_real > produc461822025y_real,A: produc461822025y_real,As: list_P693436111y_real,Bs2: list_P693436111y_real] :
% 3.10/1.62 ( ( P3 @ F2 @ As @ ( cons_P1129399039y_real @ ( F2 @ A ) @ Bs2 ) )
% 3.10/1.62 => ( P3 @ F2 @ ( cons_P1129399039y_real @ A @ As ) @ Bs2 ) )
% 3.10/1.62 => ( P3 @ A0 @ A12 @ A22 ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_205_map__tailrec__rev_Oinduct,axiom,
% 3.10/1.62 ! [P3: ( poly_real > poly_real ) > list_poly_real > list_poly_real > $o,A0: poly_real > poly_real,A12: list_poly_real,A22: list_poly_real] :
% 3.10/1.62 ( ! [F2: poly_real > poly_real,X_1: list_poly_real] : ( P3 @ F2 @ nil_poly_real @ X_1 )
% 3.10/1.62 => ( ! [F2: poly_real > poly_real,A: poly_real,As: list_poly_real,Bs2: list_poly_real] :
% 3.10/1.62 ( ( P3 @ F2 @ As @ ( cons_poly_real @ ( F2 @ A ) @ Bs2 ) )
% 3.10/1.62 => ( P3 @ F2 @ ( cons_poly_real @ A @ As ) @ Bs2 ) )
% 3.10/1.62 => ( P3 @ A0 @ A12 @ A22 ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_206_list__nonempty__induct,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,P3: list_poly_real > $o] :
% 3.10/1.62 ( ( Xs != nil_poly_real )
% 3.10/1.62 => ( ! [X3: poly_real] : ( P3 @ ( cons_poly_real @ X3 @ nil_poly_real ) )
% 3.10/1.62 => ( ! [X3: poly_real,Xs2: list_poly_real] :
% 3.10/1.62 ( ( Xs2 != nil_poly_real )
% 3.10/1.62 => ( ( P3 @ Xs2 )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) ) ) )
% 3.10/1.62 => ( P3 @ Xs ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_207_successively_Oinduct,axiom,
% 3.10/1.62 ! [P3: ( poly_real > poly_real > $o ) > list_poly_real > $o,A0: poly_real > poly_real > $o,A12: list_poly_real] :
% 3.10/1.62 ( ! [P4: poly_real > poly_real > $o] : ( P3 @ P4 @ nil_poly_real )
% 3.10/1.62 => ( ! [P4: poly_real > poly_real > $o,X3: poly_real] : ( P3 @ P4 @ ( cons_poly_real @ X3 @ nil_poly_real ) )
% 3.10/1.62 => ( ! [P4: poly_real > poly_real > $o,X3: poly_real,Y2: poly_real,Xs2: list_poly_real] :
% 3.10/1.62 ( ( P3 @ P4 @ ( cons_poly_real @ Y2 @ Xs2 ) )
% 3.10/1.62 => ( P3 @ P4 @ ( cons_poly_real @ X3 @ ( cons_poly_real @ Y2 @ Xs2 ) ) ) )
% 3.10/1.62 => ( P3 @ A0 @ A12 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_208_remdups__adj_Oinduct,axiom,
% 3.10/1.62 ! [P3: list_poly_real > $o,A0: list_poly_real] :
% 3.10/1.62 ( ( P3 @ nil_poly_real )
% 3.10/1.62 => ( ! [X3: poly_real] : ( P3 @ ( cons_poly_real @ X3 @ nil_poly_real ) )
% 3.10/1.62 => ( ! [X3: poly_real,Y2: poly_real,Xs2: list_poly_real] :
% 3.10/1.62 ( ( ( X3 = Y2 )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) ) )
% 3.10/1.62 => ( ( ( X3 != Y2 )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ Y2 @ Xs2 ) ) )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ X3 @ ( cons_poly_real @ Y2 @ Xs2 ) ) ) ) )
% 3.10/1.62 => ( P3 @ A0 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_209_sorted__wrt_Oinduct,axiom,
% 3.10/1.62 ! [P3: ( poly_real > poly_real > $o ) > list_poly_real > $o,A0: poly_real > poly_real > $o,A12: list_poly_real] :
% 3.10/1.62 ( ! [P4: poly_real > poly_real > $o] : ( P3 @ P4 @ nil_poly_real )
% 3.10/1.62 => ( ! [P4: poly_real > poly_real > $o,X3: poly_real,Ys2: list_poly_real] :
% 3.10/1.62 ( ( P3 @ P4 @ Ys2 )
% 3.10/1.62 => ( P3 @ P4 @ ( cons_poly_real @ X3 @ Ys2 ) ) )
% 3.10/1.62 => ( P3 @ A0 @ A12 ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_210_remdups__adj_Ocases,axiom,
% 3.10/1.62 ! [X: list_poly_real] :
% 3.10/1.62 ( ( X != nil_poly_real )
% 3.10/1.62 => ( ! [X3: poly_real] :
% 3.10/1.62 ( X
% 3.10/1.62 != ( cons_poly_real @ X3 @ nil_poly_real ) )
% 3.10/1.62 => ~ ! [X3: poly_real,Y2: poly_real,Xs2: list_poly_real] :
% 3.10/1.62 ( X
% 3.10/1.62 != ( cons_poly_real @ X3 @ ( cons_poly_real @ Y2 @ Xs2 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_211_shuffles_Oinduct,axiom,
% 3.10/1.62 ! [P3: list_poly_real > list_poly_real > $o,A0: list_poly_real,A12: list_poly_real] :
% 3.10/1.62 ( ! [X_1: list_poly_real] : ( P3 @ nil_poly_real @ X_1 )
% 3.10/1.62 => ( ! [Xs2: list_poly_real] : ( P3 @ Xs2 @ nil_poly_real )
% 3.10/1.62 => ( ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real] :
% 3.10/1.62 ( ( P3 @ Xs2 @ ( cons_poly_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ( ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) )
% 3.10/1.62 => ( P3 @ A0 @ A12 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_212_min__list_Oinduct,axiom,
% 3.10/1.62 ! [P3: list_poly_real > $o,A0: list_poly_real] :
% 3.10/1.62 ( ! [X3: poly_real,Xs2: list_poly_real] :
% 3.10/1.62 ( ! [X212: poly_real,X222: list_poly_real] :
% 3.10/1.62 ( ( Xs2
% 3.10/1.62 = ( cons_poly_real @ X212 @ X222 ) )
% 3.10/1.62 => ( P3 @ Xs2 ) )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) ) )
% 3.10/1.62 => ( ( P3 @ nil_poly_real )
% 3.10/1.62 => ( P3 @ A0 ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_213_min__list_Ocases,axiom,
% 3.10/1.62 ! [X: list_poly_real] :
% 3.10/1.62 ( ! [X3: poly_real,Xs2: list_poly_real] :
% 3.10/1.62 ( X
% 3.10/1.62 != ( cons_poly_real @ X3 @ Xs2 ) )
% 3.10/1.62 => ( X = nil_poly_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_214_induct__list012,axiom,
% 3.10/1.62 ! [P3: list_poly_real > $o,Xs: list_poly_real] :
% 3.10/1.62 ( ( P3 @ nil_poly_real )
% 3.10/1.62 => ( ! [X3: poly_real] : ( P3 @ ( cons_poly_real @ X3 @ nil_poly_real ) )
% 3.10/1.62 => ( ! [X3: poly_real,Y2: poly_real,Zs: list_poly_real] :
% 3.10/1.62 ( ( P3 @ Zs )
% 3.10/1.62 => ( ( P3 @ ( cons_poly_real @ Y2 @ Zs ) )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ X3 @ ( cons_poly_real @ Y2 @ Zs ) ) ) ) )
% 3.10/1.62 => ( P3 @ Xs ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_215_splice_Oinduct,axiom,
% 3.10/1.62 ! [P3: list_poly_real > list_poly_real > $o,A0: list_poly_real,A12: list_poly_real] :
% 3.10/1.62 ( ! [X_1: list_poly_real] : ( P3 @ nil_poly_real @ X_1 )
% 3.10/1.62 => ( ! [X3: poly_real,Xs2: list_poly_real,Ys2: list_poly_real] :
% 3.10/1.62 ( ( P3 @ Ys2 @ Xs2 )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ Ys2 ) )
% 3.10/1.62 => ( P3 @ A0 @ A12 ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_216_list__induct2_H,axiom,
% 3.10/1.62 ! [P3: list_poly_real > list_poly_real > $o,Xs: list_poly_real,Ys: list_poly_real] :
% 3.10/1.62 ( ( P3 @ nil_poly_real @ nil_poly_real )
% 3.10/1.62 => ( ! [X3: poly_real,Xs2: list_poly_real] : ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ nil_poly_real )
% 3.10/1.62 => ( ! [Y2: poly_real,Ys2: list_poly_real] : ( P3 @ nil_poly_real @ ( cons_poly_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ( ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real] :
% 3.10/1.62 ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) )
% 3.10/1.62 => ( P3 @ Xs @ Ys ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_217_neq__Nil__conv,axiom,
% 3.10/1.62 ! [Xs: list_poly_real] :
% 3.10/1.62 ( ( Xs != nil_poly_real )
% 3.10/1.62 = ( ? [Y3: poly_real,Ys3: list_poly_real] :
% 3.10/1.62 ( Xs
% 3.10/1.62 = ( cons_poly_real @ Y3 @ Ys3 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_218_list_Oinducts,axiom,
% 3.10/1.62 ! [P3: list_poly_real > $o,List: list_poly_real] :
% 3.10/1.62 ( ( P3 @ nil_poly_real )
% 3.10/1.62 => ( ! [X12: poly_real,X23: list_poly_real] :
% 3.10/1.62 ( ( P3 @ X23 )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ X12 @ X23 ) ) )
% 3.10/1.62 => ( P3 @ List ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_219_list_Oexhaust,axiom,
% 3.10/1.62 ! [Y: list_poly_real] :
% 3.10/1.62 ( ( Y != nil_poly_real )
% 3.10/1.62 => ~ ! [X213: poly_real,X223: list_poly_real] :
% 3.10/1.62 ( Y
% 3.10/1.62 != ( cons_poly_real @ X213 @ X223 ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_220_list_OdiscI,axiom,
% 3.10/1.62 ! [List: list_poly_real,X21: poly_real,X22: list_poly_real] :
% 3.10/1.62 ( ( List
% 3.10/1.62 = ( cons_poly_real @ X21 @ X22 ) )
% 3.10/1.62 => ( List != nil_poly_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_221_list_Odistinct_I1_J,axiom,
% 3.10/1.62 ! [X21: poly_real,X22: list_poly_real] :
% 3.10/1.62 ( nil_poly_real
% 3.10/1.62 != ( cons_poly_real @ X21 @ X22 ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_222_ord_Olexordp__eq_OCons__eq,axiom,
% 3.10/1.62 ! [Less: poly_real > poly_real > $o,X: poly_real,Y: poly_real,Xs: list_poly_real,Ys: list_poly_real] :
% 3.10/1.62 ( ~ ( Less @ X @ Y )
% 3.10/1.62 => ( ~ ( Less @ Y @ X )
% 3.10/1.62 => ( ( lexordp_eq_poly_real @ Less @ Xs @ Ys )
% 3.10/1.62 => ( lexordp_eq_poly_real @ Less @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ Y @ Ys ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_223_ord_Olexordp__eq_OCons,axiom,
% 3.10/1.62 ! [Less: poly_real > poly_real > $o,X: poly_real,Y: poly_real,Xs: list_poly_real,Ys: list_poly_real] :
% 3.10/1.62 ( ( Less @ X @ Y )
% 3.10/1.62 => ( lexordp_eq_poly_real @ Less @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ Y @ Ys ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_224_splice_Osimps_I2_J,axiom,
% 3.10/1.62 ! [X: poly_real,Xs: list_poly_real,Ys: list_poly_real] :
% 3.10/1.62 ( ( splice_poly_real @ ( cons_poly_real @ X @ Xs ) @ Ys )
% 3.10/1.62 = ( cons_poly_real @ X @ ( splice_poly_real @ Ys @ Xs ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_225_listrelp_OCons,axiom,
% 3.10/1.62 ! [R: poly_real > poly_real > $o,X: poly_real,Y: poly_real,Xs: list_poly_real,Ys: list_poly_real] :
% 3.10/1.62 ( ( R @ X @ Y )
% 3.10/1.62 => ( ( listre1609905961y_real @ R @ Xs @ Ys )
% 3.10/1.62 => ( listre1609905961y_real @ R @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ Y @ Ys ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_226_sturm__seq_Ops__first__two,axiom,
% 3.10/1.62 ! [Ps: list_poly_real,P: poly_real] :
% 3.10/1.62 ( ( sturm_1664866327rm_seq @ Ps @ P )
% 3.10/1.62 => ~ ! [Q: poly_real,Ps3: list_poly_real] :
% 3.10/1.62 ( Ps
% 3.10/1.62 != ( cons_poly_real @ P @ ( cons_poly_real @ Q @ Ps3 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_227_map__tailrec__rev_Osimps_I2_J,axiom,
% 3.10/1.62 ! [F: poly_real > poly_real,A3: poly_real,As2: list_poly_real,Bs: list_poly_real] :
% 3.10/1.62 ( ( map_ta1919289823y_real @ F @ ( cons_poly_real @ A3 @ As2 ) @ Bs )
% 3.10/1.62 = ( map_ta1919289823y_real @ F @ As2 @ ( cons_poly_real @ ( F @ A3 ) @ Bs ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_228_null__rec_I1_J,axiom,
% 3.10/1.62 ! [X: poly_real,Xs: list_poly_real] :
% 3.10/1.62 ~ ( null_poly_real @ ( cons_poly_real @ X @ Xs ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_229_member__rec_I1_J,axiom,
% 3.10/1.62 ! [X: poly_real,Xs: list_poly_real,Y: poly_real] :
% 3.10/1.62 ( ( member_poly_real @ ( cons_poly_real @ X @ Xs ) @ Y )
% 3.10/1.62 = ( ( X = Y )
% 3.10/1.62 | ( member_poly_real @ Xs @ Y ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_230_zip__eq__Nil__iff,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 3.10/1.62 ( ( ( zip_po657915297y_real @ Xs @ Ys )
% 3.10/1.62 = nil_Pr1207979855y_real )
% 3.10/1.62 = ( ( Xs = nil_poly_real )
% 3.10/1.62 | ( Ys = nil_poly_real ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_231_minus__poly__rev__list_Oinduct,axiom,
% 3.10/1.62 ! [P3: list_poly_real > list_poly_real > $o,A0: list_poly_real,A12: list_poly_real] :
