TPTP Problem File: SLH0790^1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SLH0000^1 : TPTP v8.2.0. Released v8.2.0.
% Domain : Archive of Formal Proofs
% Problem :
% Version : Especial.
% English :
% Refs : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source : [Des23]
% Names : IMP_Compiler_Reuse/0006_Compiler2/prob_00449_022881__6182458_1 [Des23]
% Status : Theorem
% Rating : ? v8.2.0
% Syntax : Number of formulae : 1466 ( 722 unt; 202 typ; 0 def)
% Number of atoms : 3192 (2046 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 10823 ( 442 ~; 46 |; 322 &;8836 @)
% ( 0 <=>;1177 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Number of types : 37 ( 36 usr)
% Number of type conns : 840 ( 840 >; 0 *; 0 +; 0 <<)
% Number of symbols : 169 ( 166 usr; 24 con; 0-4 aty)
% Number of variables : 3829 ( 103 ^;3460 !; 266 ?;3829 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2023-01-18 16:52:47.629
%------------------------------------------------------------------------------
% Could-be-implicit typings (36)
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thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
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thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
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thf(sy_c_String_Ochar_Osize__char,type,
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thf(sy_c_member_001t__Int__Oint,type,
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thf(sy_c_member_001t__List__Olist_It__String__Ochar_J,type,
member_list_char: list_char > set_list_char > $o ).
thf(sy_c_member_001t__Nat__Onat,type,
member_nat: nat > set_nat > $o ).
thf(sy_v_P,type,
p: list_instr ).
thf(sy_v_cfsa____,type,
cfsa: list_P419547167332244514st_int ).
thf(sy_v_pc_H_H____,type,
pc: int ).
thf(sy_v_pc_H____,type,
pc2: int ).
thf(sy_v_pc____,type,
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thf(sy_v_s_H_H____,type,
s: list_char > int ).
thf(sy_v_s_H____,type,
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thf(sy_v_s____,type,
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thf(sy_v_stk_H_H____,type,
stk: list_int ).
thf(sy_v_stk_H____,type,
stk2: list_int ).
thf(sy_v_stk____,type,
stk3: list_int ).
% Relevant facts (1256)
thf(fact_0_C,axiom,
( ( ord_less_eq_nat @ ( msp @ p @ pc2 ) @ ( minus_minus_nat @ ( size_size_list_int @ stk2 ) @ ( size_size_list_int @ stk3 ) ) )
& ( ord_less_eq_nat @ ( size_size_list_int @ stk3 ) @ ( size_size_list_int @ stk2 ) ) ) ).
% C
thf(fact_1__092_060open_062to__m__prog_AP_A_092_060_094bold_062_092_060turnstile_062_A_Ipc_M_Ato__m__state_A_Ivars_AP_J_As_M_A0_J_A_092_060_094bold_062_092_060rightarrow_062_092_060_094bold_062_K_A_Ipc_H_M_Aadd__m__stack_A_Ilength_Astk_H_A_N_Alength_Astk_J_Astk_H_A_Ito__m__state_A_Ivars_AP_J_As_H_J_M_Alength_Astk_H_A_N_Alength_Astk_J_092_060close_062,axiom,
star_P5461765526710342210nt_nat @ ( m_exec1 @ ( to_m_prog @ p ) ) @ ( produc8342123264692915235nt_nat @ pc3 @ ( produc2630796075472406112nt_nat @ ( to_m_state @ ( vars @ p ) @ s3 ) @ zero_zero_nat ) ) @ ( produc8342123264692915235nt_nat @ pc2 @ ( produc2630796075472406112nt_nat @ ( add_m_stack @ ( minus_minus_nat @ ( size_size_list_int @ stk2 ) @ ( size_size_list_int @ stk3 ) ) @ stk2 @ ( to_m_state @ ( vars @ p ) @ s2 ) ) @ ( minus_minus_nat @ ( size_size_list_int @ stk2 ) @ ( size_size_list_int @ stk3 ) ) ) ) ).
% \<open>to_m_prog P \<^bold>\<turnstile> (pc, to_m_state (vars P) s, 0) \<^bold>\<rightarrow>\<^bold>* (pc', add_m_stack (length stk' - length stk) stk' (to_m_state (vars P) s'), length stk' - length stk)\<close>
thf(fact_2__092_060open_062to__m__prog_AP_A_092_060_094bold_062_092_060turnstile_062_A_Ipc_H_M_Aadd__m__stack_A_Ilength_Astk_H_A_N_Alength_Astk_J_Astk_H_A_Ito__m__state_A_Ivars_AP_J_As_H_J_M_Alength_Astk_H_A_N_Alength_Astk_J_A_092_060_094bold_062_092_060rightarrow_062_A_Ipc_H_H_M_Aadd__m__stack_A_Ilength_Astk_H_A_N_Alength_Astk_A_L_Alength_Astk_H_H_A_N_Alength_Astk_H_J_Astk_H_H_A_Ito__m__state_A_Ivars_AP_J_As_H_H_J_M_Alength_Astk_H_A_N_Alength_Astk_A_L_Alength_Astk_H_H_A_N_Alength_Astk_H_J_092_060close_062,axiom,
m_exec1 @ ( to_m_prog @ p ) @ ( produc8342123264692915235nt_nat @ pc2 @ ( produc2630796075472406112nt_nat @ ( add_m_stack @ ( minus_minus_nat @ ( size_size_list_int @ stk2 ) @ ( size_size_list_int @ stk3 ) ) @ stk2 @ ( to_m_state @ ( vars @ p ) @ s2 ) ) @ ( minus_minus_nat @ ( size_size_list_int @ stk2 ) @ ( size_size_list_int @ stk3 ) ) ) ) @ ( produc8342123264692915235nt_nat @ pc @ ( produc2630796075472406112nt_nat @ ( add_m_stack @ ( minus_minus_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( size_size_list_int @ stk2 ) @ ( size_size_list_int @ stk3 ) ) @ ( size_size_list_int @ stk ) ) @ ( size_size_list_int @ stk2 ) ) @ stk @ ( to_m_state @ ( vars @ p ) @ s ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( size_size_list_int @ stk2 ) @ ( size_size_list_int @ stk3 ) ) @ ( size_size_list_int @ stk ) ) @ ( size_size_list_int @ stk2 ) ) ) ) ).
% \<open>to_m_prog P \<^bold>\<turnstile> (pc', add_m_stack (length stk' - length stk) stk' (to_m_state (vars P) s'), length stk' - length stk) \<^bold>\<rightarrow> (pc'', add_m_stack (length stk' - length stk + length stk'' - length stk') stk'' (to_m_state (vars P) s''), length stk' - length stk + length stk'' - length stk')\<close>
thf(fact_3_diff__0__eq__0,axiom,
! [N: nat] :
( ( minus_minus_nat @ zero_zero_nat @ N )
= zero_zero_nat ) ).
% diff_0_eq_0
thf(fact_4_diff__self__eq__0,axiom,
! [M: nat] :
( ( minus_minus_nat @ M @ M )
= zero_zero_nat ) ).
% diff_self_eq_0
thf(fact_5_diff__self,axiom,
! [A: int] :
( ( minus_minus_int @ A @ A )
= zero_zero_int ) ).
% diff_self
thf(fact_6_diff__0__right,axiom,
! [A: int] :
( ( minus_minus_int @ A @ zero_zero_int )
= A ) ).
% diff_0_right
thf(fact_7_zero__diff,axiom,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ) ).
% zero_diff
thf(fact_8_diff__zero,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ) ).
% diff_zero
thf(fact_9_diff__zero,axiom,
! [A: int] :
( ( minus_minus_int @ A @ zero_zero_int )
= A ) ).
% diff_zero
thf(fact_10_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_11_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
! [A: int] :
( ( minus_minus_int @ A @ A )
= zero_zero_int ) ).
% cancel_comm_monoid_add_class.diff_cancel
thf(fact_12_star__step1,axiom,
! [R: produc1019184382078353393nt_nat > produc1019184382078353393nt_nat > $o,X: produc1019184382078353393nt_nat,Y: produc1019184382078353393nt_nat] :
( ( R @ X @ Y )
=> ( star_P5461765526710342210nt_nat @ R @ X @ Y ) ) ).
% star_step1
thf(fact_13_star__step1,axiom,
! [R: produc6425607678544837394st_int > produc6425607678544837394st_int > $o,X: produc6425607678544837394st_int,Y: produc6425607678544837394st_int] :
( ( R @ X @ Y )
=> ( star_P707599355569300323st_int @ R @ X @ Y ) ) ).
% star_step1
thf(fact_14_prod_Oinject,axiom,
! [X1: list_instr,X2: list_P419547167332244514st_int,Y1: list_instr,Y2: list_P419547167332244514st_int] :
( ( ( produc7764413618310988720st_int @ X1 @ X2 )
= ( produc7764413618310988720st_int @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_15_prod_Oinject,axiom,
! [X1: int,X2: produc369741286924889929st_int,Y1: int,Y2: produc369741286924889929st_int] :
( ( ( produc5086643055186798020st_int @ X1 @ X2 )
= ( produc5086643055186798020st_int @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_16_prod_Oinject,axiom,
! [X1: int,X2: produc1534919314292393896nt_nat,Y1: int,Y2: produc1534919314292393896nt_nat] :
( ( ( produc8342123264692915235nt_nat @ X1 @ X2 )
= ( produc8342123264692915235nt_nat @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_17_prod_Oinject,axiom,
! [X1: list_char > int,X2: list_int,Y1: list_char > int,Y2: list_int] :
( ( ( produc8650753666468850689st_int @ X1 @ X2 )
= ( produc8650753666468850689st_int @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_18_prod_Oinject,axiom,
! [X1: int > int,X2: nat,Y1: int > int,Y2: nat] :
( ( ( produc2630796075472406112nt_nat @ X1 @ X2 )
= ( produc2630796075472406112nt_nat @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) ).
% prod.inject
thf(fact_19_old_Oprod_Oinject,axiom,
! [A: list_instr,B: list_P419547167332244514st_int,A2: list_instr,B2: list_P419547167332244514st_int] :
( ( ( produc7764413618310988720st_int @ A @ B )
= ( produc7764413618310988720st_int @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_20_old_Oprod_Oinject,axiom,
! [A: int,B: produc369741286924889929st_int,A2: int,B2: produc369741286924889929st_int] :
( ( ( produc5086643055186798020st_int @ A @ B )
= ( produc5086643055186798020st_int @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_21_old_Oprod_Oinject,axiom,
! [A: int,B: produc1534919314292393896nt_nat,A2: int,B2: produc1534919314292393896nt_nat] :
( ( ( produc8342123264692915235nt_nat @ A @ B )
= ( produc8342123264692915235nt_nat @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_22_old_Oprod_Oinject,axiom,
! [A: list_char > int,B: list_int,A2: list_char > int,B2: list_int] :
( ( ( produc8650753666468850689st_int @ A @ B )
= ( produc8650753666468850689st_int @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_23_old_Oprod_Oinject,axiom,
! [A: int > int,B: nat,A2: int > int,B2: nat] :
( ( ( produc2630796075472406112nt_nat @ A @ B )
= ( produc2630796075472406112nt_nat @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) ).
% old.prod.inject
thf(fact_24_add__left__cancel,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ) ).
% add_left_cancel
thf(fact_25_add__left__cancel,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
= ( B = C ) ) ).
% add_left_cancel
thf(fact_26_add__right__cancel,axiom,
! [B: nat,A: nat,C: nat] :
( ( ( plus_plus_nat @ B @ A )
= ( plus_plus_nat @ C @ A ) )
= ( B = C ) ) ).
% add_right_cancel
thf(fact_27_add__right__cancel,axiom,
! [B: int,A: int,C: int] :
( ( ( plus_plus_int @ B @ A )
= ( plus_plus_int @ C @ A ) )
= ( B = C ) ) ).
% add_right_cancel
thf(fact_28_le__zero__eq,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) ).
% le_zero_eq
thf(fact_29_add__le__cancel__left,axiom,
! [C: nat,A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ B ) ) ).
% add_le_cancel_left
thf(fact_30_add__le__cancel__left,axiom,
! [C: int,A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
= ( ord_less_eq_int @ A @ B ) ) ).
% add_le_cancel_left
thf(fact_31_add__le__cancel__right,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( ord_less_eq_nat @ A @ B ) ) ).
% add_le_cancel_right
thf(fact_32_add__le__cancel__right,axiom,
! [A: int,C: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
= ( ord_less_eq_int @ A @ B ) ) ).
% add_le_cancel_right
thf(fact_33_add__0,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ) ).
% add_0
thf(fact_34_add__0,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ) ).
% add_0
thf(fact_35_zero__eq__add__iff__both__eq__0,axiom,
! [X: nat,Y: nat] :
( ( zero_zero_nat
= ( plus_plus_nat @ X @ Y ) )
= ( ( X = zero_zero_nat )
& ( Y = zero_zero_nat ) ) ) ).
% zero_eq_add_iff_both_eq_0
thf(fact_36_add__eq__0__iff__both__eq__0,axiom,
! [X: nat,Y: nat] :
( ( ( plus_plus_nat @ X @ Y )
= zero_zero_nat )
= ( ( X = zero_zero_nat )
& ( Y = zero_zero_nat ) ) ) ).
% add_eq_0_iff_both_eq_0
thf(fact_37_add__cancel__right__right,axiom,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ) ).
% add_cancel_right_right
thf(fact_38_add__cancel__right__right,axiom,
! [A: int,B: int] :
( ( A
= ( plus_plus_int @ A @ B ) )
= ( B = zero_zero_int ) ) ).
% add_cancel_right_right
thf(fact_39_add__cancel__right__left,axiom,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ B @ A ) )
= ( B = zero_zero_nat ) ) ).
% add_cancel_right_left
thf(fact_40_add__cancel__right__left,axiom,
! [A: int,B: int] :
( ( A
= ( plus_plus_int @ B @ A ) )
= ( B = zero_zero_int ) ) ).
% add_cancel_right_left
thf(fact_41_add__cancel__left__right,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
= ( B = zero_zero_nat ) ) ).
% add_cancel_left_right
thf(fact_42_add__cancel__left__right,axiom,
! [A: int,B: int] :
( ( ( plus_plus_int @ A @ B )
= A )
= ( B = zero_zero_int ) ) ).
% add_cancel_left_right
thf(fact_43_add__cancel__left__left,axiom,
! [B: nat,A: nat] :
( ( ( plus_plus_nat @ B @ A )
= A )
= ( B = zero_zero_nat ) ) ).
% add_cancel_left_left
thf(fact_44_add__cancel__left__left,axiom,
! [B: int,A: int] :
( ( ( plus_plus_int @ B @ A )
= A )
= ( B = zero_zero_int ) ) ).
% add_cancel_left_left
thf(fact_45_double__zero__sym,axiom,
! [A: int] :
( ( zero_zero_int
= ( plus_plus_int @ A @ A ) )
= ( A = zero_zero_int ) ) ).
% double_zero_sym
thf(fact_46_add_Oright__neutral,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ) ).
% add.right_neutral
thf(fact_47_add_Oright__neutral,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ) ).
% add.right_neutral
thf(fact_48_add__diff__cancel__right_H,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ) ).
% add_diff_cancel_right'
thf(fact_49_add__diff__cancel__right_H,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
= A ) ).
% add_diff_cancel_right'
thf(fact_50_add__diff__cancel__right,axiom,
! [A: nat,C: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( minus_minus_nat @ A @ B ) ) ).
% add_diff_cancel_right
thf(fact_51_add__diff__cancel__right,axiom,
! [A: int,C: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
= ( minus_minus_int @ A @ B ) ) ).
% add_diff_cancel_right
thf(fact_52_add__diff__cancel__left_H,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ) ).
% add_diff_cancel_left'
thf(fact_53_add__diff__cancel__left_H,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
= B ) ).
% add_diff_cancel_left'
thf(fact_54_add__diff__cancel__left,axiom,
! [C: nat,A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( minus_minus_nat @ A @ B ) ) ).
% add_diff_cancel_left
thf(fact_55_add__diff__cancel__left,axiom,
! [C: int,A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
= ( minus_minus_int @ A @ B ) ) ).
% add_diff_cancel_left
thf(fact_56_diff__add__cancel,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
= A ) ).
% diff_add_cancel
thf(fact_57_add__diff__cancel,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
= A ) ).
% add_diff_cancel
thf(fact_58_le0,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% le0
thf(fact_59_bot__nat__0_Oextremum,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% bot_nat_0.extremum
thf(fact_60_Nat_Oadd__0__right,axiom,
! [M: nat] :
( ( plus_plus_nat @ M @ zero_zero_nat )
= M ) ).
% Nat.add_0_right
thf(fact_61_add__is__0,axiom,
! [M: nat,N: nat] :
( ( ( plus_plus_nat @ M @ N )
= zero_zero_nat )
= ( ( M = zero_zero_nat )
& ( N = zero_zero_nat ) ) ) ).
% add_is_0
thf(fact_62_nat__add__left__cancel__le,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( ord_less_eq_nat @ M @ N ) ) ).
% nat_add_left_cancel_le
thf(fact_63_diff__diff__cancel,axiom,
! [I: nat,N: nat] :
( ( ord_less_eq_nat @ I @ N )
=> ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
= I ) ) ).
% diff_diff_cancel
thf(fact_64_diff__diff__left,axiom,
! [I: nat,J: nat,K: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
= ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% diff_diff_left
thf(fact_65_zero__le__double__add__iff__zero__le__single__add,axiom,
! [A: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
= ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% zero_le_double_add_iff_zero_le_single_add
thf(fact_66_mem__Collect__eq,axiom,
! [A: int,P: int > $o] :
( ( member_int @ A @ ( collect_int @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_67_mem__Collect__eq,axiom,
! [A: list_char,P: list_char > $o] :
( ( member_list_char @ A @ ( collect_list_char @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_68_Collect__mem__eq,axiom,
! [A3: set_int] :
( ( collect_int
@ ^ [X3: int] : ( member_int @ X3 @ A3 ) )
= A3 ) ).
% Collect_mem_eq
thf(fact_69_Collect__mem__eq,axiom,
! [A3: set_list_char] :
( ( collect_list_char
@ ^ [X3: list_char] : ( member_list_char @ X3 @ A3 ) )
= A3 ) ).
% Collect_mem_eq
thf(fact_70_double__add__le__zero__iff__single__add__le__zero,axiom,
! [A: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
= ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% double_add_le_zero_iff_single_add_le_zero
thf(fact_71_le__add__same__cancel2,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
= ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% le_add_same_cancel2
thf(fact_72_le__add__same__cancel2,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
= ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% le_add_same_cancel2
thf(fact_73_le__add__same__cancel1,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
= ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% le_add_same_cancel1
thf(fact_74_le__add__same__cancel1,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
= ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% le_add_same_cancel1
thf(fact_75_add__le__same__cancel2,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
= ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% add_le_same_cancel2
thf(fact_76_add__le__same__cancel2,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
= ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% add_le_same_cancel2
thf(fact_77_add__le__same__cancel1,axiom,
! [B: nat,A: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
= ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% add_le_same_cancel1
thf(fact_78_add__le__same__cancel1,axiom,
! [B: int,A: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
= ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% add_le_same_cancel1
thf(fact_79_diff__ge__0__iff__ge,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
= ( ord_less_eq_int @ B @ A ) ) ).
% diff_ge_0_iff_ge
thf(fact_80_diff__add__zero,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
= zero_zero_nat ) ).
% diff_add_zero
thf(fact_81_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_82_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_83_Nat_Odiff__diff__right,axiom,
! [K: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
= ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% Nat.diff_diff_right
thf(fact_84_Nat_Oadd__diff__assoc2,axiom,
! [K: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
= ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% Nat.add_diff_assoc2
thf(fact_85_Nat_Oadd__diff__assoc,axiom,
! [K: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
= ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% Nat.add_diff_assoc
thf(fact_86_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% ab_semigroup_add_class.add_ac(1)
thf(fact_87_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% ab_semigroup_add_class.add_ac(1)
thf(fact_88_add__mono__thms__linordered__semiring_I4_J,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( I = J )
& ( K = L ) )
=> ( ( plus_plus_nat @ I @ K )
= ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(4)
thf(fact_89_add__mono__thms__linordered__semiring_I4_J,axiom,
! [I: int,J: int,K: int,L: int] :
( ( ( I = J )
& ( K = L ) )
=> ( ( plus_plus_int @ I @ K )
= ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(4)
thf(fact_90_add__mono__thms__linordered__semiring_I3_J,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I @ J )
& ( K = L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(3)
thf(fact_91_add__mono__thms__linordered__semiring_I3_J,axiom,
! [I: int,J: int,K: int,L: int] :
( ( ( ord_less_eq_int @ I @ J )
& ( K = L ) )
=> ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(3)
thf(fact_92_add__mono__thms__linordered__semiring_I2_J,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( I = J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(2)
thf(fact_93_add__mono__thms__linordered__semiring_I2_J,axiom,
! [I: int,J: int,K: int,L: int] :
( ( ( I = J )
& ( ord_less_eq_int @ K @ L ) )
=> ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(2)
thf(fact_94_add__mono__thms__linordered__semiring_I1_J,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ( ord_less_eq_nat @ I @ J )
& ( ord_less_eq_nat @ K @ L ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(1)
thf(fact_95_add__mono__thms__linordered__semiring_I1_J,axiom,
! [I: int,J: int,K: int,L: int] :
( ( ( ord_less_eq_int @ I @ J )
& ( ord_less_eq_int @ K @ L ) )
=> ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% add_mono_thms_linordered_semiring(1)
thf(fact_96_group__cancel_Oadd1,axiom,
! [A3: nat,K: nat,A: nat,B: nat] :
( ( A3
= ( plus_plus_nat @ K @ A ) )
=> ( ( plus_plus_nat @ A3 @ B )
= ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% group_cancel.add1
thf(fact_97_group__cancel_Oadd1,axiom,
! [A3: int,K: int,A: int,B: int] :
( ( A3
= ( plus_plus_int @ K @ A ) )
=> ( ( plus_plus_int @ A3 @ B )
= ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% group_cancel.add1
thf(fact_98_group__cancel_Oadd2,axiom,
! [B3: nat,K: nat,B: nat,A: nat] :
( ( B3
= ( plus_plus_nat @ K @ B ) )
=> ( ( plus_plus_nat @ A @ B3 )
= ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% group_cancel.add2
thf(fact_99_group__cancel_Oadd2,axiom,
! [B3: int,K: int,B: int,A: int] :
( ( B3
= ( plus_plus_int @ K @ B ) )
=> ( ( plus_plus_int @ A @ B3 )
= ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% group_cancel.add2
thf(fact_100_add_Oassoc,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% add.assoc
thf(fact_101_add_Oassoc,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% add.assoc
thf(fact_102_add_Oleft__cancel,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
= ( B = C ) ) ).
% add.left_cancel
thf(fact_103_add_Oright__cancel,axiom,
! [B: int,A: int,C: int] :
( ( ( plus_plus_int @ B @ A )
= ( plus_plus_int @ C @ A ) )
= ( B = C ) ) ).
% add.right_cancel
thf(fact_104_add_Ocommute,axiom,
( plus_plus_nat
= ( ^ [A4: nat,B4: nat] : ( plus_plus_nat @ B4 @ A4 ) ) ) ).
% add.commute
thf(fact_105_add_Ocommute,axiom,
( plus_plus_int
= ( ^ [A4: int,B4: int] : ( plus_plus_int @ B4 @ A4 ) ) ) ).
% add.commute
thf(fact_106_add_Oleft__commute,axiom,
! [B: nat,A: nat,C: nat] :
( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% add.left_commute
thf(fact_107_add_Oleft__commute,axiom,
! [B: int,A: int,C: int] :
( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% add.left_commute
thf(fact_108_add__mono,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% add_mono
thf(fact_109_add__mono,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% add_mono
thf(fact_110_add__left__imp__eq,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ) ).
% add_left_imp_eq
thf(fact_111_add__left__imp__eq,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
=> ( B = C ) ) ).
% add_left_imp_eq
thf(fact_112_add__right__imp__eq,axiom,
! [B: nat,A: nat,C: nat] :
( ( ( plus_plus_nat @ B @ A )
= ( plus_plus_nat @ C @ A ) )
=> ( B = C ) ) ).
% add_right_imp_eq
thf(fact_113_add__right__imp__eq,axiom,
! [B: int,A: int,C: int] :
( ( ( plus_plus_int @ B @ A )
= ( plus_plus_int @ C @ A ) )
=> ( B = C ) ) ).
% add_right_imp_eq
thf(fact_114_add__left__mono,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% add_left_mono
thf(fact_115_add__left__mono,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% add_left_mono
thf(fact_116_less__eqE,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ! [C2: nat] :
( B
!= ( plus_plus_nat @ A @ C2 ) ) ) ).
% less_eqE
thf(fact_117_add__right__mono,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% add_right_mono
thf(fact_118_add__right__mono,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% add_right_mono
thf(fact_119_le__iff__add,axiom,
( ord_less_eq_nat
= ( ^ [A4: nat,B4: nat] :
? [C3: nat] :
( B4
= ( plus_plus_nat @ A4 @ C3 ) ) ) ) ).
% le_iff_add
thf(fact_120_add__le__imp__le__left,axiom,
! [C: nat,A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ B ) ) ).
% add_le_imp_le_left
thf(fact_121_add__le__imp__le__left,axiom,
! [C: int,A: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
=> ( ord_less_eq_int @ A @ B ) ) ).
% add_le_imp_le_left
thf(fact_122_add__le__imp__le__right,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
=> ( ord_less_eq_nat @ A @ B ) ) ).
% add_le_imp_le_right
thf(fact_123_add__le__imp__le__right,axiom,
! [A: int,C: int,B: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
=> ( ord_less_eq_int @ A @ B ) ) ).
% add_le_imp_le_right
thf(fact_124_add__leE,axiom,
! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
=> ~ ( ( ord_less_eq_nat @ M @ N )
=> ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% add_leE
thf(fact_125_le__add1,axiom,
! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% le_add1
thf(fact_126_le__add2,axiom,
! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% le_add2
thf(fact_127_le__refl,axiom,
! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% le_refl
thf(fact_128_add__leD1,axiom,
! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
=> ( ord_less_eq_nat @ M @ N ) ) ).
% add_leD1
thf(fact_129_add__leD2,axiom,
! [M: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
=> ( ord_less_eq_nat @ K @ N ) ) ).
% add_leD2
thf(fact_130_le__trans,axiom,
! [I: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ord_less_eq_nat @ J @ K )
=> ( ord_less_eq_nat @ I @ K ) ) ) ).
% le_trans
thf(fact_131_eq__imp__le,axiom,
! [M: nat,N: nat] :
( ( M = N )
=> ( ord_less_eq_nat @ M @ N ) ) ).
% eq_imp_le
thf(fact_132_le__Suc__ex,axiom,
! [K: nat,L: nat] :
( ( ord_less_eq_nat @ K @ L )
=> ? [N2: nat] :
( L
= ( plus_plus_nat @ K @ N2 ) ) ) ).
% le_Suc_ex
thf(fact_133_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_134_add__le__mono,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ord_less_eq_nat @ K @ L )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% add_le_mono
thf(fact_135_add__le__mono1,axiom,
! [I: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% add_le_mono1
thf(fact_136_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_137_trans__le__add1,axiom,
! [I: nat,J: nat,M: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% trans_le_add1
thf(fact_138_trans__le__add2,axiom,
! [I: nat,J: nat,M: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% trans_le_add2
thf(fact_139_nat__le__iff__add,axiom,
( ord_less_eq_nat
= ( ^ [M2: nat,N3: nat] :
? [K2: nat] :
( N3
= ( plus_plus_nat @ M2 @ K2 ) ) ) ) ).
% nat_le_iff_add
thf(fact_140_Nat_Oex__has__greatest__nat,axiom,
! [P: nat > $o,K: nat,B: nat] :
( ( P @ K )
=> ( ! [Y3: nat] :
( ( P @ Y3 )
=> ( ord_less_eq_nat @ Y3 @ B ) )
=> ? [X4: nat] :
( ( P @ X4 )
& ! [Y4: nat] :
( ( P @ Y4 )
=> ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ) ).
% Nat.ex_has_greatest_nat
thf(fact_141_add__nonpos__eq__0__iff,axiom,
! [X: nat,Y: nat] :
( ( ord_less_eq_nat @ X @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
=> ( ( ( plus_plus_nat @ X @ Y )
= zero_zero_nat )
= ( ( X = zero_zero_nat )
& ( Y = zero_zero_nat ) ) ) ) ) ).
% add_nonpos_eq_0_iff
thf(fact_142_add__nonpos__eq__0__iff,axiom,
! [X: int,Y: int] :
( ( ord_less_eq_int @ X @ zero_zero_int )
=> ( ( ord_less_eq_int @ Y @ zero_zero_int )
=> ( ( ( plus_plus_int @ X @ Y )
= zero_zero_int )
= ( ( X = zero_zero_int )
& ( Y = zero_zero_int ) ) ) ) ) ).
% add_nonpos_eq_0_iff
thf(fact_143_add__nonneg__eq__0__iff,axiom,
! [X: nat,Y: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ X )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
=> ( ( ( plus_plus_nat @ X @ Y )
= zero_zero_nat )
= ( ( X = zero_zero_nat )
& ( Y = zero_zero_nat ) ) ) ) ) ).
% add_nonneg_eq_0_iff
thf(fact_144_add__nonneg__eq__0__iff,axiom,
! [X: int,Y: int] :
( ( ord_less_eq_int @ zero_zero_int @ X )
=> ( ( ord_less_eq_int @ zero_zero_int @ Y )
=> ( ( ( plus_plus_int @ X @ Y )
= zero_zero_int )
= ( ( X = zero_zero_int )
& ( Y = zero_zero_int ) ) ) ) ) ).
% add_nonneg_eq_0_iff
thf(fact_145_add__nonpos__nonpos,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% add_nonpos_nonpos
thf(fact_146_add__nonpos__nonpos,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ( ord_less_eq_int @ B @ zero_zero_int )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% add_nonpos_nonpos
thf(fact_147_add__nonneg__nonneg,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% add_nonneg_nonneg
thf(fact_148_add__nonneg__nonneg,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% add_nonneg_nonneg
thf(fact_149_add__increasing2,axiom,
! [C: nat,B: nat,A: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% add_increasing2
thf(fact_150_add__increasing2,axiom,
! [C: int,B: int,A: int] :
( ( ord_less_eq_int @ zero_zero_int @ C )
=> ( ( ord_less_eq_int @ B @ A )
=> ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% add_increasing2
thf(fact_151_add__decreasing2,axiom,
! [C: nat,A: nat,B: nat] :
( ( ord_less_eq_nat @ C @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% add_decreasing2
thf(fact_152_add__decreasing2,axiom,
! [C: int,A: int,B: int] :
( ( ord_less_eq_int @ C @ zero_zero_int )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% add_decreasing2
thf(fact_153_add__increasing,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% add_increasing
thf(fact_154_add__increasing,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% add_increasing
thf(fact_155_add__decreasing,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% add_decreasing
thf(fact_156_add__decreasing,axiom,
! [A: int,C: int,B: int] :
( ( ord_less_eq_int @ A @ zero_zero_int )
=> ( ( ord_less_eq_int @ C @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% add_decreasing
thf(fact_157_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ( ( minus_minus_nat @ B @ A )
= C )
= ( B
= ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
thf(fact_158_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
= B ) ) ).
% ordered_cancel_comm_monoid_diff_class.add_diff_inverse
thf(fact_159_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% ordered_cancel_comm_monoid_diff_class.diff_diff_right
thf(fact_160_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
= ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
thf(fact_161_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
= ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
thf(fact_162_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
= ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% ordered_cancel_comm_monoid_diff_class.diff_add_assoc
thf(fact_163_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% ordered_cancel_comm_monoid_diff_class.add_diff_assoc
thf(fact_164_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% ordered_cancel_comm_monoid_diff_class.le_diff_conv2
thf(fact_165_le__add__diff,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% le_add_diff
thf(fact_166_diff__add,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
= B ) ) ).
% diff_add
thf(fact_167_le__diff__eq,axiom,
! [A: int,C: int,B: int] :
( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
= ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% le_diff_eq
thf(fact_168_diff__le__eq,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
= ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% diff_le_eq
thf(fact_169_Nat_Ole__imp__diff__is__add,axiom,
! [I: nat,J: nat,K: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( ( minus_minus_nat @ J @ I )
= K )
= ( J
= ( plus_plus_nat @ K @ I ) ) ) ) ).
% Nat.le_imp_diff_is_add
thf(fact_170_Nat_Odiff__add__assoc2,axiom,
! [K: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
= ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% Nat.diff_add_assoc2
thf(fact_171_Nat_Odiff__add__assoc,axiom,
! [K: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
= ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% Nat.diff_add_assoc
thf(fact_172_Nat_Ole__diff__conv2,axiom,
! [K: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% Nat.le_diff_conv2
thf(fact_173_le__diff__conv,axiom,
! [J: nat,K: nat,I: nat] :
( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
= ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% le_diff_conv
thf(fact_174_add_Ogroup__left__neutral,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ) ).
% add.group_left_neutral
thf(fact_175_add_Ocomm__neutral,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ) ).
% add.comm_neutral
thf(fact_176_add_Ocomm__neutral,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ) ).
% add.comm_neutral
thf(fact_177_comm__monoid__add__class_Oadd__0,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ) ).
% comm_monoid_add_class.add_0
thf(fact_178_comm__monoid__add__class_Oadd__0,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ) ).
% comm_monoid_add_class.add_0
thf(fact_179_zero__le,axiom,
! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% zero_le
thf(fact_180_m__iexec_Ocases,axiom,
! [X: produc3341395906625653086nt_nat] :
~ ! [Mins: m_instr,I2: int,Ms: int > int,Sp: nat] :
( X
!= ( produc973592215685924118nt_nat @ Mins @ ( produc8342123264692915235nt_nat @ I2 @ ( produc2630796075472406112nt_nat @ Ms @ Sp ) ) ) ) ).
% m_iexec.cases
thf(fact_181_m__config__equiv_Ocases,axiom,
! [X: produc6004788045807207619nt_nat] :
~ ! [I2: int,Ms: int > int,Sp: nat,I3: int,Ms2: int > int,Sp2: nat] :
( X
!= ( produc5273850286580078715nt_nat @ ( produc8342123264692915235nt_nat @ I2 @ ( produc2630796075472406112nt_nat @ Ms @ Sp ) ) @ ( produc8342123264692915235nt_nat @ I3 @ ( produc2630796075472406112nt_nat @ Ms2 @ Sp2 ) ) ) ) ).
% m_config_equiv.cases
thf(fact_182_diff__diff__eq,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% diff_diff_eq
thf(fact_183_diff__diff__eq,axiom,
! [A: int,B: int,C: int] :
( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
= ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% diff_diff_eq
thf(fact_184_add__implies__diff,axiom,
! [C: nat,B: nat,A: nat] :
( ( ( plus_plus_nat @ C @ B )
= A )
=> ( C
= ( minus_minus_nat @ A @ B ) ) ) ).
% add_implies_diff
thf(fact_185_add__implies__diff,axiom,
! [C: int,B: int,A: int] :
( ( ( plus_plus_int @ C @ B )
= A )
=> ( C
= ( minus_minus_int @ A @ B ) ) ) ).
% add_implies_diff
thf(fact_186_diff__add__eq__diff__diff__swap,axiom,
! [A: int,B: int,C: int] :
( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% diff_add_eq_diff_diff_swap
thf(fact_187_diff__add__eq,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
= ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% diff_add_eq
thf(fact_188_diff__diff__eq2,axiom,
! [A: int,B: int,C: int] :
( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% diff_diff_eq2
thf(fact_189_add__diff__eq,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% add_diff_eq
thf(fact_190_eq__diff__eq,axiom,
! [A: int,C: int,B: int] :
( ( A
= ( minus_minus_int @ C @ B ) )
= ( ( plus_plus_int @ A @ B )
= C ) ) ).
% eq_diff_eq
thf(fact_191_diff__eq__eq,axiom,
! [A: int,B: int,C: int] :
( ( ( minus_minus_int @ A @ B )
= C )
= ( A
= ( plus_plus_int @ C @ B ) ) ) ).
% diff_eq_eq
thf(fact_192_group__cancel_Osub1,axiom,
! [A3: int,K: int,A: int,B: int] :
( ( A3
= ( plus_plus_int @ K @ A ) )
=> ( ( minus_minus_int @ A3 @ B )
= ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% group_cancel.sub1
thf(fact_193_diff__eq__diff__less__eq,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( ord_less_eq_int @ A @ B )
= ( ord_less_eq_int @ C @ D ) ) ) ).
% diff_eq_diff_less_eq
thf(fact_194_diff__right__mono,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% diff_right_mono
thf(fact_195_diff__left__mono,axiom,
! [B: int,A: int,C: int] :
( ( ord_less_eq_int @ B @ A )
=> ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% diff_left_mono
thf(fact_196_diff__mono,axiom,
! [A: int,B: int,D: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ D @ C )
=> ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% diff_mono
thf(fact_197_add__eq__self__zero,axiom,
! [M: nat,N: nat] :
( ( ( plus_plus_nat @ M @ N )
= M )
=> ( N = zero_zero_nat ) ) ).
% add_eq_self_zero
thf(fact_198_plus__nat_Oadd__0,axiom,
! [N: nat] :
( ( plus_plus_nat @ zero_zero_nat @ N )
= N ) ).
% plus_nat.add_0
thf(fact_199_le__0__eq,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) ).
% le_0_eq
thf(fact_200_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_201_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_202_less__eq__nat_Osimps_I1_J,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% less_eq_nat.simps(1)
thf(fact_203_diff__add__inverse2,axiom,
! [M: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
= M ) ).
% diff_add_inverse2
thf(fact_204_diff__add__inverse,axiom,
! [N: nat,M: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
= M ) ).
% diff_add_inverse
thf(fact_205_diff__cancel2,axiom,
! [M: nat,K: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
= ( minus_minus_nat @ M @ N ) ) ).
% diff_cancel2
thf(fact_206_Nat_Odiff__cancel,axiom,
! [K: nat,M: nat,N: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( minus_minus_nat @ M @ N ) ) ).
% Nat.diff_cancel
thf(fact_207_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_208_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_209_diff__le__self,axiom,
! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% diff_le_self
thf(fact_210_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_211_Nat_Odiff__diff__eq,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
= ( minus_minus_nat @ M @ N ) ) ) ) ).
% Nat.diff_diff_eq
thf(fact_212_le__diff__iff,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
= ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% le_diff_iff
thf(fact_213_eq__diff__iff,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( ( minus_minus_nat @ M @ K )
= ( minus_minus_nat @ N @ K ) )
= ( M = N ) ) ) ) ).
% eq_diff_iff
thf(fact_214_zero__reorient,axiom,
! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ) ).
% zero_reorient
thf(fact_215_zero__reorient,axiom,
! [X: int] :
( ( zero_zero_int = X )
= ( X = zero_zero_int ) ) ).
% zero_reorient
thf(fact_216_Pair__inject,axiom,
! [A: list_instr,B: list_P419547167332244514st_int,A2: list_instr,B2: list_P419547167332244514st_int] :
( ( ( produc7764413618310988720st_int @ A @ B )
= ( produc7764413618310988720st_int @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_217_Pair__inject,axiom,
! [A: int,B: produc369741286924889929st_int,A2: int,B2: produc369741286924889929st_int] :
( ( ( produc5086643055186798020st_int @ A @ B )
= ( produc5086643055186798020st_int @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_218_Pair__inject,axiom,
! [A: int,B: produc1534919314292393896nt_nat,A2: int,B2: produc1534919314292393896nt_nat] :
( ( ( produc8342123264692915235nt_nat @ A @ B )
= ( produc8342123264692915235nt_nat @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_219_Pair__inject,axiom,
! [A: list_char > int,B: list_int,A2: list_char > int,B2: list_int] :
( ( ( produc8650753666468850689st_int @ A @ B )
= ( produc8650753666468850689st_int @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_220_Pair__inject,axiom,
! [A: int > int,B: nat,A2: int > int,B2: nat] :
( ( ( produc2630796075472406112nt_nat @ A @ B )
= ( produc2630796075472406112nt_nat @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) ).
% Pair_inject
thf(fact_221_prod__cases,axiom,
! [P: produc4400946599758736694st_int > $o,P2: produc4400946599758736694st_int] :
( ! [A5: list_instr,B5: list_P419547167332244514st_int] : ( P @ ( produc7764413618310988720st_int @ A5 @ B5 ) )
=> ( P @ P2 ) ) ).
% prod_cases
thf(fact_222_prod__cases,axiom,
! [P: produc6425607678544837394st_int > $o,P2: produc6425607678544837394st_int] :
( ! [A5: int,B5: produc369741286924889929st_int] : ( P @ ( produc5086643055186798020st_int @ A5 @ B5 ) )
=> ( P @ P2 ) ) ).
% prod_cases
thf(fact_223_prod__cases,axiom,
! [P: produc1019184382078353393nt_nat > $o,P2: produc1019184382078353393nt_nat] :
( ! [A5: int,B5: produc1534919314292393896nt_nat] : ( P @ ( produc8342123264692915235nt_nat @ A5 @ B5 ) )
=> ( P @ P2 ) ) ).
% prod_cases
thf(fact_224_prod__cases,axiom,
! [P: produc369741286924889929st_int > $o,P2: produc369741286924889929st_int] :
( ! [A5: list_char > int,B5: list_int] : ( P @ ( produc8650753666468850689st_int @ A5 @ B5 ) )
=> ( P @ P2 ) ) ).
% prod_cases
thf(fact_225_prod__cases,axiom,
! [P: produc1534919314292393896nt_nat > $o,P2: produc1534919314292393896nt_nat] :
( ! [A5: int > int,B5: nat] : ( P @ ( produc2630796075472406112nt_nat @ A5 @ B5 ) )
=> ( P @ P2 ) ) ).
% prod_cases
thf(fact_226_surj__pair,axiom,
! [P2: produc4400946599758736694st_int] :
? [X4: list_instr,Y3: list_P419547167332244514st_int] :
( P2
= ( produc7764413618310988720st_int @ X4 @ Y3 ) ) ).
% surj_pair
thf(fact_227_surj__pair,axiom,
! [P2: produc6425607678544837394st_int] :
? [X4: int,Y3: produc369741286924889929st_int] :
( P2
= ( produc5086643055186798020st_int @ X4 @ Y3 ) ) ).
% surj_pair
thf(fact_228_surj__pair,axiom,
! [P2: produc1019184382078353393nt_nat] :
? [X4: int,Y3: produc1534919314292393896nt_nat] :
( P2
= ( produc8342123264692915235nt_nat @ X4 @ Y3 ) ) ).
% surj_pair
thf(fact_229_surj__pair,axiom,
! [P2: produc369741286924889929st_int] :
? [X4: list_char > int,Y3: list_int] :
( P2
= ( produc8650753666468850689st_int @ X4 @ Y3 ) ) ).
% surj_pair
thf(fact_230_surj__pair,axiom,
! [P2: produc1534919314292393896nt_nat] :
? [X4: int > int,Y3: nat] :
( P2
= ( produc2630796075472406112nt_nat @ X4 @ Y3 ) ) ).
% surj_pair
thf(fact_231_old_Oprod_Oexhaust,axiom,
! [Y: produc4400946599758736694st_int] :
~ ! [A5: list_instr,B5: list_P419547167332244514st_int] :
( Y
!= ( produc7764413618310988720st_int @ A5 @ B5 ) ) ).
% old.prod.exhaust
thf(fact_232_old_Oprod_Oexhaust,axiom,
! [Y: produc6425607678544837394st_int] :
~ ! [A5: int,B5: produc369741286924889929st_int] :
( Y
!= ( produc5086643055186798020st_int @ A5 @ B5 ) ) ).
% old.prod.exhaust
thf(fact_233_old_Oprod_Oexhaust,axiom,
! [Y: produc1019184382078353393nt_nat] :
~ ! [A5: int,B5: produc1534919314292393896nt_nat] :
( Y
!= ( produc8342123264692915235nt_nat @ A5 @ B5 ) ) ).
% old.prod.exhaust
thf(fact_234_old_Oprod_Oexhaust,axiom,
! [Y: produc369741286924889929st_int] :
~ ! [A5: list_char > int,B5: list_int] :
( Y
!= ( produc8650753666468850689st_int @ A5 @ B5 ) ) ).
% old.prod.exhaust
thf(fact_235_old_Oprod_Oexhaust,axiom,
! [Y: produc1534919314292393896nt_nat] :
~ ! [A5: int > int,B5: nat] :
( Y
!= ( produc2630796075472406112nt_nat @ A5 @ B5 ) ) ).
% old.prod.exhaust
thf(fact_236_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_237_diff__right__commute,axiom,
! [A: int,C: int,B: int] :
( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
= ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% diff_right_commute
thf(fact_238_diff__eq__diff__eq,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ).
% diff_eq_diff_eq
thf(fact_239_size__neq__size__imp__neq,axiom,
! [X: list_P419547167332244514st_int,Y: list_P419547167332244514st_int] :
( ( ( size_s229347708945616566st_int @ X )
!= ( size_s229347708945616566st_int @ Y ) )
=> ( X != Y ) ) ).
% size_neq_size_imp_neq
thf(fact_240_size__neq__size__imp__neq,axiom,
! [X: list_m_instr,Y: list_m_instr] :
( ( ( size_s5914166952900237872_instr @ X )
!= ( size_s5914166952900237872_instr @ Y ) )
=> ( X != Y ) ) ).
% size_neq_size_imp_neq
thf(fact_241_size__neq__size__imp__neq,axiom,
! [X: list_instr,Y: list_instr] :
( ( ( size_size_list_instr @ X )
!= ( size_size_list_instr @ Y ) )
=> ( X != Y ) ) ).
% size_neq_size_imp_neq
thf(fact_242_size__neq__size__imp__neq,axiom,
! [X: list_list_char,Y: list_list_char] :
( ( ( size_s356637359517785349t_char @ X )
!= ( size_s356637359517785349t_char @ Y ) )
=> ( X != Y ) ) ).
% size_neq_size_imp_neq
thf(fact_243_size__neq__size__imp__neq,axiom,
! [X: list_int,Y: list_int] :
( ( ( size_size_list_int @ X )
!= ( size_size_list_int @ Y ) )
=> ( X != Y ) ) ).
% size_neq_size_imp_neq
thf(fact_244_diff__commute,axiom,
! [I: nat,J: nat,K: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
= ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% diff_commute
thf(fact_245_le__iff__diff__le__0,axiom,
( ord_less_eq_int
= ( ^ [A4: int,B4: int] : ( ord_less_eq_int @ ( minus_minus_int @ A4 @ B4 ) @ zero_zero_int ) ) ) ).
% le_iff_diff_le_0
thf(fact_246_diff__add__0,axiom,
! [N: nat,M: nat] :
( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
= zero_zero_nat ) ).
% diff_add_0
thf(fact_247_star__trans,axiom,
! [R: produc1019184382078353393nt_nat > produc1019184382078353393nt_nat > $o,X: produc1019184382078353393nt_nat,Y: produc1019184382078353393nt_nat,Z: produc1019184382078353393nt_nat] :
( ( star_P5461765526710342210nt_nat @ R @ X @ Y )
=> ( ( star_P5461765526710342210nt_nat @ R @ Y @ Z )
=> ( star_P5461765526710342210nt_nat @ R @ X @ Z ) ) ) ).
% star_trans
thf(fact_248_star__trans,axiom,
! [R: produc6425607678544837394st_int > produc6425607678544837394st_int > $o,X: produc6425607678544837394st_int,Y: produc6425607678544837394st_int,Z: produc6425607678544837394st_int] :
( ( star_P707599355569300323st_int @ R @ X @ Y )
=> ( ( star_P707599355569300323st_int @ R @ Y @ Z )
=> ( star_P707599355569300323st_int @ R @ X @ Z ) ) ) ).
