TPTP Problem File: SLH0791^1.p
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- Solve Problem
%------------------------------------------------------------------------------
% 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_00609_030954__6285944_1 [Des23]
% Status : Theorem
% Rating : ? v8.2.0
% Syntax : Number of formulae : 1462 ( 704 unt; 195 typ; 0 def)
% Number of atoms : 2993 (1768 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 10324 ( 388 ~; 52 |; 225 &;8525 @)
% ( 0 <=>;1134 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Number of types : 40 ( 39 usr)
% Number of type conns : 655 ( 655 >; 0 *; 0 +; 0 <<)
% Number of symbols : 159 ( 156 usr; 20 con; 0-4 aty)
% Number of variables : 3473 ( 93 ^;3208 !; 172 ?;3473 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2023-01-18 16:59:09.354
%------------------------------------------------------------------------------
% Could-be-implicit typings (39)
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thf(ty_n_t__List__Olist_It__Int__Oint_J,type,
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thf(ty_n_t__Set__Oset_It__Num__Onum_J,type,
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thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
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thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
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thf(ty_n_t__Compiler__Om____instr,type,
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thf(ty_n_t__Compiler__Oinstr,type,
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thf(ty_n_t__String__Ochar,type,
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thf(ty_n_t__BExp__Obexp,type,
bexp: $tType ).
thf(ty_n_t__AExp__Oaexp,type,
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thf(ty_n_t__Num__Onum,type,
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thf(ty_n_t__Nat__Onat,type,
nat: $tType ).
thf(ty_n_t__Int__Oint,type,
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thf(ty_n_t__Com__Ocom,type,
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% Explicit typings (156)
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,
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thf(sy_c_Big__Step_Obig__step,type,
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thf(sy_c_Com_Ocom_OSKIP,type,
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thf(sy_c_Compiler2_Obpred,type,
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thf(sy_c_Compiler2_Ocpred,type,
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thf(sy_c_Compiler2_Oexecl,type,
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thf(sy_c_Compiler2_Oexecl__all,type,
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thf(sy_c_Compiler2_Ompred,type,
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thf(sy_c_Compiler_Oacomp,type,
acomp: aexp > list_instr ).
thf(sy_c_Compiler_Oadd__stack,type,
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thf(sy_c_Compiler_Obcomp,type,
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thf(sy_c_Compiler_Occomp,type,
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thf(sy_c_Compiler_Oexec1,type,
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thf(sy_c_Compiler_Oiexec,type,
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thf(sy_c_Compiler_Oiexec__pred,type,
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thf(sy_c_Compiler_Oinstr_OJMP,type,
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thf(sy_c_Compiler_Oinstr_OLOAD,type,
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thf(sy_c_Compiler_Oinstr_OLOADI,type,
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thf(sy_c_Compiler_Ointh_001t__Compiler__Oinstr,type,
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thf(sy_c_Compiler_Ointh_001t__Int__Oint,type,
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thf(sy_c_Compiler_Ointh_001t__List__Olist_It__String__Ochar_J,type,
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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,
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thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
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thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
minus_minus_nat: nat > nat > nat ).
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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,
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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,
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thf(sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint,type,
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thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
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thf(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum,type,
plus_plus_num: num > num > num ).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint,type,
uminus_uminus_int: int > int ).
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,
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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 ).
thf(sy_c_List_Oappend_001t__List__Olist_It__String__Ochar_J,type,
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thf(sy_c_List_Odrop_001t__Compiler__Oinstr,type,
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thf(sy_c_List_Odrop_001t__Int__Oint,type,
drop_int: nat > list_int > list_int ).
thf(sy_c_List_Odrop_001t__List__Olist_It__String__Ochar_J,type,
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thf(sy_c_List_Olist_OCons_001t__Compiler__Oinstr,type,
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thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
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thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Compiler__Oinstr_J,type,
cons_list_instr: list_instr > list_list_instr > list_list_instr ).
thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Int__Oint_J,type,
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thf(sy_c_List_Olist_OCons_001t__List__Olist_It__String__Ochar_J,type,
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thf(sy_c_List_Olist_ONil_001t__Compiler__Oinstr,type,
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thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
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thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Compiler__Oinstr_J,type,
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thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Int__Oint_J,type,
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thf(sy_c_List_Olist_ONil_001t__List__Olist_It__String__Ochar_J,type,
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nil_Pr749310521696113548st_int: list_P419547167332244514st_int ).
thf(sy_c_List_On__lists_001t__Compiler__Oinstr,type,
n_lists_instr: nat > list_instr > list_list_instr ).
thf(sy_c_List_On__lists_001t__Int__Oint,type,
n_lists_int: nat > list_int > list_list_int ).
thf(sy_c_List_On__lists_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,
n_list7311978343830957444st_int: nat > list_P419547167332244514st_int > list_l6422821129637969586st_int ).
thf(sy_c_List_Onth_001t__Compiler__Oinstr,type,
nth_instr: list_instr > nat > instr ).
thf(sy_c_List_Onth_001t__Int__Oint,type,
nth_int: list_int > nat > int ).
thf(sy_c_List_Onth_001t__List__Olist_It__String__Ochar_J,type,
nth_list_char: list_list_char > nat > list_char ).
thf(sy_c_List_Onth_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,
nth_Pr8327173284404383691st_int: list_P419547167332244514st_int > nat > produc6425607678544837394st_int ).
thf(sy_c_List_Oupto,type,
upto: int > int > list_int ).
thf(sy_c_List_Oupto__aux,type,
upto_aux: int > int > list_int > list_int ).
thf(sy_c_Nat_OSuc,type,
suc: nat > nat ).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
semiri1314217659103216013at_int: nat > int ).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
semiri1316708129612266289at_nat: nat > nat ).
thf(sy_c_Nat_Osize__class_Osize_001t__BExp__Obexp,type,
size_size_bexp: bexp > nat ).
thf(sy_c_Nat_Osize__class_Osize_001t__Com__Ocom,type,
size_size_com: com > nat ).
thf(sy_c_Nat_Osize__class_Osize_001t__Compiler__Oinstr,type,
size_size_instr: instr > nat ).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Compiler__Oinstr_J,type,
size_size_list_instr: list_instr > nat ).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
size_size_list_int: list_int > nat ).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__String__Ochar_J_J,type,
size_s356637359517785349t_char: list_list_char > nat ).
thf(sy_c_Nat_Osize__class_Osize_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,
size_s229347708945616566st_int: list_P419547167332244514st_int > nat ).
thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
size_size_num: num > nat ).
thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
size_size_char: char > nat ).
thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
neg_nu3811975205180677377ec_int: int > int ).
thf(sy_c_Num_Onum_OBit0,type,
bit0: num > num ).
thf(sy_c_Num_Onum_OOne,type,
one: num ).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
numeral_numeral_int: num > int ).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
numeral_numeral_nat: num > nat ).
thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
ord_less_int: int > int > $o ).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
ord_less_nat: nat > nat > $o ).
thf(sy_c_Orderings_Oord__class_Oless_001t__Num__Onum,type,
ord_less_num: num > num > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
ord_less_eq_int: int > int > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum,type,
ord_less_eq_num: num > num > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Int__Oint_J,type,
ord_less_eq_set_int: set_int > set_int > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Num__Onum_J,type,
ord_less_eq_set_num: set_num > set_num > $o ).
thf(sy_c_Product__Type_OPair_001_062_It__Compiler__Oinstr_M_062_It__Compiler__Oinstr_M_Eo_J_J_001t__List__Olist_It__Compiler__Oinstr_J,type,
produc7818391707689388878_instr: ( instr > instr > $o ) > list_instr > produc7133927873007960030_instr ).
thf(sy_c_Product__Type_OPair_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001t__List__Olist_It__Int__Oint_J,type,
produc8618682346314911123st_int: ( int > int > $o ) > list_int > produc5834231552977413017st_int ).
thf(sy_c_Product__Type_OPair_001_062_It__Int__Oint_Mt__Int__Oint_J_001t__Nat__Onat,type,
produc2630796075472406112nt_nat: ( int > int ) > nat > produc1534919314292393896nt_nat ).
thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_001t__Int__Oint,type,
produc5790713362662368625nt_int: ( list_char > int ) > int > produc4435102495419491129nt_int ).
thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J_001t__List__Olist_It__Int__Oint_J,type,
produc8650753666468850689st_int: ( list_char > int ) > list_int > produc369741286924889929st_int ).
thf(sy_c_Product__Type_OPair_001_062_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_M_062_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_M_Eo_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,
produc554038597315947693st_int: ( produc6425607678544837394st_int > produc6425607678544837394st_int > $o ) > list_P419547167332244514st_int > produc2468426419292222131st_int ).
thf(sy_c_Product__Type_OPair_001_Eo_001t__Int__Oint,type,
product_Pair_o_int: $o > int > product_prod_o_int ).
thf(sy_c_Product__Type_OPair_001t__BExp__Obexp_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
produc4047900504771817624_o_int: bexp > product_prod_o_int > produc1897111610453708512_o_int ).
thf(sy_c_Product__Type_OPair_001t__Com__Ocom_001_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J,type,
produc5595214716300948949ar_int: com > ( list_char > int ) > produc2931317944591925149ar_int ).
thf(sy_c_Product__Type_OPair_001t__Compiler__Oinstr_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,
produc1484136438817787418st_int: instr > produc6425607678544837394st_int > produc5995290525303592096st_int ).
thf(sy_c_Product__Type_OPair_001t__Compiler__Om____instr_001t__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Int__Oint_J_Mt__Nat__Onat_J_J,type,
produc973592215685924118nt_nat: m_instr > produc1019184382078353393nt_nat > produc3341395906625653086nt_nat ).
thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Int__Oint_J_Mt__Nat__Onat_J,type,
produc8342123264692915235nt_nat: int > produc1534919314292393896nt_nat > produc1019184382078353393nt_nat ).
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,
produc5086643055186798020st_int: int > produc369741286924889929st_int > produc6425607678544837394st_int ).
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__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__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Int__Oint_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Int__Oint_J_Mt__Nat__Onat_J_J,type,
produc5273850286580078715nt_nat: produc1019184382078353393nt_nat > produc1019184382078353393nt_nat > produc6004788045807207619nt_nat ).
thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__Int__Oint_Mt__Int__Oint_J_001t__Nat__Onat,type,
produc8715251273072885836nt_nat: produc1534919314292393896nt_nat > int > int ).
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_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__Com__Ocom_001_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J,type,
produc8829524412605799873ar_int: produc2931317944591925149ar_int > com ).
thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Int__Oint_J_Mt__Nat__Onat_J,type,
produc2827224793399753527nt_nat: produc1019184382078353393nt_nat > 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__Int__Oint_J_001t__Nat__Onat,type,
produc4411376485632109966nt_nat: produc1534919314292393896nt_nat > nat ).
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_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__Com__Ocom_001_062_It__List__Olist_It__String__Ochar_J_Mt__Int__Oint_J,type,
produc9207319146083860483ar_int: produc2931317944591925149ar_int > list_char > int ).
thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Int__Oint_J_Mt__Nat__Onat_J,type,
produc2259646285430092661nt_nat: produc1019184382078353393nt_nat > produc1534919314292393896nt_nat ).
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_Set_OCollect_001t__Int__Oint,type,
collect_int: ( int > $o ) > set_int ).
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__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_v_b,type,
b: bexp ).
thf(sy_v_c,type,
c: com ).
thf(sy_v_cfsa____,type,
cfsa: list_P419547167332244514st_int ).
thf(sy_v_k____,type,
k: nat ).
thf(sy_v_s_H____,type,
s: list_char > int ).
thf(sy_v_stk____,type,
stk: list_int ).
% Relevant facts (1257)
thf(fact_0_B,axiom,
ord_less_nat @ k @ ( size_s229347708945616566st_int @ cfsa ) ).
% B
thf(fact_1_C,axiom,
( k
!= ( minus_minus_nat @ ( size_s229347708945616566st_int @ cfsa ) @ one_one_nat ) ) ).
% C
thf(fact_2_E,axiom,
( ( plus_plus_nat @ ( suc @ k ) @ ( minus_minus_nat @ ( size_s229347708945616566st_int @ ( drop_P7838799151754935884st_int @ ( suc @ k ) @ cfsa ) ) @ one_one_nat ) )
= ( minus_minus_nat @ ( size_s229347708945616566st_int @ cfsa ) @ one_one_nat ) ) ).
% E
thf(fact_3_D,axiom,
( ( nth_Pr8327173284404383691st_int @ cfsa @ ( suc @ k ) )
= ( produc5086643055186798020st_int @ zero_zero_int @ ( produc8650753666468850689st_int @ s @ stk ) ) ) ).
% D
thf(fact_4_A,axiom,
execl_all @ ( append_instr @ ( bcomp @ ( produc4047900504771817624_o_int @ b @ ( product_Pair_o_int @ $false @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ ( ccomp @ c ) ) ) @ one_one_int ) ) ) ) @ ( append_instr @ ( ccomp @ c ) @ ( cons_instr @ ( jmp @ ( minus_minus_int @ ( minus_minus_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ ( bcomp @ ( produc4047900504771817624_o_int @ b @ ( product_Pair_o_int @ $false @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ ( ccomp @ c ) ) ) @ one_one_int ) ) ) ) ) ) ) @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ ( ccomp @ c ) ) ) ) @ one_one_int ) ) @ nil_instr ) ) ) @ cfsa ).
% A
thf(fact_5__092_060open_062cfs_A_B_Ak_A_061_A_Isize_A_Ibcomp_A_Ib_M_AFalse_M_Asize_A_Iccomp_Ac_J_A_L_A1_J_J_A_L_Asize_A_Iccomp_Ac_J_M_As_H_M_Astk_J_092_060close_062,axiom,
( ( nth_Pr8327173284404383691st_int @ cfsa @ k )
= ( produc5086643055186798020st_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ ( bcomp @ ( produc4047900504771817624_o_int @ b @ ( product_Pair_o_int @ $false @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ ( ccomp @ c ) ) ) @ one_one_int ) ) ) ) ) ) @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ ( ccomp @ c ) ) ) ) @ ( produc8650753666468850689st_int @ s @ stk ) ) ) ).
% \<open>cfs ! k = (size (bcomp (b, False, size (ccomp c) + 1)) + size (ccomp c), s', stk)\<close>
thf(fact_6_of__nat__Suc,axiom,
! [M: nat] :
( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
= ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% of_nat_Suc
thf(fact_7_of__nat__Suc,axiom,
! [M: nat] :
( ( semiri1314217659103216013at_int @ ( suc @ M ) )
= ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% of_nat_Suc
thf(fact_8_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_9_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_10_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_11_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_12_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_13_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_14_diff__minus__eq__add,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
= ( plus_plus_int @ A @ B ) ) ).
% diff_minus_eq_add
thf(fact_15_uminus__add__conv__diff,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
= ( minus_minus_int @ B @ A ) ) ).
% uminus_add_conv_diff
thf(fact_16_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_17_append__eq__append__conv,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,Us: list_P419547167332244514st_int,Vs: list_P419547167332244514st_int] :
( ( ( ( size_s229347708945616566st_int @ Xs )
= ( size_s229347708945616566st_int @ Ys ) )
| ( ( size_s229347708945616566st_int @ Us )
= ( size_s229347708945616566st_int @ Vs ) ) )
=> ( ( ( append5028292981072010935st_int @ Xs @ Us )
= ( append5028292981072010935st_int @ Ys @ Vs ) )
= ( ( Xs = Ys )
& ( Us = Vs ) ) ) ) ).
% append_eq_append_conv
thf(fact_18_append__eq__append__conv,axiom,
! [Xs: list_list_char,Ys: list_list_char,Us: list_list_char,Vs: list_list_char] :
( ( ( ( size_s356637359517785349t_char @ Xs )
= ( size_s356637359517785349t_char @ Ys ) )
| ( ( size_s356637359517785349t_char @ Us )
= ( size_s356637359517785349t_char @ Vs ) ) )
=> ( ( ( append_list_char @ Xs @ Us )
= ( append_list_char @ Ys @ Vs ) )
= ( ( Xs = Ys )
& ( Us = Vs ) ) ) ) ).
% append_eq_append_conv
thf(fact_19_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_20_append_Oright__neutral,axiom,
! [A: list_instr] :
( ( append_instr @ A @ nil_instr )
= A ) ).
% append.right_neutral
thf(fact_21_append_Oright__neutral,axiom,
! [A: list_P419547167332244514st_int] :
( ( append5028292981072010935st_int @ A @ nil_Pr749310521696113548st_int )
= A ) ).
% append.right_neutral
thf(fact_22_append_Oright__neutral,axiom,
! [A: list_int] :
( ( append_int @ A @ nil_int )
= A ) ).
% append.right_neutral
thf(fact_23_append__Nil2,axiom,
! [Xs: list_instr] :
( ( append_instr @ Xs @ nil_instr )
= Xs ) ).
% append_Nil2
thf(fact_24_append__Nil2,axiom,
! [Xs: list_P419547167332244514st_int] :
( ( append5028292981072010935st_int @ Xs @ nil_Pr749310521696113548st_int )
= Xs ) ).
% append_Nil2
thf(fact_25_append__Nil2,axiom,
! [Xs: list_int] :
( ( append_int @ Xs @ nil_int )
= Xs ) ).
% append_Nil2
thf(fact_26_append__self__conv,axiom,
! [Xs: list_instr,Ys: list_instr] :
( ( ( append_instr @ Xs @ Ys )
= Xs )
= ( Ys = nil_instr ) ) ).
% append_self_conv
thf(fact_27_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_28_append__self__conv,axiom,
! [Xs: list_int,Ys: list_int] :
( ( ( append_int @ Xs @ Ys )
= Xs )
= ( Ys = nil_int ) ) ).
% append_self_conv
thf(fact_29_self__append__conv,axiom,
! [Y: list_instr,Ys: list_instr] :
( ( Y
= ( append_instr @ Y @ Ys ) )
= ( Ys = nil_instr ) ) ).
% self_append_conv
thf(fact_30_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_31_self__append__conv,axiom,
! [Y: list_int,Ys: list_int] :
( ( Y
= ( append_int @ Y @ Ys ) )
= ( Ys = nil_int ) ) ).
% self_append_conv
thf(fact_32_append__self__conv2,axiom,
! [Xs: list_instr,Ys: list_instr] :
( ( ( append_instr @ Xs @ Ys )
= Ys )
= ( Xs = nil_instr ) ) ).
% append_self_conv2
thf(fact_33_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_34_append__self__conv2,axiom,
! [Xs: list_int,Ys: list_int] :
( ( ( append_int @ Xs @ Ys )
= Ys )
= ( Xs = nil_int ) ) ).
% append_self_conv2
thf(fact_35_self__append__conv2,axiom,
! [Y: list_instr,Xs: list_instr] :
( ( Y
= ( append_instr @ Xs @ Y ) )
= ( Xs = nil_instr ) ) ).
% self_append_conv2
thf(fact_36_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_37_self__append__conv2,axiom,
! [Y: list_int,Xs: list_int] :
( ( Y
= ( append_int @ Xs @ Y ) )
= ( Xs = nil_int ) ) ).
% self_append_conv2
thf(fact_38_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_39_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_40_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_41_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_42_neg__equal__iff__equal,axiom,
! [A: int,B: int] :
( ( ( uminus_uminus_int @ A )
= ( uminus_uminus_int @ B ) )
= ( A = B ) ) ).
% neg_equal_iff_equal
thf(fact_43_add_Oinverse__inverse,axiom,
! [A: int] :
( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
= A ) ).
% add.inverse_inverse
thf(fact_44_old_Onat_Oinject,axiom,
! [Nat: nat,Nat2: nat] :
( ( ( suc @ Nat )
= ( suc @ Nat2 ) )
= ( Nat = Nat2 ) ) ).
% old.nat.inject
thf(fact_45_nat_Oinject,axiom,
! [X2: nat,Y2: nat] :
( ( ( suc @ X2 )
= ( suc @ Y2 ) )
= ( X2 = Y2 ) ) ).
% nat.inject
thf(fact_46_list_Oinject,axiom,
! [X21: instr,X22: list_instr,Y21: instr,Y22: list_instr] :
( ( ( cons_instr @ X21 @ X22 )
= ( cons_instr @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 ) ) ) ).
% list.inject
thf(fact_47_list_Oinject,axiom,
! [X21: int,X22: list_int,Y21: int,Y22: list_int] :
( ( ( cons_int @ X21 @ X22 )
= ( cons_int @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 ) ) ) ).
% list.inject
thf(fact_48_list_Oinject,axiom,
! [X21: produc6425607678544837394st_int,X22: list_P419547167332244514st_int,Y21: produc6425607678544837394st_int,Y22: list_P419547167332244514st_int] :
( ( ( cons_P4151473878978182108st_int @ X21 @ X22 )
= ( cons_P4151473878978182108st_int @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 ) ) ) ).
% list.inject
thf(fact_49_of__nat__eq__iff,axiom,
! [M: nat,N: nat] :
( ( ( semiri1314217659103216013at_int @ M )
= ( semiri1314217659103216013at_int @ N ) )
= ( M = N ) ) ).
% of_nat_eq_iff
thf(fact_50_of__nat__eq__iff,axiom,
! [M: nat,N: nat] :
( ( ( semiri1316708129612266289at_nat @ M )
= ( semiri1316708129612266289at_nat @ N ) )
= ( M = N ) ) ).
% of_nat_eq_iff
thf(fact_51_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_52_same__append__eq,axiom,
! [Xs: list_int,Ys: list_int,Zs: list_int] :
( ( ( append_int @ Xs @ Ys )
= ( append_int @ Xs @ Zs ) )
= ( Ys = Zs ) ) ).
% same_append_eq
thf(fact_53_same__append__eq,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int] :
( ( ( append5028292981072010935st_int @ Xs @ Ys )
= ( append5028292981072010935st_int @ Xs @ Zs ) )
= ( Ys = Zs ) ) ).
% same_append_eq
thf(fact_54_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_55_append__same__eq,axiom,
! [Ys: list_int,Xs: list_int,Zs: list_int] :
( ( ( append_int @ Ys @ Xs )
= ( append_int @ Zs @ Xs ) )
= ( Ys = Zs ) ) ).
% append_same_eq
thf(fact_56_append__same__eq,axiom,
! [Ys: list_P419547167332244514st_int,Xs: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int] :
( ( ( append5028292981072010935st_int @ Ys @ Xs )
= ( append5028292981072010935st_int @ Zs @ Xs ) )
= ( Ys = Zs ) ) ).
% append_same_eq
thf(fact_57_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_58_append__assoc,axiom,
! [Xs: list_int,Ys: list_int,Zs: list_int] :
( ( append_int @ ( append_int @ Xs @ Ys ) @ Zs )
= ( append_int @ Xs @ ( append_int @ Ys @ Zs ) ) ) ).
% append_assoc
thf(fact_59_append__assoc,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int] :
( ( append5028292981072010935st_int @ ( append5028292981072010935st_int @ Xs @ Ys ) @ Zs )
= ( append5028292981072010935st_int @ Xs @ ( append5028292981072010935st_int @ Ys @ Zs ) ) ) ).
% append_assoc
thf(fact_60_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_61_append_Oassoc,axiom,
! [A: list_int,B: list_int,C: list_int] :
( ( append_int @ ( append_int @ A @ B ) @ C )
= ( append_int @ A @ ( append_int @ B @ C ) ) ) ).
% append.assoc
thf(fact_62_append_Oassoc,axiom,
! [A: list_P419547167332244514st_int,B: list_P419547167332244514st_int,C: list_P419547167332244514st_int] :
( ( append5028292981072010935st_int @ ( append5028292981072010935st_int @ A @ B ) @ C )
= ( append5028292981072010935st_int @ A @ ( append5028292981072010935st_int @ B @ C ) ) ) ).
% append.assoc
thf(fact_63_not__gr__zero,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) ).
% not_gr_zero
thf(fact_64_add__0,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ) ).
% add_0
thf(fact_65_add__0,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ) ).
% add_0
thf(fact_66_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_67_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_68_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_69_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_70_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_71_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_72_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_73_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_74_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_75_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_76_double__zero__sym,axiom,
! [A: int] :
( ( zero_zero_int
= ( plus_plus_int @ A @ A ) )
= ( A = zero_zero_int ) ) ).
% double_zero_sym
thf(fact_77_add_Oright__neutral,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ) ).
% add.right_neutral
thf(fact_78_add_Oright__neutral,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ) ).
% add.right_neutral
thf(fact_79_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_80_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_81_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_82_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_83_mem__Collect__eq,axiom,
! [A: int,P: int > $o] :
( ( member_int @ A @ ( collect_int @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_84_Collect__mem__eq,axiom,
! [A2: set_int] :
( ( collect_int
@ ^ [X3: int] : ( member_int @ X3 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_85_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_86_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_87_diff__zero,axiom,
! [A: int] :
( ( minus_minus_int @ A @ zero_zero_int )
= A ) ).
% diff_zero
thf(fact_88_diff__zero,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ) ).
% diff_zero
thf(fact_89_zero__diff,axiom,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ) ).
% zero_diff
thf(fact_90_diff__0__right,axiom,
! [A: int] :
( ( minus_minus_int @ A @ zero_zero_int )
= A ) ).
% diff_0_right
thf(fact_91_diff__self,axiom,
! [A: int] :
( ( minus_minus_int @ A @ A )
= zero_zero_int ) ).
% diff_self
thf(fact_92_neg__equal__zero,axiom,
! [A: int] :
( ( ( uminus_uminus_int @ A )
= A )
= ( A = zero_zero_int ) ) ).
% neg_equal_zero
thf(fact_93_equal__neg__zero,axiom,
! [A: int] :
( ( A
= ( uminus_uminus_int @ A ) )
= ( A = zero_zero_int ) ) ).
% equal_neg_zero
thf(fact_94_neg__equal__0__iff__equal,axiom,
! [A: int] :
( ( ( uminus_uminus_int @ A )
= zero_zero_int )
= ( A = zero_zero_int ) ) ).
% neg_equal_0_iff_equal
thf(fact_95_neg__0__equal__iff__equal,axiom,
! [A: int] :
( ( zero_zero_int
= ( uminus_uminus_int @ A ) )
= ( zero_zero_int = A ) ) ).
% neg_0_equal_iff_equal
thf(fact_96_add_Oinverse__neutral,axiom,
( ( uminus_uminus_int @ zero_zero_int )
= zero_zero_int ) ).
% add.inverse_neutral
thf(fact_97_neg__less__iff__less,axiom,
! [B: int,A: int] :
( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
= ( ord_less_int @ A @ B ) ) ).
% neg_less_iff_less
thf(fact_98_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_99_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_100_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_101_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_102_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_103_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_104_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_105_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_106_diff__add__cancel,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
= A ) ).
% diff_add_cancel
thf(fact_107_add__diff__cancel,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
= A ) ).
% add_diff_cancel
thf(fact_108_minus__add__distrib,axiom,
! [A: int,B: int] :
( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% minus_add_distrib
thf(fact_109_minus__add__cancel,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
= B ) ).
% minus_add_cancel
thf(fact_110_add__minus__cancel,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
= B ) ).
% add_minus_cancel
thf(fact_111_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_112_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_113_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_114_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_115_of__nat__0,axiom,
( ( semiri1314217659103216013at_int @ zero_zero_nat )
= zero_zero_int ) ).
% of_nat_0
thf(fact_116_of__nat__0,axiom,
( ( semiri1316708129612266289at_nat @ zero_zero_nat )
= zero_zero_nat ) ).
% of_nat_0
thf(fact_117_minus__diff__eq,axiom,
! [A: int,B: int] :
( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ B @ A ) ) ).
% minus_diff_eq
thf(fact_118_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_119_Suc__mono,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% Suc_mono
thf(fact_120_lessI,axiom,
! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% lessI
thf(fact_121_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_122_Suc__diff__diff,axiom,
! [M: nat,N: nat,K: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
= ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% Suc_diff_diff
thf(fact_123_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_124_nat__add__left__cancel__less,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( ord_less_nat @ M @ N ) ) ).
% nat_add_left_cancel_less
thf(fact_125_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_126_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_127_append__is__Nil__conv,axiom,
! [Xs: list_int,Ys: list_int] :
( ( ( append_int @ Xs @ Ys )
= nil_int )
= ( ( Xs = nil_int )
& ( Ys = nil_int ) ) ) ).
% append_is_Nil_conv
thf(fact_128_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_129_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_130_Nil__is__append__conv,axiom,
! [Xs: list_int,Ys: list_int] :
( ( nil_int
= ( append_int @ Xs @ Ys ) )
= ( ( Xs = nil_int )
& ( Ys = nil_int ) ) ) ).
% Nil_is_append_conv
thf(fact_131_diff__diff__left,axiom,
! [I: nat,J: nat,K: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
= ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% diff_diff_left
thf(fact_132_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_133_drop__drop,axiom,
! [N: nat,M: nat,Xs: list_int] :
( ( drop_int @ N @ ( drop_int @ M @ Xs ) )
= ( drop_int @ ( plus_plus_nat @ N @ M ) @ Xs ) ) ).
% drop_drop
thf(fact_134_drop__drop,axiom,
! [N: nat,M: nat,Xs: list_instr] :
( ( drop_instr @ N @ ( drop_instr @ M @ Xs ) )
= ( drop_instr @ ( plus_plus_nat @ N @ M ) @ Xs ) ) ).
% drop_drop
thf(fact_135_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_136_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_137_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_138_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_139_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_140_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_141_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_142_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_143_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_144_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_145_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_146_neg__less__0__iff__less,axiom,
! [A: int] :
( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
= ( ord_less_int @ zero_zero_int @ A ) ) ).
% neg_less_0_iff_less
thf(fact_147_neg__0__less__iff__less,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
= ( ord_less_int @ A @ zero_zero_int ) ) ).
% neg_0_less_iff_less
thf(fact_148_neg__less__pos,axiom,
! [A: int] :
( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
= ( ord_less_int @ zero_zero_int @ A ) ) ).
% neg_less_pos
thf(fact_149_less__neg__neg,axiom,
! [A: int] :
( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
= ( ord_less_int @ A @ zero_zero_int ) ) ).
% less_neg_neg
thf(fact_150_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_151_ab__left__minus,axiom,
! [A: int] :
( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
= zero_zero_int ) ).
% ab_left_minus
thf(fact_152_add_Oright__inverse,axiom,
! [A: int] :
( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
= zero_zero_int ) ).
% add.right_inverse
thf(fact_153_diff__0,axiom,
! [A: int] :
( ( minus_minus_int @ zero_zero_int @ A )
= ( uminus_uminus_int @ A ) ) ).