% 3.10/1.62 ( ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real] :
% 3.10/1.62 ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) )
% 3.10/1.62 => ( ! [Xs2: list_poly_real] : ( P3 @ Xs2 @ nil_poly_real )
% 3.10/1.62 => ( ! [Y2: poly_real,Ys2: list_poly_real] : ( P3 @ nil_poly_real @ ( cons_poly_real @ Y2 @ Ys2 ) )
% 3.10/1.62 => ( P3 @ A0 @ A12 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_232_plus__coeffs_Oinduct,axiom,
% 3.10/1.62 ! [P3: list_poly_real > list_poly_real > $o,A0: list_poly_real,A12: list_poly_real] :
% 3.10/1.62 ( ! [Xs2: list_poly_real] : ( P3 @ Xs2 @ nil_poly_real )
% 3.10/1.62 => ( ! [V: poly_real,Va: list_poly_real] : ( P3 @ nil_poly_real @ ( cons_poly_real @ V @ Va ) )
% 3.10/1.62 => ( ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real] :
% 3.10/1.62 ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.62 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) )
% 3.10/1.62 => ( P3 @ A0 @ A12 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_233_insert__Nil,axiom,
% 3.10/1.62 ! [X: poly_real] :
% 3.10/1.62 ( ( insert_poly_real @ X @ nil_poly_real )
% 3.10/1.62 = ( cons_poly_real @ X @ nil_poly_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_234_lexordp__eq__simps_I3_J,axiom,
% 3.10/1.62 ! [X: poly_real,Xs: list_poly_real] :
% 3.10/1.62 ~ ( ord_le1233681790y_real @ ( cons_poly_real @ X @ Xs ) @ nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_235_rotate1_Osimps_I2_J,axiom,
% 3.10/1.62 ! [X: poly_real,Xs: list_poly_real] :
% 3.10/1.62 ( ( rotate1_poly_real @ ( cons_poly_real @ X @ Xs ) )
% 3.10/1.62 = ( append_poly_real @ Xs @ ( cons_poly_real @ X @ nil_poly_real ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_236_bind__simps_I2_J,axiom,
% 3.10/1.62 ! [X: poly_real,Xs: list_poly_real,F: poly_real > list_poly_real] :
% 3.10/1.62 ( ( bind_p420216945y_real @ ( cons_poly_real @ X @ Xs ) @ F )
% 3.10/1.62 = ( append_poly_real @ ( F @ X ) @ ( bind_p420216945y_real @ Xs @ F ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_237_gen__length__code_I2_J,axiom,
% 3.10/1.62 ! [N: nat,X: poly_real,Xs: list_poly_real] :
% 3.10/1.62 ( ( gen_length_poly_real @ N @ ( cons_poly_real @ X @ Xs ) )
% 3.10/1.62 = ( gen_length_poly_real @ ( suc @ N ) @ Xs ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_238_append__Nil2,axiom,
% 3.10/1.62 ! [Xs: list_poly_real] :
% 3.10/1.62 ( ( append_poly_real @ Xs @ nil_poly_real )
% 3.10/1.62 = Xs ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_239_append__self__conv,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 3.10/1.62 ( ( ( append_poly_real @ Xs @ Ys )
% 3.10/1.62 = Xs )
% 3.10/1.62 = ( Ys = nil_poly_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_240_self__append__conv,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 3.10/1.62 ( ( Xs
% 3.10/1.62 = ( append_poly_real @ Xs @ Ys ) )
% 3.10/1.62 = ( Ys = nil_poly_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_241_append__self__conv2,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 3.10/1.62 ( ( ( append_poly_real @ Xs @ Ys )
% 3.10/1.62 = Ys )
% 3.10/1.62 = ( Xs = nil_poly_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_242_self__append__conv2,axiom,
% 3.10/1.62 ! [Ys: list_poly_real,Xs: list_poly_real] :
% 3.10/1.62 ( ( Ys
% 3.10/1.62 = ( append_poly_real @ Xs @ Ys ) )
% 3.10/1.62 = ( Xs = nil_poly_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_243_Nil__is__append__conv,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 3.10/1.62 ( ( nil_poly_real
% 3.10/1.62 = ( append_poly_real @ Xs @ Ys ) )
% 3.10/1.62 = ( ( Xs = nil_poly_real )
% 3.10/1.62 & ( Ys = nil_poly_real ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_244_append__is__Nil__conv,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 3.10/1.62 ( ( ( append_poly_real @ Xs @ Ys )
% 3.10/1.62 = nil_poly_real )
% 3.10/1.62 = ( ( Xs = nil_poly_real )
% 3.10/1.62 & ( Ys = nil_poly_real ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_245_append_Oright__neutral,axiom,
% 3.10/1.62 ! [A3: list_poly_real] :
% 3.10/1.62 ( ( append_poly_real @ A3 @ nil_poly_real )
% 3.10/1.62 = A3 ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_246_lexordp__eq__simps_I2_J,axiom,
% 3.10/1.62 ! [Xs: list_poly_real] :
% 3.10/1.62 ( ( ord_le1233681790y_real @ Xs @ nil_poly_real )
% 3.10/1.62 = ( Xs = nil_poly_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_247_lexordp__eq__simps_I1_J,axiom,
% 3.10/1.62 ! [Ys: list_poly_real] : ( ord_le1233681790y_real @ nil_poly_real @ Ys ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_248_append1__eq__conv,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,X: poly_real,Ys: list_poly_real,Y: poly_real] :
% 3.10/1.62 ( ( ( append_poly_real @ Xs @ ( cons_poly_real @ X @ nil_poly_real ) )
% 3.10/1.62 = ( append_poly_real @ Ys @ ( cons_poly_real @ Y @ nil_poly_real ) ) )
% 3.10/1.62 = ( ( Xs = Ys )
% 3.10/1.62 & ( X = Y ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_249_Cons__eq__appendI,axiom,
% 3.10/1.62 ! [X: poly_real,Xs1: list_poly_real,Ys: list_poly_real,Xs: list_poly_real,Zs2: list_poly_real] :
% 3.10/1.62 ( ( ( cons_poly_real @ X @ Xs1 )
% 3.10/1.62 = Ys )
% 3.10/1.62 => ( ( Xs
% 3.10/1.62 = ( append_poly_real @ Xs1 @ Zs2 ) )
% 3.10/1.62 => ( ( cons_poly_real @ X @ Xs )
% 3.10/1.62 = ( append_poly_real @ Ys @ Zs2 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_250_append__Cons,axiom,
% 3.10/1.62 ! [X: poly_real,Xs: list_poly_real,Ys: list_poly_real] :
% 3.10/1.62 ( ( append_poly_real @ ( cons_poly_real @ X @ Xs ) @ Ys )
% 3.10/1.62 = ( cons_poly_real @ X @ ( append_poly_real @ Xs @ Ys ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_251_eq__Nil__appendI,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 3.10/1.62 ( ( Xs = Ys )
% 3.10/1.62 => ( Xs
% 3.10/1.62 = ( append_poly_real @ nil_poly_real @ Ys ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_252_append__Nil,axiom,
% 3.10/1.62 ! [Ys: list_poly_real] :
% 3.10/1.62 ( ( append_poly_real @ nil_poly_real @ Ys )
% 3.10/1.62 = Ys ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_253_append_Oleft__neutral,axiom,
% 3.10/1.62 ! [A3: list_poly_real] :
% 3.10/1.62 ( ( append_poly_real @ nil_poly_real @ A3 )
% 3.10/1.62 = A3 ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_254_lexordp__eq_ONil,axiom,
% 3.10/1.62 ! [Ys: list_poly_real] : ( ord_le1233681790y_real @ nil_poly_real @ Ys ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_255_rev__induct,axiom,
% 3.10/1.62 ! [P3: list_poly_real > $o,Xs: list_poly_real] :
% 3.10/1.62 ( ( P3 @ nil_poly_real )
% 3.10/1.62 => ( ! [X3: poly_real,Xs2: list_poly_real] :
% 3.10/1.62 ( ( P3 @ Xs2 )
% 3.10/1.62 => ( P3 @ ( append_poly_real @ Xs2 @ ( cons_poly_real @ X3 @ nil_poly_real ) ) ) )
% 3.10/1.62 => ( P3 @ Xs ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_256_rev__exhaust,axiom,
% 3.10/1.62 ! [Xs: list_poly_real] :
% 3.10/1.62 ( ( Xs != nil_poly_real )
% 3.10/1.62 => ~ ! [Ys2: list_poly_real,Y2: poly_real] :
% 3.10/1.62 ( Xs
% 3.10/1.62 != ( append_poly_real @ Ys2 @ ( cons_poly_real @ Y2 @ nil_poly_real ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_257_Cons__eq__append__conv,axiom,
% 3.10/1.62 ! [X: poly_real,Xs: list_poly_real,Ys: list_poly_real,Zs2: list_poly_real] :
% 3.10/1.62 ( ( ( cons_poly_real @ X @ Xs )
% 3.10/1.62 = ( append_poly_real @ Ys @ Zs2 ) )
% 3.10/1.62 = ( ( ( Ys = nil_poly_real )
% 3.10/1.62 & ( ( cons_poly_real @ X @ Xs )
% 3.10/1.62 = Zs2 ) )
% 3.10/1.62 | ? [Ys4: list_poly_real] :
% 3.10/1.62 ( ( ( cons_poly_real @ X @ Ys4 )
% 3.10/1.62 = Ys )
% 3.10/1.62 & ( Xs
% 3.10/1.62 = ( append_poly_real @ Ys4 @ Zs2 ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_258_append__eq__Cons__conv,axiom,
% 3.10/1.62 ! [Ys: list_poly_real,Zs2: list_poly_real,X: poly_real,Xs: list_poly_real] :
% 3.10/1.62 ( ( ( append_poly_real @ Ys @ Zs2 )
% 3.10/1.62 = ( cons_poly_real @ X @ Xs ) )
% 3.10/1.62 = ( ( ( Ys = nil_poly_real )
% 3.10/1.62 & ( Zs2
% 3.10/1.62 = ( cons_poly_real @ X @ Xs ) ) )
% 3.10/1.62 | ? [Ys4: list_poly_real] :
% 3.10/1.62 ( ( Ys
% 3.10/1.62 = ( cons_poly_real @ X @ Ys4 ) )
% 3.10/1.62 & ( ( append_poly_real @ Ys4 @ Zs2 )
% 3.10/1.62 = Xs ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_259_rev__nonempty__induct,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,P3: list_poly_real > $o] :
% 3.10/1.62 ( ( Xs != nil_poly_real )
% 3.10/1.62 => ( ! [X3: poly_real] : ( P3 @ ( cons_poly_real @ X3 @ nil_poly_real ) )
% 3.10/1.62 => ( ! [X3: poly_real,Xs2: list_poly_real] :
% 3.10/1.62 ( ( Xs2 != nil_poly_real )
% 3.10/1.62 => ( ( P3 @ Xs2 )
% 3.10/1.62 => ( P3 @ ( append_poly_real @ Xs2 @ ( cons_poly_real @ X3 @ nil_poly_real ) ) ) ) )
% 3.10/1.62 => ( P3 @ Xs ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_260_maps__simps_I1_J,axiom,
% 3.10/1.62 ! [F: poly_real > list_poly_real,X: poly_real,Xs: list_poly_real] :
% 3.10/1.62 ( ( maps_p961674027y_real @ F @ ( cons_poly_real @ X @ Xs ) )
% 3.10/1.62 = ( append_poly_real @ ( F @ X ) @ ( maps_p961674027y_real @ F @ Xs ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_261_old_Onat_Oinject,axiom,
% 3.10/1.62 ! [Nat: nat,Nat2: nat] :
% 3.10/1.62 ( ( ( suc @ Nat )
% 3.10/1.62 = ( suc @ Nat2 ) )
% 3.10/1.62 = ( Nat = Nat2 ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_262_nat_Oinject,axiom,
% 3.10/1.62 ! [X2: nat,Y23: nat] :
% 3.10/1.62 ( ( ( suc @ X2 )
% 3.10/1.62 = ( suc @ Y23 ) )
% 3.10/1.62 = ( X2 = Y23 ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_263_product__lists_Osimps_I1_J,axiom,
% 3.10/1.62 ( ( produc523415045y_real @ nil_list_poly_real )
% 3.10/1.62 = ( cons_list_poly_real @ nil_poly_real @ nil_list_poly_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_264_subseqs_Osimps_I1_J,axiom,
% 3.10/1.62 ( ( subseqs_poly_real @ nil_poly_real )
% 3.10/1.62 = ( cons_list_poly_real @ nil_poly_real @ nil_list_poly_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_265_concat__eq__append__conv,axiom,
% 3.10/1.62 ! [Xss2: list_list_poly_real,Ys: list_poly_real,Zs2: list_poly_real] :
% 3.10/1.62 ( ( ( concat_poly_real @ Xss2 )
% 3.10/1.62 = ( append_poly_real @ Ys @ Zs2 ) )
% 3.10/1.62 = ( ( ( Xss2 = nil_list_poly_real )
% 3.10/1.62 => ( ( Ys = nil_poly_real )
% 3.10/1.62 & ( Zs2 = nil_poly_real ) ) )
% 3.10/1.62 & ( ( Xss2 != nil_list_poly_real )
% 3.10/1.62 => ? [Xss1: list_list_poly_real,Xs3: list_poly_real,Xs4: list_poly_real,Xss22: list_list_poly_real] :
% 3.10/1.62 ( ( Xss2
% 3.10/1.62 = ( append527544425y_real @ Xss1 @ ( cons_list_poly_real @ ( append_poly_real @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 3.10/1.62 & ( Ys
% 3.10/1.62 = ( append_poly_real @ ( concat_poly_real @ Xss1 ) @ Xs3 ) )
% 3.10/1.62 & ( Zs2
% 3.10/1.62 = ( append_poly_real @ Xs4 @ ( concat_poly_real @ Xss22 ) ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_266_concat_Osimps_I1_J,axiom,
% 3.10/1.62 ( ( concat_poly_real @ nil_list_poly_real )
% 3.10/1.62 = nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_267_Suc__inject,axiom,
% 3.10/1.62 ! [X: nat,Y: nat] :
% 3.10/1.62 ( ( ( suc @ X )
% 3.10/1.62 = ( suc @ Y ) )
