ITP001 Axioms: ITP037^5.ax
%------------------------------------------------------------------------------
% File : ITP037^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : rich_list^2.ax [Gau20]
% : HL4037^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 430 ( 15 unt; 31 typ; 0 def)
% Number of atoms : 8918 ( 348 equ; 0 cnn)
% Maximal formula atoms : 44 ( 20 avg)
% Number of connectives : 14258 ( 25 ~; 7 |; 84 &;13137 @)
% ( 62 <=>; 943 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 12 avg;13137 nst)
% Number of types : 3 ( 2 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 126 ( 123 usr; 100 con; 0-2 aty)
% Number of variables : 1496 ( 78 ^1414 !; 4 ?;1496 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(stp_c_ty_2Elist_2Elist_o,type,
tp__c_ty_2Elist_2Elist_o: $tType ).
thf(stp_inj_c_ty_2Elist_2Elist_o,type,
inj__c_ty_2Elist_2Elist_o: tp__c_ty_2Elist_2Elist_o > $i ).
thf(stp_surj_c_ty_2Elist_2Elist_o,type,
surj__c_ty_2Elist_2Elist_o: $i > tp__c_ty_2Elist_2Elist_o ).
thf(stp_inj_surj_c_ty_2Elist_2Elist_o,axiom,
! [X: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( inj__c_ty_2Elist_2Elist_o @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Elist_2Elist_o,axiom,
! [X: tp__c_ty_2Elist_2Elist_o] : ( mem @ ( inj__c_ty_2Elist_2Elist_o @ X ) @ ( ty_2Elist_2Elist @ bool ) ) ).
thf(stp_iso_mem_c_ty_2Elist_2Elist_o,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Elist_2Elist @ bool ) )
=> ( X
= ( inj__c_ty_2Elist_2Elist_o @ ( surj__c_ty_2Elist_2Elist_o @ X ) ) ) ) ).
thf(tp_c_2Erich__list_2EAND__EL,type,
c_2Erich__list_2EAND__EL: $i ).
thf(mem_c_2Erich__list_2EAND__EL,axiom,
mem @ c_2Erich__list_2EAND__EL @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ bool ) ).
thf(tp_c_2Erich__list_2EBUTLASTN,type,
c_2Erich__list_2EBUTLASTN: del > $i ).
thf(mem_c_2Erich__list_2EBUTLASTN,axiom,
! [A_27a: del] : ( mem @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ).
thf(tp_c_2Erich__list_2ECOUNT__LIST,type,
c_2Erich__list_2ECOUNT__LIST: $i ).
thf(mem_c_2Erich__list_2ECOUNT__LIST,axiom,
mem @ c_2Erich__list_2ECOUNT__LIST @ ( arr @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) ).
thf(tp_c_2Erich__list_2ECOUNT__LIST__AUX,type,
c_2Erich__list_2ECOUNT__LIST__AUX: $i ).
thf(mem_c_2Erich__list_2ECOUNT__LIST__AUX,axiom,
mem @ c_2Erich__list_2ECOUNT__LIST__AUX @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2Erich__list_2EELL,type,
c_2Erich__list_2EELL: del > $i ).
thf(mem_c_2Erich__list_2EELL,axiom,
! [A_27a: del] : ( mem @ ( c_2Erich__list_2EELL @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ A_27a ) ) ) ).
thf(tp_c_2Erich__list_2EIS__SUBLIST,type,
c_2Erich__list_2EIS__SUBLIST: del > $i ).
thf(mem_c_2Erich__list_2EIS__SUBLIST,axiom,
! [A_27a: del] : ( mem @ ( c_2Erich__list_2EIS__SUBLIST @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) ) ) ).
thf(tp_c_2Erich__list_2EIS__SUFFIX,type,
c_2Erich__list_2EIS__SUFFIX: del > $i ).
thf(mem_c_2Erich__list_2EIS__SUFFIX,axiom,
! [A_27a: del] : ( mem @ ( c_2Erich__list_2EIS__SUFFIX @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) ) ) ).
thf(tp_c_2Erich__list_2ELASTN,type,
c_2Erich__list_2ELASTN: del > $i ).
thf(mem_c_2Erich__list_2ELASTN,axiom,
! [A_27a: del] : ( mem @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ).
thf(tp_c_2Erich__list_2ELIST__ELEM__COUNT,type,
c_2Erich__list_2ELIST__ELEM__COUNT: del > $i ).
thf(mem_c_2Erich__list_2ELIST__ELEM__COUNT,axiom,
! [A_27a: del] : ( mem @ ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2Erich__list_2EOR__EL,type,
c_2Erich__list_2EOR__EL: $i ).
thf(mem_c_2Erich__list_2EOR__EL,axiom,
mem @ c_2Erich__list_2EOR__EL @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ bool ) ).
thf(tp_c_2Erich__list_2EPREFIX,type,
c_2Erich__list_2EPREFIX: del > $i ).
thf(mem_c_2Erich__list_2EPREFIX,axiom,
! [A_27a: del] : ( mem @ ( c_2Erich__list_2EPREFIX @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ).
thf(tp_c_2Erich__list_2EREPLICATE,type,
c_2Erich__list_2EREPLICATE: del > $i ).
thf(mem_c_2Erich__list_2EREPLICATE,axiom,
! [A_27a: del] : ( mem @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ).
thf(tp_c_2Erich__list_2ESCANL,type,
c_2Erich__list_2ESCANL: del > del > $i ).
thf(mem_c_2Erich__list_2ESCANL,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erich__list_2ESCANL @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27b @ ( arr @ A_27a @ A_27b ) ) @ ( arr @ A_27b @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) ) ) ) ).
thf(tp_c_2Erich__list_2ESCANR,type,
c_2Erich__list_2ESCANR: del > del > $i ).
thf(mem_c_2Erich__list_2ESCANR,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erich__list_2ESCANR @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) @ ( arr @ A_27b @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) ) ) ) ).
thf(tp_c_2Erich__list_2ESEG,type,
c_2Erich__list_2ESEG: del > $i ).
thf(mem_c_2Erich__list_2ESEG,axiom,
! [A_27a: del] : ( mem @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ).
thf(tp_c_2Erich__list_2ESPLITL,type,
c_2Erich__list_2ESPLITL: del > $i ).
thf(mem_c_2Erich__list_2ESPLITL,axiom,
! [A_27a: del] : ( mem @ ( c_2Erich__list_2ESPLITL @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ).
thf(tp_c_2Erich__list_2ESPLITP,type,
c_2Erich__list_2ESPLITP: del > $i ).
thf(mem_c_2Erich__list_2ESPLITP,axiom,
! [A_27a: del] : ( mem @ ( c_2Erich__list_2ESPLITP @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ).
thf(tp_c_2Erich__list_2ESPLITP__AUX,type,
c_2Erich__list_2ESPLITP__AUX: del > $i ).
thf(mem_c_2Erich__list_2ESPLITP__AUX,axiom,
! [A_27a: del] : ( mem @ ( c_2Erich__list_2ESPLITP__AUX @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ) ).
thf(tp_c_2Erich__list_2ESPLITR,type,
c_2Erich__list_2ESPLITR: del > $i ).
thf(mem_c_2Erich__list_2ESPLITR,axiom,
! [A_27a: del] : ( mem @ ( c_2Erich__list_2ESPLITR @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ).
thf(tp_c_2Erich__list_2ESUFFIX,type,
c_2Erich__list_2ESUFFIX: del > $i ).
thf(mem_c_2Erich__list_2ESUFFIX,axiom,
! [A_27a: del] : ( mem @ ( c_2Erich__list_2ESUFFIX @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ).
thf(tp_c_2Erich__list_2ETL__T,type,
c_2Erich__list_2ETL__T: del > $i ).
thf(mem_c_2Erich__list_2ETL__T,axiom,
! [A_27a: del] : ( mem @ ( c_2Erich__list_2ETL__T @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ).
thf(tp_c_2Erich__list_2EUNZIP__FST,type,
c_2Erich__list_2EUNZIP__FST: del > del > $i ).
thf(mem_c_2Erich__list_2EUNZIP__FST,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erich__list_2EUNZIP__FST @ A_27a @ A_27b ) @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ).
thf(tp_c_2Erich__list_2EUNZIP__SND,type,
c_2Erich__list_2EUNZIP__SND: del > del > $i ).
thf(mem_c_2Erich__list_2EUNZIP__SND,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Erich__list_2EUNZIP__SND @ A_27a @ A_27b ) @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ).
thf(tp_c_2Erich__list_2Ecommon__prefixes,type,
c_2Erich__list_2Ecommon__prefixes: del > $i ).
thf(mem_c_2Erich__list_2Ecommon__prefixes,axiom,
! [A_27a: del] : ( mem @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a ) @ ( arr @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) ) ) ).
thf(tp_c_2Erich__list_2Elongest__prefix,type,
c_2Erich__list_2Elongest__prefix: del > $i ).
thf(mem_c_2Erich__list_2Elongest__prefix,axiom,
! [A_27a: del] : ( mem @ ( c_2Erich__list_2Elongest__prefix @ A_27a ) @ ( arr @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ).
thf(ax_thm_2Erich__list_2EELL,axiom,
! [A_27a: del] :
( ! [V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0l )
= ( ap @ ( c_2Elist_2ELAST @ A_27a ) @ V0l ) ) )
& ! [V1n: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ V2l )
= ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Elist_2EFRONT @ A_27a ) @ V2l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EELL__compute,axiom,
! [A_27a: del] :
( ! [V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0l )
= ( ap @ ( c_2Elist_2ELAST @ A_27a ) @ V0l ) ) )
& ! [V1n: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ V2l )
= ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( c_2Elist_2EFRONT @ A_27a ) @ V2l ) ) ) )
& ! [V3n: tp__ty_2Enum_2Enum,V4l: $i] :
( ( mem @ V4l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ V4l )
= ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ ( ap @ ( c_2Elist_2EFRONT @ A_27a ) @ V4l ) ) ) ) ) ).
thf(ax_thm_2Erich__list_2EREPLICATE,axiom,
! [A_27a: del] :
( ! [V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0x )
= ( c_2Elist_2ENIL @ A_27a ) ) )
& ! [V1n: tp__ty_2Enum_2Enum,V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ V2x )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2x ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EREPLICATE__compute,axiom,
! [A_27a: del] :
( ! [V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0x )
= ( c_2Elist_2ENIL @ A_27a ) ) )
& ! [V1n: tp__ty_2Enum_2Enum,V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ V2x )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V2x ) ) ) )
& ! [V3n: tp__ty_2Enum_2Enum,V4x: $i] :
( ( mem @ V4x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ V4x )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4x ) @ ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ V4x ) ) ) ) ) ).
thf(ax_thm_2Erich__list_2ESCANL,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ ( arr @ A_27a @ A_27b ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27b )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESCANL @ A_27a @ A_27b ) @ V0f ) @ V1e ) @ ( c_2Elist_2ENIL @ A_27a ) )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27b ) @ V1e ) @ ( c_2Elist_2ENIL @ A_27b ) ) ) ) )
& ! [V2f: $i] :
( ( mem @ V2f @ ( arr @ A_27b @ ( arr @ A_27a @ A_27b ) ) )
=> ! [V3e: $i] :
( ( mem @ V3e @ A_27b )
=> ! [V4x: $i] :
( ( mem @ V4x @ A_27a )
=> ! [V5l: $i] :
( ( mem @ V5l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESCANL @ A_27a @ A_27b ) @ V2f ) @ V3e ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4x ) @ V5l ) )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27b ) @ V3e ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESCANL @ A_27a @ A_27b ) @ V2f ) @ ( ap @ ( ap @ V2f @ V3e ) @ V4x ) ) @ V5l ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Erich__list_2ESCANR,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27b )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESCANR @ A_27a @ A_27b ) @ V0f ) @ V1e ) @ ( c_2Elist_2ENIL @ A_27a ) )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27b ) @ V1e ) @ ( c_2Elist_2ENIL @ A_27b ) ) ) ) )
& ! [V2f: $i] :
( ( mem @ V2f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
=> ! [V3e: $i] :
( ( mem @ V3e @ A_27b )
=> ! [V4x: $i] :
( ( mem @ V4x @ A_27a )
=> ! [V5l: $i] :
( ( mem @ V5l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESCANR @ A_27a @ A_27b ) @ V2f ) @ V3e ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4x ) @ V5l ) )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27b ) @ ( ap @ ( ap @ V2f @ V4x ) @ ( ap @ ( c_2Elist_2EHD @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESCANR @ A_27a @ A_27b ) @ V2f ) @ V3e ) @ V5l ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESCANR @ A_27a @ A_27b ) @ V2f ) @ V3e ) @ V5l ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Erich__list_2ESPLITP,axiom,
! [A_27a: del] :
( ! [V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ESPLITP @ A_27a ) @ V0P ) @ ( c_2Elist_2ENIL @ A_27a ) )
= ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) )
& ! [V1P: $i] :
( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ESPLITP @ A_27a ) @ V1P ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ V3l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ V1P @ V2x ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ V3l ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ ( ap @ ( c_2Epair_2EFST @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2ESPLITP @ A_27a ) @ V1P ) @ V3l ) ) ) ) @ ( ap @ ( c_2Epair_2ESND @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2ESPLITP @ A_27a ) @ V1P ) @ V3l ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Erich__list_2ESPLITP__AUX__def,axiom,
! [A_27a: del] :
( ! [V0acc: $i] :
( ( mem @ V0acc @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1P: $i] :
( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESPLITP__AUX @ A_27a ) @ V0acc ) @ V1P ) @ ( c_2Elist_2ENIL @ A_27a ) )
= ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ V0acc ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) )
& ! [V2acc: $i] :
( ( mem @ V2acc @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V3P: $i] :
( ( mem @ V3P @ ( arr @ A_27a @ bool ) )
=> ! [V4h: $i] :
( ( mem @ V4h @ A_27a )
=> ! [V5t: $i] :
( ( mem @ V5t @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESPLITP__AUX @ A_27a ) @ V2acc ) @ V3P ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4h ) @ V5t ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ V3P @ V4h ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ V2acc ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4h ) @ V5t ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESPLITP__AUX @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V2acc ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V4h ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) @ V3P ) @ V5t ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Erich__list_2ESPLITL__def,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ( ( ap @ ( c_2Erich__list_2ESPLITL @ A_27a ) @ V0P )
= ( ap @ ( c_2Erich__list_2ESPLITP @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ bool @ bool ) @ c_2Ebool_2E_7E ) @ V0P ) ) ) ) ).
