TPTP Problem File: SLH0797^1.p
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%------------------------------------------------------------------------------
% File : SLH0000^1 : TPTP v8.2.0. Released v8.2.0.
% Domain : Archive of Formal Proofs
% Problem :
% Version : Especial.
% English :
% Refs : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source : [Des23]
% Names : IMP_Compiler_Reuse/0006_Compiler2/prob_00633_032155__6313422_1 [Des23]
% Status : Theorem
% Rating : ? v8.2.0
% Syntax : Number of formulae : 1545 ( 688 unt; 276 typ; 0 def)
% Number of atoms : 3009 (1765 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 10489 ( 468 ~; 64 |; 258 &;8519 @)
% ( 0 <=>;1180 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Number of types : 64 ( 63 usr)
% Number of type conns : 782 ( 782 >; 0 *; 0 +; 0 <<)
% Number of symbols : 216 ( 213 usr; 26 con; 0-4 aty)
% Number of variables : 3590 ( 101 ^;3318 !; 171 ?;3590 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2023-01-18 16:59:14.486
%------------------------------------------------------------------------------
% Could-be-implicit typings (63)
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list_list_list_char: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Compiler__Oinstr_Mt__Compiler__Oinstr_J,type,
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thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Compiler__Oinstr_J,type,
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thf(ty_n_t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
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thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
product_prod_nat_int: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
product_prod_int_int: $tType ).
thf(ty_n_t__List__Olist_It__List__Olist_It__Compiler__Oinstr_J_J,type,
list_list_instr: $tType ).
thf(ty_n_t__List__Olist_It__List__Olist_It__String__Ochar_J_J,type,
list_list_char: $tType ).
thf(ty_n_t__List__Olist_I_062_It__Int__Oint_Mt__Nat__Onat_J_J,type,
list_int_nat: $tType ).
thf(ty_n_t__Set__Oset_It__List__Olist_It__String__Ochar_J_J,type,
set_list_char: $tType ).
thf(ty_n_t__List__Olist_It__List__Olist_It__Int__Oint_J_J,type,
list_list_int: $tType ).
thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
product_prod_o_int: $tType ).
thf(ty_n_t__List__Olist_It__Compiler__Oinstr_J,type,
list_instr: $tType ).
thf(ty_n_t__List__Olist_It__String__Ochar_J,type,
list_char: $tType ).
thf(ty_n_t__List__Olist_It__Int__Oint_J,type,
list_int: $tType ).
thf(ty_n_t__Set__Oset_It__Num__Onum_J,type,
set_num: $tType ).
thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
set_nat: $tType ).
thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
set_int: $tType ).
thf(ty_n_t__Compiler__Oinstr,type,
instr: $tType ).
thf(ty_n_t__String__Ochar,type,
char: $tType ).
thf(ty_n_t__BExp__Obexp,type,
bexp: $tType ).
thf(ty_n_t__AExp__Oaexp,type,
aexp: $tType ).
thf(ty_n_t__Num__Onum,type,
num: $tType ).
thf(ty_n_t__Nat__Onat,type,
nat: $tType ).
thf(ty_n_t__Int__Oint,type,
int: $tType ).
thf(ty_n_t__Com__Ocom,type,
com: $tType ).
% Explicit typings (213)
thf(sy_c_AExp_Oaexp_ON,type,
n: int > aexp ).
thf(sy_c_AExp_Oaexp_OV,type,
v: list_char > aexp ).
thf(sy_c_AExp_Oaval,type,
aval: aexp > ( list_char > int ) > int ).
thf(sy_c_BExp_Obexp_OBc,type,
bc: $o > bexp ).
thf(sy_c_BExp_Obval,type,
bval: bexp > ( list_char > int ) > $o ).
thf(sy_c_Com_Ocom_OSKIP,type,
skip: com ).
thf(sy_c_Compiler2_Oapred,type,
apred: aexp > produc6425607678544837394st_int > produc6425607678544837394st_int > $o ).
thf(sy_c_Compiler2_Obpred,type,
bpred: produc1897111610453708512_o_int > produc6425607678544837394st_int > produc6425607678544837394st_int > $o ).
thf(sy_c_Compiler2_Ocpred,type,
cpred: com > produc6425607678544837394st_int > produc6425607678544837394st_int > $o ).
thf(sy_c_Compiler2_Oexecl,type,
execl: list_instr > list_P419547167332244514st_int > $o ).
thf(sy_c_Compiler2_Oexecl__all,type,
execl_all: list_instr > list_P419547167332244514st_int > $o ).
thf(sy_c_Compiler2_Ompred,type,
mpred: list_instr > list_P419547167332244514st_int > nat > nat > $o ).
thf(sy_c_Compiler_Oacomp,type,
acomp: aexp > list_instr ).
thf(sy_c_Compiler_Oaddr__of,type,
addr_of: list_list_char > list_char > int ).
thf(sy_c_Compiler_Obcomp,type,
bcomp: produc1897111610453708512_o_int > list_instr ).
thf(sy_c_Compiler_Oexec1,type,
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thf(sy_c_Compiler_Oiexec,type,
iexec: instr > produc6425607678544837394st_int > produc6425607678544837394st_int ).
thf(sy_c_Compiler_Oiexec__pred,type,
iexec_pred: produc5995290525303592096st_int > produc6425607678544837394st_int > $o ).
thf(sy_c_Compiler_Oinstr_OJMP,type,
jmp: int > instr ).
thf(sy_c_Compiler_Oinstr_OLOAD,type,
load: list_char > instr ).
thf(sy_c_Compiler_Oinstr_OLOADI,type,
loadi: int > instr ).
thf(sy_c_Compiler_Oinstr_OSTORE,type,
store: list_char > instr ).
thf(sy_c_Compiler_Ointh_001t__Compiler__Oinstr,type,
inth_instr: list_instr > int > instr ).
thf(sy_c_Compiler_Ointh_001t__Int__Oint,type,
inth_int: list_int > int > int ).
thf(sy_c_Compiler_Ointh_001t__List__Olist_It__String__Ochar_J,type,
inth_list_char: list_list_char > int > list_char ).
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inth_P8039235741264645271st_int: list_P419547167332244514st_int > int > produc6425607678544837394st_int ).
thf(sy_c_Compiler_Oto__m__state,type,
to_m_state: list_list_char > ( list_char > int ) > int > int ).
thf(sy_c_Compiler_Oto__m__state__rel,type,
to_m_state_rel: produc4189061985984568957nt_int > produc4189061985984568957nt_int > $o ).
thf(sy_c_Compiler_Oto__state,type,
to_state: list_list_char > ( int > int ) > list_char > int ).
thf(sy_c_Compiler_Ovars,type,
vars: list_instr > list_list_char ).
thf(sy_c_Fun_Ofun__upd_001t__List__Olist_It__String__Ochar_J_001t__Int__Oint,type,
fun_up8169409267500384524ar_int: ( list_char > int ) > list_char > int > list_char > int ).
thf(sy_c_GCD_Obezw,type,
bezw: nat > nat > product_prod_int_int ).
thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
abs_abs_int: int > int ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
minus_minus_int: int > int > int ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
minus_minus_nat: nat > nat > nat ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Int__Oint_J,type,
minus_minus_set_int: set_int > set_int > set_int ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J,type,
minus_269717477326218608t_char: set_list_char > set_list_char > set_list_char ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Nat__Onat_J,type,
minus_minus_set_nat: set_nat > set_nat > set_nat ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Num__Onum_J,type,
minus_minus_set_num: set_num > set_num > set_num ).
thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
one_one_int: int ).
thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
one_one_nat: nat ).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint,type,
plus_plus_int: int > int > int ).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
plus_plus_nat: nat > nat > nat ).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum,type,
plus_plus_num: num > num > num ).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
zero_zero_int: int ).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
zero_zero_nat: nat ).
thf(sy_c_If_001t__Int__Oint,type,
if_int: $o > int > int > int ).
thf(sy_c_If_001t__List__Olist_It__Compiler__Oinstr_J,type,
if_list_instr: $o > list_instr > list_instr > list_instr ).
thf(sy_c_If_001t__List__Olist_It__Int__Oint_J,type,
if_list_int: $o > list_int > list_int > list_int ).
thf(sy_c_If_001t__Nat__Onat,type,
if_nat: $o > nat > nat > nat ).
thf(sy_c_List_Oappend_001t__Compiler__Oinstr,type,
append_instr: list_instr > list_instr > list_instr ).
thf(sy_c_List_Oappend_001t__Int__Oint,type,
append_int: list_int > list_int > list_int ).
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thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__List__Olist_It__Int__Oint_J_J,type,
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thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Compiler__Oinstr_J_001t__List__Olist_It__Compiler__Oinstr_J,type,
produc7750586281064920791_instr: list_instr > list_instr > produc8891168062546637159_instr ).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Compiler__Oinstr_J_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__List__Olist_It__Int__Oint_J_J_J_J,type,
produc7764413618310988720st_int: list_instr > list_P419547167332244514st_int > produc4400946599758736694st_int ).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Int__Oint_J_001t__List__Olist_It__Int__Oint_J,type,
produc364263696895485585st_int: list_int > list_int > produc1186641810826059865st_int ).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J,type,
produc9134825680149865339t_char: list_list_char > list_list_char > produc525958773753613763t_char ).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__Int__Oint_J,type,
produc3965054194175396271nt_int: list_list_char > produc4435102495419491129nt_int > produc4189061985984568957nt_int ).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__List__Olist_It__Int__Oint_J_J_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__List__Olist_It__Int__Oint_J_J_J_J,type,
produc2639222612625641053st_int: list_P419547167332244514st_int > list_P419547167332244514st_int > produc5848496107505245989st_int ).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J,type,
produc1606739095562851931t_char: list_char > list_char > produc6859378861088059299t_char ).
thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Compiler__Oinstr,type,
produc3129998205563682742_instr: nat > instr > produc2078578717123253124_instr ).
thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Int__Oint,type,
product_Pair_nat_int: nat > int > product_prod_nat_int ).
thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__List__Olist_It__String__Ochar_J,type,
produc120197956887798346t_char: nat > list_char > produc1457211279475724562t_char ).
thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__List__Olist_It__Int__Oint_J_J_J,type,
produc2664891610604065915st_int: nat > produc6425607678544837394st_int > produc896087705980016963st_int ).
thf(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
product_Pair_num_num: num > num > product_prod_num_num ).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__List__Olist_It__Int__Oint_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__List__Olist_It__Int__Oint_J_J_J,type,
produc6552906223331971517st_int: produc6425607678544837394st_int > produc6425607678544837394st_int > produc5936699056767177093st_int ).
thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
produc6230002227079971283nt_int: produc7773217078559923341nt_int > int > option6357759511663192854e_term ).
thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_001t__Int__Oint,type,
produc9025023058967219549nt_int: produc4435102495419491129nt_int > list_char > int ).
thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_001t__List__Olist_It__Int__Oint_J,type,
produc2155683374303800813st_int: produc369741286924889929st_int > list_char > int ).
thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
produc6816164490631068361nt_int: produc2285326912895808259nt_int > produc8551481072490612790e_term > option6357759511663192854e_term ).
thf(sy_c_Product__Type_Oprod_Ofst_001_Eo_001t__Int__Oint,type,
product_fst_o_int: product_prod_o_int > $o ).
thf(sy_c_Product__Type_Oprod_Ofst_001t__BExp__Obexp_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
produc2736798884409471108_o_int: produc1897111610453708512_o_int > bexp ).
thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
product_fst_int_int: product_prod_int_int > int ).
thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__List__Olist_It__Int__Oint_J_J,type,
produc8941309049508465880st_int: produc6425607678544837394st_int > int ).
thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
produc3162348030201620241nt_int: produc7773217078559923341nt_int > product_prod_int_int ).
thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_001t__Int__Oint,type,
produc179445755590504351nt_int: produc4435102495419491129nt_int > int ).
thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_001t__List__Olist_It__Int__Oint_J,type,
produc6244060863719409455st_int: produc369741286924889929st_int > list_int ).
thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
produc7328097813583171335nt_int: produc2285326912895808259nt_int > product_prod_int_int ).
thf(sy_c_Product__Type_Oprod_Osnd_001_Eo_001t__Int__Oint,type,
product_snd_o_int: product_prod_o_int > int ).
thf(sy_c_Product__Type_Oprod_Osnd_001t__BExp__Obexp_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
produc7219675232234870470_o_int: produc1897111610453708512_o_int > product_prod_o_int ).
thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
product_snd_int_int: product_prod_int_int > int ).
thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__List__Olist_It__Int__Oint_J_J,type,
produc1296517004818028822st_int: produc6425607678544837394st_int > produc369741286924889929st_int ).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
dvd_dvd_nat: nat > nat > $o ).
thf(sy_c_Set_OCollect_001t__Int__Oint,type,
collect_int: ( int > $o ) > set_int ).
thf(sy_c_Set_OCollect_001t__List__Olist_It__String__Ochar_J,type,
collect_list_char: ( list_char > $o ) > set_list_char ).
thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
set_or4662586982721622107an_int: int > int > set_int ).
thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
set_or4665077453230672383an_nat: nat > nat > set_nat ).
thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Num__Onum,type,
set_or1222409239386451017an_num: num > num > set_num ).
thf(sy_c_Star_Ostar_001t__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__List__Olist_It__Int__Oint_J_J_J,type,
star_P707599355569300323st_int: ( produc6425607678544837394st_int > produc6425607678544837394st_int > $o ) > produc6425607678544837394st_int > produc6425607678544837394st_int > $o ).
thf(sy_c_String_Ochar_Osize__char,type,
size_char: char > nat ).
thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__Int__Oint_J_J,type,
accp_P4562858270263085236nt_int: ( produc4189061985984568957nt_int > produc4189061985984568957nt_int > $o ) > produc4189061985984568957nt_int > $o ).
thf(sy_c_member_001t__Int__Oint,type,
member_int: int > set_int > $o ).
thf(sy_c_member_001t__List__Olist_It__String__Ochar_J,type,
member_list_char: list_char > set_list_char > $o ).
thf(sy_c_member_001t__Nat__Onat,type,
member_nat: nat > set_nat > $o ).
thf(sy_c_member_001t__Num__Onum,type,
member_num: num > set_num > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Compiler__Oinstr_Mt__Compiler__Oinstr_J,type,
member8320768277060436240_instr: produc6572865875912645095_instr > set_Pr3711236633289739975_instr > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Compiler__Oinstr_J_Mt__List__Olist_It__Compiler__Oinstr_J_J,type,
member7594433970877843344_instr: produc8891168062546637159_instr > set_Pr1149628334386456903_instr > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Int__Oint_J_Mt__List__Olist_It__Int__Oint_J_J,type,
member6698963635872716290st_int: produc1186641810826059865st_int > set_Pr765067013931698361st_int > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__List__Olist_It__List__Olist_It__String__Ochar_J_J_J,type,
member5558557582278090860t_char: produc525958773753613763t_char > set_Pr5266275940962171427t_char > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__List__Olist_It__Int__Oint_J_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__List__Olist_It__Int__Oint_J_J_J_J_J,type,
member5009133577359637198st_int: produc5848496107505245989st_int > set_Pr525593282659569541st_int > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J,type,
member6023471406134104908t_char: produc6859378861088059299t_char > set_Pr4480099295215233283t_char > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__List__Olist_It__Int__Oint_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_Mt__List__Olist_It__Int__Oint_J_J_J_J,type,
member5928719113647980078st_int: produc5936699056767177093st_int > set_Pr7036172080033517285st_int > $o ).
thf(sy_v_a____,type,
a: aexp ).
thf(sy_v_cfsa____,type,
cfsa: list_P419547167332244514st_int ).
thf(sy_v_k____,type,
k: nat ).
thf(sy_v_s____,type,
s: list_char > int ).
thf(sy_v_stk____,type,
stk: list_int ).
thf(sy_v_x____,type,
x: list_char ).
% Relevant facts (1259)
thf(fact_0_C,axiom,
ord_less_nat @ k @ ( size_s229347708945616566st_int @ cfsa ) ).
% C
thf(fact_1_D,axiom,
( ( nth_Pr8327173284404383691st_int @ cfsa @ k )
= ( produc5086643055186798020st_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ ( acomp @ a ) ) ) @ ( produc8650753666468850689st_int @ s @ ( cons_int @ ( aval @ a @ s ) @ stk ) ) ) ) ).
% D
thf(fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062k_O_A_092_060lbrakk_062k_A_060_Alength_Acfs_059_Acfs_A_B_Ak_A_061_A_Isize_A_Iacomp_Aa_J_M_As_M_Aaval_Aa_As_A_D_Astk_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
~ ! [K: nat] :
( ( ord_less_nat @ K @ ( size_s229347708945616566st_int @ cfsa ) )
=> ( ( nth_Pr8327173284404383691st_int @ cfsa @ K )
!= ( produc5086643055186798020st_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ ( acomp @ a ) ) ) @ ( produc8650753666468850689st_int @ s @ ( cons_int @ ( aval @ a @ s ) @ stk ) ) ) ) ) ).
% \<open>\<And>thesis. (\<And>k. \<lbrakk>k < length cfs; cfs ! k = (size (acomp a), s, aval a s # stk)\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_3_of__nat__Suc,axiom,
! [M: nat] :
( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
= ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% of_nat_Suc
thf(fact_4_of__nat__Suc,axiom,
! [M: nat] :
( ( semiri1314217659103216013at_int @ ( suc @ M ) )
= ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% of_nat_Suc
thf(fact_5_of__nat__1,axiom,
( ( semiri1316708129612266289at_nat @ one_one_nat )
= one_one_nat ) ).
% of_nat_1
thf(fact_6_of__nat__1,axiom,
( ( semiri1314217659103216013at_int @ one_one_nat )
= one_one_int ) ).
% of_nat_1
thf(fact_7_of__nat__1__eq__iff,axiom,
! [N: nat] :
( ( one_one_nat
= ( semiri1316708129612266289at_nat @ N ) )
= ( N = one_one_nat ) ) ).
% of_nat_1_eq_iff
thf(fact_8_of__nat__1__eq__iff,axiom,
! [N: nat] :
( ( one_one_int
= ( semiri1314217659103216013at_int @ N ) )
= ( N = one_one_nat ) ) ).
% of_nat_1_eq_iff
thf(fact_9_of__nat__eq__1__iff,axiom,
! [N: nat] :
( ( ( semiri1316708129612266289at_nat @ N )
= one_one_nat )
= ( N = one_one_nat ) ) ).
% of_nat_eq_1_iff
thf(fact_10_of__nat__eq__1__iff,axiom,
! [N: nat] :
( ( ( semiri1314217659103216013at_int @ N )
= one_one_int )
= ( N = one_one_nat ) ) ).
% of_nat_eq_1_iff
thf(fact_11_of__nat__add,axiom,
! [M: nat,N: nat] :
( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
= ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% of_nat_add
thf(fact_12_of__nat__add,axiom,
! [M: nat,N: nat] :
( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% of_nat_add
thf(fact_13_B,axiom,
( ( nth_Pr8327173284404383691st_int @ cfsa @ zero_zero_nat )
= ( produc5086643055186798020st_int @ zero_zero_int @ ( produc8650753666468850689st_int @ s @ stk ) ) ) ).
% B
thf(fact_14_int__ops_I4_J,axiom,
! [A: nat] :
( ( semiri1314217659103216013at_int @ ( suc @ A ) )
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% int_ops(4)
thf(fact_15_int__Suc,axiom,
! [N: nat] :
( ( semiri1314217659103216013at_int @ ( suc @ N ) )
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% int_Suc
thf(fact_16_fun__upd__upd,axiom,
! [F: list_char > int,X: list_char,Y: int,Z: int] :
( ( fun_up8169409267500384524ar_int @ ( fun_up8169409267500384524ar_int @ F @ X @ Y ) @ X @ Z )
= ( fun_up8169409267500384524ar_int @ F @ X @ Z ) ) ).
% fun_upd_upd
thf(fact_17_fun__upd__triv,axiom,
! [F: list_char > int,X: list_char] :
( ( fun_up8169409267500384524ar_int @ F @ X @ ( F @ X ) )
= F ) ).
% fun_upd_triv
thf(fact_18_fun__upd__apply,axiom,
( fun_up8169409267500384524ar_int
= ( ^ [F2: list_char > int,X2: list_char,Y2: int,Z2: list_char] : ( if_int @ ( Z2 = X2 ) @ Y2 @ ( F2 @ Z2 ) ) ) ) ).
% fun_upd_apply
thf(fact_19_old_Onat_Oinject,axiom,
! [Nat: nat,Nat2: nat] :
( ( ( suc @ Nat )
= ( suc @ Nat2 ) )
= ( Nat = Nat2 ) ) ).
% old.nat.inject
thf(fact_20_nat_Oinject,axiom,
! [X22: nat,Y22: nat] :
( ( ( suc @ X22 )
= ( suc @ Y22 ) )
= ( X22 = Y22 ) ) ).
% nat.inject
thf(fact_21_of__nat__eq__iff,axiom,
! [M: nat,N: nat] :
( ( ( semiri1314217659103216013at_int @ M )
= ( semiri1314217659103216013at_int @ N ) )
= ( M = N ) ) ).
% of_nat_eq_iff
thf(fact_22_of__nat__eq__iff,axiom,
! [M: nat,N: nat] :
( ( ( semiri1316708129612266289at_nat @ M )
= ( semiri1316708129612266289at_nat @ N ) )
= ( M = N ) ) ).
% of_nat_eq_iff
thf(fact_23__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062s_Astk_O_Acfs_A_B_A0_A_061_A_I0_M_As_M_Astk_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
~ ! [S: list_char > int,Stk: list_int] :
( ( nth_Pr8327173284404383691st_int @ cfsa @ zero_zero_nat )
!= ( produc5086643055186798020st_int @ zero_zero_int @ ( produc8650753666468850689st_int @ S @ Stk ) ) ) ).
% \<open>\<And>thesis. (\<And>s stk. cfs ! 0 = (0, s, stk) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_24_bot__nat__0_Onot__eq__extremum,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% bot_nat_0.not_eq_extremum
thf(fact_25_neq0__conv,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% neq0_conv
thf(fact_26_less__nat__zero__code,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% less_nat_zero_code
thf(fact_27_Suc__less__eq,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
= ( ord_less_nat @ M @ N ) ) ).
% Suc_less_eq
thf(fact_28_Suc__mono,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% Suc_mono
thf(fact_29_lessI,axiom,
! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% lessI
thf(fact_30_add__is__0,axiom,
! [M: nat,N: nat] :
( ( ( plus_plus_nat @ M @ N )
= zero_zero_nat )
= ( ( M = zero_zero_nat )
& ( N = zero_zero_nat ) ) ) ).
% add_is_0
thf(fact_31_Nat_Oadd__0__right,axiom,
! [M: nat] :
( ( plus_plus_nat @ M @ zero_zero_nat )
= M ) ).
% Nat.add_0_right
thf(fact_32_add__Suc__right,axiom,
! [M: nat,N: nat] :
( ( plus_plus_nat @ M @ ( suc @ N ) )
= ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% add_Suc_right
thf(fact_33_nat__add__left__cancel__less,axiom,
! [K2: nat,M: nat,N: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ K2 @ M ) @ ( plus_plus_nat @ K2 @ N ) )
= ( ord_less_nat @ M @ N ) ) ).
% nat_add_left_cancel_less
thf(fact_34_of__nat__0,axiom,
( ( semiri1314217659103216013at_int @ zero_zero_nat )
= zero_zero_int ) ).
% of_nat_0
thf(fact_35_of__nat__0,axiom,
( ( semiri1316708129612266289at_nat @ zero_zero_nat )
= zero_zero_nat ) ).
% of_nat_0
thf(fact_36_of__nat__0__eq__iff,axiom,
! [N: nat] :
( ( zero_zero_int
= ( semiri1314217659103216013at_int @ N ) )
= ( zero_zero_nat = N ) ) ).
% of_nat_0_eq_iff
thf(fact_37_of__nat__0__eq__iff,axiom,
! [N: nat] :
( ( zero_zero_nat
= ( semiri1316708129612266289at_nat @ N ) )
= ( zero_zero_nat = N ) ) ).
% of_nat_0_eq_iff
thf(fact_38_of__nat__eq__0__iff,axiom,
! [M: nat] :
( ( ( semiri1314217659103216013at_int @ M )
= zero_zero_int )
= ( M = zero_zero_nat ) ) ).
% of_nat_eq_0_iff
thf(fact_39_of__nat__eq__0__iff,axiom,
! [M: nat] :
( ( ( semiri1316708129612266289at_nat @ M )
= zero_zero_nat )
= ( M = zero_zero_nat ) ) ).
% of_nat_eq_0_iff
thf(fact_40_of__nat__less__iff,axiom,
! [M: nat,N: nat] :
( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
= ( ord_less_nat @ M @ N ) ) ).
% of_nat_less_iff
thf(fact_41_of__nat__less__iff,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
= ( ord_less_nat @ M @ N ) ) ).
% of_nat_less_iff
thf(fact_42_zero__less__Suc,axiom,
! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% zero_less_Suc
thf(fact_43_less__Suc0,axiom,
! [N: nat] :
( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
= ( N = zero_zero_nat ) ) ).
% less_Suc0
thf(fact_44_add__gr__0,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ M )
| ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% add_gr_0
thf(fact_45_less__one,axiom,
! [N: nat] :
( ( ord_less_nat @ N @ one_one_nat )
= ( N = zero_zero_nat ) ) ).
% less_one
thf(fact_46_of__nat__0__less__iff,axiom,
! [N: nat] :
( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
= ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% of_nat_0_less_iff
thf(fact_47_of__nat__0__less__iff,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
= ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% of_nat_0_less_iff
thf(fact_48_int__ops_I1_J,axiom,
( ( semiri1314217659103216013at_int @ zero_zero_nat )
= zero_zero_int ) ).
% int_ops(1)
thf(fact_49_verit__comp__simplify1_I1_J,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ) ).
% verit_comp_simplify1(1)
thf(fact_50_verit__comp__simplify1_I1_J,axiom,
! [A: int] :
~ ( ord_less_int @ A @ A ) ).
% verit_comp_simplify1(1)
thf(fact_51_plus__nat_Oadd__0,axiom,
! [N: nat] :
( ( plus_plus_nat @ zero_zero_nat @ N )
= N ) ).
% plus_nat.add_0
thf(fact_52_bot__nat__0_Oextremum__strict,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% bot_nat_0.extremum_strict
thf(fact_53_gr0I,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% gr0I
thf(fact_54_not__gr0,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) ).
% not_gr0
thf(fact_55_mem__Collect__eq,axiom,
! [A: int,P: int > $o] :
( ( member_int @ A @ ( collect_int @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_56_mem__Collect__eq,axiom,
! [A: list_char,P: list_char > $o] :
( ( member_list_char @ A @ ( collect_list_char @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_57_Collect__mem__eq,axiom,
! [A2: set_int] :
( ( collect_int
@ ^ [X2: int] : ( member_int @ X2 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_58_Collect__mem__eq,axiom,
! [A2: set_list_char] :
( ( collect_list_char
@ ^ [X2: list_char] : ( member_list_char @ X2 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_59_add__is__1,axiom,
! [M: nat,N: nat] :
( ( ( plus_plus_nat @ M @ N )
= ( suc @ zero_zero_nat ) )
= ( ( ( M
= ( suc @ zero_zero_nat ) )
& ( N = zero_zero_nat ) )
| ( ( M = zero_zero_nat )
& ( N
= ( suc @ zero_zero_nat ) ) ) ) ) ).
% add_is_1
thf(fact_60_not__less0,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% not_less0
thf(fact_61_add__lessD1,axiom,
! [I: nat,J: nat,K2: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K2 )
=> ( ord_less_nat @ I @ K2 ) ) ).
% add_lessD1
thf(fact_62_less__zeroE,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% less_zeroE
thf(fact_63_one__is__add,axiom,
! [M: nat,N: nat] :
( ( ( suc @ zero_zero_nat )
= ( plus_plus_nat @ M @ N ) )
= ( ( ( M
= ( suc @ zero_zero_nat ) )
& ( N = zero_zero_nat ) )
| ( ( M = zero_zero_nat )
& ( N
= ( suc @ zero_zero_nat ) ) ) ) ) ).
% one_is_add
thf(fact_64_One__nat__def,axiom,
( one_one_nat
= ( suc @ zero_zero_nat ) ) ).
% One_nat_def
thf(fact_65_nat__neq__iff,axiom,
! [M: nat,N: nat] :
( ( M != N )
= ( ( ord_less_nat @ M @ N )
| ( ord_less_nat @ N @ M ) ) ) ).
% nat_neq_iff
thf(fact_66_Suc__eq__plus1,axiom,
( suc
= ( ^ [N2: nat] : ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% Suc_eq_plus1
thf(fact_67_add__less__mono,axiom,
! [I: nat,J: nat,K2: nat,L: nat] :
( ( ord_less_nat @ I @ J )
=> ( ( ord_less_nat @ K2 @ L )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K2 ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% add_less_mono
thf(fact_68_less__not__refl,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ N ) ).
% less_not_refl
thf(fact_69_not__add__less1,axiom,
! [I: nat,J: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% not_add_less1
thf(fact_70_not__add__less2,axiom,
! [J: nat,I: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% not_add_less2
thf(fact_71_plus__1__eq__Suc,axiom,
( ( plus_plus_nat @ one_one_nat )
= suc ) ).
% plus_1_eq_Suc
thf(fact_72_add__less__mono1,axiom,
! [I: nat,J: nat,K2: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K2 ) @ ( plus_plus_nat @ J @ K2 ) ) ) ).
% add_less_mono1
thf(fact_73_less__not__refl2,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ N @ M )
=> ( M != N ) ) ).
% less_not_refl2
thf(fact_74_less__not__refl3,axiom,
! [S2: nat,T: nat] :
( ( ord_less_nat @ S2 @ T )
=> ( S2 != T ) ) ).
% less_not_refl3
thf(fact_75_gr__implies__not0,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) ).
% gr_implies_not0
thf(fact_76_less__irrefl__nat,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ N ) ).
% less_irrefl_nat
thf(fact_77_nat__less__induct,axiom,
! [P: nat > $o,N: nat] :
( ! [N3: nat] :
( ! [M2: nat] :
( ( ord_less_nat @ M2 @ N3 )
=> ( P @ M2 ) )
=> ( P @ N3 ) )
=> ( P @ N ) ) ).
% nat_less_induct
thf(fact_78_trans__less__add1,axiom,
! [I: nat,J: nat,M: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% trans_less_add1
thf(fact_79_trans__less__add2,axiom,
! [I: nat,J: nat,M: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% trans_less_add2
thf(fact_80_add__eq__self__zero,axiom,
! [M: nat,N: nat] :
( ( ( plus_plus_nat @ M @ N )
= M )
=> ( N = zero_zero_nat ) ) ).
% add_eq_self_zero
thf(fact_81_infinite__descent,axiom,
! [P: nat > $o,N: nat] :
( ! [N3: nat] :
( ~ ( P @ N3 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N3 )
& ~ ( P @ M2 ) ) )
=> ( P @ N ) ) ).
% infinite_descent
thf(fact_82_less__add__eq__less,axiom,
! [K2: nat,L: nat,M: nat,N: nat] :
( ( ord_less_nat @ K2 @ L )
=> ( ( ( plus_plus_nat @ M @ L )
= ( plus_plus_nat @ K2 @ N ) )
=> ( ord_less_nat @ M @ N ) ) ) ).
% less_add_eq_less
thf(fact_83_Suc__eq__plus1__left,axiom,
( suc
= ( plus_plus_nat @ one_one_nat ) ) ).
% Suc_eq_plus1_left
thf(fact_84_infinite__descent0,axiom,
! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N3: nat] :
( ( ord_less_nat @ zero_zero_nat @ N3 )
=> ( ~ ( P @ N3 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N3 )
& ~ ( P @ M2 ) ) ) )
=> ( P @ N ) ) ) ).
% infinite_descent0
thf(fact_85_linorder__neqE__nat,axiom,
! [X: nat,Y: nat] :
( ( X != Y )
=> ( ~ ( ord_less_nat @ X @ Y )
=> ( ord_less_nat @ Y @ X ) ) ) ).
% linorder_neqE_nat
thf(fact_86_nat__induct__non__zero,axiom,
! [N: nat,P: nat > $o] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( P @ one_one_nat )
=> ( ! [N3: nat] :
( ( ord_less_nat @ zero_zero_nat @ N3 )
=> ( ( P @ N3 )
=> ( P @ ( suc @ N3 ) ) ) )
=> ( P @ N ) ) ) ) ).
% nat_induct_non_zero
thf(fact_87_less__imp__add__positive,axiom,
! [I: nat,J: nat] :
( ( ord_less_nat @ I @ J )
=> ? [K: nat] :
( ( ord_less_nat @ zero_zero_nat @ K )
& ( ( plus_plus_nat @ I @ K )
= J ) ) ) ).
% less_imp_add_positive
thf(fact_88_less__imp__Suc__add,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ? [K: nat] :
( N
= ( suc @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% less_imp_Suc_add
thf(fact_89_less__iff__Suc__add,axiom,
( ord_less_nat
= ( ^ [M3: nat,N2: nat] :
? [K3: nat] :
( N2
= ( suc @ ( plus_plus_nat @ M3 @ K3 ) ) ) ) ) ).
% less_iff_Suc_add
thf(fact_90_less__add__Suc2,axiom,
! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% less_add_Suc2
thf(fact_91_less__add__Suc1,axiom,
! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% less_add_Suc1
thf(fact_92_less__natE,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ~ ! [Q: nat] :
( N
!= ( suc @ ( plus_plus_nat @ M @ Q ) ) ) ) ).
% less_natE
thf(fact_93_less__Suc__eq__0__disj,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ( M = zero_zero_nat )
| ? [J2: nat] :
( ( M
= ( suc @ J2 ) )
& ( ord_less_nat @ J2 @ N ) ) ) ) ).
% less_Suc_eq_0_disj
thf(fact_94_gr0__implies__Suc,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ? [M4: nat] :
( N
= ( suc @ M4 ) ) ) ).
% gr0_implies_Suc
thf(fact_95_All__less__Suc2,axiom,
! [N: nat,P: nat > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( suc @ N ) )
=> ( P @ I2 ) ) )
= ( ( P @ zero_zero_nat )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ N )
=> ( P @ ( suc @ I2 ) ) ) ) ) ).
% All_less_Suc2
thf(fact_96_gr0__conv__Suc,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( ? [M3: nat] :
( N
= ( suc @ M3 ) ) ) ) ).
% gr0_conv_Suc
thf(fact_97_Ex__less__Suc2,axiom,
! [N: nat,P: nat > $o] :
( ( ? [I2: nat] :
( ( ord_less_nat @ I2 @ ( suc @ N ) )
& ( P @ I2 ) ) )
= ( ( P @ zero_zero_nat )
| ? [I2: nat] :
( ( ord_less_nat @ I2 @ N )
& ( P @ ( suc @ I2 ) ) ) ) ) ).
% Ex_less_Suc2
thf(fact_98_of__nat__less__0__iff,axiom,
! [M: nat] :
~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% of_nat_less_0_iff
thf(fact_99_of__nat__less__0__iff,axiom,
! [M: nat] :
~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% of_nat_less_0_iff
thf(fact_100_add__Suc__shift,axiom,
! [M: nat,N: nat] :
( ( plus_plus_nat @ ( suc @ M ) @ N )
= ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% add_Suc_shift
thf(fact_101_add__Suc,axiom,
! [M: nat,N: nat] :
( ( plus_plus_nat @ ( suc @ M ) @ N )
= ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% add_Suc
thf(fact_102_nat__arith_Osuc1,axiom,
! [A2: nat,K2: nat,A: nat] :
( ( A2
= ( plus_plus_nat @ K2 @ A ) )
=> ( ( suc @ A2 )
= ( plus_plus_nat @ K2 @ ( suc @ A ) ) ) ) ).
% nat_arith.suc1
thf(fact_103_verit__sum__simplify,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ) ).
% verit_sum_simplify
thf(fact_104_verit__sum__simplify,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ) ).
% verit_sum_simplify
thf(fact_105_not0__implies__Suc,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ? [M4: nat] :
( N
= ( suc @ M4 ) ) ) ).
% not0_implies_Suc
thf(fact_106_Zero__not__Suc,axiom,
! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) ).
% Zero_not_Suc
thf(fact_107_Zero__neq__Suc,axiom,
! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) ).
% Zero_neq_Suc
thf(fact_108_Suc__neq__Zero,axiom,
! [M: nat] :
( ( suc @ M )
!= zero_zero_nat ) ).
% Suc_neq_Zero
thf(fact_109_zero__induct,axiom,
! [P: nat > $o,K2: nat] :
( ( P @ K2 )
=> ( ! [N3: nat] :
( ( P @ ( suc @ N3 ) )
=> ( P @ N3 ) )
=> ( P @ zero_zero_nat ) ) ) ).
% zero_induct
thf(fact_110_diff__induct,axiom,
! [P: nat > nat > $o,M: nat,N: nat] :
( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
=> ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
=> ( ! [X3: nat,Y3: nat] :
( ( P @ X3 @ Y3 )
=> ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
=> ( P @ M @ N ) ) ) ) ).
% diff_induct
thf(fact_111_nat__induct,axiom,
! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N3: nat] :
( ( P @ N3 )
=> ( P @ ( suc @ N3 ) ) )
=> ( P @ N ) ) ) ).
% nat_induct
thf(fact_112_old_Onat_Oexhaust,axiom,
! [Y: nat] :
( ( Y != zero_zero_nat )
=> ~ ! [Nat3: nat] :
( Y
!= ( suc @ Nat3 ) ) ) ).
% old.nat.exhaust
thf(fact_113_nat_OdiscI,axiom,
! [Nat: nat,X22: nat] :
( ( Nat
= ( suc @ X22 ) )
=> ( Nat != zero_zero_nat ) ) ).
% nat.discI
thf(fact_114_old_Onat_Odistinct_I1_J,axiom,
! [Nat2: nat] :
( zero_zero_nat
!= ( suc @ Nat2 ) ) ).
% old.nat.distinct(1)
thf(fact_115_old_Onat_Odistinct_I2_J,axiom,
! [Nat2: nat] :
( ( suc @ Nat2 )
!= zero_zero_nat ) ).
% old.nat.distinct(2)
thf(fact_116_nat_Odistinct_I1_J,axiom,
! [X22: nat] :
( zero_zero_nat
!= ( suc @ X22 ) ) ).
% nat.distinct(1)
thf(fact_117_lift__Suc__mono__less__iff,axiom,
! [F: nat > nat,N: nat,M: nat] :
( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
=> ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
= ( ord_less_nat @ N @ M ) ) ) ).
% lift_Suc_mono_less_iff
thf(fact_118_lift__Suc__mono__less__iff,axiom,
! [F: nat > int,N: nat,M: nat] :
( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
=> ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
= ( ord_less_nat @ N @ M ) ) ) ).
% lift_Suc_mono_less_iff
thf(fact_119_lift__Suc__mono__less,axiom,
! [F: nat > nat,N: nat,N4: nat] :
( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
=> ( ( ord_less_nat @ N @ N4 )
=> ( ord_less_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% lift_Suc_mono_less
thf(fact_120_lift__Suc__mono__less,axiom,
! [F: nat > int,N: nat,N4: nat] :
( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
=> ( ( ord_less_nat @ N @ N4 )
=> ( ord_less_int @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% lift_Suc_mono_less
thf(fact_121_of__nat__less__imp__less,axiom,
! [M: nat,N: nat] :
( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
=> ( ord_less_nat @ M @ N ) ) ).
% of_nat_less_imp_less
thf(fact_122_of__nat__less__imp__less,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
=> ( ord_less_nat @ M @ N ) ) ).
% of_nat_less_imp_less
thf(fact_123_less__imp__of__nat__less,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% less_imp_of_nat_less
thf(fact_124_less__imp__of__nat__less,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% less_imp_of_nat_less
thf(fact_125_int__plus,axiom,
! [N: nat,M: nat] :
( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% int_plus
thf(fact_126_int__ops_I5_J,axiom,
! [A: nat,B: nat] :
( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% int_ops(5)
thf(fact_127_of__nat__neq__0,axiom,
! [N: nat] :
( ( semiri1314217659103216013at_int @ ( suc @ N ) )
!= zero_zero_int ) ).
% of_nat_neq_0
thf(fact_128_of__nat__neq__0,axiom,
! [N: nat] :
( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
!= zero_zero_nat ) ).
% of_nat_neq_0
thf(fact_129_int__ops_I2_J,axiom,
( ( semiri1314217659103216013at_int @ one_one_nat )
= one_one_int ) ).
% int_ops(2)
thf(fact_130_not__less__less__Suc__eq,axiom,
! [N: nat,M: nat] :
( ~ ( ord_less_nat @ N @ M )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
= ( N = M ) ) ) ).
% not_less_less_Suc_eq
thf(fact_131_strict__inc__induct,axiom,
! [I: nat,J: nat,P: nat > $o] :
( ( ord_less_nat @ I @ J )
=> ( ! [I3: nat] :
( ( J
= ( suc @ I3 ) )
=> ( P @ I3 ) )
=> ( ! [I3: nat] :
( ( ord_less_nat @ I3 @ J )
=> ( ( P @ ( suc @ I3 ) )
=> ( P @ I3 ) ) )
=> ( P @ I ) ) ) ) ).
% strict_inc_induct
thf(fact_132_less__Suc__induct,axiom,
! [I: nat,J: nat,P: nat > nat > $o] :
( ( ord_less_nat @ I @ J )
=> ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
=> ( ! [I3: nat,J3: nat,K: nat] :
( ( ord_less_nat @ I3 @ J3 )
=> ( ( ord_less_nat @ J3 @ K )
=> ( ( P @ I3 @ J3 )
=> ( ( P @ J3 @ K )
=> ( P @ I3 @ K ) ) ) ) )
=> ( P @ I @ J ) ) ) ) ).
% less_Suc_induct
thf(fact_133_less__trans__Suc,axiom,
! [I: nat,J: nat,K2: nat] :
( ( ord_less_nat @ I @ J )
=> ( ( ord_less_nat @ J @ K2 )
=> ( ord_less_nat @ ( suc @ I ) @ K2 ) ) ) ).
% less_trans_Suc
thf(fact_134_Suc__less__SucD,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
=> ( ord_less_nat @ M @ N ) ) ).
% Suc_less_SucD
thf(fact_135_less__antisym,axiom,
! [N: nat,M: nat] :
( ~ ( ord_less_nat @ N @ M )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
=> ( M = N ) ) ) ).
% less_antisym
thf(fact_136_Suc__less__eq2,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ ( suc @ N ) @ M )
= ( ? [M5: nat] :
( ( M
= ( suc @ M5 ) )
& ( ord_less_nat @ N @ M5 ) ) ) ) ).
% Suc_less_eq2
thf(fact_137_All__less__Suc,axiom,
! [N: nat,P: nat > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( suc @ N ) )
=> ( P @ I2 ) ) )
= ( ( P @ N )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ N )
=> ( P @ I2 ) ) ) ) ).
% All_less_Suc
thf(fact_138_not__less__eq,axiom,
! [M: nat,N: nat] :
( ( ~ ( ord_less_nat @ M @ N ) )
= ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% not_less_eq
thf(fact_139_less__Suc__eq,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ( ord_less_nat @ M @ N )
| ( M = N ) ) ) ).
% less_Suc_eq
thf(fact_140_Ex__less__Suc,axiom,
! [N: nat,P: nat > $o] :
( ( ? [I2: nat] :
( ( ord_less_nat @ I2 @ ( suc @ N ) )
& ( P @ I2 ) ) )
= ( ( P @ N )
| ? [I2: nat] :
( ( ord_less_nat @ I2 @ N )
& ( P @ I2 ) ) ) ) ).
% Ex_less_Suc
thf(fact_141_less__SucI,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% less_SucI
thf(fact_142_less__SucE,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
=> ( ~ ( ord_less_nat @ M @ N )
=> ( M = N ) ) ) ).
% less_SucE
thf(fact_143_Suc__lessI,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ( ( suc @ M )
!= N )
=> ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% Suc_lessI
thf(fact_144_Suc__lessE,axiom,
! [I: nat,K2: nat] :
( ( ord_less_nat @ ( suc @ I ) @ K2 )
=> ~ ! [J3: nat] :
( ( ord_less_nat @ I @ J3 )
=> ( K2
!= ( suc @ J3 ) ) ) ) ).
% Suc_lessE
thf(fact_145_Suc__lessD,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ N )
=> ( ord_less_nat @ M @ N ) ) ).
% Suc_lessD
thf(fact_146_Nat_OlessE,axiom,
! [I: nat,K2: nat] :
( ( ord_less_nat @ I @ K2 )
=> ( ( K2
!= ( suc @ I ) )
=> ~ ! [J3: nat] :
( ( ord_less_nat @ I @ J3 )
=> ( K2
!= ( suc @ J3 ) ) ) ) ) ).
% Nat.lessE
thf(fact_147_n__not__Suc__n,axiom,
! [N: nat] :
( N
!= ( suc @ N ) ) ).
% n_not_Suc_n
thf(fact_148_Suc__inject,axiom,
! [X: nat,Y: nat] :
( ( ( suc @ X )
= ( suc @ Y ) )
=> ( X = Y ) ) ).
% Suc_inject
thf(fact_149_size__neq__size__imp__neq,axiom,
! [X: list_int,Y: list_int] :
( ( ( size_size_list_int @ X )
!= ( size_size_list_int @ Y ) )
=> ( X != Y ) ) ).
% size_neq_size_imp_neq
thf(fact_150_size__neq__size__imp__neq,axiom,
! [X: bexp,Y: bexp] :
( ( ( size_size_bexp @ X )
!= ( size_size_bexp @ Y ) )
=> ( X != Y ) ) ).
% size_neq_size_imp_neq
thf(fact_151_size__neq__size__imp__neq,axiom,
! [X: aexp,Y: aexp] :
( ( ( size_size_aexp @ X )
!= ( size_size_aexp @ Y ) )
=> ( X != Y ) ) ).
% size_neq_size_imp_neq
thf(fact_152_size__neq__size__imp__neq,axiom,
! [X: num,Y: num] :
( ( ( size_size_num @ X )
!= ( size_size_num @ Y ) )
=> ( X != Y ) ) ).
% size_neq_size_imp_neq
thf(fact_153_size__neq__size__imp__neq,axiom,
! [X: com,Y: com] :
( ( ( size_size_com @ X )
!= ( size_size_com @ Y ) )
=> ( X != Y ) ) ).
% size_neq_size_imp_neq
thf(fact_154_int__if,axiom,
! [P: $o,A: nat,B: nat] :
( ( P
=> ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
= ( semiri1314217659103216013at_int @ A ) ) )
& ( ~ P
=> ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
= ( semiri1314217659103216013at_int @ B ) ) ) ) ).
% int_if
thf(fact_155_nat__int__comparison_I1_J,axiom,
( ( ^ [Y4: nat,Z3: nat] : ( Y4 = Z3 ) )
= ( ^ [A3: nat,B2: nat] :
( ( semiri1314217659103216013at_int @ A3 )
= ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% nat_int_comparison(1)
thf(fact_156_fun__upd__idem__iff,axiom,
! [F: list_char > int,X: list_char,Y: int] :
( ( ( fun_up8169409267500384524ar_int @ F @ X @ Y )
= F )
= ( ( F @ X )
= Y ) ) ).
