TPTP Problem File: ITP172^1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP172^1 : TPTP v8.2.0. Released v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : Sledgehammer ShadowRootMonad problem prob_623__5857930_1
% Version : Especial.
% English :
% Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% Source : [Des21]
% Names : ShadowRootMonad/prob_623__5857930_1 [Des21]
% Status : Theorem
% Rating : 0.20 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0
% Syntax : Number of formulae : 475 ( 219 unt; 132 typ; 0 def)
% Number of atoms : 716 ( 702 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 2795 ( 147 ~; 12 |; 51 &;2133 @)
% ( 0 <=>; 452 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 6 avg)
% Number of types : 26 ( 25 usr)
% Number of type conns : 402 ( 402 >; 0 *; 0 +; 0 <<)
% Number of symbols : 108 ( 107 usr; 16 con; 0-5 aty)
% Number of variables : 1120 ( 18 ^;1075 !; 27 ?;1120 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Sledgehammer 2021-02-23 15:33:17.461
%------------------------------------------------------------------------------
% Could-be-implicit typings (25)
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% Explicit typings (107)
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thf(sy_c_Option_Ooption_Osize__option_001t__DocumentPointer__Odocument____ptr_It__Sum____Type__Osum_It__ShadowRootPointer__Oshadow____root____ptr_Itf__d_J_Mtf__e_J_J,type,
size_o1635055885tr_d_e: ( docume1935157360tr_d_e > nat ) > option1330818496tr_d_e > nat ).
thf(sy_c_Option_Ooption_Osize__option_001t__ElementPointer__Oelement____ptr_Itf__a_J,type,
size_o1591053974_ptr_a: ( element_ptr_a > nat ) > option_element_ptr_a > nat ).
thf(sy_c_Option_Ooption_Osize__option_001t__ObjectClass__ORObject__ORObject____ext_It__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J_J,type,
size_o26122489on_j_k: ( rObjec1617416918on_j_k > nat ) > option841825948on_j_k > nat ).
thf(sy_c_Option_Ooption_Osize__option_001t__ObjectClass__ORObject__ORObject____ext_It__Sum____Type__Osum_It__NodeClass__ORNode__ORNode____ext_It__Sum____Type__Osum_It__ElementClass__ORElement__ORElement____ext_Itf__c_Mtf__a_Mtf__b_Mtf__d_Mt__Option__Ooption_Itf__g_J_J_Mt__Sum____Type__Osum_It__CharacterDataClass__ORCharacterData__ORCharacterData____ext_It__Option__Ooption_Itf__h_J_J_Mtf__i_J_J_J_Mt__Sum____Type__Osum_It__DocumentClass__ORDocument__ORDocument____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_It__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J_J_J_Mtf__l_J_J_J,type,
size_o310046708_j_k_l: ( rObjec1413572695_j_k_l > nat ) > option1749760295_j_k_l > nat ).
thf(sy_c_Option_Ooption_Osize__option_001t__Sum____Type__Osum_It__ShadowRootClass__ORShadowRoot__ORShadowRoot____ext_Itf__c_Mtf__a_Mtf__b_Mt__Option__Ooption_Itf__j_J_J_Mtf__k_J,type,
size_o1777465779on_j_k: ( sum_su1221287958on_j_k > nat ) > option2026120038on_j_k > nat ).
thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__DocumentPointer__Odocument____ptr_It__Sum____Type__Osum_It__ShadowRootPointer__Oshadow____root____ptr_Itf__d_J_Mtf__e_J_J_J,type,
bot_bo1111241908tr_d_e: fset_d1663890464tr_d_e ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
bot_bot_nat: nat ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
bot_bot_set_nat: set_nat ).
thf(sy_c_Product__Type_OUnity,type,
product_Unity: product_unit ).
thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(sy_c_ShadowRootClass_Otype__wf_001tf__a_001tf__b_001tf__c_001tf__d_001tf__e_001tf__f_001tf__g_001tf__h_001tf__i_001tf__j_001tf__k_001tf__l,type,
type_w92696601_j_k_l: heap_S1465075775_j_k_l > $o ).
thf(sy_c_member_001t__Nat__Onat,type,
member_nat: nat > set_nat > $o ).
thf(sy_v_h,type,
h: heap_S1465075775_j_k_l ).
thf(sy_v_h_H,type,
h2: heap_S1465075775_j_k_l ).
% Relevant facts (339)
thf(fact_0_cast_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t__inject,axiom,
! [X: rObjec1617416918on_j_k,Y: rObjec1617416918on_j_k] :
( ( ( cast_D1252964113_h_i_l @ X )
= ( cast_D1252964113_h_i_l @ Y ) )
= ( X = Y ) ) ).
% cast\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_inject
thf(fact_1_cast_092_060_094sub_062d_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r_092_060_094sub_0622_092_060_094sub_062o_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r__inject,axiom,
! [X: docume1935157360tr_d_e,Y: docume1935157360tr_d_e] :
( ( ( cast_d1608273229_b_c_f @ X )
= ( cast_d1608273229_b_c_f @ Y ) )
= ( X = Y ) ) ).
% cast\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_inject
thf(fact_2_document__ptr_Oinject_I1_J,axiom,
! [X1: nat,Y1: nat] :
( ( ( docume1511108976tr_d_e @ X1 )
= ( docume1511108976tr_d_e @ Y1 ) )
= ( X1 = Y1 ) ) ).
% document_ptr.inject(1)
thf(fact_3_RDocument_Oext__inject,axiom,
! [Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k,Nothinga2: product_unit,Doctype2: list_char,Document_element2: option_element_ptr_a,Disconnected_nodes2: list_n282880152tr_b_c,More2: option2026120038on_j_k] :
( ( ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More )
= ( rDocum427676485on_j_k @ Nothinga2 @ Doctype2 @ Document_element2 @ Disconnected_nodes2 @ More2 ) )
= ( ( Nothinga = Nothinga2 )
& ( Doctype = Doctype2 )
& ( Document_element = Document_element2 )
& ( Disconnected_nodes = Disconnected_nodes2 )
& ( More = More2 ) ) ) ).
% RDocument.ext_inject
thf(fact_4_RObject_Oext__inject,axiom,
! [Nothing: product_unit,More: rDocum326988203on_j_k,Nothing2: product_unit,More2: rDocum326988203on_j_k] :
( ( ( rObjec1303043984on_j_k @ Nothing @ More )
= ( rObjec1303043984on_j_k @ Nothing2 @ More2 ) )
= ( ( Nothing = Nothing2 )
& ( More = More2 ) ) ) ).
% RObject.ext_inject
thf(fact_5_RObject_Oext__inject,axiom,
! [Nothing: product_unit,More: product_unit,Nothing2: product_unit,More2: product_unit] :
( ( ( rObjec730108904t_unit @ Nothing @ More )
= ( rObjec730108904t_unit @ Nothing2 @ More2 ) )
= ( ( Nothing = Nothing2 )
& ( More = More2 ) ) ) ).
% RObject.ext_inject
thf(fact_6_nat_Oinject,axiom,
! [X2: nat,Y2: nat] :
( ( ( suc @ X2 )
= ( suc @ Y2 ) )
= ( X2 = Y2 ) ) ).
% nat.inject
thf(fact_7_old_Onat_Oinject,axiom,
! [Nat: nat,Nat2: nat] :
( ( ( suc @ Nat )
= ( suc @ Nat2 ) )
= ( Nat = Nat2 ) ) ).
% old.nat.inject
thf(fact_8_RDocument_Ocases__scheme,axiom,
! [R: rObjec1617416918on_j_k] :
~ ! [Nothing3: product_unit,Nothinga3: product_unit,Doctype3: list_char,Document_element3: option_element_ptr_a,Disconnected_nodes3: list_n282880152tr_b_c,More3: option2026120038on_j_k] :
( R
!= ( rObjec1303043984on_j_k @ Nothing3 @ ( rDocum427676485on_j_k @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ More3 ) ) ) ).
% RDocument.cases_scheme
thf(fact_9_RDocument_Oinduct__scheme,axiom,
! [P: rObjec1617416918on_j_k > $o,R: rObjec1617416918on_j_k] :
( ! [Nothing3: product_unit,Nothinga3: product_unit,Doctype3: list_char,Document_element3: option_element_ptr_a,Disconnected_nodes3: list_n282880152tr_b_c,More3: option2026120038on_j_k] : ( P @ ( rObjec1303043984on_j_k @ Nothing3 @ ( rDocum427676485on_j_k @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ More3 ) ) )
=> ( P @ R ) ) ).
% RDocument.induct_scheme
thf(fact_10_bot__nat__def,axiom,
bot_bot_nat = zero_zero_nat ).
% bot_nat_def
thf(fact_11_RObject_Oinduct,axiom,
! [P: rObjec103300152t_unit > $o,R: rObjec103300152t_unit] :
( ! [Nothing3: product_unit] : ( P @ ( rObjec730108904t_unit @ Nothing3 @ product_Unity ) )
=> ( P @ R ) ) ).
% RObject.induct
thf(fact_12_RObject_Ocases,axiom,
! [R: rObjec103300152t_unit] :
~ ! [Nothing3: product_unit] :
( R
!= ( rObjec730108904t_unit @ Nothing3 @ product_Unity ) ) ).
% RObject.cases
thf(fact_13_zero__reorient,axiom,
! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ) ).
% zero_reorient
thf(fact_14_n__not__Suc__n,axiom,
! [N: nat] :
( N
!= ( suc @ N ) ) ).
% n_not_Suc_n
thf(fact_15_Suc__inject,axiom,
! [X: nat,Y: nat] :
( ( ( suc @ X )
= ( suc @ Y ) )
=> ( X = Y ) ) ).
% Suc_inject
thf(fact_16_RObject_Oinduct__scheme,axiom,
! [P: rObjec1617416918on_j_k > $o,R: rObjec1617416918on_j_k] :
( ! [Nothing3: product_unit,More3: rDocum326988203on_j_k] : ( P @ ( rObjec1303043984on_j_k @ Nothing3 @ More3 ) )
=> ( P @ R ) ) ).
% RObject.induct_scheme
thf(fact_17_RObject_Oinduct__scheme,axiom,
! [P: rObjec103300152t_unit > $o,R: rObjec103300152t_unit] :
( ! [Nothing3: product_unit,More3: product_unit] : ( P @ ( rObjec730108904t_unit @ Nothing3 @ More3 ) )
=> ( P @ R ) ) ).
% RObject.induct_scheme
thf(fact_18_RObject_Ocases__scheme,axiom,
! [R: rObjec1617416918on_j_k] :
~ ! [Nothing3: product_unit,More3: rDocum326988203on_j_k] :
( R
!= ( rObjec1303043984on_j_k @ Nothing3 @ More3 ) ) ).
% RObject.cases_scheme
thf(fact_19_RObject_Ocases__scheme,axiom,
! [R: rObjec103300152t_unit] :
~ ! [Nothing3: product_unit,More3: product_unit] :
( R
!= ( rObjec730108904t_unit @ Nothing3 @ More3 ) ) ).
% RObject.cases_scheme
thf(fact_20_RDocument_Oext__induct,axiom,
! [P: rDocum326988203on_j_k > $o,R: rDocum326988203on_j_k] :
( ! [Nothinga3: product_unit,Doctype3: list_char,Document_element3: option_element_ptr_a,Disconnected_nodes3: list_n282880152tr_b_c,More3: option2026120038on_j_k] : ( P @ ( rDocum427676485on_j_k @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ More3 ) )
=> ( P @ R ) ) ).
% RDocument.ext_induct
thf(fact_21_not0__implies__Suc,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ? [M: nat] :
( N
= ( suc @ M ) ) ) ).
% not0_implies_Suc
thf(fact_22_old_Onat_Oinducts,axiom,
! [P: nat > $o,Nat: nat] :
( ( P @ zero_zero_nat )
=> ( ! [Nat3: nat] :
( ( P @ Nat3 )
=> ( P @ ( suc @ Nat3 ) ) )
=> ( P @ Nat ) ) ) ).
% old.nat.inducts
thf(fact_23_old_Onat_Oexhaust,axiom,
! [Y: nat] :
( ( Y != zero_zero_nat )
=> ~ ! [Nat3: nat] :
( Y
!= ( suc @ Nat3 ) ) ) ).
% old.nat.exhaust
thf(fact_24_Zero__not__Suc,axiom,
! [M2: nat] :
( zero_zero_nat
!= ( suc @ M2 ) ) ).
% Zero_not_Suc
thf(fact_25_Zero__neq__Suc,axiom,
! [M2: nat] :
( zero_zero_nat
!= ( suc @ M2 ) ) ).
% Zero_neq_Suc
thf(fact_26_Suc__neq__Zero,axiom,
! [M2: nat] :
( ( suc @ M2 )
!= zero_zero_nat ) ).
% Suc_neq_Zero
thf(fact_27_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_28_diff__induct,axiom,
! [P: nat > nat > $o,M2: nat,N: nat] :
( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
=> ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
=> ( ! [X3: nat,Y3: nat] :
( ( P @ X3 @ Y3 )
=> ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
=> ( P @ M2 @ N ) ) ) ) ).
% diff_induct
thf(fact_29_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_30_nat_OdiscI,axiom,
! [Nat: nat,X2: nat] :
( ( Nat
= ( suc @ X2 ) )
=> ( Nat != zero_zero_nat ) ) ).
% nat.discI
thf(fact_31_old_Onat_Odistinct_I1_J,axiom,
! [Nat2: nat] :
( zero_zero_nat
!= ( suc @ Nat2 ) ) ).
% old.nat.distinct(1)
thf(fact_32_old_Onat_Odistinct_I2_J,axiom,
! [Nat2: nat] :
( ( suc @ Nat2 )
!= zero_zero_nat ) ).
% old.nat.distinct(2)
thf(fact_33_nat_Odistinct_I1_J,axiom,
! [X2: nat] :
( zero_zero_nat
!= ( suc @ X2 ) ) ).
% nat.distinct(1)
thf(fact_34_document__ptr_Osize__gen_I1_J,axiom,
! [X: sum_su1576157353tr_d_e > nat,X1: nat] :
( ( docume1799427087tr_d_e @ X @ ( docume1511108976tr_d_e @ X1 ) )
= ( suc @ zero_zero_nat ) ) ).
% document_ptr.size_gen(1)
thf(fact_35_document__ptr_Osize_I3_J,axiom,
! [X1: nat] :
( ( size_s724035844tr_d_e @ ( docume1511108976tr_d_e @ X1 ) )
= ( suc @ zero_zero_nat ) ) ).
% document_ptr.size(3)
thf(fact_36_put_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__def,axiom,
( put_D_2126422573_h_i_l
= ( ^ [Document_ptr: docume1935157360tr_d_e,Document: rObjec1617416918on_j_k] : ( put_O_834343516_j_k_l @ ( cast_d1608273229_b_c_f @ Document_ptr ) @ ( cast_D1252964113_h_i_l @ Document ) ) ) ) ).
% put\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def
thf(fact_37_exists__least__lemma,axiom,
! [P: nat > $o] :
( ~ ( P @ zero_zero_nat )
=> ( ? [X_1: nat] : ( P @ X_1 )
=> ? [N2: nat] :
( ~ ( P @ N2 )
& ( P @ ( suc @ N2 ) ) ) ) ) ).
% exists_least_lemma
thf(fact_38_list__decode_Ocases,axiom,
! [X: nat] :
( ( X != zero_zero_nat )
=> ~ ! [N2: nat] :
( X
!= ( suc @ N2 ) ) ) ).
% list_decode.cases
thf(fact_39_object__empty,axiom,
! [X: rObjec1617416918on_j_k] :
( ( rObjec1303043984on_j_k @ product_Unity @ ( more_R1625109589on_j_k @ X ) )
= X ) ).
% object_empty
thf(fact_40_object__empty,axiom,
! [X: rObjec103300152t_unit] :
( ( rObjec730108904t_unit @ product_Unity @ ( more_Product_unit @ X ) )
= X ) ).