thf(ax_thm_2Erich__list_2ESPLITR__def,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ESPLITR @ A_27a ) @ V0P ) @ V1l )
= ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) )
@ ( ap @ ( c_2Epair_2EUNCURRY @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V2a: $i] :
( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V3b: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V3b ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V2a ) ) ) ) ) )
@ ( ap @ ( ap @ ( c_2Erich__list_2ESPLITP @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ bool @ bool ) @ c_2Ebool_2E_7E ) @ V0P ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l ) ) ) ) ) ) ).
thf(ax_thm_2Erich__list_2EPREFIX__DEF,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EPREFIX @ A_27a ) @ V0P ) @ V1l )
= ( ap @ ( c_2Epair_2EFST @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2ESPLITP @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ bool @ bool ) @ c_2Ebool_2E_7E ) @ V0P ) ) @ V1l ) ) ) ) ) ).
thf(ax_thm_2Erich__list_2ESUFFIX__DEF,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ESUFFIX @ A_27a ) @ V0P ) @ V1l )
= ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V2l_27: $i] :
( lam @ A_27a
@ ^ [V3x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ V0P @ V3x ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V3x ) @ V2l_27 ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) )
@ ( c_2Elist_2ENIL @ A_27a ) )
@ V1l ) ) ) ) ).
thf(ax_thm_2Erich__list_2EAND__EL__DEF,axiom,
( c_2Erich__list_2EAND__EL
= ( ap @ ( c_2Elist_2EEVERY @ bool ) @ ( c_2Ecombin_2EI @ bool ) ) ) ).
thf(ax_thm_2Erich__list_2EOR__EL__DEF,axiom,
( c_2Erich__list_2EOR__EL
= ( ap @ ( c_2Elist_2EEXISTS @ bool ) @ ( c_2Ecombin_2EI @ bool ) ) ) ).
thf(ax_thm_2Erich__list_2EUNZIP__FST__DEF,axiom,
! [A_27a: del,A_27b: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( ( ap @ ( c_2Erich__list_2EUNZIP__FST @ A_27a @ A_27b ) @ V0l )
= ( ap @ ( c_2Epair_2EFST @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( ap @ ( c_2Elist_2EUNZIP @ A_27a @ A_27b ) @ V0l ) ) ) ) ).
thf(ax_thm_2Erich__list_2EUNZIP__SND__DEF,axiom,
! [A_27a: del,A_27b: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) )
=> ( ( ap @ ( c_2Erich__list_2EUNZIP__SND @ A_27a @ A_27b ) @ V0l )
= ( ap @ ( c_2Epair_2ESND @ ( ty_2Elist_2Elist @ A_27b ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( c_2Elist_2EUNZIP @ A_27b @ A_27a ) @ V0l ) ) ) ) ).
thf(ax_thm_2Erich__list_2ELIST__ELEM__COUNT__DEF,axiom,
! [A_27a: del,V0e: $i] :
( ( mem @ V0e @ A_27a )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27a ) @ V0e ) @ V1l ) )
= ( surj__ty_2Enum_2Enum
@ ( ap @ ( c_2Elist_2ELENGTH @ A_27a )
@ ( ap
@ ( ap @ ( c_2Elist_2EFILTER @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V2x ) @ V0e ) ) )
@ V1l ) ) ) ) ) ) ).
thf(ax_thm_2Erich__list_2ECOUNT__LIST__def,axiom,
( ( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( c_2Elist_2ENIL @ ty_2Enum_2Enum ) ) )
& ! [V0n: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ c_2Enum_2ESUC ) @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ) ).
thf(ax_thm_2Erich__list_2ECOUNT__LIST__AUX__def,axiom,
( ! [V0l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Erich__list_2ECOUNT__LIST__AUX @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V0l ) ) )
= V0l )
& ! [V1n: tp__ty_2Enum_2Enum,V2l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Erich__list_2ECOUNT__LIST__AUX @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V2l ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Erich__list_2ECOUNT__LIST__AUX @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V2l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ECOUNT__LIST__AUX__def__compute,axiom,
( ! [V0l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Erich__list_2ECOUNT__LIST__AUX @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V0l ) ) )
= V0l )
& ! [V1n: tp__ty_2Enum_2Enum,V2l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Erich__list_2ECOUNT__LIST__AUX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V2l ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Erich__list_2ECOUNT__LIST__AUX @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V2l ) ) ) ) )
& ! [V3n: tp__ty_2Enum_2Enum,V4l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Erich__list_2ECOUNT__LIST__AUX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V4l ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Erich__list_2ECOUNT__LIST__AUX @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V4l ) ) ) ) ) ) ).
thf(ax_thm_2Erich__list_2ETL__T__def,axiom,
! [A_27a: del] :
( ( ( ap @ ( c_2Erich__list_2ETL__T @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) )
= ( c_2Elist_2ENIL @ A_27a ) )
& ! [V0h: $i] :
( ( mem @ V0h @ A_27a )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( c_2Erich__list_2ETL__T @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V0h ) @ V1t ) )
= V1t ) ) ) ) ).
thf(conj_thm_2Erich__list_2ETAKE,axiom,
! [A_27a: del] :
( ! [V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0l )
= ( c_2Elist_2ENIL @ A_27a ) ) )
& ! [V1n: tp__ty_2Enum_2Enum,V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ V3l ) )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V3l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EDROP,axiom,
! [A_27a: del] :
( ! [V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0l )
= V0l ) )
& ! [V1n: tp__ty_2Enum_2Enum,V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ V3l ) )
= ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V3l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EDROP__FUNPOW__TL,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l )
= ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2EFUNPOW @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Erich__list_2ETL__T @ A_27a ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ).
thf(conj_thm_2Erich__list_2ENOT__NULL__SNOC,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ~ ( p @ ( ap @ ( c_2Elist_2ENULL @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V0x ) @ V1l ) ) ) ) ) ).
thf(ax_thm_2Erich__list_2ELASTN__def,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1xs: $i] :
( ( mem @ V1xs @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1xs )
= ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1xs ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELASTN,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0l )
= ( c_2Elist_2ENIL @ A_27a ) ) )
& ! [V1n: tp__ty_2Enum_2Enum,V2x: $i] :
( ( mem @ V2x @ A_27b )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27b ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27b ) @ V2x ) @ V3l ) )
= ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27b ) @ V2x ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V3l ) ) ) ) ) ) ).
thf(ax_thm_2Erich__list_2EBUTLASTN__def,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1xs: $i] :
( ( mem @ V1xs @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1xs )
= ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1xs ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EBUTLASTN,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0l )
= V0l ) )
& ! [V1n: tp__ty_2Enum_2Enum,V2x: $i] :
( ( mem @ V2x @ A_27b )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27b ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27b ) @ V2x ) @ V3l ) )
= ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V3l ) ) ) ) ) ).
thf(ax_thm_2Erich__list_2EIS__SUBLIST,axiom,
! [A_27a: del] :
( ! [V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUBLIST @ A_27a ) @ V0l ) @ ( c_2Elist_2ENIL @ A_27a ) ) )
<=> $true ) )
& ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUBLIST @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1x ) @ V2l ) ) )
<=> $false ) ) )
& ! [V3x1: $i] :
( ( mem @ V3x1 @ A_27a )
=> ! [V4l1: $i] :
( ( mem @ V4l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V5x2: $i] :
( ( mem @ V5x2 @ A_27a )
=> ! [V6l2: $i] :
( ( mem @ V6l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUBLIST @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V3x1 ) @ V4l1 ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V5x2 ) @ V6l2 ) ) )
<=> ( ( ( V3x1 = V5x2 )
& ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V6l2 ) @ V4l1 ) ) )
| ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUBLIST @ A_27a ) @ V4l1 ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V5x2 ) @ V6l2 ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Erich__list_2ESEG,axiom,
! [A_27a: del] :
( ! [V0k: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0k ) ) @ V1l )
= ( c_2Elist_2ENIL @ A_27a ) ) )
& ! [V2m: tp__ty_2Enum_2Enum,V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ! [V4l: $i] :
( ( mem @ V4l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V3x ) @ V4l ) )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V3x ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V4l ) ) ) ) )
& ! [V5m: tp__ty_2Enum_2Enum,V6k: tp__ty_2Enum_2Enum,V7x: $i] :
( ( mem @ V7x @ A_27a )
=> ! [V8l: $i] :
( ( mem @ V8l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V5m ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V6k ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V7x ) @ V8l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V5m ) ) ) @ ( inj__ty_2Enum_2Enum @ V6k ) ) @ V8l ) ) ) ) ) ).
thf(ax_thm_2Erich__list_2EIS__SUFFIX,axiom,
! [A_27a: del] :
( ! [V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUFFIX @ A_27a ) @ V0l ) @ ( c_2Elist_2ENIL @ A_27a ) ) )
<=> $true ) )
& ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUFFIX @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V1x ) @ V2l ) ) )
<=> $false ) ) )
& ! [V3x1: $i] :
( ( mem @ V3x1 @ A_27a )
=> ! [V4l1: $i] :
( ( mem @ V4l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V5x2: $i] :
( ( mem @ V5x2 @ A_27a )
=> ! [V6l2: $i] :
( ( mem @ V6l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUFFIX @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V3x1 ) @ V4l1 ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V5x2 ) @ V6l2 ) ) )
<=> ( ( V3x1 = V5x2 )
& ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUFFIX @ A_27a ) @ V4l1 ) @ V6l2 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELENGTH__NOT__NULL,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) )
<=> ~ ( p @ ( ap @ ( c_2Elist_2ENULL @ A_27a ) @ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2ENOT__NIL__SNOC,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( c_2Elist_2ENIL @ A_27a )
!= ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V0x ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2ENOT__SNOC__NIL,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V0x ) @ V1l )
!= ( c_2Elist_2ENIL @ A_27a ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESNOC__EQ__LENGTH__EQ,axiom,
! [A_27a: del,V0x1: $i] :
( ( mem @ V0x1 @ A_27a )
=> ! [V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2x2: $i] :
( ( mem @ V2x2 @ A_27a )
=> ! [V3l2: $i] :
( ( mem @ V3l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V0x1 ) @ V1l1 )
= ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V2x2 ) @ V3l2 ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l1 ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V3l2 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESNOC__REVERSE__CONS,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V0x ) @ V1l )
= ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V0x ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFOLDR__SNOC,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27b )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27b ) @ V0f ) @ V1e ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V2x ) @ V3l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ V0f @ V2x ) @ V1e ) ) @ V3l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFOLDR__FOLDL,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2EMONOID @ A_27a ) @ V0f ) @ V1e ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27a ) @ V0f ) @ V1e ) @ V2l )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ A_27a ) @ V0f ) @ V1e ) @ V2l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELENGTH__FOLDR,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) )
= ( surj__ty_2Enum_2Enum
@ ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ ty_2Enum_2Enum )
@ ( lam @ A_27a
@ ^ [V1x: $i] :
( lam @ ty_2Enum_2Enum
@ ^ [V2l_27: $i] : ( ap @ c_2Enum_2ESUC @ V2l_27 ) ) ) )
@ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
@ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELENGTH__FOLDL,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) )
= ( surj__ty_2Enum_2Enum
@ ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1l_27: $i] :
( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ c_2Enum_2ESUC @ V1l_27 ) ) ) )
@ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
@ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMAP__FOLDR,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V0f ) @ V1l )
= ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ ( ty_2Elist_2Elist @ A_27b ) )
@ ( lam @ A_27a
@ ^ [V2x: $i] :
( lam @ ( ty_2Elist_2Elist @ A_27b )
@ ^ [V3l_27: $i] : ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27b ) @ ( ap @ V0f @ V2x ) ) @ V3l_27 ) ) ) )
@ ( c_2Elist_2ENIL @ A_27b ) )
@ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMAP__FOLDL,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V0f ) @ V1l )
= ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ ( ty_2Elist_2Elist @ A_27b ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27b )
@ ^ [V2l_27: $i] :
( lam @ A_27a
@ ^ [V3x: $i] : ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27b ) @ ( ap @ V0f @ V3x ) ) @ V2l_27 ) ) ) )
@ ( c_2Elist_2ENIL @ A_27b ) )
@ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFILTER__FOLDR,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V0P ) @ V1l )
= ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) )
@ ( lam @ A_27a
@ ^ [V2x: $i] :
( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V3l_27: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ V0P @ V2x ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ V3l_27 ) ) @ V3l_27 ) ) ) )
@ ( c_2Elist_2ENIL @ A_27a ) )
@ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFILTER__SNOC,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V0P ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V1x ) @ V2l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ V0P @ V1x ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V1x ) @ ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V0P ) @ V2l ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V0P ) @ V2l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFILTER__FOLDL,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V0P ) @ V1l )
= ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V2l_27: $i] :
( lam @ A_27a
@ ^ [V3x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ V0P @ V3x ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V3x ) @ V2l_27 ) ) @ V2l_27 ) ) ) )
@ ( c_2Elist_2ENIL @ A_27a ) )
@ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFILTER__COMM,axiom,
! [A_27a: del,V0f1: $i] :
( ( mem @ V0f1 @ ( arr @ A_27a @ bool ) )
=> ! [V1f2: $i] :
( ( mem @ V1f2 @ ( arr @ A_27a @ bool ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V0f1 ) @ ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V1f2 ) @ V2l ) )
= ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V1f2 ) @ ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V0f1 ) @ V2l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFILTER__IDEM,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V0f ) @ V1l ) )
= ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V0f ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFILTER__MAP,axiom,
! [A_27a: del,A_27b: del,V0f1: $i] :
( ( mem @ V0f1 @ ( arr @ A_27a @ bool ) )
=> ! [V1f2: $i] :
( ( mem @ V1f2 @ ( arr @ A_27b @ A_27a ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V0f1 ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27b @ A_27a ) @ V1f2 ) @ V2l ) )
= ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27b @ A_27a ) @ V1f2 ) @ ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27b ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27b @ bool @ A_27a ) @ V0f1 ) @ V1f2 ) ) @ V2l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELENGTH__FILTER__LEQ,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V0P ) @ V1l ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFILTER__EQ,axiom,
! [A_27a: del,V0P1: $i] :
( ( mem @ V0P1 @ ( arr @ A_27a @ bool ) )
=> ! [V1P2: $i] :
( ( mem @ V1P2 @ ( arr @ A_27a @ bool ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V0P1 ) @ V2l )
= ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V1P2 ) @ V2l ) )
<=> ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V2l ) ) )
=> ( ( p @ ( ap @ V0P1 @ V3x ) )
<=> ( p @ ( ap @ V1P2 @ V3x ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELENGTH__SEG,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1k: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1k ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1k ) ) @ V2l ) ) )
= V0n ) ) ) ).
