TPTP Problem File: ITP054^1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP054^1 : TPTP v8.2.0. Released v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : Sledgehammer FLPTheorem problem prob_1046__3303610_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_1046__3303610_1 [Des21]
% Status : Theorem
% Rating : 0.30 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% Syntax : Number of formulae : 309 ( 137 unt; 47 typ; 0 def)
% Number of atoms : 568 ( 238 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 1942 ( 88 ~; 16 |; 45 &;1532 @)
% ( 0 <=>; 261 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 179 ( 179 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 13 con; 0-4 aty)
% Number of variables : 551 ( 22 ^; 492 !; 37 ?; 551 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Sledgehammer 2021-02-23 15:31:59.069
%------------------------------------------------------------------------------
% Could-be-implicit typings (6)
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__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
list_message_p_v: $tType ).
thf(ty_n_t__Set__Oset_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
set_message_p_v: $tType ).
thf(ty_n_t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
message_p_v: $tType ).
thf(ty_n_t__Nat__Onat,type,
nat: $tType ).
% Explicit typings (41)
thf(sy_c_AsynchronousSystem_Oconfiguration_Omsgs_001tf__p_001tf__v_001tf__s_001t__Product____Type__Ounit,type,
msgs_p1029620568t_unit: config256849571t_unit > message_p_v > nat ).
thf(sy_c_AsynchronousSystem_Oenabled_001tf__p_001tf__v_001tf__s,type,
enabled_p_v_s: config256849571t_unit > message_p_v > $o ).
thf(sy_c_Execution_Oexecution_OfirstOccurrence_001tf__p_001tf__v_001tf__s,type,
firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
thf(sy_c_Execution_Oexecution_OminimalEnabled_001tf__p_001tf__v_001tf__s,type,
minimalEnabled_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > $o ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
minus_minus_nat: nat > nat > nat ).
thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
one_one_nat: nat ).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
zero_zero_nat: nat ).
thf(sy_c_If_001t__Nat__Onat,type,
if_nat: $o > nat > nat > nat ).
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_List_Olast_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit ).
thf(sy_c_List_Olast_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
last_message_p_v: list_message_p_v > message_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_Otl_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
tl_con485597044t_unit: list_c1059388851t_unit > list_c1059388851t_unit ).
thf(sy_c_List_Olist_Otl_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
tl_message_p_v: list_message_p_v > list_message_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_Olist__ex_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
list_e581556831t_unit: ( config256849571t_unit > $o ) > list_c1059388851t_unit > $o ).
thf(sy_c_List_Olist__ex_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
list_ex_message_p_v: ( message_p_v > $o ) > list_message_p_v > $o ).
thf(sy_c_List_Onth_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit ).
thf(sy_c_List_Onth_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
nth_message_p_v: list_message_p_v > nat > message_p_v ).
thf(sy_c_List_Oremdups__adj_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
remdup949903207t_unit: list_c1059388851t_unit > list_c1059388851t_unit ).
thf(sy_c_List_Oremdups__adj_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
remdup74979931ge_p_v: list_message_p_v > list_message_p_v ).
thf(sy_c_Nat_OSuc,type,
suc: 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_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
ord_less_nat: nat > nat > $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__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
collect_message_p_v: ( message_p_v > $o ) > set_message_p_v ).
thf(sy_c_member_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
member_message_p_v: message_p_v > set_message_p_v > $o ).
thf(sy_v_consumedMsg____,type,
consumedMsg: message_p_v ).
thf(sy_v_fe____,type,
fe: nat > list_c1059388851t_unit ).
thf(sy_v_firstOccSet____,type,
firstOccSet: nat > set_message_p_v ).
thf(sy_v_ft____,type,
ft: nat > list_message_p_v ).
thf(sy_v_index____,type,
index: nat ).
thf(sy_v_msg____,type,
msg: message_p_v ).
thf(sy_v_n0____,type,
n0: nat ).
thf(sy_v_n1____,type,
n1: nat ).
thf(sy_v_nMsg____,type,
nMsg: nat ).
thf(sy_v_n____,type,
n: nat ).
% Relevant facts (258)
thf(fact_0_AssumpGreaterOccurrence_I1_J,axiom,
~ ( ord_less_nat @ nMsg @ n1 ) ).
% AssumpGreaterOccurrence(1)
thf(fact_1__092_060open_062nMsg_A_060_Alength_A_Ife_Aindex_J_092_060close_062,axiom,
ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ) ).
% \<open>nMsg < length (fe index)\<close>
thf(fact_2_NotEmpty_I2_J,axiom,
( ( fe @ index )
!= nil_co1338500125t_unit ) ).
% NotEmpty(2)
thf(fact_3_AssumptionFair_I2_J,axiom,
ord_less_nat @ n0 @ ( size_s1406904903t_unit @ ( fe @ n ) ) ).
% AssumptionFair(2)
thf(fact_4_length__induct,axiom,
! [P: list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit] :
( ! [Xs2: list_c1059388851t_unit] :
( ! [Ys: list_c1059388851t_unit] :
( ( ord_less_nat @ ( size_s1406904903t_unit @ Ys ) @ ( size_s1406904903t_unit @ Xs2 ) )
=> ( P @ Ys ) )
=> ( P @ Xs2 ) )
=> ( P @ Xs ) ) ).
% length_induct
thf(fact_5_length__induct,axiom,
! [P: list_message_p_v > $o,Xs: list_message_p_v] :
( ! [Xs2: list_message_p_v] :
( ! [Ys: list_message_p_v] :
( ( ord_less_nat @ ( size_s1168481041ge_p_v @ Ys ) @ ( size_s1168481041ge_p_v @ Xs2 ) )
=> ( P @ Ys ) )
=> ( P @ Xs2 ) )
=> ( P @ Xs ) ) ).
% length_induct
thf(fact_6_SameCfgOnLow,axiom,
! [I: nat] :
( ( ord_less_nat @ I @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
=> ( ( nth_co1649820636t_unit @ ( fe @ index ) @ I )
= ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ I ) ) ) ).
% SameCfgOnLow
thf(fact_7_Ex__list__of__length,axiom,
! [N: nat] :
? [Xs2: list_c1059388851t_unit] :
( ( size_s1406904903t_unit @ Xs2 )
= N ) ).
% Ex_list_of_length
thf(fact_8_Ex__list__of__length,axiom,
! [N: nat] :
? [Xs2: list_message_p_v] :
( ( size_s1168481041ge_p_v @ Xs2 )
= N ) ).
% Ex_list_of_length
thf(fact_9_neq__if__length__neq,axiom,
! [Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ Xs )
!= ( size_s1406904903t_unit @ Ys2 ) )
=> ( Xs != Ys2 ) ) ).
% neq_if_length_neq
thf(fact_10_neq__if__length__neq,axiom,
! [Xs: list_message_p_v,Ys2: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ Xs )
!= ( size_s1168481041ge_p_v @ Ys2 ) )
=> ( Xs != Ys2 ) ) ).
% neq_if_length_neq
thf(fact_11_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_12_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_13_nat__neq__iff,axiom,
! [M: nat,N: nat] :
( ( M != N )
= ( ( ord_less_nat @ M @ N )
| ( ord_less_nat @ N @ M ) ) ) ).
% nat_neq_iff
thf(fact_14_less__not__refl,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ N ) ).
% less_not_refl
thf(fact_15_less__not__refl2,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ N @ M )
=> ( M != N ) ) ).
% less_not_refl2
thf(fact_16_less__not__refl3,axiom,
! [S: nat,T: nat] :
( ( ord_less_nat @ S @ T )
=> ( S != T ) ) ).
% less_not_refl3
thf(fact_17_less__irrefl__nat,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ N ) ).
% less_irrefl_nat
thf(fact_18_nat_Oinject,axiom,
! [X2: nat,Y2: nat] :
( ( ( suc @ X2 )
= ( suc @ Y2 ) )
= ( X2 = Y2 ) ) ).
% nat.inject
thf(fact_19_old_Onat_Oinject,axiom,
! [Nat: nat,Nat2: nat] :
( ( ( suc @ Nat )
= ( suc @ Nat2 ) )
= ( Nat = Nat2 ) ) ).
