ITP001 Axioms: ITP037^7.ax
%------------------------------------------------------------------------------
% File : ITP037^7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : rich_list.ax [Gau19]
% : HL4037^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 484 ( 153 unt; 109 typ; 0 def)
% Number of atoms : 935 ( 384 equ; 26 cnn)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 6744 ( 26 ~; 8 |; 81 &;6397 @)
% ( 30 <=>; 202 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg;6397 nst)
% Number of types : 3 ( 2 usr)
% Number of type conns : 432 ( 432 >; 0 *; 0 +; 0 <<)
% Number of symbols : 109 ( 107 usr; 5 con; 0-6 aty)
% Number of variables : 1588 ( 78 ^1398 !; 5 ?;1588 :)
% ( 107 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: $tType > $tType > $tType ).
thf(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: $tType > $tType > $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Earithmetic_2E_2B,type,
c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Epair_2E_2C,type,
c_2Epair_2E_2C:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ).
thf(c_2Earithmetic_2E_2D,type,
c_2Earithmetic_2E_2D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Enum_2E0,type,
c_2Enum_2E0: tyop_2Enum_2Enum ).
thf(c_2Eprim__rec_2E_3C,type,
c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Earithmetic_2E_3C_3D,type,
c_2Earithmetic_2E_3C_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Emin_2E_3D,type,
c_2Emin_2E_3D:
!>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
thf(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(c_2Earithmetic_2E_3E,type,
c_2Earithmetic_2E_3E: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Emin_2E_40,type,
c_2Emin_2E_40:
!>[A_27a: $tType] : ( ( A_27a > $o ) > A_27a ) ).
thf(c_2Elist_2EALL__DISTINCT,type,
c_2Elist_2EALL__DISTINCT:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).
thf(c_2Erich__list_2EAND__EL,type,
c_2Erich__list_2EAND__EL: ( tyop_2Elist_2Elist @ $o ) > $o ).
thf(c_2Elist_2EAPPEND,type,
c_2Elist_2EAPPEND:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Ecombin_2EASSOC,type,
c_2Ecombin_2EASSOC:
!>[A_27a: $tType] : ( ( A_27a > A_27a > A_27a ) > $o ) ).
thf(c_2Epred__set_2EBIGINTER,type,
c_2Epred__set_2EBIGINTER:
!>[A_27a: $tType] : ( ( ( A_27a > $o ) > $o ) > A_27a > $o ) ).
thf(c_2Earithmetic_2EBIT1,type,
c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EBIT2,type,
c_2Earithmetic_2EBIT2: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Erich__list_2EBUTLASTN,type,
c_2Erich__list_2EBUTLASTN:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Ecombin_2ECOMM,type,
c_2Ecombin_2ECOMM:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27a > A_27b ) > $o ) ).
thf(c_2Ebool_2ECOND,type,
c_2Ebool_2ECOND:
!>[A_27a: $tType] : ( $o > A_27a > A_27a > A_27a ) ).
thf(c_2Elist_2ECONS,type,
c_2Elist_2ECONS:
!>[A_27a: $tType] : ( A_27a > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Erich__list_2ECOUNT__LIST,type,
c_2Erich__list_2ECOUNT__LIST: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ).
thf(c_2Erich__list_2ECOUNT__LIST__AUX,type,
c_2Erich__list_2ECOUNT__LIST__AUX: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ).
thf(c_2Elist_2EDROP,type,
c_2Elist_2EDROP:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Elist_2EEL,type,
c_2Elist_2EEL:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > A_27a ) ).
thf(c_2Erich__list_2EELL,type,
c_2Erich__list_2EELL:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > A_27a ) ).
thf(c_2Epred__set_2EEMPTY,type,
c_2Epred__set_2EEMPTY:
!>[A_27a: $tType] : ( A_27a > $o ) ).
thf(c_2Elist_2EEVERY,type,
c_2Elist_2EEVERY:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).
thf(c_2Elist_2EEXISTS,type,
c_2Elist_2EEXISTS:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).
thf(c_2Ebool_2EF,type,
c_2Ebool_2EF: $o ).
thf(c_2Ecombin_2EFAIL,type,
c_2Ecombin_2EFAIL:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > A_27a ) ).
thf(c_2Ecombin_2EFCOMM,type,
c_2Ecombin_2EFCOMM:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( A_27a > A_27b > A_27a ) > ( A_27c > A_27a > A_27a ) > $o ) ).