% star_trans
thf(fact_249_star_Osimps,axiom,
( star_P5461765526710342210nt_nat
= ( ^ [R2: produc1019184382078353393nt_nat > produc1019184382078353393nt_nat > $o,A1: produc1019184382078353393nt_nat,A22: produc1019184382078353393nt_nat] :
( ? [X3: produc1019184382078353393nt_nat] :
( ( A1 = X3 )
& ( A22 = X3 ) )
| ? [X3: produc1019184382078353393nt_nat,Y5: produc1019184382078353393nt_nat,Z2: produc1019184382078353393nt_nat] :
( ( A1 = X3 )
& ( A22 = Z2 )
& ( R2 @ X3 @ Y5 )
& ( star_P5461765526710342210nt_nat @ R2 @ Y5 @ Z2 ) ) ) ) ) ).
% star.simps
thf(fact_250_star_Osimps,axiom,
( star_P707599355569300323st_int
= ( ^ [R2: produc6425607678544837394st_int > produc6425607678544837394st_int > $o,A1: produc6425607678544837394st_int,A22: produc6425607678544837394st_int] :
( ? [X3: produc6425607678544837394st_int] :
( ( A1 = X3 )
& ( A22 = X3 ) )
| ? [X3: produc6425607678544837394st_int,Y5: produc6425607678544837394st_int,Z2: produc6425607678544837394st_int] :
( ( A1 = X3 )
& ( A22 = Z2 )
& ( R2 @ X3 @ Y5 )
& ( star_P707599355569300323st_int @ R2 @ Y5 @ Z2 ) ) ) ) ) ).
% star.simps
thf(fact_251_star_Ocases,axiom,
! [R: produc1019184382078353393nt_nat > produc1019184382078353393nt_nat > $o,A12: produc1019184382078353393nt_nat,A23: produc1019184382078353393nt_nat] :
( ( star_P5461765526710342210nt_nat @ R @ A12 @ A23 )
=> ( ( A23 != A12 )
=> ~ ! [Y3: produc1019184382078353393nt_nat] :
( ( R @ A12 @ Y3 )
=> ~ ( star_P5461765526710342210nt_nat @ R @ Y3 @ A23 ) ) ) ) ).
% star.cases
thf(fact_252_star_Ocases,axiom,
! [R: produc6425607678544837394st_int > produc6425607678544837394st_int > $o,A12: produc6425607678544837394st_int,A23: produc6425607678544837394st_int] :
( ( star_P707599355569300323st_int @ R @ A12 @ A23 )
=> ( ( A23 != A12 )
=> ~ ! [Y3: produc6425607678544837394st_int] :
( ( R @ A12 @ Y3 )
=> ~ ( star_P707599355569300323st_int @ R @ Y3 @ A23 ) ) ) ) ).
% star.cases
thf(fact_253_star_Ostep,axiom,
! [R: produc1019184382078353393nt_nat > produc1019184382078353393nt_nat > $o,X: produc1019184382078353393nt_nat,Y: produc1019184382078353393nt_nat,Z: produc1019184382078353393nt_nat] :
( ( R @ X @ Y )
=> ( ( star_P5461765526710342210nt_nat @ R @ Y @ Z )
=> ( star_P5461765526710342210nt_nat @ R @ X @ Z ) ) ) ).
% star.step
thf(fact_254_star_Ostep,axiom,
! [R: produc6425607678544837394st_int > produc6425607678544837394st_int > $o,X: produc6425607678544837394st_int,Y: produc6425607678544837394st_int,Z: produc6425607678544837394st_int] :
( ( R @ X @ Y )
=> ( ( star_P707599355569300323st_int @ R @ Y @ Z )
=> ( star_P707599355569300323st_int @ R @ X @ Z ) ) ) ).
% star.step
thf(fact_255_star_Orefl,axiom,
! [R: produc1019184382078353393nt_nat > produc1019184382078353393nt_nat > $o,X: produc1019184382078353393nt_nat] : ( star_P5461765526710342210nt_nat @ R @ X @ X ) ).
% star.refl
thf(fact_256_star_Orefl,axiom,
! [R: produc6425607678544837394st_int > produc6425607678544837394st_int > $o,X: produc6425607678544837394st_int] : ( star_P707599355569300323st_int @ R @ X @ X ) ).
% star.refl
thf(fact_257_eq__iff__diff__eq__0,axiom,
( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
= ( ^ [A4: int,B4: int] :
( ( minus_minus_int @ A4 @ B4 )
= zero_zero_int ) ) ) ).
% eq_iff_diff_eq_0
thf(fact_258_prod__induct3,axiom,
! [P: produc6425607678544837394st_int > $o,X: produc6425607678544837394st_int] :
( ! [A5: int,B5: list_char > int,C2: list_int] : ( P @ ( produc5086643055186798020st_int @ A5 @ ( produc8650753666468850689st_int @ B5 @ C2 ) ) )
=> ( P @ X ) ) ).
% prod_induct3
thf(fact_259_prod__induct3,axiom,
! [P: produc1019184382078353393nt_nat > $o,X: produc1019184382078353393nt_nat] :
( ! [A5: int,B5: int > int,C2: nat] : ( P @ ( produc8342123264692915235nt_nat @ A5 @ ( produc2630796075472406112nt_nat @ B5 @ C2 ) ) )
=> ( P @ X ) ) ).
% prod_induct3
thf(fact_260_prod__cases3,axiom,
! [Y: produc6425607678544837394st_int] :
~ ! [A5: int,B5: list_char > int,C2: list_int] :
( Y
!= ( produc5086643055186798020st_int @ A5 @ ( produc8650753666468850689st_int @ B5 @ C2 ) ) ) ).
% prod_cases3
thf(fact_261_prod__cases3,axiom,
! [Y: produc1019184382078353393nt_nat] :
~ ! [A5: int,B5: int > int,C2: nat] :
( Y
!= ( produc8342123264692915235nt_nat @ A5 @ ( produc2630796075472406112nt_nat @ B5 @ C2 ) ) ) ).
% prod_cases3
thf(fact_262_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_263_minus__nat_Odiff__0,axiom,
! [M: nat] :
( ( minus_minus_nat @ M @ zero_zero_nat )
= M ) ).
% minus_nat.diff_0
thf(fact_264_star__induct,axiom,
! [R: produc4400946599758736694st_int > produc4400946599758736694st_int > $o,X1a: list_instr,X1b: list_P419547167332244514st_int,X2a: list_instr,X2b: list_P419547167332244514st_int,P: list_instr > list_P419547167332244514st_int > list_instr > list_P419547167332244514st_int > $o] :
( ( star_P520819168889845767st_int @ R @ ( produc7764413618310988720st_int @ X1a @ X1b ) @ ( produc7764413618310988720st_int @ X2a @ X2b ) )
=> ( ! [A5: list_instr,B5: list_P419547167332244514st_int] : ( P @ A5 @ B5 @ A5 @ B5 )
=> ( ! [A5: list_instr,B5: list_P419547167332244514st_int,Aa: list_instr,Ba: list_P419547167332244514st_int,Ab: list_instr,Bb: list_P419547167332244514st_int] :
( ( R @ ( produc7764413618310988720st_int @ A5 @ B5 ) @ ( produc7764413618310988720st_int @ Aa @ Ba ) )
=> ( ( star_P520819168889845767st_int @ R @ ( produc7764413618310988720st_int @ Aa @ Ba ) @ ( produc7764413618310988720st_int @ Ab @ Bb ) )
=> ( ( P @ Aa @ Ba @ Ab @ Bb )
=> ( P @ A5 @ B5 @ Ab @ Bb ) ) ) )
=> ( P @ X1a @ X1b @ X2a @ X2b ) ) ) ) ).
% star_induct
thf(fact_265_star__induct,axiom,
! [R: produc6425607678544837394st_int > produc6425607678544837394st_int > $o,X1a: int,X1b: produc369741286924889929st_int,X2a: int,X2b: produc369741286924889929st_int,P: int > produc369741286924889929st_int > int > produc369741286924889929st_int > $o] :
( ( star_P707599355569300323st_int @ R @ ( produc5086643055186798020st_int @ X1a @ X1b ) @ ( produc5086643055186798020st_int @ X2a @ X2b ) )
=> ( ! [A5: int,B5: produc369741286924889929st_int] : ( P @ A5 @ B5 @ A5 @ B5 )
=> ( ! [A5: int,B5: produc369741286924889929st_int,Aa: int,Ba: produc369741286924889929st_int,Ab: int,Bb: produc369741286924889929st_int] :
( ( R @ ( produc5086643055186798020st_int @ A5 @ B5 ) @ ( produc5086643055186798020st_int @ Aa @ Ba ) )
=> ( ( star_P707599355569300323st_int @ R @ ( produc5086643055186798020st_int @ Aa @ Ba ) @ ( produc5086643055186798020st_int @ Ab @ Bb ) )
=> ( ( P @ Aa @ Ba @ Ab @ Bb )
=> ( P @ A5 @ B5 @ Ab @ Bb ) ) ) )
=> ( P @ X1a @ X1b @ X2a @ X2b ) ) ) ) ).
% star_induct
thf(fact_266_star__induct,axiom,
! [R: produc1019184382078353393nt_nat > produc1019184382078353393nt_nat > $o,X1a: int,X1b: produc1534919314292393896nt_nat,X2a: int,X2b: produc1534919314292393896nt_nat,P: int > produc1534919314292393896nt_nat > int > produc1534919314292393896nt_nat > $o] :
( ( star_P5461765526710342210nt_nat @ R @ ( produc8342123264692915235nt_nat @ X1a @ X1b ) @ ( produc8342123264692915235nt_nat @ X2a @ X2b ) )
=> ( ! [A5: int,B5: produc1534919314292393896nt_nat] : ( P @ A5 @ B5 @ A5 @ B5 )
=> ( ! [A5: int,B5: produc1534919314292393896nt_nat,Aa: int,Ba: produc1534919314292393896nt_nat,Ab: int,Bb: produc1534919314292393896nt_nat] :
( ( R @ ( produc8342123264692915235nt_nat @ A5 @ B5 ) @ ( produc8342123264692915235nt_nat @ Aa @ Ba ) )
=> ( ( star_P5461765526710342210nt_nat @ R @ ( produc8342123264692915235nt_nat @ Aa @ Ba ) @ ( produc8342123264692915235nt_nat @ Ab @ Bb ) )
=> ( ( P @ Aa @ Ba @ Ab @ Bb )
=> ( P @ A5 @ B5 @ Ab @ Bb ) ) ) )
=> ( P @ X1a @ X1b @ X2a @ X2b ) ) ) ) ).
% star_induct
thf(fact_267_star__induct,axiom,
! [R: produc369741286924889929st_int > produc369741286924889929st_int > $o,X1a: list_char > int,X1b: list_int,X2a: list_char > int,X2b: list_int,P: ( list_char > int ) > list_int > ( list_char > int ) > list_int > $o] :
( ( star_P8562542470885916728st_int @ R @ ( produc8650753666468850689st_int @ X1a @ X1b ) @ ( produc8650753666468850689st_int @ X2a @ X2b ) )
=> ( ! [A5: list_char > int,B5: list_int] : ( P @ A5 @ B5 @ A5 @ B5 )
=> ( ! [A5: list_char > int,B5: list_int,Aa: list_char > int,Ba: list_int,Ab: list_char > int,Bb: list_int] :
( ( R @ ( produc8650753666468850689st_int @ A5 @ B5 ) @ ( produc8650753666468850689st_int @ Aa @ Ba ) )
=> ( ( star_P8562542470885916728st_int @ R @ ( produc8650753666468850689st_int @ Aa @ Ba ) @ ( produc8650753666468850689st_int @ Ab @ Bb ) )
=> ( ( P @ Aa @ Ba @ Ab @ Bb )
=> ( P @ A5 @ B5 @ Ab @ Bb ) ) ) )
=> ( P @ X1a @ X1b @ X2a @ X2b ) ) ) ) ).
% star_induct
thf(fact_268_star__induct,axiom,
! [R: produc1534919314292393896nt_nat > produc1534919314292393896nt_nat > $o,X1a: int > int,X1b: nat,X2a: int > int,X2b: nat,P: ( int > int ) > nat > ( int > int ) > nat > $o] :
( ( star_P2443116637854396055nt_nat @ R @ ( produc2630796075472406112nt_nat @ X1a @ X1b ) @ ( produc2630796075472406112nt_nat @ X2a @ X2b ) )
=> ( ! [A5: int > int,B5: nat] : ( P @ A5 @ B5 @ A5 @ B5 )
=> ( ! [A5: int > int,B5: nat,Aa: int > int,Ba: nat,Ab: int > int,Bb: nat] :
( ( R @ ( produc2630796075472406112nt_nat @ A5 @ B5 ) @ ( produc2630796075472406112nt_nat @ Aa @ Ba ) )
=> ( ( star_P2443116637854396055nt_nat @ R @ ( produc2630796075472406112nt_nat @ Aa @ Ba ) @ ( produc2630796075472406112nt_nat @ Ab @ Bb ) )
=> ( ( P @ Aa @ Ba @ Ab @ Bb )
=> ( P @ A5 @ B5 @ Ab @ Bb ) ) ) )
=> ( P @ X1a @ X1b @ X2a @ X2b ) ) ) ) ).
% star_induct
thf(fact_269_add__m__stack_Osimps_I1_J,axiom,
! [Uu: list_int,Ms3: int > int] :
( ( add_m_stack @ zero_zero_nat @ Uu @ Ms3 )
= Ms3 ) ).
% add_m_stack.simps(1)
thf(fact_270__092_060open_062P_A_092_060turnstile_062_A_Ipc_H_M_As_H_M_Astk_H_J_A_092_060rightarrow_062_A_Ipc_H_H_M_As_H_H_M_Astk_H_H_J_092_060close_062,axiom,
exec1 @ p @ ( produc5086643055186798020st_int @ pc2 @ ( produc8650753666468850689st_int @ s2 @ stk2 ) ) @ ( produc5086643055186798020st_int @ pc @ ( produc8650753666468850689st_int @ s @ stk ) ) ).
% \<open>P \<turnstile> (pc', s', stk') \<rightarrow> (pc'', s'', stk'')\<close>
thf(fact_271_le__add__diff__inverse2,axiom,
! [B: nat,A: nat] :
( ( ord_less_eq_nat @ B @ A )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
= A ) ) ).
% le_add_diff_inverse2
thf(fact_272_le__add__diff__inverse2,axiom,
! [B: int,A: int] :
( ( ord_less_eq_int @ B @ A )
=> ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
= A ) ) ).
% le_add_diff_inverse2
thf(fact_273_le__add__diff__inverse,axiom,
! [B: nat,A: nat] :
( ( ord_less_eq_nat @ B @ A )
=> ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
= A ) ) ).
% le_add_diff_inverse
thf(fact_274_le__add__diff__inverse,axiom,
! [B: int,A: int] :
( ( ord_less_eq_int @ B @ A )
=> ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
= A ) ) ).
% le_add_diff_inverse
thf(fact_275_exec1__m__exec1,axiom,
! [P: list_instr,Pc: int,S: list_char > int,Stk: list_int,Pc2: int,S2: list_char > int,Stk2: list_int,Sp3: nat] :
( ( exec1 @ P @ ( produc5086643055186798020st_int @ Pc @ ( produc8650753666468850689st_int @ S @ Stk ) ) @ ( produc5086643055186798020st_int @ Pc2 @ ( produc8650753666468850689st_int @ S2 @ Stk2 ) ) )
=> ( ( ord_less_eq_nat @ ( msp @ P @ Pc ) @ Sp3 )
=> ( ( ord_less_eq_nat @ Sp3 @ ( size_size_list_int @ Stk ) )
=> ( m_exec1 @ ( to_m_prog @ P ) @ ( produc8342123264692915235nt_nat @ Pc @ ( produc2630796075472406112nt_nat @ ( add_m_stack @ Sp3 @ Stk @ ( to_m_state @ ( vars @ P ) @ S ) ) @ Sp3 ) ) @ ( produc8342123264692915235nt_nat @ Pc2 @ ( produc2630796075472406112nt_nat @ ( add_m_stack @ ( minus_minus_nat @ ( plus_plus_nat @ Sp3 @ ( size_size_list_int @ Stk2 ) ) @ ( size_size_list_int @ Stk ) ) @ Stk2 @ ( to_m_state @ ( vars @ P ) @ S2 ) ) @ ( minus_minus_nat @ ( plus_plus_nat @ Sp3 @ ( size_size_list_int @ Stk2 ) ) @ ( size_size_list_int @ Stk ) ) ) ) ) ) ) ) ).
% exec1_m_exec1
thf(fact_276_double__eq__0__iff,axiom,
! [A: int] :
( ( ( plus_plus_int @ A @ A )
= zero_zero_int )
= ( A = zero_zero_int ) ) ).
% double_eq_0_iff
thf(fact_277_add__le__add__imp__diff__le,axiom,
! [I: nat,K: nat,N: nat,J: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
=> ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
=> ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% add_le_add_imp_diff_le
thf(fact_278_add__le__add__imp__diff__le,axiom,
! [I: int,K: int,N: int,J: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
=> ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
=> ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
=> ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
=> ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% add_le_add_imp_diff_le
thf(fact_279_add__le__imp__le__diff,axiom,
! [I: nat,K: nat,N: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
=> ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% add_le_imp_le_diff
thf(fact_280_add__le__imp__le__diff,axiom,
! [I: int,K: int,N: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
=> ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% add_le_imp_le_diff
thf(fact_281_order__refl,axiom,
! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% order_refl
thf(fact_282_order__refl,axiom,
! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% order_refl
thf(fact_283_dual__order_Orefl,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% dual_order.refl
thf(fact_284_dual__order_Orefl,axiom,
! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% dual_order.refl
thf(fact_285_Euclid__induct,axiom,
! [P: nat > nat > $o,A: nat,B: nat] :
( ! [A5: nat,B5: nat] :
( ( P @ A5 @ B5 )
= ( P @ B5 @ A5 ) )
=> ( ! [A5: nat] : ( P @ A5 @ zero_zero_nat )
=> ( ! [A5: nat,B5: nat] :
( ( P @ A5 @ B5 )
=> ( P @ A5 @ ( plus_plus_nat @ A5 @ B5 ) ) )
=> ( P @ A @ B ) ) ) ) ).
% Euclid_induct
thf(fact_286_verit__sum__simplify,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ) ).
% verit_sum_simplify
thf(fact_287_verit__sum__simplify,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ) ).
% verit_sum_simplify
thf(fact_288_iexec_Ocases,axiom,
! [X: produc5995290525303592096st_int] :
~ ! [Ins: instr,I2: int,S3: list_char > int,Stk3: list_int] :
( X
!= ( produc1484136438817787418st_int @ Ins @ ( produc5086643055186798020st_int @ I2 @ ( produc8650753666468850689st_int @ S3 @ Stk3 ) ) ) ) ).
% iexec.cases
thf(fact_289_exec__induct,axiom,
! [Pa: list_instr,X1a: int,X1b: list_char > int,X1c: list_int,X2a: int,X2b: list_char > int,X2c: list_int,P: int > ( list_char > int ) > list_int > int > ( list_char > int ) > list_int > $o] :
( ( star_P707599355569300323st_int @ ( exec1 @ Pa ) @ ( produc5086643055186798020st_int @ X1a @ ( produc8650753666468850689st_int @ X1b @ X1c ) ) @ ( produc5086643055186798020st_int @ X2a @ ( produc8650753666468850689st_int @ X2b @ X2c ) ) )
=> ( ! [A5: int,Aa: list_char > int,B5: list_int] : ( P @ A5 @ Aa @ B5 @ A5 @ Aa @ B5 )
=> ( ! [A5: int,Aa: list_char > int,B5: list_int,Ab: int,Ac: list_char > int,Ba: list_int,Ad: int,Ae: list_char > int,Bb: list_int] :
( ( exec1 @ Pa @ ( produc5086643055186798020st_int @ A5 @ ( produc8650753666468850689st_int @ Aa @ B5 ) ) @ ( produc5086643055186798020st_int @ Ab @ ( produc8650753666468850689st_int @ Ac @ Ba ) ) )
=> ( ( star_P707599355569300323st_int @ ( exec1 @ Pa ) @ ( produc5086643055186798020st_int @ Ab @ ( produc8650753666468850689st_int @ Ac @ Ba ) ) @ ( produc5086643055186798020st_int @ Ad @ ( produc8650753666468850689st_int @ Ae @ Bb ) ) )
=> ( ( P @ Ab @ Ac @ Ba @ Ad @ Ae @ Bb )
=> ( P @ A5 @ Aa @ B5 @ Ad @ Ae @ Bb ) ) ) )
=> ( P @ X1a @ X1b @ X1c @ X2a @ X2b @ X2c ) ) ) ) ).
% exec_induct
thf(fact_290_add__m__stack__nneg,axiom,
! [A: int,N: nat,Stk: list_int,Ms3: int > int] :
( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( add_m_stack @ N @ Stk @ Ms3 @ A )
= ( Ms3 @ A ) ) ) ).
% add_m_stack_nneg
thf(fact_291_order__antisym__conv,axiom,
! [Y: nat,X: nat] :
( ( ord_less_eq_nat @ Y @ X )
=> ( ( ord_less_eq_nat @ X @ Y )
= ( X = Y ) ) ) ).
% order_antisym_conv
thf(fact_292_order__antisym__conv,axiom,
! [Y: int,X: int] :
( ( ord_less_eq_int @ Y @ X )
=> ( ( ord_less_eq_int @ X @ Y )
= ( X = Y ) ) ) ).
% order_antisym_conv
thf(fact_293_linorder__le__cases,axiom,
! [X: nat,Y: nat] :
( ~ ( ord_less_eq_nat @ X @ Y )
=> ( ord_less_eq_nat @ Y @ X ) ) ).
% linorder_le_cases
thf(fact_294_linorder__le__cases,axiom,
! [X: int,Y: int] :
( ~ ( ord_less_eq_int @ X @ Y )
=> ( ord_less_eq_int @ Y @ X ) ) ).
% linorder_le_cases
thf(fact_295_ord__le__eq__subst,axiom,
! [A: nat,B: nat,F: nat > nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_296_ord__le__eq__subst,axiom,
! [A: nat,B: nat,F: nat > int,C: int] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_297_ord__le__eq__subst,axiom,
! [A: int,B: int,F: int > nat,C: nat] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X4: int,Y3: int] :
( ( ord_less_eq_int @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_298_ord__le__eq__subst,axiom,
! [A: int,B: int,F: int > int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X4: int,Y3: int] :
( ( ord_less_eq_int @ X4 @ Y3 )
=> ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_299_ord__eq__le__subst,axiom,
! [A: nat,F: nat > nat,B: nat,C: nat] :
( ( A
= ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_300_ord__eq__le__subst,axiom,
! [A: int,F: nat > int,B: nat,C: nat] :
( ( A
= ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_301_ord__eq__le__subst,axiom,
! [A: nat,F: int > nat,B: int,C: int] :
( ( A
= ( F @ B ) )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ! [X4: int,Y3: int] :
( ( ord_less_eq_int @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_302_ord__eq__le__subst,axiom,
! [A: int,F: int > int,B: int,C: int] :
( ( A
= ( F @ B ) )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ! [X4: int,Y3: int] :
( ( ord_less_eq_int @ X4 @ Y3 )
=> ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_303_linorder__linear,axiom,
! [X: nat,Y: nat] :
( ( ord_less_eq_nat @ X @ Y )
| ( ord_less_eq_nat @ Y @ X ) ) ).
% linorder_linear
thf(fact_304_linorder__linear,axiom,
! [X: int,Y: int] :
( ( ord_less_eq_int @ X @ Y )
| ( ord_less_eq_int @ Y @ X ) ) ).
% linorder_linear
thf(fact_305_verit__la__disequality,axiom,
! [A: nat,B: nat] :
( ( A = B )
| ~ ( ord_less_eq_nat @ A @ B )
| ~ ( ord_less_eq_nat @ B @ A ) ) ).
% verit_la_disequality
thf(fact_306_verit__la__disequality,axiom,
! [A: int,B: int] :
( ( A = B )
| ~ ( ord_less_eq_int @ A @ B )
| ~ ( ord_less_eq_int @ B @ A ) ) ).
% verit_la_disequality
thf(fact_307_order__eq__refl,axiom,
! [X: nat,Y: nat] :
( ( X = Y )
=> ( ord_less_eq_nat @ X @ Y ) ) ).
% order_eq_refl
thf(fact_308_order__eq__refl,axiom,
! [X: int,Y: int] :
( ( X = Y )
=> ( ord_less_eq_int @ X @ Y ) ) ).
% order_eq_refl
thf(fact_309_order__subst2,axiom,
! [A: nat,B: nat,F: nat > nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( F @ B ) @ C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% order_subst2
thf(fact_310_order__subst2,axiom,
! [A: nat,B: nat,F: nat > int,C: int] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_int @ ( F @ B ) @ C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% order_subst2
thf(fact_311_order__subst2,axiom,
! [A: int,B: int,F: int > nat,C: nat] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_nat @ ( F @ B ) @ C )
=> ( ! [X4: int,Y3: int] :
( ( ord_less_eq_int @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% order_subst2
thf(fact_312_order__subst2,axiom,
! [A: int,B: int,F: int > int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ ( F @ B ) @ C )
=> ( ! [X4: int,Y3: int] :
( ( ord_less_eq_int @ X4 @ Y3 )
=> ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% order_subst2
thf(fact_313_order__subst1,axiom,
! [A: nat,F: nat > nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_314_order__subst1,axiom,
! [A: nat,F: int > nat,B: int,C: int] :
( ( ord_less_eq_nat @ A @ ( F @ B ) )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ! [X4: int,Y3: int] :
( ( ord_less_eq_int @ X4 @ Y3 )
=> ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_315_order__subst1,axiom,
! [A: int,F: nat > int,B: nat,C: nat] :
( ( ord_less_eq_int @ A @ ( F @ B ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ! [X4: nat,Y3: nat] :
( ( ord_less_eq_nat @ X4 @ Y3 )
=> ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_316_order__subst1,axiom,
! [A: int,F: int > int,B: int,C: int] :
( ( ord_less_eq_int @ A @ ( F @ B ) )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ! [X4: int,Y3: int] :
( ( ord_less_eq_int @ X4 @ Y3 )
=> ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_317_Orderings_Oorder__eq__iff,axiom,
( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
= ( ^ [A4: nat,B4: nat] :
( ( ord_less_eq_nat @ A4 @ B4 )
& ( ord_less_eq_nat @ B4 @ A4 ) ) ) ) ).
% Orderings.order_eq_iff
thf(fact_318_Orderings_Oorder__eq__iff,axiom,
( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
= ( ^ [A4: int,B4: int] :
( ( ord_less_eq_int @ A4 @ B4 )
& ( ord_less_eq_int @ B4 @ A4 ) ) ) ) ).
% Orderings.order_eq_iff
thf(fact_319_antisym,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ) ).
% antisym
thf(fact_320_antisym,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( A = B ) ) ) ).
% antisym
thf(fact_321_dual__order_Otrans,axiom,
! [B: nat,A: nat,C: nat] :
( ( ord_less_eq_nat @ B @ A )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( ord_less_eq_nat @ C @ A ) ) ) ).
% dual_order.trans
thf(fact_322_dual__order_Otrans,axiom,
! [B: int,A: int,C: int] :
( ( ord_less_eq_int @ B @ A )
=> ( ( ord_less_eq_int @ C @ B )
=> ( ord_less_eq_int @ C @ A ) ) ) ).
% dual_order.trans
thf(fact_323_dual__order_Oantisym,axiom,
! [B: nat,A: nat] :
( ( ord_less_eq_nat @ B @ A )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( A = B ) ) ) ).
% dual_order.antisym
thf(fact_324_dual__order_Oantisym,axiom,
! [B: int,A: int] :
( ( ord_less_eq_int @ B @ A )
=> ( ( ord_less_eq_int @ A @ B )
=> ( A = B ) ) ) ).
% dual_order.antisym
thf(fact_325_dual__order_Oeq__iff,axiom,
( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
= ( ^ [A4: nat,B4: nat] :
( ( ord_less_eq_nat @ B4 @ A4 )
& ( ord_less_eq_nat @ A4 @ B4 ) ) ) ) ).
% dual_order.eq_iff
thf(fact_326_dual__order_Oeq__iff,axiom,
( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
= ( ^ [A4: int,B4: int] :
( ( ord_less_eq_int @ B4 @ A4 )
& ( ord_less_eq_int @ A4 @ B4 ) ) ) ) ).
% dual_order.eq_iff
thf(fact_327_linorder__wlog,axiom,
! [P: nat > nat > $o,A: nat,B: nat] :
( ! [A5: nat,B5: nat] :
( ( ord_less_eq_nat @ A5 @ B5 )
=> ( P @ A5 @ B5 ) )
=> ( ! [A5: nat,B5: nat] :
( ( P @ B5 @ A5 )
=> ( P @ A5 @ B5 ) )
=> ( P @ A @ B ) ) ) ).
% linorder_wlog
thf(fact_328_linorder__wlog,axiom,
! [P: int > int > $o,A: int,B: int] :
( ! [A5: int,B5: int] :
( ( ord_less_eq_int @ A5 @ B5 )
=> ( P @ A5 @ B5 ) )
=> ( ! [A5: int,B5: int] :
( ( P @ B5 @ A5 )
=> ( P @ A5 @ B5 ) )
=> ( P @ A @ B ) ) ) ).
% linorder_wlog
thf(fact_329_order__trans,axiom,
! [X: nat,Y: nat,Z: nat] :
( ( ord_less_eq_nat @ X @ Y )
=> ( ( ord_less_eq_nat @ Y @ Z )
=> ( ord_less_eq_nat @ X @ Z ) ) ) ).
% order_trans
thf(fact_330_order__trans,axiom,
! [X: int,Y: int,Z: int] :
( ( ord_less_eq_int @ X @ Y )
=> ( ( ord_less_eq_int @ Y @ Z )
=> ( ord_less_eq_int @ X @ Z ) ) ) ).
% order_trans
thf(fact_331_order_Otrans,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ) ).
% order.trans
thf(fact_332_order_Otrans,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ A @ C ) ) ) ).
% order.trans
thf(fact_333_order__antisym,axiom,
! [X: nat,Y: nat] :
( ( ord_less_eq_nat @ X @ Y )
=> ( ( ord_less_eq_nat @ Y @ X )
=> ( X = Y ) ) ) ).
% order_antisym
thf(fact_334_order__antisym,axiom,
! [X: int,Y: int] :
( ( ord_less_eq_int @ X @ Y )
=> ( ( ord_less_eq_int @ Y @ X )
=> ( X = Y ) ) ) ).
% order_antisym
thf(fact_335_ord__le__eq__trans,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat @ A @ C ) ) ) ).
% ord_le_eq_trans
thf(fact_336_ord__le__eq__trans,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_int @ A @ C ) ) ) ).
% ord_le_eq_trans
thf(fact_337_ord__eq__le__trans,axiom,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ) ).
% ord_eq_le_trans
thf(fact_338_ord__eq__le__trans,axiom,
! [A: int,B: int,C: int] :
( ( A = B )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ A @ C ) ) ) ).
% ord_eq_le_trans
thf(fact_339_order__class_Oorder__eq__iff,axiom,
( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
= ( ^ [X3: nat,Y5: nat] :
( ( ord_less_eq_nat @ X3 @ Y5 )
& ( ord_less_eq_nat @ Y5 @ X3 ) ) ) ) ).
% order_class.order_eq_iff
thf(fact_340_order__class_Oorder__eq__iff,axiom,
( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
= ( ^ [X3: int,Y5: int] :
( ( ord_less_eq_int @ X3 @ Y5 )
& ( ord_less_eq_int @ Y5 @ X3 ) ) ) ) ).
% order_class.order_eq_iff
thf(fact_341_le__cases3,axiom,
! [X: nat,Y: nat,Z: nat] :
( ( ( ord_less_eq_nat @ X @ Y )
=> ~ ( ord_less_eq_nat @ Y @ Z ) )
=> ( ( ( ord_less_eq_nat @ Y @ X )
=> ~ ( ord_less_eq_nat @ X @ Z ) )
=> ( ( ( ord_less_eq_nat @ X @ Z )
=> ~ ( ord_less_eq_nat @ Z @ Y ) )
=> ( ( ( ord_less_eq_nat @ Z @ Y )
=> ~ ( ord_less_eq_nat @ Y @ X ) )
=> ( ( ( ord_less_eq_nat @ Y @ Z )
=> ~ ( ord_less_eq_nat @ Z @ X ) )
=> ~ ( ( ord_less_eq_nat @ Z @ X )
=> ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% le_cases3
thf(fact_342_le__cases3,axiom,
! [X: int,Y: int,Z: int] :
( ( ( ord_less_eq_int @ X @ Y )
=> ~ ( ord_less_eq_int @ Y @ Z ) )
=> ( ( ( ord_less_eq_int @ Y @ X )
=> ~ ( ord_less_eq_int @ X @ Z ) )
=> ( ( ( ord_less_eq_int @ X @ Z )
=> ~ ( ord_less_eq_int @ Z @ Y ) )
=> ( ( ( ord_less_eq_int @ Z @ Y )
=> ~ ( ord_less_eq_int @ Y @ X ) )
=> ( ( ( ord_less_eq_int @ Y @ Z )
=> ~ ( ord_less_eq_int @ Z @ X ) )
=> ~ ( ( ord_less_eq_int @ Z @ X )
=> ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% le_cases3
thf(fact_343_nle__le,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ( ord_less_eq_nat @ B @ A )
& ( B != A ) ) ) ).
% nle_le
thf(fact_344_nle__le,axiom,
! [A: int,B: int] :
( ( ~ ( ord_less_eq_int @ A @ B ) )
= ( ( ord_less_eq_int @ B @ A )
& ( B != A ) ) ) ).
% nle_le
thf(fact_345_verit__comp__simplify1_I2_J,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% verit_comp_simplify1(2)
thf(fact_346_verit__comp__simplify1_I2_J,axiom,
! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% verit_comp_simplify1(2)
thf(fact_347_size__char__eq__0,axiom,
( size_size_char
= ( ^ [C3: char] : zero_zero_nat ) ) ).
% size_char_eq_0
thf(fact_348__092_060open_062_092_060lbrakk_062P_A_092_060Turnstile_062_Acfs_A_064_A_091_Ipc_H_M_As_H_M_Astk_H_J_093_059_Ampred_AP_A_Icfs_A_064_A_091_Ipc_H_M_As_H_M_Astk_H_J_093_J_A0_A_Ilength_Acfs_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Ato__m__prog_AP_A_092_060_094bold_062_092_060turnstile_062_A_Ipc_M_Ato__m__state_A_Ivars_AP_J_As_M_A0_J_A_092_060_094bold_062_092_060rightarrow_062_092_060_094bold_062_K_A_Ipc_H_M_Aadd__m__stack_A_Ilength_Astk_H_A_N_Alength_Astk_J_Astk_H_A_Ito__m__state_A_Ivars_AP_J_As_H_J_M_Alength_Astk_H_A_N_Alength_Astk_J_092_060close_062,axiom,
( ( execl @ p @ ( append5028292981072010935st_int @ cfsa @ ( cons_P4151473878978182108st_int @ ( produc5086643055186798020st_int @ pc2 @ ( produc8650753666468850689st_int @ s2 @ stk2 ) ) @ nil_Pr749310521696113548st_int ) ) )
=> ( ( mpred @ p @ ( append5028292981072010935st_int @ cfsa @ ( cons_P4151473878978182108st_int @ ( produc5086643055186798020st_int @ pc2 @ ( produc8650753666468850689st_int @ s2 @ stk2 ) ) @ nil_Pr749310521696113548st_int ) ) @ zero_zero_nat @ ( size_s229347708945616566st_int @ cfsa ) )
=> ( star_P5461765526710342210nt_nat @ ( m_exec1 @ ( to_m_prog @ p ) ) @ ( produc8342123264692915235nt_nat @ pc3 @ ( produc2630796075472406112nt_nat @ ( to_m_state @ ( vars @ p ) @ s3 ) @ zero_zero_nat ) ) @ ( produc8342123264692915235nt_nat @ pc2 @ ( produc2630796075472406112nt_nat @ ( add_m_stack @ ( minus_minus_nat @ ( size_size_list_int @ stk2 ) @ ( size_size_list_int @ stk3 ) ) @ stk2 @ ( to_m_state @ ( vars @ p ) @ s2 ) ) @ ( minus_minus_nat @ ( size_size_list_int @ stk2 ) @ ( size_size_list_int @ stk3 ) ) ) ) ) ) ) ).
% \<open>\<lbrakk>P \<Turnstile> cfs @ [(pc', s', stk')]; mpred P (cfs @ [(pc', s', stk')]) 0 (length cfs)\<rbrakk> \<Longrightarrow> to_m_prog P \<^bold>\<turnstile> (pc, to_m_state (vars P) s, 0) \<^bold>\<rightarrow>\<^bold>* (pc', add_m_stack (length stk' - length stk) stk' (to_m_state (vars P) s'), length stk' - length stk)\<close>
thf(fact_349_add__0__iff,axiom,
! [B: nat,A: nat] :
( ( B
= ( plus_plus_nat @ B @ A ) )
= ( A = zero_zero_nat ) ) ).
% add_0_iff
thf(fact_350_add__0__iff,axiom,
! [B: int,A: int] :
( ( B
= ( plus_plus_int @ B @ A ) )
= ( A = zero_zero_int ) ) ).
% add_0_iff
thf(fact_351_le__numeral__extra_I3_J,axiom,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% le_numeral_extra(3)
thf(fact_352_le__numeral__extra_I3_J,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% le_numeral_extra(3)
thf(fact_353_iexec__shift,axiom,
! [N: int,I4: int,S2: list_char > int,Stk2: list_int,Ins2: instr,I: int,S: list_char > int,Stk: list_int] :
( ( ( produc5086643055186798020st_int @ ( plus_plus_int @ N @ I4 ) @ ( produc8650753666468850689st_int @ S2 @ Stk2 ) )
= ( iexec @ Ins2 @ ( produc5086643055186798020st_int @ ( plus_plus_int @ N @ I ) @ ( produc8650753666468850689st_int @ S @ Stk ) ) ) )
= ( ( produc5086643055186798020st_int @ I4 @ ( produc8650753666468850689st_int @ S2 @ Stk2 ) )
= ( iexec @ Ins2 @ ( produc5086643055186798020st_int @ I @ ( produc8650753666468850689st_int @ S @ Stk ) ) ) ) ) ).
% iexec_shift
thf(fact_354_m__exec__exec,axiom,
! [P: list_instr,Pc: int,Ms3: int > int,Sp3: nat,Pc2: int,Ms4: int > int,Sp4: nat,Stk: list_int] :
( ( star_P5461765526710342210nt_nat @ ( m_exec1 @ ( to_m_prog @ P ) ) @ ( produc8342123264692915235nt_nat @ Pc @ ( produc2630796075472406112nt_nat @ Ms3 @ Sp3 ) ) @ ( produc8342123264692915235nt_nat @ Pc2 @ ( produc2630796075472406112nt_nat @ Ms4 @ Sp4 ) ) )
=> ( star_P707599355569300323st_int @ ( exec1 @ P ) @ ( produc5086643055186798020st_int @ Pc @ ( produc8650753666468850689st_int @ ( to_state @ ( vars @ P ) @ Ms3 ) @ ( append_int @ ( add_stack @ Sp3 @ Ms3 ) @ Stk ) ) ) @ ( produc5086643055186798020st_int @ Pc2 @ ( produc8650753666468850689st_int @ ( to_state @ ( vars @ P ) @ Ms4 ) @ ( append_int @ ( add_stack @ Sp4 @ Ms4 ) @ Stk ) ) ) ) ) ).
% m_exec_exec
thf(fact_355_A,axiom,
execl @ p @ ( append5028292981072010935st_int @ cfsa @ ( cons_P4151473878978182108st_int @ ( produc5086643055186798020st_int @ pc2 @ ( produc8650753666468850689st_int @ s2 @ stk2 ) ) @ ( cons_P4151473878978182108st_int @ ( produc5086643055186798020st_int @ pc @ ( produc8650753666468850689st_int @ s @ stk ) ) @ nil_Pr749310521696113548st_int ) ) ) ).
% A
thf(fact_356__092_060open_062P_A_092_060Turnstile_062_Acfs_A_064_A_091_Ipc_H_M_As_H_M_Astk_H_J_093_092_060close_062,axiom,
execl @ p @ ( append5028292981072010935st_int @ cfsa @ ( cons_P4151473878978182108st_int @ ( produc5086643055186798020st_int @ pc2 @ ( produc8650753666468850689st_int @ s2 @ stk2 ) ) @ nil_Pr749310521696113548st_int ) ) ).
% \<open>P \<Turnstile> cfs @ [(pc', s', stk')]\<close>
thf(fact_357__092_060open_062mpred_AP_A_Icfs_A_064_A_091_Ipc_H_M_As_H_M_Astk_H_J_093_J_A0_A_Ilength_Acfs_J_092_060close_062,axiom,
mpred @ p @ ( append5028292981072010935st_int @ cfsa @ ( cons_P4151473878978182108st_int @ ( produc5086643055186798020st_int @ pc2 @ ( produc8650753666468850689st_int @ s2 @ stk2 ) ) @ nil_Pr749310521696113548st_int ) ) @ zero_zero_nat @ ( size_s229347708945616566st_int @ cfsa ) ).
% \<open>mpred P (cfs @ [(pc', s', stk')]) 0 (length cfs)\<close>
thf(fact_358_B,axiom,
mpred @ p @ ( append5028292981072010935st_int @ cfsa @ ( cons_P4151473878978182108st_int @ ( produc5086643055186798020st_int @ pc2 @ ( produc8650753666468850689st_int @ s2 @ stk2 ) ) @ ( cons_P4151473878978182108st_int @ ( produc5086643055186798020st_int @ pc @ ( produc8650753666468850689st_int @ s @ stk ) ) @ nil_Pr749310521696113548st_int ) ) ) @ zero_zero_nat @ ( suc @ ( size_s229347708945616566st_int @ cfsa ) ) ).
% B
thf(fact_359__092_060open_062_Icfs_A_064_A_091_Ipc_H_M_As_H_M_Astk_H_J_093_J_A_B_A0_A_061_A_Ipc_M_As_M_Astk_J_092_060close_062,axiom,
( ( nth_Pr8327173284404383691st_int @ ( append5028292981072010935st_int @ cfsa @ ( cons_P4151473878978182108st_int @ ( produc5086643055186798020st_int @ pc2 @ ( produc8650753666468850689st_int @ s2 @ stk2 ) ) @ nil_Pr749310521696113548st_int ) ) @ zero_zero_nat )
= ( produc5086643055186798020st_int @ pc3 @ ( produc8650753666468850689st_int @ s3 @ stk3 ) ) ) ).
% \<open>(cfs @ [(pc', s', stk')]) ! 0 = (pc, s, stk)\<close>
thf(fact_360_plus__int__code_I2_J,axiom,
! [L: int] :
( ( plus_plus_int @ zero_zero_int @ L )
= L ) ).
% plus_int_code(2)
thf(fact_361_plus__int__code_I1_J,axiom,
! [K: int] :
( ( plus_plus_int @ K @ zero_zero_int )
= K ) ).
% plus_int_code(1)
thf(fact_362_minus__int__code_I1_J,axiom,
! [K: int] :
( ( minus_minus_int @ K @ zero_zero_int )
= K ) ).
% minus_int_code(1)
thf(fact_363_less__eq__int__code_I1_J,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% less_eq_int_code(1)
thf(fact_364_execl_Ocases,axiom,
! [X: produc4400946599758736694st_int] :
( ! [P3: list_instr,Cf: produc6425607678544837394st_int,Cf2: produc6425607678544837394st_int,Cfs: list_P419547167332244514st_int] :
( X
!= ( produc7764413618310988720st_int @ P3 @ ( cons_P4151473878978182108st_int @ Cf @ ( cons_P4151473878978182108st_int @ Cf2 @ Cfs ) ) ) )
=> ( ! [P3: list_instr] :
( X
!= ( produc7764413618310988720st_int @ P3 @ nil_Pr749310521696113548st_int ) )
=> ~ ! [P3: list_instr,V: produc6425607678544837394st_int] :
( X
!= ( produc7764413618310988720st_int @ P3 @ ( cons_P4151473878978182108st_int @ V @ nil_Pr749310521696113548st_int ) ) ) ) ) ).
% execl.cases
thf(fact_365_to__state__eq,axiom,
! [Ms4: int > int,Ms3: int > int,Xs: list_list_char] :
( ! [A5: int] :
( ( ord_less_eq_int @ zero_zero_int @ A5 )
=> ( ( Ms4 @ A5 )
= ( Ms3 @ A5 ) ) )
=> ( ( to_state @ Xs @ Ms4 )
= ( to_state @ Xs @ Ms3 ) ) ) ).
% to_state_eq
thf(fact_366_verit__la__generic,axiom,
! [A: int,X: int] :
( ( ord_less_eq_int @ A @ X )
| ( A = X )
| ( ord_less_eq_int @ X @ A ) ) ).
% verit_la_generic
thf(fact_367_execl_Osimps_I1_J,axiom,
! [P: list_instr,Cf3: produc6425607678544837394st_int,Cf4: produc6425607678544837394st_int,Cfs2: list_P419547167332244514st_int] :
( ( execl @ P @ ( cons_P4151473878978182108st_int @ Cf3 @ ( cons_P4151473878978182108st_int @ Cf4 @ Cfs2 ) ) )
= ( ( exec1 @ P @ Cf3 @ Cf4 )
& ( execl @ P @ ( cons_P4151473878978182108st_int @ Cf4 @ Cfs2 ) ) ) ) ).
% execl.simps(1)
thf(fact_368_execl_Oelims_I1_J,axiom,
! [X: list_instr,Xa: list_P419547167332244514st_int,Y: $o] :
( ( ( execl @ X @ Xa )
= Y )
=> ( ! [Cf: produc6425607678544837394st_int,Cf2: produc6425607678544837394st_int,Cfs: list_P419547167332244514st_int] :
( ( Xa
= ( cons_P4151473878978182108st_int @ Cf @ ( cons_P4151473878978182108st_int @ Cf2 @ Cfs ) ) )
=> ( Y
= ( ~ ( ( exec1 @ X @ Cf @ Cf2 )
& ( execl @ X @ ( cons_P4151473878978182108st_int @ Cf2 @ Cfs ) ) ) ) ) )
=> ( ( ( Xa = nil_Pr749310521696113548st_int )
=> ~ Y )
=> ~ ( ? [V: produc6425607678544837394st_int] :
( Xa
= ( cons_P4151473878978182108st_int @ V @ nil_Pr749310521696113548st_int ) )
=> ~ Y ) ) ) ) ).
% execl.elims(1)
thf(fact_369_execl_Oelims_I2_J,axiom,
! [X: list_instr,Xa: list_P419547167332244514st_int] :
( ( execl @ X @ Xa )
=> ( ! [Cf: produc6425607678544837394st_int,Cf2: produc6425607678544837394st_int,Cfs: list_P419547167332244514st_int] :
( ( Xa
= ( cons_P4151473878978182108st_int @ Cf @ ( cons_P4151473878978182108st_int @ Cf2 @ Cfs ) ) )
=> ~ ( ( exec1 @ X @ Cf @ Cf2 )
& ( execl @ X @ ( cons_P4151473878978182108st_int @ Cf2 @ Cfs ) ) ) )
=> ( ( Xa != nil_Pr749310521696113548st_int )
=> ~ ! [V: produc6425607678544837394st_int] :
( Xa
!= ( cons_P4151473878978182108st_int @ V @ nil_Pr749310521696113548st_int ) ) ) ) ) ).