% diff_0
thf(fact_154_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_155_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_156_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_157_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_158_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_159_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_160_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_161_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_162_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_163_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_164_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_165_of__nat__1,axiom,
( ( semiri1314217659103216013at_int @ one_one_nat )
= one_one_int ) ).
% of_nat_1
thf(fact_166_of__nat__1,axiom,
( ( semiri1316708129612266289at_nat @ one_one_nat )
= one_one_nat ) ).
% of_nat_1
thf(fact_167_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_168_length__append,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( size_s229347708945616566st_int @ ( append5028292981072010935st_int @ Xs @ Ys ) )
= ( plus_plus_nat @ ( size_s229347708945616566st_int @ Xs ) @ ( size_s229347708945616566st_int @ Ys ) ) ) ).
% length_append
thf(fact_169_length__append,axiom,
! [Xs: list_list_char,Ys: list_list_char] :
( ( size_s356637359517785349t_char @ ( append_list_char @ Xs @ Ys ) )
= ( plus_plus_nat @ ( size_s356637359517785349t_char @ Xs ) @ ( size_s356637359517785349t_char @ Ys ) ) ) ).
% length_append
thf(fact_170_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_171_diff__Suc__1,axiom,
! [N: nat] :
( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
= N ) ).
% diff_Suc_1
thf(fact_172_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_173_length__drop,axiom,
! [N: nat,Xs: list_instr] :
( ( size_size_list_instr @ ( drop_instr @ N @ Xs ) )
= ( minus_minus_nat @ ( size_size_list_instr @ Xs ) @ N ) ) ).
% length_drop
thf(fact_174_length__drop,axiom,
! [N: nat,Xs: list_list_char] :
( ( size_s356637359517785349t_char @ ( drop_list_char @ N @ Xs ) )
= ( minus_minus_nat @ ( size_s356637359517785349t_char @ Xs ) @ N ) ) ).
% length_drop
thf(fact_175_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_176_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_177_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_178_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_179_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_180_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_181_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_182_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_183_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_184_nth__append__length__plus,axiom,
! [Xs: list_list_char,Ys: list_list_char,N: nat] :
( ( nth_list_char @ ( append_list_char @ Xs @ Ys ) @ ( plus_plus_nat @ ( size_s356637359517785349t_char @ Xs ) @ N ) )
= ( nth_list_char @ Ys @ N ) ) ).
% nth_append_length_plus
thf(fact_185_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_186_drop__append,axiom,
! [N: nat,Xs: list_instr,Ys: list_instr] :
( ( drop_instr @ N @ ( append_instr @ Xs @ Ys ) )
= ( append_instr @ ( drop_instr @ N @ Xs ) @ ( drop_instr @ ( minus_minus_nat @ N @ ( size_size_list_instr @ Xs ) ) @ Ys ) ) ) ).
% drop_append
thf(fact_187_drop__append,axiom,
! [N: nat,Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( drop_P7838799151754935884st_int @ N @ ( append5028292981072010935st_int @ Xs @ Ys ) )
= ( append5028292981072010935st_int @ ( drop_P7838799151754935884st_int @ N @ Xs ) @ ( drop_P7838799151754935884st_int @ ( minus_minus_nat @ N @ ( size_s229347708945616566st_int @ Xs ) ) @ Ys ) ) ) ).
% drop_append
thf(fact_188_drop__append,axiom,
! [N: nat,Xs: list_list_char,Ys: list_list_char] :
( ( drop_list_char @ N @ ( append_list_char @ Xs @ Ys ) )
= ( append_list_char @ ( drop_list_char @ N @ Xs ) @ ( drop_list_char @ ( minus_minus_nat @ N @ ( size_s356637359517785349t_char @ Xs ) ) @ Ys ) ) ) ).
% drop_append
thf(fact_189_drop__append,axiom,
! [N: nat,Xs: list_int,Ys: list_int] :
( ( drop_int @ N @ ( append_int @ Xs @ Ys ) )
= ( append_int @ ( drop_int @ N @ Xs ) @ ( drop_int @ ( minus_minus_nat @ N @ ( size_size_list_int @ Xs ) ) @ Ys ) ) ) ).
% drop_append
thf(fact_190_gr__zeroI,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% gr_zeroI
thf(fact_191_not__less__zero,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% not_less_zero
thf(fact_192_gr__implies__not__zero,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) ).
% gr_implies_not_zero
thf(fact_193_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_194_add__lessD1,axiom,
! [I: nat,J: nat,K: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
=> ( ord_less_nat @ I @ K ) ) ).
% add_lessD1
thf(fact_195_Nat_Odiff__cancel,axiom,
! [K: nat,M: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( minus_minus_nat @ M @ N ) ) ).
% Nat.diff_cancel
thf(fact_196_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_197_diff__cancel2,axiom,
! [M: nat,K: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
= ( minus_minus_nat @ M @ N ) ) ).
% diff_cancel2
thf(fact_198_diff__commute,axiom,
! [I: nat,J: nat,K: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
= ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% diff_commute
thf(fact_199_add__less__mono,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ord_less_nat @ I @ J )
=> ( ( ord_less_nat @ K @ L )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% add_less_mono
thf(fact_200_less__not__refl,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ N ) ).
% less_not_refl
thf(fact_201_not__add__less1,axiom,
! [I: nat,J: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% not_add_less1
thf(fact_202_not__add__less2,axiom,
! [J: nat,I: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% not_add_less2
thf(fact_203_add__less__mono1,axiom,
! [I: nat,J: nat,K: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% add_less_mono1
thf(fact_204_less__diff__conv,axiom,
! [I: nat,J: nat,K: nat] :
( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
= ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% less_diff_conv
thf(fact_205_less__not__refl2,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ N @ M )
=> ( M != N ) ) ).
% less_not_refl2
thf(fact_206_less__not__refl3,axiom,
! [S: nat,T: nat] :
( ( ord_less_nat @ S @ T )
=> ( S != T ) ) ).
% less_not_refl3
thf(fact_207_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_208_less__irrefl__nat,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ N ) ).
% less_irrefl_nat
thf(fact_209_nat__less__induct,axiom,
! [P: nat > $o,N: nat] :
( ! [N2: nat] :
( ! [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
=> ( P @ M2 ) )
=> ( P @ N2 ) )
=> ( P @ N ) ) ).
% nat_less_induct
thf(fact_210_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_211_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_212_zero__reorient,axiom,
! [X: int] :
( ( zero_zero_int = X )
= ( X = zero_zero_int ) ) ).
% zero_reorient
thf(fact_213_zero__reorient,axiom,
! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ) ).
% zero_reorient
thf(fact_214_diff__add__inverse,axiom,
! [N: nat,M: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
= M ) ).
% diff_add_inverse
thf(fact_215_infinite__descent,axiom,
! [P: nat > $o,N: nat] :
( ! [N2: nat] :
( ~ ( P @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P @ M2 ) ) )
=> ( P @ N ) ) ).
% infinite_descent
thf(fact_216_less__add__eq__less,axiom,
! [K: nat,L: nat,M: nat,N: nat] :
( ( ord_less_nat @ K @ L )
=> ( ( ( plus_plus_nat @ M @ L )
= ( plus_plus_nat @ K @ N ) )
=> ( ord_less_nat @ M @ N ) ) ) ).
% less_add_eq_less
thf(fact_217_diff__add__inverse2,axiom,
! [M: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
= M ) ).
% diff_add_inverse2
thf(fact_218_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_219_less__imp__diff__less,axiom,
! [J: nat,K: nat,N: nat] :
( ( ord_less_nat @ J @ K )
=> ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% less_imp_diff_less
thf(fact_220_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_221_list__eq__iff__nth__eq,axiom,
( ( ^ [Y3: list_P419547167332244514st_int,Z: list_P419547167332244514st_int] : ( Y3 = Z ) )
= ( ^ [Xs2: list_P419547167332244514st_int,Ys2: list_P419547167332244514st_int] :
( ( ( size_s229347708945616566st_int @ Xs2 )
= ( size_s229347708945616566st_int @ Ys2 ) )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_s229347708945616566st_int @ Xs2 ) )
=> ( ( nth_Pr8327173284404383691st_int @ Xs2 @ I2 )
= ( nth_Pr8327173284404383691st_int @ Ys2 @ I2 ) ) ) ) ) ) ).
% list_eq_iff_nth_eq
thf(fact_222_list__eq__iff__nth__eq,axiom,
( ( ^ [Y3: list_list_char,Z: list_list_char] : ( Y3 = Z ) )
= ( ^ [Xs2: list_list_char,Ys2: list_list_char] :
( ( ( size_s356637359517785349t_char @ Xs2 )
= ( size_s356637359517785349t_char @ Ys2 ) )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_s356637359517785349t_char @ Xs2 ) )
=> ( ( nth_list_char @ Xs2 @ I2 )
= ( nth_list_char @ Ys2 @ I2 ) ) ) ) ) ) ).
% list_eq_iff_nth_eq
thf(fact_223_list__eq__iff__nth__eq,axiom,
( ( ^ [Y3: list_int,Z: list_int] : ( Y3 = Z ) )
= ( ^ [Xs2: list_int,Ys2: list_int] :
( ( ( size_size_list_int @ Xs2 )
= ( size_size_list_int @ Ys2 ) )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
=> ( ( nth_int @ Xs2 @ I2 )
= ( nth_int @ Ys2 @ I2 ) ) ) ) ) ) ).
% list_eq_iff_nth_eq
thf(fact_224_Skolem__list__nth,axiom,
! [K: nat,P: nat > produc6425607678544837394st_int > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ? [X4: produc6425607678544837394st_int] : ( P @ I2 @ X4 ) ) )
= ( ? [Xs2: list_P419547167332244514st_int] :
( ( ( size_s229347708945616566st_int @ Xs2 )
= K )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ( P @ I2 @ ( nth_Pr8327173284404383691st_int @ Xs2 @ I2 ) ) ) ) ) ) ).
% Skolem_list_nth
thf(fact_225_Skolem__list__nth,axiom,
! [K: nat,P: nat > list_char > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ? [X4: list_char] : ( P @ I2 @ X4 ) ) )
= ( ? [Xs2: list_list_char] :
( ( ( size_s356637359517785349t_char @ Xs2 )
= K )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ( P @ I2 @ ( nth_list_char @ Xs2 @ I2 ) ) ) ) ) ) ).
% Skolem_list_nth
thf(fact_226_Skolem__list__nth,axiom,
! [K: nat,P: nat > int > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ? [X4: int] : ( P @ I2 @ X4 ) ) )
= ( ? [Xs2: list_int] :
( ( ( size_size_list_int @ Xs2 )
= K )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ K )
=> ( P @ I2 @ ( nth_int @ Xs2 @ I2 ) ) ) ) ) ) ).
% Skolem_list_nth
thf(fact_227_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_228_nth__equalityI,axiom,
! [Xs: list_list_char,Ys: list_list_char] :
( ( ( size_s356637359517785349t_char @ Xs )
= ( size_s356637359517785349t_char @ Ys ) )
=> ( ! [I3: nat] :
( ( ord_less_nat @ I3 @ ( size_s356637359517785349t_char @ Xs ) )
=> ( ( nth_list_char @ Xs @ I3 )
= ( nth_list_char @ Ys @ I3 ) ) )
=> ( Xs = Ys ) ) ) ).
% nth_equalityI
thf(fact_229_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_230_diff__less__Suc,axiom,
! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% diff_less_Suc
thf(fact_231_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_232_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_233_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_234_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_235_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_236_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_237_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_238_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_239_lift__Suc__mono__less__iff,axiom,
! [F: nat > nat,N: nat,M: nat] :
( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
= ( ord_less_nat @ N @ M ) ) ) ).
% lift_Suc_mono_less_iff
thf(fact_240_lift__Suc__mono__less__iff,axiom,
! [F: nat > int,N: nat,M: nat] :
( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
= ( ord_less_nat @ N @ M ) ) ) ).
% lift_Suc_mono_less_iff
thf(fact_241_lift__Suc__mono__less,axiom,
! [F: nat > nat,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_nat @ N @ N3 )
=> ( ord_less_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% lift_Suc_mono_less
thf(fact_242_lift__Suc__mono__less,axiom,
! [F: nat > int,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_nat @ N @ N3 )
=> ( ord_less_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% lift_Suc_mono_less
thf(fact_243_less__imp__Suc__add,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ? [K2: nat] :
( N
= ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% less_imp_Suc_add
thf(fact_244_less__iff__Suc__add,axiom,
( ord_less_nat
= ( ^ [M3: nat,N4: nat] :
? [K3: nat] :
( N4
= ( suc @ ( plus_plus_nat @ M3 @ K3 ) ) ) ) ) ).
% less_iff_Suc_add
thf(fact_245_less__add__Suc2,axiom,
! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% less_add_Suc2
thf(fact_246_less__add__Suc1,axiom,
! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% less_add_Suc1
thf(fact_247_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_248_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_249_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_250_Suc__eq__plus1__left,axiom,
( suc
= ( plus_plus_nat @ one_one_nat ) ) ).
% Suc_eq_plus1_left
thf(fact_251_plus__1__eq__Suc,axiom,
( ( plus_plus_nat @ one_one_nat )
= suc ) ).
% plus_1_eq_Suc
thf(fact_252_Suc__eq__plus1,axiom,
( suc
= ( ^ [N4: nat] : ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ).
% Suc_eq_plus1
thf(fact_253_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_254_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_255_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_256_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_257_of__nat__less__0__iff,axiom,
! [M: nat] :
~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% of_nat_less_0_iff
thf(fact_258_of__nat__less__0__iff,axiom,
! [M: nat] :
~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% of_nat_less_0_iff
thf(fact_259_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_260_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_261_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_262_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_263_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_264_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_265_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_266_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_267_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_268_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_269_add__mono__thms__linordered__field_I1_J,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_nat @ I @ J )
& ( K = L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(1)
thf(fact_270_add__mono__thms__linordered__field_I1_J,axiom,
! [I: int,J: int,K: int,L: int] :
( ( ( ord_less_int @ I @ J )
& ( K = L ) )
=> ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(1)
thf(fact_271_add__mono__thms__linordered__field_I2_J,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( I = J )
& ( ord_less_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(2)
thf(fact_272_add__mono__thms__linordered__field_I2_J,axiom,
! [I: int,J: int,K: int,L: int] :
( ( ( I = J )
& ( ord_less_int @ K @ L ) )
=> ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(2)
thf(fact_273_add__mono__thms__linordered__field_I5_J,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_nat @ I @ J )
& ( ord_less_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(5)
thf(fact_274_add__mono__thms__linordered__field_I5_J,axiom,
! [I: int,J: int,K: int,L: int] :
( ( ( ord_less_int @ I @ J )
& ( ord_less_int @ K @ L ) )
=> ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(5)
thf(fact_275_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_276_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_277_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_278_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_279_zero__induct__lemma,axiom,
! [P: nat > $o,K: nat,I: nat] :
( ( P @ K )
=> ( ! [N2: nat] :
( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) )
=> ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% zero_induct_lemma
thf(fact_280_minus__less__iff,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
= ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% minus_less_iff
thf(fact_281_less__minus__iff,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
= ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% less_minus_iff
thf(fact_282_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_283_add__Suc,axiom,
! [M: nat,N: nat] :
( ( plus_plus_nat @ ( suc @ M ) @ N )
= ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% add_Suc
thf(fact_284_nat__arith_Osuc1,axiom,
! [A2: nat,K: nat,A: nat] :
( ( A2
= ( plus_plus_nat @ K @ A ) )
=> ( ( suc @ A2 )
= ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% nat_arith.suc1
thf(fact_285_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_286_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_287_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,J2: nat,K2: nat] :
( ( ord_less_nat @ I3 @ J2 )
=> ( ( ord_less_nat @ J2 @ K2 )
=> ( ( P @ I3 @ J2 )
=> ( ( P @ J2 @ K2 )
=> ( P @ I3 @ K2 ) ) ) ) )
=> ( P @ I @ J ) ) ) ) ).
% less_Suc_induct
thf(fact_288_less__trans__Suc,axiom,
! [I: nat,J: nat,K: nat] :
( ( ord_less_nat @ I @ J )
=> ( ( ord_less_nat @ J @ K )
=> ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% less_trans_Suc
thf(fact_289_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_290_less__antisym,axiom,
! [N: nat,M: nat] :
( ~ ( ord_less_nat @ N @ M )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
=> ( M = N ) ) ) ).
% less_antisym
thf(fact_291_Suc__less__eq2,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ ( suc @ N ) @ M )
= ( ? [M4: nat] :
( ( M
= ( suc @ M4 ) )
& ( ord_less_nat @ N @ M4 ) ) ) ) ).
% Suc_less_eq2
thf(fact_292_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_293_not__less__eq,axiom,
! [M: nat,N: nat] :
( ( ~ ( ord_less_nat @ M @ N ) )
= ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% not_less_eq
thf(fact_294_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_295_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_296_less__SucI,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% less_SucI
thf(fact_297_less__SucE,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
=> ( ~ ( ord_less_nat @ M @ N )
=> ( M = N ) ) ) ).
% less_SucE
thf(fact_298_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_299_Suc__lessE,axiom,
! [I: nat,K: nat] :
( ( ord_less_nat @ ( suc @ I ) @ K )
=> ~ ! [J2: nat] :
( ( ord_less_nat @ I @ J2 )
=> ( K
!= ( suc @ J2 ) ) ) ) ).
% Suc_lessE
thf(fact_300_Suc__lessD,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ N )
=> ( ord_less_nat @ M @ N ) ) ).
% Suc_lessD
thf(fact_301_Nat_OlessE,axiom,
! [I: nat,K: nat] :
( ( ord_less_nat @ I @ K )
=> ( ( K
!= ( suc @ I ) )
=> ~ ! [J2: nat] :
( ( ord_less_nat @ I @ J2 )
=> ( K
!= ( suc @ J2 ) ) ) ) ) ).
% Nat.lessE
thf(fact_302_add_Ogroup__left__neutral,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ) ).
% add.group_left_neutral
thf(fact_303_add_Ocomm__neutral,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ) ).
% add.comm_neutral
thf(fact_304_add_Ocomm__neutral,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ) ).
% add.comm_neutral
thf(fact_305_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_306_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_307_eq__iff__diff__eq__0,axiom,
( ( ^ [Y3: int,Z: int] : ( Y3 = Z ) )
= ( ^ [A3: int,B2: int] :
( ( minus_minus_int @ A3 @ B2 )
= zero_zero_int ) ) ) ).
% eq_iff_diff_eq_0
thf(fact_308_length__induct,axiom,
! [P: list_list_char > $o,Xs: list_list_char] :
( ! [Xs3: list_list_char] :
( ! [Ys3: list_list_char] :
( ( ord_less_nat @ ( size_s356637359517785349t_char @ Ys3 ) @ ( size_s356637359517785349t_char @ Xs3 ) )
=> ( P @ Ys3 ) )
=> ( P @ Xs3 ) )
=> ( P @ Xs ) ) ).
% length_induct
thf(fact_309_length__induct,axiom,
! [P: list_int > $o,Xs: list_int] :
( ! [Xs3: list_int] :
( ! [Ys3: list_int] :
( ( ord_less_nat @ ( size_size_list_int @ Ys3 ) @ ( size_size_list_int @ Xs3 ) )
=> ( P @ Ys3 ) )
=> ( P @ Xs3 ) )
=> ( P @ Xs ) ) ).
% length_induct
thf(fact_310_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_311_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_312_nth__append,axiom,
! [N: nat,Xs: list_list_char,Ys: list_list_char] :
( ( ( ord_less_nat @ N @ ( size_s356637359517785349t_char @ Xs ) )
=> ( ( nth_list_char @ ( append_list_char @ Xs @ Ys ) @ N )
= ( nth_list_char @ Xs @ N ) ) )
& ( ~ ( ord_less_nat @ N @ ( size_s356637359517785349t_char @ Xs ) )
=> ( ( nth_list_char @ ( append_list_char @ Xs @ Ys ) @ N )
= ( nth_list_char @ Ys @ ( minus_minus_nat @ N @ ( size_s356637359517785349t_char @ Xs ) ) ) ) ) ) ).
% nth_append
thf(fact_313_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_314_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_315_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_316_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_317_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_318_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_319_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_320_add_Ocommute,axiom,
( plus_plus_int
= ( ^ [A3: int,B2: int] : ( plus_plus_int @ B2 @ A3 ) ) ) ).
% add.commute
thf(fact_321_add_Ocommute,axiom,
( plus_plus_nat
= ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).
% add.commute
thf(fact_322_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_323_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_324_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_325_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_326_group__cancel_Oadd2,axiom,
! [B3: int,K: int,B: int,A: int] :
( ( B3
= ( plus_plus_int @ K @ B ) )
=> ( ( plus_plus_int @ A @ B3 )
= ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% group_cancel.add2
thf(fact_327_group__cancel_Oadd2,axiom,
! [B3: nat,K: nat,B: nat,A: nat] :
( ( B3
= ( plus_plus_nat @ K @ B ) )
=> ( ( plus_plus_nat @ A @ B3 )
= ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% group_cancel.add2
thf(fact_328_group__cancel_Oadd1,axiom,
! [A2: int,K: int,A: int,B: int] :
( ( A2
= ( plus_plus_int @ K @ A ) )
=> ( ( plus_plus_int @ A2 @ B )
= ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% group_cancel.add1
thf(fact_329_group__cancel_Oadd1,axiom,
! [A2: nat,K: nat,A: nat,B: nat] :
( ( A2
= ( plus_plus_nat @ K @ A ) )
=> ( ( plus_plus_nat @ A2 @ B )
= ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% group_cancel.add1
thf(fact_330_add__mono__thms__linordered__semiring_I4_J,axiom,
! [I: int,J: int,K: int,L: int] :
( ( ( I = J )
& ( K = L ) )
=> ( ( plus_plus_int @ I @ K )
= ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(4)
thf(fact_331_add__mono__thms__linordered__semiring_I4_J,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( I = J )
& ( K = L ) )
=> ( ( plus_plus_nat @ I @ K )
= ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(4)
thf(fact_332_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_333_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_334_one__reorient,axiom,
! [X: int] :
( ( one_one_int = X )
= ( X = one_one_int ) ) ).
% one_reorient
thf(fact_335_one__reorient,axiom,
! [X: nat] :
( ( one_one_nat = X )
= ( X = one_one_nat ) ) ).
% one_reorient
thf(fact_336_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_337_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_338_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_339_minus__equation__iff,axiom,
! [A: int,B: int] :
( ( ( uminus_uminus_int @ A )
= B )
= ( ( uminus_uminus_int @ B )
= A ) ) ).
% minus_equation_iff
thf(fact_340_equation__minus__iff,axiom,
! [A: int,B: int] :
( ( A
= ( uminus_uminus_int @ B ) )
= ( B
= ( uminus_uminus_int @ A ) ) ) ).
% equation_minus_iff
thf(fact_341_n__not__Suc__n,axiom,
! [N: nat] :
( N
!= ( suc @ N ) ) ).
% n_not_Suc_n
thf(fact_342_Suc__inject,axiom,
! [X: nat,Y: nat] :
( ( ( suc @ X )
= ( suc @ Y ) )
=> ( X = Y ) ) ).
% Suc_inject
thf(fact_343_not__Cons__self2,axiom,
! [X: instr,Xs: list_instr] :
( ( cons_instr @ X @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_344_not__Cons__self2,axiom,
! [X: int,Xs: list_int] :
( ( cons_int @ X @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_345_not__Cons__self2,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int] :
( ( cons_P4151473878978182108st_int @ X @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_346_size__neq__size__imp__neq,axiom,
! [X: list_list_char,Y: list_list_char] :
( ( ( size_s356637359517785349t_char @ X )
!= ( size_s356637359517785349t_char @ Y ) )
=> ( X != Y ) ) ).
% size_neq_size_imp_neq
thf(fact_347_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_348_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_349_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_350_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_351_neq__if__length__neq,axiom,
! [Xs: list_list_char,Ys: list_list_char] :
( ( ( size_s356637359517785349t_char @ Xs )
!= ( size_s356637359517785349t_char @ Ys ) )
=> ( Xs != Ys ) ) ).
% neq_if_length_neq
thf(fact_352_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_353_Ex__list__of__length,axiom,
! [N: nat] :
? [Xs3: list_list_char] :
( ( size_s356637359517785349t_char @ Xs3 )
= N ) ).
% Ex_list_of_length
thf(fact_354_Ex__list__of__length,axiom,
! [N: nat] :
? [Xs3: list_int] :
( ( size_size_list_int @ Xs3 )
= N ) ).
% Ex_list_of_length
thf(fact_355_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_356_append__eq__append__conv2,axiom,
! [Xs: list_int,Ys: list_int,Zs: list_int,Ts: list_int] :
( ( ( append_int @ Xs @ Ys )
= ( append_int @ Zs @ Ts ) )
= ( ? [Us2: list_int] :
( ( ( Xs
= ( append_int @ Zs @ Us2 ) )
& ( ( append_int @ Us2 @ Ys )
= Ts ) )
| ( ( ( append_int @ Xs @ Us2 )
= Zs )
& ( Ys
= ( append_int @ Us2 @ Ts ) ) ) ) ) ) ).
% append_eq_append_conv2
thf(fact_357_append__eq__append__conv2,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int,Ts: list_P419547167332244514st_int] :
( ( ( append5028292981072010935st_int @ Xs @ Ys )
= ( append5028292981072010935st_int @ Zs @ Ts ) )
= ( ? [Us2: list_P419547167332244514st_int] :
( ( ( Xs
= ( append5028292981072010935st_int @ Zs @ Us2 ) )
& ( ( append5028292981072010935st_int @ Us2 @ Ys )
= Ts ) )
| ( ( ( append5028292981072010935st_int @ Xs @ Us2 )
= Zs )
& ( Ys
= ( append5028292981072010935st_int @ Us2 @ Ts ) ) ) ) ) ) ).
% append_eq_append_conv2
thf(fact_358_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_359_append__eq__appendI,axiom,
! [Xs: list_int,Xs1: list_int,Zs: list_int,Ys: list_int,Us: list_int] :
( ( ( append_int @ Xs @ Xs1 )
= Zs )
=> ( ( Ys
= ( append_int @ Xs1 @ Us ) )
=> ( ( append_int @ Xs @ Ys )
= ( append_int @ Zs @ Us ) ) ) ) ).
% append_eq_appendI
thf(fact_360_append__eq__appendI,axiom,
! [Xs: list_P419547167332244514st_int,Xs1: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,Us: list_P419547167332244514st_int] :
( ( ( append5028292981072010935st_int @ Xs @ Xs1 )
= Zs )
=> ( ( Ys
= ( append5028292981072010935st_int @ Xs1 @ Us ) )
=> ( ( append5028292981072010935st_int @ Xs @ Ys )
= ( append5028292981072010935st_int @ Zs @ Us ) ) ) ) ).
% append_eq_appendI
thf(fact_361_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_362_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_363_neg__eq__iff__add__eq__0,axiom,
! [A: int,B: int] :
( ( ( uminus_uminus_int @ A )
= B )
= ( ( plus_plus_int @ A @ B )
= zero_zero_int ) ) ).
% neg_eq_iff_add_eq_0
thf(fact_364_eq__neg__iff__add__eq__0,axiom,
! [A: int,B: int] :
( ( A
= ( uminus_uminus_int @ B ) )
= ( ( plus_plus_int @ A @ B )
= zero_zero_int ) ) ).
% eq_neg_iff_add_eq_0
thf(fact_365_add_Oinverse__unique,axiom,
! [A: int,B: int] :
( ( ( plus_plus_int @ A @ B )
= zero_zero_int )
=> ( ( uminus_uminus_int @ A )
= B ) ) ).
% add.inverse_unique
thf(fact_366_ab__group__add__class_Oab__left__minus,axiom,
! [A: int] :
( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
= zero_zero_int ) ).
% ab_group_add_class.ab_left_minus
thf(fact_367_add__eq__0__iff,axiom,
! [A: int,B: int] :
( ( ( plus_plus_int @ A @ B )
= zero_zero_int )
= ( B
= ( uminus_uminus_int @ A ) ) ) ).
% add_eq_0_iff
thf(fact_368_nth__via__drop,axiom,
! [N: nat,Xs: list_instr,Y: instr,Ys: list_instr] :
( ( ( drop_instr @ N @ Xs )
= ( cons_instr @ Y @ Ys ) )
=> ( ( nth_instr @ Xs @ N )
= Y ) ) ).
% nth_via_drop
thf(fact_369_nth__via__drop,axiom,
! [N: nat,Xs: list_int,Y: int,Ys: list_int] :
( ( ( drop_int @ N @ Xs )
= ( cons_int @ Y @ Ys ) )
=> ( ( nth_int @ Xs @ N )
= Y ) ) ).
% nth_via_drop
thf(fact_370_nth__via__drop,axiom,
! [N: nat,Xs: list_P419547167332244514st_int,Y: produc6425607678544837394st_int,Ys: list_P419547167332244514st_int] :
( ( ( drop_P7838799151754935884st_int @ N @ Xs )
= ( cons_P4151473878978182108st_int @ Y @ Ys ) )
=> ( ( nth_Pr8327173284404383691st_int @ Xs @ N )
= Y ) ) ).
% nth_via_drop
thf(fact_371_of__nat__neq__0,axiom,
! [N: nat] :
( ( semiri1314217659103216013at_int @ ( suc @ N ) )
!= zero_zero_int ) ).
% of_nat_neq_0
thf(fact_372_of__nat__neq__0,axiom,
! [N: nat] :
( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
!= zero_zero_nat ) ).
% of_nat_neq_0
thf(fact_373_Cons__nth__drop__Suc,axiom,
! [I: nat,Xs: list_instr] :
( ( ord_less_nat @ I @ ( size_size_list_instr @ Xs ) )
=> ( ( cons_instr @ ( nth_instr @ Xs @ I ) @ ( drop_instr @ ( suc @ I ) @ Xs ) )
= ( drop_instr @ I @ Xs ) ) ) ).
% Cons_nth_drop_Suc
thf(fact_374_Cons__nth__drop__Suc,axiom,
! [I: nat,Xs: list_P419547167332244514st_int] :
( ( ord_less_nat @ I @ ( size_s229347708945616566st_int @ Xs ) )
=> ( ( cons_P4151473878978182108st_int @ ( nth_Pr8327173284404383691st_int @ Xs @ I ) @ ( drop_P7838799151754935884st_int @ ( suc @ I ) @ Xs ) )
= ( drop_P7838799151754935884st_int @ I @ Xs ) ) ) ).