% fun_upd_idem_iff
thf(fact_157_fun__upd__twist,axiom,
! [A: list_char,C: list_char,M: list_char > int,B: int,D: int] :
( ( A != C )
=> ( ( fun_up8169409267500384524ar_int @ ( fun_up8169409267500384524ar_int @ M @ A @ B ) @ C @ D )
= ( fun_up8169409267500384524ar_int @ ( fun_up8169409267500384524ar_int @ M @ C @ D ) @ A @ B ) ) ) ).
% fun_upd_twist
thf(fact_158_fun__upd__other,axiom,
! [Z: list_char,X: list_char,F: list_char > int,Y: int] :
( ( Z != X )
=> ( ( fun_up8169409267500384524ar_int @ F @ X @ Y @ Z )
= ( F @ Z ) ) ) ).
% fun_upd_other
thf(fact_159_fun__upd__same,axiom,
! [F: list_char > int,X: list_char,Y: int] :
( ( fun_up8169409267500384524ar_int @ F @ X @ Y @ X )
= Y ) ).
% fun_upd_same
thf(fact_160_fun__upd__idem,axiom,
! [F: list_char > int,X: list_char,Y: int] :
( ( ( F @ X )
= Y )
=> ( ( fun_up8169409267500384524ar_int @ F @ X @ Y )
= F ) ) ).
% fun_upd_idem
thf(fact_161_fun__upd__eqD,axiom,
! [F: list_char > int,X: list_char,Y: int,G: list_char > int,Z: int] :
( ( ( fun_up8169409267500384524ar_int @ F @ X @ Y )
= ( fun_up8169409267500384524ar_int @ G @ X @ Z ) )
=> ( Y = Z ) ) ).
% fun_upd_eqD
thf(fact_162_fun__upd__def,axiom,
( fun_up8169409267500384524ar_int
= ( ^ [F2: list_char > int,A3: list_char,B2: int,X2: list_char] : ( if_int @ ( X2 = A3 ) @ B2 @ ( F2 @ X2 ) ) ) ) ).
% fun_upd_def
thf(fact_163_nth__Cons__Suc,axiom,
! [X: int,Xs: list_int,N: nat] :
( ( nth_int @ ( cons_int @ X @ Xs ) @ ( suc @ N ) )
= ( nth_int @ Xs @ N ) ) ).
% nth_Cons_Suc
thf(fact_164_nth__Cons__Suc,axiom,
! [X: instr,Xs: list_instr,N: nat] :
( ( nth_instr @ ( cons_instr @ X @ Xs ) @ ( suc @ N ) )
= ( nth_instr @ Xs @ N ) ) ).
% nth_Cons_Suc
thf(fact_165_nth__Cons__Suc,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int,N: nat] :
( ( nth_Pr8327173284404383691st_int @ ( cons_P4151473878978182108st_int @ X @ Xs ) @ ( suc @ N ) )
= ( nth_Pr8327173284404383691st_int @ Xs @ N ) ) ).
% nth_Cons_Suc
thf(fact_166_nth__Cons__Suc,axiom,
! [X: list_char,Xs: list_list_char,N: nat] :
( ( nth_list_char @ ( cons_list_char @ X @ Xs ) @ ( suc @ N ) )
= ( nth_list_char @ Xs @ N ) ) ).
% nth_Cons_Suc
thf(fact_167_nth__Cons__0,axiom,
! [X: int,Xs: list_int] :
( ( nth_int @ ( cons_int @ X @ Xs ) @ zero_zero_nat )
= X ) ).
% nth_Cons_0
thf(fact_168_nth__Cons__0,axiom,
! [X: instr,Xs: list_instr] :
( ( nth_instr @ ( cons_instr @ X @ Xs ) @ zero_zero_nat )
= X ) ).
% nth_Cons_0
thf(fact_169_nth__Cons__0,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int] :
( ( nth_Pr8327173284404383691st_int @ ( cons_P4151473878978182108st_int @ X @ Xs ) @ zero_zero_nat )
= X ) ).
% nth_Cons_0
thf(fact_170_nth__Cons__0,axiom,
! [X: list_char,Xs: list_list_char] :
( ( nth_list_char @ ( cons_list_char @ X @ Xs ) @ zero_zero_nat )
= X ) ).
% nth_Cons_0
thf(fact_171_zero__less__double__add__iff__zero__less__single__add,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
= ( ord_less_int @ zero_zero_int @ A ) ) ).
% zero_less_double_add_iff_zero_less_single_add
thf(fact_172_double__add__less__zero__iff__single__add__less__zero,axiom,
! [A: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ) ).
% double_add_less_zero_iff_single_add_less_zero
thf(fact_173_less__add__same__cancel2,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
= ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% less_add_same_cancel2
thf(fact_174_less__add__same__cancel2,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
= ( ord_less_int @ zero_zero_int @ B ) ) ).
% less_add_same_cancel2
thf(fact_175_less__add__same__cancel1,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
= ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% less_add_same_cancel1
thf(fact_176_less__add__same__cancel1,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
= ( ord_less_int @ zero_zero_int @ B ) ) ).
% less_add_same_cancel1
thf(fact_177_add__less__same__cancel2,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
= ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% add_less_same_cancel2
thf(fact_178_add__less__same__cancel2,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
= ( ord_less_int @ A @ zero_zero_int ) ) ).
% add_less_same_cancel2
thf(fact_179_add__less__same__cancel1,axiom,
! [B: nat,A: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
= ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% add_less_same_cancel1
thf(fact_180_add__less__same__cancel1,axiom,
! [B: int,A: int] :
( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
= ( ord_less_int @ A @ zero_zero_int ) ) ).
% add_less_same_cancel1
thf(fact_181_list_Osize_I4_J,axiom,
! [X21: instr,X222: list_instr] :
( ( size_size_list_instr @ ( cons_instr @ X21 @ X222 ) )
= ( plus_plus_nat @ ( size_size_list_instr @ X222 ) @ ( suc @ zero_zero_nat ) ) ) ).
% list.size(4)
thf(fact_182_list_Osize_I4_J,axiom,
! [X21: produc6425607678544837394st_int,X222: list_P419547167332244514st_int] :
( ( size_s229347708945616566st_int @ ( cons_P4151473878978182108st_int @ X21 @ X222 ) )
= ( plus_plus_nat @ ( size_s229347708945616566st_int @ X222 ) @ ( suc @ zero_zero_nat ) ) ) ).
% list.size(4)
thf(fact_183_list_Osize_I4_J,axiom,
! [X21: list_char,X222: list_list_char] :
( ( size_s356637359517785349t_char @ ( cons_list_char @ X21 @ X222 ) )
= ( plus_plus_nat @ ( size_s356637359517785349t_char @ X222 ) @ ( suc @ zero_zero_nat ) ) ) ).
% list.size(4)
thf(fact_184_list_Osize_I4_J,axiom,
! [X21: int,X222: list_int] :
( ( size_size_list_int @ ( cons_int @ X21 @ X222 ) )
= ( plus_plus_nat @ ( size_size_list_int @ X222 ) @ ( suc @ zero_zero_nat ) ) ) ).
% list.size(4)
thf(fact_185_add__less__cancel__right,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( ord_less_nat @ A @ B ) ) ).
% add_less_cancel_right
thf(fact_186_add__less__cancel__right,axiom,
! [A: int,C: int,B: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
= ( ord_less_int @ A @ B ) ) ).
% add_less_cancel_right
thf(fact_187_add__less__cancel__left,axiom,
! [C: nat,A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) ).
% add_less_cancel_left
thf(fact_188_add__less__cancel__left,axiom,
! [C: int,A: int,B: int] :
( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
= ( ord_less_int @ A @ B ) ) ).
% add_less_cancel_left
thf(fact_189_double__eq__0__iff,axiom,
! [A: int] :
( ( ( plus_plus_int @ A @ A )
= zero_zero_int )
= ( A = zero_zero_int ) ) ).
% double_eq_0_iff
thf(fact_190_add__left__cancel,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
= ( B = C ) ) ).
% add_left_cancel
thf(fact_191_add__left__cancel,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ) ).
% add_left_cancel
thf(fact_192_add__right__cancel,axiom,
! [B: int,A: int,C: int] :
( ( ( plus_plus_int @ B @ A )
= ( plus_plus_int @ C @ A ) )
= ( B = C ) ) ).
% add_right_cancel
thf(fact_193_add__right__cancel,axiom,
! [B: nat,A: nat,C: nat] :
( ( ( plus_plus_nat @ B @ A )
= ( plus_plus_nat @ C @ A ) )
= ( B = C ) ) ).
% add_right_cancel
thf(fact_194_list_Oinject,axiom,
! [X21: int,X222: list_int,Y21: int,Y222: list_int] :
( ( ( cons_int @ X21 @ X222 )
= ( cons_int @ Y21 @ Y222 ) )
= ( ( X21 = Y21 )
& ( X222 = Y222 ) ) ) ).
% list.inject
thf(fact_195_list_Oinject,axiom,
! [X21: instr,X222: list_instr,Y21: instr,Y222: list_instr] :
( ( ( cons_instr @ X21 @ X222 )
= ( cons_instr @ Y21 @ Y222 ) )
= ( ( X21 = Y21 )
& ( X222 = Y222 ) ) ) ).
% list.inject
thf(fact_196_list_Oinject,axiom,
! [X21: produc6425607678544837394st_int,X222: list_P419547167332244514st_int,Y21: produc6425607678544837394st_int,Y222: list_P419547167332244514st_int] :
( ( ( cons_P4151473878978182108st_int @ X21 @ X222 )
= ( cons_P4151473878978182108st_int @ Y21 @ Y222 ) )
= ( ( X21 = Y21 )
& ( X222 = Y222 ) ) ) ).
% list.inject
thf(fact_197_list_Oinject,axiom,
! [X21: list_char,X222: list_list_char,Y21: list_char,Y222: list_list_char] :
( ( ( cons_list_char @ X21 @ X222 )
= ( cons_list_char @ Y21 @ Y222 ) )
= ( ( X21 = Y21 )
& ( X222 = Y222 ) ) ) ).
% list.inject
thf(fact_198_not__gr__zero,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) ).
% not_gr_zero
thf(fact_199_add_Oright__neutral,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ) ).
% add.right_neutral
thf(fact_200_add_Oright__neutral,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ) ).
% add.right_neutral
thf(fact_201_double__zero__sym,axiom,
! [A: int] :
( ( zero_zero_int
= ( plus_plus_int @ A @ A ) )
= ( A = zero_zero_int ) ) ).
% double_zero_sym
thf(fact_202_add__cancel__left__left,axiom,
! [B: nat,A: nat] :
( ( ( plus_plus_nat @ B @ A )
= A )
= ( B = zero_zero_nat ) ) ).
% add_cancel_left_left
thf(fact_203_add__cancel__left__left,axiom,
! [B: int,A: int] :
( ( ( plus_plus_int @ B @ A )
= A )
= ( B = zero_zero_int ) ) ).
% add_cancel_left_left
thf(fact_204_add__cancel__left__right,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
= ( B = zero_zero_nat ) ) ).
% add_cancel_left_right
thf(fact_205_add__cancel__left__right,axiom,
! [A: int,B: int] :
( ( ( plus_plus_int @ A @ B )
= A )
= ( B = zero_zero_int ) ) ).
% add_cancel_left_right
thf(fact_206_add__cancel__right__left,axiom,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ B @ A ) )
= ( B = zero_zero_nat ) ) ).
% add_cancel_right_left
thf(fact_207_add__cancel__right__left,axiom,
! [A: int,B: int] :
( ( A
= ( plus_plus_int @ B @ A ) )
= ( B = zero_zero_int ) ) ).
% add_cancel_right_left
thf(fact_208_add__cancel__right__right,axiom,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ) ).
% add_cancel_right_right
thf(fact_209_add__cancel__right__right,axiom,
! [A: int,B: int] :
( ( A
= ( plus_plus_int @ A @ B ) )
= ( B = zero_zero_int ) ) ).
% add_cancel_right_right
thf(fact_210_add__eq__0__iff__both__eq__0,axiom,
! [X: nat,Y: nat] :
( ( ( plus_plus_nat @ X @ Y )
= zero_zero_nat )
= ( ( X = zero_zero_nat )
& ( Y = zero_zero_nat ) ) ) ).
% add_eq_0_iff_both_eq_0
thf(fact_211_zero__eq__add__iff__both__eq__0,axiom,
! [X: nat,Y: nat] :
( ( zero_zero_nat
= ( plus_plus_nat @ X @ Y ) )
= ( ( X = zero_zero_nat )
& ( Y = zero_zero_nat ) ) ) ).
% zero_eq_add_iff_both_eq_0
thf(fact_212_add__0,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ) ).
% add_0
thf(fact_213_add__0,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ) ).
% add_0
thf(fact_214_less__int__code_I1_J,axiom,
~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% less_int_code(1)
thf(fact_215_int__gr__induct,axiom,
! [K2: int,I: int,P: int > $o] :
( ( ord_less_int @ K2 @ I )
=> ( ( P @ ( plus_plus_int @ K2 @ one_one_int ) )
=> ( ! [I3: int] :
( ( ord_less_int @ K2 @ I3 )
=> ( ( P @ I3 )
=> ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
=> ( P @ I ) ) ) ) ).
% int_gr_induct
thf(fact_216_zless__add1__eq,axiom,
! [W: int,Z: int] :
( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
= ( ( ord_less_int @ W @ Z )
| ( W = Z ) ) ) ).
% zless_add1_eq
thf(fact_217_zless__iff__Suc__zadd,axiom,
( ord_less_int
= ( ^ [W2: int,Z2: int] :
? [N2: nat] :
( Z2
= ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ) ).
% zless_iff_Suc_zadd
thf(fact_218_odd__less__0__iff,axiom,
! [Z: int] :
( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
= ( ord_less_int @ Z @ zero_zero_int ) ) ).
% odd_less_0_iff
thf(fact_219_nat__int__comparison_I2_J,axiom,
( ord_less_nat
= ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% nat_int_comparison(2)
thf(fact_220_zero__less__imp__eq__int,axiom,
! [K2: int] :
( ( ord_less_int @ zero_zero_int @ K2 )
=> ? [N3: nat] :
( ( ord_less_nat @ zero_zero_nat @ N3 )
& ( K2
= ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% zero_less_imp_eq_int
thf(fact_221_pos__int__cases,axiom,
! [K2: int] :
( ( ord_less_int @ zero_zero_int @ K2 )
=> ~ ! [N3: nat] :
( ( K2
= ( semiri1314217659103216013at_int @ N3 ) )
=> ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% pos_int_cases
thf(fact_222_zero__reorient,axiom,
! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ) ).
% zero_reorient
thf(fact_223_zero__reorient,axiom,
! [X: int] :
( ( zero_zero_int = X )
= ( X = zero_zero_int ) ) ).
% zero_reorient
thf(fact_224_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% ab_semigroup_add_class.add_ac(1)
thf(fact_225_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% ab_semigroup_add_class.add_ac(1)
thf(fact_226_add__mono__thms__linordered__semiring_I4_J,axiom,
! [I: int,J: int,K2: int,L: int] :
( ( ( I = J )
& ( K2 = L ) )
=> ( ( plus_plus_int @ I @ K2 )
= ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(4)
thf(fact_227_add__mono__thms__linordered__semiring_I4_J,axiom,
! [I: nat,J: nat,K2: nat,L: nat] :
( ( ( I = J )
& ( K2 = L ) )
=> ( ( plus_plus_nat @ I @ K2 )
= ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(4)
thf(fact_228_group__cancel_Oadd1,axiom,
! [A2: int,K2: int,A: int,B: int] :
( ( A2
= ( plus_plus_int @ K2 @ A ) )
=> ( ( plus_plus_int @ A2 @ B )
= ( plus_plus_int @ K2 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% group_cancel.add1
thf(fact_229_group__cancel_Oadd1,axiom,
! [A2: nat,K2: nat,A: nat,B: nat] :
( ( A2
= ( plus_plus_nat @ K2 @ A ) )
=> ( ( plus_plus_nat @ A2 @ B )
= ( plus_plus_nat @ K2 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% group_cancel.add1
thf(fact_230_group__cancel_Oadd2,axiom,
! [B3: int,K2: int,B: int,A: int] :
( ( B3
= ( plus_plus_int @ K2 @ B ) )
=> ( ( plus_plus_int @ A @ B3 )
= ( plus_plus_int @ K2 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% group_cancel.add2
thf(fact_231_group__cancel_Oadd2,axiom,
! [B3: nat,K2: nat,B: nat,A: nat] :
( ( B3
= ( plus_plus_nat @ K2 @ B ) )
=> ( ( plus_plus_nat @ A @ B3 )
= ( plus_plus_nat @ K2 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% group_cancel.add2
thf(fact_232_add_Oassoc,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% add.assoc
thf(fact_233_add_Oassoc,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% add.assoc
thf(fact_234_add_Oleft__cancel,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
= ( B = C ) ) ).
% add.left_cancel
thf(fact_235_add_Oright__cancel,axiom,
! [B: int,A: int,C: int] :
( ( ( plus_plus_int @ B @ A )
= ( plus_plus_int @ C @ A ) )
= ( B = C ) ) ).
% add.right_cancel
thf(fact_236_add_Ocommute,axiom,
( plus_plus_int
= ( ^ [A3: int,B2: int] : ( plus_plus_int @ B2 @ A3 ) ) ) ).
% add.commute
thf(fact_237_add_Ocommute,axiom,
( plus_plus_nat
= ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).
% add.commute
thf(fact_238_add_Oleft__commute,axiom,
! [B: int,A: int,C: int] :
( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% add.left_commute
thf(fact_239_add_Oleft__commute,axiom,
! [B: nat,A: nat,C: nat] :
( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% add.left_commute
thf(fact_240_add__left__imp__eq,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
=> ( B = C ) ) ).
% add_left_imp_eq
thf(fact_241_add__left__imp__eq,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ) ).
% add_left_imp_eq
thf(fact_242_add__right__imp__eq,axiom,
! [B: int,A: int,C: int] :
( ( ( plus_plus_int @ B @ A )
= ( plus_plus_int @ C @ A ) )
=> ( B = C ) ) ).
% add_right_imp_eq
thf(fact_243_add__right__imp__eq,axiom,
! [B: nat,A: nat,C: nat] :
( ( ( plus_plus_nat @ B @ A )
= ( plus_plus_nat @ C @ A ) )
=> ( B = C ) ) ).
% add_right_imp_eq
thf(fact_244_one__reorient,axiom,
! [X: int] :
( ( one_one_int = X )
= ( X = one_one_int ) ) ).
% one_reorient
thf(fact_245_one__reorient,axiom,
! [X: nat] :
( ( one_one_nat = X )
= ( X = one_one_nat ) ) ).
% one_reorient
thf(fact_246_not__Cons__self2,axiom,
! [X: int,Xs: list_int] :
( ( cons_int @ X @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_247_not__Cons__self2,axiom,
! [X: instr,Xs: list_instr] :
( ( cons_instr @ X @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_248_not__Cons__self2,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int] :
( ( cons_P4151473878978182108st_int @ X @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_249_not__Cons__self2,axiom,
! [X: list_char,Xs: list_list_char] :
( ( cons_list_char @ X @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_250_Ex__list__of__length,axiom,
! [N: nat] :
? [Xs2: list_int] :
( ( size_size_list_int @ Xs2 )
= N ) ).
% Ex_list_of_length
thf(fact_251_neq__if__length__neq,axiom,
! [Xs: list_int,Ys: list_int] :
( ( ( size_size_list_int @ Xs )
!= ( size_size_list_int @ Ys ) )
=> ( Xs != Ys ) ) ).
% neq_if_length_neq
thf(fact_252_int__int__eq,axiom,
! [M: nat,N: nat] :
( ( ( semiri1314217659103216013at_int @ M )
= ( semiri1314217659103216013at_int @ N ) )
= ( M = N ) ) ).
% int_int_eq
thf(fact_253_zero__less__iff__neq__zero,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ) ).
% zero_less_iff_neq_zero
thf(fact_254_gr__implies__not__zero,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) ).
% gr_implies_not_zero
thf(fact_255_not__less__zero,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% not_less_zero
thf(fact_256_gr__zeroI,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% gr_zeroI
thf(fact_257_comm__monoid__add__class_Oadd__0,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ) ).
% comm_monoid_add_class.add_0
thf(fact_258_comm__monoid__add__class_Oadd__0,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ) ).
% comm_monoid_add_class.add_0
thf(fact_259_add_Ocomm__neutral,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ) ).
% add.comm_neutral
thf(fact_260_add_Ocomm__neutral,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ) ).
% add.comm_neutral
thf(fact_261_add_Ogroup__left__neutral,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ) ).
% add.group_left_neutral
thf(fact_262_add__mono__thms__linordered__field_I5_J,axiom,
! [I: nat,J: nat,K2: nat,L: nat] :
( ( ( ord_less_nat @ I @ J )
& ( ord_less_nat @ K2 @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K2 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(5)
thf(fact_263_add__mono__thms__linordered__field_I5_J,axiom,
! [I: int,J: int,K2: int,L: int] :
( ( ( ord_less_int @ I @ J )
& ( ord_less_int @ K2 @ L ) )
=> ( ord_less_int @ ( plus_plus_int @ I @ K2 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(5)
thf(fact_264_add__mono__thms__linordered__field_I2_J,axiom,
! [I: nat,J: nat,K2: nat,L: nat] :
( ( ( I = J )
& ( ord_less_nat @ K2 @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K2 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(2)
thf(fact_265_add__mono__thms__linordered__field_I2_J,axiom,
! [I: int,J: int,K2: int,L: int] :
( ( ( I = J )
& ( ord_less_int @ K2 @ L ) )
=> ( ord_less_int @ ( plus_plus_int @ I @ K2 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(2)
thf(fact_266_add__mono__thms__linordered__field_I1_J,axiom,
! [I: nat,J: nat,K2: nat,L: nat] :
( ( ( ord_less_nat @ I @ J )
& ( K2 = L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K2 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(1)
thf(fact_267_add__mono__thms__linordered__field_I1_J,axiom,
! [I: int,J: int,K2: int,L: int] :
( ( ( ord_less_int @ I @ J )
& ( K2 = L ) )
=> ( ord_less_int @ ( plus_plus_int @ I @ K2 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(1)
thf(fact_268_add__strict__mono,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% add_strict_mono
thf(fact_269_add__strict__mono,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ C @ D )
=> ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% add_strict_mono
thf(fact_270_add__strict__left__mono,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% add_strict_left_mono
thf(fact_271_add__strict__left__mono,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% add_strict_left_mono
thf(fact_272_add__strict__right__mono,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% add_strict_right_mono
thf(fact_273_add__strict__right__mono,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% add_strict_right_mono
thf(fact_274_add__less__imp__less__left,axiom,
! [C: nat,A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ).
% add_less_imp_less_left
thf(fact_275_add__less__imp__less__left,axiom,
! [C: int,A: int,B: int] :
( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
=> ( ord_less_int @ A @ B ) ) ).
% add_less_imp_less_left
thf(fact_276_add__less__imp__less__right,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
=> ( ord_less_nat @ A @ B ) ) ).
% add_less_imp_less_right
thf(fact_277_add__less__imp__less__right,axiom,
! [A: int,C: int,B: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
=> ( ord_less_int @ A @ B ) ) ).
% add_less_imp_less_right
thf(fact_278_length__induct,axiom,
! [P: list_int > $o,Xs: list_int] :
( ! [Xs2: list_int] :
( ! [Ys2: list_int] :
( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs2 ) )
=> ( P @ Ys2 ) )
=> ( P @ Xs2 ) )
=> ( P @ Xs ) ) ).
% length_induct
thf(fact_279_plus__int__code_I2_J,axiom,
! [L: int] :
( ( plus_plus_int @ zero_zero_int @ L )
= L ) ).
% plus_int_code(2)
thf(fact_280_plus__int__code_I1_J,axiom,
! [K2: int] :
( ( plus_plus_int @ K2 @ zero_zero_int )
= K2 ) ).
% plus_int_code(1)
thf(fact_281_add__neg__neg,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ zero_zero_nat )
=> ( ( ord_less_nat @ B @ zero_zero_nat )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% add_neg_neg
thf(fact_282_add__neg__neg,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ zero_zero_int )
=> ( ( ord_less_int @ B @ zero_zero_int )
=> ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% add_neg_neg
thf(fact_283_add__pos__pos,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% add_pos_pos
thf(fact_284_add__pos__pos,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% add_pos_pos
thf(fact_285_canonically__ordered__monoid__add__class_OlessE,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ! [C2: nat] :
( ( B
= ( plus_plus_nat @ A @ C2 ) )
=> ( C2 = zero_zero_nat ) ) ) ).
% canonically_ordered_monoid_add_class.lessE
thf(fact_286_pos__add__strict,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% pos_add_strict
thf(fact_287_pos__add__strict,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% pos_add_strict
thf(fact_288_Suc__length__conv,axiom,
! [N: nat,Xs: list_instr] :
( ( ( suc @ N )
= ( size_size_list_instr @ Xs ) )
= ( ? [Y2: instr,Ys3: list_instr] :
( ( Xs
= ( cons_instr @ Y2 @ Ys3 ) )
& ( ( size_size_list_instr @ Ys3 )
= N ) ) ) ) ).
% Suc_length_conv
thf(fact_289_Suc__length__conv,axiom,
! [N: nat,Xs: list_P419547167332244514st_int] :
( ( ( suc @ N )
= ( size_s229347708945616566st_int @ Xs ) )
= ( ? [Y2: produc6425607678544837394st_int,Ys3: list_P419547167332244514st_int] :
( ( Xs
= ( cons_P4151473878978182108st_int @ Y2 @ Ys3 ) )
& ( ( size_s229347708945616566st_int @ Ys3 )
= N ) ) ) ) ).
% Suc_length_conv
thf(fact_290_Suc__length__conv,axiom,
! [N: nat,Xs: list_list_char] :
( ( ( suc @ N )
= ( size_s356637359517785349t_char @ Xs ) )
= ( ? [Y2: list_char,Ys3: list_list_char] :
( ( Xs
= ( cons_list_char @ Y2 @ Ys3 ) )
& ( ( size_s356637359517785349t_char @ Ys3 )
= N ) ) ) ) ).
% Suc_length_conv
thf(fact_291_Suc__length__conv,axiom,
! [N: nat,Xs: list_int] :
( ( ( suc @ N )
= ( size_size_list_int @ Xs ) )
= ( ? [Y2: int,Ys3: list_int] :
( ( Xs
= ( cons_int @ Y2 @ Ys3 ) )
& ( ( size_size_list_int @ Ys3 )
= N ) ) ) ) ).
% Suc_length_conv
thf(fact_292_length__Suc__conv,axiom,
! [Xs: list_instr,N: nat] :
( ( ( size_size_list_instr @ Xs )
= ( suc @ N ) )
= ( ? [Y2: instr,Ys3: list_instr] :
( ( Xs
= ( cons_instr @ Y2 @ Ys3 ) )
& ( ( size_size_list_instr @ Ys3 )
= N ) ) ) ) ).
% length_Suc_conv
thf(fact_293_length__Suc__conv,axiom,
! [Xs: list_P419547167332244514st_int,N: nat] :
( ( ( size_s229347708945616566st_int @ Xs )
= ( suc @ N ) )
= ( ? [Y2: produc6425607678544837394st_int,Ys3: list_P419547167332244514st_int] :
( ( Xs
= ( cons_P4151473878978182108st_int @ Y2 @ Ys3 ) )
& ( ( size_s229347708945616566st_int @ Ys3 )
= N ) ) ) ) ).
% length_Suc_conv
thf(fact_294_length__Suc__conv,axiom,
! [Xs: list_list_char,N: nat] :
( ( ( size_s356637359517785349t_char @ Xs )
= ( suc @ N ) )
= ( ? [Y2: list_char,Ys3: list_list_char] :
( ( Xs
= ( cons_list_char @ Y2 @ Ys3 ) )
& ( ( size_s356637359517785349t_char @ Ys3 )
= N ) ) ) ) ).
% length_Suc_conv
thf(fact_295_length__Suc__conv,axiom,
! [Xs: list_int,N: nat] :
( ( ( size_size_list_int @ Xs )
= ( suc @ N ) )
= ( ? [Y2: int,Ys3: list_int] :
( ( Xs
= ( cons_int @ Y2 @ Ys3 ) )
& ( ( size_size_list_int @ Ys3 )
= N ) ) ) ) ).
% length_Suc_conv
thf(fact_296_nth__equalityI,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( ( size_s229347708945616566st_int @ Xs )
= ( size_s229347708945616566st_int @ Ys ) )
=> ( ! [I3: nat] :
( ( ord_less_nat @ I3 @ ( size_s229347708945616566st_int @ Xs ) )
=> ( ( nth_Pr8327173284404383691st_int @ Xs @ I3 )
= ( nth_Pr8327173284404383691st_int @ Ys @ I3 ) ) )
=> ( Xs = Ys ) ) ) ).
% nth_equalityI
thf(fact_297_nth__equalityI,axiom,
! [Xs: list_int,Ys: list_int] :
( ( ( size_size_list_int @ Xs )
= ( size_size_list_int @ Ys ) )
=> ( ! [I3: nat] :
( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
=> ( ( nth_int @ Xs @ I3 )
= ( nth_int @ Ys @ I3 ) ) )
=> ( Xs = Ys ) ) ) ).
% nth_equalityI
thf(fact_298_Skolem__list__nth,axiom,
! [K2: nat,P: nat > produc6425607678544837394st_int > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ K2 )
=> ? [X4: produc6425607678544837394st_int] : ( P @ I2 @ X4 ) ) )
= ( ? [Xs3: list_P419547167332244514st_int] :
( ( ( size_s229347708945616566st_int @ Xs3 )
= K2 )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ K2 )
=> ( P @ I2 @ ( nth_Pr8327173284404383691st_int @ Xs3 @ I2 ) ) ) ) ) ) ).
% Skolem_list_nth
thf(fact_299_Skolem__list__nth,axiom,
! [K2: nat,P: nat > int > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ K2 )
=> ? [X4: int] : ( P @ I2 @ X4 ) ) )
= ( ? [Xs3: list_int] :
( ( ( size_size_list_int @ Xs3 )
= K2 )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ K2 )
=> ( P @ I2 @ ( nth_int @ Xs3 @ I2 ) ) ) ) ) ) ).
% Skolem_list_nth
thf(fact_300_list__eq__iff__nth__eq,axiom,
( ( ^ [Y4: list_P419547167332244514st_int,Z3: list_P419547167332244514st_int] : ( Y4 = Z3 ) )
= ( ^ [Xs3: list_P419547167332244514st_int,Ys3: list_P419547167332244514st_int] :
( ( ( size_s229347708945616566st_int @ Xs3 )
= ( size_s229347708945616566st_int @ Ys3 ) )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_s229347708945616566st_int @ Xs3 ) )
=> ( ( nth_Pr8327173284404383691st_int @ Xs3 @ I2 )
= ( nth_Pr8327173284404383691st_int @ Ys3 @ I2 ) ) ) ) ) ) ).
% list_eq_iff_nth_eq
thf(fact_301_list__eq__iff__nth__eq,axiom,
( ( ^ [Y4: list_int,Z3: list_int] : ( Y4 = Z3 ) )
= ( ^ [Xs3: list_int,Ys3: list_int] :
( ( ( size_size_list_int @ Xs3 )
= ( size_size_list_int @ Ys3 ) )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs3 ) )
=> ( ( nth_int @ Xs3 @ I2 )
= ( nth_int @ Ys3 @ I2 ) ) ) ) ) ) ).
% list_eq_iff_nth_eq
thf(fact_302_odd__nonzero,axiom,
! [Z: int] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
!= zero_zero_int ) ).
% odd_nonzero
thf(fact_303_zadd__int__left,axiom,
! [M: nat,N: nat,Z: int] :
( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% zadd_int_left
thf(fact_304_zero__less__two,axiom,
ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% zero_less_two
thf(fact_305_zero__less__two,axiom,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% zero_less_two
thf(fact_306_length__Cons,axiom,
! [X: instr,Xs: list_instr] :
( ( size_size_list_instr @ ( cons_instr @ X @ Xs ) )
= ( suc @ ( size_size_list_instr @ Xs ) ) ) ).
% length_Cons
thf(fact_307_length__Cons,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int] :
( ( size_s229347708945616566st_int @ ( cons_P4151473878978182108st_int @ X @ Xs ) )
= ( suc @ ( size_s229347708945616566st_int @ Xs ) ) ) ).
% length_Cons
thf(fact_308_length__Cons,axiom,
! [X: list_char,Xs: list_list_char] :
( ( size_s356637359517785349t_char @ ( cons_list_char @ X @ Xs ) )
= ( suc @ ( size_s356637359517785349t_char @ Xs ) ) ) ).
% length_Cons
thf(fact_309_length__Cons,axiom,
! [X: int,Xs: list_int] :
( ( size_size_list_int @ ( cons_int @ X @ Xs ) )
= ( suc @ ( size_size_list_int @ Xs ) ) ) ).
% length_Cons
thf(fact_310_less__add__one,axiom,
! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% less_add_one
thf(fact_311_less__add__one,axiom,
! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% less_add_one
thf(fact_312_add__mono1,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% add_mono1
thf(fact_313_add__mono1,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% add_mono1
thf(fact_314_less__numeral__extra_I1_J,axiom,
ord_less_nat @ zero_zero_nat @ one_one_nat ).
% less_numeral_extra(1)
thf(fact_315_less__numeral__extra_I1_J,axiom,
ord_less_int @ zero_zero_int @ one_one_int ).
% less_numeral_extra(1)
thf(fact_316_zero__less__one,axiom,
ord_less_nat @ zero_zero_nat @ one_one_nat ).
% zero_less_one
thf(fact_317_zero__less__one,axiom,
ord_less_int @ zero_zero_int @ one_one_int ).
% zero_less_one
thf(fact_318_not__one__less__zero,axiom,
~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% not_one_less_zero
thf(fact_319_not__one__less__zero,axiom,
~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% not_one_less_zero
thf(fact_320_add__less__zeroD,axiom,
! [X: int,Y: int] :
( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
=> ( ( ord_less_int @ X @ zero_zero_int )
| ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% add_less_zeroD
thf(fact_321_linorder__neqE__linordered__idom,axiom,
! [X: int,Y: int] :
( ( X != Y )
=> ( ~ ( ord_less_int @ X @ Y )
=> ( ord_less_int @ Y @ X ) ) ) ).
% linorder_neqE_linordered_idom
thf(fact_322_is__num__normalize_I1_J,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% is_num_normalize(1)
thf(fact_323_less__numeral__extra_I3_J,axiom,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% less_numeral_extra(3)
thf(fact_324_less__numeral__extra_I3_J,axiom,
~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% less_numeral_extra(3)
thf(fact_325_zero__neq__one,axiom,
zero_zero_nat != one_one_nat ).
% zero_neq_one
thf(fact_326_zero__neq__one,axiom,
zero_zero_int != one_one_int ).
% zero_neq_one
thf(fact_327_less__numeral__extra_I4_J,axiom,
~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% less_numeral_extra(4)
thf(fact_328_less__numeral__extra_I4_J,axiom,
~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% less_numeral_extra(4)
thf(fact_329_size__char__eq__0,axiom,
( size_size_char
= ( ^ [C3: char] : zero_zero_nat ) ) ).
% size_char_eq_0
thf(fact_330_old_Oprod_Oinject,axiom,
! [A: int,B: int,A4: int,B4: int] :
( ( ( product_Pair_int_int @ A @ B )
= ( product_Pair_int_int @ A4 @ B4 ) )
= ( ( A = A4 )
& ( B = B4 ) ) ) ).
% old.prod.inject
thf(fact_331_old_Oprod_Oinject,axiom,
! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int] :
( ( ( produc5700946648718959541nt_int @ A @ B )
= ( produc5700946648718959541nt_int @ A4 @ B4 ) )
= ( ( A = A4 )
& ( B = B4 ) ) ) ).
% old.prod.inject
thf(fact_332_old_Oprod_Oinject,axiom,
! [A: list_char > int,B: list_int,A4: list_char > int,B4: list_int] :
( ( ( produc8650753666468850689st_int @ A @ B )
= ( produc8650753666468850689st_int @ A4 @ B4 ) )
= ( ( A = A4 )
& ( B = B4 ) ) ) ).
% old.prod.inject
thf(fact_333_old_Oprod_Oinject,axiom,
! [A: list_char > int,B: int,A4: list_char > int,B4: int] :
( ( ( produc5790713362662368625nt_int @ A @ B )
= ( produc5790713362662368625nt_int @ A4 @ B4 ) )
= ( ( A = A4 )
& ( B = B4 ) ) ) ).
% old.prod.inject
thf(fact_334_old_Oprod_Oinject,axiom,
! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A4: int > option6357759511663192854e_term,B4: product_prod_int_int] :
( ( ( produc4305682042979456191nt_int @ A @ B )
= ( produc4305682042979456191nt_int @ A4 @ B4 ) )
= ( ( A = A4 )
& ( B = B4 ) ) ) ).
% old.prod.inject
thf(fact_335_prod_Oinject,axiom,
! [X1: int,X22: int,Y1: int,Y22: int] :
( ( ( product_Pair_int_int @ X1 @ X22 )
= ( product_Pair_int_int @ Y1 @ Y22 ) )
= ( ( X1 = Y1 )
& ( X22 = Y22 ) ) ) ).
% prod.inject
thf(fact_336_prod_Oinject,axiom,
! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X22: product_prod_int_int,Y1: produc8551481072490612790e_term > option6357759511663192854e_term,Y22: product_prod_int_int] :
( ( ( produc5700946648718959541nt_int @ X1 @ X22 )
= ( produc5700946648718959541nt_int @ Y1 @ Y22 ) )
= ( ( X1 = Y1 )
& ( X22 = Y22 ) ) ) ).
% prod.inject
thf(fact_337_prod_Oinject,axiom,
! [X1: list_char > int,X22: list_int,Y1: list_char > int,Y22: list_int] :
( ( ( produc8650753666468850689st_int @ X1 @ X22 )
= ( produc8650753666468850689st_int @ Y1 @ Y22 ) )
= ( ( X1 = Y1 )
& ( X22 = Y22 ) ) ) ).
% prod.inject
thf(fact_338_prod_Oinject,axiom,
! [X1: list_char > int,X22: int,Y1: list_char > int,Y22: int] :
( ( ( produc5790713362662368625nt_int @ X1 @ X22 )
= ( produc5790713362662368625nt_int @ Y1 @ Y22 ) )
= ( ( X1 = Y1 )
& ( X22 = Y22 ) ) ) ).
% prod.inject
thf(fact_339_prod_Oinject,axiom,
! [X1: int > option6357759511663192854e_term,X22: product_prod_int_int,Y1: int > option6357759511663192854e_term,Y22: product_prod_int_int] :
( ( ( produc4305682042979456191nt_int @ X1 @ X22 )
= ( produc4305682042979456191nt_int @ Y1 @ Y22 ) )
= ( ( X1 = Y1 )
& ( X22 = Y22 ) ) ) ).
% prod.inject
thf(fact_340_iexec_Ocases,axiom,
! [X: produc5995290525303592096st_int] :
~ ! [Ins: instr,I3: int,S: list_char > int,Stk: list_int] :
( X
!= ( produc1484136438817787418st_int @ Ins @ ( produc5086643055186798020st_int @ I3 @ ( produc8650753666468850689st_int @ S @ Stk ) ) ) ) ).
% iexec.cases
thf(fact_341_old_Oprod_Oexhaust,axiom,
! [Y: product_prod_int_int] :
~ ! [A5: int,B5: int] :
( Y
!= ( product_Pair_int_int @ A5 @ B5 ) ) ).
% old.prod.exhaust
thf(fact_342_old_Oprod_Oexhaust,axiom,
! [Y: produc2285326912895808259nt_int] :
~ ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] :
( Y
!= ( produc5700946648718959541nt_int @ A5 @ B5 ) ) ).
% old.prod.exhaust
thf(fact_343_old_Oprod_Oexhaust,axiom,
! [Y: produc369741286924889929st_int] :
~ ! [A5: list_char > int,B5: list_int] :
( Y
!= ( produc8650753666468850689st_int @ A5 @ B5 ) ) ).
% old.prod.exhaust
thf(fact_344_old_Oprod_Oexhaust,axiom,
! [Y: produc4435102495419491129nt_int] :
~ ! [A5: list_char > int,B5: int] :
( Y
!= ( produc5790713362662368625nt_int @ A5 @ B5 ) ) ).
% old.prod.exhaust
thf(fact_345_old_Oprod_Oexhaust,axiom,
! [Y: produc7773217078559923341nt_int] :
~ ! [A5: int > option6357759511663192854e_term,B5: product_prod_int_int] :
( Y
!= ( produc4305682042979456191nt_int @ A5 @ B5 ) ) ).
% old.prod.exhaust
thf(fact_346_surj__pair,axiom,
! [P2: product_prod_int_int] :
? [X3: int,Y3: int] :
( P2
= ( product_Pair_int_int @ X3 @ Y3 ) ) ).
% surj_pair
thf(fact_347_surj__pair,axiom,
! [P2: produc2285326912895808259nt_int] :
? [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] :
( P2
= ( produc5700946648718959541nt_int @ X3 @ Y3 ) ) ).
% surj_pair
thf(fact_348_surj__pair,axiom,
! [P2: produc369741286924889929st_int] :
? [X3: list_char > int,Y3: list_int] :
( P2
= ( produc8650753666468850689st_int @ X3 @ Y3 ) ) ).
% surj_pair
thf(fact_349_surj__pair,axiom,
! [P2: produc4435102495419491129nt_int] :
? [X3: list_char > int,Y3: int] :
( P2
= ( produc5790713362662368625nt_int @ X3 @ Y3 ) ) ).
% surj_pair
thf(fact_350_surj__pair,axiom,
! [P2: produc7773217078559923341nt_int] :
? [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] :
( P2
= ( produc4305682042979456191nt_int @ X3 @ Y3 ) ) ).
% surj_pair
thf(fact_351_prod__cases,axiom,
! [P: product_prod_int_int > $o,P2: product_prod_int_int] :
( ! [A5: int,B5: int] : ( P @ ( product_Pair_int_int @ A5 @ B5 ) )
=> ( P @ P2 ) ) ).
% prod_cases
thf(fact_352_prod__cases,axiom,
! [P: produc2285326912895808259nt_int > $o,P2: produc2285326912895808259nt_int] :
( ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] : ( P @ ( produc5700946648718959541nt_int @ A5 @ B5 ) )
=> ( P @ P2 ) ) ).
% prod_cases
thf(fact_353_prod__cases,axiom,
! [P: produc369741286924889929st_int > $o,P2: produc369741286924889929st_int] :
( ! [A5: list_char > int,B5: list_int] : ( P @ ( produc8650753666468850689st_int @ A5 @ B5 ) )
=> ( P @ P2 ) ) ).
% prod_cases
thf(fact_354_prod__cases,axiom,
! [P: produc4435102495419491129nt_int > $o,P2: produc4435102495419491129nt_int] :
( ! [A5: list_char > int,B5: int] : ( P @ ( produc5790713362662368625nt_int @ A5 @ B5 ) )
=> ( P @ P2 ) ) ).
% prod_cases
thf(fact_355_prod__cases,axiom,
! [P: produc7773217078559923341nt_int > $o,P2: produc7773217078559923341nt_int] :
( ! [A5: int > option6357759511663192854e_term,B5: product_prod_int_int] : ( P @ ( produc4305682042979456191nt_int @ A5 @ B5 ) )
=> ( P @ P2 ) ) ).
% prod_cases
thf(fact_356_Pair__inject,axiom,
! [A: int,B: int,A4: int,B4: int] :
( ( ( product_Pair_int_int @ A @ B )
= ( product_Pair_int_int @ A4 @ B4 ) )
=> ~ ( ( A = A4 )
=> ( B != B4 ) ) ) ).
% Pair_inject
thf(fact_357_Pair__inject,axiom,
! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int] :
( ( ( produc5700946648718959541nt_int @ A @ B )
= ( produc5700946648718959541nt_int @ A4 @ B4 ) )
=> ~ ( ( A = A4 )
=> ( B != B4 ) ) ) ).
% Pair_inject
thf(fact_358_Pair__inject,axiom,
! [A: list_char > int,B: list_int,A4: list_char > int,B4: list_int] :
( ( ( produc8650753666468850689st_int @ A @ B )
= ( produc8650753666468850689st_int @ A4 @ B4 ) )
=> ~ ( ( A = A4 )
=> ( B != B4 ) ) ) ).
% Pair_inject
thf(fact_359_Pair__inject,axiom,
! [A: list_char > int,B: int,A4: list_char > int,B4: int] :
( ( ( produc5790713362662368625nt_int @ A @ B )
= ( produc5790713362662368625nt_int @ A4 @ B4 ) )
=> ~ ( ( A = A4 )
=> ( B != B4 ) ) ) ).
% Pair_inject
thf(fact_360_Pair__inject,axiom,
! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A4: int > option6357759511663192854e_term,B4: product_prod_int_int] :
( ( ( produc4305682042979456191nt_int @ A @ B )
= ( produc4305682042979456191nt_int @ A4 @ B4 ) )
=> ~ ( ( A = A4 )
=> ( B != B4 ) ) ) ).
% Pair_inject
thf(fact_361_prod__cases3,axiom,
! [Y: produc2285326912895808259nt_int] :
~ ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: int,C2: int] :
( Y
!= ( produc5700946648718959541nt_int @ A5 @ ( product_Pair_int_int @ B5 @ C2 ) ) ) ).
% prod_cases3
thf(fact_362_prod__cases3,axiom,
! [Y: produc7773217078559923341nt_int] :
~ ! [A5: int > option6357759511663192854e_term,B5: int,C2: int] :
( Y
!= ( produc4305682042979456191nt_int @ A5 @ ( product_Pair_int_int @ B5 @ C2 ) ) ) ).
% prod_cases3
thf(fact_363_prod__induct3,axiom,
! [P: produc2285326912895808259nt_int > $o,X: produc2285326912895808259nt_int] :
( ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: int,C2: int] : ( P @ ( produc5700946648718959541nt_int @ A5 @ ( product_Pair_int_int @ B5 @ C2 ) ) )
=> ( P @ X ) ) ).
% prod_induct3
thf(fact_364_prod__induct3,axiom,
! [P: produc7773217078559923341nt_int > $o,X: produc7773217078559923341nt_int] :
( ! [A5: int > option6357759511663192854e_term,B5: int,C2: int] : ( P @ ( produc4305682042979456191nt_int @ A5 @ ( product_Pair_int_int @ B5 @ C2 ) ) )
=> ( P @ X ) ) ).
% prod_induct3
thf(fact_365_size_H__char__eq__0,axiom,
( size_char
= ( ^ [C3: char] : zero_zero_nat ) ) ).
% size'_char_eq_0
thf(fact_366_iexec__shift,axiom,
! [N: int,I4: int,S3: list_char > int,Stk2: list_int,Ins2: instr,I: int,S2: list_char > int,Stk3: list_int] :
( ( ( produc5086643055186798020st_int @ ( plus_plus_int @ N @ I4 ) @ ( produc8650753666468850689st_int @ S3 @ Stk2 ) )
= ( iexec @ Ins2 @ ( produc5086643055186798020st_int @ ( plus_plus_int @ N @ I ) @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) ) )
= ( ( produc5086643055186798020st_int @ I4 @ ( produc8650753666468850689st_int @ S3 @ Stk2 ) )
= ( iexec @ Ins2 @ ( produc5086643055186798020st_int @ I @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) ) ) ) ).