thf(c_2Elist_2EFILTER,type,
c_2Elist_2EFILTER:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Epred__set_2EFINITE,type,
c_2Epred__set_2EFINITE:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Elist_2EFLAT,type,
c_2Elist_2EFLAT:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ A_27a ) ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Elist_2EFOLDL,type,
c_2Elist_2EFOLDL:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27b > A_27a > A_27b ) > A_27b > ( tyop_2Elist_2Elist @ A_27a ) > A_27b ) ).
thf(c_2Elist_2EFOLDR,type,
c_2Elist_2EFOLDR:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b > A_27b ) > A_27b > ( tyop_2Elist_2Elist @ A_27a ) > A_27b ) ).
thf(c_2Elist_2EFRONT,type,
c_2Elist_2EFRONT:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Epair_2EFST,type,
c_2Epair_2EFST:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > A_27a ) ).
thf(c_2Earithmetic_2EFUNPOW,type,
c_2Earithmetic_2EFUNPOW:
!>[A_27a: $tType] : ( ( A_27a > A_27a ) > tyop_2Enum_2Enum > A_27a > A_27a ) ).
thf(c_2Elist_2EGENLIST,type,
c_2Elist_2EGENLIST:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum > A_27a ) > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Epred__set_2EGSPEC,type,
c_2Epred__set_2EGSPEC:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27b > ( tyop_2Epair_2Eprod @ A_27a @ $o ) ) > A_27a > $o ) ).
thf(c_2Elist_2EHD,type,
c_2Elist_2EHD:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > A_27a ) ).
thf(c_2Ecombin_2EI,type,
c_2Ecombin_2EI:
!>[A_27a: $tType] : ( A_27a > A_27a ) ).
thf(c_2Epred__set_2EIMAGE,type,
c_2Epred__set_2EIMAGE:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > ( A_27a > $o ) > A_27b > $o ) ).
thf(c_2Ebool_2EIN,type,
c_2Ebool_2EIN:
!>[A_27a: $tType] : ( A_27a > ( A_27a > $o ) > $o ) ).
thf(c_2Epred__set_2EINSERT,type,
c_2Epred__set_2EINSERT:
!>[A_27a: $tType] : ( A_27a > ( A_27a > $o ) > A_27a > $o ) ).
thf(c_2Erich__list_2EIS__SUBLIST,type,
c_2Erich__list_2EIS__SUBLIST:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).
thf(c_2Erich__list_2EIS__SUFFIX,type,
c_2Erich__list_2EIS__SUFFIX:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).
thf(c_2Ecombin_2EK,type,
c_2Ecombin_2EK:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > A_27a ) ).
thf(c_2Elist_2ELAST,type,
c_2Elist_2ELAST:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > A_27a ) ).
thf(c_2Erich__list_2ELASTN,type,
c_2Erich__list_2ELASTN:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Ecombin_2ELEFT__ID,type,
c_2Ecombin_2ELEFT__ID:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b > A_27b ) > A_27a > $o ) ).
thf(c_2Elist_2ELENGTH,type,
c_2Elist_2ELENGTH:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > tyop_2Enum_2Enum ) ).
thf(c_2Ebool_2ELET,type,
c_2Ebool_2ELET:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > A_27a > A_27b ) ).
thf(c_2Erich__list_2ELIST__ELEM__COUNT,type,
c_2Erich__list_2ELIST__ELEM__COUNT:
!>[A_27a: $tType] : ( A_27a > ( tyop_2Elist_2Elist @ A_27a ) > tyop_2Enum_2Enum ) ).
thf(c_2Elist_2ELIST__REL,type,
c_2Elist_2ELIST__REL:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27b ) > $o ) ).
thf(c_2Elist_2ELIST__TO__SET,type,
c_2Elist_2ELIST__TO__SET:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > A_27a > $o ) ).
thf(c_2Elist_2ELUPDATE,type,
c_2Elist_2ELUPDATE:
!>[A_27a: $tType] : ( A_27a > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Elist_2EMAP,type,
c_2Elist_2EMAP:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27b ) ) ).
thf(c_2Ecombin_2EMONOID,type,
c_2Ecombin_2EMONOID:
!>[A_27a: $tType] : ( ( A_27a > A_27a > A_27a ) > A_27a > $o ) ).