thf(conj_thm_2Erich__list_2EAPPEND__NIL,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l ) @ ( c_2Elist_2ENIL @ A_27a ) )
= V0l ) )
& ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27b ) @ ( c_2Elist_2ENIL @ A_27b ) ) @ V1l )
= V1l ) ) ) ).
thf(conj_thm_2Erich__list_2EAPPEND__FOLDR,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ V1l2 )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ECONS @ A_27a ) ) @ V1l2 ) @ V0l1 ) ) ) ) ).
thf(conj_thm_2Erich__list_2EAPPEND__FOLDL,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ V1l2 )
= ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V2l_27: $i] :
( lam @ A_27a
@ ^ [V3x: $i] : ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V3x ) @ V2l_27 ) ) ) )
@ V0l1 )
@ V1l2 ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFOLDR__APPEND,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27b )
=> ! [V2l1: $i] :
( ( mem @ V2l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V3l2: $i] :
( ( mem @ V3l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27b ) @ V0f ) @ V1e ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V2l1 ) @ V3l2 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27b ) @ V0f ) @ V1e ) @ V3l2 ) ) @ V2l1 ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFOLDL__APPEND,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27a )
=> ! [V2l1: $i] :
( ( mem @ V2l1 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V3l2: $i] :
( ( mem @ V3l2 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a ) @ V0f ) @ V1e ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27b ) @ V2l1 ) @ V3l2 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a ) @ V0f ) @ V1e ) @ V2l1 ) ) @ V3l2 ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ECONS__APPEND,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V0x ) @ V1l )
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V0x ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EASSOC__APPEND,axiom,
! [A_27a: del] : ( p @ ( ap @ ( c_2Ecombin_2EASSOC @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2EAPPEND @ A_27a ) ) ) ).
thf(conj_thm_2Erich__list_2EMONOID__APPEND__NIL,axiom,
! [A_27a: del] : ( p @ ( ap @ ( ap @ ( c_2Ecombin_2EMONOID @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2EAPPEND @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ).
thf(conj_thm_2Erich__list_2EFLAT__SNOC,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ( ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ ( ty_2Elist_2Elist @ A_27a ) ) @ V0x ) @ V1l ) )
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ V1l ) ) @ V0x ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFLAT__FOLDR,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ( ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ V0l )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2EAPPEND @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ V0l ) ) ) ).
thf(conj_thm_2Erich__list_2EFLAT__FOLDL,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ( ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ V0l )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2EAPPEND @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ V0l ) ) ) ).
thf(conj_thm_2Erich__list_2ELENGTH__FLAT,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ V0l ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Elist_2ESUM @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Elist_2Elist @ A_27a ) @ ty_2Enum_2Enum ) @ ( c_2Elist_2ELENGTH @ A_27a ) ) @ V0l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EREVERSE__FOLDR,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V0l )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ESNOC @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ V0l ) ) ) ).
thf(conj_thm_2Erich__list_2EREVERSE__FOLDL,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V0l )
= ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V1l_27: $i] :
( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ V1l_27 ) ) ) )
@ ( c_2Elist_2ENIL @ A_27a ) )
@ V0l ) ) ) ).
thf(conj_thm_2Erich__list_2EALL__EL__MAP,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27b @ A_27a ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0P ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27b @ A_27a ) @ V1f ) @ V2l ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27b ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27b @ bool @ A_27a ) @ V0P ) @ V1f ) ) @ V2l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMEM__EXISTS,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V0x ) ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESUM__FOLDR,axiom,
! [V0l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Elist_2ESUM @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V0l ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ c_2Earithmetic_2E_2B ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESUM__FOLDL,axiom,
! [V0l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Elist_2ESUM @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V0l ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ c_2Earithmetic_2E_2B ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__PREFIX,axiom,
! [A_27a: del] :
( ! [V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ V0l ) )
<=> $true ) )
& ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1x ) @ V2l ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) )
<=> $false ) ) )
& ! [V3x1: $i] :
( ( mem @ V3x1 @ A_27a )
=> ! [V4l1: $i] :
( ( mem @ V4l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V5x2: $i] :
( ( mem @ V5x2 @ A_27a )
=> ! [V6l2: $i] :
( ( mem @ V6l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V5x2 ) @ V6l2 ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V3x1 ) @ V4l1 ) ) )
<=> ( ( V3x1 = V5x2 )
& ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V6l2 ) @ V4l1 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__PREFIX__APPEND,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V1l2 ) @ V0l1 ) )
<=> ? [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
& ( V0l1
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1l2 ) @ V2l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__SUFFIX__APPEND,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUFFIX @ A_27a ) @ V0l1 ) @ V1l2 ) )
<=> ? [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
& ( V0l1
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V2l ) @ V1l2 ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__SUBLIST__APPEND,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUBLIST @ A_27a ) @ V0l1 ) @ V1l2 ) )
<=> ? [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
& ? [V3l_27: $i] :
( ( mem @ V3l_27 @ ( ty_2Elist_2Elist @ A_27a ) )
& ( V0l1
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V2l ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1l2 ) @ V3l_27 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__PREFIX__IS__SUBLIST,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V1l2 ) @ V0l1 ) )
=> ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUBLIST @ A_27a ) @ V0l1 ) @ V1l2 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__SUFFIX__IS__SUBLIST,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUFFIX @ A_27a ) @ V0l1 ) @ V1l2 ) )
=> ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUBLIST @ A_27a ) @ V0l1 ) @ V1l2 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__PREFIX__REVERSE,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l2 ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V0l1 ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUFFIX @ A_27a ) @ V0l1 ) @ V1l2 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__SUFFIX__REVERSE,axiom,
! [A_27a: del,V0l2: $i] :
( ( mem @ V0l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUFFIX @ A_27a ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l1 ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V0l2 ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V0l2 ) @ V1l1 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__SUFFIX__CONS2__E,axiom,
! [A_27a: del,V0s: $i] :
( ( mem @ V0s @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1h: $i] :
( ( mem @ V1h @ A_27a )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUFFIX @ A_27a ) @ V0s ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1h ) @ V2t ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUFFIX @ A_27a ) @ V0s ) @ V2t ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__SUFFIX__REFL,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUFFIX @ A_27a ) @ V0l ) @ V0l ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__SUBLIST__REVERSE,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUBLIST @ A_27a ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V0l1 ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l2 ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUBLIST @ A_27a ) @ V0l1 ) @ V1l2 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EPREFIX__FOLDR,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EPREFIX @ A_27a ) @ V0P ) @ V1l )
= ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) )
@ ( lam @ A_27a
@ ^ [V2x: $i] :
( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V3l_27: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ V0P @ V2x ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ V3l_27 ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) )
@ ( c_2Elist_2ENIL @ A_27a ) )
@ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EPREFIX,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EPREFIX @ A_27a ) @ V0P ) @ ( c_2Elist_2ENIL @ A_27a ) )
= ( c_2Elist_2ENIL @ A_27a ) ) )
& ! [V1P: $i] :
( ( mem @ V1P @ ( arr @ A_27b @ bool ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27b )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EPREFIX @ A_27b ) @ V1P ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27b ) @ V2x ) @ V3l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( ap @ V1P @ V2x ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27b ) @ V2x ) @ ( ap @ ( ap @ ( c_2Erich__list_2EPREFIX @ A_27b ) @ V1P ) @ V3l ) ) ) @ ( c_2Elist_2ENIL @ A_27b ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__PREFIX__PREFIX,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ ( ap @ ( ap @ ( c_2Erich__list_2EPREFIX @ A_27a ) @ V0P ) @ V1l ) ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELENGTH__SCANL,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27a )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESCANL @ A_27b @ A_27a ) @ V0f ) @ V1e ) @ V2l ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( c_2Elist_2ELENGTH @ A_27b ) @ V2l ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELENGTH__SCANR,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27b )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESCANR @ A_27a @ A_27b ) @ V0f ) @ V1e ) @ V2l ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ECOMM__MONOID__FOLDL,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
=> ( ( p @ ( ap @ ( c_2Ecombin_2ECOMM @ A_27a @ A_27a ) @ V0f ) )
=> ! [V1e_27: $i] :
( ( mem @ V1e_27 @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2EMONOID @ A_27a ) @ V0f ) @ V1e_27 ) )
=> ! [V2e: $i] :
( ( mem @ V2e @ A_27a )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ A_27a ) @ V0f ) @ V2e ) @ V3l )
= ( ap @ ( ap @ V0f @ V2e ) @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ A_27a ) @ V0f ) @ V1e_27 ) @ V3l ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ECOMM__MONOID__FOLDR,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
=> ( ( p @ ( ap @ ( c_2Ecombin_2ECOMM @ A_27a @ A_27a ) @ V0f ) )
=> ! [V1e_27: $i] :
( ( mem @ V1e_27 @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2EMONOID @ A_27a ) @ V0f ) @ V1e_27 ) )
=> ! [V2e: $i] :
( ( mem @ V2e @ A_27a )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27a ) @ V0f ) @ V2e ) @ V3l )
= ( ap @ ( ap @ V0f @ V2e ) @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27a ) @ V0f ) @ V1e_27 ) @ V3l ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFCOMM__FOLDR__APPEND,axiom,
! [A_27a: del,A_27b: del,V0g: $i] :
( ( mem @ V0g @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27b @ ( arr @ A_27a @ A_27a ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2EFCOMM @ A_27a @ A_27a @ A_27b ) @ V0g ) @ V1f ) )
=> ! [V2e: $i] :
( ( mem @ V2e @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2ELEFT__ID @ A_27a @ A_27a ) @ V0g ) @ V2e ) )
=> ! [V3l1: $i] :
( ( mem @ V3l1 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V4l2: $i] :
( ( mem @ V4l2 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27b @ A_27a ) @ V1f ) @ V2e ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27b ) @ V3l1 ) @ V4l2 ) )
= ( ap @ ( ap @ V0g @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27b @ A_27a ) @ V1f ) @ V2e ) @ V3l1 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27b @ A_27a ) @ V1f ) @ V2e ) @ V4l2 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFCOMM__FOLDL__APPEND,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2EFCOMM @ A_27a @ A_27b @ A_27a ) @ V0f ) @ V1g ) )
=> ! [V2e: $i] :
( ( mem @ V2e @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2ERIGHT__ID @ A_27a @ A_27a ) @ V1g ) @ V2e ) )
=> ! [V3l1: $i] :
( ( mem @ V3l1 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V4l2: $i] :
( ( mem @ V4l2 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a ) @ V0f ) @ V2e ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27b ) @ V3l1 ) @ V4l2 ) )
= ( ap @ ( ap @ V1g @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a ) @ V0f ) @ V2e ) @ V3l1 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a ) @ V0f ) @ V2e ) @ V4l2 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFOLDL__SINGLE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27a )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27b )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a ) @ V0f ) @ V1e ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27b ) @ V2x ) @ ( c_2Elist_2ENIL @ A_27b ) ) )
= ( ap @ ( ap @ V0f @ V1e ) @ V2x ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFOLDR__SINGLE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27b )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27b ) @ V0f ) @ V1e ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ ( c_2Elist_2ENIL @ A_27a ) ) )
= ( ap @ ( ap @ V0f @ V2x ) @ V1e ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFOLDR__CONS__NIL,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ECONS @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ V0l )
= V0l ) ) ).
thf(conj_thm_2Erich__list_2EFOLDL__SNOC__NIL,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V1xs: $i] :
( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V2x ) @ V1xs ) ) ) )
@ ( c_2Elist_2ENIL @ A_27a ) )
@ V0l )
= V0l ) ) ).