% old.nat.inject
thf(fact_20_NotEmpty_I1_J,axiom,
( ( fe @ ( suc @ index ) )
!= nil_co1338500125t_unit ) ).
% NotEmpty(1)
thf(fact_21_Suc__less__eq,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
= ( ord_less_nat @ M @ N ) ) ).
% Suc_less_eq
thf(fact_22_Suc__mono,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% Suc_mono
thf(fact_23_lessI,axiom,
! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% lessI
thf(fact_24_Suc__inject,axiom,
! [X: nat,Y: nat] :
( ( ( suc @ X )
= ( suc @ Y ) )
=> ( X = Y ) ) ).
% Suc_inject
thf(fact_25_n__not__Suc__n,axiom,
! [N: nat] :
( N
!= ( suc @ N ) ) ).
% n_not_Suc_n
thf(fact_26_not__less__less__Suc__eq,axiom,
! [N: nat,M: nat] :
( ~ ( ord_less_nat @ N @ M )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
= ( N = M ) ) ) ).
% not_less_less_Suc_eq
thf(fact_27_strict__inc__induct,axiom,
! [I2: nat,J: nat,P: nat > $o] :
( ( ord_less_nat @ I2 @ J )
=> ( ! [I3: nat] :
( ( J
= ( suc @ I3 ) )
=> ( P @ I3 ) )
=> ( ! [I3: nat] :
( ( ord_less_nat @ I3 @ J )
=> ( ( P @ ( suc @ I3 ) )
=> ( P @ I3 ) ) )
=> ( P @ I2 ) ) ) ) ).
% strict_inc_induct
thf(fact_28_less__Suc__induct,axiom,
! [I2: nat,J: nat,P: nat > nat > $o] :
( ( ord_less_nat @ I2 @ J )
=> ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
=> ( ! [I3: nat,J2: nat,K: nat] :
( ( ord_less_nat @ I3 @ J2 )
=> ( ( ord_less_nat @ J2 @ K )
=> ( ( P @ I3 @ J2 )
=> ( ( P @ J2 @ K )
=> ( P @ I3 @ K ) ) ) ) )
=> ( P @ I2 @ J ) ) ) ) ).
% less_Suc_induct
thf(fact_29_less__trans__Suc,axiom,
! [I2: nat,J: nat,K2: nat] :
( ( ord_less_nat @ I2 @ J )
=> ( ( ord_less_nat @ J @ K2 )
=> ( ord_less_nat @ ( suc @ I2 ) @ K2 ) ) ) ).
% less_trans_Suc
thf(fact_30_Suc__less__SucD,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
=> ( ord_less_nat @ M @ N ) ) ).
% Suc_less_SucD
thf(fact_31_less__antisym,axiom,
! [N: nat,M: nat] :
( ~ ( ord_less_nat @ N @ M )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
=> ( M = N ) ) ) ).
% less_antisym
thf(fact_32_Suc__less__eq2,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ ( suc @ N ) @ M )
= ( ? [M2: nat] :
( ( M
= ( suc @ M2 ) )
& ( ord_less_nat @ N @ M2 ) ) ) ) ).
% Suc_less_eq2
thf(fact_33_All__less__Suc,axiom,
! [N: nat,P: nat > $o] :
( ( ! [I4: nat] :
( ( ord_less_nat @ I4 @ ( suc @ N ) )
=> ( P @ I4 ) ) )
= ( ( P @ N )
& ! [I4: nat] :
( ( ord_less_nat @ I4 @ N )
=> ( P @ I4 ) ) ) ) ).
% All_less_Suc
thf(fact_34_not__less__eq,axiom,
! [M: nat,N: nat] :
( ( ~ ( ord_less_nat @ M @ N ) )
= ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% not_less_eq
thf(fact_35_less__Suc__eq,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ( ord_less_nat @ M @ N )
| ( M = N ) ) ) ).
% less_Suc_eq
thf(fact_36_Ex__less__Suc,axiom,
! [N: nat,P: nat > $o] :
( ( ? [I4: nat] :
( ( ord_less_nat @ I4 @ ( suc @ N ) )
& ( P @ I4 ) ) )
= ( ( P @ N )
| ? [I4: nat] :
( ( ord_less_nat @ I4 @ N )
& ( P @ I4 ) ) ) ) ).
% Ex_less_Suc
thf(fact_37_less__SucI,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% less_SucI
thf(fact_38_less__SucE,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
=> ( ~ ( ord_less_nat @ M @ N )
=> ( M = N ) ) ) ).
% less_SucE
thf(fact_39_Suc__lessI,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ( ( suc @ M )
!= N )
=> ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% Suc_lessI
thf(fact_40_Suc__lessE,axiom,
! [I2: nat,K2: nat] :
( ( ord_less_nat @ ( suc @ I2 ) @ K2 )
=> ~ ! [J2: nat] :
( ( ord_less_nat @ I2 @ J2 )
=> ( K2
!= ( suc @ J2 ) ) ) ) ).
% Suc_lessE
thf(fact_41_Suc__lessD,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ N )
=> ( ord_less_nat @ M @ N ) ) ).
% Suc_lessD
thf(fact_42_Nat_OlessE,axiom,
! [I2: nat,K2: nat] :
( ( ord_less_nat @ I2 @ K2 )
=> ( ( K2
!= ( suc @ I2 ) )
=> ~ ! [J2: nat] :
( ( ord_less_nat @ I2 @ J2 )
=> ( K2
!= ( suc @ J2 ) ) ) ) ) ).
% Nat.lessE
thf(fact_43_list__eq__iff__nth__eq,axiom,
( ( ^ [Y3: list_c1059388851t_unit,Z: list_c1059388851t_unit] : Y3 = Z )
= ( ^ [Xs3: list_c1059388851t_unit,Ys3: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ Xs3 )
= ( size_s1406904903t_unit @ Ys3 ) )
& ! [I4: nat] :
( ( ord_less_nat @ I4 @ ( size_s1406904903t_unit @ Xs3 ) )
=> ( ( nth_co1649820636t_unit @ Xs3 @ I4 )
= ( nth_co1649820636t_unit @ Ys3 @ I4 ) ) ) ) ) ) ).
% list_eq_iff_nth_eq
thf(fact_44_list__eq__iff__nth__eq,axiom,
( ( ^ [Y3: list_message_p_v,Z: list_message_p_v] : Y3 = Z )
= ( ^ [Xs3: list_message_p_v,Ys3: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ Xs3 )
= ( size_s1168481041ge_p_v @ Ys3 ) )
& ! [I4: nat] :
( ( ord_less_nat @ I4 @ ( size_s1168481041ge_p_v @ Xs3 ) )
=> ( ( nth_message_p_v @ Xs3 @ I4 )
= ( nth_message_p_v @ Ys3 @ I4 ) ) ) ) ) ) ).
% list_eq_iff_nth_eq
thf(fact_45_Skolem__list__nth,axiom,
! [K2: nat,P: nat > config256849571t_unit > $o] :
( ( ! [I4: nat] :
( ( ord_less_nat @ I4 @ K2 )
=> ? [X3: config256849571t_unit] : ( P @ I4 @ X3 ) ) )
= ( ? [Xs3: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ Xs3 )
= K2 )
& ! [I4: nat] :
( ( ord_less_nat @ I4 @ K2 )
=> ( P @ I4 @ ( nth_co1649820636t_unit @ Xs3 @ I4 ) ) ) ) ) ) ).
% Skolem_list_nth
thf(fact_46_Skolem__list__nth,axiom,
! [K2: nat,P: nat > message_p_v > $o] :
( ( ! [I4: nat] :
( ( ord_less_nat @ I4 @ K2 )
=> ? [X3: message_p_v] : ( P @ I4 @ X3 ) ) )
= ( ? [Xs3: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ Xs3 )
= K2 )
& ! [I4: nat] :
( ( ord_less_nat @ I4 @ K2 )
=> ( P @ I4 @ ( nth_message_p_v @ Xs3 @ I4 ) ) ) ) ) ) ).