% iexec_shift
thf(fact_367_Euclid__induct,axiom,
! [P: nat > nat > $o,A: nat,B: nat] :
( ! [A5: nat,B5: nat] :
( ( P @ A5 @ B5 )
= ( P @ B5 @ A5 ) )
=> ( ! [A5: nat] : ( P @ A5 @ zero_zero_nat )
=> ( ! [A5: nat,B5: nat] :
( ( P @ A5 @ B5 )
=> ( P @ A5 @ ( plus_plus_nat @ A5 @ B5 ) ) )
=> ( P @ A @ B ) ) ) ) ).
% Euclid_induct
thf(fact_368_add__0__iff,axiom,
! [B: nat,A: nat] :
( ( B
= ( plus_plus_nat @ B @ A ) )
= ( A = zero_zero_nat ) ) ).
% add_0_iff
thf(fact_369_add__0__iff,axiom,
! [B: int,A: int] :
( ( B
= ( plus_plus_int @ B @ A ) )
= ( A = zero_zero_int ) ) ).
% add_0_iff
thf(fact_370_nth__Cons__pos,axiom,
! [N: nat,X: int,Xs: list_int] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
= ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% nth_Cons_pos
thf(fact_371_nth__Cons__pos,axiom,
! [N: nat,X: instr,Xs: list_instr] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( nth_instr @ ( cons_instr @ X @ Xs ) @ N )
= ( nth_instr @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% nth_Cons_pos
thf(fact_372_nth__Cons__pos,axiom,
! [N: nat,X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( nth_Pr8327173284404383691st_int @ ( cons_P4151473878978182108st_int @ X @ Xs ) @ N )
= ( nth_Pr8327173284404383691st_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% nth_Cons_pos
thf(fact_373_nth__Cons__pos,axiom,
! [N: nat,X: list_char,Xs: list_list_char] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( nth_list_char @ ( cons_list_char @ X @ Xs ) @ N )
= ( nth_list_char @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% nth_Cons_pos
thf(fact_374_diff__self,axiom,
! [A: int] :
( ( minus_minus_int @ A @ A )
= zero_zero_int ) ).
% diff_self
thf(fact_375_diff__0__right,axiom,
! [A: int] :
( ( minus_minus_int @ A @ zero_zero_int )
= A ) ).
% diff_0_right
thf(fact_376_zero__diff,axiom,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ) ).
% zero_diff
thf(fact_377_diff__zero,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ) ).
% diff_zero
thf(fact_378_diff__zero,axiom,
! [A: int] :
( ( minus_minus_int @ A @ zero_zero_int )
= A ) ).
% diff_zero
thf(fact_379_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ) ).
% cancel_comm_monoid_add_class.diff_cancel
thf(fact_380_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
! [A: int] :
( ( minus_minus_int @ A @ A )
= zero_zero_int ) ).
% cancel_comm_monoid_add_class.diff_cancel
thf(fact_381_add__diff__cancel__right_H,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ) ).
% add_diff_cancel_right'
thf(fact_382_add__diff__cancel__right_H,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
= A ) ).
% add_diff_cancel_right'
thf(fact_383_add__diff__cancel__right,axiom,
! [A: nat,C: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( minus_minus_nat @ A @ B ) ) ).
% add_diff_cancel_right
thf(fact_384_add__diff__cancel__right,axiom,
! [A: int,C: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
= ( minus_minus_int @ A @ B ) ) ).
% add_diff_cancel_right
thf(fact_385_add__diff__cancel__left_H,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ) ).
% add_diff_cancel_left'
thf(fact_386_add__diff__cancel__left_H,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
= B ) ).
% add_diff_cancel_left'
thf(fact_387_add__diff__cancel__left,axiom,
! [C: nat,A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( minus_minus_nat @ A @ B ) ) ).
% add_diff_cancel_left
thf(fact_388_add__diff__cancel__left,axiom,
! [C: int,A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
= ( minus_minus_int @ A @ B ) ) ).
% add_diff_cancel_left
thf(fact_389_diff__add__cancel,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
= A ) ).
% diff_add_cancel
thf(fact_390_add__diff__cancel,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
= A ) ).
% add_diff_cancel
thf(fact_391_diff__0__eq__0,axiom,
! [N: nat] :
( ( minus_minus_nat @ zero_zero_nat @ N )
= zero_zero_nat ) ).
% diff_0_eq_0
thf(fact_392_diff__self__eq__0,axiom,
! [M: nat] :
( ( minus_minus_nat @ M @ M )
= zero_zero_nat ) ).
% diff_self_eq_0
thf(fact_393_Suc__diff__diff,axiom,
! [M: nat,N: nat,K2: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K2 ) )
= ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K2 ) ) ).
% Suc_diff_diff
thf(fact_394_diff__Suc__Suc,axiom,
! [M: nat,N: nat] :
( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
= ( minus_minus_nat @ M @ N ) ) ).
% diff_Suc_Suc
thf(fact_395_diff__diff__left,axiom,
! [I: nat,J: nat,K2: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K2 )
= ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K2 ) ) ) ).
% diff_diff_left
thf(fact_396_diff__gt__0__iff__gt,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
= ( ord_less_int @ B @ A ) ) ).
% diff_gt_0_iff_gt
thf(fact_397_diff__add__zero,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
= zero_zero_nat ) ).
% diff_add_zero
thf(fact_398_diff__numeral__special_I9_J,axiom,
( ( minus_minus_int @ one_one_int @ one_one_int )
= zero_zero_int ) ).
% diff_numeral_special(9)
thf(fact_399_zero__less__diff,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
= ( ord_less_nat @ M @ N ) ) ).
% zero_less_diff
thf(fact_400_diff__Suc__1,axiom,
! [N: nat] :
( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
= N ) ).
% diff_Suc_1
thf(fact_401_Suc__pred,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
= N ) ) ).
% Suc_pred
thf(fact_402_Suc__lessI2,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ( M
!= ( minus_minus_nat @ N @ one_one_nat ) )
=> ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% Suc_lessI2
thf(fact_403_Suc__diff__1,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
= N ) ) ).
% Suc_diff_1
thf(fact_404_diff__right__commute,axiom,
! [A: nat,C: nat,B: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% diff_right_commute
thf(fact_405_diff__right__commute,axiom,
! [A: int,C: int,B: int] :
( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
= ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% diff_right_commute
thf(fact_406_diff__eq__diff__eq,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ).
% diff_eq_diff_eq
thf(fact_407_diff__commute,axiom,
! [I: nat,J: nat,K2: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K2 )
= ( minus_minus_nat @ ( minus_minus_nat @ I @ K2 ) @ J ) ) ).
% diff_commute
thf(fact_408_diff__left__imp__eq,axiom,
! [A: int,B: int,C: int] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ A @ C ) )
=> ( B = C ) ) ).
% diff_left_imp_eq
thf(fact_409_eq__iff__diff__eq__0,axiom,
( ( ^ [Y4: int,Z3: int] : ( Y4 = Z3 ) )
= ( ^ [A3: int,B2: int] :
( ( minus_minus_int @ A3 @ B2 )
= zero_zero_int ) ) ) ).
% eq_iff_diff_eq_0
thf(fact_410_diff__strict__mono,axiom,
! [A: int,B: int,D: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ D @ C )
=> ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% diff_strict_mono
thf(fact_411_diff__eq__diff__less,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( ord_less_int @ A @ B )
= ( ord_less_int @ C @ D ) ) ) ).
% diff_eq_diff_less
thf(fact_412_diff__strict__left__mono,axiom,
! [B: int,A: int,C: int] :
( ( ord_less_int @ B @ A )
=> ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% diff_strict_left_mono
thf(fact_413_diff__strict__right__mono,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% diff_strict_right_mono
thf(fact_414_diff__diff__eq,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% diff_diff_eq
thf(fact_415_diff__diff__eq,axiom,
! [A: int,B: int,C: int] :
( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
= ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% diff_diff_eq
thf(fact_416_add__implies__diff,axiom,
! [C: nat,B: nat,A: nat] :
( ( ( plus_plus_nat @ C @ B )
= A )
=> ( C
= ( minus_minus_nat @ A @ B ) ) ) ).
% add_implies_diff
thf(fact_417_add__implies__diff,axiom,
! [C: int,B: int,A: int] :
( ( ( plus_plus_int @ C @ B )
= A )
=> ( C
= ( minus_minus_int @ A @ B ) ) ) ).
% add_implies_diff
thf(fact_418_diff__add__eq__diff__diff__swap,axiom,
! [A: int,B: int,C: int] :
( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% diff_add_eq_diff_diff_swap
thf(fact_419_diff__add__eq,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
= ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% diff_add_eq
thf(fact_420_diff__diff__eq2,axiom,
! [A: int,B: int,C: int] :
( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% diff_diff_eq2
thf(fact_421_add__diff__eq,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% add_diff_eq
thf(fact_422_eq__diff__eq,axiom,
! [A: int,C: int,B: int] :
( ( A
= ( minus_minus_int @ C @ B ) )
= ( ( plus_plus_int @ A @ B )
= C ) ) ).
% eq_diff_eq
thf(fact_423_diff__eq__eq,axiom,
! [A: int,B: int,C: int] :
( ( ( minus_minus_int @ A @ B )
= C )
= ( A
= ( plus_plus_int @ C @ B ) ) ) ).
% diff_eq_eq
thf(fact_424_group__cancel_Osub1,axiom,
! [A2: int,K2: int,A: int,B: int] :
( ( A2
= ( plus_plus_int @ K2 @ A ) )
=> ( ( minus_minus_int @ A2 @ B )
= ( plus_plus_int @ K2 @ ( minus_minus_int @ A @ B ) ) ) ) ).
% group_cancel.sub1
thf(fact_425_minus__nat_Odiff__0,axiom,
! [M: nat] :
( ( minus_minus_nat @ M @ zero_zero_nat )
= M ) ).
% minus_nat.diff_0
thf(fact_426_diffs0__imp__equal,axiom,
! [M: nat,N: nat] :
( ( ( minus_minus_nat @ M @ N )
= zero_zero_nat )
=> ( ( ( minus_minus_nat @ N @ M )
= zero_zero_nat )
=> ( M = N ) ) ) ).
% diffs0_imp_equal
thf(fact_427_zero__induct__lemma,axiom,
! [P: nat > $o,K2: nat,I: nat] :
( ( P @ K2 )
=> ( ! [N3: nat] :
( ( P @ ( suc @ N3 ) )
=> ( P @ N3 ) )
=> ( P @ ( minus_minus_nat @ K2 @ I ) ) ) ) ).
% zero_induct_lemma
thf(fact_428_diff__less__mono2,axiom,
! [M: nat,N: nat,L: nat] :
( ( ord_less_nat @ M @ N )
=> ( ( ord_less_nat @ M @ L )
=> ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% diff_less_mono2
thf(fact_429_less__imp__diff__less,axiom,
! [J: nat,K2: nat,N: nat] :
( ( ord_less_nat @ J @ K2 )
=> ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K2 ) ) ).
% less_imp_diff_less
thf(fact_430_Nat_Odiff__cancel,axiom,
! [K2: nat,M: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ K2 @ M ) @ ( plus_plus_nat @ K2 @ N ) )
= ( minus_minus_nat @ M @ N ) ) ).
% Nat.diff_cancel
thf(fact_431_diff__cancel2,axiom,
! [M: nat,K2: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ M @ K2 ) @ ( plus_plus_nat @ N @ K2 ) )
= ( minus_minus_nat @ M @ N ) ) ).
% diff_cancel2
thf(fact_432_diff__add__inverse,axiom,
! [N: nat,M: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
= M ) ).
% diff_add_inverse
thf(fact_433_diff__add__inverse2,axiom,
! [M: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
= M ) ).
% diff_add_inverse2
thf(fact_434_less__iff__diff__less__0,axiom,
( ord_less_int
= ( ^ [A3: int,B2: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% less_iff_diff_less_0
thf(fact_435_linordered__semidom__class_Oadd__diff__inverse,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
= A ) ) ).
% linordered_semidom_class.add_diff_inverse
thf(fact_436_linordered__semidom__class_Oadd__diff__inverse,axiom,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
= A ) ) ).
% linordered_semidom_class.add_diff_inverse
thf(fact_437_less__diff__eq,axiom,
! [A: int,C: int,B: int] :
( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
= ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% less_diff_eq
thf(fact_438_diff__less__eq,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
= ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% diff_less_eq
thf(fact_439_diff__less,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_nat @ zero_zero_nat @ M )
=> ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% diff_less
thf(fact_440_diff__less__Suc,axiom,
! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% diff_less_Suc
thf(fact_441_Suc__diff__Suc,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ N @ M )
=> ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
= ( minus_minus_nat @ M @ N ) ) ) ).
% Suc_diff_Suc
thf(fact_442_diff__add__0,axiom,
! [N: nat,M: nat] :
( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
= zero_zero_nat ) ).
% diff_add_0
thf(fact_443_less__diff__conv,axiom,
! [I: nat,J: nat,K2: nat] :
( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K2 ) )
= ( ord_less_nat @ ( plus_plus_nat @ I @ K2 ) @ J ) ) ).
% less_diff_conv
thf(fact_444_add__diff__inverse__nat,axiom,
! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
=> ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
= M ) ) ).
% add_diff_inverse_nat
thf(fact_445_diff__Suc__eq__diff__pred,axiom,
! [M: nat,N: nat] :
( ( minus_minus_nat @ M @ ( suc @ N ) )
= ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% diff_Suc_eq_diff_pred
thf(fact_446_diff__Suc__less,axiom,
! [N: nat,I: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% diff_Suc_less
thf(fact_447_nat__diff__split,axiom,
! [P: nat > $o,A: nat,B: nat] :
( ( P @ ( minus_minus_nat @ A @ B ) )
= ( ( ( ord_less_nat @ A @ B )
=> ( P @ zero_zero_nat ) )
& ! [D2: nat] :
( ( A
= ( plus_plus_nat @ B @ D2 ) )
=> ( P @ D2 ) ) ) ) ).
% nat_diff_split
thf(fact_448_nat__diff__split__asm,axiom,
! [P: nat > $o,A: nat,B: nat] :
( ( P @ ( minus_minus_nat @ A @ B ) )
= ( ~ ( ( ( ord_less_nat @ A @ B )
& ~ ( P @ zero_zero_nat ) )
| ? [D2: nat] :
( ( A
= ( plus_plus_nat @ B @ D2 ) )
& ~ ( P @ D2 ) ) ) ) ) ).
% nat_diff_split_asm
thf(fact_449_Suc__pred_H,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( N
= ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% Suc_pred'
thf(fact_450_Suc__diff__eq__diff__pred,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( minus_minus_nat @ ( suc @ M ) @ N )
= ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% Suc_diff_eq_diff_pred
thf(fact_451_add__eq__if,axiom,
( plus_plus_nat
= ( ^ [M3: nat,N2: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N2 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% add_eq_if
thf(fact_452_nth__Cons_H,axiom,
! [N: nat,X: int,Xs: list_int] :
( ( ( N = zero_zero_nat )
=> ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
= X ) )
& ( ( N != zero_zero_nat )
=> ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
= ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% nth_Cons'
thf(fact_453_nth__Cons_H,axiom,
! [N: nat,X: instr,Xs: list_instr] :
( ( ( N = zero_zero_nat )
=> ( ( nth_instr @ ( cons_instr @ X @ Xs ) @ N )
= X ) )
& ( ( N != zero_zero_nat )
=> ( ( nth_instr @ ( cons_instr @ X @ Xs ) @ N )
= ( nth_instr @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% nth_Cons'
thf(fact_454_nth__Cons_H,axiom,
! [N: nat,X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int] :
( ( ( N = zero_zero_nat )
=> ( ( nth_Pr8327173284404383691st_int @ ( cons_P4151473878978182108st_int @ X @ Xs ) @ N )
= X ) )
& ( ( N != zero_zero_nat )
=> ( ( nth_Pr8327173284404383691st_int @ ( cons_P4151473878978182108st_int @ X @ Xs ) @ N )
= ( nth_Pr8327173284404383691st_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% nth_Cons'
thf(fact_455_nth__Cons_H,axiom,
! [N: nat,X: list_char,Xs: list_list_char] :
( ( ( N = zero_zero_nat )
=> ( ( nth_list_char @ ( cons_list_char @ X @ Xs ) @ N )
= X ) )
& ( ( N != zero_zero_nat )
=> ( ( nth_list_char @ ( cons_list_char @ X @ Xs ) @ N )
= ( nth_list_char @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% nth_Cons'
thf(fact_456_nth__non__equal__first__eq,axiom,
! [X: int,Y: int,Xs: list_int,N: nat] :
( ( X != Y )
=> ( ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
= Y )
= ( ( ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
= Y )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% nth_non_equal_first_eq
thf(fact_457_nth__non__equal__first__eq,axiom,
! [X: instr,Y: instr,Xs: list_instr,N: nat] :
( ( X != Y )
=> ( ( ( nth_instr @ ( cons_instr @ X @ Xs ) @ N )
= Y )
= ( ( ( nth_instr @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
= Y )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% nth_non_equal_first_eq
thf(fact_458_nth__non__equal__first__eq,axiom,
! [X: produc6425607678544837394st_int,Y: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int,N: nat] :
( ( X != Y )
=> ( ( ( nth_Pr8327173284404383691st_int @ ( cons_P4151473878978182108st_int @ X @ Xs ) @ N )
= Y )
= ( ( ( nth_Pr8327173284404383691st_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
= Y )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% nth_non_equal_first_eq
thf(fact_459_nth__non__equal__first__eq,axiom,
! [X: list_char,Y: list_char,Xs: list_list_char,N: nat] :
( ( X != Y )
=> ( ( ( nth_list_char @ ( cons_list_char @ X @ Xs ) @ N )
= Y )
= ( ( ( nth_list_char @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
= Y )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% nth_non_equal_first_eq
thf(fact_460_dbl__inc__simps_I2_J,axiom,
( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
= one_one_int ) ).
% dbl_inc_simps(2)
thf(fact_461_nth__enumerate__eq,axiom,
! [M: nat,Xs: list_P419547167332244514st_int,N: nat] :
( ( ord_less_nat @ M @ ( size_s229347708945616566st_int @ Xs ) )
=> ( ( nth_Pr6118945435929909578st_int @ ( enumer1800257932645307117st_int @ N @ Xs ) @ M )
= ( produc2664891610604065915st_int @ ( plus_plus_nat @ N @ M ) @ ( nth_Pr8327173284404383691st_int @ Xs @ M ) ) ) ) ).
% nth_enumerate_eq
thf(fact_462_nth__enumerate__eq,axiom,
! [M: nat,Xs: list_int,N: nat] :
( ( ord_less_nat @ M @ ( size_size_list_int @ Xs ) )
=> ( ( nth_Pr3440142176431000676at_int @ ( enumerate_int @ N @ Xs ) @ M )
= ( product_Pair_nat_int @ ( plus_plus_nat @ N @ M ) @ ( nth_int @ Xs @ M ) ) ) ) ).
% nth_enumerate_eq
thf(fact_463_dbl__dec__def,axiom,
( neg_nu3811975205180677377ec_int
= ( ^ [X2: int] : ( minus_minus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% dbl_dec_def
thf(fact_464_bezw__0,axiom,
! [X: nat] :
( ( bezw @ X @ zero_zero_nat )
= ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% bezw_0
thf(fact_465_Compiler2_Oacomp__correct,axiom,
! [A: aexp,Cfs: list_P419547167332244514st_int] :
( ( execl_all @ ( acomp @ A ) @ Cfs )
=> ( apred @ A @ ( nth_Pr8327173284404383691st_int @ Cfs @ zero_zero_nat ) @ ( nth_Pr8327173284404383691st_int @ Cfs @ ( minus_minus_nat @ ( size_s229347708945616566st_int @ Cfs ) @ ( suc @ zero_zero_nat ) ) ) ) ) ).
% Compiler2.acomp_correct
thf(fact_466_in__measures_I2_J,axiom,
! [X: int,Y: int,F: int > nat,Fs: list_int_nat] :
( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ ( cons_int_nat @ F @ Fs ) ) )
= ( ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) )
| ( ( ( F @ X )
= ( F @ Y ) )
& ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ Fs ) ) ) ) ) ).
% in_measures(2)
thf(fact_467_length__enumerate,axiom,
! [N: nat,Xs: list_int] :
( ( size_s2970893825323803983at_int @ ( enumerate_int @ N @ Xs ) )
= ( size_size_list_int @ Xs ) ) ).
% length_enumerate
thf(fact_468_dbl__dec__simps_I3_J,axiom,
( ( neg_nu3811975205180677377ec_int @ one_one_int )
= one_one_int ) ).
% dbl_dec_simps(3)
thf(fact_469_enumerate__simps_I2_J,axiom,
! [N: nat,X: int,Xs: list_int] :
( ( enumerate_int @ N @ ( cons_int @ X @ Xs ) )
= ( cons_P2335045147070616083at_int @ ( product_Pair_nat_int @ N @ X ) @ ( enumerate_int @ ( suc @ N ) @ Xs ) ) ) ).
% enumerate_simps(2)
thf(fact_470_enumerate__simps_I2_J,axiom,
! [N: nat,X: instr,Xs: list_instr] :
( ( enumerate_instr @ N @ ( cons_instr @ X @ Xs ) )
= ( cons_P4643890853483612494_instr @ ( produc3129998205563682742_instr @ N @ X ) @ ( enumerate_instr @ ( suc @ N ) @ Xs ) ) ) ).
% enumerate_simps(2)
thf(fact_471_enumerate__simps_I2_J,axiom,
! [N: nat,X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int] :
( ( enumer1800257932645307117st_int @ N @ ( cons_P4151473878978182108st_int @ X @ Xs ) )
= ( cons_P6123078848854619129st_int @ ( produc2664891610604065915st_int @ N @ X ) @ ( enumer1800257932645307117st_int @ ( suc @ N ) @ Xs ) ) ) ).
% enumerate_simps(2)
thf(fact_472_enumerate__simps_I2_J,axiom,
! [N: nat,X: list_char,Xs: list_list_char] :
( ( enumerate_list_char @ N @ ( cons_list_char @ X @ Xs ) )
= ( cons_P6700496888814104776t_char @ ( produc120197956887798346t_char @ N @ X ) @ ( enumerate_list_char @ ( suc @ N ) @ Xs ) ) ) ).
% enumerate_simps(2)
thf(fact_473_full__exhaustive__int_H_Ocases,axiom,
! [X: produc2285326912895808259nt_int] :
~ ! [F3: produc8551481072490612790e_term > option6357759511663192854e_term,D3: int,I3: int] :
( X
!= ( produc5700946648718959541nt_int @ F3 @ ( product_Pair_int_int @ D3 @ I3 ) ) ) ).
% full_exhaustive_int'.cases
thf(fact_474_exhaustive__int_H_Ocases,axiom,
! [X: produc7773217078559923341nt_int] :
~ ! [F3: int > option6357759511663192854e_term,D3: int,I3: int] :
( X
!= ( produc4305682042979456191nt_int @ F3 @ ( product_Pair_int_int @ D3 @ I3 ) ) ) ).
% exhaustive_int'.cases
thf(fact_475_small__lazy_H_Ocases,axiom,
! [X: product_prod_int_int] :
~ ! [D3: int,I3: int] :
( X
!= ( product_Pair_int_int @ D3 @ I3 ) ) ).
% small_lazy'.cases
thf(fact_476_minus__int__code_I1_J,axiom,
! [K2: int] :
( ( minus_minus_int @ K2 @ zero_zero_int )
= K2 ) ).
% minus_int_code(1)
thf(fact_477_int__diff__cases,axiom,
! [Z: int] :
~ ! [M4: nat,N3: nat] :
( Z
!= ( minus_minus_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% int_diff_cases
thf(fact_478_int__less__induct,axiom,
! [I: int,K2: int,P: int > $o] :
( ( ord_less_int @ I @ K2 )
=> ( ( P @ ( minus_minus_int @ K2 @ one_one_int ) )
=> ( ! [I3: int] :
( ( ord_less_int @ I3 @ K2 )
=> ( ( P @ I3 )
=> ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
=> ( P @ I ) ) ) ) ).
% int_less_induct
thf(fact_479_measures__less,axiom,
! [F: int > nat,X: int,Y: int,Fs: list_int_nat] :
( ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) )
=> ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ ( cons_int_nat @ F @ Fs ) ) ) ) ).
% measures_less
thf(fact_480_int__ops_I6_J,axiom,
! [A: nat,B: nat] :
( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
=> ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
= zero_zero_int ) )
& ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
=> ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
= ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% int_ops(6)
thf(fact_481_dbl__inc__def,axiom,
( neg_nu5851722552734809277nc_int
= ( ^ [X2: int] : ( plus_plus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% dbl_inc_def
thf(fact_482_upto__aux__rec,axiom,
( upto_aux
= ( ^ [I2: int,J2: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J2 @ I2 ) @ Js @ ( upto_aux @ I2 @ ( minus_minus_int @ J2 @ one_one_int ) @ ( cons_int @ J2 @ Js ) ) ) ) ) ).
% upto_aux_rec
thf(fact_483_A,axiom,
execl_all @ ( append_instr @ ( acomp @ a ) @ ( cons_instr @ ( store @ x ) @ nil_instr ) ) @ cfsa ).
% A
thf(fact_484_iexec__offset,axiom,
! [Ins2: instr,Pc: int,S2: list_char > int,Stk3: list_int,Pc2: int,S3: list_char > int,Stk2: list_int,I: int] :
( ( iexec_pred @ ( produc1484136438817787418st_int @ Ins2 @ ( produc5086643055186798020st_int @ Pc @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) ) @ ( produc5086643055186798020st_int @ Pc2 @ ( produc8650753666468850689st_int @ S3 @ Stk2 ) ) )
=> ( iexec_pred @ ( produc1484136438817787418st_int @ Ins2 @ ( produc5086643055186798020st_int @ ( minus_minus_int @ Pc @ I ) @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) ) @ ( produc5086643055186798020st_int @ ( minus_minus_int @ Pc2 @ I ) @ ( produc8650753666468850689st_int @ S3 @ Stk2 ) ) ) ) ).
% iexec_offset
thf(fact_485_inth_Osimps,axiom,
! [I: int,X: int,Xs: list_int] :
( ( ( I = zero_zero_int )
=> ( ( inth_int @ ( cons_int @ X @ Xs ) @ I )
= X ) )
& ( ( I != zero_zero_int )
=> ( ( inth_int @ ( cons_int @ X @ Xs ) @ I )
= ( inth_int @ Xs @ ( minus_minus_int @ I @ one_one_int ) ) ) ) ) ).
% inth.simps
thf(fact_486_inth_Osimps,axiom,
! [I: int,X: instr,Xs: list_instr] :
( ( ( I = zero_zero_int )
=> ( ( inth_instr @ ( cons_instr @ X @ Xs ) @ I )
= X ) )
& ( ( I != zero_zero_int )
=> ( ( inth_instr @ ( cons_instr @ X @ Xs ) @ I )
= ( inth_instr @ Xs @ ( minus_minus_int @ I @ one_one_int ) ) ) ) ) ).
% inth.simps
thf(fact_487_inth_Osimps,axiom,
! [I: int,X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int] :
( ( ( I = zero_zero_int )
=> ( ( inth_P8039235741264645271st_int @ ( cons_P4151473878978182108st_int @ X @ Xs ) @ I )
= X ) )
& ( ( I != zero_zero_int )
=> ( ( inth_P8039235741264645271st_int @ ( cons_P4151473878978182108st_int @ X @ Xs ) @ I )
= ( inth_P8039235741264645271st_int @ Xs @ ( minus_minus_int @ I @ one_one_int ) ) ) ) ) ).
% inth.simps
thf(fact_488_inth_Osimps,axiom,
! [I: int,X: list_char,Xs: list_list_char] :
( ( ( I = zero_zero_int )
=> ( ( inth_list_char @ ( cons_list_char @ X @ Xs ) @ I )
= X ) )
& ( ( I != zero_zero_int )
=> ( ( inth_list_char @ ( cons_list_char @ X @ Xs ) @ I )
= ( inth_list_char @ Xs @ ( minus_minus_int @ I @ one_one_int ) ) ) ) ) ).
% inth.simps
thf(fact_489_Cons__lenlex__iff,axiom,
! [M: instr,Ms: list_instr,N: instr,Ns: list_instr,R: set_Pr3711236633289739975_instr] :
( ( member7594433970877843344_instr @ ( produc7750586281064920791_instr @ ( cons_instr @ M @ Ms ) @ ( cons_instr @ N @ Ns ) ) @ ( lenlex_instr @ R ) )
= ( ( ord_less_nat @ ( size_size_list_instr @ Ms ) @ ( size_size_list_instr @ Ns ) )
| ( ( ( size_size_list_instr @ Ms )
= ( size_size_list_instr @ Ns ) )
& ( member8320768277060436240_instr @ ( produc7105755196911784279_instr @ M @ N ) @ R ) )
| ( ( M = N )
& ( member7594433970877843344_instr @ ( produc7750586281064920791_instr @ Ms @ Ns ) @ ( lenlex_instr @ R ) ) ) ) ) ).
% Cons_lenlex_iff
thf(fact_490_Cons__lenlex__iff,axiom,
! [M: produc6425607678544837394st_int,Ms: list_P419547167332244514st_int,N: produc6425607678544837394st_int,Ns: list_P419547167332244514st_int,R: set_Pr7036172080033517285st_int] :
( ( member5009133577359637198st_int @ ( produc2639222612625641053st_int @ ( cons_P4151473878978182108st_int @ M @ Ms ) @ ( cons_P4151473878978182108st_int @ N @ Ns ) ) @ ( lenlex4038275423977926727st_int @ R ) )
= ( ( ord_less_nat @ ( size_s229347708945616566st_int @ Ms ) @ ( size_s229347708945616566st_int @ Ns ) )
| ( ( ( size_s229347708945616566st_int @ Ms )
= ( size_s229347708945616566st_int @ Ns ) )
& ( member5928719113647980078st_int @ ( produc6552906223331971517st_int @ M @ N ) @ R ) )
| ( ( M = N )
& ( member5009133577359637198st_int @ ( produc2639222612625641053st_int @ Ms @ Ns ) @ ( lenlex4038275423977926727st_int @ R ) ) ) ) ) ).
% Cons_lenlex_iff
thf(fact_491_Cons__lenlex__iff,axiom,
! [M: list_char,Ms: list_list_char,N: list_char,Ns: list_list_char,R: set_Pr4480099295215233283t_char] :
( ( member5558557582278090860t_char @ ( produc9134825680149865339t_char @ ( cons_list_char @ M @ Ms ) @ ( cons_list_char @ N @ Ns ) ) @ ( lenlex_list_char @ R ) )
= ( ( ord_less_nat @ ( size_s356637359517785349t_char @ Ms ) @ ( size_s356637359517785349t_char @ Ns ) )
| ( ( ( size_s356637359517785349t_char @ Ms )
= ( size_s356637359517785349t_char @ Ns ) )
& ( member6023471406134104908t_char @ ( produc1606739095562851931t_char @ M @ N ) @ R ) )
| ( ( M = N )
& ( member5558557582278090860t_char @ ( produc9134825680149865339t_char @ Ms @ Ns ) @ ( lenlex_list_char @ R ) ) ) ) ) ).
% Cons_lenlex_iff
thf(fact_492_Cons__lenlex__iff,axiom,
! [M: int,Ms: list_int,N: int,Ns: list_int,R: set_Pr958786334691620121nt_int] :
( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ M @ Ms ) @ ( cons_int @ N @ Ns ) ) @ ( lenlex_int @ R ) )
= ( ( ord_less_nat @ ( size_size_list_int @ Ms ) @ ( size_size_list_int @ Ns ) )
| ( ( ( size_size_list_int @ Ms )
= ( size_size_list_int @ Ns ) )
& ( member5262025264175285858nt_int @ ( product_Pair_int_int @ M @ N ) @ R ) )
| ( ( M = N )
& ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Ms @ Ns ) @ ( lenlex_int @ R ) ) ) ) ) ).
% Cons_lenlex_iff
thf(fact_493_same__append__eq,axiom,
! [Xs: list_instr,Ys: list_instr,Zs: list_instr] :
( ( ( append_instr @ Xs @ Ys )
= ( append_instr @ Xs @ Zs ) )
= ( Ys = Zs ) ) ).
% same_append_eq
thf(fact_494_append__same__eq,axiom,
! [Ys: list_instr,Xs: list_instr,Zs: list_instr] :
( ( ( append_instr @ Ys @ Xs )
= ( append_instr @ Zs @ Xs ) )
= ( Ys = Zs ) ) ).
% append_same_eq
thf(fact_495_append__assoc,axiom,
! [Xs: list_instr,Ys: list_instr,Zs: list_instr] :
( ( append_instr @ ( append_instr @ Xs @ Ys ) @ Zs )
= ( append_instr @ Xs @ ( append_instr @ Ys @ Zs ) ) ) ).
% append_assoc
thf(fact_496_append_Oassoc,axiom,
! [A: list_instr,B: list_instr,C: list_instr] :
( ( append_instr @ ( append_instr @ A @ B ) @ C )
= ( append_instr @ A @ ( append_instr @ B @ C ) ) ) ).
% append.assoc
thf(fact_497_instr_Oinject_I3_J,axiom,
! [X42: list_char,Y42: list_char] :
( ( ( store @ X42 )
= ( store @ Y42 ) )
= ( X42 = Y42 ) ) ).
% instr.inject(3)
thf(fact_498_append__is__Nil__conv,axiom,
! [Xs: list_instr,Ys: list_instr] :
( ( ( append_instr @ Xs @ Ys )
= nil_instr )
= ( ( Xs = nil_instr )
& ( Ys = nil_instr ) ) ) ).
% append_is_Nil_conv
thf(fact_499_append__is__Nil__conv,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( ( append5028292981072010935st_int @ Xs @ Ys )
= nil_Pr749310521696113548st_int )
= ( ( Xs = nil_Pr749310521696113548st_int )
& ( Ys = nil_Pr749310521696113548st_int ) ) ) ).
% append_is_Nil_conv
thf(fact_500_append__is__Nil__conv,axiom,
! [Xs: list_list_char,Ys: list_list_char] :
( ( ( append_list_char @ Xs @ Ys )
= nil_list_char )
= ( ( Xs = nil_list_char )
& ( Ys = nil_list_char ) ) ) ).
% append_is_Nil_conv
thf(fact_501_Nil__is__append__conv,axiom,
! [Xs: list_instr,Ys: list_instr] :
( ( nil_instr
= ( append_instr @ Xs @ Ys ) )
= ( ( Xs = nil_instr )
& ( Ys = nil_instr ) ) ) ).
% Nil_is_append_conv
thf(fact_502_Nil__is__append__conv,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( nil_Pr749310521696113548st_int
= ( append5028292981072010935st_int @ Xs @ Ys ) )
= ( ( Xs = nil_Pr749310521696113548st_int )
& ( Ys = nil_Pr749310521696113548st_int ) ) ) ).
% Nil_is_append_conv
thf(fact_503_Nil__is__append__conv,axiom,
! [Xs: list_list_char,Ys: list_list_char] :
( ( nil_list_char
= ( append_list_char @ Xs @ Ys ) )
= ( ( Xs = nil_list_char )
& ( Ys = nil_list_char ) ) ) ).
% Nil_is_append_conv
thf(fact_504_self__append__conv2,axiom,
! [Y: list_instr,Xs: list_instr] :
( ( Y
= ( append_instr @ Xs @ Y ) )
= ( Xs = nil_instr ) ) ).
% self_append_conv2
thf(fact_505_self__append__conv2,axiom,
! [Y: list_P419547167332244514st_int,Xs: list_P419547167332244514st_int] :
( ( Y
= ( append5028292981072010935st_int @ Xs @ Y ) )
= ( Xs = nil_Pr749310521696113548st_int ) ) ).
% self_append_conv2
thf(fact_506_self__append__conv2,axiom,
! [Y: list_list_char,Xs: list_list_char] :
( ( Y
= ( append_list_char @ Xs @ Y ) )
= ( Xs = nil_list_char ) ) ).
% self_append_conv2
thf(fact_507_append__self__conv2,axiom,
! [Xs: list_instr,Ys: list_instr] :
( ( ( append_instr @ Xs @ Ys )
= Ys )
= ( Xs = nil_instr ) ) ).
% append_self_conv2
thf(fact_508_append__self__conv2,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( ( append5028292981072010935st_int @ Xs @ Ys )
= Ys )
= ( Xs = nil_Pr749310521696113548st_int ) ) ).
% append_self_conv2
thf(fact_509_append__self__conv2,axiom,
! [Xs: list_list_char,Ys: list_list_char] :
( ( ( append_list_char @ Xs @ Ys )
= Ys )
= ( Xs = nil_list_char ) ) ).
% append_self_conv2
thf(fact_510_self__append__conv,axiom,
! [Y: list_instr,Ys: list_instr] :
( ( Y
= ( append_instr @ Y @ Ys ) )
= ( Ys = nil_instr ) ) ).
% self_append_conv
thf(fact_511_self__append__conv,axiom,
! [Y: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( Y
= ( append5028292981072010935st_int @ Y @ Ys ) )
= ( Ys = nil_Pr749310521696113548st_int ) ) ).
% self_append_conv
thf(fact_512_self__append__conv,axiom,
! [Y: list_list_char,Ys: list_list_char] :
( ( Y
= ( append_list_char @ Y @ Ys ) )
= ( Ys = nil_list_char ) ) ).
% self_append_conv
thf(fact_513_append__self__conv,axiom,
! [Xs: list_instr,Ys: list_instr] :
( ( ( append_instr @ Xs @ Ys )
= Xs )
= ( Ys = nil_instr ) ) ).
% append_self_conv
thf(fact_514_append__self__conv,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( ( append5028292981072010935st_int @ Xs @ Ys )
= Xs )
= ( Ys = nil_Pr749310521696113548st_int ) ) ).
% append_self_conv
thf(fact_515_append__self__conv,axiom,
! [Xs: list_list_char,Ys: list_list_char] :
( ( ( append_list_char @ Xs @ Ys )
= Xs )
= ( Ys = nil_list_char ) ) ).
% append_self_conv
thf(fact_516_append__Nil2,axiom,
! [Xs: list_instr] :
( ( append_instr @ Xs @ nil_instr )
= Xs ) ).
% append_Nil2
thf(fact_517_append__Nil2,axiom,
! [Xs: list_P419547167332244514st_int] :
( ( append5028292981072010935st_int @ Xs @ nil_Pr749310521696113548st_int )
= Xs ) ).
% append_Nil2
thf(fact_518_append__Nil2,axiom,
! [Xs: list_list_char] :
( ( append_list_char @ Xs @ nil_list_char )
= Xs ) ).
% append_Nil2
thf(fact_519_append_Oright__neutral,axiom,
! [A: list_instr] :
( ( append_instr @ A @ nil_instr )
= A ) ).
% append.right_neutral
thf(fact_520_append_Oright__neutral,axiom,
! [A: list_P419547167332244514st_int] :
( ( append5028292981072010935st_int @ A @ nil_Pr749310521696113548st_int )
= A ) ).
% append.right_neutral
thf(fact_521_append_Oright__neutral,axiom,
! [A: list_list_char] :
( ( append_list_char @ A @ nil_list_char )
= A ) ).
% append.right_neutral
thf(fact_522_append__eq__append__conv,axiom,
! [Xs: list_instr,Ys: list_instr,Us: list_instr,Vs: list_instr] :
( ( ( ( size_size_list_instr @ Xs )
= ( size_size_list_instr @ Ys ) )
| ( ( size_size_list_instr @ Us )
= ( size_size_list_instr @ Vs ) ) )
=> ( ( ( append_instr @ Xs @ Us )
= ( append_instr @ Ys @ Vs ) )
= ( ( Xs = Ys )
& ( Us = Vs ) ) ) ) ).
% append_eq_append_conv
thf(fact_523_append__eq__append__conv,axiom,
! [Xs: list_int,Ys: list_int,Us: list_int,Vs: list_int] :
( ( ( ( size_size_list_int @ Xs )
= ( size_size_list_int @ Ys ) )
| ( ( size_size_list_int @ Us )
= ( size_size_list_int @ Vs ) ) )
=> ( ( ( append_int @ Xs @ Us )
= ( append_int @ Ys @ Vs ) )
= ( ( Xs = Ys )
& ( Us = Vs ) ) ) ) ).
% append_eq_append_conv
thf(fact_524_enumerate__simps_I1_J,axiom,
! [N: nat] :
( ( enumerate_instr @ N @ nil_instr )
= nil_Pr5958439668630616318_instr ) ).
% enumerate_simps(1)
thf(fact_525_enumerate__simps_I1_J,axiom,
! [N: nat] :
( ( enumer1800257932645307117st_int @ N @ nil_Pr749310521696113548st_int )
= nil_Pr215578427632615497st_int ) ).
% enumerate_simps(1)
thf(fact_526_enumerate__simps_I1_J,axiom,
! [N: nat] :
( ( enumerate_list_char @ N @ nil_list_char )
= nil_Pr4704261131758228760t_char ) ).
% enumerate_simps(1)
thf(fact_527_length__0__conv,axiom,
! [Xs: list_instr] :
( ( ( size_size_list_instr @ Xs )
= zero_zero_nat )
= ( Xs = nil_instr ) ) ).
% length_0_conv
thf(fact_528_length__0__conv,axiom,
! [Xs: list_P419547167332244514st_int] :
( ( ( size_s229347708945616566st_int @ Xs )
= zero_zero_nat )
= ( Xs = nil_Pr749310521696113548st_int ) ) ).
% length_0_conv
thf(fact_529_length__0__conv,axiom,
! [Xs: list_list_char] :
( ( ( size_s356637359517785349t_char @ Xs )
= zero_zero_nat )
= ( Xs = nil_list_char ) ) ).
% length_0_conv
thf(fact_530_length__0__conv,axiom,
! [Xs: list_int] :
( ( ( size_size_list_int @ Xs )
= zero_zero_nat )
= ( Xs = nil_int ) ) ).
% length_0_conv
thf(fact_531_append1__eq__conv,axiom,
! [Xs: list_int,X: int,Ys: list_int,Y: int] :
( ( ( append_int @ Xs @ ( cons_int @ X @ nil_int ) )
= ( append_int @ Ys @ ( cons_int @ Y @ nil_int ) ) )
= ( ( Xs = Ys )
& ( X = Y ) ) ) ).
% append1_eq_conv
thf(fact_532_append1__eq__conv,axiom,
! [Xs: list_instr,X: instr,Ys: list_instr,Y: instr] :
( ( ( append_instr @ Xs @ ( cons_instr @ X @ nil_instr ) )
= ( append_instr @ Ys @ ( cons_instr @ Y @ nil_instr ) ) )
= ( ( Xs = Ys )
& ( X = Y ) ) ) ).
% append1_eq_conv
thf(fact_533_append1__eq__conv,axiom,
! [Xs: list_P419547167332244514st_int,X: produc6425607678544837394st_int,Ys: list_P419547167332244514st_int,Y: produc6425607678544837394st_int] :
( ( ( append5028292981072010935st_int @ Xs @ ( cons_P4151473878978182108st_int @ X @ nil_Pr749310521696113548st_int ) )
= ( append5028292981072010935st_int @ Ys @ ( cons_P4151473878978182108st_int @ Y @ nil_Pr749310521696113548st_int ) ) )
= ( ( Xs = Ys )
& ( X = Y ) ) ) ).
% append1_eq_conv
thf(fact_534_append1__eq__conv,axiom,
! [Xs: list_list_char,X: list_char,Ys: list_list_char,Y: list_char] :
( ( ( append_list_char @ Xs @ ( cons_list_char @ X @ nil_list_char ) )
= ( append_list_char @ Ys @ ( cons_list_char @ Y @ nil_list_char ) ) )
= ( ( Xs = Ys )
& ( X = Y ) ) ) ).
% append1_eq_conv
thf(fact_535_length__append,axiom,
! [Xs: list_instr,Ys: list_instr] :
( ( size_size_list_instr @ ( append_instr @ Xs @ Ys ) )
= ( plus_plus_nat @ ( size_size_list_instr @ Xs ) @ ( size_size_list_instr @ Ys ) ) ) ).
% length_append
thf(fact_536_length__append,axiom,
! [Xs: list_int,Ys: list_int] :
( ( size_size_list_int @ ( append_int @ Xs @ Ys ) )
= ( plus_plus_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% length_append
thf(fact_537_Nil__lenlex__iff1,axiom,
! [Ns: list_instr,R: set_Pr3711236633289739975_instr] :
( ( member7594433970877843344_instr @ ( produc7750586281064920791_instr @ nil_instr @ Ns ) @ ( lenlex_instr @ R ) )
= ( Ns != nil_instr ) ) ).
% Nil_lenlex_iff1
thf(fact_538_Nil__lenlex__iff1,axiom,
! [Ns: list_P419547167332244514st_int,R: set_Pr7036172080033517285st_int] :
( ( member5009133577359637198st_int @ ( produc2639222612625641053st_int @ nil_Pr749310521696113548st_int @ Ns ) @ ( lenlex4038275423977926727st_int @ R ) )
= ( Ns != nil_Pr749310521696113548st_int ) ) ).
% Nil_lenlex_iff1
thf(fact_539_Nil__lenlex__iff1,axiom,
! [Ns: list_list_char,R: set_Pr4480099295215233283t_char] :
( ( member5558557582278090860t_char @ ( produc9134825680149865339t_char @ nil_list_char @ Ns ) @ ( lenlex_list_char @ R ) )
= ( Ns != nil_list_char ) ) ).
% Nil_lenlex_iff1
thf(fact_540_length__greater__0__conv,axiom,
! [Xs: list_instr] :
( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_instr @ Xs ) )
= ( Xs != nil_instr ) ) ).
% length_greater_0_conv
thf(fact_541_length__greater__0__conv,axiom,
! [Xs: list_P419547167332244514st_int] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s229347708945616566st_int @ Xs ) )
= ( Xs != nil_Pr749310521696113548st_int ) ) ).
% length_greater_0_conv
thf(fact_542_length__greater__0__conv,axiom,
! [Xs: list_list_char] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s356637359517785349t_char @ Xs ) )
= ( Xs != nil_list_char ) ) ).
% length_greater_0_conv
thf(fact_543_length__greater__0__conv,axiom,
! [Xs: list_int] :
( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) )
= ( Xs != nil_int ) ) ).
% length_greater_0_conv
thf(fact_544_nth__append__length,axiom,
! [Xs: list_instr,X: instr,Ys: list_instr] :
( ( nth_instr @ ( append_instr @ Xs @ ( cons_instr @ X @ Ys ) ) @ ( size_size_list_instr @ Xs ) )
= X ) ).
% nth_append_length
thf(fact_545_nth__append__length,axiom,
! [Xs: list_P419547167332244514st_int,X: produc6425607678544837394st_int,Ys: list_P419547167332244514st_int] :
( ( nth_Pr8327173284404383691st_int @ ( append5028292981072010935st_int @ Xs @ ( cons_P4151473878978182108st_int @ X @ Ys ) ) @ ( size_s229347708945616566st_int @ Xs ) )
= X ) ).