% 3.10/1.62 => ( X = Y ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_268_n__not__Suc__n,axiom,
% 3.10/1.62 ! [N: nat] :
% 3.10/1.62 ( N
% 3.10/1.62 != ( suc @ N ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_269_butlast__snoc,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,X: poly_real] :
% 3.10/1.62 ( ( butlast_poly_real @ ( append_poly_real @ Xs @ ( cons_poly_real @ X @ nil_poly_real ) ) )
% 3.10/1.62 = Xs ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_270_enumerate__simps_I2_J,axiom,
% 3.10/1.62 ! [N: nat,X: poly_real,Xs: list_poly_real] :
% 3.10/1.62 ( ( enumerate_poly_real @ N @ ( cons_poly_real @ X @ Xs ) )
% 3.10/1.62 = ( cons_P1027346459y_real @ ( produc404352541y_real @ N @ X ) @ ( enumerate_poly_real @ ( suc @ N ) @ Xs ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_271_last__snoc,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,X: poly_real] :
% 3.10/1.62 ( ( last_poly_real @ ( append_poly_real @ Xs @ ( cons_poly_real @ X @ nil_poly_real ) ) )
% 3.10/1.62 = X ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_272_plus__coeffs_Osimps_I2_J,axiom,
% 3.10/1.62 ! [V2: poly_real,Va2: list_poly_real] :
% 3.10/1.62 ( ( plus_c288199817y_real @ nil_poly_real @ ( cons_poly_real @ V2 @ Va2 ) )
% 3.10/1.62 = ( cons_poly_real @ V2 @ Va2 ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_273_last__appendL,axiom,
% 3.10/1.62 ! [Ys: list_poly_real,Xs: list_poly_real] :
% 3.10/1.62 ( ( Ys = nil_poly_real )
% 3.10/1.62 => ( ( last_poly_real @ ( append_poly_real @ Xs @ Ys ) )
% 3.10/1.62 = ( last_poly_real @ Xs ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_274_last__appendR,axiom,
% 3.10/1.62 ! [Ys: list_poly_real,Xs: list_poly_real] :
% 3.10/1.62 ( ( Ys != nil_poly_real )
% 3.10/1.62 => ( ( last_poly_real @ ( append_poly_real @ Xs @ Ys ) )
% 3.10/1.62 = ( last_poly_real @ Ys ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_275_zip__Cons__Cons,axiom,
% 3.10/1.62 ! [X: poly_real,Xs: list_poly_real,Y: poly_real,Ys: list_poly_real] :
% 3.10/1.62 ( ( zip_po657915297y_real @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ Y @ Ys ) )
% 3.10/1.62 = ( cons_P1129399039y_real @ ( produc1867601537y_real @ X @ Y ) @ ( zip_po657915297y_real @ Xs @ Ys ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_276_append__butlast__last__id,axiom,
% 3.10/1.62 ! [Xs: list_poly_real] :
% 3.10/1.62 ( ( Xs != nil_poly_real )
% 3.10/1.62 => ( ( append_poly_real @ ( butlast_poly_real @ Xs ) @ ( cons_poly_real @ ( last_poly_real @ Xs ) @ nil_poly_real ) )
% 3.10/1.62 = Xs ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_277_butlast_Osimps_I1_J,axiom,
% 3.10/1.62 ( ( butlast_poly_real @ nil_poly_real )
% 3.10/1.62 = nil_poly_real ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_278_snoc__eq__iff__butlast,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,X: poly_real,Ys: list_poly_real] :
% 3.10/1.62 ( ( ( append_poly_real @ Xs @ ( cons_poly_real @ X @ nil_poly_real ) )
% 3.10/1.62 = Ys )
% 3.10/1.62 = ( ( Ys != nil_poly_real )
% 3.10/1.62 & ( ( butlast_poly_real @ Ys )
% 3.10/1.62 = Xs )
% 3.10/1.62 & ( ( last_poly_real @ Ys )
% 3.10/1.62 = X ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_279_last_Osimps,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,X: poly_real] :
% 3.10/1.62 ( ( ( Xs = nil_poly_real )
% 3.10/1.62 => ( ( last_poly_real @ ( cons_poly_real @ X @ Xs ) )
% 3.10/1.62 = X ) )
% 3.10/1.62 & ( ( Xs != nil_poly_real )
% 3.10/1.62 => ( ( last_poly_real @ ( cons_poly_real @ X @ Xs ) )
% 3.10/1.62 = ( last_poly_real @ Xs ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_280_last__ConsL,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,X: poly_real] :
% 3.10/1.62 ( ( Xs = nil_poly_real )
% 3.10/1.62 => ( ( last_poly_real @ ( cons_poly_real @ X @ Xs ) )
% 3.10/1.62 = X ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_281_last__ConsR,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,X: poly_real] :
% 3.10/1.62 ( ( Xs != nil_poly_real )
% 3.10/1.62 => ( ( last_poly_real @ ( cons_poly_real @ X @ Xs ) )
% 3.10/1.62 = ( last_poly_real @ Xs ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_282_zip__eq__ConsE,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,Ys: list_poly_real,Xy: produc461822025y_real,Xys: list_P693436111y_real] :
% 3.10/1.62 ( ( ( zip_po657915297y_real @ Xs @ Ys )
% 3.10/1.62 = ( cons_P1129399039y_real @ Xy @ Xys ) )
% 3.10/1.62 => ~ ! [X3: poly_real,Xs5: list_poly_real] :
% 3.10/1.62 ( ( Xs
% 3.10/1.62 = ( cons_poly_real @ X3 @ Xs5 ) )
% 3.10/1.62 => ! [Y2: poly_real,Ys5: list_poly_real] :
% 3.10/1.62 ( ( Ys
% 3.10/1.62 = ( cons_poly_real @ Y2 @ Ys5 ) )
% 3.10/1.62 => ( ( Xy
% 3.10/1.62 = ( produc1867601537y_real @ X3 @ Y2 ) )
% 3.10/1.62 => ( Xys
% 3.10/1.62 != ( zip_po657915297y_real @ Xs5 @ Ys5 ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_283_plus__coeffs_Osimps_I1_J,axiom,
% 3.10/1.62 ! [Xs: list_poly_real] :
% 3.10/1.62 ( ( plus_c288199817y_real @ Xs @ nil_poly_real )
% 3.10/1.62 = Xs ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_284_last__append,axiom,
% 3.10/1.62 ! [Ys: list_poly_real,Xs: list_poly_real] :
% 3.10/1.62 ( ( ( Ys = nil_poly_real )
% 3.10/1.62 => ( ( last_poly_real @ ( append_poly_real @ Xs @ Ys ) )
% 3.10/1.62 = ( last_poly_real @ Xs ) ) )
% 3.10/1.62 & ( ( Ys != nil_poly_real )
% 3.10/1.62 => ( ( last_poly_real @ ( append_poly_real @ Xs @ Ys ) )
% 3.10/1.62 = ( last_poly_real @ Ys ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_285_longest__common__suffix,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 3.10/1.62 ? [Ss: list_poly_real,Xs5: list_poly_real,Ys5: list_poly_real] :
% 3.10/1.62 ( ( Xs
% 3.10/1.62 = ( append_poly_real @ Xs5 @ Ss ) )
% 3.10/1.62 & ( Ys
% 3.10/1.62 = ( append_poly_real @ Ys5 @ Ss ) )
% 3.10/1.62 & ( ( Xs5 = nil_poly_real )
% 3.10/1.62 | ( Ys5 = nil_poly_real )
% 3.10/1.62 | ( ( last_poly_real @ Xs5 )
% 3.10/1.62 != ( last_poly_real @ Ys5 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_286_butlast_Osimps_I2_J,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,X: poly_real] :
% 3.10/1.62 ( ( ( Xs = nil_poly_real )
% 3.10/1.62 => ( ( butlast_poly_real @ ( cons_poly_real @ X @ Xs ) )
% 3.10/1.62 = nil_poly_real ) )
% 3.10/1.62 & ( ( Xs != nil_poly_real )
% 3.10/1.62 => ( ( butlast_poly_real @ ( cons_poly_real @ X @ Xs ) )
% 3.10/1.62 = ( cons_poly_real @ X @ ( butlast_poly_real @ Xs ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_287_butlast__append,axiom,
% 3.10/1.62 ! [Ys: list_poly_real,Xs: list_poly_real] :
% 3.10/1.62 ( ( ( Ys = nil_poly_real )
% 3.10/1.62 => ( ( butlast_poly_real @ ( append_poly_real @ Xs @ Ys ) )
% 3.10/1.62 = ( butlast_poly_real @ Xs ) ) )
% 3.10/1.62 & ( ( Ys != nil_poly_real )
% 3.10/1.62 => ( ( butlast_poly_real @ ( append_poly_real @ Xs @ Ys ) )
% 3.10/1.62 = ( append_poly_real @ Xs @ ( butlast_poly_real @ Ys ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_288_snoc__listrel1__snoc__iff,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,X: poly_real,Ys: list_poly_real,Y: poly_real,R: set_Pr483210409y_real] :
% 3.10/1.62 ( ( member403334290y_real @ ( produc1000427809y_real @ ( append_poly_real @ Xs @ ( cons_poly_real @ X @ nil_poly_real ) ) @ ( append_poly_real @ Ys @ ( cons_poly_real @ Y @ nil_poly_real ) ) ) @ ( listrel1_poly_real @ R ) )
% 3.10/1.62 = ( ( ( member403334290y_real @ ( produc1000427809y_real @ Xs @ Ys ) @ ( listrel1_poly_real @ R ) )
% 3.10/1.62 & ( X = Y ) )
% 3.10/1.62 | ( ( Xs = Ys )
% 3.10/1.62 & ( member1784523250y_real @ ( produc1867601537y_real @ X @ Y ) @ R ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_289_last__zip,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 3.10/1.62 ( ( Xs != nil_poly_real )
% 3.10/1.62 => ( ( Ys != nil_poly_real )
% 3.10/1.62 => ( ( ( size_s259235672y_real @ Xs )
% 3.10/1.62 = ( size_s259235672y_real @ Ys ) )
% 3.10/1.62 => ( ( last_P21901160y_real @ ( zip_po657915297y_real @ Xs @ Ys ) )
% 3.10/1.62 = ( produc1867601537y_real @ ( last_poly_real @ Xs ) @ ( last_poly_real @ Ys ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_290_concat__conv__foldr,axiom,
% 3.10/1.62 ( concat_poly_real
% 3.10/1.62 = ( ^ [Xss3: list_list_poly_real] : ( foldr_2117681201y_real @ append_poly_real @ Xss3 @ nil_poly_real ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_291_rotate__is__Nil__conv,axiom,
% 3.10/1.62 ! [N: nat,Xs: list_poly_real] :
% 3.10/1.62 ( ( ( rotate_poly_real @ N @ Xs )
% 3.10/1.62 = nil_poly_real )
% 3.10/1.62 = ( Xs = nil_poly_real ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_292_Cons__listrel1__Cons,axiom,
% 3.10/1.62 ! [X: poly_real,Xs: list_poly_real,Y: poly_real,Ys: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.62 ( ( member403334290y_real @ ( produc1000427809y_real @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ Y @ Ys ) ) @ ( listrel1_poly_real @ R ) )
% 3.10/1.62 = ( ( ( member1784523250y_real @ ( produc1867601537y_real @ X @ Y ) @ R )
% 3.10/1.62 & ( Xs = Ys ) )
% 3.10/1.62 | ( ( X = Y )
% 3.10/1.62 & ( member403334290y_real @ ( produc1000427809y_real @ Xs @ Ys ) @ ( listrel1_poly_real @ R ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_293_not__listrel1__Nil,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.62 ~ ( member403334290y_real @ ( produc1000427809y_real @ Xs @ nil_poly_real ) @ ( listrel1_poly_real @ R ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_294_not__Nil__listrel1,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.62 ~ ( member403334290y_real @ ( produc1000427809y_real @ nil_poly_real @ Xs ) @ ( listrel1_poly_real @ R ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_295_listrel1I2,axiom,
% 3.10/1.62 ! [Xs: list_poly_real,Ys: list_poly_real,R: set_Pr483210409y_real,X: poly_real] :
% 3.10/1.62 ( ( member403334290y_real @ ( produc1000427809y_real @ Xs @ Ys ) @ ( listrel1_poly_real @ R ) )
% 3.10/1.62 => ( member403334290y_real @ ( produc1000427809y_real @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ X @ Ys ) ) @ ( listrel1_poly_real @ R ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_296_successively_Ocases,axiom,
% 3.10/1.62 ! [X: produc1060019729y_real] :
% 3.10/1.62 ( ! [P4: poly_real > poly_real > $o] :
% 3.10/1.62 ( X
% 3.10/1.62 != ( produc1345584779y_real @ P4 @ nil_poly_real ) )
% 3.10/1.62 => ( ! [P4: poly_real > poly_real > $o,X3: poly_real] :
% 3.10/1.62 ( X
% 3.10/1.62 != ( produc1345584779y_real @ P4 @ ( cons_poly_real @ X3 @ nil_poly_real ) ) )
% 3.10/1.62 => ~ ! [P4: poly_real > poly_real > $o,X3: poly_real,Y2: poly_real,Xs2: list_poly_real] :
% 3.10/1.62 ( X
% 3.10/1.62 != ( produc1345584779y_real @ P4 @ ( cons_poly_real @ X3 @ ( cons_poly_real @ Y2 @ Xs2 ) ) ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_297_sorted__wrt_Ocases,axiom,
% 3.10/1.62 ! [X: produc1060019729y_real] :
% 3.10/1.62 ( ! [P4: poly_real > poly_real > $o] :
% 3.10/1.62 ( X
% 3.10/1.62 != ( produc1345584779y_real @ P4 @ nil_poly_real ) )
% 3.10/1.62 => ~ ! [P4: poly_real > poly_real > $o,X3: poly_real,Ys2: list_poly_real] :
% 3.10/1.62 ( X
% 3.10/1.62 != ( produc1345584779y_real @ P4 @ ( cons_poly_real @ X3 @ Ys2 ) ) ) ) ).