thf(conj_thm_2Erich__list_2EFOLDR__FOLDL__REVERSE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27b )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27b ) @ V0f ) @ V1e ) @ V2l )
= ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ A_27b )
@ ( lam @ A_27b
@ ^ [V3x: $i] :
( lam @ A_27a
@ ^ [V4y: $i] : ( ap @ ( ap @ V0f @ V4y ) @ V3x ) ) ) )
@ V1e )
@ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V2l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFOLDL__FOLDR__REVERSE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27a )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a ) @ V0f ) @ V1e ) @ V2l )
= ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDR @ A_27b @ A_27a )
@ ( lam @ A_27b
@ ^ [V3x: $i] :
( lam @ A_27a
@ ^ [V4y: $i] : ( ap @ ( ap @ V0f @ V4y ) @ V3x ) ) ) )
@ V1e )
@ ( ap @ ( c_2Elist_2EREVERSE @ A_27b ) @ V2l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFOLDR__REVERSE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27b )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27b ) @ V0f ) @ V1e ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V2l ) )
= ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ A_27b )
@ ( lam @ A_27b
@ ^ [V3x: $i] :
( lam @ A_27a
@ ^ [V4y: $i] : ( ap @ ( ap @ V0f @ V4y ) @ V3x ) ) ) )
@ V1e )
@ V2l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFOLDL__REVERSE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27a )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a ) @ V0f ) @ V1e ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27b ) @ V2l ) )
= ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDR @ A_27b @ A_27a )
@ ( lam @ A_27b
@ ^ [V3x: $i] :
( lam @ A_27a
@ ^ [V4y: $i] : ( ap @ ( ap @ V0f @ V4y ) @ V3x ) ) ) )
@ V1e )
@ V2l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFOLDR__MAP,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27b )
=> ! [V2g: $i] :
( ( mem @ V2g @ ( arr @ A_27c @ A_27a ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27c ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27b ) @ V0f ) @ V1e ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27c @ A_27a ) @ V2g ) @ V3l ) )
= ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDR @ A_27c @ A_27b )
@ ( lam @ A_27c
@ ^ [V4x: $i] :
( lam @ A_27b
@ ^ [V5y: $i] : ( ap @ ( ap @ V0f @ ( ap @ V2g @ V4x ) ) @ V5y ) ) ) )
@ V1e )
@ V3l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFOLDL__MAP,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27a )
=> ! [V2g: $i] :
( ( mem @ V2g @ ( arr @ A_27c @ A_27b ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27c ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a ) @ V0f ) @ V1e ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27c @ A_27b ) @ V2g ) @ V3l ) )
= ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDL @ A_27c @ A_27a )
@ ( lam @ A_27a
@ ^ [V4x: $i] :
( lam @ A_27c
@ ^ [V5y: $i] : ( ap @ ( ap @ V0f @ V4x ) @ ( ap @ V2g @ V5y ) ) ) ) )
@ V1e )
@ V3l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEVERY__FOLDR,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0P ) @ V1l ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ bool )
@ ( lam @ A_27a
@ ^ [V2x: $i] :
( lam @ bool
@ ^ [V3l_27: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0P @ V2x ) ) @ V3l_27 ) ) ) )
@ c_2Ebool_2ET )
@ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEVERY__FOLDL,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0P ) @ V1l ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ bool )
@ ( lam @ bool
@ ^ [V2l_27: $i] :
( lam @ A_27a
@ ^ [V3x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ V2l_27 ) @ ( ap @ V0P @ V3x ) ) ) ) )
@ c_2Ebool_2ET )
@ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEXISTS__FOLDR,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V0P ) @ V1l ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ bool )
@ ( lam @ A_27a
@ ^ [V2x: $i] :
( lam @ bool
@ ^ [V3l_27: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0P @ V2x ) ) @ V3l_27 ) ) ) )
@ c_2Ebool_2EF )
@ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEXISTS__FOLDL,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V0P ) @ V1l ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ bool )
@ ( lam @ bool
@ ^ [V2l_27: $i] :
( lam @ A_27a
@ ^ [V3x: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ V2l_27 ) @ ( ap @ V0P @ V3x ) ) ) ) )
@ c_2Ebool_2EF )
@ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEVERY__FOLDR__MAP,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0P ) @ V1l ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ bool @ bool ) @ c_2Ebool_2E_2F_5C ) @ c_2Ebool_2ET ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ bool ) @ V0P ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEVERY__FOLDL__MAP,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0P ) @ V1l ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ bool @ bool ) @ c_2Ebool_2E_2F_5C ) @ c_2Ebool_2ET ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ bool ) @ V0P ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEXISTS__FOLDR__MAP,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V0P ) @ V1l ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ bool @ bool ) @ c_2Ebool_2E_5C_2F ) @ c_2Ebool_2EF ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ bool ) @ V0P ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEXISTS__FOLDL__MAP,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V0P ) @ V1l ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ bool @ bool ) @ c_2Ebool_2E_5C_2F ) @ c_2Ebool_2EF ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ bool ) @ V0P ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFOLDR__FILTER,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27b )
=> ! [V2P: $i] :
( ( mem @ V2P @ ( arr @ A_27a @ bool ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27b ) @ V0f ) @ V1e ) @ ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V2P ) @ V3l ) )
= ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27b )
@ ( lam @ A_27a
@ ^ [V4x: $i] :
( lam @ A_27b
@ ^ [V5y: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27b ) @ ( ap @ V2P @ V4x ) ) @ ( ap @ ( ap @ V0f @ V4x ) @ V5y ) ) @ V5y ) ) ) )
@ V1e )
@ V3l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFOLDL__FILTER,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27a )
=> ! [V2P: $i] :
( ( mem @ V2P @ ( arr @ A_27b @ bool ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a ) @ V0f ) @ V1e ) @ ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27b ) @ V2P ) @ V3l ) )
= ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a )
@ ( lam @ A_27a
@ ^ [V4x: $i] :
( lam @ A_27b
@ ^ [V5y: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ V2P @ V5y ) ) @ ( ap @ ( ap @ V0f @ V4x ) @ V5y ) ) @ V4x ) ) ) )
@ V1e )
@ V3l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EASSOC__FOLDR__FLAT,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
=> ( ( p @ ( ap @ ( c_2Ecombin_2EASSOC @ A_27a ) @ V0f ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2ELEFT__ID @ A_27a @ A_27a ) @ V0f ) @ V1e ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27a ) @ V0f ) @ V1e ) @ ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ V2l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27a ) @ V0f ) @ V1e ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Elist_2Elist @ A_27a ) @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27a ) @ V0f ) @ V1e ) ) @ V2l ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EASSOC__FOLDL__FLAT,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
=> ( ( p @ ( ap @ ( c_2Ecombin_2EASSOC @ A_27a ) @ V0f ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2ERIGHT__ID @ A_27a @ A_27a ) @ V0f ) @ V1e ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ A_27a ) @ V0f ) @ V1e ) @ ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ V2l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ A_27a ) @ V0f ) @ V1e ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Elist_2Elist @ A_27a ) @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ A_27a ) @ V0f ) @ V1e ) ) @ V2l ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMAP__FLAT,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ V1l ) )
= ( ap @ ( c_2Elist_2EFLAT @ A_27b ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V0f ) ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFILTER__FLAT,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V0P ) @ ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ V1l ) )
= ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V0P ) ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEXISTS__DISJ,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p
@ ( ap
@ ( ap @ ( c_2Elist_2EEXISTS @ A_27a )
@ ( lam @ A_27a
@ ^ [V3x: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0P @ V3x ) ) @ ( ap @ V1Q @ V3x ) ) ) )
@ V2l ) )
<=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V0P ) @ V2l ) )
| ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V1Q ) @ V2l ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMEM__FOLDR,axiom,
! [A_27a: del,V0y: $i] :
( ( mem @ V0y @ A_27a )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0y ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ bool )
@ ( lam @ A_27a
@ ^ [V2x: $i] :
( lam @ bool
@ ^ [V3l_27: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V0y ) @ V2x ) ) @ V3l_27 ) ) ) )
@ c_2Ebool_2EF )
@ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMEM__FOLDL,axiom,
! [A_27a: del,V0y: $i] :
( ( mem @ V0y @ A_27a )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0y ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ bool )
@ ( lam @ bool
@ ^ [V2l_27: $i] :
( lam @ A_27a
@ ^ [V3x: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ V2l_27 ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V0y ) @ V3x ) ) ) ) )
@ c_2Ebool_2EF )
@ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ENULL__FOLDR,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Elist_2ENULL @ A_27a ) @ V0l ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ bool )
@ ( lam @ A_27a
@ ^ [V1x: $i] :
( lam @ bool
@ ^ [V2l_27: $i] : c_2Ebool_2EF ) ) )
@ c_2Ebool_2ET )
@ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2ENULL__FOLDL,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Elist_2ENULL @ A_27a ) @ V0l ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ bool )
@ ( lam @ bool
@ ^ [V1x: $i] :
( lam @ A_27a
@ ^ [V2l_27: $i] : c_2Ebool_2EF ) ) )
@ c_2Ebool_2ET )
@ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMAP__REVERSE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l ) )
= ( ap @ ( c_2Elist_2EREVERSE @ A_27b ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V0f ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESEG__LENGTH__ID,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0l )
= V0l ) ) ).
thf(conj_thm_2Erich__list_2ESEG__SUC__CONS,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V3x ) @ V2l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2l ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESEG__0__SNOC,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V2x ) @ V1l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EBUTLASTN__SEG,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l )
= ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELASTN__CONS,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ V1l ) )
= ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELENGTH__LASTN,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) )
= V0n ) ) ) ).
thf(conj_thm_2Erich__list_2ELASTN__LENGTH__ID,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) @ V0l )
= V0l ) ) ).
thf(conj_thm_2Erich__list_2ELASTN__LASTN,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum,V2m: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ V0l ) )
= ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V0l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ETAKE__SNOC,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V2x ) @ V1l ) )
= ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EBUTLASTN__SUC__FRONT,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ V1l )
= ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2EFRONT @ A_27a ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EBUTLASTN__FRONT,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2EFRONT @ A_27a ) @ V1l ) )
= ( ap @ ( c_2Elist_2EFRONT @ A_27a ) @ ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELENGTH__BUTLASTN,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EBUTLASTN__BUTLASTN,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V2l ) )
= ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ V2l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EAPPEND__BUTLASTN__LASTN,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) )
= V1l ) ) ) ).
thf(conj_thm_2Erich__list_2EAPPEND__TAKE__LASTN,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2l ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V2l ) )
= V2l ) ) ) ).
thf(conj_thm_2Erich__list_2EBUTLASTN__APPEND2,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l2 ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1l1 ) @ V2l2 ) )
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1l1 ) @ ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V2l2 ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EBUTLASTN__LENGTH__APPEND,axiom,
! [A_27a: del,V0l2: $i] :
( ( mem @ V0l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l2 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1l1 ) @ V0l2 ) )
= V1l1 ) ) ) ).
thf(conj_thm_2Erich__list_2ELASTN__LENGTH__APPEND,axiom,
! [A_27a: del,V0l2: $i] :
( ( mem @ V0l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l2 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1l1 ) @ V0l2 ) )
= V0l2 ) ) ) ).
thf(conj_thm_2Erich__list_2EBUTLASTN__CONS,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ V1l ) )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EBUTLASTN__LENGTH__CONS,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1x ) @ V0l ) )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1x ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELAST__LASTN__LAST,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
=> ( ( ap @ ( c_2Elist_2ELAST @ A_27a ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) )
= ( ap @ ( c_2Elist_2ELAST @ A_27a ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EBUTLASTN__LASTN__NIL,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) )
= ( c_2Elist_2ENIL @ A_27a ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELASTN__BUTLASTN,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V2l ) )
= ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ V2l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EBUTLASTN__LASTN,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2l ) )
= ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V2l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELASTN__1,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( V0l
!= ( c_2Elist_2ENIL @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V0l )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ ( ap @ ( c_2Elist_2ELAST @ A_27a ) @ V0l ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EBUTLASTN__1,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( V0l
!= ( c_2Elist_2ENIL @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V0l )
= ( ap @ ( c_2Elist_2EFRONT @ A_27a ) @ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EBUTLASTN__APPEND1,axiom,
! [A_27a: del,V0l2: $i] :
( ( mem @ V0l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l2 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
=> ! [V2l1: $i] :
( ( mem @ V2l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V2l1 ) @ V0l2 ) )
= ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l2 ) ) ) @ V2l1 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELASTN__APPEND2,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l2 ) ) )
=> ! [V2l1: $i] :
( ( mem @ V2l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V2l1 ) @ V1l2 ) )
= ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l2 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELASTN__APPEND1,axiom,
! [A_27a: del,V0l2: $i] :
( ( mem @ V0l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l2 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
=> ! [V2l1: $i] :
( ( mem @ V2l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V2l1 ) @ V0l2 ) )
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l2 ) ) ) @ V2l1 ) ) @ V0l2 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELASTN__MAP,axiom,
! [A_27a: del,A_27b: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ! [V2f: $i] :
( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V2f ) @ V1l ) )
= ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V2f ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EBUTLASTN__MAP,axiom,
! [A_27a: del,A_27b: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ! [V2f: $i] :
( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V2f ) @ V1l ) )
= ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V2f ) @ ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEVERY__LASTN,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0P ) @ V1l ) )
=> ! [V2m: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0P ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ V1l ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEVERY__BUTLASTN,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0P ) @ V1l ) )
=> ! [V2m: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0P ) @ ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ V1l ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ETAKE__TAKE__T,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1l ) )
= ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2ETAKE__TAKE,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ! [V2n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1l ) )
= ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EDROP__LENGTH__NIL,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) @ V0l )
= ( c_2Elist_2ENIL @ A_27a ) ) ) ).
thf(conj_thm_2Erich__list_2EBUTLASTN__LENGTH__NIL,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) @ V0l )
= ( c_2Elist_2ENIL @ A_27a ) ) ) ).