% execl.elims(2)
thf(fact_370_execl_Oelims_I3_J,axiom,
! [X: list_instr,Xa: list_P419547167332244514st_int] :
( ~ ( execl @ X @ Xa )
=> ~ ! [Cf: produc6425607678544837394st_int,Cf2: produc6425607678544837394st_int,Cfs: list_P419547167332244514st_int] :
( ( Xa
= ( cons_P4151473878978182108st_int @ Cf @ ( cons_P4151473878978182108st_int @ Cf2 @ Cfs ) ) )
=> ( ( exec1 @ X @ Cf @ Cf2 )
& ( execl @ X @ ( cons_P4151473878978182108st_int @ Cf2 @ Cfs ) ) ) ) ) ).
% execl.elims(3)
thf(fact_371_mpred__merge,axiom,
! [P: list_instr,Cfs2: list_P419547167332244514st_int,K: nat,M: nat,N: nat] :
( ( mpred @ P @ Cfs2 @ K @ M )
=> ( ( mpred @ P @ Cfs2 @ M @ N )
=> ( mpred @ P @ Cfs2 @ K @ N ) ) ) ).
% mpred_merge
thf(fact_372_execl_Osimps_I3_J,axiom,
! [P: list_instr,V2: produc6425607678544837394st_int] : ( execl @ P @ ( cons_P4151473878978182108st_int @ V2 @ nil_Pr749310521696113548st_int ) ) ).
% execl.simps(3)
thf(fact_373_execl_Osimps_I2_J,axiom,
! [P: list_instr] : ( execl @ P @ nil_Pr749310521696113548st_int ) ).
% execl.simps(2)
thf(fact_374_is__num__normalize_I1_J,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% is_num_normalize(1)
thf(fact_375_length__append,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( size_s229347708945616566st_int @ ( append5028292981072010935st_int @ Xs @ Ys ) )
= ( plus_plus_nat @ ( size_s229347708945616566st_int @ Xs ) @ ( size_s229347708945616566st_int @ Ys ) ) ) ).
% length_append
thf(fact_376_length__append,axiom,
! [Xs: list_m_instr,Ys: list_m_instr] :
( ( size_s5914166952900237872_instr @ ( append_m_instr @ Xs @ Ys ) )
= ( plus_plus_nat @ ( size_s5914166952900237872_instr @ Xs ) @ ( size_s5914166952900237872_instr @ Ys ) ) ) ).
% length_append
thf(fact_377_length__append,axiom,
! [Xs: list_instr,Ys: list_instr] :
( ( size_size_list_instr @ ( append_instr @ Xs @ Ys ) )
= ( plus_plus_nat @ ( size_size_list_instr @ Xs ) @ ( size_size_list_instr @ Ys ) ) ) ).
% length_append
thf(fact_378_length__append,axiom,
! [Xs: list_list_char,Ys: list_list_char] :
( ( size_s356637359517785349t_char @ ( append_list_char @ Xs @ Ys ) )
= ( plus_plus_nat @ ( size_s356637359517785349t_char @ Xs ) @ ( size_s356637359517785349t_char @ Ys ) ) ) ).
% length_append
thf(fact_379_length__append,axiom,
! [Xs: list_int,Ys: list_int] :
( ( size_size_list_int @ ( append_int @ Xs @ Ys ) )
= ( plus_plus_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% length_append
thf(fact_380_append1__eq__conv,axiom,
! [Xs: list_list_char,X: list_char,Ys: list_list_char,Y: list_char] :
( ( ( append_list_char @ Xs @ ( cons_list_char @ X @ nil_list_char ) )
= ( append_list_char @ Ys @ ( cons_list_char @ Y @ nil_list_char ) ) )
= ( ( Xs = Ys )
& ( X = Y ) ) ) ).
% append1_eq_conv
thf(fact_381_append1__eq__conv,axiom,
! [Xs: list_P419547167332244514st_int,X: produc6425607678544837394st_int,Ys: list_P419547167332244514st_int,Y: produc6425607678544837394st_int] :
( ( ( append5028292981072010935st_int @ Xs @ ( cons_P4151473878978182108st_int @ X @ nil_Pr749310521696113548st_int ) )
= ( append5028292981072010935st_int @ Ys @ ( cons_P4151473878978182108st_int @ Y @ nil_Pr749310521696113548st_int ) ) )
= ( ( Xs = Ys )
& ( X = Y ) ) ) ).
% append1_eq_conv
thf(fact_382_append1__eq__conv,axiom,
! [Xs: list_instr,X: instr,Ys: list_instr,Y: instr] :
( ( ( append_instr @ Xs @ ( cons_instr @ X @ nil_instr ) )
= ( append_instr @ Ys @ ( cons_instr @ Y @ nil_instr ) ) )
= ( ( Xs = Ys )
& ( X = Y ) ) ) ).
% append1_eq_conv
thf(fact_383_append1__eq__conv,axiom,
! [Xs: list_int,X: int,Ys: list_int,Y: int] :
( ( ( append_int @ Xs @ ( cons_int @ X @ nil_int ) )
= ( append_int @ Ys @ ( cons_int @ Y @ nil_int ) ) )
= ( ( Xs = Ys )
& ( X = Y ) ) ) ).
% append1_eq_conv
thf(fact_384_length__0__conv,axiom,
! [Xs: list_P419547167332244514st_int] :
( ( ( size_s229347708945616566st_int @ Xs )
= zero_zero_nat )
= ( Xs = nil_Pr749310521696113548st_int ) ) ).
% length_0_conv
thf(fact_385_length__0__conv,axiom,
! [Xs: list_m_instr] :
( ( ( size_s5914166952900237872_instr @ Xs )
= zero_zero_nat )
= ( Xs = nil_m_instr ) ) ).
% length_0_conv
thf(fact_386_length__0__conv,axiom,
! [Xs: list_instr] :
( ( ( size_size_list_instr @ Xs )
= zero_zero_nat )
= ( Xs = nil_instr ) ) ).
% length_0_conv
thf(fact_387_length__0__conv,axiom,
! [Xs: list_list_char] :
( ( ( size_s356637359517785349t_char @ Xs )
= zero_zero_nat )
= ( Xs = nil_list_char ) ) ).
% length_0_conv
thf(fact_388_length__0__conv,axiom,
! [Xs: list_int] :
( ( ( size_size_list_int @ Xs )
= zero_zero_nat )
= ( Xs = nil_int ) ) ).
% length_0_conv
thf(fact_389_append__eq__append__conv,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,Us: list_P419547167332244514st_int,Vs: list_P419547167332244514st_int] :
( ( ( ( size_s229347708945616566st_int @ Xs )
= ( size_s229347708945616566st_int @ Ys ) )
| ( ( size_s229347708945616566st_int @ Us )
= ( size_s229347708945616566st_int @ Vs ) ) )
=> ( ( ( append5028292981072010935st_int @ Xs @ Us )
= ( append5028292981072010935st_int @ Ys @ Vs ) )
= ( ( Xs = Ys )
& ( Us = Vs ) ) ) ) ).
% append_eq_append_conv
thf(fact_390_append__eq__append__conv,axiom,
! [Xs: list_m_instr,Ys: list_m_instr,Us: list_m_instr,Vs: list_m_instr] :
( ( ( ( size_s5914166952900237872_instr @ Xs )
= ( size_s5914166952900237872_instr @ Ys ) )
| ( ( size_s5914166952900237872_instr @ Us )
= ( size_s5914166952900237872_instr @ Vs ) ) )
=> ( ( ( append_m_instr @ Xs @ Us )
= ( append_m_instr @ Ys @ Vs ) )
= ( ( Xs = Ys )
& ( Us = Vs ) ) ) ) ).
% append_eq_append_conv
thf(fact_391_append__eq__append__conv,axiom,
! [Xs: list_instr,Ys: list_instr,Us: list_instr,Vs: list_instr] :
( ( ( ( size_size_list_instr @ Xs )
= ( size_size_list_instr @ Ys ) )
| ( ( size_size_list_instr @ Us )
= ( size_size_list_instr @ Vs ) ) )
=> ( ( ( append_instr @ Xs @ Us )
= ( append_instr @ Ys @ Vs ) )
= ( ( Xs = Ys )
& ( Us = Vs ) ) ) ) ).
% append_eq_append_conv
thf(fact_392_append__eq__append__conv,axiom,
! [Xs: list_list_char,Ys: list_list_char,Us: list_list_char,Vs: list_list_char] :
( ( ( ( size_s356637359517785349t_char @ Xs )
= ( size_s356637359517785349t_char @ Ys ) )
| ( ( size_s356637359517785349t_char @ Us )
= ( size_s356637359517785349t_char @ Vs ) ) )
=> ( ( ( append_list_char @ Xs @ Us )
= ( append_list_char @ Ys @ Vs ) )
= ( ( Xs = Ys )
& ( Us = Vs ) ) ) ) ).
% append_eq_append_conv
thf(fact_393_append__eq__append__conv,axiom,
! [Xs: list_int,Ys: list_int,Us: list_int,Vs: list_int] :
( ( ( ( size_size_list_int @ Xs )
= ( size_size_list_int @ Ys ) )
| ( ( size_size_list_int @ Us )
= ( size_size_list_int @ Vs ) ) )
=> ( ( ( append_int @ Xs @ Us )
= ( append_int @ Ys @ Vs ) )
= ( ( Xs = Ys )
& ( Us = Vs ) ) ) ) ).
% append_eq_append_conv
thf(fact_394_append_Oright__neutral,axiom,
! [A: list_P419547167332244514st_int] :
( ( append5028292981072010935st_int @ A @ nil_Pr749310521696113548st_int )
= A ) ).
% append.right_neutral
thf(fact_395_append_Oright__neutral,axiom,
! [A: list_instr] :
( ( append_instr @ A @ nil_instr )
= A ) ).
% append.right_neutral
thf(fact_396_append_Oright__neutral,axiom,
! [A: list_list_char] :
( ( append_list_char @ A @ nil_list_char )
= A ) ).
% append.right_neutral
thf(fact_397_append_Oright__neutral,axiom,
! [A: list_int] :
( ( append_int @ A @ nil_int )
= A ) ).
% append.right_neutral
thf(fact_398_append__Nil2,axiom,
! [Xs: list_P419547167332244514st_int] :
( ( append5028292981072010935st_int @ Xs @ nil_Pr749310521696113548st_int )
= Xs ) ).
% append_Nil2
thf(fact_399_append__Nil2,axiom,
! [Xs: list_instr] :
( ( append_instr @ Xs @ nil_instr )
= Xs ) ).
% append_Nil2
thf(fact_400_append__Nil2,axiom,
! [Xs: list_list_char] :
( ( append_list_char @ Xs @ nil_list_char )
= Xs ) ).
% append_Nil2
thf(fact_401_append__Nil2,axiom,
! [Xs: list_int] :
( ( append_int @ Xs @ nil_int )
= Xs ) ).
% append_Nil2
thf(fact_402_append__self__conv,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( ( append5028292981072010935st_int @ Xs @ Ys )
= Xs )
= ( Ys = nil_Pr749310521696113548st_int ) ) ).
% append_self_conv
thf(fact_403_append__self__conv,axiom,
! [Xs: list_instr,Ys: list_instr] :
( ( ( append_instr @ Xs @ Ys )
= Xs )
= ( Ys = nil_instr ) ) ).
% append_self_conv
thf(fact_404_append__self__conv,axiom,
! [Xs: list_list_char,Ys: list_list_char] :
( ( ( append_list_char @ Xs @ Ys )
= Xs )
= ( Ys = nil_list_char ) ) ).
% append_self_conv
thf(fact_405_append__self__conv,axiom,
! [Xs: list_int,Ys: list_int] :
( ( ( append_int @ Xs @ Ys )
= Xs )
= ( Ys = nil_int ) ) ).
% append_self_conv
thf(fact_406_nat_Oinject,axiom,
! [X2: nat,Y2: nat] :
( ( ( suc @ X2 )
= ( suc @ Y2 ) )
= ( X2 = Y2 ) ) ).
% nat.inject
thf(fact_407_old_Onat_Oinject,axiom,
! [Nat: nat,Nat2: nat] :
( ( ( suc @ Nat )
= ( suc @ Nat2 ) )
= ( Nat = Nat2 ) ) ).
% old.nat.inject
thf(fact_408_list_Oinject,axiom,
! [X21: produc6425607678544837394st_int,X22: list_P419547167332244514st_int,Y21: produc6425607678544837394st_int,Y22: list_P419547167332244514st_int] :
( ( ( cons_P4151473878978182108st_int @ X21 @ X22 )
= ( cons_P4151473878978182108st_int @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 ) ) ) ).
% list.inject
thf(fact_409_list_Oinject,axiom,
! [X21: instr,X22: list_instr,Y21: instr,Y22: list_instr] :
( ( ( cons_instr @ X21 @ X22 )
= ( cons_instr @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 ) ) ) ).
% list.inject
thf(fact_410_list_Oinject,axiom,
! [X21: int,X22: list_int,Y21: int,Y22: list_int] :
( ( ( cons_int @ X21 @ X22 )
= ( cons_int @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 ) ) ) ).
% list.inject
thf(fact_411_same__append__eq,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int] :
( ( ( append5028292981072010935st_int @ Xs @ Ys )
= ( append5028292981072010935st_int @ Xs @ Zs ) )
= ( Ys = Zs ) ) ).
% same_append_eq
thf(fact_412_same__append__eq,axiom,
! [Xs: list_int,Ys: list_int,Zs: list_int] :
( ( ( append_int @ Xs @ Ys )
= ( append_int @ Xs @ Zs ) )
= ( Ys = Zs ) ) ).
% same_append_eq
thf(fact_413_same__append__eq,axiom,
! [Xs: list_instr,Ys: list_instr,Zs: list_instr] :
( ( ( append_instr @ Xs @ Ys )
= ( append_instr @ Xs @ Zs ) )
= ( Ys = Zs ) ) ).
% same_append_eq
thf(fact_414_append__same__eq,axiom,
! [Ys: list_P419547167332244514st_int,Xs: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int] :
( ( ( append5028292981072010935st_int @ Ys @ Xs )
= ( append5028292981072010935st_int @ Zs @ Xs ) )
= ( Ys = Zs ) ) ).
% append_same_eq
thf(fact_415_append__same__eq,axiom,
! [Ys: list_int,Xs: list_int,Zs: list_int] :
( ( ( append_int @ Ys @ Xs )
= ( append_int @ Zs @ Xs ) )
= ( Ys = Zs ) ) ).
% append_same_eq
thf(fact_416_append__same__eq,axiom,
! [Ys: list_instr,Xs: list_instr,Zs: list_instr] :
( ( ( append_instr @ Ys @ Xs )
= ( append_instr @ Zs @ Xs ) )
= ( Ys = Zs ) ) ).
% append_same_eq
thf(fact_417_append__assoc,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int] :
( ( append5028292981072010935st_int @ ( append5028292981072010935st_int @ Xs @ Ys ) @ Zs )
= ( append5028292981072010935st_int @ Xs @ ( append5028292981072010935st_int @ Ys @ Zs ) ) ) ).
% append_assoc
thf(fact_418_append__assoc,axiom,
! [Xs: list_int,Ys: list_int,Zs: list_int] :
( ( append_int @ ( append_int @ Xs @ Ys ) @ Zs )
= ( append_int @ Xs @ ( append_int @ Ys @ Zs ) ) ) ).
% append_assoc
thf(fact_419_append__assoc,axiom,
! [Xs: list_instr,Ys: list_instr,Zs: list_instr] :
( ( append_instr @ ( append_instr @ Xs @ Ys ) @ Zs )
= ( append_instr @ Xs @ ( append_instr @ Ys @ Zs ) ) ) ).
% append_assoc
thf(fact_420_append_Oassoc,axiom,
! [A: list_P419547167332244514st_int,B: list_P419547167332244514st_int,C: list_P419547167332244514st_int] :
( ( append5028292981072010935st_int @ ( append5028292981072010935st_int @ A @ B ) @ C )
= ( append5028292981072010935st_int @ A @ ( append5028292981072010935st_int @ B @ C ) ) ) ).
% append.assoc
thf(fact_421_append_Oassoc,axiom,
! [A: list_int,B: list_int,C: list_int] :
( ( append_int @ ( append_int @ A @ B ) @ C )
= ( append_int @ A @ ( append_int @ B @ C ) ) ) ).
% append.assoc
thf(fact_422_append_Oassoc,axiom,
! [A: list_instr,B: list_instr,C: list_instr] :
( ( append_instr @ ( append_instr @ A @ B ) @ C )
= ( append_instr @ A @ ( append_instr @ B @ C ) ) ) ).
% append.assoc
thf(fact_423_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_424_add__Suc__right,axiom,
! [M: nat,N: nat] :
( ( plus_plus_nat @ M @ ( suc @ N ) )
= ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% add_Suc_right
thf(fact_425_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_426_Suc__diff__diff,axiom,
! [M: nat,N: nat,K: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
= ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% Suc_diff_diff
thf(fact_427_append__is__Nil__conv,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( ( append5028292981072010935st_int @ Xs @ Ys )
= nil_Pr749310521696113548st_int )
= ( ( Xs = nil_Pr749310521696113548st_int )
& ( Ys = nil_Pr749310521696113548st_int ) ) ) ).
% append_is_Nil_conv
thf(fact_428_append__is__Nil__conv,axiom,
! [Xs: list_instr,Ys: list_instr] :
( ( ( append_instr @ Xs @ Ys )
= nil_instr )
= ( ( Xs = nil_instr )
& ( Ys = nil_instr ) ) ) ).
% append_is_Nil_conv
thf(fact_429_append__is__Nil__conv,axiom,
! [Xs: list_list_char,Ys: list_list_char] :
( ( ( append_list_char @ Xs @ Ys )
= nil_list_char )
= ( ( Xs = nil_list_char )
& ( Ys = nil_list_char ) ) ) ).
% append_is_Nil_conv
thf(fact_430_append__is__Nil__conv,axiom,
! [Xs: list_int,Ys: list_int] :
( ( ( append_int @ Xs @ Ys )
= nil_int )
= ( ( Xs = nil_int )
& ( Ys = nil_int ) ) ) ).
% append_is_Nil_conv
thf(fact_431_Nil__is__append__conv,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( nil_Pr749310521696113548st_int
= ( append5028292981072010935st_int @ Xs @ Ys ) )
= ( ( Xs = nil_Pr749310521696113548st_int )
& ( Ys = nil_Pr749310521696113548st_int ) ) ) ).
% Nil_is_append_conv
thf(fact_432_Nil__is__append__conv,axiom,
! [Xs: list_instr,Ys: list_instr] :
( ( nil_instr
= ( append_instr @ Xs @ Ys ) )
= ( ( Xs = nil_instr )
& ( Ys = nil_instr ) ) ) ).
% Nil_is_append_conv
thf(fact_433_Nil__is__append__conv,axiom,
! [Xs: list_list_char,Ys: list_list_char] :
( ( nil_list_char
= ( append_list_char @ Xs @ Ys ) )
= ( ( Xs = nil_list_char )
& ( Ys = nil_list_char ) ) ) ).
% Nil_is_append_conv
thf(fact_434_Nil__is__append__conv,axiom,
! [Xs: list_int,Ys: list_int] :
( ( nil_int
= ( append_int @ Xs @ Ys ) )
= ( ( Xs = nil_int )
& ( Ys = nil_int ) ) ) ).
% Nil_is_append_conv
thf(fact_435_self__append__conv2,axiom,
! [Y: list_P419547167332244514st_int,Xs: list_P419547167332244514st_int] :
( ( Y
= ( append5028292981072010935st_int @ Xs @ Y ) )
= ( Xs = nil_Pr749310521696113548st_int ) ) ).
% self_append_conv2
thf(fact_436_self__append__conv2,axiom,
! [Y: list_instr,Xs: list_instr] :
( ( Y
= ( append_instr @ Xs @ Y ) )
= ( Xs = nil_instr ) ) ).
% self_append_conv2
thf(fact_437_self__append__conv2,axiom,
! [Y: list_list_char,Xs: list_list_char] :
( ( Y
= ( append_list_char @ Xs @ Y ) )
= ( Xs = nil_list_char ) ) ).
% self_append_conv2
thf(fact_438_self__append__conv2,axiom,
! [Y: list_int,Xs: list_int] :
( ( Y
= ( append_int @ Xs @ Y ) )
= ( Xs = nil_int ) ) ).
% self_append_conv2
thf(fact_439_append__self__conv2,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( ( append5028292981072010935st_int @ Xs @ Ys )
= Ys )
= ( Xs = nil_Pr749310521696113548st_int ) ) ).
% append_self_conv2
thf(fact_440_append__self__conv2,axiom,
! [Xs: list_instr,Ys: list_instr] :
( ( ( append_instr @ Xs @ Ys )
= Ys )
= ( Xs = nil_instr ) ) ).
% append_self_conv2
thf(fact_441_append__self__conv2,axiom,
! [Xs: list_list_char,Ys: list_list_char] :
( ( ( append_list_char @ Xs @ Ys )
= Ys )
= ( Xs = nil_list_char ) ) ).
% append_self_conv2
thf(fact_442_append__self__conv2,axiom,
! [Xs: list_int,Ys: list_int] :
( ( ( append_int @ Xs @ Ys )
= Ys )
= ( Xs = nil_int ) ) ).
% append_self_conv2
thf(fact_443_self__append__conv,axiom,
! [Y: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( Y
= ( append5028292981072010935st_int @ Y @ Ys ) )
= ( Ys = nil_Pr749310521696113548st_int ) ) ).
% self_append_conv
thf(fact_444_self__append__conv,axiom,
! [Y: list_instr,Ys: list_instr] :
( ( Y
= ( append_instr @ Y @ Ys ) )
= ( Ys = nil_instr ) ) ).
% self_append_conv
thf(fact_445_self__append__conv,axiom,
! [Y: list_list_char,Ys: list_list_char] :
( ( Y
= ( append_list_char @ Y @ Ys ) )
= ( Ys = nil_list_char ) ) ).
% self_append_conv
thf(fact_446_self__append__conv,axiom,
! [Y: list_int,Ys: list_int] :
( ( Y
= ( append_int @ Y @ Ys ) )
= ( Ys = nil_int ) ) ).
% self_append_conv
thf(fact_447_nth__Cons__0,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int] :
( ( nth_Pr8327173284404383691st_int @ ( cons_P4151473878978182108st_int @ X @ Xs ) @ zero_zero_nat )
= X ) ).
% nth_Cons_0
thf(fact_448_nth__Cons__0,axiom,
! [X: instr,Xs: list_instr] :
( ( nth_instr @ ( cons_instr @ X @ Xs ) @ zero_zero_nat )
= X ) ).
% nth_Cons_0
thf(fact_449_nth__Cons__0,axiom,
! [X: int,Xs: list_int] :
( ( nth_int @ ( cons_int @ X @ Xs ) @ zero_zero_nat )
= X ) ).
% nth_Cons_0
thf(fact_450_nth__Cons__Suc,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int,N: nat] :
( ( nth_Pr8327173284404383691st_int @ ( cons_P4151473878978182108st_int @ X @ Xs ) @ ( suc @ N ) )
= ( nth_Pr8327173284404383691st_int @ Xs @ N ) ) ).
% nth_Cons_Suc
thf(fact_451_nth__Cons__Suc,axiom,
! [X: instr,Xs: list_instr,N: nat] :
( ( nth_instr @ ( cons_instr @ X @ Xs ) @ ( suc @ N ) )
= ( nth_instr @ Xs @ N ) ) ).
% nth_Cons_Suc
thf(fact_452_nth__Cons__Suc,axiom,
! [X: int,Xs: list_int,N: nat] :
( ( nth_int @ ( cons_int @ X @ Xs ) @ ( suc @ N ) )
= ( nth_int @ Xs @ N ) ) ).
% nth_Cons_Suc
thf(fact_453_diff__Suc__diff__eq1,axiom,
! [K: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
= ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% diff_Suc_diff_eq1
thf(fact_454_diff__Suc__diff__eq2,axiom,
! [K: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
= ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% diff_Suc_diff_eq2
thf(fact_455_nth__append__length,axiom,
! [Xs: list_P419547167332244514st_int,X: produc6425607678544837394st_int,Ys: list_P419547167332244514st_int] :
( ( nth_Pr8327173284404383691st_int @ ( append5028292981072010935st_int @ Xs @ ( cons_P4151473878978182108st_int @ X @ Ys ) ) @ ( size_s229347708945616566st_int @ Xs ) )
= X ) ).
% nth_append_length
thf(fact_456_nth__append__length,axiom,
! [Xs: list_m_instr,X: m_instr,Ys: list_m_instr] :
( ( nth_m_instr @ ( append_m_instr @ Xs @ ( cons_m_instr @ X @ Ys ) ) @ ( size_s5914166952900237872_instr @ Xs ) )
= X ) ).
% nth_append_length
thf(fact_457_nth__append__length,axiom,
! [Xs: list_instr,X: instr,Ys: list_instr] :
( ( nth_instr @ ( append_instr @ Xs @ ( cons_instr @ X @ Ys ) ) @ ( size_size_list_instr @ Xs ) )
= X ) ).
% nth_append_length
thf(fact_458_nth__append__length,axiom,
! [Xs: list_list_char,X: list_char,Ys: list_list_char] :
( ( nth_list_char @ ( append_list_char @ Xs @ ( cons_list_char @ X @ Ys ) ) @ ( size_s356637359517785349t_char @ Xs ) )
= X ) ).
% nth_append_length
thf(fact_459_nth__append__length,axiom,
! [Xs: list_int,X: int,Ys: list_int] :
( ( nth_int @ ( append_int @ Xs @ ( cons_int @ X @ Ys ) ) @ ( size_size_list_int @ Xs ) )
= X ) ).
% nth_append_length
thf(fact_460_nth__append__length__plus,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,N: nat] :
( ( nth_Pr8327173284404383691st_int @ ( append5028292981072010935st_int @ Xs @ Ys ) @ ( plus_plus_nat @ ( size_s229347708945616566st_int @ Xs ) @ N ) )
= ( nth_Pr8327173284404383691st_int @ Ys @ N ) ) ).
% nth_append_length_plus
thf(fact_461_nth__append__length__plus,axiom,
! [Xs: list_m_instr,Ys: list_m_instr,N: nat] :
( ( nth_m_instr @ ( append_m_instr @ Xs @ Ys ) @ ( plus_plus_nat @ ( size_s5914166952900237872_instr @ Xs ) @ N ) )
= ( nth_m_instr @ Ys @ N ) ) ).
% nth_append_length_plus
thf(fact_462_nth__append__length__plus,axiom,
! [Xs: list_instr,Ys: list_instr,N: nat] :
( ( nth_instr @ ( append_instr @ Xs @ Ys ) @ ( plus_plus_nat @ ( size_size_list_instr @ Xs ) @ N ) )
= ( nth_instr @ Ys @ N ) ) ).
% nth_append_length_plus
thf(fact_463_nth__append__length__plus,axiom,
! [Xs: list_list_char,Ys: list_list_char,N: nat] :
( ( nth_list_char @ ( append_list_char @ Xs @ Ys ) @ ( plus_plus_nat @ ( size_s356637359517785349t_char @ Xs ) @ N ) )
= ( nth_list_char @ Ys @ N ) ) ).
% nth_append_length_plus
thf(fact_464_nth__append__length__plus,axiom,
! [Xs: list_int,Ys: list_int,N: nat] :
( ( nth_int @ ( append_int @ Xs @ Ys ) @ ( plus_plus_nat @ ( size_size_list_int @ Xs ) @ N ) )
= ( nth_int @ Ys @ N ) ) ).
% nth_append_length_plus
thf(fact_465_vars_Osimps_I1_J,axiom,
( ( vars @ nil_instr )
= nil_list_char ) ).
% vars.simps(1)
thf(fact_466_Suc__inject,axiom,
! [X: nat,Y: nat] :
( ( ( suc @ X )
= ( suc @ Y ) )
=> ( X = Y ) ) ).
% Suc_inject
thf(fact_467_n__not__Suc__n,axiom,
! [N: nat] :
( N
!= ( suc @ N ) ) ).
% n_not_Suc_n
thf(fact_468_nat_Odistinct_I1_J,axiom,
! [X2: nat] :
( zero_zero_nat
!= ( suc @ X2 ) ) ).
% nat.distinct(1)
thf(fact_469_old_Onat_Odistinct_I2_J,axiom,
! [Nat2: nat] :
( ( suc @ Nat2 )
!= zero_zero_nat ) ).
% old.nat.distinct(2)
thf(fact_470_old_Onat_Odistinct_I1_J,axiom,
! [Nat2: nat] :
( zero_zero_nat
!= ( suc @ Nat2 ) ) ).
% old.nat.distinct(1)
thf(fact_471_nat_OdiscI,axiom,
! [Nat: nat,X2: nat] :
( ( Nat
= ( suc @ X2 ) )
=> ( Nat != zero_zero_nat ) ) ).
% nat.discI
thf(fact_472_old_Onat_Oexhaust,axiom,
! [Y: nat] :
( ( Y != zero_zero_nat )
=> ~ ! [Nat3: nat] :
( Y
!= ( suc @ Nat3 ) ) ) ).
% old.nat.exhaust
thf(fact_473_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_474_diff__induct,axiom,
! [P: nat > nat > $o,M: nat,N: nat] :
( ! [X4: nat] : ( P @ X4 @ zero_zero_nat )
=> ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
=> ( ! [X4: nat,Y3: nat] :
( ( P @ X4 @ Y3 )
=> ( P @ ( suc @ X4 ) @ ( suc @ Y3 ) ) )
=> ( P @ M @ N ) ) ) ) ).
% diff_induct
thf(fact_475_zero__induct,axiom,
! [P: nat > $o,K: nat] :
( ( P @ K )
=> ( ! [N2: nat] :
( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) )
=> ( P @ zero_zero_nat ) ) ) ).
% zero_induct
thf(fact_476_Suc__neq__Zero,axiom,
! [M: nat] :
( ( suc @ M )
!= zero_zero_nat ) ).
% Suc_neq_Zero
thf(fact_477_Zero__neq__Suc,axiom,
! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) ).
% Zero_neq_Suc
thf(fact_478_Zero__not__Suc,axiom,
! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) ).
% Zero_not_Suc
thf(fact_479_not0__implies__Suc,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ? [M3: nat] :
( N
= ( suc @ M3 ) ) ) ).
% not0_implies_Suc
thf(fact_480_transitive__stepwise__le,axiom,
! [M: nat,N: nat,R3: nat > nat > $o] :
( ( ord_less_eq_nat @ M @ N )
=> ( ! [X4: nat] : ( R3 @ X4 @ X4 )
=> ( ! [X4: nat,Y3: nat,Z4: nat] :
( ( R3 @ X4 @ Y3 )
=> ( ( R3 @ Y3 @ Z4 )
=> ( R3 @ X4 @ Z4 ) ) )
=> ( ! [N2: nat] : ( R3 @ N2 @ ( suc @ N2 ) )
=> ( R3 @ M @ N ) ) ) ) ) ).
% transitive_stepwise_le
thf(fact_481_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_482_full__nat__induct,axiom,
! [P: nat > $o,N: nat] :
( ! [N2: nat] :
( ! [M4: nat] :
( ( ord_less_eq_nat @ ( suc @ M4 ) @ N2 )
=> ( P @ M4 ) )
=> ( P @ N2 ) )
=> ( P @ N ) ) ).
% full_nat_induct
thf(fact_483_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_484_Suc__n__not__le__n,axiom,
! [N: nat] :
~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% Suc_n_not_le_n
thf(fact_485_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_486_Suc__le__D,axiom,
! [N: nat,M5: nat] :
( ( ord_less_eq_nat @ ( suc @ N ) @ M5 )
=> ? [M3: nat] :
( M5
= ( suc @ M3 ) ) ) ).
% Suc_le_D
thf(fact_487_le__SucI,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% le_SucI
thf(fact_488_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_489_Suc__leD,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ M ) @ N )
=> ( ord_less_eq_nat @ M @ N ) ) ).
% Suc_leD
thf(fact_490_add__Suc__shift,axiom,
! [M: nat,N: nat] :
( ( plus_plus_nat @ ( suc @ M ) @ N )
= ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% add_Suc_shift
thf(fact_491_add__Suc,axiom,
! [M: nat,N: nat] :
( ( plus_plus_nat @ ( suc @ M ) @ N )
= ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% add_Suc
thf(fact_492_nat__arith_Osuc1,axiom,
! [A3: nat,K: nat,A: nat] :
( ( A3
= ( plus_plus_nat @ K @ A ) )
=> ( ( suc @ A3 )
= ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% nat_arith.suc1
thf(fact_493_zero__induct__lemma,axiom,
! [P: nat > $o,K: nat,I: nat] :
( ( P @ K )
=> ( ! [N2: nat] :
( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) )
=> ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% zero_induct_lemma
thf(fact_494_exec1__appendR,axiom,
! [P: list_instr,C: produc6425607678544837394st_int,C4: produc6425607678544837394st_int,P4: list_instr] :
( ( exec1 @ P @ C @ C4 )
=> ( exec1 @ ( append_instr @ P @ P4 ) @ C @ C4 ) ) ).
% exec1_appendR
thf(fact_495_Suc__length__conv,axiom,
! [N: nat,Xs: list_P419547167332244514st_int] :
( ( ( suc @ N )
= ( size_s229347708945616566st_int @ Xs ) )
= ( ? [Y5: produc6425607678544837394st_int,Ys2: list_P419547167332244514st_int] :
( ( Xs
= ( cons_P4151473878978182108st_int @ Y5 @ Ys2 ) )
& ( ( size_s229347708945616566st_int @ Ys2 )
= N ) ) ) ) ).
% Suc_length_conv
thf(fact_496_Suc__length__conv,axiom,
! [N: nat,Xs: list_m_instr] :
( ( ( suc @ N )
= ( size_s5914166952900237872_instr @ Xs ) )
= ( ? [Y5: m_instr,Ys2: list_m_instr] :
( ( Xs
= ( cons_m_instr @ Y5 @ Ys2 ) )
& ( ( size_s5914166952900237872_instr @ Ys2 )
= N ) ) ) ) ).
% Suc_length_conv
thf(fact_497_Suc__length__conv,axiom,
! [N: nat,Xs: list_instr] :
( ( ( suc @ N )
= ( size_size_list_instr @ Xs ) )
= ( ? [Y5: instr,Ys2: list_instr] :
( ( Xs
= ( cons_instr @ Y5 @ Ys2 ) )
& ( ( size_size_list_instr @ Ys2 )
= N ) ) ) ) ).
% Suc_length_conv
thf(fact_498_Suc__length__conv,axiom,
! [N: nat,Xs: list_list_char] :
( ( ( suc @ N )
= ( size_s356637359517785349t_char @ Xs ) )
= ( ? [Y5: list_char,Ys2: list_list_char] :
( ( Xs
= ( cons_list_char @ Y5 @ Ys2 ) )
& ( ( size_s356637359517785349t_char @ Ys2 )
= N ) ) ) ) ).
% Suc_length_conv
thf(fact_499_Suc__length__conv,axiom,
! [N: nat,Xs: list_int] :
( ( ( suc @ N )
= ( size_size_list_int @ Xs ) )
= ( ? [Y5: int,Ys2: list_int] :
( ( Xs
= ( cons_int @ Y5 @ Ys2 ) )
& ( ( size_size_list_int @ Ys2 )
= N ) ) ) ) ).
% Suc_length_conv
thf(fact_500_length__Suc__conv,axiom,
! [Xs: list_P419547167332244514st_int,N: nat] :
( ( ( size_s229347708945616566st_int @ Xs )
= ( suc @ N ) )
= ( ? [Y5: produc6425607678544837394st_int,Ys2: list_P419547167332244514st_int] :
( ( Xs
= ( cons_P4151473878978182108st_int @ Y5 @ Ys2 ) )
& ( ( size_s229347708945616566st_int @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv
thf(fact_501_length__Suc__conv,axiom,
! [Xs: list_m_instr,N: nat] :
( ( ( size_s5914166952900237872_instr @ Xs )
= ( suc @ N ) )
= ( ? [Y5: m_instr,Ys2: list_m_instr] :
( ( Xs
= ( cons_m_instr @ Y5 @ Ys2 ) )
& ( ( size_s5914166952900237872_instr @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv
thf(fact_502_length__Suc__conv,axiom,
! [Xs: list_instr,N: nat] :
( ( ( size_size_list_instr @ Xs )
= ( suc @ N ) )
= ( ? [Y5: instr,Ys2: list_instr] :
( ( Xs
= ( cons_instr @ Y5 @ Ys2 ) )
& ( ( size_size_list_instr @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv
thf(fact_503_length__Suc__conv,axiom,
! [Xs: list_list_char,N: nat] :
( ( ( size_s356637359517785349t_char @ Xs )
= ( suc @ N ) )
= ( ? [Y5: list_char,Ys2: list_list_char] :
( ( Xs
= ( cons_list_char @ Y5 @ Ys2 ) )
& ( ( size_s356637359517785349t_char @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv
thf(fact_504_length__Suc__conv,axiom,
! [Xs: list_int,N: nat] :
( ( ( size_size_list_int @ Xs )
= ( suc @ N ) )
= ( ? [Y5: int,Ys2: list_int] :
( ( Xs
= ( cons_int @ Y5 @ Ys2 ) )
& ( ( size_size_list_int @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv
thf(fact_505_lift__Suc__antimono__le,axiom,
! [F: nat > nat,N: nat,N4: nat] :
( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
=> ( ( ord_less_eq_nat @ N @ N4 )
=> ( ord_less_eq_nat @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% lift_Suc_antimono_le
thf(fact_506_lift__Suc__antimono__le,axiom,
! [F: nat > int,N: nat,N4: nat] :
( ! [N2: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
=> ( ( ord_less_eq_nat @ N @ N4 )
=> ( ord_less_eq_int @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% lift_Suc_antimono_le
thf(fact_507_lift__Suc__mono__le,axiom,
! [F: nat > nat,N: nat,N4: nat] :
( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_eq_nat @ N @ N4 )
=> ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% lift_Suc_mono_le
thf(fact_508_lift__Suc__mono__le,axiom,
! [F: nat > int,N: nat,N4: nat] :
( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
=> ( ( ord_less_eq_nat @ N @ N4 )
=> ( ord_less_eq_int @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% lift_Suc_mono_le
thf(fact_509_Suc__le__length__iff,axiom,
! [N: nat,Xs: list_P419547167332244514st_int] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_s229347708945616566st_int @ Xs ) )
= ( ? [X3: produc6425607678544837394st_int,Ys2: list_P419547167332244514st_int] :
( ( Xs
= ( cons_P4151473878978182108st_int @ X3 @ Ys2 ) )
& ( ord_less_eq_nat @ N @ ( size_s229347708945616566st_int @ Ys2 ) ) ) ) ) ).
% Suc_le_length_iff
thf(fact_510_Suc__le__length__iff,axiom,
! [N: nat,Xs: list_m_instr] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_s5914166952900237872_instr @ Xs ) )
= ( ? [X3: m_instr,Ys2: list_m_instr] :
( ( Xs
= ( cons_m_instr @ X3 @ Ys2 ) )
& ( ord_less_eq_nat @ N @ ( size_s5914166952900237872_instr @ Ys2 ) ) ) ) ) ).
% Suc_le_length_iff
thf(fact_511_Suc__le__length__iff,axiom,
! [N: nat,Xs: list_instr] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_instr @ Xs ) )
= ( ? [X3: instr,Ys2: list_instr] :
( ( Xs
= ( cons_instr @ X3 @ Ys2 ) )
& ( ord_less_eq_nat @ N @ ( size_size_list_instr @ Ys2 ) ) ) ) ) ).
% Suc_le_length_iff
thf(fact_512_Suc__le__length__iff,axiom,
! [N: nat,Xs: list_list_char] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_s356637359517785349t_char @ Xs ) )
= ( ? [X3: list_char,Ys2: list_list_char] :
( ( Xs
= ( cons_list_char @ X3 @ Ys2 ) )
& ( ord_less_eq_nat @ N @ ( size_s356637359517785349t_char @ Ys2 ) ) ) ) ) ).
% Suc_le_length_iff
thf(fact_513_Suc__le__length__iff,axiom,
! [N: nat,Xs: list_int] :
( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs ) )
= ( ? [X3: int,Ys2: list_int] :
( ( Xs
= ( cons_int @ X3 @ Ys2 ) )
& ( ord_less_eq_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) ) ) ).
% Suc_le_length_iff
thf(fact_514_add__is__1,axiom,
! [M: nat,N: nat] :
( ( ( plus_plus_nat @ M @ N )
= ( suc @ zero_zero_nat ) )
= ( ( ( M
= ( suc @ zero_zero_nat ) )
& ( N = zero_zero_nat ) )
| ( ( M = zero_zero_nat )
& ( N
= ( suc @ zero_zero_nat ) ) ) ) ) ).
% add_is_1
thf(fact_515_one__is__add,axiom,
! [M: nat,N: nat] :
( ( ( suc @ zero_zero_nat )
= ( plus_plus_nat @ M @ N ) )
= ( ( ( M
= ( suc @ zero_zero_nat ) )
& ( N = zero_zero_nat ) )
| ( ( M = zero_zero_nat )
& ( N
= ( suc @ zero_zero_nat ) ) ) ) ) ).
% one_is_add
thf(fact_516_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_517_add__stack_Osimps_I1_J,axiom,
! [Uu: int > int] :
( ( add_stack @ zero_zero_nat @ Uu )
= nil_int ) ).
% add_stack.simps(1)
thf(fact_518_exec__appendR,axiom,
! [P: list_instr,C: produc6425607678544837394st_int,C4: produc6425607678544837394st_int,P4: list_instr] :
( ( star_P707599355569300323st_int @ ( exec1 @ P ) @ C @ C4 )
=> ( star_P707599355569300323st_int @ ( exec1 @ ( append_instr @ P @ P4 ) ) @ C @ C4 ) ) ).
% exec_appendR
thf(fact_519_list_Osize_I4_J,axiom,
! [X21: produc6425607678544837394st_int,X22: list_P419547167332244514st_int] :
( ( size_s229347708945616566st_int @ ( cons_P4151473878978182108st_int @ X21 @ X22 ) )
= ( plus_plus_nat @ ( size_s229347708945616566st_int @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% list.size(4)
thf(fact_520_list_Osize_I4_J,axiom,
! [X21: m_instr,X22: list_m_instr] :
( ( size_s5914166952900237872_instr @ ( cons_m_instr @ X21 @ X22 ) )
= ( plus_plus_nat @ ( size_s5914166952900237872_instr @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% list.size(4)
thf(fact_521_list_Osize_I4_J,axiom,
! [X21: instr,X22: list_instr] :
( ( size_size_list_instr @ ( cons_instr @ X21 @ X22 ) )
= ( plus_plus_nat @ ( size_size_list_instr @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% list.size(4)
thf(fact_522_list_Osize_I4_J,axiom,
! [X21: list_char,X22: list_list_char] :
( ( size_s356637359517785349t_char @ ( cons_list_char @ X21 @ X22 ) )
= ( plus_plus_nat @ ( size_s356637359517785349t_char @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% list.size(4)
thf(fact_523_list_Osize_I4_J,axiom,
! [X21: int,X22: list_int] :
( ( size_size_list_int @ ( cons_int @ X21 @ X22 ) )
= ( plus_plus_nat @ ( size_size_list_int @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% list.size(4)
thf(fact_524_length__Suc__conv__rev,axiom,
! [Xs: list_P419547167332244514st_int,N: nat] :
( ( ( size_s229347708945616566st_int @ Xs )
= ( suc @ N ) )
= ( ? [Y5: produc6425607678544837394st_int,Ys2: list_P419547167332244514st_int] :
( ( Xs
= ( append5028292981072010935st_int @ Ys2 @ ( cons_P4151473878978182108st_int @ Y5 @ nil_Pr749310521696113548st_int ) ) )
& ( ( size_s229347708945616566st_int @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv_rev
thf(fact_525_length__Suc__conv__rev,axiom,
! [Xs: list_m_instr,N: nat] :
( ( ( size_s5914166952900237872_instr @ Xs )
= ( suc @ N ) )
= ( ? [Y5: m_instr,Ys2: list_m_instr] :
( ( Xs
= ( append_m_instr @ Ys2 @ ( cons_m_instr @ Y5 @ nil_m_instr ) ) )
& ( ( size_s5914166952900237872_instr @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv_rev
thf(fact_526_length__Suc__conv__rev,axiom,
! [Xs: list_instr,N: nat] :
( ( ( size_size_list_instr @ Xs )
= ( suc @ N ) )
= ( ? [Y5: instr,Ys2: list_instr] :
( ( Xs
= ( append_instr @ Ys2 @ ( cons_instr @ Y5 @ nil_instr ) ) )
& ( ( size_size_list_instr @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv_rev
thf(fact_527_length__Suc__conv__rev,axiom,
! [Xs: list_list_char,N: nat] :
( ( ( size_s356637359517785349t_char @ Xs )
= ( suc @ N ) )
= ( ? [Y5: list_char,Ys2: list_list_char] :
( ( Xs
= ( append_list_char @ Ys2 @ ( cons_list_char @ Y5 @ nil_list_char ) ) )
& ( ( size_s356637359517785349t_char @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv_rev
thf(fact_528_length__Suc__conv__rev,axiom,
! [Xs: list_int,N: nat] :
( ( ( size_size_list_int @ Xs )
= ( suc @ N ) )
= ( ? [Y5: int,Ys2: list_int] :
( ( Xs
= ( append_int @ Ys2 @ ( cons_int @ Y5 @ nil_int ) ) )
& ( ( size_size_list_int @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv_rev
thf(fact_529_not__Cons__self2,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int] :
( ( cons_P4151473878978182108st_int @ X @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_530_not__Cons__self2,axiom,
! [X: instr,Xs: list_instr] :
( ( cons_instr @ X @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_531_not__Cons__self2,axiom,
! [X: int,Xs: list_int] :
( ( cons_int @ X @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_532_Ex__list__of__length,axiom,
! [N: nat] :
? [Xs2: list_P419547167332244514st_int] :
( ( size_s229347708945616566st_int @ Xs2 )
= N ) ).
% Ex_list_of_length
thf(fact_533_Ex__list__of__length,axiom,
! [N: nat] :
? [Xs2: list_m_instr] :
( ( size_s5914166952900237872_instr @ Xs2 )
= N ) ).
% Ex_list_of_length
thf(fact_534_Ex__list__of__length,axiom,
! [N: nat] :
? [Xs2: list_instr] :
( ( size_size_list_instr @ Xs2 )
= N ) ).
% Ex_list_of_length
thf(fact_535_Ex__list__of__length,axiom,
! [N: nat] :
? [Xs2: list_list_char] :
( ( size_s356637359517785349t_char @ Xs2 )
= N ) ).
% Ex_list_of_length
thf(fact_536_Ex__list__of__length,axiom,
! [N: nat] :
? [Xs2: list_int] :
( ( size_size_list_int @ Xs2 )
= N ) ).
% Ex_list_of_length
thf(fact_537_neq__if__length__neq,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( ( size_s229347708945616566st_int @ Xs )
!= ( size_s229347708945616566st_int @ Ys ) )
=> ( Xs != Ys ) ) ).
% neq_if_length_neq
thf(fact_538_neq__if__length__neq,axiom,
! [Xs: list_m_instr,Ys: list_m_instr] :
( ( ( size_s5914166952900237872_instr @ Xs )
!= ( size_s5914166952900237872_instr @ Ys ) )
=> ( Xs != Ys ) ) ).