% Skolem_list_nth
thf(fact_47_nth__equalityI,axiom,
! [Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ Xs )
= ( size_s1406904903t_unit @ Ys2 ) )
=> ( ! [I3: nat] :
( ( ord_less_nat @ I3 @ ( size_s1406904903t_unit @ Xs ) )
=> ( ( nth_co1649820636t_unit @ Xs @ I3 )
= ( nth_co1649820636t_unit @ Ys2 @ I3 ) ) )
=> ( Xs = Ys2 ) ) ) ).
% nth_equalityI
thf(fact_48_nth__equalityI,axiom,
! [Xs: list_message_p_v,Ys2: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ Xs )
= ( size_s1168481041ge_p_v @ Ys2 ) )
=> ( ! [I3: nat] :
( ( ord_less_nat @ I3 @ ( size_s1168481041ge_p_v @ Xs ) )
=> ( ( nth_message_p_v @ Xs @ I3 )
= ( nth_message_p_v @ Ys2 @ I3 ) ) )
=> ( Xs = Ys2 ) ) ) ).
% nth_equalityI
thf(fact_49_lift__Suc__mono__less__iff,axiom,
! [F: nat > nat,N: nat,M: nat] :
( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
= ( ord_less_nat @ N @ M ) ) ) ).
% lift_Suc_mono_less_iff
thf(fact_50_mem__Collect__eq,axiom,
! [A: message_p_v,P: message_p_v > $o] :
( ( member_message_p_v @ A @ ( collect_message_p_v @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_51_Collect__mem__eq,axiom,
! [A2: set_message_p_v] :
( ( collect_message_p_v
@ ^ [X4: message_p_v] : ( member_message_p_v @ X4 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_52_Collect__cong,axiom,
! [P: message_p_v > $o,Q: message_p_v > $o] :
( ! [X5: message_p_v] :
( ( P @ X5 )
= ( Q @ X5 ) )
=> ( ( collect_message_p_v @ P )
= ( collect_message_p_v @ Q ) ) ) ).
% Collect_cong
thf(fact_53_lift__Suc__mono__less,axiom,
! [F: nat > nat,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_nat @ N @ N3 )
=> ( ord_less_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% lift_Suc_mono_less
thf(fact_54_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_55_infinite__descent,axiom,
! [P: nat > $o,N: nat] :
( ! [N2: nat] :
( ~ ( P @ N2 )
=> ? [M3: nat] :
( ( ord_less_nat @ M3 @ N2 )
& ~ ( P @ M3 ) ) )
=> ( P @ N ) ) ).
% infinite_descent
thf(fact_56_nat__less__induct,axiom,
! [P: nat > $o,N: nat] :
( ! [N2: nat] :
( ! [M3: nat] :
( ( ord_less_nat @ M3 @ N2 )
=> ( P @ M3 ) )
=> ( P @ N2 ) )
=> ( P @ N ) ) ).
% nat_less_induct
thf(fact_57_Subset,axiom,
! [MsgInSet: message_p_v] :
( ( member_message_p_v @ MsgInSet @ ( firstOccSet @ ( suc @ index ) ) )
=> ( member_message_p_v @ MsgInSet @ ( firstOccSet @ index ) ) ) ).
% Subset
thf(fact_58_IPrefixListEx,axiom,
! [I: nat] : ( prefix1615116500t_unit @ ( fe @ I ) @ ( fe @ ( suc @ I ) ) ) ).
% IPrefixListEx
thf(fact_59_AssumptionFair_I3_J,axiom,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ n0 ) @ msg ).
% AssumptionFair(3)
thf(fact_60_list__ex__length,axiom,
( list_e581556831t_unit
= ( ^ [P2: config256849571t_unit > $o,Xs3: list_c1059388851t_unit] :
? [N4: nat] :
( ( ord_less_nat @ N4 @ ( size_s1406904903t_unit @ Xs3 ) )
& ( P2 @ ( nth_co1649820636t_unit @ Xs3 @ N4 ) ) ) ) ) ).
% list_ex_length
thf(fact_61_list__ex__length,axiom,
( list_ex_message_p_v
= ( ^ [P2: message_p_v > $o,Xs3: list_message_p_v] :
? [N4: nat] :
( ( ord_less_nat @ N4 @ ( size_s1168481041ge_p_v @ Xs3 ) )
& ( P2 @ ( nth_message_p_v @ Xs3 @ N4 ) ) ) ) ) ).
% list_ex_length
thf(fact_62_AssumpGreaterOccurrence_I2_J,axiom,
firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ consumedMsg @ n1 ).
% AssumpGreaterOccurrence(2)
thf(fact_63_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_64_list__ex1__simps_I1_J,axiom,
! [P: config256849571t_unit > $o] :
~ ( list_e1598815642t_unit @ P @ nil_co1338500125t_unit ) ).
% list_ex1_simps(1)
thf(fact_65_LengthStep,axiom,
ord_less_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) ).
% LengthStep
thf(fact_66_remdups__adj__adjacent,axiom,
! [I2: nat,Xs: list_c1059388851t_unit] :
( ( ord_less_nat @ ( suc @ I2 ) @ ( size_s1406904903t_unit @ ( remdup949903207t_unit @ Xs ) ) )
=> ( ( nth_co1649820636t_unit @ ( remdup949903207t_unit @ Xs ) @ I2 )
!= ( nth_co1649820636t_unit @ ( remdup949903207t_unit @ Xs ) @ ( suc @ I2 ) ) ) ) ).
% remdups_adj_adjacent
thf(fact_67_remdups__adj__adjacent,axiom,
! [I2: nat,Xs: list_message_p_v] :
( ( ord_less_nat @ ( suc @ I2 ) @ ( size_s1168481041ge_p_v @ ( remdup74979931ge_p_v @ Xs ) ) )
=> ( ( nth_message_p_v @ ( remdup74979931ge_p_v @ Xs ) @ I2 )
!= ( nth_message_p_v @ ( remdup74979931ge_p_v @ Xs ) @ ( suc @ I2 ) ) ) ) ).
% remdups_adj_adjacent
thf(fact_68_nth__tl,axiom,
! [N: nat,Xs: list_c1059388851t_unit] :
( ( ord_less_nat @ N @ ( size_s1406904903t_unit @ ( tl_con485597044t_unit @ Xs ) ) )
=> ( ( nth_co1649820636t_unit @ ( tl_con485597044t_unit @ Xs ) @ N )
= ( nth_co1649820636t_unit @ Xs @ ( suc @ N ) ) ) ) ).
% nth_tl
thf(fact_69_nth__tl,axiom,
! [N: nat,Xs: list_message_p_v] :
( ( ord_less_nat @ N @ ( size_s1168481041ge_p_v @ ( tl_message_p_v @ Xs ) ) )
=> ( ( nth_message_p_v @ ( tl_message_p_v @ Xs ) @ N )
= ( nth_message_p_v @ Xs @ ( suc @ N ) ) ) ) ).
% nth_tl
thf(fact_70_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_71_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_72_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,N2: nat] :
( ( P @ Cfg @ FStepCfg @ FStepMsg @ N2 )
=> ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
=> ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
=> ( ! [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,N2: nat] :
( ( P @ Cfg @ FStepCfg @ FStepMsg @ N2 )
=> ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
=> ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
=> ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% infiniteExecutionCfg_infiniteExecutionMsg.induct(2)
thf(fact_73_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,A22: 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,N2: nat] :
( ( P @ Cfg @ FStepCfg @ FStepMsg @ N2 )
=> ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
=> ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
=> ( ! [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,N2: nat] :
( ( P @ Cfg @ FStepCfg @ FStepMsg @ N2 )
=> ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
=> ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
=> ( P @ A0 @ A1 @ A22 @ A3 ) ) ) ) ) ).
% infiniteExecutionCfg_infiniteExecutionMsg.induct(1)
thf(fact_74_AssumpGreaterOccurrence_I3_J,axiom,
firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg ).
% AssumpGreaterOccurrence(3)
thf(fact_75_ConsumedInSet,axiom,
member_message_p_v @ consumedMsg @ ( firstOccSet @ index ) ).