% Cons_nth_drop_Suc
thf(fact_375_Cons__nth__drop__Suc,axiom,
! [I: nat,Xs: list_list_char] :
( ( ord_less_nat @ I @ ( size_s356637359517785349t_char @ Xs ) )
=> ( ( cons_list_char @ ( nth_list_char @ Xs @ I ) @ ( drop_list_char @ ( suc @ I ) @ Xs ) )
= ( drop_list_char @ I @ Xs ) ) ) ).
% Cons_nth_drop_Suc
thf(fact_376_Cons__nth__drop__Suc,axiom,
! [I: nat,Xs: list_int] :
( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
=> ( ( cons_int @ ( nth_int @ Xs @ I ) @ ( drop_int @ ( suc @ I ) @ Xs ) )
= ( drop_int @ I @ Xs ) ) ) ).
% Cons_nth_drop_Suc
thf(fact_377_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_378_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_379_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_380_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_381_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_382_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_383_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_384_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_385_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_386_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_387_group__cancel_Osub1,axiom,
! [A2: int,K: int,A: int,B: int] :
( ( A2
= ( plus_plus_int @ K @ A ) )
=> ( ( minus_minus_int @ A2 @ B )
= ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% group_cancel.sub1
thf(fact_388_add_Oinverse__distrib__swap,axiom,
! [A: int,B: int] :
( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% add.inverse_distrib_swap
thf(fact_389_group__cancel_Oneg1,axiom,
! [A2: int,K: int,A: int] :
( ( A2
= ( plus_plus_int @ K @ A ) )
=> ( ( uminus_uminus_int @ A2 )
= ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% group_cancel.neg1
thf(fact_390_minus__diff__commute,axiom,
! [B: int,A: int] :
( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
= ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% minus_diff_commute
thf(fact_391_list__nonempty__induct,axiom,
! [Xs: list_instr,P: list_instr > $o] :
( ( Xs != nil_instr )
=> ( ! [X5: instr] : ( P @ ( cons_instr @ X5 @ nil_instr ) )
=> ( ! [X5: instr,Xs3: list_instr] :
( ( Xs3 != nil_instr )
=> ( ( P @ Xs3 )
=> ( P @ ( cons_instr @ X5 @ Xs3 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_392_list__nonempty__induct,axiom,
! [Xs: list_int,P: list_int > $o] :
( ( Xs != nil_int )
=> ( ! [X5: int] : ( P @ ( cons_int @ X5 @ nil_int ) )
=> ( ! [X5: int,Xs3: list_int] :
( ( Xs3 != nil_int )
=> ( ( P @ Xs3 )
=> ( P @ ( cons_int @ X5 @ Xs3 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_393_list__nonempty__induct,axiom,
! [Xs: list_P419547167332244514st_int,P: list_P419547167332244514st_int > $o] :
( ( Xs != nil_Pr749310521696113548st_int )
=> ( ! [X5: produc6425607678544837394st_int] : ( P @ ( cons_P4151473878978182108st_int @ X5 @ nil_Pr749310521696113548st_int ) )
=> ( ! [X5: produc6425607678544837394st_int,Xs3: list_P419547167332244514st_int] :
( ( Xs3 != nil_Pr749310521696113548st_int )
=> ( ( P @ Xs3 )
=> ( P @ ( cons_P4151473878978182108st_int @ X5 @ Xs3 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_394_list__induct2_H,axiom,
! [P: list_instr > list_instr > $o,Xs: list_instr,Ys: list_instr] :
( ( P @ nil_instr @ nil_instr )
=> ( ! [X5: instr,Xs3: list_instr] : ( P @ ( cons_instr @ X5 @ Xs3 ) @ nil_instr )
=> ( ! [Y4: instr,Ys4: list_instr] : ( P @ nil_instr @ ( cons_instr @ Y4 @ Ys4 ) )
=> ( ! [X5: instr,Xs3: list_instr,Y4: instr,Ys4: list_instr] :
( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_instr @ X5 @ Xs3 ) @ ( cons_instr @ Y4 @ Ys4 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_395_list__induct2_H,axiom,
! [P: list_instr > list_int > $o,Xs: list_instr,Ys: list_int] :
( ( P @ nil_instr @ nil_int )
=> ( ! [X5: instr,Xs3: list_instr] : ( P @ ( cons_instr @ X5 @ Xs3 ) @ nil_int )
=> ( ! [Y4: int,Ys4: list_int] : ( P @ nil_instr @ ( cons_int @ Y4 @ Ys4 ) )
=> ( ! [X5: instr,Xs3: list_instr,Y4: int,Ys4: list_int] :
( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_instr @ X5 @ Xs3 ) @ ( cons_int @ Y4 @ Ys4 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_396_list__induct2_H,axiom,
! [P: list_instr > list_P419547167332244514st_int > $o,Xs: list_instr,Ys: list_P419547167332244514st_int] :
( ( P @ nil_instr @ nil_Pr749310521696113548st_int )
=> ( ! [X5: instr,Xs3: list_instr] : ( P @ ( cons_instr @ X5 @ Xs3 ) @ nil_Pr749310521696113548st_int )
=> ( ! [Y4: produc6425607678544837394st_int,Ys4: list_P419547167332244514st_int] : ( P @ nil_instr @ ( cons_P4151473878978182108st_int @ Y4 @ Ys4 ) )
=> ( ! [X5: instr,Xs3: list_instr,Y4: produc6425607678544837394st_int,Ys4: list_P419547167332244514st_int] :
( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_instr @ X5 @ Xs3 ) @ ( cons_P4151473878978182108st_int @ Y4 @ Ys4 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_397_list__induct2_H,axiom,
! [P: list_int > list_instr > $o,Xs: list_int,Ys: list_instr] :
( ( P @ nil_int @ nil_instr )
=> ( ! [X5: int,Xs3: list_int] : ( P @ ( cons_int @ X5 @ Xs3 ) @ nil_instr )
=> ( ! [Y4: instr,Ys4: list_instr] : ( P @ nil_int @ ( cons_instr @ Y4 @ Ys4 ) )
=> ( ! [X5: int,Xs3: list_int,Y4: instr,Ys4: list_instr] :
( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_int @ X5 @ Xs3 ) @ ( cons_instr @ Y4 @ Ys4 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_398_list__induct2_H,axiom,
! [P: list_int > list_int > $o,Xs: list_int,Ys: list_int] :
( ( P @ nil_int @ nil_int )
=> ( ! [X5: int,Xs3: list_int] : ( P @ ( cons_int @ X5 @ Xs3 ) @ nil_int )
=> ( ! [Y4: int,Ys4: list_int] : ( P @ nil_int @ ( cons_int @ Y4 @ Ys4 ) )
=> ( ! [X5: int,Xs3: list_int,Y4: int,Ys4: list_int] :
( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_int @ X5 @ Xs3 ) @ ( cons_int @ Y4 @ Ys4 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_399_list__induct2_H,axiom,
! [P: list_int > list_P419547167332244514st_int > $o,Xs: list_int,Ys: list_P419547167332244514st_int] :
( ( P @ nil_int @ nil_Pr749310521696113548st_int )
=> ( ! [X5: int,Xs3: list_int] : ( P @ ( cons_int @ X5 @ Xs3 ) @ nil_Pr749310521696113548st_int )
=> ( ! [Y4: produc6425607678544837394st_int,Ys4: list_P419547167332244514st_int] : ( P @ nil_int @ ( cons_P4151473878978182108st_int @ Y4 @ Ys4 ) )
=> ( ! [X5: int,Xs3: list_int,Y4: produc6425607678544837394st_int,Ys4: list_P419547167332244514st_int] :
( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_int @ X5 @ Xs3 ) @ ( cons_P4151473878978182108st_int @ Y4 @ Ys4 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_400_list__induct2_H,axiom,
! [P: list_P419547167332244514st_int > list_instr > $o,Xs: list_P419547167332244514st_int,Ys: list_instr] :
( ( P @ nil_Pr749310521696113548st_int @ nil_instr )
=> ( ! [X5: produc6425607678544837394st_int,Xs3: list_P419547167332244514st_int] : ( P @ ( cons_P4151473878978182108st_int @ X5 @ Xs3 ) @ nil_instr )
=> ( ! [Y4: instr,Ys4: list_instr] : ( P @ nil_Pr749310521696113548st_int @ ( cons_instr @ Y4 @ Ys4 ) )
=> ( ! [X5: produc6425607678544837394st_int,Xs3: list_P419547167332244514st_int,Y4: instr,Ys4: list_instr] :
( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_P4151473878978182108st_int @ X5 @ Xs3 ) @ ( cons_instr @ Y4 @ Ys4 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_401_list__induct2_H,axiom,
! [P: list_P419547167332244514st_int > list_int > $o,Xs: list_P419547167332244514st_int,Ys: list_int] :
( ( P @ nil_Pr749310521696113548st_int @ nil_int )
=> ( ! [X5: produc6425607678544837394st_int,Xs3: list_P419547167332244514st_int] : ( P @ ( cons_P4151473878978182108st_int @ X5 @ Xs3 ) @ nil_int )
=> ( ! [Y4: int,Ys4: list_int] : ( P @ nil_Pr749310521696113548st_int @ ( cons_int @ Y4 @ Ys4 ) )
=> ( ! [X5: produc6425607678544837394st_int,Xs3: list_P419547167332244514st_int,Y4: int,Ys4: list_int] :
( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_P4151473878978182108st_int @ X5 @ Xs3 ) @ ( cons_int @ Y4 @ Ys4 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_402_list__induct2_H,axiom,
! [P: list_P419547167332244514st_int > list_P419547167332244514st_int > $o,Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( P @ nil_Pr749310521696113548st_int @ nil_Pr749310521696113548st_int )
=> ( ! [X5: produc6425607678544837394st_int,Xs3: list_P419547167332244514st_int] : ( P @ ( cons_P4151473878978182108st_int @ X5 @ Xs3 ) @ nil_Pr749310521696113548st_int )
=> ( ! [Y4: produc6425607678544837394st_int,Ys4: list_P419547167332244514st_int] : ( P @ nil_Pr749310521696113548st_int @ ( cons_P4151473878978182108st_int @ Y4 @ Ys4 ) )
=> ( ! [X5: produc6425607678544837394st_int,Xs3: list_P419547167332244514st_int,Y4: produc6425607678544837394st_int,Ys4: list_P419547167332244514st_int] :
( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_P4151473878978182108st_int @ X5 @ Xs3 ) @ ( cons_P4151473878978182108st_int @ Y4 @ Ys4 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_403_neq__Nil__conv,axiom,
! [Xs: list_instr] :
( ( Xs != nil_instr )
= ( ? [Y5: instr,Ys2: list_instr] :
( Xs
= ( cons_instr @ Y5 @ Ys2 ) ) ) ) ).
% neq_Nil_conv
thf(fact_404_neq__Nil__conv,axiom,
! [Xs: list_int] :
( ( Xs != nil_int )
= ( ? [Y5: int,Ys2: list_int] :
( Xs
= ( cons_int @ Y5 @ Ys2 ) ) ) ) ).
% neq_Nil_conv
thf(fact_405_neq__Nil__conv,axiom,
! [Xs: list_P419547167332244514st_int] :
( ( Xs != nil_Pr749310521696113548st_int )
= ( ? [Y5: produc6425607678544837394st_int,Ys2: list_P419547167332244514st_int] :
( Xs
= ( cons_P4151473878978182108st_int @ Y5 @ Ys2 ) ) ) ) ).
% neq_Nil_conv
thf(fact_406_remdups__adj_Ocases,axiom,
! [X: list_instr] :
( ( X != nil_instr )
=> ( ! [X5: instr] :
( X
!= ( cons_instr @ X5 @ nil_instr ) )
=> ~ ! [X5: instr,Y4: instr,Xs3: list_instr] :
( X
!= ( cons_instr @ X5 @ ( cons_instr @ Y4 @ Xs3 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_407_remdups__adj_Ocases,axiom,
! [X: list_int] :
( ( X != nil_int )
=> ( ! [X5: int] :
( X
!= ( cons_int @ X5 @ nil_int ) )
=> ~ ! [X5: int,Y4: int,Xs3: list_int] :
( X
!= ( cons_int @ X5 @ ( cons_int @ Y4 @ Xs3 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_408_remdups__adj_Ocases,axiom,
! [X: list_P419547167332244514st_int] :
( ( X != nil_Pr749310521696113548st_int )
=> ( ! [X5: produc6425607678544837394st_int] :
( X
!= ( cons_P4151473878978182108st_int @ X5 @ nil_Pr749310521696113548st_int ) )
=> ~ ! [X5: produc6425607678544837394st_int,Y4: produc6425607678544837394st_int,Xs3: list_P419547167332244514st_int] :
( X
!= ( cons_P4151473878978182108st_int @ X5 @ ( cons_P4151473878978182108st_int @ Y4 @ Xs3 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_409_transpose_Ocases,axiom,
! [X: list_list_instr] :
( ( X != nil_list_instr )
=> ( ! [Xss: list_list_instr] :
( X
!= ( cons_list_instr @ nil_instr @ Xss ) )
=> ~ ! [X5: instr,Xs3: list_instr,Xss: list_list_instr] :
( X
!= ( cons_list_instr @ ( cons_instr @ X5 @ Xs3 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_410_transpose_Ocases,axiom,
! [X: list_list_int] :
( ( X != nil_list_int )
=> ( ! [Xss: list_list_int] :
( X
!= ( cons_list_int @ nil_int @ Xss ) )
=> ~ ! [X5: int,Xs3: list_int,Xss: list_list_int] :
( X
!= ( cons_list_int @ ( cons_int @ X5 @ Xs3 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_411_transpose_Ocases,axiom,
! [X: list_l6422821129637969586st_int] :
( ( X != nil_li4597314861645524892st_int )
=> ( ! [Xss: list_l6422821129637969586st_int] :
( X
!= ( cons_l8648290059330449388st_int @ nil_Pr749310521696113548st_int @ Xss ) )
=> ~ ! [X5: produc6425607678544837394st_int,Xs3: list_P419547167332244514st_int,Xss: list_l6422821129637969586st_int] :
( X
!= ( cons_l8648290059330449388st_int @ ( cons_P4151473878978182108st_int @ X5 @ Xs3 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_412_min__list_Ocases,axiom,
! [X: list_int] :
( ! [X5: int,Xs3: list_int] :
( X
!= ( cons_int @ X5 @ Xs3 ) )
=> ( X = nil_int ) ) ).
% min_list.cases
thf(fact_413_list_Oexhaust,axiom,
! [Y: list_instr] :
( ( Y != nil_instr )
=> ~ ! [X212: instr,X222: list_instr] :
( Y
!= ( cons_instr @ X212 @ X222 ) ) ) ).
% list.exhaust
thf(fact_414_list_Oexhaust,axiom,
! [Y: list_int] :
( ( Y != nil_int )
=> ~ ! [X212: int,X222: list_int] :
( Y
!= ( cons_int @ X212 @ X222 ) ) ) ).
% list.exhaust
thf(fact_415_list_Oexhaust,axiom,
! [Y: list_P419547167332244514st_int] :
( ( Y != nil_Pr749310521696113548st_int )
=> ~ ! [X212: produc6425607678544837394st_int,X222: list_P419547167332244514st_int] :
( Y
!= ( cons_P4151473878978182108st_int @ X212 @ X222 ) ) ) ).
% list.exhaust
thf(fact_416_list_OdiscI,axiom,
! [List: list_instr,X21: instr,X22: list_instr] :
( ( List
= ( cons_instr @ X21 @ X22 ) )
=> ( List != nil_instr ) ) ).
% list.discI
thf(fact_417_list_OdiscI,axiom,
! [List: list_int,X21: int,X22: list_int] :
( ( List
= ( cons_int @ X21 @ X22 ) )
=> ( List != nil_int ) ) ).
% list.discI
thf(fact_418_list_OdiscI,axiom,
! [List: list_P419547167332244514st_int,X21: produc6425607678544837394st_int,X22: list_P419547167332244514st_int] :
( ( List
= ( cons_P4151473878978182108st_int @ X21 @ X22 ) )
=> ( List != nil_Pr749310521696113548st_int ) ) ).
% list.discI
thf(fact_419_list_Odistinct_I1_J,axiom,
! [X21: instr,X22: list_instr] :
( nil_instr
!= ( cons_instr @ X21 @ X22 ) ) ).
% list.distinct(1)
thf(fact_420_list_Odistinct_I1_J,axiom,
! [X21: int,X22: list_int] :
( nil_int
!= ( cons_int @ X21 @ X22 ) ) ).
% list.distinct(1)
thf(fact_421_list_Odistinct_I1_J,axiom,
! [X21: produc6425607678544837394st_int,X22: list_P419547167332244514st_int] :
( nil_Pr749310521696113548st_int
!= ( cons_P4151473878978182108st_int @ X21 @ X22 ) ) ).
% list.distinct(1)
thf(fact_422_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_423_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_424_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_425_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_426_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_427_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_428_eq__Nil__appendI,axiom,
! [Xs: list_instr,Ys: list_instr] :
( ( Xs = Ys )
=> ( Xs
= ( append_instr @ nil_instr @ Ys ) ) ) ).
% eq_Nil_appendI
thf(fact_429_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_430_eq__Nil__appendI,axiom,
! [Xs: list_int,Ys: list_int] :
( ( Xs = Ys )
=> ( Xs
= ( append_int @ nil_int @ Ys ) ) ) ).
% eq_Nil_appendI
thf(fact_431_append_Oleft__neutral,axiom,
! [A: list_instr] :
( ( append_instr @ nil_instr @ A )
= A ) ).
% append.left_neutral
thf(fact_432_append_Oleft__neutral,axiom,
! [A: list_P419547167332244514st_int] :
( ( append5028292981072010935st_int @ nil_Pr749310521696113548st_int @ A )
= A ) ).
% append.left_neutral
thf(fact_433_append_Oleft__neutral,axiom,
! [A: list_int] :
( ( append_int @ nil_int @ A )
= A ) ).
% append.left_neutral
thf(fact_434_append__Nil,axiom,
! [Ys: list_instr] :
( ( append_instr @ nil_instr @ Ys )
= Ys ) ).
% append_Nil
thf(fact_435_append__Nil,axiom,
! [Ys: list_P419547167332244514st_int] :
( ( append5028292981072010935st_int @ nil_Pr749310521696113548st_int @ Ys )
= Ys ) ).
% append_Nil
thf(fact_436_append__Nil,axiom,
! [Ys: list_int] :
( ( append_int @ nil_int @ Ys )
= Ys ) ).
% append_Nil
thf(fact_437_drop__Nil,axiom,
! [N: nat] :
( ( drop_instr @ N @ nil_instr )
= nil_instr ) ).
% drop_Nil
thf(fact_438_drop__Nil,axiom,
! [N: nat] :
( ( drop_P7838799151754935884st_int @ N @ nil_Pr749310521696113548st_int )
= nil_Pr749310521696113548st_int ) ).
% drop_Nil
thf(fact_439_drop__Nil,axiom,
! [N: nat] :
( ( drop_int @ N @ nil_int )
= nil_int ) ).
% drop_Nil
thf(fact_440_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
( minus_minus_int
= ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% ab_group_add_class.ab_diff_conv_add_uminus
thf(fact_441_diff__conv__add__uminus,axiom,
( minus_minus_int
= ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% diff_conv_add_uminus
thf(fact_442_group__cancel_Osub2,axiom,
! [B3: int,K: int,B: int,A: int] :
( ( B3
= ( plus_plus_int @ K @ B ) )
=> ( ( minus_minus_int @ A @ B3 )
= ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% group_cancel.sub2
thf(fact_443_length__Suc__conv,axiom,
! [Xs: list_instr,N: nat] :
( ( ( size_size_list_instr @ Xs )
= ( suc @ N ) )
= ( ? [Y5: instr,Ys2: list_instr] :
( ( Xs
= ( cons_instr @ Y5 @ Ys2 ) )
& ( ( size_size_list_instr @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv
thf(fact_444_length__Suc__conv,axiom,
! [Xs: list_P419547167332244514st_int,N: nat] :
( ( ( size_s229347708945616566st_int @ Xs )
= ( suc @ N ) )
= ( ? [Y5: produc6425607678544837394st_int,Ys2: list_P419547167332244514st_int] :
( ( Xs
= ( cons_P4151473878978182108st_int @ Y5 @ Ys2 ) )
& ( ( size_s229347708945616566st_int @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv
thf(fact_445_length__Suc__conv,axiom,
! [Xs: list_list_char,N: nat] :
( ( ( size_s356637359517785349t_char @ Xs )
= ( suc @ N ) )
= ( ? [Y5: list_char,Ys2: list_list_char] :
( ( Xs
= ( cons_list_char @ Y5 @ Ys2 ) )
& ( ( size_s356637359517785349t_char @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv
thf(fact_446_length__Suc__conv,axiom,
! [Xs: list_int,N: nat] :
( ( ( size_size_list_int @ Xs )
= ( suc @ N ) )
= ( ? [Y5: int,Ys2: list_int] :
( ( Xs
= ( cons_int @ Y5 @ Ys2 ) )
& ( ( size_size_list_int @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv
thf(fact_447_Suc__length__conv,axiom,
! [N: nat,Xs: list_instr] :
( ( ( suc @ N )
= ( size_size_list_instr @ Xs ) )
= ( ? [Y5: instr,Ys2: list_instr] :
( ( Xs
= ( cons_instr @ Y5 @ Ys2 ) )
& ( ( size_size_list_instr @ Ys2 )
= N ) ) ) ) ).
% Suc_length_conv
thf(fact_448_Suc__length__conv,axiom,
! [N: nat,Xs: list_P419547167332244514st_int] :
( ( ( suc @ N )
= ( size_s229347708945616566st_int @ Xs ) )
= ( ? [Y5: produc6425607678544837394st_int,Ys2: list_P419547167332244514st_int] :
( ( Xs
= ( cons_P4151473878978182108st_int @ Y5 @ Ys2 ) )
& ( ( size_s229347708945616566st_int @ Ys2 )
= N ) ) ) ) ).
% Suc_length_conv
thf(fact_449_Suc__length__conv,axiom,
! [N: nat,Xs: list_list_char] :
( ( ( suc @ N )
= ( size_s356637359517785349t_char @ Xs ) )
= ( ? [Y5: list_char,Ys2: list_list_char] :
( ( Xs
= ( cons_list_char @ Y5 @ Ys2 ) )
& ( ( size_s356637359517785349t_char @ Ys2 )
= N ) ) ) ) ).
% Suc_length_conv
thf(fact_450_Suc__length__conv,axiom,
! [N: nat,Xs: list_int] :
( ( ( suc @ N )
= ( size_size_list_int @ Xs ) )
= ( ? [Y5: int,Ys2: list_int] :
( ( Xs
= ( cons_int @ Y5 @ Ys2 ) )
& ( ( size_size_list_int @ Ys2 )
= N ) ) ) ) ).
% Suc_length_conv
thf(fact_451_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 )
=> ( ! [X5: instr,Xs3: list_instr,Y4: instr,Ys4: list_instr,Z2: instr,Zs2: list_instr] :
( ( ( size_size_list_instr @ Xs3 )
= ( size_size_list_instr @ Ys4 ) )
=> ( ( ( size_size_list_instr @ Ys4 )
= ( size_size_list_instr @ Zs2 ) )
=> ( ( P @ Xs3 @ Ys4 @ Zs2 )
=> ( P @ ( cons_instr @ X5 @ Xs3 ) @ ( cons_instr @ Y4 @ Ys4 ) @ ( cons_instr @ Z2 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_452_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 )
=> ( ! [X5: instr,Xs3: list_instr,Y4: instr,Ys4: list_instr,Z2: int,Zs2: list_int] :
( ( ( size_size_list_instr @ Xs3 )
= ( size_size_list_instr @ Ys4 ) )
=> ( ( ( size_size_list_instr @ Ys4 )
= ( size_size_list_int @ Zs2 ) )
=> ( ( P @ Xs3 @ Ys4 @ Zs2 )
=> ( P @ ( cons_instr @ X5 @ Xs3 ) @ ( cons_instr @ Y4 @ Ys4 ) @ ( cons_int @ Z2 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_453_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 )
=> ( ! [X5: instr,Xs3: list_instr,Y4: int,Ys4: list_int,Z2: instr,Zs2: list_instr] :
( ( ( size_size_list_instr @ Xs3 )
= ( size_size_list_int @ Ys4 ) )
=> ( ( ( size_size_list_int @ Ys4 )
= ( size_size_list_instr @ Zs2 ) )
=> ( ( P @ Xs3 @ Ys4 @ Zs2 )
=> ( P @ ( cons_instr @ X5 @ Xs3 ) @ ( cons_int @ Y4 @ Ys4 ) @ ( cons_instr @ Z2 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_454_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 )
=> ( ! [X5: instr,Xs3: list_instr,Y4: int,Ys4: list_int,Z2: int,Zs2: list_int] :
( ( ( size_size_list_instr @ Xs3 )
= ( size_size_list_int @ Ys4 ) )
=> ( ( ( size_size_list_int @ Ys4 )
= ( size_size_list_int @ Zs2 ) )
=> ( ( P @ Xs3 @ Ys4 @ Zs2 )
=> ( P @ ( cons_instr @ X5 @ Xs3 ) @ ( cons_int @ Y4 @ Ys4 ) @ ( cons_int @ Z2 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_455_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 )
=> ( ! [X5: int,Xs3: list_int,Y4: instr,Ys4: list_instr,Z2: instr,Zs2: list_instr] :
( ( ( size_size_list_int @ Xs3 )
= ( size_size_list_instr @ Ys4 ) )
=> ( ( ( size_size_list_instr @ Ys4 )
= ( size_size_list_instr @ Zs2 ) )
=> ( ( P @ Xs3 @ Ys4 @ Zs2 )
=> ( P @ ( cons_int @ X5 @ Xs3 ) @ ( cons_instr @ Y4 @ Ys4 ) @ ( cons_instr @ Z2 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_456_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 )
=> ( ! [X5: int,Xs3: list_int,Y4: instr,Ys4: list_instr,Z2: int,Zs2: list_int] :
( ( ( size_size_list_int @ Xs3 )
= ( size_size_list_instr @ Ys4 ) )
=> ( ( ( size_size_list_instr @ Ys4 )
= ( size_size_list_int @ Zs2 ) )
=> ( ( P @ Xs3 @ Ys4 @ Zs2 )
=> ( P @ ( cons_int @ X5 @ Xs3 ) @ ( cons_instr @ Y4 @ Ys4 ) @ ( cons_int @ Z2 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_457_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 )
=> ( ! [X5: int,Xs3: list_int,Y4: int,Ys4: list_int,Z2: instr,Zs2: list_instr] :
( ( ( size_size_list_int @ Xs3 )
= ( size_size_list_int @ Ys4 ) )
=> ( ( ( size_size_list_int @ Ys4 )
= ( size_size_list_instr @ Zs2 ) )
=> ( ( P @ Xs3 @ Ys4 @ Zs2 )
=> ( P @ ( cons_int @ X5 @ Xs3 ) @ ( cons_int @ Y4 @ Ys4 ) @ ( cons_instr @ Z2 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_458_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 )
=> ( ! [X5: int,Xs3: list_int,Y4: int,Ys4: list_int,Z2: int,Zs2: list_int] :
( ( ( size_size_list_int @ Xs3 )
= ( size_size_list_int @ Ys4 ) )
=> ( ( ( size_size_list_int @ Ys4 )
= ( size_size_list_int @ Zs2 ) )
=> ( ( P @ Xs3 @ Ys4 @ Zs2 )
=> ( P @ ( cons_int @ X5 @ Xs3 ) @ ( cons_int @ Y4 @ Ys4 ) @ ( cons_int @ Z2 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_459_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 )
=> ( ! [X5: instr,Xs3: list_instr,Y4: instr,Ys4: list_instr,Z2: list_char,Zs2: list_list_char] :
( ( ( size_size_list_instr @ Xs3 )
= ( size_size_list_instr @ Ys4 ) )
=> ( ( ( size_size_list_instr @ Ys4 )
= ( size_s356637359517785349t_char @ Zs2 ) )
=> ( ( P @ Xs3 @ Ys4 @ Zs2 )
=> ( P @ ( cons_instr @ X5 @ Xs3 ) @ ( cons_instr @ Y4 @ Ys4 ) @ ( cons_list_char @ Z2 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_460_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 )
=> ( ! [X5: instr,Xs3: list_instr,Y4: list_char,Ys4: list_list_char,Z2: instr,Zs2: list_instr] :
( ( ( size_size_list_instr @ Xs3 )
= ( size_s356637359517785349t_char @ Ys4 ) )
=> ( ( ( size_s356637359517785349t_char @ Ys4 )
= ( size_size_list_instr @ Zs2 ) )
=> ( ( P @ Xs3 @ Ys4 @ Zs2 )
=> ( P @ ( cons_instr @ X5 @ Xs3 ) @ ( cons_list_char @ Y4 @ Ys4 ) @ ( cons_instr @ Z2 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_461_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 )
=> ( ! [X5: instr,Xs3: list_instr,Y4: instr,Ys4: list_instr] :
( ( ( size_size_list_instr @ Xs3 )
= ( size_size_list_instr @ Ys4 ) )
=> ( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_instr @ X5 @ Xs3 ) @ ( cons_instr @ Y4 @ Ys4 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_462_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 )
=> ( ! [X5: instr,Xs3: list_instr,Y4: int,Ys4: list_int] :
( ( ( size_size_list_instr @ Xs3 )
= ( size_size_list_int @ Ys4 ) )
=> ( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_instr @ X5 @ Xs3 ) @ ( cons_int @ Y4 @ Ys4 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_463_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 )
=> ( ! [X5: int,Xs3: list_int,Y4: instr,Ys4: list_instr] :
( ( ( size_size_list_int @ Xs3 )
= ( size_size_list_instr @ Ys4 ) )
=> ( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_int @ X5 @ Xs3 ) @ ( cons_instr @ Y4 @ Ys4 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_464_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 )
=> ( ! [X5: int,Xs3: list_int,Y4: int,Ys4: list_int] :
( ( ( size_size_list_int @ Xs3 )
= ( size_size_list_int @ Ys4 ) )
=> ( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_int @ X5 @ Xs3 ) @ ( cons_int @ Y4 @ Ys4 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_465_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 )
=> ( ! [X5: instr,Xs3: list_instr,Y4: list_char,Ys4: list_list_char] :
( ( ( size_size_list_instr @ Xs3 )
= ( size_s356637359517785349t_char @ Ys4 ) )
=> ( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_instr @ X5 @ Xs3 ) @ ( cons_list_char @ Y4 @ Ys4 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_466_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 )
=> ( ! [X5: list_char,Xs3: list_list_char,Y4: instr,Ys4: list_instr] :
( ( ( size_s356637359517785349t_char @ Xs3 )
= ( size_size_list_instr @ Ys4 ) )
=> ( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_list_char @ X5 @ Xs3 ) @ ( cons_instr @ Y4 @ Ys4 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_467_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 )
=> ( ! [X5: list_char,Xs3: list_list_char,Y4: int,Ys4: list_int] :
( ( ( size_s356637359517785349t_char @ Xs3 )
= ( size_size_list_int @ Ys4 ) )
=> ( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_list_char @ X5 @ Xs3 ) @ ( cons_int @ Y4 @ Ys4 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_468_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 )
=> ( ! [X5: int,Xs3: list_int,Y4: list_char,Ys4: list_list_char] :
( ( ( size_size_list_int @ Xs3 )
= ( size_s356637359517785349t_char @ Ys4 ) )
=> ( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_int @ X5 @ Xs3 ) @ ( cons_list_char @ Y4 @ Ys4 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_469_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 )
=> ( ! [X5: list_char,Xs3: list_list_char,Y4: list_char,Ys4: list_list_char] :
( ( ( size_s356637359517785349t_char @ Xs3 )
= ( size_s356637359517785349t_char @ Ys4 ) )
=> ( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_list_char @ X5 @ Xs3 ) @ ( cons_list_char @ Y4 @ Ys4 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_470_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 )
=> ( ! [X5: instr,Xs3: list_instr,Y4: produc6425607678544837394st_int,Ys4: list_P419547167332244514st_int] :
( ( ( size_size_list_instr @ Xs3 )
= ( size_s229347708945616566st_int @ Ys4 ) )
=> ( ( P @ Xs3 @ Ys4 )
=> ( P @ ( cons_instr @ X5 @ Xs3 ) @ ( cons_P4151473878978182108st_int @ Y4 @ Ys4 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_471_rev__nonempty__induct,axiom,
! [Xs: list_instr,P: list_instr > $o] :
( ( Xs != nil_instr )
=> ( ! [X5: instr] : ( P @ ( cons_instr @ X5 @ nil_instr ) )
=> ( ! [X5: instr,Xs3: list_instr] :
( ( Xs3 != nil_instr )
=> ( ( P @ Xs3 )
=> ( P @ ( append_instr @ Xs3 @ ( cons_instr @ X5 @ nil_instr ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_472_rev__nonempty__induct,axiom,
! [Xs: list_int,P: list_int > $o] :
( ( Xs != nil_int )
=> ( ! [X5: int] : ( P @ ( cons_int @ X5 @ nil_int ) )
=> ( ! [X5: int,Xs3: list_int] :
( ( Xs3 != nil_int )
=> ( ( P @ Xs3 )
=> ( P @ ( append_int @ Xs3 @ ( cons_int @ X5 @ nil_int ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_473_rev__nonempty__induct,axiom,
! [Xs: list_P419547167332244514st_int,P: list_P419547167332244514st_int > $o] :
( ( Xs != nil_Pr749310521696113548st_int )
=> ( ! [X5: produc6425607678544837394st_int] : ( P @ ( cons_P4151473878978182108st_int @ X5 @ nil_Pr749310521696113548st_int ) )
=> ( ! [X5: produc6425607678544837394st_int,Xs3: list_P419547167332244514st_int] :
( ( Xs3 != nil_Pr749310521696113548st_int )
=> ( ( P @ Xs3 )
=> ( P @ ( append5028292981072010935st_int @ Xs3 @ ( cons_P4151473878978182108st_int @ X5 @ nil_Pr749310521696113548st_int ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_474_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 ) ) )
| ? [Ys5: list_instr] :
( ( Ys
= ( cons_instr @ X @ Ys5 ) )
& ( ( append_instr @ Ys5 @ Zs )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_475_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 ) ) )
| ? [Ys5: list_int] :
( ( Ys
= ( cons_int @ X @ Ys5 ) )
& ( ( append_int @ Ys5 @ Zs )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_476_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 ) ) )
| ? [Ys5: list_P419547167332244514st_int] :
( ( Ys
= ( cons_P4151473878978182108st_int @ X @ Ys5 ) )
& ( ( append5028292981072010935st_int @ Ys5 @ Zs )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_477_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 ) )
| ? [Ys5: list_instr] :
( ( ( cons_instr @ X @ Ys5 )
= Ys )
& ( Xs
= ( append_instr @ Ys5 @ Zs ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_478_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 ) )
| ? [Ys5: list_int] :
( ( ( cons_int @ X @ Ys5 )
= Ys )
& ( Xs
= ( append_int @ Ys5 @ Zs ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_479_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 ) )
| ? [Ys5: list_P419547167332244514st_int] :
( ( ( cons_P4151473878978182108st_int @ X @ Ys5 )
= Ys )
& ( Xs
= ( append5028292981072010935st_int @ Ys5 @ Zs ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_480_rev__exhaust,axiom,
! [Xs: list_instr] :
( ( Xs != nil_instr )
=> ~ ! [Ys4: list_instr,Y4: instr] :
( Xs
!= ( append_instr @ Ys4 @ ( cons_instr @ Y4 @ nil_instr ) ) ) ) ).