% object_empty
thf(fact_41_mem__Collect__eq,axiom,
! [A: nat,P: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_42_Collect__mem__eq,axiom,
! [A2: set_nat] :
( ( collect_nat
@ ^ [X4: nat] : ( member_nat @ X4 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_43_RDocument_Oupdate__convs_I1_J,axiom,
! [Nothing2: product_unit > product_unit,Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
( ( nothin1105341917on_j_k @ Nothing2 @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ ( Nothing2 @ Nothinga ) @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) ) ).
% RDocument.update_convs(1)
thf(fact_44_RDocument_Oupdate__convs_I2_J,axiom,
! [Doctype2: list_char > list_char,Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
( ( doctyp68000440on_j_k @ Doctype2 @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ ( Doctype2 @ Doctype ) @ Document_element @ Disconnected_nodes @ More ) ) ) ).
% RDocument.update_convs(2)
thf(fact_45_RDocument_Oupdate__convs_I3_J,axiom,
! [Document_element2: option_element_ptr_a > option_element_ptr_a,Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
( ( docume244715269on_j_k @ Document_element2 @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ ( Document_element2 @ Document_element ) @ Disconnected_nodes @ More ) ) ) ).
% RDocument.update_convs(3)
thf(fact_46_RDocument_Oupdate__convs_I4_J,axiom,
! [Disconnected_nodes2: list_n282880152tr_b_c > list_n282880152tr_b_c,Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
( ( discon442323090on_j_k @ Disconnected_nodes2 @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ ( Disconnected_nodes2 @ Disconnected_nodes ) @ More ) ) ) ).
% RDocument.update_convs(4)
thf(fact_47_size__neq__size__imp__neq,axiom,
! [X: docume1935157360tr_d_e,Y: docume1935157360tr_d_e] :
( ( ( size_s724035844tr_d_e @ X )
!= ( size_s724035844tr_d_e @ Y ) )
=> ( X != Y ) ) ).
% size_neq_size_imp_neq
thf(fact_48_size__neq__size__imp__neq,axiom,
! [X: list_n282880152tr_b_c,Y: list_n282880152tr_b_c] :
( ( ( size_s2106487044tr_b_c @ X )
!= ( size_s2106487044tr_b_c @ Y ) )
=> ( X != Y ) ) ).
% size_neq_size_imp_neq
thf(fact_49_size__neq__size__imp__neq,axiom,
! [X: list_char,Y: list_char] :
( ( ( size_size_list_char @ X )
!= ( size_size_list_char @ Y ) )
=> ( X != Y ) ) ).
% size_neq_size_imp_neq
thf(fact_50_size__neq__size__imp__neq,axiom,
! [X: option2026120038on_j_k,Y: option2026120038on_j_k] :
( ( ( size_s1129069050on_j_k @ X )
!= ( size_s1129069050on_j_k @ Y ) )
=> ( X != Y ) ) ).
% size_neq_size_imp_neq
thf(fact_51_size__neq__size__imp__neq,axiom,
! [X: option_element_ptr_a,Y: option_element_ptr_a] :
( ( ( size_s1129684517_ptr_a @ X )
!= ( size_s1129684517_ptr_a @ Y ) )
=> ( X != Y ) ) ).
% size_neq_size_imp_neq
thf(fact_52_RObject_Oselect__convs_I2_J,axiom,
! [Nothing: product_unit,More: rDocum326988203on_j_k] :
( ( more_R1625109589on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ More ) )
= More ) ).
% RObject.select_convs(2)
thf(fact_53_RObject_Oselect__convs_I2_J,axiom,
! [Nothing: product_unit,More: product_unit] :
( ( more_Product_unit @ ( rObjec730108904t_unit @ Nothing @ More ) )
= More ) ).
% RObject.select_convs(2)
thf(fact_54_document__ptr_Osize__neq,axiom,
! [X: docume1935157360tr_d_e] :
( ( size_s724035844tr_d_e @ X )
!= zero_zero_nat ) ).
% document_ptr.size_neq
thf(fact_55_object__more__extend__id,axiom,
! [X: rObjec103300152t_unit,Y: product_unit] :
( ( more_Product_unit @ ( extend_Product_unit @ X @ Y ) )
= Y ) ).
% object_more_extend_id
thf(fact_56_object__more__extend__id,axiom,
! [X: rObjec103300152t_unit,Y: rDocum326988203on_j_k] :
( ( more_R1625109589on_j_k @ ( extend1066431834on_j_k @ X @ Y ) )
= Y ) ).
% object_more_extend_id
thf(fact_57_RDocument_Oupdate__convs_I5_J,axiom,
! [More2: option2026120038on_j_k > option2026120038on_j_k,Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
( ( more_u1044474223_c_a_b @ More2 @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ ( More2 @ More ) ) ) ) ).
% RDocument.update_convs(5)
thf(fact_58_is__document__ptr__ref,axiom,
! [N: nat] : ( is_doc2037328342tr_d_e @ ( docume1511108976tr_d_e @ N ) ) ).
% is_document_ptr_ref
thf(fact_59_RDocument_Oselect__convs_I5_J,axiom,
! [Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
( ( more_c1453068134on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= More ) ).
% RDocument.select_convs(5)
thf(fact_60_RDocument_Oselect__convs_I4_J,axiom,
! [Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
( ( discon866287741on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= Disconnected_nodes ) ).
% RDocument.select_convs(4)
thf(fact_61_RDocument_Oselect__convs_I3_J,axiom,
! [Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
( ( docume1175131570on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= Document_element ) ).
% RDocument.select_convs(3)
thf(fact_62_RDocument_Oselect__convs_I2_J,axiom,
! [Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
( ( doctyp814403297on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= Doctype ) ).
% RDocument.select_convs(2)
thf(fact_63_RDocument_Oselect__convs_I1_J,axiom,
! [Nothing: product_unit,Nothinga: product_unit,Doctype: list_char,Document_element: option_element_ptr_a,Disconnected_nodes: list_n282880152tr_b_c,More: option2026120038on_j_k] :
( ( nothin757132294on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ ( rDocum427676485on_j_k @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= Nothinga ) ).
% RDocument.select_convs(1)
thf(fact_64_RDocument_Ounfold__congs_I6_J,axiom,
! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: option2026120038on_j_k,F: option2026120038on_j_k > option2026120038on_j_k,F2: option2026120038on_j_k > option2026120038on_j_k] :
( ( R = R2 )
=> ( ( ( more_c1453068134on_j_k @ R2 )
= V )
=> ( ! [V2: option2026120038on_j_k] :
( ( V2 = V )
=> ( ( F @ V2 )
= ( F2 @ V2 ) ) )
=> ( ( more_u1044474223_c_a_b @ F @ R )
= ( more_u1044474223_c_a_b @ F2 @ R2 ) ) ) ) ) ).
% RDocument.unfold_congs(6)
thf(fact_65_RDocument_Ofold__congs_I6_J,axiom,
! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: option2026120038on_j_k,F: option2026120038on_j_k > option2026120038on_j_k,F2: option2026120038on_j_k > option2026120038on_j_k] :
( ( R = R2 )
=> ( ( ( more_c1453068134on_j_k @ R2 )
= V )
=> ( ! [V2: option2026120038on_j_k] :
( ( V = V2 )
=> ( ( F @ V2 )
= ( F2 @ V2 ) ) )
=> ( ( more_u1044474223_c_a_b @ F @ R )
= ( more_u1044474223_c_a_b @ F2 @ R2 ) ) ) ) ) ).
% RDocument.fold_congs(6)
thf(fact_66_RDocument_Ounfold__congs_I3_J,axiom,
! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: list_char,F: list_char > list_char,F2: list_char > list_char] :
( ( R = R2 )
=> ( ( ( doctyp814403297on_j_k @ R2 )
= V )
=> ( ! [V2: list_char] :
( ( V2 = V )
=> ( ( F @ V2 )
= ( F2 @ V2 ) ) )
=> ( ( doctyp68000440on_j_k @ F @ R )
= ( doctyp68000440on_j_k @ F2 @ R2 ) ) ) ) ) ).
% RDocument.unfold_congs(3)
thf(fact_67_RDocument_Ounfold__congs_I4_J,axiom,
! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: option_element_ptr_a,F: option_element_ptr_a > option_element_ptr_a,F2: option_element_ptr_a > option_element_ptr_a] :
( ( R = R2 )
=> ( ( ( docume1175131570on_j_k @ R2 )
= V )
=> ( ! [V2: option_element_ptr_a] :
( ( V2 = V )
=> ( ( F @ V2 )
= ( F2 @ V2 ) ) )
=> ( ( docume244715269on_j_k @ F @ R )
= ( docume244715269on_j_k @ F2 @ R2 ) ) ) ) ) ).
% RDocument.unfold_congs(4)
thf(fact_68_RDocument_Ounfold__congs_I5_J,axiom,
! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: list_n282880152tr_b_c,F: list_n282880152tr_b_c > list_n282880152tr_b_c,F2: list_n282880152tr_b_c > list_n282880152tr_b_c] :
( ( R = R2 )
=> ( ( ( discon866287741on_j_k @ R2 )
= V )
=> ( ! [V2: list_n282880152tr_b_c] :
( ( V2 = V )
=> ( ( F @ V2 )
= ( F2 @ V2 ) ) )
=> ( ( discon442323090on_j_k @ F @ R )
= ( discon442323090on_j_k @ F2 @ R2 ) ) ) ) ) ).
% RDocument.unfold_congs(5)
thf(fact_69_RDocument_Ofold__congs_I3_J,axiom,
! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: list_char,F: list_char > list_char,F2: list_char > list_char] :
( ( R = R2 )
=> ( ( ( doctyp814403297on_j_k @ R2 )
= V )
=> ( ! [V2: list_char] :
( ( V = V2 )
=> ( ( F @ V2 )
= ( F2 @ V2 ) ) )
=> ( ( doctyp68000440on_j_k @ F @ R )
= ( doctyp68000440on_j_k @ F2 @ R2 ) ) ) ) ) ).
% RDocument.fold_congs(3)
thf(fact_70_RDocument_Ofold__congs_I4_J,axiom,
! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: option_element_ptr_a,F: option_element_ptr_a > option_element_ptr_a,F2: option_element_ptr_a > option_element_ptr_a] :
( ( R = R2 )
=> ( ( ( docume1175131570on_j_k @ R2 )
= V )
=> ( ! [V2: option_element_ptr_a] :
( ( V = V2 )
=> ( ( F @ V2 )
= ( F2 @ V2 ) ) )
=> ( ( docume244715269on_j_k @ F @ R )
= ( docume244715269on_j_k @ F2 @ R2 ) ) ) ) ) ).
% RDocument.fold_congs(4)
thf(fact_71_RDocument_Ofold__congs_I5_J,axiom,
! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: list_n282880152tr_b_c,F: list_n282880152tr_b_c > list_n282880152tr_b_c,F2: list_n282880152tr_b_c > list_n282880152tr_b_c] :
( ( R = R2 )
=> ( ( ( discon866287741on_j_k @ R2 )
= V )
=> ( ! [V2: list_n282880152tr_b_c] :
( ( V = V2 )
=> ( ( F @ V2 )
= ( F2 @ V2 ) ) )
=> ( ( discon442323090on_j_k @ F @ R )
= ( discon442323090on_j_k @ F2 @ R2 ) ) ) ) ) ).
% RDocument.fold_congs(5)
thf(fact_72_RDocument_Ounfold__congs_I2_J,axiom,
! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: product_unit,F: product_unit > product_unit,F2: product_unit > product_unit] :
( ( R = R2 )
=> ( ( ( nothin757132294on_j_k @ R2 )
= V )
=> ( ! [V2: product_unit] :
( ( V2 = V )
=> ( ( F @ V2 )
= ( F2 @ V2 ) ) )
=> ( ( nothin1105341917on_j_k @ F @ R )
= ( nothin1105341917on_j_k @ F2 @ R2 ) ) ) ) ) ).
% RDocument.unfold_congs(2)
thf(fact_73_RDocument_Ofold__congs_I2_J,axiom,
! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k,V: product_unit,F: product_unit > product_unit,F2: product_unit > product_unit] :
( ( R = R2 )
=> ( ( ( nothin757132294on_j_k @ R2 )
= V )
=> ( ! [V2: product_unit] :
( ( V = V2 )
=> ( ( F @ V2 )
= ( F2 @ V2 ) ) )
=> ( ( nothin1105341917on_j_k @ F @ R )
= ( nothin1105341917on_j_k @ F2 @ R2 ) ) ) ) ) ).
% RDocument.fold_congs(2)
thf(fact_74_length__0__conv,axiom,
! [Xs: list_l118626078tr_b_c] :
( ( ( size_s9369994tr_b_c @ Xs )
= zero_zero_nat )
= ( Xs = nil_li198338206tr_b_c ) ) ).
% length_0_conv
thf(fact_75_length__0__conv,axiom,
! [Xs: list_list_char] :
( ( ( size_s2008079621t_char @ Xs )
= zero_zero_nat )
= ( Xs = nil_list_char ) ) ).
% length_0_conv
thf(fact_76_length__0__conv,axiom,
! [Xs: list_char] :
( ( ( size_size_list_char @ Xs )
= zero_zero_nat )
= ( Xs = nil_char ) ) ).
% length_0_conv
thf(fact_77_length__0__conv,axiom,
! [Xs: list_n282880152tr_b_c] :
( ( ( size_s2106487044tr_b_c @ Xs )
= zero_zero_nat )
= ( Xs = nil_no279930520tr_b_c ) ) ).
% length_0_conv
thf(fact_78_RDocument_Osurjective,axiom,
! [R: rObjec1617416918on_j_k] :
( R
= ( rObjec1303043984on_j_k @ ( nothin1567949605on_j_k @ R ) @ ( rDocum427676485on_j_k @ ( nothin757132294on_j_k @ R ) @ ( doctyp814403297on_j_k @ R ) @ ( docume1175131570on_j_k @ R ) @ ( discon866287741on_j_k @ R ) @ ( more_c1453068134on_j_k @ R ) ) ) ) ).
% RDocument.surjective
thf(fact_79_RDocument_Oequality,axiom,
! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k] :
( ( ( nothin1567949605on_j_k @ R )
= ( nothin1567949605on_j_k @ R2 ) )
=> ( ( ( nothin757132294on_j_k @ R )
= ( nothin757132294on_j_k @ R2 ) )
=> ( ( ( doctyp814403297on_j_k @ R )
= ( doctyp814403297on_j_k @ R2 ) )
=> ( ( ( docume1175131570on_j_k @ R )
= ( docume1175131570on_j_k @ R2 ) )
=> ( ( ( discon866287741on_j_k @ R )
= ( discon866287741on_j_k @ R2 ) )
=> ( ( ( more_c1453068134on_j_k @ R )
= ( more_c1453068134on_j_k @ R2 ) )
=> ( R = R2 ) ) ) ) ) ) ) ).
% RDocument.equality
thf(fact_80_option_Osize_I3_J,axiom,
( ( size_s7667464on_j_k @ none_R1587534007on_j_k )
= ( suc @ zero_zero_nat ) ) ).
% option.size(3)
thf(fact_81_option_Osize_I3_J,axiom,
( ( size_s1129684517_ptr_a @ none_element_ptr_a )
= ( suc @ zero_zero_nat ) ) ).
% option.size(3)
thf(fact_82_option_Osize_I3_J,axiom,
( ( size_s1129069050on_j_k @ none_S1393028981on_j_k )
= ( suc @ zero_zero_nat ) ) ).
% option.size(3)
thf(fact_83_list_Osize_I3_J,axiom,
( ( size_s9369994tr_b_c @ nil_li198338206tr_b_c )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_84_list_Osize_I3_J,axiom,
( ( size_s2008079621t_char @ nil_list_char )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_85_list_Osize_I3_J,axiom,
( ( size_size_list_char @ nil_char )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_86_list_Osize_I3_J,axiom,
( ( size_s2106487044tr_b_c @ nil_no279930520tr_b_c )
= zero_zero_nat ) ).