% ConsumedInSet
thf(fact_76_SameMsgOnLow,axiom,
! [I: nat] :
( ( ord_less_nat @ I @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
=> ( ( nth_message_p_v @ ( ft @ index ) @ I )
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I ) ) ) ).
% SameMsgOnLow
thf(fact_77_neq0__conv,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% neq0_conv
thf(fact_78_less__nat__zero__code,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% less_nat_zero_code
thf(fact_79_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_80_ConsumedMsg_I1_J,axiom,
minimalEnabled_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ consumedMsg ).
% ConsumedMsg(1)
thf(fact_81_remdups__adj__Nil__iff,axiom,
! [Xs: list_message_p_v] :
( ( ( remdup74979931ge_p_v @ Xs )
= nil_message_p_v )
= ( Xs = nil_message_p_v ) ) ).
% remdups_adj_Nil_iff
thf(fact_82_remdups__adj__Nil__iff,axiom,
! [Xs: list_c1059388851t_unit] :
( ( ( remdup949903207t_unit @ Xs )
= nil_co1338500125t_unit )
= ( Xs = nil_co1338500125t_unit ) ) ).
% remdups_adj_Nil_iff
thf(fact_83_list__ex__simps_I2_J,axiom,
! [P: message_p_v > $o] :
~ ( list_ex_message_p_v @ P @ nil_message_p_v ) ).
% list_ex_simps(2)
thf(fact_84_list__ex__simps_I2_J,axiom,
! [P: config256849571t_unit > $o] :
~ ( list_e581556831t_unit @ P @ nil_co1338500125t_unit ) ).
% list_ex_simps(2)
thf(fact_85_SmallIndex,axiom,
! [NMsg: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ NMsg )
=> ( ord_less_nat @ NMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ) ).
% SmallIndex
thf(fact_86_zero__less__Suc,axiom,
! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% zero_less_Suc
thf(fact_87_less__Suc0,axiom,
! [N: nat] :
( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
= ( N = zero_zero_nat ) ) ).
% less_Suc0
thf(fact_88_length__0__conv,axiom,
! [Xs: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ Xs )
= zero_zero_nat )
= ( Xs = nil_co1338500125t_unit ) ) ).
% length_0_conv
thf(fact_89_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_90_AssumptionFairContr,axiom,
! [N5: nat] :
( ( ord_less_eq_nat @ n @ N5 )
=> ! [N0: nat] :
( ( ord_less_nat @ N0 @ ( size_s1168481041ge_p_v @ ( ft @ N5 ) ) )
=> ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) @ N0 )
=> ( msg
!= ( nth_message_p_v @ ( ft @ N5 ) @ N0 ) ) ) ) ) ).
% AssumptionFairContr
thf(fact_91_AssumptionFirstOccSetDecrOrConsumed_I1_J,axiom,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ index ) ) @ msg ).
% AssumptionFirstOccSetDecrOrConsumed(1)
thf(fact_92_AssumptionCase1ImplThesis_H,axiom,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ n ) ) @ msg ).
% AssumptionCase1ImplThesis'
thf(fact_93_remdups__adj_Osimps_I1_J,axiom,
( ( remdup74979931ge_p_v @ nil_message_p_v )
= nil_message_p_v ) ).
% remdups_adj.simps(1)
thf(fact_94_remdups__adj_Osimps_I1_J,axiom,
( ( remdup949903207t_unit @ nil_co1338500125t_unit )
= nil_co1338500125t_unit ) ).
% remdups_adj.simps(1)
thf(fact_95_list_Osel_I2_J,axiom,
( ( tl_message_p_v @ nil_message_p_v )
= nil_message_p_v ) ).
% list.sel(2)
thf(fact_96_list_Osel_I2_J,axiom,
( ( tl_con485597044t_unit @ nil_co1338500125t_unit )
= nil_co1338500125t_unit ) ).
% list.sel(2)
thf(fact_97_not0__implies__Suc,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ? [M4: nat] :
( N
= ( suc @ M4 ) ) ) ).
% not0_implies_Suc
thf(fact_98_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_99_old_Onat_Oexhaust,axiom,
! [Y: nat] :
( ( Y != zero_zero_nat )
=> ~ ! [Nat3: nat] :
( Y
!= ( suc @ Nat3 ) ) ) ).
% old.nat.exhaust
thf(fact_100_Zero__not__Suc,axiom,
! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) ).
% Zero_not_Suc
thf(fact_101_Zero__neq__Suc,axiom,
! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) ).
% Zero_neq_Suc
thf(fact_102_Suc__neq__Zero,axiom,
! [M: nat] :
( ( suc @ M )
!= zero_zero_nat ) ).
% Suc_neq_Zero
thf(fact_103_zero__induct,axiom,
! [P: nat > $o,K2: nat] :
( ( P @ K2 )
=> ( ! [N2: nat] :
( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) )
=> ( P @ zero_zero_nat ) ) ) ).
% zero_induct
thf(fact_104_diff__induct,axiom,
! [P: nat > nat > $o,M: nat,N: nat] :
( ! [X5: nat] : ( P @ X5 @ zero_zero_nat )
=> ( ! [Y4: nat] : ( P @ zero_zero_nat @ ( suc @ Y4 ) )
=> ( ! [X5: nat,Y4: nat] :
( ( P @ X5 @ Y4 )
=> ( P @ ( suc @ X5 ) @ ( suc @ Y4 ) ) )
=> ( P @ M @ N ) ) ) ) ).
% diff_induct
thf(fact_105_nat__induct,axiom,
! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) )
=> ( P @ N ) ) ) ).
% nat_induct
thf(fact_106_nat_OdiscI,axiom,
! [Nat: nat,X2: nat] :
( ( Nat
= ( suc @ X2 ) )
=> ( Nat != zero_zero_nat ) ) ).
% nat.discI
thf(fact_107_old_Onat_Odistinct_I1_J,axiom,
! [Nat2: nat] :
( zero_zero_nat
!= ( suc @ Nat2 ) ) ).
% old.nat.distinct(1)
thf(fact_108_old_Onat_Odistinct_I2_J,axiom,
! [Nat2: nat] :
( ( suc @ Nat2 )
!= zero_zero_nat ) ).
% old.nat.distinct(2)
thf(fact_109_nat_Odistinct_I1_J,axiom,
! [X2: nat] :
( zero_zero_nat
!= ( suc @ X2 ) ) ).
% nat.distinct(1)
thf(fact_110_gr0I,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% gr0I
thf(fact_111_not__gr0,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) ).
% not_gr0
thf(fact_112_not__less0,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% not_less0
thf(fact_113_less__zeroE,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% less_zeroE
thf(fact_114_gr__implies__not0,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) ).
% gr_implies_not0
thf(fact_115_infinite__descent0,axiom,
! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ~ ( P @ N2 )
=> ? [M3: nat] :
( ( ord_less_nat @ M3 @ N2 )
& ~ ( P @ M3 ) ) ) )
=> ( P @ N ) ) ) ).
% infinite_descent0
thf(fact_116_bot__nat__0_Oextremum__strict,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% bot_nat_0.extremum_strict
thf(fact_117_less__Suc__eq__0__disj,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ( M = zero_zero_nat )
| ? [J3: nat] :
( ( M
= ( suc @ J3 ) )
& ( ord_less_nat @ J3 @ N ) ) ) ) ).
% less_Suc_eq_0_disj
thf(fact_118_gr0__implies__Suc,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ? [M4: nat] :
( N
= ( suc @ M4 ) ) ) ).
% gr0_implies_Suc
thf(fact_119_All__less__Suc2,axiom,
! [N: nat,P: nat > $o] :
( ( ! [I4: nat] :
( ( ord_less_nat @ I4 @ ( suc @ N ) )
=> ( P @ I4 ) ) )
= ( ( P @ zero_zero_nat )
& ! [I4: nat] :
( ( ord_less_nat @ I4 @ N )
=> ( P @ ( suc @ I4 ) ) ) ) ) ).
% All_less_Suc2
thf(fact_120_gr0__conv__Suc,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( ? [M5: nat] :
( N
= ( suc @ M5 ) ) ) ) ).