% rev_exhaust
thf(fact_481_rev__exhaust,axiom,
! [Xs: list_int] :
( ( Xs != nil_int )
=> ~ ! [Ys4: list_int,Y4: int] :
( Xs
!= ( append_int @ Ys4 @ ( cons_int @ Y4 @ nil_int ) ) ) ) ).
% rev_exhaust
thf(fact_482_rev__exhaust,axiom,
! [Xs: list_P419547167332244514st_int] :
( ( Xs != nil_Pr749310521696113548st_int )
=> ~ ! [Ys4: list_P419547167332244514st_int,Y4: produc6425607678544837394st_int] :
( Xs
!= ( append5028292981072010935st_int @ Ys4 @ ( cons_P4151473878978182108st_int @ Y4 @ nil_Pr749310521696113548st_int ) ) ) ) ).
% rev_exhaust
thf(fact_483_rev__induct,axiom,
! [P: list_instr > $o,Xs: list_instr] :
( ( P @ nil_instr )
=> ( ! [X5: instr,Xs3: list_instr] :
( ( P @ Xs3 )
=> ( P @ ( append_instr @ Xs3 @ ( cons_instr @ X5 @ nil_instr ) ) ) )
=> ( P @ Xs ) ) ) ).
% rev_induct
thf(fact_484_rev__induct,axiom,
! [P: list_int > $o,Xs: list_int] :
( ( P @ nil_int )
=> ( ! [X5: int,Xs3: list_int] :
( ( P @ Xs3 )
=> ( P @ ( append_int @ Xs3 @ ( cons_int @ X5 @ nil_int ) ) ) )
=> ( P @ Xs ) ) ) ).
% rev_induct
thf(fact_485_rev__induct,axiom,
! [P: list_P419547167332244514st_int > $o,Xs: list_P419547167332244514st_int] :
( ( P @ nil_Pr749310521696113548st_int )
=> ( ! [X5: produc6425607678544837394st_int,Xs3: list_P419547167332244514st_int] :
( ( P @ Xs3 )
=> ( P @ ( append5028292981072010935st_int @ Xs3 @ ( cons_P4151473878978182108st_int @ X5 @ nil_Pr749310521696113548st_int ) ) ) )
=> ( P @ Xs ) ) ) ).
% rev_induct
thf(fact_486_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,X5: instr,Xs4: list_instr,Y4: instr,Ys6: list_instr] :
( ( X5 != Y4 )
& ( Xs
= ( append_instr @ Pre @ ( append_instr @ ( cons_instr @ X5 @ nil_instr ) @ Xs4 ) ) )
& ( Ys
= ( append_instr @ Pre @ ( append_instr @ ( cons_instr @ Y4 @ nil_instr ) @ Ys6 ) ) ) ) ) ) ).
% same_length_different
thf(fact_487_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,X5: produc6425607678544837394st_int,Xs4: list_P419547167332244514st_int,Y4: produc6425607678544837394st_int,Ys6: list_P419547167332244514st_int] :
( ( X5 != Y4 )
& ( Xs
= ( append5028292981072010935st_int @ Pre @ ( append5028292981072010935st_int @ ( cons_P4151473878978182108st_int @ X5 @ nil_Pr749310521696113548st_int ) @ Xs4 ) ) )
& ( Ys
= ( append5028292981072010935st_int @ Pre @ ( append5028292981072010935st_int @ ( cons_P4151473878978182108st_int @ Y4 @ nil_Pr749310521696113548st_int ) @ Ys6 ) ) ) ) ) ) ).
% same_length_different
thf(fact_488_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,X5: list_char,Xs4: list_list_char,Y4: list_char,Ys6: list_list_char] :
( ( X5 != Y4 )
& ( Xs
= ( append_list_char @ Pre @ ( append_list_char @ ( cons_list_char @ X5 @ nil_list_char ) @ Xs4 ) ) )
& ( Ys
= ( append_list_char @ Pre @ ( append_list_char @ ( cons_list_char @ Y4 @ nil_list_char ) @ Ys6 ) ) ) ) ) ) ).
% same_length_different
thf(fact_489_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,X5: int,Xs4: list_int,Y4: int,Ys6: list_int] :
( ( X5 != Y4 )
& ( Xs
= ( append_int @ Pre @ ( append_int @ ( cons_int @ X5 @ nil_int ) @ Xs4 ) ) )
& ( Ys
= ( append_int @ Pre @ ( append_int @ ( cons_int @ Y4 @ nil_int ) @ Ys6 ) ) ) ) ) ) ).
% same_length_different
thf(fact_490_length__Suc__conv__rev,axiom,
! [Xs: list_instr,N: nat] :
( ( ( size_size_list_instr @ Xs )
= ( suc @ N ) )
= ( ? [Y5: instr,Ys2: list_instr] :
( ( Xs
= ( append_instr @ Ys2 @ ( cons_instr @ Y5 @ nil_instr ) ) )
& ( ( size_size_list_instr @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv_rev
thf(fact_491_length__Suc__conv__rev,axiom,
! [Xs: list_P419547167332244514st_int,N: nat] :
( ( ( size_s229347708945616566st_int @ Xs )
= ( suc @ N ) )
= ( ? [Y5: produc6425607678544837394st_int,Ys2: list_P419547167332244514st_int] :
( ( Xs
= ( append5028292981072010935st_int @ Ys2 @ ( cons_P4151473878978182108st_int @ Y5 @ nil_Pr749310521696113548st_int ) ) )
& ( ( size_s229347708945616566st_int @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv_rev
thf(fact_492_length__Suc__conv__rev,axiom,
! [Xs: list_list_char,N: nat] :
( ( ( size_s356637359517785349t_char @ Xs )
= ( suc @ N ) )
= ( ? [Y5: list_char,Ys2: list_list_char] :
( ( Xs
= ( append_list_char @ Ys2 @ ( cons_list_char @ Y5 @ nil_list_char ) ) )
& ( ( size_s356637359517785349t_char @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv_rev
thf(fact_493_length__Suc__conv__rev,axiom,
! [Xs: list_int,N: nat] :
( ( ( size_size_list_int @ Xs )
= ( suc @ N ) )
= ( ? [Y5: int,Ys2: list_int] :
( ( Xs
= ( append_int @ Ys2 @ ( cons_int @ Y5 @ nil_int ) ) )
& ( ( size_size_list_int @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv_rev
thf(fact_494_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_495_diff__numeral__special_I12_J,axiom,
( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
= zero_zero_int ) ).
% diff_numeral_special(12)
thf(fact_496_add__neg__numeral__special_I7_J,axiom,
( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
= zero_zero_int ) ).
% add_neg_numeral_special(7)
thf(fact_497_add__neg__numeral__special_I8_J,axiom,
( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
= zero_zero_int ) ).
% add_neg_numeral_special(8)
thf(fact_498_verit__minus__simplify_I3_J,axiom,
! [B: int] :
( ( minus_minus_int @ zero_zero_int @ B )
= ( uminus_uminus_int @ B ) ) ).
% verit_minus_simplify(3)
thf(fact_499_diff__numeral__special_I9_J,axiom,
( ( minus_minus_int @ one_one_int @ one_one_int )
= zero_zero_int ) ).
% diff_numeral_special(9)
thf(fact_500_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_501_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_502_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_503_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_504_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_505_int__Suc,axiom,
! [N: nat] :
( ( semiri1314217659103216013at_int @ ( suc @ N ) )
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% int_Suc
thf(fact_506_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_507_less__minus__one__simps_I1_J,axiom,
ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% less_minus_one_simps(1)
thf(fact_508_verit__minus__simplify_I4_J,axiom,
! [B: int] :
( ( uminus_uminus_int @ ( uminus_uminus_int @ B ) )
= B ) ).
% verit_minus_simplify(4)
thf(fact_509_instr_Oinject_I4_J,axiom,
! [X52: int,Y52: int] :
( ( ( jmp @ X52 )
= ( jmp @ Y52 ) )
= ( X52 = Y52 ) ) ).
% instr.inject(4)
thf(fact_510_less__nat__zero__code,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% less_nat_zero_code
thf(fact_511_neq0__conv,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% neq0_conv
thf(fact_512_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_513_Nat_Oadd__0__right,axiom,
! [M: nat] :
( ( plus_plus_nat @ M @ zero_zero_nat )
= M ) ).
% Nat.add_0_right
thf(fact_514_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_515_diff__self__eq__0,axiom,
! [M: nat] :
( ( minus_minus_nat @ M @ M )
= zero_zero_nat ) ).
% diff_self_eq_0
thf(fact_516_diff__0__eq__0,axiom,
! [N: nat] :
( ( minus_minus_nat @ zero_zero_nat @ N )
= zero_zero_nat ) ).
% diff_0_eq_0
thf(fact_517_drop0,axiom,
( ( drop_P7838799151754935884st_int @ zero_zero_nat )
= ( ^ [X3: list_P419547167332244514st_int] : X3 ) ) ).
% drop0
thf(fact_518_drop0,axiom,
( ( drop_int @ zero_zero_nat )
= ( ^ [X3: list_int] : X3 ) ) ).
% drop0
thf(fact_519_drop0,axiom,
( ( drop_instr @ zero_zero_nat )
= ( ^ [X3: list_instr] : X3 ) ) ).
% drop0
thf(fact_520_less__Suc0,axiom,
! [N: nat] :
( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
= ( N = zero_zero_nat ) ) ).
% less_Suc0
thf(fact_521_zero__less__Suc,axiom,
! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% zero_less_Suc
thf(fact_522_length__0__conv,axiom,
! [Xs: list_instr] :
( ( ( size_size_list_instr @ Xs )
= zero_zero_nat )
= ( Xs = nil_instr ) ) ).
% length_0_conv
thf(fact_523_length__0__conv,axiom,
! [Xs: list_P419547167332244514st_int] :
( ( ( size_s229347708945616566st_int @ Xs )
= zero_zero_nat )
= ( Xs = nil_Pr749310521696113548st_int ) ) ).
% length_0_conv
thf(fact_524_length__0__conv,axiom,
! [Xs: list_list_char] :
( ( ( size_s356637359517785349t_char @ Xs )
= zero_zero_nat )
= ( Xs = nil_list_char ) ) ).
% length_0_conv
thf(fact_525_length__0__conv,axiom,
! [Xs: list_int] :
( ( ( size_size_list_int @ Xs )
= zero_zero_nat )
= ( Xs = nil_int ) ) ).
% length_0_conv
thf(fact_526_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_527_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_528_nth__Cons__0,axiom,
! [X: instr,Xs: list_instr] :
( ( nth_instr @ ( cons_instr @ X @ Xs ) @ zero_zero_nat )
= X ) ).
% nth_Cons_0
thf(fact_529_nth__Cons__0,axiom,
! [X: int,Xs: list_int] :
( ( nth_int @ ( cons_int @ X @ Xs ) @ zero_zero_nat )
= X ) ).
% nth_Cons_0
thf(fact_530_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_531_less__one,axiom,
! [N: nat] :
( ( ord_less_nat @ N @ one_one_nat )
= ( N = zero_zero_nat ) ) ).
% less_one
thf(fact_532_negative__eq__positive,axiom,
! [N: nat,M: nat] :
( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
= ( semiri1314217659103216013at_int @ M ) )
= ( ( N = zero_zero_nat )
& ( M = zero_zero_nat ) ) ) ).
% negative_eq_positive
thf(fact_533_negative__zless,axiom,
! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% negative_zless
thf(fact_534_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_535_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_536_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_537_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_538_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_539_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_540_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_541_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_542_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_543_instr_Osize_I12_J,axiom,
! [X52: int] :
( ( size_size_instr @ ( jmp @ X52 ) )
= zero_zero_nat ) ).
% instr.size(12)
thf(fact_544_less__int__code_I1_J,axiom,
~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% less_int_code(1)
thf(fact_545_zero__less__imp__eq__int,axiom,
! [K: int] :
( ( ord_less_int @ zero_zero_int @ K )
=> ? [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
& ( K
= ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% zero_less_imp_eq_int
thf(fact_546_pos__int__cases,axiom,
! [K: int] :
( ( ord_less_int @ zero_zero_int @ K )
=> ~ ! [N2: nat] :
( ( K
= ( semiri1314217659103216013at_int @ N2 ) )
=> ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% pos_int_cases
thf(fact_547_nat_Odistinct_I1_J,axiom,
! [X2: nat] :
( zero_zero_nat
!= ( suc @ X2 ) ) ).
% nat.distinct(1)
thf(fact_548_old_Onat_Odistinct_I2_J,axiom,
! [Nat2: nat] :
( ( suc @ Nat2 )
!= zero_zero_nat ) ).
% old.nat.distinct(2)
thf(fact_549_old_Onat_Odistinct_I1_J,axiom,
! [Nat2: nat] :
( zero_zero_nat
!= ( suc @ Nat2 ) ) ).
% old.nat.distinct(1)
thf(fact_550_nat_OdiscI,axiom,
! [Nat: nat,X2: nat] :
( ( Nat
= ( suc @ X2 ) )
=> ( Nat != zero_zero_nat ) ) ).
% nat.discI
thf(fact_551_old_Onat_Oexhaust,axiom,
! [Y: nat] :
( ( Y != zero_zero_nat )
=> ~ ! [Nat3: nat] :
( Y
!= ( suc @ Nat3 ) ) ) ).
% old.nat.exhaust
thf(fact_552_nat__induct,axiom,
! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) )
=> ( P @ N ) ) ) ).
% nat_induct
thf(fact_553_diff__induct,axiom,
! [P: nat > nat > $o,M: nat,N: nat] :
( ! [X5: nat] : ( P @ X5 @ zero_zero_nat )
=> ( ! [Y4: nat] : ( P @ zero_zero_nat @ ( suc @ Y4 ) )
=> ( ! [X5: nat,Y4: nat] :
( ( P @ X5 @ Y4 )
=> ( P @ ( suc @ X5 ) @ ( suc @ Y4 ) ) )
=> ( P @ M @ N ) ) ) ) ).
% diff_induct
thf(fact_554_zero__induct,axiom,
! [P: nat > $o,K: nat] :
( ( P @ K )
=> ( ! [N2: nat] :
( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) )
=> ( P @ zero_zero_nat ) ) ) ).
% zero_induct
thf(fact_555_Suc__neq__Zero,axiom,
! [M: nat] :
( ( suc @ M )
!= zero_zero_nat ) ).
% Suc_neq_Zero
thf(fact_556_Zero__neq__Suc,axiom,
! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) ).
% Zero_neq_Suc
thf(fact_557_Zero__not__Suc,axiom,
! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) ).
% Zero_not_Suc
thf(fact_558_not0__implies__Suc,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ? [M5: nat] :
( N
= ( suc @ M5 ) ) ) ).
% not0_implies_Suc
thf(fact_559_infinite__descent0,axiom,
! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ~ ( P @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P @ M2 ) ) ) )
=> ( P @ N ) ) ) ).
% infinite_descent0
thf(fact_560_gr__implies__not0,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) ).
% gr_implies_not0
thf(fact_561_less__zeroE,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% less_zeroE
thf(fact_562_not__less0,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% not_less0
thf(fact_563_not__gr0,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) ).
% not_gr0
thf(fact_564_gr0I,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% gr0I
thf(fact_565_bot__nat__0_Oextremum__strict,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% bot_nat_0.extremum_strict
thf(fact_566_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_567_plus__nat_Oadd__0,axiom,
! [N: nat] :
( ( plus_plus_nat @ zero_zero_nat @ N )
= N ) ).
% plus_nat.add_0
thf(fact_568_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_569_minus__nat_Odiff__0,axiom,
! [M: nat] :
( ( minus_minus_nat @ M @ zero_zero_nat )
= M ) ).
% minus_nat.diff_0
thf(fact_570_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_571_drop__0,axiom,
! [Xs: list_P419547167332244514st_int] :
( ( drop_P7838799151754935884st_int @ zero_zero_nat @ Xs )
= Xs ) ).
% drop_0
thf(fact_572_drop__0,axiom,
! [Xs: list_int] :
( ( drop_int @ zero_zero_nat @ Xs )
= Xs ) ).
% drop_0
thf(fact_573_drop__0,axiom,
! [Xs: list_instr] :
( ( drop_instr @ zero_zero_nat @ Xs )
= Xs ) ).
% drop_0
thf(fact_574_int__gr__induct,axiom,
! [K: int,I: int,P: int > $o] :
( ( ord_less_int @ K @ I )
=> ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
=> ( ! [I3: int] :
( ( ord_less_int @ K @ I3 )
=> ( ( P @ I3 )
=> ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
=> ( P @ I ) ) ) ) ).
% int_gr_induct
thf(fact_575_zless__add1__eq,axiom,
! [W: int,Z3: int] :
( ( ord_less_int @ W @ ( plus_plus_int @ Z3 @ one_one_int ) )
= ( ( ord_less_int @ W @ Z3 )
| ( W = Z3 ) ) ) ).
% zless_add1_eq
thf(fact_576_not__int__zless__negative,axiom,
! [N: nat,M: nat] :
~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% not_int_zless_negative
thf(fact_577_int__less__induct,axiom,
! [I: int,K: int,P: int > $o] :
( ( ord_less_int @ I @ K )
=> ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
=> ( ! [I3: int] :
( ( ord_less_int @ I3 @ K )
=> ( ( P @ I3 )
=> ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
=> ( P @ I ) ) ) ) ).
% int_less_induct
thf(fact_578_int__ops_I1_J,axiom,
( ( semiri1314217659103216013at_int @ zero_zero_nat )
= zero_zero_int ) ).
% int_ops(1)
thf(fact_579_neg__int__cases,axiom,
! [K: int] :
( ( ord_less_int @ K @ zero_zero_int )
=> ~ ! [N2: nat] :
( ( K
= ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
=> ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% neg_int_cases
thf(fact_580_sorted__wrt_Ocases,axiom,
! [X: produc7133927873007960030_instr] :
( ! [P2: instr > instr > $o] :
( X
!= ( produc7818391707689388878_instr @ P2 @ nil_instr ) )
=> ~ ! [P2: instr > instr > $o,X5: instr,Ys4: list_instr] :
( X
!= ( produc7818391707689388878_instr @ P2 @ ( cons_instr @ X5 @ Ys4 ) ) ) ) ).
% sorted_wrt.cases
thf(fact_581_sorted__wrt_Ocases,axiom,
! [X: produc5834231552977413017st_int] :
( ! [P2: int > int > $o] :
( X
!= ( produc8618682346314911123st_int @ P2 @ nil_int ) )
=> ~ ! [P2: int > int > $o,X5: int,Ys4: list_int] :
( X
!= ( produc8618682346314911123st_int @ P2 @ ( cons_int @ X5 @ Ys4 ) ) ) ) ).
% sorted_wrt.cases
thf(fact_582_sorted__wrt_Ocases,axiom,
! [X: produc2468426419292222131st_int] :
( ! [P2: produc6425607678544837394st_int > produc6425607678544837394st_int > $o] :
( X
!= ( produc554038597315947693st_int @ P2 @ nil_Pr749310521696113548st_int ) )
=> ~ ! [P2: produc6425607678544837394st_int > produc6425607678544837394st_int > $o,X5: produc6425607678544837394st_int,Ys4: list_P419547167332244514st_int] :
( X
!= ( produc554038597315947693st_int @ P2 @ ( cons_P4151473878978182108st_int @ X5 @ Ys4 ) ) ) ) ).
% sorted_wrt.cases
thf(fact_583_successively_Ocases,axiom,
! [X: produc7133927873007960030_instr] :
( ! [P2: instr > instr > $o] :
( X
!= ( produc7818391707689388878_instr @ P2 @ nil_instr ) )
=> ( ! [P2: instr > instr > $o,X5: instr] :
( X
!= ( produc7818391707689388878_instr @ P2 @ ( cons_instr @ X5 @ nil_instr ) ) )
=> ~ ! [P2: instr > instr > $o,X5: instr,Y4: instr,Xs3: list_instr] :
( X
!= ( produc7818391707689388878_instr @ P2 @ ( cons_instr @ X5 @ ( cons_instr @ Y4 @ Xs3 ) ) ) ) ) ) ).
% successively.cases
thf(fact_584_successively_Ocases,axiom,
! [X: produc5834231552977413017st_int] :
( ! [P2: int > int > $o] :
( X
!= ( produc8618682346314911123st_int @ P2 @ nil_int ) )
=> ( ! [P2: int > int > $o,X5: int] :
( X
!= ( produc8618682346314911123st_int @ P2 @ ( cons_int @ X5 @ nil_int ) ) )
=> ~ ! [P2: int > int > $o,X5: int,Y4: int,Xs3: list_int] :
( X
!= ( produc8618682346314911123st_int @ P2 @ ( cons_int @ X5 @ ( cons_int @ Y4 @ Xs3 ) ) ) ) ) ) ).
% successively.cases
thf(fact_585_successively_Ocases,axiom,
! [X: produc2468426419292222131st_int] :
( ! [P2: produc6425607678544837394st_int > produc6425607678544837394st_int > $o] :
( X
!= ( produc554038597315947693st_int @ P2 @ nil_Pr749310521696113548st_int ) )
=> ( ! [P2: produc6425607678544837394st_int > produc6425607678544837394st_int > $o,X5: produc6425607678544837394st_int] :
( X
!= ( produc554038597315947693st_int @ P2 @ ( cons_P4151473878978182108st_int @ X5 @ nil_Pr749310521696113548st_int ) ) )
=> ~ ! [P2: produc6425607678544837394st_int > produc6425607678544837394st_int > $o,X5: produc6425607678544837394st_int,Y4: produc6425607678544837394st_int,Xs3: list_P419547167332244514st_int] :
( X
!= ( produc554038597315947693st_int @ P2 @ ( cons_P4151473878978182108st_int @ X5 @ ( cons_P4151473878978182108st_int @ Y4 @ Xs3 ) ) ) ) ) ) ).
% successively.cases
thf(fact_586_zless__iff__Suc__zadd,axiom,
( ord_less_int
= ( ^ [W2: int,Z4: int] :
? [N4: nat] :
( Z4
= ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) ) ) ) ).
% zless_iff_Suc_zadd
thf(fact_587_odd__less__0__iff,axiom,
! [Z3: int] :
( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z3 ) @ Z3 ) @ zero_zero_int )
= ( ord_less_int @ Z3 @ zero_zero_int ) ) ).
% odd_less_0_iff
thf(fact_588_int__cases4,axiom,
! [M: int] :
( ! [N2: nat] :
( M
!= ( semiri1314217659103216013at_int @ N2 ) )
=> ~ ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( M
!= ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% int_cases4
thf(fact_589_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_590_gr0__conv__Suc,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( ? [M3: nat] :
( N
= ( suc @ M3 ) ) ) ) ).
% gr0_conv_Suc
thf(fact_591_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_592_gr0__implies__Suc,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ? [M5: nat] :
( N
= ( suc @ M5 ) ) ) ).
% gr0_implies_Suc
thf(fact_593_less__Suc__eq__0__disj,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ( M = zero_zero_nat )
| ? [J3: nat] :
( ( M
= ( suc @ J3 ) )
& ( ord_less_nat @ J3 @ N ) ) ) ) ).
% less_Suc_eq_0_disj
thf(fact_594_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_595_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_596_list_Osize_I3_J,axiom,
( ( size_size_list_instr @ nil_instr )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_597_list_Osize_I3_J,axiom,
( ( size_s229347708945616566st_int @ nil_Pr749310521696113548st_int )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_598_list_Osize_I3_J,axiom,
( ( size_s356637359517785349t_char @ nil_list_char )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_599_list_Osize_I3_J,axiom,
( ( size_size_list_int @ nil_int )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_600_less__imp__add__positive,axiom,
! [I: nat,J: nat] :
( ( ord_less_nat @ I @ J )
=> ? [K2: nat] :
( ( ord_less_nat @ zero_zero_nat @ K2 )
& ( ( plus_plus_nat @ I @ K2 )
= J ) ) ) ).
% less_imp_add_positive
thf(fact_601_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_602_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_603_One__nat__def,axiom,
( one_one_nat
= ( suc @ zero_zero_nat ) ) ).
% One_nat_def
thf(fact_604_negD,axiom,
! [X: int] :
( ( ord_less_int @ X @ zero_zero_int )
=> ? [N2: nat] :
( X
= ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% negD
thf(fact_605_negative__zless__0,axiom,
! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% negative_zless_0
thf(fact_606_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_607_int__cases3,axiom,
! [K: int] :
( ( K != zero_zero_int )
=> ( ! [N2: nat] :
( ( K
= ( semiri1314217659103216013at_int @ N2 ) )
=> ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
=> ~ ! [N2: nat] :
( ( K
= ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
=> ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% int_cases3
thf(fact_608_verit__comp__simplify1_I1_J,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ) ).
% verit_comp_simplify1(1)
thf(fact_609_verit__comp__simplify1_I1_J,axiom,
! [A: int] :
~ ( ord_less_int @ A @ A ) ).
% verit_comp_simplify1(1)
thf(fact_610_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_611_verit__negate__coefficient_I3_J,axiom,
! [A: int,B: int] :
( ( A = B )
=> ( ( uminus_uminus_int @ A )
= ( uminus_uminus_int @ B ) ) ) ).
% verit_negate_coefficient(3)
thf(fact_612_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_613_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_614_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_615_nat__induct__non__zero,axiom,
! [N: nat,P: nat > $o] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( P @ one_one_nat )
=> ( ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) ) )
=> ( P @ N ) ) ) ) ).
