TPTP Problem File: ITP055^1.p
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%------------------------------------------------------------------------------
% File : ITP055^1 : TPTP v8.2.0. Released v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : Sledgehammer FLPTheorem problem prob_1231__3305662_1
% Version : Especial.
% English :
% Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% Source : [Des21]
% Names : FLPTheorem/prob_1231__3305662_1 [Des21]
% Status : Theorem
% Rating : 0.20 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% Syntax : Number of formulae : 414 ( 186 unt; 72 typ; 0 def)
% Number of atoms : 741 ( 451 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 3000 ( 179 ~; 10 |; 38 &;2297 @)
% ( 0 <=>; 476 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Number of types : 15 ( 14 usr)
% Number of type conns : 520 ( 520 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 58 usr; 14 con; 0-4 aty)
% Number of variables : 1101 ( 11 ^;1046 !; 44 ?;1101 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Sledgehammer 2021-02-23 15:32:18.186
%------------------------------------------------------------------------------
% Could-be-implicit typings (14)
thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J_J,type,
list_l1584713811t_unit: $tType ).
thf(ty_n_t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
list_l611321411t_unit: $tType ).
thf(ty_n_t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
list_c1059388851t_unit: $tType ).
thf(ty_n_t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
config256849571t_unit: $tType ).
thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J_J,type,
list_l1341496881ge_p_v: $tType ).
thf(ty_n_t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
list_l1619404459ge_p_v: $tType ).
thf(ty_n_t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
list_message_p_v: $tType ).
thf(ty_n_t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
message_p_v: $tType ).
thf(ty_n_t__AsynchronousSystem__OmessageValue_Itf__v_J,type,
messageValue_v: $tType ).
thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
set_nat: $tType ).
thf(ty_n_t__Nat__Onat,type,
nat: $tType ).
thf(ty_n_t__Int__Oint,type,
int: $tType ).
thf(ty_n_tf__s,type,
s: $tType ).
thf(ty_n_tf__p,type,
p: $tType ).
% Explicit typings (58)
thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_001tf__p_001tf__s_001tf__v,type,
fLPThe9398366_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o ).
thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_OinfiniteExecutionCfg_001tf__p_001tf__v_001tf__s,type,
fLPThe1519354920_p_v_s: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_c1059388851t_unit ).
thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_OinfiniteExecutionMsg_001tf__p_001tf__v_001tf__s,type,
fLPThe536531371_p_v_s: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_message_p_v ).
thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
one_one_int: int ).
thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
one_one_nat: nat ).
thf(sy_c_Groups_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_Int_Onat,type,
nat2: int > nat ).
thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
ring_1_of_int_int: int > int ).
thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
thf(sy_c_ListUtilities_OprefixList_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
prefix747844452t_unit: list_l611321411t_unit > list_l611321411t_unit > $o ).
thf(sy_c_ListUtilities_OprefixList_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
prefix1465223476ge_p_v: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o ).
thf(sy_c_List_Ogen__length_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
gen_le193291088t_unit: nat > list_c1059388851t_unit > nat ).
thf(sy_c_List_Ogen__length_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
gen_le697204914ge_p_v: nat > list_message_p_v > nat ).
thf(sy_c_List_Oinsert_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
insert1308755079t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
thf(sy_c_List_Oinsert_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
insert_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).
thf(sy_c_List_Olist_OCons_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
cons_c1162654829t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
thf(sy_c_List_Olist_OCons_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
cons_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).
thf(sy_c_List_Olist_OCons_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
cons_l1083444861t_unit: list_c1059388851t_unit > list_l611321411t_unit > list_l611321411t_unit ).
thf(sy_c_List_Olist_OCons_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
cons_l233104475ge_p_v: list_message_p_v > list_l1619404459ge_p_v > list_l1619404459ge_p_v ).
thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
cons_l1777019405t_unit: list_l611321411t_unit > list_l1584713811t_unit > list_l1584713811t_unit ).
thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
cons_l1383421281ge_p_v: list_l1619404459ge_p_v > list_l1341496881ge_p_v > list_l1341496881ge_p_v ).
thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
nil_co1338500125t_unit: list_c1059388851t_unit ).
thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
nil_message_p_v: list_message_p_v ).
thf(sy_c_List_Olist_ONil_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
nil_li307996205t_unit: list_l611321411t_unit ).
thf(sy_c_List_Olist_ONil_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
nil_list_message_p_v: list_l1619404459ge_p_v ).
thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
nil_li2108369341t_unit: list_l1584713811t_unit ).
thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
nil_li835338673ge_p_v: list_l1341496881ge_p_v ).
thf(sy_c_List_Olist__ex1_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
list_e1598815642t_unit: ( config256849571t_unit > $o ) > list_c1059388851t_unit > $o ).
thf(sy_c_List_Olist__ex1_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
list_ex1_message_p_v: ( message_p_v > $o ) > list_message_p_v > $o ).
thf(sy_c_List_On__lists_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
n_list1987762709t_unit: nat > list_c1059388851t_unit > list_l611321411t_unit ).
thf(sy_c_List_On__lists_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
n_lists_message_p_v: nat > list_message_p_v > list_l1619404459ge_p_v ).
thf(sy_c_List_Onths_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
nths_c890550943t_unit: list_c1059388851t_unit > set_nat > list_c1059388851t_unit ).
thf(sy_c_List_Onths_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
nths_message_p_v: list_message_p_v > set_nat > list_message_p_v ).
thf(sy_c_List_Oproduct__lists_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
produc663212148t_unit: list_l611321411t_unit > list_l611321411t_unit ).
thf(sy_c_List_Oproduct__lists_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
produc1505827982ge_p_v: list_l1619404459ge_p_v > list_l1619404459ge_p_v ).
thf(sy_c_List_Osubseqs_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
subseq1144048270t_unit: list_c1059388851t_unit > list_l611321411t_unit ).
thf(sy_c_List_Osubseqs_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
subseqs_message_p_v: list_message_p_v > list_l1619404459ge_p_v ).
thf(sy_c_Nat_OSuc,type,
suc: nat > nat ).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
semiri2019852685at_int: nat > int ).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
semiri1382578993at_nat: nat > nat ).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
size_s1406904903t_unit: list_c1059388851t_unit > nat ).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
size_s1168481041ge_p_v: list_message_p_v > nat ).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
size_s503142615t_unit: list_l611321411t_unit > nat ).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
size_s1809856791ge_p_v: list_l1619404459ge_p_v > 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__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_Set_OCollect_001t__Nat__Onat,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(sy_c_member_001t__Nat__Onat,type,
member_nat: nat > set_nat > $o ).
thf(sy_v_cfg____,type,
cfg: config256849571t_unit ).
thf(sy_v_fe____,type,
fe: nat > list_c1059388851t_unit ).
thf(sy_v_m____,type,
m: nat ).
thf(sy_v_n____,type,
n: nat ).
thf(sy_v_na____,type,
na: nat ).
% Relevant facts (341)
thf(fact_0__092_060open_062m_A_060_An_092_060close_062,axiom,
ord_less_nat @ m @ na ).
% \<open>m < n\<close>
thf(fact_1_MLessN,axiom,
ord_less_nat @ m @ n ).
% MLessN
thf(fact_2_IA_I1_J,axiom,
( ( ord_less_nat @ m @ na )
=> ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ) ) ).
% IA(1)
thf(fact_3__092_060open_062m_A_061_An_A_092_060or_062_Am_A_060_An_092_060close_062,axiom,
( ( m = na )
| ( ord_less_nat @ m @ na ) ) ).
% \<open>m = n \<or> m < n\<close>
thf(fact_4_IA_I2_J,axiom,
ord_less_nat @ m @ ( suc @ na ) ).
% IA(2)
thf(fact_5_PrefixListTransitive,axiom,
! [L1: list_message_p_v,L2: list_message_p_v,L3: list_message_p_v] :
( ( prefix47729710ge_p_v @ L1 @ L2 )
=> ( ( prefix47729710ge_p_v @ L2 @ L3 )
=> ( prefix47729710ge_p_v @ L1 @ L3 ) ) ) ).
% PrefixListTransitive
thf(fact_6_PrefixListTransitive,axiom,
! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit,L3: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ L1 @ L2 )
=> ( ( prefix1615116500t_unit @ L2 @ L3 )
=> ( prefix1615116500t_unit @ L1 @ L3 ) ) ) ).
% PrefixListTransitive
thf(fact_7_FE_I1_J,axiom,
( ( fe @ zero_zero_nat )
= ( cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit ) ) ).
% FE(1)
thf(fact_8_prefixList_Ointros_I2_J,axiom,
! [Xa: list_l611321411t_unit,Xb: list_l611321411t_unit,X: list_c1059388851t_unit] :
( ( prefix747844452t_unit @ Xa @ Xb )
=> ( prefix747844452t_unit @ ( cons_l1083444861t_unit @ X @ Xa ) @ ( cons_l1083444861t_unit @ X @ Xb ) ) ) ).
% prefixList.intros(2)
thf(fact_9_prefixList_Ointros_I2_J,axiom,
! [Xa: list_l1619404459ge_p_v,Xb: list_l1619404459ge_p_v,X: list_message_p_v] :
( ( prefix1465223476ge_p_v @ Xa @ Xb )
=> ( prefix1465223476ge_p_v @ ( cons_l233104475ge_p_v @ X @ Xa ) @ ( cons_l233104475ge_p_v @ X @ Xb ) ) ) ).
% prefixList.intros(2)
thf(fact_10_prefixList_Ointros_I2_J,axiom,
! [Xa: list_message_p_v,Xb: list_message_p_v,X: message_p_v] :
( ( prefix47729710ge_p_v @ Xa @ Xb )
=> ( prefix47729710ge_p_v @ ( cons_message_p_v @ X @ Xa ) @ ( cons_message_p_v @ X @ Xb ) ) ) ).
% prefixList.intros(2)
thf(fact_11_prefixList_Ointros_I2_J,axiom,
! [Xa: list_c1059388851t_unit,Xb: list_c1059388851t_unit,X: config256849571t_unit] :
( ( prefix1615116500t_unit @ Xa @ Xb )
=> ( prefix1615116500t_unit @ ( cons_c1162654829t_unit @ X @ Xa ) @ ( cons_c1162654829t_unit @ X @ Xb ) ) ) ).
% prefixList.intros(2)
thf(fact_12_PrefixListMonotonicity,axiom,
! [L1: list_message_p_v,L2: list_message_p_v] :
( ( prefix47729710ge_p_v @ L1 @ L2 )
=> ( ord_less_nat @ ( size_s1168481041ge_p_v @ L1 ) @ ( size_s1168481041ge_p_v @ L2 ) ) ) ).
% PrefixListMonotonicity
thf(fact_13_PrefixListMonotonicity,axiom,
! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ L1 @ L2 )
=> ( ord_less_nat @ ( size_s1406904903t_unit @ L1 ) @ ( size_s1406904903t_unit @ L2 ) ) ) ).
% PrefixListMonotonicity
thf(fact_14_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
! [P: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,Q: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,A4: config256849571t_unit,A5: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,A6: list_c1059388851t_unit > list_message_p_v > list_message_p_v,A7: nat] :
( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( P @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
=> ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
=> ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
=> ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
=> ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
=> ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
=> ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
=> ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
=> ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% infiniteExecutionCfg_infiniteExecutionMsg.induct(2)
thf(fact_15_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
! [P: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,Q: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,A0: config256849571t_unit,A1: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,A2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,A3: nat] :
( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( P @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
=> ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
=> ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
=> ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
=> ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
=> ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
=> ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
=> ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
=> ( P @ A0 @ A1 @ A2 @ A3 ) ) ) ) ) ).
% infiniteExecutionCfg_infiniteExecutionMsg.induct(1)
thf(fact_16_prefixList_Ointros_I1_J,axiom,
! [X: list_c1059388851t_unit,Xs: list_l611321411t_unit] : ( prefix747844452t_unit @ nil_li307996205t_unit @ ( cons_l1083444861t_unit @ X @ Xs ) ) ).
% prefixList.intros(1)
thf(fact_17_prefixList_Ointros_I1_J,axiom,
! [X: list_message_p_v,Xs: list_l1619404459ge_p_v] : ( prefix1465223476ge_p_v @ nil_list_message_p_v @ ( cons_l233104475ge_p_v @ X @ Xs ) ) ).
% prefixList.intros(1)
thf(fact_18_prefixList_Ointros_I1_J,axiom,
! [X: message_p_v,Xs: list_message_p_v] : ( prefix47729710ge_p_v @ nil_message_p_v @ ( cons_message_p_v @ X @ Xs ) ) ).
% prefixList.intros(1)
thf(fact_19_prefixList_Ointros_I1_J,axiom,
! [X: config256849571t_unit,Xs: list_c1059388851t_unit] : ( prefix1615116500t_unit @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ X @ Xs ) ) ).
% prefixList.intros(1)
thf(fact_20_prefixList_Ocases,axiom,
! [A1: list_l611321411t_unit,A2: list_l611321411t_unit] :
( ( prefix747844452t_unit @ A1 @ A2 )
=> ( ( ( A1 = nil_li307996205t_unit )
=> ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
( A2
!= ( cons_l1083444861t_unit @ X2 @ Xs2 ) ) )
=> ~ ! [Xa2: list_l611321411t_unit,Xb2: list_l611321411t_unit,X2: list_c1059388851t_unit] :
( ( A1
= ( cons_l1083444861t_unit @ X2 @ Xa2 ) )
=> ( ( A2
= ( cons_l1083444861t_unit @ X2 @ Xb2 ) )
=> ~ ( prefix747844452t_unit @ Xa2 @ Xb2 ) ) ) ) ) ).
% prefixList.cases
thf(fact_21_prefixList_Ocases,axiom,
! [A1: list_l1619404459ge_p_v,A2: list_l1619404459ge_p_v] :
( ( prefix1465223476ge_p_v @ A1 @ A2 )
=> ( ( ( A1 = nil_list_message_p_v )
=> ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
( A2
!= ( cons_l233104475ge_p_v @ X2 @ Xs2 ) ) )
=> ~ ! [Xa2: list_l1619404459ge_p_v,Xb2: list_l1619404459ge_p_v,X2: list_message_p_v] :
( ( A1
= ( cons_l233104475ge_p_v @ X2 @ Xa2 ) )
=> ( ( A2
= ( cons_l233104475ge_p_v @ X2 @ Xb2 ) )
=> ~ ( prefix1465223476ge_p_v @ Xa2 @ Xb2 ) ) ) ) ) ).