% list.size(3)
thf(fact_87_document__ptr_Osize_I4_J,axiom,
! [X2: sum_su1576157353tr_d_e] :
( ( size_s724035844tr_d_e @ ( docume1825929374tr_d_e @ X2 ) )
= ( suc @ zero_zero_nat ) ) ).
% document_ptr.size(4)
thf(fact_88_RObject_Osurjective,axiom,
! [R: rObjec1617416918on_j_k] :
( R
= ( rObjec1303043984on_j_k @ ( nothin1567949605on_j_k @ R ) @ ( more_R1625109589on_j_k @ R ) ) ) ).
% RObject.surjective
thf(fact_89_RObject_Osurjective,axiom,
! [R: rObjec103300152t_unit] :
( R
= ( rObjec730108904t_unit @ ( nothing_Product_unit @ R ) @ ( more_Product_unit @ R ) ) ) ).
% RObject.surjective
thf(fact_90_document__ptr_Oinject_I2_J,axiom,
! [X2: sum_su1576157353tr_d_e,Y2: sum_su1576157353tr_d_e] :
( ( ( docume1825929374tr_d_e @ X2 )
= ( docume1825929374tr_d_e @ Y2 ) )
= ( X2 = Y2 ) ) ).
% document_ptr.inject(2)
thf(fact_91_neq__if__length__neq,axiom,
! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
( ( ( size_s2106487044tr_b_c @ Xs )
!= ( size_s2106487044tr_b_c @ Ys ) )
=> ( Xs != Ys ) ) ).
% neq_if_length_neq
thf(fact_92_neq__if__length__neq,axiom,
! [Xs: list_char,Ys: list_char] :
( ( ( size_size_list_char @ Xs )
!= ( size_size_list_char @ Ys ) )
=> ( Xs != Ys ) ) ).
% neq_if_length_neq
thf(fact_93_Ex__list__of__length,axiom,
! [N: nat] :
? [Xs2: list_n282880152tr_b_c] :
( ( size_s2106487044tr_b_c @ Xs2 )
= N ) ).
% Ex_list_of_length
thf(fact_94_Ex__list__of__length,axiom,
! [N: nat] :
? [Xs2: list_char] :
( ( size_size_list_char @ Xs2 )
= N ) ).
% Ex_list_of_length
thf(fact_95_document__ptr_Odistinct_I1_J,axiom,
! [X1: nat,X2: sum_su1576157353tr_d_e] :
( ( docume1511108976tr_d_e @ X1 )
!= ( docume1825929374tr_d_e @ X2 ) ) ).
% document_ptr.distinct(1)
thf(fact_96_document__ptr_Oinduct,axiom,
! [P: docume1935157360tr_d_e > $o,Document_ptr2: docume1935157360tr_d_e] :
( ! [X3: nat] : ( P @ ( docume1511108976tr_d_e @ X3 ) )
=> ( ! [X3: sum_su1576157353tr_d_e] : ( P @ ( docume1825929374tr_d_e @ X3 ) )
=> ( P @ Document_ptr2 ) ) ) ).
% document_ptr.induct
thf(fact_97_document__ptr_Oexhaust,axiom,
! [Y: docume1935157360tr_d_e] :
( ! [X12: nat] :
( Y
!= ( docume1511108976tr_d_e @ X12 ) )
=> ~ ! [X22: sum_su1576157353tr_d_e] :
( Y
!= ( docume1825929374tr_d_e @ X22 ) ) ) ).
% document_ptr.exhaust
thf(fact_98_RObject_Oselect__convs_I1_J,axiom,
! [Nothing: product_unit,More: rDocum326988203on_j_k] :
( ( nothin1567949605on_j_k @ ( rObjec1303043984on_j_k @ Nothing @ More ) )
= Nothing ) ).
% RObject.select_convs(1)
thf(fact_99_RObject_Oselect__convs_I1_J,axiom,
! [Nothing: product_unit,More: product_unit] :
( ( nothing_Product_unit @ ( rObjec730108904t_unit @ Nothing @ More ) )
= Nothing ) ).
% RObject.select_convs(1)
thf(fact_100_RObject_Oequality,axiom,
! [R: rObjec1617416918on_j_k,R2: rObjec1617416918on_j_k] :
( ( ( nothin1567949605on_j_k @ R )
= ( nothin1567949605on_j_k @ R2 ) )
=> ( ( ( more_R1625109589on_j_k @ R )
= ( more_R1625109589on_j_k @ R2 ) )
=> ( R = R2 ) ) ) ).
% RObject.equality
thf(fact_101_RObject_Oequality,axiom,
! [R: rObjec103300152t_unit,R2: rObjec103300152t_unit] :
( ( ( nothing_Product_unit @ R )
= ( nothing_Product_unit @ R2 ) )
=> ( ( ( more_Product_unit @ R )
= ( more_Product_unit @ R2 ) )
=> ( R = R2 ) ) ) ).
% RObject.equality
thf(fact_102_option_Osize__neq,axiom,
! [X: option2026120038on_j_k] :
( ( size_s1129069050on_j_k @ X )
!= zero_zero_nat ) ).
% option.size_neq
thf(fact_103_option_Osize__neq,axiom,
! [X: option_element_ptr_a] :
( ( size_s1129684517_ptr_a @ X )
!= zero_zero_nat ) ).
% option.size_neq
thf(fact_104_option_Osize__gen_I1_J,axiom,
! [X: rObjec1617416918on_j_k > nat] :
( ( size_o26122489on_j_k @ X @ none_R1587534007on_j_k )
= ( suc @ zero_zero_nat ) ) ).
% option.size_gen(1)
thf(fact_105_option_Osize__gen_I1_J,axiom,
! [X: element_ptr_a > nat] :
( ( size_o1591053974_ptr_a @ X @ none_element_ptr_a )
= ( suc @ zero_zero_nat ) ) ).
% option.size_gen(1)
thf(fact_106_option_Osize__gen_I1_J,axiom,
! [X: sum_su1221287958on_j_k > nat] :
( ( size_o1777465779on_j_k @ X @ none_S1393028981on_j_k )
= ( suc @ zero_zero_nat ) ) ).
% option.size_gen(1)
thf(fact_107_length__code,axiom,
( size_s2106487044tr_b_c
= ( gen_le955068453tr_b_c @ zero_zero_nat ) ) ).
% length_code
thf(fact_108_length__code,axiom,
( size_size_list_char
= ( gen_length_char @ zero_zero_nat ) ) ).
% length_code
thf(fact_109_document__ptr_Osize__gen_I2_J,axiom,
! [X: sum_su1576157353tr_d_e > nat,X2: sum_su1576157353tr_d_e] :
( ( docume1799427087tr_d_e @ X @ ( docume1825929374tr_d_e @ X2 ) )
= ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% document_ptr.size_gen(2)
thf(fact_110_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__none,axiom,
! [Obj: rObjec1413572695_j_k_l] :
( ( ( cast_O1034441233_j_k_l @ Obj )
= none_R1587534007on_j_k )
= ( ~ ? [Document: rObjec1617416918on_j_k] :
( ( cast_D1252964113_h_i_l @ Document )
= Obj ) ) ) ).
% cast\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>2\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_none
thf(fact_111_list__ex1__simps_I1_J,axiom,
! [P: list_n282880152tr_b_c > $o] :
~ ( list_e529904353tr_b_c @ P @ nil_li198338206tr_b_c ) ).
% list_ex1_simps(1)
thf(fact_112_list__ex1__simps_I1_J,axiom,
! [P: list_char > $o] :
~ ( list_ex1_list_char @ P @ nil_list_char ) ).
% list_ex1_simps(1)
thf(fact_113_list__ex1__simps_I1_J,axiom,
! [P: char > $o] :
~ ( list_ex1_char @ P @ nil_char ) ).
% list_ex1_simps(1)
thf(fact_114_list__ex1__simps_I1_J,axiom,
! [P: node_p1234578834tr_b_c > $o] :
~ ( list_e469495899tr_b_c @ P @ nil_no279930520tr_b_c ) ).
% list_ex1_simps(1)
thf(fact_115_is__document__kind__def,axiom,
( is_doc1417632087_j_k_l
= ( ^ [Ptr: rObjec1413572695_j_k_l] :
( ( cast_O1034441233_j_k_l @ Ptr )
!= none_R1587534007on_j_k ) ) ) ).
% is_document_kind_def
thf(fact_116_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_117_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_118_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_119_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_120_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_121_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_122_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_123_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_124_add_Oright__neutral,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ) ).
% add.right_neutral
thf(fact_125_add_Oleft__neutral,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ) ).
% add.left_neutral
thf(fact_126_add__Suc__right,axiom,
! [M2: nat,N: nat] :
( ( plus_plus_nat @ M2 @ ( suc @ N ) )
= ( suc @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% add_Suc_right
thf(fact_127_Nat_Oadd__0__right,axiom,
! [M2: nat] :
( ( plus_plus_nat @ M2 @ zero_zero_nat )
= M2 ) ).
% Nat.add_0_right
thf(fact_128_add__is__0,axiom,
! [M2: nat,N: nat] :
( ( ( plus_plus_nat @ M2 @ N )
= zero_zero_nat )
= ( ( M2 = zero_zero_nat )
& ( N = zero_zero_nat ) ) ) ).
% add_is_0
thf(fact_129_gen__length__def,axiom,
( gen_le955068453tr_b_c
= ( ^ [N3: nat,Xs3: list_n282880152tr_b_c] : ( plus_plus_nat @ N3 @ ( size_s2106487044tr_b_c @ Xs3 ) ) ) ) ).
% gen_length_def
thf(fact_130_gen__length__def,axiom,
( gen_length_char
= ( ^ [N3: nat,Xs3: list_char] : ( plus_plus_nat @ N3 @ ( size_size_list_char @ Xs3 ) ) ) ) ).
% gen_length_def
thf(fact_131_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_132_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_133_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_134_add_Ocommute,axiom,
( plus_plus_nat
= ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).
% add.commute
thf(fact_135_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_136_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_137_group__cancel_Oadd1,axiom,
! [A2: nat,K: nat,A: nat,B: nat] :
( ( A2
= ( plus_plus_nat @ K @ A ) )
=> ( ( plus_plus_nat @ A2 @ B )
= ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% group_cancel.add1
thf(fact_138_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_139_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_140_add_Ocomm__neutral,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ) ).
% add.comm_neutral
thf(fact_141_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_142_add__Suc,axiom,
! [M2: nat,N: nat] :
( ( plus_plus_nat @ ( suc @ M2 ) @ N )
= ( suc @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% add_Suc
thf(fact_143_nat__arith_Osuc1,axiom,
! [A2: nat,K: nat,A: nat] :
( ( A2
= ( plus_plus_nat @ K @ A ) )
=> ( ( suc @ A2 )
= ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% nat_arith.suc1
thf(fact_144_add__Suc__shift,axiom,
! [M2: nat,N: nat] :
( ( plus_plus_nat @ ( suc @ M2 ) @ N )
= ( plus_plus_nat @ M2 @ ( suc @ N ) ) ) ).
% add_Suc_shift
thf(fact_145_add__eq__self__zero,axiom,
! [M2: nat,N: nat] :
( ( ( plus_plus_nat @ M2 @ N )
= M2 )
=> ( N = zero_zero_nat ) ) ).
% add_eq_self_zero
thf(fact_146_plus__nat_Oadd__0,axiom,
! [N: nat] :
( ( plus_plus_nat @ zero_zero_nat @ N )
= N ) ).
% plus_nat.add_0
thf(fact_147_one__is__add,axiom,
! [M2: nat,N: nat] :
( ( ( suc @ zero_zero_nat )
= ( plus_plus_nat @ M2 @ N ) )
= ( ( ( M2
= ( suc @ zero_zero_nat ) )
& ( N = zero_zero_nat ) )
| ( ( M2 = zero_zero_nat )
& ( N
= ( suc @ zero_zero_nat ) ) ) ) ) ).
% one_is_add
thf(fact_148_add__is__1,axiom,
! [M2: nat,N: nat] :
( ( ( plus_plus_nat @ M2 @ N )
= ( suc @ zero_zero_nat ) )
= ( ( ( M2
= ( suc @ zero_zero_nat ) )
& ( N = zero_zero_nat ) )
| ( ( M2 = zero_zero_nat )
& ( N
= ( suc @ zero_zero_nat ) ) ) ) ) ).
% add_is_1
thf(fact_149_gen__length__code_I1_J,axiom,
! [N: nat] :
( ( gen_le170886571tr_b_c @ N @ nil_li198338206tr_b_c )
= N ) ).
% gen_length_code(1)
thf(fact_150_gen__length__code_I1_J,axiom,
! [N: nat] :
( ( gen_length_list_char @ N @ nil_list_char )
= N ) ).
% gen_length_code(1)
thf(fact_151_gen__length__code_I1_J,axiom,
! [N: nat] :
( ( gen_length_char @ N @ nil_char )
= N ) ).
% gen_length_code(1)
thf(fact_152_gen__length__code_I1_J,axiom,
! [N: nat] :
( ( gen_le955068453tr_b_c @ N @ nil_no279930520tr_b_c )
= N ) ).
% gen_length_code(1)
thf(fact_153_Euclid__induct,axiom,
! [P: nat > nat > $o,A: nat,B: nat] :
( ! [A4: nat,B4: nat] :
( ( P @ A4 @ B4 )
= ( P @ B4 @ A4 ) )
=> ( ! [A4: nat] : ( P @ A4 @ zero_zero_nat )
=> ( ! [A4: nat,B4: nat] :
( ( P @ A4 @ B4 )
=> ( P @ A4 @ ( plus_plus_nat @ A4 @ B4 ) ) )
=> ( P @ A @ B ) ) ) ) ).
% Euclid_induct
thf(fact_154_triangle__Suc,axiom,
! [N: nat] :
( ( nat_triangle @ ( suc @ N ) )
= ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% triangle_Suc
thf(fact_155_verit__sum__simplify,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ) ).
% verit_sum_simplify
thf(fact_156_add__0__iff,axiom,
! [B: nat,A: nat] :
( ( B
= ( plus_plus_nat @ B @ A ) )
= ( A = zero_zero_nat ) ) ).
% add_0_iff
thf(fact_157_option_Osize__gen_I2_J,axiom,
! [X: rObjec1617416918on_j_k > nat,X2: rObjec1617416918on_j_k] :
( ( size_o26122489on_j_k @ X @ ( some_R67702331on_j_k @ X2 ) )
= ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% option.size_gen(2)
thf(fact_158_option_Osize__gen_I2_J,axiom,
! [X: docume1935157360tr_d_e > nat,X2: docume1935157360tr_d_e] :
( ( size_o1635055885tr_d_e @ X @ ( some_d1631029323tr_d_e @ X2 ) )
= ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% option.size_gen(2)
thf(fact_159_option_Osize__gen_I2_J,axiom,
! [X: rObjec1413572695_j_k_l > nat,X2: rObjec1413572695_j_k_l] :
( ( size_o310046708_j_k_l @ X @ ( some_R1598191922_j_k_l @ X2 ) )
= ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% option.size_gen(2)
thf(fact_160_option_Osize__gen_I2_J,axiom,
! [X: sum_su1221287958on_j_k > nat,X2: sum_su1221287958on_j_k] :
( ( size_o1777465779on_j_k @ X @ ( some_S1960742641on_j_k @ X2 ) )
= ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% option.size_gen(2)
thf(fact_161_option_Osize__gen_I2_J,axiom,
! [X: element_ptr_a > nat,X2: element_ptr_a] :
( ( size_o1591053974_ptr_a @ X @ ( some_element_ptr_a @ X2 ) )
= ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% option.size_gen(2)
thf(fact_162_option_Oinject,axiom,
! [X2: sum_su1221287958on_j_k,Y2: sum_su1221287958on_j_k] :
( ( ( some_S1960742641on_j_k @ X2 )
= ( some_S1960742641on_j_k @ Y2 ) )
= ( X2 = Y2 ) ) ).
% option.inject
thf(fact_163_option_Oinject,axiom,
! [X2: element_ptr_a,Y2: element_ptr_a] :
( ( ( some_element_ptr_a @ X2 )
= ( some_element_ptr_a @ Y2 ) )
= ( X2 = Y2 ) ) ).