thf(c_2Elist_2ENIL,type,
c_2Elist_2ENIL:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist @ A_27a ) ).
thf(c_2Elist_2ENULL,type,
c_2Elist_2ENULL:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).
thf(c_2Earithmetic_2ENUMERAL,type,
c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Erich__list_2EOR__EL,type,
c_2Erich__list_2EOR__EL: ( tyop_2Elist_2Elist @ $o ) > $o ).
thf(c_2Eprim__rec_2EPRE,type,
c_2Eprim__rec_2EPRE: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Erich__list_2EPREFIX,type,
c_2Erich__list_2EPREFIX:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Erich__list_2EREPLICATE,type,
c_2Erich__list_2EREPLICATE:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > A_27a > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Elist_2EREVERSE,type,
c_2Elist_2EREVERSE:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Ecombin_2ERIGHT__ID,type,
c_2Ecombin_2ERIGHT__ID:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b > A_27a ) > A_27b > $o ) ).
thf(c_2Erich__list_2ESCANL,type,
c_2Erich__list_2ESCANL:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27b > A_27a > A_27b ) > A_27b > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27b ) ) ).
thf(c_2Erich__list_2ESCANR,type,
c_2Erich__list_2ESCANR:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b > A_27b ) > A_27b > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27b ) ) ).
thf(c_2Erich__list_2ESEG,type,
c_2Erich__list_2ESEG:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Epair_2ESND,type,
c_2Epair_2ESND:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > A_27b ) ).
thf(c_2Elist_2ESNOC,type,
c_2Elist_2ESNOC:
!>[A_27a: $tType] : ( A_27a > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Erich__list_2ESPLITL,type,
c_2Erich__list_2ESPLITL:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ).
thf(c_2Erich__list_2ESPLITP,type,
c_2Erich__list_2ESPLITP:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ).
thf(c_2Erich__list_2ESPLITP__AUX,type,
c_2Erich__list_2ESPLITP__AUX:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > ( A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ).
thf(c_2Erich__list_2ESPLITR,type,
c_2Erich__list_2ESPLITR:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ).
thf(c_2Enum_2ESUC,type,
c_2Enum_2ESUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Erich__list_2ESUFFIX,type,
c_2Erich__list_2ESUFFIX:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Elist_2ESUM,type,
c_2Elist_2ESUM: ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ET,type,
c_2Ebool_2ET: $o ).
thf(c_2Elist_2ETAKE,type,
c_2Elist_2ETAKE:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Elist_2ETL,type,
c_2Elist_2ETL:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Erich__list_2ETL__T,type,
c_2Erich__list_2ETL__T:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Epair_2EUNCURRY,type,
c_2Epair_2EUNCURRY:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( A_27a > A_27b > A_27c ) > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > A_27c ) ).
thf(c_2Elist_2EUNIQUE,type,
c_2Elist_2EUNIQUE:
!>[A_27a: $tType] : ( A_27a > ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).
thf(c_2Elist_2EUNZIP,type,
c_2Elist_2EUNZIP:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) > ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) ).
thf(c_2Erich__list_2EUNZIP__FST,type,
c_2Erich__list_2EUNZIP__FST:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Erich__list_2EUNZIP__SND,type,
c_2Erich__list_2EUNZIP__SND:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Earithmetic_2EZERO,type,
c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).
thf(c_2Elist_2EZIP,type,
c_2Elist_2EZIP:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) ) > ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Erich__list_2Ecommon__prefixes,type,
c_2Erich__list_2Ecommon__prefixes:
!>[A_27a: $tType] : ( ( ( tyop_2Elist_2Elist @ A_27a ) > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).
thf(c_2Epred__set_2Ecount,type,
c_2Epred__set_2Ecount: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Elist_2EisPREFIX,type,
c_2Elist_2EisPREFIX:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).
thf(c_2Epred__set_2Eis__measure__maximal,type,
c_2Epred__set_2Eis__measure__maximal:
!>[A_27a: $tType] : ( ( A_27a > tyop_2Enum_2Enum ) > ( A_27a > $o ) > A_27a > $o ) ).