thf(conj_thm_2Erich__list_2EDROP__APPEND,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1l1 ) @ V2l2 ) )
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l1 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l1 ) ) ) @ V2l2 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EDROP__APPEND1,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l1 ) ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1l1 ) @ V2l2 ) )
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l1 ) ) @ V2l2 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EDROP__APPEND2,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l1 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ V2l2 ) )
= ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l1 ) ) ) @ V2l2 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EDROP__DROP__T,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V2l ) )
= ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ V2l ) ) ) ).
thf(conj_thm_2Erich__list_2EDROP__DROP,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V2l ) )
= ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ V2l ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELASTN__SEG,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l )
= ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2ETAKE__SEG,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l )
= ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EDROP__SEG,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l )
= ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EDROP__SNOC,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V2x ) @ V1l ) )
= ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V2x ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EAPPEND__BUTLASTN__DROP,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V2l ) ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2l ) )
= V2l ) ) ) ).
thf(conj_thm_2Erich__list_2ESEG__SEG,axiom,
! [A_27a: del,V0n1: tp__ty_2Enum_2Enum,V1m1: tp__ty_2Enum_2Enum,V2n2: tp__ty_2Enum_2Enum,V3m2: tp__ty_2Enum_2Enum,V4l: $i] :
( ( mem @ V4l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n1 ) ) @ ( inj__ty_2Enum_2Enum @ V1m1 ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V4l ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n2 ) ) @ ( inj__ty_2Enum_2Enum @ V3m2 ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n1 ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n2 ) ) @ ( inj__ty_2Enum_2Enum @ V3m2 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n1 ) ) @ ( inj__ty_2Enum_2Enum @ V1m1 ) ) @ V4l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n2 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m1 ) ) @ ( inj__ty_2Enum_2Enum @ V3m2 ) ) ) @ V4l ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESEG__APPEND1,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2l1: $i] :
( ( mem @ V2l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l1 ) ) )
=> ! [V3l2: $i] :
( ( mem @ V3l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V2l1 ) @ V3l2 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V2l1 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESEG__APPEND2,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum,V3l2: $i] :
( ( mem @ V3l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l1 ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V3l2 ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ V3l2 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l1 ) ) ) @ V3l2 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESEG__TAKE__DROP,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V2l )
= ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V2l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESEG__APPEND,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2n: tp__ty_2Enum_2Enum,V3l2: $i] :
( ( mem @ V3l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l1 ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l1 ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V3l2 ) ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1l1 ) @ V3l2 ) )
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l1 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1l1 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l1 ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V3l2 ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESEG__LENGTH__SNOC,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V1x ) @ V0l ) )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1x ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESEG__SNOC,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) )
=> ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V3x ) @ V2l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V2l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EELL__SEG,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l )
= ( ap @ ( c_2Elist_2EHD @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESNOC__FOLDR,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V0x ) @ V1l )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ECONS @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V0x ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMEM__FOLDR__MAP,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ bool @ bool ) @ c_2Ebool_2E_5C_2F ) @ c_2Ebool_2EF ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ bool ) @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V0x ) ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMEM__FOLDL__MAP,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ bool @ bool ) @ c_2Ebool_2E_5C_2F ) @ c_2Ebool_2EF ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ bool ) @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V0x ) ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFILTER__FILTER,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V0P ) @ ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V1Q ) @ V2l ) )
= ( ap
@ ( ap @ ( c_2Elist_2EFILTER @ A_27a )
@ ( lam @ A_27a
@ ^ [V3x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0P @ V3x ) ) @ ( ap @ V1Q @ V3x ) ) ) )
@ V2l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFCOMM__FOLDR__FLAT,axiom,
! [A_27a: del,A_27b: del,V0g: $i] :
( ( mem @ V0g @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27b @ ( arr @ A_27a @ A_27a ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2EFCOMM @ A_27a @ A_27a @ A_27b ) @ V0g ) @ V1f ) )
=> ! [V2e: $i] :
( ( mem @ V2e @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2ELEFT__ID @ A_27a @ A_27a ) @ V0g ) @ V2e ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ A_27b ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27b @ A_27a ) @ V1f ) @ V2e ) @ ( ap @ ( c_2Elist_2EFLAT @ A_27b ) @ V3l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27a ) @ V0g ) @ V2e ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Elist_2Elist @ A_27b ) @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27b @ A_27a ) @ V1f ) @ V2e ) ) @ V3l ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFCOMM__FOLDL__FLAT,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2EFCOMM @ A_27a @ A_27b @ A_27a ) @ V0f ) @ V1g ) )
=> ! [V2e: $i] :
( ( mem @ V2e @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ecombin_2ERIGHT__ID @ A_27a @ A_27a ) @ V1g ) @ V2e ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ A_27b ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a ) @ V0f ) @ V2e ) @ ( ap @ ( c_2Elist_2EFLAT @ A_27b ) @ V3l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ A_27a ) @ V1g ) @ V2e ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Elist_2Elist @ A_27b ) @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a ) @ V0f ) @ V2e ) ) @ V3l ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFOLDR__MAP__REVERSE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
=> ( ! [V1a: $i] :
( ( mem @ V1a @ A_27a )
=> ! [V2b: $i] :
( ( mem @ V2b @ A_27a )
=> ! [V3c: $i] :
( ( mem @ V3c @ A_27a )
=> ( ( ap @ ( ap @ V0f @ V1a ) @ ( ap @ ( ap @ V0f @ V2b ) @ V3c ) )
= ( ap @ ( ap @ V0f @ V2b ) @ ( ap @ ( ap @ V0f @ V1a ) @ V3c ) ) ) ) ) )
=> ! [V4e: $i] :
( ( mem @ V4e @ A_27a )
=> ! [V5g: $i] :
( ( mem @ V5g @ ( arr @ A_27b @ A_27a ) )
=> ! [V6l: $i] :
( ( mem @ V6l @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27a ) @ V0f ) @ V4e ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27b @ A_27a ) @ V5g ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27b ) @ V6l ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27a ) @ V0f ) @ V4e ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27b @ A_27a ) @ V5g ) @ V6l ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFOLDR__FILTER__REVERSE,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
=> ( ! [V1a: $i] :
( ( mem @ V1a @ A_27a )
=> ! [V2b: $i] :
( ( mem @ V2b @ A_27a )
=> ! [V3c: $i] :
( ( mem @ V3c @ A_27a )
=> ( ( ap @ ( ap @ V0f @ V1a ) @ ( ap @ ( ap @ V0f @ V2b ) @ V3c ) )
= ( ap @ ( ap @ V0f @ V2b ) @ ( ap @ ( ap @ V0f @ V1a ) @ V3c ) ) ) ) ) )
=> ! [V4e: $i] :
( ( mem @ V4e @ A_27a )
=> ! [V5P: $i] :
( ( mem @ V5P @ ( arr @ A_27a @ bool ) )
=> ! [V6l: $i] :
( ( mem @ V6l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27a ) @ V0f ) @ V4e ) @ ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V5P ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V6l ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27a ) @ V0f ) @ V4e ) @ ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V5P ) @ V6l ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ECOMM__ASSOC__FOLDR__REVERSE,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
=> ( ( p @ ( ap @ ( c_2Ecombin_2ECOMM @ A_27a @ A_27a ) @ V0f ) )
=> ( ( p @ ( ap @ ( c_2Ecombin_2EASSOC @ A_27a ) @ V0f ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27a )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27a ) @ V0f ) @ V1e ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V2l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27a ) @ V0f ) @ V1e ) @ V2l ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ECOMM__ASSOC__FOLDL__REVERSE,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) )
=> ( ( p @ ( ap @ ( c_2Ecombin_2ECOMM @ A_27a @ A_27a ) @ V0f ) )
=> ( ( p @ ( ap @ ( c_2Ecombin_2EASSOC @ A_27a ) @ V0f ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27a )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ A_27a ) @ V0f ) @ V1e ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V2l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27a @ A_27a ) @ V0f ) @ V1e ) @ V2l ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EELL__LAST,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ~ ( p @ ( ap @ ( c_2Elist_2ENULL @ A_27a ) @ V0l ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0l )
= ( ap @ ( c_2Elist_2ELAST @ A_27a ) @ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EELL__0__SNOC,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V1x ) @ V0l ) )
= V1x ) ) ) ).
thf(conj_thm_2Erich__list_2EELL__SNOC,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V1x ) @ V2l ) )
= ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ V2l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EELL__SUC__SNOC,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V1x ) @ V2l ) )
= ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V2l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EELL__CONS,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ V1l ) )
= ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EELL__LENGTH__CONS,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1x ) @ V0l ) )
= V1x ) ) ) ).
thf(conj_thm_2Erich__list_2EELL__LENGTH__SNOC,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V1x ) @ V0l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( c_2Elist_2ENULL @ A_27a ) @ V0l ) ) @ V1x ) @ ( ap @ ( c_2Elist_2EHD @ A_27a ) @ V0l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EELL__APPEND2,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l2 ) ) )
=> ! [V2l1: $i] :
( ( mem @ V2l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V2l1 ) @ V1l2 ) )
= ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l2 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EELL__APPEND1,axiom,
! [A_27a: del,V0l2: $i] :
( ( mem @ V0l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l2 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
=> ! [V2l1: $i] :
( ( mem @ V2l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V2l1 ) @ V0l2 ) )
= ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l2 ) ) ) @ V2l1 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EELL__PRE__LENGTH,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( V0l
!= ( c_2Elist_2ENIL @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) ) @ V0l )
= ( ap @ ( c_2Elist_2EHD @ A_27a ) @ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEL__PRE__LENGTH,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( V0l
!= ( c_2Elist_2ENIL @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) ) @ V0l )
= ( ap @ ( c_2Elist_2ELAST @ A_27a ) @ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEL__ELL,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l )
= ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEL__LENGTH__APPEND,axiom,
! [A_27a: del,V0l2: $i] :
( ( mem @ V0l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ~ ( p @ ( ap @ ( c_2Elist_2ENULL @ A_27a ) @ V0l2 ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l1 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1l1 ) @ V0l2 ) )
= ( ap @ ( c_2Elist_2EHD @ A_27a ) @ V0l2 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EELL__EL,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l )
= ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EELL__MAP,axiom,
! [A_27a: del,A_27b: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2f: $i] :
( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V2f ) @ V1l ) )
= ( ap @ V2f @ ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELENGTH__FRONT,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( V0l
!= ( c_2Elist_2ENIL @ A_27a ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ ( ap @ ( c_2Elist_2EFRONT @ A_27a ) @ V0l ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EDROP__LENGTH__APPEND,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l1 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ V1l2 ) )
= V1l2 ) ) ) ).
thf(conj_thm_2Erich__list_2ETAKE__APPEND,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1l1 ) @ V2l2 ) )
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l1 ) ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l1 ) ) ) @ V2l2 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ETAKE__APPEND1,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l1 ) ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1l1 ) @ V2l2 ) )
= ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l1 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ETAKE__APPEND2,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l1 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ V2l2 ) )
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l1 ) ) ) @ V2l2 ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ETAKE__LENGTH__APPEND,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l1 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ V1l2 ) )
= V0l1 ) ) ) ).
thf(conj_thm_2Erich__list_2EREVERSE__FLAT,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ( ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ V0l ) )
= ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ ( ap @ ( c_2Elist_2EREVERSE @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2EREVERSE @ A_27a ) ) @ V0l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMAP__FILTER,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27a ) )
=> ! [V1P: $i] :
( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ( ( p @ ( ap @ V1P @ ( ap @ V0f @ V3x ) ) )
<=> ( p @ ( ap @ V1P @ V3x ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V1P ) @ V2l ) )
= ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V1P ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27a ) @ V0f ) @ V2l ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFLAT__REVERSE,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ( ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ ( ap @ ( c_2Elist_2EREVERSE @ ( ty_2Elist_2Elist @ A_27a ) ) @ V0l ) )
= ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2EREVERSE @ A_27a ) ) @ V0l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFLAT__FLAT,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
=> ( ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ ( ap @ ( c_2Elist_2EFLAT @ ( ty_2Elist_2Elist @ A_27a ) ) @ V0l ) )
= ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2EFLAT @ A_27a ) ) @ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEVERY__REVERSE,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0P ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0P ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEXISTS__REVERSE,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V0P ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V0P ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEVERY__SEG,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0P ) @ V1l ) )
=> ! [V2m: tp__ty_2Enum_2Enum,V3k: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3k ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0P ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3k ) ) @ V1l ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEVERY__TAKE,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0P ) @ V1l ) )
=> ! [V2m: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0P ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ V1l ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEVERY__DROP,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0P ) @ V1l ) )
=> ! [V2m: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0P ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ V1l ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEXISTS__SEG,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1k: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1k ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) )
=> ! [V3P: $i] :
( ( mem @ V3P @ ( arr @ A_27a @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V3P ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1k ) ) @ V2l ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V3P ) @ V2l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEXISTS__TAKE__IMP,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1m: tp__ty_2Enum_2Enum,V2P: $i] :
( ( mem @ V2P @ ( arr @ A_27a @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V2P ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V0l ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V2P ) @ V0l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEXISTS__DROP__IMP,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1m: tp__ty_2Enum_2Enum,V2P: $i] :
( ( mem @ V2P @ ( arr @ A_27a @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V2P ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V0l ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V2P ) @ V0l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEXISTS__TAKE,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ! [V2P: $i] :
( ( mem @ V2P @ ( arr @ A_27a @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V2P ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1l ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V2P ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEXISTS__DROP,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ! [V2P: $i] :
( ( mem @ V2P @ ( arr @ A_27a @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V2P ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1l ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V2P ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEXISTS__LASTN,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ! [V2P: $i] :
( ( mem @ V2P @ ( arr @ A_27a @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V2P ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1l ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V2P ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEXISTS__BUTLASTN,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ! [V2P: $i] :
( ( mem @ V2P @ ( arr @ A_27a @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V2P ) @ ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1l ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V2P ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMEM__SEG,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) )
=> ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V2l ) ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V3x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V2l ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMEM__TAKE__IMP,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1m: tp__ty_2Enum_2Enum,V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V0l ) ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V0l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMEM__DROP__IMP,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1m: tp__ty_2Enum_2Enum,V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V0l ) ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V0l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMEM__TAKE,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1l ) ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMEM__DROP,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1l ) ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMEM__BUTLASTN,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1l ) ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMEM__LASTN,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1l ) ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EZIP__SNOC,axiom,
! [A_27a: del,A_27b: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l1 ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27b ) @ V1l2 ) ) )
=> ! [V2x1: $i] :
( ( mem @ V2x1 @ A_27a )
=> ! [V3x2: $i] :
( ( mem @ V3x2 @ A_27b )
=> ( ( ap @ ( c_2Elist_2EZIP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V2x1 ) @ V0l1 ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27b ) @ V3x2 ) @ V1l2 ) ) )
= ( ap @ ( ap @ ( c_2Elist_2ESNOC @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V2x1 ) @ V3x2 ) ) @ ( ap @ ( c_2Elist_2EZIP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ V0l1 ) @ V1l2 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EUNZIP__SNOC,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( ( ap @ ( c_2Elist_2EUNZIP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0x ) @ V1l ) )
= ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V0x ) ) @ ( ap @ ( c_2Epair_2EFST @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( ap @ ( c_2Elist_2EUNZIP @ A_27a @ A_27b ) @ V1l ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27b ) @ ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ V0x ) ) @ ( ap @ ( c_2Epair_2ESND @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( ap @ ( c_2Elist_2EUNZIP @ A_27a @ A_27b ) @ V1l ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELENGTH__UNZIP__FST,axiom,
! [A_27a: del,A_27b: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ ( ap @ ( c_2Erich__list_2EUNZIP__FST @ A_27a @ A_27b ) @ V0l ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELENGTH__UNZIP__SND,axiom,
! [A_27a: del,A_27b: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27b ) @ ( ap @ ( c_2Erich__list_2EUNZIP__SND @ A_27b @ A_27a ) @ V0l ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESUM__REVERSE,axiom,
! [V0l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Elist_2ESUM @ ( ap @ ( c_2Elist_2EREVERSE @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V0l ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Elist_2ESUM @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V0l ) ) ) ) ).