% gr0_conv_Suc
thf(fact_121_Ex__less__Suc2,axiom,
! [N: nat,P: nat > $o] :
( ( ? [I4: nat] :
( ( ord_less_nat @ I4 @ ( suc @ N ) )
& ( P @ I4 ) ) )
= ( ( P @ zero_zero_nat )
| ? [I4: nat] :
( ( ord_less_nat @ I4 @ N )
& ( P @ ( suc @ I4 ) ) ) ) ) ).
% Ex_less_Suc2
thf(fact_122_list_Osize_I3_J,axiom,
( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_123_list_Osize_I3_J,axiom,
( ( size_s1168481041ge_p_v @ nil_message_p_v )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_124_MinImplFirstOcc,axiom,
! [Msg: message_p_v] :
( ( minimalEnabled_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ Msg )
=> ( member_message_p_v @ Msg @ ( firstOccSet @ index ) ) ) ).
% MinImplFirstOcc
thf(fact_125_Case2ImplThesis,axiom,
( ? [N0: nat] :
( ( ord_less_eq_nat @ n0 @ N0 )
& ( ord_less_nat @ N0 @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) )
& ( ( nth_message_p_v @ ( ft @ n ) @ N0 )
= msg ) )
=> ? [N6: nat] :
( ( ord_less_eq_nat @ n @ N6 )
& ? [N02: nat] :
( ( ord_less_eq_nat @ n0 @ N02 )
& ( ord_less_nat @ N02 @ ( size_s1168481041ge_p_v @ ( ft @ N6 ) ) )
& ( msg
= ( nth_message_p_v @ ( ft @ N6 ) @ N02 ) ) ) ) ) ).
% Case2ImplThesis
thf(fact_126_MessageStaysOrConsumed,axiom,
! [N1: nat,N22: nat,N: nat,Msg2: message_p_v] :
( ( ( ord_less_eq_nat @ N1 @ N22 )
& ( ord_less_nat @ N22 @ ( size_s1406904903t_unit @ ( fe @ N ) ) )
& ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ N ) @ N1 ) @ Msg2 ) )
=> ( ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ N ) @ N22 ) @ Msg2 )
| ? [N02: nat] :
( ( ord_less_eq_nat @ N1 @ N02 )
& ( ord_less_nat @ N02 @ ( size_s1168481041ge_p_v @ ( ft @ N ) ) )
& ( ( nth_message_p_v @ ( ft @ N ) @ N02 )
= Msg2 ) ) ) ) ).
% MessageStaysOrConsumed
thf(fact_127_NotConsumedIntermediate,axiom,
! [I: nat] :
( ( ord_less_nat @ I @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
=> ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ I )
=> ( ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I )
!= msg ) ) ) ).
% NotConsumedIntermediate
thf(fact_128__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ift_A_ISuc_Aindex_J_J_O_Alength_A_Ift_Aindex_J_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062,axiom,
~ ? [I: nat] :
( ( ord_less_nat @ I @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
& ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ I )
& ( msg
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I ) ) ) ).
% \<open>\<not> (\<exists>i<length (ft (Suc index)). length (ft index) \<le> i \<and> msg = ft (Suc index) ! i)\<close>
thf(fact_129_Nitpick_Osize__list__simp_I2_J,axiom,
( size_s1406904903t_unit
= ( ^ [Xs3: list_c1059388851t_unit] : ( if_nat @ ( Xs3 = nil_co1338500125t_unit ) @ zero_zero_nat @ ( suc @ ( size_s1406904903t_unit @ ( tl_con485597044t_unit @ Xs3 ) ) ) ) ) ) ).
% Nitpick.size_list_simp(2)
thf(fact_130_Nitpick_Osize__list__simp_I2_J,axiom,
( size_s1168481041ge_p_v
= ( ^ [Xs3: list_message_p_v] : ( if_nat @ ( Xs3 = nil_message_p_v ) @ zero_zero_nat @ ( suc @ ( size_s1168481041ge_p_v @ ( tl_message_p_v @ Xs3 ) ) ) ) ) ) ).
% Nitpick.size_list_simp(2)
thf(fact_131_not__gr__zero,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) ).
% not_gr_zero
thf(fact_132_le__zero__eq,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) ).
% le_zero_eq
thf(fact_133_bot__nat__0_Oextremum,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% bot_nat_0.extremum
thf(fact_134_le0,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% le0
thf(fact_135_Suc__le__mono,axiom,
! [N: nat,M: nat] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
= ( ord_less_eq_nat @ N @ M ) ) ).
% Suc_le_mono
thf(fact_136_EnabledInSuc,axiom,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msg ).
% EnabledInSuc
thf(fact_137_MinImplAllBigger,axiom,
! [Msg: message_p_v] :
( ( minimalEnabled_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ Msg )
=> ? [OccM: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ Msg @ OccM )
& ! [Msg3: message_p_v,OccM2: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ Msg3 @ OccM2 )
=> ( ord_less_eq_nat @ OccM @ OccM2 ) ) ) ) ).
% MinImplAllBigger
thf(fact_138_last__remdups__adj,axiom,
! [Xs: list_message_p_v] :
( ( last_message_p_v @ ( remdup74979931ge_p_v @ Xs ) )
= ( last_message_p_v @ Xs ) ) ).
% last_remdups_adj
thf(fact_139_last__remdups__adj,axiom,
! [Xs: list_c1059388851t_unit] :
( ( last_c571238084t_unit @ ( remdup949903207t_unit @ Xs ) )
= ( last_c571238084t_unit @ Xs ) ) ).
% last_remdups_adj
thf(fact_140_EnabledOrConsumedAtLast,axiom,
( ( enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ n ) ) @ msg )
| ? [N02: nat] :
( ( ord_less_eq_nat @ n0 @ N02 )
& ( ord_less_nat @ N02 @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) )
& ( ( nth_message_p_v @ ( ft @ n ) @ N02 )
= msg ) ) ) ).
% EnabledOrConsumedAtLast
thf(fact_141_zero__le,axiom,
! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% zero_le
thf(fact_142_lift__Suc__antimono__le,axiom,
! [F: nat > nat,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% lift_Suc_antimono_le
thf(fact_143_lift__Suc__mono__le,axiom,
! [F: nat > nat,N: nat,N3: nat] :
( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_eq_nat @ N @ N3 )
=> ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% lift_Suc_mono_le
thf(fact_144_Nat_Oex__has__greatest__nat,axiom,
! [P: nat > $o,K2: nat,B: nat] :
( ( P @ K2 )
=> ( ! [Y4: nat] :
( ( P @ Y4 )
=> ( ord_less_eq_nat @ Y4 @ B ) )
=> ? [X5: nat] :
( ( P @ X5 )
& ! [Y5: nat] :
( ( P @ Y5 )
=> ( ord_less_eq_nat @ Y5 @ X5 ) ) ) ) ) ).
% Nat.ex_has_greatest_nat
thf(fact_145_nat__le__linear,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
| ( ord_less_eq_nat @ N @ M ) ) ).
% nat_le_linear
thf(fact_146_le__antisym,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( ord_less_eq_nat @ N @ M )
=> ( M = N ) ) ) ).
% le_antisym
thf(fact_147_eq__imp__le,axiom,
! [M: nat,N: nat] :
( ( M = N )
=> ( ord_less_eq_nat @ M @ N ) ) ).
% eq_imp_le
thf(fact_148_le__trans,axiom,
! [I2: nat,J: nat,K2: nat] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( ord_less_eq_nat @ J @ K2 )
=> ( ord_less_eq_nat @ I2 @ K2 ) ) ) ).
% le_trans
thf(fact_149_le__refl,axiom,
! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% le_refl
thf(fact_150_bot__nat__0_Oextremum__uniqueI,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ) ).
% bot_nat_0.extremum_uniqueI
thf(fact_151_bot__nat__0_Oextremum__unique,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ) ).
% bot_nat_0.extremum_unique
thf(fact_152_le__0__eq,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) ).
