TPTP Problem File: ITP172^2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP172^2 : 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 : 0.00 v7.5.0
% Syntax : Number of formulae : 421 ( 182 unt; 113 typ; 0 def)
% Number of atoms : 596 ( 479 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 5645 ( 86 ~; 8 |; 41 &;5224 @)
% ( 0 <=>; 286 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 7 avg)
% Number of types : 16 ( 15 usr)
% Number of type conns : 306 ( 306 >; 0 *; 0 +; 0 <<)
% Number of symbols : 99 ( 98 usr; 3 con; 0-14 aty)
% Number of variables : 1455 ( 16 ^;1233 !; 22 ?;1455 :)
% ( 184 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : This file was generated by Sledgehammer 2021-02-23 16:18:20.160
%------------------------------------------------------------------------------
% Could-be-implicit typings (35)
thf(ty_t_CharacterDataClass_ORCharacterData_ORCharacterData__ext,type,
rCharacterData_ext: $tType > $tType ).
thf(ty_t_ShadowRootClass_ORShadowRoot_ORShadowRoot__ext,type,
rShadowRoot_ext: $tType > $tType > $tType > $tType > $tType ).
thf(ty_t_CharacterDataPointer_Ocharacter__data__ptr,type,
character_data_ptr: $tType > $tType ).
thf(ty_t_DocumentClass_ORDocument_ORDocument__ext,type,
rDocument_ext: $tType > $tType > $tType > $tType > $tType ).
thf(ty_t_ElementClass_ORElement_ORElement__ext,type,
rElement_ext: $tType > $tType > $tType > $tType > $tType > $tType ).
thf(ty_t_ShadowRootPointer_Oshadow__root__ptr,type,
shadow_root_ptr: $tType > $tType ).
thf(ty_t_ObjectClass_ORObject_ORObject__ext,type,
rObject_ext: $tType > $tType ).
thf(ty_t_DocumentPointer_Odocument__ptr,type,
document_ptr: $tType > $tType ).
thf(ty_t_NodeClass_ORNode_ORNode__ext,type,
rNode_ext: $tType > $tType ).
thf(ty_t_ElementPointer_Oelement__ptr,type,
element_ptr: $tType > $tType ).
thf(ty_t_ObjectPointer_Oobject__ptr,type,
object_ptr: $tType > $tType ).
thf(ty_t_Heap__Error__Monad_Oprog,type,
heap_Error_prog: $tType > $tType > $tType > $tType ).
thf(ty_t_NodePointer_Onode__ptr,type,
node_ptr: $tType > $tType ).
thf(ty_t_Product__Type_Ounit,type,
product_unit: $tType ).
thf(ty_t_Product__Type_Oprod,type,
product_prod: $tType > $tType > $tType ).
thf(ty_t_ObjectClass_Oheap,type,
heap: $tType > $tType > $tType ).
thf(ty_t_Sum__Type_Osum,type,
sum_sum: $tType > $tType > $tType ).
thf(ty_t_Option_Ooption,type,
option: $tType > $tType ).
thf(ty_t_String_Ochar,type,
char: $tType ).
thf(ty_t_List_Olist,type,
list: $tType > $tType ).
thf(ty_t_FSet_Ofset,type,
fset: $tType > $tType ).
thf(ty_t_Set_Oset,type,
set: $tType > $tType ).
thf(ty_t_Nat_Onat,type,
nat: $tType ).
thf(ty_tf_l,type,
l: $tType ).
thf(ty_tf_k,type,
k: $tType ).
thf(ty_tf_j,type,
j: $tType ).
thf(ty_tf_i,type,
i: $tType ).
thf(ty_tf_h,type,
h: $tType ).
thf(ty_tf_g,type,
g: $tType ).
thf(ty_tf_f,type,
f: $tType ).
thf(ty_tf_e,type,
e: $tType ).
thf(ty_tf_d,type,
d: $tType ).
thf(ty_tf_c,type,
c: $tType ).
thf(ty_tf_b,type,
b: $tType ).
thf(ty_tf_a,type,
a: $tType ).
% Explicit typings (78)
thf(sy_cl_HOL_Otype,type,
type:
!>[A: $tType] : $o ).
thf(sy_cl_Nat_Osize,type,
size:
!>[A: $tType] : $o ).
thf(sy_cl_Groups_Ozero,type,
zero:
!>[A: $tType] : $o ).
thf(sy_cl_Orderings_Obot,type,
bot:
!>[A: $tType] : $o ).
thf(sy_cl_Orderings_Oord,type,
ord:
!>[A: $tType] : $o ).
thf(sy_cl_Groups_Ogroup__add,type,
group_add:
!>[A: $tType] : $o ).
thf(sy_cl_Groups_Omonoid__add,type,
monoid_add:
!>[A: $tType] : $o ).
thf(sy_cl_Orderings_Olinorder,type,
linorder:
!>[A: $tType] : $o ).
thf(sy_cl_Groups_Osemigroup__add,type,
semigroup_add:
!>[A: $tType] : $o ).
thf(sy_cl_Groups_Ocomm__monoid__add,type,
comm_monoid_add:
!>[A: $tType] : $o ).
thf(sy_cl_Groups_Oab__semigroup__add,type,
ab_semigroup_add:
!>[A: $tType] : $o ).
thf(sy_cl_Groups_Ocancel__semigroup__add,type,
cancel_semigroup_add:
!>[A: $tType] : $o ).
thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
cancel1352612707id_add:
!>[A: $tType] : $o ).
thf(sy_cl_Groups_Olinordered__ab__group__add,type,
linord219039673up_add:
!>[A: $tType] : $o ).
thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
ordere779506340up_add:
!>[A: $tType] : $o ).
thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
canoni770627133id_add:
!>[A: $tType] : $o ).
thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
semiri456707255roduct:
!>[A: $tType] : $o ).
thf(sy_c_DocumentClass_ORDocument_ORDocument__ext,type,
rDocument_ext2:
!>[Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType] : ( product_unit > ( list @ char ) > ( option @ ( element_ptr @ Element_ptr ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) ) > Z > ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) ).
thf(sy_c_DocumentClass_ORDocument_Odisconnected__nodes,type,
disconnected_nodes:
!>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) ) ) ).
thf(sy_c_DocumentClass_ORDocument_Odisconnected__nodes__update,type,
discon1635973971update:
!>[Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType] : ( ( ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) ) ).
thf(sy_c_DocumentClass_ORDocument_Odoctype,type,
doctype:
!>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( list @ char ) ) ).
thf(sy_c_DocumentClass_ORDocument_Odoctype__update,type,
doctype_update:
!>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( ( list @ char ) > ( list @ char ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) ) ).
thf(sy_c_DocumentClass_ORDocument_Odocument__element,type,
document_element:
!>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( option @ ( element_ptr @ Element_ptr ) ) ) ).
thf(sy_c_DocumentClass_ORDocument_Odocument__element__update,type,
docume446011358update:
!>[Element_ptr: $tType,Node_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( ( option @ ( element_ptr @ Element_ptr ) ) > ( option @ ( element_ptr @ Element_ptr ) ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) ) ).
thf(sy_c_DocumentClass_ORDocument_Omore,type,
more:
!>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > Z ) ).
thf(sy_c_DocumentClass_ORDocument_Omore__update,type,
more_update:
!>[Z: $tType,Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType] : ( ( Z > Z ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) ) ).
thf(sy_c_DocumentClass_ORDocument_Onothing,type,
nothing:
!>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > product_unit ) ).
thf(sy_c_DocumentClass_ORDocument_Onothing__update,type,
nothing_update:
!>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Z: $tType] : ( ( product_unit > product_unit ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) ) ).
thf(sy_c_DocumentClass_Ocast_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,type,
cast_D42511940_e_c_t:
!>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Document: $tType,Shadow_root_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Object: $tType] : ( ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) ) > ( rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) ) ).
thf(sy_c_DocumentClass_Ocast_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,type,
cast_O1159777348_e_n_t:
!>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Shadow_root_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Document: $tType,Object: $tType] : ( ( rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) > ( option @ ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) ) ) ) ).
thf(sy_c_DocumentClass_Odocument__ptrs,type,
document_ptrs:
!>[Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Shadow_root_ptr: $tType,Document_ptr: $tType,Object_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Document: $tType,Object: $tType] : ( ( heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) > ( fset @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) ) ) ).
thf(sy_c_DocumentClass_Oget_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,type,
get_D_o_c_u_m_e_n_t:
!>[Shadow_root_ptr: $tType,Document_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Object_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Document: $tType,Object: $tType] : ( ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) > ( heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) > ( option @ ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) ) ) ) ).
thf(sy_c_DocumentClass_Ois__document__kind,type,
is_document_kind:
!>[Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Shadow_root_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Document: $tType,Object: $tType] : ( ( rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) > $o ) ).
thf(sy_c_DocumentClass_Oput_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,type,
put_D_o_c_u_m_e_n_t:
!>[Shadow_root_ptr: $tType,Document_ptr: $tType,Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Document: $tType,Object_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Object: $tType] : ( ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) > ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) ) > ( heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) > ( heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) ) ).
thf(sy_c_DocumentPointer_Ocast_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,type,
cast_d1427782271_p_t_r:
!>[Document_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Object_ptr: $tType] : ( ( document_ptr @ Document_ptr ) > ( object_ptr @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ Document_ptr ) @ Object_ptr ) ) ) ) ).
thf(sy_c_DocumentPointer_Ocast_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_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_092_060_094sub_062___092_060_094sub_062p_092_060_094sub_062t_092_060_094sub_062r,type,
cast_o823910367_p_t_r:
!>[Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Document_ptr: $tType,Object_ptr: $tType] : ( ( object_ptr @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ Document_ptr ) @ Object_ptr ) ) ) > ( option @ ( document_ptr @ Document_ptr ) ) ) ).
thf(sy_c_DocumentPointer_Odocument__ptr_OExt,type,
document_Ext:
!>[Document_ptr: $tType] : ( Document_ptr > ( document_ptr @ Document_ptr ) ) ).
thf(sy_c_DocumentPointer_Odocument__ptr_ORef,type,
document_Ref:
!>[Document_ptr: $tType] : ( nat > ( document_ptr @ Document_ptr ) ) ).
thf(sy_c_DocumentPointer_Odocument__ptr_Osize__document__ptr,type,
docume1907984069nt_ptr:
!>[Document_ptr: $tType] : ( ( Document_ptr > nat ) > ( document_ptr @ Document_ptr ) > nat ) ).
thf(sy_c_DocumentPointer_Ois__document__ptr_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,type,
is_doc697300620_p_t_r:
!>[Document_ptr: $tType] : ( ( document_ptr @ Document_ptr ) > $o ) ).
thf(sy_c_Groups_Oplus__class_Oplus,type,
plus_plus:
!>[A: $tType] : ( A > A > A ) ).
thf(sy_c_Groups_Ozero__class_Ozero,type,
zero_zero:
!>[A: $tType] : A ).
thf(sy_c_Heap__Error__Monad_Oprog_OProg,type,
heap_Error_Prog:
!>[Heap: $tType,E: $tType,Result: $tType] : ( ( Heap > ( sum_sum @ E @ ( product_prod @ Result @ Heap ) ) ) > ( heap_Error_prog @ Heap @ E @ Result ) ) ).
thf(sy_c_Heap__Error__Monad_Oprog_Osize__prog,type,
heap_Error_size_prog:
!>[Heap: $tType,E: $tType,Result: $tType] : ( ( Heap > nat ) > ( E > nat ) > ( Result > nat ) > ( heap_Error_prog @ Heap @ E @ Result ) > nat ) ).
thf(sy_c_List_Oappend,type,
append:
!>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
thf(sy_c_List_Ocount__list,type,
count_list:
!>[A: $tType] : ( ( list @ A ) > A > nat ) ).
thf(sy_c_List_Ogen__length,type,
gen_length:
!>[A: $tType] : ( nat > ( list @ A ) > nat ) ).
thf(sy_c_List_Oinsert,type,
insert:
!>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
thf(sy_c_List_Olist_OCons,type,
cons:
!>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
thf(sy_c_List_Olist_ONil,type,
nil:
!>[A: $tType] : ( list @ A ) ).
thf(sy_c_List_Olist__ex1,type,
list_ex1:
!>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
thf(sy_c_List_On__lists,type,
n_lists:
!>[A: $tType] : ( nat > ( list @ A ) > ( list @ ( list @ A ) ) ) ).
thf(sy_c_List_Onths,type,
nths:
!>[A: $tType] : ( ( list @ A ) > ( set @ nat ) > ( list @ A ) ) ).
thf(sy_c_List_Oproduct__lists,type,
product_lists:
!>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
thf(sy_c_List_Osplice,type,
splice:
!>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
thf(sy_c_List_Osubseqs,type,
subseqs:
!>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
thf(sy_c_Nat_OSuc,type,
suc: nat > nat ).
thf(sy_c_Nat_Osize__class_Osize,type,
size_size:
!>[A: $tType] : ( A > nat ) ).
thf(sy_c_Nat__Bijection_Oset__decode,type,
nat_set_decode: nat > ( set @ nat ) ).
thf(sy_c_Nat__Bijection_Oset__encode,type,
nat_set_encode: ( set @ nat ) > nat ).
thf(sy_c_Nat__Bijection_Otriangle,type,
nat_triangle: nat > nat ).
thf(sy_c_ObjectClass_ORObject_ORObject__ext,type,
rObject_ext2:
!>[Z: $tType] : ( product_unit > Z > ( rObject_ext @ Z ) ) ).
thf(sy_c_ObjectClass_ORObject_Oextend,type,
extend:
!>[Z: $tType] : ( ( rObject_ext @ product_unit ) > Z > ( rObject_ext @ Z ) ) ).
thf(sy_c_ObjectClass_ORObject_Omore,type,
more2:
!>[Z: $tType] : ( ( rObject_ext @ Z ) > Z ) ).
thf(sy_c_ObjectClass_ORObject_Onothing,type,
nothing2:
!>[Z: $tType] : ( ( rObject_ext @ Z ) > product_unit ) ).
thf(sy_c_ObjectClass_Oget_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t,type,
get_O_b_j_e_c_t:
!>[Object_ptr: $tType,Object: $tType] : ( ( object_ptr @ Object_ptr ) > ( heap @ Object_ptr @ Object ) > ( option @ ( rObject_ext @ Object ) ) ) ).
thf(sy_c_ObjectClass_Oput_092_060_094sub_062O_092_060_094sub_062b_092_060_094sub_062j_092_060_094sub_062e_092_060_094sub_062c_092_060_094sub_062t,type,
put_O_b_j_e_c_t:
!>[Object_ptr: $tType,Object: $tType] : ( ( object_ptr @ Object_ptr ) > ( rObject_ext @ Object ) > ( heap @ Object_ptr @ Object ) > ( heap @ Object_ptr @ Object ) ) ).
thf(sy_c_Option_Obind,type,
bind:
!>[A: $tType,B: $tType] : ( ( option @ A ) > ( A > ( option @ B ) ) > ( option @ B ) ) ).
thf(sy_c_Option_Ooption_ONone,type,
none:
!>[A: $tType] : ( option @ A ) ).
thf(sy_c_Option_Ooption_OSome,type,
some:
!>[A: $tType] : ( A > ( option @ A ) ) ).
thf(sy_c_Option_Ooption_Osize__option,type,
size_option:
!>[A: $tType] : ( ( A > nat ) > ( option @ A ) > nat ) ).
thf(sy_c_Orderings_Obot__class_Obot,type,
bot_bot:
!>[A: $tType] : A ).
thf(sy_c_Product__Type_OUnity,type,
product_Unity: product_unit ).
thf(sy_c_Set_OCollect,type,
collect:
!>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
thf(sy_c_ShadowRootClass_Otype__wf,type,
type_wf:
!>[A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F: $tType,G: $tType,H: $tType,I: $tType,J: $tType,K: $tType,L: $tType] : ( ( heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ A ) @ ( sum_sum @ ( character_data_ptr @ B ) @ C ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ D ) @ E ) ) @ F ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ C @ A @ B @ D @ ( option @ G ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ H ) ) @ I ) ) ) @ ( sum_sum @ ( rDocument_ext @ C @ A @ B @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ C @ A @ B @ ( option @ J ) ) @ K ) ) ) @ L ) ) ) > $o ) ).
thf(sy_c_member,type,
member:
!>[A: $tType] : ( A > ( set @ A ) > $o ) ).
thf(sy_v_h,type,
h2: heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ a ) @ ( sum_sum @ ( character_data_ptr @ b ) @ c ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ d ) @ e ) ) @ f ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ c @ a @ b @ d @ ( option @ g ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ h ) ) @ i ) ) ) @ ( sum_sum @ ( rDocument_ext @ c @ a @ b @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) @ l ) ) ).
thf(sy_v_h_H,type,
h3: heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ a ) @ ( sum_sum @ ( character_data_ptr @ b ) @ c ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ d ) @ e ) ) @ f ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ c @ a @ b @ d @ ( option @ g ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ h ) ) @ i ) ) ) @ ( sum_sum @ ( rDocument_ext @ c @ a @ b @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) @ l ) ) ).