thf(stp_c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum,type,
tp__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum: $tType ).
thf(stp_inj_c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum,type,
inj__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum: tp__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum > $i ).
thf(stp_surj_c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum,type,
surj__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum: $i > tp__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum ).
thf(stp_inj_surj_c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum,axiom,
! [X: tp__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( inj__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum,axiom,
! [X: tp__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum] : ( mem @ ( inj__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum @ X ) @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) ) ).
thf(stp_iso_mem_c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) )
=> ( X
= ( inj__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( surj__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum @ X ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESUM__FLAT,axiom,
! [V0l: tp__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Elist_2ESUM @ ( ap @ ( c_2Elist_2EFLAT @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V0l ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Elist_2ESUM @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) @ c_2Elist_2ESUM ) @ ( inj__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V0l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEL__APPEND1,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l1 ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1l1 ) @ V2l2 ) )
= ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l1 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEL__APPEND2,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l1 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ V2l2 ) )
= ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l1 ) ) ) @ V2l2 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELUPDATE__APPEND2,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2n: tp__ty_2Enum_2Enum,V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l1 ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELUPDATE @ A_27a ) @ V3x ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ V1l2 ) )
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELUPDATE @ A_27a ) @ V3x ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l1 ) ) ) @ V1l2 ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELUPDATE__APPEND1,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2n: tp__ty_2Enum_2Enum,V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l1 ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELUPDATE @ A_27a ) @ V3x ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ V1l2 ) )
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELUPDATE @ A_27a ) @ V3x ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V0l1 ) ) @ V1l2 ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2Eis__prefix__el,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V1l1 ) @ V2l2 ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l1 ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l2 ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l1 )
= ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V2l2 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEL__CONS,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1x ) @ V2l ) )
= ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ V2l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESEG1,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEL__SEG,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l )
= ( ap @ ( c_2Elist_2EHD @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESEG__CONS,axiom,
! [A_27a: del,V0j: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2h: $i] :
( ( mem @ V2h @ A_27a )
=> ! [V3t: $i] :
( ( mem @ V3t @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0j ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0j ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V3t ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0j ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2h ) @ V3t ) )
= ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0j ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V3t ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESEG__SUC__EL,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1i: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ V2l )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ V2l ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V2l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ETAKE__SEG__DROP,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1i: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ V2l ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ V2l ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ V2l ) )
= V2l ) ) ) ).
thf(conj_thm_2Erich__list_2EEL__MEM,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ETL__SNOC,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( c_2Elist_2ETL @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V0x ) @ V1l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( c_2Elist_2ENULL @ A_27a ) @ V1l ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V0x ) @ ( ap @ ( c_2Elist_2ETL @ A_27a ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEL__REVERSE__ELL,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l ) )
= ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EELL__LENGTH__APPEND,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ~ ( p @ ( ap @ ( c_2Elist_2ENULL @ A_27a ) @ V0l1 ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l2 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ V1l2 ) )
= ( ap @ ( c_2Elist_2ELAST @ A_27a ) @ V0l1 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EELL__MEM,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EELL__REVERSE,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l ) )
= ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EELL__REVERSE__EL,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EELL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l ) )
= ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2ETAKE__BUTLASTN,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l )
= ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EBUTLASTN__TAKE,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l )
= ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELASTN__DROP,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l )
= ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EDROP__LASTN,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l )
= ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESEG__LASTN__BUTLASTN,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V2l )
= ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ V2l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EDROP__REVERSE,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l ) )
= ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EBUTLASTN__REVERSE,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l ) )
= ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELASTN__REVERSE,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l ) )
= ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ETAKE__REVERSE,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l ) )
= ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESEG__REVERSE,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V2l ) )
= ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ V2l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELENGTH__REPLICATE,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1x ) ) )
= V0n ) ) ).
thf(conj_thm_2Erich__list_2EMEM__REPLICATE,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1x ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EAND__EL__FOLDL,axiom,
! [V0l: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ c_2Erich__list_2EAND__EL @ ( inj__c_ty_2Elist_2Elist_o @ V0l ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ bool @ bool ) @ c_2Ebool_2E_2F_5C ) @ c_2Ebool_2ET ) @ ( inj__c_ty_2Elist_2Elist_o @ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EAND__EL__FOLDR,axiom,
! [V0l: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ c_2Erich__list_2EAND__EL @ ( inj__c_ty_2Elist_2Elist_o @ V0l ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ bool @ bool ) @ c_2Ebool_2E_2F_5C ) @ c_2Ebool_2ET ) @ ( inj__c_ty_2Elist_2Elist_o @ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EOR__EL__FOLDL,axiom,
! [V0l: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ c_2Erich__list_2EOR__EL @ ( inj__c_ty_2Elist_2Elist_o @ V0l ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ bool @ bool ) @ c_2Ebool_2E_5C_2F ) @ c_2Ebool_2EF ) @ ( inj__c_ty_2Elist_2Elist_o @ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EOR__EL__FOLDR,axiom,
! [V0l: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ c_2Erich__list_2EOR__EL @ ( inj__c_ty_2Elist_2Elist_o @ V0l ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ bool @ bool ) @ c_2Ebool_2E_5C_2F ) @ c_2Ebool_2EF ) @ ( inj__c_ty_2Elist_2Elist_o @ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__PREFIX__NIL,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ V0x ) )
& ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V0x ) @ ( c_2Elist_2ENIL @ A_27a ) ) )
<=> ( V0x
= ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__PREFIX__REFL,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V0x ) @ V0x ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__PREFIX__ANTISYM,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V0x ) @ V1y ) )
& ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V1y ) @ V0x ) ) )
=> ( V0x = V1y ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__PREFIX__TRANS,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2z: $i] :
( ( mem @ V2z @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V1y ) @ V0x ) )
& ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V2z ) @ V1y ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V2z ) @ V0x ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__PREFIX__BUTLAST,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ ( ap @ ( c_2Elist_2EFRONT @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V0x ) @ V1y ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V0x ) @ V1y ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__PREFIX__LENGTH,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V0x ) @ V1y ) )
=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0x ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1y ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__PREFIX__LENGTH__ANTI,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V0x ) @ V1y ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0x ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1y ) ) ) )
<=> ( V0x = V1y ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__PREFIX__SNOC,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2z: $i] :
( ( mem @ V2z @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V2z ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V0x ) @ V1y ) ) )
<=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V2z ) @ V1y ) )
| ( V2z
= ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V0x ) @ V1y ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__PREFIX__APPEND1,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0a ) @ V1b ) ) @ V2c ) )
=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V0a ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__PREFIX__APPEND2,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V0a ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1b ) @ V2c ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V0a ) @ V1b ) )
| ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__PREFIX__APPENDS,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0a ) @ V1b ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0a ) @ V2c ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V1b ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__PREFIX__APPEND3,axiom,
! [A_27a: del,V0c: $i] :
( ( mem @ V0c @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V1a ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1a ) @ V0c ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2Eprefixes__is__prefix__total,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V1l1 ) @ V0l ) )
& ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V2l2 ) @ V0l ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V1l1 ) @ V2l2 ) )
| ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V2l2 ) @ V1l1 ) ) ) ) ) ) ) ).
thf(ax_thm_2Erich__list_2Ecommon__prefixes__def,axiom,
! [A_27a: del,V0s: $i] :
( ( mem @ V0s @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) )
=> ( ( ap @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a ) @ V0s )
= ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V1p: $i] :
( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) @ V1p )
@ ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Elist_2Elist @ A_27a ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V2m: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Elist_2Elist @ A_27a ) ) @ V2m ) @ V0s ) ) @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V1p ) @ V2m ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2Ecommon__prefixes__BIGINTER,axiom,
! [A_27a: del,V0s: $i] :
( ( mem @ V0s @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) )
=> ( ( ap @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a ) @ V0s )
= ( ap @ ( c_2Epred__set_2EBIGINTER @ ( ty_2Elist_2Elist @ A_27a ) )
@ ( ap
@ ( ap @ ( c_2Epred__set_2EIMAGE @ ( ty_2Elist_2Elist @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V1l: $i] :
( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V2p: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) @ V2p ) @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V2p ) @ V1l ) ) ) ) ) )
@ V0s ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFINITE__prefix,axiom,
! [A_27a: del,V0b: $i] :
( ( mem @ V0b @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( p
@ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Elist_2Elist @ A_27a ) )
@ ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V1a: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) @ V1a ) @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V1a ) @ V0b ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFINITE__common__prefixes,axiom,
! [A_27a: del,V0s: $i] :
( ( mem @ V0s @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) )
=> ( ( V0s
!= ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a ) @ V0s ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2Ecommon__prefixes__NONEMPTY,axiom,
! [A_27a: del,V0s: $i] :
( ( mem @ V0s @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) )
=> ( ( ap @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a ) @ V0s )
!= ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ).
thf(ax_thm_2Erich__list_2Elongest__prefix__def,axiom,
! [A_27a: del,V0s: $i] :
( ( mem @ V0s @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) )
=> ( ( ap @ ( c_2Erich__list_2Elongest__prefix @ A_27a ) @ V0s )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) ) @ V0s ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) @ ( c_2Elist_2ENIL @ A_27a ) )
@ ( ap @ ( c_2Emin_2E_40 @ ( ty_2Elist_2Elist @ A_27a ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V1x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2Eis__measure__maximal @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ELENGTH @ A_27a ) ) @ ( ap @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a ) @ V0s ) ) @ V1x ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2Etwo__common__prefixes,axiom,
! [A_27a: del,V0s: $i] :
( ( mem @ V0s @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) )
=> ! [V1p1: $i] :
( ( mem @ V1p1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2p2: $i] :
( ( mem @ V2p2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( V0s
!= ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27a ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Elist_2Elist @ A_27a ) ) @ V1p1 ) @ ( ap @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a ) @ V0s ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Elist_2Elist @ A_27a ) ) @ V2p2 ) @ ( ap @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a ) @ V0s ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V1p1 ) @ V2p2 ) )
| ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V2p2 ) @ V1p1 ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2Elongest__prefix__UNIQUE,axiom,
! [A_27a: del,V0s: $i] :
( ( mem @ V0s @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2y: $i] :
( ( mem @ V2y @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( V0s
!= ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27a ) ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2Eis__measure__maximal @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ELENGTH @ A_27a ) ) @ ( ap @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a ) @ V0s ) ) @ V1x ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2Eis__measure__maximal @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ELENGTH @ A_27a ) ) @ ( ap @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a ) @ V0s ) ) @ V2y ) ) )
=> ( V1x = V2y ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2Ecommon__prefixes__NIL,axiom,
! [A_27a: del,V0s: $i] :
( ( mem @ V0s @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ V0s ) )
=> ( ( ap @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a ) @ V0s )
= ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2Elongest__prefix__NIL,axiom,
! [A_27a: del,V0s: $i] :
( ( mem @ V0s @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ V0s ) )
=> ( ( ap @ ( c_2Erich__list_2Elongest__prefix @ A_27a ) @ V0s )
= ( c_2Elist_2ENIL @ A_27a ) ) ) ) ).
thf(conj_thm_2Erich__list_2ENIL__IN__common__prefixes,axiom,
! [A_27a: del,V0s: $i] :
( ( mem @ V0s @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( ap @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a ) @ V0s ) ) ) ) ).