% prefixList.cases
thf(fact_22_prefixList_Ocases,axiom,
! [A1: list_message_p_v,A2: list_message_p_v] :
( ( prefix47729710ge_p_v @ A1 @ A2 )
=> ( ( ( A1 = nil_message_p_v )
=> ! [X2: message_p_v,Xs2: list_message_p_v] :
( A2
!= ( cons_message_p_v @ X2 @ Xs2 ) ) )
=> ~ ! [Xa2: list_message_p_v,Xb2: list_message_p_v,X2: message_p_v] :
( ( A1
= ( cons_message_p_v @ X2 @ Xa2 ) )
=> ( ( A2
= ( cons_message_p_v @ X2 @ Xb2 ) )
=> ~ ( prefix47729710ge_p_v @ Xa2 @ Xb2 ) ) ) ) ) ).
% prefixList.cases
thf(fact_23_prefixList_Ocases,axiom,
! [A1: list_c1059388851t_unit,A2: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ A1 @ A2 )
=> ( ( ( A1 = nil_co1338500125t_unit )
=> ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] :
( A2
!= ( cons_c1162654829t_unit @ X2 @ Xs2 ) ) )
=> ~ ! [Xa2: list_c1059388851t_unit,Xb2: list_c1059388851t_unit,X2: config256849571t_unit] :
( ( A1
= ( cons_c1162654829t_unit @ X2 @ Xa2 ) )
=> ( ( A2
= ( cons_c1162654829t_unit @ X2 @ Xb2 ) )
=> ~ ( prefix1615116500t_unit @ Xa2 @ Xb2 ) ) ) ) ) ).
% prefixList.cases
thf(fact_24_prefixList_Osimps,axiom,
( prefix747844452t_unit
= ( ^ [A12: list_l611321411t_unit,A22: list_l611321411t_unit] :
( ? [X3: list_c1059388851t_unit,Xs3: list_l611321411t_unit] :
( ( A12 = nil_li307996205t_unit )
& ( A22
= ( cons_l1083444861t_unit @ X3 @ Xs3 ) ) )
| ? [Xa3: list_l611321411t_unit,Xb3: list_l611321411t_unit,X3: list_c1059388851t_unit] :
( ( A12
= ( cons_l1083444861t_unit @ X3 @ Xa3 ) )
& ( A22
= ( cons_l1083444861t_unit @ X3 @ Xb3 ) )
& ( prefix747844452t_unit @ Xa3 @ Xb3 ) ) ) ) ) ).
% prefixList.simps
thf(fact_25_prefixList_Osimps,axiom,
( prefix1465223476ge_p_v
= ( ^ [A12: list_l1619404459ge_p_v,A22: list_l1619404459ge_p_v] :
( ? [X3: list_message_p_v,Xs3: list_l1619404459ge_p_v] :
( ( A12 = nil_list_message_p_v )
& ( A22
= ( cons_l233104475ge_p_v @ X3 @ Xs3 ) ) )
| ? [Xa3: list_l1619404459ge_p_v,Xb3: list_l1619404459ge_p_v,X3: list_message_p_v] :
( ( A12
= ( cons_l233104475ge_p_v @ X3 @ Xa3 ) )
& ( A22
= ( cons_l233104475ge_p_v @ X3 @ Xb3 ) )
& ( prefix1465223476ge_p_v @ Xa3 @ Xb3 ) ) ) ) ) ).
% prefixList.simps
thf(fact_26_prefixList_Osimps,axiom,
( prefix47729710ge_p_v
= ( ^ [A12: list_message_p_v,A22: list_message_p_v] :
( ? [X3: message_p_v,Xs3: list_message_p_v] :
( ( A12 = nil_message_p_v )
& ( A22
= ( cons_message_p_v @ X3 @ Xs3 ) ) )
| ? [Xa3: list_message_p_v,Xb3: list_message_p_v,X3: message_p_v] :
( ( A12
= ( cons_message_p_v @ X3 @ Xa3 ) )
& ( A22
= ( cons_message_p_v @ X3 @ Xb3 ) )
& ( prefix47729710ge_p_v @ Xa3 @ Xb3 ) ) ) ) ) ).
% prefixList.simps
thf(fact_27_prefixList_Osimps,axiom,
( prefix1615116500t_unit
= ( ^ [A12: list_c1059388851t_unit,A22: list_c1059388851t_unit] :
( ? [X3: config256849571t_unit,Xs3: list_c1059388851t_unit] :
( ( A12 = nil_co1338500125t_unit )
& ( A22
= ( cons_c1162654829t_unit @ X3 @ Xs3 ) ) )
| ? [Xa3: list_c1059388851t_unit,Xb3: list_c1059388851t_unit,X3: config256849571t_unit] :
( ( A12
= ( cons_c1162654829t_unit @ X3 @ Xa3 ) )
& ( A22
= ( cons_c1162654829t_unit @ X3 @ Xb3 ) )
& ( prefix1615116500t_unit @ Xa3 @ Xb3 ) ) ) ) ) ).
% prefixList.simps
thf(fact_28_prefixList_Oinducts,axiom,
! [X1: list_l611321411t_unit,X22: list_l611321411t_unit,P: list_l611321411t_unit > list_l611321411t_unit > $o] :
( ( prefix747844452t_unit @ X1 @ X22 )
=> ( ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit] : ( P @ nil_li307996205t_unit @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) )
=> ( ! [Xa2: list_l611321411t_unit,Xb2: list_l611321411t_unit,X2: list_c1059388851t_unit] :
( ( prefix747844452t_unit @ Xa2 @ Xb2 )
=> ( ( P @ Xa2 @ Xb2 )
=> ( P @ ( cons_l1083444861t_unit @ X2 @ Xa2 ) @ ( cons_l1083444861t_unit @ X2 @ Xb2 ) ) ) )
=> ( P @ X1 @ X22 ) ) ) ) ).
% prefixList.inducts
thf(fact_29_prefixList_Oinducts,axiom,
! [X1: list_l1619404459ge_p_v,X22: list_l1619404459ge_p_v,P: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o] :
( ( prefix1465223476ge_p_v @ X1 @ X22 )
=> ( ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v] : ( P @ nil_list_message_p_v @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) )
=> ( ! [Xa2: list_l1619404459ge_p_v,Xb2: list_l1619404459ge_p_v,X2: list_message_p_v] :
( ( prefix1465223476ge_p_v @ Xa2 @ Xb2 )
=> ( ( P @ Xa2 @ Xb2 )
=> ( P @ ( cons_l233104475ge_p_v @ X2 @ Xa2 ) @ ( cons_l233104475ge_p_v @ X2 @ Xb2 ) ) ) )
=> ( P @ X1 @ X22 ) ) ) ) ).
% prefixList.inducts
thf(fact_30_prefixList_Oinducts,axiom,
! [X1: list_message_p_v,X22: list_message_p_v,P: list_message_p_v > list_message_p_v > $o] :
( ( prefix47729710ge_p_v @ X1 @ X22 )
=> ( ! [X2: message_p_v,Xs2: list_message_p_v] : ( P @ nil_message_p_v @ ( cons_message_p_v @ X2 @ Xs2 ) )
=> ( ! [Xa2: list_message_p_v,Xb2: list_message_p_v,X2: message_p_v] :
( ( prefix47729710ge_p_v @ Xa2 @ Xb2 )
=> ( ( P @ Xa2 @ Xb2 )
=> ( P @ ( cons_message_p_v @ X2 @ Xa2 ) @ ( cons_message_p_v @ X2 @ Xb2 ) ) ) )
=> ( P @ X1 @ X22 ) ) ) ) ).
% prefixList.inducts
thf(fact_31_prefixList_Oinducts,axiom,
! [X1: list_c1059388851t_unit,X22: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
( ( prefix1615116500t_unit @ X1 @ X22 )
=> ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) )
=> ( ! [Xa2: list_c1059388851t_unit,Xb2: list_c1059388851t_unit,X2: config256849571t_unit] :
( ( prefix1615116500t_unit @ Xa2 @ Xb2 )
=> ( ( P @ Xa2 @ Xb2 )
=> ( P @ ( cons_c1162654829t_unit @ X2 @ Xa2 ) @ ( cons_c1162654829t_unit @ X2 @ Xb2 ) ) ) )
=> ( P @ X1 @ X22 ) ) ) ) ).
% prefixList.inducts
thf(fact_32_NatPredicateTippingPoint,axiom,
! [N2: nat,Pr: nat > $o] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ( Pr @ zero_zero_nat )
=> ( ~ ( Pr @ N2 )
=> ? [N: nat] :
( ( ord_less_nat @ N @ N2 )
& ( Pr @ N )
& ~ ( Pr @ ( suc @ N ) ) ) ) ) ) ).
% NatPredicateTippingPoint
thf(fact_33_infiniteExecutionCfg_Osimps_I1_J,axiom,
! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
= ( cons_c1162654829t_unit @ Cfg2 @ nil_co1338500125t_unit ) ) ).
% infiniteExecutionCfg.simps(1)
thf(fact_34_length__greater__0__conv,axiom,
! [Xs: list_l611321411t_unit] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s503142615t_unit @ Xs ) )
= ( Xs != nil_li307996205t_unit ) ) ).
% length_greater_0_conv
thf(fact_35_length__greater__0__conv,axiom,
! [Xs: list_l1619404459ge_p_v] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1809856791ge_p_v @ Xs ) )
= ( Xs != nil_list_message_p_v ) ) ).
% length_greater_0_conv
thf(fact_36_length__greater__0__conv,axiom,
! [Xs: list_message_p_v] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1168481041ge_p_v @ Xs ) )
= ( Xs != nil_message_p_v ) ) ).
% length_greater_0_conv
thf(fact_37_length__greater__0__conv,axiom,
! [Xs: list_c1059388851t_unit] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ Xs ) )
= ( Xs != nil_co1338500125t_unit ) ) ).
% length_greater_0_conv
thf(fact_38_length__0__conv,axiom,
! [Xs: list_l611321411t_unit] :
( ( ( size_s503142615t_unit @ Xs )
= zero_zero_nat )
= ( Xs = nil_li307996205t_unit ) ) ).
% length_0_conv
thf(fact_39_length__0__conv,axiom,
! [Xs: list_l1619404459ge_p_v] :
( ( ( size_s1809856791ge_p_v @ Xs )
= zero_zero_nat )
= ( Xs = nil_list_message_p_v ) ) ).
% length_0_conv
thf(fact_40_length__0__conv,axiom,
! [Xs: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ Xs )
= zero_zero_nat )
= ( Xs = nil_message_p_v ) ) ).
% length_0_conv
thf(fact_41_length__0__conv,axiom,
! [Xs: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ Xs )
= zero_zero_nat )
= ( Xs = nil_co1338500125t_unit ) ) ).
% length_0_conv
thf(fact_42_less__Suc0,axiom,
! [N3: nat] :
( ( ord_less_nat @ N3 @ ( suc @ zero_zero_nat ) )
= ( N3 = zero_zero_nat ) ) ).
% less_Suc0
thf(fact_43_zero__less__Suc,axiom,
! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N3 ) ) ).
% zero_less_Suc
thf(fact_44_lessI,axiom,
! [N3: nat] : ( ord_less_nat @ N3 @ ( suc @ N3 ) ) ).
% lessI
thf(fact_45_Suc__mono,axiom,
! [M: nat,N3: nat] :
( ( ord_less_nat @ M @ N3 )
=> ( ord_less_nat @ ( suc @ M ) @ ( suc @ N3 ) ) ) ).
% Suc_mono
thf(fact_46_Suc__less__eq,axiom,
! [M: nat,N3: nat] :
( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N3 ) )
= ( ord_less_nat @ M @ N3 ) ) ).
% Suc_less_eq
thf(fact_47_neq0__conv,axiom,
! [N3: nat] :
( ( N3 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% neq0_conv
thf(fact_48_less__nat__zero__code,axiom,
! [N3: nat] :
~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).
% less_nat_zero_code
thf(fact_49_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_50_list_Oinject,axiom,
! [X21: message_p_v,X222: list_message_p_v,Y21: message_p_v,Y22: list_message_p_v] :
( ( ( cons_message_p_v @ X21 @ X222 )
= ( cons_message_p_v @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X222 = Y22 ) ) ) ).
% list.inject
thf(fact_51_list_Oinject,axiom,
! [X21: list_c1059388851t_unit,X222: list_l611321411t_unit,Y21: list_c1059388851t_unit,Y22: list_l611321411t_unit] :
( ( ( cons_l1083444861t_unit @ X21 @ X222 )
= ( cons_l1083444861t_unit @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X222 = Y22 ) ) ) ).
% list.inject
thf(fact_52_list_Oinject,axiom,
! [X21: list_message_p_v,X222: list_l1619404459ge_p_v,Y21: list_message_p_v,Y22: list_l1619404459ge_p_v] :
( ( ( cons_l233104475ge_p_v @ X21 @ X222 )
= ( cons_l233104475ge_p_v @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X222 = Y22 ) ) ) ).
% list.inject
thf(fact_53_list_Oinject,axiom,
! [X21: config256849571t_unit,X222: list_c1059388851t_unit,Y21: config256849571t_unit,Y22: list_c1059388851t_unit] :
( ( ( cons_c1162654829t_unit @ X21 @ X222 )
= ( cons_c1162654829t_unit @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X222 = Y22 ) ) ) ).
% list.inject
thf(fact_54_old_Onat_Oinject,axiom,
! [Nat: nat,Nat2: nat] :
( ( ( suc @ Nat )
= ( suc @ Nat2 ) )
= ( Nat = Nat2 ) ) ).
% old.nat.inject
thf(fact_55_nat_Oinject,axiom,
! [X22: nat,Y2: nat] :
( ( ( suc @ X22 )
= ( suc @ Y2 ) )
= ( X22 = Y2 ) ) ).