% nat_induct_non_zero
thf(fact_616_nat__int__comparison_I1_J,axiom,
( ( ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
= ( ^ [A3: nat,B2: nat] :
( ( semiri1314217659103216013at_int @ A3 )
= ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% nat_int_comparison(1)
thf(fact_617_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_618_int__int__eq,axiom,
! [M: nat,N: nat] :
( ( ( semiri1314217659103216013at_int @ M )
= ( semiri1314217659103216013at_int @ N ) )
= ( M = N ) ) ).
% int_int_eq
thf(fact_619_list_Osize_I4_J,axiom,
! [X21: instr,X22: list_instr] :
( ( size_size_list_instr @ ( cons_instr @ X21 @ X22 ) )
= ( plus_plus_nat @ ( size_size_list_instr @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% list.size(4)
thf(fact_620_list_Osize_I4_J,axiom,
! [X21: produc6425607678544837394st_int,X22: list_P419547167332244514st_int] :
( ( size_s229347708945616566st_int @ ( cons_P4151473878978182108st_int @ X21 @ X22 ) )
= ( plus_plus_nat @ ( size_s229347708945616566st_int @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% list.size(4)
thf(fact_621_list_Osize_I4_J,axiom,
! [X21: list_char,X22: list_list_char] :
( ( size_s356637359517785349t_char @ ( cons_list_char @ X21 @ X22 ) )
= ( plus_plus_nat @ ( size_s356637359517785349t_char @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% list.size(4)
thf(fact_622_list_Osize_I4_J,axiom,
! [X21: int,X22: list_int] :
( ( size_size_list_int @ ( cons_int @ X21 @ X22 ) )
= ( plus_plus_nat @ ( size_size_list_int @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% list.size(4)
thf(fact_623_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_624_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_625_add__eq__if,axiom,
( plus_plus_nat
= ( ^ [M3: nat,N4: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N4 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N4 ) ) ) ) ) ).
% add_eq_if
thf(fact_626_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_627_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_628_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_629_drop__Cons_H,axiom,
! [N: nat,X: instr,Xs: list_instr] :
( ( ( N = zero_zero_nat )
=> ( ( drop_instr @ N @ ( cons_instr @ X @ Xs ) )
= ( cons_instr @ X @ Xs ) ) )
& ( ( N != zero_zero_nat )
=> ( ( drop_instr @ N @ ( cons_instr @ X @ Xs ) )
= ( drop_instr @ ( minus_minus_nat @ N @ one_one_nat ) @ Xs ) ) ) ) ).
% drop_Cons'
thf(fact_630_drop__Cons_H,axiom,
! [N: nat,X: int,Xs: list_int] :
( ( ( N = zero_zero_nat )
=> ( ( drop_int @ N @ ( cons_int @ X @ Xs ) )
= ( cons_int @ X @ Xs ) ) )
& ( ( N != zero_zero_nat )
=> ( ( drop_int @ N @ ( cons_int @ X @ Xs ) )
= ( drop_int @ ( minus_minus_nat @ N @ one_one_nat ) @ Xs ) ) ) ) ).
% drop_Cons'
thf(fact_631_drop__Cons_H,axiom,
! [N: nat,X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int] :
( ( ( N = zero_zero_nat )
=> ( ( drop_P7838799151754935884st_int @ N @ ( cons_P4151473878978182108st_int @ X @ Xs ) )
= ( cons_P4151473878978182108st_int @ X @ Xs ) ) )
& ( ( N != zero_zero_nat )
=> ( ( drop_P7838799151754935884st_int @ N @ ( cons_P4151473878978182108st_int @ X @ Xs ) )
= ( drop_P7838799151754935884st_int @ ( minus_minus_nat @ N @ one_one_nat ) @ Xs ) ) ) ) ).
% drop_Cons'
thf(fact_632_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_633_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_634_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_635_less__numeral__extra_I3_J,axiom,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% less_numeral_extra(3)
thf(fact_636_less__numeral__extra_I3_J,axiom,
~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% less_numeral_extra(3)
thf(fact_637_verit__sum__simplify,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ) ).
% verit_sum_simplify
thf(fact_638_verit__sum__simplify,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ) ).
% verit_sum_simplify
thf(fact_639_less__numeral__extra_I4_J,axiom,
~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% less_numeral_extra(4)
thf(fact_640_less__numeral__extra_I4_J,axiom,
~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% less_numeral_extra(4)
thf(fact_641_verit__negate__coefficient_I2_J,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% verit_negate_coefficient(2)
thf(fact_642_is__num__normalize_I8_J,axiom,
! [A: int,B: int] :
( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% is_num_normalize(8)
thf(fact_643_one__neq__neg__one,axiom,
( one_one_int
!= ( uminus_uminus_int @ one_one_int ) ) ).
% one_neq_neg_one
thf(fact_644_plus__int__code_I2_J,axiom,
! [L: int] :
( ( plus_plus_int @ zero_zero_int @ L )
= L ) ).
% plus_int_code(2)
thf(fact_645_plus__int__code_I1_J,axiom,
! [K: int] :
( ( plus_plus_int @ K @ zero_zero_int )
= K ) ).
% plus_int_code(1)
thf(fact_646_uminus__int__code_I1_J,axiom,
( ( uminus_uminus_int @ zero_zero_int )
= zero_zero_int ) ).
% uminus_int_code(1)
thf(fact_647_minus__int__code_I1_J,axiom,
! [K: int] :
( ( minus_minus_int @ K @ zero_zero_int )
= K ) ).
% minus_int_code(1)
thf(fact_648_int__cases2,axiom,
! [Z3: int] :
( ! [N2: nat] :
( Z3
!= ( semiri1314217659103216013at_int @ N2 ) )
=> ~ ! [N2: nat] :
( Z3
!= ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% int_cases2
thf(fact_649_int__diff__cases,axiom,
! [Z3: int] :
~ ! [M5: nat,N2: nat] :
( Z3
!= ( minus_minus_int @ ( semiri1314217659103216013at_int @ M5 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% int_diff_cases
thf(fact_650_less__numeral__extra_I1_J,axiom,
ord_less_nat @ zero_zero_nat @ one_one_nat ).
% less_numeral_extra(1)
thf(fact_651_less__numeral__extra_I1_J,axiom,
ord_less_int @ zero_zero_int @ one_one_int ).
% less_numeral_extra(1)
thf(fact_652_zero__neq__neg__one,axiom,
( zero_zero_int
!= ( uminus_uminus_int @ one_one_int ) ) ).
% zero_neq_neg_one
thf(fact_653_less__minus__one__simps_I4_J,axiom,
~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% less_minus_one_simps(4)
thf(fact_654_less__minus__one__simps_I2_J,axiom,
ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% less_minus_one_simps(2)
thf(fact_655_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_656_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_657_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_658_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_659_int__cases,axiom,
! [Z3: int] :
( ! [N2: nat] :
( Z3
!= ( semiri1314217659103216013at_int @ N2 ) )
=> ~ ! [N2: nat] :
( Z3
!= ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% int_cases
thf(fact_660_int__of__nat__induct,axiom,
! [P: int > $o,Z3: int] :
( ! [N2: nat] : ( P @ ( semiri1314217659103216013at_int @ N2 ) )
=> ( ! [N2: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) )
=> ( P @ Z3 ) ) ) ).
% int_of_nat_induct
thf(fact_661_odd__nonzero,axiom,
! [Z3: int] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z3 ) @ Z3 )
!= zero_zero_int ) ).
% odd_nonzero
thf(fact_662_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_663_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_664_zadd__int__left,axiom,
! [M: nat,N: nat,Z3: int] :
( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z3 ) )
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z3 ) ) ).
% zadd_int_left
thf(fact_665_int__ops_I2_J,axiom,
( ( semiri1314217659103216013at_int @ one_one_nat )
= one_one_int ) ).
% int_ops(2)
thf(fact_666_minus__int__code_I2_J,axiom,
! [L: int] :
( ( minus_minus_int @ zero_zero_int @ L )
= ( uminus_uminus_int @ L ) ) ).
% minus_int_code(2)
thf(fact_667_less__minus__one__simps_I3_J,axiom,
~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% less_minus_one_simps(3)
thf(fact_668_zero__less__two,axiom,
ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% zero_less_two
thf(fact_669_zero__less__two,axiom,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% zero_less_two
thf(fact_670_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_671_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_672_n__lists__Nil,axiom,
! [N: nat] :
( ( ( N = zero_zero_nat )
=> ( ( n_lists_int @ N @ nil_int )
= ( cons_list_int @ nil_int @ nil_list_int ) ) )
& ( ( N != zero_zero_nat )
=> ( ( n_lists_int @ N @ nil_int )
= nil_list_int ) ) ) ).
% n_lists_Nil
thf(fact_673_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_674_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_675_less__add__one,axiom,
! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% less_add_one
thf(fact_676_less__add__one,axiom,
! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% less_add_one
thf(fact_677_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_678_zero__neq__one,axiom,
zero_zero_int != one_one_int ).
% zero_neq_one
thf(fact_679_zero__neq__one,axiom,
zero_zero_nat != one_one_nat ).
% zero_neq_one
thf(fact_680_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_681_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_682_n__lists_Osimps_I1_J,axiom,
! [Xs: list_int] :
( ( n_lists_int @ zero_zero_nat @ Xs )
= ( cons_list_int @ nil_int @ nil_list_int ) ) ).
% n_lists.simps(1)
thf(fact_683_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_684_not__one__less__zero,axiom,
~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% not_one_less_zero
thf(fact_685_not__one__less__zero,axiom,
~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% not_one_less_zero
thf(fact_686_zero__less__one,axiom,
ord_less_nat @ zero_zero_nat @ one_one_nat ).
% zero_less_one
thf(fact_687_zero__less__one,axiom,
ord_less_int @ zero_zero_int @ one_one_int ).
% zero_less_one
thf(fact_688_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_689_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_690_dbl__dec__simps_I2_J,axiom,
( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
= ( uminus_uminus_int @ one_one_int ) ) ).
% dbl_dec_simps(2)
thf(fact_691_upto__aux__rec,axiom,
( upto_aux
= ( ^ [I2: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I2 ) @ Js @ ( upto_aux @ I2 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% upto_aux_rec
thf(fact_692_dbl__dec__simps_I3_J,axiom,
( ( neg_nu3811975205180677377ec_int @ one_one_int )
= one_one_int ) ).
% dbl_dec_simps(3)
thf(fact_693_dbl__dec__def,axiom,
( neg_nu3811975205180677377ec_int
= ( ^ [X3: int] : ( minus_minus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% dbl_dec_def
thf(fact_694_size__char__eq__0,axiom,
( size_size_char
= ( ^ [C3: char] : zero_zero_nat ) ) ).
% size_char_eq_0
thf(fact_695_prod_Oinject,axiom,
! [X1: int,X2: produc1534919314292393896nt_nat,Y1: int,Y2: produc1534919314292393896nt_nat] :
( ( ( produc8342123264692915235nt_nat @ X1 @ X2 )
= ( produc8342123264692915235nt_nat @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_696_prod_Oinject,axiom,
! [X1: com,X2: list_char > int,Y1: com,Y2: list_char > int] :
( ( ( produc5595214716300948949ar_int @ X1 @ X2 )
= ( produc5595214716300948949ar_int @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_697_prod_Oinject,axiom,
! [X1: list_char > int,X2: list_int,Y1: list_char > int,Y2: list_int] :
( ( ( produc8650753666468850689st_int @ X1 @ X2 )
= ( produc8650753666468850689st_int @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_698_prod_Oinject,axiom,
! [X1: list_char > int,X2: int,Y1: list_char > int,Y2: int] :
( ( ( produc5790713362662368625nt_int @ X1 @ X2 )
= ( produc5790713362662368625nt_int @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_699_prod_Oinject,axiom,
! [X1: int > int,X2: nat,Y1: int > int,Y2: nat] :
( ( ( produc2630796075472406112nt_nat @ X1 @ X2 )
= ( produc2630796075472406112nt_nat @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_700_old_Oprod_Oinject,axiom,
! [A: int,B: produc1534919314292393896nt_nat,A4: int,B4: produc1534919314292393896nt_nat] :
( ( ( produc8342123264692915235nt_nat @ A @ B )
= ( produc8342123264692915235nt_nat @ A4 @ B4 ) )
= ( ( A = A4 )
& ( B = B4 ) ) ) ).
% old.prod.inject
thf(fact_701_old_Oprod_Oinject,axiom,
! [A: com,B: list_char > int,A4: com,B4: list_char > int] :
( ( ( produc5595214716300948949ar_int @ A @ B )
= ( produc5595214716300948949ar_int @ A4 @ B4 ) )
= ( ( A = A4 )
& ( B = B4 ) ) ) ).
% old.prod.inject
thf(fact_702_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_703_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_704_old_Oprod_Oinject,axiom,
! [A: int > int,B: nat,A4: int > int,B4: nat] :
( ( ( produc2630796075472406112nt_nat @ A @ B )
= ( produc2630796075472406112nt_nat @ A4 @ B4 ) )
= ( ( A = A4 )
& ( B = B4 ) ) ) ).
% old.prod.inject
thf(fact_705_shuffles_Ocases,axiom,
! [X: produc8891168062546637159_instr] :
( ! [Ys4: list_instr] :
( X
!= ( produc7750586281064920791_instr @ nil_instr @ Ys4 ) )
=> ( ! [Xs3: list_instr] :
( X
!= ( produc7750586281064920791_instr @ Xs3 @ nil_instr ) )
=> ~ ! [X5: instr,Xs3: list_instr,Y4: instr,Ys4: list_instr] :
( X
!= ( produc7750586281064920791_instr @ ( cons_instr @ X5 @ Xs3 ) @ ( cons_instr @ Y4 @ Ys4 ) ) ) ) ) ).
% shuffles.cases
thf(fact_706_shuffles_Ocases,axiom,
! [X: produc1186641810826059865st_int] :
( ! [Ys4: list_int] :
( X
!= ( produc364263696895485585st_int @ nil_int @ Ys4 ) )
=> ( ! [Xs3: list_int] :
( X
!= ( produc364263696895485585st_int @ Xs3 @ nil_int ) )
=> ~ ! [X5: int,Xs3: list_int,Y4: int,Ys4: list_int] :
( X
!= ( produc364263696895485585st_int @ ( cons_int @ X5 @ Xs3 ) @ ( cons_int @ Y4 @ Ys4 ) ) ) ) ) ).
% shuffles.cases
thf(fact_707_shuffles_Ocases,axiom,
! [X: produc5848496107505245989st_int] :
( ! [Ys4: list_P419547167332244514st_int] :
( X
!= ( produc2639222612625641053st_int @ nil_Pr749310521696113548st_int @ Ys4 ) )
=> ( ! [Xs3: list_P419547167332244514st_int] :
( X
!= ( produc2639222612625641053st_int @ Xs3 @ nil_Pr749310521696113548st_int ) )
=> ~ ! [X5: produc6425607678544837394st_int,Xs3: list_P419547167332244514st_int,Y4: produc6425607678544837394st_int,Ys4: list_P419547167332244514st_int] :
( X
!= ( produc2639222612625641053st_int @ ( cons_P4151473878978182108st_int @ X5 @ Xs3 ) @ ( cons_P4151473878978182108st_int @ Y4 @ Ys4 ) ) ) ) ) ).
% shuffles.cases
thf(fact_708_splice_Ocases,axiom,
! [X: produc8891168062546637159_instr] :
( ! [Ys4: list_instr] :
( X
!= ( produc7750586281064920791_instr @ nil_instr @ Ys4 ) )
=> ~ ! [X5: instr,Xs3: list_instr,Ys4: list_instr] :
( X
!= ( produc7750586281064920791_instr @ ( cons_instr @ X5 @ Xs3 ) @ Ys4 ) ) ) ).
% splice.cases
thf(fact_709_splice_Ocases,axiom,
! [X: produc1186641810826059865st_int] :
( ! [Ys4: list_int] :
( X
!= ( produc364263696895485585st_int @ nil_int @ Ys4 ) )
=> ~ ! [X5: int,Xs3: list_int,Ys4: list_int] :
( X
!= ( produc364263696895485585st_int @ ( cons_int @ X5 @ Xs3 ) @ Ys4 ) ) ) ).
% splice.cases
thf(fact_710_splice_Ocases,axiom,
! [X: produc5848496107505245989st_int] :
( ! [Ys4: list_P419547167332244514st_int] :
( X
!= ( produc2639222612625641053st_int @ nil_Pr749310521696113548st_int @ Ys4 ) )
=> ~ ! [X5: produc6425607678544837394st_int,Xs3: list_P419547167332244514st_int,Ys4: list_P419547167332244514st_int] :
( X
!= ( produc2639222612625641053st_int @ ( cons_P4151473878978182108st_int @ X5 @ Xs3 ) @ Ys4 ) ) ) ).
% splice.cases
thf(fact_711_iexec_Ocases,axiom,
! [X: produc5995290525303592096st_int] :
~ ! [Ins: instr,I3: int,S2: list_char > int,Stk: list_int] :
( X
!= ( produc1484136438817787418st_int @ Ins @ ( produc5086643055186798020st_int @ I3 @ ( produc8650753666468850689st_int @ S2 @ Stk ) ) ) ) ).
% iexec.cases
thf(fact_712_Pair__inject,axiom,
! [A: int,B: produc1534919314292393896nt_nat,A4: int,B4: produc1534919314292393896nt_nat] :
( ( ( produc8342123264692915235nt_nat @ A @ B )
= ( produc8342123264692915235nt_nat @ A4 @ B4 ) )
=> ~ ( ( A = A4 )
=> ( B != B4 ) ) ) ).
% Pair_inject
thf(fact_713_Pair__inject,axiom,
! [A: com,B: list_char > int,A4: com,B4: list_char > int] :
( ( ( produc5595214716300948949ar_int @ A @ B )
= ( produc5595214716300948949ar_int @ A4 @ B4 ) )
=> ~ ( ( A = A4 )
=> ( B != B4 ) ) ) ).
% Pair_inject
thf(fact_714_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_715_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_716_Pair__inject,axiom,
! [A: int > int,B: nat,A4: int > int,B4: nat] :
( ( ( produc2630796075472406112nt_nat @ A @ B )
= ( produc2630796075472406112nt_nat @ A4 @ B4 ) )
=> ~ ( ( A = A4 )
=> ( B != B4 ) ) ) ).
% Pair_inject
thf(fact_717_prod__cases,axiom,
! [P: produc1019184382078353393nt_nat > $o,P3: produc1019184382078353393nt_nat] :
( ! [A5: int,B5: produc1534919314292393896nt_nat] : ( P @ ( produc8342123264692915235nt_nat @ A5 @ B5 ) )
=> ( P @ P3 ) ) ).
% prod_cases
thf(fact_718_prod__cases,axiom,
! [P: produc2931317944591925149ar_int > $o,P3: produc2931317944591925149ar_int] :
( ! [A5: com,B5: list_char > int] : ( P @ ( produc5595214716300948949ar_int @ A5 @ B5 ) )
=> ( P @ P3 ) ) ).
% prod_cases
thf(fact_719_prod__cases,axiom,
! [P: produc369741286924889929st_int > $o,P3: produc369741286924889929st_int] :
( ! [A5: list_char > int,B5: list_int] : ( P @ ( produc8650753666468850689st_int @ A5 @ B5 ) )
=> ( P @ P3 ) ) ).
% prod_cases
thf(fact_720_prod__cases,axiom,
! [P: produc4435102495419491129nt_int > $o,P3: produc4435102495419491129nt_int] :
( ! [A5: list_char > int,B5: int] : ( P @ ( produc5790713362662368625nt_int @ A5 @ B5 ) )
=> ( P @ P3 ) ) ).
% prod_cases
thf(fact_721_prod__cases,axiom,
! [P: produc1534919314292393896nt_nat > $o,P3: produc1534919314292393896nt_nat] :
( ! [A5: int > int,B5: nat] : ( P @ ( produc2630796075472406112nt_nat @ A5 @ B5 ) )
=> ( P @ P3 ) ) ).
% prod_cases
thf(fact_722_surj__pair,axiom,
! [P3: produc1019184382078353393nt_nat] :
? [X5: int,Y4: produc1534919314292393896nt_nat] :
( P3
= ( produc8342123264692915235nt_nat @ X5 @ Y4 ) ) ).
% surj_pair
thf(fact_723_surj__pair,axiom,
! [P3: produc2931317944591925149ar_int] :
? [X5: com,Y4: list_char > int] :
( P3
= ( produc5595214716300948949ar_int @ X5 @ Y4 ) ) ).
% surj_pair
thf(fact_724_surj__pair,axiom,
! [P3: produc369741286924889929st_int] :
? [X5: list_char > int,Y4: list_int] :
( P3
= ( produc8650753666468850689st_int @ X5 @ Y4 ) ) ).
% surj_pair
thf(fact_725_surj__pair,axiom,
! [P3: produc4435102495419491129nt_int] :
? [X5: list_char > int,Y4: int] :
( P3
= ( produc5790713362662368625nt_int @ X5 @ Y4 ) ) ).
% surj_pair
thf(fact_726_surj__pair,axiom,
! [P3: produc1534919314292393896nt_nat] :
? [X5: int > int,Y4: nat] :
( P3
= ( produc2630796075472406112nt_nat @ X5 @ Y4 ) ) ).
% surj_pair
thf(fact_727_old_Oprod_Oexhaust,axiom,
! [Y: produc1019184382078353393nt_nat] :
~ ! [A5: int,B5: produc1534919314292393896nt_nat] :
( Y
!= ( produc8342123264692915235nt_nat @ A5 @ B5 ) ) ).
% old.prod.exhaust
thf(fact_728_old_Oprod_Oexhaust,axiom,
! [Y: produc2931317944591925149ar_int] :
~ ! [A5: com,B5: list_char > int] :
( Y
!= ( produc5595214716300948949ar_int @ A5 @ B5 ) ) ).
% old.prod.exhaust
thf(fact_729_old_Oprod_Oexhaust,axiom,
! [Y: produc369741286924889929st_int] :
~ ! [A5: list_char > int,B5: list_int] :
( Y
!= ( produc8650753666468850689st_int @ A5 @ B5 ) ) ).
% old.prod.exhaust
thf(fact_730_old_Oprod_Oexhaust,axiom,
! [Y: produc4435102495419491129nt_int] :
~ ! [A5: list_char > int,B5: int] :
( Y
!= ( produc5790713362662368625nt_int @ A5 @ B5 ) ) ).
% old.prod.exhaust
thf(fact_731_old_Oprod_Oexhaust,axiom,
! [Y: produc1534919314292393896nt_nat] :
~ ! [A5: int > int,B5: nat] :
( Y
!= ( produc2630796075472406112nt_nat @ A5 @ B5 ) ) ).
% old.prod.exhaust
thf(fact_732_prod__induct3,axiom,
! [P: produc1019184382078353393nt_nat > $o,X: produc1019184382078353393nt_nat] :
( ! [A5: int,B5: int > int,C2: nat] : ( P @ ( produc8342123264692915235nt_nat @ A5 @ ( produc2630796075472406112nt_nat @ B5 @ C2 ) ) )
=> ( P @ X ) ) ).
% prod_induct3
thf(fact_733_prod__cases3,axiom,
! [Y: produc1019184382078353393nt_nat] :
~ ! [A5: int,B5: int > int,C2: nat] :
( Y
!= ( produc8342123264692915235nt_nat @ A5 @ ( produc2630796075472406112nt_nat @ B5 @ C2 ) ) ) ).
% prod_cases3
thf(fact_734_size_H__char__eq__0,axiom,
( size_char
= ( ^ [C3: char] : zero_zero_nat ) ) ).
% size'_char_eq_0
thf(fact_735_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_736_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_737_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_738_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_739_JmpE,axiom,
! [I: int,Pc: int,S: list_char > int,Stk2: list_int,Cf: produc6425607678544837394st_int] :
( ( iexec_pred @ ( produc1484136438817787418st_int @ ( jmp @ I ) @ ( produc5086643055186798020st_int @ Pc @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) ) @ Cf )
=> ( Cf
= ( produc5086643055186798020st_int @ ( plus_plus_int @ ( plus_plus_int @ Pc @ one_one_int ) @ I ) @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) ) ) ).
% JmpE
thf(fact_740_iexec__offset,axiom,
! [Ins2: instr,Pc: int,S: list_char > int,Stk2: list_int,Pc2: int,S3: list_char > int,Stk3: list_int,I: int] :
( ( iexec_pred @ ( produc1484136438817787418st_int @ Ins2 @ ( produc5086643055186798020st_int @ Pc @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) ) @ ( produc5086643055186798020st_int @ Pc2 @ ( produc8650753666468850689st_int @ S3 @ Stk3 ) ) )
=> ( iexec_pred @ ( produc1484136438817787418st_int @ Ins2 @ ( produc5086643055186798020st_int @ ( minus_minus_int @ Pc @ I ) @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) ) @ ( produc5086643055186798020st_int @ ( minus_minus_int @ Pc2 @ I ) @ ( produc8650753666468850689st_int @ S3 @ Stk3 ) ) ) ) ).
% iexec_offset
thf(fact_741_LoadIE,axiom,
! [I: int,Pc: int,S: list_char > int,Stk2: list_int,Cf: produc6425607678544837394st_int] :
( ( iexec_pred @ ( produc1484136438817787418st_int @ ( loadi @ I ) @ ( produc5086643055186798020st_int @ Pc @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) ) @ Cf )
=> ( Cf
= ( produc5086643055186798020st_int @ ( plus_plus_int @ Pc @ one_one_int ) @ ( produc8650753666468850689st_int @ S @ ( cons_int @ I @ Stk2 ) ) ) ) ) ).
% LoadIE
thf(fact_742_LoadE,axiom,
! [X: list_char,Pc: int,S: list_char > int,Stk2: list_int,Cf: produc6425607678544837394st_int] :
( ( iexec_pred @ ( produc1484136438817787418st_int @ ( load @ X ) @ ( produc5086643055186798020st_int @ Pc @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) ) @ Cf )
=> ( Cf
= ( produc5086643055186798020st_int @ ( plus_plus_int @ Pc @ one_one_int ) @ ( produc8650753666468850689st_int @ S @ ( cons_int @ ( S @ X ) @ Stk2 ) ) ) ) ) ).
% LoadE
thf(fact_743_inth__append,axiom,
! [I: int,Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_s229347708945616566st_int @ Xs ) ) )
=> ( ( inth_P8039235741264645271st_int @ ( append5028292981072010935st_int @ Xs @ Ys ) @ I )
= ( inth_P8039235741264645271st_int @ Xs @ I ) ) )
& ( ~ ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_s229347708945616566st_int @ Xs ) ) )
=> ( ( inth_P8039235741264645271st_int @ ( append5028292981072010935st_int @ Xs @ Ys ) @ I )
= ( inth_P8039235741264645271st_int @ Ys @ ( minus_minus_int @ I @ ( semiri1314217659103216013at_int @ ( size_s229347708945616566st_int @ Xs ) ) ) ) ) ) ) ) ).
% inth_append
thf(fact_744_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_745_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_746_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_747_iexec__shift,axiom,
! [N: int,I4: int,S3: list_char > int,Stk3: list_int,Ins2: instr,I: int,S: list_char > int,Stk2: list_int] :
( ( ( produc5086643055186798020st_int @ ( plus_plus_int @ N @ I4 ) @ ( produc8650753666468850689st_int @ S3 @ Stk3 ) )
= ( iexec @ Ins2 @ ( produc5086643055186798020st_int @ ( plus_plus_int @ N @ I ) @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) ) )
= ( ( produc5086643055186798020st_int @ I4 @ ( produc8650753666468850689st_int @ S3 @ Stk3 ) )
= ( iexec @ Ins2 @ ( produc5086643055186798020st_int @ I @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) ) ) ) ).
% iexec_shift
thf(fact_748_instr_Oinject_I2_J,axiom,
! [X2: list_char,Y2: list_char] :
( ( ( load @ X2 )
= ( load @ Y2 ) )
= ( X2 = Y2 ) ) ).
% instr.inject(2)
thf(fact_749_instr_Oinject_I1_J,axiom,
! [X1: int,Y1: int] :
( ( ( loadi @ X1 )
= ( loadi @ Y1 ) )
= ( X1 = Y1 ) ) ).
% instr.inject(1)
thf(fact_750_le__zero__eq,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) ).
% le_zero_eq
thf(fact_751_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_752_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_753_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_754_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_755_neg__le__iff__le,axiom,
! [B: int,A: int] :
( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
= ( ord_less_eq_int @ A @ B ) ) ).
% neg_le_iff_le
thf(fact_756_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_757_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_758_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_759_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_760_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_761_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_762_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_763_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_764_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_765_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_766_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_767_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_768_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_769_neg__less__eq__nonneg,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
= ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% neg_less_eq_nonneg
thf(fact_770_less__eq__neg__nonpos,axiom,
! [A: int] :
( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
= ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% less_eq_neg_nonpos
thf(fact_771_neg__le__0__iff__le,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
= ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% neg_le_0_iff_le
thf(fact_772_neg__0__le__iff__le,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
= ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% neg_0_le_iff_le
thf(fact_773_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_774_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_775_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_776_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_777_negative__zle,axiom,
! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% negative_zle
thf(fact_778_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_779_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_780_zle__add1__eq__le,axiom,
! [W: int,Z3: int] :
( ( ord_less_int @ W @ ( plus_plus_int @ Z3 @ one_one_int ) )
= ( ord_less_eq_int @ W @ Z3 ) ) ).
% zle_add1_eq_le
thf(fact_781_zle__diff1__eq,axiom,
! [W: int,Z3: int] :
( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z3 @ one_one_int ) )
= ( ord_less_int @ W @ Z3 ) ) ).
% zle_diff1_eq
thf(fact_782_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_783_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_784_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_785_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_786_verit__comp__simplify1_I2_J,axiom,
! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% verit_comp_simplify1(2)
thf(fact_787_verit__comp__simplify1_I2_J,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% verit_comp_simplify1(2)
thf(fact_788_verit__comp__simplify1_I2_J,axiom,
! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% verit_comp_simplify1(2)
thf(fact_789_instr_Odistinct_I1_J,axiom,
! [X1: int,X2: list_char] :
( ( loadi @ X1 )
!= ( load @ X2 ) ) ).