% 3.10/1.62
% 3.10/1.62 thf(fact_298_Suc__length__conv,axiom,
% 3.10/1.62 ! [N: nat,Xs: list_poly_real] :
% 3.10/1.62 ( ( ( suc @ N )
% 3.10/1.62 = ( size_s259235672y_real @ Xs ) )
% 3.10/1.62 = ( ? [Y3: poly_real,Ys3: list_poly_real] :
% 3.10/1.63 ( ( Xs
% 3.10/1.63 = ( cons_poly_real @ Y3 @ Ys3 ) )
% 3.10/1.63 & ( ( size_s259235672y_real @ Ys3 )
% 3.10/1.63 = N ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_299_length__Suc__conv,axiom,
% 3.10/1.63 ! [Xs: list_poly_real,N: nat] :
% 3.10/1.63 ( ( ( size_s259235672y_real @ Xs )
% 3.10/1.63 = ( suc @ N ) )
% 3.10/1.63 = ( ? [Y3: poly_real,Ys3: list_poly_real] :
% 3.10/1.63 ( ( Xs
% 3.10/1.63 = ( cons_poly_real @ Y3 @ Ys3 ) )
% 3.10/1.63 & ( ( size_s259235672y_real @ Ys3 )
% 3.10/1.63 = N ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_300_list__induct4,axiom,
% 3.10/1.63 ! [Xs: list_poly_real,Ys: list_poly_real,Zs2: list_poly_real,Ws: list_poly_real,P3: list_poly_real > list_poly_real > list_poly_real > list_poly_real > $o] :
% 3.10/1.63 ( ( ( size_s259235672y_real @ Xs )
% 3.10/1.63 = ( size_s259235672y_real @ Ys ) )
% 3.10/1.63 => ( ( ( size_s259235672y_real @ Ys )
% 3.10/1.63 = ( size_s259235672y_real @ Zs2 ) )
% 3.10/1.63 => ( ( ( size_s259235672y_real @ Zs2 )
% 3.10/1.63 = ( size_s259235672y_real @ Ws ) )
% 3.10/1.63 => ( ( P3 @ nil_poly_real @ nil_poly_real @ nil_poly_real @ nil_poly_real )
% 3.10/1.63 => ( ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real,Z: poly_real,Zs: list_poly_real,W: poly_real,Ws2: list_poly_real] :
% 3.10/1.63 ( ( ( size_s259235672y_real @ Xs2 )
% 3.10/1.63 = ( size_s259235672y_real @ Ys2 ) )
% 3.10/1.63 => ( ( ( size_s259235672y_real @ Ys2 )
% 3.10/1.63 = ( size_s259235672y_real @ Zs ) )
% 3.10/1.63 => ( ( ( size_s259235672y_real @ Zs )
% 3.10/1.63 = ( size_s259235672y_real @ Ws2 ) )
% 3.10/1.63 => ( ( P3 @ Xs2 @ Ys2 @ Zs @ Ws2 )
% 3.10/1.63 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) @ ( cons_poly_real @ Z @ Zs ) @ ( cons_poly_real @ W @ Ws2 ) ) ) ) ) )
% 3.10/1.63 => ( P3 @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_301_list__induct3,axiom,
% 3.10/1.63 ! [Xs: list_poly_real,Ys: list_poly_real,Zs2: list_poly_real,P3: list_poly_real > list_poly_real > list_poly_real > $o] :
% 3.10/1.63 ( ( ( size_s259235672y_real @ Xs )
% 3.10/1.63 = ( size_s259235672y_real @ Ys ) )
% 3.10/1.63 => ( ( ( size_s259235672y_real @ Ys )
% 3.10/1.63 = ( size_s259235672y_real @ Zs2 ) )
% 3.10/1.63 => ( ( P3 @ nil_poly_real @ nil_poly_real @ nil_poly_real )
% 3.10/1.63 => ( ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real,Z: poly_real,Zs: list_poly_real] :
% 3.10/1.63 ( ( ( size_s259235672y_real @ Xs2 )
% 3.10/1.63 = ( size_s259235672y_real @ Ys2 ) )
% 3.10/1.63 => ( ( ( size_s259235672y_real @ Ys2 )
% 3.10/1.63 = ( size_s259235672y_real @ Zs ) )
% 3.10/1.63 => ( ( P3 @ Xs2 @ Ys2 @ Zs )
% 3.10/1.63 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) @ ( cons_poly_real @ Z @ Zs ) ) ) ) )
% 3.10/1.63 => ( P3 @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_302_list__induct2,axiom,
% 3.10/1.63 ! [Xs: list_poly_real,Ys: list_poly_real,P3: list_poly_real > list_poly_real > $o] :
% 3.10/1.63 ( ( ( size_s259235672y_real @ Xs )
% 3.10/1.63 = ( size_s259235672y_real @ Ys ) )
% 3.10/1.63 => ( ( P3 @ nil_poly_real @ nil_poly_real )
% 3.10/1.63 => ( ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real] :
% 3.10/1.63 ( ( ( size_s259235672y_real @ Xs2 )
% 3.10/1.63 = ( size_s259235672y_real @ Ys2 ) )
% 3.10/1.63 => ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.63 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) )
% 3.10/1.63 => ( P3 @ Xs @ Ys ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_303_pderiv__coeffs__code_Ocases,axiom,
% 3.10/1.63 ! [X: produc796638169y_real] :
% 3.10/1.63 ( ! [F2: poly_real,X3: poly_real,Xs2: list_poly_real] :
% 3.10/1.63 ( X
% 3.10/1.63 != ( produc490255505y_real @ F2 @ ( cons_poly_real @ X3 @ Xs2 ) ) )
% 3.10/1.63 => ~ ! [F2: poly_real] :
% 3.10/1.63 ( X
% 3.10/1.63 != ( produc490255505y_real @ F2 @ nil_poly_real ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_304_shuffles_Ocases,axiom,
% 3.10/1.63 ! [X: produc1426596841y_real] :
% 3.10/1.63 ( ! [Ys2: list_poly_real] :
% 3.10/1.63 ( X
% 3.10/1.63 != ( produc1000427809y_real @ nil_poly_real @ Ys2 ) )
% 3.10/1.63 => ( ! [Xs2: list_poly_real] :
% 3.10/1.63 ( X
% 3.10/1.63 != ( produc1000427809y_real @ Xs2 @ nil_poly_real ) )
% 3.10/1.63 => ~ ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real] :
% 3.10/1.63 ( X
% 3.10/1.63 != ( produc1000427809y_real @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_305_plus__coeffs_Ocases,axiom,
% 3.10/1.63 ! [X: produc1426596841y_real] :
% 3.10/1.63 ( ! [Xs2: list_poly_real] :
% 3.10/1.63 ( X
% 3.10/1.63 != ( produc1000427809y_real @ Xs2 @ nil_poly_real ) )
% 3.10/1.63 => ( ! [V: poly_real,Va: list_poly_real] :
% 3.10/1.63 ( X
% 3.10/1.63 != ( produc1000427809y_real @ nil_poly_real @ ( cons_poly_real @ V @ Va ) ) )
% 3.10/1.63 => ~ ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real] :
% 3.10/1.63 ( X
% 3.10/1.63 != ( produc1000427809y_real @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_306_minus__poly__rev__list_Ocases,axiom,
% 3.10/1.63 ! [X: produc1426596841y_real] :
% 3.10/1.63 ( ! [X3: poly_real,Xs2: list_poly_real,Y2: poly_real,Ys2: list_poly_real] :
% 3.10/1.63 ( X
% 3.10/1.63 != ( produc1000427809y_real @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) )
% 3.10/1.63 => ( ! [Xs2: list_poly_real] :
% 3.10/1.63 ( X
% 3.10/1.63 != ( produc1000427809y_real @ Xs2 @ nil_poly_real ) )
% 3.10/1.63 => ~ ! [Y2: poly_real,Ys2: list_poly_real] :
% 3.10/1.63 ( X
% 3.10/1.63 != ( produc1000427809y_real @ nil_poly_real @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_307_Cons__listrel1E2,axiom,
% 3.10/1.63 ! [Xs: list_poly_real,Y: poly_real,Ys: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ( ( member403334290y_real @ ( produc1000427809y_real @ Xs @ ( cons_poly_real @ Y @ Ys ) ) @ ( listrel1_poly_real @ R ) )
% 3.10/1.63 => ( ! [X3: poly_real] :
% 3.10/1.63 ( ( Xs
% 3.10/1.63 = ( cons_poly_real @ X3 @ Ys ) )
% 3.10/1.63 => ~ ( member1784523250y_real @ ( produc1867601537y_real @ X3 @ Y ) @ R ) )
% 3.10/1.63 => ~ ! [Zs: list_poly_real] :
% 3.10/1.63 ( ( Xs
% 3.10/1.63 = ( cons_poly_real @ Y @ Zs ) )
% 3.10/1.63 => ~ ( member403334290y_real @ ( produc1000427809y_real @ Zs @ Ys ) @ ( listrel1_poly_real @ R ) ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_308_Cons__listrel1E1,axiom,
% 3.10/1.63 ! [X: poly_real,Xs: list_poly_real,Ys: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ( ( member403334290y_real @ ( produc1000427809y_real @ ( cons_poly_real @ X @ Xs ) @ Ys ) @ ( listrel1_poly_real @ R ) )
% 3.10/1.63 => ( ! [Y2: poly_real] :
% 3.10/1.63 ( ( Ys
% 3.10/1.63 = ( cons_poly_real @ Y2 @ Xs ) )
% 3.10/1.63 => ~ ( member1784523250y_real @ ( produc1867601537y_real @ X @ Y2 ) @ R ) )
% 3.10/1.63 => ~ ! [Zs: list_poly_real] :
% 3.10/1.63 ( ( Ys
% 3.10/1.63 = ( cons_poly_real @ X @ Zs ) )
% 3.10/1.63 => ~ ( member403334290y_real @ ( produc1000427809y_real @ Xs @ Zs ) @ ( listrel1_poly_real @ R ) ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_309_listrel1I1,axiom,
% 3.10/1.63 ! [X: poly_real,Y: poly_real,R: set_Pr483210409y_real,Xs: list_poly_real] :
% 3.10/1.63 ( ( member1784523250y_real @ ( produc1867601537y_real @ X @ Y ) @ R )
% 3.10/1.63 => ( member403334290y_real @ ( produc1000427809y_real @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ Y @ Xs ) ) @ ( listrel1_poly_real @ R ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_310_same__length__different,axiom,
% 3.10/1.63 ! [Xs: list_poly_real,Ys: list_poly_real] :
% 3.10/1.63 ( ( Xs != Ys )
% 3.10/1.63 => ( ( ( size_s259235672y_real @ Xs )
% 3.10/1.63 = ( size_s259235672y_real @ Ys ) )
% 3.10/1.63 => ? [Pre: list_poly_real,X3: poly_real,Xs5: list_poly_real,Y2: poly_real,Ys5: list_poly_real] :
% 3.10/1.63 ( ( X3 != Y2 )
% 3.10/1.63 & ( Xs
% 3.10/1.63 = ( append_poly_real @ Pre @ ( append_poly_real @ ( cons_poly_real @ X3 @ nil_poly_real ) @ Xs5 ) ) )
% 3.10/1.63 & ( Ys
% 3.10/1.63 = ( append_poly_real @ Pre @ ( append_poly_real @ ( cons_poly_real @ Y2 @ nil_poly_real ) @ Ys5 ) ) ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_311_listrel1E,axiom,
% 3.10/1.63 ! [Xs: list_poly_real,Ys: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ( ( member403334290y_real @ ( produc1000427809y_real @ Xs @ Ys ) @ ( listrel1_poly_real @ R ) )
% 3.10/1.63 => ~ ! [X3: poly_real,Y2: poly_real] :
% 3.10/1.63 ( ( member1784523250y_real @ ( produc1867601537y_real @ X3 @ Y2 ) @ R )
% 3.10/1.63 => ! [Us: list_poly_real,Vs: list_poly_real] :
% 3.10/1.63 ( ( Xs
% 3.10/1.63 = ( append_poly_real @ Us @ ( cons_poly_real @ X3 @ Vs ) ) )
% 3.10/1.63 => ( Ys
% 3.10/1.63 != ( append_poly_real @ Us @ ( cons_poly_real @ Y2 @ Vs ) ) ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_312_listrel1I,axiom,
% 3.10/1.63 ! [X: poly_real,Y: poly_real,R: set_Pr483210409y_real,Xs: list_poly_real,Us2: list_poly_real,Vs2: list_poly_real,Ys: list_poly_real] :
% 3.10/1.63 ( ( member1784523250y_real @ ( produc1867601537y_real @ X @ Y ) @ R )
% 3.10/1.63 => ( ( Xs
% 3.10/1.63 = ( append_poly_real @ Us2 @ ( cons_poly_real @ X @ Vs2 ) ) )
% 3.10/1.63 => ( ( Ys
% 3.10/1.63 = ( append_poly_real @ Us2 @ ( cons_poly_real @ Y @ Vs2 ) ) )
% 3.10/1.63 => ( member403334290y_real @ ( produc1000427809y_real @ Xs @ Ys ) @ ( listrel1_poly_real @ R ) ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_313_length__append__singleton,axiom,
% 3.10/1.63 ! [Xs: list_poly_real,X: poly_real] :
% 3.10/1.63 ( ( size_s259235672y_real @ ( append_poly_real @ Xs @ ( cons_poly_real @ X @ nil_poly_real ) ) )
% 3.10/1.63 = ( suc @ ( size_s259235672y_real @ Xs ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_314_subset__eq__mset__impl_Ocases,axiom,
% 3.10/1.63 ! [X: produc1426596841y_real] :
% 3.10/1.63 ( ! [Ys2: list_poly_real] :
% 3.10/1.63 ( X
% 3.10/1.63 != ( produc1000427809y_real @ nil_poly_real @ Ys2 ) )
% 3.10/1.63 => ~ ! [X3: poly_real,Xs2: list_poly_real,Ys2: list_poly_real] :
% 3.10/1.63 ( X
% 3.10/1.63 != ( produc1000427809y_real @ ( cons_poly_real @ X3 @ Xs2 ) @ Ys2 ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_315_length__Cons,axiom,
% 3.10/1.63 ! [X: poly_real,Xs: list_poly_real] :
% 3.10/1.63 ( ( size_s259235672y_real @ ( cons_poly_real @ X @ Xs ) )
% 3.10/1.63 = ( suc @ ( size_s259235672y_real @ Xs ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_316_Cons__in__lex,axiom,
% 3.10/1.63 ! [X: poly_real,Xs: list_poly_real,Y: poly_real,Ys: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ( ( member403334290y_real @ ( produc1000427809y_real @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ Y @ Ys ) ) @ ( lex_poly_real @ R ) )
% 3.10/1.63 = ( ( ( member1784523250y_real @ ( produc1867601537y_real @ X @ Y ) @ R )
% 3.10/1.63 & ( ( size_s259235672y_real @ Xs )