% neq_if_length_neq
thf(fact_539_neq__if__length__neq,axiom,
! [Xs: list_instr,Ys: list_instr] :
( ( ( size_size_list_instr @ Xs )
!= ( size_size_list_instr @ Ys ) )
=> ( Xs != Ys ) ) ).
% neq_if_length_neq
thf(fact_540_neq__if__length__neq,axiom,
! [Xs: list_list_char,Ys: list_list_char] :
( ( ( size_s356637359517785349t_char @ Xs )
!= ( size_s356637359517785349t_char @ Ys ) )
=> ( Xs != Ys ) ) ).
% neq_if_length_neq
thf(fact_541_neq__if__length__neq,axiom,
! [Xs: list_int,Ys: list_int] :
( ( ( size_size_list_int @ Xs )
!= ( size_size_list_int @ Ys ) )
=> ( Xs != Ys ) ) ).
% neq_if_length_neq
thf(fact_542_append__eq__append__conv2,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int,Ts: list_P419547167332244514st_int] :
( ( ( append5028292981072010935st_int @ Xs @ Ys )
= ( append5028292981072010935st_int @ Zs @ Ts ) )
= ( ? [Us2: list_P419547167332244514st_int] :
( ( ( Xs
= ( append5028292981072010935st_int @ Zs @ Us2 ) )
& ( ( append5028292981072010935st_int @ Us2 @ Ys )
= Ts ) )
| ( ( ( append5028292981072010935st_int @ Xs @ Us2 )
= Zs )
& ( Ys
= ( append5028292981072010935st_int @ Us2 @ Ts ) ) ) ) ) ) ).
% append_eq_append_conv2
thf(fact_543_append__eq__append__conv2,axiom,
! [Xs: list_int,Ys: list_int,Zs: list_int,Ts: list_int] :
( ( ( append_int @ Xs @ Ys )
= ( append_int @ Zs @ Ts ) )
= ( ? [Us2: list_int] :
( ( ( Xs
= ( append_int @ Zs @ Us2 ) )
& ( ( append_int @ Us2 @ Ys )
= Ts ) )
| ( ( ( append_int @ Xs @ Us2 )
= Zs )
& ( Ys
= ( append_int @ Us2 @ Ts ) ) ) ) ) ) ).
% append_eq_append_conv2
thf(fact_544_append__eq__append__conv2,axiom,
! [Xs: list_instr,Ys: list_instr,Zs: list_instr,Ts: list_instr] :
( ( ( append_instr @ Xs @ Ys )
= ( append_instr @ Zs @ Ts ) )
= ( ? [Us2: list_instr] :
( ( ( Xs
= ( append_instr @ Zs @ Us2 ) )
& ( ( append_instr @ Us2 @ Ys )
= Ts ) )
| ( ( ( append_instr @ Xs @ Us2 )
= Zs )
& ( Ys
= ( append_instr @ Us2 @ Ts ) ) ) ) ) ) ).
% append_eq_append_conv2
thf(fact_545_append__eq__appendI,axiom,
! [Xs: list_P419547167332244514st_int,Xs1: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,Us: list_P419547167332244514st_int] :
( ( ( append5028292981072010935st_int @ Xs @ Xs1 )
= Zs )
=> ( ( Ys
= ( append5028292981072010935st_int @ Xs1 @ Us ) )
=> ( ( append5028292981072010935st_int @ Xs @ Ys )
= ( append5028292981072010935st_int @ Zs @ Us ) ) ) ) ).
% append_eq_appendI
thf(fact_546_append__eq__appendI,axiom,
! [Xs: list_int,Xs1: list_int,Zs: list_int,Ys: list_int,Us: list_int] :
( ( ( append_int @ Xs @ Xs1 )
= Zs )
=> ( ( Ys
= ( append_int @ Xs1 @ Us ) )
=> ( ( append_int @ Xs @ Ys )
= ( append_int @ Zs @ Us ) ) ) ) ).
% append_eq_appendI
thf(fact_547_append__eq__appendI,axiom,
! [Xs: list_instr,Xs1: list_instr,Zs: list_instr,Ys: list_instr,Us: list_instr] :
( ( ( append_instr @ Xs @ Xs1 )
= Zs )
=> ( ( Ys
= ( append_instr @ Xs1 @ Us ) )
=> ( ( append_instr @ Xs @ Ys )
= ( append_instr @ Zs @ Us ) ) ) ) ).
% append_eq_appendI
thf(fact_548_list__nonempty__induct,axiom,
! [Xs: list_list_char,P: list_list_char > $o] :
( ( Xs != nil_list_char )
=> ( ! [X4: list_char] : ( P @ ( cons_list_char @ X4 @ nil_list_char ) )
=> ( ! [X4: list_char,Xs2: list_list_char] :
( ( Xs2 != nil_list_char )
=> ( ( P @ Xs2 )
=> ( P @ ( cons_list_char @ X4 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_549_list__nonempty__induct,axiom,
! [Xs: list_P419547167332244514st_int,P: list_P419547167332244514st_int > $o] :
( ( Xs != nil_Pr749310521696113548st_int )
=> ( ! [X4: produc6425607678544837394st_int] : ( P @ ( cons_P4151473878978182108st_int @ X4 @ nil_Pr749310521696113548st_int ) )
=> ( ! [X4: produc6425607678544837394st_int,Xs2: list_P419547167332244514st_int] :
( ( Xs2 != nil_Pr749310521696113548st_int )
=> ( ( P @ Xs2 )
=> ( P @ ( cons_P4151473878978182108st_int @ X4 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_550_list__nonempty__induct,axiom,
! [Xs: list_instr,P: list_instr > $o] :
( ( Xs != nil_instr )
=> ( ! [X4: instr] : ( P @ ( cons_instr @ X4 @ nil_instr ) )
=> ( ! [X4: instr,Xs2: list_instr] :
( ( Xs2 != nil_instr )
=> ( ( P @ Xs2 )
=> ( P @ ( cons_instr @ X4 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_551_list__nonempty__induct,axiom,
! [Xs: list_int,P: list_int > $o] :
( ( Xs != nil_int )
=> ( ! [X4: int] : ( P @ ( cons_int @ X4 @ nil_int ) )
=> ( ! [X4: int,Xs2: list_int] :
( ( Xs2 != nil_int )
=> ( ( P @ Xs2 )
=> ( P @ ( cons_int @ X4 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_552_list__induct2_H,axiom,
! [P: list_instr > list_instr > $o,Xs: list_instr,Ys: list_instr] :
( ( P @ nil_instr @ nil_instr )
=> ( ! [X4: instr,Xs2: list_instr] : ( P @ ( cons_instr @ X4 @ Xs2 ) @ nil_instr )
=> ( ! [Y3: instr,Ys3: list_instr] : ( P @ nil_instr @ ( cons_instr @ Y3 @ Ys3 ) )
=> ( ! [X4: instr,Xs2: list_instr,Y3: instr,Ys3: list_instr] :
( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_instr @ X4 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys3 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_553_list__induct2_H,axiom,
! [P: list_instr > list_int > $o,Xs: list_instr,Ys: list_int] :
( ( P @ nil_instr @ nil_int )
=> ( ! [X4: instr,Xs2: list_instr] : ( P @ ( cons_instr @ X4 @ Xs2 ) @ nil_int )
=> ( ! [Y3: int,Ys3: list_int] : ( P @ nil_instr @ ( cons_int @ Y3 @ Ys3 ) )
=> ( ! [X4: instr,Xs2: list_instr,Y3: int,Ys3: list_int] :
( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_instr @ X4 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_554_list__induct2_H,axiom,
! [P: list_int > list_instr > $o,Xs: list_int,Ys: list_instr] :
( ( P @ nil_int @ nil_instr )
=> ( ! [X4: int,Xs2: list_int] : ( P @ ( cons_int @ X4 @ Xs2 ) @ nil_instr )
=> ( ! [Y3: instr,Ys3: list_instr] : ( P @ nil_int @ ( cons_instr @ Y3 @ Ys3 ) )
=> ( ! [X4: int,Xs2: list_int,Y3: instr,Ys3: list_instr] :
( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_int @ X4 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys3 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_555_list__induct2_H,axiom,
! [P: list_int > list_int > $o,Xs: list_int,Ys: list_int] :
( ( P @ nil_int @ nil_int )
=> ( ! [X4: int,Xs2: list_int] : ( P @ ( cons_int @ X4 @ Xs2 ) @ nil_int )
=> ( ! [Y3: int,Ys3: list_int] : ( P @ nil_int @ ( cons_int @ Y3 @ Ys3 ) )
=> ( ! [X4: int,Xs2: list_int,Y3: int,Ys3: list_int] :
( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_int @ X4 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_556_list__induct2_H,axiom,
! [P: list_list_char > list_instr > $o,Xs: list_list_char,Ys: list_instr] :
( ( P @ nil_list_char @ nil_instr )
=> ( ! [X4: list_char,Xs2: list_list_char] : ( P @ ( cons_list_char @ X4 @ Xs2 ) @ nil_instr )
=> ( ! [Y3: instr,Ys3: list_instr] : ( P @ nil_list_char @ ( cons_instr @ Y3 @ Ys3 ) )
=> ( ! [X4: list_char,Xs2: list_list_char,Y3: instr,Ys3: list_instr] :
( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_list_char @ X4 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys3 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_557_list__induct2_H,axiom,
! [P: list_list_char > list_int > $o,Xs: list_list_char,Ys: list_int] :
( ( P @ nil_list_char @ nil_int )
=> ( ! [X4: list_char,Xs2: list_list_char] : ( P @ ( cons_list_char @ X4 @ Xs2 ) @ nil_int )
=> ( ! [Y3: int,Ys3: list_int] : ( P @ nil_list_char @ ( cons_int @ Y3 @ Ys3 ) )
=> ( ! [X4: list_char,Xs2: list_list_char,Y3: int,Ys3: list_int] :
( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_list_char @ X4 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_558_list__induct2_H,axiom,
! [P: list_instr > list_list_char > $o,Xs: list_instr,Ys: list_list_char] :
( ( P @ nil_instr @ nil_list_char )
=> ( ! [X4: instr,Xs2: list_instr] : ( P @ ( cons_instr @ X4 @ Xs2 ) @ nil_list_char )
=> ( ! [Y3: list_char,Ys3: list_list_char] : ( P @ nil_instr @ ( cons_list_char @ Y3 @ Ys3 ) )
=> ( ! [X4: instr,Xs2: list_instr,Y3: list_char,Ys3: list_list_char] :
( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_instr @ X4 @ Xs2 ) @ ( cons_list_char @ Y3 @ Ys3 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_559_list__induct2_H,axiom,
! [P: list_int > list_list_char > $o,Xs: list_int,Ys: list_list_char] :
( ( P @ nil_int @ nil_list_char )
=> ( ! [X4: int,Xs2: list_int] : ( P @ ( cons_int @ X4 @ Xs2 ) @ nil_list_char )
=> ( ! [Y3: list_char,Ys3: list_list_char] : ( P @ nil_int @ ( cons_list_char @ Y3 @ Ys3 ) )
=> ( ! [X4: int,Xs2: list_int,Y3: list_char,Ys3: list_list_char] :
( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_int @ X4 @ Xs2 ) @ ( cons_list_char @ Y3 @ Ys3 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_560_list__induct2_H,axiom,
! [P: list_list_char > list_list_char > $o,Xs: list_list_char,Ys: list_list_char] :
( ( P @ nil_list_char @ nil_list_char )
=> ( ! [X4: list_char,Xs2: list_list_char] : ( P @ ( cons_list_char @ X4 @ Xs2 ) @ nil_list_char )
=> ( ! [Y3: list_char,Ys3: list_list_char] : ( P @ nil_list_char @ ( cons_list_char @ Y3 @ Ys3 ) )
=> ( ! [X4: list_char,Xs2: list_list_char,Y3: list_char,Ys3: list_list_char] :
( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_list_char @ X4 @ Xs2 ) @ ( cons_list_char @ Y3 @ Ys3 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_561_list__induct2_H,axiom,
! [P: list_P419547167332244514st_int > list_instr > $o,Xs: list_P419547167332244514st_int,Ys: list_instr] :
( ( P @ nil_Pr749310521696113548st_int @ nil_instr )
=> ( ! [X4: produc6425607678544837394st_int,Xs2: list_P419547167332244514st_int] : ( P @ ( cons_P4151473878978182108st_int @ X4 @ Xs2 ) @ nil_instr )
=> ( ! [Y3: instr,Ys3: list_instr] : ( P @ nil_Pr749310521696113548st_int @ ( cons_instr @ Y3 @ Ys3 ) )
=> ( ! [X4: produc6425607678544837394st_int,Xs2: list_P419547167332244514st_int,Y3: instr,Ys3: list_instr] :
( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_P4151473878978182108st_int @ X4 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys3 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_562_neq__Nil__conv,axiom,
! [Xs: list_list_char] :
( ( Xs != nil_list_char )
= ( ? [Y5: list_char,Ys2: list_list_char] :
( Xs
= ( cons_list_char @ Y5 @ Ys2 ) ) ) ) ).
% neq_Nil_conv
thf(fact_563_neq__Nil__conv,axiom,
! [Xs: list_P419547167332244514st_int] :
( ( Xs != nil_Pr749310521696113548st_int )
= ( ? [Y5: produc6425607678544837394st_int,Ys2: list_P419547167332244514st_int] :
( Xs
= ( cons_P4151473878978182108st_int @ Y5 @ Ys2 ) ) ) ) ).
% neq_Nil_conv
thf(fact_564_neq__Nil__conv,axiom,
! [Xs: list_instr] :
( ( Xs != nil_instr )
= ( ? [Y5: instr,Ys2: list_instr] :
( Xs
= ( cons_instr @ Y5 @ Ys2 ) ) ) ) ).
% neq_Nil_conv
thf(fact_565_neq__Nil__conv,axiom,
! [Xs: list_int] :
( ( Xs != nil_int )
= ( ? [Y5: int,Ys2: list_int] :
( Xs
= ( cons_int @ Y5 @ Ys2 ) ) ) ) ).
% neq_Nil_conv
thf(fact_566_remdups__adj_Ocases,axiom,
! [X: list_list_char] :
( ( X != nil_list_char )
=> ( ! [X4: list_char] :
( X
!= ( cons_list_char @ X4 @ nil_list_char ) )
=> ~ ! [X4: list_char,Y3: list_char,Xs2: list_list_char] :
( X
!= ( cons_list_char @ X4 @ ( cons_list_char @ Y3 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_567_remdups__adj_Ocases,axiom,
! [X: list_P419547167332244514st_int] :
( ( X != nil_Pr749310521696113548st_int )
=> ( ! [X4: produc6425607678544837394st_int] :
( X
!= ( cons_P4151473878978182108st_int @ X4 @ nil_Pr749310521696113548st_int ) )
=> ~ ! [X4: produc6425607678544837394st_int,Y3: produc6425607678544837394st_int,Xs2: list_P419547167332244514st_int] :
( X
!= ( cons_P4151473878978182108st_int @ X4 @ ( cons_P4151473878978182108st_int @ Y3 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_568_remdups__adj_Ocases,axiom,
! [X: list_instr] :
( ( X != nil_instr )
=> ( ! [X4: instr] :
( X
!= ( cons_instr @ X4 @ nil_instr ) )
=> ~ ! [X4: instr,Y3: instr,Xs2: list_instr] :
( X
!= ( cons_instr @ X4 @ ( cons_instr @ Y3 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_569_remdups__adj_Ocases,axiom,
! [X: list_int] :
( ( X != nil_int )
=> ( ! [X4: int] :
( X
!= ( cons_int @ X4 @ nil_int ) )
=> ~ ! [X4: int,Y3: int,Xs2: list_int] :
( X
!= ( cons_int @ X4 @ ( cons_int @ Y3 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_570_transpose_Ocases,axiom,
! [X: list_list_list_char] :
( ( X != nil_list_list_char )
=> ( ! [Xss: list_list_list_char] :
( X
!= ( cons_list_list_char @ nil_list_char @ Xss ) )
=> ~ ! [X4: list_char,Xs2: list_list_char,Xss: list_list_list_char] :
( X
!= ( cons_list_list_char @ ( cons_list_char @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_571_transpose_Ocases,axiom,
! [X: list_list_char] :
( ( X != nil_list_char )
=> ( ! [Xss: list_list_char] :
( X
!= ( cons_list_char @ nil_char @ Xss ) )
=> ~ ! [X4: char,Xs2: list_char,Xss: list_list_char] :
( X
!= ( cons_list_char @ ( cons_char @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_572_transpose_Ocases,axiom,
! [X: list_l6422821129637969586st_int] :
( ( X != nil_li4597314861645524892st_int )
=> ( ! [Xss: list_l6422821129637969586st_int] :
( X
!= ( cons_l8648290059330449388st_int @ nil_Pr749310521696113548st_int @ Xss ) )
=> ~ ! [X4: produc6425607678544837394st_int,Xs2: list_P419547167332244514st_int,Xss: list_l6422821129637969586st_int] :
( X
!= ( cons_l8648290059330449388st_int @ ( cons_P4151473878978182108st_int @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_573_transpose_Ocases,axiom,
! [X: list_list_instr] :
( ( X != nil_list_instr )
=> ( ! [Xss: list_list_instr] :
( X
!= ( cons_list_instr @ nil_instr @ Xss ) )
=> ~ ! [X4: instr,Xs2: list_instr,Xss: list_list_instr] :
( X
!= ( cons_list_instr @ ( cons_instr @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_574_transpose_Ocases,axiom,
! [X: list_list_int] :
( ( X != nil_list_int )
=> ( ! [Xss: list_list_int] :
( X
!= ( cons_list_int @ nil_int @ Xss ) )
=> ~ ! [X4: int,Xs2: list_int,Xss: list_list_int] :
( X
!= ( cons_list_int @ ( cons_int @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_575_min__list_Ocases,axiom,
! [X: list_int] :
( ! [X4: int,Xs2: list_int] :
( X
!= ( cons_int @ X4 @ Xs2 ) )
=> ( X = nil_int ) ) ).
% min_list.cases
thf(fact_576_list_Oexhaust,axiom,
! [Y: list_list_char] :
( ( Y != nil_list_char )
=> ~ ! [X212: list_char,X222: list_list_char] :
( Y
!= ( cons_list_char @ X212 @ X222 ) ) ) ).
% list.exhaust
thf(fact_577_list_Oexhaust,axiom,
! [Y: list_P419547167332244514st_int] :
( ( Y != nil_Pr749310521696113548st_int )
=> ~ ! [X212: produc6425607678544837394st_int,X222: list_P419547167332244514st_int] :
( Y
!= ( cons_P4151473878978182108st_int @ X212 @ X222 ) ) ) ).
% list.exhaust
thf(fact_578_list_Oexhaust,axiom,
! [Y: list_instr] :
( ( Y != nil_instr )
=> ~ ! [X212: instr,X222: list_instr] :
( Y
!= ( cons_instr @ X212 @ X222 ) ) ) ).
% list.exhaust
thf(fact_579_list_Oexhaust,axiom,
! [Y: list_int] :
( ( Y != nil_int )
=> ~ ! [X212: int,X222: list_int] :
( Y
!= ( cons_int @ X212 @ X222 ) ) ) ).
% list.exhaust
thf(fact_580_list_OdiscI,axiom,
! [List: list_list_char,X21: list_char,X22: list_list_char] :
( ( List
= ( cons_list_char @ X21 @ X22 ) )
=> ( List != nil_list_char ) ) ).
% list.discI
thf(fact_581_list_OdiscI,axiom,
! [List: list_P419547167332244514st_int,X21: produc6425607678544837394st_int,X22: list_P419547167332244514st_int] :
( ( List
= ( cons_P4151473878978182108st_int @ X21 @ X22 ) )
=> ( List != nil_Pr749310521696113548st_int ) ) ).
% list.discI
thf(fact_582_list_OdiscI,axiom,
! [List: list_instr,X21: instr,X22: list_instr] :
( ( List
= ( cons_instr @ X21 @ X22 ) )
=> ( List != nil_instr ) ) ).
% list.discI
thf(fact_583_list_OdiscI,axiom,
! [List: list_int,X21: int,X22: list_int] :
( ( List
= ( cons_int @ X21 @ X22 ) )
=> ( List != nil_int ) ) ).
% list.discI
thf(fact_584_list_Odistinct_I1_J,axiom,
! [X21: list_char,X22: list_list_char] :
( nil_list_char
!= ( cons_list_char @ X21 @ X22 ) ) ).
% list.distinct(1)
thf(fact_585_list_Odistinct_I1_J,axiom,
! [X21: produc6425607678544837394st_int,X22: list_P419547167332244514st_int] :
( nil_Pr749310521696113548st_int
!= ( cons_P4151473878978182108st_int @ X21 @ X22 ) ) ).
% list.distinct(1)
thf(fact_586_list_Odistinct_I1_J,axiom,
! [X21: instr,X22: list_instr] :
( nil_instr
!= ( cons_instr @ X21 @ X22 ) ) ).
% list.distinct(1)
thf(fact_587_list_Odistinct_I1_J,axiom,
! [X21: int,X22: list_int] :
( nil_int
!= ( cons_int @ X21 @ X22 ) ) ).
% list.distinct(1)
thf(fact_588_map__tailrec__rev_Ocases,axiom,
! [X: produc8882982558199175111st_int] :
( ! [F2: instr > produc6425607678544837394st_int,Bs: list_P419547167332244514st_int] :
( X
!= ( produc5788636948506852673st_int @ F2 @ ( produc7764413618310988720st_int @ nil_instr @ Bs ) ) )
=> ~ ! [F2: instr > produc6425607678544837394st_int,A5: instr,As: list_instr,Bs: list_P419547167332244514st_int] :
( X
!= ( produc5788636948506852673st_int @ F2 @ ( produc7764413618310988720st_int @ ( cons_instr @ A5 @ As ) @ Bs ) ) ) ) ).
% map_tailrec_rev.cases
thf(fact_589_successively_Ocases,axiom,
! [X: produc8794813868974875620t_char] :
( ! [P3: list_char > list_char > $o] :
( X
!= ( produc1436111165245395422t_char @ P3 @ nil_list_char ) )
=> ( ! [P3: list_char > list_char > $o,X4: list_char] :
( X
!= ( produc1436111165245395422t_char @ P3 @ ( cons_list_char @ X4 @ nil_list_char ) ) )
=> ~ ! [P3: list_char > list_char > $o,X4: list_char,Y3: list_char,Xs2: list_list_char] :
( X
!= ( produc1436111165245395422t_char @ P3 @ ( cons_list_char @ X4 @ ( cons_list_char @ Y3 @ Xs2 ) ) ) ) ) ) ).
% successively.cases
thf(fact_590_successively_Ocases,axiom,
! [X: produc2468426419292222131st_int] :
( ! [P3: produc6425607678544837394st_int > produc6425607678544837394st_int > $o] :
( X
!= ( produc554038597315947693st_int @ P3 @ nil_Pr749310521696113548st_int ) )
=> ( ! [P3: produc6425607678544837394st_int > produc6425607678544837394st_int > $o,X4: produc6425607678544837394st_int] :
( X
!= ( produc554038597315947693st_int @ P3 @ ( cons_P4151473878978182108st_int @ X4 @ nil_Pr749310521696113548st_int ) ) )
=> ~ ! [P3: produc6425607678544837394st_int > produc6425607678544837394st_int > $o,X4: produc6425607678544837394st_int,Y3: produc6425607678544837394st_int,Xs2: list_P419547167332244514st_int] :
( X
!= ( produc554038597315947693st_int @ P3 @ ( cons_P4151473878978182108st_int @ X4 @ ( cons_P4151473878978182108st_int @ Y3 @ Xs2 ) ) ) ) ) ) ).
% successively.cases
thf(fact_591_successively_Ocases,axiom,
! [X: produc7133927873007960030_instr] :
( ! [P3: instr > instr > $o] :
( X
!= ( produc7818391707689388878_instr @ P3 @ nil_instr ) )
=> ( ! [P3: instr > instr > $o,X4: instr] :
( X
!= ( produc7818391707689388878_instr @ P3 @ ( cons_instr @ X4 @ nil_instr ) ) )
=> ~ ! [P3: instr > instr > $o,X4: instr,Y3: instr,Xs2: list_instr] :
( X
!= ( produc7818391707689388878_instr @ P3 @ ( cons_instr @ X4 @ ( cons_instr @ Y3 @ Xs2 ) ) ) ) ) ) ).
% successively.cases
thf(fact_592_successively_Ocases,axiom,
! [X: produc5834231552977413017st_int] :
( ! [P3: int > int > $o] :
( X
!= ( produc8618682346314911123st_int @ P3 @ nil_int ) )
=> ( ! [P3: int > int > $o,X4: int] :
( X
!= ( produc8618682346314911123st_int @ P3 @ ( cons_int @ X4 @ nil_int ) ) )
=> ~ ! [P3: int > int > $o,X4: int,Y3: int,Xs2: list_int] :
( X
!= ( produc8618682346314911123st_int @ P3 @ ( cons_int @ X4 @ ( cons_int @ Y3 @ Xs2 ) ) ) ) ) ) ).
% successively.cases
thf(fact_593_sorted__wrt_Ocases,axiom,
! [X: produc8794813868974875620t_char] :
( ! [P3: list_char > list_char > $o] :
( X
!= ( produc1436111165245395422t_char @ P3 @ nil_list_char ) )
=> ~ ! [P3: list_char > list_char > $o,X4: list_char,Ys3: list_list_char] :
( X
!= ( produc1436111165245395422t_char @ P3 @ ( cons_list_char @ X4 @ Ys3 ) ) ) ) ).
% sorted_wrt.cases
thf(fact_594_sorted__wrt_Ocases,axiom,
! [X: produc2468426419292222131st_int] :
( ! [P3: produc6425607678544837394st_int > produc6425607678544837394st_int > $o] :
( X
!= ( produc554038597315947693st_int @ P3 @ nil_Pr749310521696113548st_int ) )
=> ~ ! [P3: produc6425607678544837394st_int > produc6425607678544837394st_int > $o,X4: produc6425607678544837394st_int,Ys3: list_P419547167332244514st_int] :
( X
!= ( produc554038597315947693st_int @ P3 @ ( cons_P4151473878978182108st_int @ X4 @ Ys3 ) ) ) ) ).
% sorted_wrt.cases
thf(fact_595_sorted__wrt_Ocases,axiom,
! [X: produc7133927873007960030_instr] :
( ! [P3: instr > instr > $o] :
( X
!= ( produc7818391707689388878_instr @ P3 @ nil_instr ) )
=> ~ ! [P3: instr > instr > $o,X4: instr,Ys3: list_instr] :
( X
!= ( produc7818391707689388878_instr @ P3 @ ( cons_instr @ X4 @ Ys3 ) ) ) ) ).
% sorted_wrt.cases
thf(fact_596_sorted__wrt_Ocases,axiom,
! [X: produc5834231552977413017st_int] :
( ! [P3: int > int > $o] :
( X
!= ( produc8618682346314911123st_int @ P3 @ nil_int ) )
=> ~ ! [P3: int > int > $o,X4: int,Ys3: list_int] :
( X
!= ( produc8618682346314911123st_int @ P3 @ ( cons_int @ X4 @ Ys3 ) ) ) ) ).
% sorted_wrt.cases
thf(fact_597_shuffles_Ocases,axiom,
! [X: produc525958773753613763t_char] :
( ! [Ys3: list_list_char] :
( X
!= ( produc9134825680149865339t_char @ nil_list_char @ Ys3 ) )
=> ( ! [Xs2: list_list_char] :
( X
!= ( produc9134825680149865339t_char @ Xs2 @ nil_list_char ) )
=> ~ ! [X4: list_char,Xs2: list_list_char,Y3: list_char,Ys3: list_list_char] :
( X
!= ( produc9134825680149865339t_char @ ( cons_list_char @ X4 @ Xs2 ) @ ( cons_list_char @ Y3 @ Ys3 ) ) ) ) ) ).
% shuffles.cases
thf(fact_598_shuffles_Ocases,axiom,
! [X: produc5848496107505245989st_int] :
( ! [Ys3: list_P419547167332244514st_int] :
( X
!= ( produc2639222612625641053st_int @ nil_Pr749310521696113548st_int @ Ys3 ) )
=> ( ! [Xs2: list_P419547167332244514st_int] :
( X
!= ( produc2639222612625641053st_int @ Xs2 @ nil_Pr749310521696113548st_int ) )
=> ~ ! [X4: produc6425607678544837394st_int,Xs2: list_P419547167332244514st_int,Y3: produc6425607678544837394st_int,Ys3: list_P419547167332244514st_int] :
( X
!= ( produc2639222612625641053st_int @ ( cons_P4151473878978182108st_int @ X4 @ Xs2 ) @ ( cons_P4151473878978182108st_int @ Y3 @ Ys3 ) ) ) ) ) ).
% shuffles.cases
thf(fact_599_shuffles_Ocases,axiom,
! [X: produc8891168062546637159_instr] :
( ! [Ys3: list_instr] :
( X
!= ( produc7750586281064920791_instr @ nil_instr @ Ys3 ) )
=> ( ! [Xs2: list_instr] :
( X
!= ( produc7750586281064920791_instr @ Xs2 @ nil_instr ) )
=> ~ ! [X4: instr,Xs2: list_instr,Y3: instr,Ys3: list_instr] :
( X
!= ( produc7750586281064920791_instr @ ( cons_instr @ X4 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys3 ) ) ) ) ) ).
% shuffles.cases
thf(fact_600_shuffles_Ocases,axiom,
! [X: produc1186641810826059865st_int] :
( ! [Ys3: list_int] :
( X
!= ( produc364263696895485585st_int @ nil_int @ Ys3 ) )
=> ( ! [Xs2: list_int] :
( X
!= ( produc364263696895485585st_int @ Xs2 @ nil_int ) )
=> ~ ! [X4: int,Xs2: list_int,Y3: int,Ys3: list_int] :
( X
!= ( produc364263696895485585st_int @ ( cons_int @ X4 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) ) ) ) ).
% shuffles.cases
thf(fact_601_splice_Ocases,axiom,
! [X: produc525958773753613763t_char] :
( ! [Ys3: list_list_char] :
( X
!= ( produc9134825680149865339t_char @ nil_list_char @ Ys3 ) )
=> ~ ! [X4: list_char,Xs2: list_list_char,Ys3: list_list_char] :
( X
!= ( produc9134825680149865339t_char @ ( cons_list_char @ X4 @ Xs2 ) @ Ys3 ) ) ) ).
% splice.cases
thf(fact_602_splice_Ocases,axiom,
! [X: produc5848496107505245989st_int] :
( ! [Ys3: list_P419547167332244514st_int] :
( X
!= ( produc2639222612625641053st_int @ nil_Pr749310521696113548st_int @ Ys3 ) )
=> ~ ! [X4: produc6425607678544837394st_int,Xs2: list_P419547167332244514st_int,Ys3: list_P419547167332244514st_int] :
( X
!= ( produc2639222612625641053st_int @ ( cons_P4151473878978182108st_int @ X4 @ Xs2 ) @ Ys3 ) ) ) ).
% splice.cases
thf(fact_603_splice_Ocases,axiom,
! [X: produc8891168062546637159_instr] :
( ! [Ys3: list_instr] :
( X
!= ( produc7750586281064920791_instr @ nil_instr @ Ys3 ) )
=> ~ ! [X4: instr,Xs2: list_instr,Ys3: list_instr] :
( X
!= ( produc7750586281064920791_instr @ ( cons_instr @ X4 @ Xs2 ) @ Ys3 ) ) ) ).
% splice.cases
thf(fact_604_splice_Ocases,axiom,
! [X: produc1186641810826059865st_int] :
( ! [Ys3: list_int] :
( X
!= ( produc364263696895485585st_int @ nil_int @ Ys3 ) )
=> ~ ! [X4: int,Xs2: list_int,Ys3: list_int] :
( X
!= ( produc364263696895485585st_int @ ( cons_int @ X4 @ Xs2 ) @ Ys3 ) ) ) ).
% splice.cases
thf(fact_605_Cons__eq__appendI,axiom,
! [X: produc6425607678544837394st_int,Xs1: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,Xs: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int] :
( ( ( cons_P4151473878978182108st_int @ X @ Xs1 )
= Ys )
=> ( ( Xs
= ( append5028292981072010935st_int @ Xs1 @ Zs ) )
=> ( ( cons_P4151473878978182108st_int @ X @ Xs )
= ( append5028292981072010935st_int @ Ys @ Zs ) ) ) ) ).
% Cons_eq_appendI
thf(fact_606_Cons__eq__appendI,axiom,
! [X: instr,Xs1: list_instr,Ys: list_instr,Xs: list_instr,Zs: list_instr] :
( ( ( cons_instr @ X @ Xs1 )
= Ys )
=> ( ( Xs
= ( append_instr @ Xs1 @ Zs ) )
=> ( ( cons_instr @ X @ Xs )
= ( append_instr @ Ys @ Zs ) ) ) ) ).
% Cons_eq_appendI
thf(fact_607_Cons__eq__appendI,axiom,
! [X: int,Xs1: list_int,Ys: list_int,Xs: list_int,Zs: list_int] :
( ( ( cons_int @ X @ Xs1 )
= Ys )
=> ( ( Xs
= ( append_int @ Xs1 @ Zs ) )
=> ( ( cons_int @ X @ Xs )
= ( append_int @ Ys @ Zs ) ) ) ) ).
% Cons_eq_appendI
thf(fact_608_append__Cons,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( append5028292981072010935st_int @ ( cons_P4151473878978182108st_int @ X @ Xs ) @ Ys )
= ( cons_P4151473878978182108st_int @ X @ ( append5028292981072010935st_int @ Xs @ Ys ) ) ) ).
% append_Cons
thf(fact_609_append__Cons,axiom,
! [X: instr,Xs: list_instr,Ys: list_instr] :
( ( append_instr @ ( cons_instr @ X @ Xs ) @ Ys )
= ( cons_instr @ X @ ( append_instr @ Xs @ Ys ) ) ) ).
% append_Cons
thf(fact_610_append__Cons,axiom,
! [X: int,Xs: list_int,Ys: list_int] :
( ( append_int @ ( cons_int @ X @ Xs ) @ Ys )
= ( cons_int @ X @ ( append_int @ Xs @ Ys ) ) ) ).
% append_Cons
thf(fact_611_eq__Nil__appendI,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( Xs = Ys )
=> ( Xs
= ( append5028292981072010935st_int @ nil_Pr749310521696113548st_int @ Ys ) ) ) ).
% eq_Nil_appendI
thf(fact_612_eq__Nil__appendI,axiom,
! [Xs: list_instr,Ys: list_instr] :
( ( Xs = Ys )
=> ( Xs
= ( append_instr @ nil_instr @ Ys ) ) ) ).
% eq_Nil_appendI
thf(fact_613_eq__Nil__appendI,axiom,
! [Xs: list_list_char,Ys: list_list_char] :
( ( Xs = Ys )
=> ( Xs
= ( append_list_char @ nil_list_char @ Ys ) ) ) ).
% eq_Nil_appendI
thf(fact_614_eq__Nil__appendI,axiom,
! [Xs: list_int,Ys: list_int] :
( ( Xs = Ys )
=> ( Xs
= ( append_int @ nil_int @ Ys ) ) ) ).
% eq_Nil_appendI
thf(fact_615_append_Oleft__neutral,axiom,
! [A: list_P419547167332244514st_int] :
( ( append5028292981072010935st_int @ nil_Pr749310521696113548st_int @ A )
= A ) ).
% append.left_neutral
thf(fact_616_append_Oleft__neutral,axiom,
! [A: list_instr] :
( ( append_instr @ nil_instr @ A )
= A ) ).
% append.left_neutral
thf(fact_617_append_Oleft__neutral,axiom,
! [A: list_list_char] :
( ( append_list_char @ nil_list_char @ A )
= A ) ).
% append.left_neutral
thf(fact_618_append_Oleft__neutral,axiom,
! [A: list_int] :
( ( append_int @ nil_int @ A )
= A ) ).
% append.left_neutral
thf(fact_619_append__Nil,axiom,
! [Ys: list_P419547167332244514st_int] :
( ( append5028292981072010935st_int @ nil_Pr749310521696113548st_int @ Ys )
= Ys ) ).
% append_Nil
thf(fact_620_append__Nil,axiom,
! [Ys: list_instr] :
( ( append_instr @ nil_instr @ Ys )
= Ys ) ).
% append_Nil
thf(fact_621_append__Nil,axiom,
! [Ys: list_list_char] :
( ( append_list_char @ nil_list_char @ Ys )
= Ys ) ).
% append_Nil
thf(fact_622_append__Nil,axiom,
! [Ys: list_int] :
( ( append_int @ nil_int @ Ys )
= Ys ) ).
% append_Nil
thf(fact_623_list_Osize_I3_J,axiom,
( ( size_s229347708945616566st_int @ nil_Pr749310521696113548st_int )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_624_list_Osize_I3_J,axiom,
( ( size_s5914166952900237872_instr @ nil_m_instr )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_625_list_Osize_I3_J,axiom,
( ( size_size_list_instr @ nil_instr )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_626_list_Osize_I3_J,axiom,
( ( size_s356637359517785349t_char @ nil_list_char )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_627_list_Osize_I3_J,axiom,
( ( size_size_list_int @ nil_int )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_628_list__induct2,axiom,
! [Xs: list_m_instr,Ys: list_m_instr,P: list_m_instr > list_m_instr > $o] :
( ( ( size_s5914166952900237872_instr @ Xs )
= ( size_s5914166952900237872_instr @ Ys ) )
=> ( ( P @ nil_m_instr @ nil_m_instr )
=> ( ! [X4: m_instr,Xs2: list_m_instr,Y3: m_instr,Ys3: list_m_instr] :
( ( ( size_s5914166952900237872_instr @ Xs2 )
= ( size_s5914166952900237872_instr @ Ys3 ) )
=> ( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_m_instr @ X4 @ Xs2 ) @ ( cons_m_instr @ Y3 @ Ys3 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_629_list__induct2,axiom,
! [Xs: list_m_instr,Ys: list_instr,P: list_m_instr > list_instr > $o] :
( ( ( size_s5914166952900237872_instr @ Xs )
= ( size_size_list_instr @ Ys ) )
=> ( ( P @ nil_m_instr @ nil_instr )
=> ( ! [X4: m_instr,Xs2: list_m_instr,Y3: instr,Ys3: list_instr] :
( ( ( size_s5914166952900237872_instr @ Xs2 )
= ( size_size_list_instr @ Ys3 ) )
=> ( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_m_instr @ X4 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys3 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_630_list__induct2,axiom,
! [Xs: list_m_instr,Ys: list_int,P: list_m_instr > list_int > $o] :
( ( ( size_s5914166952900237872_instr @ Xs )
= ( size_size_list_int @ Ys ) )
=> ( ( P @ nil_m_instr @ nil_int )
=> ( ! [X4: m_instr,Xs2: list_m_instr,Y3: int,Ys3: list_int] :
( ( ( size_s5914166952900237872_instr @ Xs2 )
= ( size_size_list_int @ Ys3 ) )
=> ( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_m_instr @ X4 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_631_list__induct2,axiom,
! [Xs: list_instr,Ys: list_m_instr,P: list_instr > list_m_instr > $o] :
( ( ( size_size_list_instr @ Xs )
= ( size_s5914166952900237872_instr @ Ys ) )
=> ( ( P @ nil_instr @ nil_m_instr )
=> ( ! [X4: instr,Xs2: list_instr,Y3: m_instr,Ys3: list_m_instr] :
( ( ( size_size_list_instr @ Xs2 )
= ( size_s5914166952900237872_instr @ Ys3 ) )
=> ( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_instr @ X4 @ Xs2 ) @ ( cons_m_instr @ Y3 @ Ys3 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_632_list__induct2,axiom,
! [Xs: list_instr,Ys: list_instr,P: list_instr > list_instr > $o] :
( ( ( size_size_list_instr @ Xs )
= ( size_size_list_instr @ Ys ) )
=> ( ( P @ nil_instr @ nil_instr )
=> ( ! [X4: instr,Xs2: list_instr,Y3: instr,Ys3: list_instr] :
( ( ( size_size_list_instr @ Xs2 )
= ( size_size_list_instr @ Ys3 ) )
=> ( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_instr @ X4 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys3 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_633_list__induct2,axiom,
! [Xs: list_instr,Ys: list_int,P: list_instr > list_int > $o] :
( ( ( size_size_list_instr @ Xs )
= ( size_size_list_int @ Ys ) )
=> ( ( P @ nil_instr @ nil_int )
=> ( ! [X4: instr,Xs2: list_instr,Y3: int,Ys3: list_int] :
( ( ( size_size_list_instr @ Xs2 )
= ( size_size_list_int @ Ys3 ) )
=> ( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_instr @ X4 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_634_list__induct2,axiom,
! [Xs: list_int,Ys: list_m_instr,P: list_int > list_m_instr > $o] :
( ( ( size_size_list_int @ Xs )
= ( size_s5914166952900237872_instr @ Ys ) )
=> ( ( P @ nil_int @ nil_m_instr )
=> ( ! [X4: int,Xs2: list_int,Y3: m_instr,Ys3: list_m_instr] :
( ( ( size_size_list_int @ Xs2 )
= ( size_s5914166952900237872_instr @ Ys3 ) )
=> ( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_int @ X4 @ Xs2 ) @ ( cons_m_instr @ Y3 @ Ys3 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_635_list__induct2,axiom,
! [Xs: list_int,Ys: list_instr,P: list_int > list_instr > $o] :
( ( ( size_size_list_int @ Xs )
= ( size_size_list_instr @ Ys ) )
=> ( ( P @ nil_int @ nil_instr )
=> ( ! [X4: int,Xs2: list_int,Y3: instr,Ys3: list_instr] :
( ( ( size_size_list_int @ Xs2 )
= ( size_size_list_instr @ Ys3 ) )
=> ( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_int @ X4 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys3 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_636_list__induct2,axiom,
! [Xs: list_int,Ys: list_int,P: list_int > list_int > $o] :
( ( ( size_size_list_int @ Xs )
= ( size_size_list_int @ Ys ) )
=> ( ( P @ nil_int @ nil_int )
=> ( ! [X4: int,Xs2: list_int,Y3: int,Ys3: list_int] :
( ( ( size_size_list_int @ Xs2 )
= ( size_size_list_int @ Ys3 ) )
=> ( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_int @ X4 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_637_list__induct2,axiom,
! [Xs: list_m_instr,Ys: list_list_char,P: list_m_instr > list_list_char > $o] :
( ( ( size_s5914166952900237872_instr @ Xs )
= ( size_s356637359517785349t_char @ Ys ) )
=> ( ( P @ nil_m_instr @ nil_list_char )
=> ( ! [X4: m_instr,Xs2: list_m_instr,Y3: list_char,Ys3: list_list_char] :
( ( ( size_s5914166952900237872_instr @ Xs2 )
= ( size_s356637359517785349t_char @ Ys3 ) )
=> ( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_m_instr @ X4 @ Xs2 ) @ ( cons_list_char @ Y3 @ Ys3 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_638_list__induct3,axiom,
! [Xs: list_m_instr,Ys: list_m_instr,Zs: list_m_instr,P: list_m_instr > list_m_instr > list_m_instr > $o] :
( ( ( size_s5914166952900237872_instr @ Xs )
= ( size_s5914166952900237872_instr @ Ys ) )
=> ( ( ( size_s5914166952900237872_instr @ Ys )
= ( size_s5914166952900237872_instr @ Zs ) )
=> ( ( P @ nil_m_instr @ nil_m_instr @ nil_m_instr )
=> ( ! [X4: m_instr,Xs2: list_m_instr,Y3: m_instr,Ys3: list_m_instr,Z4: m_instr,Zs2: list_m_instr] :
( ( ( size_s5914166952900237872_instr @ Xs2 )
= ( size_s5914166952900237872_instr @ Ys3 ) )
=> ( ( ( size_s5914166952900237872_instr @ Ys3 )
= ( size_s5914166952900237872_instr @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs2 )
=> ( P @ ( cons_m_instr @ X4 @ Xs2 ) @ ( cons_m_instr @ Y3 @ Ys3 ) @ ( cons_m_instr @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_639_list__induct3,axiom,
! [Xs: list_m_instr,Ys: list_m_instr,Zs: list_instr,P: list_m_instr > list_m_instr > list_instr > $o] :
( ( ( size_s5914166952900237872_instr @ Xs )
= ( size_s5914166952900237872_instr @ Ys ) )
=> ( ( ( size_s5914166952900237872_instr @ Ys )
= ( size_size_list_instr @ Zs ) )
=> ( ( P @ nil_m_instr @ nil_m_instr @ nil_instr )
=> ( ! [X4: m_instr,Xs2: list_m_instr,Y3: m_instr,Ys3: list_m_instr,Z4: instr,Zs2: list_instr] :
( ( ( size_s5914166952900237872_instr @ Xs2 )
= ( size_s5914166952900237872_instr @ Ys3 ) )
=> ( ( ( size_s5914166952900237872_instr @ Ys3 )
= ( size_size_list_instr @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs2 )
=> ( P @ ( cons_m_instr @ X4 @ Xs2 ) @ ( cons_m_instr @ Y3 @ Ys3 ) @ ( cons_instr @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_640_list__induct3,axiom,
! [Xs: list_m_instr,Ys: list_m_instr,Zs: list_int,P: list_m_instr > list_m_instr > list_int > $o] :
( ( ( size_s5914166952900237872_instr @ Xs )
= ( size_s5914166952900237872_instr @ Ys ) )
=> ( ( ( size_s5914166952900237872_instr @ Ys )
= ( size_size_list_int @ Zs ) )
=> ( ( P @ nil_m_instr @ nil_m_instr @ nil_int )
=> ( ! [X4: m_instr,Xs2: list_m_instr,Y3: m_instr,Ys3: list_m_instr,Z4: int,Zs2: list_int] :
( ( ( size_s5914166952900237872_instr @ Xs2 )
= ( size_s5914166952900237872_instr @ Ys3 ) )
=> ( ( ( size_s5914166952900237872_instr @ Ys3 )
= ( size_size_list_int @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs2 )
=> ( P @ ( cons_m_instr @ X4 @ Xs2 ) @ ( cons_m_instr @ Y3 @ Ys3 ) @ ( cons_int @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_641_list__induct3,axiom,
! [Xs: list_m_instr,Ys: list_instr,Zs: list_m_instr,P: list_m_instr > list_instr > list_m_instr > $o] :
( ( ( size_s5914166952900237872_instr @ Xs )
= ( size_size_list_instr @ Ys ) )
=> ( ( ( size_size_list_instr @ Ys )
= ( size_s5914166952900237872_instr @ Zs ) )
=> ( ( P @ nil_m_instr @ nil_instr @ nil_m_instr )
=> ( ! [X4: m_instr,Xs2: list_m_instr,Y3: instr,Ys3: list_instr,Z4: m_instr,Zs2: list_m_instr] :
( ( ( size_s5914166952900237872_instr @ Xs2 )
= ( size_size_list_instr @ Ys3 ) )
=> ( ( ( size_size_list_instr @ Ys3 )
= ( size_s5914166952900237872_instr @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs2 )
=> ( P @ ( cons_m_instr @ X4 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys3 ) @ ( cons_m_instr @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_642_list__induct3,axiom,
! [Xs: list_m_instr,Ys: list_instr,Zs: list_instr,P: list_m_instr > list_instr > list_instr > $o] :
( ( ( size_s5914166952900237872_instr @ Xs )
= ( size_size_list_instr @ Ys ) )
=> ( ( ( size_size_list_instr @ Ys )
= ( size_size_list_instr @ Zs ) )
=> ( ( P @ nil_m_instr @ nil_instr @ nil_instr )
=> ( ! [X4: m_instr,Xs2: list_m_instr,Y3: instr,Ys3: list_instr,Z4: instr,Zs2: list_instr] :
( ( ( size_s5914166952900237872_instr @ Xs2 )
= ( size_size_list_instr @ Ys3 ) )
=> ( ( ( size_size_list_instr @ Ys3 )
= ( size_size_list_instr @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs2 )
=> ( P @ ( cons_m_instr @ X4 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys3 ) @ ( cons_instr @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_643_list__induct3,axiom,
! [Xs: list_m_instr,Ys: list_instr,Zs: list_int,P: list_m_instr > list_instr > list_int > $o] :
( ( ( size_s5914166952900237872_instr @ Xs )
= ( size_size_list_instr @ Ys ) )
=> ( ( ( size_size_list_instr @ Ys )
= ( size_size_list_int @ Zs ) )
=> ( ( P @ nil_m_instr @ nil_instr @ nil_int )
=> ( ! [X4: m_instr,Xs2: list_m_instr,Y3: instr,Ys3: list_instr,Z4: int,Zs2: list_int] :
( ( ( size_s5914166952900237872_instr @ Xs2 )
= ( size_size_list_instr @ Ys3 ) )
=> ( ( ( size_size_list_instr @ Ys3 )
= ( size_size_list_int @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs2 )
=> ( P @ ( cons_m_instr @ X4 @ Xs2 ) @ ( cons_instr @ Y3 @ Ys3 ) @ ( cons_int @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_644_list__induct3,axiom,
! [Xs: list_m_instr,Ys: list_int,Zs: list_m_instr,P: list_m_instr > list_int > list_m_instr > $o] :
( ( ( size_s5914166952900237872_instr @ Xs )
= ( size_size_list_int @ Ys ) )
=> ( ( ( size_size_list_int @ Ys )
= ( size_s5914166952900237872_instr @ Zs ) )
=> ( ( P @ nil_m_instr @ nil_int @ nil_m_instr )
=> ( ! [X4: m_instr,Xs2: list_m_instr,Y3: int,Ys3: list_int,Z4: m_instr,Zs2: list_m_instr] :
( ( ( size_s5914166952900237872_instr @ Xs2 )
= ( size_size_list_int @ Ys3 ) )
=> ( ( ( size_size_list_int @ Ys3 )
= ( size_s5914166952900237872_instr @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs2 )
=> ( P @ ( cons_m_instr @ X4 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) @ ( cons_m_instr @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_645_list__induct3,axiom,
! [Xs: list_m_instr,Ys: list_int,Zs: list_instr,P: list_m_instr > list_int > list_instr > $o] :
( ( ( size_s5914166952900237872_instr @ Xs )
= ( size_size_list_int @ Ys ) )
=> ( ( ( size_size_list_int @ Ys )
= ( size_size_list_instr @ Zs ) )
=> ( ( P @ nil_m_instr @ nil_int @ nil_instr )
=> ( ! [X4: m_instr,Xs2: list_m_instr,Y3: int,Ys3: list_int,Z4: instr,Zs2: list_instr] :
( ( ( size_s5914166952900237872_instr @ Xs2 )
= ( size_size_list_int @ Ys3 ) )
=> ( ( ( size_size_list_int @ Ys3 )
= ( size_size_list_instr @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs2 )
=> ( P @ ( cons_m_instr @ X4 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) @ ( cons_instr @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_646_list__induct3,axiom,
! [Xs: list_m_instr,Ys: list_int,Zs: list_int,P: list_m_instr > list_int > list_int > $o] :
( ( ( size_s5914166952900237872_instr @ Xs )
= ( size_size_list_int @ Ys ) )
=> ( ( ( size_size_list_int @ Ys )
= ( size_size_list_int @ Zs ) )
=> ( ( P @ nil_m_instr @ nil_int @ nil_int )
=> ( ! [X4: m_instr,Xs2: list_m_instr,Y3: int,Ys3: list_int,Z4: int,Zs2: list_int] :
( ( ( size_s5914166952900237872_instr @ Xs2 )
= ( size_size_list_int @ Ys3 ) )
=> ( ( ( size_size_list_int @ Ys3 )
= ( size_size_list_int @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs2 )
=> ( P @ ( cons_m_instr @ X4 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) @ ( cons_int @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_647_list__induct3,axiom,
! [Xs: list_instr,Ys: list_m_instr,Zs: list_m_instr,P: list_instr > list_m_instr > list_m_instr > $o] :
( ( ( size_size_list_instr @ Xs )
= ( size_s5914166952900237872_instr @ Ys ) )
=> ( ( ( size_s5914166952900237872_instr @ Ys )
= ( size_s5914166952900237872_instr @ Zs ) )
=> ( ( P @ nil_instr @ nil_m_instr @ nil_m_instr )
=> ( ! [X4: instr,Xs2: list_instr,Y3: m_instr,Ys3: list_m_instr,Z4: m_instr,Zs2: list_m_instr] :
( ( ( size_size_list_instr @ Xs2 )
= ( size_s5914166952900237872_instr @ Ys3 ) )
=> ( ( ( size_s5914166952900237872_instr @ Ys3 )
= ( size_s5914166952900237872_instr @ Zs2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs2 )
=> ( P @ ( cons_instr @ X4 @ Xs2 ) @ ( cons_m_instr @ Y3 @ Ys3 ) @ ( cons_m_instr @ Z4 @ Zs2 ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% list_induct3
thf(fact_648_impossible__Cons,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,X: produc6425607678544837394st_int] :
( ( ord_less_eq_nat @ ( size_s229347708945616566st_int @ Xs ) @ ( size_s229347708945616566st_int @ Ys ) )
=> ( Xs
!= ( cons_P4151473878978182108st_int @ X @ Ys ) ) ) ).