% nat.inject
thf(fact_56_not__Cons__self2,axiom,
! [X: message_p_v,Xs: list_message_p_v] :
( ( cons_message_p_v @ X @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_57_not__Cons__self2,axiom,
! [X: list_c1059388851t_unit,Xs: list_l611321411t_unit] :
( ( cons_l1083444861t_unit @ X @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_58_not__Cons__self2,axiom,
! [X: list_message_p_v,Xs: list_l1619404459ge_p_v] :
( ( cons_l233104475ge_p_v @ X @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_59_not__Cons__self2,axiom,
! [X: config256849571t_unit,Xs: list_c1059388851t_unit] :
( ( cons_c1162654829t_unit @ X @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_60_n__not__Suc__n,axiom,
! [N3: nat] :
( N3
!= ( suc @ N3 ) ) ).
% n_not_Suc_n
thf(fact_61_Suc__inject,axiom,
! [X: nat,Y: nat] :
( ( ( suc @ X )
= ( suc @ Y ) )
=> ( X = Y ) ) ).
% Suc_inject
thf(fact_62_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_63_infinite__descent,axiom,
! [P: nat > $o,N3: nat] :
( ! [N: nat] :
( ~ ( P @ N )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N )
& ~ ( P @ M2 ) ) )
=> ( P @ N3 ) ) ).
% infinite_descent
thf(fact_64_nat__less__induct,axiom,
! [P: nat > $o,N3: nat] :
( ! [N: nat] :
( ! [M2: nat] :
( ( ord_less_nat @ M2 @ N )
=> ( P @ M2 ) )
=> ( P @ N ) )
=> ( P @ N3 ) ) ).
% nat_less_induct
thf(fact_65_less__irrefl__nat,axiom,
! [N3: nat] :
~ ( ord_less_nat @ N3 @ N3 ) ).
% less_irrefl_nat
thf(fact_66_less__not__refl3,axiom,
! [S: nat,T: nat] :
( ( ord_less_nat @ S @ T )
=> ( S != T ) ) ).
% less_not_refl3
thf(fact_67_less__not__refl2,axiom,
! [N3: nat,M: nat] :
( ( ord_less_nat @ N3 @ M )
=> ( M != N3 ) ) ).
% less_not_refl2
thf(fact_68_mem__Collect__eq,axiom,
! [A: nat,P: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_69_Collect__mem__eq,axiom,
! [A8: set_nat] :
( ( collect_nat
@ ^ [X3: nat] : ( member_nat @ X3 @ A8 ) )
= A8 ) ).
% Collect_mem_eq
thf(fact_70_less__not__refl,axiom,
! [N3: nat] :
~ ( ord_less_nat @ N3 @ N3 ) ).
% less_not_refl
thf(fact_71_nat__neq__iff,axiom,
! [M: nat,N3: nat] :
( ( M != N3 )
= ( ( ord_less_nat @ M @ N3 )
| ( ord_less_nat @ N3 @ M ) ) ) ).
% nat_neq_iff
thf(fact_72_size__neq__size__imp__neq,axiom,
! [X: list_message_p_v,Y: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ X )
!= ( size_s1168481041ge_p_v @ Y ) )
=> ( X != Y ) ) ).
% size_neq_size_imp_neq
thf(fact_73_size__neq__size__imp__neq,axiom,
! [X: list_c1059388851t_unit,Y: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ X )
!= ( size_s1406904903t_unit @ Y ) )
=> ( X != Y ) ) ).
% size_neq_size_imp_neq
thf(fact_74_neq__if__length__neq,axiom,
! [Xs: list_message_p_v,Ys: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ Xs )
!= ( size_s1168481041ge_p_v @ Ys ) )
=> ( Xs != Ys ) ) ).
% neq_if_length_neq
thf(fact_75_neq__if__length__neq,axiom,
! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ Xs )
!= ( size_s1406904903t_unit @ Ys ) )
=> ( Xs != Ys ) ) ).
% neq_if_length_neq
thf(fact_76_Ex__list__of__length,axiom,
! [N3: nat] :
? [Xs2: list_message_p_v] :
( ( size_s1168481041ge_p_v @ Xs2 )
= N3 ) ).
% Ex_list_of_length
thf(fact_77_Ex__list__of__length,axiom,
! [N3: nat] :
? [Xs2: list_c1059388851t_unit] :
( ( size_s1406904903t_unit @ Xs2 )
= N3 ) ).
% Ex_list_of_length
thf(fact_78_not0__implies__Suc,axiom,
! [N3: nat] :
( ( N3 != zero_zero_nat )
=> ? [M3: nat] :
( N3
= ( suc @ M3 ) ) ) ).
% not0_implies_Suc
thf(fact_79_old_Onat_Oinducts,axiom,
! [P: nat > $o,Nat: nat] :
( ( P @ zero_zero_nat )
=> ( ! [Nat3: nat] :
( ( P @ Nat3 )
=> ( P @ ( suc @ Nat3 ) ) )
=> ( P @ Nat ) ) ) ).
% old.nat.inducts
thf(fact_80_old_Onat_Oexhaust,axiom,
! [Y: nat] :
( ( Y != zero_zero_nat )
=> ~ ! [Nat3: nat] :
( Y
!= ( suc @ Nat3 ) ) ) ).
% old.nat.exhaust
thf(fact_81_Zero__not__Suc,axiom,
! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) ).
% Zero_not_Suc
thf(fact_82_Zero__neq__Suc,axiom,
! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) ).
% Zero_neq_Suc
thf(fact_83_Suc__neq__Zero,axiom,
! [M: nat] :
( ( suc @ M )
!= zero_zero_nat ) ).
% Suc_neq_Zero
thf(fact_84_zero__induct,axiom,
! [P: nat > $o,K: nat] :
( ( P @ K )
=> ( ! [N: nat] :
( ( P @ ( suc @ N ) )
=> ( P @ N ) )
=> ( P @ zero_zero_nat ) ) ) ).
% zero_induct
thf(fact_85_diff__induct,axiom,
! [P: nat > nat > $o,M: nat,N3: nat] :
( ! [X2: nat] : ( P @ X2 @ zero_zero_nat )
=> ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
=> ( ! [X2: nat,Y3: nat] :
( ( P @ X2 @ Y3 )
=> ( P @ ( suc @ X2 ) @ ( suc @ Y3 ) ) )
=> ( P @ M @ N3 ) ) ) ) ).
% diff_induct
thf(fact_86_nat__induct,axiom,
! [P: nat > $o,N3: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N: nat] :
( ( P @ N )
=> ( P @ ( suc @ N ) ) )
=> ( P @ N3 ) ) ) ).
% nat_induct
thf(fact_87_nat_OdiscI,axiom,
! [Nat: nat,X22: nat] :
( ( Nat
= ( suc @ X22 ) )
=> ( Nat != zero_zero_nat ) ) ).
% nat.discI
thf(fact_88_old_Onat_Odistinct_I1_J,axiom,
! [Nat2: nat] :
( zero_zero_nat
!= ( suc @ Nat2 ) ) ).
% old.nat.distinct(1)
thf(fact_89_old_Onat_Odistinct_I2_J,axiom,
! [Nat2: nat] :
( ( suc @ Nat2 )
!= zero_zero_nat ) ).
% old.nat.distinct(2)
thf(fact_90_nat_Odistinct_I1_J,axiom,
! [X22: nat] :
( zero_zero_nat
!= ( suc @ X22 ) ) ).
% nat.distinct(1)
thf(fact_91_bot__nat__0_Oextremum__strict,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% bot_nat_0.extremum_strict
thf(fact_92_infinite__descent0,axiom,
! [P: nat > $o,N3: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ~ ( P @ N )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N )
& ~ ( P @ M2 ) ) ) )
=> ( P @ N3 ) ) ) ).
% infinite_descent0
thf(fact_93_gr__implies__not0,axiom,
! [M: nat,N3: nat] :
( ( ord_less_nat @ M @ N3 )
=> ( N3 != zero_zero_nat ) ) ).
% gr_implies_not0
thf(fact_94_less__zeroE,axiom,
! [N3: nat] :
~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).
% less_zeroE
thf(fact_95_not__less0,axiom,
! [N3: nat] :
~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).
% not_less0
thf(fact_96_not__gr0,axiom,
! [N3: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
= ( N3 = zero_zero_nat ) ) ).
% not_gr0
thf(fact_97_gr0I,axiom,
! [N3: nat] :
( ( N3 != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% gr0I
thf(fact_98_not__less__less__Suc__eq,axiom,
! [N3: nat,M: nat] :
( ~ ( ord_less_nat @ N3 @ M )
=> ( ( ord_less_nat @ N3 @ ( suc @ M ) )
= ( N3 = M ) ) ) ).
% not_less_less_Suc_eq
thf(fact_99_strict__inc__induct,axiom,
! [I: nat,J: nat,P: nat > $o] :
( ( ord_less_nat @ I @ J )
=> ( ! [I2: nat] :
( ( J
= ( suc @ I2 ) )
=> ( P @ I2 ) )
=> ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ J )
=> ( ( P @ ( suc @ I2 ) )
=> ( P @ I2 ) ) )
=> ( P @ I ) ) ) ) ).
% strict_inc_induct
thf(fact_100_less__Suc__induct,axiom,
! [I: nat,J: nat,P: nat > nat > $o] :
( ( ord_less_nat @ I @ J )
=> ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
=> ( ! [I2: nat,J2: nat,K2: nat] :
( ( ord_less_nat @ I2 @ J2 )
=> ( ( ord_less_nat @ J2 @ K2 )
=> ( ( P @ I2 @ J2 )
=> ( ( P @ J2 @ K2 )
=> ( P @ I2 @ K2 ) ) ) ) )
=> ( P @ I @ J ) ) ) ) ).
% less_Suc_induct
thf(fact_101_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_102_Suc__less__SucD,axiom,
! [M: nat,N3: nat] :
( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N3 ) )
=> ( ord_less_nat @ M @ N3 ) ) ).
% Suc_less_SucD
thf(fact_103_less__antisym,axiom,
! [N3: nat,M: nat] :
( ~ ( ord_less_nat @ N3 @ M )
=> ( ( ord_less_nat @ N3 @ ( suc @ M ) )
=> ( M = N3 ) ) ) ).
% less_antisym
thf(fact_104_Suc__less__eq2,axiom,
! [N3: nat,M: nat] :
( ( ord_less_nat @ ( suc @ N3 ) @ M )
= ( ? [M4: nat] :
( ( M
= ( suc @ M4 ) )
& ( ord_less_nat @ N3 @ M4 ) ) ) ) ).
% Suc_less_eq2
thf(fact_105_All__less__Suc,axiom,
! [N3: nat,P: nat > $o] :
( ( ! [I3: nat] :
( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
=> ( P @ I3 ) ) )
= ( ( P @ N3 )
& ! [I3: nat] :
( ( ord_less_nat @ I3 @ N3 )
=> ( P @ I3 ) ) ) ) ).
% All_less_Suc
thf(fact_106_not__less__eq,axiom,
! [M: nat,N3: nat] :
( ( ~ ( ord_less_nat @ M @ N3 ) )
= ( ord_less_nat @ N3 @ ( suc @ M ) ) ) ).
% not_less_eq
thf(fact_107_less__Suc__eq,axiom,
! [M: nat,N3: nat] :
( ( ord_less_nat @ M @ ( suc @ N3 ) )
= ( ( ord_less_nat @ M @ N3 )
| ( M = N3 ) ) ) ).
% less_Suc_eq
thf(fact_108_Ex__less__Suc,axiom,
! [N3: nat,P: nat > $o] :
( ( ? [I3: nat] :
( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
& ( P @ I3 ) ) )
= ( ( P @ N3 )
| ? [I3: nat] :
( ( ord_less_nat @ I3 @ N3 )
& ( P @ I3 ) ) ) ) ).
% Ex_less_Suc
thf(fact_109_less__SucI,axiom,
! [M: nat,N3: nat] :
( ( ord_less_nat @ M @ N3 )
=> ( ord_less_nat @ M @ ( suc @ N3 ) ) ) ).
% less_SucI
thf(fact_110_less__SucE,axiom,
! [M: nat,N3: nat] :
( ( ord_less_nat @ M @ ( suc @ N3 ) )
=> ( ~ ( ord_less_nat @ M @ N3 )
=> ( M = N3 ) ) ) ).
% less_SucE
thf(fact_111_Suc__lessI,axiom,
! [M: nat,N3: nat] :
( ( ord_less_nat @ M @ N3 )
=> ( ( ( suc @ M )
!= N3 )
=> ( ord_less_nat @ ( suc @ M ) @ N3 ) ) ) ).
% Suc_lessI
thf(fact_112_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_113_Suc__lessD,axiom,
! [M: nat,N3: nat] :
( ( ord_less_nat @ ( suc @ M ) @ N3 )
=> ( ord_less_nat @ M @ N3 ) ) ).
% Suc_lessD
thf(fact_114_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_115_map__tailrec__rev_Oinduct,axiom,
! [P: ( message_p_v > config256849571t_unit ) > list_message_p_v > list_c1059388851t_unit > $o,A0: message_p_v > config256849571t_unit,A1: list_message_p_v,A2: list_c1059388851t_unit] :
( ! [F: message_p_v > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_message_p_v @ X_1 )
=> ( ! [F: message_p_v > config256849571t_unit,A9: message_p_v,As: list_message_p_v,Bs: list_c1059388851t_unit] :
( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A9 ) @ Bs ) )
=> ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
=> ( P @ A0 @ A1 @ A2 ) ) ) ).
% map_tailrec_rev.induct
thf(fact_116_map__tailrec__rev_Oinduct,axiom,
! [P: ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit,A1: list_c1059388851t_unit,A2: list_c1059388851t_unit] :
( ! [F: config256849571t_unit > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_co1338500125t_unit @ X_1 )
=> ( ! [F: config256849571t_unit > config256849571t_unit,A9: config256849571t_unit,As: list_c1059388851t_unit,Bs: list_c1059388851t_unit] :
( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A9 ) @ Bs ) )
=> ( P @ F @ ( cons_c1162654829t_unit @ A9 @ As ) @ Bs ) )
=> ( P @ A0 @ A1 @ A2 ) ) ) ).