thf(c_2Erich__list_2Elongest__prefix,type,
c_2Erich__list_2Elongest__prefix:
!>[A_27a: $tType] : ( ( ( tyop_2Elist_2Elist @ A_27a ) > $o ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Ecombin_2Eo,type,
c_2Ecombin_2Eo:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( A_27c > A_27b ) > ( A_27a > A_27c ) > A_27a > A_27b ) ).
thf(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $o > $o ).
thf(logicdef_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(logicdef_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(logicdef_2E_7E,axiom,
! [V0: $o] :
( ( c_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(logicdef_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0: A_27a,V1: A_27a] :
( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
<=> ( V0 = V1 ) ) ).
thf(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_21 @ A_27a @ V0f )
<=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_3F @ A_27a @ V0f )
<=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(thm_2Erich__list_2Elongest__prefix__def,axiom,
! [A_27a: $tType,V0s: ( tyop_2Elist_2Elist @ A_27a ) > $o] :
( ( c_2Erich__list_2Elongest__prefix @ A_27a @ V0s )
= ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Emin_2E_3D @ ( ( tyop_2Elist_2Elist @ A_27a ) > $o ) @ V0s @ ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( c_2Elist_2ENIL @ A_27a )
@ ( c_2Emin_2E_40 @ ( tyop_2Elist_2Elist @ A_27a )
@ ^ [V1x: tyop_2Elist_2Elist @ A_27a] : ( c_2Epred__set_2Eis__measure__maximal @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ELENGTH @ A_27a ) @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a @ V0s ) @ V1x ) ) ) ) ).
thf(thm_2Erich__list_2Ecommon__prefixes__def,axiom,
! [A_27a: $tType,V0s: ( tyop_2Elist_2Elist @ A_27a ) > $o] :
( ( c_2Erich__list_2Ecommon__prefixes @ A_27a @ V0s )
= ( c_2Epred__set_2EGSPEC @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a )
@ ^ [V1p: tyop_2Elist_2Elist @ A_27a] :
( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ $o @ V1p
@ ( c_2Ebool_2E_21 @ ( tyop_2Elist_2Elist @ A_27a )
@ ^ [V2m: tyop_2Elist_2Elist @ A_27a] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Ebool_2EIN @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m @ V0s ) @ ( c_2Elist_2EisPREFIX @ A_27a @ V1p @ V2m ) ) ) ) ) ) ).
thf(thm_2Erich__list_2EELL,axiom,
! [A_27a: $tType] :
( ! [V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EELL @ A_27a @ c_2Enum_2E0 @ V0l )
= ( c_2Elist_2ELAST @ A_27a @ V0l ) )
& ! [V1n: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EELL @ A_27a @ ( c_2Enum_2ESUC @ V1n ) @ V2l )
= ( c_2Erich__list_2EELL @ A_27a @ V1n @ ( c_2Elist_2EFRONT @ A_27a @ V2l ) ) ) ) ).
thf(thm_2Erich__list_2EREPLICATE,axiom,
! [A_27a: $tType] :
( ! [V0x: A_27a] :
( ( c_2Erich__list_2EREPLICATE @ A_27a @ c_2Enum_2E0 @ V0x )
= ( c_2Elist_2ENIL @ A_27a ) )
& ! [V1n: tyop_2Enum_2Enum,V2x: A_27a] :
( ( c_2Erich__list_2EREPLICATE @ A_27a @ ( c_2Enum_2ESUC @ V1n ) @ V2x )
= ( c_2Elist_2ECONS @ A_27a @ V2x @ ( c_2Erich__list_2EREPLICATE @ A_27a @ V1n @ V2x ) ) ) ) ).
thf(thm_2Erich__list_2ESCANL,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0f: A_27b > A_27a > A_27b,V1e: A_27b] :
( ( c_2Erich__list_2ESCANL @ A_27a @ A_27b @ V0f @ V1e @ ( c_2Elist_2ENIL @ A_27a ) )
= ( c_2Elist_2ECONS @ A_27b @ V1e @ ( c_2Elist_2ENIL @ A_27b ) ) )
& ! [V2f: A_27b > A_27a > A_27b,V3e: A_27b,V4x: A_27a,V5l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ESCANL @ A_27a @ A_27b @ V2f @ V3e @ ( c_2Elist_2ECONS @ A_27a @ V4x @ V5l ) )
= ( c_2Elist_2ECONS @ A_27b @ V3e @ ( c_2Erich__list_2ESCANL @ A_27a @ A_27b @ V2f @ ( V2f @ V3e @ V4x ) @ V5l ) ) ) ) ).