% nth_append_length
thf(fact_546_nth__append__length,axiom,
! [Xs: list_list_char,X: list_char,Ys: list_list_char] :
( ( nth_list_char @ ( append_list_char @ Xs @ ( cons_list_char @ X @ Ys ) ) @ ( size_s356637359517785349t_char @ Xs ) )
= X ) ).
% nth_append_length
thf(fact_547_nth__append__length,axiom,
! [Xs: list_int,X: int,Ys: list_int] :
( ( nth_int @ ( append_int @ Xs @ ( cons_int @ X @ Ys ) ) @ ( size_size_list_int @ Xs ) )
= X ) ).
% nth_append_length
thf(fact_548_nth__append__length__plus,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,N: nat] :
( ( nth_Pr8327173284404383691st_int @ ( append5028292981072010935st_int @ Xs @ Ys ) @ ( plus_plus_nat @ ( size_s229347708945616566st_int @ Xs ) @ N ) )
= ( nth_Pr8327173284404383691st_int @ Ys @ N ) ) ).
% nth_append_length_plus
thf(fact_549_nth__append__length__plus,axiom,
! [Xs: list_instr,Ys: list_instr,N: nat] :
( ( nth_instr @ ( append_instr @ Xs @ Ys ) @ ( plus_plus_nat @ ( size_size_list_instr @ Xs ) @ N ) )
= ( nth_instr @ Ys @ N ) ) ).
% nth_append_length_plus
thf(fact_550_nth__append__length__plus,axiom,
! [Xs: list_int,Ys: list_int,N: nat] :
( ( nth_int @ ( append_int @ Xs @ Ys ) @ ( plus_plus_nat @ ( size_size_list_int @ Xs ) @ N ) )
= ( nth_int @ Ys @ N ) ) ).
% nth_append_length_plus
thf(fact_551_Nil__lenlex__iff2,axiom,
! [Ns: list_instr,R: set_Pr3711236633289739975_instr] :
~ ( member7594433970877843344_instr @ ( produc7750586281064920791_instr @ Ns @ nil_instr ) @ ( lenlex_instr @ R ) ) ).
% Nil_lenlex_iff2
thf(fact_552_Nil__lenlex__iff2,axiom,
! [Ns: list_P419547167332244514st_int,R: set_Pr7036172080033517285st_int] :
~ ( member5009133577359637198st_int @ ( produc2639222612625641053st_int @ Ns @ nil_Pr749310521696113548st_int ) @ ( lenlex4038275423977926727st_int @ R ) ) ).
% Nil_lenlex_iff2
thf(fact_553_Nil__lenlex__iff2,axiom,
! [Ns: list_list_char,R: set_Pr4480099295215233283t_char] :
~ ( member5558557582278090860t_char @ ( produc9134825680149865339t_char @ Ns @ nil_list_char ) @ ( lenlex_list_char @ R ) ) ).
% Nil_lenlex_iff2
thf(fact_554_lenlex__append1,axiom,
! [Us: list_instr,Xs: list_instr,R2: set_Pr3711236633289739975_instr,Vs: list_instr,Ys: list_instr] :
( ( member7594433970877843344_instr @ ( produc7750586281064920791_instr @ Us @ Xs ) @ ( lenlex_instr @ R2 ) )
=> ( ( ( size_size_list_instr @ Vs )
= ( size_size_list_instr @ Ys ) )
=> ( member7594433970877843344_instr @ ( produc7750586281064920791_instr @ ( append_instr @ Us @ Vs ) @ ( append_instr @ Xs @ Ys ) ) @ ( lenlex_instr @ R2 ) ) ) ) ).
% lenlex_append1
thf(fact_555_lenlex__append1,axiom,
! [Us: list_int,Xs: list_int,R2: set_Pr958786334691620121nt_int,Vs: list_int,Ys: list_int] :
( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Us @ Xs ) @ ( lenlex_int @ R2 ) )
=> ( ( ( size_size_list_int @ Vs )
= ( size_size_list_int @ Ys ) )
=> ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( append_int @ Us @ Vs ) @ ( append_int @ Xs @ Ys ) ) @ ( lenlex_int @ R2 ) ) ) ) ).
% lenlex_append1
thf(fact_556_rev__nonempty__induct,axiom,
! [Xs: list_int,P: list_int > $o] :
( ( Xs != nil_int )
=> ( ! [X3: int] : ( P @ ( cons_int @ X3 @ nil_int ) )
=> ( ! [X3: int,Xs2: list_int] :
( ( Xs2 != nil_int )
=> ( ( P @ Xs2 )
=> ( P @ ( append_int @ Xs2 @ ( cons_int @ X3 @ nil_int ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_557_rev__nonempty__induct,axiom,
! [Xs: list_instr,P: list_instr > $o] :
( ( Xs != nil_instr )
=> ( ! [X3: instr] : ( P @ ( cons_instr @ X3 @ nil_instr ) )
=> ( ! [X3: instr,Xs2: list_instr] :
( ( Xs2 != nil_instr )
=> ( ( P @ Xs2 )
=> ( P @ ( append_instr @ Xs2 @ ( cons_instr @ X3 @ nil_instr ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_558_rev__nonempty__induct,axiom,
! [Xs: list_P419547167332244514st_int,P: list_P419547167332244514st_int > $o] :
( ( Xs != nil_Pr749310521696113548st_int )
=> ( ! [X3: produc6425607678544837394st_int] : ( P @ ( cons_P4151473878978182108st_int @ X3 @ nil_Pr749310521696113548st_int ) )
=> ( ! [X3: produc6425607678544837394st_int,Xs2: list_P419547167332244514st_int] :
( ( Xs2 != nil_Pr749310521696113548st_int )
=> ( ( P @ Xs2 )
=> ( P @ ( append5028292981072010935st_int @ Xs2 @ ( cons_P4151473878978182108st_int @ X3 @ nil_Pr749310521696113548st_int ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_559_rev__nonempty__induct,axiom,
! [Xs: list_list_char,P: list_list_char > $o] :
( ( Xs != nil_list_char )
=> ( ! [X3: list_char] : ( P @ ( cons_list_char @ X3 @ nil_list_char ) )
=> ( ! [X3: list_char,Xs2: list_list_char] :
( ( Xs2 != nil_list_char )
=> ( ( P @ Xs2 )
=> ( P @ ( append_list_char @ Xs2 @ ( cons_list_char @ X3 @ nil_list_char ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_560_append__eq__Cons__conv,axiom,
! [Ys: list_int,Zs: list_int,X: int,Xs: list_int] :
( ( ( append_int @ Ys @ Zs )
= ( cons_int @ X @ Xs ) )
= ( ( ( Ys = nil_int )
& ( Zs
= ( cons_int @ X @ Xs ) ) )
| ? [Ys4: list_int] :
( ( Ys
= ( cons_int @ X @ Ys4 ) )
& ( ( append_int @ Ys4 @ Zs )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_561_append__eq__Cons__conv,axiom,
! [Ys: list_instr,Zs: list_instr,X: instr,Xs: list_instr] :
( ( ( append_instr @ Ys @ Zs )
= ( cons_instr @ X @ Xs ) )
= ( ( ( Ys = nil_instr )
& ( Zs
= ( cons_instr @ X @ Xs ) ) )
| ? [Ys4: list_instr] :
( ( Ys
= ( cons_instr @ X @ Ys4 ) )
& ( ( append_instr @ Ys4 @ Zs )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_562_append__eq__Cons__conv,axiom,
! [Ys: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int,X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int] :
( ( ( append5028292981072010935st_int @ Ys @ Zs )
= ( cons_P4151473878978182108st_int @ X @ Xs ) )
= ( ( ( Ys = nil_Pr749310521696113548st_int )
& ( Zs
= ( cons_P4151473878978182108st_int @ X @ Xs ) ) )
| ? [Ys4: list_P419547167332244514st_int] :
( ( Ys
= ( cons_P4151473878978182108st_int @ X @ Ys4 ) )
& ( ( append5028292981072010935st_int @ Ys4 @ Zs )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_563_append__eq__Cons__conv,axiom,
! [Ys: list_list_char,Zs: list_list_char,X: list_char,Xs: list_list_char] :
( ( ( append_list_char @ Ys @ Zs )
= ( cons_list_char @ X @ Xs ) )
= ( ( ( Ys = nil_list_char )
& ( Zs
= ( cons_list_char @ X @ Xs ) ) )
| ? [Ys4: list_list_char] :
( ( Ys
= ( cons_list_char @ X @ Ys4 ) )
& ( ( append_list_char @ Ys4 @ Zs )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_564_Cons__eq__append__conv,axiom,
! [X: int,Xs: list_int,Ys: list_int,Zs: list_int] :
( ( ( cons_int @ X @ Xs )
= ( append_int @ Ys @ Zs ) )
= ( ( ( Ys = nil_int )
& ( ( cons_int @ X @ Xs )
= Zs ) )
| ? [Ys4: list_int] :
( ( ( cons_int @ X @ Ys4 )
= Ys )
& ( Xs
= ( append_int @ Ys4 @ Zs ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_565_Cons__eq__append__conv,axiom,
! [X: instr,Xs: list_instr,Ys: list_instr,Zs: list_instr] :
( ( ( cons_instr @ X @ Xs )
= ( append_instr @ Ys @ Zs ) )
= ( ( ( Ys = nil_instr )
& ( ( cons_instr @ X @ Xs )
= Zs ) )
| ? [Ys4: list_instr] :
( ( ( cons_instr @ X @ Ys4 )
= Ys )
& ( Xs
= ( append_instr @ Ys4 @ Zs ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_566_Cons__eq__append__conv,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int] :
( ( ( cons_P4151473878978182108st_int @ X @ Xs )
= ( append5028292981072010935st_int @ Ys @ Zs ) )
= ( ( ( Ys = nil_Pr749310521696113548st_int )
& ( ( cons_P4151473878978182108st_int @ X @ Xs )
= Zs ) )
| ? [Ys4: list_P419547167332244514st_int] :
( ( ( cons_P4151473878978182108st_int @ X @ Ys4 )
= Ys )
& ( Xs
= ( append5028292981072010935st_int @ Ys4 @ Zs ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_567_Cons__eq__append__conv,axiom,
! [X: list_char,Xs: list_list_char,Ys: list_list_char,Zs: list_list_char] :
( ( ( cons_list_char @ X @ Xs )
= ( append_list_char @ Ys @ Zs ) )
= ( ( ( Ys = nil_list_char )
& ( ( cons_list_char @ X @ Xs )
= Zs ) )
| ? [Ys4: list_list_char] :
( ( ( cons_list_char @ X @ Ys4 )
= Ys )
& ( Xs
= ( append_list_char @ Ys4 @ Zs ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_568_rev__exhaust,axiom,
! [Xs: list_int] :
( ( Xs != nil_int )
=> ~ ! [Ys5: list_int,Y3: int] :
( Xs
!= ( append_int @ Ys5 @ ( cons_int @ Y3 @ nil_int ) ) ) ) ).
% rev_exhaust
thf(fact_569_rev__exhaust,axiom,
! [Xs: list_instr] :
( ( Xs != nil_instr )
=> ~ ! [Ys5: list_instr,Y3: instr] :
( Xs
!= ( append_instr @ Ys5 @ ( cons_instr @ Y3 @ nil_instr ) ) ) ) ).
% rev_exhaust
thf(fact_570_rev__exhaust,axiom,
! [Xs: list_P419547167332244514st_int] :
( ( Xs != nil_Pr749310521696113548st_int )
=> ~ ! [Ys5: list_P419547167332244514st_int,Y3: produc6425607678544837394st_int] :
( Xs
!= ( append5028292981072010935st_int @ Ys5 @ ( cons_P4151473878978182108st_int @ Y3 @ nil_Pr749310521696113548st_int ) ) ) ) ).
% rev_exhaust
thf(fact_571_rev__exhaust,axiom,
! [Xs: list_list_char] :
( ( Xs != nil_list_char )
=> ~ ! [Ys5: list_list_char,Y3: list_char] :
( Xs
!= ( append_list_char @ Ys5 @ ( cons_list_char @ Y3 @ nil_list_char ) ) ) ) ).
% rev_exhaust
thf(fact_572_rev__induct,axiom,
! [P: list_int > $o,Xs: list_int] :
( ( P @ nil_int )
=> ( ! [X3: int,Xs2: list_int] :
( ( P @ Xs2 )
=> ( P @ ( append_int @ Xs2 @ ( cons_int @ X3 @ nil_int ) ) ) )
=> ( P @ Xs ) ) ) ).
% rev_induct
thf(fact_573_rev__induct,axiom,
! [P: list_instr > $o,Xs: list_instr] :
( ( P @ nil_instr )
=> ( ! [X3: instr,Xs2: list_instr] :
( ( P @ Xs2 )
=> ( P @ ( append_instr @ Xs2 @ ( cons_instr @ X3 @ nil_instr ) ) ) )
=> ( P @ Xs ) ) ) ).
% rev_induct
thf(fact_574_rev__induct,axiom,
! [P: list_P419547167332244514st_int > $o,Xs: list_P419547167332244514st_int] :
( ( P @ nil_Pr749310521696113548st_int )
=> ( ! [X3: produc6425607678544837394st_int,Xs2: list_P419547167332244514st_int] :
( ( P @ Xs2 )
=> ( P @ ( append5028292981072010935st_int @ Xs2 @ ( cons_P4151473878978182108st_int @ X3 @ nil_Pr749310521696113548st_int ) ) ) )
=> ( P @ Xs ) ) ) ).
% rev_induct
thf(fact_575_rev__induct,axiom,
! [P: list_list_char > $o,Xs: list_list_char] :
( ( P @ nil_list_char )
=> ( ! [X3: list_char,Xs2: list_list_char] :
( ( P @ Xs2 )
=> ( P @ ( append_list_char @ Xs2 @ ( cons_list_char @ X3 @ nil_list_char ) ) ) )
=> ( P @ Xs ) ) ) ).
% rev_induct
thf(fact_576_transpose_Ocases,axiom,
! [X: list_list_int] :
( ( X != nil_list_int )
=> ( ! [Xss: list_list_int] :
( X
!= ( cons_list_int @ nil_int @ Xss ) )
=> ~ ! [X3: int,Xs2: list_int,Xss: list_list_int] :
( X
!= ( cons_list_int @ ( cons_int @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_577_transpose_Ocases,axiom,
! [X: list_list_instr] :
( ( X != nil_list_instr )
=> ( ! [Xss: list_list_instr] :
( X
!= ( cons_list_instr @ nil_instr @ Xss ) )
=> ~ ! [X3: instr,Xs2: list_instr,Xss: list_list_instr] :
( X
!= ( cons_list_instr @ ( cons_instr @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_578_transpose_Ocases,axiom,
! [X: list_l6422821129637969586st_int] :
( ( X != nil_li4597314861645524892st_int )
=> ( ! [Xss: list_l6422821129637969586st_int] :
( X
!= ( cons_l8648290059330449388st_int @ nil_Pr749310521696113548st_int @ Xss ) )
=> ~ ! [X3: produc6425607678544837394st_int,Xs2: list_P419547167332244514st_int,Xss: list_l6422821129637969586st_int] :
( X
!= ( cons_l8648290059330449388st_int @ ( cons_P4151473878978182108st_int @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_579_transpose_Ocases,axiom,
! [X: list_list_list_char] :
( ( X != nil_list_list_char )
=> ( ! [Xss: list_list_list_char] :
( X
!= ( cons_list_list_char @ nil_list_char @ Xss ) )
=> ~ ! [X3: list_char,Xs2: list_list_char,Xss: list_list_list_char] :
( X
!= ( cons_list_list_char @ ( cons_list_char @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_580_transpose_Ocases,axiom,
! [X: list_list_char] :
( ( X != nil_list_char )
=> ( ! [Xss: list_list_char] :
( X
!= ( cons_list_char @ nil_char @ Xss ) )
=> ~ ! [X3: char,Xs2: list_char,Xss: list_list_char] :
( X
!= ( cons_list_char @ ( cons_char @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_581_same__length__different,axiom,
! [Xs: list_instr,Ys: list_instr] :
( ( Xs != Ys )
=> ( ( ( size_size_list_instr @ Xs )
= ( size_size_list_instr @ Ys ) )
=> ? [Pre: list_instr,X3: instr,Xs4: list_instr,Y3: instr,Ys6: list_instr] :
( ( X3 != Y3 )
& ( Xs
= ( append_instr @ Pre @ ( append_instr @ ( cons_instr @ X3 @ nil_instr ) @ Xs4 ) ) )
& ( Ys
= ( append_instr @ Pre @ ( append_instr @ ( cons_instr @ Y3 @ nil_instr ) @ Ys6 ) ) ) ) ) ) ).
% same_length_different
thf(fact_582_same__length__different,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( Xs != Ys )
=> ( ( ( size_s229347708945616566st_int @ Xs )
= ( size_s229347708945616566st_int @ Ys ) )
=> ? [Pre: list_P419547167332244514st_int,X3: produc6425607678544837394st_int,Xs4: list_P419547167332244514st_int,Y3: produc6425607678544837394st_int,Ys6: list_P419547167332244514st_int] :
( ( X3 != Y3 )
& ( Xs
= ( append5028292981072010935st_int @ Pre @ ( append5028292981072010935st_int @ ( cons_P4151473878978182108st_int @ X3 @ nil_Pr749310521696113548st_int ) @ Xs4 ) ) )
& ( Ys
= ( append5028292981072010935st_int @ Pre @ ( append5028292981072010935st_int @ ( cons_P4151473878978182108st_int @ Y3 @ nil_Pr749310521696113548st_int ) @ Ys6 ) ) ) ) ) ) ).
% same_length_different
thf(fact_583_same__length__different,axiom,
! [Xs: list_list_char,Ys: list_list_char] :
( ( Xs != Ys )
=> ( ( ( size_s356637359517785349t_char @ Xs )
= ( size_s356637359517785349t_char @ Ys ) )
=> ? [Pre: list_list_char,X3: list_char,Xs4: list_list_char,Y3: list_char,Ys6: list_list_char] :
( ( X3 != Y3 )
& ( Xs
= ( append_list_char @ Pre @ ( append_list_char @ ( cons_list_char @ X3 @ nil_list_char ) @ Xs4 ) ) )
& ( Ys
= ( append_list_char @ Pre @ ( append_list_char @ ( cons_list_char @ Y3 @ nil_list_char ) @ Ys6 ) ) ) ) ) ) ).
% same_length_different
thf(fact_584_same__length__different,axiom,
! [Xs: list_int,Ys: list_int] :
( ( Xs != Ys )
=> ( ( ( size_size_list_int @ Xs )
= ( size_size_list_int @ Ys ) )
=> ? [Pre: list_int,X3: int,Xs4: list_int,Y3: int,Ys6: list_int] :
( ( X3 != Y3 )
& ( Xs
= ( append_int @ Pre @ ( append_int @ ( cons_int @ X3 @ nil_int ) @ Xs4 ) ) )
& ( Ys
= ( append_int @ Pre @ ( append_int @ ( cons_int @ Y3 @ nil_int ) @ Ys6 ) ) ) ) ) ) ).
% same_length_different
thf(fact_585_append__eq__append__conv2,axiom,
! [Xs: list_instr,Ys: list_instr,Zs: list_instr,Ts: list_instr] :
( ( ( append_instr @ Xs @ Ys )
= ( append_instr @ Zs @ Ts ) )
= ( ? [Us2: list_instr] :
( ( ( Xs
= ( append_instr @ Zs @ Us2 ) )
& ( ( append_instr @ Us2 @ Ys )
= Ts ) )
| ( ( ( append_instr @ Xs @ Us2 )
= Zs )
& ( Ys
= ( append_instr @ Us2 @ Ts ) ) ) ) ) ) ).
% append_eq_append_conv2
thf(fact_586_append__eq__appendI,axiom,
! [Xs: list_instr,Xs1: list_instr,Zs: list_instr,Ys: list_instr,Us: list_instr] :
( ( ( append_instr @ Xs @ Xs1 )
= Zs )
=> ( ( Ys
= ( append_instr @ Xs1 @ Us ) )
=> ( ( append_instr @ Xs @ Ys )
= ( append_instr @ Zs @ Us ) ) ) ) ).
% append_eq_appendI
thf(fact_587_eq__Nil__appendI,axiom,
! [Xs: list_instr,Ys: list_instr] :
( ( Xs = Ys )
=> ( Xs
= ( append_instr @ nil_instr @ Ys ) ) ) ).
% eq_Nil_appendI
thf(fact_588_eq__Nil__appendI,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( Xs = Ys )
=> ( Xs
= ( append5028292981072010935st_int @ nil_Pr749310521696113548st_int @ Ys ) ) ) ).
% eq_Nil_appendI
thf(fact_589_eq__Nil__appendI,axiom,
! [Xs: list_list_char,Ys: list_list_char] :
( ( Xs = Ys )
=> ( Xs
= ( append_list_char @ nil_list_char @ Ys ) ) ) ).
% eq_Nil_appendI
thf(fact_590_append_Oleft__neutral,axiom,
! [A: list_instr] :
( ( append_instr @ nil_instr @ A )
= A ) ).
% append.left_neutral
thf(fact_591_append_Oleft__neutral,axiom,
! [A: list_P419547167332244514st_int] :
( ( append5028292981072010935st_int @ nil_Pr749310521696113548st_int @ A )
= A ) ).
% append.left_neutral
thf(fact_592_append_Oleft__neutral,axiom,
! [A: list_list_char] :
( ( append_list_char @ nil_list_char @ A )
= A ) ).
% append.left_neutral
thf(fact_593_append__Nil,axiom,
! [Ys: list_instr] :
( ( append_instr @ nil_instr @ Ys )
= Ys ) ).
% append_Nil
thf(fact_594_append__Nil,axiom,
! [Ys: list_P419547167332244514st_int] :
( ( append5028292981072010935st_int @ nil_Pr749310521696113548st_int @ Ys )
= Ys ) ).
% append_Nil
thf(fact_595_append__Nil,axiom,
! [Ys: list_list_char] :
( ( append_list_char @ nil_list_char @ Ys )
= Ys ) ).
% append_Nil
thf(fact_596_append__Cons,axiom,
! [X: int,Xs: list_int,Ys: list_int] :
( ( append_int @ ( cons_int @ X @ Xs ) @ Ys )
= ( cons_int @ X @ ( append_int @ Xs @ Ys ) ) ) ).
% append_Cons
thf(fact_597_append__Cons,axiom,
! [X: instr,Xs: list_instr,Ys: list_instr] :
( ( append_instr @ ( cons_instr @ X @ Xs ) @ Ys )
= ( cons_instr @ X @ ( append_instr @ Xs @ Ys ) ) ) ).
% append_Cons
thf(fact_598_append__Cons,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( append5028292981072010935st_int @ ( cons_P4151473878978182108st_int @ X @ Xs ) @ Ys )
= ( cons_P4151473878978182108st_int @ X @ ( append5028292981072010935st_int @ Xs @ Ys ) ) ) ).
% append_Cons
thf(fact_599_append__Cons,axiom,
! [X: list_char,Xs: list_list_char,Ys: list_list_char] :
( ( append_list_char @ ( cons_list_char @ X @ Xs ) @ Ys )
= ( cons_list_char @ X @ ( append_list_char @ Xs @ Ys ) ) ) ).
% append_Cons
thf(fact_600_Cons__eq__appendI,axiom,
! [X: int,Xs1: list_int,Ys: list_int,Xs: list_int,Zs: list_int] :
( ( ( cons_int @ X @ Xs1 )
= Ys )
=> ( ( Xs
= ( append_int @ Xs1 @ Zs ) )
=> ( ( cons_int @ X @ Xs )
= ( append_int @ Ys @ Zs ) ) ) ) ).
% Cons_eq_appendI
thf(fact_601_Cons__eq__appendI,axiom,
! [X: instr,Xs1: list_instr,Ys: list_instr,Xs: list_instr,Zs: list_instr] :
( ( ( cons_instr @ X @ Xs1 )
= Ys )
=> ( ( Xs
= ( append_instr @ Xs1 @ Zs ) )
=> ( ( cons_instr @ X @ Xs )
= ( append_instr @ Ys @ Zs ) ) ) ) ).
% Cons_eq_appendI
thf(fact_602_Cons__eq__appendI,axiom,
! [X: produc6425607678544837394st_int,Xs1: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,Xs: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int] :
( ( ( cons_P4151473878978182108st_int @ X @ Xs1 )
= Ys )
=> ( ( Xs
= ( append5028292981072010935st_int @ Xs1 @ Zs ) )
=> ( ( cons_P4151473878978182108st_int @ X @ Xs )
= ( append5028292981072010935st_int @ Ys @ Zs ) ) ) ) ).
% Cons_eq_appendI
thf(fact_603_Cons__eq__appendI,axiom,
! [X: list_char,Xs1: list_list_char,Ys: list_list_char,Xs: list_list_char,Zs: list_list_char] :
( ( ( cons_list_char @ X @ Xs1 )
= Ys )
=> ( ( Xs
= ( append_list_char @ Xs1 @ Zs ) )
=> ( ( cons_list_char @ X @ Xs )
= ( append_list_char @ Ys @ Zs ) ) ) ) ).
% Cons_eq_appendI
thf(fact_604_list_Odistinct_I1_J,axiom,
! [X21: int,X222: list_int] :
( nil_int
!= ( cons_int @ X21 @ X222 ) ) ).
% list.distinct(1)
thf(fact_605_list_Odistinct_I1_J,axiom,
! [X21: instr,X222: list_instr] :
( nil_instr
!= ( cons_instr @ X21 @ X222 ) ) ).
% list.distinct(1)
thf(fact_606_list_Odistinct_I1_J,axiom,
! [X21: produc6425607678544837394st_int,X222: list_P419547167332244514st_int] :
( nil_Pr749310521696113548st_int
!= ( cons_P4151473878978182108st_int @ X21 @ X222 ) ) ).
% list.distinct(1)
thf(fact_607_list_Odistinct_I1_J,axiom,
! [X21: list_char,X222: list_list_char] :
( nil_list_char
!= ( cons_list_char @ X21 @ X222 ) ) ).
% list.distinct(1)
thf(fact_608_list_OdiscI,axiom,
! [List: list_int,X21: int,X222: list_int] :
( ( List
= ( cons_int @ X21 @ X222 ) )
=> ( List != nil_int ) ) ).
% list.discI
thf(fact_609_list_OdiscI,axiom,
! [List: list_instr,X21: instr,X222: list_instr] :
( ( List
= ( cons_instr @ X21 @ X222 ) )
=> ( List != nil_instr ) ) ).
% list.discI
thf(fact_610_list_OdiscI,axiom,
! [List: list_P419547167332244514st_int,X21: produc6425607678544837394st_int,X222: list_P419547167332244514st_int] :
( ( List
= ( cons_P4151473878978182108st_int @ X21 @ X222 ) )
=> ( List != nil_Pr749310521696113548st_int ) ) ).
% list.discI
thf(fact_611_list_OdiscI,axiom,
! [List: list_list_char,X21: list_char,X222: list_list_char] :
( ( List
= ( cons_list_char @ X21 @ X222 ) )
=> ( List != nil_list_char ) ) ).
% list.discI
thf(fact_612_list_Oexhaust,axiom,
! [Y: list_int] :
( ( Y != nil_int )
=> ~ ! [X212: int,X223: list_int] :
( Y
!= ( cons_int @ X212 @ X223 ) ) ) ).
% list.exhaust
thf(fact_613_list_Oexhaust,axiom,
! [Y: list_instr] :
( ( Y != nil_instr )
=> ~ ! [X212: instr,X223: list_instr] :
( Y
!= ( cons_instr @ X212 @ X223 ) ) ) ).
% list.exhaust
thf(fact_614_list_Oexhaust,axiom,
! [Y: list_P419547167332244514st_int] :
( ( Y != nil_Pr749310521696113548st_int )
=> ~ ! [X212: produc6425607678544837394st_int,X223: list_P419547167332244514st_int] :
( Y
!= ( cons_P4151473878978182108st_int @ X212 @ X223 ) ) ) ).
% list.exhaust
thf(fact_615_list_Oexhaust,axiom,
! [Y: list_list_char] :
( ( Y != nil_list_char )
=> ~ ! [X212: list_char,X223: list_list_char] :
( Y
!= ( cons_list_char @ X212 @ X223 ) ) ) ).
% list.exhaust
thf(fact_616_min__list_Ocases,axiom,
! [X: list_int] :
( ! [X3: int,Xs2: list_int] :
( X
!= ( cons_int @ X3 @ Xs2 ) )
=> ( X = nil_int ) ) ).
% min_list.cases
thf(fact_617_remdups__adj_Ocases,axiom,
! [X: list_int] :
( ( X != nil_int )
=> ( ! [X3: int] :
( X
!= ( cons_int @ X3 @ nil_int ) )
=> ~ ! [X3: int,Y3: int,Xs2: list_int] :
( X
!= ( cons_int @ X3 @ ( cons_int @ Y3 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_618_remdups__adj_Ocases,axiom,
! [X: list_instr] :
( ( X != nil_instr )
=> ( ! [X3: instr] :
( X
!= ( cons_instr @ X3 @ nil_instr ) )
=> ~ ! [X3: instr,Y3: instr,Xs2: list_instr] :
( X
!= ( cons_instr @ X3 @ ( cons_instr @ Y3 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_619_remdups__adj_Ocases,axiom,
! [X: list_P419547167332244514st_int] :
( ( X != nil_Pr749310521696113548st_int )
=> ( ! [X3: produc6425607678544837394st_int] :
( X
!= ( cons_P4151473878978182108st_int @ X3 @ nil_Pr749310521696113548st_int ) )
=> ~ ! [X3: produc6425607678544837394st_int,Y3: produc6425607678544837394st_int,Xs2: list_P419547167332244514st_int] :
( X
!= ( cons_P4151473878978182108st_int @ X3 @ ( cons_P4151473878978182108st_int @ Y3 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_620_remdups__adj_Ocases,axiom,
! [X: list_list_char] :
( ( X != nil_list_char )
=> ( ! [X3: list_char] :
( X
!= ( cons_list_char @ X3 @ nil_list_char ) )
=> ~ ! [X3: list_char,Y3: list_char,Xs2: list_list_char] :
( X
!= ( cons_list_char @ X3 @ ( cons_list_char @ Y3 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_621_neq__Nil__conv,axiom,
! [Xs: list_int] :
( ( Xs != nil_int )
= ( ? [Y2: int,Ys3: list_int] :
( Xs
= ( cons_int @ Y2 @ Ys3 ) ) ) ) ).
% neq_Nil_conv
thf(fact_622_neq__Nil__conv,axiom,
! [Xs: list_instr] :
( ( Xs != nil_instr )
= ( ? [Y2: instr,Ys3: list_instr] :
( Xs
= ( cons_instr @ Y2 @ Ys3 ) ) ) ) ).
% neq_Nil_conv
thf(fact_623_neq__Nil__conv,axiom,
! [Xs: list_P419547167332244514st_int] :
( ( Xs != nil_Pr749310521696113548st_int )
= ( ? [Y2: produc6425607678544837394st_int,Ys3: list_P419547167332244514st_int] :
( Xs
= ( cons_P4151473878978182108st_int @ Y2 @ Ys3 ) ) ) ) ).
% neq_Nil_conv
thf(fact_624_neq__Nil__conv,axiom,
! [Xs: list_list_char] :
( ( Xs != nil_list_char )
= ( ? [Y2: list_char,Ys3: list_list_char] :
( Xs
= ( cons_list_char @ Y2 @ Ys3 ) ) ) ) ).
% neq_Nil_conv
thf(fact_625_list__induct2_H,axiom,
! [P: list_int > list_int > $o,Xs: list_int,Ys: list_int] :
( ( P @ nil_int @ nil_int )
=> ( ! [X3: int,Xs2: list_int] : ( P @ ( cons_int @ X3 @ Xs2 ) @ nil_int )
=> ( ! [Y3: int,Ys5: list_int] : ( P @ nil_int @ ( cons_int @ Y3 @ Ys5 ) )
=> ( ! [X3: int,Xs2: list_int,Y3: int,Ys5: list_int] :
( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys5 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_626_list__induct2_H,axiom,
! [P: list_int > list_instr > $o,Xs: list_int,Ys: list_instr] :
( ( P @ nil_int @ nil_instr )
=> ( ! [X3: int,Xs2: list_int] : ( P @ ( cons_int @ X3 @ Xs2 ) @ nil_instr )
=> ( ! [Y3: instr,Ys5: list_instr] : ( P @ nil_int @ ( cons_instr @ Y3 @ Ys5 ) )
=> ( ! [X3: int,Xs2: list_int,Y3: instr,Ys5: list_instr] :
( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys5 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_627_list__induct2_H,axiom,
! [P: list_instr > list_int > $o,Xs: list_instr,Ys: list_int] :
( ( P @ nil_instr @ nil_int )
=> ( ! [X3: instr,Xs2: list_instr] : ( P @ ( cons_instr @ X3 @ Xs2 ) @ nil_int )
=> ( ! [Y3: int,Ys5: list_int] : ( P @ nil_instr @ ( cons_int @ Y3 @ Ys5 ) )
=> ( ! [X3: instr,Xs2: list_instr,Y3: int,Ys5: list_int] :
( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_instr @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys5 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_628_list__induct2_H,axiom,
! [P: list_instr > list_instr > $o,Xs: list_instr,Ys: list_instr] :
( ( P @ nil_instr @ nil_instr )
=> ( ! [X3: instr,Xs2: list_instr] : ( P @ ( cons_instr @ X3 @ Xs2 ) @ nil_instr )
=> ( ! [Y3: instr,Ys5: list_instr] : ( P @ nil_instr @ ( cons_instr @ Y3 @ Ys5 ) )
=> ( ! [X3: instr,Xs2: list_instr,Y3: instr,Ys5: list_instr] :
( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_instr @ X3 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys5 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_629_list__induct2_H,axiom,
! [P: list_int > list_list_char > $o,Xs: list_int,Ys: list_list_char] :
( ( P @ nil_int @ nil_list_char )
=> ( ! [X3: int,Xs2: list_int] : ( P @ ( cons_int @ X3 @ Xs2 ) @ nil_list_char )
=> ( ! [Y3: list_char,Ys5: list_list_char] : ( P @ nil_int @ ( cons_list_char @ Y3 @ Ys5 ) )
=> ( ! [X3: int,Xs2: list_int,Y3: list_char,Ys5: list_list_char] :
( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_list_char @ Y3 @ Ys5 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_630_list__induct2_H,axiom,
! [P: list_instr > list_list_char > $o,Xs: list_instr,Ys: list_list_char] :
( ( P @ nil_instr @ nil_list_char )
=> ( ! [X3: instr,Xs2: list_instr] : ( P @ ( cons_instr @ X3 @ Xs2 ) @ nil_list_char )
=> ( ! [Y3: list_char,Ys5: list_list_char] : ( P @ nil_instr @ ( cons_list_char @ Y3 @ Ys5 ) )
=> ( ! [X3: instr,Xs2: list_instr,Y3: list_char,Ys5: list_list_char] :
( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_instr @ X3 @ Xs2 ) @ ( cons_list_char @ Y3 @ Ys5 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_631_list__induct2_H,axiom,
! [P: list_list_char > list_int > $o,Xs: list_list_char,Ys: list_int] :
( ( P @ nil_list_char @ nil_int )
=> ( ! [X3: list_char,Xs2: list_list_char] : ( P @ ( cons_list_char @ X3 @ Xs2 ) @ nil_int )
=> ( ! [Y3: int,Ys5: list_int] : ( P @ nil_list_char @ ( cons_int @ Y3 @ Ys5 ) )
=> ( ! [X3: list_char,Xs2: list_list_char,Y3: int,Ys5: list_int] :
( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_list_char @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys5 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_632_list__induct2_H,axiom,
! [P: list_list_char > list_instr > $o,Xs: list_list_char,Ys: list_instr] :
( ( P @ nil_list_char @ nil_instr )
=> ( ! [X3: list_char,Xs2: list_list_char] : ( P @ ( cons_list_char @ X3 @ Xs2 ) @ nil_instr )
=> ( ! [Y3: instr,Ys5: list_instr] : ( P @ nil_list_char @ ( cons_instr @ Y3 @ Ys5 ) )
=> ( ! [X3: list_char,Xs2: list_list_char,Y3: instr,Ys5: list_instr] :
( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_list_char @ X3 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys5 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_633_list__induct2_H,axiom,
! [P: list_list_char > list_list_char > $o,Xs: list_list_char,Ys: list_list_char] :
( ( P @ nil_list_char @ nil_list_char )
=> ( ! [X3: list_char,Xs2: list_list_char] : ( P @ ( cons_list_char @ X3 @ Xs2 ) @ nil_list_char )
=> ( ! [Y3: list_char,Ys5: list_list_char] : ( P @ nil_list_char @ ( cons_list_char @ Y3 @ Ys5 ) )
=> ( ! [X3: list_char,Xs2: list_list_char,Y3: list_char,Ys5: list_list_char] :
( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_list_char @ X3 @ Xs2 ) @ ( cons_list_char @ Y3 @ Ys5 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_634_list__induct2_H,axiom,
! [P: list_int > list_P419547167332244514st_int > $o,Xs: list_int,Ys: list_P419547167332244514st_int] :
( ( P @ nil_int @ nil_Pr749310521696113548st_int )
=> ( ! [X3: int,Xs2: list_int] : ( P @ ( cons_int @ X3 @ Xs2 ) @ nil_Pr749310521696113548st_int )
=> ( ! [Y3: produc6425607678544837394st_int,Ys5: list_P419547167332244514st_int] : ( P @ nil_int @ ( cons_P4151473878978182108st_int @ Y3 @ Ys5 ) )
=> ( ! [X3: int,Xs2: list_int,Y3: produc6425607678544837394st_int,Ys5: list_P419547167332244514st_int] :
( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_P4151473878978182108st_int @ Y3 @ Ys5 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_635_list__nonempty__induct,axiom,
! [Xs: list_int,P: list_int > $o] :
( ( Xs != nil_int )
=> ( ! [X3: int] : ( P @ ( cons_int @ X3 @ nil_int ) )
=> ( ! [X3: int,Xs2: list_int] :
( ( Xs2 != nil_int )
=> ( ( P @ Xs2 )
=> ( P @ ( cons_int @ X3 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_636_list__nonempty__induct,axiom,
! [Xs: list_instr,P: list_instr > $o] :
( ( Xs != nil_instr )
=> ( ! [X3: instr] : ( P @ ( cons_instr @ X3 @ nil_instr ) )
=> ( ! [X3: instr,Xs2: list_instr] :
( ( Xs2 != nil_instr )
=> ( ( P @ Xs2 )
=> ( P @ ( cons_instr @ X3 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_637_list__nonempty__induct,axiom,
! [Xs: list_P419547167332244514st_int,P: list_P419547167332244514st_int > $o] :
( ( Xs != nil_Pr749310521696113548st_int )
=> ( ! [X3: produc6425607678544837394st_int] : ( P @ ( cons_P4151473878978182108st_int @ X3 @ nil_Pr749310521696113548st_int ) )
=> ( ! [X3: produc6425607678544837394st_int,Xs2: list_P419547167332244514st_int] :
( ( Xs2 != nil_Pr749310521696113548st_int )
=> ( ( P @ Xs2 )
=> ( P @ ( cons_P4151473878978182108st_int @ X3 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_638_list__nonempty__induct,axiom,
! [Xs: list_list_char,P: list_list_char > $o] :
( ( Xs != nil_list_char )
=> ( ! [X3: list_char] : ( P @ ( cons_list_char @ X3 @ nil_list_char ) )
=> ( ! [X3: list_char,Xs2: list_list_char] :
( ( Xs2 != nil_list_char )
=> ( ( P @ Xs2 )
=> ( P @ ( cons_list_char @ X3 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_639_splice_Ocases,axiom,
! [X: produc1186641810826059865st_int] :
( ! [Ys5: list_int] :
( X
!= ( produc364263696895485585st_int @ nil_int @ Ys5 ) )
=> ~ ! [X3: int,Xs2: list_int,Ys5: list_int] :
( X
!= ( produc364263696895485585st_int @ ( cons_int @ X3 @ Xs2 ) @ Ys5 ) ) ) ).
% splice.cases
thf(fact_640_splice_Ocases,axiom,
! [X: produc8891168062546637159_instr] :
( ! [Ys5: list_instr] :
( X
!= ( produc7750586281064920791_instr @ nil_instr @ Ys5 ) )
=> ~ ! [X3: instr,Xs2: list_instr,Ys5: list_instr] :
( X
!= ( produc7750586281064920791_instr @ ( cons_instr @ X3 @ Xs2 ) @ Ys5 ) ) ) ).
% splice.cases
thf(fact_641_splice_Ocases,axiom,
! [X: produc5848496107505245989st_int] :
( ! [Ys5: list_P419547167332244514st_int] :
( X
!= ( produc2639222612625641053st_int @ nil_Pr749310521696113548st_int @ Ys5 ) )
=> ~ ! [X3: produc6425607678544837394st_int,Xs2: list_P419547167332244514st_int,Ys5: list_P419547167332244514st_int] :
( X
!= ( produc2639222612625641053st_int @ ( cons_P4151473878978182108st_int @ X3 @ Xs2 ) @ Ys5 ) ) ) ).
% splice.cases
thf(fact_642_splice_Ocases,axiom,
! [X: produc525958773753613763t_char] :
( ! [Ys5: list_list_char] :
( X
!= ( produc9134825680149865339t_char @ nil_list_char @ Ys5 ) )
=> ~ ! [X3: list_char,Xs2: list_list_char,Ys5: list_list_char] :
( X
!= ( produc9134825680149865339t_char @ ( cons_list_char @ X3 @ Xs2 ) @ Ys5 ) ) ) ).
% splice.cases
thf(fact_643_shuffles_Ocases,axiom,
! [X: produc1186641810826059865st_int] :
( ! [Ys5: list_int] :
( X
!= ( produc364263696895485585st_int @ nil_int @ Ys5 ) )
=> ( ! [Xs2: list_int] :
( X
!= ( produc364263696895485585st_int @ Xs2 @ nil_int ) )
=> ~ ! [X3: int,Xs2: list_int,Y3: int,Ys5: list_int] :
( X
!= ( produc364263696895485585st_int @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys5 ) ) ) ) ) ).
% shuffles.cases
thf(fact_644_shuffles_Ocases,axiom,
! [X: produc8891168062546637159_instr] :
( ! [Ys5: list_instr] :
( X
!= ( produc7750586281064920791_instr @ nil_instr @ Ys5 ) )
=> ( ! [Xs2: list_instr] :
( X
!= ( produc7750586281064920791_instr @ Xs2 @ nil_instr ) )
=> ~ ! [X3: instr,Xs2: list_instr,Y3: instr,Ys5: list_instr] :
( X
!= ( produc7750586281064920791_instr @ ( cons_instr @ X3 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys5 ) ) ) ) ) ).
% shuffles.cases
thf(fact_645_shuffles_Ocases,axiom,
! [X: produc5848496107505245989st_int] :
( ! [Ys5: list_P419547167332244514st_int] :
( X
!= ( produc2639222612625641053st_int @ nil_Pr749310521696113548st_int @ Ys5 ) )
=> ( ! [Xs2: list_P419547167332244514st_int] :
( X
!= ( produc2639222612625641053st_int @ Xs2 @ nil_Pr749310521696113548st_int ) )
=> ~ ! [X3: produc6425607678544837394st_int,Xs2: list_P419547167332244514st_int,Y3: produc6425607678544837394st_int,Ys5: list_P419547167332244514st_int] :
( X
!= ( produc2639222612625641053st_int @ ( cons_P4151473878978182108st_int @ X3 @ Xs2 ) @ ( cons_P4151473878978182108st_int @ Y3 @ Ys5 ) ) ) ) ) ).
% shuffles.cases
thf(fact_646_shuffles_Ocases,axiom,
! [X: produc525958773753613763t_char] :
( ! [Ys5: list_list_char] :
( X
!= ( produc9134825680149865339t_char @ nil_list_char @ Ys5 ) )
=> ( ! [Xs2: list_list_char] :
( X
!= ( produc9134825680149865339t_char @ Xs2 @ nil_list_char ) )
=> ~ ! [X3: list_char,Xs2: list_list_char,Y3: list_char,Ys5: list_list_char] :
( X
!= ( produc9134825680149865339t_char @ ( cons_list_char @ X3 @ Xs2 ) @ ( cons_list_char @ Y3 @ Ys5 ) ) ) ) ) ).
% shuffles.cases
thf(fact_647_sorted__wrt_Ocases,axiom,
! [X: produc5834231552977413017st_int] :
( ! [P3: int > int > $o] :
( X
!= ( produc8618682346314911123st_int @ P3 @ nil_int ) )
=> ~ ! [P3: int > int > $o,X3: int,Ys5: list_int] :
( X
!= ( produc8618682346314911123st_int @ P3 @ ( cons_int @ X3 @ Ys5 ) ) ) ) ).
% sorted_wrt.cases
thf(fact_648_sorted__wrt_Ocases,axiom,
! [X: produc7133927873007960030_instr] :
( ! [P3: instr > instr > $o] :
( X
!= ( produc7818391707689388878_instr @ P3 @ nil_instr ) )
=> ~ ! [P3: instr > instr > $o,X3: instr,Ys5: list_instr] :
( X
!= ( produc7818391707689388878_instr @ P3 @ ( cons_instr @ X3 @ Ys5 ) ) ) ) ).
% sorted_wrt.cases
thf(fact_649_sorted__wrt_Ocases,axiom,
! [X: produc2468426419292222131st_int] :
( ! [P3: produc6425607678544837394st_int > produc6425607678544837394st_int > $o] :
( X
!= ( produc554038597315947693st_int @ P3 @ nil_Pr749310521696113548st_int ) )
=> ~ ! [P3: produc6425607678544837394st_int > produc6425607678544837394st_int > $o,X3: produc6425607678544837394st_int,Ys5: list_P419547167332244514st_int] :
( X
!= ( produc554038597315947693st_int @ P3 @ ( cons_P4151473878978182108st_int @ X3 @ Ys5 ) ) ) ) ).
% sorted_wrt.cases
thf(fact_650_sorted__wrt_Ocases,axiom,
! [X: produc8794813868974875620t_char] :
( ! [P3: list_char > list_char > $o] :
( X
!= ( produc1436111165245395422t_char @ P3 @ nil_list_char ) )
=> ~ ! [P3: list_char > list_char > $o,X3: list_char,Ys5: list_list_char] :
( X
!= ( produc1436111165245395422t_char @ P3 @ ( cons_list_char @ X3 @ Ys5 ) ) ) ) ).
% sorted_wrt.cases
thf(fact_651_successively_Ocases,axiom,
! [X: produc5834231552977413017st_int] :
( ! [P3: int > int > $o] :
( X
!= ( produc8618682346314911123st_int @ P3 @ nil_int ) )
=> ( ! [P3: int > int > $o,X3: int] :
( X
!= ( produc8618682346314911123st_int @ P3 @ ( cons_int @ X3 @ nil_int ) ) )
=> ~ ! [P3: int > int > $o,X3: int,Y3: int,Xs2: list_int] :
( X
!= ( produc8618682346314911123st_int @ P3 @ ( cons_int @ X3 @ ( cons_int @ Y3 @ Xs2 ) ) ) ) ) ) ).