% option.inject
thf(fact_164_option_Oinject,axiom,
! [X2: rObjec1617416918on_j_k,Y2: rObjec1617416918on_j_k] :
( ( ( some_R67702331on_j_k @ X2 )
= ( some_R67702331on_j_k @ Y2 ) )
= ( X2 = Y2 ) ) ).
% option.inject
thf(fact_165_option_Oinject,axiom,
! [X2: docume1935157360tr_d_e,Y2: docume1935157360tr_d_e] :
( ( ( some_d1631029323tr_d_e @ X2 )
= ( some_d1631029323tr_d_e @ Y2 ) )
= ( X2 = Y2 ) ) ).
% option.inject
thf(fact_166_option_Oinject,axiom,
! [X2: rObjec1413572695_j_k_l,Y2: rObjec1413572695_j_k_l] :
( ( ( some_R1598191922_j_k_l @ X2 )
= ( some_R1598191922_j_k_l @ Y2 ) )
= ( X2 = Y2 ) ) ).
% option.inject
thf(fact_167_not__Some__eq,axiom,
! [X: option841825948on_j_k] :
( ( ! [Y4: rObjec1617416918on_j_k] :
( X
!= ( some_R67702331on_j_k @ Y4 ) ) )
= ( X = none_R1587534007on_j_k ) ) ).
% not_Some_eq
thf(fact_168_not__Some__eq,axiom,
! [X: option1330818496tr_d_e] :
( ( ! [Y4: docume1935157360tr_d_e] :
( X
!= ( some_d1631029323tr_d_e @ Y4 ) ) )
= ( X = none_d1458959567tr_d_e ) ) ).
% not_Some_eq
thf(fact_169_not__Some__eq,axiom,
! [X: option1749760295_j_k_l] :
( ( ! [Y4: rObjec1413572695_j_k_l] :
( X
!= ( some_R1598191922_j_k_l @ Y4 ) ) )
= ( X = none_R1773662646_j_k_l ) ) ).
% not_Some_eq
thf(fact_170_not__Some__eq,axiom,
! [X: option_element_ptr_a] :
( ( ! [Y4: element_ptr_a] :
( X
!= ( some_element_ptr_a @ Y4 ) ) )
= ( X = none_element_ptr_a ) ) ).
% not_Some_eq
thf(fact_171_not__Some__eq,axiom,
! [X: option2026120038on_j_k] :
( ( ! [Y4: sum_su1221287958on_j_k] :
( X
!= ( some_S1960742641on_j_k @ Y4 ) ) )
= ( X = none_S1393028981on_j_k ) ) ).
% not_Some_eq
thf(fact_172_not__None__eq,axiom,
! [X: option841825948on_j_k] :
( ( X != none_R1587534007on_j_k )
= ( ? [Y4: rObjec1617416918on_j_k] :
( X
= ( some_R67702331on_j_k @ Y4 ) ) ) ) ).
% not_None_eq
thf(fact_173_not__None__eq,axiom,
! [X: option1330818496tr_d_e] :
( ( X != none_d1458959567tr_d_e )
= ( ? [Y4: docume1935157360tr_d_e] :
( X
= ( some_d1631029323tr_d_e @ Y4 ) ) ) ) ).
% not_None_eq
thf(fact_174_not__None__eq,axiom,
! [X: option1749760295_j_k_l] :
( ( X != none_R1773662646_j_k_l )
= ( ? [Y4: rObjec1413572695_j_k_l] :
( X
= ( some_R1598191922_j_k_l @ Y4 ) ) ) ) ).
% not_None_eq
thf(fact_175_not__None__eq,axiom,
! [X: option_element_ptr_a] :
( ( X != none_element_ptr_a )
= ( ? [Y4: element_ptr_a] :
( X
= ( some_element_ptr_a @ Y4 ) ) ) ) ).
% not_None_eq
thf(fact_176_not__None__eq,axiom,
! [X: option2026120038on_j_k] :
( ( X != none_S1393028981on_j_k )
= ( ? [Y4: sum_su1221287958on_j_k] :
( X
= ( some_S1960742641on_j_k @ Y4 ) ) ) ) ).
% not_None_eq
thf(fact_177_triangle__0,axiom,
( ( nat_triangle @ zero_zero_nat )
= zero_zero_nat ) ).
% triangle_0
thf(fact_178_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__inv,axiom,
! [Document2: rObjec1617416918on_j_k] :
( ( cast_O1034441233_j_k_l @ ( cast_D1252964113_h_i_l @ Document2 ) )
= ( some_R67702331on_j_k @ Document2 ) ) ).
% cast\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>2\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_inv
thf(fact_179_cast_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t_092_060_094sub_0622_092_060_094sub_062D_092_060_094sub_062o_092_060_094sub_062c_092_060_094sub_062u_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062n_092_060_094sub_062t__some,axiom,
! [Obj: rObjec1413572695_j_k_l,Document2: rObjec1617416918on_j_k] :
( ( ( cast_O1034441233_j_k_l @ Obj )
= ( some_R67702331on_j_k @ Document2 ) )
= ( ( cast_D1252964113_h_i_l @ Document2 )
= Obj ) ) ).
% cast\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>2\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_some
thf(fact_180_option_Odistinct_I1_J,axiom,
! [X2: rObjec1617416918on_j_k] :
( none_R1587534007on_j_k
!= ( some_R67702331on_j_k @ X2 ) ) ).
% option.distinct(1)
thf(fact_181_option_Odistinct_I1_J,axiom,
! [X2: docume1935157360tr_d_e] :
( none_d1458959567tr_d_e
!= ( some_d1631029323tr_d_e @ X2 ) ) ).
% option.distinct(1)
thf(fact_182_option_Odistinct_I1_J,axiom,
! [X2: rObjec1413572695_j_k_l] :
( none_R1773662646_j_k_l
!= ( some_R1598191922_j_k_l @ X2 ) ) ).
% option.distinct(1)
thf(fact_183_option_Odistinct_I1_J,axiom,
! [X2: element_ptr_a] :
( none_element_ptr_a
!= ( some_element_ptr_a @ X2 ) ) ).
% option.distinct(1)
thf(fact_184_option_Odistinct_I1_J,axiom,
! [X2: sum_su1221287958on_j_k] :
( none_S1393028981on_j_k
!= ( some_S1960742641on_j_k @ X2 ) ) ).
% option.distinct(1)
thf(fact_185_option_OdiscI,axiom,
! [Option: option841825948on_j_k,X2: rObjec1617416918on_j_k] :
( ( Option
= ( some_R67702331on_j_k @ X2 ) )
=> ( Option != none_R1587534007on_j_k ) ) ).
% option.discI
thf(fact_186_option_OdiscI,axiom,
! [Option: option1330818496tr_d_e,X2: docume1935157360tr_d_e] :
( ( Option
= ( some_d1631029323tr_d_e @ X2 ) )
=> ( Option != none_d1458959567tr_d_e ) ) ).
% option.discI
thf(fact_187_option_OdiscI,axiom,
! [Option: option1749760295_j_k_l,X2: rObjec1413572695_j_k_l] :
( ( Option
= ( some_R1598191922_j_k_l @ X2 ) )
=> ( Option != none_R1773662646_j_k_l ) ) ).
% option.discI
thf(fact_188_option_OdiscI,axiom,
! [Option: option_element_ptr_a,X2: element_ptr_a] :
( ( Option
= ( some_element_ptr_a @ X2 ) )
=> ( Option != none_element_ptr_a ) ) ).
% option.discI
thf(fact_189_option_OdiscI,axiom,
! [Option: option2026120038on_j_k,X2: sum_su1221287958on_j_k] :
( ( Option
= ( some_S1960742641on_j_k @ X2 ) )
=> ( Option != none_S1393028981on_j_k ) ) ).
% option.discI
thf(fact_190_option_Oexhaust,axiom,
! [Y: option_element_ptr_a] :
( ( Y != none_element_ptr_a )
=> ~ ! [X22: element_ptr_a] :
( Y
!= ( some_element_ptr_a @ X22 ) ) ) ).
% option.exhaust
thf(fact_191_option_Oexhaust,axiom,
! [Y: option2026120038on_j_k] :
( ( Y != none_S1393028981on_j_k )
=> ~ ! [X22: sum_su1221287958on_j_k] :
( Y
!= ( some_S1960742641on_j_k @ X22 ) ) ) ).
% option.exhaust
thf(fact_192_option_Oinducts,axiom,
! [P: option_element_ptr_a > $o,Option: option_element_ptr_a] :
( ( P @ none_element_ptr_a )
=> ( ! [X3: element_ptr_a] : ( P @ ( some_element_ptr_a @ X3 ) )
=> ( P @ Option ) ) ) ).
% option.inducts
thf(fact_193_option_Oinducts,axiom,
! [P: option2026120038on_j_k > $o,Option: option2026120038on_j_k] :
( ( P @ none_S1393028981on_j_k )
=> ( ! [X3: sum_su1221287958on_j_k] : ( P @ ( some_S1960742641on_j_k @ X3 ) )
=> ( P @ Option ) ) ) ).
% option.inducts
thf(fact_194_split__option__ex,axiom,
( ( ^ [P2: option_element_ptr_a > $o] :
? [X5: option_element_ptr_a] : ( P2 @ X5 ) )
= ( ^ [P3: option_element_ptr_a > $o] :
( ( P3 @ none_element_ptr_a )
| ? [X4: element_ptr_a] : ( P3 @ ( some_element_ptr_a @ X4 ) ) ) ) ) ).
% split_option_ex
thf(fact_195_split__option__ex,axiom,
( ( ^ [P2: option2026120038on_j_k > $o] :
? [X5: option2026120038on_j_k] : ( P2 @ X5 ) )
= ( ^ [P3: option2026120038on_j_k > $o] :
( ( P3 @ none_S1393028981on_j_k )
| ? [X4: sum_su1221287958on_j_k] : ( P3 @ ( some_S1960742641on_j_k @ X4 ) ) ) ) ) ).
% split_option_ex
thf(fact_196_split__option__all,axiom,
( ( ^ [P2: option_element_ptr_a > $o] :
! [X5: option_element_ptr_a] : ( P2 @ X5 ) )
= ( ^ [P3: option_element_ptr_a > $o] :
( ( P3 @ none_element_ptr_a )
& ! [X4: element_ptr_a] : ( P3 @ ( some_element_ptr_a @ X4 ) ) ) ) ) ).
% split_option_all
thf(fact_197_split__option__all,axiom,
( ( ^ [P2: option2026120038on_j_k > $o] :
! [X5: option2026120038on_j_k] : ( P2 @ X5 ) )
= ( ^ [P3: option2026120038on_j_k > $o] :
( ( P3 @ none_S1393028981on_j_k )
& ! [X4: sum_su1221287958on_j_k] : ( P3 @ ( some_S1960742641on_j_k @ X4 ) ) ) ) ) ).
% split_option_all
thf(fact_198_combine__options__cases,axiom,
! [X: option_element_ptr_a,P: option_element_ptr_a > option_element_ptr_a > $o,Y: option_element_ptr_a] :
( ( ( X = none_element_ptr_a )
=> ( P @ X @ Y ) )
=> ( ( ( Y = none_element_ptr_a )
=> ( P @ X @ Y ) )
=> ( ! [A4: element_ptr_a,B4: element_ptr_a] :
( ( X
= ( some_element_ptr_a @ A4 ) )
=> ( ( Y
= ( some_element_ptr_a @ B4 ) )
=> ( P @ X @ Y ) ) )
=> ( P @ X @ Y ) ) ) ) ).
% combine_options_cases
thf(fact_199_combine__options__cases,axiom,
! [X: option_element_ptr_a,P: option_element_ptr_a > option2026120038on_j_k > $o,Y: option2026120038on_j_k] :
( ( ( X = none_element_ptr_a )
=> ( P @ X @ Y ) )
=> ( ( ( Y = none_S1393028981on_j_k )
=> ( P @ X @ Y ) )
=> ( ! [A4: element_ptr_a,B4: sum_su1221287958on_j_k] :
( ( X
= ( some_element_ptr_a @ A4 ) )
=> ( ( Y
= ( some_S1960742641on_j_k @ B4 ) )
=> ( P @ X @ Y ) ) )
=> ( P @ X @ Y ) ) ) ) ).
% combine_options_cases
thf(fact_200_combine__options__cases,axiom,
! [X: option2026120038on_j_k,P: option2026120038on_j_k > option_element_ptr_a > $o,Y: option_element_ptr_a] :
( ( ( X = none_S1393028981on_j_k )
=> ( P @ X @ Y ) )
=> ( ( ( Y = none_element_ptr_a )
=> ( P @ X @ Y ) )
=> ( ! [A4: sum_su1221287958on_j_k,B4: element_ptr_a] :
( ( X
= ( some_S1960742641on_j_k @ A4 ) )
=> ( ( Y
= ( some_element_ptr_a @ B4 ) )
=> ( P @ X @ Y ) ) )
=> ( P @ X @ Y ) ) ) ) ).
% combine_options_cases
thf(fact_201_combine__options__cases,axiom,
! [X: option2026120038on_j_k,P: option2026120038on_j_k > option2026120038on_j_k > $o,Y: option2026120038on_j_k] :
( ( ( X = none_S1393028981on_j_k )
=> ( P @ X @ Y ) )
=> ( ( ( Y = none_S1393028981on_j_k )
=> ( P @ X @ Y ) )
=> ( ! [A4: sum_su1221287958on_j_k,B4: sum_su1221287958on_j_k] :
( ( X
= ( some_S1960742641on_j_k @ A4 ) )
=> ( ( Y
= ( some_S1960742641on_j_k @ B4 ) )
=> ( P @ X @ Y ) ) )
=> ( P @ X @ Y ) ) ) ) ).
% combine_options_cases
thf(fact_202_document__ptr__casts__commute2,axiom,
! [Document_ptr2: docume1935157360tr_d_e] :
( ( cast_o761049241_d_e_f @ ( cast_d1608273229_b_c_f @ Document_ptr2 ) )
= ( some_d1631029323tr_d_e @ Document_ptr2 ) ) ).
% document_ptr_casts_commute2
thf(fact_203_document__ptr__casts__commute,axiom,
! [Ptr2: object945351580_d_e_f,Document_ptr2: docume1935157360tr_d_e] :
( ( ( cast_o761049241_d_e_f @ Ptr2 )
= ( some_d1631029323tr_d_e @ Document_ptr2 ) )
= ( ( cast_d1608273229_b_c_f @ Document_ptr2 )
= Ptr2 ) ) ).
% document_ptr_casts_commute
thf(fact_204_get__document__ptr__simp,axiom,
! [Ptr2: object945351580_d_e_f,Document_ptr2: docume1935157360tr_d_e,Obj: rObjec1413572695_j_k_l,H: heap_S1465075775_j_k_l] :
( ( ( Ptr2
= ( cast_d1608273229_b_c_f @ Document_ptr2 ) )
=> ( ( get_D_1192261494_j_k_l @ Document_ptr2 @ ( put_O_834343516_j_k_l @ Ptr2 @ Obj @ H ) )
= ( cast_O1034441233_j_k_l @ Obj ) ) )
& ( ( Ptr2
!= ( cast_d1608273229_b_c_f @ Document_ptr2 ) )
=> ( ( get_D_1192261494_j_k_l @ Document_ptr2 @ ( put_O_834343516_j_k_l @ Ptr2 @ Obj @ H ) )
= ( get_D_1192261494_j_k_l @ Document_ptr2 @ H ) ) ) ) ).
% get_document_ptr_simp
thf(fact_205_split__Nil__iff,axiom,
! [Xs: list_char,Ys: list_char] :
( ( ( splice_char @ Xs @ Ys )
= nil_char )
= ( ( Xs = nil_char )
& ( Ys = nil_char ) ) ) ).