% Relevant facts (251)
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,
! [I: $tType,G: $tType,F: $tType,E: $tType,D: $tType,H: $tType,C: $tType,B: $tType,A: $tType,X: rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ H ) ),Y: rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ H ) )] :
( ( ( cast_D42511940_e_c_t @ A @ B @ C @ H @ D @ E @ F @ G @ I @ X )
= ( cast_D42511940_e_c_t @ A @ B @ C @ H @ D @ E @ F @ G @ I @ 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,
! [E: $tType,C: $tType,B: $tType,A: $tType,D: $tType,X: document_ptr @ D,Y: document_ptr @ D] :
( ( ( cast_d1427782271_p_t_r @ D @ A @ B @ C @ E @ X )
= ( cast_d1427782271_p_t_r @ D @ A @ B @ C @ E @ 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,
! [Document_ptr: $tType,X1: nat,Y1: nat] :
( ( ( document_Ref @ Document_ptr @ X1 )
= ( document_Ref @ Document_ptr @ Y1 ) )
= ( X1 = Y1 ) ) ).
% document_ptr.inject(1)
thf(fact_3_RDocument_Oext__inject,axiom,
! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z,Nothinga2: product_unit,Doctype2: list @ char,Document_element2: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes2: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More2: Z] :
( ( ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More )
= ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ 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,
! [Z: $tType,Nothing: product_unit,More: Z,Nothing2: product_unit,More2: Z] :
( ( ( rObject_ext2 @ Z @ Nothing @ More )
= ( rObject_ext2 @ Z @ Nothing2 @ More2 ) )
= ( ( Nothing = Nothing2 )
& ( More = More2 ) ) ) ).
% RObject.ext_inject
thf(fact_5_nat_Oinject,axiom,
! [X2: nat,Y2: nat] :
( ( ( suc @ X2 )
= ( suc @ Y2 ) )
= ( X2 = Y2 ) ) ).
% nat.inject
thf(fact_6_old_Onat_Oinject,axiom,
! [Nat: nat,Nat2: nat] :
( ( ( suc @ Nat )
= ( suc @ Nat2 ) )
= ( Nat = Nat2 ) ) ).
% old.nat.inject
thf(fact_7_bot__apply,axiom,
! [C: $tType,D: $tType] :
( ( bot @ C )
=> ( ( bot_bot @ ( D > C ) )
= ( ^ [X3: D] : ( bot_bot @ C ) ) ) ) ).
% bot_apply
thf(fact_8_RDocument_Ocases__scheme,axiom,
! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z )] :
~ ! [Nothing3: product_unit,Nothinga3: product_unit,Doctype3: list @ char,Document_element3: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes3: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More3: Z] :
( R
!= ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing3 @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ More3 ) ) ) ).
% RDocument.cases_scheme
thf(fact_9_RDocument_Oinduct__scheme,axiom,
! [Z: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Node_ptr: $tType,P: ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) ) > $o,R: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z )] :
( ! [Nothing3: product_unit,Nothinga3: product_unit,Doctype3: list @ char,Document_element3: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes3: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More3: Z] : ( P @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing3 @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ More3 ) ) )
=> ( P @ R ) ) ).
% RDocument.induct_scheme
thf(fact_10_RDocument_Oinduct,axiom,
! [Character_data_ptr: $tType,Element_ptr: $tType,Node_ptr: $tType,P: ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ product_unit ) ) > $o,R: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ product_unit )] :
( ! [Nothing3: product_unit,Nothinga3: product_unit,Doctype3: list @ char,Document_element3: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes3: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) )] : ( P @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ product_unit ) @ Nothing3 @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ product_unit @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ product_Unity ) ) )
=> ( P @ R ) ) ).
% RDocument.induct
thf(fact_11_RDocument_Ocases,axiom,
! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ product_unit )] :
~ ! [Nothing3: product_unit,Nothinga3: product_unit,Doctype3: list @ char,Document_element3: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes3: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) )] :
( R
!= ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ product_unit ) @ Nothing3 @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ product_unit @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ product_Unity ) ) ) ).
% RDocument.cases
thf(fact_12_bot__nat__def,axiom,
( ( bot_bot @ nat )
= ( zero_zero @ nat ) ) ).
% bot_nat_def
thf(fact_13_RObject_Oinduct,axiom,
! [P: ( rObject_ext @ product_unit ) > $o,R: rObject_ext @ product_unit] :
( ! [Nothing3: product_unit] : ( P @ ( rObject_ext2 @ product_unit @ Nothing3 @ product_Unity ) )
=> ( P @ R ) ) ).
% RObject.induct
thf(fact_14_RObject_Ocases,axiom,
! [R: rObject_ext @ product_unit] :
~ ! [Nothing3: product_unit] :
( R
!= ( rObject_ext2 @ product_unit @ Nothing3 @ product_Unity ) ) ).
% RObject.cases
thf(fact_15_zero__reorient,axiom,
! [A: $tType] :
( ( zero @ A )
=> ! [X: A] :
( ( ( zero_zero @ A )
= X )
= ( X
= ( zero_zero @ A ) ) ) ) ).
% zero_reorient
thf(fact_16_bot__fun__def,axiom,
! [B: $tType,A: $tType] :
( ( bot @ B )
=> ( ( bot_bot @ ( A > B ) )
= ( ^ [X3: A] : ( bot_bot @ B ) ) ) ) ).
% bot_fun_def
thf(fact_17_n__not__Suc__n,axiom,
! [N: nat] :
( N
!= ( suc @ N ) ) ).
% n_not_Suc_n
thf(fact_18_Suc__inject,axiom,
! [X: nat,Y: nat] :
( ( ( suc @ X )
= ( suc @ Y ) )
=> ( X = Y ) ) ).
% Suc_inject
thf(fact_19_RObject_Oinduct__scheme,axiom,
! [Z: $tType,P: ( rObject_ext @ Z ) > $o,R: rObject_ext @ Z] :
( ! [Nothing3: product_unit,More3: Z] : ( P @ ( rObject_ext2 @ Z @ Nothing3 @ More3 ) )
=> ( P @ R ) ) ).
% RObject.induct_scheme
thf(fact_20_RObject_Ocases__scheme,axiom,
! [Z: $tType,R: rObject_ext @ Z] :
~ ! [Nothing3: product_unit,More3: Z] :
( R
!= ( rObject_ext2 @ Z @ Nothing3 @ More3 ) ) ).
% RObject.cases_scheme
thf(fact_21_RDocument_Oext__induct,axiom,
! [Z: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Node_ptr: $tType,P: ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) > $o,R: rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z] :
( ! [Nothinga3: product_unit,Doctype3: list @ char,Document_element3: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes3: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More3: Z] : ( P @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga3 @ Doctype3 @ Document_element3 @ Disconnected_nodes3 @ More3 ) )
=> ( P @ R ) ) ).
% RDocument.ext_induct
thf(fact_22_not0__implies__Suc,axiom,
! [N: nat] :
( ( N
!= ( zero_zero @ nat ) )
=> ? [M: nat] :
( N
= ( suc @ M ) ) ) ).
% not0_implies_Suc
thf(fact_23_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_24_old_Onat_Oexhaust,axiom,
! [Y: nat] :
( ( Y
!= ( zero_zero @ nat ) )
=> ~ ! [Nat3: nat] :
( Y
!= ( suc @ Nat3 ) ) ) ).
% old.nat.exhaust
thf(fact_25_Zero__not__Suc,axiom,
! [M2: nat] :
( ( zero_zero @ nat )
!= ( suc @ M2 ) ) ).
% Zero_not_Suc
thf(fact_26_Zero__neq__Suc,axiom,
! [M2: nat] :
( ( zero_zero @ nat )
!= ( suc @ M2 ) ) ).
% Zero_neq_Suc
thf(fact_27_Suc__neq__Zero,axiom,
! [M2: nat] :
( ( suc @ M2 )
!= ( zero_zero @ nat ) ) ).
% Suc_neq_Zero
thf(fact_28_zero__induct,axiom,
! [P: nat > $o,K2: nat] :
( ( P @ K2 )
=> ( ! [N2: nat] :
( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) )
=> ( P @ ( zero_zero @ nat ) ) ) ) ).
% zero_induct
thf(fact_29_diff__induct,axiom,
! [P: nat > nat > $o,M2: nat,N: nat] :
( ! [X4: nat] : ( P @ X4 @ ( zero_zero @ nat ) )
=> ( ! [Y3: nat] : ( P @ ( zero_zero @ nat ) @ ( suc @ Y3 ) )
=> ( ! [X4: nat,Y3: nat] :
( ( P @ X4 @ Y3 )
=> ( P @ ( suc @ X4 ) @ ( suc @ Y3 ) ) )
=> ( P @ M2 @ N ) ) ) ) ).
% diff_induct
thf(fact_30_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_31_nat_OdiscI,axiom,
! [Nat: nat,X2: nat] :
( ( Nat
= ( suc @ X2 ) )
=> ( Nat
!= ( zero_zero @ nat ) ) ) ).
% nat.discI
thf(fact_32_old_Onat_Odistinct_I1_J,axiom,
! [Nat2: nat] :
( ( zero_zero @ nat )
!= ( suc @ Nat2 ) ) ).
% old.nat.distinct(1)
thf(fact_33_old_Onat_Odistinct_I2_J,axiom,
! [Nat4: nat] :
( ( suc @ Nat4 )
!= ( zero_zero @ nat ) ) ).
% old.nat.distinct(2)
thf(fact_34_nat_Odistinct_I1_J,axiom,
! [X2: nat] :
( ( zero_zero @ nat )
!= ( suc @ X2 ) ) ).
% nat.distinct(1)
thf(fact_35_document__ptr_Osize__gen_I1_J,axiom,
! [Document_ptr: $tType,X: Document_ptr > nat,X1: nat] :
( ( docume1907984069nt_ptr @ Document_ptr @ X @ ( document_Ref @ Document_ptr @ X1 ) )
= ( suc @ ( zero_zero @ nat ) ) ) ).
% document_ptr.size_gen(1)
thf(fact_36_document__ptr_Osize_I3_J,axiom,
! [Document_ptr: $tType,X1: nat] :
( ( size_size @ ( document_ptr @ Document_ptr ) @ ( document_Ref @ Document_ptr @ X1 ) )
= ( suc @ ( zero_zero @ nat ) ) ) ).
% document_ptr.size(3)
thf(fact_37_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,
! [Node_ptr: $tType,Element_ptr: $tType,Character_data_ptr: $tType,Document: $tType,Object_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Object: $tType,Document_ptr: $tType,Shadow_root_ptr: $tType] :
( ( put_D_o_c_u_m_e_n_t @ Shadow_root_ptr @ Document_ptr @ Node_ptr @ Element_ptr @ Character_data_ptr @ Document @ Object_ptr @ Element @ CharacterData @ Node @ Object )
= ( ^ [Document_ptr2: document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ),Document2: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) )] : ( put_O_b_j_e_c_t @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) @ ( cast_d1427782271_p_t_r @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) @ Element_ptr @ Character_data_ptr @ Node_ptr @ Object_ptr @ Document_ptr2 ) @ ( cast_D42511940_e_c_t @ Node_ptr @ Element_ptr @ Character_data_ptr @ Document @ Shadow_root_ptr @ Element @ CharacterData @ Node @ Object @ Document2 ) ) ) ) ).
% put\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def
thf(fact_38_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_39_dependent__nat__choice,axiom,
! [A: $tType,P: nat > A > $o,Q: nat > A > A > $o] :
( ? [X_1: A] : ( P @ ( zero_zero @ nat ) @ X_1 )
=> ( ! [X4: A,N2: nat] :
( ( P @ N2 @ X4 )
=> ? [Y4: A] :
( ( P @ ( suc @ N2 ) @ Y4 )
& ( Q @ N2 @ X4 @ Y4 ) ) )
=> ? [F2: nat > A] :
! [N3: nat] :
( ( P @ N3 @ ( F2 @ N3 ) )
& ( Q @ N3 @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) ) ) ) ) ).
% dependent_nat_choice
thf(fact_40_list__decode_Ocases,axiom,
! [X: nat] :
( ( X
!= ( zero_zero @ nat ) )
=> ~ ! [N2: nat] :
( X
!= ( suc @ N2 ) ) ) ).
% list_decode.cases
thf(fact_41_object__empty,axiom,
! [A: $tType,X: rObject_ext @ A] :
( ( rObject_ext2 @ A @ product_Unity @ ( more2 @ A @ X ) )
= X ) ).
% object_empty
thf(fact_42_mem__Collect__eq,axiom,
! [A: $tType,A2: A,P: A > $o] :
( ( member @ A @ A2 @ ( collect @ A @ P ) )
= ( P @ A2 ) ) ).
% mem_Collect_eq
thf(fact_43_Collect__mem__eq,axiom,
! [A: $tType,A3: set @ A] :
( ( collect @ A
@ ^ [X3: A] : ( member @ A @ X3 @ A3 ) )
= A3 ) ).
% Collect_mem_eq
thf(fact_44_Collect__cong,axiom,
! [A: $tType,P: A > $o,Q: A > $o] :
( ! [X4: A] :
( ( P @ X4 )
= ( Q @ X4 ) )
=> ( ( collect @ A @ P )
= ( collect @ A @ Q ) ) ) ).
% Collect_cong
thf(fact_45_ext,axiom,
! [B: $tType,A: $tType,F3: A > B,G2: A > B] :
( ! [X4: A] :
( ( F3 @ X4 )
= ( G2 @ X4 ) )
=> ( F3 = G2 ) ) ).