% impossible_Cons
thf(fact_649_impossible__Cons,axiom,
! [Xs: list_m_instr,Ys: list_m_instr,X: m_instr] :
( ( ord_less_eq_nat @ ( size_s5914166952900237872_instr @ Xs ) @ ( size_s5914166952900237872_instr @ Ys ) )
=> ( Xs
!= ( cons_m_instr @ X @ Ys ) ) ) ).
% impossible_Cons
thf(fact_650_impossible__Cons,axiom,
! [Xs: list_instr,Ys: list_instr,X: instr] :
( ( ord_less_eq_nat @ ( size_size_list_instr @ Xs ) @ ( size_size_list_instr @ Ys ) )
=> ( Xs
!= ( cons_instr @ X @ Ys ) ) ) ).
% impossible_Cons
thf(fact_651_impossible__Cons,axiom,
! [Xs: list_list_char,Ys: list_list_char,X: list_char] :
( ( ord_less_eq_nat @ ( size_s356637359517785349t_char @ Xs ) @ ( size_s356637359517785349t_char @ Ys ) )
=> ( Xs
!= ( cons_list_char @ X @ Ys ) ) ) ).
% impossible_Cons
thf(fact_652_impossible__Cons,axiom,
! [Xs: list_int,Ys: list_int,X: int] :
( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys ) )
=> ( Xs
!= ( cons_int @ X @ Ys ) ) ) ).
% impossible_Cons
thf(fact_653_rev__nonempty__induct,axiom,
! [Xs: list_list_char,P: list_list_char > $o] :
( ( Xs != nil_list_char )
=> ( ! [X4: list_char] : ( P @ ( cons_list_char @ X4 @ nil_list_char ) )
=> ( ! [X4: list_char,Xs2: list_list_char] :
( ( Xs2 != nil_list_char )
=> ( ( P @ Xs2 )
=> ( P @ ( append_list_char @ Xs2 @ ( cons_list_char @ X4 @ nil_list_char ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_654_rev__nonempty__induct,axiom,
! [Xs: list_P419547167332244514st_int,P: list_P419547167332244514st_int > $o] :
( ( Xs != nil_Pr749310521696113548st_int )
=> ( ! [X4: produc6425607678544837394st_int] : ( P @ ( cons_P4151473878978182108st_int @ X4 @ nil_Pr749310521696113548st_int ) )
=> ( ! [X4: produc6425607678544837394st_int,Xs2: list_P419547167332244514st_int] :
( ( Xs2 != nil_Pr749310521696113548st_int )
=> ( ( P @ Xs2 )
=> ( P @ ( append5028292981072010935st_int @ Xs2 @ ( cons_P4151473878978182108st_int @ X4 @ nil_Pr749310521696113548st_int ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_655_rev__nonempty__induct,axiom,
! [Xs: list_instr,P: list_instr > $o] :
( ( Xs != nil_instr )
=> ( ! [X4: instr] : ( P @ ( cons_instr @ X4 @ nil_instr ) )
=> ( ! [X4: instr,Xs2: list_instr] :
( ( Xs2 != nil_instr )
=> ( ( P @ Xs2 )
=> ( P @ ( append_instr @ Xs2 @ ( cons_instr @ X4 @ nil_instr ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_656_rev__nonempty__induct,axiom,
! [Xs: list_int,P: list_int > $o] :
( ( Xs != nil_int )
=> ( ! [X4: int] : ( P @ ( cons_int @ X4 @ nil_int ) )
=> ( ! [X4: int,Xs2: list_int] :
( ( Xs2 != nil_int )
=> ( ( P @ Xs2 )
=> ( P @ ( append_int @ Xs2 @ ( cons_int @ X4 @ nil_int ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_657_append__eq__Cons__conv,axiom,
! [Ys: list_list_char,Zs: list_list_char,X: list_char,Xs: list_list_char] :
( ( ( append_list_char @ Ys @ Zs )
= ( cons_list_char @ X @ Xs ) )
= ( ( ( Ys = nil_list_char )
& ( Zs
= ( cons_list_char @ X @ Xs ) ) )
| ? [Ys4: list_list_char] :
( ( Ys
= ( cons_list_char @ X @ Ys4 ) )
& ( ( append_list_char @ Ys4 @ Zs )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_658_append__eq__Cons__conv,axiom,
! [Ys: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int,X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int] :
( ( ( append5028292981072010935st_int @ Ys @ Zs )
= ( cons_P4151473878978182108st_int @ X @ Xs ) )
= ( ( ( Ys = nil_Pr749310521696113548st_int )
& ( Zs
= ( cons_P4151473878978182108st_int @ X @ Xs ) ) )
| ? [Ys4: list_P419547167332244514st_int] :
( ( Ys
= ( cons_P4151473878978182108st_int @ X @ Ys4 ) )
& ( ( append5028292981072010935st_int @ Ys4 @ Zs )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_659_append__eq__Cons__conv,axiom,
! [Ys: list_instr,Zs: list_instr,X: instr,Xs: list_instr] :
( ( ( append_instr @ Ys @ Zs )
= ( cons_instr @ X @ Xs ) )
= ( ( ( Ys = nil_instr )
& ( Zs
= ( cons_instr @ X @ Xs ) ) )
| ? [Ys4: list_instr] :
( ( Ys
= ( cons_instr @ X @ Ys4 ) )
& ( ( append_instr @ Ys4 @ Zs )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_660_append__eq__Cons__conv,axiom,
! [Ys: list_int,Zs: list_int,X: int,Xs: list_int] :
( ( ( append_int @ Ys @ Zs )
= ( cons_int @ X @ Xs ) )
= ( ( ( Ys = nil_int )
& ( Zs
= ( cons_int @ X @ Xs ) ) )
| ? [Ys4: list_int] :
( ( Ys
= ( cons_int @ X @ Ys4 ) )
& ( ( append_int @ Ys4 @ Zs )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_661_Cons__eq__append__conv,axiom,
! [X: list_char,Xs: list_list_char,Ys: list_list_char,Zs: list_list_char] :
( ( ( cons_list_char @ X @ Xs )
= ( append_list_char @ Ys @ Zs ) )
= ( ( ( Ys = nil_list_char )
& ( ( cons_list_char @ X @ Xs )
= Zs ) )
| ? [Ys4: list_list_char] :
( ( ( cons_list_char @ X @ Ys4 )
= Ys )
& ( Xs
= ( append_list_char @ Ys4 @ Zs ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_662_Cons__eq__append__conv,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int] :
( ( ( cons_P4151473878978182108st_int @ X @ Xs )
= ( append5028292981072010935st_int @ Ys @ Zs ) )
= ( ( ( Ys = nil_Pr749310521696113548st_int )
& ( ( cons_P4151473878978182108st_int @ X @ Xs )
= Zs ) )
| ? [Ys4: list_P419547167332244514st_int] :
( ( ( cons_P4151473878978182108st_int @ X @ Ys4 )
= Ys )
& ( Xs
= ( append5028292981072010935st_int @ Ys4 @ Zs ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_663_Cons__eq__append__conv,axiom,
! [X: instr,Xs: list_instr,Ys: list_instr,Zs: list_instr] :
( ( ( cons_instr @ X @ Xs )
= ( append_instr @ Ys @ Zs ) )
= ( ( ( Ys = nil_instr )
& ( ( cons_instr @ X @ Xs )
= Zs ) )
| ? [Ys4: list_instr] :
( ( ( cons_instr @ X @ Ys4 )
= Ys )
& ( Xs
= ( append_instr @ Ys4 @ Zs ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_664_Cons__eq__append__conv,axiom,
! [X: int,Xs: list_int,Ys: list_int,Zs: list_int] :
( ( ( cons_int @ X @ Xs )
= ( append_int @ Ys @ Zs ) )
= ( ( ( Ys = nil_int )
& ( ( cons_int @ X @ Xs )
= Zs ) )
| ? [Ys4: list_int] :
( ( ( cons_int @ X @ Ys4 )
= Ys )
& ( Xs
= ( append_int @ Ys4 @ Zs ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_665_rev__exhaust,axiom,
! [Xs: list_list_char] :
( ( Xs != nil_list_char )
=> ~ ! [Ys3: list_list_char,Y3: list_char] :
( Xs
!= ( append_list_char @ Ys3 @ ( cons_list_char @ Y3 @ nil_list_char ) ) ) ) ).
% rev_exhaust
thf(fact_666_rev__exhaust,axiom,
! [Xs: list_P419547167332244514st_int] :
( ( Xs != nil_Pr749310521696113548st_int )
=> ~ ! [Ys3: list_P419547167332244514st_int,Y3: produc6425607678544837394st_int] :
( Xs
!= ( append5028292981072010935st_int @ Ys3 @ ( cons_P4151473878978182108st_int @ Y3 @ nil_Pr749310521696113548st_int ) ) ) ) ).
% rev_exhaust
thf(fact_667_rev__exhaust,axiom,
! [Xs: list_instr] :
( ( Xs != nil_instr )
=> ~ ! [Ys3: list_instr,Y3: instr] :
( Xs
!= ( append_instr @ Ys3 @ ( cons_instr @ Y3 @ nil_instr ) ) ) ) ).
% rev_exhaust
thf(fact_668_rev__exhaust,axiom,
! [Xs: list_int] :
( ( Xs != nil_int )
=> ~ ! [Ys3: list_int,Y3: int] :
( Xs
!= ( append_int @ Ys3 @ ( cons_int @ Y3 @ nil_int ) ) ) ) ).
% rev_exhaust
thf(fact_669_rev__induct,axiom,
! [P: list_list_char > $o,Xs: list_list_char] :
( ( P @ nil_list_char )
=> ( ! [X4: list_char,Xs2: list_list_char] :
( ( P @ Xs2 )
=> ( P @ ( append_list_char @ Xs2 @ ( cons_list_char @ X4 @ nil_list_char ) ) ) )
=> ( P @ Xs ) ) ) ).
% rev_induct
thf(fact_670_rev__induct,axiom,
! [P: list_P419547167332244514st_int > $o,Xs: list_P419547167332244514st_int] :
( ( P @ nil_Pr749310521696113548st_int )
=> ( ! [X4: produc6425607678544837394st_int,Xs2: list_P419547167332244514st_int] :
( ( P @ Xs2 )
=> ( P @ ( append5028292981072010935st_int @ Xs2 @ ( cons_P4151473878978182108st_int @ X4 @ nil_Pr749310521696113548st_int ) ) ) )
=> ( P @ Xs ) ) ) ).
% rev_induct
thf(fact_671_rev__induct,axiom,
! [P: list_instr > $o,Xs: list_instr] :
( ( P @ nil_instr )
=> ( ! [X4: instr,Xs2: list_instr] :
( ( P @ Xs2 )
=> ( P @ ( append_instr @ Xs2 @ ( cons_instr @ X4 @ nil_instr ) ) ) )
=> ( P @ Xs ) ) ) ).
% rev_induct
thf(fact_672_rev__induct,axiom,
! [P: list_int > $o,Xs: list_int] :
( ( P @ nil_int )
=> ( ! [X4: int,Xs2: list_int] :
( ( P @ Xs2 )
=> ( P @ ( append_int @ Xs2 @ ( cons_int @ X4 @ nil_int ) ) ) )
=> ( P @ Xs ) ) ) ).
% rev_induct
thf(fact_673_same__length__different,axiom,
! [Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( Xs != Ys )
=> ( ( ( size_s229347708945616566st_int @ Xs )
= ( size_s229347708945616566st_int @ Ys ) )
=> ? [Pre: list_P419547167332244514st_int,X4: produc6425607678544837394st_int,Xs3: list_P419547167332244514st_int,Y3: produc6425607678544837394st_int,Ys5: list_P419547167332244514st_int] :
( ( X4 != Y3 )
& ( Xs
= ( append5028292981072010935st_int @ Pre @ ( append5028292981072010935st_int @ ( cons_P4151473878978182108st_int @ X4 @ nil_Pr749310521696113548st_int ) @ Xs3 ) ) )
& ( Ys
= ( append5028292981072010935st_int @ Pre @ ( append5028292981072010935st_int @ ( cons_P4151473878978182108st_int @ Y3 @ nil_Pr749310521696113548st_int ) @ Ys5 ) ) ) ) ) ) ).
% same_length_different
thf(fact_674_same__length__different,axiom,
! [Xs: list_m_instr,Ys: list_m_instr] :
( ( Xs != Ys )
=> ( ( ( size_s5914166952900237872_instr @ Xs )
= ( size_s5914166952900237872_instr @ Ys ) )
=> ? [Pre: list_m_instr,X4: m_instr,Xs3: list_m_instr,Y3: m_instr,Ys5: list_m_instr] :
( ( X4 != Y3 )
& ( Xs
= ( append_m_instr @ Pre @ ( append_m_instr @ ( cons_m_instr @ X4 @ nil_m_instr ) @ Xs3 ) ) )
& ( Ys
= ( append_m_instr @ Pre @ ( append_m_instr @ ( cons_m_instr @ Y3 @ nil_m_instr ) @ Ys5 ) ) ) ) ) ) ).
% same_length_different
thf(fact_675_same__length__different,axiom,
! [Xs: list_instr,Ys: list_instr] :
( ( Xs != Ys )
=> ( ( ( size_size_list_instr @ Xs )
= ( size_size_list_instr @ Ys ) )
=> ? [Pre: list_instr,X4: instr,Xs3: list_instr,Y3: instr,Ys5: list_instr] :
( ( X4 != Y3 )
& ( Xs
= ( append_instr @ Pre @ ( append_instr @ ( cons_instr @ X4 @ nil_instr ) @ Xs3 ) ) )
& ( Ys
= ( append_instr @ Pre @ ( append_instr @ ( cons_instr @ Y3 @ nil_instr ) @ Ys5 ) ) ) ) ) ) ).
% same_length_different
thf(fact_676_same__length__different,axiom,
! [Xs: list_list_char,Ys: list_list_char] :
( ( Xs != Ys )
=> ( ( ( size_s356637359517785349t_char @ Xs )
= ( size_s356637359517785349t_char @ Ys ) )
=> ? [Pre: list_list_char,X4: list_char,Xs3: list_list_char,Y3: list_char,Ys5: list_list_char] :
( ( X4 != Y3 )
& ( Xs
= ( append_list_char @ Pre @ ( append_list_char @ ( cons_list_char @ X4 @ nil_list_char ) @ Xs3 ) ) )
& ( Ys
= ( append_list_char @ Pre @ ( append_list_char @ ( cons_list_char @ Y3 @ nil_list_char ) @ Ys5 ) ) ) ) ) ) ).
% same_length_different
thf(fact_677_same__length__different,axiom,
! [Xs: list_int,Ys: list_int] :
( ( Xs != Ys )
=> ( ( ( size_size_list_int @ Xs )
= ( size_size_list_int @ Ys ) )
=> ? [Pre: list_int,X4: int,Xs3: list_int,Y3: int,Ys5: list_int] :
( ( X4 != Y3 )
& ( Xs
= ( append_int @ Pre @ ( append_int @ ( cons_int @ X4 @ nil_int ) @ Xs3 ) ) )
& ( Ys
= ( append_int @ Pre @ ( append_int @ ( cons_int @ Y3 @ nil_int ) @ Ys5 ) ) ) ) ) ) ).
% same_length_different
thf(fact_678_length__append__singleton,axiom,
! [Xs: list_P419547167332244514st_int,X: produc6425607678544837394st_int] :
( ( size_s229347708945616566st_int @ ( append5028292981072010935st_int @ Xs @ ( cons_P4151473878978182108st_int @ X @ nil_Pr749310521696113548st_int ) ) )
= ( suc @ ( size_s229347708945616566st_int @ Xs ) ) ) ).
% length_append_singleton
thf(fact_679_length__append__singleton,axiom,
! [Xs: list_m_instr,X: m_instr] :
( ( size_s5914166952900237872_instr @ ( append_m_instr @ Xs @ ( cons_m_instr @ X @ nil_m_instr ) ) )
= ( suc @ ( size_s5914166952900237872_instr @ Xs ) ) ) ).
% length_append_singleton
thf(fact_680_length__append__singleton,axiom,
! [Xs: list_instr,X: instr] :
( ( size_size_list_instr @ ( append_instr @ Xs @ ( cons_instr @ X @ nil_instr ) ) )
= ( suc @ ( size_size_list_instr @ Xs ) ) ) ).
% length_append_singleton
thf(fact_681_length__append__singleton,axiom,
! [Xs: list_list_char,X: list_char] :
( ( size_s356637359517785349t_char @ ( append_list_char @ Xs @ ( cons_list_char @ X @ nil_list_char ) ) )
= ( suc @ ( size_s356637359517785349t_char @ Xs ) ) ) ).
% length_append_singleton
thf(fact_682_length__append__singleton,axiom,
! [Xs: list_int,X: int] :
( ( size_size_list_int @ ( append_int @ Xs @ ( cons_int @ X @ nil_int ) ) )
= ( suc @ ( size_size_list_int @ Xs ) ) ) ).
% length_append_singleton
thf(fact_683_size_H__char__eq__0,axiom,
( size_char
= ( ^ [C3: char] : zero_zero_nat ) ) ).
% size'_char_eq_0
thf(fact_684_exec__append__trans,axiom,
! [P: list_instr,S: list_char > int,Stk: list_int,I4: int,S2: list_char > int,Stk2: list_int,P4: list_instr,I5: int,S4: list_char > int,Stk4: list_int,J2: int] :
( ( star_P707599355569300323st_int @ ( exec1 @ P ) @ ( produc5086643055186798020st_int @ zero_zero_int @ ( produc8650753666468850689st_int @ S @ Stk ) ) @ ( produc5086643055186798020st_int @ I4 @ ( produc8650753666468850689st_int @ S2 @ Stk2 ) ) )
=> ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P ) ) @ I4 )
=> ( ( star_P707599355569300323st_int @ ( exec1 @ P4 ) @ ( produc5086643055186798020st_int @ ( minus_minus_int @ I4 @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P ) ) ) @ ( produc8650753666468850689st_int @ S2 @ Stk2 ) ) @ ( produc5086643055186798020st_int @ I5 @ ( produc8650753666468850689st_int @ S4 @ Stk4 ) ) )
=> ( ( J2
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P ) ) @ I5 ) )
=> ( star_P707599355569300323st_int @ ( exec1 @ ( append_instr @ P @ P4 ) ) @ ( produc5086643055186798020st_int @ zero_zero_int @ ( produc8650753666468850689st_int @ S @ Stk ) ) @ ( produc5086643055186798020st_int @ J2 @ ( produc8650753666468850689st_int @ S4 @ Stk4 ) ) ) ) ) ) ) ).
% exec_append_trans
thf(fact_685_length__Cons,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int] :
( ( size_s229347708945616566st_int @ ( cons_P4151473878978182108st_int @ X @ Xs ) )
= ( suc @ ( size_s229347708945616566st_int @ Xs ) ) ) ).
% length_Cons
thf(fact_686_length__Cons,axiom,
! [X: m_instr,Xs: list_m_instr] :
( ( size_s5914166952900237872_instr @ ( cons_m_instr @ X @ Xs ) )
= ( suc @ ( size_s5914166952900237872_instr @ Xs ) ) ) ).
% length_Cons
thf(fact_687_length__Cons,axiom,
! [X: instr,Xs: list_instr] :
( ( size_size_list_instr @ ( cons_instr @ X @ Xs ) )
= ( suc @ ( size_size_list_instr @ Xs ) ) ) ).
% length_Cons
thf(fact_688_length__Cons,axiom,
! [X: list_char,Xs: list_list_char] :
( ( size_s356637359517785349t_char @ ( cons_list_char @ X @ Xs ) )
= ( suc @ ( size_s356637359517785349t_char @ Xs ) ) ) ).
% length_Cons
thf(fact_689_length__Cons,axiom,
! [X: int,Xs: list_int] :
( ( size_size_list_int @ ( cons_int @ X @ Xs ) )
= ( suc @ ( size_size_list_int @ Xs ) ) ) ).
% length_Cons
thf(fact_690_exec__appendL__if,axiom,
! [P4: list_instr,I: int,P: list_instr,S: list_char > int,Stk: list_int,J: int,S2: list_char > int,Stk2: list_int,I4: int] :
( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P4 ) ) @ I )
=> ( ( star_P707599355569300323st_int @ ( exec1 @ P ) @ ( produc5086643055186798020st_int @ ( minus_minus_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P4 ) ) ) @ ( produc8650753666468850689st_int @ S @ Stk ) ) @ ( produc5086643055186798020st_int @ J @ ( produc8650753666468850689st_int @ S2 @ Stk2 ) ) )
=> ( ( I4
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P4 ) ) @ J ) )
=> ( star_P707599355569300323st_int @ ( exec1 @ ( append_instr @ P4 @ P ) ) @ ( produc5086643055186798020st_int @ I @ ( produc8650753666468850689st_int @ S @ Stk ) ) @ ( produc5086643055186798020st_int @ I4 @ ( produc8650753666468850689st_int @ S2 @ Stk2 ) ) ) ) ) ) ).
% exec_appendL_if
thf(fact_691_exec__Cons__1,axiom,
! [P: list_instr,S: list_char > int,Stk: list_int,J: int,T: list_char > int,Stk2: list_int,Ins2: instr] :
( ( star_P707599355569300323st_int @ ( exec1 @ P ) @ ( produc5086643055186798020st_int @ zero_zero_int @ ( produc8650753666468850689st_int @ S @ Stk ) ) @ ( produc5086643055186798020st_int @ J @ ( produc8650753666468850689st_int @ T @ Stk2 ) ) )
=> ( star_P707599355569300323st_int @ ( exec1 @ ( cons_instr @ Ins2 @ P ) ) @ ( produc5086643055186798020st_int @ one_one_int @ ( produc8650753666468850689st_int @ S @ Stk ) ) @ ( produc5086643055186798020st_int @ ( plus_plus_int @ one_one_int @ J ) @ ( produc8650753666468850689st_int @ T @ Stk2 ) ) ) ) ).
% exec_Cons_1
thf(fact_692_iexec__offset,axiom,
! [Ins2: instr,Pc: int,S: list_char > int,Stk: list_int,Pc2: int,S2: list_char > int,Stk2: list_int,I: int] :
( ( iexec_pred @ ( produc1484136438817787418st_int @ Ins2 @ ( produc5086643055186798020st_int @ Pc @ ( produc8650753666468850689st_int @ S @ Stk ) ) ) @ ( produc5086643055186798020st_int @ Pc2 @ ( produc8650753666468850689st_int @ S2 @ Stk2 ) ) )
=> ( iexec_pred @ ( produc1484136438817787418st_int @ Ins2 @ ( produc5086643055186798020st_int @ ( minus_minus_int @ Pc @ I ) @ ( produc8650753666468850689st_int @ S @ Stk ) ) ) @ ( produc5086643055186798020st_int @ ( minus_minus_int @ Pc2 @ I ) @ ( produc8650753666468850689st_int @ S2 @ Stk2 ) ) ) ) ).
% iexec_offset
thf(fact_693_of__nat__eq__iff,axiom,
! [M: nat,N: nat] :
( ( ( semiri1314217659103216013at_int @ M )
= ( semiri1314217659103216013at_int @ N ) )
= ( M = N ) ) ).
% of_nat_eq_iff
thf(fact_694_of__nat__eq__1__iff,axiom,
! [N: nat] :
( ( ( semiri1316708129612266289at_nat @ N )
= one_one_nat )
= ( N = one_one_nat ) ) ).
% of_nat_eq_1_iff
thf(fact_695_of__nat__eq__1__iff,axiom,
! [N: nat] :
( ( ( semiri1314217659103216013at_int @ N )
= one_one_int )
= ( N = one_one_nat ) ) ).
% of_nat_eq_1_iff
thf(fact_696_of__nat__1__eq__iff,axiom,
! [N: nat] :
( ( one_one_nat
= ( semiri1316708129612266289at_nat @ N ) )
= ( N = one_one_nat ) ) ).
% of_nat_1_eq_iff
thf(fact_697_of__nat__1__eq__iff,axiom,
! [N: nat] :
( ( one_one_int
= ( semiri1314217659103216013at_int @ N ) )
= ( N = one_one_nat ) ) ).
% of_nat_1_eq_iff
thf(fact_698_of__nat__1,axiom,
( ( semiri1316708129612266289at_nat @ one_one_nat )
= one_one_nat ) ).
% of_nat_1
thf(fact_699_of__nat__1,axiom,
( ( semiri1314217659103216013at_int @ one_one_nat )
= one_one_int ) ).
% of_nat_1
thf(fact_700_diff__numeral__special_I9_J,axiom,
( ( minus_minus_int @ one_one_int @ one_one_int )
= zero_zero_int ) ).
% diff_numeral_special(9)
thf(fact_701_of__nat__eq__0__iff,axiom,
! [M: nat] :
( ( ( semiri1316708129612266289at_nat @ M )
= zero_zero_nat )
= ( M = zero_zero_nat ) ) ).
% of_nat_eq_0_iff
thf(fact_702_of__nat__eq__0__iff,axiom,
! [M: nat] :
( ( ( semiri1314217659103216013at_int @ M )
= zero_zero_int )
= ( M = zero_zero_nat ) ) ).
% of_nat_eq_0_iff
thf(fact_703_of__nat__0__eq__iff,axiom,
! [N: nat] :
( ( zero_zero_nat
= ( semiri1316708129612266289at_nat @ N ) )
= ( zero_zero_nat = N ) ) ).
% of_nat_0_eq_iff
thf(fact_704_of__nat__0__eq__iff,axiom,
! [N: nat] :
( ( zero_zero_int
= ( semiri1314217659103216013at_int @ N ) )
= ( zero_zero_nat = N ) ) ).
% of_nat_0_eq_iff
thf(fact_705_of__nat__0,axiom,
( ( semiri1316708129612266289at_nat @ zero_zero_nat )
= zero_zero_nat ) ).
% of_nat_0
thf(fact_706_of__nat__0,axiom,
( ( semiri1314217659103216013at_int @ zero_zero_nat )
= zero_zero_int ) ).
% of_nat_0
thf(fact_707_of__nat__le__iff,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
= ( ord_less_eq_nat @ M @ N ) ) ).
% of_nat_le_iff
thf(fact_708_of__nat__le__iff,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
= ( ord_less_eq_nat @ M @ N ) ) ).
% of_nat_le_iff
thf(fact_709_of__nat__add,axiom,
! [M: nat,N: nat] :
( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
= ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% of_nat_add
thf(fact_710_of__nat__add,axiom,
! [M: nat,N: nat] :
( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% of_nat_add
thf(fact_711_of__nat__le__0__iff,axiom,
! [M: nat] :
( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
= ( M = zero_zero_nat ) ) ).
% of_nat_le_0_iff
thf(fact_712_of__nat__le__0__iff,axiom,
! [M: nat] :
( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
= ( M = zero_zero_nat ) ) ).
% of_nat_le_0_iff
thf(fact_713_of__nat__Suc,axiom,
! [M: nat] :
( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
= ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% of_nat_Suc
thf(fact_714_of__nat__Suc,axiom,
! [M: nat] :
( ( semiri1314217659103216013at_int @ ( suc @ M ) )
= ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% of_nat_Suc
thf(fact_715_int__int__eq,axiom,
! [M: nat,N: nat] :
( ( ( semiri1314217659103216013at_int @ M )
= ( semiri1314217659103216013at_int @ N ) )
= ( M = N ) ) ).
% int_int_eq
thf(fact_716_int__if,axiom,
! [P: $o,A: nat,B: nat] :
( ( P
=> ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
= ( semiri1314217659103216013at_int @ A ) ) )
& ( ~ P
=> ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
= ( semiri1314217659103216013at_int @ B ) ) ) ) ).
% int_if
thf(fact_717_nat__int__comparison_I1_J,axiom,
( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
= ( ^ [A4: nat,B4: nat] :
( ( semiri1314217659103216013at_int @ A4 )
= ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% nat_int_comparison(1)
thf(fact_718_one__reorient,axiom,
! [X: int] :
( ( one_one_int = X )
= ( X = one_one_int ) ) ).
% one_reorient
thf(fact_719_one__reorient,axiom,
! [X: nat] :
( ( one_one_nat = X )
= ( X = one_one_nat ) ) ).
% one_reorient
thf(fact_720_int__Suc,axiom,
! [N: nat] :
( ( semiri1314217659103216013at_int @ ( suc @ N ) )
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% int_Suc
thf(fact_721_int__ops_I4_J,axiom,
! [A: nat] :
( ( semiri1314217659103216013at_int @ ( suc @ A ) )
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% int_ops(4)
thf(fact_722_le__numeral__extra_I4_J,axiom,
ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% le_numeral_extra(4)
thf(fact_723_le__numeral__extra_I4_J,axiom,
ord_less_eq_int @ one_one_int @ one_one_int ).
% le_numeral_extra(4)
thf(fact_724_zero__neq__one,axiom,
zero_zero_nat != one_one_nat ).
% zero_neq_one
thf(fact_725_zero__neq__one,axiom,
zero_zero_int != one_one_int ).
% zero_neq_one
thf(fact_726_int__diff__cases,axiom,
! [Z: int] :
~ ! [M3: nat,N2: nat] :
( Z
!= ( minus_minus_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% int_diff_cases
thf(fact_727_of__nat__0__le__iff,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% of_nat_0_le_iff
thf(fact_728_of__nat__0__le__iff,axiom,
! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% of_nat_0_le_iff
thf(fact_729_of__nat__neq__0,axiom,
! [N: nat] :
( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
!= zero_zero_nat ) ).
% of_nat_neq_0
thf(fact_730_of__nat__neq__0,axiom,
! [N: nat] :
( ( semiri1314217659103216013at_int @ ( suc @ N ) )
!= zero_zero_int ) ).
% of_nat_neq_0
thf(fact_731_of__nat__mono,axiom,
! [I: nat,J: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% of_nat_mono
thf(fact_732_of__nat__mono,axiom,
! [I: nat,J: nat] :
( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% of_nat_mono
thf(fact_733_int__ops_I1_J,axiom,
( ( semiri1314217659103216013at_int @ zero_zero_nat )
= zero_zero_int ) ).
% int_ops(1)
thf(fact_734_zle__int,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
= ( ord_less_eq_nat @ M @ N ) ) ).
% zle_int
thf(fact_735_nat__int__comparison_I3_J,axiom,
( ord_less_eq_nat
= ( ^ [A4: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% nat_int_comparison(3)
thf(fact_736_nonneg__int__cases,axiom,
! [K: int] :
( ( ord_less_eq_int @ zero_zero_int @ K )
=> ~ ! [N2: nat] :
( K
!= ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% nonneg_int_cases
thf(fact_737_zero__le__imp__eq__int,axiom,
! [K: int] :
( ( ord_less_eq_int @ zero_zero_int @ K )
=> ? [N2: nat] :
( K
= ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% zero_le_imp_eq_int
thf(fact_738_zadd__int__left,axiom,
! [M: nat,N: nat,Z: int] :
( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% zadd_int_left
thf(fact_739_int__plus,axiom,
! [N: nat,M: nat] :
( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% int_plus
thf(fact_740_int__ops_I5_J,axiom,
! [A: nat,B: nat] :
( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
= ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% int_ops(5)
thf(fact_741_not__one__le__zero,axiom,
~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% not_one_le_zero
thf(fact_742_not__one__le__zero,axiom,
~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% not_one_le_zero
thf(fact_743_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% linordered_nonzero_semiring_class.zero_le_one
thf(fact_744_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
ord_less_eq_int @ zero_zero_int @ one_one_int ).
% linordered_nonzero_semiring_class.zero_le_one
thf(fact_745_zero__less__one__class_Ozero__le__one,axiom,
ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% zero_less_one_class.zero_le_one
thf(fact_746_zero__less__one__class_Ozero__le__one,axiom,
ord_less_eq_int @ zero_zero_int @ one_one_int ).
% zero_less_one_class.zero_le_one
thf(fact_747_zle__iff__zadd,axiom,
( ord_less_eq_int
= ( ^ [W: int,Z2: int] :
? [N3: nat] :
( Z2
= ( plus_plus_int @ W @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% zle_iff_zadd
thf(fact_748_odd__nonzero,axiom,
! [Z: int] :
( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
!= zero_zero_int ) ).
% odd_nonzero
thf(fact_749_int__ge__induct,axiom,
! [K: int,I: int,P: int > $o] :
( ( ord_less_eq_int @ K @ I )
=> ( ( P @ K )
=> ( ! [I2: int] :
( ( ord_less_eq_int @ K @ I2 )
=> ( ( P @ I2 )
=> ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
=> ( P @ I ) ) ) ) ).
% int_ge_induct
thf(fact_750_int__le__induct,axiom,
! [I: int,K: int,P: int > $o] :
( ( ord_less_eq_int @ I @ K )
=> ( ( P @ K )
=> ( ! [I2: int] :
( ( ord_less_eq_int @ I2 @ K )
=> ( ( P @ I2 )
=> ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
=> ( P @ I ) ) ) ) ).
% int_le_induct
thf(fact_751_of__nat__diff,axiom,
! [N: nat,M: nat] :
( ( ord_less_eq_nat @ N @ M )
=> ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
= ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% of_nat_diff
thf(fact_752_of__nat__diff,axiom,
! [N: nat,M: nat] :
( ( ord_less_eq_nat @ N @ M )
=> ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
= ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% of_nat_diff
thf(fact_753_int__induct,axiom,
! [P: int > $o,K: int,I: int] :
( ( P @ K )
=> ( ! [I2: int] :
( ( ord_less_eq_int @ K @ I2 )
=> ( ( P @ I2 )
=> ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
=> ( ! [I2: int] :
( ( ord_less_eq_int @ I2 @ K )
=> ( ( P @ I2 )
=> ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
=> ( P @ I ) ) ) ) ).
% int_induct
thf(fact_754_iexec__pred_Ocases,axiom,
! [A12: produc5995290525303592096st_int,A23: produc6425607678544837394st_int] :
( ( iexec_pred @ A12 @ A23 )
=> ~ ! [Ins: instr,Cf: produc6425607678544837394st_int] :
( ( A12
= ( produc1484136438817787418st_int @ Ins @ Cf ) )
=> ( A23
!= ( iexec @ Ins @ Cf ) ) ) ) ).
% iexec_pred.cases
thf(fact_755_iexec__pred_Osimps,axiom,
( iexec_pred
= ( ^ [A1: produc5995290525303592096st_int,A22: produc6425607678544837394st_int] :
? [Ins3: instr,Cf5: produc6425607678544837394st_int] :
( ( A1
= ( produc1484136438817787418st_int @ Ins3 @ Cf5 ) )
& ( A22
= ( iexec @ Ins3 @ Cf5 ) ) ) ) ) ).
% iexec_pred.simps
thf(fact_756_iexec__pred_Ointros,axiom,
! [Ins2: instr,Cf3: produc6425607678544837394st_int] : ( iexec_pred @ ( produc1484136438817787418st_int @ Ins2 @ Cf3 ) @ ( iexec @ Ins2 @ Cf3 ) ) ).
% iexec_pred.intros
thf(fact_757_iexec__simp,axiom,
! [Ins2: instr,Cf3: produc6425607678544837394st_int,Cf4: produc6425607678544837394st_int] :
( ( iexec_pred @ ( produc1484136438817787418st_int @ Ins2 @ Cf3 ) @ Cf4 )
= ( Cf4
= ( iexec @ Ins2 @ Cf3 ) ) ) ).
% iexec_simp
thf(fact_758_exec1__appendL,axiom,
! [P: list_instr,I: int,S: list_char > int,Stk: list_int,I4: int,S2: list_char > int,Stk2: list_int,P4: list_instr] :
( ( exec1 @ P @ ( produc5086643055186798020st_int @ I @ ( produc8650753666468850689st_int @ S @ Stk ) ) @ ( produc5086643055186798020st_int @ I4 @ ( produc8650753666468850689st_int @ S2 @ Stk2 ) ) )
=> ( exec1 @ ( append_instr @ P4 @ P ) @ ( produc5086643055186798020st_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P4 ) ) @ I ) @ ( produc8650753666468850689st_int @ S @ Stk ) ) @ ( produc5086643055186798020st_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P4 ) ) @ I4 ) @ ( produc8650753666468850689st_int @ S2 @ Stk2 ) ) ) ) ).
% exec1_appendL
thf(fact_759_exec__appendL,axiom,
! [P: list_instr,I: int,S: list_char > int,Stk: list_int,I4: int,S2: list_char > int,Stk2: list_int,P4: list_instr] :
( ( star_P707599355569300323st_int @ ( exec1 @ P ) @ ( produc5086643055186798020st_int @ I @ ( produc8650753666468850689st_int @ S @ Stk ) ) @ ( produc5086643055186798020st_int @ I4 @ ( produc8650753666468850689st_int @ S2 @ Stk2 ) ) )
=> ( star_P707599355569300323st_int @ ( exec1 @ ( append_instr @ P4 @ P ) ) @ ( produc5086643055186798020st_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P4 ) ) @ I ) @ ( produc8650753666468850689st_int @ S @ Stk ) ) @ ( produc5086643055186798020st_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P4 ) ) @ I4 ) @ ( produc8650753666468850689st_int @ S2 @ Stk2 ) ) ) ) ).
% exec_appendL
thf(fact_760_n__lists__Nil,axiom,
! [N: nat] :
( ( ( N = zero_zero_nat )
=> ( ( n_lists_char @ N @ nil_char )
= ( cons_list_char @ nil_char @ nil_list_char ) ) )
& ( ( N != zero_zero_nat )
=> ( ( n_lists_char @ N @ nil_char )
= nil_list_char ) ) ) ).
% n_lists_Nil
thf(fact_761_n__lists__Nil,axiom,
! [N: nat] :
( ( ( N = zero_zero_nat )
=> ( ( n_list7311978343830957444st_int @ N @ nil_Pr749310521696113548st_int )
= ( cons_l8648290059330449388st_int @ nil_Pr749310521696113548st_int @ nil_li4597314861645524892st_int ) ) )
& ( ( N != zero_zero_nat )
=> ( ( n_list7311978343830957444st_int @ N @ nil_Pr749310521696113548st_int )
= nil_li4597314861645524892st_int ) ) ) ).
% n_lists_Nil
thf(fact_762_n__lists__Nil,axiom,
! [N: nat] :
( ( ( N = zero_zero_nat )
=> ( ( n_lists_instr @ N @ nil_instr )
= ( cons_list_instr @ nil_instr @ nil_list_instr ) ) )
& ( ( N != zero_zero_nat )
=> ( ( n_lists_instr @ N @ nil_instr )
= nil_list_instr ) ) ) ).
% n_lists_Nil
thf(fact_763_n__lists__Nil,axiom,
! [N: nat] :
( ( ( N = zero_zero_nat )
=> ( ( n_lists_list_char @ N @ nil_list_char )
= ( cons_list_list_char @ nil_list_char @ nil_list_list_char ) ) )
& ( ( N != zero_zero_nat )
=> ( ( n_lists_list_char @ N @ nil_list_char )
= nil_list_list_char ) ) ) ).
% n_lists_Nil
thf(fact_764_n__lists__Nil,axiom,
! [N: nat] :
( ( ( N = zero_zero_nat )
=> ( ( n_lists_int @ N @ nil_int )
= ( cons_list_int @ nil_int @ nil_list_int ) ) )
& ( ( N != zero_zero_nat )
=> ( ( n_lists_int @ N @ nil_int )
= nil_list_int ) ) ) ).
% n_lists_Nil
thf(fact_765_LoadIE,axiom,
! [I: int,Pc: int,S: list_char > int,Stk: list_int,Cf3: produc6425607678544837394st_int] :
( ( iexec_pred @ ( produc1484136438817787418st_int @ ( loadi @ I ) @ ( produc5086643055186798020st_int @ Pc @ ( produc8650753666468850689st_int @ S @ Stk ) ) ) @ Cf3 )
=> ( Cf3
= ( produc5086643055186798020st_int @ ( plus_plus_int @ Pc @ one_one_int ) @ ( produc8650753666468850689st_int @ S @ ( cons_int @ I @ Stk ) ) ) ) ) ).
% LoadIE
thf(fact_766_LoadE,axiom,
! [X: list_char,Pc: int,S: list_char > int,Stk: list_int,Cf3: produc6425607678544837394st_int] :
( ( iexec_pred @ ( produc1484136438817787418st_int @ ( load @ X ) @ ( produc5086643055186798020st_int @ Pc @ ( produc8650753666468850689st_int @ S @ Stk ) ) ) @ Cf3 )
=> ( Cf3
= ( produc5086643055186798020st_int @ ( plus_plus_int @ Pc @ one_one_int ) @ ( produc8650753666468850689st_int @ S @ ( cons_int @ ( S @ X ) @ Stk ) ) ) ) ) ).
% LoadE
thf(fact_767_JmpE,axiom,
! [I: int,Pc: int,S: list_char > int,Stk: list_int,Cf3: produc6425607678544837394st_int] :
( ( iexec_pred @ ( produc1484136438817787418st_int @ ( jmp @ I ) @ ( produc5086643055186798020st_int @ Pc @ ( produc8650753666468850689st_int @ S @ Stk ) ) ) @ Cf3 )
=> ( Cf3
= ( produc5086643055186798020st_int @ ( plus_plus_int @ ( plus_plus_int @ Pc @ one_one_int ) @ I ) @ ( produc8650753666468850689st_int @ S @ Stk ) ) ) ) ).
% JmpE
thf(fact_768_n__lists_Osimps_I1_J,axiom,
! [Xs: list_char] :
( ( n_lists_char @ zero_zero_nat @ Xs )
= ( cons_list_char @ nil_char @ nil_list_char ) ) ).
% n_lists.simps(1)
thf(fact_769_n__lists_Osimps_I1_J,axiom,
! [Xs: list_P419547167332244514st_int] :
( ( n_list7311978343830957444st_int @ zero_zero_nat @ Xs )
= ( cons_l8648290059330449388st_int @ nil_Pr749310521696113548st_int @ nil_li4597314861645524892st_int ) ) ).
% n_lists.simps(1)
thf(fact_770_n__lists_Osimps_I1_J,axiom,
! [Xs: list_instr] :
( ( n_lists_instr @ zero_zero_nat @ Xs )
= ( cons_list_instr @ nil_instr @ nil_list_instr ) ) ).