% split_Nil_iff
thf(fact_206_split__Nil__iff,axiom,
! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
( ( ( splice1294941035tr_b_c @ Xs @ Ys )
= nil_no279930520tr_b_c )
= ( ( Xs = nil_no279930520tr_b_c )
& ( Ys = nil_no279930520tr_b_c ) ) ) ).
% split_Nil_iff
thf(fact_207_splice__Nil2,axiom,
! [Xs: list_char] :
( ( splice_char @ Xs @ nil_char )
= Xs ) ).
% splice_Nil2
thf(fact_208_splice__Nil2,axiom,
! [Xs: list_n282880152tr_b_c] :
( ( splice1294941035tr_b_c @ Xs @ nil_no279930520tr_b_c )
= Xs ) ).
% splice_Nil2
thf(fact_209_splice_Osimps_I1_J,axiom,
! [Ys: list_char] :
( ( splice_char @ nil_char @ Ys )
= Ys ) ).
% splice.simps(1)
thf(fact_210_splice_Osimps_I1_J,axiom,
! [Ys: list_n282880152tr_b_c] :
( ( splice1294941035tr_b_c @ nil_no279930520tr_b_c @ Ys )
= Ys ) ).
% splice.simps(1)
thf(fact_211_get__object__ptr__simp1,axiom,
! [Object_ptr: object945351580_d_e_f,Object: rObjec1413572695_j_k_l,H: heap_S1465075775_j_k_l] :
( ( get_O_623850005_j_k_l @ Object_ptr @ ( put_O_834343516_j_k_l @ Object_ptr @ Object @ H ) )
= ( some_R1598191922_j_k_l @ Object ) ) ).
% get_object_ptr_simp1
thf(fact_212_count__list_Osimps_I1_J,axiom,
! [Y: char] :
( ( count_list_char @ nil_char @ Y )
= zero_zero_nat ) ).
% count_list.simps(1)
thf(fact_213_count__list_Osimps_I1_J,axiom,
! [Y: node_p1234578834tr_b_c] :
( ( count_2128515342tr_b_c @ nil_no279930520tr_b_c @ Y )
= zero_zero_nat ) ).
% count_list.simps(1)
thf(fact_214_get__object__ptr__simp2,axiom,
! [Object_ptr: object945351580_d_e_f,Object_ptr2: object945351580_d_e_f,Object: rObjec1413572695_j_k_l,H: heap_S1465075775_j_k_l] :
( ( Object_ptr != Object_ptr2 )
=> ( ( get_O_623850005_j_k_l @ Object_ptr @ ( put_O_834343516_j_k_l @ Object_ptr2 @ Object @ H ) )
= ( get_O_623850005_j_k_l @ Object_ptr @ H ) ) ) ).
% get_object_ptr_simp2
thf(fact_215_transpose_Ocases,axiom,
! [X: list_list_char] :
( ( X != nil_list_char )
=> ( ! [Xss: list_list_char] :
( X
!= ( cons_list_char @ nil_char @ Xss ) )
=> ~ ! [X3: char,Xs2: list_char,Xss: list_list_char] :
( X
!= ( cons_list_char @ ( cons_char @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_216_transpose_Ocases,axiom,
! [X: list_l118626078tr_b_c] :
( ( X != nil_li198338206tr_b_c )
=> ( ! [Xss: list_l118626078tr_b_c] :
( X
!= ( cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ Xss ) )
=> ~ ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Xss: list_l118626078tr_b_c] :
( X
!= ( cons_l1809994318tr_b_c @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_217_list_Odistinct_I1_J,axiom,
! [X21: char,X222: list_char] :
( nil_char
!= ( cons_char @ X21 @ X222 ) ) ).
% list.distinct(1)
thf(fact_218_list_Odistinct_I1_J,axiom,
! [X21: node_p1234578834tr_b_c,X222: list_n282880152tr_b_c] :
( nil_no279930520tr_b_c
!= ( cons_n413985352tr_b_c @ X21 @ X222 ) ) ).
% list.distinct(1)
thf(fact_219_list_OdiscI,axiom,
! [List: list_char,X21: char,X222: list_char] :
( ( List
= ( cons_char @ X21 @ X222 ) )
=> ( List != nil_char ) ) ).
% list.discI
thf(fact_220_list_OdiscI,axiom,
! [List: list_n282880152tr_b_c,X21: node_p1234578834tr_b_c,X222: list_n282880152tr_b_c] :
( ( List
= ( cons_n413985352tr_b_c @ X21 @ X222 ) )
=> ( List != nil_no279930520tr_b_c ) ) ).
% list.discI
thf(fact_221_list_Oexhaust,axiom,
! [Y: list_char] :
( ( Y != nil_char )
=> ~ ! [X212: char,X223: list_char] :
( Y
!= ( cons_char @ X212 @ X223 ) ) ) ).
% list.exhaust
thf(fact_222_list_Oexhaust,axiom,
! [Y: list_n282880152tr_b_c] :
( ( Y != nil_no279930520tr_b_c )
=> ~ ! [X212: node_p1234578834tr_b_c,X223: list_n282880152tr_b_c] :
( Y
!= ( cons_n413985352tr_b_c @ X212 @ X223 ) ) ) ).
% list.exhaust
thf(fact_223_list_Oinducts,axiom,
! [P: list_char > $o,List: list_char] :
( ( P @ nil_char )
=> ( ! [X12: char,X22: list_char] :
( ( P @ X22 )
=> ( P @ ( cons_char @ X12 @ X22 ) ) )
=> ( P @ List ) ) ) ).
% list.inducts
thf(fact_224_list_Oinducts,axiom,
! [P: list_n282880152tr_b_c > $o,List: list_n282880152tr_b_c] :
( ( P @ nil_no279930520tr_b_c )
=> ( ! [X12: node_p1234578834tr_b_c,X22: list_n282880152tr_b_c] :
( ( P @ X22 )
=> ( P @ ( cons_n413985352tr_b_c @ X12 @ X22 ) ) )
=> ( P @ List ) ) ) ).
% list.inducts
thf(fact_225_neq__Nil__conv,axiom,
! [Xs: list_char] :
( ( Xs != nil_char )
= ( ? [Y4: char,Ys2: list_char] :
( Xs
= ( cons_char @ Y4 @ Ys2 ) ) ) ) ).
% neq_Nil_conv
thf(fact_226_neq__Nil__conv,axiom,
! [Xs: list_n282880152tr_b_c] :
( ( Xs != nil_no279930520tr_b_c )
= ( ? [Y4: node_p1234578834tr_b_c,Ys2: list_n282880152tr_b_c] :
( Xs
= ( cons_n413985352tr_b_c @ Y4 @ Ys2 ) ) ) ) ).
% neq_Nil_conv
thf(fact_227_list__induct2_H,axiom,
! [P: list_char > list_char > $o,Xs: list_char,Ys: list_char] :
( ( P @ nil_char @ nil_char )
=> ( ! [X3: char,Xs2: list_char] : ( P @ ( cons_char @ X3 @ Xs2 ) @ nil_char )
=> ( ! [Y3: char,Ys3: list_char] : ( P @ nil_char @ ( cons_char @ Y3 @ Ys3 ) )
=> ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char] :
( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_228_list__induct2_H,axiom,
! [P: list_char > list_n282880152tr_b_c > $o,Xs: list_char,Ys: list_n282880152tr_b_c] :
( ( P @ nil_char @ nil_no279930520tr_b_c )
=> ( ! [X3: char,Xs2: list_char] : ( P @ ( cons_char @ X3 @ Xs2 ) @ nil_no279930520tr_b_c )
=> ( ! [Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] : ( P @ nil_char @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) )
=> ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] :
( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_229_list__induct2_H,axiom,
! [P: list_n282880152tr_b_c > list_char > $o,Xs: list_n282880152tr_b_c,Ys: list_char] :
( ( P @ nil_no279930520tr_b_c @ nil_char )
=> ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] : ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ nil_char )
=> ( ! [Y3: char,Ys3: list_char] : ( P @ nil_no279930520tr_b_c @ ( cons_char @ Y3 @ Ys3 ) )
=> ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char] :
( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_230_list__induct2_H,axiom,
! [P: list_n282880152tr_b_c > list_n282880152tr_b_c > $o,Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
( ( P @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c )
=> ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] : ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ nil_no279930520tr_b_c )
=> ( ! [Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] : ( P @ nil_no279930520tr_b_c @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) )
=> ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] :
( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_231_splice_Oinduct,axiom,
! [P: list_char > list_char > $o,A0: list_char,A1: list_char] :
( ! [X_12: list_char] : ( P @ nil_char @ X_12 )
=> ( ! [X3: char,Xs2: list_char,Ys3: list_char] :
( ( P @ Ys3 @ Xs2 )
=> ( P @ ( cons_char @ X3 @ Xs2 ) @ Ys3 ) )
=> ( P @ A0 @ A1 ) ) ) ).
% splice.induct
thf(fact_232_splice_Oinduct,axiom,
! [P: list_n282880152tr_b_c > list_n282880152tr_b_c > $o,A0: list_n282880152tr_b_c,A1: list_n282880152tr_b_c] :
( ! [X_12: list_n282880152tr_b_c] : ( P @ nil_no279930520tr_b_c @ X_12 )
=> ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Ys3: list_n282880152tr_b_c] :
( ( P @ Ys3 @ Xs2 )
=> ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ Ys3 ) )
=> ( P @ A0 @ A1 ) ) ) ).
% splice.induct
thf(fact_233_induct__list012,axiom,
! [P: list_char > $o,Xs: list_char] :
( ( P @ nil_char )
=> ( ! [X3: char] : ( P @ ( cons_char @ X3 @ nil_char ) )
=> ( ! [X3: char,Y3: char,Zs: list_char] :
( ( P @ Zs )
=> ( ( P @ ( cons_char @ Y3 @ Zs ) )
=> ( P @ ( cons_char @ X3 @ ( cons_char @ Y3 @ Zs ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% induct_list012
thf(fact_234_induct__list012,axiom,
! [P: list_n282880152tr_b_c > $o,Xs: list_n282880152tr_b_c] :
( ( P @ nil_no279930520tr_b_c )
=> ( ! [X3: node_p1234578834tr_b_c] : ( P @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) )
=> ( ! [X3: node_p1234578834tr_b_c,Y3: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c] :
( ( P @ Zs )
=> ( ( P @ ( cons_n413985352tr_b_c @ Y3 @ Zs ) )
=> ( P @ ( cons_n413985352tr_b_c @ X3 @ ( cons_n413985352tr_b_c @ Y3 @ Zs ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% induct_list012
thf(fact_235_shuffles_Oinduct,axiom,
! [P: list_char > list_char > $o,A0: list_char,A1: list_char] :
( ! [X_12: list_char] : ( P @ nil_char @ X_12 )
=> ( ! [Xs2: list_char] : ( P @ Xs2 @ nil_char )
=> ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char] :
( ( P @ Xs2 @ ( cons_char @ Y3 @ Ys3 ) )
=> ( ( P @ ( cons_char @ X3 @ Xs2 ) @ Ys3 )
=> ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) ) ) )
=> ( P @ A0 @ A1 ) ) ) ) ).
% shuffles.induct
thf(fact_236_shuffles_Oinduct,axiom,
! [P: list_n282880152tr_b_c > list_n282880152tr_b_c > $o,A0: list_n282880152tr_b_c,A1: list_n282880152tr_b_c] :
( ! [X_12: list_n282880152tr_b_c] : ( P @ nil_no279930520tr_b_c @ X_12 )
=> ( ! [Xs2: list_n282880152tr_b_c] : ( P @ Xs2 @ nil_no279930520tr_b_c )
=> ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] :
( ( P @ Xs2 @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) )
=> ( ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ Ys3 )
=> ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) ) ) )
=> ( P @ A0 @ A1 ) ) ) ) ).
% shuffles.induct
thf(fact_237_remdups__adj_Ocases,axiom,
! [X: list_char] :
( ( X != nil_char )
=> ( ! [X3: char] :
( X
!= ( cons_char @ X3 @ nil_char ) )
=> ~ ! [X3: char,Y3: char,Xs2: list_char] :
( X
!= ( cons_char @ X3 @ ( cons_char @ Y3 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_238_remdups__adj_Ocases,axiom,
! [X: list_n282880152tr_b_c] :
( ( X != nil_no279930520tr_b_c )
=> ( ! [X3: node_p1234578834tr_b_c] :
( X
!= ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) )
=> ~ ! [X3: node_p1234578834tr_b_c,Y3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
( X
!= ( cons_n413985352tr_b_c @ X3 @ ( cons_n413985352tr_b_c @ Y3 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_239_sorted__wrt_Oinduct,axiom,
! [P: ( char > char > $o ) > list_char > $o,A0: char > char > $o,A1: list_char] :
( ! [P4: char > char > $o] : ( P @ P4 @ nil_char )
=> ( ! [P4: char > char > $o,X3: char,Ys3: list_char] :
( ( P @ P4 @ Ys3 )
=> ( P @ P4 @ ( cons_char @ X3 @ Ys3 ) ) )
=> ( P @ A0 @ A1 ) ) ) ).
% sorted_wrt.induct
thf(fact_240_sorted__wrt_Oinduct,axiom,
! [P: ( node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o ) > list_n282880152tr_b_c > $o,A0: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o,A1: list_n282880152tr_b_c] :
( ! [P4: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o] : ( P @ P4 @ nil_no279930520tr_b_c )
=> ( ! [P4: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o,X3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] :
( ( P @ P4 @ Ys3 )
=> ( P @ P4 @ ( cons_n413985352tr_b_c @ X3 @ Ys3 ) ) )
=> ( P @ A0 @ A1 ) ) ) ).
% sorted_wrt.induct
thf(fact_241_remdups__adj_Oinduct,axiom,
! [P: list_char > $o,A0: list_char] :
( ( P @ nil_char )
=> ( ! [X3: char] : ( P @ ( cons_char @ X3 @ nil_char ) )
=> ( ! [X3: char,Y3: char,Xs2: list_char] :
( ( ( X3 = Y3 )
=> ( P @ ( cons_char @ X3 @ Xs2 ) ) )
=> ( ( ( X3 != Y3 )
=> ( P @ ( cons_char @ Y3 @ Xs2 ) ) )
=> ( P @ ( cons_char @ X3 @ ( cons_char @ Y3 @ Xs2 ) ) ) ) )
=> ( P @ A0 ) ) ) ) ).
% remdups_adj.induct
thf(fact_242_remdups__adj_Oinduct,axiom,
! [P: list_n282880152tr_b_c > $o,A0: list_n282880152tr_b_c] :
( ( P @ nil_no279930520tr_b_c )
=> ( ! [X3: node_p1234578834tr_b_c] : ( P @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) )
=> ( ! [X3: node_p1234578834tr_b_c,Y3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
( ( ( X3 = Y3 )
=> ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) ) )
=> ( ( ( X3 != Y3 )
=> ( P @ ( cons_n413985352tr_b_c @ Y3 @ Xs2 ) ) )
=> ( P @ ( cons_n413985352tr_b_c @ X3 @ ( cons_n413985352tr_b_c @ Y3 @ Xs2 ) ) ) ) )
=> ( P @ A0 ) ) ) ) ).
% remdups_adj.induct
thf(fact_243_successively_Oinduct,axiom,
! [P: ( char > char > $o ) > list_char > $o,A0: char > char > $o,A1: list_char] :
( ! [P4: char > char > $o] : ( P @ P4 @ nil_char )
=> ( ! [P4: char > char > $o,X3: char] : ( P @ P4 @ ( cons_char @ X3 @ nil_char ) )
=> ( ! [P4: char > char > $o,X3: char,Y3: char,Xs2: list_char] :
( ( P @ P4 @ ( cons_char @ Y3 @ Xs2 ) )
=> ( P @ P4 @ ( cons_char @ X3 @ ( cons_char @ Y3 @ Xs2 ) ) ) )
=> ( P @ A0 @ A1 ) ) ) ) ).