% ext
thf(fact_46_RDocument_Oupdate__convs_I1_J,axiom,
! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,Nothing2: product_unit > product_unit,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
( ( nothing_update @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ Nothing2 @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ ( Nothing2 @ Nothinga ) @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) ) ).
% RDocument.update_convs(1)
thf(fact_47_RDocument_Oupdate__convs_I2_J,axiom,
! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,Doctype2: ( list @ char ) > ( list @ char ),Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
( ( doctype_update @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ Doctype2 @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ ( Doctype2 @ Doctype ) @ Document_element @ Disconnected_nodes @ More ) ) ) ).
% RDocument.update_convs(2)
thf(fact_48_RDocument_Oupdate__convs_I3_J,axiom,
! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,Document_element2: ( option @ ( element_ptr @ Element_ptr ) ) > ( option @ ( element_ptr @ Element_ptr ) ),Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
( ( docume446011358update @ Element_ptr @ Node_ptr @ Character_data_ptr @ Z @ Document_element2 @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ ( Document_element2 @ Document_element ) @ Disconnected_nodes @ More ) ) ) ).
% RDocument.update_convs(3)
thf(fact_49_RDocument_Oupdate__convs_I4_J,axiom,
! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,Disconnected_nodes2: ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) ),Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
( ( discon1635973971update @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Disconnected_nodes2 @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ ( Disconnected_nodes2 @ Disconnected_nodes ) @ More ) ) ) ).
% RDocument.update_convs(4)
thf(fact_50_size__neq__size__imp__neq,axiom,
! [A: $tType] :
( ( size @ A )
=> ! [X: A,Y: A] :
( ( ( size_size @ A @ X )
!= ( size_size @ A @ Y ) )
=> ( X != Y ) ) ) ).
% size_neq_size_imp_neq
thf(fact_51_RObject_Oselect__convs_I2_J,axiom,
! [Z: $tType,Nothing: product_unit,More: Z] :
( ( more2 @ Z @ ( rObject_ext2 @ Z @ Nothing @ More ) )
= More ) ).
% RObject.select_convs(2)
thf(fact_52_document__ptr_Osize__neq,axiom,
! [Document_ptr: $tType,X: document_ptr @ Document_ptr] :
( ( size_size @ ( document_ptr @ Document_ptr ) @ X )
!= ( zero_zero @ nat ) ) ).
% document_ptr.size_neq
thf(fact_53_object__more__extend__id,axiom,
! [A: $tType,X: rObject_ext @ product_unit,Y: A] :
( ( more2 @ A @ ( extend @ A @ X @ Y ) )
= Y ) ).
% object_more_extend_id
thf(fact_54_RDocument_Oupdate__convs_I5_J,axiom,
! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Z: $tType,More2: Z > Z,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
( ( more_update @ Z @ Node_ptr @ Element_ptr @ Character_data_ptr @ More2 @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ ( More2 @ More ) ) ) ) ).
% RDocument.update_convs(5)
thf(fact_55_is__document__ptr__ref,axiom,
! [A: $tType,N: nat] : ( is_doc697300620_p_t_r @ A @ ( document_Ref @ A @ N ) ) ).
% is_document_ptr_ref
thf(fact_56_RDocument_Oselect__convs_I5_J,axiom,
! [Node_ptr: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Z: $tType,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
( ( more @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= More ) ).
% RDocument.select_convs(5)
thf(fact_57_RDocument_Oselect__convs_I4_J,axiom,
! [Z: $tType,Node_ptr: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
( ( disconnected_nodes @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= Disconnected_nodes ) ).
% RDocument.select_convs(4)
thf(fact_58_RDocument_Oselect__convs_I3_J,axiom,
! [Z: $tType,Node_ptr: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
( ( document_element @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= Document_element ) ).
% RDocument.select_convs(3)
thf(fact_59_RDocument_Oselect__convs_I2_J,axiom,
! [Z: $tType,Node_ptr: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
( ( doctype @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= Doctype ) ).
% RDocument.select_convs(2)
thf(fact_60_RDocument_Oselect__convs_I1_J,axiom,
! [Z: $tType,Node_ptr: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Nothing: product_unit,Nothinga: product_unit,Doctype: list @ char,Document_element: option @ ( element_ptr @ Element_ptr ),Disconnected_nodes: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ),More: Z] :
( ( nothing @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ Nothing @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ Nothinga @ Doctype @ Document_element @ Disconnected_nodes @ More ) ) )
= Nothinga ) ).
% RDocument.select_convs(1)
thf(fact_61_RDocument_Ounfold__congs_I6_J,axiom,
! [A: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ A ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ A ),V: A,F3: A > A,F4: A > A] :
( ( R = R2 )
=> ( ( ( more @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ A @ R2 )
= V )
=> ( ! [V2: A] :
( ( V2 = V )
=> ( ( F3 @ V2 )
= ( F4 @ V2 ) ) )
=> ( ( more_update @ A @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ F3 @ R )
= ( more_update @ A @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ F4 @ R2 ) ) ) ) ) ).
% RDocument.unfold_congs(6)
thf(fact_62_RDocument_Ofold__congs_I6_J,axiom,
! [A: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ A ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ A ),V: A,F3: A > A,F4: A > A] :
( ( R = R2 )
=> ( ( ( more @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ A @ R2 )
= V )
=> ( ! [V2: A] :
( ( V = V2 )
=> ( ( F3 @ V2 )
= ( F4 @ V2 ) ) )
=> ( ( more_update @ A @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ F3 @ R )
= ( more_update @ A @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ F4 @ R2 ) ) ) ) ) ).
% RDocument.fold_congs(6)
thf(fact_63_heap_Osize__neq,axiom,
! [Object_ptr: $tType,Object: $tType,X: heap @ Object_ptr @ Object] :
( ( size_size @ ( heap @ Object_ptr @ Object ) @ X )
!= ( zero_zero @ nat ) ) ).
% heap.size_neq
thf(fact_64_RDocument_Ounfold__congs_I3_J,axiom,
! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: list @ char,F3: ( list @ char ) > ( list @ char ),F4: ( list @ char ) > ( list @ char )] :
( ( R = R2 )
=> ( ( ( doctype @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
= V )
=> ( ! [V2: list @ char] :
( ( V2 = V )
=> ( ( F3 @ V2 )
= ( F4 @ V2 ) ) )
=> ( ( doctype_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F3 @ R )
= ( doctype_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% RDocument.unfold_congs(3)
thf(fact_65_RDocument_Ounfold__congs_I4_J,axiom,
! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: option @ ( element_ptr @ Element_ptr2 ),F3: ( option @ ( element_ptr @ Element_ptr2 ) ) > ( option @ ( element_ptr @ Element_ptr2 ) ),F4: ( option @ ( element_ptr @ Element_ptr2 ) ) > ( option @ ( element_ptr @ Element_ptr2 ) )] :
( ( R = R2 )
=> ( ( ( document_element @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
= V )
=> ( ! [V2: option @ ( element_ptr @ Element_ptr2 )] :
( ( V2 = V )
=> ( ( F3 @ V2 )
= ( F4 @ V2 ) ) )
=> ( ( docume446011358update @ Element_ptr2 @ Node_ptr2 @ Character_data_ptr2 @ Z2 @ F3 @ R )
= ( docume446011358update @ Element_ptr2 @ Node_ptr2 @ Character_data_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% RDocument.unfold_congs(4)
thf(fact_66_RDocument_Ounfold__congs_I5_J,axiom,
! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ),F3: ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) ),F4: ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) )] :
( ( R = R2 )
=> ( ( ( disconnected_nodes @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
= V )
=> ( ! [V2: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) )] :
( ( V2 = V )
=> ( ( F3 @ V2 )
= ( F4 @ V2 ) ) )
=> ( ( discon1635973971update @ Element_ptr2 @ Character_data_ptr2 @ Node_ptr2 @ Z2 @ F3 @ R )
= ( discon1635973971update @ Element_ptr2 @ Character_data_ptr2 @ Node_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% RDocument.unfold_congs(5)
thf(fact_67_RDocument_Ofold__congs_I3_J,axiom,
! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: list @ char,F3: ( list @ char ) > ( list @ char ),F4: ( list @ char ) > ( list @ char )] :
( ( R = R2 )
=> ( ( ( doctype @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
= V )
=> ( ! [V2: list @ char] :
( ( V = V2 )
=> ( ( F3 @ V2 )
= ( F4 @ V2 ) ) )
=> ( ( doctype_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F3 @ R )
= ( doctype_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% RDocument.fold_congs(3)
thf(fact_68_RDocument_Ofold__congs_I4_J,axiom,
! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: option @ ( element_ptr @ Element_ptr2 ),F3: ( option @ ( element_ptr @ Element_ptr2 ) ) > ( option @ ( element_ptr @ Element_ptr2 ) ),F4: ( option @ ( element_ptr @ Element_ptr2 ) ) > ( option @ ( element_ptr @ Element_ptr2 ) )] :
( ( R = R2 )
=> ( ( ( document_element @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
= V )
=> ( ! [V2: option @ ( element_ptr @ Element_ptr2 )] :
( ( V = V2 )
=> ( ( F3 @ V2 )
= ( F4 @ V2 ) ) )
=> ( ( docume446011358update @ Element_ptr2 @ Node_ptr2 @ Character_data_ptr2 @ Z2 @ F3 @ R )
= ( docume446011358update @ Element_ptr2 @ Node_ptr2 @ Character_data_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% RDocument.fold_congs(4)
thf(fact_69_RDocument_Ofold__congs_I5_J,axiom,
! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ),F3: ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) ),F4: ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) ) > ( list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) ) )] :
( ( R = R2 )
=> ( ( ( disconnected_nodes @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
= V )
=> ( ! [V2: list @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr2 ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr2 ) @ Node_ptr2 ) ) )] :
( ( V = V2 )
=> ( ( F3 @ V2 )
= ( F4 @ V2 ) ) )
=> ( ( discon1635973971update @ Element_ptr2 @ Character_data_ptr2 @ Node_ptr2 @ Z2 @ F3 @ R )
= ( discon1635973971update @ Element_ptr2 @ Character_data_ptr2 @ Node_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% RDocument.fold_congs(5)
thf(fact_70_RDocument_Ounfold__congs_I2_J,axiom,
! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: product_unit,F3: product_unit > product_unit,F4: product_unit > product_unit] :
( ( R = R2 )
=> ( ( ( nothing @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
= V )
=> ( ! [V2: product_unit] :
( ( V2 = V )
=> ( ( F3 @ V2 )
= ( F4 @ V2 ) ) )
=> ( ( nothing_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F3 @ R )
= ( nothing_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% RDocument.unfold_congs(2)
thf(fact_71_RDocument_Ofold__congs_I2_J,axiom,
! [Z2: $tType,Character_data_ptr2: $tType,Element_ptr2: $tType,Node_ptr2: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 ),V: product_unit,F3: product_unit > product_unit,F4: product_unit > product_unit] :
( ( R = R2 )
=> ( ( ( nothing @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ R2 )
= V )
=> ( ! [V2: product_unit] :
( ( V = V2 )
=> ( ( F3 @ V2 )
= ( F4 @ V2 ) ) )
=> ( ( nothing_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F3 @ R )
= ( nothing_update @ Node_ptr2 @ Element_ptr2 @ Character_data_ptr2 @ Z2 @ F4 @ R2 ) ) ) ) ) ).
% RDocument.fold_congs(2)
thf(fact_72_length__0__conv,axiom,
! [A: $tType,Xs: list @ A] :
( ( ( size_size @ ( list @ A ) @ Xs )
= ( zero_zero @ nat ) )
= ( Xs
= ( nil @ A ) ) ) ).
% length_0_conv
thf(fact_73_RDocument_Osurjective,axiom,
! [Z: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Node_ptr: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z )] :
( R
= ( rObject_ext2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ ( nothing2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ R ) @ ( rDocument_ext2 @ Element_ptr @ Character_data_ptr @ Node_ptr @ Z @ ( nothing @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R ) @ ( doctype @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R ) @ ( document_element @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R ) @ ( disconnected_nodes @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R ) @ ( more @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R ) ) ) ) ).
% RDocument.surjective
thf(fact_74_RDocument_Oequality,axiom,
! [Z: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Node_ptr: $tType,R: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ),R2: rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z )] :
( ( ( nothing2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ R )
= ( nothing2 @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z ) @ R2 ) )
=> ( ( ( nothing @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R )
= ( nothing @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R2 ) )
=> ( ( ( doctype @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R )
= ( doctype @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R2 ) )
=> ( ( ( document_element @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R )
= ( document_element @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R2 ) )
=> ( ( ( disconnected_nodes @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R )
= ( disconnected_nodes @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R2 ) )
=> ( ( ( more @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R )
= ( more @ Node_ptr @ Element_ptr @ Character_data_ptr @ Z @ R2 ) )
=> ( R = R2 ) ) ) ) ) ) ) ).
% RDocument.equality
thf(fact_75_option_Osize_I3_J,axiom,
! [A: $tType] :
( ( size_size @ ( option @ A ) @ ( none @ A ) )
= ( suc @ ( zero_zero @ nat ) ) ) ).
% option.size(3)
thf(fact_76_list_Osize_I3_J,axiom,
! [A: $tType] :
( ( size_size @ ( list @ A ) @ ( nil @ A ) )
= ( zero_zero @ nat ) ) ).
% list.size(3)
thf(fact_77_document__ptr_Osize_I4_J,axiom,
! [Document_ptr: $tType,X2: Document_ptr] :
( ( size_size @ ( document_ptr @ Document_ptr ) @ ( document_Ext @ Document_ptr @ X2 ) )
= ( suc @ ( zero_zero @ nat ) ) ) ).
% document_ptr.size(4)
thf(fact_78_RObject_Osurjective,axiom,
! [Z: $tType,R: rObject_ext @ Z] :
( R
= ( rObject_ext2 @ Z @ ( nothing2 @ Z @ R ) @ ( more2 @ Z @ R ) ) ) ).
% RObject.surjective
thf(fact_79_document__ptr_Oinject_I2_J,axiom,
! [Document_ptr: $tType,X2: Document_ptr,Y2: Document_ptr] :
( ( ( document_Ext @ Document_ptr @ X2 )
= ( document_Ext @ Document_ptr @ Y2 ) )
= ( X2 = Y2 ) ) ).
% document_ptr.inject(2)
thf(fact_80_neq__if__length__neq,axiom,
! [A: $tType,Xs: list @ A,Ys: list @ A] :
( ( ( size_size @ ( list @ A ) @ Xs )
!= ( size_size @ ( list @ A ) @ Ys ) )
=> ( Xs != Ys ) ) ).
% neq_if_length_neq
thf(fact_81_Ex__list__of__length,axiom,
! [A: $tType,N: nat] :
? [Xs2: list @ A] :
( ( size_size @ ( list @ A ) @ Xs2 )
= N ) ).
% Ex_list_of_length
thf(fact_82_document__ptr_Odistinct_I1_J,axiom,
! [Document_ptr: $tType,X1: nat,X2: Document_ptr] :
( ( document_Ref @ Document_ptr @ X1 )
!= ( document_Ext @ Document_ptr @ X2 ) ) ).