% 3.10/1.63 = ( size_s259235672y_real @ Ys ) ) )
% 3.10/1.63 | ( ( X = Y )
% 3.10/1.63 & ( member403334290y_real @ ( produc1000427809y_real @ Xs @ Ys ) @ ( lex_poly_real @ R ) ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_317_Nil2__notin__lex,axiom,
% 3.10/1.63 ! [Xs: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ~ ( member403334290y_real @ ( produc1000427809y_real @ Xs @ nil_poly_real ) @ ( lex_poly_real @ R ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_318_Nil__notin__lex,axiom,
% 3.10/1.63 ! [Ys: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ~ ( member403334290y_real @ ( produc1000427809y_real @ nil_poly_real @ Ys ) @ ( lex_poly_real @ R ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_319_SuccD,axiom,
% 3.10/1.63 ! [K: poly_real,Kl: set_list_poly_real,Kl2: list_poly_real] :
% 3.10/1.63 ( ( member_poly_real2 @ K @ ( bNF_Gr1644259033y_real @ Kl @ Kl2 ) )
% 3.10/1.63 => ( member708095579y_real @ ( append_poly_real @ Kl2 @ ( cons_poly_real @ K @ nil_poly_real ) ) @ Kl ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_320_SuccI,axiom,
% 3.10/1.63 ! [Kl2: list_poly_real,K: poly_real,Kl: set_list_poly_real] :
% 3.10/1.63 ( ( member708095579y_real @ ( append_poly_real @ Kl2 @ ( cons_poly_real @ K @ nil_poly_real ) ) @ Kl )
% 3.10/1.63 => ( member_poly_real2 @ K @ ( bNF_Gr1644259033y_real @ Kl @ Kl2 ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_321_empty__Shift,axiom,
% 3.10/1.63 ! [Kl: set_list_poly_real,K: poly_real] :
% 3.10/1.63 ( ( member708095579y_real @ nil_poly_real @ Kl )
% 3.10/1.63 => ( ( member_poly_real2 @ K @ ( bNF_Gr1644259033y_real @ Kl @ nil_poly_real ) )
% 3.10/1.63 => ( member708095579y_real @ nil_poly_real @ ( bNF_Gr851617109y_real @ Kl @ K ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_322_Succ__Shift,axiom,
% 3.10/1.63 ! [Kl: set_list_poly_real,K: poly_real,Kl2: list_poly_real] :
% 3.10/1.63 ( ( bNF_Gr1644259033y_real @ ( bNF_Gr851617109y_real @ Kl @ K ) @ Kl2 )
% 3.10/1.63 = ( bNF_Gr1644259033y_real @ Kl @ ( cons_poly_real @ K @ Kl2 ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_323_ShiftD,axiom,
% 3.10/1.63 ! [Kl2: list_poly_real,Kl: set_list_poly_real,K: poly_real] :
% 3.10/1.63 ( ( member708095579y_real @ Kl2 @ ( bNF_Gr851617109y_real @ Kl @ K ) )
% 3.10/1.63 => ( member708095579y_real @ ( cons_poly_real @ K @ Kl2 ) @ Kl ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_324_Suc__mult__cancel1,axiom,
% 3.10/1.63 ! [K: nat,M: nat,N: nat] :
% 3.10/1.63 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 3.10/1.63 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 3.10/1.63 = ( M = N ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_325_lexord__append__left__rightI,axiom,
% 3.10/1.63 ! [A3: poly_real,B: poly_real,R: set_Pr483210409y_real,U: list_poly_real,X: list_poly_real,Y: list_poly_real] :
% 3.10/1.63 ( ( member1784523250y_real @ ( produc1867601537y_real @ A3 @ B ) @ R )
% 3.10/1.63 => ( member403334290y_real @ ( produc1000427809y_real @ ( append_poly_real @ U @ ( cons_poly_real @ A3 @ X ) ) @ ( append_poly_real @ U @ ( cons_poly_real @ B @ Y ) ) ) @ ( lexord_poly_real @ R ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_326_listrel_Oinducts,axiom,
% 3.10/1.63 ! [X1: list_poly_real,X2: list_poly_real,R: set_Pr483210409y_real,P3: list_poly_real > list_poly_real > $o] :
% 3.10/1.63 ( ( member403334290y_real @ ( produc1000427809y_real @ X1 @ X2 ) @ ( listre572247515y_real @ R ) )
% 3.10/1.63 => ( ( P3 @ nil_poly_real @ nil_poly_real )
% 3.10/1.63 => ( ! [X3: poly_real,Y2: poly_real,Xs2: list_poly_real,Ys2: list_poly_real] :
% 3.10/1.63 ( ( member1784523250y_real @ ( produc1867601537y_real @ X3 @ Y2 ) @ R )
% 3.10/1.63 => ( ( member403334290y_real @ ( produc1000427809y_real @ Xs2 @ Ys2 ) @ ( listre572247515y_real @ R ) )
% 3.10/1.63 => ( ( P3 @ Xs2 @ Ys2 )
% 3.10/1.63 => ( P3 @ ( cons_poly_real @ X3 @ Xs2 ) @ ( cons_poly_real @ Y2 @ Ys2 ) ) ) ) )
% 3.10/1.63 => ( P3 @ X1 @ X2 ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_327_lexord__cons__cons,axiom,
% 3.10/1.63 ! [A3: poly_real,X: list_poly_real,B: poly_real,Y: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ( ( member403334290y_real @ ( produc1000427809y_real @ ( cons_poly_real @ A3 @ X ) @ ( cons_poly_real @ B @ Y ) ) @ ( lexord_poly_real @ R ) )
% 3.10/1.63 = ( ( member1784523250y_real @ ( produc1867601537y_real @ A3 @ B ) @ R )
% 3.10/1.63 | ( ( A3 = B )
% 3.10/1.63 & ( member403334290y_real @ ( produc1000427809y_real @ X @ Y ) @ ( lexord_poly_real @ R ) ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_328_lexord__Nil__left,axiom,
% 3.10/1.63 ! [Y: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ( ( member403334290y_real @ ( produc1000427809y_real @ nil_poly_real @ Y ) @ ( lexord_poly_real @ R ) )
% 3.10/1.63 = ( ? [A5: poly_real,X4: list_poly_real] :
% 3.10/1.63 ( Y
% 3.10/1.63 = ( cons_poly_real @ A5 @ X4 ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_329_lexord__Nil__right,axiom,
% 3.10/1.63 ! [X: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ~ ( member403334290y_real @ ( produc1000427809y_real @ X @ nil_poly_real ) @ ( lexord_poly_real @ R ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_330_listrel__Nil2,axiom,
% 3.10/1.63 ! [Xs: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ( ( member403334290y_real @ ( produc1000427809y_real @ Xs @ nil_poly_real ) @ ( listre572247515y_real @ R ) )
% 3.10/1.63 => ( Xs = nil_poly_real ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_331_listrel__Nil1,axiom,
% 3.10/1.63 ! [Xs: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ( ( member403334290y_real @ ( produc1000427809y_real @ nil_poly_real @ Xs ) @ ( listre572247515y_real @ R ) )
% 3.10/1.63 => ( Xs = nil_poly_real ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_332_listrel_ONil,axiom,
% 3.10/1.63 ! [R: set_Pr483210409y_real] : ( member403334290y_real @ ( produc1000427809y_real @ nil_poly_real @ nil_poly_real ) @ ( listre572247515y_real @ R ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_333_listrel__Cons2,axiom,
% 3.10/1.63 ! [Xs: list_poly_real,Y: poly_real,Ys: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ( ( member403334290y_real @ ( produc1000427809y_real @ Xs @ ( cons_poly_real @ Y @ Ys ) ) @ ( listre572247515y_real @ R ) )
% 3.10/1.63 => ~ ! [X3: poly_real,Xs2: list_poly_real] :
% 3.10/1.63 ( ( Xs
% 3.10/1.63 = ( cons_poly_real @ X3 @ Xs2 ) )
% 3.10/1.63 => ( ( member1784523250y_real @ ( produc1867601537y_real @ X3 @ Y ) @ R )
% 3.10/1.63 => ~ ( member403334290y_real @ ( produc1000427809y_real @ Xs2 @ Ys ) @ ( listre572247515y_real @ R ) ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_334_listrel__Cons1,axiom,
% 3.10/1.63 ! [Y: poly_real,Ys: list_poly_real,Xs: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ( ( member403334290y_real @ ( produc1000427809y_real @ ( cons_poly_real @ Y @ Ys ) @ Xs ) @ ( listre572247515y_real @ R ) )
% 3.10/1.63 => ~ ! [Y2: poly_real,Ys2: list_poly_real] :
% 3.10/1.63 ( ( Xs
% 3.10/1.63 = ( cons_poly_real @ Y2 @ Ys2 ) )
% 3.10/1.63 => ( ( member1784523250y_real @ ( produc1867601537y_real @ Y @ Y2 ) @ R )
% 3.10/1.63 => ~ ( member403334290y_real @ ( produc1000427809y_real @ Ys @ Ys2 ) @ ( listre572247515y_real @ R ) ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_335_listrel_OCons,axiom,
% 3.10/1.63 ! [X: poly_real,Y: poly_real,R: set_Pr483210409y_real,Xs: list_poly_real,Ys: list_poly_real] :
% 3.10/1.63 ( ( member1784523250y_real @ ( produc1867601537y_real @ X @ Y ) @ R )
% 3.10/1.63 => ( ( member403334290y_real @ ( produc1000427809y_real @ Xs @ Ys ) @ ( listre572247515y_real @ R ) )
% 3.10/1.63 => ( member403334290y_real @ ( produc1000427809y_real @ ( cons_poly_real @ X @ Xs ) @ ( cons_poly_real @ Y @ Ys ) ) @ ( listre572247515y_real @ R ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_336_lexord__append__rightI,axiom,
% 3.10/1.63 ! [Y: list_poly_real,X: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ( ? [B2: poly_real,Z2: list_poly_real] :
% 3.10/1.63 ( Y
% 3.10/1.63 = ( cons_poly_real @ B2 @ Z2 ) )
% 3.10/1.63 => ( member403334290y_real @ ( produc1000427809y_real @ X @ ( append_poly_real @ X @ Y ) ) @ ( lexord_poly_real @ R ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_337_listrel_Ocases,axiom,
% 3.10/1.63 ! [A12: list_poly_real,A22: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ( ( member403334290y_real @ ( produc1000427809y_real @ A12 @ A22 ) @ ( listre572247515y_real @ R ) )
% 3.10/1.63 => ( ( ( A12 = nil_poly_real )
% 3.10/1.63 => ( A22 != nil_poly_real ) )
% 3.10/1.63 => ~ ! [X3: poly_real,Y2: poly_real,Xs2: list_poly_real] :
% 3.10/1.63 ( ( A12
% 3.10/1.63 = ( cons_poly_real @ X3 @ Xs2 ) )
% 3.10/1.63 => ! [Ys2: list_poly_real] :
% 3.10/1.63 ( ( A22
% 3.10/1.63 = ( cons_poly_real @ Y2 @ Ys2 ) )
% 3.10/1.63 => ( ( member1784523250y_real @ ( produc1867601537y_real @ X3 @ Y2 ) @ R )
% 3.10/1.63 => ~ ( member403334290y_real @ ( produc1000427809y_real @ Xs2 @ Ys2 ) @ ( listre572247515y_real @ R ) ) ) ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_338_listrel_Osimps,axiom,
% 3.10/1.63 ! [A12: list_poly_real,A22: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ( ( member403334290y_real @ ( produc1000427809y_real @ A12 @ A22 ) @ ( listre572247515y_real @ R ) )
% 3.10/1.63 = ( ( ( A12 = nil_poly_real )
% 3.10/1.63 & ( A22 = nil_poly_real ) )
% 3.10/1.63 | ? [X4: poly_real,Y3: poly_real,Xs3: list_poly_real,Ys3: list_poly_real] :
% 3.10/1.63 ( ( A12
% 3.10/1.63 = ( cons_poly_real @ X4 @ Xs3 ) )
% 3.10/1.63 & ( A22
% 3.10/1.63 = ( cons_poly_real @ Y3 @ Ys3 ) )
% 3.10/1.63 & ( member1784523250y_real @ ( produc1867601537y_real @ X4 @ Y3 ) @ R )
% 3.10/1.63 & ( member403334290y_real @ ( produc1000427809y_real @ Xs3 @ Ys3 ) @ ( listre572247515y_real @ R ) ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_339_map__tailrec__rev_Opelims,axiom,
% 3.10/1.63 ! [X: poly_real > poly_real,Xa: list_poly_real,Xb: list_poly_real,Y: list_poly_real] :
% 3.10/1.63 ( ( ( map_ta1919289823y_real @ X @ Xa @ Xb )
% 3.10/1.63 = Y )
% 3.10/1.63 => ( ( accp_P948088014y_real @ map_ta954657966y_real @ ( produc2087464649y_real @ X @ ( produc1000427809y_real @ Xa @ Xb ) ) )
% 3.10/1.63 => ( ( ( Xa = nil_poly_real )
% 3.10/1.63 => ( ( Y = Xb )
% 3.10/1.63 => ~ ( accp_P948088014y_real @ map_ta954657966y_real @ ( produc2087464649y_real @ X @ ( produc1000427809y_real @ nil_poly_real @ Xb ) ) ) ) )
% 3.10/1.63 => ~ ! [A: poly_real,As: list_poly_real] :
% 3.10/1.63 ( ( Xa
% 3.10/1.63 = ( cons_poly_real @ A @ As ) )
% 3.10/1.63 => ( ( Y
% 3.10/1.63 = ( map_ta1919289823y_real @ X @ As @ ( cons_poly_real @ ( X @ A ) @ Xb ) ) )
% 3.10/1.63 => ~ ( accp_P948088014y_real @ map_ta954657966y_real @ ( produc2087464649y_real @ X @ ( produc1000427809y_real @ ( cons_poly_real @ A @ As ) @ Xb ) ) ) ) ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_340_Nil__lenlex__iff1,axiom,