% instr.distinct(1)
thf(fact_790_lift__Suc__antimono__le,axiom,
! [F: nat > int,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% lift_Suc_antimono_le
thf(fact_791_lift__Suc__antimono__le,axiom,
! [F: nat > nat,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% lift_Suc_antimono_le
thf(fact_792_lift__Suc__antimono__le,axiom,
! [F: nat > num,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% lift_Suc_antimono_le
thf(fact_793_lift__Suc__mono__le,axiom,
! [F: nat > int,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% lift_Suc_mono_le
thf(fact_794_lift__Suc__mono__le,axiom,
! [F: nat > nat,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% lift_Suc_mono_le
thf(fact_795_lift__Suc__mono__le,axiom,
! [F: nat > num,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_num @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% lift_Suc_mono_le
thf(fact_796_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_797_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_798_less__eq__int__code_I1_J,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% less_eq_int_code(1)
thf(fact_799_le__numeral__extra_I4_J,axiom,
ord_less_eq_int @ one_one_int @ one_one_int ).
% le_numeral_extra(4)
thf(fact_800_le__numeral__extra_I4_J,axiom,
ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% le_numeral_extra(4)
thf(fact_801_add__mono__thms__linordered__semiring_I3_J,axiom,
! [I: int,J: int,K: int,L: int] :
( ( ( ord_less_eq_int @ I @ J )
& ( K = L ) )
=> ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(3)
thf(fact_802_add__mono__thms__linordered__semiring_I3_J,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I @ J )
& ( K = L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(3)
thf(fact_803_add__mono__thms__linordered__semiring_I2_J,axiom,
! [I: int,J: int,K: int,L: int] :
( ( ( I = J )
& ( ord_less_eq_int @ K @ L ) )
=> ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(2)
thf(fact_804_add__mono__thms__linordered__semiring_I2_J,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( I = J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(2)
thf(fact_805_add__mono__thms__linordered__semiring_I1_J,axiom,
! [I: int,J: int,K: int,L: int] :
( ( ( ord_less_eq_int @ I @ J )
& ( ord_less_eq_int @ K @ L ) )
=> ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(1)
thf(fact_806_add__mono__thms__linordered__semiring_I1_J,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I @ J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(1)
thf(fact_807_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_808_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_809_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_810_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_811_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_812_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_813_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_814_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_815_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_816_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_817_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_818_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_819_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_820_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_821_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_822_le__numeral__extra_I3_J,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% le_numeral_extra(3)
thf(fact_823_le__numeral__extra_I3_J,axiom,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% le_numeral_extra(3)
thf(fact_824_zero__le,axiom,
! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% zero_le
thf(fact_825_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_826_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_827_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_828_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_829_le__imp__neg__le,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% le_imp_neg_le
thf(fact_830_minus__le__iff,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
= ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% minus_le_iff
thf(fact_831_le__minus__iff,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
= ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% le_minus_iff
thf(fact_832_instr_Odistinct_I17_J,axiom,
! [X2: list_char,X52: int] :
( ( load @ X2 )
!= ( jmp @ X52 ) ) ).
% instr.distinct(17)
thf(fact_833_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_834_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_835_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_836_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_837_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_838_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_839_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_840_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_841_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_842_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_843_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_844_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_845_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_846_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_847_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_848_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_849_not__one__le__zero,axiom,
~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% not_one_le_zero
thf(fact_850_not__one__le__zero,axiom,
~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% not_one_le_zero
thf(fact_851_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_852_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_853_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_854_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_855_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_856_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_857_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_858_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_859_add__mono__thms__linordered__field_I3_J,axiom,
! [I: int,J: int,K: int,L: int] :
( ( ( ord_less_int @ I @ J )
& ( ord_less_eq_int @ K @ L ) )
=> ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(3)
thf(fact_860_add__mono__thms__linordered__field_I3_J,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_nat @ I @ J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(3)
thf(fact_861_add__mono__thms__linordered__field_I4_J,axiom,
! [I: int,J: int,K: int,L: int] :
( ( ( ord_less_eq_int @ I @ J )
& ( ord_less_int @ K @ L ) )
=> ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(4)
thf(fact_862_add__mono__thms__linordered__field_I4_J,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I @ J )
& ( ord_less_nat @ K @ L ) )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_field(4)
thf(fact_863_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_864_instr_Odistinct_I7_J,axiom,
! [X1: int,X52: int] :
( ( loadi @ X1 )
!= ( jmp @ X52 ) ) ).
% instr.distinct(7)
thf(fact_865_add__le__add__imp__diff__le,axiom,
! [I: int,K: int,N: int,J: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
=> ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
=> ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
=> ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
=> ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% add_le_add_imp_diff_le
thf(fact_866_add__le__add__imp__diff__le,axiom,
! [I: nat,K: nat,N: nat,J: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
=> ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
=> ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% add_le_add_imp_diff_le
thf(fact_867_add__le__imp__le__diff,axiom,
! [I: int,K: int,N: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
=> ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% add_le_imp_le_diff
thf(fact_868_add__le__imp__le__diff,axiom,
! [I: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
=> ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% add_le_imp_le_diff
thf(fact_869_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_870_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_871_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_872_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_873_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_874_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_875_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_876_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_877_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_878_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_879_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_880_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_881_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_882_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_883_le__minus__one__simps_I2_J,axiom,
ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% le_minus_one_simps(2)
thf(fact_884_le__minus__one__simps_I4_J,axiom,
~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% le_minus_one_simps(4)
thf(fact_885_zero__le__imp__eq__int,axiom,
! [K: int] :
( ( ord_less_eq_int @ zero_zero_int @ K )
=> ? [N2: nat] :
( K
= ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% zero_le_imp_eq_int
thf(fact_886_nonneg__int__cases,axiom,
! [K: int] :
( ( ord_less_eq_int @ zero_zero_int @ K )
=> ~ ! [N2: nat] :
( K
!= ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% nonneg_int_cases
thf(fact_887_int__ge__induct,axiom,
! [K: int,I: int,P: int > $o] :
( ( ord_less_eq_int @ K @ I )
=> ( ( P @ K )
=> ( ! [I3: int] :
( ( ord_less_eq_int @ K @ I3 )
=> ( ( P @ I3 )
=> ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
=> ( P @ I ) ) ) ) ).
% int_ge_induct
thf(fact_888_zle__iff__zadd,axiom,
( ord_less_eq_int
= ( ^ [W2: int,Z4: int] :
? [N4: nat] :
( Z4
= ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% zle_iff_zadd
thf(fact_889_int__le__induct,axiom,
! [I: int,K: int,P: int > $o] :
( ( ord_less_eq_int @ I @ K )
=> ( ( P @ K )
=> ( ! [I3: int] :
( ( ord_less_eq_int @ I3 @ K )
=> ( ( P @ I3 )
=> ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
=> ( P @ I ) ) ) ) ).
% int_le_induct
thf(fact_890_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_891_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_892_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_893_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_894_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_895_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_896_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_897_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_898_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_899_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_900_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_901_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_902_le__minus__one__simps_I1_J,axiom,
ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% le_minus_one_simps(1)
thf(fact_903_le__minus__one__simps_I3_J,axiom,
~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% le_minus_one_simps(3)
thf(fact_904_int__zle__neg,axiom,
! [N: nat,M: nat] :
( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
= ( ( N = zero_zero_nat )
& ( M = zero_zero_nat ) ) ) ).
% int_zle_neg
thf(fact_905_int__one__le__iff__zero__less,axiom,
! [Z3: int] :
( ( ord_less_eq_int @ one_one_int @ Z3 )
= ( ord_less_int @ zero_zero_int @ Z3 ) ) ).
% int_one_le_iff_zero_less
thf(fact_906_nonpos__int__cases,axiom,
! [K: int] :
( ( ord_less_eq_int @ K @ zero_zero_int )
=> ~ ! [N2: nat] :
( K
!= ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% nonpos_int_cases
thf(fact_907_negative__zle__0,axiom,
! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% negative_zle_0
thf(fact_908_zless__imp__add1__zle,axiom,
! [W: int,Z3: int] :
( ( ord_less_int @ W @ Z3 )
=> ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z3 ) ) ).
% zless_imp_add1_zle
thf(fact_909_add1__zle__eq,axiom,
! [W: int,Z3: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z3 )
= ( ord_less_int @ W @ Z3 ) ) ).
% add1_zle_eq
thf(fact_910_int__induct,axiom,
! [P: int > $o,K: int,I: int] :
( ( P @ K )
=> ( ! [I3: int] :
( ( ord_less_eq_int @ K @ I3 )
=> ( ( P @ I3 )
=> ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
=> ( ! [I3: int] :
( ( ord_less_eq_int @ I3 @ K )
=> ( ( P @ I3 )
=> ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
=> ( P @ I ) ) ) ) ).
% int_induct
thf(fact_911_instr_Osize_I9_J,axiom,
! [X2: list_char] :
( ( size_size_instr @ ( load @ X2 ) )
= zero_zero_nat ) ).
% instr.size(9)
thf(fact_912_instr_Osize_I8_J,axiom,
! [X1: int] :
( ( size_size_instr @ ( loadi @ X1 ) )
= zero_zero_nat ) ).
% instr.size(8)
thf(fact_913_not__zle__0__negative,axiom,
! [N: nat] :
~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% not_zle_0_negative
thf(fact_914_le__imp__0__less,axiom,
! [Z3: int] :
( ( ord_less_eq_int @ zero_zero_int @ Z3 )
=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z3 ) ) ) ).
% le_imp_0_less
thf(fact_915_iexec__pred_Ocases,axiom,
! [A1: produc5995290525303592096st_int,A22: produc6425607678544837394st_int] :
( ( iexec_pred @ A1 @ A22 )
=> ~ ! [Ins: instr,Cf2: produc6425607678544837394st_int] :
( ( A1
= ( produc1484136438817787418st_int @ Ins @ Cf2 ) )
=> ( A22
!= ( iexec @ Ins @ Cf2 ) ) ) ) ).
% iexec_pred.cases
thf(fact_916_iexec__pred_Osimps,axiom,
( iexec_pred
= ( ^ [A12: produc5995290525303592096st_int,A23: produc6425607678544837394st_int] :
? [Ins3: instr,Cf3: produc6425607678544837394st_int] :
( ( A12
= ( produc1484136438817787418st_int @ Ins3 @ Cf3 ) )
& ( A23
= ( iexec @ Ins3 @ Cf3 ) ) ) ) ) ).
% iexec_pred.simps
thf(fact_917_iexec__pred_Ointros,axiom,
! [Ins2: instr,Cf: produc6425607678544837394st_int] : ( iexec_pred @ ( produc1484136438817787418st_int @ Ins2 @ Cf ) @ ( iexec @ Ins2 @ Cf ) ) ).
% iexec_pred.intros
thf(fact_918_iexec__simp,axiom,
! [Ins2: instr,Cf: produc6425607678544837394st_int,Cf4: produc6425607678544837394st_int] :
( ( iexec_pred @ ( produc1484136438817787418st_int @ Ins2 @ Cf ) @ Cf4 )
= ( Cf4
= ( iexec @ Ins2 @ Cf ) ) ) ).
% iexec_simp
thf(fact_919_exec1I,axiom,
! [C4: produc6425607678544837394st_int,P: list_instr,I: int,S: list_char > int,Stk2: list_int] :
( ( C4
= ( iexec @ ( inth_instr @ P @ I ) @ ( produc5086643055186798020st_int @ I @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) ) )
=> ( ( 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 @ S @ Stk2 ) ) @ C4 ) ) ) ) ).
% exec1I
thf(fact_920_m__config__equiv_Osimps,axiom,
! [I: int,Ms: int > int,Sp: nat,I4: int,Ms2: int > int,Sp2: nat] :
( ( m_config_equiv @ ( produc8342123264692915235nt_nat @ I @ ( produc2630796075472406112nt_nat @ Ms @ Sp ) ) @ ( produc8342123264692915235nt_nat @ I4 @ ( produc2630796075472406112nt_nat @ Ms2 @ Sp2 ) ) )
= ( ( I = I4 )
& ( Sp = Sp2 )
& ! [A3: int] :
( ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ Sp ) ) @ A3 )
=> ( ( Ms @ A3 )
= ( Ms2 @ A3 ) ) ) ) ) ).
% m_config_equiv.simps
thf(fact_921_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_922_bot__nat__0_Oextremum,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% bot_nat_0.extremum
thf(fact_923_le0,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% le0
thf(fact_924_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_925_nat__add__left__cancel__le,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( ord_less_eq_nat @ M @ N ) ) ).
% nat_add_left_cancel_le
thf(fact_926_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_927_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_928_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_929_Nat_Odiff__diff__right,axiom,
! [K: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
= ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% Nat.diff_diff_right
thf(fact_930_Nat_Oadd__diff__assoc2,axiom,
! [K: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
= ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% Nat.add_diff_assoc2
thf(fact_931_Nat_Oadd__diff__assoc,axiom,
! [K: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
= ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% Nat.add_diff_assoc
thf(fact_932_diff__Suc__diff__eq1,axiom,
! [K: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
= ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% diff_Suc_diff_eq1
thf(fact_933_diff__Suc__diff__eq2,axiom,
! [K: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
= ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% diff_Suc_diff_eq2
thf(fact_934_drop__all,axiom,
! [Xs: list_instr,N: nat] :
( ( ord_less_eq_nat @ ( size_size_list_instr @ Xs ) @ N )
=> ( ( drop_instr @ N @ Xs )
= nil_instr ) ) ).
% drop_all
thf(fact_935_drop__all,axiom,
! [Xs: list_P419547167332244514st_int,N: nat] :
( ( ord_less_eq_nat @ ( size_s229347708945616566st_int @ Xs ) @ N )
=> ( ( drop_P7838799151754935884st_int @ N @ Xs )
= nil_Pr749310521696113548st_int ) ) ).
% drop_all
thf(fact_936_drop__all,axiom,
! [Xs: list_list_char,N: nat] :
( ( ord_less_eq_nat @ ( size_s356637359517785349t_char @ Xs ) @ N )
=> ( ( drop_list_char @ N @ Xs )
= nil_list_char ) ) ).
% drop_all
thf(fact_937_drop__all,axiom,
! [Xs: list_int,N: nat] :
( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N )
=> ( ( drop_int @ N @ Xs )
= nil_int ) ) ).
% drop_all
thf(fact_938_drop__eq__Nil,axiom,
! [N: nat,Xs: list_instr] :
( ( ( drop_instr @ N @ Xs )
= nil_instr )
= ( ord_less_eq_nat @ ( size_size_list_instr @ Xs ) @ N ) ) ).
% drop_eq_Nil
thf(fact_939_drop__eq__Nil,axiom,
! [N: nat,Xs: list_P419547167332244514st_int] :
( ( ( drop_P7838799151754935884st_int @ N @ Xs )
= nil_Pr749310521696113548st_int )
= ( ord_less_eq_nat @ ( size_s229347708945616566st_int @ Xs ) @ N ) ) ).
% drop_eq_Nil
thf(fact_940_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_941_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_942_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_943_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_944_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_945_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_946_nth__drop,axiom,
! [N: nat,Xs: list_P419547167332244514st_int,I: nat] :
( ( ord_less_eq_nat @ N @ ( size_s229347708945616566st_int @ Xs ) )
=> ( ( nth_Pr8327173284404383691st_int @ ( drop_P7838799151754935884st_int @ N @ Xs ) @ I )
= ( nth_Pr8327173284404383691st_int @ Xs @ ( plus_plus_nat @ N @ I ) ) ) ) ).
% nth_drop
thf(fact_947_nth__drop,axiom,
! [N: nat,Xs: list_instr,I: nat] :
( ( ord_less_eq_nat @ N @ ( size_size_list_instr @ Xs ) )
=> ( ( nth_instr @ ( drop_instr @ N @ Xs ) @ I )
= ( nth_instr @ Xs @ ( plus_plus_nat @ N @ I ) ) ) ) ).
% nth_drop
thf(fact_948_nth__drop,axiom,
! [N: nat,Xs: list_list_char,I: nat] :
( ( ord_less_eq_nat @ N @ ( size_s356637359517785349t_char @ Xs ) )
=> ( ( nth_list_char @ ( drop_list_char @ N @ Xs ) @ I )
= ( nth_list_char @ Xs @ ( plus_plus_nat @ N @ I ) ) ) ) ).
% nth_drop
thf(fact_949_nth__drop,axiom,
! [N: nat,Xs: list_int,I: nat] :
( ( ord_less_eq_nat @ N @ ( size_size_list_int @ Xs ) )
=> ( ( nth_int @ ( drop_int @ N @ Xs ) @ I )
= ( nth_int @ Xs @ ( plus_plus_nat @ N @ I ) ) ) ) ).
% nth_drop
thf(fact_950_Nat_Oex__has__greatest__nat,axiom,
! [P: nat > $o,K: nat,B: nat] :
( ( P @ K )
=> ( ! [Y4: nat] :
( ( P @ Y4 )
=> ( ord_less_eq_nat @ Y4 @ B ) )
=> ? [X5: nat] :
( ( P @ X5 )
& ! [Y6: nat] :
( ( P @ Y6 )
=> ( ord_less_eq_nat @ Y6 @ X5 ) ) ) ) ) ).
% Nat.ex_has_greatest_nat
thf(fact_951_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_952_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_953_eq__imp__le,axiom,
! [M: nat,N: nat] :
( ( M = N )
=> ( ord_less_eq_nat @ M @ N ) ) ).
% eq_imp_le
thf(fact_954_le__trans,axiom,
! [I: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ord_less_eq_nat @ J @ K )
=> ( ord_less_eq_nat @ I @ K ) ) ) ).
% le_trans
thf(fact_955_le__refl,axiom,
! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% le_refl
thf(fact_956_nat__le__iff__add,axiom,
( ord_less_eq_nat
= ( ^ [M3: nat,N4: nat] :
? [K3: nat] :
( N4
= ( plus_plus_nat @ M3 @ K3 ) ) ) ) ).
% nat_le_iff_add
thf(fact_957_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_958_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_959_add__le__mono1,axiom,
! [I: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% add_le_mono1
thf(fact_960_add__le__mono,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ord_less_eq_nat @ K @ L )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% add_le_mono
thf(fact_961_le__Suc__ex,axiom,
! [K: nat,L: nat] :
( ( ord_less_eq_nat @ K @ L )
=> ? [N2: nat] :
( L
= ( plus_plus_nat @ K @ N2 ) ) ) ).
% le_Suc_ex
thf(fact_962_add__leD2,axiom,
! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
=> ( ord_less_eq_nat @ K @ N ) ) ).
% add_leD2
thf(fact_963_add__leD1,axiom,
! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
=> ( ord_less_eq_nat @ M @ N ) ) ).
% add_leD1
thf(fact_964_le__add2,axiom,
! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% le_add2
thf(fact_965_le__add1,axiom,
! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% le_add1
thf(fact_966_add__leE,axiom,
! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
=> ~ ( ( ord_less_eq_nat @ M @ N )
=> ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% add_leE
thf(fact_967_less__mono__imp__le__mono,axiom,
! [F: nat > nat,I: nat,J: nat] :
( ! [I3: nat,J2: nat] :
( ( ord_less_nat @ I3 @ J2 )
=> ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
=> ( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% less_mono_imp_le_mono
thf(fact_968_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_969_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_970_le__eq__less__or__eq,axiom,
( ord_less_eq_nat
= ( ^ [M3: nat,N4: nat] :
( ( ord_less_nat @ M3 @ N4 )
| ( M3 = N4 ) ) ) ) ).
% le_eq_less_or_eq
thf(fact_971_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_972_nat__less__le,axiom,
( ord_less_nat
= ( ^ [M3: nat,N4: nat] :
( ( ord_less_eq_nat @ M3 @ N4 )
& ( M3 != N4 ) ) ) ) ).
% nat_less_le
thf(fact_973_Suc__leD,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
=> ( ord_less_eq_nat @ M @ N ) ) ).
% Suc_leD
thf(fact_974_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_975_le__SucI,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% le_SucI
thf(fact_976_Suc__le__D,axiom,
! [N: nat,M6: nat] :
( ( ord_less_eq_nat @ ( suc @ N ) @ M6 )
=> ? [M5: nat] :
( M6
= ( suc @ M5 ) ) ) ).
% Suc_le_D
thf(fact_977_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_978_Suc__n__not__le__n,axiom,
! [N: nat] :
~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% Suc_n_not_le_n
thf(fact_979_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_980_full__nat__induct,axiom,
! [P: nat > $o,N: nat] :
( ! [N2: nat] :
( ! [M2: nat] :
( ( ord_less_eq_nat @ ( suc @ M2 ) @ N2 )
=> ( P @ M2 ) )
=> ( P @ N2 ) )
=> ( P @ N ) ) ).
% full_nat_induct
thf(fact_981_nat__induct__at__least,axiom,
! [M: nat,N: nat,P: nat > $o] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( P @ M )
=> ( ! [N2: nat] :
( ( ord_less_eq_nat @ M @ N2 )
=> ( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) ) )
=> ( P @ N ) ) ) ) ).
% nat_induct_at_least
thf(fact_982_transitive__stepwise__le,axiom,
! [M: nat,N: nat,R: nat > nat > $o] :
( ( ord_less_eq_nat @ M @ N )
=> ( ! [X5: nat] : ( R @ X5 @ X5 )
=> ( ! [X5: nat,Y4: nat,Z2: nat] :
( ( R @ X5 @ Y4 )
=> ( ( R @ Y4 @ Z2 )
=> ( R @ X5 @ Z2 ) ) )
=> ( ! [N2: nat] : ( R @ N2 @ ( suc @ N2 ) )
=> ( R @ M @ N ) ) ) ) ) ).
% transitive_stepwise_le
thf(fact_983_less__eq__nat_Osimps_I1_J,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% less_eq_nat.simps(1)
thf(fact_984_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_985_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_986_le__0__eq,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) ).
% le_0_eq
thf(fact_987_bounded__Max__nat,axiom,
! [P: nat > $o,X: nat,M7: nat] :
( ( P @ X )
=> ( ! [X5: nat] :
( ( P @ X5 )
=> ( ord_less_eq_nat @ X5 @ M7 ) )
=> ~ ! [M5: nat] :
( ( P @ M5 )
=> ~ ! [X6: nat] :
( ( P @ X6 )
=> ( ord_less_eq_nat @ X6 @ M5 ) ) ) ) ) ).
% bounded_Max_nat
thf(fact_988_eq__diff__iff,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( ( minus_minus_nat @ M @ K )
= ( minus_minus_nat @ N @ K ) )
= ( M = N ) ) ) ) ).
% eq_diff_iff
thf(fact_989_le__diff__iff,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
= ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% le_diff_iff
thf(fact_990_Nat_Odiff__diff__eq,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
= ( minus_minus_nat @ M @ N ) ) ) ) ).
% Nat.diff_diff_eq
thf(fact_991_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_992_diff__le__self,axiom,
! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% diff_le_self
thf(fact_993_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_994_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_995_m__iexec_Ocases,axiom,
! [X: produc3341395906625653086nt_nat] :
~ ! [Mins: m_instr,I3: int,Ms3: int > int,Sp3: nat] :
( X
!= ( produc973592215685924118nt_nat @ Mins @ ( produc8342123264692915235nt_nat @ I3 @ ( produc2630796075472406112nt_nat @ Ms3 @ Sp3 ) ) ) ) ).
% m_iexec.cases
thf(fact_996_m__config__equiv_Ocases,axiom,
! [X: produc6004788045807207619nt_nat] :
~ ! [I3: int,Ms3: int > int,Sp3: nat,I5: int,Ms4: int > int,Sp4: nat] :
( X
!= ( produc5273850286580078715nt_nat @ ( produc8342123264692915235nt_nat @ I3 @ ( produc2630796075472406112nt_nat @ Ms3 @ Sp3 ) ) @ ( produc8342123264692915235nt_nat @ I5 @ ( produc2630796075472406112nt_nat @ Ms4 @ Sp4 ) ) ) ) ).
% m_config_equiv.cases
thf(fact_997_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_998_ex__least__nat__le,axiom,
! [P: nat > $o,N: nat] :
( ( P @ N )
=> ( ~ ( P @ zero_zero_nat )
=> ? [K2: nat] :
( ( ord_less_eq_nat @ K2 @ N )
& ! [I6: nat] :
( ( ord_less_nat @ I6 @ K2 )
=> ~ ( P @ I6 ) )
& ( P @ K2 ) ) ) ) ).
% ex_least_nat_le
thf(fact_999_Suc__leI,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% Suc_leI
thf(fact_1000_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_1001_dec__induct,axiom,
! [I: nat,J: nat,P: nat > $o] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( P @ I )
=> ( ! [N2: nat] :
( ( ord_less_eq_nat @ I @ N2 )
=> ( ( ord_less_nat @ N2 @ J )
=> ( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) ) ) )
=> ( P @ J ) ) ) ) ).
% dec_induct
thf(fact_1002_inc__induct,axiom,
! [I: nat,J: nat,P: nat > $o] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( P @ J )
=> ( ! [N2: nat] :
( ( ord_less_eq_nat @ I @ N2 )
=> ( ( ord_less_nat @ N2 @ J )
=> ( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) ) ) )
=> ( P @ I ) ) ) ) ).
% inc_induct
thf(fact_1003_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_1004_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_1005_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_1006_less__eq__Suc__le,axiom,
( ord_less_nat
= ( ^ [N4: nat] : ( ord_less_eq_nat @ ( suc @ N4 ) ) ) ) ).
% less_eq_Suc_le
thf(fact_1007_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_1008_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_1009_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_1010_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_1011_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_1012_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_1013_mono__nat__linear__lb,axiom,
! [F: nat > nat,M: nat,K: nat] :
( ! [M5: nat,N2: nat] :
( ( ord_less_nat @ M5 @ N2 )
=> ( ord_less_nat @ ( F @ M5 ) @ ( F @ N2 ) ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% mono_nat_linear_lb
thf(fact_1014_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_1015_less__diff__iff,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
= ( ord_less_nat @ M @ N ) ) ) ) ).
% less_diff_iff
thf(fact_1016_Nat_Ole__imp__diff__is__add,axiom,
! [I: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ( minus_minus_nat @ J @ I )
= K )
= ( J
= ( plus_plus_nat @ K @ I ) ) ) ) ).
% Nat.le_imp_diff_is_add
thf(fact_1017_Nat_Odiff__add__assoc2,axiom,
! [K: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
= ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% Nat.diff_add_assoc2
thf(fact_1018_Nat_Odiff__add__assoc,axiom,
! [K: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
= ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% Nat.diff_add_assoc
thf(fact_1019_Nat_Ole__diff__conv2,axiom,
! [K: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% Nat.le_diff_conv2
thf(fact_1020_le__diff__conv,axiom,
! [J: nat,K: nat,I: nat] :
( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
= ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% le_diff_conv
thf(fact_1021_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_1022_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_1023_ex__least__nat__less,axiom,
! [P: nat > $o,N: nat] :
( ( P @ N )
=> ( ~ ( P @ zero_zero_nat )
=> ? [K2: nat] :
( ( ord_less_nat @ K2 @ N )
& ! [I6: nat] :
( ( ord_less_eq_nat @ I6 @ K2 )
=> ~ ( P @ I6 ) )
& ( P @ ( suc @ K2 ) ) ) ) ) ).
% ex_least_nat_less
thf(fact_1024_Suc__le__length__iff,axiom,
! [N: nat,Xs: list_instr] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_instr @ Xs ) )
= ( ? [X3: instr,Ys2: list_instr] :
( ( Xs
= ( cons_instr @ X3 @ Ys2 ) )
& ( ord_less_eq_nat @ N @ ( size_size_list_instr @ Ys2 ) ) ) ) ) ).
% Suc_le_length_iff
thf(fact_1025_Suc__le__length__iff,axiom,
! [N: nat,Xs: list_P419547167332244514st_int] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_s229347708945616566st_int @ Xs ) )
= ( ? [X3: produc6425607678544837394st_int,Ys2: list_P419547167332244514st_int] :
( ( Xs
= ( cons_P4151473878978182108st_int @ X3 @ Ys2 ) )
& ( ord_less_eq_nat @ N @ ( size_s229347708945616566st_int @ Ys2 ) ) ) ) ) ).
% Suc_le_length_iff
thf(fact_1026_Suc__le__length__iff,axiom,
! [N: nat,Xs: list_list_char] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_s356637359517785349t_char @ Xs ) )
= ( ? [X3: list_char,Ys2: list_list_char] :
( ( Xs
= ( cons_list_char @ X3 @ Ys2 ) )
& ( ord_less_eq_nat @ N @ ( size_s356637359517785349t_char @ Ys2 ) ) ) ) ) ).
% Suc_le_length_iff
thf(fact_1027_Suc__le__length__iff,axiom,
! [N: nat,Xs: list_int] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs ) )
= ( ? [X3: int,Ys2: list_int] :
( ( Xs
= ( cons_int @ X3 @ Ys2 ) )
& ( ord_less_eq_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) ) ) ).
% Suc_le_length_iff
thf(fact_1028_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_1029_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_1030_less__diff__conv2,axiom,
! [K: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
= ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% less_diff_conv2
thf(fact_1031_exec1__appendL,axiom,
! [P: list_instr,I: int,S: list_char > int,Stk2: list_int,I4: int,S3: list_char > int,Stk3: list_int,P4: list_instr] :
( ( exec1 @ P @ ( produc5086643055186798020st_int @ I @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) @ ( produc5086643055186798020st_int @ I4 @ ( produc8650753666468850689st_int @ S3 @ Stk3 ) ) )
=> ( exec1 @ ( append_instr @ P4 @ P ) @ ( produc5086643055186798020st_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P4 ) ) @ I ) @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) @ ( produc5086643055186798020st_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P4 ) ) @ I4 ) @ ( produc8650753666468850689st_int @ S3 @ Stk3 ) ) ) ) ).
% exec1_appendL
thf(fact_1032_to__m__state_Osimps,axiom,
( to_m_state
= ( ^ [Xs2: 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 @ Xs2 ) ) ) )
@ ( S4 @ ( inth_list_char @ Xs2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs2 ) ) @ A3 ) ) )
@ zero_zero_int ) ) ) ).
% to_m_state.simps
thf(fact_1033_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_1034_exec__append__trans,axiom,
! [P: list_instr,S: list_char > int,Stk2: list_int,I4: int,S3: list_char > int,Stk3: list_int,P4: list_instr,I7: int,S5: list_char > int,Stk4: list_int,J4: int] :
( ( star_P707599355569300323st_int @ ( exec1 @ P ) @ ( produc5086643055186798020st_int @ zero_zero_int @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) @ ( produc5086643055186798020st_int @ I4 @ ( produc8650753666468850689st_int @ S3 @ Stk3 ) ) )
=> ( ( 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 @ Stk3 ) ) @ ( produc5086643055186798020st_int @ I7 @ ( produc8650753666468850689st_int @ S5 @ Stk4 ) ) )
=> ( ( J4
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P ) ) @ I7 ) )
=> ( star_P707599355569300323st_int @ ( exec1 @ ( append_instr @ P @ P4 ) ) @ ( produc5086643055186798020st_int @ zero_zero_int @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) @ ( produc5086643055186798020st_int @ J4 @ ( produc8650753666468850689st_int @ S5 @ Stk4 ) ) ) ) ) ) ) ).