% document_ptr.distinct(1)
thf(fact_83_document__ptr_Oinduct,axiom,
! [Document_ptr: $tType,P: ( document_ptr @ Document_ptr ) > $o,Document_ptr3: document_ptr @ Document_ptr] :
( ! [X4: nat] : ( P @ ( document_Ref @ Document_ptr @ X4 ) )
=> ( ! [X4: Document_ptr] : ( P @ ( document_Ext @ Document_ptr @ X4 ) )
=> ( P @ Document_ptr3 ) ) ) ).
% document_ptr.induct
thf(fact_84_document__ptr_Oexhaust,axiom,
! [Document_ptr: $tType,Y: document_ptr @ Document_ptr] :
( ! [X12: nat] :
( Y
!= ( document_Ref @ Document_ptr @ X12 ) )
=> ~ ! [X22: Document_ptr] :
( Y
!= ( document_Ext @ Document_ptr @ X22 ) ) ) ).
% document_ptr.exhaust
thf(fact_85_RObject_Oselect__convs_I1_J,axiom,
! [Z: $tType,Nothing: product_unit,More: Z] :
( ( nothing2 @ Z @ ( rObject_ext2 @ Z @ Nothing @ More ) )
= Nothing ) ).
% RObject.select_convs(1)
thf(fact_86_RObject_Oequality,axiom,
! [Z: $tType,R: rObject_ext @ Z,R2: rObject_ext @ Z] :
( ( ( nothing2 @ Z @ R )
= ( nothing2 @ Z @ R2 ) )
=> ( ( ( more2 @ Z @ R )
= ( more2 @ Z @ R2 ) )
=> ( R = R2 ) ) ) ).
% RObject.equality
thf(fact_87_option_Osize__neq,axiom,
! [A: $tType,X: option @ A] :
( ( size_size @ ( option @ A ) @ X )
!= ( zero_zero @ nat ) ) ).
% option.size_neq
thf(fact_88_option_Osize__gen_I1_J,axiom,
! [A: $tType,X: A > nat] :
( ( size_option @ A @ X @ ( none @ A ) )
= ( suc @ ( zero_zero @ nat ) ) ) ).
% option.size_gen(1)
thf(fact_89_length__code,axiom,
! [A: $tType] :
( ( size_size @ ( list @ A ) )
= ( gen_length @ A @ ( zero_zero @ nat ) ) ) ).
% length_code
thf(fact_90_document__ptr_Osize__gen_I2_J,axiom,
! [Document_ptr: $tType,X: Document_ptr > nat,X2: Document_ptr] :
( ( docume1907984069nt_ptr @ Document_ptr @ X @ ( document_Ext @ Document_ptr @ X2 ) )
= ( plus_plus @ nat @ ( X @ X2 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% document_ptr.size_gen(2)
thf(fact_91_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,
! [E: $tType,F: $tType,G: $tType,H: $tType,I: $tType,D: $tType,C: $tType,B: $tType,A: $tType,Obj: rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ F ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ G ) ) @ H ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ I ) )] :
( ( ( cast_O1159777348_e_n_t @ A @ B @ C @ E @ F @ G @ H @ D @ I @ Obj )
= ( none @ ( rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) ) ) )
= ( ~ ? [Document2: rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) )] :
( ( cast_D42511940_e_c_t @ A @ B @ C @ D @ E @ F @ G @ H @ I @ 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_none
thf(fact_92_list__ex1__simps_I1_J,axiom,
! [A: $tType,P: A > $o] :
~ ( list_ex1 @ A @ P @ ( nil @ A ) ) ).
% list_ex1_simps(1)
thf(fact_93_is__document__kind__def,axiom,
! [Object: $tType,Document: $tType,Node: $tType,CharacterData: $tType,Element: $tType,Shadow_root_ptr: $tType,Character_data_ptr: $tType,Element_ptr: $tType,Node_ptr: $tType] :
( ( is_document_kind @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ Element @ CharacterData @ Node @ Document @ Object )
= ( ^ [Ptr: rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) )] :
( ( cast_O1159777348_e_n_t @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ Element @ CharacterData @ Node @ Document @ Object @ Ptr )
!= ( none @ ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) ) ) ) ) ) ).
% is_document_kind_def
thf(fact_94_add__right__cancel,axiom,
! [A: $tType] :
( ( cancel_semigroup_add @ A )
=> ! [B2: A,A2: A,C2: A] :
( ( ( plus_plus @ A @ B2 @ A2 )
= ( plus_plus @ A @ C2 @ A2 ) )
= ( B2 = C2 ) ) ) ).
% add_right_cancel
thf(fact_95_add__left__cancel,axiom,
! [A: $tType] :
( ( cancel_semigroup_add @ A )
=> ! [A2: A,B2: A,C2: A] :
( ( ( plus_plus @ A @ A2 @ B2 )
= ( plus_plus @ A @ A2 @ C2 ) )
= ( B2 = C2 ) ) ) ).
% add_left_cancel
thf(fact_96_zero__eq__add__iff__both__eq__0,axiom,
! [A: $tType] :
( ( canoni770627133id_add @ A )
=> ! [X: A,Y: A] :
( ( ( zero_zero @ A )
= ( plus_plus @ A @ X @ Y ) )
= ( ( X
= ( zero_zero @ A ) )
& ( Y
= ( zero_zero @ A ) ) ) ) ) ).
% zero_eq_add_iff_both_eq_0
thf(fact_97_add__eq__0__iff__both__eq__0,axiom,
! [A: $tType] :
( ( canoni770627133id_add @ A )
=> ! [X: A,Y: A] :
( ( ( plus_plus @ A @ X @ Y )
= ( zero_zero @ A ) )
= ( ( X
= ( zero_zero @ A ) )
& ( Y
= ( zero_zero @ A ) ) ) ) ) ).
% add_eq_0_iff_both_eq_0
thf(fact_98_add__cancel__right__right,axiom,
! [A: $tType] :
( ( cancel1352612707id_add @ A )
=> ! [A2: A,B2: A] :
( ( A2
= ( plus_plus @ A @ A2 @ B2 ) )
= ( B2
= ( zero_zero @ A ) ) ) ) ).
% add_cancel_right_right
thf(fact_99_add__cancel__right__left,axiom,
! [A: $tType] :
( ( cancel1352612707id_add @ A )
=> ! [A2: A,B2: A] :
( ( A2
= ( plus_plus @ A @ B2 @ A2 ) )
= ( B2
= ( zero_zero @ A ) ) ) ) ).
% add_cancel_right_left
thf(fact_100_add__cancel__left__right,axiom,
! [A: $tType] :
( ( cancel1352612707id_add @ A )
=> ! [A2: A,B2: A] :
( ( ( plus_plus @ A @ A2 @ B2 )
= A2 )
= ( B2
= ( zero_zero @ A ) ) ) ) ).
% add_cancel_left_right
thf(fact_101_add__cancel__left__left,axiom,
! [A: $tType] :
( ( cancel1352612707id_add @ A )
=> ! [B2: A,A2: A] :
( ( ( plus_plus @ A @ B2 @ A2 )
= A2 )
= ( B2
= ( zero_zero @ A ) ) ) ) ).
% add_cancel_left_left
thf(fact_102_double__zero__sym,axiom,
! [A: $tType] :
( ( linord219039673up_add @ A )
=> ! [A2: A] :
( ( ( zero_zero @ A )
= ( plus_plus @ A @ A2 @ A2 ) )
= ( A2
= ( zero_zero @ A ) ) ) ) ).
% double_zero_sym
thf(fact_103_double__zero,axiom,
! [A: $tType] :
( ( linord219039673up_add @ A )
=> ! [A2: A] :
( ( ( plus_plus @ A @ A2 @ A2 )
= ( zero_zero @ A ) )
= ( A2
= ( zero_zero @ A ) ) ) ) ).
% double_zero
thf(fact_104_add_Oright__neutral,axiom,
! [A: $tType] :
( ( monoid_add @ A )
=> ! [A2: A] :
( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
= A2 ) ) ).
% add.right_neutral
thf(fact_105_add_Oleft__neutral,axiom,
! [A: $tType] :
( ( monoid_add @ A )
=> ! [A2: A] :
( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
= A2 ) ) ).
% add.left_neutral
thf(fact_106_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_107_Nat_Oadd__0__right,axiom,
! [M2: nat] :
( ( plus_plus @ nat @ M2 @ ( zero_zero @ nat ) )
= M2 ) ).
% Nat.add_0_right
thf(fact_108_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_109_gen__length__def,axiom,
! [A: $tType] :
( ( gen_length @ A )
= ( ^ [N4: nat,Xs3: list @ A] : ( plus_plus @ nat @ N4 @ ( size_size @ ( list @ A ) @ Xs3 ) ) ) ) ).
% gen_length_def
thf(fact_110_add__right__imp__eq,axiom,
! [A: $tType] :
( ( cancel_semigroup_add @ A )
=> ! [B2: A,A2: A,C2: A] :
( ( ( plus_plus @ A @ B2 @ A2 )
= ( plus_plus @ A @ C2 @ A2 ) )
=> ( B2 = C2 ) ) ) ).
% add_right_imp_eq
thf(fact_111_add__left__imp__eq,axiom,
! [A: $tType] :
( ( cancel_semigroup_add @ A )
=> ! [A2: A,B2: A,C2: A] :
( ( ( plus_plus @ A @ A2 @ B2 )
= ( plus_plus @ A @ A2 @ C2 ) )
=> ( B2 = C2 ) ) ) ).
% add_left_imp_eq
thf(fact_112_add_Oleft__commute,axiom,
! [A: $tType] :
( ( ab_semigroup_add @ A )
=> ! [B2: A,A2: A,C2: A] :
( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C2 ) )
= ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% add.left_commute
thf(fact_113_add_Ocommute,axiom,
! [A: $tType] :
( ( ab_semigroup_add @ A )
=> ( ( plus_plus @ A )
= ( ^ [A4: A,B3: A] : ( plus_plus @ A @ B3 @ A4 ) ) ) ) ).
% add.commute
thf(fact_114_add_Oright__cancel,axiom,
! [A: $tType] :
( ( group_add @ A )
=> ! [B2: A,A2: A,C2: A] :
( ( ( plus_plus @ A @ B2 @ A2 )
= ( plus_plus @ A @ C2 @ A2 ) )
= ( B2 = C2 ) ) ) ).
% add.right_cancel
thf(fact_115_add_Oleft__cancel,axiom,
! [A: $tType] :
( ( group_add @ A )
=> ! [A2: A,B2: A,C2: A] :
( ( ( plus_plus @ A @ A2 @ B2 )
= ( plus_plus @ A @ A2 @ C2 ) )
= ( B2 = C2 ) ) ) ).
% add.left_cancel
thf(fact_116_add_Oassoc,axiom,
! [A: $tType] :
( ( semigroup_add @ A )
=> ! [A2: A,B2: A,C2: A] :
( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
= ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% add.assoc
thf(fact_117_group__cancel_Oadd2,axiom,
! [A: $tType] :
( ( comm_monoid_add @ A )
=> ! [B4: A,K2: A,B2: A,A2: A] :
( ( B4
= ( plus_plus @ A @ K2 @ B2 ) )
=> ( ( plus_plus @ A @ A2 @ B4 )
= ( plus_plus @ A @ K2 @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% group_cancel.add2
thf(fact_118_group__cancel_Oadd1,axiom,
! [A: $tType] :
( ( comm_monoid_add @ A )
=> ! [A3: A,K2: A,A2: A,B2: A] :
( ( A3
= ( plus_plus @ A @ K2 @ A2 ) )
=> ( ( plus_plus @ A @ A3 @ B2 )
= ( plus_plus @ A @ K2 @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% group_cancel.add1
thf(fact_119_add__mono__thms__linordered__semiring_I4_J,axiom,
! [A: $tType] :
( ( ordere779506340up_add @ A )
=> ! [I2: A,J2: A,K2: A,L2: A] :
( ( ( I2 = J2 )
& ( K2 = L2 ) )
=> ( ( plus_plus @ A @ I2 @ K2 )
= ( plus_plus @ A @ J2 @ L2 ) ) ) ) ).
% add_mono_thms_linordered_semiring(4)
thf(fact_120_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [A: $tType] :
( ( ab_semigroup_add @ A )
=> ! [A2: A,B2: A,C2: A] :
( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C2 )
= ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% ab_semigroup_add_class.add_ac(1)
thf(fact_121_add_Ogroup__left__neutral,axiom,
! [A: $tType] :
( ( group_add @ A )
=> ! [A2: A] :
( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
= A2 ) ) ).
% add.group_left_neutral
thf(fact_122_add_Ocomm__neutral,axiom,
! [A: $tType] :
( ( comm_monoid_add @ A )
=> ! [A2: A] :
( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
= A2 ) ) ).
% add.comm_neutral
thf(fact_123_comm__monoid__add__class_Oadd__0,axiom,
! [A: $tType] :
( ( comm_monoid_add @ A )
=> ! [A2: A] :
( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
= A2 ) ) ).
% comm_monoid_add_class.add_0
thf(fact_124_add__Suc,axiom,
! [M2: nat,N: nat] :
( ( plus_plus @ nat @ ( suc @ M2 ) @ N )
= ( suc @ ( plus_plus @ nat @ M2 @ N ) ) ) ).
% add_Suc
thf(fact_125_nat__arith_Osuc1,axiom,
! [A3: nat,K2: nat,A2: nat] :
( ( A3
= ( plus_plus @ nat @ K2 @ A2 ) )
=> ( ( suc @ A3 )
= ( plus_plus @ nat @ K2 @ ( suc @ A2 ) ) ) ) ).
% nat_arith.suc1
thf(fact_126_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_127_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_128_plus__nat_Oadd__0,axiom,
! [N: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ N )
= N ) ).
% plus_nat.add_0
thf(fact_129_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_130_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_131_gen__length__code_I1_J,axiom,
! [A: $tType,N: nat] :
( ( gen_length @ A @ N @ ( nil @ A ) )
= N ) ).
% gen_length_code(1)
thf(fact_132_Euclid__induct,axiom,
! [P: nat > nat > $o,A2: nat,B2: nat] :
( ! [A5: nat,B5: nat] :
( ( P @ A5 @ B5 )
= ( P @ B5 @ A5 ) )
=> ( ! [A5: nat] : ( P @ A5 @ ( zero_zero @ nat ) )
=> ( ! [A5: nat,B5: nat] :
( ( P @ A5 @ B5 )
=> ( P @ A5 @ ( plus_plus @ nat @ A5 @ B5 ) ) )
=> ( P @ A2 @ B2 ) ) ) ) ).
% Euclid_induct
thf(fact_133_triangle__Suc,axiom,
! [N: nat] :
( ( nat_triangle @ ( suc @ N ) )
= ( plus_plus @ nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% triangle_Suc
thf(fact_134_verit__sum__simplify,axiom,
! [A: $tType] :
( ( cancel1352612707id_add @ A )
=> ! [A2: A] :
( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
= A2 ) ) ).
% verit_sum_simplify
thf(fact_135_add__0__iff,axiom,
! [A: $tType] :
( ( semiri456707255roduct @ A )
=> ! [B2: A,A2: A] :
( ( B2
= ( plus_plus @ A @ B2 @ A2 ) )
= ( A2
= ( zero_zero @ A ) ) ) ) ).