% n_lists.simps(1)
thf(fact_771_n__lists_Osimps_I1_J,axiom,
! [Xs: list_list_char] :
( ( n_lists_list_char @ zero_zero_nat @ Xs )
= ( cons_list_list_char @ nil_list_char @ nil_list_list_char ) ) ).
% n_lists.simps(1)
thf(fact_772_n__lists_Osimps_I1_J,axiom,
! [Xs: list_int] :
( ( n_lists_int @ zero_zero_nat @ Xs )
= ( cons_list_int @ nil_int @ nil_list_int ) ) ).
% n_lists.simps(1)
thf(fact_773_instr_Oinject_I4_J,axiom,
! [X5: int,Y52: int] :
( ( ( jmp @ X5 )
= ( jmp @ Y52 ) )
= ( X5 = Y52 ) ) ).
% instr.inject(4)
thf(fact_774_instr_Oinject_I2_J,axiom,
! [X2: list_char,Y2: list_char] :
( ( ( load @ X2 )
= ( load @ Y2 ) )
= ( X2 = Y2 ) ) ).
% instr.inject(2)
thf(fact_775_instr_Oinject_I1_J,axiom,
! [X1: int,Y1: int] :
( ( ( loadi @ X1 )
= ( loadi @ Y1 ) )
= ( X1 = Y1 ) ) ).
% instr.inject(1)
thf(fact_776_diff__Suc__1,axiom,
! [N: nat] :
( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
= N ) ).
% diff_Suc_1
thf(fact_777_instr_Odistinct_I17_J,axiom,
! [X2: list_char,X5: int] :
( ( load @ X2 )
!= ( jmp @ X5 ) ) ).
% instr.distinct(17)
thf(fact_778_instr_Odistinct_I7_J,axiom,
! [X1: int,X5: int] :
( ( loadi @ X1 )
!= ( jmp @ X5 ) ) ).
% instr.distinct(7)
thf(fact_779_instr_Odistinct_I1_J,axiom,
! [X1: int,X2: list_char] :
( ( loadi @ X1 )
!= ( load @ X2 ) ) ).
% instr.distinct(1)
thf(fact_780_instr_Osize_I12_J,axiom,
! [X5: int] :
( ( size_size_instr @ ( jmp @ X5 ) )
= zero_zero_nat ) ).
% instr.size(12)
thf(fact_781_instr_Osize_I9_J,axiom,
! [X2: list_char] :
( ( size_size_instr @ ( load @ X2 ) )
= zero_zero_nat ) ).
% instr.size(9)
thf(fact_782_instr_Osize_I8_J,axiom,
! [X1: int] :
( ( size_size_instr @ ( loadi @ X1 ) )
= zero_zero_nat ) ).
% instr.size(8)
thf(fact_783_One__nat__def,axiom,
( one_one_nat
= ( suc @ zero_zero_nat ) ) ).
% One_nat_def
thf(fact_784_Suc__eq__plus1__left,axiom,
( suc
= ( plus_plus_nat @ one_one_nat ) ) ).
% Suc_eq_plus1_left
thf(fact_785_plus__1__eq__Suc,axiom,
( ( plus_plus_nat @ one_one_nat )
= suc ) ).
% plus_1_eq_Suc
thf(fact_786_Suc__eq__plus1,axiom,
( suc
= ( ^ [N3: nat] : ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ).
% Suc_eq_plus1
thf(fact_787_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_788_int__ops_I2_J,axiom,
( ( semiri1314217659103216013at_int @ one_one_nat )
= one_one_int ) ).
% int_ops(2)
thf(fact_789_add__eq__if,axiom,
( plus_plus_nat
= ( ^ [M2: nat,N3: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ N3 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% add_eq_if
thf(fact_790_nth__Cons_H,axiom,
! [N: nat,X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int] :
( ( ( N = zero_zero_nat )
=> ( ( nth_Pr8327173284404383691st_int @ ( cons_P4151473878978182108st_int @ X @ Xs ) @ N )
= X ) )
& ( ( N != zero_zero_nat )
=> ( ( nth_Pr8327173284404383691st_int @ ( cons_P4151473878978182108st_int @ X @ Xs ) @ N )
= ( nth_Pr8327173284404383691st_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% nth_Cons'
thf(fact_791_nth__Cons_H,axiom,
! [N: nat,X: instr,Xs: list_instr] :
( ( ( N = zero_zero_nat )
=> ( ( nth_instr @ ( cons_instr @ X @ Xs ) @ N )
= X ) )
& ( ( N != zero_zero_nat )
=> ( ( nth_instr @ ( cons_instr @ X @ Xs ) @ N )
= ( nth_instr @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% nth_Cons'
thf(fact_792_nth__Cons_H,axiom,
! [N: nat,X: int,Xs: list_int] :
( ( ( N = zero_zero_nat )
=> ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
= X ) )
& ( ( N != zero_zero_nat )
=> ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
= ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% nth_Cons'
thf(fact_793_inth_Osimps,axiom,
! [I: int,X: list_char,Xs: list_list_char] :
( ( ( I = zero_zero_int )
=> ( ( inth_list_char @ ( cons_list_char @ X @ Xs ) @ I )
= X ) )
& ( ( I != zero_zero_int )
=> ( ( inth_list_char @ ( cons_list_char @ X @ Xs ) @ I )
= ( inth_list_char @ Xs @ ( minus_minus_int @ I @ one_one_int ) ) ) ) ) ).
% inth.simps
thf(fact_794_inth_Osimps,axiom,
! [I: int,X: m_instr,Xs: list_m_instr] :
( ( ( I = zero_zero_int )
=> ( ( inth_m_instr @ ( cons_m_instr @ X @ Xs ) @ I )
= X ) )
& ( ( I != zero_zero_int )
=> ( ( inth_m_instr @ ( cons_m_instr @ X @ Xs ) @ I )
= ( inth_m_instr @ Xs @ ( minus_minus_int @ I @ one_one_int ) ) ) ) ) ).
% inth.simps
thf(fact_795_inth_Osimps,axiom,
! [I: int,X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int] :
( ( ( I = zero_zero_int )
=> ( ( inth_P8039235741264645271st_int @ ( cons_P4151473878978182108st_int @ X @ Xs ) @ I )
= X ) )
& ( ( I != zero_zero_int )
=> ( ( inth_P8039235741264645271st_int @ ( cons_P4151473878978182108st_int @ X @ Xs ) @ I )
= ( inth_P8039235741264645271st_int @ Xs @ ( minus_minus_int @ I @ one_one_int ) ) ) ) ) ).
% inth.simps
thf(fact_796_inth_Osimps,axiom,
! [I: int,X: instr,Xs: list_instr] :
( ( ( I = zero_zero_int )
=> ( ( inth_instr @ ( cons_instr @ X @ Xs ) @ I )
= X ) )
& ( ( I != zero_zero_int )
=> ( ( inth_instr @ ( cons_instr @ X @ Xs ) @ I )
= ( inth_instr @ Xs @ ( minus_minus_int @ I @ one_one_int ) ) ) ) ) ).
% inth.simps
thf(fact_797_inth_Osimps,axiom,
! [I: int,X: int,Xs: list_int] :
( ( ( I = zero_zero_int )
=> ( ( inth_int @ ( cons_int @ X @ Xs ) @ I )
= X ) )
& ( ( I != zero_zero_int )
=> ( ( inth_int @ ( cons_int @ X @ Xs ) @ I )
= ( inth_int @ Xs @ ( minus_minus_int @ I @ one_one_int ) ) ) ) ) ).
% inth.simps
thf(fact_798_m__exec1__exec1,axiom,
! [P: list_instr,Pc: int,Ms3: int > int,Sp3: nat,Pc2: int,Ms4: int > int,Sp4: nat,Stk: list_int] :
( ( m_exec1 @ ( map_instr_m_instr @ ( to_m_instr @ ( vars @ P ) ) @ P ) @ ( produc8342123264692915235nt_nat @ Pc @ ( produc2630796075472406112nt_nat @ Ms3 @ Sp3 ) ) @ ( produc8342123264692915235nt_nat @ Pc2 @ ( produc2630796075472406112nt_nat @ Ms4 @ Sp4 ) ) )
=> ( exec1 @ P @ ( produc5086643055186798020st_int @ Pc @ ( produc8650753666468850689st_int @ ( to_state @ ( vars @ P ) @ Ms3 ) @ ( append_int @ ( add_stack @ Sp3 @ Ms3 ) @ Stk ) ) ) @ ( produc5086643055186798020st_int @ Pc2 @ ( produc8650753666468850689st_int @ ( to_state @ ( vars @ P ) @ Ms4 ) @ ( append_int @ ( add_stack @ Sp4 @ Ms4 ) @ Stk ) ) ) ) ) ).
% m_exec1_exec1
thf(fact_799_upto__rec2,axiom,
! [I: int,J: int] :
( ( ord_less_eq_int @ I @ J )
=> ( ( upto @ I @ J )
= ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% upto_rec2
thf(fact_800_upto__split3,axiom,
! [I: int,J: int,K: int] :
( ( ord_less_eq_int @ I @ J )
=> ( ( ord_less_eq_int @ J @ K )
=> ( ( upto @ I @ K )
= ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% upto_split3
thf(fact_801_list_Omap__disc__iff,axiom,
! [F: instr > instr,A: list_instr] :
( ( ( map_instr_instr @ F @ A )
= nil_instr )
= ( A = nil_instr ) ) ).
% list.map_disc_iff
thf(fact_802_list_Omap__disc__iff,axiom,
! [F: int > instr,A: list_int] :
( ( ( map_int_instr @ F @ A )
= nil_instr )
= ( A = nil_int ) ) ).
% list.map_disc_iff
thf(fact_803_list_Omap__disc__iff,axiom,
! [F: instr > int,A: list_instr] :
( ( ( map_instr_int @ F @ A )
= nil_int )
= ( A = nil_instr ) ) ).
% list.map_disc_iff
thf(fact_804_list_Omap__disc__iff,axiom,
! [F: int > int,A: list_int] :
( ( ( map_int_int @ F @ A )
= nil_int )
= ( A = nil_int ) ) ).
% list.map_disc_iff
thf(fact_805_list_Omap__disc__iff,axiom,
! [F: instr > m_instr,A: list_instr] :
( ( ( map_instr_m_instr @ F @ A )
= nil_m_instr )
= ( A = nil_instr ) ) ).
% list.map_disc_iff
thf(fact_806_list_Omap__disc__iff,axiom,
! [F: list_char > instr,A: list_list_char] :
( ( ( map_list_char_instr @ F @ A )
= nil_instr )
= ( A = nil_list_char ) ) ).
% list.map_disc_iff
thf(fact_807_list_Omap__disc__iff,axiom,
! [F: instr > list_char,A: list_instr] :
( ( ( map_instr_list_char @ F @ A )
= nil_list_char )
= ( A = nil_instr ) ) ).
% list.map_disc_iff
thf(fact_808_list_Omap__disc__iff,axiom,
! [F: int > list_char,A: list_int] :
( ( ( map_int_list_char @ F @ A )
= nil_list_char )
= ( A = nil_int ) ) ).
% list.map_disc_iff
thf(fact_809_list_Omap__disc__iff,axiom,
! [F: list_char > int,A: list_list_char] :
( ( ( map_list_char_int @ F @ A )
= nil_int )
= ( A = nil_list_char ) ) ).
% list.map_disc_iff
thf(fact_810_list_Omap__disc__iff,axiom,
! [F: list_char > list_char,A: list_list_char] :
( ( ( map_li116305933131242120t_char @ F @ A )
= nil_list_char )
= ( A = nil_list_char ) ) ).
% list.map_disc_iff
thf(fact_811_Nil__is__map__conv,axiom,
! [F: instr > instr,Xs: list_instr] :
( ( nil_instr
= ( map_instr_instr @ F @ Xs ) )
= ( Xs = nil_instr ) ) ).
% Nil_is_map_conv
thf(fact_812_Nil__is__map__conv,axiom,
! [F: int > instr,Xs: list_int] :
( ( nil_instr
= ( map_int_instr @ F @ Xs ) )
= ( Xs = nil_int ) ) ).
% Nil_is_map_conv
thf(fact_813_Nil__is__map__conv,axiom,
! [F: instr > int,Xs: list_instr] :
( ( nil_int
= ( map_instr_int @ F @ Xs ) )
= ( Xs = nil_instr ) ) ).
% Nil_is_map_conv
thf(fact_814_Nil__is__map__conv,axiom,
! [F: int > int,Xs: list_int] :
( ( nil_int
= ( map_int_int @ F @ Xs ) )
= ( Xs = nil_int ) ) ).
% Nil_is_map_conv
thf(fact_815_Nil__is__map__conv,axiom,
! [F: instr > m_instr,Xs: list_instr] :
( ( nil_m_instr
= ( map_instr_m_instr @ F @ Xs ) )
= ( Xs = nil_instr ) ) ).
% Nil_is_map_conv
thf(fact_816_Nil__is__map__conv,axiom,
! [F: list_char > instr,Xs: list_list_char] :
( ( nil_instr
= ( map_list_char_instr @ F @ Xs ) )
= ( Xs = nil_list_char ) ) ).
% Nil_is_map_conv
thf(fact_817_Nil__is__map__conv,axiom,
! [F: instr > list_char,Xs: list_instr] :
( ( nil_list_char
= ( map_instr_list_char @ F @ Xs ) )
= ( Xs = nil_instr ) ) ).
% Nil_is_map_conv
thf(fact_818_Nil__is__map__conv,axiom,
! [F: int > list_char,Xs: list_int] :
( ( nil_list_char
= ( map_int_list_char @ F @ Xs ) )
= ( Xs = nil_int ) ) ).
% Nil_is_map_conv
thf(fact_819_Nil__is__map__conv,axiom,
! [F: list_char > int,Xs: list_list_char] :
( ( nil_int
= ( map_list_char_int @ F @ Xs ) )
= ( Xs = nil_list_char ) ) ).
% Nil_is_map_conv
thf(fact_820_Nil__is__map__conv,axiom,
! [F: list_char > list_char,Xs: list_list_char] :
( ( nil_list_char
= ( map_li116305933131242120t_char @ F @ Xs ) )
= ( Xs = nil_list_char ) ) ).
% Nil_is_map_conv
thf(fact_821_map__is__Nil__conv,axiom,
! [F: instr > instr,Xs: list_instr] :
( ( ( map_instr_instr @ F @ Xs )
= nil_instr )
= ( Xs = nil_instr ) ) ).
% map_is_Nil_conv
thf(fact_822_map__is__Nil__conv,axiom,
! [F: int > instr,Xs: list_int] :
( ( ( map_int_instr @ F @ Xs )
= nil_instr )
= ( Xs = nil_int ) ) ).
% map_is_Nil_conv
thf(fact_823_map__is__Nil__conv,axiom,
! [F: instr > int,Xs: list_instr] :
( ( ( map_instr_int @ F @ Xs )
= nil_int )
= ( Xs = nil_instr ) ) ).
% map_is_Nil_conv
thf(fact_824_map__is__Nil__conv,axiom,
! [F: int > int,Xs: list_int] :
( ( ( map_int_int @ F @ Xs )
= nil_int )
= ( Xs = nil_int ) ) ).
% map_is_Nil_conv
thf(fact_825_map__is__Nil__conv,axiom,
! [F: instr > m_instr,Xs: list_instr] :
( ( ( map_instr_m_instr @ F @ Xs )
= nil_m_instr )
= ( Xs = nil_instr ) ) ).
% map_is_Nil_conv
thf(fact_826_map__is__Nil__conv,axiom,
! [F: list_char > instr,Xs: list_list_char] :
( ( ( map_list_char_instr @ F @ Xs )
= nil_instr )
= ( Xs = nil_list_char ) ) ).
% map_is_Nil_conv
thf(fact_827_map__is__Nil__conv,axiom,
! [F: instr > list_char,Xs: list_instr] :
( ( ( map_instr_list_char @ F @ Xs )
= nil_list_char )
= ( Xs = nil_instr ) ) ).
% map_is_Nil_conv
thf(fact_828_map__is__Nil__conv,axiom,
! [F: int > list_char,Xs: list_int] :
( ( ( map_int_list_char @ F @ Xs )
= nil_list_char )
= ( Xs = nil_int ) ) ).
% map_is_Nil_conv
thf(fact_829_map__is__Nil__conv,axiom,
! [F: list_char > int,Xs: list_list_char] :
( ( ( map_list_char_int @ F @ Xs )
= nil_int )
= ( Xs = nil_list_char ) ) ).
% map_is_Nil_conv
thf(fact_830_map__is__Nil__conv,axiom,
! [F: list_char > list_char,Xs: list_list_char] :
( ( ( map_li116305933131242120t_char @ F @ Xs )
= nil_list_char )
= ( Xs = nil_list_char ) ) ).
% map_is_Nil_conv
thf(fact_831_length__map,axiom,
! [F: m_instr > m_instr,Xs: list_m_instr] :
( ( size_s5914166952900237872_instr @ ( map_m_instr_m_instr @ F @ Xs ) )
= ( size_s5914166952900237872_instr @ Xs ) ) ).
% length_map
thf(fact_832_length__map,axiom,
! [F: instr > m_instr,Xs: list_instr] :
( ( size_s5914166952900237872_instr @ ( map_instr_m_instr @ F @ Xs ) )
= ( size_size_list_instr @ Xs ) ) ).
% length_map
thf(fact_833_length__map,axiom,
! [F: int > m_instr,Xs: list_int] :
( ( size_s5914166952900237872_instr @ ( map_int_m_instr @ F @ Xs ) )
= ( size_size_list_int @ Xs ) ) ).
% length_map
thf(fact_834_length__map,axiom,
! [F: m_instr > instr,Xs: list_m_instr] :
( ( size_size_list_instr @ ( map_m_instr_instr @ F @ Xs ) )
= ( size_s5914166952900237872_instr @ Xs ) ) ).
% length_map
thf(fact_835_length__map,axiom,
! [F: instr > instr,Xs: list_instr] :
( ( size_size_list_instr @ ( map_instr_instr @ F @ Xs ) )
= ( size_size_list_instr @ Xs ) ) ).
% length_map
thf(fact_836_length__map,axiom,
! [F: int > instr,Xs: list_int] :
( ( size_size_list_instr @ ( map_int_instr @ F @ Xs ) )
= ( size_size_list_int @ Xs ) ) ).
% length_map
thf(fact_837_length__map,axiom,
! [F: m_instr > int,Xs: list_m_instr] :
( ( size_size_list_int @ ( map_m_instr_int @ F @ Xs ) )
= ( size_s5914166952900237872_instr @ Xs ) ) ).
% length_map
thf(fact_838_length__map,axiom,
! [F: instr > int,Xs: list_instr] :
( ( size_size_list_int @ ( map_instr_int @ F @ Xs ) )
= ( size_size_list_instr @ Xs ) ) ).
% length_map
thf(fact_839_length__map,axiom,
! [F: int > int,Xs: list_int] :
( ( size_size_list_int @ ( map_int_int @ F @ Xs ) )
= ( size_size_list_int @ Xs ) ) ).
% length_map
thf(fact_840_length__map,axiom,
! [F: list_char > m_instr,Xs: list_list_char] :
( ( size_s5914166952900237872_instr @ ( map_li1986238532096774195_instr @ F @ Xs ) )
= ( size_s356637359517785349t_char @ Xs ) ) ).
% length_map
thf(fact_841_map__append,axiom,
! [F: produc6425607678544837394st_int > produc6425607678544837394st_int,Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( map_Pr8625093460839654122st_int @ F @ ( append5028292981072010935st_int @ Xs @ Ys ) )
= ( append5028292981072010935st_int @ ( map_Pr8625093460839654122st_int @ F @ Xs ) @ ( map_Pr8625093460839654122st_int @ F @ Ys ) ) ) ).
% map_append
thf(fact_842_map__append,axiom,
! [F: produc6425607678544837394st_int > int,Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( map_Pr3224476576807795204nt_int @ F @ ( append5028292981072010935st_int @ Xs @ Ys ) )
= ( append_int @ ( map_Pr3224476576807795204nt_int @ F @ Xs ) @ ( map_Pr3224476576807795204nt_int @ F @ Ys ) ) ) ).
% map_append
thf(fact_843_map__append,axiom,
! [F: produc6425607678544837394st_int > instr,Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( map_Pr7514435936640407687_instr @ F @ ( append5028292981072010935st_int @ Xs @ Ys ) )
= ( append_instr @ ( map_Pr7514435936640407687_instr @ F @ Xs ) @ ( map_Pr7514435936640407687_instr @ F @ Ys ) ) ) ).
% map_append
thf(fact_844_map__append,axiom,
! [F: int > produc6425607678544837394st_int,Xs: list_int,Ys: list_int] :
( ( map_in8512336359594627332st_int @ F @ ( append_int @ Xs @ Ys ) )
= ( append5028292981072010935st_int @ ( map_in8512336359594627332st_int @ F @ Xs ) @ ( map_in8512336359594627332st_int @ F @ Ys ) ) ) ).
% map_append
thf(fact_845_map__append,axiom,
! [F: int > int,Xs: list_int,Ys: list_int] :
( ( map_int_int @ F @ ( append_int @ Xs @ Ys ) )
= ( append_int @ ( map_int_int @ F @ Xs ) @ ( map_int_int @ F @ Ys ) ) ) ).
% map_append
thf(fact_846_map__append,axiom,
! [F: int > instr,Xs: list_int,Ys: list_int] :
( ( map_int_instr @ F @ ( append_int @ Xs @ Ys ) )
= ( append_instr @ ( map_int_instr @ F @ Xs ) @ ( map_int_instr @ F @ Ys ) ) ) ).
% map_append
thf(fact_847_map__append,axiom,
! [F: instr > produc6425607678544837394st_int,Xs: list_instr,Ys: list_instr] :
( ( map_in7259965606695656109st_int @ F @ ( append_instr @ Xs @ Ys ) )
= ( append5028292981072010935st_int @ ( map_in7259965606695656109st_int @ F @ Xs ) @ ( map_in7259965606695656109st_int @ F @ Ys ) ) ) ).
% map_append
thf(fact_848_map__append,axiom,
! [F: instr > int,Xs: list_instr,Ys: list_instr] :
( ( map_instr_int @ F @ ( append_instr @ Xs @ Ys ) )
= ( append_int @ ( map_instr_int @ F @ Xs ) @ ( map_instr_int @ F @ Ys ) ) ) ).
% map_append
thf(fact_849_map__append,axiom,
! [F: instr > instr,Xs: list_instr,Ys: list_instr] :
( ( map_instr_instr @ F @ ( append_instr @ Xs @ Ys ) )
= ( append_instr @ ( map_instr_instr @ F @ Xs ) @ ( map_instr_instr @ F @ Ys ) ) ) ).
% map_append
thf(fact_850_map__append,axiom,
! [F: instr > m_instr,Xs: list_instr,Ys: list_instr] :
( ( map_instr_m_instr @ F @ ( append_instr @ Xs @ Ys ) )
= ( append_m_instr @ ( map_instr_m_instr @ F @ Xs ) @ ( map_instr_m_instr @ F @ Ys ) ) ) ).
% map_append
thf(fact_851_upto__single,axiom,
! [I: int] :
( ( upto @ I @ I )
= ( cons_int @ I @ nil_int ) ) ).
% upto_single
thf(fact_852_nth__upto,axiom,
! [I: int,K: nat,J: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
=> ( ( nth_int @ ( upto @ I @ J ) @ K )
= ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% nth_upto
thf(fact_853_map__eq__Cons__conv,axiom,
! [F: instr > m_instr,Xs: list_instr,Y: m_instr,Ys: list_m_instr] :
( ( ( map_instr_m_instr @ F @ Xs )
= ( cons_m_instr @ Y @ Ys ) )
= ( ? [Z2: instr,Zs3: list_instr] :
( ( Xs
= ( cons_instr @ Z2 @ Zs3 ) )
& ( ( F @ Z2 )
= Y )
& ( ( map_instr_m_instr @ F @ Zs3 )
= Ys ) ) ) ) ).
% map_eq_Cons_conv
thf(fact_854_map__eq__Cons__conv,axiom,
! [F: produc6425607678544837394st_int > produc6425607678544837394st_int,Xs: list_P419547167332244514st_int,Y: produc6425607678544837394st_int,Ys: list_P419547167332244514st_int] :
( ( ( map_Pr8625093460839654122st_int @ F @ Xs )
= ( cons_P4151473878978182108st_int @ Y @ Ys ) )
= ( ? [Z2: produc6425607678544837394st_int,Zs3: list_P419547167332244514st_int] :
( ( Xs
= ( cons_P4151473878978182108st_int @ Z2 @ Zs3 ) )
& ( ( F @ Z2 )
= Y )
& ( ( map_Pr8625093460839654122st_int @ F @ Zs3 )
= Ys ) ) ) ) ).
% map_eq_Cons_conv
thf(fact_855_map__eq__Cons__conv,axiom,
! [F: instr > produc6425607678544837394st_int,Xs: list_instr,Y: produc6425607678544837394st_int,Ys: list_P419547167332244514st_int] :
( ( ( map_in7259965606695656109st_int @ F @ Xs )
= ( cons_P4151473878978182108st_int @ Y @ Ys ) )
= ( ? [Z2: instr,Zs3: list_instr] :
( ( Xs
= ( cons_instr @ Z2 @ Zs3 ) )
& ( ( F @ Z2 )
= Y )
& ( ( map_in7259965606695656109st_int @ F @ Zs3 )
= Ys ) ) ) ) ).
% map_eq_Cons_conv
thf(fact_856_map__eq__Cons__conv,axiom,
! [F: int > produc6425607678544837394st_int,Xs: list_int,Y: produc6425607678544837394st_int,Ys: list_P419547167332244514st_int] :
( ( ( map_in8512336359594627332st_int @ F @ Xs )
= ( cons_P4151473878978182108st_int @ Y @ Ys ) )
= ( ? [Z2: int,Zs3: list_int] :
( ( Xs
= ( cons_int @ Z2 @ Zs3 ) )
& ( ( F @ Z2 )
= Y )
& ( ( map_in8512336359594627332st_int @ F @ Zs3 )
= Ys ) ) ) ) ).
% map_eq_Cons_conv
thf(fact_857_map__eq__Cons__conv,axiom,
! [F: produc6425607678544837394st_int > instr,Xs: list_P419547167332244514st_int,Y: instr,Ys: list_instr] :
( ( ( map_Pr7514435936640407687_instr @ F @ Xs )
= ( cons_instr @ Y @ Ys ) )
= ( ? [Z2: produc6425607678544837394st_int,Zs3: list_P419547167332244514st_int] :
( ( Xs
= ( cons_P4151473878978182108st_int @ Z2 @ Zs3 ) )
& ( ( F @ Z2 )
= Y )
& ( ( map_Pr7514435936640407687_instr @ F @ Zs3 )
= Ys ) ) ) ) ).
% map_eq_Cons_conv
thf(fact_858_map__eq__Cons__conv,axiom,
! [F: instr > instr,Xs: list_instr,Y: instr,Ys: list_instr] :
( ( ( map_instr_instr @ F @ Xs )
= ( cons_instr @ Y @ Ys ) )
= ( ? [Z2: instr,Zs3: list_instr] :
( ( Xs
= ( cons_instr @ Z2 @ Zs3 ) )
& ( ( F @ Z2 )
= Y )
& ( ( map_instr_instr @ F @ Zs3 )
= Ys ) ) ) ) ).
% map_eq_Cons_conv
thf(fact_859_map__eq__Cons__conv,axiom,
! [F: int > instr,Xs: list_int,Y: instr,Ys: list_instr] :
( ( ( map_int_instr @ F @ Xs )
= ( cons_instr @ Y @ Ys ) )
= ( ? [Z2: int,Zs3: list_int] :
( ( Xs
= ( cons_int @ Z2 @ Zs3 ) )
& ( ( F @ Z2 )
= Y )
& ( ( map_int_instr @ F @ Zs3 )
= Ys ) ) ) ) ).
% map_eq_Cons_conv
thf(fact_860_map__eq__Cons__conv,axiom,
! [F: produc6425607678544837394st_int > int,Xs: list_P419547167332244514st_int,Y: int,Ys: list_int] :
( ( ( map_Pr3224476576807795204nt_int @ F @ Xs )
= ( cons_int @ Y @ Ys ) )
= ( ? [Z2: produc6425607678544837394st_int,Zs3: list_P419547167332244514st_int] :
( ( Xs
= ( cons_P4151473878978182108st_int @ Z2 @ Zs3 ) )
& ( ( F @ Z2 )
= Y )
& ( ( map_Pr3224476576807795204nt_int @ F @ Zs3 )
= Ys ) ) ) ) ).
% map_eq_Cons_conv
thf(fact_861_map__eq__Cons__conv,axiom,
! [F: instr > int,Xs: list_instr,Y: int,Ys: list_int] :
( ( ( map_instr_int @ F @ Xs )
= ( cons_int @ Y @ Ys ) )
= ( ? [Z2: instr,Zs3: list_instr] :
( ( Xs
= ( cons_instr @ Z2 @ Zs3 ) )
& ( ( F @ Z2 )
= Y )
& ( ( map_instr_int @ F @ Zs3 )
= Ys ) ) ) ) ).
% map_eq_Cons_conv
thf(fact_862_map__eq__Cons__conv,axiom,
! [F: int > int,Xs: list_int,Y: int,Ys: list_int] :
( ( ( map_int_int @ F @ Xs )
= ( cons_int @ Y @ Ys ) )
= ( ? [Z2: int,Zs3: list_int] :
( ( Xs
= ( cons_int @ Z2 @ Zs3 ) )
& ( ( F @ Z2 )
= Y )
& ( ( map_int_int @ F @ Zs3 )
= Ys ) ) ) ) ).
% map_eq_Cons_conv
thf(fact_863_Cons__eq__map__conv,axiom,
! [X: m_instr,Xs: list_m_instr,F: instr > m_instr,Ys: list_instr] :
( ( ( cons_m_instr @ X @ Xs )
= ( map_instr_m_instr @ F @ Ys ) )
= ( ? [Z2: instr,Zs3: list_instr] :
( ( Ys
= ( cons_instr @ Z2 @ Zs3 ) )
& ( X
= ( F @ Z2 ) )
& ( Xs
= ( map_instr_m_instr @ F @ Zs3 ) ) ) ) ) ).
% Cons_eq_map_conv
thf(fact_864_Cons__eq__map__conv,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int,F: produc6425607678544837394st_int > produc6425607678544837394st_int,Ys: list_P419547167332244514st_int] :
( ( ( cons_P4151473878978182108st_int @ X @ Xs )
= ( map_Pr8625093460839654122st_int @ F @ Ys ) )
= ( ? [Z2: produc6425607678544837394st_int,Zs3: list_P419547167332244514st_int] :
( ( Ys
= ( cons_P4151473878978182108st_int @ Z2 @ Zs3 ) )
& ( X
= ( F @ Z2 ) )
& ( Xs
= ( map_Pr8625093460839654122st_int @ F @ Zs3 ) ) ) ) ) ).
% Cons_eq_map_conv
thf(fact_865_Cons__eq__map__conv,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int,F: instr > produc6425607678544837394st_int,Ys: list_instr] :
( ( ( cons_P4151473878978182108st_int @ X @ Xs )
= ( map_in7259965606695656109st_int @ F @ Ys ) )
= ( ? [Z2: instr,Zs3: list_instr] :
( ( Ys
= ( cons_instr @ Z2 @ Zs3 ) )
& ( X
= ( F @ Z2 ) )
& ( Xs
= ( map_in7259965606695656109st_int @ F @ Zs3 ) ) ) ) ) ).
% Cons_eq_map_conv
thf(fact_866_Cons__eq__map__conv,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int,F: int > produc6425607678544837394st_int,Ys: list_int] :
( ( ( cons_P4151473878978182108st_int @ X @ Xs )
= ( map_in8512336359594627332st_int @ F @ Ys ) )
= ( ? [Z2: int,Zs3: list_int] :
( ( Ys
= ( cons_int @ Z2 @ Zs3 ) )
& ( X
= ( F @ Z2 ) )
& ( Xs
= ( map_in8512336359594627332st_int @ F @ Zs3 ) ) ) ) ) ).
% Cons_eq_map_conv
thf(fact_867_Cons__eq__map__conv,axiom,
! [X: instr,Xs: list_instr,F: produc6425607678544837394st_int > instr,Ys: list_P419547167332244514st_int] :
( ( ( cons_instr @ X @ Xs )
= ( map_Pr7514435936640407687_instr @ F @ Ys ) )
= ( ? [Z2: produc6425607678544837394st_int,Zs3: list_P419547167332244514st_int] :
( ( Ys
= ( cons_P4151473878978182108st_int @ Z2 @ Zs3 ) )
& ( X
= ( F @ Z2 ) )
& ( Xs
= ( map_Pr7514435936640407687_instr @ F @ Zs3 ) ) ) ) ) ).
% Cons_eq_map_conv
thf(fact_868_Cons__eq__map__conv,axiom,
! [X: instr,Xs: list_instr,F: instr > instr,Ys: list_instr] :
( ( ( cons_instr @ X @ Xs )
= ( map_instr_instr @ F @ Ys ) )
= ( ? [Z2: instr,Zs3: list_instr] :
( ( Ys
= ( cons_instr @ Z2 @ Zs3 ) )
& ( X
= ( F @ Z2 ) )
& ( Xs
= ( map_instr_instr @ F @ Zs3 ) ) ) ) ) ).
% Cons_eq_map_conv
thf(fact_869_Cons__eq__map__conv,axiom,
! [X: instr,Xs: list_instr,F: int > instr,Ys: list_int] :
( ( ( cons_instr @ X @ Xs )
= ( map_int_instr @ F @ Ys ) )
= ( ? [Z2: int,Zs3: list_int] :
( ( Ys
= ( cons_int @ Z2 @ Zs3 ) )
& ( X
= ( F @ Z2 ) )
& ( Xs
= ( map_int_instr @ F @ Zs3 ) ) ) ) ) ).
% Cons_eq_map_conv
thf(fact_870_Cons__eq__map__conv,axiom,
! [X: int,Xs: list_int,F: produc6425607678544837394st_int > int,Ys: list_P419547167332244514st_int] :
( ( ( cons_int @ X @ Xs )
= ( map_Pr3224476576807795204nt_int @ F @ Ys ) )
= ( ? [Z2: produc6425607678544837394st_int,Zs3: list_P419547167332244514st_int] :
( ( Ys
= ( cons_P4151473878978182108st_int @ Z2 @ Zs3 ) )
& ( X
= ( F @ Z2 ) )
& ( Xs
= ( map_Pr3224476576807795204nt_int @ F @ Zs3 ) ) ) ) ) ).
% Cons_eq_map_conv
thf(fact_871_Cons__eq__map__conv,axiom,
! [X: int,Xs: list_int,F: instr > int,Ys: list_instr] :
( ( ( cons_int @ X @ Xs )
= ( map_instr_int @ F @ Ys ) )
= ( ? [Z2: instr,Zs3: list_instr] :
( ( Ys
= ( cons_instr @ Z2 @ Zs3 ) )
& ( X
= ( F @ Z2 ) )
& ( Xs
= ( map_instr_int @ F @ Zs3 ) ) ) ) ) ).
% Cons_eq_map_conv
thf(fact_872_Cons__eq__map__conv,axiom,
! [X: int,Xs: list_int,F: int > int,Ys: list_int] :
( ( ( cons_int @ X @ Xs )
= ( map_int_int @ F @ Ys ) )
= ( ? [Z2: int,Zs3: list_int] :
( ( Ys
= ( cons_int @ Z2 @ Zs3 ) )
& ( X
= ( F @ Z2 ) )
& ( Xs
= ( map_int_int @ F @ Zs3 ) ) ) ) ) ).
% Cons_eq_map_conv
thf(fact_873_map__eq__Cons__D,axiom,
! [F: instr > m_instr,Xs: list_instr,Y: m_instr,Ys: list_m_instr] :
( ( ( map_instr_m_instr @ F @ Xs )
= ( cons_m_instr @ Y @ Ys ) )
=> ? [Z4: instr,Zs2: list_instr] :
( ( Xs
= ( cons_instr @ Z4 @ Zs2 ) )
& ( ( F @ Z4 )
= Y )
& ( ( map_instr_m_instr @ F @ Zs2 )
= Ys ) ) ) ).
% map_eq_Cons_D
thf(fact_874_map__eq__Cons__D,axiom,
! [F: produc6425607678544837394st_int > produc6425607678544837394st_int,Xs: list_P419547167332244514st_int,Y: produc6425607678544837394st_int,Ys: list_P419547167332244514st_int] :
( ( ( map_Pr8625093460839654122st_int @ F @ Xs )
= ( cons_P4151473878978182108st_int @ Y @ Ys ) )
=> ? [Z4: produc6425607678544837394st_int,Zs2: list_P419547167332244514st_int] :
( ( Xs
= ( cons_P4151473878978182108st_int @ Z4 @ Zs2 ) )
& ( ( F @ Z4 )
= Y )
& ( ( map_Pr8625093460839654122st_int @ F @ Zs2 )
= Ys ) ) ) ).
% map_eq_Cons_D
thf(fact_875_map__eq__Cons__D,axiom,
! [F: instr > produc6425607678544837394st_int,Xs: list_instr,Y: produc6425607678544837394st_int,Ys: list_P419547167332244514st_int] :
( ( ( map_in7259965606695656109st_int @ F @ Xs )
= ( cons_P4151473878978182108st_int @ Y @ Ys ) )
=> ? [Z4: instr,Zs2: list_instr] :
( ( Xs
= ( cons_instr @ Z4 @ Zs2 ) )
& ( ( F @ Z4 )
= Y )
& ( ( map_in7259965606695656109st_int @ F @ Zs2 )
= Ys ) ) ) ).
% map_eq_Cons_D
thf(fact_876_map__eq__Cons__D,axiom,
! [F: int > produc6425607678544837394st_int,Xs: list_int,Y: produc6425607678544837394st_int,Ys: list_P419547167332244514st_int] :
( ( ( map_in8512336359594627332st_int @ F @ Xs )
= ( cons_P4151473878978182108st_int @ Y @ Ys ) )
=> ? [Z4: int,Zs2: list_int] :
( ( Xs
= ( cons_int @ Z4 @ Zs2 ) )
& ( ( F @ Z4 )
= Y )
& ( ( map_in8512336359594627332st_int @ F @ Zs2 )
= Ys ) ) ) ).
% map_eq_Cons_D
thf(fact_877_map__eq__Cons__D,axiom,
! [F: produc6425607678544837394st_int > instr,Xs: list_P419547167332244514st_int,Y: instr,Ys: list_instr] :
( ( ( map_Pr7514435936640407687_instr @ F @ Xs )
= ( cons_instr @ Y @ Ys ) )
=> ? [Z4: produc6425607678544837394st_int,Zs2: list_P419547167332244514st_int] :
( ( Xs
= ( cons_P4151473878978182108st_int @ Z4 @ Zs2 ) )
& ( ( F @ Z4 )
= Y )
& ( ( map_Pr7514435936640407687_instr @ F @ Zs2 )
= Ys ) ) ) ).
% map_eq_Cons_D
thf(fact_878_map__eq__Cons__D,axiom,
! [F: instr > instr,Xs: list_instr,Y: instr,Ys: list_instr] :
( ( ( map_instr_instr @ F @ Xs )
= ( cons_instr @ Y @ Ys ) )
=> ? [Z4: instr,Zs2: list_instr] :
( ( Xs
= ( cons_instr @ Z4 @ Zs2 ) )
& ( ( F @ Z4 )
= Y )
& ( ( map_instr_instr @ F @ Zs2 )
= Ys ) ) ) ).
% map_eq_Cons_D
thf(fact_879_map__eq__Cons__D,axiom,
! [F: int > instr,Xs: list_int,Y: instr,Ys: list_instr] :
( ( ( map_int_instr @ F @ Xs )
= ( cons_instr @ Y @ Ys ) )
=> ? [Z4: int,Zs2: list_int] :
( ( Xs
= ( cons_int @ Z4 @ Zs2 ) )
& ( ( F @ Z4 )
= Y )
& ( ( map_int_instr @ F @ Zs2 )
= Ys ) ) ) ).
% map_eq_Cons_D
thf(fact_880_map__eq__Cons__D,axiom,
! [F: produc6425607678544837394st_int > int,Xs: list_P419547167332244514st_int,Y: int,Ys: list_int] :
( ( ( map_Pr3224476576807795204nt_int @ F @ Xs )
= ( cons_int @ Y @ Ys ) )
=> ? [Z4: produc6425607678544837394st_int,Zs2: list_P419547167332244514st_int] :
( ( Xs
= ( cons_P4151473878978182108st_int @ Z4 @ Zs2 ) )
& ( ( F @ Z4 )
= Y )
& ( ( map_Pr3224476576807795204nt_int @ F @ Zs2 )
= Ys ) ) ) ).
% map_eq_Cons_D
thf(fact_881_map__eq__Cons__D,axiom,
! [F: instr > int,Xs: list_instr,Y: int,Ys: list_int] :
( ( ( map_instr_int @ F @ Xs )
= ( cons_int @ Y @ Ys ) )
=> ? [Z4: instr,Zs2: list_instr] :
( ( Xs
= ( cons_instr @ Z4 @ Zs2 ) )
& ( ( F @ Z4 )
= Y )
& ( ( map_instr_int @ F @ Zs2 )
= Ys ) ) ) ).
% map_eq_Cons_D
thf(fact_882_map__eq__Cons__D,axiom,
! [F: int > int,Xs: list_int,Y: int,Ys: list_int] :
( ( ( map_int_int @ F @ Xs )
= ( cons_int @ Y @ Ys ) )
=> ? [Z4: int,Zs2: list_int] :
( ( Xs
= ( cons_int @ Z4 @ Zs2 ) )
& ( ( F @ Z4 )
= Y )
& ( ( map_int_int @ F @ Zs2 )
= Ys ) ) ) ).
% map_eq_Cons_D
thf(fact_883_Cons__eq__map__D,axiom,
! [X: m_instr,Xs: list_m_instr,F: instr > m_instr,Ys: list_instr] :
( ( ( cons_m_instr @ X @ Xs )
= ( map_instr_m_instr @ F @ Ys ) )
=> ? [Z4: instr,Zs2: list_instr] :
( ( Ys
= ( cons_instr @ Z4 @ Zs2 ) )
& ( X
= ( F @ Z4 ) )
& ( Xs
= ( map_instr_m_instr @ F @ Zs2 ) ) ) ) ).
% Cons_eq_map_D
thf(fact_884_Cons__eq__map__D,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int,F: produc6425607678544837394st_int > produc6425607678544837394st_int,Ys: list_P419547167332244514st_int] :
( ( ( cons_P4151473878978182108st_int @ X @ Xs )
= ( map_Pr8625093460839654122st_int @ F @ Ys ) )
=> ? [Z4: produc6425607678544837394st_int,Zs2: list_P419547167332244514st_int] :
( ( Ys
= ( cons_P4151473878978182108st_int @ Z4 @ Zs2 ) )
& ( X
= ( F @ Z4 ) )
& ( Xs
= ( map_Pr8625093460839654122st_int @ F @ Zs2 ) ) ) ) ).
% Cons_eq_map_D
thf(fact_885_Cons__eq__map__D,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int,F: instr > produc6425607678544837394st_int,Ys: list_instr] :
( ( ( cons_P4151473878978182108st_int @ X @ Xs )
= ( map_in7259965606695656109st_int @ F @ Ys ) )
=> ? [Z4: instr,Zs2: list_instr] :
( ( Ys
= ( cons_instr @ Z4 @ Zs2 ) )
& ( X
= ( F @ Z4 ) )
& ( Xs
= ( map_in7259965606695656109st_int @ F @ Zs2 ) ) ) ) ).
% Cons_eq_map_D
thf(fact_886_Cons__eq__map__D,axiom,
! [X: produc6425607678544837394st_int,Xs: list_P419547167332244514st_int,F: int > produc6425607678544837394st_int,Ys: list_int] :
( ( ( cons_P4151473878978182108st_int @ X @ Xs )
= ( map_in8512336359594627332st_int @ F @ Ys ) )
=> ? [Z4: int,Zs2: list_int] :
( ( Ys
= ( cons_int @ Z4 @ Zs2 ) )
& ( X
= ( F @ Z4 ) )
& ( Xs
= ( map_in8512336359594627332st_int @ F @ Zs2 ) ) ) ) ).
% Cons_eq_map_D
thf(fact_887_Cons__eq__map__D,axiom,
! [X: instr,Xs: list_instr,F: produc6425607678544837394st_int > instr,Ys: list_P419547167332244514st_int] :
( ( ( cons_instr @ X @ Xs )
= ( map_Pr7514435936640407687_instr @ F @ Ys ) )
=> ? [Z4: produc6425607678544837394st_int,Zs2: list_P419547167332244514st_int] :
( ( Ys
= ( cons_P4151473878978182108st_int @ Z4 @ Zs2 ) )
& ( X
= ( F @ Z4 ) )
& ( Xs
= ( map_Pr7514435936640407687_instr @ F @ Zs2 ) ) ) ) ).
% Cons_eq_map_D
thf(fact_888_Cons__eq__map__D,axiom,
! [X: instr,Xs: list_instr,F: instr > instr,Ys: list_instr] :
( ( ( cons_instr @ X @ Xs )
= ( map_instr_instr @ F @ Ys ) )
=> ? [Z4: instr,Zs2: list_instr] :
( ( Ys
= ( cons_instr @ Z4 @ Zs2 ) )
& ( X
= ( F @ Z4 ) )
& ( Xs
= ( map_instr_instr @ F @ Zs2 ) ) ) ) ).
% Cons_eq_map_D
thf(fact_889_Cons__eq__map__D,axiom,
! [X: instr,Xs: list_instr,F: int > instr,Ys: list_int] :
( ( ( cons_instr @ X @ Xs )
= ( map_int_instr @ F @ Ys ) )
=> ? [Z4: int,Zs2: list_int] :
( ( Ys
= ( cons_int @ Z4 @ Zs2 ) )
& ( X
= ( F @ Z4 ) )
& ( Xs
= ( map_int_instr @ F @ Zs2 ) ) ) ) ).
% Cons_eq_map_D
thf(fact_890_Cons__eq__map__D,axiom,
! [X: int,Xs: list_int,F: produc6425607678544837394st_int > int,Ys: list_P419547167332244514st_int] :
( ( ( cons_int @ X @ Xs )
= ( map_Pr3224476576807795204nt_int @ F @ Ys ) )
=> ? [Z4: produc6425607678544837394st_int,Zs2: list_P419547167332244514st_int] :
( ( Ys
= ( cons_P4151473878978182108st_int @ Z4 @ Zs2 ) )
& ( X
= ( F @ Z4 ) )
& ( Xs
= ( map_Pr3224476576807795204nt_int @ F @ Zs2 ) ) ) ) ).
% Cons_eq_map_D
thf(fact_891_Cons__eq__map__D,axiom,
! [X: int,Xs: list_int,F: instr > int,Ys: list_instr] :
( ( ( cons_int @ X @ Xs )
= ( map_instr_int @ F @ Ys ) )
=> ? [Z4: instr,Zs2: list_instr] :
( ( Ys
= ( cons_instr @ Z4 @ Zs2 ) )
& ( X
= ( F @ Z4 ) )
& ( Xs
= ( map_instr_int @ F @ Zs2 ) ) ) ) ).
% Cons_eq_map_D
thf(fact_892_Cons__eq__map__D,axiom,
! [X: int,Xs: list_int,F: int > int,Ys: list_int] :
( ( ( cons_int @ X @ Xs )
= ( map_int_int @ F @ Ys ) )
=> ? [Z4: int,Zs2: list_int] :
( ( Ys
= ( cons_int @ Z4 @ Zs2 ) )
& ( X
= ( F @ Z4 ) )
& ( Xs
= ( map_int_int @ F @ Zs2 ) ) ) ) ).