% successively.induct
thf(fact_244_successively_Oinduct,axiom,
! [P: ( node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o ) > list_n282880152tr_b_c > $o,A0: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o,A1: list_n282880152tr_b_c] :
( ! [P4: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o] : ( P @ P4 @ nil_no279930520tr_b_c )
=> ( ! [P4: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o,X3: node_p1234578834tr_b_c] : ( P @ P4 @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) )
=> ( ! [P4: node_p1234578834tr_b_c > node_p1234578834tr_b_c > $o,X3: node_p1234578834tr_b_c,Y3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
( ( P @ P4 @ ( cons_n413985352tr_b_c @ Y3 @ Xs2 ) )
=> ( P @ P4 @ ( cons_n413985352tr_b_c @ X3 @ ( cons_n413985352tr_b_c @ Y3 @ Xs2 ) ) ) )
=> ( P @ A0 @ A1 ) ) ) ) ).
% successively.induct
thf(fact_245_list__nonempty__induct,axiom,
! [Xs: list_char,P: list_char > $o] :
( ( Xs != nil_char )
=> ( ! [X3: char] : ( P @ ( cons_char @ X3 @ nil_char ) )
=> ( ! [X3: char,Xs2: list_char] :
( ( Xs2 != nil_char )
=> ( ( P @ Xs2 )
=> ( P @ ( cons_char @ X3 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_246_list__nonempty__induct,axiom,
! [Xs: list_n282880152tr_b_c,P: list_n282880152tr_b_c > $o] :
( ( Xs != nil_no279930520tr_b_c )
=> ( ! [X3: node_p1234578834tr_b_c] : ( P @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) )
=> ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
( ( Xs2 != nil_no279930520tr_b_c )
=> ( ( P @ Xs2 )
=> ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_247_list__induct4,axiom,
! [Xs: list_char,Ys: list_char,Zs2: list_char,Ws: list_char,P: list_char > list_char > list_char > list_char > $o] :
( ( ( size_size_list_char @ Xs )
= ( size_size_list_char @ Ys ) )
=> ( ( ( size_size_list_char @ Ys )
= ( size_size_list_char @ Zs2 ) )
=> ( ( ( size_size_list_char @ Zs2 )
= ( size_size_list_char @ Ws ) )
=> ( ( P @ nil_char @ nil_char @ nil_char @ nil_char )
=> ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char,Z: char,Zs: list_char,W: char,Ws2: list_char] :
( ( ( size_size_list_char @ Xs2 )
= ( size_size_list_char @ Ys3 ) )
=> ( ( ( size_size_list_char @ Ys3 )
= ( size_size_list_char @ Zs ) )
=> ( ( ( size_size_list_char @ Zs )
= ( size_size_list_char @ Ws2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
=> ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) @ ( cons_char @ W @ Ws2 ) ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% list_induct4
thf(fact_248_list__induct4,axiom,
! [Xs: list_char,Ys: list_char,Zs2: list_char,Ws: list_n282880152tr_b_c,P: list_char > list_char > list_char > list_n282880152tr_b_c > $o] :
( ( ( size_size_list_char @ Xs )
= ( size_size_list_char @ Ys ) )
=> ( ( ( size_size_list_char @ Ys )
= ( size_size_list_char @ Zs2 ) )
=> ( ( ( size_size_list_char @ Zs2 )
= ( size_s2106487044tr_b_c @ Ws ) )
=> ( ( P @ nil_char @ nil_char @ nil_char @ nil_no279930520tr_b_c )
=> ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char,Z: char,Zs: list_char,W: node_p1234578834tr_b_c,Ws2: list_n282880152tr_b_c] :
( ( ( size_size_list_char @ Xs2 )
= ( size_size_list_char @ Ys3 ) )
=> ( ( ( size_size_list_char @ Ys3 )
= ( size_size_list_char @ Zs ) )
=> ( ( ( size_size_list_char @ Zs )
= ( size_s2106487044tr_b_c @ Ws2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
=> ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) @ ( cons_n413985352tr_b_c @ W @ Ws2 ) ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% list_induct4
thf(fact_249_list__induct4,axiom,
! [Xs: list_char,Ys: list_char,Zs2: list_n282880152tr_b_c,Ws: list_char,P: list_char > list_char > list_n282880152tr_b_c > list_char > $o] :
( ( ( size_size_list_char @ Xs )
= ( size_size_list_char @ Ys ) )
=> ( ( ( size_size_list_char @ Ys )
= ( size_s2106487044tr_b_c @ Zs2 ) )
=> ( ( ( size_s2106487044tr_b_c @ Zs2 )
= ( size_size_list_char @ Ws ) )
=> ( ( P @ nil_char @ nil_char @ nil_no279930520tr_b_c @ nil_char )
=> ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c,W: char,Ws2: list_char] :
( ( ( size_size_list_char @ Xs2 )
= ( size_size_list_char @ Ys3 ) )
=> ( ( ( size_size_list_char @ Ys3 )
= ( size_s2106487044tr_b_c @ Zs ) )
=> ( ( ( size_s2106487044tr_b_c @ Zs )
= ( size_size_list_char @ Ws2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
=> ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) @ ( cons_char @ W @ Ws2 ) ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% list_induct4
thf(fact_250_list__induct4,axiom,
! [Xs: list_char,Ys: list_n282880152tr_b_c,Zs2: list_char,Ws: list_char,P: list_char > list_n282880152tr_b_c > list_char > list_char > $o] :
( ( ( size_size_list_char @ Xs )
= ( size_s2106487044tr_b_c @ Ys ) )
=> ( ( ( size_s2106487044tr_b_c @ Ys )
= ( size_size_list_char @ Zs2 ) )
=> ( ( ( size_size_list_char @ Zs2 )
= ( size_size_list_char @ Ws ) )
=> ( ( P @ nil_char @ nil_no279930520tr_b_c @ nil_char @ nil_char )
=> ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: char,Zs: list_char,W: char,Ws2: list_char] :
( ( ( size_size_list_char @ Xs2 )
= ( size_s2106487044tr_b_c @ Ys3 ) )
=> ( ( ( size_s2106487044tr_b_c @ Ys3 )
= ( size_size_list_char @ Zs ) )
=> ( ( ( size_size_list_char @ Zs )
= ( size_size_list_char @ Ws2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
=> ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) @ ( cons_char @ W @ Ws2 ) ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% list_induct4
thf(fact_251_list__induct4,axiom,
! [Xs: list_n282880152tr_b_c,Ys: list_char,Zs2: list_char,Ws: list_char,P: list_n282880152tr_b_c > list_char > list_char > list_char > $o] :
( ( ( size_s2106487044tr_b_c @ Xs )
= ( size_size_list_char @ Ys ) )
=> ( ( ( size_size_list_char @ Ys )
= ( size_size_list_char @ Zs2 ) )
=> ( ( ( size_size_list_char @ Zs2 )
= ( size_size_list_char @ Ws ) )
=> ( ( P @ nil_no279930520tr_b_c @ nil_char @ nil_char @ nil_char )
=> ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char,Z: char,Zs: list_char,W: char,Ws2: list_char] :
( ( ( size_s2106487044tr_b_c @ Xs2 )
= ( size_size_list_char @ Ys3 ) )
=> ( ( ( size_size_list_char @ Ys3 )
= ( size_size_list_char @ Zs ) )
=> ( ( ( size_size_list_char @ Zs )
= ( size_size_list_char @ Ws2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
=> ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) @ ( cons_char @ W @ Ws2 ) ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% list_induct4
thf(fact_252_list__induct4,axiom,
! [Xs: list_char,Ys: list_char,Zs2: list_n282880152tr_b_c,Ws: list_n282880152tr_b_c,P: list_char > list_char > list_n282880152tr_b_c > list_n282880152tr_b_c > $o] :
( ( ( size_size_list_char @ Xs )
= ( size_size_list_char @ Ys ) )
=> ( ( ( size_size_list_char @ Ys )
= ( size_s2106487044tr_b_c @ Zs2 ) )
=> ( ( ( size_s2106487044tr_b_c @ Zs2 )
= ( size_s2106487044tr_b_c @ Ws ) )
=> ( ( P @ nil_char @ nil_char @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c )
=> ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c,W: node_p1234578834tr_b_c,Ws2: list_n282880152tr_b_c] :
( ( ( size_size_list_char @ Xs2 )
= ( size_size_list_char @ Ys3 ) )
=> ( ( ( size_size_list_char @ Ys3 )
= ( size_s2106487044tr_b_c @ Zs ) )
=> ( ( ( size_s2106487044tr_b_c @ Zs )
= ( size_s2106487044tr_b_c @ Ws2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
=> ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) @ ( cons_n413985352tr_b_c @ W @ Ws2 ) ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% list_induct4
thf(fact_253_list__induct4,axiom,
! [Xs: list_char,Ys: list_n282880152tr_b_c,Zs2: list_char,Ws: list_n282880152tr_b_c,P: list_char > list_n282880152tr_b_c > list_char > list_n282880152tr_b_c > $o] :
( ( ( size_size_list_char @ Xs )
= ( size_s2106487044tr_b_c @ Ys ) )
=> ( ( ( size_s2106487044tr_b_c @ Ys )
= ( size_size_list_char @ Zs2 ) )
=> ( ( ( size_size_list_char @ Zs2 )
= ( size_s2106487044tr_b_c @ Ws ) )
=> ( ( P @ nil_char @ nil_no279930520tr_b_c @ nil_char @ nil_no279930520tr_b_c )
=> ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: char,Zs: list_char,W: node_p1234578834tr_b_c,Ws2: list_n282880152tr_b_c] :
( ( ( size_size_list_char @ Xs2 )
= ( size_s2106487044tr_b_c @ Ys3 ) )
=> ( ( ( size_s2106487044tr_b_c @ Ys3 )
= ( size_size_list_char @ Zs ) )
=> ( ( ( size_size_list_char @ Zs )
= ( size_s2106487044tr_b_c @ Ws2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
=> ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) @ ( cons_n413985352tr_b_c @ W @ Ws2 ) ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% list_induct4
thf(fact_254_list__induct4,axiom,
! [Xs: list_char,Ys: list_n282880152tr_b_c,Zs2: list_n282880152tr_b_c,Ws: list_char,P: list_char > list_n282880152tr_b_c > list_n282880152tr_b_c > list_char > $o] :
( ( ( size_size_list_char @ Xs )
= ( size_s2106487044tr_b_c @ Ys ) )
=> ( ( ( size_s2106487044tr_b_c @ Ys )
= ( size_s2106487044tr_b_c @ Zs2 ) )
=> ( ( ( size_s2106487044tr_b_c @ Zs2 )
= ( size_size_list_char @ Ws ) )
=> ( ( P @ nil_char @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c @ nil_char )
=> ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c,W: char,Ws2: list_char] :
( ( ( size_size_list_char @ Xs2 )
= ( size_s2106487044tr_b_c @ Ys3 ) )
=> ( ( ( size_s2106487044tr_b_c @ Ys3 )
= ( size_s2106487044tr_b_c @ Zs ) )
=> ( ( ( size_s2106487044tr_b_c @ Zs )
= ( size_size_list_char @ Ws2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
=> ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) @ ( cons_char @ W @ Ws2 ) ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% list_induct4
thf(fact_255_list__induct4,axiom,
! [Xs: list_n282880152tr_b_c,Ys: list_char,Zs2: list_char,Ws: list_n282880152tr_b_c,P: list_n282880152tr_b_c > list_char > list_char > list_n282880152tr_b_c > $o] :
( ( ( size_s2106487044tr_b_c @ Xs )
= ( size_size_list_char @ Ys ) )
=> ( ( ( size_size_list_char @ Ys )
= ( size_size_list_char @ Zs2 ) )
=> ( ( ( size_size_list_char @ Zs2 )
= ( size_s2106487044tr_b_c @ Ws ) )
=> ( ( P @ nil_no279930520tr_b_c @ nil_char @ nil_char @ nil_no279930520tr_b_c )
=> ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char,Z: char,Zs: list_char,W: node_p1234578834tr_b_c,Ws2: list_n282880152tr_b_c] :
( ( ( size_s2106487044tr_b_c @ Xs2 )
= ( size_size_list_char @ Ys3 ) )
=> ( ( ( size_size_list_char @ Ys3 )
= ( size_size_list_char @ Zs ) )
=> ( ( ( size_size_list_char @ Zs )
= ( size_s2106487044tr_b_c @ Ws2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
=> ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) @ ( cons_n413985352tr_b_c @ W @ Ws2 ) ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% list_induct4
thf(fact_256_list__induct4,axiom,
! [Xs: list_n282880152tr_b_c,Ys: list_char,Zs2: list_n282880152tr_b_c,Ws: list_char,P: list_n282880152tr_b_c > list_char > list_n282880152tr_b_c > list_char > $o] :
( ( ( size_s2106487044tr_b_c @ Xs )
= ( size_size_list_char @ Ys ) )
=> ( ( ( size_size_list_char @ Ys )
= ( size_s2106487044tr_b_c @ Zs2 ) )
=> ( ( ( size_s2106487044tr_b_c @ Zs2 )
= ( size_size_list_char @ Ws ) )
=> ( ( P @ nil_no279930520tr_b_c @ nil_char @ nil_no279930520tr_b_c @ nil_char )
=> ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c,W: char,Ws2: list_char] :
( ( ( size_s2106487044tr_b_c @ Xs2 )
= ( size_size_list_char @ Ys3 ) )
=> ( ( ( size_size_list_char @ Ys3 )
= ( size_s2106487044tr_b_c @ Zs ) )
=> ( ( ( size_s2106487044tr_b_c @ Zs )
= ( size_size_list_char @ Ws2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
=> ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) @ ( cons_char @ W @ Ws2 ) ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% list_induct4
thf(fact_257_list__induct3,axiom,
! [Xs: list_char,Ys: list_char,Zs2: list_char,P: list_char > list_char > list_char > $o] :
( ( ( size_size_list_char @ Xs )
= ( size_size_list_char @ Ys ) )
=> ( ( ( size_size_list_char @ Ys )
= ( size_size_list_char @ Zs2 ) )
=> ( ( P @ nil_char @ nil_char @ nil_char )
=> ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char,Z: char,Zs: list_char] :
( ( ( size_size_list_char @ Xs2 )
= ( size_size_list_char @ Ys3 ) )
=> ( ( ( size_size_list_char @ Ys3 )
= ( size_size_list_char @ Zs ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs )
=> ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% list_induct3
thf(fact_258_list__induct3,axiom,
! [Xs: list_char,Ys: list_char,Zs2: list_n282880152tr_b_c,P: list_char > list_char > list_n282880152tr_b_c > $o] :
( ( ( size_size_list_char @ Xs )
= ( size_size_list_char @ Ys ) )
=> ( ( ( size_size_list_char @ Ys )
= ( size_s2106487044tr_b_c @ Zs2 ) )
=> ( ( P @ nil_char @ nil_char @ nil_no279930520tr_b_c )
=> ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c] :
( ( ( size_size_list_char @ Xs2 )
= ( size_size_list_char @ Ys3 ) )
=> ( ( ( size_size_list_char @ Ys3 )
= ( size_s2106487044tr_b_c @ Zs ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs )
=> ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% list_induct3
thf(fact_259_list__induct3,axiom,
! [Xs: list_char,Ys: list_n282880152tr_b_c,Zs2: list_char,P: list_char > list_n282880152tr_b_c > list_char > $o] :