% successively.cases
thf(fact_652_successively_Ocases,axiom,
! [X: produc7133927873007960030_instr] :
( ! [P3: instr > instr > $o] :
( X
!= ( produc7818391707689388878_instr @ P3 @ nil_instr ) )
=> ( ! [P3: instr > instr > $o,X3: instr] :
( X
!= ( produc7818391707689388878_instr @ P3 @ ( cons_instr @ X3 @ nil_instr ) ) )
=> ~ ! [P3: instr > instr > $o,X3: instr,Y3: instr,Xs2: list_instr] :
( X
!= ( produc7818391707689388878_instr @ P3 @ ( cons_instr @ X3 @ ( cons_instr @ Y3 @ Xs2 ) ) ) ) ) ) ).
% successively.cases
thf(fact_653_successively_Ocases,axiom,
! [X: produc2468426419292222131st_int] :
( ! [P3: produc6425607678544837394st_int > produc6425607678544837394st_int > $o] :
( X
!= ( produc554038597315947693st_int @ P3 @ nil_Pr749310521696113548st_int ) )
=> ( ! [P3: produc6425607678544837394st_int > produc6425607678544837394st_int > $o,X3: produc6425607678544837394st_int] :
( X
!= ( produc554038597315947693st_int @ P3 @ ( cons_P4151473878978182108st_int @ X3 @ nil_Pr749310521696113548st_int ) ) )
=> ~ ! [P3: produc6425607678544837394st_int > produc6425607678544837394st_int > $o,X3: produc6425607678544837394st_int,Y3: produc6425607678544837394st_int,Xs2: list_P419547167332244514st_int] :
( X
!= ( produc554038597315947693st_int @ P3 @ ( cons_P4151473878978182108st_int @ X3 @ ( cons_P4151473878978182108st_int @ Y3 @ Xs2 ) ) ) ) ) ) ).
% successively.cases
thf(fact_654_successively_Ocases,axiom,
! [X: produc8794813868974875620t_char] :
( ! [P3: list_char > list_char > $o] :
( X
!= ( produc1436111165245395422t_char @ P3 @ nil_list_char ) )
=> ( ! [P3: list_char > list_char > $o,X3: list_char] :
( X
!= ( produc1436111165245395422t_char @ P3 @ ( cons_list_char @ X3 @ nil_list_char ) ) )
=> ~ ! [P3: list_char > list_char > $o,X3: list_char,Y3: list_char,Xs2: list_list_char] :
( X
!= ( produc1436111165245395422t_char @ P3 @ ( cons_list_char @ X3 @ ( cons_list_char @ Y3 @ Xs2 ) ) ) ) ) ) ).
% successively.cases
thf(fact_655_length__append__singleton,axiom,
! [Xs: list_instr,X: instr] :
( ( size_size_list_instr @ ( append_instr @ Xs @ ( cons_instr @ X @ nil_instr ) ) )
= ( suc @ ( size_size_list_instr @ Xs ) ) ) ).
% length_append_singleton
thf(fact_656_length__append__singleton,axiom,
! [Xs: list_P419547167332244514st_int,X: produc6425607678544837394st_int] :
( ( size_s229347708945616566st_int @ ( append5028292981072010935st_int @ Xs @ ( cons_P4151473878978182108st_int @ X @ nil_Pr749310521696113548st_int ) ) )
= ( suc @ ( size_s229347708945616566st_int @ Xs ) ) ) ).
% length_append_singleton
thf(fact_657_length__append__singleton,axiom,
! [Xs: list_list_char,X: list_char] :
( ( size_s356637359517785349t_char @ ( append_list_char @ Xs @ ( cons_list_char @ X @ nil_list_char ) ) )
= ( suc @ ( size_s356637359517785349t_char @ Xs ) ) ) ).
% length_append_singleton
thf(fact_658_length__append__singleton,axiom,
! [Xs: list_int,X: int] :
( ( size_size_list_int @ ( append_int @ Xs @ ( cons_int @ X @ nil_int ) ) )
= ( suc @ ( size_size_list_int @ Xs ) ) ) ).
% length_append_singleton
thf(fact_659_length__Suc__conv__rev,axiom,
! [Xs: list_instr,N: nat] :
( ( ( size_size_list_instr @ Xs )
= ( suc @ N ) )
= ( ? [Y2: instr,Ys3: list_instr] :
( ( Xs
= ( append_instr @ Ys3 @ ( cons_instr @ Y2 @ nil_instr ) ) )
& ( ( size_size_list_instr @ Ys3 )
= N ) ) ) ) ).
% length_Suc_conv_rev
thf(fact_660_length__Suc__conv__rev,axiom,
! [Xs: list_P419547167332244514st_int,N: nat] :
( ( ( size_s229347708945616566st_int @ Xs )
= ( suc @ N ) )
= ( ? [Y2: produc6425607678544837394st_int,Ys3: list_P419547167332244514st_int] :
( ( Xs
= ( append5028292981072010935st_int @ Ys3 @ ( cons_P4151473878978182108st_int @ Y2 @ nil_Pr749310521696113548st_int ) ) )
& ( ( size_s229347708945616566st_int @ Ys3 )
= N ) ) ) ) ).
% length_Suc_conv_rev
thf(fact_661_length__Suc__conv__rev,axiom,
! [Xs: list_list_char,N: nat] :
( ( ( size_s356637359517785349t_char @ Xs )
= ( suc @ N ) )
= ( ? [Y2: list_char,Ys3: list_list_char] :
( ( Xs
= ( append_list_char @ Ys3 @ ( cons_list_char @ Y2 @ nil_list_char ) ) )
& ( ( size_s356637359517785349t_char @ Ys3 )
= N ) ) ) ) ).
% length_Suc_conv_rev
thf(fact_662_length__Suc__conv__rev,axiom,
! [Xs: list_int,N: nat] :
( ( ( size_size_list_int @ Xs )
= ( suc @ N ) )
= ( ? [Y2: int,Ys3: list_int] :
( ( Xs
= ( append_int @ Ys3 @ ( cons_int @ Y2 @ nil_int ) ) )
& ( ( size_size_list_int @ Ys3 )
= N ) ) ) ) ).
% length_Suc_conv_rev
thf(fact_663_enumerate__append__eq,axiom,
! [N: nat,Xs: list_instr,Ys: list_instr] :
( ( enumerate_instr @ N @ ( append_instr @ Xs @ Ys ) )
= ( append227978101926261161_instr @ ( enumerate_instr @ N @ Xs ) @ ( enumerate_instr @ ( plus_plus_nat @ N @ ( size_size_list_instr @ Xs ) ) @ Ys ) ) ) ).
% enumerate_append_eq
thf(fact_664_enumerate__append__eq,axiom,
! [N: nat,Xs: list_int,Ys: list_int] :
( ( enumerate_int @ N @ ( append_int @ Xs @ Ys ) )
= ( append6031344391939132024at_int @ ( enumerate_int @ N @ Xs ) @ ( enumerate_int @ ( plus_plus_nat @ N @ ( size_size_list_int @ Xs ) ) @ Ys ) ) ) ).
% enumerate_append_eq
thf(fact_665_lenlex__irreflexive,axiom,
! [R: set_Pr958786334691620121nt_int,Xs: list_int] :
( ! [X3: int] :
~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ X3 ) @ R )
=> ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Xs ) @ ( lenlex_int @ R ) ) ) ).
% lenlex_irreflexive
thf(fact_666_instr_Osize_I11_J,axiom,
! [X42: list_char] :
( ( size_size_instr @ ( store @ X42 ) )
= zero_zero_nat ) ).
% instr.size(11)
thf(fact_667_list_Osize_I3_J,axiom,
( ( size_size_list_instr @ nil_instr )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_668_list_Osize_I3_J,axiom,
( ( size_s229347708945616566st_int @ nil_Pr749310521696113548st_int )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_669_list_Osize_I3_J,axiom,
( ( size_s356637359517785349t_char @ nil_list_char )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_670_list_Osize_I3_J,axiom,
( ( size_size_list_int @ nil_int )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_671_list__induct3,axiom,
! [Xs: list_instr,Ys: list_instr,Zs: list_instr,P: list_instr > list_instr > list_instr > $o] :
( ( ( size_size_list_instr @ Xs )
= ( size_size_list_instr @ Ys ) )
=> ( ( ( size_size_list_instr @ Ys )
= ( size_size_list_instr @ Zs ) )
=> ( ( P @ nil_instr @ nil_instr @ nil_instr )
=> ( ! [X3: instr,Xs2: list_instr,Y3: instr,Ys5: list_instr,Z4: instr,Zs2: list_instr] :
( ( ( size_size_list_instr @ Xs2 )
= ( size_size_list_instr @ Ys5 ) )
=> ( ( ( size_size_list_instr @ Ys5 )
= ( size_size_list_instr @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys5 @ Zs2 )
=> ( P @ ( cons_instr @ X3 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys5 ) @ ( cons_instr @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_672_list__induct3,axiom,
! [Xs: list_instr,Ys: list_instr,Zs: list_int,P: list_instr > list_instr > list_int > $o] :
( ( ( size_size_list_instr @ Xs )
= ( size_size_list_instr @ Ys ) )
=> ( ( ( size_size_list_instr @ Ys )
= ( size_size_list_int @ Zs ) )
=> ( ( P @ nil_instr @ nil_instr @ nil_int )
=> ( ! [X3: instr,Xs2: list_instr,Y3: instr,Ys5: list_instr,Z4: int,Zs2: list_int] :
( ( ( size_size_list_instr @ Xs2 )
= ( size_size_list_instr @ Ys5 ) )
=> ( ( ( size_size_list_instr @ Ys5 )
= ( size_size_list_int @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys5 @ Zs2 )
=> ( P @ ( cons_instr @ X3 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys5 ) @ ( cons_int @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_673_list__induct3,axiom,
! [Xs: list_instr,Ys: list_int,Zs: list_instr,P: list_instr > list_int > list_instr > $o] :
( ( ( size_size_list_instr @ Xs )
= ( size_size_list_int @ Ys ) )
=> ( ( ( size_size_list_int @ Ys )
= ( size_size_list_instr @ Zs ) )
=> ( ( P @ nil_instr @ nil_int @ nil_instr )
=> ( ! [X3: instr,Xs2: list_instr,Y3: int,Ys5: list_int,Z4: instr,Zs2: list_instr] :
( ( ( size_size_list_instr @ Xs2 )
= ( size_size_list_int @ Ys5 ) )
=> ( ( ( size_size_list_int @ Ys5 )
= ( size_size_list_instr @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys5 @ Zs2 )
=> ( P @ ( cons_instr @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys5 ) @ ( cons_instr @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_674_list__induct3,axiom,
! [Xs: list_instr,Ys: list_int,Zs: list_int,P: list_instr > list_int > list_int > $o] :
( ( ( size_size_list_instr @ Xs )
= ( size_size_list_int @ Ys ) )
=> ( ( ( size_size_list_int @ Ys )
= ( size_size_list_int @ Zs ) )
=> ( ( P @ nil_instr @ nil_int @ nil_int )
=> ( ! [X3: instr,Xs2: list_instr,Y3: int,Ys5: list_int,Z4: int,Zs2: list_int] :
( ( ( size_size_list_instr @ Xs2 )
= ( size_size_list_int @ Ys5 ) )
=> ( ( ( size_size_list_int @ Ys5 )
= ( size_size_list_int @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys5 @ Zs2 )
=> ( P @ ( cons_instr @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys5 ) @ ( cons_int @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_675_list__induct3,axiom,
! [Xs: list_int,Ys: list_instr,Zs: list_instr,P: list_int > list_instr > list_instr > $o] :
( ( ( size_size_list_int @ Xs )
= ( size_size_list_instr @ Ys ) )
=> ( ( ( size_size_list_instr @ Ys )
= ( size_size_list_instr @ Zs ) )
=> ( ( P @ nil_int @ nil_instr @ nil_instr )
=> ( ! [X3: int,Xs2: list_int,Y3: instr,Ys5: list_instr,Z4: instr,Zs2: list_instr] :
( ( ( size_size_list_int @ Xs2 )
= ( size_size_list_instr @ Ys5 ) )
=> ( ( ( size_size_list_instr @ Ys5 )
= ( size_size_list_instr @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys5 @ Zs2 )
=> ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys5 ) @ ( cons_instr @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_676_list__induct3,axiom,
! [Xs: list_int,Ys: list_instr,Zs: list_int,P: list_int > list_instr > list_int > $o] :
( ( ( size_size_list_int @ Xs )
= ( size_size_list_instr @ Ys ) )
=> ( ( ( size_size_list_instr @ Ys )
= ( size_size_list_int @ Zs ) )
=> ( ( P @ nil_int @ nil_instr @ nil_int )
=> ( ! [X3: int,Xs2: list_int,Y3: instr,Ys5: list_instr,Z4: int,Zs2: list_int] :
( ( ( size_size_list_int @ Xs2 )
= ( size_size_list_instr @ Ys5 ) )
=> ( ( ( size_size_list_instr @ Ys5 )
= ( size_size_list_int @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys5 @ Zs2 )
=> ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys5 ) @ ( cons_int @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_677_list__induct3,axiom,
! [Xs: list_int,Ys: list_int,Zs: list_instr,P: list_int > list_int > list_instr > $o] :
( ( ( size_size_list_int @ Xs )
= ( size_size_list_int @ Ys ) )
=> ( ( ( size_size_list_int @ Ys )
= ( size_size_list_instr @ Zs ) )
=> ( ( P @ nil_int @ nil_int @ nil_instr )
=> ( ! [X3: int,Xs2: list_int,Y3: int,Ys5: list_int,Z4: instr,Zs2: list_instr] :
( ( ( size_size_list_int @ Xs2 )
= ( size_size_list_int @ Ys5 ) )
=> ( ( ( size_size_list_int @ Ys5 )
= ( size_size_list_instr @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys5 @ Zs2 )
=> ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys5 ) @ ( cons_instr @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_678_list__induct3,axiom,
! [Xs: list_int,Ys: list_int,Zs: list_int,P: list_int > list_int > list_int > $o] :
( ( ( size_size_list_int @ Xs )
= ( size_size_list_int @ Ys ) )
=> ( ( ( size_size_list_int @ Ys )
= ( size_size_list_int @ Zs ) )
=> ( ( P @ nil_int @ nil_int @ nil_int )
=> ( ! [X3: int,Xs2: list_int,Y3: int,Ys5: list_int,Z4: int,Zs2: list_int] :
( ( ( size_size_list_int @ Xs2 )
= ( size_size_list_int @ Ys5 ) )
=> ( ( ( size_size_list_int @ Ys5 )
= ( size_size_list_int @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys5 @ Zs2 )
=> ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys5 ) @ ( cons_int @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_679_list__induct3,axiom,
! [Xs: list_instr,Ys: list_instr,Zs: list_list_char,P: list_instr > list_instr > list_list_char > $o] :
( ( ( size_size_list_instr @ Xs )
= ( size_size_list_instr @ Ys ) )
=> ( ( ( size_size_list_instr @ Ys )
= ( size_s356637359517785349t_char @ Zs ) )
=> ( ( P @ nil_instr @ nil_instr @ nil_list_char )
=> ( ! [X3: instr,Xs2: list_instr,Y3: instr,Ys5: list_instr,Z4: list_char,Zs2: list_list_char] :
( ( ( size_size_list_instr @ Xs2 )
= ( size_size_list_instr @ Ys5 ) )
=> ( ( ( size_size_list_instr @ Ys5 )
= ( size_s356637359517785349t_char @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys5 @ Zs2 )
=> ( P @ ( cons_instr @ X3 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys5 ) @ ( cons_list_char @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_680_list__induct3,axiom,
! [Xs: list_instr,Ys: list_list_char,Zs: list_instr,P: list_instr > list_list_char > list_instr > $o] :
( ( ( size_size_list_instr @ Xs )
= ( size_s356637359517785349t_char @ Ys ) )
=> ( ( ( size_s356637359517785349t_char @ Ys )
= ( size_size_list_instr @ Zs ) )
=> ( ( P @ nil_instr @ nil_list_char @ nil_instr )
=> ( ! [X3: instr,Xs2: list_instr,Y3: list_char,Ys5: list_list_char,Z4: instr,Zs2: list_instr] :
( ( ( size_size_list_instr @ Xs2 )
= ( size_s356637359517785349t_char @ Ys5 ) )
=> ( ( ( size_s356637359517785349t_char @ Ys5 )
= ( size_size_list_instr @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys5 @ Zs2 )
=> ( P @ ( cons_instr @ X3 @ Xs2 ) @ ( cons_list_char @ Y3 @ Ys5 ) @ ( cons_instr @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_681_list__induct2,axiom,
! [Xs: list_instr,Ys: list_instr,P: list_instr > list_instr > $o] :
( ( ( size_size_list_instr @ Xs )
= ( size_size_list_instr @ Ys ) )
=> ( ( P @ nil_instr @ nil_instr )
=> ( ! [X3: instr,Xs2: list_instr,Y3: instr,Ys5: list_instr] :
( ( ( size_size_list_instr @ Xs2 )
= ( size_size_list_instr @ Ys5 ) )
=> ( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_instr @ X3 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys5 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_682_list__induct2,axiom,
! [Xs: list_instr,Ys: list_int,P: list_instr > list_int > $o] :
( ( ( size_size_list_instr @ Xs )
= ( size_size_list_int @ Ys ) )
=> ( ( P @ nil_instr @ nil_int )
=> ( ! [X3: instr,Xs2: list_instr,Y3: int,Ys5: list_int] :
( ( ( size_size_list_instr @ Xs2 )
= ( size_size_list_int @ Ys5 ) )
=> ( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_instr @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys5 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_683_list__induct2,axiom,
! [Xs: list_int,Ys: list_instr,P: list_int > list_instr > $o] :
( ( ( size_size_list_int @ Xs )
= ( size_size_list_instr @ Ys ) )
=> ( ( P @ nil_int @ nil_instr )
=> ( ! [X3: int,Xs2: list_int,Y3: instr,Ys5: list_instr] :
( ( ( size_size_list_int @ Xs2 )
= ( size_size_list_instr @ Ys5 ) )
=> ( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys5 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_684_list__induct2,axiom,
! [Xs: list_int,Ys: list_int,P: list_int > list_int > $o] :
( ( ( size_size_list_int @ Xs )
= ( size_size_list_int @ Ys ) )
=> ( ( P @ nil_int @ nil_int )
=> ( ! [X3: int,Xs2: list_int,Y3: int,Ys5: list_int] :
( ( ( size_size_list_int @ Xs2 )
= ( size_size_list_int @ Ys5 ) )
=> ( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys5 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_685_list__induct2,axiom,
! [Xs: list_instr,Ys: list_list_char,P: list_instr > list_list_char > $o] :
( ( ( size_size_list_instr @ Xs )
= ( size_s356637359517785349t_char @ Ys ) )
=> ( ( P @ nil_instr @ nil_list_char )
=> ( ! [X3: instr,Xs2: list_instr,Y3: list_char,Ys5: list_list_char] :
( ( ( size_size_list_instr @ Xs2 )
= ( size_s356637359517785349t_char @ Ys5 ) )
=> ( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_instr @ X3 @ Xs2 ) @ ( cons_list_char @ Y3 @ Ys5 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_686_list__induct2,axiom,
! [Xs: list_list_char,Ys: list_instr,P: list_list_char > list_instr > $o] :
( ( ( size_s356637359517785349t_char @ Xs )
= ( size_size_list_instr @ Ys ) )
=> ( ( P @ nil_list_char @ nil_instr )
=> ( ! [X3: list_char,Xs2: list_list_char,Y3: instr,Ys5: list_instr] :
( ( ( size_s356637359517785349t_char @ Xs2 )
= ( size_size_list_instr @ Ys5 ) )
=> ( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_list_char @ X3 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys5 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_687_list__induct2,axiom,
! [Xs: list_list_char,Ys: list_int,P: list_list_char > list_int > $o] :
( ( ( size_s356637359517785349t_char @ Xs )
= ( size_size_list_int @ Ys ) )
=> ( ( P @ nil_list_char @ nil_int )
=> ( ! [X3: list_char,Xs2: list_list_char,Y3: int,Ys5: list_int] :
( ( ( size_s356637359517785349t_char @ Xs2 )
= ( size_size_list_int @ Ys5 ) )
=> ( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_list_char @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys5 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_688_list__induct2,axiom,
! [Xs: list_int,Ys: list_list_char,P: list_int > list_list_char > $o] :
( ( ( size_size_list_int @ Xs )
= ( size_s356637359517785349t_char @ Ys ) )
=> ( ( P @ nil_int @ nil_list_char )
=> ( ! [X3: int,Xs2: list_int,Y3: list_char,Ys5: list_list_char] :
( ( ( size_size_list_int @ Xs2 )
= ( size_s356637359517785349t_char @ Ys5 ) )
=> ( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_list_char @ Y3 @ Ys5 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_689_list__induct2,axiom,
! [Xs: list_list_char,Ys: list_list_char,P: list_list_char > list_list_char > $o] :
( ( ( size_s356637359517785349t_char @ Xs )
= ( size_s356637359517785349t_char @ Ys ) )
=> ( ( P @ nil_list_char @ nil_list_char )
=> ( ! [X3: list_char,Xs2: list_list_char,Y3: list_char,Ys5: list_list_char] :
( ( ( size_s356637359517785349t_char @ Xs2 )
= ( size_s356637359517785349t_char @ Ys5 ) )
=> ( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_list_char @ X3 @ Xs2 ) @ ( cons_list_char @ Y3 @ Ys5 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_690_list__induct2,axiom,
! [Xs: list_instr,Ys: list_P419547167332244514st_int,P: list_instr > list_P419547167332244514st_int > $o] :
( ( ( size_size_list_instr @ Xs )
= ( size_s229347708945616566st_int @ Ys ) )
=> ( ( P @ nil_instr @ nil_Pr749310521696113548st_int )
=> ( ! [X3: instr,Xs2: list_instr,Y3: produc6425607678544837394st_int,Ys5: list_P419547167332244514st_int] :
( ( ( size_size_list_instr @ Xs2 )
= ( size_s229347708945616566st_int @ Ys5 ) )
=> ( ( P @ Xs2 @ Ys5 )
=> ( P @ ( cons_instr @ X3 @ Xs2 ) @ ( cons_P4151473878978182108st_int @ Y3 @ Ys5 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_691_nth__append,axiom,
! [N: nat,Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( ( ord_less_nat @ N @ ( size_s229347708945616566st_int @ Xs ) )
=> ( ( nth_Pr8327173284404383691st_int @ ( append5028292981072010935st_int @ Xs @ Ys ) @ N )
= ( nth_Pr8327173284404383691st_int @ Xs @ N ) ) )
& ( ~ ( ord_less_nat @ N @ ( size_s229347708945616566st_int @ Xs ) )
=> ( ( nth_Pr8327173284404383691st_int @ ( append5028292981072010935st_int @ Xs @ Ys ) @ N )
= ( nth_Pr8327173284404383691st_int @ Ys @ ( minus_minus_nat @ N @ ( size_s229347708945616566st_int @ Xs ) ) ) ) ) ) ).
% nth_append
thf(fact_692_nth__append,axiom,
! [N: nat,Xs: list_instr,Ys: list_instr] :
( ( ( ord_less_nat @ N @ ( size_size_list_instr @ Xs ) )
=> ( ( nth_instr @ ( append_instr @ Xs @ Ys ) @ N )
= ( nth_instr @ Xs @ N ) ) )
& ( ~ ( ord_less_nat @ N @ ( size_size_list_instr @ Xs ) )
=> ( ( nth_instr @ ( append_instr @ Xs @ Ys ) @ N )
= ( nth_instr @ Ys @ ( minus_minus_nat @ N @ ( size_size_list_instr @ Xs ) ) ) ) ) ) ).
% nth_append
thf(fact_693_nth__append,axiom,
! [N: nat,Xs: list_int,Ys: list_int] :
( ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
=> ( ( nth_int @ ( append_int @ Xs @ Ys ) @ N )
= ( nth_int @ Xs @ N ) ) )
& ( ~ ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
=> ( ( nth_int @ ( append_int @ Xs @ Ys ) @ N )
= ( nth_int @ Ys @ ( minus_minus_nat @ N @ ( size_size_list_int @ Xs ) ) ) ) ) ) ).
% nth_append
thf(fact_694_iexec__simp,axiom,
! [Ins2: instr,Cf: produc6425607678544837394st_int,Cf2: produc6425607678544837394st_int] :
( ( iexec_pred @ ( produc1484136438817787418st_int @ Ins2 @ Cf ) @ Cf2 )
= ( Cf2
= ( iexec @ Ins2 @ Cf ) ) ) ).
% iexec_simp
thf(fact_695_iexec__pred_Ointros,axiom,
! [Ins2: instr,Cf: produc6425607678544837394st_int] : ( iexec_pred @ ( produc1484136438817787418st_int @ Ins2 @ Cf ) @ ( iexec @ Ins2 @ Cf ) ) ).
% iexec_pred.intros
thf(fact_696_iexec__pred_Osimps,axiom,
( iexec_pred
= ( ^ [A1: produc5995290525303592096st_int,A22: produc6425607678544837394st_int] :
? [Ins3: instr,Cf3: produc6425607678544837394st_int] :
( ( A1
= ( produc1484136438817787418st_int @ Ins3 @ Cf3 ) )
& ( A22
= ( iexec @ Ins3 @ Cf3 ) ) ) ) ) ).
% iexec_pred.simps
thf(fact_697_iexec__pred_Ocases,axiom,
! [A12: produc5995290525303592096st_int,A23: produc6425607678544837394st_int] :
( ( iexec_pred @ A12 @ A23 )
=> ~ ! [Ins: instr,Cf4: produc6425607678544837394st_int] :
( ( A12
= ( produc1484136438817787418st_int @ Ins @ Cf4 ) )
=> ( A23
!= ( iexec @ Ins @ Cf4 ) ) ) ) ).
% iexec_pred.cases
thf(fact_698_LoadIE,axiom,
! [I: int,Pc: int,S2: list_char > int,Stk3: list_int,Cf: produc6425607678544837394st_int] :
( ( iexec_pred @ ( produc1484136438817787418st_int @ ( loadi @ I ) @ ( produc5086643055186798020st_int @ Pc @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) ) @ Cf )
=> ( Cf
= ( produc5086643055186798020st_int @ ( plus_plus_int @ Pc @ one_one_int ) @ ( produc8650753666468850689st_int @ S2 @ ( cons_int @ I @ Stk3 ) ) ) ) ) ).
% LoadIE
thf(fact_699_LoadE,axiom,
! [X: list_char,Pc: int,S2: list_char > int,Stk3: list_int,Cf: produc6425607678544837394st_int] :
( ( iexec_pred @ ( produc1484136438817787418st_int @ ( load @ X ) @ ( produc5086643055186798020st_int @ Pc @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) ) @ Cf )
=> ( Cf
= ( produc5086643055186798020st_int @ ( plus_plus_int @ Pc @ one_one_int ) @ ( produc8650753666468850689st_int @ S2 @ ( cons_int @ ( S2 @ X ) @ Stk3 ) ) ) ) ) ).
% LoadE
thf(fact_700_JmpE,axiom,
! [I: int,Pc: int,S2: list_char > int,Stk3: list_int,Cf: produc6425607678544837394st_int] :
( ( iexec_pred @ ( produc1484136438817787418st_int @ ( jmp @ I ) @ ( produc5086643055186798020st_int @ Pc @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) ) @ Cf )
=> ( Cf
= ( produc5086643055186798020st_int @ ( plus_plus_int @ ( plus_plus_int @ Pc @ one_one_int ) @ I ) @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) ) ) ).
% JmpE
thf(fact_701__092_060open_062_092_060exists_062k_060length_Acfs_O_Aapred_Aa_A_Ioff_A_091_093_A_Icfs_A_B_A0_J_J_A_Ioff_A_091_093_A_Icfs_A_B_Ak_J_J_092_060close_062,axiom,
? [K: nat] :
( ( ord_less_nat @ K @ ( size_s229347708945616566st_int @ cfsa ) )
& ( apred @ a @ ( produc5086643055186798020st_int @ ( minus_minus_int @ ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ cfsa @ zero_zero_nat ) ) @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ nil_instr ) ) ) @ ( produc1296517004818028822st_int @ ( nth_Pr8327173284404383691st_int @ cfsa @ zero_zero_nat ) ) ) @ ( produc5086643055186798020st_int @ ( minus_minus_int @ ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ cfsa @ K ) ) @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ nil_instr ) ) ) @ ( produc1296517004818028822st_int @ ( nth_Pr8327173284404383691st_int @ cfsa @ K ) ) ) ) ) ).
% \<open>\<exists>k<length cfs. apred a (off [] (cfs ! 0)) (off [] (cfs ! k))\<close>
thf(fact_702_inth__append,axiom,
! [I: int,Xs: list_instr,Ys: list_instr] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ Xs ) ) )
=> ( ( inth_instr @ ( append_instr @ Xs @ Ys ) @ I )
= ( inth_instr @ Xs @ I ) ) )
& ( ~ ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ Xs ) ) )
=> ( ( inth_instr @ ( append_instr @ Xs @ Ys ) @ I )
= ( inth_instr @ Ys @ ( minus_minus_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ Xs ) ) ) ) ) ) ) ) ).
% inth_append
thf(fact_703_inth__append,axiom,
! [I: int,Xs: list_list_char,Ys: list_list_char] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs ) ) )
=> ( ( inth_list_char @ ( append_list_char @ Xs @ Ys ) @ I )
= ( inth_list_char @ Xs @ I ) ) )
& ( ~ ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs ) ) )
=> ( ( inth_list_char @ ( append_list_char @ Xs @ Ys ) @ I )
= ( inth_list_char @ Ys @ ( minus_minus_int @ I @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs ) ) ) ) ) ) ) ) ).
% inth_append
thf(fact_704_inth__append,axiom,
! [I: int,Xs: list_int,Ys: list_int] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_int @ Xs ) ) )
=> ( ( inth_int @ ( append_int @ Xs @ Ys ) @ I )
= ( inth_int @ Xs @ I ) ) )
& ( ~ ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_int @ Xs ) ) )
=> ( ( inth_int @ ( append_int @ Xs @ Ys ) @ I )
= ( inth_int @ Ys @ ( minus_minus_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_int @ Xs ) ) ) ) ) ) ) ) ).
% inth_append
thf(fact_705_instr_Oinject_I4_J,axiom,
! [X5: int,Y5: int] :
( ( ( jmp @ X5 )
= ( jmp @ Y5 ) )
= ( X5 = Y5 ) ) ).
% instr.inject(4)
thf(fact_706_instr_Oinject_I2_J,axiom,
! [X22: list_char,Y22: list_char] :
( ( ( load @ X22 )
= ( load @ Y22 ) )
= ( X22 = Y22 ) ) ).
% instr.inject(2)
thf(fact_707_instr_Oinject_I1_J,axiom,
! [X1: int,Y1: int] :
( ( ( loadi @ X1 )
= ( loadi @ Y1 ) )
= ( X1 = Y1 ) ) ).
% instr.inject(1)
thf(fact_708_le__zero__eq,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) ).
% le_zero_eq
thf(fact_709_add__le__cancel__left,axiom,
! [C: int,A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
= ( ord_less_eq_int @ A @ B ) ) ).
% add_le_cancel_left
thf(fact_710_add__le__cancel__left,axiom,
! [C: nat,A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ B ) ) ).
% add_le_cancel_left
thf(fact_711_add__le__cancel__right,axiom,
! [A: int,C: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
= ( ord_less_eq_int @ A @ B ) ) ).
% add_le_cancel_right
thf(fact_712_add__le__cancel__right,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( ord_less_eq_nat @ A @ B ) ) ).
% add_le_cancel_right
thf(fact_713_of__nat__le__iff,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
= ( ord_less_eq_nat @ M @ N ) ) ).
% of_nat_le_iff
thf(fact_714_of__nat__le__iff,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
= ( ord_less_eq_nat @ M @ N ) ) ).
% of_nat_le_iff
thf(fact_715_in__measures_I1_J,axiom,
! [X: int,Y: int] :
~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ nil_int_nat ) ) ).
% in_measures(1)
thf(fact_716_zero__le__double__add__iff__zero__le__single__add,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
= ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% zero_le_double_add_iff_zero_le_single_add
thf(fact_717_double__add__le__zero__iff__single__add__le__zero,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
= ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% double_add_le_zero_iff_single_add_le_zero
thf(fact_718_le__add__same__cancel2,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
= ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% le_add_same_cancel2
thf(fact_719_le__add__same__cancel2,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
= ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% le_add_same_cancel2
thf(fact_720_le__add__same__cancel1,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
= ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% le_add_same_cancel1
thf(fact_721_le__add__same__cancel1,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
= ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% le_add_same_cancel1
thf(fact_722_add__le__same__cancel2,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
= ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% add_le_same_cancel2
thf(fact_723_add__le__same__cancel2,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
= ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% add_le_same_cancel2
thf(fact_724_add__le__same__cancel1,axiom,
! [B: int,A: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
= ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% add_le_same_cancel1
thf(fact_725_add__le__same__cancel1,axiom,
! [B: nat,A: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
= ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% add_le_same_cancel1
thf(fact_726_diff__ge__0__iff__ge,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
= ( ord_less_eq_int @ B @ A ) ) ).
% diff_ge_0_iff_ge
thf(fact_727_le__add__diff__inverse2,axiom,
! [B: int,A: int] :
( ( ord_less_eq_int @ B @ A )
=> ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
= A ) ) ).
% le_add_diff_inverse2
thf(fact_728_le__add__diff__inverse2,axiom,
! [B: nat,A: nat] :
( ( ord_less_eq_nat @ B @ A )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
= A ) ) ).
% le_add_diff_inverse2
thf(fact_729_le__add__diff__inverse,axiom,
! [B: int,A: int] :
( ( ord_less_eq_int @ B @ A )
=> ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
= A ) ) ).
% le_add_diff_inverse
thf(fact_730_le__add__diff__inverse,axiom,
! [B: nat,A: nat] :
( ( ord_less_eq_nat @ B @ A )
=> ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
= A ) ) ).
% le_add_diff_inverse
thf(fact_731_prod_Ocollapse,axiom,
! [Prod: product_prod_int_int] :
( ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) )
= Prod ) ).
% prod.collapse
thf(fact_732_prod_Ocollapse,axiom,
! [Prod: produc2285326912895808259nt_int] :
( ( produc5700946648718959541nt_int @ ( produc6816164490631068361nt_int @ Prod ) @ ( produc7328097813583171335nt_int @ Prod ) )
= Prod ) ).
% prod.collapse
thf(fact_733_prod_Ocollapse,axiom,
! [Prod: produc4435102495419491129nt_int] :
( ( produc5790713362662368625nt_int @ ( produc9025023058967219549nt_int @ Prod ) @ ( produc179445755590504351nt_int @ Prod ) )
= Prod ) ).
% prod.collapse
thf(fact_734_prod_Ocollapse,axiom,
! [Prod: produc7773217078559923341nt_int] :
( ( produc4305682042979456191nt_int @ ( produc6230002227079971283nt_int @ Prod ) @ ( produc3162348030201620241nt_int @ Prod ) )
= Prod ) ).
% prod.collapse
thf(fact_735_prod_Ocollapse,axiom,
! [Prod: produc6425607678544837394st_int] :
( ( produc5086643055186798020st_int @ ( produc8941309049508465880st_int @ Prod ) @ ( produc1296517004818028822st_int @ Prod ) )
= Prod ) ).
% prod.collapse
thf(fact_736_prod_Ocollapse,axiom,
! [Prod: product_prod_o_int] :
( ( product_Pair_o_int @ ( product_fst_o_int @ Prod ) @ ( product_snd_o_int @ Prod ) )
= Prod ) ).
% prod.collapse
thf(fact_737_prod_Ocollapse,axiom,
! [Prod: produc1897111610453708512_o_int] :
( ( produc4047900504771817624_o_int @ ( produc2736798884409471108_o_int @ Prod ) @ ( produc7219675232234870470_o_int @ Prod ) )
= Prod ) ).
% prod.collapse
thf(fact_738_prod_Ocollapse,axiom,
! [Prod: produc369741286924889929st_int] :
( ( produc8650753666468850689st_int @ ( produc2155683374303800813st_int @ Prod ) @ ( produc6244060863719409455st_int @ Prod ) )
= Prod ) ).
% prod.collapse
thf(fact_739_of__nat__le__0__iff,axiom,
! [M: nat] :
( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
= ( M = zero_zero_nat ) ) ).
% of_nat_le_0_iff
thf(fact_740_of__nat__le__0__iff,axiom,
! [M: nat] :
( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
= ( M = zero_zero_nat ) ) ).
% of_nat_le_0_iff
thf(fact_741_zle__add1__eq__le,axiom,
! [W: int,Z: int] :
( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
= ( ord_less_eq_int @ W @ Z ) ) ).
% zle_add1_eq_le
thf(fact_742_zle__diff1__eq,axiom,
! [W: int,Z: int] :
( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
= ( ord_less_int @ W @ Z ) ) ).
% zle_diff1_eq
thf(fact_743_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
! [P: int > int > $o,X: int,Y: int,A: product_prod_int_int] :
( ( P @ X @ Y )
=> ( ( A
= ( product_Pair_int_int @ X @ Y ) )
=> ( P @ ( product_fst_int_int @ A ) @ ( product_snd_int_int @ A ) ) ) ) ).
% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_744_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
! [P: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int,A: produc2285326912895808259nt_int] :
( ( P @ X @ Y )
=> ( ( A
= ( produc5700946648718959541nt_int @ X @ Y ) )
=> ( P @ ( produc6816164490631068361nt_int @ A ) @ ( produc7328097813583171335nt_int @ A ) ) ) ) ).
% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_745_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
! [P: ( list_char > int ) > int > $o,X: list_char > int,Y: int,A: produc4435102495419491129nt_int] :
( ( P @ X @ Y )
=> ( ( A
= ( produc5790713362662368625nt_int @ X @ Y ) )
=> ( P @ ( produc9025023058967219549nt_int @ A ) @ ( produc179445755590504351nt_int @ A ) ) ) ) ).
% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_746_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
! [P: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,X: int > option6357759511663192854e_term,Y: product_prod_int_int,A: produc7773217078559923341nt_int] :
( ( P @ X @ Y )
=> ( ( A
= ( produc4305682042979456191nt_int @ X @ Y ) )
=> ( P @ ( produc6230002227079971283nt_int @ A ) @ ( produc3162348030201620241nt_int @ A ) ) ) ) ).
% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_747_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
! [P: int > produc369741286924889929st_int > $o,X: int,Y: produc369741286924889929st_int,A: produc6425607678544837394st_int] :
( ( P @ X @ Y )
=> ( ( A
= ( produc5086643055186798020st_int @ X @ Y ) )
=> ( P @ ( produc8941309049508465880st_int @ A ) @ ( produc1296517004818028822st_int @ A ) ) ) ) ).
% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_748_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
! [P: $o > int > $o,X: $o,Y: int,A: product_prod_o_int] :
( ( P @ X @ Y )
=> ( ( A
= ( product_Pair_o_int @ X @ Y ) )
=> ( P @ ( product_fst_o_int @ A ) @ ( product_snd_o_int @ A ) ) ) ) ).
% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_749_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
! [P: bexp > product_prod_o_int > $o,X: bexp,Y: product_prod_o_int,A: produc1897111610453708512_o_int] :
( ( P @ X @ Y )
=> ( ( A
= ( produc4047900504771817624_o_int @ X @ Y ) )
=> ( P @ ( produc2736798884409471108_o_int @ A ) @ ( produc7219675232234870470_o_int @ A ) ) ) ) ).
% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_750_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
! [P: ( list_char > int ) > list_int > $o,X: list_char > int,Y: list_int,A: produc369741286924889929st_int] :
( ( P @ X @ Y )
=> ( ( A
= ( produc8650753666468850689st_int @ X @ Y ) )
=> ( P @ ( produc2155683374303800813st_int @ A ) @ ( produc6244060863719409455st_int @ A ) ) ) ) ).
% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_751_surjective__pairing,axiom,
! [T: product_prod_int_int] :
( T
= ( product_Pair_int_int @ ( product_fst_int_int @ T ) @ ( product_snd_int_int @ T ) ) ) ).
% surjective_pairing
thf(fact_752_surjective__pairing,axiom,
! [T: produc2285326912895808259nt_int] :
( T
= ( produc5700946648718959541nt_int @ ( produc6816164490631068361nt_int @ T ) @ ( produc7328097813583171335nt_int @ T ) ) ) ).
% surjective_pairing
thf(fact_753_surjective__pairing,axiom,
! [T: produc4435102495419491129nt_int] :
( T
= ( produc5790713362662368625nt_int @ ( produc9025023058967219549nt_int @ T ) @ ( produc179445755590504351nt_int @ T ) ) ) ).
% surjective_pairing
thf(fact_754_surjective__pairing,axiom,
! [T: produc7773217078559923341nt_int] :
( T
= ( produc4305682042979456191nt_int @ ( produc6230002227079971283nt_int @ T ) @ ( produc3162348030201620241nt_int @ T ) ) ) ).
% surjective_pairing
thf(fact_755_surjective__pairing,axiom,
! [T: produc6425607678544837394st_int] :
( T
= ( produc5086643055186798020st_int @ ( produc8941309049508465880st_int @ T ) @ ( produc1296517004818028822st_int @ T ) ) ) ).
% surjective_pairing
thf(fact_756_surjective__pairing,axiom,
! [T: product_prod_o_int] :
( T
= ( product_Pair_o_int @ ( product_fst_o_int @ T ) @ ( product_snd_o_int @ T ) ) ) ).
% surjective_pairing
thf(fact_757_surjective__pairing,axiom,
! [T: produc1897111610453708512_o_int] :
( T
= ( produc4047900504771817624_o_int @ ( produc2736798884409471108_o_int @ T ) @ ( produc7219675232234870470_o_int @ T ) ) ) ).
% surjective_pairing
thf(fact_758_surjective__pairing,axiom,
! [T: produc369741286924889929st_int] :
( T
= ( produc8650753666468850689st_int @ ( produc2155683374303800813st_int @ T ) @ ( produc6244060863719409455st_int @ T ) ) ) ).
% surjective_pairing
thf(fact_759_prod_Oexhaust__sel,axiom,
! [Prod: product_prod_int_int] :
( Prod
= ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ).
% prod.exhaust_sel
thf(fact_760_prod_Oexhaust__sel,axiom,
! [Prod: produc2285326912895808259nt_int] :
( Prod
= ( produc5700946648718959541nt_int @ ( produc6816164490631068361nt_int @ Prod ) @ ( produc7328097813583171335nt_int @ Prod ) ) ) ).
% prod.exhaust_sel
thf(fact_761_prod_Oexhaust__sel,axiom,
! [Prod: produc4435102495419491129nt_int] :
( Prod
= ( produc5790713362662368625nt_int @ ( produc9025023058967219549nt_int @ Prod ) @ ( produc179445755590504351nt_int @ Prod ) ) ) ).
% prod.exhaust_sel
thf(fact_762_prod_Oexhaust__sel,axiom,
! [Prod: produc7773217078559923341nt_int] :
( Prod
= ( produc4305682042979456191nt_int @ ( produc6230002227079971283nt_int @ Prod ) @ ( produc3162348030201620241nt_int @ Prod ) ) ) ).
% prod.exhaust_sel
thf(fact_763_prod_Oexhaust__sel,axiom,
! [Prod: produc6425607678544837394st_int] :
( Prod
= ( produc5086643055186798020st_int @ ( produc8941309049508465880st_int @ Prod ) @ ( produc1296517004818028822st_int @ Prod ) ) ) ).
% prod.exhaust_sel
thf(fact_764_prod_Oexhaust__sel,axiom,
! [Prod: product_prod_o_int] :
( Prod
= ( product_Pair_o_int @ ( product_fst_o_int @ Prod ) @ ( product_snd_o_int @ Prod ) ) ) ).
% prod.exhaust_sel
thf(fact_765_prod_Oexhaust__sel,axiom,
! [Prod: produc1897111610453708512_o_int] :
( Prod
= ( produc4047900504771817624_o_int @ ( produc2736798884409471108_o_int @ Prod ) @ ( produc7219675232234870470_o_int @ Prod ) ) ) ).
% prod.exhaust_sel
thf(fact_766_prod_Oexhaust__sel,axiom,
! [Prod: produc369741286924889929st_int] :
( Prod
= ( produc8650753666468850689st_int @ ( produc2155683374303800813st_int @ Prod ) @ ( produc6244060863719409455st_int @ Prod ) ) ) ).
% prod.exhaust_sel
thf(fact_767_snd__eqD,axiom,
! [X: int,Y: int,A: int] :
( ( ( product_snd_int_int @ ( product_Pair_int_int @ X @ Y ) )
= A )
=> ( Y = A ) ) ).
% snd_eqD
thf(fact_768_snd__eqD,axiom,
! [X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int,A: product_prod_int_int] :
( ( ( produc7328097813583171335nt_int @ ( produc5700946648718959541nt_int @ X @ Y ) )
= A )
=> ( Y = A ) ) ).
% snd_eqD
thf(fact_769_snd__eqD,axiom,
! [X: list_char > int,Y: int,A: int] :
( ( ( produc179445755590504351nt_int @ ( produc5790713362662368625nt_int @ X @ Y ) )
= A )
=> ( Y = A ) ) ).
% snd_eqD
thf(fact_770_snd__eqD,axiom,
! [X: int > option6357759511663192854e_term,Y: product_prod_int_int,A: product_prod_int_int] :
( ( ( produc3162348030201620241nt_int @ ( produc4305682042979456191nt_int @ X @ Y ) )
= A )
=> ( Y = A ) ) ).
% snd_eqD
thf(fact_771_snd__eqD,axiom,
! [X: int,Y: produc369741286924889929st_int,A: produc369741286924889929st_int] :
( ( ( produc1296517004818028822st_int @ ( produc5086643055186798020st_int @ X @ Y ) )
= A )
=> ( Y = A ) ) ).
% snd_eqD
thf(fact_772_snd__eqD,axiom,
! [X: $o,Y: int,A: int] :
( ( ( product_snd_o_int @ ( product_Pair_o_int @ X @ Y ) )
= A )
=> ( Y = A ) ) ).
% snd_eqD
thf(fact_773_snd__eqD,axiom,
! [X: bexp,Y: product_prod_o_int,A: product_prod_o_int] :
( ( ( produc7219675232234870470_o_int @ ( produc4047900504771817624_o_int @ X @ Y ) )
= A )
=> ( Y = A ) ) ).
% snd_eqD
thf(fact_774_snd__eqD,axiom,
! [X: list_char > int,Y: list_int,A: list_int] :
( ( ( produc6244060863719409455st_int @ ( produc8650753666468850689st_int @ X @ Y ) )
= A )
=> ( Y = A ) ) ).
% snd_eqD
thf(fact_775_snd__conv,axiom,
! [X1: int,X22: int] :
( ( product_snd_int_int @ ( product_Pair_int_int @ X1 @ X22 ) )
= X22 ) ).