thf(thm_2Erich__list_2ESCANR,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0f: A_27a > A_27b > A_27b,V1e: A_27b] :
( ( c_2Erich__list_2ESCANR @ A_27a @ A_27b @ V0f @ V1e @ ( c_2Elist_2ENIL @ A_27a ) )
= ( c_2Elist_2ECONS @ A_27b @ V1e @ ( c_2Elist_2ENIL @ A_27b ) ) )
& ! [V2f: A_27a > A_27b > A_27b,V3e: A_27b,V4x: A_27a,V5l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ESCANR @ A_27a @ A_27b @ V2f @ V3e @ ( c_2Elist_2ECONS @ A_27a @ V4x @ V5l ) )
= ( c_2Elist_2ECONS @ A_27b @ ( V2f @ V4x @ ( c_2Elist_2EHD @ A_27b @ ( c_2Erich__list_2ESCANR @ A_27a @ A_27b @ V2f @ V3e @ V5l ) ) ) @ ( c_2Erich__list_2ESCANR @ A_27a @ A_27b @ V2f @ V3e @ V5l ) ) ) ) ).
thf(thm_2Erich__list_2ESPLITP,axiom,
! [A_27a: $tType] :
( ! [V0P: A_27a > $o] :
( ( c_2Erich__list_2ESPLITP @ A_27a @ V0P @ ( c_2Elist_2ENIL @ A_27a ) )
= ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) ) )
& ! [V1P: A_27a > $o,V2x: A_27a,V3l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ESPLITP @ A_27a @ V1P @ ( c_2Elist_2ECONS @ A_27a @ V2x @ V3l ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( V1P @ V2x ) @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) @ ( c_2Elist_2ECONS @ A_27a @ V2x @ V3l ) ) @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS @ A_27a @ V2x @ ( c_2Epair_2EFST @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Erich__list_2ESPLITP @ A_27a @ V1P @ V3l ) ) ) @ ( c_2Epair_2ESND @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Erich__list_2ESPLITP @ A_27a @ V1P @ V3l ) ) ) ) ) ) ).
thf(thm_2Erich__list_2ESPLITP__AUX__def,axiom,
! [A_27a: $tType] :
( ! [V0acc: tyop_2Elist_2Elist @ A_27a,V1P: A_27a > $o] :
( ( c_2Erich__list_2ESPLITP__AUX @ A_27a @ V0acc @ V1P @ ( c_2Elist_2ENIL @ A_27a ) )
= ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) @ V0acc @ ( c_2Elist_2ENIL @ A_27a ) ) )
& ! [V2acc: tyop_2Elist_2Elist @ A_27a,V3P: A_27a > $o,V4h: A_27a,V5t: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ESPLITP__AUX @ A_27a @ V2acc @ V3P @ ( c_2Elist_2ECONS @ A_27a @ V4h @ V5t ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( V3P @ V4h ) @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) @ V2acc @ ( c_2Elist_2ECONS @ A_27a @ V4h @ V5t ) ) @ ( c_2Erich__list_2ESPLITP__AUX @ A_27a @ ( c_2Elist_2EAPPEND @ A_27a @ V2acc @ ( c_2Elist_2ECONS @ A_27a @ V4h @ ( c_2Elist_2ENIL @ A_27a ) ) ) @ V3P @ V5t ) ) ) ) ).
thf(thm_2Erich__list_2ESPLITL__def,axiom,
! [A_27a: $tType,V0P: A_27a > $o] :
( ( c_2Erich__list_2ESPLITL @ A_27a @ V0P )
= ( c_2Erich__list_2ESPLITP @ A_27a @ ( c_2Ecombin_2Eo @ A_27a @ $o @ $o @ c_2Ebool_2E_7E @ V0P ) ) ) ).