% add_0_iff
thf(fact_136_option_Osize__gen_I2_J,axiom,
! [A: $tType,X: A > nat,X2: A] :
( ( size_option @ A @ X @ ( some @ A @ X2 ) )
= ( plus_plus @ nat @ ( X @ X2 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% option.size_gen(2)
thf(fact_137_option_Oinject,axiom,
! [A: $tType,X2: A,Y2: A] :
( ( ( some @ A @ X2 )
= ( some @ A @ Y2 ) )
= ( X2 = Y2 ) ) ).
% option.inject
thf(fact_138_not__Some__eq,axiom,
! [A: $tType,X: option @ A] :
( ( ! [Y5: A] :
( X
!= ( some @ A @ Y5 ) ) )
= ( X
= ( none @ A ) ) ) ).
% not_Some_eq
thf(fact_139_not__None__eq,axiom,
! [A: $tType,X: option @ A] :
( ( X
!= ( none @ A ) )
= ( ? [Y5: A] :
( X
= ( some @ A @ Y5 ) ) ) ) ).
% not_None_eq
thf(fact_140_triangle__0,axiom,
( ( nat_triangle @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ) ).
% triangle_0
thf(fact_141_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,
! [I: $tType,H: $tType,G: $tType,F: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,Document3: rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) )] :
( ( cast_O1159777348_e_n_t @ A @ B @ C @ E @ F @ G @ H @ D @ I @ ( cast_D42511940_e_c_t @ A @ B @ C @ D @ E @ F @ G @ H @ I @ Document3 ) )
= ( some @ ( rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) ) @ Document3 ) ) ).
% 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_142_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,
! [I: $tType,D: $tType,H: $tType,G: $tType,F: $tType,E: $tType,C: $tType,B: $tType,A: $tType,Obj: rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ F ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ G ) ) @ H ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ I ) ),Document3: rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) )] :
( ( ( cast_O1159777348_e_n_t @ A @ B @ C @ E @ F @ G @ H @ D @ I @ Obj )
= ( some @ ( rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) ) @ Document3 ) )
= ( ( cast_D42511940_e_c_t @ A @ B @ C @ D @ E @ F @ G @ H @ I @ Document3 )
= 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_143_option_Odistinct_I1_J,axiom,
! [A: $tType,X2: A] :
( ( none @ A )
!= ( some @ A @ X2 ) ) ).
% option.distinct(1)
thf(fact_144_option_OdiscI,axiom,
! [A: $tType,Option: option @ A,X2: A] :
( ( Option
= ( some @ A @ X2 ) )
=> ( Option
!= ( none @ A ) ) ) ).
% option.discI
thf(fact_145_option_Oexhaust,axiom,
! [A: $tType,Y: option @ A] :
( ( Y
!= ( none @ A ) )
=> ~ ! [X22: A] :
( Y
!= ( some @ A @ X22 ) ) ) ).
% option.exhaust
thf(fact_146_option_Oinducts,axiom,
! [A: $tType,P: ( option @ A ) > $o,Option: option @ A] :
( ( P @ ( none @ A ) )
=> ( ! [X4: A] : ( P @ ( some @ A @ X4 ) )
=> ( P @ Option ) ) ) ).
% option.inducts
thf(fact_147_split__option__ex,axiom,
! [A: $tType] :
( ( ^ [P2: ( option @ A ) > $o] :
? [X5: option @ A] : ( P2 @ X5 ) )
= ( ^ [P3: ( option @ A ) > $o] :
( ( P3 @ ( none @ A ) )
| ? [X3: A] : ( P3 @ ( some @ A @ X3 ) ) ) ) ) ).
% split_option_ex
thf(fact_148_split__option__all,axiom,
! [A: $tType] :
( ( ^ [P2: ( option @ A ) > $o] :
! [X5: option @ A] : ( P2 @ X5 ) )
= ( ^ [P3: ( option @ A ) > $o] :
( ( P3 @ ( none @ A ) )
& ! [X3: A] : ( P3 @ ( some @ A @ X3 ) ) ) ) ) ).
% split_option_all
thf(fact_149_combine__options__cases,axiom,
! [A: $tType,B: $tType,X: option @ A,P: ( option @ A ) > ( option @ B ) > $o,Y: option @ B] :
( ( ( X
= ( none @ A ) )
=> ( P @ X @ Y ) )
=> ( ( ( Y
= ( none @ B ) )
=> ( P @ X @ Y ) )
=> ( ! [A5: A,B5: B] :
( ( X
= ( some @ A @ A5 ) )
=> ( ( Y
= ( some @ B @ B5 ) )
=> ( P @ X @ Y ) ) )
=> ( P @ X @ Y ) ) ) ) ).
% combine_options_cases
thf(fact_150_option_Osize_I4_J,axiom,
! [A: $tType,X2: A] :
( ( size_size @ ( option @ A ) @ ( some @ A @ X2 ) )
= ( suc @ ( zero_zero @ nat ) ) ) ).
% option.size(4)
thf(fact_151_document__ptr__casts__commute2,axiom,
! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,Document_ptr3: document_ptr @ A] :
( ( cast_o823910367_p_t_r @ B @ C @ D @ A @ E @ ( cast_d1427782271_p_t_r @ A @ B @ C @ D @ E @ Document_ptr3 ) )
= ( some @ ( document_ptr @ A ) @ Document_ptr3 ) ) ).
% document_ptr_casts_commute2
thf(fact_152_document__ptr__casts__commute,axiom,
! [E: $tType,A: $tType,D: $tType,C: $tType,B: $tType,Ptr2: object_ptr @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ B ) @ ( sum_sum @ ( character_data_ptr @ C ) @ D ) ) ) @ ( sum_sum @ ( document_ptr @ A ) @ E ) ),Document_ptr3: document_ptr @ A] :
( ( ( cast_o823910367_p_t_r @ B @ C @ D @ A @ E @ Ptr2 )
= ( some @ ( document_ptr @ A ) @ Document_ptr3 ) )
= ( ( cast_d1427782271_p_t_r @ A @ B @ C @ D @ E @ Document_ptr3 )
= Ptr2 ) ) ).
% document_ptr_casts_commute
thf(fact_153_length__splice,axiom,
! [A: $tType,Xs: list @ A,Ys: list @ A] :
( ( size_size @ ( list @ A ) @ ( splice @ A @ Xs @ Ys ) )
= ( plus_plus @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( size_size @ ( list @ A ) @ Ys ) ) ) ).
% length_splice
thf(fact_154_get__document__ptr__simp,axiom,
! [K: $tType,D: $tType,J: $tType,I: $tType,H: $tType,G: $tType,F: $tType,E: $tType,A: $tType,C: $tType,B: $tType,Ptr2: object_ptr @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ B ) @ ( sum_sum @ ( character_data_ptr @ C ) @ A ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) ) @ G ) ),Document_ptr3: document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ),Obj: rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ H ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ I ) ) @ J ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ K ) ),H2: heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ B ) @ ( sum_sum @ ( character_data_ptr @ C ) @ A ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) ) @ G ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ H ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ I ) ) @ J ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ K ) )] :
( ( ( Ptr2
= ( cast_d1427782271_p_t_r @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) @ B @ C @ A @ G @ Document_ptr3 ) )
=> ( ( get_D_o_c_u_m_e_n_t @ E @ F @ B @ C @ A @ G @ H @ I @ J @ D @ K @ Document_ptr3 @ ( put_O_b_j_e_c_t @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ B ) @ ( sum_sum @ ( character_data_ptr @ C ) @ A ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) ) @ G ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ H ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ I ) ) @ J ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ K ) ) @ Ptr2 @ Obj @ H2 ) )
= ( cast_O1159777348_e_n_t @ A @ B @ C @ E @ H @ I @ J @ D @ K @ Obj ) ) )
& ( ( Ptr2
!= ( cast_d1427782271_p_t_r @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) @ B @ C @ A @ G @ Document_ptr3 ) )
=> ( ( get_D_o_c_u_m_e_n_t @ E @ F @ B @ C @ A @ G @ H @ I @ J @ D @ K @ Document_ptr3 @ ( put_O_b_j_e_c_t @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ B ) @ ( sum_sum @ ( character_data_ptr @ C ) @ A ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) ) @ G ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ H ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ I ) ) @ J ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ K ) ) @ Ptr2 @ Obj @ H2 ) )
= ( get_D_o_c_u_m_e_n_t @ E @ F @ B @ C @ A @ G @ H @ I @ J @ D @ K @ Document_ptr3 @ H2 ) ) ) ) ).
% get_document_ptr_simp
thf(fact_155_split__Nil__iff,axiom,
! [A: $tType,Xs: list @ A,Ys: list @ A] :
( ( ( splice @ A @ Xs @ Ys )
= ( nil @ A ) )
= ( ( Xs
= ( nil @ A ) )
& ( Ys
= ( nil @ A ) ) ) ) ).
% split_Nil_iff
thf(fact_156_splice__Nil2,axiom,
! [A: $tType,Xs: list @ A] :
( ( splice @ A @ Xs @ ( nil @ A ) )
= Xs ) ).
% splice_Nil2
thf(fact_157_get__document__ptr__simp2,axiom,
! [K: $tType,F: $tType,J: $tType,I: $tType,H: $tType,G: $tType,B: $tType,A: $tType,C: $tType,E: $tType,D: $tType,Document_ptr3: document_ptr @ ( sum_sum @ ( shadow_root_ptr @ A ) @ B ),Document_ptr4: document_ptr @ ( sum_sum @ ( shadow_root_ptr @ A ) @ B ),Document3: rObject_ext @ ( rDocument_ext @ C @ D @ E @ ( option @ F ) ),H2: heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ D ) @ ( sum_sum @ ( character_data_ptr @ E ) @ C ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ A ) @ B ) ) @ G ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ C @ D @ E @ A @ ( option @ H ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ I ) ) @ J ) ) ) @ ( sum_sum @ ( rDocument_ext @ C @ D @ E @ ( option @ F ) ) @ K ) )] :
( ( Document_ptr3 != Document_ptr4 )
=> ( ( get_D_o_c_u_m_e_n_t @ A @ B @ D @ E @ C @ G @ H @ I @ J @ F @ K @ Document_ptr3 @ ( put_D_o_c_u_m_e_n_t @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ Document_ptr4 @ Document3 @ H2 ) )
= ( get_D_o_c_u_m_e_n_t @ A @ B @ D @ E @ C @ G @ H @ I @ J @ F @ K @ Document_ptr3 @ H2 ) ) ) ).
% get_document_ptr_simp2
thf(fact_158_get__document__ptr__simp1,axiom,
! [E: $tType,F: $tType,G: $tType,H: $tType,I: $tType,J: $tType,K: $tType,D: $tType,C: $tType,B: $tType,A: $tType,Document_ptr3: document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ),Document3: rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ),H2: heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ B ) @ ( sum_sum @ ( character_data_ptr @ C ) @ A ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ E ) @ F ) ) @ G ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ A @ B @ C @ E @ ( option @ H ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ I ) ) @ J ) ) ) @ ( sum_sum @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) @ K ) )] :
( ( get_D_o_c_u_m_e_n_t @ E @ F @ B @ C @ A @ G @ H @ I @ J @ D @ K @ Document_ptr3 @ ( put_D_o_c_u_m_e_n_t @ E @ F @ A @ B @ C @ D @ G @ H @ I @ J @ K @ Document_ptr3 @ Document3 @ H2 ) )
= ( some @ ( rObject_ext @ ( rDocument_ext @ A @ B @ C @ ( option @ D ) ) ) @ Document3 ) ) ).
% get_document_ptr_simp1
thf(fact_159_splice_Osimps_I1_J,axiom,
! [A: $tType,Ys: list @ A] :
( ( splice @ A @ ( nil @ A ) @ Ys )
= Ys ) ).
% splice.simps(1)
thf(fact_160_get__object__ptr__simp1,axiom,
! [B: $tType,A: $tType,Object_ptr2: object_ptr @ B,Object2: rObject_ext @ A,H2: heap @ B @ A] :
( ( get_O_b_j_e_c_t @ B @ A @ Object_ptr2 @ ( put_O_b_j_e_c_t @ B @ A @ Object_ptr2 @ Object2 @ H2 ) )
= ( some @ ( rObject_ext @ A ) @ Object2 ) ) ).
% get_object_ptr_simp1
thf(fact_161_list_Osize_I4_J,axiom,
! [A: $tType,X21: A,X222: list @ A] :
( ( size_size @ ( list @ A ) @ ( cons @ A @ X21 @ X222 ) )
= ( plus_plus @ nat @ ( size_size @ ( list @ A ) @ X222 ) @ ( suc @ ( zero_zero @ nat ) ) ) ) ).
% list.size(4)
thf(fact_162_count__list_Osimps_I1_J,axiom,
! [A: $tType,Y: A] :
( ( count_list @ A @ ( nil @ A ) @ Y )
= ( zero_zero @ nat ) ) ).
% count_list.simps(1)
thf(fact_163_list_Oinject,axiom,
! [A: $tType,X21: A,X222: list @ A,Y21: A,Y22: list @ A] :
( ( ( cons @ A @ X21 @ X222 )
= ( cons @ A @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X222 = Y22 ) ) ) ).
% list.inject
thf(fact_164_get__object__ptr__simp2,axiom,
! [B: $tType,A: $tType,Object_ptr2: object_ptr @ A,Object_ptr3: object_ptr @ A,Object2: rObject_ext @ B,H2: heap @ A @ B] :
( ( Object_ptr2 != Object_ptr3 )
=> ( ( get_O_b_j_e_c_t @ A @ B @ Object_ptr2 @ ( put_O_b_j_e_c_t @ A @ B @ Object_ptr3 @ Object2 @ H2 ) )
= ( get_O_b_j_e_c_t @ A @ B @ Object_ptr2 @ H2 ) ) ) ).
% get_object_ptr_simp2
thf(fact_165_splice_Osimps_I2_J,axiom,
! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
( ( splice @ A @ ( cons @ A @ X @ Xs ) @ Ys )
= ( cons @ A @ X @ ( splice @ A @ Ys @ Xs ) ) ) ).
% splice.simps(2)
thf(fact_166_not__Cons__self2,axiom,
! [A: $tType,X: A,Xs: list @ A] :
( ( cons @ A @ X @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_167_transpose_Ocases,axiom,
! [A: $tType,X: list @ ( list @ A )] :
( ( X
!= ( nil @ ( list @ A ) ) )
=> ( ! [Xss: list @ ( list @ A )] :
( X
!= ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
=> ~ ! [X4: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
( X
!= ( cons @ ( list @ A ) @ ( cons @ A @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_168_list_Odistinct_I1_J,axiom,
! [A: $tType,X21: A,X222: list @ A] :
( ( nil @ A )
!= ( cons @ A @ X21 @ X222 ) ) ).
% list.distinct(1)
thf(fact_169_list_OdiscI,axiom,
! [A: $tType,List: list @ A,X21: A,X222: list @ A] :
( ( List
= ( cons @ A @ X21 @ X222 ) )
=> ( List
!= ( nil @ A ) ) ) ).
% list.discI
thf(fact_170_list_Oexhaust,axiom,
! [A: $tType,Y: list @ A] :
( ( Y
!= ( nil @ A ) )
=> ~ ! [X212: A,X223: list @ A] :
( Y
!= ( cons @ A @ X212 @ X223 ) ) ) ).
% list.exhaust
thf(fact_171_list_Oinducts,axiom,
! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
( ( P @ ( nil @ A ) )
=> ( ! [X12: A,X22: list @ A] :
( ( P @ X22 )
=> ( P @ ( cons @ A @ X12 @ X22 ) ) )
=> ( P @ List ) ) ) ).