% 3.10/1.63 ! [Ns: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ( ( member403334290y_real @ ( produc1000427809y_real @ nil_poly_real @ Ns ) @ ( lenlex_poly_real @ R ) )
% 3.10/1.63 = ( Ns != nil_poly_real ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_341_Nil__lenlex__iff2,axiom,
% 3.10/1.63 ! [Ns: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ~ ( member403334290y_real @ ( produc1000427809y_real @ Ns @ nil_poly_real ) @ ( lenlex_poly_real @ R ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_342_Cons__lenlex__iff,axiom,
% 3.10/1.63 ! [M: poly_real,Ms: list_poly_real,N: poly_real,Ns: list_poly_real,R: set_Pr483210409y_real] :
% 3.10/1.63 ( ( member403334290y_real @ ( produc1000427809y_real @ ( cons_poly_real @ M @ Ms ) @ ( cons_poly_real @ N @ Ns ) ) @ ( lenlex_poly_real @ R ) )
% 3.10/1.63 = ( ( ord_less_nat @ ( size_s259235672y_real @ Ms ) @ ( size_s259235672y_real @ Ns ) )
% 3.10/1.63 | ( ( ( size_s259235672y_real @ Ms )
% 3.10/1.63 = ( size_s259235672y_real @ Ns ) )
% 3.10/1.63 & ( member1784523250y_real @ ( produc1867601537y_real @ M @ N ) @ R ) )
% 3.10/1.63 | ( ( M = N )
% 3.10/1.63 & ( member403334290y_real @ ( produc1000427809y_real @ Ms @ Ns ) @ ( lenlex_poly_real @ R ) ) ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_343_Suc__less__eq,axiom,
% 3.10/1.63 ! [M: nat,N: nat] :
% 3.10/1.63 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 3.10/1.63 = ( ord_less_nat @ M @ N ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_344_Suc__mono,axiom,
% 3.10/1.63 ! [M: nat,N: nat] :
% 3.10/1.63 ( ( ord_less_nat @ M @ N )
% 3.10/1.63 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_345_lessI,axiom,
% 3.10/1.63 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_346_list_Omap__disc__iff,axiom,
% 3.10/1.63 ! [F: poly_real > poly_real,A3: list_poly_real] :
% 3.10/1.63 ( ( ( map_po2132607150y_real @ F @ A3 )
% 3.10/1.63 = nil_poly_real )
% 3.10/1.63 = ( A3 = nil_poly_real ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_347_map__is__Nil__conv,axiom,
% 3.10/1.63 ! [F: poly_real > poly_real,Xs: list_poly_real] :
% 3.10/1.63 ( ( ( map_po2132607150y_real @ F @ Xs )
% 3.10/1.63 = nil_poly_real )
% 3.10/1.63 = ( Xs = nil_poly_real ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(fact_348_Nil__is__map__conv,axiom,
% 3.10/1.63 ! [F: poly_real > poly_real,Xs: list_poly_real] :
% 3.10/1.63 ( ( nil_poly_real
% 3.10/1.63 = ( map_po2132607150y_real @ F @ Xs ) )
% 3.10/1.63 = ( Xs = nil_poly_real ) ) ).
% 3.10/1.63
% 3.10/1.63 thf(conj_0,conjecture,
% 3.10/1.63 ~ ( sturm_891428828rm_seq @ nil_poly_real ) ).
% 3.10/1.63 ------------------------
% 3.10/1.67 % (23856)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_23528 for (2999ds/27Mi)
% 3.10/1.67 % (23857)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23528 for (2999ds/2Mi)
% 3.10/1.67 % (23854)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23528 for (2999ds/183Mi)
% 3.10/1.67 % (23857)Instruction limit reached!
% 3.10/1.67 % (23857)------------------------------
% 3.10/1.67 % (23857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.67 % (23857)Termination reason: Unknown
% 3.10/1.67 % (23857)Termination phase: shuffling
% 3.10/1.67
% 3.10/1.67 % (23857)Memory used [KB]: 1535
% 3.10/1.67 % (23857)Time elapsed: 0.002 s
% 3.10/1.67 % (23857)Instructions burned: 2 (million)
% 3.10/1.67 % (23857)------------------------------
% 3.10/1.67 % (23857)------------------------------
% 3.10/1.67 % (23860)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23528 for (2999ds/18Mi)
% 3.10/1.67 % (23855)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_23528 for (2999ds/4Mi)
% 3.10/1.67 % (23860)Instruction limit reached!
% 3.10/1.67 % (23860)------------------------------
% 3.10/1.67 % (23860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.67 % (23860)Termination reason: Unknown
% 3.10/1.67 % (23860)Termination phase: shuffling
% 3.10/1.67
% 3.10/1.67 % (23860)Memory used [KB]: 1918
% 3.10/1.67 % (23860)Time elapsed: 0.008 s
% 3.10/1.67 % (23860)Instructions burned: 20 (million)
% 3.10/1.67 % (23860)------------------------------
% 3.10/1.67 % (23860)------------------------------
% 3.10/1.67 % (23858)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_23528 for (2999ds/2Mi)
% 3.10/1.67 % (23859)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_23528 for (2999ds/275Mi)
% 3.10/1.67 % (23856)Instruction limit reached!
% 3.10/1.67 % (23856)------------------------------
% 3.10/1.67 % (23856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.67 % (23856)Termination reason: Unknown
% 3.10/1.67 % (23856)Termination phase: shuffling
% 3.10/1.67
% 3.10/1.67 % (23856)Memory used [KB]: 2174
% 3.10/1.67 % (23856)Time elapsed: 0.010 s
% 3.10/1.67 % (23856)Instructions burned: 27 (million)
% 3.10/1.67 % (23856)------------------------------
% 3.10/1.67 % (23856)------------------------------
% 3.10/1.68 % (23858)Instruction limit reached!
% 3.10/1.68 % (23858)------------------------------
% 3.10/1.68 % (23858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.68 % (23858)Termination reason: Unknown
% 3.10/1.68 % (23858)Termination phase: shuffling
% 3.10/1.68
% 3.10/1.68 % (23858)Memory used [KB]: 1663
% 3.10/1.68 % (23858)Time elapsed: 0.004 s
% 3.10/1.68 % (23858)Instructions burned: 3 (million)
% 3.10/1.68 % (23858)------------------------------
% 3.10/1.68 % (23858)------------------------------
% 3.10/1.68 % (23855)Instruction limit reached!
% 3.10/1.68 % (23855)------------------------------
% 3.10/1.68 % (23855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.68 % (23855)Termination reason: Unknown
% 3.10/1.68 % (23855)Termination phase: shuffling
% 3.10/1.68
% 3.10/1.68 % (23855)Memory used [KB]: 1663
% 3.10/1.68 % (23855)Time elapsed: 0.005 s
% 3.10/1.68 % (23855)Instructions burned: 5 (million)
% 3.10/1.68 % (23855)------------------------------
% 3.10/1.68 % (23855)------------------------------
% 3.10/1.68 % (23863)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_23528 for (2999ds/15Mi)
% 3.10/1.68 % (23862)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_23528 for (2999ds/37Mi)
% 3.10/1.68 % (23861)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23528 for (2999ds/3Mi)
% 3.10/1.69 % (23861)Instruction limit reached!
% 3.10/1.69 % (23861)------------------------------
% 3.10/1.69 % (23861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.69 % (23861)Termination reason: Unknown
% 3.10/1.69 % (23861)Termination phase: shuffling
% 3.10/1.69
% 3.10/1.69 % (23861)Memory used [KB]: 1663
% 3.10/1.69 % (23861)Time elapsed: 0.004 s
% 3.10/1.69 % (23861)Instructions burned: 3 (million)
% 3.10/1.69 % (23861)------------------------------
% 3.10/1.69 % (23861)------------------------------
% 3.10/1.69 % (23863)Instruction limit reached!
% 3.10/1.69 % (23863)------------------------------
% 3.10/1.69 % (23863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.69 % (23863)Termination reason: Unknown
% 3.10/1.69 % (23863)Termination phase: shuffling
% 3.10/1.69
% 3.10/1.69 % (23863)Memory used [KB]: 1918
% 3.10/1.69 % (23863)Time elapsed: 0.006 s
% 3.10/1.69 % (23863)Instructions burned: 15 (million)
% 3.10/1.69 % (23863)------------------------------
% 3.10/1.69 % (23863)------------------------------
% 3.10/1.69 % (23864)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23528 for (2999ds/3Mi)
% 3.10/1.69 % (23865)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_23528 for (2999ds/1041Mi)
% 3.10/1.69 % (23864)Instruction limit reached!
% 3.10/1.69 % (23864)------------------------------
% 3.10/1.69 % (23864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.69 % (23864)Termination reason: Unknown
% 3.10/1.69 % (23864)Termination phase: shuffling
% 3.10/1.69
% 3.10/1.69 % (23862)Instruction limit reached!
% 3.10/1.69 % (23862)------------------------------
% 3.10/1.69 % (23862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.69 % (23864)Memory used [KB]: 1535
% 3.10/1.69 % (23862)Termination reason: Unknown
% 3.10/1.69 % (23864)Time elapsed: 0.004 s
% 3.10/1.69 % (23862)Termination phase: shuffling
% 3.10/1.69 % (23864)Instructions burned: 3 (million)
% 3.10/1.69
% 3.10/1.69 % (23862)Memory used [KB]: 2302
% 3.10/1.69 % (23864)------------------------------
% 3.10/1.69 % (23864)------------------------------
% 3.10/1.69 % (23862)Time elapsed: 0.013 s
% 3.10/1.69 % (23862)Instructions burned: 38 (million)
% 3.10/1.69 % (23862)------------------------------
% 3.10/1.69 % (23862)------------------------------
% 3.14/1.70 % (23867)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_23528 for (2999ds/16Mi)
% 3.14/1.70 % (23867)Instruction limit reached!
% 3.14/1.70 % (23867)------------------------------
% 3.14/1.70 % (23867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.70 % (23867)Termination reason: Unknown
% 3.14/1.70 % (23867)Termination phase: shuffling
% 3.14/1.70
% 3.14/1.70 % (23867)Memory used [KB]: 1918
% 3.14/1.70 % (23867)Time elapsed: 0.006 s
% 3.14/1.70 % (23867)Instructions burned: 16 (million)
% 3.14/1.70 % (23867)------------------------------
% 3.14/1.70 % (23867)------------------------------
% 3.14/1.70 % (23866)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23528 for (2999ds/7Mi)
% 3.14/1.71 % (23869)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_23528 for (2999ds/3Mi)
% 3.14/1.71 % (23859)First to succeed.
% 3.14/1.71 % (23869)Instruction limit reached!
% 3.14/1.71 % (23869)------------------------------
% 3.14/1.71 % (23869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.71 % (23869)Termination reason: Unknown
% 3.14/1.71 % (23869)Termination phase: shuffling
% 3.14/1.71
% 3.14/1.71 % (23869)Memory used [KB]: 1663
% 3.14/1.71 % (23869)Time elapsed: 0.003 s
% 3.14/1.71 % (23869)Instructions burned: 3 (million)
% 3.14/1.71 % (23869)------------------------------
% 3.14/1.71 % (23869)------------------------------
% 3.14/1.71 % (23859)Refutation found. Thanks to Tanya!
% 3.14/1.71 % SZS status Theorem for DTF2THF_23528
% 3.14/1.71 % SZS output start Proof for DTF2THF_23528
% 3.14/1.71 thf(type_def_5, type, set_list_poly_real: $tType).
% 3.14/1.71 thf(type_def_6, type, poly_real: $tType).
% 3.14/1.71 thf(type_def_8, type, list_poly_real: $tType).
% 3.14/1.71 thf(type_def_9, type, set_poly_real: $tType).
% 3.14/1.71 thf(type_def_10, type, nat: $tType).
% 3.14/1.71 thf(type_def_11, type, list_list_poly_real: $tType).
% 3.14/1.71 thf(type_def_12, type, list_P736648811y_real: $tType).
% 3.14/1.71 thf(type_def_13, type, list_P693436111y_real: $tType).
% 3.14/1.71 thf(type_def_14, type, produc321349221y_real: $tType).
% 3.14/1.71 thf(type_def_15, type, produc461822025y_real: $tType).
% 3.14/1.71 thf(type_def_16, type, list_P1001591419y_real: $tType).
% 3.14/1.71 thf(type_def_17, type, list_P991700890y_real: $tType).
% 3.14/1.71 thf(type_def_18, type, list_P657095678y_real: $tType).
% 3.14/1.71 thf(type_def_19, type, set_Pr483210409y_real: $tType).