% le_0_eq
thf(fact_153_less__eq__nat_Osimps_I1_J,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% less_eq_nat.simps(1)
thf(fact_154_Suc__leD,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
=> ( ord_less_eq_nat @ M @ N ) ) ).
% Suc_leD
thf(fact_155_le__SucE,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ ( suc @ N ) )
=> ( ~ ( ord_less_eq_nat @ M @ N )
=> ( M
= ( suc @ N ) ) ) ) ).
% le_SucE
thf(fact_156_le__SucI,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% le_SucI
thf(fact_157_Suc__le__D,axiom,
! [N: nat,M6: nat] :
( ( ord_less_eq_nat @ ( suc @ N ) @ M6 )
=> ? [M4: nat] :
( M6
= ( suc @ M4 ) ) ) ).
% Suc_le_D
thf(fact_158_le__Suc__eq,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ ( suc @ N ) )
= ( ( ord_less_eq_nat @ M @ N )
| ( M
= ( suc @ N ) ) ) ) ).
% le_Suc_eq
thf(fact_159_Suc__n__not__le__n,axiom,
! [N: nat] :
~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% Suc_n_not_le_n
thf(fact_160_not__less__eq__eq,axiom,
! [M: nat,N: nat] :
( ( ~ ( ord_less_eq_nat @ M @ N ) )
= ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% not_less_eq_eq
thf(fact_161_full__nat__induct,axiom,
! [P: nat > $o,N: nat] :
( ! [N2: nat] :
( ! [M3: nat] :
( ( ord_less_eq_nat @ ( suc @ M3 ) @ N2 )
=> ( P @ M3 ) )
=> ( P @ N2 ) )
=> ( P @ N ) ) ).
% full_nat_induct
thf(fact_162_nat__induct__at__least,axiom,
! [M: nat,N: nat,P: nat > $o] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( P @ M )
=> ( ! [N2: nat] :
( ( ord_less_eq_nat @ M @ N2 )
=> ( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) ) )
=> ( P @ N ) ) ) ) ).
% nat_induct_at_least
thf(fact_163_transitive__stepwise__le,axiom,
! [M: nat,N: nat,R: nat > nat > $o] :
( ( ord_less_eq_nat @ M @ N )
=> ( ! [X5: nat] : ( R @ X5 @ X5 )
=> ( ! [X5: nat,Y4: nat,Z2: nat] :
( ( R @ X5 @ Y4 )
=> ( ( R @ Y4 @ Z2 )
=> ( R @ X5 @ Z2 ) ) )
=> ( ! [N2: nat] : ( R @ N2 @ ( suc @ N2 ) )
=> ( R @ M @ N ) ) ) ) ) ).
% transitive_stepwise_le
thf(fact_164_less__mono__imp__le__mono,axiom,
! [F: nat > nat,I2: nat,J: nat] :
( ! [I3: nat,J2: nat] :
( ( ord_less_nat @ I3 @ J2 )
=> ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
=> ( ( ord_less_eq_nat @ I2 @ J )
=> ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% less_mono_imp_le_mono
thf(fact_165_le__neq__implies__less,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( M != N )
=> ( ord_less_nat @ M @ N ) ) ) ).
% le_neq_implies_less
thf(fact_166_less__or__eq__imp__le,axiom,
! [M: nat,N: nat] :
( ( ( ord_less_nat @ M @ N )
| ( M = N ) )
=> ( ord_less_eq_nat @ M @ N ) ) ).
% less_or_eq_imp_le
thf(fact_167_le__eq__less__or__eq,axiom,
( ord_less_eq_nat
= ( ^ [M5: nat,N4: nat] :
( ( ord_less_nat @ M5 @ N4 )
| ( M5 = N4 ) ) ) ) ).
% le_eq_less_or_eq
thf(fact_168_less__imp__le__nat,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ N ) ) ).
% less_imp_le_nat
thf(fact_169_nat__less__le,axiom,
( ord_less_nat
= ( ^ [M5: nat,N4: nat] :
( ( ord_less_eq_nat @ M5 @ N4 )
& ( M5 != N4 ) ) ) ) ).
% nat_less_le
thf(fact_170_ex__least__nat__le,axiom,
! [P: nat > $o,N: nat] :
( ( P @ N )
=> ( ~ ( P @ zero_zero_nat )
=> ? [K: nat] :
( ( ord_less_eq_nat @ K @ N )
& ! [I: nat] :
( ( ord_less_nat @ I @ K )
=> ~ ( P @ I ) )
& ( P @ K ) ) ) ) ).
% ex_least_nat_le
thf(fact_171_Suc__leI,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% Suc_leI
thf(fact_172_Suc__le__eq,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
= ( ord_less_nat @ M @ N ) ) ).
% Suc_le_eq
thf(fact_173_dec__induct,axiom,
! [I2: nat,J: nat,P: nat > $o] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( P @ I2 )
=> ( ! [N2: nat] :
( ( ord_less_eq_nat @ I2 @ N2 )
=> ( ( ord_less_nat @ N2 @ J )
=> ( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) ) ) )
=> ( P @ J ) ) ) ) ).
% dec_induct
thf(fact_174_inc__induct,axiom,
! [I2: nat,J: nat,P: nat > $o] :
( ( ord_less_eq_nat @ I2 @ J )
=> ( ( P @ J )
=> ( ! [N2: nat] :
( ( ord_less_eq_nat @ I2 @ N2 )
=> ( ( ord_less_nat @ N2 @ J )
=> ( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) ) ) )
=> ( P @ I2 ) ) ) ) ).
% inc_induct
thf(fact_175_Suc__le__lessD,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
=> ( ord_less_nat @ M @ N ) ) ).
% Suc_le_lessD
thf(fact_176_le__less__Suc__eq,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
= ( N = M ) ) ) ).
% le_less_Suc_eq
thf(fact_177_less__Suc__eq__le,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ord_less_eq_nat @ M @ N ) ) ).
% less_Suc_eq_le
thf(fact_178_less__eq__Suc__le,axiom,
( ord_less_nat
= ( ^ [N4: nat] : ( ord_less_eq_nat @ ( suc @ N4 ) ) ) ) ).
% less_eq_Suc_le
thf(fact_179_le__imp__less__Suc,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% le_imp_less_Suc
thf(fact_180_remdups__adj__length,axiom,
! [Xs: list_c1059388851t_unit] : ( ord_less_eq_nat @ ( size_s1406904903t_unit @ ( remdup949903207t_unit @ Xs ) ) @ ( size_s1406904903t_unit @ Xs ) ) ).
% remdups_adj_length
thf(fact_181_remdups__adj__length,axiom,
! [Xs: list_message_p_v] : ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( remdup74979931ge_p_v @ Xs ) ) @ ( size_s1168481041ge_p_v @ Xs ) ) ).
% remdups_adj_length
thf(fact_182_last__tl,axiom,
! [Xs: list_message_p_v] :
( ( ( Xs = nil_message_p_v )
| ( ( tl_message_p_v @ Xs )
!= nil_message_p_v ) )
=> ( ( last_message_p_v @ ( tl_message_p_v @ Xs ) )
= ( last_message_p_v @ Xs ) ) ) ).
% last_tl
thf(fact_183_last__tl,axiom,
! [Xs: list_c1059388851t_unit] :
( ( ( Xs = nil_co1338500125t_unit )
| ( ( tl_con485597044t_unit @ Xs )
!= nil_co1338500125t_unit ) )
=> ( ( last_c571238084t_unit @ ( tl_con485597044t_unit @ Xs ) )
= ( last_c571238084t_unit @ Xs ) ) ) ).
% last_tl
thf(fact_184_ex__least__nat__less,axiom,
! [P: nat > $o,N: nat] :
( ( P @ N )
=> ( ~ ( P @ zero_zero_nat )
=> ? [K: nat] :
( ( ord_less_nat @ K @ N )
& ! [I: nat] :
( ( ord_less_eq_nat @ I @ K )
=> ~ ( P @ I ) )
& ( P @ ( suc @ K ) ) ) ) ) ).
% ex_least_nat_less
thf(fact_185_zero__reorient,axiom,
! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ) ).