% map_tailrec_rev.induct
thf(fact_117_map__tailrec__rev_Oinduct,axiom,
! [P: ( message_p_v > message_p_v ) > list_message_p_v > list_message_p_v > $o,A0: message_p_v > message_p_v,A1: list_message_p_v,A2: list_message_p_v] :
( ! [F: message_p_v > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_message_p_v @ X_1 )
=> ( ! [F: message_p_v > message_p_v,A9: message_p_v,As: list_message_p_v,Bs: list_message_p_v] :
( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
=> ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
=> ( P @ A0 @ A1 @ A2 ) ) ) ).
% map_tailrec_rev.induct
thf(fact_118_map__tailrec__rev_Oinduct,axiom,
! [P: ( list_message_p_v > message_p_v ) > list_l1619404459ge_p_v > list_message_p_v > $o,A0: list_message_p_v > message_p_v,A1: list_l1619404459ge_p_v,A2: list_message_p_v] :
( ! [F: list_message_p_v > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_list_message_p_v @ X_1 )
=> ( ! [F: list_message_p_v > message_p_v,A9: list_message_p_v,As: list_l1619404459ge_p_v,Bs: list_message_p_v] :
( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
=> ( P @ F @ ( cons_l233104475ge_p_v @ A9 @ As ) @ Bs ) )
=> ( P @ A0 @ A1 @ A2 ) ) ) ).
% map_tailrec_rev.induct
thf(fact_119_map__tailrec__rev_Oinduct,axiom,
! [P: ( message_p_v > list_message_p_v ) > list_message_p_v > list_l1619404459ge_p_v > $o,A0: message_p_v > list_message_p_v,A1: list_message_p_v,A2: list_l1619404459ge_p_v] :
( ! [F: message_p_v > list_message_p_v,X_1: list_l1619404459ge_p_v] : ( P @ F @ nil_message_p_v @ X_1 )
=> ( ! [F: message_p_v > list_message_p_v,A9: message_p_v,As: list_message_p_v,Bs: list_l1619404459ge_p_v] :
( ( P @ F @ As @ ( cons_l233104475ge_p_v @ ( F @ A9 ) @ Bs ) )
=> ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
=> ( P @ A0 @ A1 @ A2 ) ) ) ).
% map_tailrec_rev.induct
thf(fact_120_map__tailrec__rev_Oinduct,axiom,
! [P: ( config256849571t_unit > message_p_v ) > list_c1059388851t_unit > list_message_p_v > $o,A0: config256849571t_unit > message_p_v,A1: list_c1059388851t_unit,A2: list_message_p_v] :
( ! [F: config256849571t_unit > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_co1338500125t_unit @ X_1 )
=> ( ! [F: config256849571t_unit > message_p_v,A9: config256849571t_unit,As: list_c1059388851t_unit,Bs: list_message_p_v] :
( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
=> ( P @ F @ ( cons_c1162654829t_unit @ A9 @ As ) @ Bs ) )
=> ( P @ A0 @ A1 @ A2 ) ) ) ).
% map_tailrec_rev.induct
thf(fact_121_map__tailrec__rev_Oinduct,axiom,
! [P: ( list_message_p_v > list_message_p_v ) > list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o,A0: list_message_p_v > list_message_p_v,A1: list_l1619404459ge_p_v,A2: list_l1619404459ge_p_v] :
( ! [F: list_message_p_v > list_message_p_v,X_1: list_l1619404459ge_p_v] : ( P @ F @ nil_list_message_p_v @ X_1 )
=> ( ! [F: list_message_p_v > list_message_p_v,A9: list_message_p_v,As: list_l1619404459ge_p_v,Bs: list_l1619404459ge_p_v] :
( ( P @ F @ As @ ( cons_l233104475ge_p_v @ ( F @ A9 ) @ Bs ) )
=> ( P @ F @ ( cons_l233104475ge_p_v @ A9 @ As ) @ Bs ) )
=> ( P @ A0 @ A1 @ A2 ) ) ) ).
% map_tailrec_rev.induct
thf(fact_122_map__tailrec__rev_Oinduct,axiom,
! [P: ( list_message_p_v > config256849571t_unit ) > list_l1619404459ge_p_v > list_c1059388851t_unit > $o,A0: list_message_p_v > config256849571t_unit,A1: list_l1619404459ge_p_v,A2: list_c1059388851t_unit] :
( ! [F: list_message_p_v > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_list_message_p_v @ X_1 )
=> ( ! [F: list_message_p_v > config256849571t_unit,A9: list_message_p_v,As: list_l1619404459ge_p_v,Bs: list_c1059388851t_unit] :
( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A9 ) @ Bs ) )
=> ( P @ F @ ( cons_l233104475ge_p_v @ A9 @ As ) @ Bs ) )
=> ( P @ A0 @ A1 @ A2 ) ) ) ).
% map_tailrec_rev.induct
thf(fact_123_map__tailrec__rev_Oinduct,axiom,
! [P: ( list_c1059388851t_unit > message_p_v ) > list_l611321411t_unit > list_message_p_v > $o,A0: list_c1059388851t_unit > message_p_v,A1: list_l611321411t_unit,A2: list_message_p_v] :
( ! [F: list_c1059388851t_unit > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_li307996205t_unit @ X_1 )
=> ( ! [F: list_c1059388851t_unit > message_p_v,A9: list_c1059388851t_unit,As: list_l611321411t_unit,Bs: list_message_p_v] :
( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
=> ( P @ F @ ( cons_l1083444861t_unit @ A9 @ As ) @ Bs ) )
=> ( P @ A0 @ A1 @ A2 ) ) ) ).
% map_tailrec_rev.induct
thf(fact_124_map__tailrec__rev_Oinduct,axiom,
! [P: ( message_p_v > list_c1059388851t_unit ) > list_message_p_v > list_l611321411t_unit > $o,A0: message_p_v > list_c1059388851t_unit,A1: list_message_p_v,A2: list_l611321411t_unit] :
( ! [F: message_p_v > list_c1059388851t_unit,X_1: list_l611321411t_unit] : ( P @ F @ nil_message_p_v @ X_1 )
=> ( ! [F: message_p_v > list_c1059388851t_unit,A9: message_p_v,As: list_message_p_v,Bs: list_l611321411t_unit] :
( ( P @ F @ As @ ( cons_l1083444861t_unit @ ( F @ A9 ) @ Bs ) )
=> ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
=> ( P @ A0 @ A1 @ A2 ) ) ) ).
% map_tailrec_rev.induct
thf(fact_125_list__nonempty__induct,axiom,
! [Xs: list_l611321411t_unit,P: list_l611321411t_unit > $o] :
( ( Xs != nil_li307996205t_unit )
=> ( ! [X2: list_c1059388851t_unit] : ( P @ ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
=> ( ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
( ( Xs2 != nil_li307996205t_unit )
=> ( ( P @ Xs2 )
=> ( P @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_126_list__nonempty__induct,axiom,
! [Xs: list_l1619404459ge_p_v,P: list_l1619404459ge_p_v > $o] :
( ( Xs != nil_list_message_p_v )
=> ( ! [X2: list_message_p_v] : ( P @ ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
=> ( ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
( ( Xs2 != nil_list_message_p_v )
=> ( ( P @ Xs2 )
=> ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_127_list__nonempty__induct,axiom,
! [Xs: list_message_p_v,P: list_message_p_v > $o] :
( ( Xs != nil_message_p_v )
=> ( ! [X2: message_p_v] : ( P @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
=> ( ! [X2: message_p_v,Xs2: list_message_p_v] :
( ( Xs2 != nil_message_p_v )
=> ( ( P @ Xs2 )
=> ( P @ ( cons_message_p_v @ X2 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_128_list__nonempty__induct,axiom,
! [Xs: list_c1059388851t_unit,P: list_c1059388851t_unit > $o] :
( ( Xs != nil_co1338500125t_unit )
=> ( ! [X2: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
=> ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] :
( ( Xs2 != nil_co1338500125t_unit )
=> ( ( P @ Xs2 )
=> ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_129_successively_Oinduct,axiom,
! [P: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_l611321411t_unit > $o,A0: list_c1059388851t_unit > list_c1059388851t_unit > $o,A1: list_l611321411t_unit] :
( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o] : ( P @ P2 @ nil_li307996205t_unit )
=> ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X2: list_c1059388851t_unit] : ( P @ P2 @ ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
=> ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X2: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
( ( P @ P2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) )
=> ( P @ P2 @ ( cons_l1083444861t_unit @ X2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) )
=> ( P @ A0 @ A1 ) ) ) ) ).
% successively.induct
thf(fact_130_successively_Oinduct,axiom,
! [P: ( list_message_p_v > list_message_p_v > $o ) > list_l1619404459ge_p_v > $o,A0: list_message_p_v > list_message_p_v > $o,A1: list_l1619404459ge_p_v] :
( ! [P2: list_message_p_v > list_message_p_v > $o] : ( P @ P2 @ nil_list_message_p_v )
=> ( ! [P2: list_message_p_v > list_message_p_v > $o,X2: list_message_p_v] : ( P @ P2 @ ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
=> ( ! [P2: list_message_p_v > list_message_p_v > $o,X2: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
( ( P @ P2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) )
=> ( P @ P2 @ ( cons_l233104475ge_p_v @ X2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) )
=> ( P @ A0 @ A1 ) ) ) ) ).
% successively.induct
thf(fact_131_successively_Oinduct,axiom,
! [P: ( message_p_v > message_p_v > $o ) > list_message_p_v > $o,A0: message_p_v > message_p_v > $o,A1: list_message_p_v] :
( ! [P2: message_p_v > message_p_v > $o] : ( P @ P2 @ nil_message_p_v )
=> ( ! [P2: message_p_v > message_p_v > $o,X2: message_p_v] : ( P @ P2 @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
=> ( ! [P2: message_p_v > message_p_v > $o,X2: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
( ( P @ P2 @ ( cons_message_p_v @ Y3 @ Xs2 ) )
=> ( P @ P2 @ ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) )
=> ( P @ A0 @ A1 ) ) ) ) ).
% successively.induct
thf(fact_132_successively_Oinduct,axiom,
! [P: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit > $o,A1: list_c1059388851t_unit] :
( ! [P2: config256849571t_unit > config256849571t_unit > $o] : ( P @ P2 @ nil_co1338500125t_unit )
=> ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X2: config256849571t_unit] : ( P @ P2 @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
=> ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X2: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
( ( P @ P2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) )
=> ( P @ P2 @ ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) )
=> ( P @ A0 @ A1 ) ) ) ) ).
% successively.induct
thf(fact_133_remdups__adj_Oinduct,axiom,
! [P: list_l611321411t_unit > $o,A0: list_l611321411t_unit] :
( ( P @ nil_li307996205t_unit )
=> ( ! [X2: list_c1059388851t_unit] : ( P @ ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
=> ( ! [X2: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
( ( ( X2 = Y3 )
=> ( P @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) ) )
=> ( ( ( X2 != Y3 )
=> ( P @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) )
=> ( P @ ( cons_l1083444861t_unit @ X2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) ) )
=> ( P @ A0 ) ) ) ) ).
% remdups_adj.induct
thf(fact_134_remdups__adj_Oinduct,axiom,
! [P: list_l1619404459ge_p_v > $o,A0: list_l1619404459ge_p_v] :
( ( P @ nil_list_message_p_v )
=> ( ! [X2: list_message_p_v] : ( P @ ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
=> ( ! [X2: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
( ( ( X2 = Y3 )
=> ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) ) )
=> ( ( ( X2 != Y3 )
=> ( P @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) )
=> ( P @ ( cons_l233104475ge_p_v @ X2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) ) )
=> ( P @ A0 ) ) ) ) ).
% remdups_adj.induct
thf(fact_135_remdups__adj_Oinduct,axiom,
! [P: list_message_p_v > $o,A0: list_message_p_v] :
( ( P @ nil_message_p_v )
=> ( ! [X2: message_p_v] : ( P @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
=> ( ! [X2: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
( ( ( X2 = Y3 )
=> ( P @ ( cons_message_p_v @ X2 @ Xs2 ) ) )
=> ( ( ( X2 != Y3 )
=> ( P @ ( cons_message_p_v @ Y3 @ Xs2 ) ) )
=> ( P @ ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) ) )
=> ( P @ A0 ) ) ) ) ).
% remdups_adj.induct
thf(fact_136_remdups__adj_Oinduct,axiom,
! [P: list_c1059388851t_unit > $o,A0: list_c1059388851t_unit] :
( ( P @ nil_co1338500125t_unit )
=> ( ! [X2: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
=> ( ! [X2: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
( ( ( X2 = Y3 )
=> ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) ) )
=> ( ( ( X2 != Y3 )
=> ( P @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) )
=> ( P @ ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) ) )
=> ( P @ A0 ) ) ) ) ).
% remdups_adj.induct
thf(fact_137_sorted__wrt_Oinduct,axiom,
! [P: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_l611321411t_unit > $o,A0: list_c1059388851t_unit > list_c1059388851t_unit > $o,A1: list_l611321411t_unit] :
( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o] : ( P @ P2 @ nil_li307996205t_unit )
=> ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X2: list_c1059388851t_unit,Ys2: list_l611321411t_unit] :
( ( P @ P2 @ Ys2 )
=> ( P @ P2 @ ( cons_l1083444861t_unit @ X2 @ Ys2 ) ) )
=> ( P @ A0 @ A1 ) ) ) ).
% sorted_wrt.induct
thf(fact_138_sorted__wrt_Oinduct,axiom,
! [P: ( list_message_p_v > list_message_p_v > $o ) > list_l1619404459ge_p_v > $o,A0: list_message_p_v > list_message_p_v > $o,A1: list_l1619404459ge_p_v] :
( ! [P2: list_message_p_v > list_message_p_v > $o] : ( P @ P2 @ nil_list_message_p_v )
=> ( ! [P2: list_message_p_v > list_message_p_v > $o,X2: list_message_p_v,Ys2: list_l1619404459ge_p_v] :
( ( P @ P2 @ Ys2 )
=> ( P @ P2 @ ( cons_l233104475ge_p_v @ X2 @ Ys2 ) ) )
=> ( P @ A0 @ A1 ) ) ) ).