% snd_conv
thf(fact_776_snd__conv,axiom,
! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X22: product_prod_int_int] :
( ( produc7328097813583171335nt_int @ ( produc5700946648718959541nt_int @ X1 @ X22 ) )
= X22 ) ).
% snd_conv
thf(fact_777_snd__conv,axiom,
! [X1: list_char > int,X22: int] :
( ( produc179445755590504351nt_int @ ( produc5790713362662368625nt_int @ X1 @ X22 ) )
= X22 ) ).
% snd_conv
thf(fact_778_snd__conv,axiom,
! [X1: int > option6357759511663192854e_term,X22: product_prod_int_int] :
( ( produc3162348030201620241nt_int @ ( produc4305682042979456191nt_int @ X1 @ X22 ) )
= X22 ) ).
% snd_conv
thf(fact_779_snd__conv,axiom,
! [X1: int,X22: produc369741286924889929st_int] :
( ( produc1296517004818028822st_int @ ( produc5086643055186798020st_int @ X1 @ X22 ) )
= X22 ) ).
% snd_conv
thf(fact_780_snd__conv,axiom,
! [X1: $o,X22: int] :
( ( product_snd_o_int @ ( product_Pair_o_int @ X1 @ X22 ) )
= X22 ) ).
% snd_conv
thf(fact_781_snd__conv,axiom,
! [X1: bexp,X22: product_prod_o_int] :
( ( produc7219675232234870470_o_int @ ( produc4047900504771817624_o_int @ X1 @ X22 ) )
= X22 ) ).
% snd_conv
thf(fact_782_snd__conv,axiom,
! [X1: list_char > int,X22: list_int] :
( ( produc6244060863719409455st_int @ ( produc8650753666468850689st_int @ X1 @ X22 ) )
= X22 ) ).
% snd_conv
thf(fact_783_fst__eqD,axiom,
! [X: int,Y: int,A: int] :
( ( ( product_fst_int_int @ ( product_Pair_int_int @ X @ Y ) )
= A )
=> ( X = A ) ) ).
% fst_eqD
thf(fact_784_fst__eqD,axiom,
! [X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int,A: produc8551481072490612790e_term > option6357759511663192854e_term] :
( ( ( produc6816164490631068361nt_int @ ( produc5700946648718959541nt_int @ X @ Y ) )
= A )
=> ( X = A ) ) ).
% fst_eqD
thf(fact_785_fst__eqD,axiom,
! [X: list_char > int,Y: list_int,A: list_char > int] :
( ( ( produc2155683374303800813st_int @ ( produc8650753666468850689st_int @ X @ Y ) )
= A )
=> ( X = A ) ) ).
% fst_eqD
thf(fact_786_fst__eqD,axiom,
! [X: list_char > int,Y: int,A: list_char > int] :
( ( ( produc9025023058967219549nt_int @ ( produc5790713362662368625nt_int @ X @ Y ) )
= A )
=> ( X = A ) ) ).
% fst_eqD
thf(fact_787_fst__eqD,axiom,
! [X: int > option6357759511663192854e_term,Y: product_prod_int_int,A: int > option6357759511663192854e_term] :
( ( ( produc6230002227079971283nt_int @ ( produc4305682042979456191nt_int @ X @ Y ) )
= A )
=> ( X = A ) ) ).
% fst_eqD
thf(fact_788_fst__eqD,axiom,
! [X: int,Y: produc369741286924889929st_int,A: int] :
( ( ( produc8941309049508465880st_int @ ( produc5086643055186798020st_int @ X @ Y ) )
= A )
=> ( X = A ) ) ).
% fst_eqD
thf(fact_789_fst__conv,axiom,
! [X1: int,X22: int] :
( ( product_fst_int_int @ ( product_Pair_int_int @ X1 @ X22 ) )
= X1 ) ).
% fst_conv
thf(fact_790_fst__conv,axiom,
! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X22: product_prod_int_int] :
( ( produc6816164490631068361nt_int @ ( produc5700946648718959541nt_int @ X1 @ X22 ) )
= X1 ) ).
% fst_conv
thf(fact_791_fst__conv,axiom,
! [X1: list_char > int,X22: list_int] :
( ( produc2155683374303800813st_int @ ( produc8650753666468850689st_int @ X1 @ X22 ) )
= X1 ) ).
% fst_conv
thf(fact_792_fst__conv,axiom,
! [X1: list_char > int,X22: int] :
( ( produc9025023058967219549nt_int @ ( produc5790713362662368625nt_int @ X1 @ X22 ) )
= X1 ) ).
% fst_conv
thf(fact_793_fst__conv,axiom,
! [X1: int > option6357759511663192854e_term,X22: product_prod_int_int] :
( ( produc6230002227079971283nt_int @ ( produc4305682042979456191nt_int @ X1 @ X22 ) )
= X1 ) ).
% fst_conv
thf(fact_794_fst__conv,axiom,
! [X1: int,X22: produc369741286924889929st_int] :
( ( produc8941309049508465880st_int @ ( produc5086643055186798020st_int @ X1 @ X22 ) )
= X1 ) ).
% fst_conv
thf(fact_795_verit__comp__simplify1_I2_J,axiom,
! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% verit_comp_simplify1(2)
thf(fact_796_verit__comp__simplify1_I2_J,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% verit_comp_simplify1(2)
thf(fact_797_verit__comp__simplify1_I2_J,axiom,
! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% verit_comp_simplify1(2)
thf(fact_798_verit__la__generic,axiom,
! [A: int,X: int] :
( ( ord_less_eq_int @ A @ X )
| ( A = X )
| ( ord_less_eq_int @ X @ A ) ) ).
% verit_la_generic
thf(fact_799_verit__la__disequality,axiom,
! [A: int,B: int] :
( ( A = B )
| ~ ( ord_less_eq_int @ A @ B )
| ~ ( ord_less_eq_int @ B @ A ) ) ).
% verit_la_disequality
thf(fact_800_verit__la__disequality,axiom,
! [A: nat,B: nat] :
( ( A = B )
| ~ ( ord_less_eq_nat @ A @ B )
| ~ ( ord_less_eq_nat @ B @ A ) ) ).
% verit_la_disequality
thf(fact_801_verit__la__disequality,axiom,
! [A: num,B: num] :
( ( A = B )
| ~ ( ord_less_eq_num @ A @ B )
| ~ ( ord_less_eq_num @ B @ A ) ) ).
% verit_la_disequality
thf(fact_802_of__nat__mono,axiom,
! [I: nat,J: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% of_nat_mono
thf(fact_803_of__nat__mono,axiom,
! [I: nat,J: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% of_nat_mono
thf(fact_804_lift__Suc__mono__le,axiom,
! [F: nat > int,N: nat,N4: nat] :
( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
=> ( ( ord_less_eq_nat @ N @ N4 )
=> ( ord_less_eq_int @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% lift_Suc_mono_le
thf(fact_805_lift__Suc__mono__le,axiom,
! [F: nat > nat,N: nat,N4: nat] :
( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
=> ( ( ord_less_eq_nat @ N @ N4 )
=> ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% lift_Suc_mono_le
thf(fact_806_lift__Suc__mono__le,axiom,
! [F: nat > num,N: nat,N4: nat] :
( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
=> ( ( ord_less_eq_nat @ N @ N4 )
=> ( ord_less_eq_num @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% lift_Suc_mono_le
thf(fact_807_lift__Suc__antimono__le,axiom,
! [F: nat > int,N: nat,N4: nat] :
( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
=> ( ( ord_less_eq_nat @ N @ N4 )
=> ( ord_less_eq_int @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% lift_Suc_antimono_le
thf(fact_808_lift__Suc__antimono__le,axiom,
! [F: nat > nat,N: nat,N4: nat] :
( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
=> ( ( ord_less_eq_nat @ N @ N4 )
=> ( ord_less_eq_nat @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% lift_Suc_antimono_le
thf(fact_809_lift__Suc__antimono__le,axiom,
! [F: nat > num,N: nat,N4: nat] :
( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
=> ( ( ord_less_eq_nat @ N @ N4 )
=> ( ord_less_eq_num @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% lift_Suc_antimono_le
thf(fact_810_instr_Odistinct_I17_J,axiom,
! [X22: list_char,X5: int] :
( ( load @ X22 )
!= ( jmp @ X5 ) ) ).
% instr.distinct(17)
thf(fact_811_instr_Odistinct_I7_J,axiom,
! [X1: int,X5: int] :
( ( loadi @ X1 )
!= ( jmp @ X5 ) ) ).
% instr.distinct(7)
thf(fact_812_instr_Odistinct_I1_J,axiom,
! [X1: int,X22: list_char] :
( ( loadi @ X1 )
!= ( load @ X22 ) ) ).
% instr.distinct(1)
thf(fact_813_prod_Oexpand,axiom,
! [Prod: produc6425607678544837394st_int,Prod2: produc6425607678544837394st_int] :
( ( ( ( produc8941309049508465880st_int @ Prod )
= ( produc8941309049508465880st_int @ Prod2 ) )
& ( ( produc1296517004818028822st_int @ Prod )
= ( produc1296517004818028822st_int @ Prod2 ) ) )
=> ( Prod = Prod2 ) ) ).
% prod.expand
thf(fact_814_prod_Oexpand,axiom,
! [Prod: product_prod_o_int,Prod2: product_prod_o_int] :
( ( ( ( product_fst_o_int @ Prod )
= ( product_fst_o_int @ Prod2 ) )
& ( ( product_snd_o_int @ Prod )
= ( product_snd_o_int @ Prod2 ) ) )
=> ( Prod = Prod2 ) ) ).
% prod.expand
thf(fact_815_prod_Oexpand,axiom,
! [Prod: produc1897111610453708512_o_int,Prod2: produc1897111610453708512_o_int] :
( ( ( ( produc2736798884409471108_o_int @ Prod )
= ( produc2736798884409471108_o_int @ Prod2 ) )
& ( ( produc7219675232234870470_o_int @ Prod )
= ( produc7219675232234870470_o_int @ Prod2 ) ) )
=> ( Prod = Prod2 ) ) ).
% prod.expand
thf(fact_816_prod_Oexpand,axiom,
! [Prod: produc369741286924889929st_int,Prod2: produc369741286924889929st_int] :
( ( ( ( produc2155683374303800813st_int @ Prod )
= ( produc2155683374303800813st_int @ Prod2 ) )
& ( ( produc6244060863719409455st_int @ Prod )
= ( produc6244060863719409455st_int @ Prod2 ) ) )
=> ( Prod = Prod2 ) ) ).
% prod.expand
thf(fact_817_prod__eqI,axiom,
! [P2: produc6425607678544837394st_int,Q2: produc6425607678544837394st_int] :
( ( ( produc8941309049508465880st_int @ P2 )
= ( produc8941309049508465880st_int @ Q2 ) )
=> ( ( ( produc1296517004818028822st_int @ P2 )
= ( produc1296517004818028822st_int @ Q2 ) )
=> ( P2 = Q2 ) ) ) ).
% prod_eqI
thf(fact_818_prod__eqI,axiom,
! [P2: product_prod_o_int,Q2: product_prod_o_int] :
( ( ( product_fst_o_int @ P2 )
= ( product_fst_o_int @ Q2 ) )
=> ( ( ( product_snd_o_int @ P2 )
= ( product_snd_o_int @ Q2 ) )
=> ( P2 = Q2 ) ) ) ).
% prod_eqI
thf(fact_819_prod__eqI,axiom,
! [P2: produc1897111610453708512_o_int,Q2: produc1897111610453708512_o_int] :
( ( ( produc2736798884409471108_o_int @ P2 )
= ( produc2736798884409471108_o_int @ Q2 ) )
=> ( ( ( produc7219675232234870470_o_int @ P2 )
= ( produc7219675232234870470_o_int @ Q2 ) )
=> ( P2 = Q2 ) ) ) ).
% prod_eqI
thf(fact_820_prod__eqI,axiom,
! [P2: produc369741286924889929st_int,Q2: produc369741286924889929st_int] :
( ( ( produc2155683374303800813st_int @ P2 )
= ( produc2155683374303800813st_int @ Q2 ) )
=> ( ( ( produc6244060863719409455st_int @ P2 )
= ( produc6244060863719409455st_int @ Q2 ) )
=> ( P2 = Q2 ) ) ) ).
% prod_eqI
thf(fact_821_prod__eq__iff,axiom,
( ( ^ [Y4: produc6425607678544837394st_int,Z3: produc6425607678544837394st_int] : ( Y4 = Z3 ) )
= ( ^ [S4: produc6425607678544837394st_int,T2: produc6425607678544837394st_int] :
( ( ( produc8941309049508465880st_int @ S4 )
= ( produc8941309049508465880st_int @ T2 ) )
& ( ( produc1296517004818028822st_int @ S4 )
= ( produc1296517004818028822st_int @ T2 ) ) ) ) ) ).
% prod_eq_iff
thf(fact_822_prod__eq__iff,axiom,
( ( ^ [Y4: product_prod_o_int,Z3: product_prod_o_int] : ( Y4 = Z3 ) )
= ( ^ [S4: product_prod_o_int,T2: product_prod_o_int] :
( ( ( product_fst_o_int @ S4 )
= ( product_fst_o_int @ T2 ) )
& ( ( product_snd_o_int @ S4 )
= ( product_snd_o_int @ T2 ) ) ) ) ) ).
% prod_eq_iff
thf(fact_823_prod__eq__iff,axiom,
( ( ^ [Y4: produc1897111610453708512_o_int,Z3: produc1897111610453708512_o_int] : ( Y4 = Z3 ) )
= ( ^ [S4: produc1897111610453708512_o_int,T2: produc1897111610453708512_o_int] :
( ( ( produc2736798884409471108_o_int @ S4 )
= ( produc2736798884409471108_o_int @ T2 ) )
& ( ( produc7219675232234870470_o_int @ S4 )
= ( produc7219675232234870470_o_int @ T2 ) ) ) ) ) ).
% prod_eq_iff
thf(fact_824_prod__eq__iff,axiom,
( ( ^ [Y4: produc369741286924889929st_int,Z3: produc369741286924889929st_int] : ( Y4 = Z3 ) )
= ( ^ [S4: produc369741286924889929st_int,T2: produc369741286924889929st_int] :
( ( ( produc2155683374303800813st_int @ S4 )
= ( produc2155683374303800813st_int @ T2 ) )
& ( ( produc6244060863719409455st_int @ S4 )
= ( produc6244060863719409455st_int @ T2 ) ) ) ) ) ).
% prod_eq_iff
thf(fact_825_zero__le,axiom,
! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% zero_le
thf(fact_826_le__numeral__extra_I3_J,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% le_numeral_extra(3)
thf(fact_827_le__numeral__extra_I3_J,axiom,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% le_numeral_extra(3)
thf(fact_828_verit__comp__simplify1_I3_J,axiom,
! [B4: int,A4: int] :
( ( ~ ( ord_less_eq_int @ B4 @ A4 ) )
= ( ord_less_int @ A4 @ B4 ) ) ).
% verit_comp_simplify1(3)
thf(fact_829_verit__comp__simplify1_I3_J,axiom,
! [B4: nat,A4: nat] :
( ( ~ ( ord_less_eq_nat @ B4 @ A4 ) )
= ( ord_less_nat @ A4 @ B4 ) ) ).
% verit_comp_simplify1(3)
thf(fact_830_verit__comp__simplify1_I3_J,axiom,
! [B4: num,A4: num] :
( ( ~ ( ord_less_eq_num @ B4 @ A4 ) )
= ( ord_less_num @ A4 @ B4 ) ) ).
% verit_comp_simplify1(3)
thf(fact_831_add__mono__thms__linordered__semiring_I3_J,axiom,
! [I: int,J: int,K2: int,L: int] :
( ( ( ord_less_eq_int @ I @ J )
& ( K2 = L ) )
=> ( ord_less_eq_int @ ( plus_plus_int @ I @ K2 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(3)
thf(fact_832_add__mono__thms__linordered__semiring_I3_J,axiom,
! [I: nat,J: nat,K2: nat,L: nat] :
( ( ( ord_less_eq_nat @ I @ J )
& ( K2 = L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K2 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(3)
thf(fact_833_add__mono__thms__linordered__semiring_I2_J,axiom,
! [I: int,J: int,K2: int,L: int] :
( ( ( I = J )
& ( ord_less_eq_int @ K2 @ L ) )
=> ( ord_less_eq_int @ ( plus_plus_int @ I @ K2 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(2)
thf(fact_834_add__mono__thms__linordered__semiring_I2_J,axiom,
! [I: nat,J: nat,K2: nat,L: nat] :
( ( ( I = J )
& ( ord_less_eq_nat @ K2 @ L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K2 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(2)
thf(fact_835_add__mono__thms__linordered__semiring_I1_J,axiom,
! [I: int,J: int,K2: int,L: int] :
( ( ( ord_less_eq_int @ I @ J )
& ( ord_less_eq_int @ K2 @ L ) )
=> ( ord_less_eq_int @ ( plus_plus_int @ I @ K2 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(1)
thf(fact_836_add__mono__thms__linordered__semiring_I1_J,axiom,
! [I: nat,J: nat,K2: nat,L: nat] :
( ( ( ord_less_eq_nat @ I @ J )
& ( ord_less_eq_nat @ K2 @ L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K2 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(1)
thf(fact_837_add__mono,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% add_mono
thf(fact_838_add__mono,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% add_mono
thf(fact_839_add__left__mono,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% add_left_mono
thf(fact_840_add__left__mono,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% add_left_mono
thf(fact_841_less__eqE,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ! [C2: nat] :
( B
!= ( plus_plus_nat @ A @ C2 ) ) ) ).
% less_eqE
thf(fact_842_add__right__mono,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% add_right_mono
thf(fact_843_add__right__mono,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% add_right_mono
thf(fact_844_le__iff__add,axiom,
( ord_less_eq_nat
= ( ^ [A3: nat,B2: nat] :
? [C3: nat] :
( B2
= ( plus_plus_nat @ A3 @ C3 ) ) ) ) ).
% le_iff_add
thf(fact_845_add__le__imp__le__left,axiom,
! [C: int,A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
=> ( ord_less_eq_int @ A @ B ) ) ).
% add_le_imp_le_left
thf(fact_846_add__le__imp__le__left,axiom,
! [C: nat,A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ) ).
% add_le_imp_le_left
thf(fact_847_add__le__imp__le__right,axiom,
! [A: int,C: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
=> ( ord_less_eq_int @ A @ B ) ) ).
% add_le_imp_le_right
thf(fact_848_add__le__imp__le__right,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
=> ( ord_less_eq_nat @ A @ B ) ) ).
% add_le_imp_le_right
thf(fact_849_le__numeral__extra_I4_J,axiom,
ord_less_eq_int @ one_one_int @ one_one_int ).
% le_numeral_extra(4)
thf(fact_850_le__numeral__extra_I4_J,axiom,
ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% le_numeral_extra(4)
thf(fact_851_diff__mono,axiom,
! [A: int,B: int,D: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ D @ C )
=> ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% diff_mono
thf(fact_852_diff__left__mono,axiom,
! [B: int,A: int,C: int] :
( ( ord_less_eq_int @ B @ A )
=> ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% diff_left_mono
thf(fact_853_diff__right__mono,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% diff_right_mono
thf(fact_854_diff__eq__diff__less__eq,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( ord_less_eq_int @ A @ B )
= ( ord_less_eq_int @ C @ D ) ) ) ).
% diff_eq_diff_less_eq
thf(fact_855_less__eq__int__code_I1_J,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% less_eq_int_code(1)
thf(fact_856_instr_Osize_I12_J,axiom,
! [X5: int] :
( ( size_size_instr @ ( jmp @ X5 ) )
= zero_zero_nat ) ).
% instr.size(12)
thf(fact_857_instr_Osize_I9_J,axiom,
! [X22: list_char] :
( ( size_size_instr @ ( load @ X22 ) )
= zero_zero_nat ) ).
% instr.size(9)
thf(fact_858_instr_Osize_I8_J,axiom,
! [X1: int] :
( ( size_size_instr @ ( loadi @ X1 ) )
= zero_zero_nat ) ).
% instr.size(8)
thf(fact_859_instr_Odistinct_I31_J,axiom,
! [X42: list_char,X5: int] :
( ( store @ X42 )
!= ( jmp @ X5 ) ) ).
% instr.distinct(31)
thf(fact_860_instr_Odistinct_I15_J,axiom,
! [X22: list_char,X42: list_char] :
( ( load @ X22 )
!= ( store @ X42 ) ) ).
% instr.distinct(15)
thf(fact_861_add__nonpos__eq__0__iff,axiom,
! [X: int,Y: int] :
( ( ord_less_eq_int @ X @ zero_zero_int )
=> ( ( ord_less_eq_int @ Y @ zero_zero_int )
=> ( ( ( plus_plus_int @ X @ Y )
= zero_zero_int )
= ( ( X = zero_zero_int )
& ( Y = zero_zero_int ) ) ) ) ) ).
% add_nonpos_eq_0_iff
thf(fact_862_add__nonpos__eq__0__iff,axiom,
! [X: nat,Y: nat] :
( ( ord_less_eq_nat @ X @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
=> ( ( ( plus_plus_nat @ X @ Y )
= zero_zero_nat )
= ( ( X = zero_zero_nat )
& ( Y = zero_zero_nat ) ) ) ) ) ).
% add_nonpos_eq_0_iff
thf(fact_863_add__nonneg__eq__0__iff,axiom,
! [X: int,Y: int] :
( ( ord_less_eq_int @ zero_zero_int @ X )
=> ( ( ord_less_eq_int @ zero_zero_int @ Y )
=> ( ( ( plus_plus_int @ X @ Y )
= zero_zero_int )
= ( ( X = zero_zero_int )
& ( Y = zero_zero_int ) ) ) ) ) ).
% add_nonneg_eq_0_iff
thf(fact_864_add__nonneg__eq__0__iff,axiom,
! [X: nat,Y: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ X )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
=> ( ( ( plus_plus_nat @ X @ Y )
= zero_zero_nat )
= ( ( X = zero_zero_nat )
& ( Y = zero_zero_nat ) ) ) ) ) ).
% add_nonneg_eq_0_iff
thf(fact_865_add__nonpos__nonpos,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ( ord_less_eq_int @ B @ zero_zero_int )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% add_nonpos_nonpos
thf(fact_866_add__nonpos__nonpos,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% add_nonpos_nonpos
thf(fact_867_add__nonneg__nonneg,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% add_nonneg_nonneg
thf(fact_868_add__nonneg__nonneg,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% add_nonneg_nonneg
thf(fact_869_add__increasing2,axiom,
! [C: int,B: int,A: int] :
( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_eq_int @ B @ A )
=> ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% add_increasing2
thf(fact_870_add__increasing2,axiom,
! [C: nat,B: nat,A: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% add_increasing2
thf(fact_871_add__decreasing2,axiom,
! [C: int,A: int,B: int] :
( ( ord_less_eq_int @ C @ zero_zero_int )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% add_decreasing2
thf(fact_872_add__decreasing2,axiom,
! [C: nat,A: nat,B: nat] :
( ( ord_less_eq_nat @ C @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% add_decreasing2
thf(fact_873_add__increasing,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% add_increasing
thf(fact_874_add__increasing,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% add_increasing
thf(fact_875_add__decreasing,axiom,
! [A: int,C: int,B: int] :
( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ( ord_less_eq_int @ C @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% add_decreasing
thf(fact_876_add__decreasing,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% add_decreasing
thf(fact_877_not__one__le__zero,axiom,
~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% not_one_le_zero
thf(fact_878_not__one__le__zero,axiom,
~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% not_one_le_zero
thf(fact_879_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
ord_less_eq_int @ zero_zero_int @ one_one_int ).
% linordered_nonzero_semiring_class.zero_le_one
thf(fact_880_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% linordered_nonzero_semiring_class.zero_le_one
thf(fact_881_zero__less__one__class_Ozero__le__one,axiom,
ord_less_eq_int @ zero_zero_int @ one_one_int ).
% zero_less_one_class.zero_le_one
thf(fact_882_zero__less__one__class_Ozero__le__one,axiom,
ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% zero_less_one_class.zero_le_one
thf(fact_883_add__mono__thms__linordered__field_I4_J,axiom,
! [I: int,J: int,K2: int,L: int] :
( ( ( ord_less_eq_int @ I @ J )
& ( ord_less_int @ K2 @ L ) )
=> ( ord_less_int @ ( plus_plus_int @ I @ K2 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(4)
thf(fact_884_add__mono__thms__linordered__field_I4_J,axiom,
! [I: nat,J: nat,K2: nat,L: nat] :
( ( ( ord_less_eq_nat @ I @ J )
& ( ord_less_nat @ K2 @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K2 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(4)
thf(fact_885_add__mono__thms__linordered__field_I3_J,axiom,
! [I: int,J: int,K2: int,L: int] :
( ( ( ord_less_int @ I @ J )
& ( ord_less_eq_int @ K2 @ L ) )
=> ( ord_less_int @ ( plus_plus_int @ I @ K2 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(3)
thf(fact_886_add__mono__thms__linordered__field_I3_J,axiom,
! [I: nat,J: nat,K2: nat,L: nat] :
( ( ( ord_less_nat @ I @ J )
& ( ord_less_eq_nat @ K2 @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K2 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(3)
thf(fact_887_add__le__less__mono,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ C @ D )
=> ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% add_le_less_mono
thf(fact_888_add__le__less__mono,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% add_le_less_mono
thf(fact_889_add__less__le__mono,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% add_less_le_mono
thf(fact_890_add__less__le__mono,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% add_less_le_mono
thf(fact_891_le__iff__diff__le__0,axiom,
( ord_less_eq_int
= ( ^ [A3: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% le_iff_diff_le_0
thf(fact_892_add__le__add__imp__diff__le,axiom,
! [I: int,K2: int,N: int,J: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ I @ K2 ) @ N )
=> ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K2 ) )
=> ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K2 ) @ N )
=> ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K2 ) )
=> ( ord_less_eq_int @ ( minus_minus_int @ N @ K2 ) @ J ) ) ) ) ) ).
% add_le_add_imp_diff_le
thf(fact_893_add__le__add__imp__diff__le,axiom,
! [I: nat,K2: nat,N: nat,J: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K2 ) @ N )
=> ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K2 ) )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K2 ) @ N )
=> ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K2 ) )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K2 ) @ J ) ) ) ) ) ).
% add_le_add_imp_diff_le
thf(fact_894_add__le__imp__le__diff,axiom,
! [I: int,K2: int,N: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ I @ K2 ) @ N )
=> ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K2 ) ) ) ).
% add_le_imp_le_diff
thf(fact_895_add__le__imp__le__diff,axiom,
! [I: nat,K2: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K2 ) @ N )
=> ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K2 ) ) ) ).
% add_le_imp_le_diff
thf(fact_896_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ( ( minus_minus_nat @ B @ A )
= C )
= ( B
= ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
thf(fact_897_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
= B ) ) ).
% ordered_cancel_comm_monoid_diff_class.add_diff_inverse
thf(fact_898_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% ordered_cancel_comm_monoid_diff_class.diff_diff_right
thf(fact_899_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
= ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
thf(fact_900_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
= ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
thf(fact_901_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
= ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% ordered_cancel_comm_monoid_diff_class.diff_add_assoc
thf(fact_902_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% ordered_cancel_comm_monoid_diff_class.add_diff_assoc
thf(fact_903_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% ordered_cancel_comm_monoid_diff_class.le_diff_conv2
thf(fact_904_le__add__diff,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% le_add_diff
thf(fact_905_diff__add,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
= B ) ) ).
% diff_add
thf(fact_906_le__diff__eq,axiom,
! [A: int,C: int,B: int] :
( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
= ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% le_diff_eq
thf(fact_907_diff__le__eq,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
= ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% diff_le_eq
thf(fact_908_of__nat__0__le__iff,axiom,
! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% of_nat_0_le_iff
thf(fact_909_of__nat__0__le__iff,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% of_nat_0_le_iff
thf(fact_910_instr_Odistinct_I5_J,axiom,
! [X1: int,X42: list_char] :
( ( loadi @ X1 )
!= ( store @ X42 ) ) ).
% instr.distinct(5)
thf(fact_911_zero__le__imp__eq__int,axiom,
! [K2: int] :
( ( ord_less_eq_int @ zero_zero_int @ K2 )
=> ? [N3: nat] :
( K2
= ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% zero_le_imp_eq_int
thf(fact_912_nonneg__int__cases,axiom,
! [K2: int] :
( ( ord_less_eq_int @ zero_zero_int @ K2 )
=> ~ ! [N3: nat] :
( K2
!= ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% nonneg_int_cases
thf(fact_913_int__ge__induct,axiom,
! [K2: int,I: int,P: int > $o] :
( ( ord_less_eq_int @ K2 @ I )
=> ( ( P @ K2 )
=> ( ! [I3: int] :
( ( ord_less_eq_int @ K2 @ I3 )
=> ( ( P @ I3 )
=> ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
=> ( P @ I ) ) ) ) ).
% int_ge_induct
thf(fact_914_zle__iff__zadd,axiom,
( ord_less_eq_int
= ( ^ [W2: int,Z2: int] :
? [N2: nat] :
( Z2
= ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% zle_iff_zadd
thf(fact_915_int__le__induct,axiom,
! [I: int,K2: int,P: int > $o] :
( ( ord_less_eq_int @ I @ K2 )
=> ( ( P @ K2 )
=> ( ! [I3: int] :
( ( ord_less_eq_int @ I3 @ K2 )
=> ( ( P @ I3 )
=> ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
=> ( P @ I ) ) ) ) ).
% int_le_induct
thf(fact_916_add__strict__increasing2,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% add_strict_increasing2
thf(fact_917_add__strict__increasing2,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% add_strict_increasing2
thf(fact_918_add__strict__increasing,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% add_strict_increasing
thf(fact_919_add__strict__increasing,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% add_strict_increasing
thf(fact_920_add__pos__nonneg,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% add_pos_nonneg
thf(fact_921_add__pos__nonneg,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% add_pos_nonneg
thf(fact_922_add__nonpos__neg,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ( ord_less_int @ B @ zero_zero_int )
=> ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% add_nonpos_neg
thf(fact_923_add__nonpos__neg,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_nat @ B @ zero_zero_nat )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% add_nonpos_neg
thf(fact_924_add__nonneg__pos,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_int @ zero_zero_int @ B )
=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% add_nonneg_pos
thf(fact_925_add__nonneg__pos,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% add_nonneg_pos
thf(fact_926_add__neg__nonpos,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ zero_zero_int )
=> ( ( ord_less_eq_int @ B @ zero_zero_int )
=> ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% add_neg_nonpos
thf(fact_927_add__neg__nonpos,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% add_neg_nonpos
thf(fact_928_int__one__le__iff__zero__less,axiom,
! [Z: int] :
( ( ord_less_eq_int @ one_one_int @ Z )
= ( ord_less_int @ zero_zero_int @ Z ) ) ).
% int_one_le_iff_zero_less
thf(fact_929_add1__zle__eq,axiom,
! [W: int,Z: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
= ( ord_less_int @ W @ Z ) ) ).
% add1_zle_eq
thf(fact_930_zless__imp__add1__zle,axiom,
! [W: int,Z: int] :
( ( ord_less_int @ W @ Z )
=> ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% zless_imp_add1_zle
thf(fact_931_int__induct,axiom,
! [P: int > $o,K2: int,I: int] :
( ( P @ K2 )
=> ( ! [I3: int] :
( ( ord_less_eq_int @ K2 @ I3 )
=> ( ( P @ I3 )
=> ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
=> ( ! [I3: int] :
( ( ord_less_eq_int @ I3 @ K2 )
=> ( ( P @ I3 )
=> ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
=> ( P @ I ) ) ) ) ).
% int_induct
thf(fact_932_le__imp__0__less,axiom,
! [Z: int] :
( ( ord_less_eq_int @ zero_zero_int @ Z )
=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% le_imp_0_less
thf(fact_933_execl__next,axiom,
! [P: list_instr,Cfs: list_P419547167332244514st_int,K2: nat] :
( ( execl @ P @ Cfs )
=> ( ( ord_less_nat @ K2 @ ( size_s229347708945616566st_int @ Cfs ) )
=> ( ( K2
!= ( minus_minus_nat @ ( size_s229347708945616566st_int @ Cfs ) @ one_one_nat ) )
=> ( ( iexec_pred @ ( produc1484136438817787418st_int @ ( inth_instr @ P @ ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs @ K2 ) ) ) @ ( nth_Pr8327173284404383691st_int @ Cfs @ K2 ) ) @ ( nth_Pr8327173284404383691st_int @ Cfs @ ( suc @ K2 ) ) )
& ( ord_less_eq_int @ zero_zero_int @ ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs @ K2 ) ) )
& ( ord_less_int @ ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs @ K2 ) ) @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P ) ) ) ) ) ) ) ).
% execl_next
thf(fact_934_n__lists__Nil,axiom,
! [N: nat] :
( ( ( N = zero_zero_nat )
=> ( ( n_lists_instr @ N @ nil_instr )
= ( cons_list_instr @ nil_instr @ nil_list_instr ) ) )
& ( ( N != zero_zero_nat )
=> ( ( n_lists_instr @ N @ nil_instr )
= nil_list_instr ) ) ) ).
% n_lists_Nil
thf(fact_935_n__lists__Nil,axiom,
! [N: nat] :
( ( ( N = zero_zero_nat )
=> ( ( n_list7311978343830957444st_int @ N @ nil_Pr749310521696113548st_int )
= ( cons_l8648290059330449388st_int @ nil_Pr749310521696113548st_int @ nil_li4597314861645524892st_int ) ) )
& ( ( N != zero_zero_nat )
=> ( ( n_list7311978343830957444st_int @ N @ nil_Pr749310521696113548st_int )
= nil_li4597314861645524892st_int ) ) ) ).
% n_lists_Nil
thf(fact_936_n__lists__Nil,axiom,
! [N: nat] :
( ( ( N = zero_zero_nat )
=> ( ( n_lists_list_char @ N @ nil_list_char )
= ( cons_list_list_char @ nil_list_char @ nil_list_list_char ) ) )
& ( ( N != zero_zero_nat )
=> ( ( n_lists_list_char @ N @ nil_list_char )
= nil_list_list_char ) ) ) ).
% n_lists_Nil
thf(fact_937_n__lists__Nil,axiom,
! [N: nat] :
( ( ( N = zero_zero_nat )
=> ( ( n_lists_char @ N @ nil_char )
= ( cons_list_char @ nil_char @ nil_list_char ) ) )
& ( ( N != zero_zero_nat )
=> ( ( n_lists_char @ N @ nil_char )
= nil_list_char ) ) ) ).
% n_lists_Nil
thf(fact_938_exec1I,axiom,
! [C4: produc6425607678544837394st_int,P: list_instr,I: int,S2: list_char > int,Stk3: list_int] :
( ( C4
= ( iexec @ ( inth_instr @ P @ I ) @ ( produc5086643055186798020st_int @ I @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P ) ) )
=> ( exec1 @ P @ ( produc5086643055186798020st_int @ I @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) @ C4 ) ) ) ) ).
% exec1I
thf(fact_939_conjI__realizer,axiom,
! [P: int > $o,P2: int,Q3: int > $o,Q2: int] :
( ( P @ P2 )
=> ( ( Q3 @ Q2 )
=> ( ( P @ ( product_fst_int_int @ ( product_Pair_int_int @ P2 @ Q2 ) ) )
& ( Q3 @ ( product_snd_int_int @ ( product_Pair_int_int @ P2 @ Q2 ) ) ) ) ) ) ).
% conjI_realizer
thf(fact_940_conjI__realizer,axiom,
! [P: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > $o,P2: produc8551481072490612790e_term > option6357759511663192854e_term,Q3: product_prod_int_int > $o,Q2: product_prod_int_int] :
( ( P @ P2 )
=> ( ( Q3 @ Q2 )
=> ( ( P @ ( produc6816164490631068361nt_int @ ( produc5700946648718959541nt_int @ P2 @ Q2 ) ) )
& ( Q3 @ ( produc7328097813583171335nt_int @ ( produc5700946648718959541nt_int @ P2 @ Q2 ) ) ) ) ) ) ).
% conjI_realizer
thf(fact_941_conjI__realizer,axiom,
! [P: ( list_char > int ) > $o,P2: list_char > int,Q3: int > $o,Q2: int] :
( ( P @ P2 )
=> ( ( Q3 @ Q2 )
=> ( ( P @ ( produc9025023058967219549nt_int @ ( produc5790713362662368625nt_int @ P2 @ Q2 ) ) )
& ( Q3 @ ( produc179445755590504351nt_int @ ( produc5790713362662368625nt_int @ P2 @ Q2 ) ) ) ) ) ) ).
% conjI_realizer
thf(fact_942_conjI__realizer,axiom,
! [P: ( int > option6357759511663192854e_term ) > $o,P2: int > option6357759511663192854e_term,Q3: product_prod_int_int > $o,Q2: product_prod_int_int] :
( ( P @ P2 )
=> ( ( Q3 @ Q2 )
=> ( ( P @ ( produc6230002227079971283nt_int @ ( produc4305682042979456191nt_int @ P2 @ Q2 ) ) )
& ( Q3 @ ( produc3162348030201620241nt_int @ ( produc4305682042979456191nt_int @ P2 @ Q2 ) ) ) ) ) ) ).
% conjI_realizer
thf(fact_943_conjI__realizer,axiom,
! [P: int > $o,P2: int,Q3: produc369741286924889929st_int > $o,Q2: produc369741286924889929st_int] :
( ( P @ P2 )
=> ( ( Q3 @ Q2 )
=> ( ( P @ ( produc8941309049508465880st_int @ ( produc5086643055186798020st_int @ P2 @ Q2 ) ) )
& ( Q3 @ ( produc1296517004818028822st_int @ ( produc5086643055186798020st_int @ P2 @ Q2 ) ) ) ) ) ) ).
% conjI_realizer
thf(fact_944_conjI__realizer,axiom,
! [P: $o > $o,P2: $o,Q3: int > $o,Q2: int] :
( ( P @ P2 )
=> ( ( Q3 @ Q2 )
=> ( ( P @ ( product_fst_o_int @ ( product_Pair_o_int @ P2 @ Q2 ) ) )
& ( Q3 @ ( product_snd_o_int @ ( product_Pair_o_int @ P2 @ Q2 ) ) ) ) ) ) ).
% conjI_realizer
thf(fact_945_conjI__realizer,axiom,
! [P: bexp > $o,P2: bexp,Q3: product_prod_o_int > $o,Q2: product_prod_o_int] :
( ( P @ P2 )
=> ( ( Q3 @ Q2 )
=> ( ( P @ ( produc2736798884409471108_o_int @ ( produc4047900504771817624_o_int @ P2 @ Q2 ) ) )
& ( Q3 @ ( produc7219675232234870470_o_int @ ( produc4047900504771817624_o_int @ P2 @ Q2 ) ) ) ) ) ) ).
% conjI_realizer
thf(fact_946_conjI__realizer,axiom,
! [P: ( list_char > int ) > $o,P2: list_char > int,Q3: list_int > $o,Q2: list_int] :
( ( P @ P2 )
=> ( ( Q3 @ Q2 )
=> ( ( P @ ( produc2155683374303800813st_int @ ( produc8650753666468850689st_int @ P2 @ Q2 ) ) )
& ( Q3 @ ( produc6244060863719409455st_int @ ( produc8650753666468850689st_int @ P2 @ Q2 ) ) ) ) ) ) ).
% conjI_realizer
thf(fact_947_bot__nat__0_Oextremum,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% bot_nat_0.extremum
thf(fact_948_le0,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% le0
thf(fact_949_Suc__le__mono,axiom,
! [N: nat,M: nat] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
= ( ord_less_eq_nat @ N @ M ) ) ).
% Suc_le_mono
thf(fact_950_nat__add__left__cancel__le,axiom,
! [K2: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ K2 @ M ) @ ( plus_plus_nat @ K2 @ N ) )
= ( ord_less_eq_nat @ M @ N ) ) ).
% nat_add_left_cancel_le
thf(fact_951_diff__diff__cancel,axiom,
! [I: nat,N: nat] :
( ( ord_less_eq_nat @ I @ N )
=> ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
= I ) ) ).
% diff_diff_cancel
thf(fact_952_diff__is__0__eq_H,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( minus_minus_nat @ M @ N )
= zero_zero_nat ) ) ).
% diff_is_0_eq'
thf(fact_953_diff__is__0__eq,axiom,
! [M: nat,N: nat] :
( ( ( minus_minus_nat @ M @ N )
= zero_zero_nat )
= ( ord_less_eq_nat @ M @ N ) ) ).
% diff_is_0_eq
thf(fact_954_Nat_Odiff__diff__right,axiom,
! [K2: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K2 @ J )
=> ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K2 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ I @ K2 ) @ J ) ) ) ).
% Nat.diff_diff_right
thf(fact_955_Nat_Oadd__diff__assoc2,axiom,
! [K2: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K2 @ J )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K2 ) @ I )
= ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K2 ) ) ) ).
% Nat.add_diff_assoc2
thf(fact_956_Nat_Oadd__diff__assoc,axiom,
! [K2: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K2 @ J )
=> ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K2 ) )
= ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K2 ) ) ) ).
% Nat.add_diff_assoc
thf(fact_957_diff__Suc__diff__eq1,axiom,
! [K2: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K2 @ J )
=> ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K2 ) ) )
= ( minus_minus_nat @ ( plus_plus_nat @ I @ K2 ) @ ( suc @ J ) ) ) ) ).
% diff_Suc_diff_eq1
thf(fact_958_diff__Suc__diff__eq2,axiom,
! [K2: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K2 @ J )
=> ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K2 ) ) @ I )
= ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K2 @ I ) ) ) ) ).
% diff_Suc_diff_eq2
thf(fact_959_execl_Osimps_I1_J,axiom,
! [P: list_instr,Cf: produc6425607678544837394st_int,Cf2: produc6425607678544837394st_int,Cfs: list_P419547167332244514st_int] :
( ( execl @ P @ ( cons_P4151473878978182108st_int @ Cf @ ( cons_P4151473878978182108st_int @ Cf2 @ Cfs ) ) )
= ( ( exec1 @ P @ Cf @ Cf2 )
& ( execl @ P @ ( cons_P4151473878978182108st_int @ Cf2 @ Cfs ) ) ) ) ).
% execl.simps(1)
thf(fact_960_execl_Osimps_I3_J,axiom,
! [P: list_instr,V: produc6425607678544837394st_int] : ( execl @ P @ ( cons_P4151473878978182108st_int @ V @ nil_Pr749310521696113548st_int ) ) ).
% execl.simps(3)
thf(fact_961_execl_Oelims_I1_J,axiom,
! [X: list_instr,Xa: list_P419547167332244514st_int,Y: $o] :
( ( ( execl @ X @ Xa )
= Y )
=> ( ! [Cf4: produc6425607678544837394st_int,Cf5: produc6425607678544837394st_int,Cfs2: list_P419547167332244514st_int] :
( ( Xa
= ( cons_P4151473878978182108st_int @ Cf4 @ ( cons_P4151473878978182108st_int @ Cf5 @ Cfs2 ) ) )
=> ( Y
= ( ~ ( ( exec1 @ X @ Cf4 @ Cf5 )
& ( execl @ X @ ( cons_P4151473878978182108st_int @ Cf5 @ Cfs2 ) ) ) ) ) )
=> ( ( ( Xa = nil_Pr749310521696113548st_int )
=> ~ Y )
=> ~ ( ? [V2: produc6425607678544837394st_int] :
( Xa
= ( cons_P4151473878978182108st_int @ V2 @ nil_Pr749310521696113548st_int ) )
=> ~ Y ) ) ) ) ).
% execl.elims(1)
thf(fact_962_execl_Oelims_I2_J,axiom,
! [X: list_instr,Xa: list_P419547167332244514st_int] :
( ( execl @ X @ Xa )
=> ( ! [Cf4: produc6425607678544837394st_int,Cf5: produc6425607678544837394st_int,Cfs2: list_P419547167332244514st_int] :
( ( Xa
= ( cons_P4151473878978182108st_int @ Cf4 @ ( cons_P4151473878978182108st_int @ Cf5 @ Cfs2 ) ) )
=> ~ ( ( exec1 @ X @ Cf4 @ Cf5 )
& ( execl @ X @ ( cons_P4151473878978182108st_int @ Cf5 @ Cfs2 ) ) ) )
=> ( ( Xa != nil_Pr749310521696113548st_int )
=> ~ ! [V2: produc6425607678544837394st_int] :
( Xa
!= ( cons_P4151473878978182108st_int @ V2 @ nil_Pr749310521696113548st_int ) ) ) ) ) ).
% execl.elims(2)
thf(fact_963_execl_Oelims_I3_J,axiom,
! [X: list_instr,Xa: list_P419547167332244514st_int] :
( ~ ( execl @ X @ Xa )
=> ~ ! [Cf4: produc6425607678544837394st_int,Cf5: produc6425607678544837394st_int,Cfs2: list_P419547167332244514st_int] :
( ( Xa
= ( cons_P4151473878978182108st_int @ Cf4 @ ( cons_P4151473878978182108st_int @ Cf5 @ Cfs2 ) ) )
=> ( ( exec1 @ X @ Cf4 @ Cf5 )
& ( execl @ X @ ( cons_P4151473878978182108st_int @ Cf5 @ Cfs2 ) ) ) ) ) ).
% execl.elims(3)
thf(fact_964_execl_Osimps_I2_J,axiom,
! [P: list_instr] : ( execl @ P @ nil_Pr749310521696113548st_int ) ).
% execl.simps(2)
thf(fact_965_bounded__Max__nat,axiom,
! [P: nat > $o,X: nat,M6: nat] :
( ( P @ X )
=> ( ! [X3: nat] :
( ( P @ X3 )
=> ( ord_less_eq_nat @ X3 @ M6 ) )
=> ~ ! [M4: nat] :
( ( P @ M4 )
=> ~ ! [X6: nat] :
( ( P @ X6 )
=> ( ord_less_eq_nat @ X6 @ M4 ) ) ) ) ) ).
% bounded_Max_nat
thf(fact_966_le__refl,axiom,
! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% le_refl
thf(fact_967_le__trans,axiom,
! [I: nat,J: nat,K2: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ord_less_eq_nat @ J @ K2 )
=> ( ord_less_eq_nat @ I @ K2 ) ) ) ).
% le_trans
thf(fact_968_eq__imp__le,axiom,
! [M: nat,N: nat] :
( ( M = N )
=> ( ord_less_eq_nat @ M @ N ) ) ).
% eq_imp_le
thf(fact_969_le__antisym,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( ord_less_eq_nat @ N @ M )
=> ( M = N ) ) ) ).
% le_antisym
thf(fact_970_nat__le__linear,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
| ( ord_less_eq_nat @ N @ M ) ) ).
% nat_le_linear
thf(fact_971_Nat_Oex__has__greatest__nat,axiom,
! [P: nat > $o,K2: nat,B: nat] :
( ( P @ K2 )
=> ( ! [Y3: nat] :
( ( P @ Y3 )
=> ( ord_less_eq_nat @ Y3 @ B ) )
=> ? [X3: nat] :
( ( P @ X3 )
& ! [Y6: nat] :
( ( P @ Y6 )
=> ( ord_less_eq_nat @ Y6 @ X3 ) ) ) ) ) ).