% 3.14/1.71 thf(type_def_20, type, set_Pr1405268809y_real: $tType).
% 3.14/1.71 thf(type_def_21, type, list_l1245274212y_real: $tType).
% 3.14/1.71 thf(type_def_22, type, list_l6097393y_real: $tType).
% 3.14/1.71 thf(type_def_23, type, list_l343759061y_real: $tType).
% 3.14/1.71 thf(type_def_24, type, list_nat: $tType).
% 3.14/1.71 thf(type_def_25, type, option1330723604y_real: $tType).
% 3.14/1.71 thf(type_def_26, type, option_poly_real: $tType).
% 3.14/1.71 thf(type_def_27, type, option988260395y_real: $tType).
% 3.14/1.71 thf(type_def_28, type, option293660815y_real: $tType).
% 3.14/1.71 thf(type_def_29, type, produc1456530199y_real: $tType).
% 3.14/1.71 thf(type_def_30, type, produc1060019729y_real: $tType).
% 3.14/1.71 thf(type_def_31, type, produc1426596841y_real: $tType).
% 3.14/1.71 thf(type_def_32, type, produc796638169y_real: $tType).
% 3.14/1.71 thf(func_def_0, type, produc1456530199y_real: $tType).
% 3.14/1.71 thf(func_def_1, type, produc1060019729y_real: $tType).
% 3.14/1.71 thf(func_def_2, type, list_P657095678y_real: $tType).
% 3.14/1.71 thf(func_def_3, type, set_Pr1405268809y_real: $tType).
% 3.14/1.71 thf(func_def_4, type, produc1426596841y_real: $tType).
% 3.14/1.71 thf(func_def_5, type, list_l343759061y_real: $tType).
% 3.14/1.71 thf(func_def_6, type, list_P991700890y_real: $tType).
% 3.14/1.71 thf(func_def_7, type, option293660815y_real: $tType).
% 3.14/1.71 thf(func_def_8, type, produc796638169y_real: $tType).
% 3.14/1.71 thf(func_def_9, type, list_P693436111y_real: $tType).
% 3.14/1.71 thf(func_def_10, type, set_Pr483210409y_real: $tType).
% 3.14/1.71 thf(func_def_11, type, list_P1001591419y_real: $tType).
% 3.14/1.71 thf(func_def_12, type, list_l6097393y_real: $tType).
% 3.14/1.71 thf(func_def_13, type, produc461822025y_real: $tType).
% 3.14/1.71 thf(func_def_14, type, option988260395y_real: $tType).
% 3.14/1.71 thf(func_def_15, type, list_P736648811y_real: $tType).
% 3.14/1.71 thf(func_def_16, type, list_l1245274212y_real: $tType).
% 3.14/1.71 thf(func_def_17, type, produc321349221y_real: $tType).
% 3.14/1.71 thf(func_def_18, type, option1330723604y_real: $tType).
% 3.14/1.71 thf(func_def_19, type, list_list_poly_real: $tType).
% 3.14/1.71 thf(func_def_20, type, set_list_poly_real: $tType).
% 3.14/1.71 thf(func_def_21, type, option_poly_real: $tType).
% 3.14/1.71 thf(func_def_22, type, list_poly_real: $tType).
% 3.14/1.71 thf(func_def_23, type, set_poly_real: $tType).
% 3.14/1.71 thf(func_def_24, type, poly_real: $tType).
% 3.14/1.71 thf(func_def_25, type, list_nat: $tType).
% 3.14/1.71 thf(func_def_26, type, nat: $tType).
% 3.14/1.71 thf(func_def_27, type, bNF_Gr851617109y_real: set_list_poly_real > poly_real > set_list_poly_real).
% 3.14/1.71 thf(func_def_28, type, bNF_Gr1644259033y_real: set_list_poly_real > list_poly_real > set_poly_real).
% 3.14/1.71 thf(func_def_29, type, times_times_nat: nat > nat > nat).
% 3.14/1.71 thf(func_def_30, type, append527544425y_real: list_list_poly_real > list_list_poly_real > list_list_poly_real).
% 3.14/1.71 thf(func_def_31, type, append_poly_real: list_poly_real > list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_32, type, bind_l1810664209y_real: list_list_poly_real > (list_poly_real > list_list_poly_real) > list_list_poly_real).
% 3.14/1.71 thf(func_def_33, type, bind_l146959617y_real: list_list_poly_real > (list_poly_real > list_poly_real) > list_poly_real).
% 3.14/1.71 thf(func_def_34, type, bind_l429098840y_real: list_list_poly_real > (list_poly_real > list_P736648811y_real) > list_P736648811y_real).
% 3.14/1.71 thf(func_def_35, type, bind_p1226679937y_real: list_poly_real > (poly_real > list_list_poly_real) > list_list_poly_real).
% 3.14/1.71 thf(func_def_36, type, bind_p420216945y_real: list_poly_real > (poly_real > list_poly_real) > list_poly_real).
% 3.14/1.71 thf(func_def_37, type, bind_p600434664y_real: list_poly_real > (poly_real > list_P736648811y_real) > list_P736648811y_real).
% 3.14/1.71 thf(func_def_38, type, bind_p988182092y_real: list_poly_real > (poly_real > list_P693436111y_real) > list_P693436111y_real).
% 3.14/1.71 thf(func_def_39, type, bind_P1861132770y_real: list_P736648811y_real > (produc321349221y_real > list_list_poly_real) > list_list_poly_real).
% 3.14/1.71 thf(func_def_40, type, bind_P755425362y_real: list_P736648811y_real > (produc321349221y_real > list_poly_real) > list_poly_real).
% 3.14/1.71 thf(func_def_41, type, bind_P120560694y_real: list_P693436111y_real > (produc461822025y_real > list_poly_real) > list_poly_real).
% 3.14/1.71 thf(func_def_42, type, butlast_poly_real: list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_43, type, concat_poly_real: list_list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_44, type, enumer1433313439y_real: nat > list_list_poly_real > list_P1001591419y_real).
% 3.14/1.71 thf(func_def_45, type, enumerate_poly_real: nat > list_poly_real > list_P736648811y_real).
% 3.14/1.71 thf(func_def_46, type, enumer1123002698y_real: nat > list_P736648811y_real > list_P991700890y_real).
% 3.14/1.71 thf(func_def_47, type, enumer1015405230y_real: nat > list_P693436111y_real > list_P657095678y_real).
% 3.14/1.71 thf(func_def_48, type, foldr_2117681201y_real: (list_poly_real > list_poly_real > list_poly_real) > list_list_poly_real > list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_49, type, gen_le1160603377y_real: nat > list_list_poly_real > nat).
% 3.14/1.71 thf(func_def_50, type, gen_length_poly_real: nat > list_poly_real > nat).
% 3.14/1.71 thf(func_def_51, type, gen_le904455032y_real: nat > list_P736648811y_real > nat).
% 3.14/1.71 thf(func_def_52, type, gen_le1524582876y_real: nat > list_P693436111y_real > nat).
% 3.14/1.71 thf(func_def_53, type, insert_poly_real: poly_real > list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_54, type, last_poly_real: list_poly_real > poly_real).
% 3.14/1.71 thf(func_def_55, type, last_P21901160y_real: list_P693436111y_real > produc461822025y_real).
% 3.14/1.71 thf(func_def_56, type, lenlex_poly_real: set_Pr483210409y_real > set_Pr1405268809y_real).
% 3.14/1.71 thf(func_def_57, type, lex_poly_real: set_Pr483210409y_real > set_Pr1405268809y_real).
% 3.14/1.71 thf(func_def_58, type, lexord_poly_real: set_Pr483210409y_real > set_Pr1405268809y_real).
% 3.14/1.71 thf(func_def_59, type, cons_l2022919326y_real: list_list_poly_real > list_l1245274212y_real > list_l1245274212y_real).
% 3.14/1.71 thf(func_def_60, type, cons_list_poly_real: list_poly_real > list_list_poly_real > list_list_poly_real).
% 3.14/1.71 thf(func_def_61, type, cons_l730969377y_real: list_P736648811y_real > list_l6097393y_real > list_l6097393y_real).
% 3.14/1.71 thf(func_def_62, type, cons_l677353093y_real: list_P693436111y_real > list_l343759061y_real > list_l343759061y_real).
% 3.14/1.71 thf(func_def_63, type, cons_poly_real: poly_real > list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_64, type, cons_P1027346459y_real: produc321349221y_real > list_P736648811y_real > list_P736648811y_real).
% 3.14/1.71 thf(func_def_65, type, cons_P1129399039y_real: produc461822025y_real > list_P693436111y_real > list_P693436111y_real).
% 3.14/1.71 thf(func_def_66, type, nil_li2088348750y_real: list_l1245274212y_real).
% 3.14/1.71 thf(func_def_67, type, nil_list_poly_real: list_list_poly_real).
% 3.14/1.71 thf(func_def_68, type, nil_li579690865y_real: list_l6097393y_real).
% 3.14/1.71 thf(func_def_69, type, nil_li1299462869y_real: list_l343759061y_real).
% 3.14/1.71 thf(func_def_70, type, nil_nat: list_nat).
% 3.14/1.71 thf(func_def_71, type, nil_poly_real: list_poly_real).
% 3.14/1.71 thf(func_def_72, type, nil_Pr1161137915y_real: list_P1001591419y_real).
% 3.14/1.71 thf(func_def_73, type, nil_Pr1492526187y_real: list_P736648811y_real).
% 3.14/1.71 thf(func_def_74, type, nil_Pr570652676y_real: list_P991700890y_real).
% 3.14/1.71 thf(func_def_75, type, nil_Pr2056488424y_real: list_P657095678y_real).
% 3.14/1.71 thf(func_def_76, type, nil_Pr1207979855y_real: list_P693436111y_real).
% 3.14/1.71 thf(func_def_77, type, map_po2132607150y_real: (poly_real > poly_real) > list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_78, type, list_e367462459y_real: (list_poly_real > $o) > list_list_poly_real > $o).
% 3.14/1.71 thf(func_def_79, type, list_ex1_poly_real: (poly_real > $o) > list_poly_real > $o).
% 3.14/1.71 thf(func_def_80, type, list_e1892536494y_real: (produc321349221y_real > $o) > list_P736648811y_real > $o).
% 3.14/1.71 thf(func_def_81, type, list_e1507538962y_real: (produc461822025y_real > $o) > list_P693436111y_real > $o).
% 3.14/1.71 thf(func_def_82, type, list_e809719936y_real: (list_poly_real > $o) > list_list_poly_real > $o).
% 3.14/1.71 thf(func_def_83, type, list_ex_poly_real: (poly_real > $o) > list_poly_real > $o).
% 3.14/1.71 thf(func_def_84, type, list_e2093379497y_real: (produc321349221y_real > $o) > list_P736648811y_real > $o).
% 3.14/1.71 thf(func_def_85, type, list_e1312221069y_real: (produc461822025y_real > $o) > list_P693436111y_real > $o).
% 3.14/1.71 thf(func_def_86, type, listrel1_poly_real: set_Pr483210409y_real > set_Pr1405268809y_real).
% 3.14/1.71 thf(func_def_87, type, listre572247515y_real: set_Pr483210409y_real > set_Pr1405268809y_real).
% 3.14/1.71 thf(func_def_88, type, listre1763068361y_real: (list_poly_real > list_poly_real > $o) > list_list_poly_real > list_list_poly_real > $o).
% 3.14/1.71 thf(func_def_89, type, listre713353145y_real: (list_poly_real > poly_real > $o) > list_list_poly_real > list_poly_real > $o).
% 3.14/1.71 thf(func_def_90, type, listre1037026976y_real: (list_poly_real > produc321349221y_real > $o) > list_list_poly_real > list_P736648811y_real > $o).
% 3.14/1.71 thf(func_def_91, type, listre1793073465y_real: (poly_real > list_poly_real > $o) > list_poly_real > list_list_poly_real > $o).
% 3.14/1.71 thf(func_def_92, type, listre1609905961y_real: (poly_real > poly_real > $o) > list_poly_real > list_poly_real > $o).
% 3.14/1.71 thf(func_def_93, type, listre889482032y_real: (poly_real > produc321349221y_real > $o) > list_poly_real > list_P736648811y_real > $o).
% 3.14/1.71 thf(func_def_94, type, listre471999892y_real: (poly_real > produc461822025y_real > $o) > list_poly_real > list_P693436111y_real > $o).
% 3.14/1.71 thf(func_def_95, type, listre321577258y_real: (produc321349221y_real > list_poly_real > $o) > list_P736648811y_real > list_list_poly_real > $o).
% 3.14/1.71 thf(func_def_96, type, listre1044472730y_real: (produc321349221y_real > poly_real > $o) > list_P736648811y_real > list_poly_real > $o).
% 3.14/1.71 thf(func_def_97, type, listre1751862142y_real: (produc461822025y_real > poly_real > $o) > list_P693436111y_real > list_poly_real > $o).
% 3.14/1.71 thf(func_def_98, type, map_fi357666132y_real: (list_poly_real > option1330723604y_real) > list_list_poly_real > list_list_poly_real).
% 3.14/1.71 thf(func_def_99, type, map_fi1988340932y_real: (list_poly_real > option_poly_real) > list_list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_100, type, map_fi2104453077y_real: (list_poly_real > option988260395y_real) > list_list_poly_real > list_P736648811y_real).
% 3.14/1.71 thf(func_def_101, type, map_fi920577604y_real: (poly_real > option1330723604y_real) > list_poly_real > list_list_poly_real).
% 3.14/1.71 thf(func_def_102, type, map_fi1183202740y_real: (poly_real > option_poly_real) > list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_103, type, map_fi740944613y_real: (poly_real > option988260395y_real) > list_poly_real > list_P736648811y_real).
% 3.14/1.71 thf(func_def_104, type, map_fi1117002953y_real: (poly_real > option293660815y_real) > list_poly_real > list_P693436111y_real).
% 3.14/1.71 thf(func_def_105, type, map_fi1389003359y_real: (produc321349221y_real > option1330723604y_real) > list_P736648811y_real > list_list_poly_real).