% sorted_wrt.induct
thf(fact_139_sorted__wrt_Oinduct,axiom,
! [P: ( message_p_v > message_p_v > $o ) > list_message_p_v > $o,A0: message_p_v > message_p_v > $o,A1: list_message_p_v] :
( ! [P2: message_p_v > message_p_v > $o] : ( P @ P2 @ nil_message_p_v )
=> ( ! [P2: message_p_v > message_p_v > $o,X2: message_p_v,Ys2: list_message_p_v] :
( ( P @ P2 @ Ys2 )
=> ( P @ P2 @ ( cons_message_p_v @ X2 @ Ys2 ) ) )
=> ( P @ A0 @ A1 ) ) ) ).
% sorted_wrt.induct
thf(fact_140_sorted__wrt_Oinduct,axiom,
! [P: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit > $o,A1: list_c1059388851t_unit] :
( ! [P2: config256849571t_unit > config256849571t_unit > $o] : ( P @ P2 @ nil_co1338500125t_unit )
=> ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X2: config256849571t_unit,Ys2: list_c1059388851t_unit] :
( ( P @ P2 @ Ys2 )
=> ( P @ P2 @ ( cons_c1162654829t_unit @ X2 @ Ys2 ) ) )
=> ( P @ A0 @ A1 ) ) ) ).
% sorted_wrt.induct
thf(fact_141_remdups__adj_Ocases,axiom,
! [X: list_l611321411t_unit] :
( ( X != nil_li307996205t_unit )
=> ( ! [X2: list_c1059388851t_unit] :
( X
!= ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
=> ~ ! [X2: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
( X
!= ( cons_l1083444861t_unit @ X2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_142_remdups__adj_Ocases,axiom,
! [X: list_l1619404459ge_p_v] :
( ( X != nil_list_message_p_v )
=> ( ! [X2: list_message_p_v] :
( X
!= ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
=> ~ ! [X2: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
( X
!= ( cons_l233104475ge_p_v @ X2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_143_remdups__adj_Ocases,axiom,
! [X: list_message_p_v] :
( ( X != nil_message_p_v )
=> ( ! [X2: message_p_v] :
( X
!= ( cons_message_p_v @ X2 @ nil_message_p_v ) )
=> ~ ! [X2: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
( X
!= ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_144_remdups__adj_Ocases,axiom,
! [X: list_c1059388851t_unit] :
( ( X != nil_co1338500125t_unit )
=> ( ! [X2: config256849571t_unit] :
( X
!= ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
=> ~ ! [X2: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
( X
!= ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_145_transpose_Ocases,axiom,
! [X: list_l1584713811t_unit] :
( ( X != nil_li2108369341t_unit )
=> ( ! [Xss: list_l1584713811t_unit] :
( X
!= ( cons_l1777019405t_unit @ nil_li307996205t_unit @ Xss ) )
=> ~ ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit,Xss: list_l1584713811t_unit] :
( X
!= ( cons_l1777019405t_unit @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_146_transpose_Ocases,axiom,
! [X: list_l1341496881ge_p_v] :
( ( X != nil_li835338673ge_p_v )
=> ( ! [Xss: list_l1341496881ge_p_v] :
( X
!= ( cons_l1383421281ge_p_v @ nil_list_message_p_v @ Xss ) )
=> ~ ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v,Xss: list_l1341496881ge_p_v] :
( X
!= ( cons_l1383421281ge_p_v @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_147_transpose_Ocases,axiom,
! [X: list_l1619404459ge_p_v] :
( ( X != nil_list_message_p_v )
=> ( ! [Xss: list_l1619404459ge_p_v] :
( X
!= ( cons_l233104475ge_p_v @ nil_message_p_v @ Xss ) )
=> ~ ! [X2: message_p_v,Xs2: list_message_p_v,Xss: list_l1619404459ge_p_v] :
( X
!= ( cons_l233104475ge_p_v @ ( cons_message_p_v @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_148_transpose_Ocases,axiom,
! [X: list_l611321411t_unit] :
( ( X != nil_li307996205t_unit )
=> ( ! [Xss: list_l611321411t_unit] :
( X
!= ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ Xss ) )
=> ~ ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Xss: list_l611321411t_unit] :
( X
!= ( cons_l1083444861t_unit @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_149_shuffles_Oinduct,axiom,
! [P: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o,A0: list_l1619404459ge_p_v,A1: list_l1619404459ge_p_v] :
( ! [X_1: list_l1619404459ge_p_v] : ( P @ nil_list_message_p_v @ X_1 )
=> ( ! [Xs2: list_l1619404459ge_p_v] : ( P @ Xs2 @ nil_list_message_p_v )
=> ( ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v,Y3: list_message_p_v,Ys2: list_l1619404459ge_p_v] :
( ( P @ Xs2 @ ( cons_l233104475ge_p_v @ Y3 @ Ys2 ) )
=> ( ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) @ Ys2 )
=> ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) @ ( cons_l233104475ge_p_v @ Y3 @ Ys2 ) ) ) )
=> ( P @ A0 @ A1 ) ) ) ) ).
% shuffles.induct
thf(fact_150_shuffles_Oinduct,axiom,
! [P: list_message_p_v > list_message_p_v > $o,A0: list_message_p_v,A1: list_message_p_v] :
( ! [X_1: list_message_p_v] : ( P @ nil_message_p_v @ X_1 )
=> ( ! [Xs2: list_message_p_v] : ( P @ Xs2 @ nil_message_p_v )
=> ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v] :
( ( P @ Xs2 @ ( cons_message_p_v @ Y3 @ Ys2 ) )
=> ( ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ Ys2 )
=> ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) ) )
=> ( P @ A0 @ A1 ) ) ) ) ).
% shuffles.induct
thf(fact_151_shuffles_Oinduct,axiom,
! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: list_c1059388851t_unit,A1: list_c1059388851t_unit] :
( ! [X_1: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ X_1 )
=> ( ! [Xs2: list_c1059388851t_unit] : ( P @ Xs2 @ nil_co1338500125t_unit )
=> ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
( ( P @ Xs2 @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) )
=> ( ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ Ys2 )
=> ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) ) )
=> ( P @ A0 @ A1 ) ) ) ) ).
% shuffles.induct
thf(fact_152_induct__list012,axiom,
! [P: list_message_p_v > $o,Xs: list_message_p_v] :
( ( P @ nil_message_p_v )
=> ( ! [X2: message_p_v] : ( P @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
=> ( ! [X2: message_p_v,Y3: message_p_v,Zs: list_message_p_v] :
( ( P @ Zs )
=> ( ( P @ ( cons_message_p_v @ Y3 @ Zs ) )
=> ( P @ ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Zs ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% induct_list012
thf(fact_153_induct__list012,axiom,
! [P: list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit] :
( ( P @ nil_co1338500125t_unit )
=> ( ! [X2: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
=> ( ! [X2: config256849571t_unit,Y3: config256849571t_unit,Zs: list_c1059388851t_unit] :
( ( P @ Zs )
=> ( ( P @ ( cons_c1162654829t_unit @ Y3 @ Zs ) )
=> ( P @ ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Zs ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% induct_list012
thf(fact_154_splice_Oinduct,axiom,
! [P: list_message_p_v > list_message_p_v > $o,A0: list_message_p_v,A1: list_message_p_v] :
( ! [X_1: list_message_p_v] : ( P @ nil_message_p_v @ X_1 )
=> ( ! [X2: message_p_v,Xs2: list_message_p_v,Ys2: list_message_p_v] :
( ( P @ Ys2 @ Xs2 )
=> ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ Ys2 ) )
=> ( P @ A0 @ A1 ) ) ) ).
% splice.induct
thf(fact_155_splice_Oinduct,axiom,
! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: list_c1059388851t_unit,A1: list_c1059388851t_unit] :
( ! [X_1: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ X_1 )
=> ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
( ( P @ Ys2 @ Xs2 )
=> ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ Ys2 ) )
=> ( P @ A0 @ A1 ) ) ) ).
% splice.induct
thf(fact_156_list__induct2_H,axiom,
! [P: list_message_p_v > list_message_p_v > $o,Xs: list_message_p_v,Ys: list_message_p_v] :
( ( P @ nil_message_p_v @ nil_message_p_v )
=> ( ! [X2: message_p_v,Xs2: list_message_p_v] : ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ nil_message_p_v )
=> ( ! [Y3: message_p_v,Ys2: list_message_p_v] : ( P @ nil_message_p_v @ ( cons_message_p_v @ Y3 @ Ys2 ) )
=> ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v] :
( ( P @ Xs2 @ Ys2 )
=> ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_157_list__induct2_H,axiom,
! [P: list_message_p_v > list_c1059388851t_unit > $o,Xs: list_message_p_v,Ys: list_c1059388851t_unit] :
( ( P @ nil_message_p_v @ nil_co1338500125t_unit )
=> ( ! [X2: message_p_v,Xs2: list_message_p_v] : ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ nil_co1338500125t_unit )
=> ( ! [Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] : ( P @ nil_message_p_v @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) )
=> ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
( ( P @ Xs2 @ Ys2 )
=> ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_158_list__induct2_H,axiom,
! [P: list_c1059388851t_unit > list_message_p_v > $o,Xs: list_c1059388851t_unit,Ys: list_message_p_v] :
( ( P @ nil_co1338500125t_unit @ nil_message_p_v )
=> ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ nil_message_p_v )
=> ( ! [Y3: message_p_v,Ys2: list_message_p_v] : ( P @ nil_co1338500125t_unit @ ( cons_message_p_v @ Y3 @ Ys2 ) )
=> ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v] :
( ( P @ Xs2 @ Ys2 )
=> ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_159_list__induct2_H,axiom,
! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
=> ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ nil_co1338500125t_unit )
=> ( ! [Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) )
=> ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
( ( P @ Xs2 @ Ys2 )
=> ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_160_neq__Nil__conv,axiom,
! [Xs: list_message_p_v] :
( ( Xs != nil_message_p_v )
= ( ? [Y4: message_p_v,Ys3: list_message_p_v] :
( Xs
= ( cons_message_p_v @ Y4 @ Ys3 ) ) ) ) ).
% neq_Nil_conv
thf(fact_161_neq__Nil__conv,axiom,
! [Xs: list_c1059388851t_unit] :
( ( Xs != nil_co1338500125t_unit )
= ( ? [Y4: config256849571t_unit,Ys3: list_c1059388851t_unit] :
( Xs
= ( cons_c1162654829t_unit @ Y4 @ Ys3 ) ) ) ) ).
% neq_Nil_conv
thf(fact_162_list_Oinducts,axiom,
! [P: list_message_p_v > $o,List: list_message_p_v] :
( ( P @ nil_message_p_v )
=> ( ! [X12: message_p_v,X23: list_message_p_v] :
( ( P @ X23 )
=> ( P @ ( cons_message_p_v @ X12 @ X23 ) ) )
=> ( P @ List ) ) ) ).
% list.inducts
thf(fact_163_list_Oinducts,axiom,
! [P: list_c1059388851t_unit > $o,List: list_c1059388851t_unit] :
( ( P @ nil_co1338500125t_unit )
=> ( ! [X12: config256849571t_unit,X23: list_c1059388851t_unit] :
( ( P @ X23 )
=> ( P @ ( cons_c1162654829t_unit @ X12 @ X23 ) ) )
=> ( P @ List ) ) ) ).
% list.inducts
thf(fact_164_list_Oexhaust,axiom,
! [Y: list_message_p_v] :
( ( Y != nil_message_p_v )
=> ~ ! [X212: message_p_v,X223: list_message_p_v] :
( Y
!= ( cons_message_p_v @ X212 @ X223 ) ) ) ).
% list.exhaust
thf(fact_165_list_Oexhaust,axiom,
! [Y: list_c1059388851t_unit] :
( ( Y != nil_co1338500125t_unit )
=> ~ ! [X212: config256849571t_unit,X223: list_c1059388851t_unit] :
( Y
!= ( cons_c1162654829t_unit @ X212 @ X223 ) ) ) ).
% list.exhaust
thf(fact_166_list_OdiscI,axiom,
! [List: list_message_p_v,X21: message_p_v,X222: list_message_p_v] :
( ( List
= ( cons_message_p_v @ X21 @ X222 ) )
=> ( List != nil_message_p_v ) ) ).
% list.discI
thf(fact_167_list_OdiscI,axiom,
! [List: list_c1059388851t_unit,X21: config256849571t_unit,X222: list_c1059388851t_unit] :
( ( List
= ( cons_c1162654829t_unit @ X21 @ X222 ) )
=> ( List != nil_co1338500125t_unit ) ) ).
% list.discI
thf(fact_168_list_Odistinct_I1_J,axiom,
! [X21: message_p_v,X222: list_message_p_v] :
( nil_message_p_v
!= ( cons_message_p_v @ X21 @ X222 ) ) ).
% list.distinct(1)
thf(fact_169_list_Odistinct_I1_J,axiom,
! [X21: config256849571t_unit,X222: list_c1059388851t_unit] :
( nil_co1338500125t_unit
!= ( cons_c1162654829t_unit @ X21 @ X222 ) ) ).
% list.distinct(1)
thf(fact_170_length__induct,axiom,
! [P: list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit] :
( ! [Xs2: list_c1059388851t_unit] :
( ! [Ys4: list_c1059388851t_unit] :
( ( ord_less_nat @ ( size_s1406904903t_unit @ Ys4 ) @ ( size_s1406904903t_unit @ Xs2 ) )
=> ( P @ Ys4 ) )
=> ( P @ Xs2 ) )
=> ( P @ Xs ) ) ).
% length_induct
thf(fact_171_lift__Suc__mono__less__iff,axiom,
! [F2: nat > nat,N3: nat,M: nat] :
( ! [N: nat] : ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
=> ( ( ord_less_nat @ ( F2 @ N3 ) @ ( F2 @ M ) )
= ( ord_less_nat @ N3 @ M ) ) ) ).
% lift_Suc_mono_less_iff
thf(fact_172_lift__Suc__mono__less__iff,axiom,
! [F2: nat > int,N3: nat,M: nat] :
( ! [N: nat] : ( ord_less_int @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
=> ( ( ord_less_int @ ( F2 @ N3 ) @ ( F2 @ M ) )
= ( ord_less_nat @ N3 @ M ) ) ) ).
% lift_Suc_mono_less_iff
thf(fact_173_lift__Suc__mono__less,axiom,
! [F2: nat > nat,N3: nat,N4: nat] :
( ! [N: nat] : ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
=> ( ( ord_less_nat @ N3 @ N4 )
=> ( ord_less_nat @ ( F2 @ N3 ) @ ( F2 @ N4 ) ) ) ) ).