% list.inducts
thf(fact_172_neq__Nil__conv,axiom,
! [A: $tType,Xs: list @ A] :
( ( Xs
!= ( nil @ A ) )
= ( ? [Y5: A,Ys2: list @ A] :
( Xs
= ( cons @ A @ Y5 @ Ys2 ) ) ) ) ).
% neq_Nil_conv
thf(fact_173_list__induct2_H,axiom,
! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
( ( P @ ( nil @ A ) @ ( nil @ B ) )
=> ( ! [X4: A,Xs2: list @ A] : ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( nil @ B ) )
=> ( ! [Y3: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y3 @ Ys3 ) )
=> ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_174_splice_Oinduct,axiom,
! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
( ! [X_12: list @ A] : ( P @ ( nil @ A ) @ X_12 )
=> ( ! [X4: A,Xs2: list @ A,Ys3: list @ A] :
( ( P @ Ys3 @ Xs2 )
=> ( P @ ( cons @ A @ X4 @ Xs2 ) @ Ys3 ) )
=> ( P @ A0 @ A1 ) ) ) ).
% splice.induct
thf(fact_175_induct__list012,axiom,
! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
( ( P @ ( nil @ A ) )
=> ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
=> ( ! [X4: A,Y3: A,Zs: list @ A] :
( ( P @ Zs )
=> ( ( P @ ( cons @ A @ Y3 @ Zs ) )
=> ( P @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Zs ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% induct_list012
thf(fact_176_min__list_Ocases,axiom,
! [A: $tType] :
( ( ord @ A )
=> ! [X: list @ A] :
( ! [X4: A,Xs2: list @ A] :
( X
!= ( cons @ A @ X4 @ Xs2 ) )
=> ( X
= ( nil @ A ) ) ) ) ).
% min_list.cases
thf(fact_177_min__list_Oinduct,axiom,
! [A: $tType] :
( ( ord @ A )
=> ! [P: ( list @ A ) > $o,A0: list @ A] :
( ! [X4: A,Xs2: list @ A] :
( ! [X213: A,X224: list @ A] :
( ( Xs2
= ( cons @ A @ X213 @ X224 ) )
=> ( P @ Xs2 ) )
=> ( P @ ( cons @ A @ X4 @ Xs2 ) ) )
=> ( ( P @ ( nil @ A ) )
=> ( P @ A0 ) ) ) ) ).
% min_list.induct
thf(fact_178_shuffles_Oinduct,axiom,
! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
( ! [X_12: list @ A] : ( P @ ( nil @ A ) @ X_12 )
=> ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
=> ( ! [X4: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
( ( P @ Xs2 @ ( cons @ A @ Y3 @ Ys3 ) )
=> ( ( P @ ( cons @ A @ X4 @ Xs2 ) @ Ys3 )
=> ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) )
=> ( P @ A0 @ A1 ) ) ) ) ).
% shuffles.induct
thf(fact_179_remdups__adj_Ocases,axiom,
! [A: $tType,X: list @ A] :
( ( X
!= ( nil @ A ) )
=> ( ! [X4: A] :
( X
!= ( cons @ A @ X4 @ ( nil @ A ) ) )
=> ~ ! [X4: A,Y3: A,Xs2: list @ A] :
( X
!= ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_180_sorted__wrt_Oinduct,axiom,
! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
( ! [P4: A > A > $o] : ( P @ P4 @ ( nil @ A ) )
=> ( ! [P4: A > A > $o,X4: A,Ys3: list @ A] :
( ( P @ P4 @ Ys3 )
=> ( P @ P4 @ ( cons @ A @ X4 @ Ys3 ) ) )
=> ( P @ A0 @ A1 ) ) ) ).
% sorted_wrt.induct
thf(fact_181_remdups__adj_Oinduct,axiom,
! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
( ( P @ ( nil @ A ) )
=> ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
=> ( ! [X4: A,Y3: A,Xs2: list @ A] :
( ( ( X4 = Y3 )
=> ( P @ ( cons @ A @ X4 @ Xs2 ) ) )
=> ( ( ( X4 != Y3 )
=> ( P @ ( cons @ A @ Y3 @ Xs2 ) ) )
=> ( P @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) )
=> ( P @ A0 ) ) ) ) ).
% remdups_adj.induct
thf(fact_182_arg__min__list_Oinduct,axiom,
! [B: $tType,A: $tType] :
( ( linorder @ B )
=> ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
( ! [F2: A > B,X4: A] : ( P @ F2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
=> ( ! [F2: A > B,X4: A,Y3: A,Zs: list @ A] :
( ( P @ F2 @ ( cons @ A @ Y3 @ Zs ) )
=> ( P @ F2 @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Zs ) ) ) )
=> ( ! [A5: A > B] : ( P @ A5 @ ( nil @ A ) )
=> ( P @ A0 @ A1 ) ) ) ) ) ).
% arg_min_list.induct
thf(fact_183_successively_Oinduct,axiom,
! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
( ! [P4: A > A > $o] : ( P @ P4 @ ( nil @ A ) )
=> ( ! [P4: A > A > $o,X4: A] : ( P @ P4 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
=> ( ! [P4: A > A > $o,X4: A,Y3: A,Xs2: list @ A] :
( ( P @ P4 @ ( cons @ A @ Y3 @ Xs2 ) )
=> ( P @ P4 @ ( cons @ A @ X4 @ ( cons @ A @ Y3 @ Xs2 ) ) ) )
=> ( P @ A0 @ A1 ) ) ) ) ).
% successively.induct
thf(fact_184_list__nonempty__induct,axiom,
! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
( ( Xs
!= ( nil @ A ) )
=> ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
=> ( ! [X4: A,Xs2: list @ A] :
( ( Xs2
!= ( nil @ A ) )
=> ( ( P @ Xs2 )
=> ( P @ ( cons @ A @ X4 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_185_map__tailrec__rev_Oinduct,axiom,
! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
( ! [F2: A > B,X_12: list @ B] : ( P @ F2 @ ( nil @ A ) @ X_12 )
=> ( ! [F2: A > B,A5: A,As: list @ A,Bs: list @ B] :
( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A5 ) @ Bs ) )
=> ( P @ F2 @ ( cons @ A @ A5 @ As ) @ Bs ) )
=> ( P @ A0 @ A1 @ A22 ) ) ) ).
% map_tailrec_rev.induct
thf(fact_186_strict__sorted_Ocases,axiom,
! [A: $tType] :
( ( linorder @ A )
=> ! [X: list @ A] :
( ( X
!= ( nil @ A ) )
=> ~ ! [X4: A,Ys3: list @ A] :
( X
!= ( cons @ A @ X4 @ Ys3 ) ) ) ) ).
% strict_sorted.cases
thf(fact_187_strict__sorted_Oinduct,axiom,
! [A: $tType] :
( ( linorder @ A )
=> ! [P: ( list @ A ) > $o,A0: list @ A] :
( ( P @ ( nil @ A ) )
=> ( ! [X4: A,Ys3: list @ A] :
( ( P @ Ys3 )
=> ( P @ ( cons @ A @ X4 @ Ys3 ) ) )
=> ( P @ A0 ) ) ) ) ).
% strict_sorted.induct
thf(fact_188_length__Suc__conv,axiom,
! [A: $tType,Xs: list @ A,N: nat] :
( ( ( size_size @ ( list @ A ) @ Xs )
= ( suc @ N ) )
= ( ? [Y5: A,Ys2: list @ A] :
( ( Xs
= ( cons @ A @ Y5 @ Ys2 ) )
& ( ( size_size @ ( list @ A ) @ Ys2 )
= N ) ) ) ) ).
% length_Suc_conv
thf(fact_189_Suc__length__conv,axiom,
! [A: $tType,N: nat,Xs: list @ A] :
( ( ( suc @ N )
= ( size_size @ ( list @ A ) @ Xs ) )
= ( ? [Y5: A,Ys2: list @ A] :
( ( Xs
= ( cons @ A @ Y5 @ Ys2 ) )
& ( ( size_size @ ( list @ A ) @ Ys2 )
= N ) ) ) ) ).
% Suc_length_conv
thf(fact_190_list__induct4,axiom,
! [C: $tType,A: $tType,B: $tType,D: $tType,Xs: list @ A,Ys: list @ B,Zs2: list @ C,Ws: list @ D,P: ( list @ A ) > ( list @ B ) > ( list @ C ) > ( list @ D ) > $o] :
( ( ( size_size @ ( list @ A ) @ Xs )
= ( size_size @ ( list @ B ) @ Ys ) )
=> ( ( ( size_size @ ( list @ B ) @ Ys )
= ( size_size @ ( list @ C ) @ Zs2 ) )
=> ( ( ( size_size @ ( list @ C ) @ Zs2 )
= ( size_size @ ( list @ D ) @ Ws ) )
=> ( ( P @ ( nil @ A ) @ ( nil @ B ) @ ( nil @ C ) @ ( nil @ D ) )
=> ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B,Z3: C,Zs: list @ C,W: D,Ws2: list @ D] :
( ( ( size_size @ ( list @ A ) @ Xs2 )
= ( size_size @ ( list @ B ) @ Ys3 ) )
=> ( ( ( size_size @ ( list @ B ) @ Ys3 )
= ( size_size @ ( list @ C ) @ Zs ) )
=> ( ( ( size_size @ ( list @ C ) @ Zs )
= ( size_size @ ( list @ D ) @ Ws2 ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs @ Ws2 )
=> ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) @ ( cons @ C @ Z3 @ Zs ) @ ( cons @ D @ W @ Ws2 ) ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 @ Ws ) ) ) ) ) ) ).
% list_induct4
thf(fact_191_list__induct3,axiom,
! [B: $tType,A: $tType,C: $tType,Xs: list @ A,Ys: list @ B,Zs2: list @ C,P: ( list @ A ) > ( list @ B ) > ( list @ C ) > $o] :
( ( ( size_size @ ( list @ A ) @ Xs )
= ( size_size @ ( list @ B ) @ Ys ) )
=> ( ( ( size_size @ ( list @ B ) @ Ys )
= ( size_size @ ( list @ C ) @ Zs2 ) )
=> ( ( P @ ( nil @ A ) @ ( nil @ B ) @ ( nil @ C ) )
=> ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B,Z3: C,Zs: list @ C] :
( ( ( size_size @ ( list @ A ) @ Xs2 )
= ( size_size @ ( list @ B ) @ Ys3 ) )
=> ( ( ( size_size @ ( list @ B ) @ Ys3 )
= ( size_size @ ( list @ C ) @ Zs ) )
=> ( ( P @ Xs2 @ Ys3 @ Zs )
=> ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) @ ( cons @ C @ Z3 @ Zs ) ) ) ) )
=> ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% list_induct3
thf(fact_192_list__induct2,axiom,
! [A: $tType,B: $tType,Xs: list @ A,Ys: list @ B,P: ( list @ A ) > ( list @ B ) > $o] :
( ( ( size_size @ ( list @ A ) @ Xs )
= ( size_size @ ( list @ B ) @ Ys ) )
=> ( ( P @ ( nil @ A ) @ ( nil @ B ) )
=> ( ! [X4: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
( ( ( size_size @ ( list @ A ) @ Xs2 )
= ( size_size @ ( list @ B ) @ Ys3 ) )
=> ( ( P @ Xs2 @ Ys3 )
=> ( P @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ).
% list_induct2
thf(fact_193_splice_Oelims,axiom,
! [A: $tType,X: list @ A,Xa: list @ A,Y: list @ A] :
( ( ( splice @ A @ X @ Xa )
= Y )
=> ( ( ( X
= ( nil @ A ) )
=> ( Y != Xa ) )
=> ~ ! [X4: A,Xs2: list @ A] :
( ( X
= ( cons @ A @ X4 @ Xs2 ) )
=> ( Y
!= ( cons @ A @ X4 @ ( splice @ A @ Xa @ Xs2 ) ) ) ) ) ) ).
% splice.elims
thf(fact_194_gen__length__code_I2_J,axiom,
! [B: $tType,N: nat,X: B,Xs: list @ B] :
( ( gen_length @ B @ N @ ( cons @ B @ X @ Xs ) )
= ( gen_length @ B @ ( suc @ N ) @ Xs ) ) ).
% gen_length_code(2)
thf(fact_195_get__object__ptr__simp,axiom,
! [A: $tType,B: $tType,Ptr2: object_ptr @ B,Object_ptr2: object_ptr @ B,Obj: rObject_ext @ A,H2: heap @ B @ A] :
( ( ( Ptr2 = Object_ptr2 )
=> ( ( get_O_b_j_e_c_t @ B @ A @ Object_ptr2 @ ( put_O_b_j_e_c_t @ B @ A @ Ptr2 @ Obj @ H2 ) )
= ( some @ ( rObject_ext @ A ) @ Obj ) ) )
& ( ( Ptr2 != Object_ptr2 )
=> ( ( get_O_b_j_e_c_t @ B @ A @ Object_ptr2 @ ( put_O_b_j_e_c_t @ B @ A @ Ptr2 @ Obj @ H2 ) )
= ( get_O_b_j_e_c_t @ B @ A @ Object_ptr2 @ H2 ) ) ) ) ).
% get_object_ptr_simp
thf(fact_196_length__Cons,axiom,
! [A: $tType,X: A,Xs: list @ A] :
( ( size_size @ ( list @ A ) @ ( cons @ A @ X @ Xs ) )
= ( suc @ ( size_size @ ( list @ A ) @ Xs ) ) ) ).
% length_Cons
thf(fact_197_map__M_Oinduct,axiom,
! [Heap: $tType,E: $tType,Result: $tType,X6: $tType,P: ( X6 > ( heap_Error_prog @ Heap @ E @ Result ) ) > ( list @ X6 ) > $o,A0: X6 > ( heap_Error_prog @ Heap @ E @ Result ),A1: list @ X6] :
( ! [F2: X6 > ( heap_Error_prog @ Heap @ E @ Result )] : ( P @ F2 @ ( nil @ X6 ) )
=> ( ! [F2: X6 > ( heap_Error_prog @ Heap @ E @ Result ),X4: X6,Xs2: list @ X6] :
( ! [Xa2: Result] : ( P @ F2 @ Xs2 )
=> ( P @ F2 @ ( cons @ X6 @ X4 @ Xs2 ) ) )
=> ( P @ A0 @ A1 ) ) ) ).
% map_M.induct
thf(fact_198_prog_Osize__neq,axiom,
! [Heap: $tType,E: $tType,Result: $tType,X: heap_Error_prog @ Heap @ E @ Result] :
( ( size_size @ ( heap_Error_prog @ Heap @ E @ Result ) @ X )
!= ( zero_zero @ nat ) ) ).
% prog.size_neq
thf(fact_199_forall__M_Oinduct,axiom,
! [Heap: $tType,E: $tType,Result: $tType,Y6: $tType,P: ( Y6 > ( heap_Error_prog @ Heap @ E @ Result ) ) > ( list @ Y6 ) > $o,A0: Y6 > ( heap_Error_prog @ Heap @ E @ Result ),A1: list @ Y6] :
( ! [P4: Y6 > ( heap_Error_prog @ Heap @ E @ Result )] : ( P @ P4 @ ( nil @ Y6 ) )
=> ( ! [P4: Y6 > ( heap_Error_prog @ Heap @ E @ Result ),X4: Y6,Xs2: list @ Y6] :
( ! [Xa2: Result] : ( P @ P4 @ Xs2 )
=> ( P @ P4 @ ( cons @ Y6 @ X4 @ Xs2 ) ) )
=> ( P @ A0 @ A1 ) ) ) ).