% Cons_eq_map_D
thf(fact_893_list_Osimps_I9_J,axiom,
! [F: produc6425607678544837394st_int > produc6425607678544837394st_int,X21: produc6425607678544837394st_int,X22: list_P419547167332244514st_int] :
( ( map_Pr8625093460839654122st_int @ F @ ( cons_P4151473878978182108st_int @ X21 @ X22 ) )
= ( cons_P4151473878978182108st_int @ ( F @ X21 ) @ ( map_Pr8625093460839654122st_int @ F @ X22 ) ) ) ).
% list.simps(9)
thf(fact_894_list_Osimps_I9_J,axiom,
! [F: produc6425607678544837394st_int > instr,X21: produc6425607678544837394st_int,X22: list_P419547167332244514st_int] :
( ( map_Pr7514435936640407687_instr @ F @ ( cons_P4151473878978182108st_int @ X21 @ X22 ) )
= ( cons_instr @ ( F @ X21 ) @ ( map_Pr7514435936640407687_instr @ F @ X22 ) ) ) ).
% list.simps(9)
thf(fact_895_list_Osimps_I9_J,axiom,
! [F: produc6425607678544837394st_int > int,X21: produc6425607678544837394st_int,X22: list_P419547167332244514st_int] :
( ( map_Pr3224476576807795204nt_int @ F @ ( cons_P4151473878978182108st_int @ X21 @ X22 ) )
= ( cons_int @ ( F @ X21 ) @ ( map_Pr3224476576807795204nt_int @ F @ X22 ) ) ) ).
% list.simps(9)
thf(fact_896_list_Osimps_I9_J,axiom,
! [F: instr > m_instr,X21: instr,X22: list_instr] :
( ( map_instr_m_instr @ F @ ( cons_instr @ X21 @ X22 ) )
= ( cons_m_instr @ ( F @ X21 ) @ ( map_instr_m_instr @ F @ X22 ) ) ) ).
% list.simps(9)
thf(fact_897_list_Osimps_I9_J,axiom,
! [F: instr > produc6425607678544837394st_int,X21: instr,X22: list_instr] :
( ( map_in7259965606695656109st_int @ F @ ( cons_instr @ X21 @ X22 ) )
= ( cons_P4151473878978182108st_int @ ( F @ X21 ) @ ( map_in7259965606695656109st_int @ F @ X22 ) ) ) ).
% list.simps(9)
thf(fact_898_list_Osimps_I9_J,axiom,
! [F: instr > instr,X21: instr,X22: list_instr] :
( ( map_instr_instr @ F @ ( cons_instr @ X21 @ X22 ) )
= ( cons_instr @ ( F @ X21 ) @ ( map_instr_instr @ F @ X22 ) ) ) ).
% list.simps(9)
thf(fact_899_list_Osimps_I9_J,axiom,
! [F: instr > int,X21: instr,X22: list_instr] :
( ( map_instr_int @ F @ ( cons_instr @ X21 @ X22 ) )
= ( cons_int @ ( F @ X21 ) @ ( map_instr_int @ F @ X22 ) ) ) ).
% list.simps(9)
thf(fact_900_list_Osimps_I9_J,axiom,
! [F: int > produc6425607678544837394st_int,X21: int,X22: list_int] :
( ( map_in8512336359594627332st_int @ F @ ( cons_int @ X21 @ X22 ) )
= ( cons_P4151473878978182108st_int @ ( F @ X21 ) @ ( map_in8512336359594627332st_int @ F @ X22 ) ) ) ).
% list.simps(9)
thf(fact_901_list_Osimps_I9_J,axiom,
! [F: int > instr,X21: int,X22: list_int] :
( ( map_int_instr @ F @ ( cons_int @ X21 @ X22 ) )
= ( cons_instr @ ( F @ X21 ) @ ( map_int_instr @ F @ X22 ) ) ) ).
% list.simps(9)
thf(fact_902_list_Osimps_I9_J,axiom,
! [F: int > int,X21: int,X22: list_int] :
( ( map_int_int @ F @ ( cons_int @ X21 @ X22 ) )
= ( cons_int @ ( F @ X21 ) @ ( map_int_int @ F @ X22 ) ) ) ).
% list.simps(9)
thf(fact_903_append__eq__map__conv,axiom,
! [Ys: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int,F: produc6425607678544837394st_int > produc6425607678544837394st_int,Xs: list_P419547167332244514st_int] :
( ( ( append5028292981072010935st_int @ Ys @ Zs )
= ( map_Pr8625093460839654122st_int @ F @ Xs ) )
= ( ? [Us2: list_P419547167332244514st_int,Vs2: list_P419547167332244514st_int] :
( ( Xs
= ( append5028292981072010935st_int @ Us2 @ Vs2 ) )
& ( Ys
= ( map_Pr8625093460839654122st_int @ F @ Us2 ) )
& ( Zs
= ( map_Pr8625093460839654122st_int @ F @ Vs2 ) ) ) ) ) ).
% append_eq_map_conv
thf(fact_904_append__eq__map__conv,axiom,
! [Ys: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int,F: int > produc6425607678544837394st_int,Xs: list_int] :
( ( ( append5028292981072010935st_int @ Ys @ Zs )
= ( map_in8512336359594627332st_int @ F @ Xs ) )
= ( ? [Us2: list_int,Vs2: list_int] :
( ( Xs
= ( append_int @ Us2 @ Vs2 ) )
& ( Ys
= ( map_in8512336359594627332st_int @ F @ Us2 ) )
& ( Zs
= ( map_in8512336359594627332st_int @ F @ Vs2 ) ) ) ) ) ).
% append_eq_map_conv
thf(fact_905_append__eq__map__conv,axiom,
! [Ys: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int,F: instr > produc6425607678544837394st_int,Xs: list_instr] :
( ( ( append5028292981072010935st_int @ Ys @ Zs )
= ( map_in7259965606695656109st_int @ F @ Xs ) )
= ( ? [Us2: list_instr,Vs2: list_instr] :
( ( Xs
= ( append_instr @ Us2 @ Vs2 ) )
& ( Ys
= ( map_in7259965606695656109st_int @ F @ Us2 ) )
& ( Zs
= ( map_in7259965606695656109st_int @ F @ Vs2 ) ) ) ) ) ).
% append_eq_map_conv
thf(fact_906_append__eq__map__conv,axiom,
! [Ys: list_int,Zs: list_int,F: produc6425607678544837394st_int > int,Xs: list_P419547167332244514st_int] :
( ( ( append_int @ Ys @ Zs )
= ( map_Pr3224476576807795204nt_int @ F @ Xs ) )
= ( ? [Us2: list_P419547167332244514st_int,Vs2: list_P419547167332244514st_int] :
( ( Xs
= ( append5028292981072010935st_int @ Us2 @ Vs2 ) )
& ( Ys
= ( map_Pr3224476576807795204nt_int @ F @ Us2 ) )
& ( Zs
= ( map_Pr3224476576807795204nt_int @ F @ Vs2 ) ) ) ) ) ).
% append_eq_map_conv
thf(fact_907_append__eq__map__conv,axiom,
! [Ys: list_int,Zs: list_int,F: int > int,Xs: list_int] :
( ( ( append_int @ Ys @ Zs )
= ( map_int_int @ F @ Xs ) )
= ( ? [Us2: list_int,Vs2: list_int] :
( ( Xs
= ( append_int @ Us2 @ Vs2 ) )
& ( Ys
= ( map_int_int @ F @ Us2 ) )
& ( Zs
= ( map_int_int @ F @ Vs2 ) ) ) ) ) ).
% append_eq_map_conv
thf(fact_908_append__eq__map__conv,axiom,
! [Ys: list_int,Zs: list_int,F: instr > int,Xs: list_instr] :
( ( ( append_int @ Ys @ Zs )
= ( map_instr_int @ F @ Xs ) )
= ( ? [Us2: list_instr,Vs2: list_instr] :
( ( Xs
= ( append_instr @ Us2 @ Vs2 ) )
& ( Ys
= ( map_instr_int @ F @ Us2 ) )
& ( Zs
= ( map_instr_int @ F @ Vs2 ) ) ) ) ) ).
% append_eq_map_conv
thf(fact_909_append__eq__map__conv,axiom,
! [Ys: list_instr,Zs: list_instr,F: produc6425607678544837394st_int > instr,Xs: list_P419547167332244514st_int] :
( ( ( append_instr @ Ys @ Zs )
= ( map_Pr7514435936640407687_instr @ F @ Xs ) )
= ( ? [Us2: list_P419547167332244514st_int,Vs2: list_P419547167332244514st_int] :
( ( Xs
= ( append5028292981072010935st_int @ Us2 @ Vs2 ) )
& ( Ys
= ( map_Pr7514435936640407687_instr @ F @ Us2 ) )
& ( Zs
= ( map_Pr7514435936640407687_instr @ F @ Vs2 ) ) ) ) ) ).
% append_eq_map_conv
thf(fact_910_append__eq__map__conv,axiom,
! [Ys: list_instr,Zs: list_instr,F: int > instr,Xs: list_int] :
( ( ( append_instr @ Ys @ Zs )
= ( map_int_instr @ F @ Xs ) )
= ( ? [Us2: list_int,Vs2: list_int] :
( ( Xs
= ( append_int @ Us2 @ Vs2 ) )
& ( Ys
= ( map_int_instr @ F @ Us2 ) )
& ( Zs
= ( map_int_instr @ F @ Vs2 ) ) ) ) ) ).
% append_eq_map_conv
thf(fact_911_append__eq__map__conv,axiom,
! [Ys: list_instr,Zs: list_instr,F: instr > instr,Xs: list_instr] :
( ( ( append_instr @ Ys @ Zs )
= ( map_instr_instr @ F @ Xs ) )
= ( ? [Us2: list_instr,Vs2: list_instr] :
( ( Xs
= ( append_instr @ Us2 @ Vs2 ) )
& ( Ys
= ( map_instr_instr @ F @ Us2 ) )
& ( Zs
= ( map_instr_instr @ F @ Vs2 ) ) ) ) ) ).
% append_eq_map_conv
thf(fact_912_append__eq__map__conv,axiom,
! [Ys: list_m_instr,Zs: list_m_instr,F: instr > m_instr,Xs: list_instr] :
( ( ( append_m_instr @ Ys @ Zs )
= ( map_instr_m_instr @ F @ Xs ) )
= ( ? [Us2: list_instr,Vs2: list_instr] :
( ( Xs
= ( append_instr @ Us2 @ Vs2 ) )
& ( Ys
= ( map_instr_m_instr @ F @ Us2 ) )
& ( Zs
= ( map_instr_m_instr @ F @ Vs2 ) ) ) ) ) ).
% append_eq_map_conv
thf(fact_913_map__eq__append__conv,axiom,
! [F: produc6425607678544837394st_int > produc6425607678544837394st_int,Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int] :
( ( ( map_Pr8625093460839654122st_int @ F @ Xs )
= ( append5028292981072010935st_int @ Ys @ Zs ) )
= ( ? [Us2: list_P419547167332244514st_int,Vs2: list_P419547167332244514st_int] :
( ( Xs
= ( append5028292981072010935st_int @ Us2 @ Vs2 ) )
& ( Ys
= ( map_Pr8625093460839654122st_int @ F @ Us2 ) )
& ( Zs
= ( map_Pr8625093460839654122st_int @ F @ Vs2 ) ) ) ) ) ).
% map_eq_append_conv
thf(fact_914_map__eq__append__conv,axiom,
! [F: int > produc6425607678544837394st_int,Xs: list_int,Ys: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int] :
( ( ( map_in8512336359594627332st_int @ F @ Xs )
= ( append5028292981072010935st_int @ Ys @ Zs ) )
= ( ? [Us2: list_int,Vs2: list_int] :
( ( Xs
= ( append_int @ Us2 @ Vs2 ) )
& ( Ys
= ( map_in8512336359594627332st_int @ F @ Us2 ) )
& ( Zs
= ( map_in8512336359594627332st_int @ F @ Vs2 ) ) ) ) ) ).
% map_eq_append_conv
thf(fact_915_map__eq__append__conv,axiom,
! [F: instr > produc6425607678544837394st_int,Xs: list_instr,Ys: list_P419547167332244514st_int,Zs: list_P419547167332244514st_int] :
( ( ( map_in7259965606695656109st_int @ F @ Xs )
= ( append5028292981072010935st_int @ Ys @ Zs ) )
= ( ? [Us2: list_instr,Vs2: list_instr] :
( ( Xs
= ( append_instr @ Us2 @ Vs2 ) )
& ( Ys
= ( map_in7259965606695656109st_int @ F @ Us2 ) )
& ( Zs
= ( map_in7259965606695656109st_int @ F @ Vs2 ) ) ) ) ) ).
% map_eq_append_conv
thf(fact_916_map__eq__append__conv,axiom,
! [F: produc6425607678544837394st_int > int,Xs: list_P419547167332244514st_int,Ys: list_int,Zs: list_int] :
( ( ( map_Pr3224476576807795204nt_int @ F @ Xs )
= ( append_int @ Ys @ Zs ) )
= ( ? [Us2: list_P419547167332244514st_int,Vs2: list_P419547167332244514st_int] :
( ( Xs
= ( append5028292981072010935st_int @ Us2 @ Vs2 ) )
& ( Ys
= ( map_Pr3224476576807795204nt_int @ F @ Us2 ) )
& ( Zs
= ( map_Pr3224476576807795204nt_int @ F @ Vs2 ) ) ) ) ) ).
% map_eq_append_conv
thf(fact_917_map__eq__append__conv,axiom,
! [F: int > int,Xs: list_int,Ys: list_int,Zs: list_int] :
( ( ( map_int_int @ F @ Xs )
= ( append_int @ Ys @ Zs ) )
= ( ? [Us2: list_int,Vs2: list_int] :
( ( Xs
= ( append_int @ Us2 @ Vs2 ) )
& ( Ys
= ( map_int_int @ F @ Us2 ) )
& ( Zs
= ( map_int_int @ F @ Vs2 ) ) ) ) ) ).
% map_eq_append_conv
thf(fact_918_map__eq__append__conv,axiom,
! [F: instr > int,Xs: list_instr,Ys: list_int,Zs: list_int] :
( ( ( map_instr_int @ F @ Xs )
= ( append_int @ Ys @ Zs ) )
= ( ? [Us2: list_instr,Vs2: list_instr] :
( ( Xs
= ( append_instr @ Us2 @ Vs2 ) )
& ( Ys
= ( map_instr_int @ F @ Us2 ) )
& ( Zs
= ( map_instr_int @ F @ Vs2 ) ) ) ) ) ).
% map_eq_append_conv
thf(fact_919_map__eq__append__conv,axiom,
! [F: produc6425607678544837394st_int > instr,Xs: list_P419547167332244514st_int,Ys: list_instr,Zs: list_instr] :
( ( ( map_Pr7514435936640407687_instr @ F @ Xs )
= ( append_instr @ Ys @ Zs ) )
= ( ? [Us2: list_P419547167332244514st_int,Vs2: list_P419547167332244514st_int] :
( ( Xs
= ( append5028292981072010935st_int @ Us2 @ Vs2 ) )
& ( Ys
= ( map_Pr7514435936640407687_instr @ F @ Us2 ) )
& ( Zs
= ( map_Pr7514435936640407687_instr @ F @ Vs2 ) ) ) ) ) ).
% map_eq_append_conv
thf(fact_920_map__eq__append__conv,axiom,
! [F: int > instr,Xs: list_int,Ys: list_instr,Zs: list_instr] :
( ( ( map_int_instr @ F @ Xs )
= ( append_instr @ Ys @ Zs ) )
= ( ? [Us2: list_int,Vs2: list_int] :
( ( Xs
= ( append_int @ Us2 @ Vs2 ) )
& ( Ys
= ( map_int_instr @ F @ Us2 ) )
& ( Zs
= ( map_int_instr @ F @ Vs2 ) ) ) ) ) ).
% map_eq_append_conv
thf(fact_921_map__eq__append__conv,axiom,
! [F: instr > instr,Xs: list_instr,Ys: list_instr,Zs: list_instr] :
( ( ( map_instr_instr @ F @ Xs )
= ( append_instr @ Ys @ Zs ) )
= ( ? [Us2: list_instr,Vs2: list_instr] :
( ( Xs
= ( append_instr @ Us2 @ Vs2 ) )
& ( Ys
= ( map_instr_instr @ F @ Us2 ) )
& ( Zs
= ( map_instr_instr @ F @ Vs2 ) ) ) ) ) ).
% map_eq_append_conv
thf(fact_922_map__eq__append__conv,axiom,
! [F: instr > m_instr,Xs: list_instr,Ys: list_m_instr,Zs: list_m_instr] :
( ( ( map_instr_m_instr @ F @ Xs )
= ( append_m_instr @ Ys @ Zs ) )
= ( ? [Us2: list_instr,Vs2: list_instr] :
( ( Xs
= ( append_instr @ Us2 @ Vs2 ) )
& ( Ys
= ( map_instr_m_instr @ F @ Us2 ) )
& ( Zs
= ( map_instr_m_instr @ F @ Vs2 ) ) ) ) ) ).
% map_eq_append_conv
thf(fact_923_map__eq__imp__length__eq,axiom,
! [F: produc6425607678544837394st_int > m_instr,Xs: list_P419547167332244514st_int,G: instr > m_instr,Ys: list_instr] :
( ( ( map_Pr1330222860079180132_instr @ F @ Xs )
= ( map_instr_m_instr @ G @ Ys ) )
=> ( ( size_s229347708945616566st_int @ Xs )
= ( size_size_list_instr @ Ys ) ) ) ).
% map_eq_imp_length_eq
thf(fact_924_map__eq__imp__length__eq,axiom,
! [F: m_instr > m_instr,Xs: list_m_instr,G: instr > m_instr,Ys: list_instr] :
( ( ( map_m_instr_m_instr @ F @ Xs )
= ( map_instr_m_instr @ G @ Ys ) )
=> ( ( size_s5914166952900237872_instr @ Xs )
= ( size_size_list_instr @ Ys ) ) ) ).
% map_eq_imp_length_eq
thf(fact_925_map__eq__imp__length__eq,axiom,
! [F: instr > m_instr,Xs: list_instr,G: produc6425607678544837394st_int > m_instr,Ys: list_P419547167332244514st_int] :
( ( ( map_instr_m_instr @ F @ Xs )
= ( map_Pr1330222860079180132_instr @ G @ Ys ) )
=> ( ( size_size_list_instr @ Xs )
= ( size_s229347708945616566st_int @ Ys ) ) ) ).
% map_eq_imp_length_eq
thf(fact_926_map__eq__imp__length__eq,axiom,
! [F: instr > m_instr,Xs: list_instr,G: m_instr > m_instr,Ys: list_m_instr] :
( ( ( map_instr_m_instr @ F @ Xs )
= ( map_m_instr_m_instr @ G @ Ys ) )
=> ( ( size_size_list_instr @ Xs )
= ( size_s5914166952900237872_instr @ Ys ) ) ) ).
% map_eq_imp_length_eq
thf(fact_927_map__eq__imp__length__eq,axiom,
! [F: instr > m_instr,Xs: list_instr,G: instr > m_instr,Ys: list_instr] :
( ( ( map_instr_m_instr @ F @ Xs )
= ( map_instr_m_instr @ G @ Ys ) )
=> ( ( size_size_list_instr @ Xs )
= ( size_size_list_instr @ Ys ) ) ) ).
% map_eq_imp_length_eq
thf(fact_928_map__eq__imp__length__eq,axiom,
! [F: instr > m_instr,Xs: list_instr,G: list_char > m_instr,Ys: list_list_char] :
( ( ( map_instr_m_instr @ F @ Xs )
= ( map_li1986238532096774195_instr @ G @ Ys ) )
=> ( ( size_size_list_instr @ Xs )
= ( size_s356637359517785349t_char @ Ys ) ) ) ).
% map_eq_imp_length_eq
thf(fact_929_map__eq__imp__length__eq,axiom,
! [F: instr > m_instr,Xs: list_instr,G: int > m_instr,Ys: list_int] :
( ( ( map_instr_m_instr @ F @ Xs )
= ( map_int_m_instr @ G @ Ys ) )
=> ( ( size_size_list_instr @ Xs )
= ( size_size_list_int @ Ys ) ) ) ).
% map_eq_imp_length_eq
thf(fact_930_map__eq__imp__length__eq,axiom,
! [F: list_char > m_instr,Xs: list_list_char,G: instr > m_instr,Ys: list_instr] :
( ( ( map_li1986238532096774195_instr @ F @ Xs )
= ( map_instr_m_instr @ G @ Ys ) )
=> ( ( size_s356637359517785349t_char @ Xs )
= ( size_size_list_instr @ Ys ) ) ) ).
% map_eq_imp_length_eq
thf(fact_931_map__eq__imp__length__eq,axiom,
! [F: int > m_instr,Xs: list_int,G: instr > m_instr,Ys: list_instr] :
( ( ( map_int_m_instr @ F @ Xs )
= ( map_instr_m_instr @ G @ Ys ) )
=> ( ( size_size_list_int @ Xs )
= ( size_size_list_instr @ Ys ) ) ) ).
% map_eq_imp_length_eq
thf(fact_932_list_Osimps_I8_J,axiom,
! [F: instr > instr] :
( ( map_instr_instr @ F @ nil_instr )
= nil_instr ) ).
% list.simps(8)
thf(fact_933_list_Osimps_I8_J,axiom,
! [F: instr > int] :
( ( map_instr_int @ F @ nil_instr )
= nil_int ) ).
% list.simps(8)
thf(fact_934_list_Osimps_I8_J,axiom,
! [F: int > instr] :
( ( map_int_instr @ F @ nil_int )
= nil_instr ) ).
% list.simps(8)
thf(fact_935_list_Osimps_I8_J,axiom,
! [F: int > int] :
( ( map_int_int @ F @ nil_int )
= nil_int ) ).
% list.simps(8)
thf(fact_936_list_Osimps_I8_J,axiom,
! [F: instr > m_instr] :
( ( map_instr_m_instr @ F @ nil_instr )
= nil_m_instr ) ).
% list.simps(8)
thf(fact_937_list_Osimps_I8_J,axiom,
! [F: instr > list_char] :
( ( map_instr_list_char @ F @ nil_instr )
= nil_list_char ) ).
% list.simps(8)
thf(fact_938_list_Osimps_I8_J,axiom,
! [F: list_char > instr] :
( ( map_list_char_instr @ F @ nil_list_char )
= nil_instr ) ).
% list.simps(8)
thf(fact_939_list_Osimps_I8_J,axiom,
! [F: list_char > int] :
( ( map_list_char_int @ F @ nil_list_char )
= nil_int ) ).
% list.simps(8)
thf(fact_940_list_Osimps_I8_J,axiom,
! [F: int > list_char] :
( ( map_int_list_char @ F @ nil_int )
= nil_list_char ) ).
% list.simps(8)
thf(fact_941_list_Osimps_I8_J,axiom,
! [F: list_char > list_char] :
( ( map_li116305933131242120t_char @ F @ nil_list_char )
= nil_list_char ) ).
% list.simps(8)
thf(fact_942_to__m__prog_Osimps,axiom,
( to_m_prog
= ( ^ [P5: list_instr] : ( map_instr_m_instr @ ( to_m_instr @ ( vars @ P5 ) ) @ P5 ) ) ) ).
% to_m_prog.simps
thf(fact_943_to__m__prog_Oelims,axiom,
! [X: list_instr,Y: list_m_instr] :
( ( ( to_m_prog @ X )
= Y )
=> ( Y
= ( map_instr_m_instr @ ( to_m_instr @ ( vars @ X ) ) @ X ) ) ) ).
% to_m_prog.elims
thf(fact_944_upto__rec1,axiom,
! [I: int,J: int] :
( ( ord_less_eq_int @ I @ J )
=> ( ( upto @ I @ J )
= ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% upto_rec1
thf(fact_945_upto__split2,axiom,
! [I: int,J: int,K: int] :
( ( ord_less_eq_int @ I @ J )
=> ( ( ord_less_eq_int @ J @ K )
=> ( ( upto @ I @ K )
= ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% upto_split2
thf(fact_946_upto__split1,axiom,
! [I: int,J: int,K: int] :
( ( ord_less_eq_int @ I @ J )
=> ( ( ord_less_eq_int @ J @ K )
=> ( ( upto @ I @ K )
= ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% upto_split1
thf(fact_947_upto_Osimps,axiom,
( upto
= ( ^ [I6: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I6 @ J3 ) @ ( cons_int @ I6 @ ( upto @ ( plus_plus_int @ I6 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% upto.simps
thf(fact_948_upto_Oelims,axiom,
! [X: int,Xa: int,Y: list_int] :
( ( ( upto @ X @ Xa )
= Y )
=> ( ( ( ord_less_eq_int @ X @ Xa )
=> ( Y
= ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
& ( ~ ( ord_less_eq_int @ X @ Xa )
=> ( Y = nil_int ) ) ) ) ).
% upto.elims
thf(fact_949_exec1I,axiom,
! [C4: produc6425607678544837394st_int,P: list_instr,I: int,S: list_char > int,Stk: list_int] :
( ( C4
= ( iexec @ ( inth_instr @ P @ I ) @ ( produc5086643055186798020st_int @ I @ ( produc8650753666468850689st_int @ S @ Stk ) ) ) )
=> ( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P ) ) )
=> ( exec1 @ P @ ( produc5086643055186798020st_int @ I @ ( produc8650753666468850689st_int @ S @ Stk ) ) @ C4 ) ) ) ) ).
% exec1I
thf(fact_950_inth__append,axiom,
! [I: int,Xs: list_P419547167332244514st_int,Ys: list_P419547167332244514st_int] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_s229347708945616566st_int @ Xs ) ) )
=> ( ( inth_P8039235741264645271st_int @ ( append5028292981072010935st_int @ Xs @ Ys ) @ I )
= ( inth_P8039235741264645271st_int @ Xs @ I ) ) )
& ( ~ ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_s229347708945616566st_int @ Xs ) ) )
=> ( ( inth_P8039235741264645271st_int @ ( append5028292981072010935st_int @ Xs @ Ys ) @ I )
= ( inth_P8039235741264645271st_int @ Ys @ ( minus_minus_int @ I @ ( semiri1314217659103216013at_int @ ( size_s229347708945616566st_int @ Xs ) ) ) ) ) ) ) ) ).
% inth_append
thf(fact_951_inth__append,axiom,
! [I: int,Xs: list_m_instr,Ys: list_m_instr] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_s5914166952900237872_instr @ Xs ) ) )
=> ( ( inth_m_instr @ ( append_m_instr @ Xs @ Ys ) @ I )
= ( inth_m_instr @ Xs @ I ) ) )
& ( ~ ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_s5914166952900237872_instr @ Xs ) ) )
=> ( ( inth_m_instr @ ( append_m_instr @ Xs @ Ys ) @ I )
= ( inth_m_instr @ Ys @ ( minus_minus_int @ I @ ( semiri1314217659103216013at_int @ ( size_s5914166952900237872_instr @ Xs ) ) ) ) ) ) ) ) ).
% inth_append
thf(fact_952_inth__append,axiom,
! [I: int,Xs: list_instr,Ys: list_instr] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ Xs ) ) )
=> ( ( inth_instr @ ( append_instr @ Xs @ Ys ) @ I )
= ( inth_instr @ Xs @ I ) ) )
& ( ~ ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ Xs ) ) )
=> ( ( inth_instr @ ( append_instr @ Xs @ Ys ) @ I )
= ( inth_instr @ Ys @ ( minus_minus_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ Xs ) ) ) ) ) ) ) ) ).
% inth_append
thf(fact_953_inth__append,axiom,
! [I: int,Xs: list_list_char,Ys: list_list_char] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs ) ) )
=> ( ( inth_list_char @ ( append_list_char @ Xs @ Ys ) @ I )
= ( inth_list_char @ Xs @ I ) ) )
& ( ~ ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs ) ) )
=> ( ( inth_list_char @ ( append_list_char @ Xs @ Ys ) @ I )
= ( inth_list_char @ Ys @ ( minus_minus_int @ I @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs ) ) ) ) ) ) ) ) ).
% inth_append
thf(fact_954_inth__append,axiom,
! [I: int,Xs: list_int,Ys: list_int] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_int @ Xs ) ) )
=> ( ( inth_int @ ( append_int @ Xs @ Ys ) @ I )
= ( inth_int @ Xs @ I ) ) )
& ( ~ ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_int @ Xs ) ) )
=> ( ( inth_int @ ( append_int @ Xs @ Ys ) @ I )
= ( inth_int @ Ys @ ( minus_minus_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_int @ Xs ) ) ) ) ) ) ) ) ).
% inth_append
thf(fact_955_msp__def,axiom,
( msp
= ( ^ [P5: list_instr,I6: int] : ( m_msp @ ( to_m_instr @ nil_list_char @ ( inth_instr @ P5 @ I6 ) ) ) ) ) ).
% msp_def
thf(fact_956_upto__rec__numeral_I1_J,axiom,
! [M: num,N: num] :
( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
=> ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
= ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
& ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
=> ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
= nil_int ) ) ) ).
% upto_rec_numeral(1)
thf(fact_957_numeral__eq__iff,axiom,
! [M: num,N: num] :
( ( ( numeral_numeral_int @ M )
= ( numeral_numeral_int @ N ) )
= ( M = N ) ) ).
% numeral_eq_iff
thf(fact_958_numeral__eq__iff,axiom,
! [M: num,N: num] :
( ( ( numeral_numeral_nat @ M )
= ( numeral_numeral_nat @ N ) )
= ( M = N ) ) ).
% numeral_eq_iff
thf(fact_959_not__gr__zero,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) ).
% not_gr_zero
thf(fact_960_numeral__le__iff,axiom,
! [M: num,N: num] :
( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
= ( ord_less_eq_num @ M @ N ) ) ).
% numeral_le_iff
thf(fact_961_numeral__le__iff,axiom,
! [M: num,N: num] :
( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
= ( ord_less_eq_num @ M @ N ) ) ).
% numeral_le_iff
thf(fact_962_numeral__less__iff,axiom,
! [M: num,N: num] :
( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
= ( ord_less_num @ M @ N ) ) ).
% numeral_less_iff
thf(fact_963_numeral__less__iff,axiom,
! [M: num,N: num] :
( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
= ( ord_less_num @ M @ N ) ) ).
% numeral_less_iff
thf(fact_964_add__less__cancel__right,axiom,
! [A: int,C: int,B: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
= ( ord_less_int @ A @ B ) ) ).
% add_less_cancel_right
thf(fact_965_add__less__cancel__right,axiom,
! [A: nat,C: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
= ( ord_less_nat @ A @ B ) ) ).
% add_less_cancel_right
thf(fact_966_add__less__cancel__left,axiom,
! [C: int,A: int,B: int] :
( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
= ( ord_less_int @ A @ B ) ) ).
% add_less_cancel_left
thf(fact_967_add__less__cancel__left,axiom,
! [C: nat,A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_nat @ A @ B ) ) ).
% add_less_cancel_left
thf(fact_968_numeral__plus__numeral,axiom,
! [M: num,N: num] :
( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
= ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% numeral_plus_numeral
thf(fact_969_numeral__plus__numeral,axiom,
! [M: num,N: num] :
( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
= ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% numeral_plus_numeral
thf(fact_970_add__numeral__left,axiom,
! [V2: num,W2: num,Z: int] :
( ( plus_plus_int @ ( numeral_numeral_int @ V2 ) @ ( plus_plus_int @ ( numeral_numeral_int @ W2 ) @ Z ) )
= ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V2 @ W2 ) ) @ Z ) ) ).
% add_numeral_left
thf(fact_971_add__numeral__left,axiom,
! [V2: num,W2: num,Z: nat] :
( ( plus_plus_nat @ ( numeral_numeral_nat @ V2 ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W2 ) @ Z ) )
= ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V2 @ W2 ) ) @ Z ) ) ).
% add_numeral_left
thf(fact_972_of__nat__less__iff,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
= ( ord_less_nat @ M @ N ) ) ).
% of_nat_less_iff
thf(fact_973_of__nat__less__iff,axiom,
! [M: nat,N: nat] :
( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
= ( ord_less_nat @ M @ N ) ) ).
% of_nat_less_iff
thf(fact_974_of__nat__numeral,axiom,
! [N: num] :
( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
= ( numeral_numeral_nat @ N ) ) ).
% of_nat_numeral
thf(fact_975_of__nat__numeral,axiom,
! [N: num] :
( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
= ( numeral_numeral_int @ N ) ) ).
% of_nat_numeral
thf(fact_976_add__less__same__cancel1,axiom,
! [B: int,A: int] :
( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
= ( ord_less_int @ A @ zero_zero_int ) ) ).
% add_less_same_cancel1
thf(fact_977_add__less__same__cancel1,axiom,
! [B: nat,A: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
= ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% add_less_same_cancel1
thf(fact_978_add__less__same__cancel2,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
= ( ord_less_int @ A @ zero_zero_int ) ) ).
% add_less_same_cancel2
thf(fact_979_add__less__same__cancel2,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
= ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% add_less_same_cancel2
thf(fact_980_less__add__same__cancel1,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
= ( ord_less_int @ zero_zero_int @ B ) ) ).
% less_add_same_cancel1
thf(fact_981_less__add__same__cancel1,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
= ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% less_add_same_cancel1
thf(fact_982_less__add__same__cancel2,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
= ( ord_less_int @ zero_zero_int @ B ) ) ).
% less_add_same_cancel2
thf(fact_983_less__add__same__cancel2,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
= ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% less_add_same_cancel2
thf(fact_984_double__add__less__zero__iff__single__add__less__zero,axiom,
! [A: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ) ).
% double_add_less_zero_iff_single_add_less_zero
thf(fact_985_zero__less__double__add__iff__zero__less__single__add,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
= ( ord_less_int @ zero_zero_int @ A ) ) ).
% zero_less_double_add_iff_zero_less_single_add
thf(fact_986_diff__gt__0__iff__gt,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
= ( ord_less_int @ B @ A ) ) ).
% diff_gt_0_iff_gt
thf(fact_987_upto__Nil,axiom,
! [I: int,J: int] :
( ( ( upto @ I @ J )
= nil_int )
= ( ord_less_int @ J @ I ) ) ).
% upto_Nil
thf(fact_988_upto__Nil2,axiom,
! [I: int,J: int] :
( ( nil_int
= ( upto @ I @ J ) )
= ( ord_less_int @ J @ I ) ) ).
% upto_Nil2
thf(fact_989_upto__empty,axiom,
! [J: int,I: int] :
( ( ord_less_int @ J @ I )
=> ( ( upto @ I @ J )
= nil_int ) ) ).
% upto_empty
thf(fact_990_of__nat__0__less__iff,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
= ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% of_nat_0_less_iff
thf(fact_991_of__nat__0__less__iff,axiom,
! [N: nat] :
( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
= ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% of_nat_0_less_iff
thf(fact_992_zle__add1__eq__le,axiom,
! [W2: int,Z: int] :
( ( ord_less_int @ W2 @ ( plus_plus_int @ Z @ one_one_int ) )
= ( ord_less_eq_int @ W2 @ Z ) ) ).
% zle_add1_eq_le
thf(fact_993_zle__diff1__eq,axiom,
! [W2: int,Z: int] :
( ( ord_less_eq_int @ W2 @ ( minus_minus_int @ Z @ one_one_int ) )
= ( ord_less_int @ W2 @ Z ) ) ).
% zle_diff1_eq
thf(fact_994_inth__map,axiom,
! [I: int,Xs: list_m_instr,F: m_instr > instr] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_s5914166952900237872_instr @ Xs ) ) )
=> ( ( inth_instr @ ( map_m_instr_instr @ F @ Xs ) @ I )
= ( F @ ( inth_m_instr @ Xs @ I ) ) ) ) ) ).
% inth_map
thf(fact_995_inth__map,axiom,
! [I: int,Xs: list_m_instr,F: m_instr > m_instr] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_s5914166952900237872_instr @ Xs ) ) )
=> ( ( inth_m_instr @ ( map_m_instr_m_instr @ F @ Xs ) @ I )
= ( F @ ( inth_m_instr @ Xs @ I ) ) ) ) ) ).
% inth_map
thf(fact_996_inth__map,axiom,
! [I: int,Xs: list_instr,F: instr > instr] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ Xs ) ) )
=> ( ( inth_instr @ ( map_instr_instr @ F @ Xs ) @ I )
= ( F @ ( inth_instr @ Xs @ I ) ) ) ) ) ).
% inth_map
thf(fact_997_inth__map,axiom,
! [I: int,Xs: list_instr,F: instr > m_instr] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ Xs ) ) )
=> ( ( inth_m_instr @ ( map_instr_m_instr @ F @ Xs ) @ I )
= ( F @ ( inth_instr @ Xs @ I ) ) ) ) ) ).
% inth_map
thf(fact_998_inth__map,axiom,
! [I: int,Xs: list_int,F: int > instr] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_int @ Xs ) ) )
=> ( ( inth_instr @ ( map_int_instr @ F @ Xs ) @ I )
= ( F @ ( inth_int @ Xs @ I ) ) ) ) ) ).
% inth_map
thf(fact_999_inth__map,axiom,
! [I: int,Xs: list_int,F: int > m_instr] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_int @ Xs ) ) )
=> ( ( inth_m_instr @ ( map_int_m_instr @ F @ Xs ) @ I )
= ( F @ ( inth_int @ Xs @ I ) ) ) ) ) ).
% inth_map
thf(fact_1000_inth__map,axiom,
! [I: int,Xs: list_m_instr,F: m_instr > list_char] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_s5914166952900237872_instr @ Xs ) ) )
=> ( ( inth_list_char @ ( map_m_3283148507038589619t_char @ F @ Xs ) @ I )
= ( F @ ( inth_m_instr @ Xs @ I ) ) ) ) ) ).
% inth_map
thf(fact_1001_inth__map,axiom,
! [I: int,Xs: list_instr,F: instr > list_char] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ Xs ) ) )
=> ( ( inth_list_char @ ( map_instr_list_char @ F @ Xs ) @ I )
= ( F @ ( inth_instr @ Xs @ I ) ) ) ) ) ).
% inth_map
thf(fact_1002_inth__map,axiom,
! [I: int,Xs: list_list_char,F: list_char > instr] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs ) ) )
=> ( ( inth_instr @ ( map_list_char_instr @ F @ Xs ) @ I )
= ( F @ ( inth_list_char @ Xs @ I ) ) ) ) ) ).
% inth_map
thf(fact_1003_inth__map,axiom,
! [I: int,Xs: list_list_char,F: list_char > m_instr] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs ) ) )
=> ( ( inth_m_instr @ ( map_li1986238532096774195_instr @ F @ Xs ) @ I )
= ( F @ ( inth_list_char @ Xs @ I ) ) ) ) ) ).
% inth_map
thf(fact_1004_zero__neq__numeral,axiom,
! [N: num] :
( zero_zero_int
!= ( numeral_numeral_int @ N ) ) ).
% zero_neq_numeral
thf(fact_1005_zero__neq__numeral,axiom,
! [N: num] :
( zero_zero_nat
!= ( numeral_numeral_nat @ N ) ) ).
% zero_neq_numeral
thf(fact_1006_not__numeral__less__zero,axiom,
! [N: num] :
~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% not_numeral_less_zero
thf(fact_1007_not__numeral__less__zero,axiom,
! [N: num] :
~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% not_numeral_less_zero
thf(fact_1008_zero__less__numeral,axiom,
! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% zero_less_numeral
thf(fact_1009_zero__less__numeral,axiom,
! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% zero_less_numeral
thf(fact_1010_verit__comp__simplify1_I1_J,axiom,
! [A: int] :
~ ( ord_less_int @ A @ A ) ).
% verit_comp_simplify1(1)
thf(fact_1011_verit__comp__simplify1_I1_J,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ) ).
% verit_comp_simplify1(1)
thf(fact_1012_lt__ex,axiom,
! [X: int] :
? [Y3: int] : ( ord_less_int @ Y3 @ X ) ).
% lt_ex
thf(fact_1013_gt__ex,axiom,
! [X: int] :
? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% gt_ex
thf(fact_1014_gt__ex,axiom,
! [X: nat] :
? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% gt_ex
thf(fact_1015_less__imp__neq,axiom,
! [X: int,Y: int] :
( ( ord_less_int @ X @ Y )
=> ( X != Y ) ) ).
% less_imp_neq
thf(fact_1016_less__imp__neq,axiom,
! [X: nat,Y: nat] :
( ( ord_less_nat @ X @ Y )
=> ( X != Y ) ) ).
% less_imp_neq
thf(fact_1017_order_Oasym,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ) ).
% order.asym
thf(fact_1018_order_Oasym,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ) ).
% order.asym
thf(fact_1019_ord__eq__less__trans,axiom,
! [A: int,B: int,C: int] :
( ( A = B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ) ).
% ord_eq_less_trans
thf(fact_1020_ord__eq__less__trans,axiom,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ) ).
% ord_eq_less_trans
thf(fact_1021_ord__less__eq__trans,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( B = C )
=> ( ord_less_int @ A @ C ) ) ) ).
% ord_less_eq_trans
thf(fact_1022_ord__less__eq__trans,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_nat @ A @ C ) ) ) ).
% ord_less_eq_trans
thf(fact_1023_less__induct,axiom,
! [P: nat > $o,A: nat] :
( ! [X4: nat] :
( ! [Y4: nat] :
( ( ord_less_nat @ Y4 @ X4 )
=> ( P @ Y4 ) )
=> ( P @ X4 ) )
=> ( P @ A ) ) ).
% less_induct
thf(fact_1024_antisym__conv3,axiom,
! [Y: int,X: int] :
( ~ ( ord_less_int @ Y @ X )
=> ( ( ~ ( ord_less_int @ X @ Y ) )
= ( X = Y ) ) ) ).
% antisym_conv3
thf(fact_1025_antisym__conv3,axiom,
! [Y: nat,X: nat] :
( ~ ( ord_less_nat @ Y @ X )
=> ( ( ~ ( ord_less_nat @ X @ Y ) )
= ( X = Y ) ) ) ).
% antisym_conv3
thf(fact_1026_linorder__cases,axiom,
! [X: int,Y: int] :
( ~ ( ord_less_int @ X @ Y )
=> ( ( X != Y )
=> ( ord_less_int @ Y @ X ) ) ) ).
% linorder_cases
thf(fact_1027_linorder__cases,axiom,
! [X: nat,Y: nat] :
( ~ ( ord_less_nat @ X @ Y )
=> ( ( X != Y )
=> ( ord_less_nat @ Y @ X ) ) ) ).
% linorder_cases
thf(fact_1028_dual__order_Oasym,axiom,
! [B: int,A: int] :
( ( ord_less_int @ B @ A )
=> ~ ( ord_less_int @ A @ B ) ) ).
% dual_order.asym
thf(fact_1029_dual__order_Oasym,axiom,
! [B: nat,A: nat] :
( ( ord_less_nat @ B @ A )
=> ~ ( ord_less_nat @ A @ B ) ) ).
% dual_order.asym
thf(fact_1030_dual__order_Oirrefl,axiom,
! [A: int] :
~ ( ord_less_int @ A @ A ) ).
% dual_order.irrefl
thf(fact_1031_dual__order_Oirrefl,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ) ).
% dual_order.irrefl
thf(fact_1032_exists__least__iff,axiom,
( ( ^ [P6: nat > $o] :
? [X6: nat] : ( P6 @ X6 ) )
= ( ^ [P5: nat > $o] :
? [N3: nat] :
( ( P5 @ N3 )
& ! [M2: nat] :
( ( ord_less_nat @ M2 @ N3 )
=> ~ ( P5 @ M2 ) ) ) ) ) ).
% exists_least_iff
thf(fact_1033_linorder__less__wlog,axiom,
! [P: int > int > $o,A: int,B: int] :
( ! [A5: int,B5: int] :
( ( ord_less_int @ A5 @ B5 )
=> ( P @ A5 @ B5 ) )
=> ( ! [A5: int] : ( P @ A5 @ A5 )
=> ( ! [A5: int,B5: int] :
( ( P @ B5 @ A5 )
=> ( P @ A5 @ B5 ) )
=> ( P @ A @ B ) ) ) ) ).
% linorder_less_wlog
thf(fact_1034_linorder__less__wlog,axiom,
! [P: nat > nat > $o,A: nat,B: nat] :
( ! [A5: nat,B5: nat] :
( ( ord_less_nat @ A5 @ B5 )
=> ( P @ A5 @ B5 ) )
=> ( ! [A5: nat] : ( P @ A5 @ A5 )
=> ( ! [A5: nat,B5: nat] :
( ( P @ B5 @ A5 )
=> ( P @ A5 @ B5 ) )
=> ( P @ A @ B ) ) ) ) ).
% linorder_less_wlog
thf(fact_1035_order_Ostrict__trans,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ) ).
% order.strict_trans
thf(fact_1036_order_Ostrict__trans,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ) ).
% order.strict_trans
thf(fact_1037_not__less__iff__gr__or__eq,axiom,
! [X: int,Y: int] :
( ( ~ ( ord_less_int @ X @ Y ) )
= ( ( ord_less_int @ Y @ X )
| ( X = Y ) ) ) ).
% not_less_iff_gr_or_eq
thf(fact_1038_not__less__iff__gr__or__eq,axiom,
! [X: nat,Y: nat] :
( ( ~ ( ord_less_nat @ X @ Y ) )
= ( ( ord_less_nat @ Y @ X )
| ( X = Y ) ) ) ).
% not_less_iff_gr_or_eq
thf(fact_1039_dual__order_Ostrict__trans,axiom,
! [B: int,A: int,C: int] :
( ( ord_less_int @ B @ A )
=> ( ( ord_less_int @ C @ B )
=> ( ord_less_int @ C @ A ) ) ) ).
% dual_order.strict_trans
thf(fact_1040_dual__order_Ostrict__trans,axiom,
! [B: nat,A: nat,C: nat] :
( ( ord_less_nat @ B @ A )
=> ( ( ord_less_nat @ C @ B )
=> ( ord_less_nat @ C @ A ) ) ) ).
% dual_order.strict_trans
thf(fact_1041_order_Ostrict__implies__not__eq,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ) ).
% order.strict_implies_not_eq
thf(fact_1042_order_Ostrict__implies__not__eq,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ) ).
% order.strict_implies_not_eq
thf(fact_1043_dual__order_Ostrict__implies__not__eq,axiom,
! [B: int,A: int] :
( ( ord_less_int @ B @ A )
=> ( A != B ) ) ).
% dual_order.strict_implies_not_eq
thf(fact_1044_dual__order_Ostrict__implies__not__eq,axiom,
! [B: nat,A: nat] :
( ( ord_less_nat @ B @ A )
=> ( A != B ) ) ).
% dual_order.strict_implies_not_eq
thf(fact_1045_linorder__neqE__linordered__idom,axiom,
! [X: int,Y: int] :
( ( X != Y )
=> ( ~ ( ord_less_int @ X @ Y )
=> ( ord_less_int @ Y @ X ) ) ) ).
% linorder_neqE_linordered_idom
thf(fact_1046_linorder__neqE,axiom,
! [X: int,Y: int] :
( ( X != Y )
=> ( ~ ( ord_less_int @ X @ Y )
=> ( ord_less_int @ Y @ X ) ) ) ).
% linorder_neqE
thf(fact_1047_linorder__neqE,axiom,
! [X: nat,Y: nat] :
( ( X != Y )
=> ( ~ ( ord_less_nat @ X @ Y )
=> ( ord_less_nat @ Y @ X ) ) ) ).