% lift_Suc_mono_less
thf(fact_174_lift__Suc__mono__less,axiom,
! [F2: nat > int,N3: nat,N4: nat] :
( ! [N: nat] : ( ord_less_int @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
=> ( ( ord_less_nat @ N3 @ N4 )
=> ( ord_less_int @ ( F2 @ N3 ) @ ( F2 @ N4 ) ) ) ) ).
% lift_Suc_mono_less
thf(fact_175_less__Suc__eq__0__disj,axiom,
! [M: nat,N3: nat] :
( ( ord_less_nat @ M @ ( suc @ N3 ) )
= ( ( M = zero_zero_nat )
| ? [J3: nat] :
( ( M
= ( suc @ J3 ) )
& ( ord_less_nat @ J3 @ N3 ) ) ) ) ).
% less_Suc_eq_0_disj
thf(fact_176_gr0__implies__Suc,axiom,
! [N3: nat] :
( ( ord_less_nat @ zero_zero_nat @ N3 )
=> ? [M3: nat] :
( N3
= ( suc @ M3 ) ) ) ).
% gr0_implies_Suc
thf(fact_177_All__less__Suc2,axiom,
! [N3: nat,P: nat > $o] :
( ( ! [I3: nat] :
( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
=> ( P @ I3 ) ) )
= ( ( P @ zero_zero_nat )
& ! [I3: nat] :
( ( ord_less_nat @ I3 @ N3 )
=> ( P @ ( suc @ I3 ) ) ) ) ) ).
% All_less_Suc2
thf(fact_178_gr0__conv__Suc,axiom,
! [N3: nat] :
( ( ord_less_nat @ zero_zero_nat @ N3 )
= ( ? [M5: nat] :
( N3
= ( suc @ M5 ) ) ) ) ).
% gr0_conv_Suc
thf(fact_179_Ex__less__Suc2,axiom,
! [N3: nat,P: nat > $o] :
( ( ? [I3: nat] :
( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
& ( P @ I3 ) ) )
= ( ( P @ zero_zero_nat )
| ? [I3: nat] :
( ( ord_less_nat @ I3 @ N3 )
& ( P @ ( suc @ I3 ) ) ) ) ) ).
% Ex_less_Suc2
thf(fact_180_length__Suc__conv,axiom,
! [Xs: list_c1059388851t_unit,N3: nat] :
( ( ( size_s1406904903t_unit @ Xs )
= ( suc @ N3 ) )
= ( ? [Y4: config256849571t_unit,Ys3: list_c1059388851t_unit] :
( ( Xs
= ( cons_c1162654829t_unit @ Y4 @ Ys3 ) )
& ( ( size_s1406904903t_unit @ Ys3 )
= N3 ) ) ) ) ).
% length_Suc_conv
thf(fact_181_Suc__length__conv,axiom,
! [N3: nat,Xs: list_c1059388851t_unit] :
( ( ( suc @ N3 )
= ( size_s1406904903t_unit @ Xs ) )
= ( ? [Y4: config256849571t_unit,Ys3: list_c1059388851t_unit] :
( ( Xs
= ( cons_c1162654829t_unit @ Y4 @ Ys3 ) )
& ( ( size_s1406904903t_unit @ Ys3 )
= N3 ) ) ) ) ).
% Suc_length_conv
thf(fact_182_list_Osize_I3_J,axiom,
( ( size_s1168481041ge_p_v @ nil_message_p_v )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_183_list_Osize_I3_J,axiom,
( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_184_list__induct3,axiom,
! [Xs: list_message_p_v,Ys: list_message_p_v,Zs2: list_message_p_v,P: list_message_p_v > list_message_p_v > list_message_p_v > $o] :
( ( ( size_s1168481041ge_p_v @ Xs )
= ( size_s1168481041ge_p_v @ Ys ) )
=> ( ( ( size_s1168481041ge_p_v @ Ys )
= ( size_s1168481041ge_p_v @ Zs2 ) )
=> ( ( P @ nil_message_p_v @ nil_message_p_v @ nil_message_p_v )
=> ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v,Z: message_p_v,Zs: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ Xs2 )
= ( size_s1168481041ge_p_v @ Ys2 ) )
=> ( ( ( size_s1168481041ge_p_v @ Ys2 )
= ( size_s1168481041ge_p_v @ Zs ) )
=> ( ( P @ Xs2 @ Ys2 @ Zs )
=> ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% list_induct3
thf(fact_185_list__induct3,axiom,
! [Xs: list_message_p_v,Ys: list_message_p_v,Zs2: list_c1059388851t_unit,P: list_message_p_v > list_message_p_v > list_c1059388851t_unit > $o] :
( ( ( size_s1168481041ge_p_v @ Xs )
= ( size_s1168481041ge_p_v @ Ys ) )
=> ( ( ( size_s1168481041ge_p_v @ Ys )
= ( size_s1406904903t_unit @ Zs2 ) )
=> ( ( P @ nil_message_p_v @ nil_message_p_v @ nil_co1338500125t_unit )
=> ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
( ( ( size_s1168481041ge_p_v @ Xs2 )
= ( size_s1168481041ge_p_v @ Ys2 ) )
=> ( ( ( size_s1168481041ge_p_v @ Ys2 )
= ( size_s1406904903t_unit @ Zs ) )
=> ( ( P @ Xs2 @ Ys2 @ Zs )
=> ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% list_induct3
thf(fact_186_list__induct3,axiom,
! [Xs: list_message_p_v,Ys: list_c1059388851t_unit,Zs2: list_message_p_v,P: list_message_p_v > list_c1059388851t_unit > list_message_p_v > $o] :
( ( ( size_s1168481041ge_p_v @ Xs )
= ( size_s1406904903t_unit @ Ys ) )
=> ( ( ( size_s1406904903t_unit @ Ys )
= ( size_s1168481041ge_p_v @ Zs2 ) )
=> ( ( P @ nil_message_p_v @ nil_co1338500125t_unit @ nil_message_p_v )
=> ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: message_p_v,Zs: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ Xs2 )
= ( size_s1406904903t_unit @ Ys2 ) )
=> ( ( ( size_s1406904903t_unit @ Ys2 )
= ( size_s1168481041ge_p_v @ Zs ) )
=> ( ( P @ Xs2 @ Ys2 @ Zs )
=> ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% list_induct3
thf(fact_187_list__induct3,axiom,
! [Xs: list_message_p_v,Ys: list_c1059388851t_unit,Zs2: list_c1059388851t_unit,P: list_message_p_v > list_c1059388851t_unit > list_c1059388851t_unit > $o] :
( ( ( size_s1168481041ge_p_v @ Xs )
= ( size_s1406904903t_unit @ Ys ) )
=> ( ( ( size_s1406904903t_unit @ Ys )
= ( size_s1406904903t_unit @ Zs2 ) )
=> ( ( P @ nil_message_p_v @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
=> ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
( ( ( size_s1168481041ge_p_v @ Xs2 )
= ( size_s1406904903t_unit @ Ys2 ) )
=> ( ( ( size_s1406904903t_unit @ Ys2 )
= ( size_s1406904903t_unit @ Zs ) )
=> ( ( P @ Xs2 @ Ys2 @ Zs )
=> ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% list_induct3
thf(fact_188_list__induct3,axiom,
! [Xs: list_c1059388851t_unit,Ys: list_message_p_v,Zs2: list_message_p_v,P: list_c1059388851t_unit > list_message_p_v > list_message_p_v > $o] :
( ( ( size_s1406904903t_unit @ Xs )
= ( size_s1168481041ge_p_v @ Ys ) )
=> ( ( ( size_s1168481041ge_p_v @ Ys )
= ( size_s1168481041ge_p_v @ Zs2 ) )
=> ( ( P @ nil_co1338500125t_unit @ nil_message_p_v @ nil_message_p_v )
=> ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v,Z: message_p_v,Zs: list_message_p_v] :
( ( ( size_s1406904903t_unit @ Xs2 )
= ( size_s1168481041ge_p_v @ Ys2 ) )
=> ( ( ( size_s1168481041ge_p_v @ Ys2 )
= ( size_s1168481041ge_p_v @ Zs ) )
=> ( ( P @ Xs2 @ Ys2 @ Zs )
=> ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% list_induct3
thf(fact_189_list__induct3,axiom,
! [Xs: list_c1059388851t_unit,Ys: list_message_p_v,Zs2: list_c1059388851t_unit,P: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit > $o] :
( ( ( size_s1406904903t_unit @ Xs )
= ( size_s1168481041ge_p_v @ Ys ) )
=> ( ( ( size_s1168481041ge_p_v @ Ys )
= ( size_s1406904903t_unit @ Zs2 ) )
=> ( ( P @ nil_co1338500125t_unit @ nil_message_p_v @ nil_co1338500125t_unit )
=> ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ Xs2 )
= ( size_s1168481041ge_p_v @ Ys2 ) )
=> ( ( ( size_s1168481041ge_p_v @ Ys2 )
= ( size_s1406904903t_unit @ Zs ) )
=> ( ( P @ Xs2 @ Ys2 @ Zs )
=> ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% list_induct3
thf(fact_190_list__induct3,axiom,
! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit,Zs2: list_message_p_v,P: list_c1059388851t_unit > list_c1059388851t_unit > list_message_p_v > $o] :
( ( ( size_s1406904903t_unit @ Xs )
= ( size_s1406904903t_unit @ Ys ) )
=> ( ( ( size_s1406904903t_unit @ Ys )
= ( size_s1168481041ge_p_v @ Zs2 ) )
=> ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit @ nil_message_p_v )
=> ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: message_p_v,Zs: list_message_p_v] :
( ( ( size_s1406904903t_unit @ Xs2 )
= ( size_s1406904903t_unit @ Ys2 ) )
=> ( ( ( size_s1406904903t_unit @ Ys2 )
= ( size_s1168481041ge_p_v @ Zs ) )
=> ( ( P @ Xs2 @ Ys2 @ Zs )
=> ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% list_induct3
thf(fact_191_list__induct3,axiom,
! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit,Zs2: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o] :
( ( ( size_s1406904903t_unit @ Xs )
= ( size_s1406904903t_unit @ Ys ) )
=> ( ( ( size_s1406904903t_unit @ Ys )
= ( size_s1406904903t_unit @ Zs2 ) )
=> ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
=> ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ Xs2 )
= ( size_s1406904903t_unit @ Ys2 ) )
=> ( ( ( size_s1406904903t_unit @ Ys2 )
= ( size_s1406904903t_unit @ Zs ) )
=> ( ( P @ Xs2 @ Ys2 @ Zs )
=> ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% list_induct3
thf(fact_192_list__induct2,axiom,
! [Xs: list_message_p_v,Ys: list_message_p_v,P: list_message_p_v > list_message_p_v > $o] :
( ( ( size_s1168481041ge_p_v @ Xs )
= ( size_s1168481041ge_p_v @ Ys ) )
=> ( ( P @ nil_message_p_v @ nil_message_p_v )
=> ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ Xs2 )
= ( size_s1168481041ge_p_v @ Ys2 ) )
=> ( ( P @ Xs2 @ Ys2 )
=> ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_193_list__induct2,axiom,
! [Xs: list_message_p_v,Ys: list_c1059388851t_unit,P: list_message_p_v > list_c1059388851t_unit > $o] :
( ( ( size_s1168481041ge_p_v @ Xs )
= ( size_s1406904903t_unit @ Ys ) )
=> ( ( P @ nil_message_p_v @ nil_co1338500125t_unit )
=> ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
( ( ( size_s1168481041ge_p_v @ Xs2 )
= ( size_s1406904903t_unit @ Ys2 ) )
=> ( ( P @ Xs2 @ Ys2 )
=> ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_194_list__induct2,axiom,
! [Xs: list_c1059388851t_unit,Ys: list_message_p_v,P: list_c1059388851t_unit > list_message_p_v > $o] :
( ( ( size_s1406904903t_unit @ Xs )
= ( size_s1168481041ge_p_v @ Ys ) )
=> ( ( P @ nil_co1338500125t_unit @ nil_message_p_v )
=> ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v] :
( ( ( size_s1406904903t_unit @ Xs2 )
= ( size_s1168481041ge_p_v @ Ys2 ) )
=> ( ( P @ Xs2 @ Ys2 )
=> ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_195_list__induct2,axiom,
! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
( ( ( size_s1406904903t_unit @ Xs )
= ( size_s1406904903t_unit @ Ys ) )
=> ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
=> ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ Xs2 )
= ( size_s1406904903t_unit @ Ys2 ) )
=> ( ( P @ Xs2 @ Ys2 )
=> ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_196_infiniteExecutionCfg_Oelims,axiom,
! [X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_c1059388851t_unit] :
( ( ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ Xc )
= Y )
=> ( ( ( Xc = zero_zero_nat )
=> ( Y
!= ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) )
=> ~ ! [N: nat] :
( ( Xc
= ( suc @ N ) )
=> ( Y
!= ( Xa @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ).
% infiniteExecutionCfg.elims
thf(fact_197_infiniteExecutionMsg_Oelims,axiom,
! [X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_message_p_v] :
( ( ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ Xc )
= Y )
=> ( ( ( Xc = zero_zero_nat )
=> ( Y != nil_message_p_v ) )
=> ~ ! [N: nat] :
( ( Xc
= ( suc @ N ) )
=> ( Y
!= ( Xb @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ).
% infiniteExecutionMsg.elims
thf(fact_198_infiniteExecutionMsg_Osimps_I2_J,axiom,
! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
= ( FStepMsg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ).
% infiniteExecutionMsg.simps(2)
thf(fact_199_infiniteExecutionCfg_Osimps_I2_J,axiom,
! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
= ( FStepCfg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ).
% infiniteExecutionCfg.simps(2)
thf(fact_200_infiniteExecutionMsg_Osimps_I1_J,axiom,
! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
= nil_message_p_v ) ).
% infiniteExecutionMsg.simps(1)
thf(fact_201_not__gr__zero,axiom,
! [N3: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
= ( N3 = zero_zero_nat ) ) ).