% forall_M.induct
thf(fact_200_filter__M_Oinduct,axiom,
! [Heap: $tType,E: $tType,X6: $tType,P: ( X6 > ( heap_Error_prog @ Heap @ E @ $o ) ) > ( list @ X6 ) > $o,A0: X6 > ( heap_Error_prog @ Heap @ E @ $o ),A1: list @ X6] :
( ! [P4: X6 > ( heap_Error_prog @ Heap @ E @ $o )] : ( P @ P4 @ ( nil @ X6 ) )
=> ( ! [P4: X6 > ( heap_Error_prog @ Heap @ E @ $o ),X4: X6,Xs2: list @ X6] :
( ! [Xa2: $o] : ( P @ P4 @ Xs2 )
=> ( P @ P4 @ ( cons @ X6 @ X4 @ Xs2 ) ) )
=> ( P @ A0 @ A1 ) ) ) ).
% filter_M.induct
thf(fact_201_fold__M_Oinduct,axiom,
! [Result: $tType,E: $tType,Heap: $tType,Y6: $tType,P: ( Result > Y6 > ( heap_Error_prog @ Heap @ E @ Result ) ) > Result > ( list @ Y6 ) > $o,A0: Result > Y6 > ( heap_Error_prog @ Heap @ E @ Result ),A1: Result,A22: list @ Y6] :
( ! [F2: Result > Y6 > ( heap_Error_prog @ Heap @ E @ Result ),D2: Result] : ( P @ F2 @ D2 @ ( nil @ Y6 ) )
=> ( ! [F2: Result > Y6 > ( heap_Error_prog @ Heap @ E @ Result ),D2: Result,X4: Y6,Xs2: list @ Y6] :
( ! [Xa2: Result] : ( P @ F2 @ Xa2 @ Xs2 )
=> ( P @ F2 @ D2 @ ( cons @ Y6 @ X4 @ Xs2 ) ) )
=> ( P @ A0 @ A1 @ A22 ) ) ) ).
% fold_M.induct
thf(fact_202_n__lists__Nil,axiom,
! [A: $tType,N: nat] :
( ( ( N
= ( zero_zero @ nat ) )
=> ( ( n_lists @ A @ N @ ( nil @ A ) )
= ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) )
& ( ( N
!= ( zero_zero @ nat ) )
=> ( ( n_lists @ A @ N @ ( nil @ A ) )
= ( nil @ ( list @ A ) ) ) ) ) ).
% n_lists_Nil
thf(fact_203_n__lists_Osimps_I1_J,axiom,
! [A: $tType,Xs: list @ A] :
( ( n_lists @ A @ ( zero_zero @ nat ) @ Xs )
= ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% n_lists.simps(1)
thf(fact_204_product__lists_Osimps_I1_J,axiom,
! [A: $tType] :
( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
= ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% product_lists.simps(1)
thf(fact_205_subseqs_Osimps_I1_J,axiom,
! [A: $tType] :
( ( subseqs @ A @ ( nil @ A ) )
= ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% subseqs.simps(1)
thf(fact_206_insert__Nil,axiom,
! [A: $tType,X: A] :
( ( insert @ A @ X @ ( nil @ A ) )
= ( cons @ A @ X @ ( nil @ A ) ) ) ).
% insert_Nil
thf(fact_207_nths__singleton,axiom,
! [A: $tType,A3: set @ nat,X: A] :
( ( ( member @ nat @ ( zero_zero @ nat ) @ A3 )
=> ( ( nths @ A @ ( cons @ A @ X @ ( nil @ A ) ) @ A3 )
= ( cons @ A @ X @ ( nil @ A ) ) ) )
& ( ~ ( member @ nat @ ( zero_zero @ nat ) @ A3 )
=> ( ( nths @ A @ ( cons @ A @ X @ ( nil @ A ) ) @ A3 )
= ( nil @ A ) ) ) ) ).
% nths_singleton
thf(fact_208_nths__nil,axiom,
! [A: $tType,A3: set @ nat] :
( ( nths @ A @ ( nil @ A ) @ A3 )
= ( nil @ A ) ) ).
% nths_nil
thf(fact_209_nths__empty,axiom,
! [A: $tType,Xs: list @ A] :
( ( nths @ A @ Xs @ ( bot_bot @ ( set @ nat ) ) )
= ( nil @ A ) ) ).
% nths_empty
thf(fact_210_prog_Osize_I2_J,axiom,
! [Heap: $tType,E: $tType,Result: $tType,X: Heap > ( sum_sum @ E @ ( product_prod @ Result @ Heap ) )] :
( ( size_size @ ( heap_Error_prog @ Heap @ E @ Result ) @ ( heap_Error_Prog @ Heap @ E @ Result @ X ) )
= ( suc @ ( zero_zero @ nat ) ) ) ).
% prog.size(2)
thf(fact_211_get_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,
! [Element_ptr: $tType,Character_data_ptr: $tType,Node_ptr: $tType,Object_ptr: $tType,Element: $tType,CharacterData: $tType,Node: $tType,Document: $tType,Object: $tType,Document_ptr: $tType,Shadow_root_ptr: $tType] :
( ( get_D_o_c_u_m_e_n_t @ Shadow_root_ptr @ Document_ptr @ Element_ptr @ Character_data_ptr @ Node_ptr @ Object_ptr @ Element @ CharacterData @ Node @ Document @ Object )
= ( ^ [Document_ptr2: document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ),H3: heap @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) )] : ( bind @ ( rObject_ext @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) ) @ ( rObject_ext @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) ) @ ( get_O_b_j_e_c_t @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ Element_ptr ) @ ( sum_sum @ ( character_data_ptr @ Character_data_ptr ) @ Node_ptr ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) ) @ Object_ptr ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ ( option @ Element ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ CharacterData ) ) @ Node ) ) ) @ ( sum_sum @ ( rDocument_ext @ Node_ptr @ Element_ptr @ Character_data_ptr @ ( option @ Document ) ) @ Object ) ) @ ( cast_d1427782271_p_t_r @ ( sum_sum @ ( shadow_root_ptr @ Shadow_root_ptr ) @ Document_ptr ) @ Element_ptr @ Character_data_ptr @ Node_ptr @ Object_ptr @ Document_ptr2 ) @ H3 ) @ ( cast_O1159777348_e_n_t @ Node_ptr @ Element_ptr @ Character_data_ptr @ Shadow_root_ptr @ Element @ CharacterData @ Node @ Document @ Object ) ) ) ) ).
% get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def
thf(fact_212_bind__runit,axiom,
! [A: $tType,X: option @ A] :
( ( bind @ A @ A @ X @ ( some @ A ) )
= X ) ).
% bind_runit
thf(fact_213_bind__split__asm,axiom,
! [A: $tType,B: $tType,P: ( option @ A ) > $o,M2: option @ B,F3: B > ( option @ A )] :
( ( P @ ( bind @ B @ A @ M2 @ F3 ) )
= ( ~ ( ( ( M2
= ( none @ B ) )
& ~ ( P @ ( none @ A ) ) )
| ? [X3: B] :
( ( M2
= ( some @ B @ X3 ) )
& ~ ( P @ ( F3 @ X3 ) ) ) ) ) ) ).
% bind_split_asm
thf(fact_214_bind__split,axiom,
! [A: $tType,B: $tType,P: ( option @ A ) > $o,M2: option @ B,F3: B > ( option @ A )] :
( ( P @ ( bind @ B @ A @ M2 @ F3 ) )
= ( ( ( M2
= ( none @ B ) )
=> ( P @ ( none @ A ) ) )
& ! [V3: B] :
( ( M2
= ( some @ B @ V3 ) )
=> ( P @ ( F3 @ V3 ) ) ) ) ) ).
% bind_split
thf(fact_215_Option_Obind__cong,axiom,
! [B: $tType,A: $tType,X: option @ A,Y: option @ A,F3: A > ( option @ B ),G2: A > ( option @ B )] :
( ( X = Y )
=> ( ! [A5: A] :
( ( Y
= ( some @ A @ A5 ) )
=> ( ( F3 @ A5 )
= ( G2 @ A5 ) ) )
=> ( ( bind @ A @ B @ X @ F3 )
= ( bind @ A @ B @ Y @ G2 ) ) ) ) ).
% Option.bind_cong
thf(fact_216_bind_Obind__lunit,axiom,
! [B: $tType,A: $tType,X: A,F3: A > ( option @ B )] :
( ( bind @ A @ B @ ( some @ A @ X ) @ F3 )
= ( F3 @ X ) ) ).
% bind.bind_lunit
thf(fact_217_bind__eq__Some__conv,axiom,
! [A: $tType,B: $tType,F3: option @ B,G2: B > ( option @ A ),X: A] :
( ( ( bind @ B @ A @ F3 @ G2 )
= ( some @ A @ X ) )
= ( ? [Y5: B] :
( ( F3
= ( some @ B @ Y5 ) )
& ( ( G2 @ Y5 )
= ( some @ A @ X ) ) ) ) ) ).
% bind_eq_Some_conv
thf(fact_218_bind_Obind__lzero,axiom,
! [A: $tType,B: $tType,F3: A > ( option @ B )] :
( ( bind @ A @ B @ ( none @ A ) @ F3 )
= ( none @ B ) ) ).
% bind.bind_lzero
thf(fact_219_bind__option__cong__code,axiom,
! [B: $tType,A: $tType,X: option @ A,Y: option @ A,F3: A > ( option @ B )] :
( ( X = Y )
=> ( ( bind @ A @ B @ X @ F3 )
= ( bind @ A @ B @ Y @ F3 ) ) ) ).
% bind_option_cong_code
thf(fact_220_prog_Osize__gen,axiom,
! [Heap: $tType,E: $tType,Result: $tType,Xc: Heap > nat,Xb: E > nat,Xa: Result > nat,X: Heap > ( sum_sum @ E @ ( product_prod @ Result @ Heap ) )] :
( ( heap_Error_size_prog @ Heap @ E @ Result @ Xc @ Xb @ Xa @ ( heap_Error_Prog @ Heap @ E @ Result @ X ) )
= ( suc @ ( zero_zero @ nat ) ) ) ).
% prog.size_gen
thf(fact_221_set__encode__empty,axiom,
( ( nat_set_encode @ ( bot_bot @ ( set @ nat ) ) )
= ( zero_zero @ nat ) ) ).
% set_encode_empty
thf(fact_222_set__decode__zero,axiom,
( ( nat_set_decode @ ( zero_zero @ nat ) )
= ( bot_bot @ ( set @ nat ) ) ) ).
% set_decode_zero
thf(fact_223_length__append__singleton,axiom,
! [A: $tType,Xs: list @ A,X: A] :
( ( size_size @ ( list @ A ) @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
= ( suc @ ( size_size @ ( list @ A ) @ Xs ) ) ) ).
% length_append_singleton
thf(fact_224_same__append__eq,axiom,
! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
( ( ( append @ A @ Xs @ Ys )
= ( append @ A @ Xs @ Zs2 ) )
= ( Ys = Zs2 ) ) ).
% same_append_eq
thf(fact_225_append__same__eq,axiom,
! [A: $tType,Ys: list @ A,Xs: list @ A,Zs2: list @ A] :
( ( ( append @ A @ Ys @ Xs )
= ( append @ A @ Zs2 @ Xs ) )
= ( Ys = Zs2 ) ) ).
% append_same_eq
thf(fact_226_append__assoc,axiom,
! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs2 )
= ( append @ A @ Xs @ ( append @ A @ Ys @ Zs2 ) ) ) ).
% append_assoc
thf(fact_227_append_Oassoc,axiom,
! [A: $tType,A2: list @ A,B2: list @ A,C2: list @ A] :
( ( append @ A @ ( append @ A @ A2 @ B2 ) @ C2 )
= ( append @ A @ A2 @ ( append @ A @ B2 @ C2 ) ) ) ).
% append.assoc
thf(fact_228_append__Nil2,axiom,
! [A: $tType,Xs: list @ A] :
( ( append @ A @ Xs @ ( nil @ A ) )
= Xs ) ).
% append_Nil2
thf(fact_229_append__self__conv,axiom,
! [A: $tType,Xs: list @ A,Ys: list @ A] :
( ( ( append @ A @ Xs @ Ys )
= Xs )
= ( Ys
= ( nil @ A ) ) ) ).
% append_self_conv
thf(fact_230_self__append__conv,axiom,
! [A: $tType,Xs: list @ A,Ys: list @ A] :
( ( Xs
= ( append @ A @ Xs @ Ys ) )
= ( Ys
= ( nil @ A ) ) ) ).
% self_append_conv
thf(fact_231_append__self__conv2,axiom,
! [A: $tType,Xs: list @ A,Ys: list @ A] :
( ( ( append @ A @ Xs @ Ys )
= Ys )
= ( Xs
= ( nil @ A ) ) ) ).
% append_self_conv2
thf(fact_232_self__append__conv2,axiom,
! [A: $tType,Ys: list @ A,Xs: list @ A] :
( ( Ys
= ( append @ A @ Xs @ Ys ) )
= ( Xs
= ( nil @ A ) ) ) ).
% self_append_conv2
thf(fact_233_Nil__is__append__conv,axiom,
! [A: $tType,Xs: list @ A,Ys: list @ A] :
( ( ( nil @ A )
= ( append @ A @ Xs @ Ys ) )
= ( ( Xs
= ( nil @ A ) )
& ( Ys
= ( nil @ A ) ) ) ) ).
% Nil_is_append_conv
thf(fact_234_append__is__Nil__conv,axiom,
! [A: $tType,Xs: list @ A,Ys: list @ A] :
( ( ( append @ A @ Xs @ Ys )
= ( nil @ A ) )
= ( ( Xs
= ( nil @ A ) )
& ( Ys
= ( nil @ A ) ) ) ) ).
% append_is_Nil_conv
thf(fact_235_append_Oright__neutral,axiom,
! [A: $tType,A2: list @ A] :
( ( append @ A @ A2 @ ( nil @ A ) )
= A2 ) ).
% append.right_neutral
thf(fact_236_append__eq__append__conv,axiom,
! [A: $tType,Xs: list @ A,Ys: list @ A,Us: list @ A,Vs: list @ A] :
( ( ( ( size_size @ ( list @ A ) @ Xs )
= ( size_size @ ( list @ A ) @ Ys ) )
| ( ( size_size @ ( list @ A ) @ Us )
= ( size_size @ ( list @ A ) @ Vs ) ) )
=> ( ( ( append @ A @ Xs @ Us )
= ( append @ A @ Ys @ Vs ) )
= ( ( Xs = Ys )
& ( Us = Vs ) ) ) ) ).
% append_eq_append_conv
thf(fact_237_set__decode__inverse,axiom,
! [N: nat] :
( ( nat_set_encode @ ( nat_set_decode @ N ) )
= N ) ).
% set_decode_inverse
thf(fact_238_append1__eq__conv,axiom,
! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
= ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
= ( ( Xs = Ys )
& ( X = Y ) ) ) ).