% Nat.ex_has_greatest_nat
thf(fact_972_le__0__eq,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) ).
% le_0_eq
thf(fact_973_bot__nat__0_Oextremum__uniqueI,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ) ).
% bot_nat_0.extremum_uniqueI
thf(fact_974_bot__nat__0_Oextremum__unique,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ) ).
% bot_nat_0.extremum_unique
thf(fact_975_less__eq__nat_Osimps_I1_J,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% less_eq_nat.simps(1)
thf(fact_976_Suc__leD,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
=> ( ord_less_eq_nat @ M @ N ) ) ).
% Suc_leD
thf(fact_977_le__SucE,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ ( suc @ N ) )
=> ( ~ ( ord_less_eq_nat @ M @ N )
=> ( M
= ( suc @ N ) ) ) ) ).
% le_SucE
thf(fact_978_le__SucI,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% le_SucI
thf(fact_979_Suc__le__D,axiom,
! [N: nat,M7: nat] :
( ( ord_less_eq_nat @ ( suc @ N ) @ M7 )
=> ? [M4: nat] :
( M7
= ( suc @ M4 ) ) ) ).
% Suc_le_D
thf(fact_980_le__Suc__eq,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ ( suc @ N ) )
= ( ( ord_less_eq_nat @ M @ N )
| ( M
= ( suc @ N ) ) ) ) ).
% le_Suc_eq
thf(fact_981_Suc__n__not__le__n,axiom,
! [N: nat] :
~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% Suc_n_not_le_n
thf(fact_982_not__less__eq__eq,axiom,
! [M: nat,N: nat] :
( ( ~ ( ord_less_eq_nat @ M @ N ) )
= ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% not_less_eq_eq
thf(fact_983_full__nat__induct,axiom,
! [P: nat > $o,N: nat] :
( ! [N3: nat] :
( ! [M2: nat] :
( ( ord_less_eq_nat @ ( suc @ M2 ) @ N3 )
=> ( P @ M2 ) )
=> ( P @ N3 ) )
=> ( P @ N ) ) ).
% full_nat_induct
thf(fact_984_nat__induct__at__least,axiom,
! [M: nat,N: nat,P: nat > $o] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( P @ M )
=> ( ! [N3: nat] :
( ( ord_less_eq_nat @ M @ N3 )
=> ( ( P @ N3 )
=> ( P @ ( suc @ N3 ) ) ) )
=> ( P @ N ) ) ) ) ).
% nat_induct_at_least
thf(fact_985_transitive__stepwise__le,axiom,
! [M: nat,N: nat,R2: nat > nat > $o] :
( ( ord_less_eq_nat @ M @ N )
=> ( ! [X3: nat] : ( R2 @ X3 @ X3 )
=> ( ! [X3: nat,Y3: nat,Z4: nat] :
( ( R2 @ X3 @ Y3 )
=> ( ( R2 @ Y3 @ Z4 )
=> ( R2 @ X3 @ Z4 ) ) )
=> ( ! [N3: nat] : ( R2 @ N3 @ ( suc @ N3 ) )
=> ( R2 @ M @ N ) ) ) ) ) ).
% transitive_stepwise_le
thf(fact_986_less__mono__imp__le__mono,axiom,
! [F: nat > nat,I: nat,J: nat] :
( ! [I3: nat,J3: nat] :
( ( ord_less_nat @ I3 @ J3 )
=> ( ord_less_nat @ ( F @ I3 ) @ ( F @ J3 ) ) )
=> ( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% less_mono_imp_le_mono
thf(fact_987_le__neq__implies__less,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( M != N )
=> ( ord_less_nat @ M @ N ) ) ) ).
% le_neq_implies_less
thf(fact_988_less__or__eq__imp__le,axiom,
! [M: nat,N: nat] :
( ( ( ord_less_nat @ M @ N )
| ( M = N ) )
=> ( ord_less_eq_nat @ M @ N ) ) ).
% less_or_eq_imp_le
thf(fact_989_le__eq__less__or__eq,axiom,
( ord_less_eq_nat
= ( ^ [M3: nat,N2: nat] :
( ( ord_less_nat @ M3 @ N2 )
| ( M3 = N2 ) ) ) ) ).
% le_eq_less_or_eq
thf(fact_990_less__imp__le__nat,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ N ) ) ).
% less_imp_le_nat
thf(fact_991_nat__less__le,axiom,
( ord_less_nat
= ( ^ [M3: nat,N2: nat] :
( ( ord_less_eq_nat @ M3 @ N2 )
& ( M3 != N2 ) ) ) ) ).
% nat_less_le
thf(fact_992_nat__le__iff__add,axiom,
( ord_less_eq_nat
= ( ^ [M3: nat,N2: nat] :
? [K3: nat] :
( N2
= ( plus_plus_nat @ M3 @ K3 ) ) ) ) ).
% nat_le_iff_add
thf(fact_993_trans__le__add2,axiom,
! [I: nat,J: nat,M: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% trans_le_add2
thf(fact_994_trans__le__add1,axiom,
! [I: nat,J: nat,M: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% trans_le_add1
thf(fact_995_add__le__mono1,axiom,
! [I: nat,J: nat,K2: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K2 ) @ ( plus_plus_nat @ J @ K2 ) ) ) ).
% add_le_mono1
thf(fact_996_add__le__mono,axiom,
! [I: nat,J: nat,K2: nat,L: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ord_less_eq_nat @ K2 @ L )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K2 ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% add_le_mono
thf(fact_997_le__Suc__ex,axiom,
! [K2: nat,L: nat] :
( ( ord_less_eq_nat @ K2 @ L )
=> ? [N3: nat] :
( L
= ( plus_plus_nat @ K2 @ N3 ) ) ) ).
% le_Suc_ex
thf(fact_998_add__leD2,axiom,
! [M: nat,K2: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K2 ) @ N )
=> ( ord_less_eq_nat @ K2 @ N ) ) ).
% add_leD2
thf(fact_999_add__leD1,axiom,
! [M: nat,K2: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K2 ) @ N )
=> ( ord_less_eq_nat @ M @ N ) ) ).
% add_leD1
thf(fact_1000_le__add2,axiom,
! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% le_add2
thf(fact_1001_le__add1,axiom,
! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% le_add1
thf(fact_1002_add__leE,axiom,
! [M: nat,K2: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K2 ) @ N )
=> ~ ( ( ord_less_eq_nat @ M @ N )
=> ~ ( ord_less_eq_nat @ K2 @ N ) ) ) ).
% add_leE
thf(fact_1003_eq__diff__iff,axiom,
! [K2: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K2 @ M )
=> ( ( ord_less_eq_nat @ K2 @ N )
=> ( ( ( minus_minus_nat @ M @ K2 )
= ( minus_minus_nat @ N @ K2 ) )
= ( M = N ) ) ) ) ).
% eq_diff_iff
thf(fact_1004_le__diff__iff,axiom,
! [K2: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K2 @ M )
=> ( ( ord_less_eq_nat @ K2 @ N )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K2 ) @ ( minus_minus_nat @ N @ K2 ) )
= ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% le_diff_iff
thf(fact_1005_Nat_Odiff__diff__eq,axiom,
! [K2: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K2 @ M )
=> ( ( ord_less_eq_nat @ K2 @ N )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K2 ) @ ( minus_minus_nat @ N @ K2 ) )
= ( minus_minus_nat @ M @ N ) ) ) ) ).
% Nat.diff_diff_eq
thf(fact_1006_diff__le__mono,axiom,
! [M: nat,N: nat,L: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% diff_le_mono
thf(fact_1007_diff__le__self,axiom,
! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% diff_le_self
thf(fact_1008_le__diff__iff_H,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ A @ C )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
= ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% le_diff_iff'
thf(fact_1009_diff__le__mono2,axiom,
! [M: nat,N: nat,L: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% diff_le_mono2
thf(fact_1010_exec1__appendR,axiom,
! [P: list_instr,C: produc6425607678544837394st_int,C4: produc6425607678544837394st_int,P4: list_instr] :
( ( exec1 @ P @ C @ C4 )
=> ( exec1 @ ( append_instr @ P @ P4 ) @ C @ C4 ) ) ).
% exec1_appendR
thf(fact_1011_ex__least__nat__le,axiom,
! [P: nat > $o,N: nat] :
( ( P @ N )
=> ( ~ ( P @ zero_zero_nat )
=> ? [K: nat] :
( ( ord_less_eq_nat @ K @ N )
& ! [I5: nat] :
( ( ord_less_nat @ I5 @ K )
=> ~ ( P @ I5 ) )
& ( P @ K ) ) ) ) ).
% ex_least_nat_le
thf(fact_1012_le__imp__less__Suc,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% le_imp_less_Suc
thf(fact_1013_less__eq__Suc__le,axiom,
( ord_less_nat
= ( ^ [N2: nat] : ( ord_less_eq_nat @ ( suc @ N2 ) ) ) ) ).
% less_eq_Suc_le
thf(fact_1014_less__Suc__eq__le,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ord_less_eq_nat @ M @ N ) ) ).
% less_Suc_eq_le
thf(fact_1015_le__less__Suc__eq,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
= ( N = M ) ) ) ).
% le_less_Suc_eq
thf(fact_1016_Suc__le__lessD,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
=> ( ord_less_nat @ M @ N ) ) ).
% Suc_le_lessD
thf(fact_1017_inc__induct,axiom,
! [I: nat,J: nat,P: nat > $o] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( P @ J )
=> ( ! [N3: nat] :
( ( ord_less_eq_nat @ I @ N3 )
=> ( ( ord_less_nat @ N3 @ J )
=> ( ( P @ ( suc @ N3 ) )
=> ( P @ N3 ) ) ) )
=> ( P @ I ) ) ) ) ).
% inc_induct
thf(fact_1018_dec__induct,axiom,
! [I: nat,J: nat,P: nat > $o] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( P @ I )
=> ( ! [N3: nat] :
( ( ord_less_eq_nat @ I @ N3 )
=> ( ( ord_less_nat @ N3 @ J )
=> ( ( P @ N3 )
=> ( P @ ( suc @ N3 ) ) ) ) )
=> ( P @ J ) ) ) ) ).
% dec_induct
thf(fact_1019_Suc__le__eq,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
= ( ord_less_nat @ M @ N ) ) ).
% Suc_le_eq
thf(fact_1020_Suc__leI,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% Suc_leI
thf(fact_1021_impossible__Cons,axiom,
! [Xs: list_instr,Ys: list_instr,X: instr] :
( ( ord_less_eq_nat @ ( size_size_list_instr @ Xs ) @ ( size_size_list_instr @ Ys ) )
=> ( Xs
!= ( cons_instr @ X @ Ys ) ) ) ).
% impossible_Cons
thf(fact_1022_impossible__Cons,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,X: produc6425607678544837394st_int] :
( ( ord_less_eq_nat @ ( size_s229347708945616566st_int @ Xs ) @ ( size_s229347708945616566st_int @ Ys ) )
=> ( Xs
!= ( cons_P4151473878978182108st_int @ X @ Ys ) ) ) ).
% impossible_Cons
thf(fact_1023_impossible__Cons,axiom,
! [Xs: list_list_char,Ys: list_list_char,X: list_char] :
( ( ord_less_eq_nat @ ( size_s356637359517785349t_char @ Xs ) @ ( size_s356637359517785349t_char @ Ys ) )
=> ( Xs
!= ( cons_list_char @ X @ Ys ) ) ) ).
% impossible_Cons
thf(fact_1024_impossible__Cons,axiom,
! [Xs: list_int,Ys: list_int,X: int] :
( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys ) )
=> ( Xs
!= ( cons_int @ X @ Ys ) ) ) ).
% impossible_Cons
thf(fact_1025_Suc__diff__le,axiom,
! [N: nat,M: nat] :
( ( ord_less_eq_nat @ N @ M )
=> ( ( minus_minus_nat @ ( suc @ M ) @ N )
= ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% Suc_diff_le
thf(fact_1026_mono__nat__linear__lb,axiom,
! [F: nat > nat,M: nat,K2: nat] :
( ! [M4: nat,N3: nat] :
( ( ord_less_nat @ M4 @ N3 )
=> ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K2 ) @ ( F @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% mono_nat_linear_lb
thf(fact_1027_less__diff__iff,axiom,
! [K2: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K2 @ M )
=> ( ( ord_less_eq_nat @ K2 @ N )
=> ( ( ord_less_nat @ ( minus_minus_nat @ M @ K2 ) @ ( minus_minus_nat @ N @ K2 ) )
= ( ord_less_nat @ M @ N ) ) ) ) ).
% less_diff_iff
thf(fact_1028_diff__less__mono,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% diff_less_mono
thf(fact_1029_Nat_Ole__imp__diff__is__add,axiom,
! [I: nat,J: nat,K2: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ( minus_minus_nat @ J @ I )
= K2 )
= ( J
= ( plus_plus_nat @ K2 @ I ) ) ) ) ).
% Nat.le_imp_diff_is_add
thf(fact_1030_Nat_Odiff__add__assoc2,axiom,
! [K2: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K2 @ J )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K2 )
= ( plus_plus_nat @ ( minus_minus_nat @ J @ K2 ) @ I ) ) ) ).
% Nat.diff_add_assoc2
thf(fact_1031_Nat_Odiff__add__assoc,axiom,
! [K2: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K2 @ J )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K2 )
= ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K2 ) ) ) ) ).
% Nat.diff_add_assoc
thf(fact_1032_Nat_Ole__diff__conv2,axiom,
! [K2: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K2 @ J )
=> ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K2 ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K2 ) @ J ) ) ) ).
% Nat.le_diff_conv2
thf(fact_1033_le__diff__conv,axiom,
! [J: nat,K2: nat,I: nat] :
( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K2 ) @ I )
= ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K2 ) ) ) ).
% le_diff_conv
thf(fact_1034_zle__int,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
= ( ord_less_eq_nat @ M @ N ) ) ).
% zle_int
thf(fact_1035_nat__int__comparison_I3_J,axiom,
( ord_less_eq_nat
= ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% nat_int_comparison(3)
thf(fact_1036_ex__least__nat__less,axiom,
! [P: nat > $o,N: nat] :
( ( P @ N )
=> ( ~ ( P @ zero_zero_nat )
=> ? [K: nat] :
( ( ord_less_nat @ K @ N )
& ! [I5: nat] :
( ( ord_less_eq_nat @ I5 @ K )
=> ~ ( P @ I5 ) )
& ( P @ ( suc @ K ) ) ) ) ) ).
% ex_least_nat_less
thf(fact_1037_Suc__le__length__iff,axiom,
! [N: nat,Xs: list_instr] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_instr @ Xs ) )
= ( ? [X2: instr,Ys3: list_instr] :
( ( Xs
= ( cons_instr @ X2 @ Ys3 ) )
& ( ord_less_eq_nat @ N @ ( size_size_list_instr @ Ys3 ) ) ) ) ) ).
% Suc_le_length_iff
thf(fact_1038_Suc__le__length__iff,axiom,
! [N: nat,Xs: list_P419547167332244514st_int] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_s229347708945616566st_int @ Xs ) )
= ( ? [X2: produc6425607678544837394st_int,Ys3: list_P419547167332244514st_int] :
( ( Xs
= ( cons_P4151473878978182108st_int @ X2 @ Ys3 ) )
& ( ord_less_eq_nat @ N @ ( size_s229347708945616566st_int @ Ys3 ) ) ) ) ) ).
% Suc_le_length_iff
thf(fact_1039_Suc__le__length__iff,axiom,
! [N: nat,Xs: list_list_char] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_s356637359517785349t_char @ Xs ) )
= ( ? [X2: list_char,Ys3: list_list_char] :
( ( Xs
= ( cons_list_char @ X2 @ Ys3 ) )
& ( ord_less_eq_nat @ N @ ( size_s356637359517785349t_char @ Ys3 ) ) ) ) ) ).
% Suc_le_length_iff
thf(fact_1040_Suc__le__length__iff,axiom,
! [N: nat,Xs: list_int] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs ) )
= ( ? [X2: int,Ys3: list_int] :
( ( Xs
= ( cons_int @ X2 @ Ys3 ) )
& ( ord_less_eq_nat @ N @ ( size_size_list_int @ Ys3 ) ) ) ) ) ).
% Suc_le_length_iff
thf(fact_1041_of__nat__diff,axiom,
! [N: nat,M: nat] :
( ( ord_less_eq_nat @ N @ M )
=> ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
= ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% of_nat_diff
thf(fact_1042_of__nat__diff,axiom,
! [N: nat,M: nat] :
( ( ord_less_eq_nat @ N @ M )
=> ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
= ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% of_nat_diff
thf(fact_1043_less__diff__conv2,axiom,
! [K2: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K2 @ J )
=> ( ( ord_less_nat @ ( minus_minus_nat @ J @ K2 ) @ I )
= ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K2 ) ) ) ) ).
% less_diff_conv2
thf(fact_1044_lenlex__length,axiom,
! [Ms: list_int,Ns: list_int,R: set_Pr958786334691620121nt_int] :
( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Ms @ Ns ) @ ( lenlex_int @ R ) )
=> ( ord_less_eq_nat @ ( size_size_list_int @ Ms ) @ ( size_size_list_int @ Ns ) ) ) ).
% lenlex_length
thf(fact_1045_measures__lesseq,axiom,
! [F: int > nat,X: int,Y: int,Fs: list_int_nat] :
( ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) )
=> ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ Fs ) )
=> ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ ( cons_int_nat @ F @ Fs ) ) ) ) ) ).
% measures_lesseq
thf(fact_1046_exec1__appendL,axiom,
! [P: list_instr,I: int,S2: list_char > int,Stk3: list_int,I4: int,S3: list_char > int,Stk2: list_int,P4: list_instr] :
( ( exec1 @ P @ ( produc5086643055186798020st_int @ I @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) @ ( produc5086643055186798020st_int @ I4 @ ( produc8650753666468850689st_int @ S3 @ Stk2 ) ) )
=> ( exec1 @ ( append_instr @ P4 @ P ) @ ( produc5086643055186798020st_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P4 ) ) @ I ) @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) @ ( produc5086643055186798020st_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P4 ) ) @ I4 ) @ ( produc8650753666468850689st_int @ S3 @ Stk2 ) ) ) ) ).
% exec1_appendL
thf(fact_1047_n__lists_Osimps_I1_J,axiom,
! [Xs: list_instr] :
( ( n_lists_instr @ zero_zero_nat @ Xs )
= ( cons_list_instr @ nil_instr @ nil_list_instr ) ) ).
% n_lists.simps(1)
thf(fact_1048_n__lists_Osimps_I1_J,axiom,
! [Xs: list_P419547167332244514st_int] :
( ( n_list7311978343830957444st_int @ zero_zero_nat @ Xs )
= ( cons_l8648290059330449388st_int @ nil_Pr749310521696113548st_int @ nil_li4597314861645524892st_int ) ) ).
% n_lists.simps(1)
thf(fact_1049_n__lists_Osimps_I1_J,axiom,
! [Xs: list_list_char] :
( ( n_lists_list_char @ zero_zero_nat @ Xs )
= ( cons_list_list_char @ nil_list_char @ nil_list_list_char ) ) ).
% n_lists.simps(1)
thf(fact_1050_n__lists_Osimps_I1_J,axiom,
! [Xs: list_char] :
( ( n_lists_char @ zero_zero_nat @ Xs )
= ( cons_list_char @ nil_char @ nil_list_char ) ) ).
% n_lists.simps(1)
thf(fact_1051_exec1__def,axiom,
( exec1
= ( ^ [P5: list_instr,Cf3: produc6425607678544837394st_int,Cf6: produc6425607678544837394st_int] :
( ( iexec_pred @ ( produc1484136438817787418st_int @ ( inth_instr @ P5 @ ( produc8941309049508465880st_int @ Cf3 ) ) @ Cf3 ) @ Cf6 )
& ( ord_less_eq_int @ zero_zero_int @ ( produc8941309049508465880st_int @ Cf3 ) )
& ( ord_less_int @ ( produc8941309049508465880st_int @ Cf3 ) @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P5 ) ) ) ) ) ) ).
% exec1_def
thf(fact_1052_exI__realizer,axiom,
! [P: int > int > $o,Y: int,X: int] :
( ( P @ Y @ X )
=> ( P @ ( product_snd_int_int @ ( product_Pair_int_int @ X @ Y ) ) @ ( product_fst_int_int @ ( product_Pair_int_int @ X @ Y ) ) ) ) ).
% exI_realizer
thf(fact_1053_exI__realizer,axiom,
! [P: product_prod_int_int > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > $o,Y: product_prod_int_int,X: produc8551481072490612790e_term > option6357759511663192854e_term] :
( ( P @ Y @ X )
=> ( P @ ( produc7328097813583171335nt_int @ ( produc5700946648718959541nt_int @ X @ Y ) ) @ ( produc6816164490631068361nt_int @ ( produc5700946648718959541nt_int @ X @ Y ) ) ) ) ).
% exI_realizer
thf(fact_1054_exI__realizer,axiom,
! [P: int > ( list_char > int ) > $o,Y: int,X: list_char > int] :
( ( P @ Y @ X )
=> ( P @ ( produc179445755590504351nt_int @ ( produc5790713362662368625nt_int @ X @ Y ) ) @ ( produc9025023058967219549nt_int @ ( produc5790713362662368625nt_int @ X @ Y ) ) ) ) ).
% exI_realizer
thf(fact_1055_exI__realizer,axiom,
! [P: product_prod_int_int > ( int > option6357759511663192854e_term ) > $o,Y: product_prod_int_int,X: int > option6357759511663192854e_term] :
( ( P @ Y @ X )
=> ( P @ ( produc3162348030201620241nt_int @ ( produc4305682042979456191nt_int @ X @ Y ) ) @ ( produc6230002227079971283nt_int @ ( produc4305682042979456191nt_int @ X @ Y ) ) ) ) ).
% exI_realizer
thf(fact_1056_exI__realizer,axiom,
! [P: produc369741286924889929st_int > int > $o,Y: produc369741286924889929st_int,X: int] :
( ( P @ Y @ X )
=> ( P @ ( produc1296517004818028822st_int @ ( produc5086643055186798020st_int @ X @ Y ) ) @ ( produc8941309049508465880st_int @ ( produc5086643055186798020st_int @ X @ Y ) ) ) ) ).
% exI_realizer
thf(fact_1057_exI__realizer,axiom,
! [P: int > $o > $o,Y: int,X: $o] :
( ( P @ Y @ X )
=> ( P @ ( product_snd_o_int @ ( product_Pair_o_int @ X @ Y ) ) @ ( product_fst_o_int @ ( product_Pair_o_int @ X @ Y ) ) ) ) ).
% exI_realizer
thf(fact_1058_exI__realizer,axiom,
! [P: product_prod_o_int > bexp > $o,Y: product_prod_o_int,X: bexp] :
( ( P @ Y @ X )
=> ( P @ ( produc7219675232234870470_o_int @ ( produc4047900504771817624_o_int @ X @ Y ) ) @ ( produc2736798884409471108_o_int @ ( produc4047900504771817624_o_int @ X @ Y ) ) ) ) ).
% exI_realizer
thf(fact_1059_exI__realizer,axiom,
! [P: list_int > ( list_char > int ) > $o,Y: list_int,X: list_char > int] :
( ( P @ Y @ X )
=> ( P @ ( produc6244060863719409455st_int @ ( produc8650753666468850689st_int @ X @ Y ) ) @ ( produc2155683374303800813st_int @ ( produc8650753666468850689st_int @ X @ Y ) ) ) ) ).
% exI_realizer
thf(fact_1060_zdiff__int__split,axiom,
! [P: int > $o,X: nat,Y: nat] :
( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
= ( ( ( ord_less_eq_nat @ Y @ X )
=> ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
& ( ( ord_less_nat @ X @ Y )
=> ( P @ zero_zero_int ) ) ) ) ).
% zdiff_int_split
thf(fact_1061_exec__append__trans,axiom,
! [P: list_instr,S2: list_char > int,Stk3: list_int,I4: int,S3: list_char > int,Stk2: list_int,P4: list_instr,I6: int,S5: list_char > int,Stk4: list_int,J4: int] :
( ( star_P707599355569300323st_int @ ( exec1 @ P ) @ ( produc5086643055186798020st_int @ zero_zero_int @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) @ ( produc5086643055186798020st_int @ I4 @ ( produc8650753666468850689st_int @ S3 @ Stk2 ) ) )
=> ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P ) ) @ I4 )
=> ( ( star_P707599355569300323st_int @ ( exec1 @ P4 ) @ ( produc5086643055186798020st_int @ ( minus_minus_int @ I4 @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P ) ) ) @ ( produc8650753666468850689st_int @ S3 @ Stk2 ) ) @ ( produc5086643055186798020st_int @ I6 @ ( produc8650753666468850689st_int @ S5 @ Stk4 ) ) )
=> ( ( J4
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P ) ) @ I6 ) )
=> ( star_P707599355569300323st_int @ ( exec1 @ ( append_instr @ P @ P4 ) ) @ ( produc5086643055186798020st_int @ zero_zero_int @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) @ ( produc5086643055186798020st_int @ J4 @ ( produc8650753666468850689st_int @ S5 @ Stk4 ) ) ) ) ) ) ) ).
% exec_append_trans
thf(fact_1062_Compiler_Oacomp__correct,axiom,
! [A: aexp,S2: list_char > int,Stk3: list_int] : ( star_P707599355569300323st_int @ ( exec1 @ ( acomp @ A ) ) @ ( produc5086643055186798020st_int @ zero_zero_int @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) @ ( produc5086643055186798020st_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ ( acomp @ A ) ) ) @ ( produc8650753666468850689st_int @ S2 @ ( cons_int @ ( aval @ A @ S2 ) @ Stk3 ) ) ) ) ).
% Compiler.acomp_correct
thf(fact_1063_exec__Cons__1,axiom,
! [P: list_instr,S2: list_char > int,Stk3: list_int,J: int,T: list_char > int,Stk2: list_int,Ins2: instr] :
( ( star_P707599355569300323st_int @ ( exec1 @ P ) @ ( produc5086643055186798020st_int @ zero_zero_int @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) @ ( produc5086643055186798020st_int @ J @ ( produc8650753666468850689st_int @ T @ Stk2 ) ) )
=> ( star_P707599355569300323st_int @ ( exec1 @ ( cons_instr @ Ins2 @ P ) ) @ ( produc5086643055186798020st_int @ one_one_int @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) @ ( produc5086643055186798020st_int @ ( plus_plus_int @ one_one_int @ J ) @ ( produc8650753666468850689st_int @ T @ Stk2 ) ) ) ) ).
% exec_Cons_1
thf(fact_1064_exec__appendL__if,axiom,
! [P4: list_instr,I: int,P: list_instr,S2: list_char > int,Stk3: list_int,J: int,S3: list_char > int,Stk2: list_int,I4: int] :
( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P4 ) ) @ I )
=> ( ( star_P707599355569300323st_int @ ( exec1 @ P ) @ ( produc5086643055186798020st_int @ ( minus_minus_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P4 ) ) ) @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) @ ( produc5086643055186798020st_int @ J @ ( produc8650753666468850689st_int @ S3 @ Stk2 ) ) )
=> ( ( I4
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P4 ) ) @ J ) )
=> ( star_P707599355569300323st_int @ ( exec1 @ ( append_instr @ P4 @ P ) ) @ ( produc5086643055186798020st_int @ I @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) @ ( produc5086643055186798020st_int @ I4 @ ( produc8650753666468850689st_int @ S3 @ Stk2 ) ) ) ) ) ) ).
% exec_appendL_if
thf(fact_1065_execl_Ocases,axiom,
! [X: produc4400946599758736694st_int] :
( ! [P3: list_instr,Cf4: produc6425607678544837394st_int,Cf5: produc6425607678544837394st_int,Cfs2: list_P419547167332244514st_int] :
( X
!= ( produc7764413618310988720st_int @ P3 @ ( cons_P4151473878978182108st_int @ Cf4 @ ( cons_P4151473878978182108st_int @ Cf5 @ Cfs2 ) ) ) )
=> ( ! [P3: list_instr] :
( X
!= ( produc7764413618310988720st_int @ P3 @ nil_Pr749310521696113548st_int ) )
=> ~ ! [P3: list_instr,V2: produc6425607678544837394st_int] :
( X
!= ( produc7764413618310988720st_int @ P3 @ ( cons_P4151473878978182108st_int @ V2 @ nil_Pr749310521696113548st_int ) ) ) ) ) ).
% execl.cases
thf(fact_1066_mpred__merge,axiom,
! [P: list_instr,Cfs: list_P419547167332244514st_int,K2: nat,M: nat,N: nat] :
( ( mpred @ P @ Cfs @ K2 @ M )
=> ( ( mpred @ P @ Cfs @ M @ N )
=> ( mpred @ P @ Cfs @ K2 @ N ) ) ) ).
% mpred_merge
thf(fact_1067_exec__appendR,axiom,
! [P: list_instr,C: produc6425607678544837394st_int,C4: produc6425607678544837394st_int,P4: list_instr] :
( ( star_P707599355569300323st_int @ ( exec1 @ P ) @ C @ C4 )
=> ( star_P707599355569300323st_int @ ( exec1 @ ( append_instr @ P @ P4 ) ) @ C @ C4 ) ) ).
% exec_appendR
thf(fact_1068_pinf_I1_J,axiom,
! [P: nat > $o,P4: nat > $o,Q3: nat > $o,Q4: nat > $o] :
( ? [Z5: nat] :
! [X3: nat] :
( ( ord_less_nat @ Z5 @ X3 )
=> ( ( P @ X3 )
= ( P4 @ X3 ) ) )
=> ( ? [Z5: nat] :
! [X3: nat] :
( ( ord_less_nat @ Z5 @ X3 )
=> ( ( Q3 @ X3 )
= ( Q4 @ X3 ) ) )
=> ? [Z4: nat] :
! [X6: nat] :
( ( ord_less_nat @ Z4 @ X6 )
=> ( ( ( P @ X6 )
& ( Q3 @ X6 ) )
= ( ( P4 @ X6 )
& ( Q4 @ X6 ) ) ) ) ) ) ).
% pinf(1)
thf(fact_1069_pinf_I1_J,axiom,
! [P: int > $o,P4: int > $o,Q3: int > $o,Q4: int > $o] :
( ? [Z5: int] :
! [X3: int] :
( ( ord_less_int @ Z5 @ X3 )
=> ( ( P @ X3 )
= ( P4 @ X3 ) ) )
=> ( ? [Z5: int] :
! [X3: int] :
( ( ord_less_int @ Z5 @ X3 )
=> ( ( Q3 @ X3 )
= ( Q4 @ X3 ) ) )
=> ? [Z4: int] :
! [X6: int] :
( ( ord_less_int @ Z4 @ X6 )
=> ( ( ( P @ X6 )
& ( Q3 @ X6 ) )
= ( ( P4 @ X6 )
& ( Q4 @ X6 ) ) ) ) ) ) ).
% pinf(1)
thf(fact_1070_pinf_I2_J,axiom,
! [P: nat > $o,P4: nat > $o,Q3: nat > $o,Q4: nat > $o] :
( ? [Z5: nat] :
! [X3: nat] :
( ( ord_less_nat @ Z5 @ X3 )
=> ( ( P @ X3 )
= ( P4 @ X3 ) ) )
=> ( ? [Z5: nat] :
! [X3: nat] :
( ( ord_less_nat @ Z5 @ X3 )
=> ( ( Q3 @ X3 )
= ( Q4 @ X3 ) ) )
=> ? [Z4: nat] :
! [X6: nat] :
( ( ord_less_nat @ Z4 @ X6 )
=> ( ( ( P @ X6 )
| ( Q3 @ X6 ) )
= ( ( P4 @ X6 )
| ( Q4 @ X6 ) ) ) ) ) ) ).
% pinf(2)
thf(fact_1071_pinf_I2_J,axiom,
! [P: int > $o,P4: int > $o,Q3: int > $o,Q4: int > $o] :
( ? [Z5: int] :
! [X3: int] :
( ( ord_less_int @ Z5 @ X3 )
=> ( ( P @ X3 )
= ( P4 @ X3 ) ) )
=> ( ? [Z5: int] :
! [X3: int] :
( ( ord_less_int @ Z5 @ X3 )
=> ( ( Q3 @ X3 )
= ( Q4 @ X3 ) ) )
=> ? [Z4: int] :
! [X6: int] :
( ( ord_less_int @ Z4 @ X6 )
=> ( ( ( P @ X6 )
| ( Q3 @ X6 ) )
= ( ( P4 @ X6 )
| ( Q4 @ X6 ) ) ) ) ) ) ).
% pinf(2)
thf(fact_1072_pinf_I3_J,axiom,
! [T: nat] :
? [Z4: nat] :
! [X6: nat] :
( ( ord_less_nat @ Z4 @ X6 )
=> ( X6 != T ) ) ).
% pinf(3)
thf(fact_1073_pinf_I3_J,axiom,
! [T: int] :
? [Z4: int] :
! [X6: int] :
( ( ord_less_int @ Z4 @ X6 )
=> ( X6 != T ) ) ).
% pinf(3)
thf(fact_1074_pinf_I4_J,axiom,
! [T: nat] :
? [Z4: nat] :
! [X6: nat] :
( ( ord_less_nat @ Z4 @ X6 )
=> ( X6 != T ) ) ).
% pinf(4)
thf(fact_1075_pinf_I4_J,axiom,
! [T: int] :
? [Z4: int] :
! [X6: int] :
( ( ord_less_int @ Z4 @ X6 )
=> ( X6 != T ) ) ).
% pinf(4)
thf(fact_1076_pinf_I5_J,axiom,
! [T: nat] :
? [Z4: nat] :
! [X6: nat] :
( ( ord_less_nat @ Z4 @ X6 )
=> ~ ( ord_less_nat @ X6 @ T ) ) ).
% pinf(5)
thf(fact_1077_pinf_I5_J,axiom,
! [T: int] :
? [Z4: int] :
! [X6: int] :
( ( ord_less_int @ Z4 @ X6 )
=> ~ ( ord_less_int @ X6 @ T ) ) ).
% pinf(5)
thf(fact_1078_pinf_I7_J,axiom,
! [T: nat] :
? [Z4: nat] :
! [X6: nat] :
( ( ord_less_nat @ Z4 @ X6 )
=> ( ord_less_nat @ T @ X6 ) ) ).
% pinf(7)
thf(fact_1079_pinf_I7_J,axiom,
! [T: int] :
? [Z4: int] :
! [X6: int] :
( ( ord_less_int @ Z4 @ X6 )
=> ( ord_less_int @ T @ X6 ) ) ).
% pinf(7)
thf(fact_1080_minf_I1_J,axiom,
! [P: nat > $o,P4: nat > $o,Q3: nat > $o,Q4: nat > $o] :
( ? [Z5: nat] :
! [X3: nat] :
( ( ord_less_nat @ X3 @ Z5 )
=> ( ( P @ X3 )
= ( P4 @ X3 ) ) )
=> ( ? [Z5: nat] :
! [X3: nat] :
( ( ord_less_nat @ X3 @ Z5 )
=> ( ( Q3 @ X3 )
= ( Q4 @ X3 ) ) )
=> ? [Z4: nat] :
! [X6: nat] :
( ( ord_less_nat @ X6 @ Z4 )
=> ( ( ( P @ X6 )
& ( Q3 @ X6 ) )
= ( ( P4 @ X6 )
& ( Q4 @ X6 ) ) ) ) ) ) ).
% minf(1)
thf(fact_1081_minf_I1_J,axiom,
! [P: int > $o,P4: int > $o,Q3: int > $o,Q4: int > $o] :
( ? [Z5: int] :
! [X3: int] :
( ( ord_less_int @ X3 @ Z5 )
=> ( ( P @ X3 )
= ( P4 @ X3 ) ) )
=> ( ? [Z5: int] :
! [X3: int] :
( ( ord_less_int @ X3 @ Z5 )
=> ( ( Q3 @ X3 )
= ( Q4 @ X3 ) ) )
=> ? [Z4: int] :
! [X6: int] :
( ( ord_less_int @ X6 @ Z4 )
=> ( ( ( P @ X6 )
& ( Q3 @ X6 ) )
= ( ( P4 @ X6 )
& ( Q4 @ X6 ) ) ) ) ) ) ).
% minf(1)
thf(fact_1082_minf_I2_J,axiom,
! [P: nat > $o,P4: nat > $o,Q3: nat > $o,Q4: nat > $o] :
( ? [Z5: nat] :
! [X3: nat] :
( ( ord_less_nat @ X3 @ Z5 )
=> ( ( P @ X3 )
= ( P4 @ X3 ) ) )
=> ( ? [Z5: nat] :
! [X3: nat] :
( ( ord_less_nat @ X3 @ Z5 )
=> ( ( Q3 @ X3 )
= ( Q4 @ X3 ) ) )
=> ? [Z4: nat] :
! [X6: nat] :
( ( ord_less_nat @ X6 @ Z4 )
=> ( ( ( P @ X6 )
| ( Q3 @ X6 ) )
= ( ( P4 @ X6 )
| ( Q4 @ X6 ) ) ) ) ) ) ).
% minf(2)
thf(fact_1083_minf_I2_J,axiom,
! [P: int > $o,P4: int > $o,Q3: int > $o,Q4: int > $o] :
( ? [Z5: int] :
! [X3: int] :
( ( ord_less_int @ X3 @ Z5 )
=> ( ( P @ X3 )
= ( P4 @ X3 ) ) )
=> ( ? [Z5: int] :
! [X3: int] :
( ( ord_less_int @ X3 @ Z5 )
=> ( ( Q3 @ X3 )
= ( Q4 @ X3 ) ) )
=> ? [Z4: int] :
! [X6: int] :
( ( ord_less_int @ X6 @ Z4 )
=> ( ( ( P @ X6 )
| ( Q3 @ X6 ) )
= ( ( P4 @ X6 )
| ( Q4 @ X6 ) ) ) ) ) ) ).
% minf(2)
thf(fact_1084_minf_I3_J,axiom,
! [T: nat] :
? [Z4: nat] :
! [X6: nat] :
( ( ord_less_nat @ X6 @ Z4 )
=> ( X6 != T ) ) ).
% minf(3)
thf(fact_1085_minf_I3_J,axiom,
! [T: int] :
? [Z4: int] :
! [X6: int] :
( ( ord_less_int @ X6 @ Z4 )
=> ( X6 != T ) ) ).
% minf(3)
thf(fact_1086_minf_I4_J,axiom,
! [T: nat] :
? [Z4: nat] :
! [X6: nat] :
( ( ord_less_nat @ X6 @ Z4 )
=> ( X6 != T ) ) ).
% minf(4)
thf(fact_1087_minf_I4_J,axiom,
! [T: int] :
? [Z4: int] :
! [X6: int] :
( ( ord_less_int @ X6 @ Z4 )
=> ( X6 != T ) ) ).
% minf(4)
thf(fact_1088_minf_I5_J,axiom,
! [T: nat] :
? [Z4: nat] :
! [X6: nat] :
( ( ord_less_nat @ X6 @ Z4 )
=> ( ord_less_nat @ X6 @ T ) ) ).
% minf(5)
thf(fact_1089_minf_I5_J,axiom,
! [T: int] :
? [Z4: int] :
! [X6: int] :
( ( ord_less_int @ X6 @ Z4 )
=> ( ord_less_int @ X6 @ T ) ) ).
% minf(5)
thf(fact_1090_minf_I7_J,axiom,
! [T: nat] :
? [Z4: nat] :
! [X6: nat] :
( ( ord_less_nat @ X6 @ Z4 )
=> ~ ( ord_less_nat @ T @ X6 ) ) ).
% minf(7)
thf(fact_1091_minf_I7_J,axiom,
! [T: int] :
? [Z4: int] :
! [X6: int] :
( ( ord_less_int @ X6 @ Z4 )
=> ~ ( ord_less_int @ T @ X6 ) ) ).
% minf(7)
thf(fact_1092_exec__induct,axiom,
! [Pa: list_instr,X1a: int,X1b: list_char > int,X1c: list_int,X2a: int,X2b: list_char > int,X2c: list_int,P: int > ( list_char > int ) > list_int > int > ( list_char > int ) > list_int > $o] :
( ( star_P707599355569300323st_int @ ( exec1 @ Pa ) @ ( produc5086643055186798020st_int @ X1a @ ( produc8650753666468850689st_int @ X1b @ X1c ) ) @ ( produc5086643055186798020st_int @ X2a @ ( produc8650753666468850689st_int @ X2b @ X2c ) ) )
=> ( ! [A5: int,Aa: list_char > int,B5: list_int] : ( P @ A5 @ Aa @ B5 @ A5 @ Aa @ B5 )
=> ( ! [A5: int,Aa: list_char > int,B5: list_int,Ab: int,Ac: list_char > int,Ba: list_int,Ad: int,Ae: list_char > int,Bb: list_int] :
( ( exec1 @ Pa @ ( produc5086643055186798020st_int @ A5 @ ( produc8650753666468850689st_int @ Aa @ B5 ) ) @ ( produc5086643055186798020st_int @ Ab @ ( produc8650753666468850689st_int @ Ac @ Ba ) ) )
=> ( ( star_P707599355569300323st_int @ ( exec1 @ Pa ) @ ( produc5086643055186798020st_int @ Ab @ ( produc8650753666468850689st_int @ Ac @ Ba ) ) @ ( produc5086643055186798020st_int @ Ad @ ( produc8650753666468850689st_int @ Ae @ Bb ) ) )
=> ( ( P @ Ab @ Ac @ Ba @ Ad @ Ae @ Bb )
=> ( P @ A5 @ Aa @ B5 @ Ad @ Ae @ Bb ) ) ) )
=> ( P @ X1a @ X1b @ X1c @ X2a @ X2b @ X2c ) ) ) ) ).
% exec_induct
thf(fact_1093_pinf_I6_J,axiom,
! [T: int] :
? [Z4: int] :
! [X6: int] :
( ( ord_less_int @ Z4 @ X6 )
=> ~ ( ord_less_eq_int @ X6 @ T ) ) ).
% pinf(6)
thf(fact_1094_pinf_I6_J,axiom,
! [T: nat] :
? [Z4: nat] :
! [X6: nat] :
( ( ord_less_nat @ Z4 @ X6 )
=> ~ ( ord_less_eq_nat @ X6 @ T ) ) ).
% pinf(6)
thf(fact_1095_pinf_I6_J,axiom,
! [T: num] :
? [Z4: num] :
! [X6: num] :
( ( ord_less_num @ Z4 @ X6 )
=> ~ ( ord_less_eq_num @ X6 @ T ) ) ).
% pinf(6)
thf(fact_1096_pinf_I8_J,axiom,
! [T: int] :
? [Z4: int] :
! [X6: int] :
( ( ord_less_int @ Z4 @ X6 )
=> ( ord_less_eq_int @ T @ X6 ) ) ).
% pinf(8)
thf(fact_1097_pinf_I8_J,axiom,
! [T: nat] :
? [Z4: nat] :
! [X6: nat] :
( ( ord_less_nat @ Z4 @ X6 )
=> ( ord_less_eq_nat @ T @ X6 ) ) ).
% pinf(8)
thf(fact_1098_pinf_I8_J,axiom,
! [T: num] :
? [Z4: num] :
! [X6: num] :
( ( ord_less_num @ Z4 @ X6 )
=> ( ord_less_eq_num @ T @ X6 ) ) ).
% pinf(8)
thf(fact_1099_minf_I6_J,axiom,
! [T: int] :
? [Z4: int] :
! [X6: int] :
( ( ord_less_int @ X6 @ Z4 )
=> ( ord_less_eq_int @ X6 @ T ) ) ).
% minf(6)
thf(fact_1100_minf_I6_J,axiom,
! [T: nat] :
? [Z4: nat] :
! [X6: nat] :
( ( ord_less_nat @ X6 @ Z4 )
=> ( ord_less_eq_nat @ X6 @ T ) ) ).
% minf(6)
thf(fact_1101_minf_I6_J,axiom,
! [T: num] :
? [Z4: num] :
! [X6: num] :
( ( ord_less_num @ X6 @ Z4 )
=> ( ord_less_eq_num @ X6 @ T ) ) ).
% minf(6)
thf(fact_1102_minf_I8_J,axiom,
! [T: int] :
? [Z4: int] :
! [X6: int] :
( ( ord_less_int @ X6 @ Z4 )
=> ~ ( ord_less_eq_int @ T @ X6 ) ) ).
% minf(8)
thf(fact_1103_minf_I8_J,axiom,
! [T: nat] :
? [Z4: nat] :
! [X6: nat] :
( ( ord_less_nat @ X6 @ Z4 )
=> ~ ( ord_less_eq_nat @ T @ X6 ) ) ).
% minf(8)
thf(fact_1104_minf_I8_J,axiom,
! [T: num] :
? [Z4: num] :
! [X6: num] :
( ( ord_less_num @ X6 @ Z4 )
=> ~ ( ord_less_eq_num @ T @ X6 ) ) ).
% minf(8)
thf(fact_1105_imp__le__cong,axiom,
! [X: int,X7: int,P: $o,P4: $o] :
( ( X = X7 )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
=> ( P = P4 ) )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ X )
=> P )
= ( ( ord_less_eq_int @ zero_zero_int @ X7 )
=> P4 ) ) ) ) ).
% imp_le_cong
thf(fact_1106_conj__le__cong,axiom,
! [X: int,X7: int,P: $o,P4: $o] :
( ( X = X7 )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
=> ( P = P4 ) )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ X )
& P )
= ( ( ord_less_eq_int @ zero_zero_int @ X7 )
& P4 ) ) ) ) ).
% conj_le_cong
thf(fact_1107_exec__appendL,axiom,
! [P: list_instr,I: int,S2: list_char > int,Stk3: list_int,I4: int,S3: list_char > int,Stk2: list_int,P4: list_instr] :
( ( star_P707599355569300323st_int @ ( exec1 @ P ) @ ( produc5086643055186798020st_int @ I @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) @ ( produc5086643055186798020st_int @ I4 @ ( produc8650753666468850689st_int @ S3 @ Stk2 ) ) )
=> ( star_P707599355569300323st_int @ ( exec1 @ ( append_instr @ P4 @ P ) ) @ ( produc5086643055186798020st_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P4 ) ) @ I ) @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) @ ( produc5086643055186798020st_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P4 ) ) @ I4 ) @ ( produc8650753666468850689st_int @ S3 @ Stk2 ) ) ) ) ).
% exec_appendL
thf(fact_1108_execl__all__def,axiom,
( execl_all
= ( ^ [P5: list_instr,Cfs3: list_P419547167332244514st_int] :
( ( execl @ P5 @ Cfs3 )
& ( Cfs3 != nil_Pr749310521696113548st_int )
& ( ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs3 @ zero_zero_nat ) )
= zero_zero_int )
& ~ ( member_int @ ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs3 @ ( minus_minus_nat @ ( size_s229347708945616566st_int @ Cfs3 ) @ one_one_nat ) ) ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P5 ) ) ) ) ) ) ) ).