% not_gr_zero
thf(fact_202_length__Cons,axiom,
! [X: config256849571t_unit,Xs: list_c1059388851t_unit] :
( ( size_s1406904903t_unit @ ( cons_c1162654829t_unit @ X @ Xs ) )
= ( suc @ ( size_s1406904903t_unit @ Xs ) ) ) ).
% length_Cons
thf(fact_203_zero__reorient,axiom,
! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ) ).
% zero_reorient
thf(fact_204_zero__reorient,axiom,
! [X: int] :
( ( zero_zero_int = X )
= ( X = zero_zero_int ) ) ).
% zero_reorient
thf(fact_205_gr__zeroI,axiom,
! [N3: nat] :
( ( N3 != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% gr_zeroI
thf(fact_206_not__less__zero,axiom,
! [N3: nat] :
~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).
% not_less_zero
thf(fact_207_gr__implies__not__zero,axiom,
! [M: nat,N3: nat] :
( ( ord_less_nat @ M @ N3 )
=> ( N3 != zero_zero_nat ) ) ).
% gr_implies_not_zero
thf(fact_208_zero__less__iff__neq__zero,axiom,
! [N3: nat] :
( ( ord_less_nat @ zero_zero_nat @ N3 )
= ( N3 != zero_zero_nat ) ) ).
% zero_less_iff_neq_zero
thf(fact_209_n__lists__Nil,axiom,
! [N3: nat] :
( ( ( N3 = zero_zero_nat )
=> ( ( n_list1987762709t_unit @ N3 @ nil_co1338500125t_unit )
= ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) )
& ( ( N3 != zero_zero_nat )
=> ( ( n_list1987762709t_unit @ N3 @ nil_co1338500125t_unit )
= nil_li307996205t_unit ) ) ) ).
% n_lists_Nil
thf(fact_210_n__lists__Nil,axiom,
! [N3: nat] :
( ( ( N3 = zero_zero_nat )
=> ( ( n_lists_message_p_v @ N3 @ nil_message_p_v )
= ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) )
& ( ( N3 != zero_zero_nat )
=> ( ( n_lists_message_p_v @ N3 @ nil_message_p_v )
= nil_list_message_p_v ) ) ) ).
% n_lists_Nil
thf(fact_211_flpPseudoConsensus_OinfiniteExecutionCfg_Oelims,axiom,
! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_c1059388851t_unit] :
( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
=> ( ( ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ Xc )
= Y )
=> ( ( ( Xc = zero_zero_nat )
=> ( Y
!= ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) )
=> ~ ! [N: nat] :
( ( Xc
= ( suc @ N ) )
=> ( Y
!= ( Xa @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ) ).
% flpPseudoConsensus.infiniteExecutionCfg.elims
thf(fact_212_n__lists_Osimps_I1_J,axiom,
! [Xs: list_c1059388851t_unit] :
( ( n_list1987762709t_unit @ zero_zero_nat @ Xs )
= ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).
% n_lists.simps(1)
thf(fact_213_n__lists_Osimps_I1_J,axiom,
! [Xs: list_message_p_v] :
( ( n_lists_message_p_v @ zero_zero_nat @ Xs )
= ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).
% n_lists.simps(1)
thf(fact_214_flpPseudoConsensus_OinfiniteExecutionMsg_Oelims,axiom,
! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_message_p_v] :
( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
=> ( ( ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ Xc )
= Y )
=> ( ( ( Xc = zero_zero_nat )
=> ( Y != nil_message_p_v ) )
=> ~ ! [N: nat] :
( ( Xc
= ( suc @ N ) )
=> ( Y
!= ( Xb @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ) ).
% flpPseudoConsensus.infiniteExecutionMsg.elims
thf(fact_215_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I2_J,axiom,
! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
=> ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
= ( FStepMsg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ) ).
% flpPseudoConsensus.infiniteExecutionMsg.simps(2)
thf(fact_216_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I2_J,axiom,
! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
=> ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
= ( FStepCfg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ) ).
% flpPseudoConsensus.infiniteExecutionCfg.simps(2)
thf(fact_217_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I1_J,axiom,
! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
=> ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
= nil_message_p_v ) ) ).
% flpPseudoConsensus.infiniteExecutionMsg.simps(1)
thf(fact_218_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I1_J,axiom,
! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
=> ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
= ( cons_c1162654829t_unit @ Cfg2 @ nil_co1338500125t_unit ) ) ) ).
% flpPseudoConsensus.infiniteExecutionCfg.simps(1)
thf(fact_219_less__numeral__extra_I3_J,axiom,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% less_numeral_extra(3)
thf(fact_220_less__numeral__extra_I3_J,axiom,
~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% less_numeral_extra(3)
thf(fact_221_product__lists_Osimps_I1_J,axiom,
( ( produc663212148t_unit @ nil_li307996205t_unit )
= ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).
% product_lists.simps(1)
thf(fact_222_product__lists_Osimps_I1_J,axiom,
( ( produc1505827982ge_p_v @ nil_list_message_p_v )
= ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).
% product_lists.simps(1)
thf(fact_223_subseqs_Osimps_I1_J,axiom,
( ( subseq1144048270t_unit @ nil_co1338500125t_unit )
= ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).
% subseqs.simps(1)
thf(fact_224_subseqs_Osimps_I1_J,axiom,
( ( subseqs_message_p_v @ nil_message_p_v )
= ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).
% subseqs.simps(1)
thf(fact_225_length__code,axiom,
( size_s1406904903t_unit
= ( gen_le193291088t_unit @ zero_zero_nat ) ) ).
% length_code
thf(fact_226_gen__length__code_I2_J,axiom,
! [N3: nat,X: config256849571t_unit,Xs: list_c1059388851t_unit] :
( ( gen_le193291088t_unit @ N3 @ ( cons_c1162654829t_unit @ X @ Xs ) )
= ( gen_le193291088t_unit @ ( suc @ N3 ) @ Xs ) ) ).
% gen_length_code(2)
thf(fact_227_gen__length__code_I1_J,axiom,
! [N3: nat] :
( ( gen_le193291088t_unit @ N3 @ nil_co1338500125t_unit )
= N3 ) ).
% gen_length_code(1)
thf(fact_228_gen__length__code_I1_J,axiom,
! [N3: nat] :
( ( gen_le697204914ge_p_v @ N3 @ nil_message_p_v )
= N3 ) ).
% gen_length_code(1)
thf(fact_229_insert__Nil,axiom,
! [X: message_p_v] :
( ( insert_message_p_v @ X @ nil_message_p_v )
= ( cons_message_p_v @ X @ nil_message_p_v ) ) ).
% insert_Nil
thf(fact_230_insert__Nil,axiom,
! [X: config256849571t_unit] :
( ( insert1308755079t_unit @ X @ nil_co1338500125t_unit )
= ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) ).
% insert_Nil
thf(fact_231_nths__singleton,axiom,
! [A8: set_nat,X: message_p_v] :
( ( ( member_nat @ zero_zero_nat @ A8 )
=> ( ( nths_message_p_v @ ( cons_message_p_v @ X @ nil_message_p_v ) @ A8 )
= ( cons_message_p_v @ X @ nil_message_p_v ) ) )
& ( ~ ( member_nat @ zero_zero_nat @ A8 )
=> ( ( nths_message_p_v @ ( cons_message_p_v @ X @ nil_message_p_v ) @ A8 )
= nil_message_p_v ) ) ) ).
% nths_singleton
thf(fact_232_nths__singleton,axiom,
! [A8: set_nat,X: config256849571t_unit] :
( ( ( member_nat @ zero_zero_nat @ A8 )
=> ( ( nths_c890550943t_unit @ ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) @ A8 )
= ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) )
& ( ~ ( member_nat @ zero_zero_nat @ A8 )
=> ( ( nths_c890550943t_unit @ ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) @ A8 )
= nil_co1338500125t_unit ) ) ) ).
% nths_singleton
thf(fact_233_of__nat__0__less__iff,axiom,
! [N3: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N3 ) )
= ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% of_nat_0_less_iff
thf(fact_234_of__nat__0__less__iff,axiom,
! [N3: nat] :
( ( ord_less_int @ zero_zero_int @ ( semiri2019852685at_int @ N3 ) )
= ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% of_nat_0_less_iff
thf(fact_235_of__nat__eq__iff,axiom,
! [M: nat,N3: nat] :
( ( ( semiri2019852685at_int @ M )
= ( semiri2019852685at_int @ N3 ) )
= ( M = N3 ) ) ).
% of_nat_eq_iff
thf(fact_236_nths__nil,axiom,
! [A8: set_nat] :
( ( nths_c890550943t_unit @ nil_co1338500125t_unit @ A8 )
= nil_co1338500125t_unit ) ).
% nths_nil
thf(fact_237_nths__nil,axiom,
! [A8: set_nat] :
( ( nths_message_p_v @ nil_message_p_v @ A8 )
= nil_message_p_v ) ).
% nths_nil
thf(fact_238_of__nat__0,axiom,
( ( semiri1382578993at_nat @ zero_zero_nat )
= zero_zero_nat ) ).
% of_nat_0
thf(fact_239_of__nat__0,axiom,
( ( semiri2019852685at_int @ zero_zero_nat )
= zero_zero_int ) ).
% of_nat_0
thf(fact_240_of__nat__0__eq__iff,axiom,
! [N3: nat] :
( ( zero_zero_nat
= ( semiri1382578993at_nat @ N3 ) )
= ( zero_zero_nat = N3 ) ) ).
% of_nat_0_eq_iff
thf(fact_241_of__nat__0__eq__iff,axiom,
! [N3: nat] :
( ( zero_zero_int
= ( semiri2019852685at_int @ N3 ) )
= ( zero_zero_nat = N3 ) ) ).
% of_nat_0_eq_iff
thf(fact_242_of__nat__eq__0__iff,axiom,
! [M: nat] :
( ( ( semiri1382578993at_nat @ M )
= zero_zero_nat )
= ( M = zero_zero_nat ) ) ).
% of_nat_eq_0_iff
thf(fact_243_of__nat__eq__0__iff,axiom,
! [M: nat] :
( ( ( semiri2019852685at_int @ M )
= zero_zero_int )
= ( M = zero_zero_nat ) ) ).
% of_nat_eq_0_iff
thf(fact_244_of__nat__less__iff,axiom,
! [M: nat,N3: nat] :
( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N3 ) )
= ( ord_less_nat @ M @ N3 ) ) ).
% of_nat_less_iff
thf(fact_245_of__nat__less__iff,axiom,
! [M: nat,N3: nat] :
( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) )
= ( ord_less_nat @ M @ N3 ) ) ).
% of_nat_less_iff
thf(fact_246_of__nat__less__0__iff,axiom,
! [M: nat] :
~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ) ).
% of_nat_less_0_iff
thf(fact_247_of__nat__less__0__iff,axiom,
! [M: nat] :
~ ( ord_less_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int ) ).
% of_nat_less_0_iff
thf(fact_248_of__nat__neq__0,axiom,
! [N3: nat] :
( ( semiri1382578993at_nat @ ( suc @ N3 ) )
!= zero_zero_nat ) ).
% of_nat_neq_0
thf(fact_249_of__nat__neq__0,axiom,
! [N3: nat] :
( ( semiri2019852685at_int @ ( suc @ N3 ) )
!= zero_zero_int ) ).
% of_nat_neq_0
thf(fact_250_less__imp__of__nat__less,axiom,
! [M: nat,N3: nat] :
( ( ord_less_nat @ M @ N3 )
=> ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N3 ) ) ) ).
% less_imp_of_nat_less
thf(fact_251_less__imp__of__nat__less,axiom,
! [M: nat,N3: nat] :
( ( ord_less_nat @ M @ N3 )
=> ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) ) ) ).
% less_imp_of_nat_less
thf(fact_252_of__nat__less__imp__less,axiom,
! [M: nat,N3: nat] :
( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N3 ) )
=> ( ord_less_nat @ M @ N3 ) ) ).
% of_nat_less_imp_less
thf(fact_253_of__nat__less__imp__less,axiom,
! [M: nat,N3: nat] :
( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) )
=> ( ord_less_nat @ M @ N3 ) ) ).
% of_nat_less_imp_less
thf(fact_254_nths__all,axiom,
! [Xs: list_c1059388851t_unit,I4: set_nat] :
( ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( size_s1406904903t_unit @ Xs ) )
=> ( member_nat @ I2 @ I4 ) )
=> ( ( nths_c890550943t_unit @ Xs @ I4 )
= Xs ) ) ).
% nths_all
thf(fact_255_pos__int__cases,axiom,
! [K: int] :
( ( ord_less_int @ zero_zero_int @ K )
=> ~ ! [N: nat] :
( ( K
= ( semiri2019852685at_int @ N ) )
=> ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% pos_int_cases
thf(fact_256_zero__less__imp__eq__int,axiom,
! [K: int] :
( ( ord_less_int @ zero_zero_int @ K )
=> ? [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
& ( K
= ( semiri2019852685at_int @ N ) ) ) ) ).
% zero_less_imp_eq_int
thf(fact_257_list__ex1__simps_I1_J,axiom,
! [P: config256849571t_unit > $o] :
~ ( list_e1598815642t_unit @ P @ nil_co1338500125t_unit ) ).
% list_ex1_simps(1)
thf(fact_258_list__ex1__simps_I1_J,axiom,
! [P: message_p_v > $o] :
~ ( list_ex1_message_p_v @ P @ nil_message_p_v ) ).
% list_ex1_simps(1)
thf(fact_259_nat__int__comparison_I2_J,axiom,
( ord_less_nat
= ( ^ [A10: nat,B: nat] : ( ord_less_int @ ( semiri2019852685at_int @ A10 ) @ ( semiri2019852685at_int @ B ) ) ) ) ).
% nat_int_comparison(2)
thf(fact_260_int__ops_I1_J,axiom,
( ( semiri2019852685at_int @ zero_zero_nat )
= zero_zero_int ) ).
% int_ops(1)
thf(fact_261_neg__int__cases,axiom,
! [K: int] :
( ( ord_less_int @ K @ zero_zero_int )
=> ~ ! [N: nat] :
( ( K
= ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) ) )
=> ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% neg_int_cases
thf(fact_262_neg__equal__iff__equal,axiom,
! [A: int,B2: int] :
( ( ( uminus_uminus_int @ A )
= ( uminus_uminus_int @ B2 ) )
= ( A = B2 ) ) ).