( ( ( size_size_list_char @ Xs )
= ( size_s2106487044tr_b_c @ Ys ) )
=> ( ( ( size_s2106487044tr_b_c @ Ys )
= ( size_size_list_char @ Zs2 ) )
=> ( ( P @ nil_char @ nil_no279930520tr_b_c @ nil_char )
=> ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: char,Zs: list_char] :
( ( ( size_size_list_char @ Xs2 )
= ( size_s2106487044tr_b_c @ Ys3 ) )
=> ( ( ( size_s2106487044tr_b_c @ Ys3 )
= ( size_size_list_char @ Zs ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs )
=> ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% list_induct3
thf(fact_260_list__induct3,axiom,
! [Xs: list_char,Ys: list_n282880152tr_b_c,Zs2: list_n282880152tr_b_c,P: list_char > list_n282880152tr_b_c > list_n282880152tr_b_c > $o] :
( ( ( size_size_list_char @ Xs )
= ( size_s2106487044tr_b_c @ Ys ) )
=> ( ( ( size_s2106487044tr_b_c @ Ys )
= ( size_s2106487044tr_b_c @ Zs2 ) )
=> ( ( P @ nil_char @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c )
=> ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c] :
( ( ( size_size_list_char @ Xs2 )
= ( size_s2106487044tr_b_c @ Ys3 ) )
=> ( ( ( size_s2106487044tr_b_c @ Ys3 )
= ( size_s2106487044tr_b_c @ Zs ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs )
=> ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% list_induct3
thf(fact_261_list__induct3,axiom,
! [Xs: list_n282880152tr_b_c,Ys: list_char,Zs2: list_char,P: list_n282880152tr_b_c > list_char > list_char > $o] :
( ( ( size_s2106487044tr_b_c @ Xs )
= ( size_size_list_char @ Ys ) )
=> ( ( ( size_size_list_char @ Ys )
= ( size_size_list_char @ Zs2 ) )
=> ( ( P @ nil_no279930520tr_b_c @ nil_char @ nil_char )
=> ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char,Z: char,Zs: list_char] :
( ( ( size_s2106487044tr_b_c @ Xs2 )
= ( size_size_list_char @ Ys3 ) )
=> ( ( ( size_size_list_char @ Ys3 )
= ( size_size_list_char @ Zs ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs )
=> ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% list_induct3
thf(fact_262_list__induct3,axiom,
! [Xs: list_n282880152tr_b_c,Ys: list_char,Zs2: list_n282880152tr_b_c,P: list_n282880152tr_b_c > list_char > list_n282880152tr_b_c > $o] :
( ( ( size_s2106487044tr_b_c @ Xs )
= ( size_size_list_char @ Ys ) )
=> ( ( ( size_size_list_char @ Ys )
= ( size_s2106487044tr_b_c @ Zs2 ) )
=> ( ( P @ nil_no279930520tr_b_c @ nil_char @ nil_no279930520tr_b_c )
=> ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c] :
( ( ( size_s2106487044tr_b_c @ Xs2 )
= ( size_size_list_char @ Ys3 ) )
=> ( ( ( size_size_list_char @ Ys3 )
= ( size_s2106487044tr_b_c @ Zs ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs )
=> ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% list_induct3
thf(fact_263_list__induct3,axiom,
! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c,Zs2: list_char,P: list_n282880152tr_b_c > list_n282880152tr_b_c > list_char > $o] :
( ( ( size_s2106487044tr_b_c @ Xs )
= ( size_s2106487044tr_b_c @ Ys ) )
=> ( ( ( size_s2106487044tr_b_c @ Ys )
= ( size_size_list_char @ Zs2 ) )
=> ( ( P @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c @ nil_char )
=> ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: char,Zs: list_char] :
( ( ( size_s2106487044tr_b_c @ Xs2 )
= ( size_s2106487044tr_b_c @ Ys3 ) )
=> ( ( ( size_s2106487044tr_b_c @ Ys3 )
= ( size_size_list_char @ Zs ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs )
=> ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_char @ Z @ Zs ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% list_induct3
thf(fact_264_list__induct3,axiom,
! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c,Zs2: list_n282880152tr_b_c,P: list_n282880152tr_b_c > list_n282880152tr_b_c > list_n282880152tr_b_c > $o] :
( ( ( size_s2106487044tr_b_c @ Xs )
= ( size_s2106487044tr_b_c @ Ys ) )
=> ( ( ( size_s2106487044tr_b_c @ Ys )
= ( size_s2106487044tr_b_c @ Zs2 ) )
=> ( ( P @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c )
=> ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c,Z: node_p1234578834tr_b_c,Zs: list_n282880152tr_b_c] :
( ( ( size_s2106487044tr_b_c @ Xs2 )
= ( size_s2106487044tr_b_c @ Ys3 ) )
=> ( ( ( size_s2106487044tr_b_c @ Ys3 )
= ( size_s2106487044tr_b_c @ Zs ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs )
=> ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) @ ( cons_n413985352tr_b_c @ Z @ Zs ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% list_induct3
thf(fact_265_list__induct2,axiom,
! [Xs: list_char,Ys: list_char,P: list_char > list_char > $o] :
( ( ( size_size_list_char @ Xs )
= ( size_size_list_char @ Ys ) )
=> ( ( P @ nil_char @ nil_char )
=> ( ! [X3: char,Xs2: list_char,Y3: char,Ys3: list_char] :
( ( ( size_size_list_char @ Xs2 )
= ( size_size_list_char @ Ys3 ) )
=> ( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_266_list__induct2,axiom,
! [Xs: list_char,Ys: list_n282880152tr_b_c,P: list_char > list_n282880152tr_b_c > $o] :
( ( ( size_size_list_char @ Xs )
= ( size_s2106487044tr_b_c @ Ys ) )
=> ( ( P @ nil_char @ nil_no279930520tr_b_c )
=> ( ! [X3: char,Xs2: list_char,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] :
( ( ( size_size_list_char @ Xs2 )
= ( size_s2106487044tr_b_c @ Ys3 ) )
=> ( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_char @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_267_list__induct2,axiom,
! [Xs: list_n282880152tr_b_c,Ys: list_char,P: list_n282880152tr_b_c > list_char > $o] :
( ( ( size_s2106487044tr_b_c @ Xs )
= ( size_size_list_char @ Ys ) )
=> ( ( P @ nil_no279930520tr_b_c @ nil_char )
=> ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: char,Ys3: list_char] :
( ( ( size_s2106487044tr_b_c @ Xs2 )
= ( size_size_list_char @ Ys3 ) )
=> ( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_char @ Y3 @ Ys3 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_268_list__induct2,axiom,
! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c,P: list_n282880152tr_b_c > list_n282880152tr_b_c > $o] :
( ( ( size_s2106487044tr_b_c @ Xs )
= ( size_s2106487044tr_b_c @ Ys ) )
=> ( ( P @ nil_no279930520tr_b_c @ nil_no279930520tr_b_c )
=> ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c,Y3: node_p1234578834tr_b_c,Ys3: list_n282880152tr_b_c] :
( ( ( size_s2106487044tr_b_c @ Xs2 )
= ( size_s2106487044tr_b_c @ Ys3 ) )
=> ( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons_n413985352tr_b_c @ X3 @ Xs2 ) @ ( cons_n413985352tr_b_c @ Y3 @ Ys3 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_269_splice_Oelims,axiom,
! [X: list_char,Xa: list_char,Y: list_char] :
( ( ( splice_char @ X @ Xa )
= Y )
=> ( ( ( X = nil_char )
=> ( Y != Xa ) )
=> ~ ! [X3: char,Xs2: list_char] :
( ( X
= ( cons_char @ X3 @ Xs2 ) )
=> ( Y
!= ( cons_char @ X3 @ ( splice_char @ Xa @ Xs2 ) ) ) ) ) ) ).
% splice.elims
thf(fact_270_splice_Oelims,axiom,
! [X: list_n282880152tr_b_c,Xa: list_n282880152tr_b_c,Y: list_n282880152tr_b_c] :
( ( ( splice1294941035tr_b_c @ X @ Xa )
= Y )
=> ( ( ( X = nil_no279930520tr_b_c )
=> ( Y != Xa ) )
=> ~ ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
( ( X
= ( cons_n413985352tr_b_c @ X3 @ Xs2 ) )
=> ( Y
!= ( cons_n413985352tr_b_c @ X3 @ ( splice1294941035tr_b_c @ Xa @ Xs2 ) ) ) ) ) ) ).
% splice.elims
thf(fact_271_get__object__ptr__simp,axiom,
! [Ptr2: object945351580_d_e_f,Object_ptr: object945351580_d_e_f,Obj: rObjec1413572695_j_k_l,H: heap_S1465075775_j_k_l] :
( ( ( Ptr2 = Object_ptr )
=> ( ( get_O_623850005_j_k_l @ Object_ptr @ ( put_O_834343516_j_k_l @ Ptr2 @ Obj @ H ) )
= ( some_R1598191922_j_k_l @ Obj ) ) )
& ( ( Ptr2 != Object_ptr )
=> ( ( get_O_623850005_j_k_l @ Object_ptr @ ( put_O_834343516_j_k_l @ Ptr2 @ Obj @ H ) )
= ( get_O_623850005_j_k_l @ Object_ptr @ H ) ) ) ) ).
% get_object_ptr_simp
thf(fact_272_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_273_n__lists__Nil,axiom,
! [N: nat] :
( ( ( N = zero_zero_nat )
=> ( ( n_list1807568544tr_b_c @ N @ nil_no279930520tr_b_c )
= ( cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c ) ) )
& ( ( N != zero_zero_nat )
=> ( ( n_list1807568544tr_b_c @ N @ nil_no279930520tr_b_c )
= nil_li198338206tr_b_c ) ) ) ).
% n_lists_Nil
thf(fact_274_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_275_n__lists_Osimps_I1_J,axiom,
! [Xs: list_n282880152tr_b_c] :
( ( n_list1807568544tr_b_c @ zero_zero_nat @ Xs )
= ( cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c ) ) ).
% n_lists.simps(1)
thf(fact_276_product__lists_Osimps_I1_J,axiom,
( ( product_lists_char @ nil_list_char )
= ( cons_list_char @ nil_char @ nil_list_char ) ) ).
% product_lists.simps(1)
thf(fact_277_product__lists_Osimps_I1_J,axiom,
( ( produc1509350401tr_b_c @ nil_li198338206tr_b_c )
= ( cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c ) ) ).
% product_lists.simps(1)
thf(fact_278_subseqs_Osimps_I1_J,axiom,
( ( subseqs_char @ nil_char )
= ( cons_list_char @ nil_char @ nil_list_char ) ) ).
% subseqs.simps(1)
thf(fact_279_subseqs_Osimps_I1_J,axiom,
( ( subseq1828679783tr_b_c @ nil_no279930520tr_b_c )
= ( cons_l1809994318tr_b_c @ nil_no279930520tr_b_c @ nil_li198338206tr_b_c ) ) ).
% subseqs.simps(1)
thf(fact_280_insert__Nil,axiom,
! [X: char] :
( ( insert_char @ X @ nil_char )
= ( cons_char @ X @ nil_char ) ) ).
% insert_Nil
thf(fact_281_insert__Nil,axiom,
! [X: node_p1234578834tr_b_c] :
( ( insert678865070tr_b_c @ X @ nil_no279930520tr_b_c )
= ( cons_n413985352tr_b_c @ X @ nil_no279930520tr_b_c ) ) ).
% insert_Nil
thf(fact_282_nths__singleton,axiom,
! [A2: set_nat,X: char] :
( ( ( member_nat @ zero_zero_nat @ A2 )
=> ( ( nths_char @ ( cons_char @ X @ nil_char ) @ A2 )
= ( cons_char @ X @ nil_char ) ) )
& ( ~ ( member_nat @ zero_zero_nat @ A2 )
=> ( ( nths_char @ ( cons_char @ X @ nil_char ) @ A2 )
= nil_char ) ) ) ).
% nths_singleton
thf(fact_283_nths__singleton,axiom,
! [A2: set_nat,X: node_p1234578834tr_b_c] :
( ( ( member_nat @ zero_zero_nat @ A2 )
=> ( ( nths_n1256675478tr_b_c @ ( cons_n413985352tr_b_c @ X @ nil_no279930520tr_b_c ) @ A2 )
= ( cons_n413985352tr_b_c @ X @ nil_no279930520tr_b_c ) ) )
& ( ~ ( member_nat @ zero_zero_nat @ A2 )
=> ( ( nths_n1256675478tr_b_c @ ( cons_n413985352tr_b_c @ X @ nil_no279930520tr_b_c ) @ A2 )
= nil_no279930520tr_b_c ) ) ) ).
% nths_singleton
thf(fact_284_nths__nil,axiom,
! [A2: set_nat] :
( ( nths_char @ nil_char @ A2 )
= nil_char ) ).
% nths_nil
thf(fact_285_nths__nil,axiom,
! [A2: set_nat] :
( ( nths_n1256675478tr_b_c @ nil_no279930520tr_b_c @ A2 )
= nil_no279930520tr_b_c ) ).
% nths_nil
thf(fact_286_nths__empty,axiom,
! [Xs: list_char] :
( ( nths_char @ Xs @ bot_bot_set_nat )
= nil_char ) ).
% nths_empty
thf(fact_287_nths__empty,axiom,
! [Xs: list_n282880152tr_b_c] :
( ( nths_n1256675478tr_b_c @ Xs @ bot_bot_set_nat )
= nil_no279930520tr_b_c ) ).
% nths_empty
thf(fact_288_bind__split__asm,axiom,
! [P: option_element_ptr_a > $o,M2: option_element_ptr_a,F: element_ptr_a > option_element_ptr_a] :
( ( P @ ( bind_e22036734_ptr_a @ M2 @ F ) )
= ( ~ ( ( ( M2 = none_element_ptr_a )
& ~ ( P @ none_element_ptr_a ) )
| ? [X4: element_ptr_a] :
( ( M2
= ( some_element_ptr_a @ X4 ) )
& ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).
% bind_split_asm
thf(fact_289_bind__split__asm,axiom,
! [P: option2026120038on_j_k > $o,M2: option_element_ptr_a,F: element_ptr_a > option2026120038on_j_k] :
( ( P @ ( bind_e1012152651on_j_k @ M2 @ F ) )
= ( ~ ( ( ( M2 = none_element_ptr_a )
& ~ ( P @ none_S1393028981on_j_k ) )
| ? [X4: element_ptr_a] :
( ( M2
= ( some_element_ptr_a @ X4 ) )
& ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).
% bind_split_asm
thf(fact_290_bind__split__asm,axiom,
! [P: option_element_ptr_a > $o,M2: option2026120038on_j_k,F: sum_su1221287958on_j_k > option_element_ptr_a] :
( ( P @ ( bind_S287509021_ptr_a @ M2 @ F ) )
= ( ~ ( ( ( M2 = none_S1393028981on_j_k )
& ~ ( P @ none_element_ptr_a ) )
| ? [X4: sum_su1221287958on_j_k] :
( ( M2
= ( some_S1960742641on_j_k @ X4 ) )
& ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).
% bind_split_asm
thf(fact_291_bind__split__asm,axiom,
! [P: option2026120038on_j_k > $o,M2: option2026120038on_j_k,F: sum_su1221287958on_j_k > option2026120038on_j_k] :
( ( P @ ( bind_S607117548on_j_k @ M2 @ F ) )
= ( ~ ( ( ( M2 = none_S1393028981on_j_k )
& ~ ( P @ none_S1393028981on_j_k ) )
| ? [X4: sum_su1221287958on_j_k] :
( ( M2
= ( some_S1960742641on_j_k @ X4 ) )
& ~ ( P @ ( F @ X4 ) ) ) ) ) ) ).
% bind_split_asm
thf(fact_292_bind__split,axiom,
! [P: option_element_ptr_a > $o,M2: option_element_ptr_a,F: element_ptr_a > option_element_ptr_a] :
( ( P @ ( bind_e22036734_ptr_a @ M2 @ F ) )
= ( ( ( M2 = none_element_ptr_a )
=> ( P @ none_element_ptr_a ) )
& ! [V3: element_ptr_a] :
( ( M2
= ( some_element_ptr_a @ V3 ) )
=> ( P @ ( F @ V3 ) ) ) ) ) ).
% bind_split
thf(fact_293_bind__split,axiom,
! [P: option2026120038on_j_k > $o,M2: option_element_ptr_a,F: element_ptr_a > option2026120038on_j_k] :
( ( P @ ( bind_e1012152651on_j_k @ M2 @ F ) )
= ( ( ( M2 = none_element_ptr_a )
=> ( P @ none_S1393028981on_j_k ) )
& ! [V3: element_ptr_a] :
( ( M2
= ( some_element_ptr_a @ V3 ) )
=> ( P @ ( F @ V3 ) ) ) ) ) ).