% exec_append_trans
thf(fact_1035_exec__appendL__if,axiom,
! [P4: list_instr,I: int,P: list_instr,S: list_char > int,Stk2: list_int,J: int,S3: list_char > int,Stk3: 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 @ S @ Stk2 ) ) @ ( produc5086643055186798020st_int @ J @ ( produc8650753666468850689st_int @ S3 @ Stk3 ) ) )
=> ( ( 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 @ S @ Stk2 ) ) @ ( produc5086643055186798020st_int @ I4 @ ( produc8650753666468850689st_int @ S3 @ Stk3 ) ) ) ) ) ) ).
% exec_appendL_if
thf(fact_1036_exec__Cons__1,axiom,
! [P: list_instr,S: list_char > int,Stk2: list_int,J: int,T: list_char > int,Stk3: list_int,Ins2: instr] :
( ( star_P707599355569300323st_int @ ( exec1 @ P ) @ ( produc5086643055186798020st_int @ zero_zero_int @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) @ ( produc5086643055186798020st_int @ J @ ( produc8650753666468850689st_int @ T @ Stk3 ) ) )
=> ( star_P707599355569300323st_int @ ( exec1 @ ( cons_instr @ Ins2 @ P ) ) @ ( produc5086643055186798020st_int @ one_one_int @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) @ ( produc5086643055186798020st_int @ ( plus_plus_int @ one_one_int @ J ) @ ( produc8650753666468850689st_int @ T @ Stk3 ) ) ) ) ).
% exec_Cons_1
thf(fact_1037_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_1038_minf_I7_J,axiom,
! [T: nat] :
? [Z2: nat] :
! [X6: nat] :
( ( ord_less_nat @ X6 @ Z2 )
=> ~ ( ord_less_nat @ T @ X6 ) ) ).
% minf(7)
thf(fact_1039_minf_I7_J,axiom,
! [T: int] :
? [Z2: int] :
! [X6: int] :
( ( ord_less_int @ X6 @ Z2 )
=> ~ ( ord_less_int @ T @ X6 ) ) ).
% minf(7)
thf(fact_1040_minf_I5_J,axiom,
! [T: nat] :
? [Z2: nat] :
! [X6: nat] :
( ( ord_less_nat @ X6 @ Z2 )
=> ( ord_less_nat @ X6 @ T ) ) ).
% minf(5)
thf(fact_1041_minf_I5_J,axiom,
! [T: int] :
? [Z2: int] :
! [X6: int] :
( ( ord_less_int @ X6 @ Z2 )
=> ( ord_less_int @ X6 @ T ) ) ).
% minf(5)
thf(fact_1042_minf_I4_J,axiom,
! [T: nat] :
? [Z2: nat] :
! [X6: nat] :
( ( ord_less_nat @ X6 @ Z2 )
=> ( X6 != T ) ) ).
% minf(4)
thf(fact_1043_minf_I4_J,axiom,
! [T: int] :
? [Z2: int] :
! [X6: int] :
( ( ord_less_int @ X6 @ Z2 )
=> ( X6 != T ) ) ).
% minf(4)
thf(fact_1044_minf_I3_J,axiom,
! [T: nat] :
? [Z2: nat] :
! [X6: nat] :
( ( ord_less_nat @ X6 @ Z2 )
=> ( X6 != T ) ) ).
% minf(3)
thf(fact_1045_minf_I3_J,axiom,
! [T: int] :
? [Z2: int] :
! [X6: int] :
( ( ord_less_int @ X6 @ Z2 )
=> ( X6 != T ) ) ).
% minf(3)
thf(fact_1046_minf_I2_J,axiom,
! [P: nat > $o,P4: nat > $o,Q2: nat > $o,Q3: nat > $o] :
( ? [Z5: nat] :
! [X5: nat] :
( ( ord_less_nat @ X5 @ Z5 )
=> ( ( P @ X5 )
= ( P4 @ X5 ) ) )
=> ( ? [Z5: nat] :
! [X5: nat] :
( ( ord_less_nat @ X5 @ Z5 )
=> ( ( Q2 @ X5 )
= ( Q3 @ X5 ) ) )
=> ? [Z2: nat] :
! [X6: nat] :
( ( ord_less_nat @ X6 @ Z2 )
=> ( ( ( P @ X6 )
| ( Q2 @ X6 ) )
= ( ( P4 @ X6 )
| ( Q3 @ X6 ) ) ) ) ) ) ).
% minf(2)
thf(fact_1047_minf_I2_J,axiom,
! [P: int > $o,P4: int > $o,Q2: int > $o,Q3: int > $o] :
( ? [Z5: int] :
! [X5: int] :
( ( ord_less_int @ X5 @ Z5 )
=> ( ( P @ X5 )
= ( P4 @ X5 ) ) )
=> ( ? [Z5: int] :
! [X5: int] :
( ( ord_less_int @ X5 @ Z5 )
=> ( ( Q2 @ X5 )
= ( Q3 @ X5 ) ) )
=> ? [Z2: int] :
! [X6: int] :
( ( ord_less_int @ X6 @ Z2 )
=> ( ( ( P @ X6 )
| ( Q2 @ X6 ) )
= ( ( P4 @ X6 )
| ( Q3 @ X6 ) ) ) ) ) ) ).
% minf(2)
thf(fact_1048_minf_I1_J,axiom,
! [P: nat > $o,P4: nat > $o,Q2: nat > $o,Q3: nat > $o] :
( ? [Z5: nat] :
! [X5: nat] :
( ( ord_less_nat @ X5 @ Z5 )
=> ( ( P @ X5 )
= ( P4 @ X5 ) ) )
=> ( ? [Z5: nat] :
! [X5: nat] :
( ( ord_less_nat @ X5 @ Z5 )
=> ( ( Q2 @ X5 )
= ( Q3 @ X5 ) ) )
=> ? [Z2: nat] :
! [X6: nat] :
( ( ord_less_nat @ X6 @ Z2 )
=> ( ( ( P @ X6 )
& ( Q2 @ X6 ) )
= ( ( P4 @ X6 )
& ( Q3 @ X6 ) ) ) ) ) ) ).
% minf(1)
thf(fact_1049_minf_I1_J,axiom,
! [P: int > $o,P4: int > $o,Q2: int > $o,Q3: int > $o] :
( ? [Z5: int] :
! [X5: int] :
( ( ord_less_int @ X5 @ Z5 )
=> ( ( P @ X5 )
= ( P4 @ X5 ) ) )
=> ( ? [Z5: int] :
! [X5: int] :
( ( ord_less_int @ X5 @ Z5 )
=> ( ( Q2 @ X5 )
= ( Q3 @ X5 ) ) )
=> ? [Z2: int] :
! [X6: int] :
( ( ord_less_int @ X6 @ Z2 )
=> ( ( ( P @ X6 )
& ( Q2 @ X6 ) )
= ( ( P4 @ X6 )
& ( Q3 @ X6 ) ) ) ) ) ) ).
% minf(1)
thf(fact_1050_pinf_I7_J,axiom,
! [T: nat] :
? [Z2: nat] :
! [X6: nat] :
( ( ord_less_nat @ Z2 @ X6 )
=> ( ord_less_nat @ T @ X6 ) ) ).
% pinf(7)
thf(fact_1051_pinf_I7_J,axiom,
! [T: int] :
? [Z2: int] :
! [X6: int] :
( ( ord_less_int @ Z2 @ X6 )
=> ( ord_less_int @ T @ X6 ) ) ).
% pinf(7)
thf(fact_1052_pinf_I5_J,axiom,
! [T: nat] :
? [Z2: nat] :
! [X6: nat] :
( ( ord_less_nat @ Z2 @ X6 )
=> ~ ( ord_less_nat @ X6 @ T ) ) ).
% pinf(5)
thf(fact_1053_pinf_I5_J,axiom,
! [T: int] :
? [Z2: int] :
! [X6: int] :
( ( ord_less_int @ Z2 @ X6 )
=> ~ ( ord_less_int @ X6 @ T ) ) ).
% pinf(5)
thf(fact_1054_pinf_I4_J,axiom,
! [T: nat] :
? [Z2: nat] :
! [X6: nat] :
( ( ord_less_nat @ Z2 @ X6 )
=> ( X6 != T ) ) ).
% pinf(4)
thf(fact_1055_pinf_I4_J,axiom,
! [T: int] :
? [Z2: int] :
! [X6: int] :
( ( ord_less_int @ Z2 @ X6 )
=> ( X6 != T ) ) ).
% pinf(4)
thf(fact_1056_pinf_I3_J,axiom,
! [T: nat] :
? [Z2: nat] :
! [X6: nat] :
( ( ord_less_nat @ Z2 @ X6 )
=> ( X6 != T ) ) ).
% pinf(3)
thf(fact_1057_pinf_I3_J,axiom,
! [T: int] :
? [Z2: int] :
! [X6: int] :
( ( ord_less_int @ Z2 @ X6 )
=> ( X6 != T ) ) ).
% pinf(3)
thf(fact_1058_pinf_I2_J,axiom,
! [P: nat > $o,P4: nat > $o,Q2: nat > $o,Q3: nat > $o] :
( ? [Z5: nat] :
! [X5: nat] :
( ( ord_less_nat @ Z5 @ X5 )
=> ( ( P @ X5 )
= ( P4 @ X5 ) ) )
=> ( ? [Z5: nat] :
! [X5: nat] :
( ( ord_less_nat @ Z5 @ X5 )
=> ( ( Q2 @ X5 )
= ( Q3 @ X5 ) ) )
=> ? [Z2: nat] :
! [X6: nat] :
( ( ord_less_nat @ Z2 @ X6 )
=> ( ( ( P @ X6 )
| ( Q2 @ X6 ) )
= ( ( P4 @ X6 )
| ( Q3 @ X6 ) ) ) ) ) ) ).
% pinf(2)
thf(fact_1059_pinf_I2_J,axiom,
! [P: int > $o,P4: int > $o,Q2: int > $o,Q3: int > $o] :
( ? [Z5: int] :
! [X5: int] :
( ( ord_less_int @ Z5 @ X5 )
=> ( ( P @ X5 )
= ( P4 @ X5 ) ) )
=> ( ? [Z5: int] :
! [X5: int] :
( ( ord_less_int @ Z5 @ X5 )
=> ( ( Q2 @ X5 )
= ( Q3 @ X5 ) ) )
=> ? [Z2: int] :
! [X6: int] :
( ( ord_less_int @ Z2 @ X6 )
=> ( ( ( P @ X6 )
| ( Q2 @ X6 ) )
= ( ( P4 @ X6 )
| ( Q3 @ X6 ) ) ) ) ) ) ).
% pinf(2)
thf(fact_1060_pinf_I1_J,axiom,
! [P: nat > $o,P4: nat > $o,Q2: nat > $o,Q3: nat > $o] :
( ? [Z5: nat] :
! [X5: nat] :
( ( ord_less_nat @ Z5 @ X5 )
=> ( ( P @ X5 )
= ( P4 @ X5 ) ) )
=> ( ? [Z5: nat] :
! [X5: nat] :
( ( ord_less_nat @ Z5 @ X5 )
=> ( ( Q2 @ X5 )
= ( Q3 @ X5 ) ) )
=> ? [Z2: nat] :
! [X6: nat] :
( ( ord_less_nat @ Z2 @ X6 )
=> ( ( ( P @ X6 )
& ( Q2 @ X6 ) )
= ( ( P4 @ X6 )
& ( Q3 @ X6 ) ) ) ) ) ) ).
% pinf(1)
thf(fact_1061_pinf_I1_J,axiom,
! [P: int > $o,P4: int > $o,Q2: int > $o,Q3: int > $o] :
( ? [Z5: int] :
! [X5: int] :
( ( ord_less_int @ Z5 @ X5 )
=> ( ( P @ X5 )
= ( P4 @ X5 ) ) )
=> ( ? [Z5: int] :
! [X5: int] :
( ( ord_less_int @ Z5 @ X5 )
=> ( ( Q2 @ X5 )
= ( Q3 @ X5 ) ) )
=> ? [Z2: int] :
! [X6: int] :
( ( ord_less_int @ Z2 @ X6 )
=> ( ( ( P @ X6 )
& ( Q2 @ X6 ) )
= ( ( P4 @ X6 )
& ( Q3 @ X6 ) ) ) ) ) ) ).
% pinf(1)
thf(fact_1062_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_1063_minf_I8_J,axiom,
! [T: int] :
? [Z2: int] :
! [X6: int] :
( ( ord_less_int @ X6 @ Z2 )
=> ~ ( ord_less_eq_int @ T @ X6 ) ) ).
% minf(8)
thf(fact_1064_minf_I8_J,axiom,
! [T: nat] :
? [Z2: nat] :
! [X6: nat] :
( ( ord_less_nat @ X6 @ Z2 )
=> ~ ( ord_less_eq_nat @ T @ X6 ) ) ).
% minf(8)
thf(fact_1065_minf_I8_J,axiom,
! [T: num] :
? [Z2: num] :
! [X6: num] :
( ( ord_less_num @ X6 @ Z2 )
=> ~ ( ord_less_eq_num @ T @ X6 ) ) ).
% minf(8)
thf(fact_1066_minf_I6_J,axiom,
! [T: int] :
? [Z2: int] :
! [X6: int] :
( ( ord_less_int @ X6 @ Z2 )
=> ( ord_less_eq_int @ X6 @ T ) ) ).
% minf(6)
thf(fact_1067_minf_I6_J,axiom,
! [T: nat] :
? [Z2: nat] :
! [X6: nat] :
( ( ord_less_nat @ X6 @ Z2 )
=> ( ord_less_eq_nat @ X6 @ T ) ) ).
% minf(6)
thf(fact_1068_minf_I6_J,axiom,
! [T: num] :
? [Z2: num] :
! [X6: num] :
( ( ord_less_num @ X6 @ Z2 )
=> ( ord_less_eq_num @ X6 @ T ) ) ).
% minf(6)
thf(fact_1069_pinf_I8_J,axiom,
! [T: int] :
? [Z2: int] :
! [X6: int] :
( ( ord_less_int @ Z2 @ X6 )
=> ( ord_less_eq_int @ T @ X6 ) ) ).
% pinf(8)
thf(fact_1070_pinf_I8_J,axiom,
! [T: nat] :
? [Z2: nat] :
! [X6: nat] :
( ( ord_less_nat @ Z2 @ X6 )
=> ( ord_less_eq_nat @ T @ X6 ) ) ).
% pinf(8)
thf(fact_1071_pinf_I8_J,axiom,
! [T: num] :
? [Z2: num] :
! [X6: num] :
( ( ord_less_num @ Z2 @ X6 )
=> ( ord_less_eq_num @ T @ X6 ) ) ).
% pinf(8)
thf(fact_1072_pinf_I6_J,axiom,
! [T: int] :
? [Z2: int] :
! [X6: int] :
( ( ord_less_int @ Z2 @ X6 )
=> ~ ( ord_less_eq_int @ X6 @ T ) ) ).
% pinf(6)
thf(fact_1073_pinf_I6_J,axiom,
! [T: nat] :
? [Z2: nat] :
! [X6: nat] :
( ( ord_less_nat @ Z2 @ X6 )
=> ~ ( ord_less_eq_nat @ X6 @ T ) ) ).
% pinf(6)
thf(fact_1074_pinf_I6_J,axiom,
! [T: num] :
? [Z2: num] :
! [X6: num] :
( ( ord_less_num @ Z2 @ X6 )
=> ~ ( ord_less_eq_num @ X6 @ T ) ) ).
% pinf(6)
thf(fact_1075_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_1076_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_1077_exec__appendL,axiom,
! [P: list_instr,I: int,S: list_char > int,Stk2: list_int,I4: int,S3: list_char > int,Stk3: list_int,P4: list_instr] :
( ( star_P707599355569300323st_int @ ( exec1 @ P ) @ ( produc5086643055186798020st_int @ I @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) @ ( produc5086643055186798020st_int @ I4 @ ( produc8650753666468850689st_int @ S3 @ Stk3 ) ) )
=> ( star_P707599355569300323st_int @ ( exec1 @ ( append_instr @ P4 @ P ) ) @ ( produc5086643055186798020st_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P4 ) ) @ I ) @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) @ ( produc5086643055186798020st_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P4 ) ) @ I4 ) @ ( produc8650753666468850689st_int @ S3 @ Stk3 ) ) ) ) ).
% exec_appendL
thf(fact_1078_Compiler_Obcomp__correct,axiom,
! [I: int,B: bexp,F: $o,S: list_char > int,Stk2: 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 @ S @ Stk2 ) )
@ ( 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 @ S ) )
@ I
@ zero_zero_int ) )
@ ( produc8650753666468850689st_int @ S @ Stk2 ) ) ) ) ).
% Compiler.bcomp_correct
thf(fact_1079_exec1__def,axiom,
( exec1
= ( ^ [P5: list_instr,Cf3: produc6425607678544837394st_int,Cf5: produc6425607678544837394st_int] :
( ( iexec_pred @ ( produc1484136438817787418st_int @ ( inth_instr @ P5 @ ( produc8941309049508465880st_int @ Cf3 ) ) @ Cf3 ) @ Cf5 )
& ( 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_1080_fst__eqD,axiom,
! [X: int,Y: produc1534919314292393896nt_nat,A: int] :
( ( ( produc2827224793399753527nt_nat @ ( produc8342123264692915235nt_nat @ X @ Y ) )
= A )
=> ( X = A ) ) ).
% fst_eqD
thf(fact_1081_fst__eqD,axiom,
! [X: com,Y: list_char > int,A: com] :
( ( ( produc8829524412605799873ar_int @ ( produc5595214716300948949ar_int @ X @ Y ) )
= A )
=> ( X = A ) ) ).
% fst_eqD
thf(fact_1082_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_1083_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_1084_fst__eqD,axiom,
! [X: int > int,Y: nat,A: int > int] :
( ( ( produc8715251273072885836nt_nat @ ( produc2630796075472406112nt_nat @ X @ Y ) )
= A )
=> ( X = A ) ) ).
% fst_eqD
thf(fact_1085_fst__eqD,axiom,
! [X: int,Y: produc369741286924889929st_int,A: int] :
( ( ( produc8941309049508465880st_int @ ( produc5086643055186798020st_int @ X @ Y ) )
= A )
=> ( X = A ) ) ).
% fst_eqD
thf(fact_1086_fst__conv,axiom,
! [X1: int,X2: produc1534919314292393896nt_nat] :
( ( produc2827224793399753527nt_nat @ ( produc8342123264692915235nt_nat @ X1 @ X2 ) )
= X1 ) ).
% fst_conv
thf(fact_1087_fst__conv,axiom,
! [X1: com,X2: list_char > int] :
( ( produc8829524412605799873ar_int @ ( produc5595214716300948949ar_int @ X1 @ X2 ) )
= X1 ) ).
% fst_conv
thf(fact_1088_fst__conv,axiom,
! [X1: list_char > int,X2: list_int] :
( ( produc2155683374303800813st_int @ ( produc8650753666468850689st_int @ X1 @ X2 ) )
= X1 ) ).
% fst_conv
thf(fact_1089_fst__conv,axiom,
! [X1: list_char > int,X2: int] :
( ( produc9025023058967219549nt_int @ ( produc5790713362662368625nt_int @ X1 @ X2 ) )
= X1 ) ).
% fst_conv
thf(fact_1090_fst__conv,axiom,
! [X1: int > int,X2: nat] :
( ( produc8715251273072885836nt_nat @ ( produc2630796075472406112nt_nat @ X1 @ X2 ) )
= X1 ) ).
% fst_conv
thf(fact_1091_fst__conv,axiom,
! [X1: int,X2: produc369741286924889929st_int] :
( ( produc8941309049508465880st_int @ ( produc5086643055186798020st_int @ X1 @ X2 ) )
= X1 ) ).
% fst_conv
thf(fact_1092_execl__next,axiom,
! [P: list_instr,Cfs: list_P419547167332244514st_int,K: nat] :
( ( execl @ P @ Cfs )
=> ( ( ord_less_nat @ K @ ( size_s229347708945616566st_int @ Cfs ) )
=> ( ( K
!= ( minus_minus_nat @ ( size_s229347708945616566st_int @ Cfs ) @ one_one_nat ) )
=> ( ( iexec_pred @ ( produc1484136438817787418st_int @ ( inth_instr @ P @ ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs @ K ) ) ) @ ( nth_Pr8327173284404383691st_int @ Cfs @ K ) ) @ ( nth_Pr8327173284404383691st_int @ Cfs @ ( suc @ K ) ) )
& ( ord_less_eq_int @ zero_zero_int @ ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs @ K ) ) )
& ( ord_less_int @ ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs @ K ) ) @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P ) ) ) ) ) ) ) ).
% execl_next
thf(fact_1093_ccomp__bigstep,axiom,
! [C: com,S: list_char > int,T: list_char > int,Stk2: list_int] :
( ( big_big_step @ ( produc5595214716300948949ar_int @ C @ S ) @ T )
=> ( star_P707599355569300323st_int @ ( exec1 @ ( ccomp @ C ) ) @ ( produc5086643055186798020st_int @ zero_zero_int @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) @ ( produc5086643055186798020st_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ ( ccomp @ C ) ) ) @ ( produc8650753666468850689st_int @ T @ Stk2 ) ) ) ) ).
% ccomp_bigstep
thf(fact_1094_prod_Ocollapse,axiom,
! [Prod: produc1019184382078353393nt_nat] :
( ( produc8342123264692915235nt_nat @ ( produc2827224793399753527nt_nat @ Prod ) @ ( produc2259646285430092661nt_nat @ Prod ) )
= Prod ) ).
% prod.collapse
thf(fact_1095_prod_Ocollapse,axiom,
! [Prod: produc2931317944591925149ar_int] :
( ( produc5595214716300948949ar_int @ ( produc8829524412605799873ar_int @ Prod ) @ ( produc9207319146083860483ar_int @ Prod ) )
= Prod ) ).
% prod.collapse
thf(fact_1096_prod_Ocollapse,axiom,
! [Prod: produc4435102495419491129nt_int] :
( ( produc5790713362662368625nt_int @ ( produc9025023058967219549nt_int @ Prod ) @ ( produc179445755590504351nt_int @ Prod ) )
= Prod ) ).
% prod.collapse
thf(fact_1097_prod_Ocollapse,axiom,
! [Prod: produc1534919314292393896nt_nat] :
( ( produc2630796075472406112nt_nat @ ( produc8715251273072885836nt_nat @ Prod ) @ ( produc4411376485632109966nt_nat @ Prod ) )
= Prod ) ).
% prod.collapse
thf(fact_1098_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_1099_prod_Ocollapse,axiom,
! [Prod: produc1897111610453708512_o_int] :
( ( produc4047900504771817624_o_int @ ( produc2736798884409471108_o_int @ Prod ) @ ( produc7219675232234870470_o_int @ Prod ) )
= Prod ) ).
% prod.collapse
thf(fact_1100_prod_Ocollapse,axiom,
! [Prod: produc369741286924889929st_int] :
( ( produc8650753666468850689st_int @ ( produc2155683374303800813st_int @ Prod ) @ ( produc6244060863719409455st_int @ Prod ) )
= Prod ) ).
% prod.collapse
thf(fact_1101_prod_Ocollapse,axiom,
! [Prod: produc6425607678544837394st_int] :
( ( produc5086643055186798020st_int @ ( produc8941309049508465880st_int @ Prod ) @ ( produc1296517004818028822st_int @ Prod ) )
= Prod ) ).
% prod.collapse
thf(fact_1102_prod_Oexhaust__sel,axiom,
! [Prod: produc1019184382078353393nt_nat] :
( Prod
= ( produc8342123264692915235nt_nat @ ( produc2827224793399753527nt_nat @ Prod ) @ ( produc2259646285430092661nt_nat @ Prod ) ) ) ).
% prod.exhaust_sel
thf(fact_1103_prod_Oexhaust__sel,axiom,
! [Prod: produc2931317944591925149ar_int] :
( Prod
= ( produc5595214716300948949ar_int @ ( produc8829524412605799873ar_int @ Prod ) @ ( produc9207319146083860483ar_int @ Prod ) ) ) ).
% prod.exhaust_sel
thf(fact_1104_prod_Oexhaust__sel,axiom,
! [Prod: produc4435102495419491129nt_int] :
( Prod
= ( produc5790713362662368625nt_int @ ( produc9025023058967219549nt_int @ Prod ) @ ( produc179445755590504351nt_int @ Prod ) ) ) ).
% prod.exhaust_sel
thf(fact_1105_prod_Oexhaust__sel,axiom,
! [Prod: produc1534919314292393896nt_nat] :
( Prod
= ( produc2630796075472406112nt_nat @ ( produc8715251273072885836nt_nat @ Prod ) @ ( produc4411376485632109966nt_nat @ Prod ) ) ) ).
% prod.exhaust_sel
thf(fact_1106_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_1107_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_1108_prod_Oexhaust__sel,axiom,
! [Prod: produc369741286924889929st_int] :
( Prod
= ( produc8650753666468850689st_int @ ( produc2155683374303800813st_int @ Prod ) @ ( produc6244060863719409455st_int @ Prod ) ) ) ).
% prod.exhaust_sel
thf(fact_1109_prod_Oexhaust__sel,axiom,
! [Prod: produc6425607678544837394st_int] :
( Prod
= ( produc5086643055186798020st_int @ ( produc8941309049508465880st_int @ Prod ) @ ( produc1296517004818028822st_int @ Prod ) ) ) ).
% prod.exhaust_sel
thf(fact_1110_surjective__pairing,axiom,
! [T: produc1019184382078353393nt_nat] :
( T
= ( produc8342123264692915235nt_nat @ ( produc2827224793399753527nt_nat @ T ) @ ( produc2259646285430092661nt_nat @ T ) ) ) ).
% surjective_pairing
thf(fact_1111_surjective__pairing,axiom,
! [T: produc2931317944591925149ar_int] :
( T
= ( produc5595214716300948949ar_int @ ( produc8829524412605799873ar_int @ T ) @ ( produc9207319146083860483ar_int @ T ) ) ) ).
% surjective_pairing
thf(fact_1112_surjective__pairing,axiom,
! [T: produc4435102495419491129nt_int] :
( T
= ( produc5790713362662368625nt_int @ ( produc9025023058967219549nt_int @ T ) @ ( produc179445755590504351nt_int @ T ) ) ) ).
% surjective_pairing
thf(fact_1113_surjective__pairing,axiom,
! [T: produc1534919314292393896nt_nat] :
( T
= ( produc2630796075472406112nt_nat @ ( produc8715251273072885836nt_nat @ T ) @ ( produc4411376485632109966nt_nat @ T ) ) ) ).
% surjective_pairing
thf(fact_1114_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_1115_surjective__pairing,axiom,
! [T: produc1897111610453708512_o_int] :
( T
= ( produc4047900504771817624_o_int @ ( produc2736798884409471108_o_int @ T ) @ ( produc7219675232234870470_o_int @ T ) ) ) ).
% surjective_pairing
thf(fact_1116_surjective__pairing,axiom,
! [T: produc369741286924889929st_int] :
( T
= ( produc8650753666468850689st_int @ ( produc2155683374303800813st_int @ T ) @ ( produc6244060863719409455st_int @ T ) ) ) ).
% surjective_pairing
thf(fact_1117_surjective__pairing,axiom,
! [T: produc6425607678544837394st_int] :
( T
= ( produc5086643055186798020st_int @ ( produc8941309049508465880st_int @ T ) @ ( produc1296517004818028822st_int @ T ) ) ) ).
% surjective_pairing
thf(fact_1118_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
! [P: int > produc1534919314292393896nt_nat > $o,X: int,Y: produc1534919314292393896nt_nat,A: produc1019184382078353393nt_nat] :
( ( P @ X @ Y )
=> ( ( A
= ( produc8342123264692915235nt_nat @ X @ Y ) )
=> ( P @ ( produc2827224793399753527nt_nat @ A ) @ ( produc2259646285430092661nt_nat @ A ) ) ) ) ).
% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_1119_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
! [P: com > ( list_char > int ) > $o,X: com,Y: list_char > int,A: produc2931317944591925149ar_int] :
( ( P @ X @ Y )
=> ( ( A
= ( produc5595214716300948949ar_int @ X @ Y ) )
=> ( P @ ( produc8829524412605799873ar_int @ A ) @ ( produc9207319146083860483ar_int @ A ) ) ) ) ).
% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_1120_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_1121_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
! [P: ( int > int ) > nat > $o,X: int > int,Y: nat,A: produc1534919314292393896nt_nat] :
( ( P @ X @ Y )
=> ( ( A
= ( produc2630796075472406112nt_nat @ X @ Y ) )
=> ( P @ ( produc8715251273072885836nt_nat @ A ) @ ( produc4411376485632109966nt_nat @ A ) ) ) ) ).
% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_1122_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_1123_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_1124_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_1125_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_1126_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_1127_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_1128_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_1129_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_1130_prod__eqI,axiom,
! [P3: product_prod_o_int,Q4: product_prod_o_int] :
( ( ( product_fst_o_int @ P3 )
= ( product_fst_o_int @ Q4 ) )
=> ( ( ( product_snd_o_int @ P3 )
= ( product_snd_o_int @ Q4 ) )
=> ( P3 = Q4 ) ) ) ).
% prod_eqI
thf(fact_1131_prod__eqI,axiom,
! [P3: produc1897111610453708512_o_int,Q4: produc1897111610453708512_o_int] :
( ( ( produc2736798884409471108_o_int @ P3 )
= ( produc2736798884409471108_o_int @ Q4 ) )
=> ( ( ( produc7219675232234870470_o_int @ P3 )
= ( produc7219675232234870470_o_int @ Q4 ) )
=> ( P3 = Q4 ) ) ) ).
% prod_eqI
thf(fact_1132_prod__eqI,axiom,
! [P3: produc369741286924889929st_int,Q4: produc369741286924889929st_int] :
( ( ( produc2155683374303800813st_int @ P3 )
= ( produc2155683374303800813st_int @ Q4 ) )
=> ( ( ( produc6244060863719409455st_int @ P3 )
= ( produc6244060863719409455st_int @ Q4 ) )
=> ( P3 = Q4 ) ) ) ).