% zero_reorient
thf(fact_186_remdups__adj__length__ge1,axiom,
! [Xs: list_c1059388851t_unit] :
( ( Xs != nil_co1338500125t_unit )
=> ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_s1406904903t_unit @ ( remdup949903207t_unit @ Xs ) ) ) ) ).
% remdups_adj_length_ge1
thf(fact_187_remdups__adj__length__ge1,axiom,
! [Xs: list_message_p_v] :
( ( Xs != nil_message_p_v )
=> ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_s1168481041ge_p_v @ ( remdup74979931ge_p_v @ Xs ) ) ) ) ).
% remdups_adj_length_ge1
thf(fact_188_zero__less__iff__neq__zero,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ) ).
% zero_less_iff_neq_zero
thf(fact_189_gr__implies__not__zero,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) ).
% gr_implies_not_zero
thf(fact_190_not__less__zero,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% not_less_zero
thf(fact_191_gr__zeroI,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% gr_zeroI
thf(fact_192_LastOfIndex,axiom,
( ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) )
= ( last_c571238084t_unit @ ( fe @ index ) ) ) ).
% LastOfIndex
thf(fact_193__092_060open_062_092_060And_062n0_Amsg_O_A_092_060forall_062n_O_Aexecution_OfirstOccurrence_A_Ife_An_J_A_Ift_An_J_Amsg_An0_A_092_060longrightarrow_062_Amsg_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062,axiom,
! [Msg2: message_p_v,N03: nat,N7: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ N7 ) @ ( ft @ N7 ) @ Msg2 @ N03 )
=> ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ ( last_c571238084t_unit @ ( fe @ N7 ) ) @ Msg2 ) ) ) ).
% \<open>\<And>n0 msg. \<forall>n. execution.firstOccurrence (fe n) (ft n) msg n0 \<longrightarrow> msg \<in># msgs (last (fe n))\<close>
thf(fact_194__092_060open_062_092_060forall_062n_O_A_092_060forall_062msg_H_092_060in_062firstOccSet_An_O_Amsg_H_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062,axiom,
! [N7: nat,X6: message_p_v] :
( ( member_message_p_v @ X6 @ ( firstOccSet @ N7 ) )
=> ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ ( last_c571238084t_unit @ ( fe @ N7 ) ) @ X6 ) ) ) ).
% \<open>\<forall>n. \<forall>msg'\<in>firstOccSet n. msg' \<in># msgs (last (fe n))\<close>
thf(fact_195_PrefixSameOnLow,axiom,
! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ L1 @ L2 )
=> ! [Index: nat] :
( ( ord_less_nat @ Index @ ( size_s1406904903t_unit @ L1 ) )
=> ( ( nth_co1649820636t_unit @ L1 @ Index )
= ( nth_co1649820636t_unit @ L2 @ Index ) ) ) ) ).
% PrefixSameOnLow
thf(fact_196_PrefixSameOnLow,axiom,
! [L1: list_message_p_v,L2: list_message_p_v] :
( ( prefix47729710ge_p_v @ L1 @ L2 )
=> ! [Index: nat] :
( ( ord_less_nat @ Index @ ( size_s1168481041ge_p_v @ L1 ) )
=> ( ( nth_message_p_v @ L1 @ Index )
= ( nth_message_p_v @ L2 @ Index ) ) ) ) ).
% PrefixSameOnLow
thf(fact_197_IPrefixList,axiom,
! [I: nat] : ( prefix47729710ge_p_v @ ( ft @ I ) @ ( ft @ ( suc @ I ) ) ) ).
% IPrefixList
thf(fact_198_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ) ).
% cancel_comm_monoid_add_class.diff_cancel
thf(fact_199_diff__zero,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ) ).
% diff_zero
thf(fact_200_zero__diff,axiom,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ) ).
% zero_diff
thf(fact_201_diff__0__eq__0,axiom,
! [N: nat] :
( ( minus_minus_nat @ zero_zero_nat @ N )
= zero_zero_nat ) ).
% diff_0_eq_0
thf(fact_202_diff__self__eq__0,axiom,
! [M: nat] :
( ( minus_minus_nat @ M @ M )
= zero_zero_nat ) ).
% diff_self_eq_0
thf(fact_203_Suc__diff__diff,axiom,
! [M: nat,N: nat,K2: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K2 ) )
= ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K2 ) ) ).
% Suc_diff_diff
thf(fact_204_diff__Suc__Suc,axiom,
! [M: nat,N: nat] :
( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
= ( minus_minus_nat @ M @ N ) ) ).
% diff_Suc_Suc
thf(fact_205_diff__diff__cancel,axiom,
! [I2: nat,N: nat] :
( ( ord_less_eq_nat @ I2 @ N )
=> ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I2 ) )
= I2 ) ) ).
% diff_diff_cancel
thf(fact_206_zero__less__diff,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
= ( ord_less_nat @ M @ N ) ) ).
% zero_less_diff
thf(fact_207_diff__is__0__eq_H,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( minus_minus_nat @ M @ N )
= zero_zero_nat ) ) ).
% diff_is_0_eq'
thf(fact_208_diff__is__0__eq,axiom,
! [M: nat,N: nat] :
( ( ( minus_minus_nat @ M @ N )
= zero_zero_nat )
= ( ord_less_eq_nat @ M @ N ) ) ).
% diff_is_0_eq
thf(fact_209_Suc__pred,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
= N ) ) ).
% Suc_pred
thf(fact_210_diff__right__commute,axiom,
! [A: nat,C: nat,B: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% diff_right_commute
thf(fact_211_diff__le__mono2,axiom,
! [M: nat,N: nat,L: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% diff_le_mono2
thf(fact_212_le__diff__iff_H,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ A @ C )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
= ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% le_diff_iff'
thf(fact_213_diff__le__self,axiom,
! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% diff_le_self
thf(fact_214_diff__le__mono,axiom,
! [M: nat,N: nat,L: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% diff_le_mono
thf(fact_215_Nat_Odiff__diff__eq,axiom,
! [K2: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K2 @ M )
=> ( ( ord_less_eq_nat @ K2 @ N )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K2 ) @ ( minus_minus_nat @ N @ K2 ) )
= ( minus_minus_nat @ M @ N ) ) ) ) ).
% Nat.diff_diff_eq
thf(fact_216_le__diff__iff,axiom,
! [K2: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K2 @ M )
=> ( ( ord_less_eq_nat @ K2 @ N )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K2 ) @ ( minus_minus_nat @ N @ K2 ) )
= ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% le_diff_iff
thf(fact_217_eq__diff__iff,axiom,
! [K2: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K2 @ M )
=> ( ( ord_less_eq_nat @ K2 @ N )
=> ( ( ( minus_minus_nat @ M @ K2 )
= ( minus_minus_nat @ N @ K2 ) )
= ( M = N ) ) ) ) ).
% eq_diff_iff
thf(fact_218_minus__nat_Odiff__0,axiom,
! [M: nat] :
( ( minus_minus_nat @ M @ zero_zero_nat )
= M ) ).
% minus_nat.diff_0
thf(fact_219_diffs0__imp__equal,axiom,
! [M: nat,N: nat] :
( ( ( minus_minus_nat @ M @ N )
= zero_zero_nat )
=> ( ( ( minus_minus_nat @ N @ M )
= zero_zero_nat )
=> ( M = N ) ) ) ).
% diffs0_imp_equal
thf(fact_220_zero__induct__lemma,axiom,
! [P: nat > $o,K2: nat,I2: nat] :
( ( P @ K2 )
=> ( ! [N2: nat] :
( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) )
=> ( P @ ( minus_minus_nat @ K2 @ I2 ) ) ) ) ).
% zero_induct_lemma
thf(fact_221_less__imp__diff__less,axiom,
! [J: nat,K2: nat,N: nat] :
( ( ord_less_nat @ J @ K2 )
=> ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K2 ) ) ).
% less_imp_diff_less
thf(fact_222_diff__less__mono2,axiom,
! [M: nat,N: nat,L: nat] :
( ( ord_less_nat @ M @ N )
=> ( ( ord_less_nat @ M @ L )
=> ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% diff_less_mono2
thf(fact_223_diff__commute,axiom,
! [I2: nat,J: nat,K2: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K2 )
= ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K2 ) @ J ) ) ).