% linorder_neqE
thf(fact_1048_order__less__asym,axiom,
! [X: int,Y: int] :
( ( ord_less_int @ X @ Y )
=> ~ ( ord_less_int @ Y @ X ) ) ).
% order_less_asym
thf(fact_1049_order__less__asym,axiom,
! [X: nat,Y: nat] :
( ( ord_less_nat @ X @ Y )
=> ~ ( ord_less_nat @ Y @ X ) ) ).
% order_less_asym
thf(fact_1050_linorder__neq__iff,axiom,
! [X: int,Y: int] :
( ( X != Y )
= ( ( ord_less_int @ X @ Y )
| ( ord_less_int @ Y @ X ) ) ) ).
% linorder_neq_iff
thf(fact_1051_linorder__neq__iff,axiom,
! [X: nat,Y: nat] :
( ( X != Y )
= ( ( ord_less_nat @ X @ Y )
| ( ord_less_nat @ Y @ X ) ) ) ).
% linorder_neq_iff
thf(fact_1052_order__less__asym_H,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ) ).
% order_less_asym'
thf(fact_1053_order__less__asym_H,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ) ).
% order_less_asym'
thf(fact_1054_less__int__code_I1_J,axiom,
~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% less_int_code(1)
thf(fact_1055_int__gr__induct,axiom,
! [K: int,I: int,P: int > $o] :
( ( ord_less_int @ K @ I )
=> ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
=> ( ! [I2: int] :
( ( ord_less_int @ K @ I2 )
=> ( ( P @ I2 )
=> ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
=> ( P @ I ) ) ) ) ).
% int_gr_induct
thf(fact_1056_zless__add1__eq,axiom,
! [W2: int,Z: int] :
( ( ord_less_int @ W2 @ ( plus_plus_int @ Z @ one_one_int ) )
= ( ( ord_less_int @ W2 @ Z )
| ( W2 = Z ) ) ) ).
% zless_add1_eq
thf(fact_1057_int__less__induct,axiom,
! [I: int,K: int,P: int > $o] :
( ( ord_less_int @ I @ K )
=> ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
=> ( ! [I2: int] :
( ( ord_less_int @ I2 @ K )
=> ( ( P @ I2 )
=> ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
=> ( P @ I ) ) ) ) ).
% int_less_induct
thf(fact_1058_zless__iff__Suc__zadd,axiom,
( ord_less_int
= ( ^ [W: int,Z2: int] :
? [N3: nat] :
( Z2
= ( plus_plus_int @ W @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ) ).
% zless_iff_Suc_zadd
thf(fact_1059_int__one__le__iff__zero__less,axiom,
! [Z: int] :
( ( ord_less_eq_int @ one_one_int @ Z )
= ( ord_less_int @ zero_zero_int @ Z ) ) ).
% int_one_le_iff_zero_less
thf(fact_1060_odd__less__0__iff,axiom,
! [Z: int] :
( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
= ( ord_less_int @ Z @ zero_zero_int ) ) ).
% odd_less_0_iff
thf(fact_1061_zless__imp__add1__zle,axiom,
! [W2: int,Z: int] :
( ( ord_less_int @ W2 @ Z )
=> ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z ) ) ).
% zless_imp_add1_zle
thf(fact_1062_add1__zle__eq,axiom,
! [W2: int,Z: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z )
= ( ord_less_int @ W2 @ Z ) ) ).
% add1_zle_eq
thf(fact_1063_le__imp__0__less,axiom,
! [Z: int] :
( ( ord_less_eq_int @ zero_zero_int @ Z )
=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% le_imp_0_less
thf(fact_1064_int__ops_I6_J,axiom,
! [A: nat,B: nat] :
( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
=> ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
= zero_zero_int ) )
& ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
=> ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
= ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% int_ops(6)
thf(fact_1065_to__m__state_Osimps,axiom,
( to_m_state
= ( ^ [Xs4: list_list_char,S5: list_char > int,A4: int] :
( if_int
@ ( ( ord_less_int @ zero_zero_int @ A4 )
& ( ord_less_eq_int @ A4 @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs4 ) ) ) )
@ ( S5 @ ( inth_list_char @ Xs4 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ Xs4 ) ) @ A4 ) ) )
@ zero_zero_int ) ) ) ).
% to_m_state.simps
thf(fact_1066_to__m__state_Oelims,axiom,
! [X: list_list_char,Xa: list_char > int,Xb: int,Y: int] :
( ( ( to_m_state @ X @ Xa @ Xb )
= Y )
=> ( ( ( ( ord_less_int @ zero_zero_int @ Xb )
& ( ord_less_eq_int @ Xb @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ X ) ) ) )
=> ( Y
= ( Xa @ ( inth_list_char @ X @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ X ) ) @ Xb ) ) ) ) )
& ( ~ ( ( ord_less_int @ zero_zero_int @ Xb )
& ( ord_less_eq_int @ Xb @ ( semiri1314217659103216013at_int @ ( size_s356637359517785349t_char @ X ) ) ) )
=> ( Y = zero_zero_int ) ) ) ) ).
% to_m_state.elims
thf(fact_1067_upto__aux__rec,axiom,
( upto_aux
= ( ^ [I6: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I6 ) @ Js @ ( upto_aux @ I6 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% upto_aux_rec
thf(fact_1068_less__nat__zero__code,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% less_nat_zero_code
thf(fact_1069_neq0__conv,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% neq0_conv
thf(fact_1070_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_1071_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_1072_Suc__mono,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% Suc_mono
thf(fact_1073_lessI,axiom,
! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% lessI
thf(fact_1074_nat__add__left__cancel__less,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
= ( ord_less_nat @ M @ N ) ) ).
% nat_add_left_cancel_less
thf(fact_1075_less__Suc0,axiom,
! [N: nat] :
( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
= ( N = zero_zero_nat ) ) ).
% less_Suc0
thf(fact_1076_zero__less__Suc,axiom,
! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% zero_less_Suc
thf(fact_1077_add__gr__0,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ M )
| ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% add_gr_0
thf(fact_1078_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_1079_less__one,axiom,
! [N: nat] :
( ( ord_less_nat @ N @ one_one_nat )
= ( N = zero_zero_nat ) ) ).
% less_one
thf(fact_1080_int__eq__iff__numeral,axiom,
! [M: nat,V2: num] :
( ( ( semiri1314217659103216013at_int @ M )
= ( numeral_numeral_int @ V2 ) )
= ( M
= ( numeral_numeral_nat @ V2 ) ) ) ).
% int_eq_iff_numeral
thf(fact_1081_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_1082_Suc__lessI2,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ( M
!= ( minus_minus_nat @ N @ one_one_nat ) )
=> ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% Suc_lessI2
thf(fact_1083_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_1084_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_1085_less__not__refl,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ N ) ).
% less_not_refl
thf(fact_1086_less__not__refl2,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ N @ M )
=> ( M != N ) ) ).
% less_not_refl2
thf(fact_1087_less__not__refl3,axiom,
! [S: nat,T: nat] :
( ( ord_less_nat @ S @ T )
=> ( S != T ) ) ).
% less_not_refl3
thf(fact_1088_less__irrefl__nat,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ N ) ).
% less_irrefl_nat
thf(fact_1089_nat__less__induct,axiom,
! [P: nat > $o,N: nat] :
( ! [N2: nat] :
( ! [M4: nat] :
( ( ord_less_nat @ M4 @ N2 )
=> ( P @ M4 ) )
=> ( P @ N2 ) )
=> ( P @ N ) ) ).
% nat_less_induct
thf(fact_1090_infinite__descent,axiom,
! [P: nat > $o,N: nat] :
( ! [N2: nat] :
( ~ ( P @ N2 )
=> ? [M4: nat] :
( ( ord_less_nat @ M4 @ N2 )
& ~ ( P @ M4 ) ) )
=> ( P @ N ) ) ).
% infinite_descent
thf(fact_1091_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_1092_less__imp__diff__less,axiom,
! [J: nat,K: nat,N: nat] :
( ( ord_less_nat @ J @ K )
=> ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% less_imp_diff_less
thf(fact_1093_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_1094_add__lessD1,axiom,
! [I: nat,J: nat,K: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
=> ( ord_less_nat @ I @ K ) ) ).
% add_lessD1
thf(fact_1095_add__less__mono,axiom,
! [I: nat,J: nat,K: nat,L: nat] :
( ( ord_less_nat @ I @ J )
=> ( ( ord_less_nat @ K @ L )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% add_less_mono
thf(fact_1096_not__add__less1,axiom,
! [I: nat,J: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% not_add_less1
thf(fact_1097_not__add__less2,axiom,
! [J: nat,I: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% not_add_less2
thf(fact_1098_add__less__mono1,axiom,
! [I: nat,J: nat,K: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% add_less_mono1
thf(fact_1099_trans__less__add1,axiom,
! [I: nat,J: nat,M: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% trans_less_add1
thf(fact_1100_trans__less__add2,axiom,
! [I: nat,J: nat,M: nat] :
( ( ord_less_nat @ I @ J )
=> ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% trans_less_add2
thf(fact_1101_less__add__eq__less,axiom,
! [K: nat,L: nat,M: nat,N: nat] :
( ( ord_less_nat @ K @ L )
=> ( ( ( plus_plus_nat @ M @ L )
= ( plus_plus_nat @ K @ N ) )
=> ( ord_less_nat @ M @ N ) ) ) ).
% less_add_eq_less
thf(fact_1102_nat__less__le,axiom,
( ord_less_nat
= ( ^ [M2: nat,N3: nat] :
( ( ord_less_eq_nat @ M2 @ N3 )
& ( M2 != N3 ) ) ) ) ).
% nat_less_le
thf(fact_1103_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_1104_le__eq__less__or__eq,axiom,
( ord_less_eq_nat
= ( ^ [M2: nat,N3: nat] :
( ( ord_less_nat @ M2 @ N3 )
| ( M2 = N3 ) ) ) ) ).
% le_eq_less_or_eq
thf(fact_1105_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_1106_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_1107_less__mono__imp__le__mono,axiom,
! [F: nat > nat,I: nat,J: nat] :
( ! [I2: nat,J4: nat] :
( ( ord_less_nat @ I2 @ J4 )
=> ( ord_less_nat @ ( F @ I2 ) @ ( F @ J4 ) ) )
=> ( ( ord_less_eq_nat @ I @ J )
=> ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% less_mono_imp_le_mono
thf(fact_1108_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_1109_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_1110_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,J4: nat,K3: nat] :
( ( ord_less_nat @ I2 @ J4 )
=> ( ( ord_less_nat @ J4 @ K3 )
=> ( ( P @ I2 @ J4 )
=> ( ( P @ J4 @ K3 )
=> ( P @ I2 @ K3 ) ) ) ) )
=> ( P @ I @ J ) ) ) ) ).
% less_Suc_induct
thf(fact_1111_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_1112_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_1113_less__antisym,axiom,
! [N: nat,M: nat] :
( ~ ( ord_less_nat @ N @ M )
=> ( ( ord_less_nat @ N @ ( suc @ M ) )
=> ( M = N ) ) ) ).
% less_antisym
thf(fact_1114_Suc__less__eq2,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ ( suc @ N ) @ M )
= ( ? [M6: nat] :
( ( M
= ( suc @ M6 ) )
& ( ord_less_nat @ N @ M6 ) ) ) ) ).
% Suc_less_eq2
thf(fact_1115_All__less__Suc,axiom,
! [N: nat,P: nat > $o] :
( ( ! [I6: nat] :
( ( ord_less_nat @ I6 @ ( suc @ N ) )
=> ( P @ I6 ) ) )
= ( ( P @ N )
& ! [I6: nat] :
( ( ord_less_nat @ I6 @ N )
=> ( P @ I6 ) ) ) ) ).
% All_less_Suc
thf(fact_1116_not__less__eq,axiom,
! [M: nat,N: nat] :
( ( ~ ( ord_less_nat @ M @ N ) )
= ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% not_less_eq
thf(fact_1117_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_1118_Ex__less__Suc,axiom,
! [N: nat,P: nat > $o] :
( ( ? [I6: nat] :
( ( ord_less_nat @ I6 @ ( suc @ N ) )
& ( P @ I6 ) ) )
= ( ( P @ N )
| ? [I6: nat] :
( ( ord_less_nat @ I6 @ N )
& ( P @ I6 ) ) ) ) ).
% Ex_less_Suc
thf(fact_1119_less__SucI,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% less_SucI
thf(fact_1120_less__SucE,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
=> ( ~ ( ord_less_nat @ M @ N )
=> ( M = N ) ) ) ).
% less_SucE
thf(fact_1121_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_1122_Suc__lessE,axiom,
! [I: nat,K: nat] :
( ( ord_less_nat @ ( suc @ I ) @ K )
=> ~ ! [J4: nat] :
( ( ord_less_nat @ I @ J4 )
=> ( K
!= ( suc @ J4 ) ) ) ) ).
% Suc_lessE
thf(fact_1123_Suc__lessD,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ ( suc @ M ) @ N )
=> ( ord_less_nat @ M @ N ) ) ).
% Suc_lessD
thf(fact_1124_Nat_OlessE,axiom,
! [I: nat,K: nat] :
( ( ord_less_nat @ I @ K )
=> ( ( K
!= ( suc @ I ) )
=> ~ ! [J4: nat] :
( ( ord_less_nat @ I @ J4 )
=> ( K
!= ( suc @ J4 ) ) ) ) ) ).
% Nat.lessE
thf(fact_1125_infinite__descent0,axiom,
! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ~ ( P @ N2 )
=> ? [M4: nat] :
( ( ord_less_nat @ M4 @ N2 )
& ~ ( P @ M4 ) ) ) )
=> ( P @ N ) ) ) ).
% infinite_descent0
thf(fact_1126_gr__implies__not0,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) ).
% gr_implies_not0
thf(fact_1127_less__zeroE,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% less_zeroE
thf(fact_1128_not__less0,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% not_less0
thf(fact_1129_not__gr0,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) ).
% not_gr0
thf(fact_1130_gr0I,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% gr0I
thf(fact_1131_bot__nat__0_Oextremum__strict,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% bot_nat_0.extremum_strict
thf(fact_1132_Ex__less__Suc2,axiom,
! [N: nat,P: nat > $o] :
( ( ? [I6: nat] :
( ( ord_less_nat @ I6 @ ( suc @ N ) )
& ( P @ I6 ) ) )
= ( ( P @ zero_zero_nat )
| ? [I6: nat] :
( ( ord_less_nat @ I6 @ N )
& ( P @ ( suc @ I6 ) ) ) ) ) ).
% Ex_less_Suc2
thf(fact_1133_gr0__conv__Suc,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( ? [M2: nat] :
( N
= ( suc @ M2 ) ) ) ) ).
% gr0_conv_Suc
thf(fact_1134_All__less__Suc2,axiom,
! [N: nat,P: nat > $o] :
( ( ! [I6: nat] :
( ( ord_less_nat @ I6 @ ( suc @ N ) )
=> ( P @ I6 ) ) )
= ( ( P @ zero_zero_nat )
& ! [I6: nat] :
( ( ord_less_nat @ I6 @ N )
=> ( P @ ( suc @ I6 ) ) ) ) ) ).
% All_less_Suc2
thf(fact_1135_gr0__implies__Suc,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ? [M3: nat] :
( N
= ( suc @ M3 ) ) ) ).
% gr0_implies_Suc
thf(fact_1136_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_1137_ex__least__nat__le,axiom,
! [P: nat > $o,N: nat] :
( ( P @ N )
=> ( ~ ( P @ zero_zero_nat )
=> ? [K3: nat] :
( ( ord_less_eq_nat @ K3 @ N )
& ! [I7: nat] :
( ( ord_less_nat @ I7 @ K3 )
=> ~ ( P @ I7 ) )
& ( P @ K3 ) ) ) ) ).
% ex_least_nat_le
thf(fact_1138_Suc__leI,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% Suc_leI
thf(fact_1139_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_1140_dec__induct,axiom,
! [I: nat,J: nat,P: nat > $o] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( P @ I )
=> ( ! [N2: nat] :
( ( ord_less_eq_nat @ I @ N2 )
=> ( ( ord_less_nat @ N2 @ J )
=> ( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) ) ) )
=> ( P @ J ) ) ) ) ).
% dec_induct
thf(fact_1141_inc__induct,axiom,
! [I: nat,J: nat,P: nat > $o] :
( ( ord_less_eq_nat @ I @ J )
=> ( ( P @ J )
=> ( ! [N2: nat] :
( ( ord_less_eq_nat @ I @ N2 )
=> ( ( ord_less_nat @ N2 @ J )
=> ( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) ) ) )
=> ( P @ I ) ) ) ) ).
% inc_induct
thf(fact_1142_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_1143_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_1144_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_1145_less__eq__Suc__le,axiom,
( ord_less_nat
= ( ^ [N3: nat] : ( ord_less_eq_nat @ ( suc @ N3 ) ) ) ) ).
% less_eq_Suc_le
thf(fact_1146_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_1147_less__imp__add__positive,axiom,
! [I: nat,J: nat] :
( ( ord_less_nat @ I @ J )
=> ? [K3: nat] :
( ( ord_less_nat @ zero_zero_nat @ K3 )
& ( ( plus_plus_nat @ I @ K3 )
= J ) ) ) ).
% less_imp_add_positive
thf(fact_1148_less__natE,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ~ ! [Q: nat] :
( N
!= ( suc @ ( plus_plus_nat @ M @ Q ) ) ) ) ).
% less_natE
thf(fact_1149_less__add__Suc1,axiom,
! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% less_add_Suc1
thf(fact_1150_less__add__Suc2,axiom,
! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% less_add_Suc2
thf(fact_1151_less__iff__Suc__add,axiom,
( ord_less_nat
= ( ^ [M2: nat,N3: nat] :
? [K2: nat] :
( N3
= ( suc @ ( plus_plus_nat @ M2 @ K2 ) ) ) ) ) ).
% less_iff_Suc_add
thf(fact_1152_less__imp__Suc__add,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ? [K3: nat] :
( N
= ( suc @ ( plus_plus_nat @ M @ K3 ) ) ) ) ).
% less_imp_Suc_add
thf(fact_1153_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_1154_diff__less__Suc,axiom,
! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% diff_less_Suc
thf(fact_1155_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_1156_mono__nat__linear__lb,axiom,
! [F: nat > nat,M: nat,K: nat] :
( ! [M3: nat,N2: nat] :
( ( ord_less_nat @ M3 @ N2 )
=> ( ord_less_nat @ ( F @ M3 ) @ ( F @ N2 ) ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% mono_nat_linear_lb
thf(fact_1157_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_1158_less__diff__iff,axiom,
! [K: nat,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ M )
=> ( ( ord_less_eq_nat @ K @ N )
=> ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
= ( ord_less_nat @ M @ N ) ) ) ) ).
% less_diff_iff
thf(fact_1159_int__ops_I3_J,axiom,
! [N: num] :
( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
= ( numeral_numeral_int @ N ) ) ).
% int_ops(3)
thf(fact_1160_add__diff__inverse__nat,axiom,
! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
=> ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
= M ) ) ).
% add_diff_inverse_nat
thf(fact_1161_less__diff__conv,axiom,
! [I: nat,J: nat,K: nat] :
( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
= ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% less_diff_conv
thf(fact_1162_nat__int__comparison_I2_J,axiom,
( ord_less_nat
= ( ^ [A4: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% nat_int_comparison(2)
thf(fact_1163_ex__least__nat__less,axiom,
! [P: nat > $o,N: nat] :
( ( P @ N )
=> ( ~ ( P @ zero_zero_nat )
=> ? [K3: nat] :
( ( ord_less_nat @ K3 @ N )
& ! [I7: nat] :
( ( ord_less_eq_nat @ I7 @ K3 )
=> ~ ( P @ I7 ) )
& ( P @ ( suc @ K3 ) ) ) ) ) ).
% ex_least_nat_less
thf(fact_1164_diff__Suc__less,axiom,
! [N: nat,I: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% diff_Suc_less
thf(fact_1165_nat__diff__split__asm,axiom,
! [P: nat > $o,A: nat,B: nat] :
( ( P @ ( minus_minus_nat @ A @ B ) )
= ( ~ ( ( ( ord_less_nat @ A @ B )
& ~ ( P @ zero_zero_nat ) )
| ? [D2: nat] :
( ( A
= ( plus_plus_nat @ B @ D2 ) )
& ~ ( P @ D2 ) ) ) ) ) ).
% nat_diff_split_asm
thf(fact_1166_nat__diff__split,axiom,
! [P: nat > $o,A: nat,B: nat] :
( ( P @ ( minus_minus_nat @ A @ B ) )
= ( ( ( ord_less_nat @ A @ B )
=> ( P @ zero_zero_nat ) )
& ! [D2: nat] :
( ( A
= ( plus_plus_nat @ B @ D2 ) )
=> ( P @ D2 ) ) ) ) ).
% nat_diff_split
thf(fact_1167_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_1168_less__diff__conv2,axiom,
! [K: nat,J: nat,I: nat] :
( ( ord_less_eq_nat @ K @ J )
=> ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
= ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% less_diff_conv2
thf(fact_1169_add__stack__nnil,axiom,
! [N: nat,Ms3: int > int] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( add_stack @ N @ Ms3 )
!= nil_int ) ) ).
% add_stack_nnil
thf(fact_1170_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_1171_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_1172_zero__less__imp__eq__int,axiom,
! [K: int] :
( ( ord_less_int @ zero_zero_int @ K )
=> ? [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
& ( K
= ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% zero_less_imp_eq_int
thf(fact_1173_pos__int__cases,axiom,
! [K: int] :
( ( ord_less_int @ zero_zero_int @ K )
=> ~ ! [N2: nat] :
( ( K
= ( semiri1314217659103216013at_int @ N2 ) )
=> ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% pos_int_cases
thf(fact_1174_upto__code,axiom,
( upto
= ( ^ [I6: int,J3: int] : ( upto_aux @ I6 @ J3 @ nil_int ) ) ) ).
% upto_code
thf(fact_1175_upto__aux__def,axiom,
( upto_aux
= ( ^ [I6: int,J3: int] : ( append_int @ ( upto @ I6 @ J3 ) ) ) ) ).
% upto_aux_def
thf(fact_1176_zdiff__int__split,axiom,
! [P: int > $o,X: nat,Y: nat] :
( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
= ( ( ( ord_less_eq_nat @ Y @ X )
=> ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
& ( ( ord_less_nat @ X @ Y )
=> ( P @ zero_zero_int ) ) ) ) ).
% zdiff_int_split
thf(fact_1177_execl__next,axiom,
! [P: list_instr,Cfs2: list_P419547167332244514st_int,K: nat] :
( ( execl @ P @ Cfs2 )
=> ( ( ord_less_nat @ K @ ( size_s229347708945616566st_int @ Cfs2 ) )
=> ( ( K
!= ( minus_minus_nat @ ( size_s229347708945616566st_int @ Cfs2 ) @ one_one_nat ) )
=> ( ( iexec_pred @ ( produc1484136438817787418st_int @ ( inth_instr @ P @ ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs2 @ K ) ) ) @ ( nth_Pr8327173284404383691st_int @ Cfs2 @ K ) ) @ ( nth_Pr8327173284404383691st_int @ Cfs2 @ ( suc @ K ) ) )
& ( ord_less_eq_int @ zero_zero_int @ ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs2 @ K ) ) )
& ( ord_less_int @ ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs2 @ K ) ) @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P ) ) ) ) ) ) ) ).
% execl_next
thf(fact_1178_conj__le__cong,axiom,
! [X: int,X7: int,P: $o,P4: $o] :
( ( X = X7 )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
=> ( P = P4 ) )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ X )
& P )
= ( ( ord_less_eq_int @ zero_zero_int @ X7 )
& P4 ) ) ) ) ).
% conj_le_cong
thf(fact_1179_imp__le__cong,axiom,
! [X: int,X7: int,P: $o,P4: $o] :
( ( X = X7 )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
=> ( P = P4 ) )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ X )
=> P )
= ( ( ord_less_eq_int @ zero_zero_int @ X7 )
=> P4 ) ) ) ) ).
% imp_le_cong
thf(fact_1180_exec1__def,axiom,
( exec1
= ( ^ [P5: list_instr,Cf5: produc6425607678544837394st_int,Cf6: produc6425607678544837394st_int] :
( ( iexec_pred @ ( produc1484136438817787418st_int @ ( inth_instr @ P5 @ ( produc8941309049508465880st_int @ Cf5 ) ) @ Cf5 ) @ Cf6 )
& ( ord_less_eq_int @ zero_zero_int @ ( produc8941309049508465880st_int @ Cf5 ) )
& ( ord_less_int @ ( produc8941309049508465880st_int @ Cf5 ) @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P5 ) ) ) ) ) ) ).
% exec1_def
thf(fact_1181_bounded__Max__nat,axiom,
! [P: nat > $o,X: nat,M7: nat] :
( ( P @ X )
=> ( ! [X4: nat] :
( ( P @ X4 )
=> ( ord_less_eq_nat @ X4 @ M7 ) )
=> ~ ! [M3: nat] :
( ( P @ M3 )
=> ~ ! [X8: nat] :
( ( P @ X8 )
=> ( ord_less_eq_nat @ X8 @ M3 ) ) ) ) ) ).
% bounded_Max_nat
thf(fact_1182_execl__last,axiom,
! [P: list_instr,Cfs2: list_P419547167332244514st_int,K: nat] :
( ( execl @ P @ Cfs2 )
=> ( ( ord_less_nat @ K @ ( size_s229347708945616566st_int @ Cfs2 ) )
=> ( ~ ( member_int @ ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs2 @ K ) ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P ) ) ) )
=> ( ( minus_minus_nat @ ( size_s229347708945616566st_int @ Cfs2 ) @ one_one_nat )
= K ) ) ) ) ).
% execl_last
thf(fact_1183_upto__rec__numeral_I4_J,axiom,
! [M: num,N: num] :
( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
=> ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
= ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
& ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
=> ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
= nil_int ) ) ) ).
% upto_rec_numeral(4)
thf(fact_1184_negative__eq__positive,axiom,
! [N: nat,M: nat] :
( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
= ( semiri1314217659103216013at_int @ M ) )
= ( ( N = zero_zero_nat )
& ( M = zero_zero_nat ) ) ) ).
% negative_eq_positive
thf(fact_1185_negative__zle,axiom,
! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% negative_zle
thf(fact_1186_negative__zless,axiom,
! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% negative_zless
thf(fact_1187_upto__rec__numeral_I2_J,axiom,
! [M: num,N: num] :
( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
=> ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
= ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
& ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
=> ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
= nil_int ) ) ) ).
% upto_rec_numeral(2)
thf(fact_1188_upto__rec__numeral_I3_J,axiom,
! [M: num,N: num] :
( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
=> ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
= ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
& ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
=> ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
= nil_int ) ) ) ).
% upto_rec_numeral(3)
thf(fact_1189_add__stack__eq,axiom,
! [M: nat,Ms4: int > int,Ms3: int > int,N: nat] :
( ! [X4: int] :
( ( member_int @ X4 @ ( set_or4662586982721622107an_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) @ zero_zero_int ) )
=> ( ( Ms4 @ X4 )
= ( Ms3 @ X4 ) ) )
=> ( ( M = N )
=> ( ( add_stack @ M @ Ms4 )
= ( add_stack @ N @ Ms3 ) ) ) ) ).
% add_stack_eq
thf(fact_1190_int__cases2,axiom,
! [Z: int] :
( ! [N2: nat] :
( Z
!= ( semiri1314217659103216013at_int @ N2 ) )
=> ~ ! [N2: nat] :
( Z
!= ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% int_cases2
thf(fact_1191_uminus__int__code_I1_J,axiom,
( ( uminus_uminus_int @ zero_zero_int )
= zero_zero_int ) ).
% uminus_int_code(1)
thf(fact_1192_minus__int__code_I2_J,axiom,
! [L: int] :
( ( minus_minus_int @ zero_zero_int @ L )
= ( uminus_uminus_int @ L ) ) ).
% minus_int_code(2)
thf(fact_1193_not__int__zless__negative,axiom,
! [N: nat,M: nat] :
~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% not_int_zless_negative
thf(fact_1194_int__cases,axiom,
! [Z: int] :
( ! [N2: nat] :
( Z
!= ( semiri1314217659103216013at_int @ N2 ) )
=> ~ ! [N2: nat] :
( Z
!= ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% int_cases
thf(fact_1195_int__of__nat__induct,axiom,
! [P: int > $o,Z: int] :
( ! [N2: nat] : ( P @ ( semiri1314217659103216013at_int @ N2 ) )
=> ( ! [N2: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) )
=> ( P @ Z ) ) ) ).
% int_of_nat_induct
thf(fact_1196_int__cases4,axiom,
! [M: int] :
( ! [N2: nat] :
( M
!= ( semiri1314217659103216013at_int @ N2 ) )
=> ~ ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( M
!= ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% int_cases4
thf(fact_1197_int__zle__neg,axiom,
! [N: nat,M: nat] :
( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
= ( ( N = zero_zero_nat )
& ( M = zero_zero_nat ) ) ) ).
% int_zle_neg
thf(fact_1198_nonpos__int__cases,axiom,
! [K: int] :
( ( ord_less_eq_int @ K @ zero_zero_int )
=> ~ ! [N2: nat] :
( K
!= ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% nonpos_int_cases
thf(fact_1199_negative__zle__0,axiom,
! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% negative_zle_0
thf(fact_1200_add__stack__eq2,axiom,
! [N: nat,Ms4: int > int,I: int,Ms3: int > int] :
( ! [X4: int] :
( ( member_int @ X4 @ ( set_or4662586982721622107an_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) )
=> ( ( ( X4
= ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
=> ( ( Ms4 @ X4 )
= I ) )
& ( ( X4
!= ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
=> ( ( Ms4 @ X4 )
= ( Ms3 @ X4 ) ) ) ) )
=> ( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( add_stack @ N @ Ms4 )
= ( cons_int @ I @ ( add_stack @ ( minus_minus_nat @ N @ one_one_nat ) @ Ms3 ) ) ) ) ) ).
% add_stack_eq2
thf(fact_1201_int__cases3,axiom,
! [K: int] :
( ( K != zero_zero_int )
=> ( ! [N2: nat] :
( ( K
= ( semiri1314217659103216013at_int @ N2 ) )
=> ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
=> ~ ! [N2: nat] :
( ( K
= ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
=> ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% int_cases3
thf(fact_1202_not__zle__0__negative,axiom,
! [N: nat] :
~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% not_zle_0_negative
thf(fact_1203_negative__zless__0,axiom,
! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% negative_zless_0
thf(fact_1204_negD,axiom,
! [X: int] :
( ( ord_less_int @ X @ zero_zero_int )
=> ? [N2: nat] :
( X
= ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% negD
thf(fact_1205_add__stack_Osimps_I2_J,axiom,
! [N: nat,Ms3: int > int] :
( ( add_stack @ ( suc @ N ) @ Ms3 )
= ( cons_int @ ( Ms3 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) @ ( add_stack @ N @ Ms3 ) ) ) ).
% add_stack.simps(2)
thf(fact_1206_neg__int__cases,axiom,
! [K: int] :
( ( ord_less_int @ K @ zero_zero_int )
=> ~ ! [N2: nat] :
( ( K
= ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
=> ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% neg_int_cases
thf(fact_1207_execl__all__def,axiom,
( execl_all
= ( ^ [P5: list_instr,Cfs3: list_P419547167332244514st_int] :
( ( execl @ P5 @ Cfs3 )
& ( Cfs3 != nil_Pr749310521696113548st_int )
& ( ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs3 @ zero_zero_nat ) )
= zero_zero_int )
& ~ ( member_int @ ( produc8941309049508465880st_int @ ( nth_Pr8327173284404383691st_int @ Cfs3 @ ( minus_minus_nat @ ( size_s229347708945616566st_int @ Cfs3 ) @ one_one_nat ) ) ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P5 ) ) ) ) ) ) ) ).
% execl_all_def
thf(fact_1208_ex__nat__less__eq,axiom,
! [N: nat,P: nat > $o] :
( ( ? [M2: nat] :
( ( ord_less_nat @ M2 @ N )
& ( P @ M2 ) ) )
= ( ? [X3: nat] :
( ( member_nat @ X3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
& ( P @ X3 ) ) ) ) ).
% ex_nat_less_eq
thf(fact_1209_all__nat__less__eq,axiom,
! [N: nat,P: nat > $o] :
( ( ! [M2: nat] :
( ( ord_less_nat @ M2 @ N )
=> ( P @ M2 ) ) )
= ( ! [X3: nat] :
( ( member_nat @ X3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
=> ( P @ X3 ) ) ) ) ).
% all_nat_less_eq
thf(fact_1210_m__config__equiv_Osimps,axiom,
! [I: int,Ms3: int > int,Sp3: nat,I4: int,Ms4: int > int,Sp4: nat] :
( ( m_config_equiv @ ( produc8342123264692915235nt_nat @ I @ ( produc2630796075472406112nt_nat @ Ms3 @ Sp3 ) ) @ ( produc8342123264692915235nt_nat @ I4 @ ( produc2630796075472406112nt_nat @ Ms4 @ Sp4 ) ) )
= ( ( I = I4 )
& ( Sp3 = Sp4 )
& ! [A4: int] :
( ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ Sp3 ) ) @ A4 )
=> ( ( Ms3 @ A4 )
= ( Ms4 @ A4 ) ) ) ) ) ).
% m_config_equiv.simps
thf(fact_1211_m__exec1__def,axiom,
( m_exec1
= ( ^ [MP: list_m_instr,Mcf: produc1019184382078353393nt_nat,Mcf2: produc1019184382078353393nt_nat] :
( ( m_config_equiv @ Mcf2 @ ( m_iexec @ ( inth_m_instr @ MP @ ( produc2827224793399753527nt_nat @ Mcf ) ) @ Mcf ) )
& ( ord_less_eq_int @ zero_zero_int @ ( produc2827224793399753527nt_nat @ Mcf ) )
& ( ord_less_int @ ( produc2827224793399753527nt_nat @ Mcf ) @ ( semiri1314217659103216013at_int @ ( size_s5914166952900237872_instr @ MP ) ) )
& ( ord_less_eq_nat @ ( m_msp @ ( inth_m_instr @ MP @ ( produc2827224793399753527nt_nat @ Mcf ) ) ) @ ( produc4411376485632109966nt_nat @ ( produc2259646285430092661nt_nat @ Mcf ) ) ) ) ) ) ).
% m_exec1_def
thf(fact_1212_add__m__stack__nth,axiom,
! [N: nat,A: int,Stk: list_int,Ms3: int > int] :
( ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ A )
=> ( ( ord_less_eq_nat @ N @ ( size_size_list_int @ Stk ) )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( add_m_stack @ N @ Stk @ Ms3 @ A )
= ( Ms3 @ A ) ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ A )
=> ( ( add_m_stack @ N @ Stk @ Ms3 @ A )
= ( nth_int @ Stk @ ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ A ) ) ) ) ) ) ) ) ).
% add_m_stack_nth
thf(fact_1213_nat__int,axiom,
! [N: nat] :
( ( nat2 @ ( semiri1314217659103216013at_int @ N ) )
= N ) ).
% nat_int
thf(fact_1214_nat__numeral,axiom,
! [K: num] :
( ( nat2 @ ( numeral_numeral_int @ K ) )
= ( numeral_numeral_nat @ K ) ) ).
% nat_numeral
thf(fact_1215_nat__1,axiom,
( ( nat2 @ one_one_int )
= ( suc @ zero_zero_nat ) ) ).
% nat_1
thf(fact_1216_nat__0__iff,axiom,
! [I: int] :
( ( ( nat2 @ I )
= zero_zero_nat )
= ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% nat_0_iff
thf(fact_1217_nat__le__0,axiom,
! [Z: int] :
( ( ord_less_eq_int @ Z @ zero_zero_int )
=> ( ( nat2 @ Z )
= zero_zero_nat ) ) ).
% nat_le_0
thf(fact_1218_zless__nat__conj,axiom,
! [W2: int,Z: int] :
( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
= ( ( ord_less_int @ zero_zero_int @ Z )
& ( ord_less_int @ W2 @ Z ) ) ) ).
% zless_nat_conj
thf(fact_1219_nat__neg__numeral,axiom,
! [K: num] :
( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
= zero_zero_nat ) ).
% nat_neg_numeral
thf(fact_1220_nat__zminus__int,axiom,
! [N: nat] :
( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
= zero_zero_nat ) ).
% nat_zminus_int
thf(fact_1221_int__nat__eq,axiom,
! [Z: int] :
( ( ( ord_less_eq_int @ zero_zero_int @ Z )
=> ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
= Z ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
=> ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
= zero_zero_int ) ) ) ).
% int_nat_eq
thf(fact_1222_zero__less__nat__eq,axiom,
! [Z: int] :
( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
= ( ord_less_int @ zero_zero_int @ Z ) ) ).
% zero_less_nat_eq
thf(fact_1223_diff__nat__numeral,axiom,
! [V2: num,V3: num] :
( ( minus_minus_nat @ ( numeral_numeral_nat @ V2 ) @ ( numeral_numeral_nat @ V3 ) )
= ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% diff_nat_numeral
thf(fact_1224_one__less__nat__eq,axiom,
! [Z: int] :
( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
= ( ord_less_int @ one_one_int @ Z ) ) ).
% one_less_nat_eq
thf(fact_1225_length__upto,axiom,
! [I: int,J: int] :
( ( size_size_list_int @ ( upto @ I @ J ) )
= ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% length_upto
thf(fact_1226_nat__numeral__diff__1,axiom,
! [V2: num] :
( ( minus_minus_nat @ ( numeral_numeral_nat @ V2 ) @ one_one_nat )
= ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V2 ) @ one_one_int ) ) ) ).
% nat_numeral_diff_1
thf(fact_1227_nat__zero__as__int,axiom,
( zero_zero_nat
= ( nat2 @ zero_zero_int ) ) ).
% nat_zero_as_int
thf(fact_1228_nat__numeral__as__int,axiom,
( numeral_numeral_nat
= ( ^ [I6: num] : ( nat2 @ ( numeral_numeral_int @ I6 ) ) ) ) ).
% nat_numeral_as_int
thf(fact_1229_nat__one__as__int,axiom,
( one_one_nat
= ( nat2 @ one_one_int ) ) ).
% nat_one_as_int
thf(fact_1230_int__minus,axiom,
! [N: nat,M: nat] :
( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M ) )
= ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% int_minus
thf(fact_1231_nat__int__add,axiom,
! [A: nat,B: nat] :
( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
= ( plus_plus_nat @ A @ B ) ) ).
% nat_int_add
thf(fact_1232_int__eq__iff,axiom,
! [M: nat,Z: int] :
( ( ( semiri1314217659103216013at_int @ M )
= Z )
= ( ( M
= ( nat2 @ Z ) )
& ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% int_eq_iff
thf(fact_1233_nat__0__le,axiom,
! [Z: int] :
( ( ord_less_eq_int @ zero_zero_int @ Z )
=> ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
= Z ) ) ).
% nat_0_le
thf(fact_1234_nat__le__iff,axiom,
! [X: int,N: nat] :
( ( ord_less_eq_nat @ ( nat2 @ X ) @ N )
= ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% nat_le_iff
thf(fact_1235_zless__nat__eq__int__zless,axiom,
! [M: nat,Z: int] :
( ( ord_less_nat @ M @ ( nat2 @ Z ) )
= ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% zless_nat_eq_int_zless
thf(fact_1236_nat__mono__iff,axiom,
! [Z: int,W2: int] :
( ( ord_less_int @ zero_zero_int @ Z )
=> ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
= ( ord_less_int @ W2 @ Z ) ) ) ).
% nat_mono_iff
thf(fact_1237_ex__nat,axiom,
( ( ^ [P6: nat > $o] :
? [X6: nat] : ( P6 @ X6 ) )
= ( ^ [P5: nat > $o] :
? [X3: int] :
( ( ord_less_eq_int @ zero_zero_int @ X3 )
& ( P5 @ ( nat2 @ X3 ) ) ) ) ) ).
% ex_nat
thf(fact_1238_all__nat,axiom,
( ( ^ [P6: nat > $o] :
! [X6: nat] : ( P6 @ X6 ) )
= ( ^ [P5: nat > $o] :
! [X3: int] :
( ( ord_less_eq_int @ zero_zero_int @ X3 )
=> ( P5 @ ( nat2 @ X3 ) ) ) ) ) ).
% all_nat
thf(fact_1239_eq__nat__nat__iff,axiom,
! [Z: int,Z5: int] :
( ( ord_less_eq_int @ zero_zero_int @ Z )
=> ( ( ord_less_eq_int @ zero_zero_int @ Z5 )
=> ( ( ( nat2 @ Z )
= ( nat2 @ Z5 ) )
= ( Z = Z5 ) ) ) ) ).
% eq_nat_nat_iff
thf(fact_1240_nat__mono,axiom,
! [X: int,Y: int] :
( ( ord_less_eq_int @ X @ Y )
=> ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).
% nat_mono
thf(fact_1241_nat__eq__iff,axiom,
! [W2: int,M: nat] :
( ( ( nat2 @ W2 )
= M )
= ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
=> ( W2
= ( semiri1314217659103216013at_int @ M ) ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
=> ( M = zero_zero_nat ) ) ) ) ).
% nat_eq_iff
thf(fact_1242_nat__eq__iff2,axiom,
! [M: nat,W2: int] :
( ( M
= ( nat2 @ W2 ) )
= ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
=> ( W2
= ( semiri1314217659103216013at_int @ M ) ) )
& ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
=> ( M = zero_zero_nat ) ) ) ) ).
% nat_eq_iff2
thf(fact_1243_split__nat,axiom,
! [P: nat > $o,I: int] :
( ( P @ ( nat2 @ I ) )
= ( ! [N3: nat] :
( ( I
= ( semiri1314217659103216013at_int @ N3 ) )
=> ( P @ N3 ) )
& ( ( ord_less_int @ I @ zero_zero_int )
=> ( P @ zero_zero_nat ) ) ) ) ).
% split_nat
thf(fact_1244_nat__less__eq__zless,axiom,
! [W2: int,Z: int] :
( ( ord_less_eq_int @ zero_zero_int @ W2 )
=> ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
= ( ord_less_int @ W2 @ Z ) ) ) ).
% nat_less_eq_zless
thf(fact_1245_le__nat__iff,axiom,
! [K: int,N: nat] :
( ( ord_less_eq_int @ zero_zero_int @ K )
=> ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
= ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% le_nat_iff
thf(fact_1246_nat__le__eq__zle,axiom,
! [W2: int,Z: int] :
( ( ( ord_less_int @ zero_zero_int @ W2 )
| ( ord_less_eq_int @ zero_zero_int @ Z ) )
=> ( ( ord_less_eq_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
= ( ord_less_eq_int @ W2 @ Z ) ) ) ).
% nat_le_eq_zle
thf(fact_1247_nat__add__distrib,axiom,
! [Z: int,Z5: int] :
( ( ord_less_eq_int @ zero_zero_int @ Z )
=> ( ( ord_less_eq_int @ zero_zero_int @ Z5 )
=> ( ( nat2 @ ( plus_plus_int @ Z @ Z5 ) )
= ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) ) ) ) ) ).
% nat_add_distrib
thf(fact_1248_Suc__as__int,axiom,
( suc
= ( ^ [A4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ one_one_int ) ) ) ) ).
% Suc_as_int
thf(fact_1249_nat__diff__distrib_H,axiom,
! [X: int,Y: int] :
( ( ord_less_eq_int @ zero_zero_int @ X )
=> ( ( ord_less_eq_int @ zero_zero_int @ Y )
=> ( ( nat2 @ ( minus_minus_int @ X @ Y ) )
= ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% nat_diff_distrib'
thf(fact_1250_nat__diff__distrib,axiom,
! [Z5: int,Z: int] :
( ( ord_less_eq_int @ zero_zero_int @ Z5 )
=> ( ( ord_less_eq_int @ Z5 @ Z )
=> ( ( nat2 @ ( minus_minus_int @ Z @ Z5 ) )
= ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) ) ) ) ) ).
% nat_diff_distrib
thf(fact_1251_Suc__nat__eq__nat__zadd1,axiom,
! [Z: int] :
( ( ord_less_eq_int @ zero_zero_int @ Z )
=> ( ( suc @ ( nat2 @ Z ) )
= ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% Suc_nat_eq_nat_zadd1
thf(fact_1252_nat__less__iff,axiom,
! [W2: int,M: nat] :
( ( ord_less_eq_int @ zero_zero_int @ W2 )
=> ( ( ord_less_nat @ ( nat2 @ W2 ) @ M )
= ( ord_less_int @ W2 @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% nat_less_iff
thf(fact_1253_mpred__drop,axiom,
! [K: nat,Cfs2: list_P419547167332244514st_int,P: list_instr,M: nat,N: nat] :
( ( ord_less_eq_nat @ K @ ( size_s229347708945616566st_int @ Cfs2 ) )
=> ( ( ord_less_eq_nat @ ( size_size_list_int @ ( produc6244060863719409455st_int @ ( produc1296517004818028822st_int @ ( nth_Pr8327173284404383691st_int @ Cfs2 @ zero_zero_nat ) ) ) ) @ ( size_size_list_int @ ( produc6244060863719409455st_int @ ( produc1296517004818028822st_int @ ( nth_Pr8327173284404383691st_int @ Cfs2 @ K ) ) ) ) )
=> ( ( mpred @ P @ ( drop_P7838799151754935884st_int @ K @ Cfs2 ) @ M @ N )
=> ( mpred @ P @ Cfs2 @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) ) ) ) ) ).
% mpred_drop
thf(fact_1254_vars__load,axiom,
! [I: int,P: list_instr,X: list_char] :
( ( ord_less_eq_int @ zero_zero_int @ I )
=> ( ( ord_less_int @ I @ ( semiri1314217659103216013at_int @ ( size_size_list_instr @ P ) ) )
=> ( ( ( inth_instr @ P @ I )
= ( load @ X ) )
=> ( member_list_char @ X @ ( set_list_char2 @ ( vars @ P ) ) ) ) ) ) ).
% vars_load
thf(fact_1255_execl__drop,axiom,
! [P: list_instr,Cfs2: list_P419547167332244514st_int,N: nat] :
( ( execl @ P @ Cfs2 )
=> ( execl @ P @ ( drop_P7838799151754935884st_int @ N @ Cfs2 ) ) ) ).
% execl_drop
% Helper facts (7)
thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
! [X: int,Y: int] :
( ( if_int @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
! [X: int,Y: int] :
( ( if_int @ $true @ X @ Y )
= X ) ).
thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
! [X: nat,Y: nat] :
( ( if_nat @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
! [X: nat,Y: nat] :
( ( if_nat @ $true @ X @ Y )
= X ) ).
thf(help_If_3_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ) ).
thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
! [X: list_int,Y: list_int] :
( ( if_list_int @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
! [X: list_int,Y: list_int] :
( ( if_list_int @ $true @ X @ Y )
= X ) ).
% Conjectures (1)
thf(conj_0,conjecture,
star_P5461765526710342210nt_nat @ ( m_exec1 @ ( to_m_prog @ p ) ) @ ( produc8342123264692915235nt_nat @ pc3 @ ( produc2630796075472406112nt_nat @ ( to_m_state @ ( vars @ p ) @ s3 ) @ zero_zero_nat ) ) @ ( produc8342123264692915235nt_nat @ pc @ ( produc2630796075472406112nt_nat @ ( add_m_stack @ ( minus_minus_nat @ ( size_size_list_int @ stk ) @ ( size_size_list_int @ stk3 ) ) @ stk @ ( to_m_state @ ( vars @ p ) @ s ) ) @ ( minus_minus_nat @ ( size_size_list_int @ stk ) @ ( size_size_list_int @ stk3 ) ) ) ) ).
%------------------------------------------------------------------------------