thf(conj_thm_2Erich__list_2Elongest__prefix__EMPTY,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Erich__list_2Elongest__prefix @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27a ) ) )
= ( c_2Elist_2ENIL @ A_27a ) ) ).
thf(conj_thm_2Erich__list_2Elongest__prefix__SING,axiom,
! [A_27a: del,V0s: $i] :
( ( mem @ V0s @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( c_2Erich__list_2Elongest__prefix @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27a ) ) @ V0s ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
= V0s ) ) ).
thf(conj_thm_2Erich__list_2Ecommon__prefixes__PAIR,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ A_27b )
=> ! [V2xs: $i] :
( ( mem @ V2xs @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V3b: $i] :
( ( mem @ V3b @ A_27b )
=> ! [V4ys: $i] :
( ( mem @ V4ys @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ( ap @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27a ) ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) )
= ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
& ( ( ap @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27a ) ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) )
= ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27a ) ) ) )
& ( ( ap @ ( c_2Erich__list_2Ecommon__prefixes @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27b ) @ V1a ) @ V2xs ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27b ) @ V3b ) @ V4ys ) ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27b ) ) ) ) )
= ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( c_2Elist_2ENIL @ A_27b ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ ( ty_2Elist_2Elist @ A_27b ) @ bool ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27b ) @ V1a ) @ V3b ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ( ty_2Elist_2Elist @ A_27b ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( ap @ ( c_2Elist_2ECONS @ A_27b ) @ V1a ) ) @ ( ap @ ( c_2Erich__list_2Ecommon__prefixes @ A_27b ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27b ) ) @ V2xs ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27b ) ) @ V4ys ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27b ) ) ) ) ) ) ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27b ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2Elongest__prefix__PAIR,axiom,
! [A_27a: del,V0ys: $i] :
( ( mem @ V0ys @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1xs: $i] :
( ( mem @ V1xs @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ! [V3y: $i] :
( ( mem @ V3y @ A_27a )
=> ( ( ( ap @ ( c_2Erich__list_2Elongest__prefix @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27a ) ) @ V0ys ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) )
= ( c_2Elist_2ENIL @ A_27a ) )
& ( ( ap @ ( c_2Erich__list_2Elongest__prefix @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27a ) ) @ V1xs ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) )
= ( c_2Elist_2ENIL @ A_27a ) )
& ( ( ap @ ( c_2Erich__list_2Elongest__prefix @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ V1xs ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V3y ) @ V0ys ) ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V2x ) @ V3y ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x ) @ ( ap @ ( c_2Erich__list_2Elongest__prefix @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27a ) ) @ V1xs ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Elist_2Elist @ A_27a ) ) @ V0ys ) @ ( c_2Epred__set_2EEMPTY @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ECOUNT__LIST__GENLIST,axiom,
! [V0n: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Elist_2EGENLIST @ ty_2Enum_2Enum ) @ ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELENGTH__COUNT__LIST,axiom,
! [V0n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Enum_2Enum ) @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
= V0n ) ).
thf(conj_thm_2Erich__list_2EEL__COUNT__LIST,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Elist_2EEL @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
= V0m ) ) ).
thf(conj_thm_2Erich__list_2EMEM__COUNT__LIST,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ ty_2Enum_2Enum ) @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
thf(conj_thm_2Erich__list_2ECOUNT__LIST__SNOC,axiom,
( ( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( c_2Elist_2ENIL @ ty_2Enum_2Enum ) ) )
& ! [V0n: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ECOUNT__LIST__COUNT,axiom,
! [V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( c_2Elist_2ELIST__TO__SET @ ty_2Enum_2Enum ) @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( ap @ c_2Epred__set_2Ecount @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ).
thf(conj_thm_2Erich__list_2ECOUNT__LIST__ADD,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum
@ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ty_2Enum_2Enum ) @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
@ ( ap
@ ( ap @ ( c_2Elist_2EMAP @ ty_2Enum_2Enum @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2n_27: $i] : ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V2n_27 ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
@ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEL__DROP,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2l ) )
= ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ V2l ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESNOC__EL__TAKE,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) )
= ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ V1l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EZIP__TAKE__LEQ,axiom,
! [A_27a: del,A_27b: del,V0n: tp__ty_2Enum_2Enum,V1a: $i] :
( ( mem @ V1a @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2b: $i] :
( ( mem @ V2b @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1a ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1a ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27b ) @ V2b ) ) ) )
=> ( ( ap @ ( c_2Elist_2EZIP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V2b ) ) )
= ( ap @ ( ap @ ( c_2Elist_2ETAKE @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2EZIP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ V1a ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27b ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1a ) ) @ V2b ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EZIP__TAKE,axiom,
! [A_27a: del,A_27b: del,V0n: tp__ty_2Enum_2Enum,V1a: $i] :
( ( mem @ V1a @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2b: $i] :
( ( mem @ V2b @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1a ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1a ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27b ) @ V2b ) ) ) )
=> ( ( ap @ ( c_2Elist_2EZIP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V2b ) ) )
= ( ap @ ( ap @ ( c_2Elist_2ETAKE @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2EZIP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ V1a ) @ V2b ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEL__TAKE,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V2l ) )
= ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ V2l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EZIP__APPEND,axiom,
! [A_27a: del,A_27b: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V3d: $i] :
( ( mem @ V3d @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0a ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27b ) @ V1b ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2c ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27b ) @ V3d ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( c_2Elist_2EZIP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ V0a ) @ V1b ) ) ) @ ( ap @ ( c_2Elist_2EZIP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ V2c ) @ V3d ) ) )
= ( ap @ ( c_2Elist_2EZIP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0a ) @ V2c ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27b ) @ V1b ) @ V3d ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EAPPEND__ASSOC__CONS,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1h: $i] :
( ( mem @ V1h @ A_27a )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V3l3: $i] :
( ( mem @ V3l3 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1h ) @ V2l2 ) ) ) @ V3l3 )
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1h ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V2l2 ) @ V3l3 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EAPPEND__SNOC1,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ V1x ) @ V0l1 ) ) @ V2l2 )
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1x ) @ V2l2 ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFOLDL__MAP2,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27a )
=> ! [V2g: $i] :
( ( mem @ V2g @ ( arr @ A_27c @ A_27b ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27c ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a ) @ V0f ) @ V1e ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27c @ A_27b ) @ V2g ) @ V3l ) )
= ( ap
@ ( ap
@ ( ap @ ( c_2Elist_2EFOLDL @ A_27c @ A_27a )
@ ( lam @ A_27a
@ ^ [V4x: $i] :
( lam @ A_27c
@ ^ [V5y: $i] : ( ap @ ( ap @ V0f @ V4x ) @ ( ap @ V2g @ V5y ) ) ) ) )
@ V1e )
@ V3l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESPLITP__EVERY,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p
@ ( ap
@ ( ap @ ( c_2Elist_2EEVERY @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0P @ V2x ) ) ) )
@ V1l ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ESPLITP @ A_27a ) @ V0P ) @ V1l )
= ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ V1l ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMEM__FRONT,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ A_27a )
=> ! [V2y: $i] :
( ( mem @ V2y @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2y ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( c_2Elist_2EFRONT @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1e ) @ V0l ) ) ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V2y ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1e ) @ V0l ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EFRONT__APPEND,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2e: $i] :
( ( mem @ V2e @ A_27a )
=> ( ( ap @ ( c_2Elist_2EFRONT @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2e ) @ V1l2 ) ) )
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ ( ap @ ( c_2Elist_2EFRONT @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2e ) @ V1l2 ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEL__FRONT,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ ( ap @ ( c_2Elist_2EFRONT @ A_27a ) @ V0l ) ) ) )
& ~ ( p @ ( ap @ ( c_2Elist_2ENULL @ A_27a ) @ V0l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Elist_2EFRONT @ A_27a ) @ V0l ) )
= ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V0l ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMEM__LAST,axiom,
! [A_27a: del,V0e: $i] :
( ( mem @ V0e @ A_27a )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ ( c_2Elist_2ELAST @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V0e ) @ V1l ) ) ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V0e ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EDROP__CONS__EL,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMEM__LAST__FRONT,axiom,
! [A_27a: del,V0e: $i] :
( ( mem @ V0e @ A_27a )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2h: $i] :
( ( mem @ V2h @ A_27a )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0e ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) )
& ( V0e
!= ( ap @ ( c_2Elist_2ELAST @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2h ) @ V1l ) ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0e ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ ( ap @ ( c_2Elist_2EFRONT @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2h ) @ V1l ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELIST__ELEM__COUNT__THM,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del] :
( ! [V0e: $i] :
( ( mem @ V0e @ A_27a )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27a ) @ V0e ) @ ( c_2Elist_2ENIL @ A_27a ) ) )
= fo__c_2Enum_2E0 ) )
& ! [V1e: $i] :
( ( mem @ V1e @ A_27b )
=> ! [V2l1: $i] :
( ( mem @ V2l1 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V3l2: $i] :
( ( mem @ V3l2 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27b ) @ V1e ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27b ) @ V2l1 ) @ V3l2 ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27b ) @ V1e ) @ V2l1 ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27b ) @ V1e ) @ V3l2 ) ) ) ) ) ) )
& ! [V4e: $i] :
( ( mem @ V4e @ A_27c )
=> ! [V5h: $i] :
( ( mem @ V5h @ A_27c )
=> ! [V6l: $i] :
( ( mem @ V6l @ ( ty_2Elist_2Elist @ A_27c ) )
=> ( ( V5h = V4e )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27c ) @ V4e ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27c ) @ V5h ) @ V6l ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27c ) @ V4e ) @ V6l ) ) ) ) ) ) ) )
& ! [V7e: $i] :
( ( mem @ V7e @ A_27d )
=> ! [V8h: $i] :
( ( mem @ V8h @ A_27d )
=> ! [V9l: $i] :
( ( mem @ V9l @ ( ty_2Elist_2Elist @ A_27d ) )
=> ( ( V8h != V7e )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27d ) @ V7e ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27d ) @ V8h ) @ V9l ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27d ) @ V7e ) @ V9l ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELIST__ELEM__COUNT__MEM,axiom,
! [A_27a: del,V0e: $i] :
( ( mem @ V0e @ A_27a )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( ap @ ( ap @ ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27a ) @ V0e ) @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V0e ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELIST__TO__SET__EQ__SING,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1ls: $i] :
( ( mem @ V1ls @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1ls )
= ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ A_27a ) @ V0x ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
<=> ( ( V1ls
!= ( c_2Elist_2ENIL @ A_27a ) )
& ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V0x ) ) @ V1ls ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EREPLICATE__GENLIST,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1x )
= ( ap @ ( ap @ ( c_2Elist_2EGENLIST @ A_27a ) @ ( ap @ ( c_2Ecombin_2EK @ A_27a @ ty_2Enum_2Enum ) @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEL__REPLICATE,axiom,
! [A_27a: del,V0n1: tp__ty_2Enum_2Enum,V1n2: tp__ty_2Enum_2Enum,V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n1 ) ) @ ( inj__ty_2Enum_2Enum @ V1n2 ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n1 ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n2 ) ) @ V2x ) )
= V2x ) ) ) ).
thf(conj_thm_2Erich__list_2EEVERY__REPLICATE,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ bool ) )
=> ! [V1n: tp__ty_2Enum_2Enum,V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2x ) ) )
<=> ( ( V1n = fo__c_2Enum_2E0 )
| ( p @ ( ap @ V0f @ V2x ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EALL__DISTINCT__DROP,axiom,
! [A_27a: del,V0ls: $i] :
( ( mem @ V0ls @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( c_2Elist_2EALL__DISTINCT @ A_27a ) @ V0ls ) )
=> ( p @ ( ap @ ( c_2Elist_2EALL__DISTINCT @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V0ls ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMAP__SND__FILTER__NEQ,axiom,
! [A_27a: del,A_27b: del,V0z: $i] :
( ( mem @ V0z @ A_27a )
=> ! [V1ls: $i] :
( ( mem @ V1ls @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ ( c_2Epair_2ESND @ A_27b @ A_27a ) )
@ ( ap
@ ( ap @ ( c_2Elist_2EFILTER @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) )
@ ( ap @ ( c_2Epair_2EUNCURRY @ A_27b @ A_27a @ bool )
@ ( lam @ A_27b
@ ^ [V2x: $i] :
( lam @ A_27a
@ ^ [V3y: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V3y ) @ V0z ) ) ) ) ) )
@ V1ls ) )
= ( ap
@ ( ap @ ( c_2Elist_2EFILTER @ A_27a )
@ ( lam @ A_27a
@ ^ [V4y: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V0z ) @ V4y ) ) ) )
@ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ ( c_2Epair_2ESND @ A_27b @ A_27a ) ) @ V1ls ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMEM__SING__APPEND,axiom,
! [A_27a: del,V0d: $i] :
( ( mem @ V0d @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ A_27a )
=> ( ! [V2a: $i] :
( ( mem @ V2a @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V3c: $i] :
( ( mem @ V3c @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( V0d
!= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V2a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1b ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) @ V3c ) ) ) )
<=> ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ V1b ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V0d ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEL__LENGTH__APPEND__rwt,axiom,
! [A_27a: del,V0l2: $i] :
( ( mem @ V0l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum,V2l1: $i] :
( ( mem @ V2l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ~ ( p @ ( ap @ ( c_2Elist_2ENULL @ A_27a ) @ V0l2 ) )
& ( V1n
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l1 ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V2l1 ) @ V0l2 ) )
= ( ap @ ( c_2Elist_2EHD @ A_27a ) @ V0l2 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EMAP__FST__funs,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0funs: $i] :
( ( mem @ V0funs @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) ) ) )
=> ( ( ap
@ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) ) @ A_27a )
@ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27a )
@ ( lam @ A_27a
@ ^ [V1x: $i] :
( ap @ ( c_2Epair_2EUNCURRY @ A_27b @ A_27c @ A_27a )
@ ( lam @ A_27b
@ ^ [V2y: $i] :
( lam @ A_27c
@ ^ [V3z: $i] : V1x ) ) ) ) ) )
@ V0funs )
= ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) ) @ A_27a ) @ ( c_2Epair_2EFST @ A_27a @ ( ty_2Epair_2Eprod @ A_27b @ A_27c ) ) ) @ V0funs ) ) ) ).