% execl_all_def
thf(fact_1109_Compiler2_Obcomp__correct,axiom,
! [X: produc1897111610453708512_o_int,Cfs: list_P419547167332244514st_int] :
( ( execl_all @ ( bcomp @ X ) @ Cfs )
=> ( ( ord_less_eq_int @ zero_zero_int @ ( product_snd_o_int @ ( produc7219675232234870470_o_int @ X ) ) )
=> ( bpred @ X @ ( nth_Pr8327173284404383691st_int @ Cfs @ zero_zero_nat ) @ ( nth_Pr8327173284404383691st_int @ Cfs @ ( minus_minus_nat @ ( size_s229347708945616566st_int @ Cfs ) @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% Compiler2.bcomp_correct
thf(fact_1110_ivl__diff,axiom,
! [I: num,N: num,M: num] :
( ( ord_less_eq_num @ I @ N )
=> ( ( minus_minus_set_num @ ( set_or1222409239386451017an_num @ I @ M ) @ ( set_or1222409239386451017an_num @ I @ N ) )
= ( set_or1222409239386451017an_num @ N @ M ) ) ) ).
% ivl_diff
thf(fact_1111_ivl__diff,axiom,
! [I: int,N: int,M: int] :
( ( ord_less_eq_int @ I @ N )
=> ( ( minus_minus_set_int @ ( set_or4662586982721622107an_int @ I @ M ) @ ( set_or4662586982721622107an_int @ I @ N ) )
= ( set_or4662586982721622107an_int @ N @ M ) ) ) ).
% ivl_diff
thf(fact_1112_ivl__diff,axiom,
! [I: nat,N: nat,M: nat] :
( ( ord_less_eq_nat @ I @ N )
=> ( ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ I @ M ) @ ( set_or4665077453230672383an_nat @ I @ N ) )
= ( set_or4665077453230672383an_nat @ N @ M ) ) ) ).
% ivl_diff
thf(fact_1113_ivl__subset,axiom,
! [I: num,J: num,M: num,N: num] :
( ( ord_less_eq_set_num @ ( set_or1222409239386451017an_num @ I @ J ) @ ( set_or1222409239386451017an_num @ M @ N ) )
= ( ( ord_less_eq_num @ J @ I )
| ( ( ord_less_eq_num @ M @ I )
& ( ord_less_eq_num @ J @ N ) ) ) ) ).
% ivl_subset
thf(fact_1114_ivl__subset,axiom,
! [I: int,J: int,M: int,N: int] :
( ( ord_less_eq_set_int @ ( set_or4662586982721622107an_int @ I @ J ) @ ( set_or4662586982721622107an_int @ M @ N ) )
= ( ( ord_less_eq_int @ J @ I )
| ( ( ord_less_eq_int @ M @ I )
& ( ord_less_eq_int @ J @ N ) ) ) ) ).
% ivl_subset
thf(fact_1115_ivl__subset,axiom,
! [I: nat,J: nat,M: nat,N: nat] :
( ( ord_less_eq_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ M @ N ) )
= ( ( ord_less_eq_nat @ J @ I )
| ( ( ord_less_eq_nat @ M @ I )
& ( ord_less_eq_nat @ J @ N ) ) ) ) ).
% ivl_subset
thf(fact_1116_atLeastLessThan__iff,axiom,
! [I: num,L: num,U: num] :
( ( member_num @ I @ ( set_or1222409239386451017an_num @ L @ U ) )
= ( ( ord_less_eq_num @ L @ I )
& ( ord_less_num @ I @ U ) ) ) ).
% atLeastLessThan_iff
thf(fact_1117_atLeastLessThan__iff,axiom,
! [I: int,L: int,U: int] :
( ( member_int @ I @ ( set_or4662586982721622107an_int @ L @ U ) )
= ( ( ord_less_eq_int @ L @ I )
& ( ord_less_int @ I @ U ) ) ) ).
% atLeastLessThan_iff
thf(fact_1118_atLeastLessThan__iff,axiom,
! [I: nat,L: nat,U: nat] :
( ( member_nat @ I @ ( set_or4665077453230672383an_nat @ L @ U ) )
= ( ( ord_less_eq_nat @ L @ I )
& ( ord_less_nat @ I @ U ) ) ) ).
% atLeastLessThan_iff
thf(fact_1119_atLeastLessThan__inj_I2_J,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( set_or4662586982721622107an_int @ A @ B )
= ( set_or4662586982721622107an_int @ C @ D ) )
=> ( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ C @ D )
=> ( B = D ) ) ) ) ).
% atLeastLessThan_inj(2)
thf(fact_1120_atLeastLessThan__inj_I2_J,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( set_or4665077453230672383an_nat @ A @ B )
= ( set_or4665077453230672383an_nat @ C @ D ) )
=> ( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( B = D ) ) ) ) ).
% atLeastLessThan_inj(2)
thf(fact_1121_atLeastLessThan__inj_I1_J,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( set_or4662586982721622107an_int @ A @ B )
= ( set_or4662586982721622107an_int @ C @ D ) )
=> ( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ C @ D )
=> ( A = C ) ) ) ) ).
% atLeastLessThan_inj(1)
thf(fact_1122_atLeastLessThan__inj_I1_J,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( set_or4665077453230672383an_nat @ A @ B )
= ( set_or4665077453230672383an_nat @ C @ D ) )
=> ( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( A = C ) ) ) ) ).
% atLeastLessThan_inj(1)
thf(fact_1123_Ico__eq__Ico,axiom,
! [L: int,H: int,L2: int,H2: int] :
( ( ( set_or4662586982721622107an_int @ L @ H )
= ( set_or4662586982721622107an_int @ L2 @ H2 ) )
= ( ( ( L = L2 )
& ( H = H2 ) )
| ( ~ ( ord_less_int @ L @ H )
& ~ ( ord_less_int @ L2 @ H2 ) ) ) ) ).
% Ico_eq_Ico
thf(fact_1124_Ico__eq__Ico,axiom,
! [L: nat,H: nat,L2: nat,H2: nat] :
( ( ( set_or4665077453230672383an_nat @ L @ H )
= ( set_or4665077453230672383an_nat @ L2 @ H2 ) )
= ( ( ( L = L2 )
& ( H = H2 ) )
| ( ~ ( ord_less_nat @ L @ H )
& ~ ( ord_less_nat @ L2 @ H2 ) ) ) ) ).
% Ico_eq_Ico
thf(fact_1125_atLeastLessThan__eq__iff,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ C @ D )
=> ( ( ( set_or4662586982721622107an_int @ A @ B )
= ( set_or4662586982721622107an_int @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ) ) ) ).
% atLeastLessThan_eq_iff
thf(fact_1126_atLeastLessThan__eq__iff,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( ( ( set_or4665077453230672383an_nat @ A @ B )
= ( set_or4665077453230672383an_nat @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ) ) ) ).
% atLeastLessThan_eq_iff
thf(fact_1127_atLeastLessThan__subset__iff,axiom,
! [A: num,B: num,C: num,D: num] :
( ( ord_less_eq_set_num @ ( set_or1222409239386451017an_num @ A @ B ) @ ( set_or1222409239386451017an_num @ C @ D ) )
=> ( ( ord_less_eq_num @ B @ A )
| ( ( ord_less_eq_num @ C @ A )
& ( ord_less_eq_num @ B @ D ) ) ) ) ).
% atLeastLessThan_subset_iff
thf(fact_1128_atLeastLessThan__subset__iff,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_set_int @ ( set_or4662586982721622107an_int @ A @ B ) @ ( set_or4662586982721622107an_int @ C @ D ) )
=> ( ( ord_less_eq_int @ B @ A )
| ( ( ord_less_eq_int @ C @ A )
& ( ord_less_eq_int @ B @ D ) ) ) ) ).
% atLeastLessThan_subset_iff
thf(fact_1129_atLeastLessThan__subset__iff,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_set_nat @ ( set_or4665077453230672383an_nat @ A @ B ) @ ( set_or4665077453230672383an_nat @ C @ D ) )
=> ( ( ord_less_eq_nat @ B @ A )
| ( ( ord_less_eq_nat @ C @ A )
& ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% atLeastLessThan_subset_iff
thf(fact_1130_execl__last,axiom,
! [P: list_instr,Cfs: list_P419547167332244514st_int,K2: nat] :
( ( execl @ P @ Cfs )
=> ( ( ord_less_nat @ K2 @ ( size_s229347708945616566st_int @ Cfs ) )
=> ( ~ ( member_int @ ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs @ K2 ) ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P ) ) ) )
=> ( ( minus_minus_nat @ ( size_s229347708945616566st_int @ Cfs ) @ one_one_nat )
= K2 ) ) ) ) ).
% execl_last
thf(fact_1131_Compiler_Obcomp__correct,axiom,
! [I: int,B: bexp,F: $o,S2: list_char > int,Stk3: list_int] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( star_P707599355569300323st_int @ ( exec1 @ ( bcomp @ ( produc4047900504771817624_o_int @ B @ ( product_Pair_o_int @ F @ I ) ) ) ) @ ( produc5086643055186798020st_int @ zero_zero_int @ ( produc8650753666468850689st_int @ S2 @ Stk3 ) )
@ ( produc5086643055186798020st_int
@ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ ( bcomp @ ( produc4047900504771817624_o_int @ B @ ( product_Pair_o_int @ F @ I ) ) ) ) )
@ ( if_int
@ ( F
= ( bval @ B @ S2 ) )
@ I
@ zero_zero_int ) )
@ ( produc8650753666468850689st_int @ S2 @ Stk3 ) ) ) ) ).
% Compiler.bcomp_correct
thf(fact_1132_to__m__state_Osimps,axiom,
( to_m_state
= ( ^ [Xs3: list_list_char,S4: list_char > int,A3: int] :
( if_int
@ ( ( ord_less_int @ zero_zero_int @ A3 )
& ( ord_less_eq_int @ A3 @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs3 ) ) ) )
@ ( S4 @ ( inth_list_char @ Xs3 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs3 ) ) @ A3 ) ) )
@ zero_zero_int ) ) ) ).
% to_m_state.simps
thf(fact_1133_to__m__state_Oelims,axiom,
! [X: list_list_char,Xa: list_char > int,Xb: int,Y: int] :
( ( ( to_m_state @ X @ Xa @ Xb )
= Y )
=> ( ( ( ( ord_less_int @ zero_zero_int @ Xb )
& ( ord_less_eq_int @ Xb @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ X ) ) ) )
=> ( Y
= ( Xa @ ( inth_list_char @ X @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ X ) ) @ Xb ) ) ) ) )
& ( ~ ( ( ord_less_int @ zero_zero_int @ Xb )
& ( ord_less_eq_int @ Xb @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ X ) ) ) )
=> ( Y = zero_zero_int ) ) ) ) ).
% to_m_state.elims
thf(fact_1134_ex__nat__less__eq,axiom,
! [N: nat,P: nat > $o] :
( ( ? [M3: nat] :
( ( ord_less_nat @ M3 @ N )
& ( P @ M3 ) ) )
= ( ? [X2: nat] :
( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
& ( P @ X2 ) ) ) ) ).
% ex_nat_less_eq
thf(fact_1135_all__nat__less__eq,axiom,
! [N: nat,P: nat > $o] :
( ( ! [M3: nat] :
( ( ord_less_nat @ M3 @ N )
=> ( P @ M3 ) ) )
= ( ! [X2: nat] :
( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
=> ( P @ X2 ) ) ) ) ).
% all_nat_less_eq
thf(fact_1136_mpred__drop,axiom,
! [K2: nat,Cfs: list_P419547167332244514st_int,P: list_instr,M: nat,N: nat] :
( ( ord_less_eq_nat @ K2 @ ( size_s229347708945616566st_int @ Cfs ) )
=> ( ( ord_less_eq_nat @ ( size_size_list_int @ ( produc6244060863719409455st_int @ ( produc1296517004818028822st_int @ ( nth_Pr8327173284404383691st_int @ Cfs @ zero_zero_nat ) ) ) ) @ ( size_size_list_int @ ( produc6244060863719409455st_int @ ( produc1296517004818028822st_int @ ( nth_Pr8327173284404383691st_int @ Cfs @ K2 ) ) ) ) )
=> ( ( mpred @ P @ ( drop_P7838799151754935884st_int @ K2 @ Cfs ) @ M @ N )
=> ( mpred @ P @ Cfs @ ( plus_plus_nat @ K2 @ M ) @ ( plus_plus_nat @ K2 @ N ) ) ) ) ) ).
% mpred_drop
thf(fact_1137_DiffI,axiom,
! [C: int,A2: set_int,B3: set_int] :
( ( member_int @ C @ A2 )
=> ( ~ ( member_int @ C @ B3 )
=> ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ) ).
% DiffI
thf(fact_1138_DiffI,axiom,
! [C: list_char,A2: set_list_char,B3: set_list_char] :
( ( member_list_char @ C @ A2 )
=> ( ~ ( member_list_char @ C @ B3 )
=> ( member_list_char @ C @ ( minus_269717477326218608t_char @ A2 @ B3 ) ) ) ) ).
% DiffI
thf(fact_1139_Diff__iff,axiom,
! [C: int,A2: set_int,B3: set_int] :
( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
= ( ( member_int @ C @ A2 )
& ~ ( member_int @ C @ B3 ) ) ) ).
% Diff_iff
thf(fact_1140_Diff__iff,axiom,
! [C: list_char,A2: set_list_char,B3: set_list_char] :
( ( member_list_char @ C @ ( minus_269717477326218608t_char @ A2 @ B3 ) )
= ( ( member_list_char @ C @ A2 )
& ~ ( member_list_char @ C @ B3 ) ) ) ).
% Diff_iff
thf(fact_1141_drop0,axiom,
( ( drop_P7838799151754935884st_int @ zero_zero_nat )
= ( ^ [X2: list_P419547167332244514st_int] : X2 ) ) ).
% drop0
thf(fact_1142_drop__drop,axiom,
! [N: nat,M: nat,Xs: list_P419547167332244514st_int] :
( ( drop_P7838799151754935884st_int @ N @ ( drop_P7838799151754935884st_int @ M @ Xs ) )
= ( drop_P7838799151754935884st_int @ ( plus_plus_nat @ N @ M ) @ Xs ) ) ).
% drop_drop
thf(fact_1143_drop__Suc__Cons,axiom,
! [N: nat,X: int,Xs: list_int] :
( ( drop_int @ ( suc @ N ) @ ( cons_int @ X @ Xs ) )
= ( drop_int @ N @ Xs ) ) ).
% drop_Suc_Cons
thf(fact_1144_drop__Suc__Cons,axiom,
! [N: nat,X: instr,Xs: list_instr] :
( ( drop_instr @ ( suc @ N ) @ ( cons_instr @ X @ Xs ) )
= ( drop_instr @ N @ Xs ) ) ).
% drop_Suc_Cons
thf(fact_1145_drop__Suc__Cons,axiom,
! [N: nat,X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int] :
( ( drop_P7838799151754935884st_int @ ( suc @ N ) @ ( cons_P4151473878978182108st_int @ X @ Xs ) )
= ( drop_P7838799151754935884st_int @ N @ Xs ) ) ).
% drop_Suc_Cons
thf(fact_1146_drop__Suc__Cons,axiom,
! [N: nat,X: list_char,Xs: list_list_char] :
( ( drop_list_char @ ( suc @ N ) @ ( cons_list_char @ X @ Xs ) )
= ( drop_list_char @ N @ Xs ) ) ).
% drop_Suc_Cons
thf(fact_1147_length__drop,axiom,
! [N: nat,Xs: list_P419547167332244514st_int] :
( ( size_s229347708945616566st_int @ ( drop_P7838799151754935884st_int @ N @ Xs ) )
= ( minus_minus_nat @ ( size_s229347708945616566st_int @ Xs ) @ N ) ) ).
% length_drop
thf(fact_1148_length__drop,axiom,
! [N: nat,Xs: list_int] :
( ( size_size_list_int @ ( drop_int @ N @ Xs ) )
= ( minus_minus_nat @ ( size_size_list_int @ Xs ) @ N ) ) ).
% length_drop
thf(fact_1149_drop__eq__Nil2,axiom,
! [N: nat,Xs: list_instr] :
( ( nil_instr
= ( drop_instr @ N @ Xs ) )
= ( ord_less_eq_nat @ ( size_size_list_instr @ Xs ) @ N ) ) ).
% drop_eq_Nil2
thf(fact_1150_drop__eq__Nil2,axiom,
! [N: nat,Xs: list_P419547167332244514st_int] :
( ( nil_Pr749310521696113548st_int
= ( drop_P7838799151754935884st_int @ N @ Xs ) )
= ( ord_less_eq_nat @ ( size_s229347708945616566st_int @ Xs ) @ N ) ) ).
% drop_eq_Nil2
thf(fact_1151_drop__eq__Nil2,axiom,
! [N: nat,Xs: list_list_char] :
( ( nil_list_char
= ( drop_list_char @ N @ Xs ) )
= ( ord_less_eq_nat @ ( size_s356637359517785349t_char @ Xs ) @ N ) ) ).
% drop_eq_Nil2
thf(fact_1152_drop__eq__Nil2,axiom,
! [N: nat,Xs: list_int] :
( ( nil_int
= ( drop_int @ N @ Xs ) )
= ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ).
% drop_eq_Nil2
thf(fact_1153_drop__eq__Nil,axiom,
! [N: nat,Xs: list_list_char] :
( ( ( drop_list_char @ N @ Xs )
= nil_list_char )
= ( ord_less_eq_nat @ ( size_s356637359517785349t_char @ Xs ) @ N ) ) ).
% drop_eq_Nil
thf(fact_1154_drop__eq__Nil,axiom,
! [N: nat,Xs: list_int] :
( ( ( drop_int @ N @ Xs )
= nil_int )
= ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ).
% drop_eq_Nil
thf(fact_1155_execl__drop,axiom,
! [P: list_instr,Cfs: list_P419547167332244514st_int,N: nat] :
( ( execl @ P @ Cfs )
=> ( execl @ P @ ( drop_P7838799151754935884st_int @ N @ Cfs ) ) ) ).
% execl_drop
thf(fact_1156_to__m__state_Opelims,axiom,
! [X: list_list_char,Xa: list_char > int,Xb: int,Y: int] :
( ( ( to_m_state @ X @ Xa @ Xb )
= Y )
=> ( ( accp_P4562858270263085236nt_int @ to_m_state_rel @ ( produc3965054194175396271nt_int @ X @ ( produc5790713362662368625nt_int @ Xa @ Xb ) ) )
=> ~ ( ( ( ( ( ord_less_int @ zero_zero_int @ Xb )
& ( ord_less_eq_int @ Xb @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ X ) ) ) )
=> ( Y
= ( Xa @ ( inth_list_char @ X @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ X ) ) @ Xb ) ) ) ) )
& ( ~ ( ( ord_less_int @ zero_zero_int @ Xb )
& ( ord_less_eq_int @ Xb @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ X ) ) ) )
=> ( Y = zero_zero_int ) ) )
=> ~ ( accp_P4562858270263085236nt_int @ to_m_state_rel @ ( produc3965054194175396271nt_int @ X @ ( produc5790713362662368625nt_int @ Xa @ Xb ) ) ) ) ) ) ).
% to_m_state.pelims
thf(fact_1157_nat0__intermed__int__val,axiom,
! [N: nat,F: nat > int,K2: int] :
( ! [I3: nat] :
( ( ord_less_nat @ I3 @ N )
=> ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
=> ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K2 )
=> ( ( ord_less_eq_int @ K2 @ ( F @ N ) )
=> ? [I3: nat] :
( ( ord_less_eq_nat @ I3 @ N )
& ( ( F @ I3 )
= K2 ) ) ) ) ) ).
% nat0_intermed_int_val
thf(fact_1158_zabs__less__one__iff,axiom,
! [Z: int] :
( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
= ( Z = zero_zero_int ) ) ).
% zabs_less_one_iff
thf(fact_1159_to__m__state_Ocases,axiom,
! [X: produc4189061985984568957nt_int] :
~ ! [Xs2: list_list_char,S: list_char > int,A5: int] :
( X
!= ( produc3965054194175396271nt_int @ Xs2 @ ( produc5790713362662368625nt_int @ S @ A5 ) ) ) ).
% to_m_state.cases
thf(fact_1160_nat__intermed__int__val,axiom,
! [M: nat,N: nat,F: nat > int,K2: int] :
( ! [I3: nat] :
( ( ( ord_less_eq_nat @ M @ I3 )
& ( ord_less_nat @ I3 @ N ) )
=> ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
=> ( ( ord_less_eq_nat @ M @ N )
=> ( ( ord_less_eq_int @ ( F @ M ) @ K2 )
=> ( ( ord_less_eq_int @ K2 @ ( F @ N ) )
=> ? [I3: nat] :
( ( ord_less_eq_nat @ M @ I3 )
& ( ord_less_eq_nat @ I3 @ N )
& ( ( F @ I3 )
= K2 ) ) ) ) ) ) ).
% nat_intermed_int_val
thf(fact_1161_nat__ivt__aux,axiom,
! [N: nat,F: nat > int,K2: int] :
( ! [I3: nat] :
( ( ord_less_nat @ I3 @ N )
=> ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
=> ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K2 )
=> ( ( ord_less_eq_int @ K2 @ ( F @ N ) )
=> ? [I3: nat] :
( ( ord_less_eq_nat @ I3 @ N )
& ( ( F @ I3 )
= K2 ) ) ) ) ) ).
% nat_ivt_aux
thf(fact_1162_nat__descend__induct,axiom,
! [N: nat,P: nat > $o,M: nat] :
( ! [K: nat] :
( ( ord_less_nat @ N @ K )
=> ( P @ K ) )
=> ( ! [K: nat] :
( ( ord_less_eq_nat @ K @ N )
=> ( ! [I5: nat] :
( ( ord_less_nat @ K @ I5 )
=> ( P @ I5 ) )
=> ( P @ K ) ) )
=> ( P @ M ) ) ) ).
% nat_descend_induct
thf(fact_1163_execl__all__SKIP,axiom,
! [Cfs: list_P419547167332244514st_int] :
( ( execl_all @ nil_instr @ Cfs )
=> ( ( cpred @ skip @ ( nth_Pr8327173284404383691st_int @ Cfs @ zero_zero_nat ) @ ( nth_Pr8327173284404383691st_int @ Cfs @ ( minus_minus_nat @ ( size_s229347708945616566st_int @ Cfs ) @ ( suc @ zero_zero_nat ) ) ) )
& ( ( size_s229347708945616566st_int @ Cfs )
= ( suc @ zero_zero_nat ) ) ) ) ).
% execl_all_SKIP
thf(fact_1164_bcomp_Osimps_I1_J,axiom,
! [V: $o,F: $o,I: int] :
( ( ( V = F )
=> ( ( bcomp @ ( produc4047900504771817624_o_int @ ( bc @ V ) @ ( product_Pair_o_int @ F @ I ) ) )
= ( cons_instr @ ( jmp @ I ) @ nil_instr ) ) )
& ( ( V = ~ F )
=> ( ( bcomp @ ( produc4047900504771817624_o_int @ ( bc @ V ) @ ( product_Pair_o_int @ F @ I ) ) )
= nil_instr ) ) ) ).
% bcomp.simps(1)
thf(fact_1165_com_Osize_I6_J,axiom,
( ( size_size_com @ skip )
= zero_zero_nat ) ).
% com.size(6)
thf(fact_1166_bexp_Osize_I5_J,axiom,
! [X1: $o] :
( ( size_size_bexp @ ( bc @ X1 ) )
= zero_zero_nat ) ).
% bexp.size(5)
thf(fact_1167_vars__store,axiom,
! [I: int,P: list_instr,X: list_char] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P ) ) )
=> ( ( ( inth_instr @ P @ I )
= ( store @ X ) )
=> ( member_list_char @ X @ ( set_list_char2 @ ( vars @ P ) ) ) ) ) ) ).
% vars_store
thf(fact_1168_vars__load,axiom,
! [I: int,P: list_instr,X: list_char] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P ) ) )
=> ( ( ( inth_instr @ P @ I )
= ( load @ X ) )
=> ( member_list_char @ X @ ( set_list_char2 @ ( vars @ P ) ) ) ) ) ) ).
% vars_load
thf(fact_1169_vars_Osimps_I1_J,axiom,
( ( vars @ nil_instr )
= nil_list_char ) ).
% vars.simps(1)
thf(fact_1170_addr__of__correct,axiom,
! [X: list_char,Xs: list_list_char] :
( ( member_list_char @ X @ ( set_list_char2 @ Xs ) )
=> ( ( inth_list_char @ Xs @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs ) ) @ ( addr_of @ Xs @ X ) ) )
= X ) ) ).
% addr_of_correct
thf(fact_1171_addr__of__neq2,axiom,
! [X: list_char,Xs: list_list_char,X7: list_char] :
( ( member_list_char @ X @ ( set_list_char2 @ Xs ) )
=> ( ( X7 != X )
=> ( ( addr_of @ Xs @ X7 )
!= ( addr_of @ Xs @ X ) ) ) ) ).
% addr_of_neq2
thf(fact_1172_addr__of_Osimps_I1_J,axiom,
! [Uu: list_char] :
( ( addr_of @ nil_list_char @ Uu )
= zero_zero_int ) ).
% addr_of.simps(1)
thf(fact_1173_addr__of__nneg,axiom,
! [Xs: list_list_char,X: list_char] : ( ord_less_eq_int @ zero_zero_int @ ( addr_of @ Xs @ X ) ) ).
% addr_of_nneg
thf(fact_1174_addr__of__nset,axiom,
! [X: list_char,Xs: list_list_char] :
( ~ ( member_list_char @ X @ ( set_list_char2 @ Xs ) )
=> ( ( addr_of @ Xs @ X )
= zero_zero_int ) ) ).
% addr_of_nset
thf(fact_1175_addr__of__max,axiom,
! [Xs: list_list_char,X: list_char] : ( ord_less_eq_int @ ( addr_of @ Xs @ X ) @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs ) ) ) ).
% addr_of_max
thf(fact_1176_addr__of__set,axiom,
! [X: list_char,Xs: list_list_char] :
( ( member_list_char @ X @ ( set_list_char2 @ Xs ) )
=> ( ord_less_int @ zero_zero_int @ ( addr_of @ Xs @ X ) ) ) ).
% addr_of_set
thf(fact_1177_addr__of__neq,axiom,
! [Xs: list_list_char,X: list_char] :
( ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs ) ) )
!= ( addr_of @ Xs @ X ) ) ).
% addr_of_neq
thf(fact_1178_addr__of_Osimps_I2_J,axiom,
! [X: list_char,Y: list_char,Xs: list_list_char] :
( ( ( X = Y )
=> ( ( addr_of @ ( cons_list_char @ X @ Xs ) @ Y )
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs ) ) @ one_one_int ) ) )
& ( ( X != Y )
=> ( ( addr_of @ ( cons_list_char @ X @ Xs ) @ Y )
= ( addr_of @ Xs @ Y ) ) ) ) ).
% addr_of.simps(2)
thf(fact_1179_to__state__upd,axiom,
! [Xs: list_list_char,X: list_char,Ms2: int > int,I: int,Ms: int > int] :
( ! [A5: int] :
( ( ord_less_eq_int @ zero_zero_int @ A5 )
=> ( ( ( A5
= ( addr_of @ Xs @ X ) )
=> ( ( Ms2 @ A5 )
= I ) )
& ( ( A5
!= ( addr_of @ Xs @ X ) )
=> ( ( Ms2 @ A5 )
= ( Ms @ A5 ) ) ) ) )
=> ( ( member_list_char @ X @ ( set_list_char2 @ Xs ) )
=> ( ( to_state @ Xs @ Ms2 )
= ( fun_up8169409267500384524ar_int @ ( to_state @ Xs @ Ms ) @ X @ I ) ) ) ) ).
% to_state_upd
thf(fact_1180_addr__of__unique,axiom,
! [Xs: list_list_char,A: int] :
( ( distinct_list_char @ Xs )
=> ( ( ord_less_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ A @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs ) ) )
=> ( ( addr_of @ Xs @ ( inth_list_char @ Xs @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs ) ) @ A ) ) )
= A ) ) ) ) ).
% addr_of_unique
thf(fact_1181_to__state_Osimps,axiom,
( to_state
= ( ^ [Xs3: list_list_char,Ms3: int > int,X2: list_char] : ( Ms3 @ ( addr_of @ Xs3 @ X2 ) ) ) ) ).
% to_state.simps
thf(fact_1182_to__state_Oelims,axiom,
! [X: list_list_char,Xa: int > int,Xb: list_char,Y: int] :
( ( ( to_state @ X @ Xa @ Xb )
= Y )
=> ( Y
= ( Xa @ ( addr_of @ X @ Xb ) ) ) ) ).
% to_state.elims
thf(fact_1183_vars__dist,axiom,
! [P: list_instr] : ( distinct_list_char @ ( vars @ P ) ) ).
% vars_dist
thf(fact_1184_to__state__eq,axiom,
! [Ms2: int > int,Ms: int > int,Xs: list_list_char] :
( ! [A5: int] :
( ( ord_less_eq_int @ zero_zero_int @ A5 )
=> ( ( Ms2 @ A5 )
= ( Ms @ A5 ) ) )
=> ( ( to_state @ Xs @ Ms2 )
= ( to_state @ Xs @ Ms ) ) ) ).
% to_state_eq
thf(fact_1185_execl__all__Bc,axiom,
! [V: $o,F: $o,I: int,Cfs: list_P419547167332244514st_int] :
( ( execl_all @ ( if_list_instr @ ( V = F ) @ ( cons_instr @ ( jmp @ I ) @ nil_instr ) @ nil_instr ) @ Cfs )
=> ( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( bpred @ ( produc4047900504771817624_o_int @ ( bc @ V ) @ ( product_Pair_o_int @ F @ I ) ) @ ( nth_Pr8327173284404383691st_int @ Cfs @ zero_zero_nat ) @ ( nth_Pr8327173284404383691st_int @ Cfs @ ( minus_minus_nat @ ( size_s229347708945616566st_int @ Cfs ) @ ( suc @ zero_zero_nat ) ) ) )
& ( ( V = F )
=> ( ( size_s229347708945616566st_int @ Cfs )
= ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
& ( ( V = ~ F )
=> ( ( size_s229347708945616566st_int @ Cfs )
= one_one_nat ) )
& ( ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs @ zero_zero_nat ) )
= zero_zero_int ) ) ) ) ).
% execl_all_Bc
thf(fact_1186_verit__eq__simplify_I8_J,axiom,
! [X22: num,Y22: num] :
( ( ( bit0 @ X22 )
= ( bit0 @ Y22 ) )
= ( X22 = Y22 ) ) ).
% verit_eq_simplify(8)
thf(fact_1187_Suc__numeral,axiom,
! [N: num] :
( ( suc @ ( numeral_numeral_nat @ N ) )
= ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% Suc_numeral
thf(fact_1188_add__2__eq__Suc,axiom,
! [N: nat] :
( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
= ( suc @ ( suc @ N ) ) ) ).
% add_2_eq_Suc
thf(fact_1189_add__2__eq__Suc_H,axiom,
! [N: nat] :
( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= ( suc @ ( suc @ N ) ) ) ).
% add_2_eq_Suc'
thf(fact_1190_Suc__1,axiom,
( ( suc @ one_one_nat )
= ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% Suc_1
thf(fact_1191_less__2__cases,axiom,
! [N: nat] :
( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
=> ( ( N = zero_zero_nat )
| ( N
= ( suc @ zero_zero_nat ) ) ) ) ).
% less_2_cases
thf(fact_1192_less__2__cases__iff,axiom,
! [N: nat] :
( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= ( ( N = zero_zero_nat )
| ( N
= ( suc @ zero_zero_nat ) ) ) ) ).
% less_2_cases_iff
thf(fact_1193_le__num__One__iff,axiom,
! [X: num] :
( ( ord_less_eq_num @ X @ one )
= ( X = one ) ) ).
% le_num_One_iff
thf(fact_1194_numeral__1__eq__Suc__0,axiom,
( ( numeral_numeral_nat @ one )
= ( suc @ zero_zero_nat ) ) ).
% numeral_1_eq_Suc_0
thf(fact_1195_Suc__nat__number__of__add,axiom,
! [V: num,N: nat] :
( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
= ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% Suc_nat_number_of_add
thf(fact_1196_verit__eq__simplify_I10_J,axiom,
! [X22: num] :
( one
!= ( bit0 @ X22 ) ) ).
% verit_eq_simplify(10)
thf(fact_1197_numerals_I1_J,axiom,
( ( numeral_numeral_nat @ one )
= one_one_nat ) ).
% numerals(1)
thf(fact_1198_add__One__commute,axiom,
! [N: num] :
( ( plus_plus_num @ one @ N )
= ( plus_plus_num @ N @ one ) ) ).
% add_One_commute
thf(fact_1199_nat__1__add__1,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% nat_1_add_1
thf(fact_1200_numeral__2__eq__2,axiom,
( ( numeral_numeral_nat @ ( bit0 @ one ) )
= ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% numeral_2_eq_2
thf(fact_1201_num_Osize_I4_J,axiom,
( ( size_size_num @ one )
= zero_zero_nat ) ).
% num.size(4)
thf(fact_1202_num_Osize_I5_J,axiom,
! [X22: num] :
( ( size_size_num @ ( bit0 @ X22 ) )
= ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% num.size(5)
thf(fact_1203_nat__induct2,axiom,
! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ( P @ one_one_nat )
=> ( ! [N3: nat] :
( ( P @ N3 )
=> ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
=> ( P @ N ) ) ) ) ).
% nat_induct2
thf(fact_1204_execl__all__N,axiom,
! [I: int,Cfs: list_P419547167332244514st_int] :
( ( execl_all @ ( cons_instr @ ( loadi @ I ) @ nil_instr ) @ Cfs )
=> ( ( apred @ ( n @ I ) @ ( nth_Pr8327173284404383691st_int @ Cfs @ zero_zero_nat ) @ ( nth_Pr8327173284404383691st_int @ Cfs @ ( minus_minus_nat @ ( size_s229347708945616566st_int @ Cfs ) @ ( suc @ zero_zero_nat ) ) ) )
& ( ( size_s229347708945616566st_int @ Cfs )
= ( numeral_numeral_nat @ ( bit0 @ one ) ) )
& ( ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs @ zero_zero_nat ) )
= zero_zero_int ) ) ) ).
% execl_all_N
thf(fact_1205_int__eq__iff__numeral,axiom,
! [M: nat,V: num] :
( ( ( semiri1314217659103216013at_int @ M )
= ( numeral_numeral_int @ V ) )
= ( M
= ( numeral_numeral_nat @ V ) ) ) ).
% int_eq_iff_numeral
thf(fact_1206_int__ops_I3_J,axiom,
! [N: num] :
( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
= ( numeral_numeral_int @ N ) ) ).
% int_ops(3)
thf(fact_1207_acomp_Osimps_I1_J,axiom,
! [I: int] :
( ( acomp @ ( n @ I ) )
= ( cons_instr @ ( loadi @ I ) @ nil_instr ) ) ).
% acomp.simps(1)
thf(fact_1208_execl__all__V,axiom,
! [X: list_char,Cfs: list_P419547167332244514st_int] :
( ( execl_all @ ( cons_instr @ ( load @ X ) @ nil_instr ) @ Cfs )
=> ( ( apred @ ( v @ X ) @ ( nth_Pr8327173284404383691st_int @ Cfs @ zero_zero_nat ) @ ( nth_Pr8327173284404383691st_int @ Cfs @ ( minus_minus_nat @ ( size_s229347708945616566st_int @ Cfs ) @ ( suc @ zero_zero_nat ) ) ) )
& ( ( size_s229347708945616566st_int @ Cfs )
= ( numeral_numeral_nat @ ( bit0 @ one ) ) )
& ( ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs @ zero_zero_nat ) )
= zero_zero_int ) ) ) ).
% execl_all_V
thf(fact_1209_acomp_Osimps_I2_J,axiom,
! [X: list_char] :
( ( acomp @ ( v @ X ) )
= ( cons_instr @ ( load @ X ) @ nil_instr ) ) ).
% acomp.simps(2)
thf(fact_1210_num_Osize__gen_I2_J,axiom,
! [X22: num] :
( ( size_num @ ( bit0 @ X22 ) )
= ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% num.size_gen(2)
thf(fact_1211_num_Osize__gen_I1_J,axiom,
( ( size_num @ one )
= zero_zero_nat ) ).
% num.size_gen(1)
thf(fact_1212_divmod__BitM__2__eq,axiom,
! [M: num] :
( ( unique5403075989570733136od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
= ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% divmod_BitM_2_eq
thf(fact_1213_eval__nat__numeral_I2_J,axiom,
! [N: num] :
( ( numeral_numeral_nat @ ( bit0 @ N ) )
= ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% eval_nat_numeral(2)
thf(fact_1214_BitM__plus__one,axiom,
! [N: num] :
( ( plus_plus_num @ ( bitM @ N ) @ one )
= ( bit0 @ N ) ) ).
% BitM_plus_one
thf(fact_1215_one__plus__BitM,axiom,
! [N: num] :
( ( plus_plus_num @ one @ ( bitM @ N ) )
= ( bit0 @ N ) ) ).
% one_plus_BitM
thf(fact_1216_verit__eq__simplify_I9_J,axiom,
! [X32: num,Y32: num] :
( ( ( bit1 @ X32 )
= ( bit1 @ Y32 ) )
= ( X32 = Y32 ) ) ).
% verit_eq_simplify(9)
thf(fact_1217_num_Oexhaust,axiom,
! [Y: num] :
( ( Y != one )
=> ( ! [X23: num] :
( Y
!= ( bit0 @ X23 ) )
=> ~ ! [X33: num] :
( Y
!= ( bit1 @ X33 ) ) ) ) ).
% num.exhaust
thf(fact_1218_verit__eq__simplify_I14_J,axiom,
! [X22: num,X32: num] :
( ( bit0 @ X22 )
!= ( bit1 @ X32 ) ) ).
% verit_eq_simplify(14)
thf(fact_1219_verit__eq__simplify_I12_J,axiom,
! [X32: num] :
( one
!= ( bit1 @ X32 ) ) ).
% verit_eq_simplify(12)
thf(fact_1220_eval__nat__numeral_I3_J,axiom,
! [N: num] :
( ( numeral_numeral_nat @ ( bit1 @ N ) )
= ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% eval_nat_numeral(3)
thf(fact_1221_numeral__3__eq__3,axiom,
( ( numeral_numeral_nat @ ( bit1 @ one ) )
= ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% numeral_3_eq_3
thf(fact_1222_Suc3__eq__add__3,axiom,
! [N: nat] :
( ( suc @ ( suc @ ( suc @ N ) ) )
= ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% Suc3_eq_add_3
thf(fact_1223_num_Osize__gen_I3_J,axiom,
! [X32: num] :
( ( size_num @ ( bit1 @ X32 ) )
= ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% num.size_gen(3)
thf(fact_1224_num_Osize_I6_J,axiom,
! [X32: num] :
( ( size_size_num @ ( bit1 @ X32 ) )
= ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% num.size(6)
thf(fact_1225_xor__num_Ocases,axiom,
! [X: product_prod_num_num] :
( ( X
!= ( product_Pair_num_num @ one @ one ) )
=> ( ! [N3: num] :
( X
!= ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
=> ( ! [N3: num] :
( X
!= ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
=> ( ! [M4: num] :
( X
!= ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) )
=> ( ! [M4: num,N3: num] :
( X
!= ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) )
=> ( ! [M4: num,N3: num] :
( X
!= ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) )
=> ( ! [M4: num] :
( X
!= ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) )
=> ( ! [M4: num,N3: num] :
( X
!= ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) )
=> ~ ! [M4: num,N3: num] :
( X
!= ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% xor_num.cases
thf(fact_1226_aval_Osimps_I1_J,axiom,
! [N: int,S2: list_char > int] :
( ( aval @ ( n @ N ) @ S2 )
= N ) ).
% aval.simps(1)
thf(fact_1227_aexp_Osize_I5_J,axiom,
! [X22: list_char] :
( ( size_size_aexp @ ( v @ X22 ) )
= zero_zero_nat ) ).
% aexp.size(5)
thf(fact_1228_aexp_Osize_I4_J,axiom,
! [X1: int] :
( ( size_size_aexp @ ( n @ X1 ) )
= zero_zero_nat ) ).
% aexp.size(4)
thf(fact_1229_aval_Osimps_I2_J,axiom,
! [X: list_char,S2: list_char > int] :
( ( aval @ ( v @ X ) @ S2 )
= ( S2 @ X ) ) ).
% aval.simps(2)
thf(fact_1230_Parity_Oadjust__mod__def,axiom,
( adjust_mod
= ( ^ [L3: num,R3: int] : ( if_int @ ( R3 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ ( numeral_numeral_int @ L3 ) @ R3 ) ) ) ) ).
% Parity.adjust_mod_def
thf(fact_1231_even__diff__nat,axiom,
! [M: nat,N: nat] :
( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
= ( ( ord_less_nat @ M @ N )
| ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% even_diff_nat
thf(fact_1232_odd__Suc__minus__one,axiom,
! [N: nat] :
( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
=> ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
= N ) ) ).
% odd_Suc_minus_one
thf(fact_1233_nat__dvd__1__iff__1,axiom,
! [M: nat] :
( ( dvd_dvd_nat @ M @ one_one_nat )
= ( M = one_one_nat ) ) ).
% nat_dvd_1_iff_1
thf(fact_1234_dvd__1__left,axiom,
! [K2: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K2 ) ).
% dvd_1_left
thf(fact_1235_dvd__1__iff__1,axiom,
! [M: nat] :
( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
= ( M
= ( suc @ zero_zero_nat ) ) ) ).
% dvd_1_iff_1
thf(fact_1236_even__Suc__Suc__iff,axiom,
! [N: nat] :
( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
= ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% even_Suc_Suc_iff
thf(fact_1237_even__Suc,axiom,
! [N: nat] :
( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
= ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% even_Suc
thf(fact_1238_gcd__nat_Oasym,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
=> ~ ( ( dvd_dvd_nat @ B @ A )
& ( B != A ) ) ) ).
% gcd_nat.asym
thf(fact_1239_gcd__nat_Orefl,axiom,
! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% gcd_nat.refl
thf(fact_1240_gcd__nat_Otrans,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ A @ C ) ) ) ).
% gcd_nat.trans
thf(fact_1241_gcd__nat_Oeq__iff,axiom,
( ( ^ [Y4: nat,Z3: nat] : ( Y4 = Z3 ) )
= ( ^ [A3: nat,B2: nat] :
( ( dvd_dvd_nat @ A3 @ B2 )
& ( dvd_dvd_nat @ B2 @ A3 ) ) ) ) ).
% gcd_nat.eq_iff
thf(fact_1242_gcd__nat_Oirrefl,axiom,
! [A: nat] :
~ ( ( dvd_dvd_nat @ A @ A )
& ( A != A ) ) ).
% gcd_nat.irrefl
thf(fact_1243_gcd__nat_Oantisym,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ B @ A )
=> ( A = B ) ) ) ).
% gcd_nat.antisym
thf(fact_1244_gcd__nat_Ostrict__trans,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
=> ( ( ( dvd_dvd_nat @ B @ C )
& ( B != C ) )
=> ( ( dvd_dvd_nat @ A @ C )
& ( A != C ) ) ) ) ).
% gcd_nat.strict_trans
thf(fact_1245_gcd__nat_Ostrict__trans1,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( ( dvd_dvd_nat @ B @ C )
& ( B != C ) )
=> ( ( dvd_dvd_nat @ A @ C )
& ( A != C ) ) ) ) ).
% gcd_nat.strict_trans1
thf(fact_1246_gcd__nat_Ostrict__trans2,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
=> ( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ A @ C )
& ( A != C ) ) ) ) ).
% gcd_nat.strict_trans2
thf(fact_1247_gcd__nat_Ostrict__iff__not,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
= ( ( dvd_dvd_nat @ A @ B )
& ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% gcd_nat.strict_iff_not
thf(fact_1248_gcd__nat_Oorder__iff__strict,axiom,
( dvd_dvd_nat
= ( ^ [A3: nat,B2: nat] :
( ( ( dvd_dvd_nat @ A3 @ B2 )
& ( A3 != B2 ) )
| ( A3 = B2 ) ) ) ) ).
% gcd_nat.order_iff_strict
thf(fact_1249_gcd__nat_Ostrict__iff__order,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
= ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) ) ) ).
% gcd_nat.strict_iff_order
thf(fact_1250_gcd__nat_Ostrict__implies__order,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
=> ( dvd_dvd_nat @ A @ B ) ) ).
% gcd_nat.strict_implies_order
thf(fact_1251_gcd__nat_Ostrict__implies__not__eq,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
=> ( A != B ) ) ).
% gcd_nat.strict_implies_not_eq
thf(fact_1252_gcd__nat_Onot__eq__order__implies__strict,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) ) ) ) ).
% gcd_nat.not_eq_order_implies_strict
thf(fact_1253_dvd__antisym,axiom,
! [M: nat,N: nat] :
( ( dvd_dvd_nat @ M @ N )
=> ( ( dvd_dvd_nat @ N @ M )
=> ( M = N ) ) ) ).
% dvd_antisym
thf(fact_1254_gcd__nat_Oextremum__uniqueI,axiom,
! [A: nat] :
( ( dvd_dvd_nat @ zero_zero_nat @ A )
=> ( A = zero_zero_nat ) ) ).
% gcd_nat.extremum_uniqueI
thf(fact_1255_gcd__nat_Onot__eq__extremum,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ( dvd_dvd_nat @ A @ zero_zero_nat )
& ( A != zero_zero_nat ) ) ) ).
% gcd_nat.not_eq_extremum
thf(fact_1256_gcd__nat_Oextremum__unique,axiom,
! [A: nat] :
( ( dvd_dvd_nat @ zero_zero_nat @ A )
= ( A = zero_zero_nat ) ) ).
% gcd_nat.extremum_unique
thf(fact_1257_gcd__nat_Oextremum__strict,axiom,
! [A: nat] :
~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
& ( zero_zero_nat != A ) ) ).
% gcd_nat.extremum_strict
thf(fact_1258_gcd__nat_Oextremum,axiom,
! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% gcd_nat.extremum
% Helper facts (9)
thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
! [X: int,Y: int] :
( ( if_int @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
! [X: int,Y: int] :
( ( if_int @ $true @ X @ Y )
= X ) ).
thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
! [X: nat,Y: nat] :
( ( if_nat @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
! [X: nat,Y: nat] :
( ( if_nat @ $true @ X @ Y )
= X ) ).
thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
! [X: list_int,Y: list_int] :
( ( if_list_int @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
! [X: list_int,Y: list_int] :
( ( if_list_int @ $true @ X @ Y )
= X ) ).
thf(help_If_3_1_If_001t__List__Olist_It__Compiler__Oinstr_J_T,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ) ).
thf(help_If_2_1_If_001t__List__Olist_It__Compiler__Oinstr_J_T,axiom,
! [X: list_instr,Y: list_instr] :
( ( if_list_instr @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__List__Olist_It__Compiler__Oinstr_J_T,axiom,
! [X: list_instr,Y: list_instr] :
( ( if_list_instr @ $true @ X @ Y )
= X ) ).
% Conjectures (1)
thf(conj_0,conjecture,
( ( nth_Pr8327173284404383691st_int @ cfsa @ ( suc @ k ) )
= ( produc5086643055186798020st_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ ( acomp @ a ) ) ) @ one_one_int ) @ ( produc8650753666468850689st_int @ ( fun_up8169409267500384524ar_int @ s @ x @ ( aval @ a @ s ) ) @ stk ) ) ) ).
%------------------------------------------------------------------------------