% 3.14/1.71 thf(func_def_106, type, map_fi895935311y_real: (produc321349221y_real > option_poly_real) > list_P736648811y_real > list_poly_real).
% 3.14/1.71 thf(func_def_107, type, map_fi249381555y_real: (produc461822025y_real > option_poly_real) > list_P693436111y_real > list_poly_real).
% 3.14/1.71 thf(func_def_108, type, map_ta316995199y_real: (list_poly_real > list_poly_real) > list_list_poly_real > list_list_poly_real > list_list_poly_real).
% 3.14/1.71 thf(func_def_109, type, map_ta434235247y_real: (list_poly_real > poly_real) > list_list_poly_real > list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_110, type, map_ta1674185578y_real: (list_poly_real > produc321349221y_real) > list_list_poly_real > list_P736648811y_real > list_P736648811y_real).
% 3.14/1.71 thf(func_def_111, type, map_ta1513955567y_real: (poly_real > list_poly_real) > list_poly_real > list_list_poly_real > list_list_poly_real).
% 3.14/1.71 thf(func_def_112, type, map_ta1919289823y_real: (poly_real > poly_real) > list_poly_real > list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_113, type, map_ta632757498y_real: (poly_real > produc321349221y_real) > list_poly_real > list_P736648811y_real > list_P736648811y_real).
% 3.14/1.71 thf(func_def_114, type, map_ta920933982y_real: (poly_real > produc461822025y_real) > list_poly_real > list_P693436111y_real > list_P693436111y_real).
% 3.14/1.71 thf(func_def_115, type, map_ta958735860y_real: (produc321349221y_real > list_poly_real) > list_P736648811y_real > list_list_poly_real > list_list_poly_real).
% 3.14/1.71 thf(func_def_116, type, map_ta787748196y_real: (produc321349221y_real > poly_real) > list_P736648811y_real > list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_117, type, map_ta53312584y_real: (produc461822025y_real > poly_real) > list_P693436111y_real > list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_118, type, map_ta954657966y_real: produc1456530199y_real > produc1456530199y_real > $o).
% 3.14/1.71 thf(func_def_119, type, maps_l502643659y_real: (list_poly_real > list_list_poly_real) > list_list_poly_real > list_list_poly_real).
% 3.14/1.71 thf(func_def_120, type, maps_l337560251y_real: (list_poly_real > list_poly_real) > list_list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_121, type, maps_l770007326y_real: (list_poly_real > list_P736648811y_real) > list_list_poly_real > list_P736648811y_real).
% 3.14/1.71 thf(func_def_122, type, maps_p1417280571y_real: (poly_real > list_list_poly_real) > list_poly_real > list_list_poly_real).
% 3.14/1.71 thf(func_def_123, type, maps_p961674027y_real: (poly_real > list_poly_real) > list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_124, type, maps_p2108677294y_real: (poly_real > list_P736648811y_real) > list_poly_real > list_P736648811y_real).
% 3.14/1.71 thf(func_def_125, type, maps_p86983698y_real: (poly_real > list_P693436111y_real) > list_poly_real > list_P693436111y_real).
% 3.14/1.71 thf(func_def_126, type, maps_P54557608y_real: (produc321349221y_real > list_list_poly_real) > list_P736648811y_real > list_list_poly_real).
% 3.14/1.71 thf(func_def_127, type, maps_P116184344y_real: (produc321349221y_real > list_poly_real) > list_P736648811y_real > list_poly_real).
% 3.14/1.71 thf(func_def_128, type, maps_P1366845948y_real: (produc461822025y_real > list_poly_real) > list_P693436111y_real > list_poly_real).
% 3.14/1.71 thf(func_def_129, type, member1829603177y_real: list_list_poly_real > list_poly_real > $o).
% 3.14/1.71 thf(func_def_130, type, member_poly_real: list_poly_real > poly_real > $o).
% 3.14/1.71 thf(func_def_131, type, member1782690048y_real: list_P736648811y_real > produc321349221y_real > $o).
% 3.14/1.71 thf(func_def_132, type, member202023780y_real: list_P693436111y_real > produc461822025y_real > $o).
% 3.14/1.71 thf(func_def_133, type, null_list_poly_real: list_list_poly_real > $o).
% 3.14/1.71 thf(func_def_134, type, null_poly_real: list_poly_real > $o).
% 3.14/1.71 thf(func_def_135, type, null_P89569907y_real: list_P736648811y_real > $o).
% 3.14/1.71 thf(func_def_136, type, null_P1782853975y_real: list_P693436111y_real > $o).
% 3.14/1.71 thf(func_def_137, type, lexord1324236152y_real: (list_poly_real > list_poly_real > $o) > list_list_poly_real > list_list_poly_real > $o).
% 3.14/1.71 thf(func_def_138, type, lexordp_eq_poly_real: (poly_real > poly_real > $o) > list_poly_real > list_poly_real > $o).
% 3.14/1.71 thf(func_def_139, type, lexord834705585y_real: (produc321349221y_real > produc321349221y_real > $o) > list_P736648811y_real > list_P736648811y_real > $o).
% 3.14/1.71 thf(func_def_140, type, lexord1053351061y_real: (produc461822025y_real > produc461822025y_real > $o) > list_P693436111y_real > list_P693436111y_real > $o).
% 3.14/1.71 thf(func_def_141, type, ord_le1233681790y_real: list_poly_real > list_poly_real > $o).
% 3.14/1.71 thf(func_def_142, type, produc1360353227y_real: list_nat > list_poly_real > list_P736648811y_real).
% 3.14/1.71 thf(func_def_143, type, produc1733309743y_real: list_poly_real > list_poly_real > list_P693436111y_real).
% 3.14/1.71 thf(func_def_144, type, produc523415045y_real: list_list_poly_real > list_list_poly_real).
% 3.14/1.71 thf(func_def_145, type, rotate717473073y_real: list_list_poly_real > list_list_poly_real).
% 3.14/1.71 thf(func_def_146, type, rotate1_poly_real: list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_147, type, rotate623875384y_real: list_P736648811y_real > list_P736648811y_real).
% 3.14/1.71 thf(func_def_148, type, rotate867081116y_real: list_P693436111y_real > list_P693436111y_real).
% 3.14/1.71 thf(func_def_149, type, rotate_poly_real: nat > list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_150, type, splice2080530731y_real: list_list_poly_real > list_list_poly_real > list_list_poly_real).
% 3.14/1.71 thf(func_def_151, type, splice_poly_real: list_poly_real > list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_152, type, splice1383748542y_real: list_P736648811y_real > list_P736648811y_real > list_P736648811y_real).
% 3.14/1.71 thf(func_def_153, type, splice1321784098y_real: list_P693436111y_real > list_P693436111y_real > list_P693436111y_real).
% 3.14/1.71 thf(func_def_154, type, subseqs_poly_real: list_poly_real > list_list_poly_real).
% 3.14/1.71 thf(func_def_155, type, zip_nat_poly_real: list_nat > list_poly_real > list_P736648811y_real).
% 3.14/1.71 thf(func_def_156, type, zip_po657915297y_real: list_poly_real > list_poly_real > list_P693436111y_real).
% 3.14/1.71 thf(func_def_157, type, suc: nat > nat).
% 3.14/1.71 thf(func_def_158, type, size_s259235672y_real: list_poly_real > nat).
% 3.14/1.71 thf(func_def_159, type, ord_less_nat: nat > nat > $o).
% 3.14/1.71 thf(func_def_160, type, plus_c288199817y_real: list_poly_real > list_poly_real > list_poly_real).
% 3.14/1.71 thf(func_def_161, type, produc1345584779y_real: (poly_real > poly_real > $o) > list_poly_real > produc1060019729y_real).
% 3.14/1.71 thf(func_def_162, type, produc2087464649y_real: (poly_real > poly_real) > produc1426596841y_real > produc1456530199y_real).
% 3.14/1.71 thf(func_def_163, type, produc1000427809y_real: list_poly_real > list_poly_real > produc1426596841y_real).
% 3.14/1.71 thf(func_def_164, type, produc404352541y_real: nat > poly_real > produc321349221y_real).
% 3.14/1.71 thf(func_def_165, type, produc490255505y_real: poly_real > list_poly_real > produc796638169y_real).
% 3.14/1.71 thf(func_def_166, type, produc1867601537y_real: poly_real > poly_real > produc461822025y_real).
% 3.14/1.71 thf(func_def_167, type, collec1537941401y_real: (list_poly_real > $o) > set_list_poly_real).
% 3.14/1.71 thf(func_def_168, type, collect_poly_real: (poly_real > $o) > set_poly_real).
% 3.14/1.71 thf(func_def_169, type, collec1459394516y_real: (produc1426596841y_real > $o) > set_Pr1405268809y_real).
% 3.14/1.71 thf(func_def_170, type, collec329281332y_real: (produc461822025y_real > $o) > set_Pr483210409y_real).
% 3.14/1.71 thf(func_def_171, type, sturm_891428828rm_seq: list_poly_real > $o).
% 3.14/1.71 thf(func_def_172, type, sturm_1664866327rm_seq: list_poly_real > poly_real > $o).
% 3.14/1.71 thf(func_def_173, type, sturm_1683633594axioms: list_poly_real > poly_real > $o).
% 3.14/1.71 thf(func_def_174, type, accp_P948088014y_real: (produc1456530199y_real > produc1456530199y_real > $o) > produc1456530199y_real > $o).
% 3.14/1.71 thf(func_def_175, type, member708095579y_real: list_poly_real > set_list_poly_real > $o).
% 3.14/1.71 thf(func_def_176, type, member_poly_real2: poly_real > set_poly_real > $o).
% 3.14/1.71 thf(func_def_177, type, member403334290y_real: produc1426596841y_real > set_Pr1405268809y_real > $o).
% 3.14/1.71 thf(func_def_178, type, member1784523250y_real: produc461822025y_real > set_Pr483210409y_real > $o).
% 3.14/1.71 thf(func_def_195, type, sK0: list_poly_real > poly_real > poly_real).
% 3.14/1.71 thf(func_def_196, type, sK1: list_poly_real > poly_real > list_poly_real).
% 3.14/1.71 thf(f786,plain,(
% 3.14/1.71 $false),
% 3.14/1.71 inference(subsumption_resolution,[status(thm)],[f784,f785])).
% 3.14/1.71 thf(f785,plain,(
% 3.14/1.71 ((sturm_891428828rm_seq @ nil_poly_real) != $true)),
% 3.14/1.71 inference(equality_resolution,[status(thm)],[f782])).
% 3.14/1.71 thf(f782,plain,(
% 3.14/1.71 ( ! [X0 : list_poly_real] : (((sturm_891428828rm_seq @ X0) != $true) | (nil_poly_real != X0)) )),
% 3.14/1.71 inference(cnf_transformation,[status(thm)],[f777])).
% 3.14/1.71 thf(f777,plain,(
% 3.14/1.71 ! [X0 : list_poly_real] : (((sturm_891428828rm_seq @ X0) != $true) | (nil_poly_real != X0))),
% 3.14/1.71 inference(ennf_transformation,[status(thm)],[f636])).
% 3.14/1.71 thf(f636,plain,(
% 3.14/1.71 ! [X0 : list_poly_real] : (((sturm_891428828rm_seq @ X0) = $true) => (nil_poly_real != X0))),
% 3.14/1.71 inference(fool_elimination,[status(thm)],[f635])).
% 3.14/1.71 thf(f635,plain,(
% 3.14/1.71 ! [X0 : list_poly_real] : ((sturm_891428828rm_seq @ X0) => (nil_poly_real != X0))),
% 3.14/1.71 inference(rectify,[status(thm)],[f1])).
% 3.14/1.71 thf(f1,axiom,(
% 3.14/1.71 ! [X0 : list_poly_real] : ((sturm_891428828rm_seq @ X0) => (nil_poly_real != X0))),
% 3.14/1.71 file('/export/starexec/sandbox/tmp/tmp.MilWfgdHi9/DTF2THF_23528.p',fact_0_quasi__sturm__seq_Ops__not__Nil)).
% 3.14/1.71 thf(f784,plain,(
% 3.14/1.71 ((sturm_891428828rm_seq @ nil_poly_real) = $true)),
% 3.14/1.71 inference(cnf_transformation,[status(thm)],[f775])).
% 3.14/1.71 thf(f775,plain,(
% 3.14/1.71 ((sturm_891428828rm_seq @ nil_poly_real) = $true)),
% 3.14/1.71 inference(flattening,[status(thm)],[f428])).
% 3.14/1.71 thf(f428,plain,(
% 3.14/1.71 ~~((sturm_891428828rm_seq @ nil_poly_real) = $true)),
% 3.14/1.71 inference(fool_elimination,[status(thm)],[f427])).
% 3.14/1.71 thf(f427,plain,(
% 3.14/1.71 ~~(sturm_891428828rm_seq @ nil_poly_real)),
% 3.14/1.71 inference(rectify,[status(thm)],[f351])).
% 3.14/1.71 thf(f351,negated_conjecture,(
% 3.14/1.71 ~~(sturm_891428828rm_seq @ nil_poly_real)),
% 3.14/1.71 inference(negated_conjecture,[status(cth)],[f350])).
% 3.14/1.71 thf(f350,conjecture,(
% 3.14/1.71 ~(sturm_891428828rm_seq @ nil_poly_real)),
% 3.14/1.71 file('/export/starexec/sandbox/tmp/tmp.MilWfgdHi9/DTF2THF_23528.p',conj_0)).
% 3.14/1.71 % SZS output end Proof for DTF2THF_23528
% 3.14/1.71 % (23859)------------------------------
% 3.14/1.71 % (23859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.71 % (23859)Termination reason: Refutation
% 3.14/1.71
% 3.14/1.71 % (23859)Memory used [KB]: 6780
% 3.14/1.71 % (23859)Time elapsed: 0.035 s
% 3.14/1.71 % (23859)Instructions burned: 56 (million)
% 3.14/1.71 % (23859)------------------------------
% 3.14/1.71 % (23859)------------------------------
% 3.14/1.71 % (23853)Success in time 0.076 s
%------------------------------------------------------------------------------