thf(conj_thm_2Erich__list_2ETAKE__PRE__LENGTH,axiom,
! [A_27a: del,V0ls: $i] :
( ( mem @ V0ls @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( V0ls
!= ( c_2Elist_2ENIL @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0ls ) ) ) @ V0ls )
= ( ap @ ( c_2Elist_2EFRONT @ A_27a ) @ V0ls ) ) ) ) ).
thf(conj_thm_2Erich__list_2EDROP__LENGTH__NIL__rwt,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1m: tp__ty_2Enum_2Enum] :
( ( V1m
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V0l )
= ( c_2Elist_2ENIL @ A_27a ) ) ) ) ).
thf(conj_thm_2Erich__list_2EDROP__EL__CONS,axiom,
! [A_27a: del,V0ls: $i] :
( ( mem @ V0ls @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0ls ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V0ls )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V0ls ) ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V0ls ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ETAKE__EL__SNOC,axiom,
! [A_27a: del,V0ls: $i] :
( ( mem @ V0ls @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0ls ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V0ls )
= ( ap @ ( ap @ ( c_2Elist_2ESNOC @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V0ls ) ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V0ls ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EREVERSE__DROP,axiom,
! [A_27a: del,V0ls: $i] :
( ( mem @ V0ls @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0ls ) ) )
=> ( ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V0ls ) )
= ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0ls ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ V0ls ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELENGTH__FILTER__LESS,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1ls: $i] :
( ( mem @ V1ls @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ bool @ bool ) @ c_2Ebool_2E_7E ) @ V0P ) ) @ V1ls ) )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V0P ) @ V1ls ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1ls ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEVERY2__APPEND,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
=> ! [V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V3l3: $i] :
( ( mem @ V3l3 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V4l4: $i] :
( ( mem @ V4l4 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0R ) @ V1l1 ) @ V2l2 ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0R ) @ V3l3 ) @ V4l4 ) ) )
<=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0R ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1l1 ) @ V3l3 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27b ) @ V2l2 ) @ V4l4 ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l1 ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27b ) @ V2l2 ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V3l3 ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27b ) @ V4l4 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELIST__REL__APPEND__IMP,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
=> ! [V1xs: $i] :
( ( mem @ V1xs @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2ys: $i] :
( ( mem @ V2ys @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V3xs1: $i] :
( ( mem @ V3xs1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V4ys1: $i] :
( ( mem @ V4ys1 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0P ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1xs ) @ V3xs1 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27b ) @ V2ys ) @ V4ys1 ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1xs ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27b ) @ V2ys ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0P ) @ V1xs ) @ V2ys ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0P ) @ V3xs1 ) @ V4ys1 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEVERY2__APPEND__suff,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
=> ! [V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V3l3: $i] :
( ( mem @ V3l3 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V4l4: $i] :
( ( mem @ V4l4 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0R ) @ V1l1 ) @ V2l2 ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0R ) @ V3l3 ) @ V4l4 ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0R ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1l1 ) @ V3l3 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27b ) @ V2l2 ) @ V4l4 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEVERY2__DROP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
=> ! [V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V3n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0R ) @ V1l1 ) @ V2l2 ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0R ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V1l1 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V2l2 ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEVERY2__TAKE,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
=> ! [V1xs: $i] :
( ( mem @ V1xs @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2ys: $i] :
( ( mem @ V2ys @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V3n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0P ) @ V1xs ) @ V2ys ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0P ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V1xs ) ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V2ys ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELIST__REL__APPEND__SING,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
=> ! [V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2x1: $i] :
( ( mem @ V2x1 @ A_27a )
=> ! [V3l2: $i] :
( ( mem @ V3l2 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V4x2: $i] :
( ( mem @ V4x2 @ A_27b )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0R ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V1l1 ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V2x1 ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27b ) @ V3l2 ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27b ) @ V4x2 ) @ ( c_2Elist_2ENIL @ A_27b ) ) ) ) )
<=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0R ) @ V1l1 ) @ V3l2 ) )
& ( p @ ( ap @ ( ap @ V0R @ V2x1 ) @ V4x2 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELIST__REL__GENLIST,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V2l: tp__ty_2Enum_2Enum,V3g: $i] :
( ( mem @ V3g @ ( arr @ ty_2Enum_2Enum @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0P ) @ ( ap @ ( ap @ ( c_2Elist_2EGENLIST @ A_27a ) @ V1f ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EGENLIST @ A_27b ) @ V3g ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) ) )
<=> ! [V4i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4i ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) )
=> ( p @ ( ap @ ( ap @ V0P @ ( ap @ V1f @ ( inj__ty_2Enum_2Enum @ V4i ) ) ) @ ( ap @ V3g @ ( inj__ty_2Enum_2Enum @ V4i ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EALL__DISTINCT__MEM__ZIP__MAP,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
=> ! [V2ls: $i] :
( ( mem @ V2ls @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Elist_2EALL__DISTINCT @ A_27a ) @ V2ls ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1x ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( c_2Elist_2EZIP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ V2ls ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V0f ) @ V2ls ) ) ) ) ) )
<=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ A_27a ) @ ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V1x ) ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V2ls ) ) )
& ( ( ap @ ( c_2Epair_2ESND @ A_27a @ A_27b ) @ V1x )
= ( ap @ V0f @ ( ap @ ( c_2Epair_2EFST @ A_27a @ A_27b ) @ V1x ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EREVERSE__ZIP,axiom,
! [A_27a: del,A_27b: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l1 ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27b ) @ V1l2 ) ) )
=> ( ( ap @ ( c_2Elist_2EREVERSE @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( c_2Elist_2EZIP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ V0l1 ) @ V1l2 ) ) )
= ( ap @ ( c_2Elist_2EZIP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V0l1 ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27b ) @ V1l2 ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EEVERY2__REVERSE1,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
=> ! [V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0R ) @ V1l1 ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27b ) @ V2l2 ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0R ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l1 ) ) @ V2l2 ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELIST__REL__REVERSE__EQ,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
=> ! [V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0R ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l1 ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27b ) @ V2l2 ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0R ) @ V1l1 ) @ V2l2 ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2Eevery__count__list,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ ty_2Enum_2Enum ) @ V0P ) @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
<=> ! [V2m: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
=> ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2Ecount__list__sub1,axiom,
! [V0n: tp__ty_2Enum_2Enum] :
( ( V0n != fo__c_2Enum_2E0 )
=> ( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ c_2Enum_2ESUC ) @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2Eel__map__count,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1f: $i] :
( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V2m: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ty_2Enum_2Enum @ A_27a ) @ V1f ) @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) )
= ( ap @ V1f @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EZIP__COUNT__LIST,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( V0n
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l1 ) ) )
=> ( ( ap @ ( c_2Elist_2EZIP @ A_27a @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) @ V1l1 ) @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
= ( ap
@ ( ap @ ( c_2Elist_2EGENLIST @ ( ty_2Epair_2Eprod @ A_27a @ ty_2Enum_2Enum ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2n: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ V2n ) @ V1l1 ) ) @ V2n ) ) )
@ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l1 ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2Emap__replicate,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1n: tp__ty_2Enum_2Enum,V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2x ) )
= ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ V0f @ V2x ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EREPLICATE__NIL,axiom,
! [A_27a: del,V0x: tp__ty_2Enum_2Enum,V1y: $i] :
( ( mem @ V1y @ A_27a )
=> ( ( ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ V1y )
= ( c_2Elist_2ENIL @ A_27a ) )
<=> ( V0x = fo__c_2Enum_2E0 ) ) ) ).
thf(conj_thm_2Erich__list_2EREPLICATE__APPEND,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1a: $i] :
( ( mem @ V1a @ A_27a )
=> ! [V2m: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1a ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ V1a ) )
= ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ V1a ) ) ) ).
thf(conj_thm_2Erich__list_2EDROP__REPLICATE,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2a: $i] :
( ( mem @ V2a @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V2a ) )
= ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ V2a ) ) ) ).
thf(conj_thm_2Erich__list_2ELIST__REL__REPLICATE__same,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
=> ! [V1n: tp__ty_2Enum_2Enum,V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ! [V3y: $i] :
( ( mem @ V3y @ A_27b )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0P ) @ ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2x ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2EREPLICATE @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V3y ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
=> ( p @ ( ap @ ( ap @ V0P @ V2x ) @ V3y ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2Etake__drop__partition,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V2l ) ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V2l ) ) )
= ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V2l ) ) ) ) ).
thf(conj_thm_2Erich__list_2Eall__distinct__count__list,axiom,
! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( c_2Elist_2EALL__DISTINCT @ ty_2Enum_2Enum ) @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
thf(conj_thm_2Erich__list_2Elist__rel__lastn,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
=> ! [V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V3n: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l1 ) ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0f ) @ V1l1 ) @ V2l2 ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V1l1 ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V2l2 ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2Elist__rel__butlastn,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
=> ! [V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V3n: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l1 ) ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0f ) @ V1l1 ) @ V2l2 ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V1l1 ) ) @ ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V2l2 ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EUNIQUE__LIST__ELEM__COUNT,axiom,
! [A_27a: del,V0e: $i] :
( ( mem @ V0e @ A_27a )
=> ! [V1L: $i] :
( ( mem @ V1L @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EUNIQUE @ A_27a ) @ V0e ) @ V1L ) )
<=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27a ) @ V0e ) @ V1L ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ECOUNT__LIST__compute,axiom,
! [V0n: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ c_2Erich__list_2ECOUNT__LIST @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Erich__list_2ECOUNT__LIST__AUX @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( c_2Elist_2ENIL @ ty_2Enum_2Enum ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESPLITP__compute,axiom,
! [A_27a: del] :
( ( c_2Erich__list_2ESPLITP @ A_27a )
= ( ap @ ( c_2Erich__list_2ESPLITP__AUX @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ).
thf(conj_thm_2Erich__list_2EIS__SUFFIX__compute,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Erich__list_2EIS__SUFFIX @ A_27a ) @ V0l1 ) @ V1l2 ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l2 ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V0l1 ) ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ESEG__compute,axiom,
! [A_27a: del] :
( ! [V0k: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0k ) ) @ V1l )
= ( c_2Elist_2ENIL @ A_27a ) ) )
& ! [V2m: tp__ty_2Enum_2Enum,V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ! [V4l: $i] :
( ( mem @ V4l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V3x ) @ V4l ) )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V3x ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V4l ) ) ) ) )
& ! [V5m: tp__ty_2Enum_2Enum,V6x: $i] :
( ( mem @ V6x @ A_27a )
=> ! [V7l: $i] :
( ( mem @ V7l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V5m ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V6x ) @ V7l ) )
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V6x ) @ ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V5m ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V7l ) ) ) ) )
& ! [V8m: tp__ty_2Enum_2Enum,V9k: tp__ty_2Enum_2Enum,V10x: $i] :
( ( mem @ V10x @ A_27a )
=> ! [V11l: $i] :
( ( mem @ V11l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V8m ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V9k ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V10x ) @ V11l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V8m ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V9k ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V11l ) ) ) )
& ! [V12m: tp__ty_2Enum_2Enum,V13k: tp__ty_2Enum_2Enum,V14x: $i] :
( ( mem @ V14x @ A_27a )
=> ! [V15l: $i] :
( ( mem @ V15l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V12m ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V13k ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V14x ) @ V15l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V12m ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V13k ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V15l ) ) ) )
& ! [V16m: tp__ty_2Enum_2Enum,V17k: tp__ty_2Enum_2Enum,V18x: $i] :
( ( mem @ V18x @ A_27a )
=> ! [V19l: $i] :
( ( mem @ V19l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V16m ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V17k ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V18x ) @ V19l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V16m ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V17k ) ) ) ) @ V19l ) ) ) )
& ! [V20m: tp__ty_2Enum_2Enum,V21k: tp__ty_2Enum_2Enum,V22x: $i] :
( ( mem @ V22x @ A_27a )
=> ! [V23l: $i] :
( ( mem @ V23l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V20m ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V21k ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V22x ) @ V23l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Erich__list_2ESEG @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V20m ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V21k ) ) ) ) @ V23l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2EBUTLASTN__compute,axiom,
! [A_27a: del,V0longer_20than_20list: $i] :
( ( mem @ V0longer_20than_20list @ bool )
=> ! [V1n: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2l )
= ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ A_27a ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3m: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V3m ) ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V3m ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ V2l ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EFAIL @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ bool ) @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) ) @ V0longer_20than_20list ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2l ) ) ) )
@ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) ) ) ) ).
thf(conj_thm_2Erich__list_2ELASTN__compute,axiom,
! [A_27a: del,V0longer_20than_20list: $i] :
( ( mem @ V0longer_20than_20list @ bool )
=> ! [V1n: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Erich__list_2ELASTN @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2l )
= ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ A_27a ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3m: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V3m ) ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V3m ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ V2l ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EFAIL @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ bool ) @ ( c_2Erich__list_2ELASTN @ A_27a ) ) @ V0longer_20than_20list ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2l ) ) ) )
@ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) ) ) ) ).
%------------------------------------------------------------------------------