% prod_eqI
thf(fact_1133_prod__eqI,axiom,
! [P3: produc6425607678544837394st_int,Q4: produc6425607678544837394st_int] :
( ( ( produc8941309049508465880st_int @ P3 )
= ( produc8941309049508465880st_int @ Q4 ) )
=> ( ( ( produc1296517004818028822st_int @ P3 )
= ( produc1296517004818028822st_int @ Q4 ) )
=> ( P3 = Q4 ) ) ) ).
% prod_eqI
thf(fact_1134_prod__eq__iff,axiom,
( ( ^ [Y3: product_prod_o_int,Z: product_prod_o_int] : ( Y3 = Z ) )
= ( ^ [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_1135_prod__eq__iff,axiom,
( ( ^ [Y3: produc1897111610453708512_o_int,Z: produc1897111610453708512_o_int] : ( Y3 = Z ) )
= ( ^ [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_1136_prod__eq__iff,axiom,
( ( ^ [Y3: produc369741286924889929st_int,Z: produc369741286924889929st_int] : ( Y3 = Z ) )
= ( ^ [S4: produc369741286924889929st_int,T2: produc369741286924889929st_int] :
( ( ( produc2155683374303800813st_int @ S4 )
= ( produc2155683374303800813st_int @ T2 ) )
& ( ( produc6244060863719409455st_int @ S4 )
= ( produc6244060863719409455st_int @ T2 ) ) ) ) ) ).
% prod_eq_iff
thf(fact_1137_prod__eq__iff,axiom,
( ( ^ [Y3: produc6425607678544837394st_int,Z: produc6425607678544837394st_int] : ( Y3 = Z ) )
= ( ^ [S4: produc6425607678544837394st_int,T2: produc6425607678544837394st_int] :
( ( ( produc8941309049508465880st_int @ S4 )
= ( produc8941309049508465880st_int @ T2 ) )
& ( ( produc1296517004818028822st_int @ S4 )
= ( produc1296517004818028822st_int @ T2 ) ) ) ) ) ).
% prod_eq_iff
thf(fact_1138_execl_Oelims_I3_J,axiom,
! [X: list_instr,Xa: list_P419547167332244514st_int] :
( ~ ( execl @ X @ Xa )
=> ~ ! [Cf2: produc6425607678544837394st_int,Cf6: produc6425607678544837394st_int,Cfs2: list_P419547167332244514st_int] :
( ( Xa
= ( cons_P4151473878978182108st_int @ Cf2 @ ( cons_P4151473878978182108st_int @ Cf6 @ Cfs2 ) ) )
=> ( ( exec1 @ X @ Cf2 @ Cf6 )
& ( execl @ X @ ( cons_P4151473878978182108st_int @ Cf6 @ Cfs2 ) ) ) ) ) ).
% execl.elims(3)
thf(fact_1139_execl_Oelims_I2_J,axiom,
! [X: list_instr,Xa: list_P419547167332244514st_int] :
( ( execl @ X @ Xa )
=> ( ! [Cf2: produc6425607678544837394st_int,Cf6: produc6425607678544837394st_int,Cfs2: list_P419547167332244514st_int] :
( ( Xa
= ( cons_P4151473878978182108st_int @ Cf2 @ ( cons_P4151473878978182108st_int @ Cf6 @ Cfs2 ) ) )
=> ~ ( ( exec1 @ X @ Cf2 @ Cf6 )
& ( execl @ X @ ( cons_P4151473878978182108st_int @ Cf6 @ Cfs2 ) ) ) )
=> ( ( Xa != nil_Pr749310521696113548st_int )
=> ~ ! [V: produc6425607678544837394st_int] :
( Xa
!= ( cons_P4151473878978182108st_int @ V @ nil_Pr749310521696113548st_int ) ) ) ) ) ).
% execl.elims(2)
thf(fact_1140_execl_Oelims_I1_J,axiom,
! [X: list_instr,Xa: list_P419547167332244514st_int,Y: $o] :
( ( ( execl @ X @ Xa )
= Y )
=> ( ! [Cf2: produc6425607678544837394st_int,Cf6: produc6425607678544837394st_int,Cfs2: list_P419547167332244514st_int] :
( ( Xa
= ( cons_P4151473878978182108st_int @ Cf2 @ ( cons_P4151473878978182108st_int @ Cf6 @ Cfs2 ) ) )
=> ( Y
= ( ~ ( ( exec1 @ X @ Cf2 @ Cf6 )
& ( execl @ X @ ( cons_P4151473878978182108st_int @ Cf6 @ Cfs2 ) ) ) ) ) )
=> ( ( ( Xa = nil_Pr749310521696113548st_int )
=> ~ Y )
=> ~ ( ? [V: produc6425607678544837394st_int] :
( Xa
= ( cons_P4151473878978182108st_int @ V @ nil_Pr749310521696113548st_int ) )
=> ~ Y ) ) ) ) ).
% execl.elims(1)
thf(fact_1141_execl_Osimps_I1_J,axiom,
! [P: list_instr,Cf: produc6425607678544837394st_int,Cf4: produc6425607678544837394st_int,Cfs: list_P419547167332244514st_int] :
( ( execl @ P @ ( cons_P4151473878978182108st_int @ Cf @ ( cons_P4151473878978182108st_int @ Cf4 @ Cfs ) ) )
= ( ( exec1 @ P @ Cf @ Cf4 )
& ( execl @ P @ ( cons_P4151473878978182108st_int @ Cf4 @ Cfs ) ) ) ) ).
% execl.simps(1)
thf(fact_1142_execl_Osimps_I3_J,axiom,
! [P: list_instr,V2: produc6425607678544837394st_int] : ( execl @ P @ ( cons_P4151473878978182108st_int @ V2 @ nil_Pr749310521696113548st_int ) ) ).
% execl.simps(3)
thf(fact_1143_execl_Osimps_I2_J,axiom,
! [P: list_instr] : ( execl @ P @ nil_Pr749310521696113548st_int ) ).
% execl.simps(2)
thf(fact_1144_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_1145_snd__conv,axiom,
! [X1: int,X2: produc1534919314292393896nt_nat] :
( ( produc2259646285430092661nt_nat @ ( produc8342123264692915235nt_nat @ X1 @ X2 ) )
= X2 ) ).
% snd_conv
thf(fact_1146_snd__conv,axiom,
! [X1: com,X2: list_char > int] :
( ( produc9207319146083860483ar_int @ ( produc5595214716300948949ar_int @ X1 @ X2 ) )
= X2 ) ).
% snd_conv
thf(fact_1147_snd__conv,axiom,
! [X1: list_char > int,X2: int] :
( ( produc179445755590504351nt_int @ ( produc5790713362662368625nt_int @ X1 @ X2 ) )
= X2 ) ).
% snd_conv
thf(fact_1148_snd__conv,axiom,
! [X1: int > int,X2: nat] :
( ( produc4411376485632109966nt_nat @ ( produc2630796075472406112nt_nat @ X1 @ X2 ) )
= X2 ) ).
% snd_conv
thf(fact_1149_snd__conv,axiom,
! [X1: $o,X2: int] :
( ( product_snd_o_int @ ( product_Pair_o_int @ X1 @ X2 ) )
= X2 ) ).
% snd_conv
thf(fact_1150_snd__conv,axiom,
! [X1: bexp,X2: product_prod_o_int] :
( ( produc7219675232234870470_o_int @ ( produc4047900504771817624_o_int @ X1 @ X2 ) )
= X2 ) ).
% snd_conv
thf(fact_1151_snd__conv,axiom,
! [X1: list_char > int,X2: list_int] :
( ( produc6244060863719409455st_int @ ( produc8650753666468850689st_int @ X1 @ X2 ) )
= X2 ) ).
% snd_conv
thf(fact_1152_snd__conv,axiom,
! [X1: int,X2: produc369741286924889929st_int] :
( ( produc1296517004818028822st_int @ ( produc5086643055186798020st_int @ X1 @ X2 ) )
= X2 ) ).
% snd_conv
thf(fact_1153_snd__eqD,axiom,
! [X: int,Y: produc1534919314292393896nt_nat,A: produc1534919314292393896nt_nat] :
( ( ( produc2259646285430092661nt_nat @ ( produc8342123264692915235nt_nat @ X @ Y ) )
= A )
=> ( Y = A ) ) ).
% snd_eqD
thf(fact_1154_snd__eqD,axiom,
! [X: com,Y: list_char > int,A: list_char > int] :
( ( ( produc9207319146083860483ar_int @ ( produc5595214716300948949ar_int @ X @ Y ) )
= A )
=> ( Y = A ) ) ).
% snd_eqD
thf(fact_1155_snd__eqD,axiom,
! [X: list_char > int,Y: int,A: int] :
( ( ( produc179445755590504351nt_int @ ( produc5790713362662368625nt_int @ X @ Y ) )
= A )
=> ( Y = A ) ) ).
% snd_eqD
thf(fact_1156_snd__eqD,axiom,
! [X: int > int,Y: nat,A: nat] :
( ( ( produc4411376485632109966nt_nat @ ( produc2630796075472406112nt_nat @ X @ Y ) )
= A )
=> ( Y = A ) ) ).
% snd_eqD
thf(fact_1157_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_1158_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_1159_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_1160_snd__eqD,axiom,
! [X: int,Y: produc369741286924889929st_int,A: produc369741286924889929st_int] :
( ( ( produc1296517004818028822st_int @ ( produc5086643055186798020st_int @ X @ Y ) )
= A )
=> ( Y = A ) ) ).
% snd_eqD
thf(fact_1161_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_1162_exI__realizer,axiom,
! [P: produc1534919314292393896nt_nat > int > $o,Y: produc1534919314292393896nt_nat,X: int] :
( ( P @ Y @ X )
=> ( P @ ( produc2259646285430092661nt_nat @ ( produc8342123264692915235nt_nat @ X @ Y ) ) @ ( produc2827224793399753527nt_nat @ ( produc8342123264692915235nt_nat @ X @ Y ) ) ) ) ).
% exI_realizer
thf(fact_1163_exI__realizer,axiom,
! [P: ( list_char > int ) > com > $o,Y: list_char > int,X: com] :
( ( P @ Y @ X )
=> ( P @ ( produc9207319146083860483ar_int @ ( produc5595214716300948949ar_int @ X @ Y ) ) @ ( produc8829524412605799873ar_int @ ( produc5595214716300948949ar_int @ X @ Y ) ) ) ) ).
% exI_realizer
thf(fact_1164_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_1165_exI__realizer,axiom,
! [P: nat > ( int > int ) > $o,Y: nat,X: int > int] :
( ( P @ Y @ X )
=> ( P @ ( produc4411376485632109966nt_nat @ ( produc2630796075472406112nt_nat @ X @ Y ) ) @ ( produc8715251273072885836nt_nat @ ( produc2630796075472406112nt_nat @ X @ Y ) ) ) ) ).
% exI_realizer
thf(fact_1166_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_1167_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_1168_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_1169_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_1170_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_1171_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_1172_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_1173_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_1174_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_1175_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_1176_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_1177_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_1178_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_1179_execl_Ocases,axiom,
! [X: produc4400946599758736694st_int] :
( ! [P2: list_instr,Cf2: produc6425607678544837394st_int,Cf6: produc6425607678544837394st_int,Cfs2: list_P419547167332244514st_int] :
( X
!= ( produc7764413618310988720st_int @ P2 @ ( cons_P4151473878978182108st_int @ Cf2 @ ( cons_P4151473878978182108st_int @ Cf6 @ Cfs2 ) ) ) )
=> ( ! [P2: list_instr] :
( X
!= ( produc7764413618310988720st_int @ P2 @ nil_Pr749310521696113548st_int ) )
=> ~ ! [P2: list_instr,V: produc6425607678544837394st_int] :
( X
!= ( produc7764413618310988720st_int @ P2 @ ( cons_P4151473878978182108st_int @ V @ nil_Pr749310521696113548st_int ) ) ) ) ) ).
% execl.cases
thf(fact_1180_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_1181_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_1182_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_1183_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_1184_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_1185_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_1186_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_1187_execl__last,axiom,
! [P: list_instr,Cfs: list_P419547167332244514st_int,K: nat] :
( ( execl @ P @ Cfs )
=> ( ( ord_less_nat @ K @ ( size_s229347708945616566st_int @ Cfs ) )
=> ( ~ ( member_int @ ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs @ K ) ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P ) ) ) )
=> ( ( minus_minus_nat @ ( size_s229347708945616566st_int @ Cfs ) @ one_one_nat )
= K ) ) ) ) ).
% execl_last
thf(fact_1188_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_1189_ex__nat__less__eq,axiom,
! [N: nat,P: nat > $o] :
( ( ? [M3: nat] :
( ( ord_less_nat @ M3 @ N )
& ( P @ M3 ) ) )
= ( ? [X3: nat] :
( ( member_nat @ X3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
& ( P @ X3 ) ) ) ) ).
% ex_nat_less_eq
thf(fact_1190_all__nat__less__eq,axiom,
! [N: nat,P: nat > $o] :
( ( ! [M3: nat] :
( ( ord_less_nat @ M3 @ N )
=> ( P @ M3 ) ) )
= ( ! [X3: nat] :
( ( member_nat @ X3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
=> ( P @ X3 ) ) ) ) ).
% all_nat_less_eq
thf(fact_1191_mpred__merge,axiom,
! [P: list_instr,Cfs: list_P419547167332244514st_int,K: nat,M: nat,N: nat] :
( ( mpred @ P @ Cfs @ K @ M )
=> ( ( mpred @ P @ Cfs @ M @ N )
=> ( mpred @ P @ Cfs @ K @ N ) ) ) ).
% mpred_merge
thf(fact_1192_mpred__drop,axiom,
! [K: nat,Cfs: list_P419547167332244514st_int,P: list_instr,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ ( 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 @ K ) ) ) ) )
=> ( ( mpred @ P @ ( drop_P7838799151754935884st_int @ K @ Cfs ) @ M @ N )
=> ( mpred @ P @ Cfs @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) ) ) ) ) ).
% mpred_drop
thf(fact_1193_add__stack__eq2,axiom,
! [N: nat,Ms2: int > int,I: int,Ms: int > int] :
( ! [X5: int] :
( ( member_int @ X5 @ ( set_or4662586982721622107an_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) )
=> ( ( ( X5
= ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
=> ( ( Ms2 @ X5 )
= I ) )
& ( ( X5
!= ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
=> ( ( Ms2 @ X5 )
= ( Ms @ X5 ) ) ) ) )
=> ( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( add_stack @ N @ Ms2 )
= ( cons_int @ I @ ( add_stack @ ( minus_minus_nat @ N @ one_one_nat ) @ Ms ) ) ) ) ) ).
% add_stack_eq2
thf(fact_1194_add__stack_Osimps_I1_J,axiom,
! [Uu: int > int] :
( ( add_stack @ zero_zero_nat @ Uu )
= nil_int ) ).
% add_stack.simps(1)
thf(fact_1195_add__stack__nnil,axiom,
! [N: nat,Ms: int > int] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( add_stack @ N @ Ms )
!= nil_int ) ) ).
% add_stack_nnil
thf(fact_1196_add__stack_Osimps_I2_J,axiom,
! [N: nat,Ms: int > int] :
( ( add_stack @ ( suc @ N ) @ Ms )
= ( cons_int @ ( Ms @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) @ ( add_stack @ N @ Ms ) ) ) ).
% add_stack.simps(2)
thf(fact_1197_add__stack__eq,axiom,
! [M: nat,Ms2: int > int,Ms: int > int,N: nat] :
( ! [X5: int] :
( ( member_int @ X5 @ ( set_or4662586982721622107an_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) @ zero_zero_int ) )
=> ( ( Ms2 @ X5 )
= ( Ms @ X5 ) ) )
=> ( ( M = N )
=> ( ( add_stack @ M @ Ms2 )
= ( add_stack @ N @ Ms ) ) ) ) ).
% add_stack_eq
thf(fact_1198_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_1199_nat0__intermed__int__val,axiom,
! [N: nat,F: nat > int,K: 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 ) @ K )
=> ( ( ord_less_eq_int @ K @ ( F @ N ) )
=> ? [I3: nat] :
( ( ord_less_eq_nat @ I3 @ N )
& ( ( F @ I3 )
= K ) ) ) ) ) ).
% nat0_intermed_int_val
thf(fact_1200_zabs__less__one__iff,axiom,
! [Z3: int] :
( ( ord_less_int @ ( abs_abs_int @ Z3 ) @ one_one_int )
= ( Z3 = zero_zero_int ) ) ).
% zabs_less_one_iff
thf(fact_1201_to__m__state_Ocases,axiom,
! [X: produc4189061985984568957nt_int] :
~ ! [Xs3: list_list_char,S2: list_char > int,A5: int] :
( X
!= ( produc3965054194175396271nt_int @ Xs3 @ ( produc5790713362662368625nt_int @ S2 @ A5 ) ) ) ).
% to_m_state.cases
thf(fact_1202_zabs__def,axiom,
( abs_abs_int
= ( ^ [I2: int] : ( if_int @ ( ord_less_int @ I2 @ zero_zero_int ) @ ( uminus_uminus_int @ I2 ) @ I2 ) ) ) ).
% zabs_def
thf(fact_1203_nat__intermed__int__val,axiom,
! [M: nat,N: nat,F: nat > int,K: 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 ) @ K )
=> ( ( ord_less_eq_int @ K @ ( F @ N ) )
=> ? [I3: nat] :
( ( ord_less_eq_nat @ M @ I3 )
& ( ord_less_eq_nat @ I3 @ N )
& ( ( F @ I3 )
= K ) ) ) ) ) ) ).
% nat_intermed_int_val
thf(fact_1204_nat__ivt__aux,axiom,
! [N: nat,F: nat > int,K: 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 ) @ K )
=> ( ( ord_less_eq_int @ K @ ( F @ N ) )
=> ? [I3: nat] :
( ( ord_less_eq_nat @ I3 @ N )
& ( ( F @ I3 )
= K ) ) ) ) ) ).
% nat_ivt_aux
thf(fact_1205_big__step__determ,axiom,
! [C: com,S: list_char > int,T: list_char > int,U: list_char > int] :
( ( big_big_step @ ( produc5595214716300948949ar_int @ C @ S ) @ T )
=> ( ( big_big_step @ ( produc5595214716300948949ar_int @ C @ S ) @ U )
=> ( U = T ) ) ) ).
% big_step_determ
thf(fact_1206_sim__trans,axiom,
! [C: com,C4: com,C5: com] :
( ! [S2: list_char > int,T3: list_char > int] :
( ( big_big_step @ ( produc5595214716300948949ar_int @ C @ S2 ) @ T3 )
= ( big_big_step @ ( produc5595214716300948949ar_int @ C4 @ S2 ) @ T3 ) )
=> ( ! [S2: list_char > int,T3: list_char > int] :
( ( big_big_step @ ( produc5595214716300948949ar_int @ C4 @ S2 ) @ T3 )
= ( big_big_step @ ( produc5595214716300948949ar_int @ C5 @ S2 ) @ T3 ) )
=> ! [S6: list_char > int,T4: list_char > int] :
( ( big_big_step @ ( produc5595214716300948949ar_int @ C @ S6 ) @ T4 )
= ( big_big_step @ ( produc5595214716300948949ar_int @ C5 @ S6 ) @ T4 ) ) ) ) ).
% sim_trans
thf(fact_1207_sim__sym,axiom,
! [C: com,C4: com] :
( ( ! [S4: list_char > int,T2: list_char > int] :
( ( big_big_step @ ( produc5595214716300948949ar_int @ C @ S4 ) @ T2 )
= ( big_big_step @ ( produc5595214716300948949ar_int @ C4 @ S4 ) @ T2 ) ) )
= ( ! [S4: list_char > int,T2: list_char > int] :
( ( big_big_step @ ( produc5595214716300948949ar_int @ C4 @ S4 ) @ T2 )
= ( big_big_step @ ( produc5595214716300948949ar_int @ C @ S4 ) @ T2 ) ) ) ) ).
% sim_sym
thf(fact_1208_sim__refl,axiom,
! [C: com,S6: list_char > int,T4: list_char > int] :
( ( big_big_step @ ( produc5595214716300948949ar_int @ C @ S6 ) @ T4 )
= ( big_big_step @ ( produc5595214716300948949ar_int @ C @ S6 ) @ T4 ) ) ).
% sim_refl
thf(fact_1209_nat__descend__induct,axiom,
! [N: nat,P: nat > $o,M: nat] :
( ! [K2: nat] :
( ( ord_less_nat @ N @ K2 )
=> ( P @ K2 ) )
=> ( ! [K2: nat] :
( ( ord_less_eq_nat @ K2 @ N )
=> ( ! [I6: nat] :
( ( ord_less_nat @ K2 @ I6 )
=> ( P @ I6 ) )
=> ( P @ K2 ) ) )
=> ( P @ M ) ) ) ).
% nat_descend_induct
thf(fact_1210_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_1211_SkipE,axiom,
! [S: list_char > int,T: list_char > int] :
( ( big_big_step @ ( produc5595214716300948949ar_int @ skip @ S ) @ T )
=> ( T = S ) ) ).
% SkipE
thf(fact_1212_Skip,axiom,
! [S: list_char > int] : ( big_big_step @ ( produc5595214716300948949ar_int @ skip @ S ) @ S ) ).
% Skip
thf(fact_1213_ccomp_Osimps_I1_J,axiom,
( ( ccomp @ skip )
= nil_instr ) ).
% ccomp.simps(1)
thf(fact_1214_com_Osize_I6_J,axiom,
( ( size_size_com @ skip )
= zero_zero_nat ) ).
% com.size(6)
thf(fact_1215_bcomp_Osimps_I1_J,axiom,
! [V2: $o,F: $o,I: int] :
( ( ( V2 = F )
=> ( ( bcomp @ ( produc4047900504771817624_o_int @ ( bc @ V2 ) @ ( product_Pair_o_int @ F @ I ) ) )
= ( cons_instr @ ( jmp @ I ) @ nil_instr ) ) )
& ( ( V2 = ~ F )
=> ( ( bcomp @ ( produc4047900504771817624_o_int @ ( bc @ V2 ) @ ( product_Pair_o_int @ F @ I ) ) )
= nil_instr ) ) ) ).
% bcomp.simps(1)
thf(fact_1216_bexp_Osize_I5_J,axiom,
! [X1: $o] :
( ( size_size_bexp @ ( bc @ X1 ) )
= zero_zero_nat ) ).
% bexp.size(5)
thf(fact_1217_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_1218_execl__all__Bc,axiom,
! [V2: $o,F: $o,I: int,Cfs: list_P419547167332244514st_int] :
( ( execl_all @ ( if_list_instr @ ( V2 = F ) @ ( cons_instr @ ( jmp @ I ) @ nil_instr ) @ nil_instr ) @ Cfs )
=> ( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( bpred @ ( produc4047900504771817624_o_int @ ( bc @ V2 ) @ ( 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 ) ) ) )
& ( ( V2 = F )
=> ( ( size_s229347708945616566st_int @ Cfs )
= ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
& ( ( V2 = ~ 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_1219_verit__eq__simplify_I8_J,axiom,
! [X2: num,Y2: num] :
( ( ( bit0 @ X2 )
= ( bit0 @ Y2 ) )
= ( X2 = Y2 ) ) ).
% verit_eq_simplify(8)
thf(fact_1220_Suc__numeral,axiom,
! [N: num] :
( ( suc @ ( numeral_numeral_nat @ N ) )
= ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% Suc_numeral
thf(fact_1221_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_1222_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_1223_Suc__1,axiom,
( ( suc @ one_one_nat )
= ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% Suc_1
thf(fact_1224_num_Osize_I4_J,axiom,
( ( size_size_num @ one )
= zero_zero_nat ) ).
% num.size(4)
thf(fact_1225_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_1226_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_1227_le__num__One__iff,axiom,
! [X: num] :
( ( ord_less_eq_num @ X @ one )
= ( X = one ) ) ).
% le_num_One_iff
thf(fact_1228_numeral__1__eq__Suc__0,axiom,
( ( numeral_numeral_nat @ one )
= ( suc @ zero_zero_nat ) ) ).
% numeral_1_eq_Suc_0
thf(fact_1229_Suc__nat__number__of__add,axiom,
! [V2: num,N: nat] :
( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V2 ) @ N ) )
= ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V2 @ one ) ) @ N ) ) ).
% Suc_nat_number_of_add
thf(fact_1230_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_1231_verit__eq__simplify_I10_J,axiom,
! [X2: num] :
( one
!= ( bit0 @ X2 ) ) ).
% verit_eq_simplify(10)
thf(fact_1232_add__One__commute,axiom,
! [N: num] :
( ( plus_plus_num @ one @ N )
= ( plus_plus_num @ N @ one ) ) ).
% add_One_commute
thf(fact_1233_numeral__2__eq__2,axiom,
( ( numeral_numeral_nat @ ( bit0 @ one ) )
= ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% numeral_2_eq_2
thf(fact_1234_numerals_I1_J,axiom,
( ( numeral_numeral_nat @ one )
= one_one_nat ) ).
% numerals(1)
thf(fact_1235_num_Osize_I5_J,axiom,
! [X2: num] :
( ( size_size_num @ ( bit0 @ X2 ) )
= ( plus_plus_nat @ ( size_size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% num.size(5)
thf(fact_1236_nat__induct2,axiom,
! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ( P @ one_one_nat )
=> ( ! [N2: nat] :
( ( P @ N2 )
=> ( P @ ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
=> ( P @ N ) ) ) ) ).
% nat_induct2
thf(fact_1237_int__eq__iff__numeral,axiom,
! [M: nat,V2: num] :
( ( ( semiri1314217659103216013at_int @ M )
= ( numeral_numeral_int @ V2 ) )
= ( M
= ( numeral_numeral_nat @ V2 ) ) ) ).
% int_eq_iff_numeral
thf(fact_1238_int__ops_I3_J,axiom,
! [N: num] :
( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
= ( numeral_numeral_int @ N ) ) ).
% int_ops(3)
thf(fact_1239_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_1240_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_1241_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_1242_acomp_Osimps_I2_J,axiom,
! [X: list_char] :
( ( acomp @ ( v @ X ) )
= ( cons_instr @ ( load @ X ) @ nil_instr ) ) ).
% acomp.simps(2)
thf(fact_1243_acomp_Osimps_I1_J,axiom,
! [I: int] :
( ( acomp @ ( n @ I ) )
= ( cons_instr @ ( loadi @ I ) @ nil_instr ) ) ).
% acomp.simps(1)
thf(fact_1244_Compiler_Oacomp__correct,axiom,
! [A: aexp,S: list_char > int,Stk2: list_int] : ( star_P707599355569300323st_int @ ( exec1 @ ( acomp @ A ) ) @ ( produc5086643055186798020st_int @ zero_zero_int @ ( produc8650753666468850689st_int @ S @ Stk2 ) ) @ ( produc5086643055186798020st_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ ( acomp @ A ) ) ) @ ( produc8650753666468850689st_int @ S @ ( cons_int @ ( aval @ A @ S ) @ Stk2 ) ) ) ) ).
% Compiler.acomp_correct
thf(fact_1245_upto__rec__numeral_I2_J,axiom,
! [M: num,N: num] :
( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
=> ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
= ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
& ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
=> ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
= nil_int ) ) ) ).
% upto_rec_numeral(2)
thf(fact_1246_upto__empty,axiom,
! [J: int,I: int] :
( ( ord_less_int @ J @ I )
=> ( ( upto @ I @ J )
= nil_int ) ) ).
% upto_empty
thf(fact_1247_upto__Nil2,axiom,
! [I: int,J: int] :
( ( nil_int
= ( upto @ I @ J ) )
= ( ord_less_int @ J @ I ) ) ).
% upto_Nil2
thf(fact_1248_upto__Nil,axiom,
! [I: int,J: int] :
( ( ( upto @ I @ J )
= nil_int )
= ( ord_less_int @ J @ I ) ) ).
% upto_Nil
thf(fact_1249_upto__single,axiom,
! [I: int] :
( ( upto @ I @ I )
= ( cons_int @ I @ nil_int ) ) ).
% upto_single
thf(fact_1250_nth__upto,axiom,
! [I: int,K: nat,J: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
=> ( ( nth_int @ ( upto @ I @ J ) @ K )
= ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% nth_upto
thf(fact_1251_upto__rec__numeral_I1_J,axiom,
! [M: num,N: num] :
( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
=> ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
= ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
& ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
=> ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
= nil_int ) ) ) ).
% upto_rec_numeral(1)
thf(fact_1252_upto__rec__numeral_I4_J,axiom,
! [M: num,N: num] :
( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
=> ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
= ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
& ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
=> ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
= nil_int ) ) ) ).
% upto_rec_numeral(4)
thf(fact_1253_upto__rec__numeral_I3_J,axiom,
! [M: num,N: num] :
( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
=> ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
= ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
& ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
=> ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
= nil_int ) ) ) ).
% upto_rec_numeral(3)
thf(fact_1254_upto__aux__def,axiom,
( upto_aux
= ( ^ [I2: int,J3: int] : ( append_int @ ( upto @ I2 @ J3 ) ) ) ) ).
% upto_aux_def
thf(fact_1255_upto__split1,axiom,
! [I: int,J: int,K: int] :
( ( ord_less_eq_int @ I @ J )
=> ( ( ord_less_eq_int @ J @ K )
=> ( ( upto @ I @ K )
= ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% upto_split1
thf(fact_1256_upto__split2,axiom,
! [I: int,J: int,K: int] :
( ( ord_less_eq_int @ I @ J )
=> ( ( ord_less_eq_int @ J @ K )
=> ( ( upto @ I @ K )
= ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% upto_split2
% 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,
execl_all @ ( append_instr @ ( bcomp @ ( produc4047900504771817624_o_int @ b @ ( product_Pair_o_int @ $false @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ ( ccomp @ c ) ) ) @ one_one_int ) ) ) ) @ ( append_instr @ ( ccomp @ c ) @ ( cons_instr @ ( jmp @ ( minus_minus_int @ ( minus_minus_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ ( bcomp @ ( produc4047900504771817624_o_int @ b @ ( product_Pair_o_int @ $false @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ ( ccomp @ c ) ) ) @ one_one_int ) ) ) ) ) ) ) @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ ( ccomp @ c ) ) ) ) @ one_one_int ) ) @ nil_instr ) ) ) @ ( drop_P7838799151754935884st_int @ ( suc @ k ) @ cfsa ) ).
%------------------------------------------------------------------------------