% append1_eq_conv
thf(fact_239_length__append,axiom,
! [A: $tType,Xs: list @ A,Ys: list @ A] :
( ( size_size @ ( list @ A ) @ ( append @ A @ Xs @ Ys ) )
= ( plus_plus @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( size_size @ ( list @ A ) @ Ys ) ) ) ).
% length_append
thf(fact_240_append__eq__append__conv2,axiom,
! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A,Ts: list @ A] :
( ( ( append @ A @ Xs @ Ys )
= ( append @ A @ Zs2 @ Ts ) )
= ( ? [Us2: list @ A] :
( ( ( Xs
= ( append @ A @ Zs2 @ Us2 ) )
& ( ( append @ A @ Us2 @ Ys )
= Ts ) )
| ( ( ( append @ A @ Xs @ Us2 )
= Zs2 )
& ( Ys
= ( append @ A @ Us2 @ Ts ) ) ) ) ) ) ).
% append_eq_append_conv2
thf(fact_241_append__eq__appendI,axiom,
! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs2: list @ A,Ys: list @ A,Us: list @ A] :
( ( ( append @ A @ Xs @ Xs1 )
= Zs2 )
=> ( ( Ys
= ( append @ A @ Xs1 @ Us ) )
=> ( ( append @ A @ Xs @ Ys )
= ( append @ A @ Zs2 @ Us ) ) ) ) ).
% append_eq_appendI
thf(fact_242_rev__induct,axiom,
! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
( ( P @ ( nil @ A ) )
=> ( ! [X4: A,Xs2: list @ A] :
( ( P @ Xs2 )
=> ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) )
=> ( P @ Xs ) ) ) ).
% rev_induct
thf(fact_243_rev__exhaust,axiom,
! [A: $tType,Xs: list @ A] :
( ( Xs
!= ( nil @ A ) )
=> ~ ! [Ys3: list @ A,Y3: A] :
( Xs
!= ( append @ A @ Ys3 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) ) ) ).
% rev_exhaust
thf(fact_244_Cons__eq__append__conv,axiom,
! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
( ( ( cons @ A @ X @ Xs )
= ( append @ A @ Ys @ Zs2 ) )
= ( ( ( Ys
= ( nil @ A ) )
& ( ( cons @ A @ X @ Xs )
= Zs2 ) )
| ? [Ys4: list @ A] :
( ( ( cons @ A @ X @ Ys4 )
= Ys )
& ( Xs
= ( append @ A @ Ys4 @ Zs2 ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_245_append__eq__Cons__conv,axiom,
! [A: $tType,Ys: list @ A,Zs2: list @ A,X: A,Xs: list @ A] :
( ( ( append @ A @ Ys @ Zs2 )
= ( cons @ A @ X @ Xs ) )
= ( ( ( Ys
= ( nil @ A ) )
& ( Zs2
= ( cons @ A @ X @ Xs ) ) )
| ? [Ys4: list @ A] :
( ( Ys
= ( cons @ A @ X @ Ys4 ) )
& ( ( append @ A @ Ys4 @ Zs2 )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_246_rev__nonempty__induct,axiom,
! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
( ( Xs
!= ( nil @ A ) )
=> ( ! [X4: A] : ( P @ ( cons @ A @ X4 @ ( nil @ A ) ) )
=> ( ! [X4: A,Xs2: list @ A] :
( ( Xs2
!= ( nil @ A ) )
=> ( ( P @ Xs2 )
=> ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_247_eq__Nil__appendI,axiom,
! [A: $tType,Xs: list @ A,Ys: list @ A] :
( ( Xs = Ys )
=> ( Xs
= ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% eq_Nil_appendI
thf(fact_248_append__Nil,axiom,
! [A: $tType,Ys: list @ A] :
( ( append @ A @ ( nil @ A ) @ Ys )
= Ys ) ).
% append_Nil
thf(fact_249_append_Oleft__neutral,axiom,
! [A: $tType,A2: list @ A] :
( ( append @ A @ ( nil @ A ) @ A2 )
= A2 ) ).
% append.left_neutral
thf(fact_250_append__Cons,axiom,
! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys )
= ( cons @ A @ X @ ( append @ A @ Xs @ Ys ) ) ) ).
% append_Cons
% Type constructors (53)
thf(tcon_fun___Orderings_Oord,axiom,
! [A6: $tType,A7: $tType] :
( ( ord @ A7 )
=> ( ord @ ( A6 > A7 ) ) ) ).
thf(tcon_fun___Orderings_Obot,axiom,
! [A6: $tType,A7: $tType] :
( ( bot @ A7 )
=> ( bot @ ( A6 > A7 ) ) ) ).
thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
semiri456707255roduct @ nat ).
thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
canoni770627133id_add @ nat ).
thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
ordere779506340up_add @ nat ).
thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
cancel1352612707id_add @ nat ).
thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
cancel_semigroup_add @ nat ).
thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
ab_semigroup_add @ nat ).
thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
comm_monoid_add @ nat ).
thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
semigroup_add @ nat ).
thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
linorder @ nat ).
thf(tcon_Nat_Onat___Groups_Omonoid__add,axiom,
monoid_add @ nat ).
thf(tcon_Nat_Onat___Orderings_Oord_1,axiom,
ord @ nat ).
thf(tcon_Nat_Onat___Orderings_Obot_2,axiom,
bot @ nat ).
thf(tcon_Nat_Onat___Groups_Ozero,axiom,
zero @ nat ).
thf(tcon_Nat_Onat___Nat_Osize,axiom,
size @ nat ).
thf(tcon_Set_Oset___Orderings_Oord_3,axiom,
! [A6: $tType] : ( ord @ ( set @ A6 ) ) ).
thf(tcon_Set_Oset___Orderings_Obot_4,axiom,
! [A6: $tType] : ( bot @ ( set @ A6 ) ) ).
thf(tcon_HOL_Obool___Orderings_Olinorder_5,axiom,
linorder @ $o ).
thf(tcon_HOL_Obool___Orderings_Oord_6,axiom,
ord @ $o ).
thf(tcon_HOL_Obool___Orderings_Obot_7,axiom,
bot @ $o ).
thf(tcon_FSet_Ofset___Orderings_Oord_8,axiom,
! [A6: $tType] : ( ord @ ( fset @ A6 ) ) ).
thf(tcon_FSet_Ofset___Orderings_Obot_9,axiom,
! [A6: $tType] : ( bot @ ( fset @ A6 ) ) ).
thf(tcon_FSet_Ofset___Nat_Osize_10,axiom,
! [A6: $tType] : ( size @ ( fset @ A6 ) ) ).
thf(tcon_List_Olist___Nat_Osize_11,axiom,
! [A6: $tType] : ( size @ ( list @ A6 ) ) ).
thf(tcon_String_Ochar___Nat_Osize_12,axiom,
size @ char ).
thf(tcon_Sum__Type_Osum___Orderings_Olinorder_13,axiom,
! [A6: $tType,A7: $tType] :
( ( ( linorder @ A6 )
& ( linorder @ A7 ) )
=> ( linorder @ ( sum_sum @ A6 @ A7 ) ) ) ).
thf(tcon_Sum__Type_Osum___Orderings_Oord_14,axiom,
! [A6: $tType,A7: $tType] :
( ( ( linorder @ A6 )
& ( linorder @ A7 ) )
=> ( ord @ ( sum_sum @ A6 @ A7 ) ) ) ).
thf(tcon_Sum__Type_Osum___Nat_Osize_15,axiom,
! [A6: $tType,A7: $tType] : ( size @ ( sum_sum @ A6 @ A7 ) ) ).
thf(tcon_Option_Ooption___Nat_Osize_16,axiom,
! [A6: $tType] : ( size @ ( option @ A6 ) ) ).
thf(tcon_ObjectClass_Oheap___Nat_Osize_17,axiom,
! [A6: $tType,A7: $tType] : ( size @ ( heap @ A6 @ A7 ) ) ).
thf(tcon_Product__Type_Ounit___Orderings_Olinorder_18,axiom,
linorder @ product_unit ).
thf(tcon_Product__Type_Ounit___Orderings_Oord_19,axiom,
ord @ product_unit ).
thf(tcon_Product__Type_Ounit___Orderings_Obot_20,axiom,
bot @ product_unit ).
thf(tcon_NodePointer_Onode__ptr___Orderings_Olinorder_21,axiom,
! [A6: $tType] :
( ( linorder @ A6 )
=> ( linorder @ ( node_ptr @ A6 ) ) ) ).
thf(tcon_NodePointer_Onode__ptr___Orderings_Oord_22,axiom,
! [A6: $tType] :
( ( linorder @ A6 )
=> ( ord @ ( node_ptr @ A6 ) ) ) ).
thf(tcon_NodePointer_Onode__ptr___Nat_Osize_23,axiom,
! [A6: $tType] : ( size @ ( node_ptr @ A6 ) ) ).
thf(tcon_Heap__Error__Monad_Oprog___Nat_Osize_24,axiom,
! [A6: $tType,A7: $tType,A8: $tType] : ( size @ ( heap_Error_prog @ A6 @ A7 @ A8 ) ) ).
thf(tcon_ObjectPointer_Oobject__ptr___Orderings_Olinorder_25,axiom,
! [A6: $tType] :
( ( linorder @ A6 )
=> ( linorder @ ( object_ptr @ A6 ) ) ) ).
thf(tcon_ObjectPointer_Oobject__ptr___Orderings_Oord_26,axiom,
! [A6: $tType] :
( ( linorder @ A6 )
=> ( ord @ ( object_ptr @ A6 ) ) ) ).
thf(tcon_ObjectPointer_Oobject__ptr___Nat_Osize_27,axiom,
! [A6: $tType] : ( size @ ( object_ptr @ A6 ) ) ).
thf(tcon_ElementPointer_Oelement__ptr___Orderings_Olinorder_28,axiom,
! [A6: $tType] :
( ( linorder @ A6 )
=> ( linorder @ ( element_ptr @ A6 ) ) ) ).
thf(tcon_ElementPointer_Oelement__ptr___Orderings_Oord_29,axiom,
! [A6: $tType] :
( ( linorder @ A6 )
=> ( ord @ ( element_ptr @ A6 ) ) ) ).
thf(tcon_ElementPointer_Oelement__ptr___Nat_Osize_30,axiom,
! [A6: $tType] : ( size @ ( element_ptr @ A6 ) ) ).
thf(tcon_DocumentPointer_Odocument__ptr___Orderings_Olinorder_31,axiom,
! [A6: $tType] :
( ( linorder @ A6 )
=> ( linorder @ ( document_ptr @ A6 ) ) ) ).
thf(tcon_DocumentPointer_Odocument__ptr___Orderings_Oord_32,axiom,
! [A6: $tType] :
( ( linorder @ A6 )
=> ( ord @ ( document_ptr @ A6 ) ) ) ).
thf(tcon_DocumentPointer_Odocument__ptr___Nat_Osize_33,axiom,
! [A6: $tType] : ( size @ ( document_ptr @ A6 ) ) ).
thf(tcon_ShadowRootPointer_Oshadow__root__ptr___Orderings_Olinorder_34,axiom,
! [A6: $tType] :
( ( linorder @ A6 )
=> ( linorder @ ( shadow_root_ptr @ A6 ) ) ) ).
thf(tcon_ShadowRootPointer_Oshadow__root__ptr___Orderings_Oord_35,axiom,
! [A6: $tType] :
( ( linorder @ A6 )
=> ( ord @ ( shadow_root_ptr @ A6 ) ) ) ).
thf(tcon_ShadowRootPointer_Oshadow__root__ptr___Nat_Osize_36,axiom,
! [A6: $tType] : ( size @ ( shadow_root_ptr @ A6 ) ) ).
thf(tcon_CharacterDataPointer_Ocharacter__data__ptr___Orderings_Olinorder_37,axiom,
! [A6: $tType] :
( ( linorder @ A6 )
=> ( linorder @ ( character_data_ptr @ A6 ) ) ) ).
thf(tcon_CharacterDataPointer_Ocharacter__data__ptr___Orderings_Oord_38,axiom,
! [A6: $tType] :
( ( linorder @ A6 )
=> ( ord @ ( character_data_ptr @ A6 ) ) ) ).
thf(tcon_CharacterDataPointer_Ocharacter__data__ptr___Nat_Osize_39,axiom,
! [A6: $tType] : ( size @ ( character_data_ptr @ A6 ) ) ).
% Conjectures (4)
thf(conj_0,hypothesis,
( ( document_ptrs @ a @ b @ c @ d @ e @ f @ g @ h @ i @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) @ l @ h2 )
= ( bot_bot @ ( fset @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ d ) @ e ) ) ) ) ) ).
thf(conj_1,hypothesis,
( h3
= ( put_O_b_j_e_c_t @ ( sum_sum @ ( node_ptr @ ( sum_sum @ ( element_ptr @ a ) @ ( sum_sum @ ( character_data_ptr @ b ) @ c ) ) ) @ ( sum_sum @ ( document_ptr @ ( sum_sum @ ( shadow_root_ptr @ d ) @ e ) ) @ f ) ) @ ( sum_sum @ ( rNode_ext @ ( sum_sum @ ( rElement_ext @ c @ a @ b @ d @ ( option @ g ) ) @ ( sum_sum @ ( rCharacterData_ext @ ( option @ h ) ) @ i ) ) ) @ ( sum_sum @ ( rDocument_ext @ c @ a @ b @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) @ l ) ) @ ( cast_d1427782271_p_t_r @ ( sum_sum @ ( shadow_root_ptr @ d ) @ e ) @ a @ b @ c @ f @ ( document_Ref @ ( sum_sum @ ( shadow_root_ptr @ d ) @ e ) @ ( suc @ ( zero_zero @ nat ) ) ) ) @ ( cast_D42511940_e_c_t @ c @ a @ b @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) @ d @ g @ h @ i @ l @ ( rObject_ext2 @ ( rDocument_ext @ c @ a @ b @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) @ product_Unity @ ( rDocument_ext2 @ a @ b @ c @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) @ product_Unity @ ( nil @ char ) @ ( none @ ( element_ptr @ a ) ) @ ( nil @ ( node_ptr @ ( sum_sum @ ( element_ptr @ a ) @ ( sum_sum @ ( character_data_ptr @ b ) @ c ) ) ) ) @ ( none @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) ) ) @ h2 ) ) ).
thf(conj_2,hypothesis,
type_wf @ a @ b @ c @ d @ e @ f @ g @ h @ i @ j @ k @ l @ h2 ).
thf(conj_3,conjecture,
is_document_kind @ c @ a @ b @ d @ g @ h @ i @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) @ l @ ( cast_D42511940_e_c_t @ c @ a @ b @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) @ d @ g @ h @ i @ l @ ( rObject_ext2 @ ( rDocument_ext @ c @ a @ b @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) @ product_Unity @ ( rDocument_ext2 @ a @ b @ c @ ( option @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) @ product_Unity @ ( nil @ char ) @ ( none @ ( element_ptr @ a ) ) @ ( nil @ ( node_ptr @ ( sum_sum @ ( element_ptr @ a ) @ ( sum_sum @ ( character_data_ptr @ b ) @ c ) ) ) ) @ ( none @ ( sum_sum @ ( rShadowRoot_ext @ c @ a @ b @ ( option @ j ) ) @ k ) ) ) ) ) ).
%------------------------------------------------------------------------------