% neg_equal_iff_equal
thf(fact_263_add_Oinverse__inverse,axiom,
! [A: int] :
( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
= A ) ).
% add.inverse_inverse
thf(fact_264_add_Oinverse__neutral,axiom,
( ( uminus_uminus_int @ zero_zero_int )
= zero_zero_int ) ).
% add.inverse_neutral
thf(fact_265_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_266_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_267_equal__neg__zero,axiom,
! [A: int] :
( ( A
= ( uminus_uminus_int @ A ) )
= ( A = zero_zero_int ) ) ).
% equal_neg_zero
thf(fact_268_neg__equal__zero,axiom,
! [A: int] :
( ( ( uminus_uminus_int @ A )
= A )
= ( A = zero_zero_int ) ) ).
% neg_equal_zero
thf(fact_269_neg__less__iff__less,axiom,
! [B2: int,A: int] :
( ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) )
= ( ord_less_int @ A @ B2 ) ) ).
% neg_less_iff_less
thf(fact_270_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_271_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_272_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_273_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_274_negative__eq__positive,axiom,
! [N3: nat,M: nat] :
( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ N3 ) )
= ( semiri2019852685at_int @ M ) )
= ( ( N3 = zero_zero_nat )
& ( M = zero_zero_nat ) ) ) ).
% negative_eq_positive
thf(fact_275_negative__zless,axiom,
! [N3: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N3 ) ) ) @ ( semiri2019852685at_int @ M ) ) ).
% negative_zless
thf(fact_276_minus__less__iff,axiom,
! [A: int,B2: int] :
( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B2 )
= ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ A ) ) ).
% minus_less_iff
thf(fact_277_less__minus__iff,axiom,
! [A: int,B2: int] :
( ( ord_less_int @ A @ ( uminus_uminus_int @ B2 ) )
= ( ord_less_int @ B2 @ ( uminus_uminus_int @ A ) ) ) ).
% less_minus_iff
thf(fact_278_verit__negate__coefficient_I2_J,axiom,
! [A: int,B2: int] :
( ( ord_less_int @ A @ B2 )
=> ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) ) ) ).
% verit_negate_coefficient(2)
thf(fact_279_minus__equation__iff,axiom,
! [A: int,B2: int] :
( ( ( uminus_uminus_int @ A )
= B2 )
= ( ( uminus_uminus_int @ B2 )
= A ) ) ).
% minus_equation_iff
thf(fact_280_equation__minus__iff,axiom,
! [A: int,B2: int] :
( ( A
= ( uminus_uminus_int @ B2 ) )
= ( B2
= ( uminus_uminus_int @ A ) ) ) ).
% equation_minus_iff
thf(fact_281_int__cases,axiom,
! [Z2: int] :
( ! [N: nat] :
( Z2
!= ( semiri2019852685at_int @ N ) )
=> ~ ! [N: nat] :
( Z2
!= ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N ) ) ) ) ) ).
% int_cases
thf(fact_282_int__of__nat__induct,axiom,
! [P: int > $o,Z2: int] :
( ! [N: nat] : ( P @ ( semiri2019852685at_int @ N ) )
=> ( ! [N: nat] : ( P @ ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N ) ) ) )
=> ( P @ Z2 ) ) ) ).
% int_of_nat_induct
thf(fact_283_int__cases4,axiom,
! [M: int] :
( ! [N: nat] :
( M
!= ( semiri2019852685at_int @ N ) )
=> ~ ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( M
!= ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) ) ) ) ) ).
% int_cases4
thf(fact_284_verit__comp__simplify1_I1_J,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ) ).
% verit_comp_simplify1(1)
thf(fact_285_verit__comp__simplify1_I1_J,axiom,
! [A: int] :
~ ( ord_less_int @ A @ A ) ).
% verit_comp_simplify1(1)
thf(fact_286_int__cases3,axiom,
! [K: int] :
( ( K != zero_zero_int )
=> ( ! [N: nat] :
( ( K
= ( semiri2019852685at_int @ N ) )
=> ~ ( ord_less_nat @ zero_zero_nat @ N ) )
=> ~ ! [N: nat] :
( ( K
= ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) ) )
=> ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% int_cases3
thf(fact_287_negative__zless__0,axiom,
! [N3: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N3 ) ) ) @ zero_zero_int ) ).
% negative_zless_0
thf(fact_288_negD,axiom,
! [X: int] :
( ( ord_less_int @ X @ zero_zero_int )
=> ? [N: nat] :
( X
= ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N ) ) ) ) ) ).
% negD
thf(fact_289_zero__less__nat__eq,axiom,
! [Z2: int] :
( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z2 ) )
= ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% zero_less_nat_eq
thf(fact_290_of__int__0__less__iff,axiom,
! [Z2: int] :
( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
= ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% of_int_0_less_iff
thf(fact_291_of__int__0,axiom,
( ( ring_1_of_int_int @ zero_zero_int )
= zero_zero_int ) ).
% of_int_0
thf(fact_292_of__int__0__eq__iff,axiom,
! [Z2: int] :
( ( zero_zero_int
= ( ring_1_of_int_int @ Z2 ) )
= ( Z2 = zero_zero_int ) ) ).
% of_int_0_eq_iff
thf(fact_293_of__int__eq__0__iff,axiom,
! [Z2: int] :
( ( ( ring_1_of_int_int @ Z2 )
= zero_zero_int )
= ( Z2 = zero_zero_int ) ) ).
% of_int_eq_0_iff
thf(fact_294_of__int__less__iff,axiom,
! [W: int,Z2: int] :
( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z2 ) )
= ( ord_less_int @ W @ Z2 ) ) ).
% of_int_less_iff
thf(fact_295_zless__nat__conj,axiom,
! [W: int,Z2: int] :
( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z2 ) )
= ( ( ord_less_int @ zero_zero_int @ Z2 )
& ( ord_less_int @ W @ Z2 ) ) ) ).
% zless_nat_conj
thf(fact_296_nat__zminus__int,axiom,
! [N3: nat] :
( ( nat2 @ ( uminus_uminus_int @ ( semiri2019852685at_int @ N3 ) ) )
= zero_zero_nat ) ).
% nat_zminus_int
thf(fact_297_of__int__less__0__iff,axiom,
! [Z2: int] :
( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
= ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% of_int_less_0_iff
thf(fact_298_nat__zero__as__int,axiom,
( zero_zero_nat
= ( nat2 @ zero_zero_int ) ) ).
% nat_zero_as_int
thf(fact_299_nat__mono__iff,axiom,
! [Z2: int,W: int] :
( ( ord_less_int @ zero_zero_int @ Z2 )
=> ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z2 ) )
= ( ord_less_int @ W @ Z2 ) ) ) ).
% nat_mono_iff
thf(fact_300_zless__nat__eq__int__zless,axiom,
! [M: nat,Z2: int] :
( ( ord_less_nat @ M @ ( nat2 @ Z2 ) )
= ( ord_less_int @ ( semiri2019852685at_int @ M ) @ Z2 ) ) ).
% zless_nat_eq_int_zless
thf(fact_301_of__int__pos,axiom,
! [Z2: int] :
( ( ord_less_int @ zero_zero_int @ Z2 )
=> ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% of_int_pos
thf(fact_302_of__nat__less__of__int__iff,axiom,
! [N3: nat,X: int] :
( ( ord_less_int @ ( semiri2019852685at_int @ N3 ) @ ( ring_1_of_int_int @ X ) )
= ( ord_less_int @ ( semiri2019852685at_int @ N3 ) @ X ) ) ).
% of_nat_less_of_int_iff
thf(fact_303_split__nat,axiom,
! [P: nat > $o,I: int] :
( ( P @ ( nat2 @ I ) )
= ( ! [N5: nat] :
( ( I
= ( semiri2019852685at_int @ N5 ) )
=> ( P @ N5 ) )
& ( ( ord_less_int @ I @ zero_zero_int )
=> ( P @ zero_zero_nat ) ) ) ) ).
% split_nat
thf(fact_304_one__less__nat__eq,axiom,
! [Z2: int] :
( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z2 ) )
= ( ord_less_int @ one_one_int @ Z2 ) ) ).
% one_less_nat_eq
thf(fact_305_nat__less__iff,axiom,
! [W: int,M: nat] :
( ( ord_less_eq_int @ zero_zero_int @ W )
=> ( ( ord_less_nat @ ( nat2 @ W ) @ M )
= ( ord_less_int @ W @ ( semiri2019852685at_int @ M ) ) ) ) ).
% nat_less_iff
thf(fact_306_le__zero__eq,axiom,
! [N3: nat] :
( ( ord_less_eq_nat @ N3 @ zero_zero_nat )
= ( N3 = zero_zero_nat ) ) ).
% le_zero_eq
thf(fact_307_neg__le__iff__le,axiom,
! [B2: int,A: int] :
( ( ord_less_eq_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) )
= ( ord_less_eq_int @ A @ B2 ) ) ).
% neg_le_iff_le
thf(fact_308_of__nat__le__iff,axiom,
! [M: nat,N3: nat] :
( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) )
= ( ord_less_eq_nat @ M @ N3 ) ) ).
% of_nat_le_iff
thf(fact_309_of__nat__1,axiom,
( ( semiri2019852685at_int @ one_one_nat )
= one_one_int ) ).
% of_nat_1
thf(fact_310_of__nat__1__eq__iff,axiom,
! [N3: nat] :
( ( one_one_int
= ( semiri2019852685at_int @ N3 ) )
= ( N3 = one_one_nat ) ) ).
% of_nat_1_eq_iff
thf(fact_311_of__nat__eq__1__iff,axiom,
! [N3: nat] :
( ( ( semiri2019852685at_int @ N3 )
= one_one_int )
= ( N3 = one_one_nat ) ) ).
% of_nat_eq_1_iff
thf(fact_312_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_313_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_314_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_315_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_316_of__nat__le__0__iff,axiom,
! [M: nat] :
( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat )
= ( M = zero_zero_nat ) ) ).
% of_nat_le_0_iff
thf(fact_317_of__nat__le__0__iff,axiom,
! [M: nat] :
( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int )
= ( M = zero_zero_nat ) ) ).
% of_nat_le_0_iff
thf(fact_318_nat__1,axiom,
( ( nat2 @ one_one_int )
= ( suc @ zero_zero_nat ) ) ).
% nat_1
thf(fact_319_nat__le__0,axiom,
! [Z2: int] :
( ( ord_less_eq_int @ Z2 @ zero_zero_int )
=> ( ( nat2 @ Z2 )
= zero_zero_nat ) ) ).
% nat_le_0
thf(fact_320_nat__0__iff,axiom,
! [I: int] :
( ( ( nat2 @ I )
= zero_zero_nat )
= ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% nat_0_iff
thf(fact_321_of__int__le__0__iff,axiom,
! [Z2: int] :
( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
= ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% of_int_le_0_iff
thf(fact_322_of__int__0__le__iff,axiom,
! [Z2: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
= ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% of_int_0_le_iff
thf(fact_323_of__int__less__1__iff,axiom,
! [Z2: int] :
( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ one_one_int )
= ( ord_less_int @ Z2 @ one_one_int ) ) ).
% of_int_less_1_iff
thf(fact_324_of__int__1__less__iff,axiom,
! [Z2: int] :
( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z2 ) )
= ( ord_less_int @ one_one_int @ Z2 ) ) ).
% of_int_1_less_iff
thf(fact_325_of__int__nonneg,axiom,
! [Z2: int] :
( ( ord_less_eq_int @ zero_zero_int @ Z2 )
=> ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% of_int_nonneg
thf(fact_326_verit__comp__simplify1_I3_J,axiom,
! [B3: nat,A11: nat] :
( ( ~ ( ord_less_eq_nat @ B3 @ A11 ) )
= ( ord_less_nat @ A11 @ B3 ) ) ).
% verit_comp_simplify1(3)
thf(fact_327_verit__comp__simplify1_I3_J,axiom,
! [B3: int,A11: int] :
( ( ~ ( ord_less_eq_int @ B3 @ A11 ) )
= ( ord_less_int @ A11 @ B3 ) ) ).
% verit_comp_simplify1(3)
thf(fact_328_le__numeral__extra_I4_J,axiom,
ord_less_eq_int @ one_one_int @ one_one_int ).
% le_numeral_extra(4)
thf(fact_329_one__reorient,axiom,
! [X: int] :
( ( one_one_int = X )
= ( X = one_one_int ) ) ).
% one_reorient
thf(fact_330_lift__Suc__antimono__le,axiom,
! [F2: nat > int,N3: nat,N4: nat] :
( ! [N: nat] : ( ord_less_eq_int @ ( F2 @ ( suc @ N ) ) @ ( F2 @ N ) )
=> ( ( ord_less_eq_nat @ N3 @ N4 )
=> ( ord_less_eq_int @ ( F2 @ N4 ) @ ( F2 @ N3 ) ) ) ) ).
% lift_Suc_antimono_le
thf(fact_331_lift__Suc__mono__le,axiom,
! [F2: nat > int,N3: nat,N4: nat] :
( ! [N: nat] : ( ord_less_eq_int @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
=> ( ( ord_less_eq_nat @ N3 @ N4 )
=> ( ord_less_eq_int @ ( F2 @ N3 ) @ ( F2 @ N4 ) ) ) ) ).
% lift_Suc_mono_le
thf(fact_332_zero__le,axiom,
! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% zero_le
thf(fact_333_le__numeral__extra_I3_J,axiom,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% le_numeral_extra(3)
thf(fact_334_le__numeral__extra_I3_J,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% le_numeral_extra(3)
thf(fact_335_less__numeral__extra_I4_J,axiom,
~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% less_numeral_extra(4)
thf(fact_336_less__numeral__extra_I4_J,axiom,
~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% less_numeral_extra(4)
thf(fact_337_of__nat__mono,axiom,
! [I: nat,J: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_int @ ( semiri2019852685at_int @ I ) @ ( semiri2019852685at_int @ J ) ) ) ).
% of_nat_mono
thf(fact_338_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_339_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_340_zero__neq__neg__one,axiom,
( zero_zero_int
!= ( uminus_uminus_int @ one_one_int ) ) ).
% zero_neq_neg_one
% Conjectures (1)
thf(conj_0,conjecture,
prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ).
%------------------------------------------------------------------------------