% diff_commute
thf(fact_224_diff__less,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_nat @ zero_zero_nat @ M )
=> ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% diff_less
thf(fact_225_diff__less__Suc,axiom,
! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% diff_less_Suc
thf(fact_226_Suc__diff__Suc,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ N @ M )
=> ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
= ( minus_minus_nat @ M @ N ) ) ) ).
% Suc_diff_Suc
thf(fact_227_Suc__diff__le,axiom,
! [N: nat,M: nat] :
( ( ord_less_eq_nat @ N @ M )
=> ( ( minus_minus_nat @ ( suc @ M ) @ N )
= ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% Suc_diff_le
thf(fact_228_less__diff__iff,axiom,
! [K2: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K2 @ M )
=> ( ( ord_less_eq_nat @ K2 @ N )
=> ( ( ord_less_nat @ ( minus_minus_nat @ M @ K2 ) @ ( minus_minus_nat @ N @ K2 ) )
= ( ord_less_nat @ M @ N ) ) ) ) ).
% less_diff_iff
thf(fact_229_diff__less__mono,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% diff_less_mono
thf(fact_230_diff__Suc__less,axiom,
! [N: nat,I2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I2 ) ) @ N ) ) ).
% diff_Suc_less
thf(fact_231_MinPredicate,axiom,
! [P: nat > $o] :
( ? [X_1: nat] : ( P @ X_1 )
=> ? [N04: nat] :
( ( P @ N04 )
& ! [N5: nat] :
( ( P @ N5 )
=> ( ord_less_eq_nat @ N04 @ N5 ) ) ) ) ).
% MinPredicate
thf(fact_232_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_233_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_234_KeepProperty,axiom,
! [Low: nat,P: nat > $o,Q: nat > $o] :
( ! [I3: nat] :
( ( ord_less_eq_nat @ Low @ I3 )
=> ( ( P @ I3 )
=> ( ( P @ ( suc @ I3 ) )
& ( Q @ I3 ) ) ) )
=> ( ( P @ Low )
=> ! [I: nat] :
( ( ord_less_eq_nat @ Low @ I )
=> ( Q @ I ) ) ) ) ).
% KeepProperty
thf(fact_235_NatPredicateTippingPoint,axiom,
! [N22: nat,Pr: nat > $o] :
( ( ord_less_nat @ zero_zero_nat @ N22 )
=> ( ( Pr @ zero_zero_nat )
=> ( ~ ( Pr @ N22 )
=> ? [N2: nat] :
( ( ord_less_nat @ N2 @ N22 )
& ( Pr @ N2 )
& ~ ( Pr @ ( suc @ N2 ) ) ) ) ) ) ).
% NatPredicateTippingPoint
thf(fact_236_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_237_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_238_EnabledOrConsumed,axiom,
( ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ) @ msg )
| ? [N02: nat] :
( ( ord_less_eq_nat @ n0 @ N02 )
& ( ord_less_nat @ N02 @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) )
& ( ( nth_message_p_v @ ( ft @ n ) @ N02 )
= msg ) ) ) ).
% EnabledOrConsumed
thf(fact_239__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_O_Alength_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062,axiom,
~ ? [I: nat] :
( ( ord_less_nat @ I @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) )
& ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ I )
& ( msg
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I ) ) ) ).
% \<open>\<not> (\<exists>i<length (fe (Suc index)) - 1. length (fe index) - 1 \<le> i \<and> msg = ft (Suc index) ! i)\<close>
thf(fact_240_EnabledIntermediate,axiom,
! [I: nat] :
( ( ord_less_nat @ I @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ I )
=> ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ I ) @ msg ) ) ) ).
% EnabledIntermediate
thf(fact_241__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Alength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_092_060close_062,axiom,
ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) ).
% \<open>length (fe index) - 1 \<le> length (fe (Suc index)) - 1\<close>
thf(fact_242_less__one,axiom,
! [N: nat] :
( ( ord_less_nat @ N @ one_one_nat )
= ( N = zero_zero_nat ) ) ).
% less_one
thf(fact_243__092_060open_062enabled_A_Ife_A_ISuc_Aindex_J_A_B_A_Ilength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_J_J_Amsg_092_060close_062,axiom,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) ) @ msg ).
% \<open>enabled (fe (Suc index) ! (length (fe (Suc index)) - 1)) msg\<close>
thf(fact_244_diff__Suc__1,axiom,
! [N: nat] :
( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
= N ) ).
% diff_Suc_1
thf(fact_245_length__tl,axiom,
! [Xs: list_c1059388851t_unit] :
( ( size_s1406904903t_unit @ ( tl_con485597044t_unit @ Xs ) )
= ( minus_minus_nat @ ( size_s1406904903t_unit @ Xs ) @ one_one_nat ) ) ).
% length_tl
thf(fact_246_length__tl,axiom,
! [Xs: list_message_p_v] :
( ( size_s1168481041ge_p_v @ ( tl_message_p_v @ Xs ) )
= ( minus_minus_nat @ ( size_s1168481041ge_p_v @ Xs ) @ one_one_nat ) ) ).
% length_tl
thf(fact_247_Suc__diff__1,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
= N ) ) ).
% Suc_diff_1
thf(fact_248_one__reorient,axiom,
! [X: nat] :
( ( one_one_nat = X )
= ( X = one_one_nat ) ) ).
% one_reorient
thf(fact_249_One__nat__def,axiom,
( one_one_nat
= ( suc @ zero_zero_nat ) ) ).
% One_nat_def
thf(fact_250_MinPredicate2,axiom,
! [P: nat > $o] :
( ? [X_1: nat] : ( P @ X_1 )
=> ? [N04: nat] :
( ( P @ N04 )
& ( ( N04 = zero_zero_nat )
| ~ ( P @ ( minus_minus_nat @ N04 @ one_one_nat ) ) ) ) ) ).
% MinPredicate2
thf(fact_251_diff__Suc__eq__diff__pred,axiom,
! [M: nat,N: nat] :
( ( minus_minus_nat @ M @ ( suc @ N ) )
= ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% diff_Suc_eq_diff_pred
thf(fact_252_nat__induct__non__zero,axiom,
! [N: nat,P: nat > $o] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( P @ one_one_nat )
=> ( ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) ) )
=> ( P @ N ) ) ) ) ).
% nat_induct_non_zero
thf(fact_253_Suc__pred_H,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( N
= ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% Suc_pred'
thf(fact_254_Suc__diff__eq__diff__pred,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( minus_minus_nat @ ( suc @ M ) @ N )
= ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% Suc_diff_eq_diff_pred
thf(fact_255_last__conv__nth,axiom,
! [Xs: list_c1059388851t_unit] :
( ( Xs != nil_co1338500125t_unit )
=> ( ( last_c571238084t_unit @ Xs )
= ( nth_co1649820636t_unit @ Xs @ ( minus_minus_nat @ ( size_s1406904903t_unit @ Xs ) @ one_one_nat ) ) ) ) ).
% last_conv_nth
thf(fact_256_last__conv__nth,axiom,
! [Xs: list_message_p_v] :
( ( Xs != nil_message_p_v )
=> ( ( last_message_p_v @ Xs )
= ( nth_message_p_v @ Xs @ ( minus_minus_nat @ ( size_s1168481041ge_p_v @ Xs ) @ one_one_nat ) ) ) ) ).
% last_conv_nth
thf(fact_257_enabled__def,axiom,
( enabled_p_v_s
= ( ^ [Cfg2: config256849571t_unit,Msg4: message_p_v] : ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ Cfg2 @ Msg4 ) ) ) ) ).
% enabled_def
% Helper facts (3)
thf(help_If_3_1_If_001t__Nat__Onat_T,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ) ).
thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
! [X: nat,Y: nat] :
( ( if_nat @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
! [X: nat,Y: nat] :
( ( if_nat @ $true @ X @ Y )
= X ) ).
% Conjectures (1)
thf(conj_0,conjecture,
ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ).
%------------------------------------------------------------------------------