% bind_split
thf(fact_294_bind__split,axiom,
! [P: option_element_ptr_a > $o,M2: option2026120038on_j_k,F: sum_su1221287958on_j_k > option_element_ptr_a] :
( ( P @ ( bind_S287509021_ptr_a @ M2 @ F ) )
= ( ( ( M2 = none_S1393028981on_j_k )
=> ( P @ none_element_ptr_a ) )
& ! [V3: sum_su1221287958on_j_k] :
( ( M2
= ( some_S1960742641on_j_k @ V3 ) )
=> ( P @ ( F @ V3 ) ) ) ) ) ).
% bind_split
thf(fact_295_bind__split,axiom,
! [P: option2026120038on_j_k > $o,M2: option2026120038on_j_k,F: sum_su1221287958on_j_k > option2026120038on_j_k] :
( ( P @ ( bind_S607117548on_j_k @ M2 @ F ) )
= ( ( ( M2 = none_S1393028981on_j_k )
=> ( P @ none_S1393028981on_j_k ) )
& ! [V3: sum_su1221287958on_j_k] :
( ( M2
= ( some_S1960742641on_j_k @ V3 ) )
=> ( P @ ( F @ V3 ) ) ) ) ) ).
% bind_split
thf(fact_296_bind_Obind__lzero,axiom,
! [F: element_ptr_a > option_element_ptr_a] :
( ( bind_e22036734_ptr_a @ none_element_ptr_a @ F )
= none_element_ptr_a ) ).
% bind.bind_lzero
thf(fact_297_bind_Obind__lzero,axiom,
! [F: element_ptr_a > option2026120038on_j_k] :
( ( bind_e1012152651on_j_k @ none_element_ptr_a @ F )
= none_S1393028981on_j_k ) ).
% bind.bind_lzero
thf(fact_298_bind_Obind__lzero,axiom,
! [F: sum_su1221287958on_j_k > option_element_ptr_a] :
( ( bind_S287509021_ptr_a @ none_S1393028981on_j_k @ F )
= none_element_ptr_a ) ).
% bind.bind_lzero
thf(fact_299_bind_Obind__lzero,axiom,
! [F: sum_su1221287958on_j_k > option2026120038on_j_k] :
( ( bind_S607117548on_j_k @ none_S1393028981on_j_k @ F )
= none_S1393028981on_j_k ) ).
% bind.bind_lzero
thf(fact_300_set__encode__empty,axiom,
( ( nat_set_encode @ bot_bot_set_nat )
= zero_zero_nat ) ).
% set_encode_empty
thf(fact_301_set__decode__zero,axiom,
( ( nat_set_decode @ zero_zero_nat )
= bot_bot_set_nat ) ).
% set_decode_zero
thf(fact_302_length__append__singleton,axiom,
! [Xs: list_char,X: char] :
( ( size_size_list_char @ ( append_char @ Xs @ ( cons_char @ X @ nil_char ) ) )
= ( suc @ ( size_size_list_char @ Xs ) ) ) ).
% length_append_singleton
thf(fact_303_length__append__singleton,axiom,
! [Xs: list_n282880152tr_b_c,X: node_p1234578834tr_b_c] :
( ( size_s2106487044tr_b_c @ ( append846395565tr_b_c @ Xs @ ( cons_n413985352tr_b_c @ X @ nil_no279930520tr_b_c ) ) )
= ( suc @ ( size_s2106487044tr_b_c @ Xs ) ) ) ).
% length_append_singleton
thf(fact_304_append__Nil2,axiom,
! [Xs: list_char] :
( ( append_char @ Xs @ nil_char )
= Xs ) ).
% append_Nil2
thf(fact_305_append__Nil2,axiom,
! [Xs: list_n282880152tr_b_c] :
( ( append846395565tr_b_c @ Xs @ nil_no279930520tr_b_c )
= Xs ) ).
% append_Nil2
thf(fact_306_append__self__conv,axiom,
! [Xs: list_char,Ys: list_char] :
( ( ( append_char @ Xs @ Ys )
= Xs )
= ( Ys = nil_char ) ) ).
% append_self_conv
thf(fact_307_append__self__conv,axiom,
! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
( ( ( append846395565tr_b_c @ Xs @ Ys )
= Xs )
= ( Ys = nil_no279930520tr_b_c ) ) ).
% append_self_conv
thf(fact_308_self__append__conv,axiom,
! [Xs: list_char,Ys: list_char] :
( ( Xs
= ( append_char @ Xs @ Ys ) )
= ( Ys = nil_char ) ) ).
% self_append_conv
thf(fact_309_self__append__conv,axiom,
! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
( ( Xs
= ( append846395565tr_b_c @ Xs @ Ys ) )
= ( Ys = nil_no279930520tr_b_c ) ) ).
% self_append_conv
thf(fact_310_append__self__conv2,axiom,
! [Xs: list_char,Ys: list_char] :
( ( ( append_char @ Xs @ Ys )
= Ys )
= ( Xs = nil_char ) ) ).
% append_self_conv2
thf(fact_311_append__self__conv2,axiom,
! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
( ( ( append846395565tr_b_c @ Xs @ Ys )
= Ys )
= ( Xs = nil_no279930520tr_b_c ) ) ).
% append_self_conv2
thf(fact_312_self__append__conv2,axiom,
! [Ys: list_char,Xs: list_char] :
( ( Ys
= ( append_char @ Xs @ Ys ) )
= ( Xs = nil_char ) ) ).
% self_append_conv2
thf(fact_313_self__append__conv2,axiom,
! [Ys: list_n282880152tr_b_c,Xs: list_n282880152tr_b_c] :
( ( Ys
= ( append846395565tr_b_c @ Xs @ Ys ) )
= ( Xs = nil_no279930520tr_b_c ) ) ).
% self_append_conv2
thf(fact_314_Nil__is__append__conv,axiom,
! [Xs: list_char,Ys: list_char] :
( ( nil_char
= ( append_char @ Xs @ Ys ) )
= ( ( Xs = nil_char )
& ( Ys = nil_char ) ) ) ).
% Nil_is_append_conv
thf(fact_315_Nil__is__append__conv,axiom,
! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
( ( nil_no279930520tr_b_c
= ( append846395565tr_b_c @ Xs @ Ys ) )
= ( ( Xs = nil_no279930520tr_b_c )
& ( Ys = nil_no279930520tr_b_c ) ) ) ).
% Nil_is_append_conv
thf(fact_316_append__is__Nil__conv,axiom,
! [Xs: list_char,Ys: list_char] :
( ( ( append_char @ Xs @ Ys )
= nil_char )
= ( ( Xs = nil_char )
& ( Ys = nil_char ) ) ) ).
% append_is_Nil_conv
thf(fact_317_append__is__Nil__conv,axiom,
! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
( ( ( append846395565tr_b_c @ Xs @ Ys )
= nil_no279930520tr_b_c )
= ( ( Xs = nil_no279930520tr_b_c )
& ( Ys = nil_no279930520tr_b_c ) ) ) ).
% append_is_Nil_conv
thf(fact_318_append_Oright__neutral,axiom,
! [A: list_char] :
( ( append_char @ A @ nil_char )
= A ) ).
% append.right_neutral
thf(fact_319_append_Oright__neutral,axiom,
! [A: list_n282880152tr_b_c] :
( ( append846395565tr_b_c @ A @ nil_no279930520tr_b_c )
= A ) ).
% append.right_neutral
thf(fact_320_set__decode__inverse,axiom,
! [N: nat] :
( ( nat_set_encode @ ( nat_set_decode @ N ) )
= N ) ).
% set_decode_inverse
thf(fact_321_append1__eq__conv,axiom,
! [Xs: list_char,X: char,Ys: list_char,Y: char] :
( ( ( append_char @ Xs @ ( cons_char @ X @ nil_char ) )
= ( append_char @ Ys @ ( cons_char @ Y @ nil_char ) ) )
= ( ( Xs = Ys )
& ( X = Y ) ) ) ).
% append1_eq_conv
thf(fact_322_append1__eq__conv,axiom,
! [Xs: list_n282880152tr_b_c,X: node_p1234578834tr_b_c,Ys: list_n282880152tr_b_c,Y: node_p1234578834tr_b_c] :
( ( ( append846395565tr_b_c @ Xs @ ( cons_n413985352tr_b_c @ X @ nil_no279930520tr_b_c ) )
= ( append846395565tr_b_c @ Ys @ ( cons_n413985352tr_b_c @ Y @ nil_no279930520tr_b_c ) ) )
= ( ( Xs = Ys )
& ( X = Y ) ) ) ).
% append1_eq_conv
thf(fact_323_rev__induct,axiom,
! [P: list_char > $o,Xs: list_char] :
( ( P @ nil_char )
=> ( ! [X3: char,Xs2: list_char] :
( ( P @ Xs2 )
=> ( P @ ( append_char @ Xs2 @ ( cons_char @ X3 @ nil_char ) ) ) )
=> ( P @ Xs ) ) ) ).
% rev_induct
thf(fact_324_rev__induct,axiom,
! [P: list_n282880152tr_b_c > $o,Xs: list_n282880152tr_b_c] :
( ( P @ nil_no279930520tr_b_c )
=> ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
( ( P @ Xs2 )
=> ( P @ ( append846395565tr_b_c @ Xs2 @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) ) ) )
=> ( P @ Xs ) ) ) ).
% rev_induct
thf(fact_325_rev__exhaust,axiom,
! [Xs: list_char] :
( ( Xs != nil_char )
=> ~ ! [Ys3: list_char,Y3: char] :
( Xs
!= ( append_char @ Ys3 @ ( cons_char @ Y3 @ nil_char ) ) ) ) ).
% rev_exhaust
thf(fact_326_rev__exhaust,axiom,
! [Xs: list_n282880152tr_b_c] :
( ( Xs != nil_no279930520tr_b_c )
=> ~ ! [Ys3: list_n282880152tr_b_c,Y3: node_p1234578834tr_b_c] :
( Xs
!= ( append846395565tr_b_c @ Ys3 @ ( cons_n413985352tr_b_c @ Y3 @ nil_no279930520tr_b_c ) ) ) ) ).
% rev_exhaust
thf(fact_327_Cons__eq__append__conv,axiom,
! [X: char,Xs: list_char,Ys: list_char,Zs2: list_char] :
( ( ( cons_char @ X @ Xs )
= ( append_char @ Ys @ Zs2 ) )
= ( ( ( Ys = nil_char )
& ( ( cons_char @ X @ Xs )
= Zs2 ) )
| ? [Ys4: list_char] :
( ( ( cons_char @ X @ Ys4 )
= Ys )
& ( Xs
= ( append_char @ Ys4 @ Zs2 ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_328_Cons__eq__append__conv,axiom,
! [X: node_p1234578834tr_b_c,Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c,Zs2: list_n282880152tr_b_c] :
( ( ( cons_n413985352tr_b_c @ X @ Xs )
= ( append846395565tr_b_c @ Ys @ Zs2 ) )
= ( ( ( Ys = nil_no279930520tr_b_c )
& ( ( cons_n413985352tr_b_c @ X @ Xs )
= Zs2 ) )
| ? [Ys4: list_n282880152tr_b_c] :
( ( ( cons_n413985352tr_b_c @ X @ Ys4 )
= Ys )
& ( Xs
= ( append846395565tr_b_c @ Ys4 @ Zs2 ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_329_append__eq__Cons__conv,axiom,
! [Ys: list_char,Zs2: list_char,X: char,Xs: list_char] :
( ( ( append_char @ Ys @ Zs2 )
= ( cons_char @ X @ Xs ) )
= ( ( ( Ys = nil_char )
& ( Zs2
= ( cons_char @ X @ Xs ) ) )
| ? [Ys4: list_char] :
( ( Ys
= ( cons_char @ X @ Ys4 ) )
& ( ( append_char @ Ys4 @ Zs2 )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_330_append__eq__Cons__conv,axiom,
! [Ys: list_n282880152tr_b_c,Zs2: list_n282880152tr_b_c,X: node_p1234578834tr_b_c,Xs: list_n282880152tr_b_c] :
( ( ( append846395565tr_b_c @ Ys @ Zs2 )
= ( cons_n413985352tr_b_c @ X @ Xs ) )
= ( ( ( Ys = nil_no279930520tr_b_c )
& ( Zs2
= ( cons_n413985352tr_b_c @ X @ Xs ) ) )
| ? [Ys4: list_n282880152tr_b_c] :
( ( Ys
= ( cons_n413985352tr_b_c @ X @ Ys4 ) )
& ( ( append846395565tr_b_c @ Ys4 @ Zs2 )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_331_rev__nonempty__induct,axiom,
! [Xs: list_char,P: list_char > $o] :
( ( Xs != nil_char )
=> ( ! [X3: char] : ( P @ ( cons_char @ X3 @ nil_char ) )
=> ( ! [X3: char,Xs2: list_char] :
( ( Xs2 != nil_char )
=> ( ( P @ Xs2 )
=> ( P @ ( append_char @ Xs2 @ ( cons_char @ X3 @ nil_char ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_332_rev__nonempty__induct,axiom,
! [Xs: list_n282880152tr_b_c,P: list_n282880152tr_b_c > $o] :
( ( Xs != nil_no279930520tr_b_c )
=> ( ! [X3: node_p1234578834tr_b_c] : ( P @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) )
=> ( ! [X3: node_p1234578834tr_b_c,Xs2: list_n282880152tr_b_c] :
( ( Xs2 != nil_no279930520tr_b_c )
=> ( ( P @ Xs2 )
=> ( P @ ( append846395565tr_b_c @ Xs2 @ ( cons_n413985352tr_b_c @ X3 @ nil_no279930520tr_b_c ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_333_eq__Nil__appendI,axiom,
! [Xs: list_char,Ys: list_char] :
( ( Xs = Ys )
=> ( Xs
= ( append_char @ nil_char @ Ys ) ) ) ).
% eq_Nil_appendI
thf(fact_334_eq__Nil__appendI,axiom,
! [Xs: list_n282880152tr_b_c,Ys: list_n282880152tr_b_c] :
( ( Xs = Ys )
=> ( Xs
= ( append846395565tr_b_c @ nil_no279930520tr_b_c @ Ys ) ) ) ).
% eq_Nil_appendI
thf(fact_335_append__Nil,axiom,
! [Ys: list_char] :
( ( append_char @ nil_char @ Ys )
= Ys ) ).
% append_Nil
thf(fact_336_append__Nil,axiom,
! [Ys: list_n282880152tr_b_c] :
( ( append846395565tr_b_c @ nil_no279930520tr_b_c @ Ys )
= Ys ) ).
% append_Nil
thf(fact_337_append_Oleft__neutral,axiom,
! [A: list_char] :
( ( append_char @ nil_char @ A )
= A ) ).
% append.left_neutral
thf(fact_338_append_Oleft__neutral,axiom,
! [A: list_n282880152tr_b_c] :
( ( append846395565tr_b_c @ nil_no279930520tr_b_c @ A )
= A ) ).
% append.left_neutral
% Conjectures (4)
thf(conj_0,hypothesis,
( ( docume1070804385_j_k_l @ h )
= bot_bo1111241908tr_d_e ) ).
thf(conj_1,hypothesis,
( h2
= ( put_O_834343516_j_k_l @ ( cast_d1608273229_b_c_f @ ( docume1511108976tr_d_e @ ( suc @ zero_zero_nat ) ) ) @ ( cast_D1252964113_h_i_l @ ( rObjec1303043984on_j_k @ product_Unity @ ( rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k ) ) ) @ h ) ) ).
thf(conj_2,hypothesis,
type_w92696601_j_k_l @ h ).
thf(conj_3,conjecture,
is_doc1417632087_j_k_l @ ( cast_D1252964113_h_i_l @ ( rObjec1303043984on_j_k @ product_Unity @ ( rDocum427676485on_j_k @ product_Unity @ nil_char @ none_element_ptr_a @ nil_no279930520tr_b_c @ none_S1393028981on_j_k ) ) ) ).
%------------------------------------------------------------------------------