thf(thm_2Erich__list_2ESPLITR__def,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ESPLITR @ A_27a @ V0P @ V1l )
= ( c_2Ebool_2ELET @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) )
@ ( c_2Epair_2EUNCURRY @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) )
@ ^ [V2a: tyop_2Elist_2Elist @ A_27a,V3b: tyop_2Elist_2Elist @ A_27a] : ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EREVERSE @ A_27a @ V3b ) @ ( c_2Elist_2EREVERSE @ A_27a @ V2a ) ) )
@ ( c_2Erich__list_2ESPLITP @ A_27a @ ( c_2Ecombin_2Eo @ A_27a @ $o @ $o @ c_2Ebool_2E_7E @ V0P ) @ ( c_2Elist_2EREVERSE @ A_27a @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2EPREFIX__DEF,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EPREFIX @ A_27a @ V0P @ V1l )
= ( c_2Epair_2EFST @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Erich__list_2ESPLITP @ A_27a @ ( c_2Ecombin_2Eo @ A_27a @ $o @ $o @ c_2Ebool_2E_7E @ V0P ) @ V1l ) ) ) ).
thf(thm_2Erich__list_2ESUFFIX__DEF,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ESUFFIX @ A_27a @ V0P @ V1l )
= ( c_2Elist_2EFOLDL @ A_27a @ ( tyop_2Elist_2Elist @ A_27a )
@ ^ [V2l_27: tyop_2Elist_2Elist @ A_27a,V3x: A_27a] : ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ A_27a ) @ ( V0P @ V3x ) @ ( c_2Elist_2ESNOC @ A_27a @ V3x @ V2l_27 ) @ ( c_2Elist_2ENIL @ A_27a ) )
@ ( c_2Elist_2ENIL @ A_27a )
@ V1l ) ) ).
thf(thm_2Erich__list_2EAND__EL__DEF,axiom,
( c_2Erich__list_2EAND__EL
= ( c_2Elist_2EEVERY @ $o @ ( c_2Ecombin_2EI @ $o ) ) ) ).
thf(thm_2Erich__list_2EOR__EL__DEF,axiom,
( c_2Erich__list_2EOR__EL
= ( c_2Elist_2EEXISTS @ $o @ ( c_2Ecombin_2EI @ $o ) ) ) ).
thf(thm_2Erich__list_2EUNZIP__FST__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0l: tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b )] :
( ( c_2Erich__list_2EUNZIP__FST @ A_27a @ A_27b @ V0l )
= ( c_2Epair_2EFST @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EUNZIP @ A_27a @ A_27b @ V0l ) ) ) ).
thf(thm_2Erich__list_2EUNZIP__SND__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,V0l: tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a )] :
( ( c_2Erich__list_2EUNZIP__SND @ A_27a @ A_27b @ V0l )
= ( c_2Epair_2ESND @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EUNZIP @ A_27b @ A_27a @ V0l ) ) ) ).
thf(thm_2Erich__list_2ELIST__ELEM__COUNT__DEF,axiom,
! [A_27a: $tType,V0e: A_27a,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27a @ V0e @ V1l )
= ( c_2Elist_2ELENGTH @ A_27a
@ ( c_2Elist_2EFILTER @ A_27a
@ ^ [V2x: A_27a] : ( c_2Emin_2E_3D @ A_27a @ V2x @ V0e )
@ V1l ) ) ) ).
thf(thm_2Erich__list_2ECOUNT__LIST__def,axiom,
( ( ( c_2Erich__list_2ECOUNT__LIST @ c_2Enum_2E0 )
= ( c_2Elist_2ENIL @ tyop_2Enum_2Enum ) )
& ! [V0n: tyop_2Enum_2Enum] :
( ( c_2Erich__list_2ECOUNT__LIST @ ( c_2Enum_2ESUC @ V0n ) )
= ( c_2Elist_2ECONS @ tyop_2Enum_2Enum @ c_2Enum_2E0 @ ( c_2Elist_2EMAP @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Enum_2ESUC @ ( c_2Erich__list_2ECOUNT__LIST @ V0n ) ) ) ) ) ).
thf(thm_2Erich__list_2ECOUNT__LIST__AUX__def,axiom,
( ! [V0l: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
( ( c_2Erich__list_2ECOUNT__LIST__AUX @ c_2Enum_2E0 @ V0l )
= V0l )
& ! [V1n: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
( ( c_2Erich__list_2ECOUNT__LIST__AUX @ ( c_2Enum_2ESUC @ V1n ) @ V2l )
= ( c_2Erich__list_2ECOUNT__LIST__AUX @ V1n @ ( c_2Elist_2ECONS @ tyop_2Enum_2Enum @ V1n @ V2l ) ) ) ) ).
thf(thm_2Erich__list_2ETL__T__def,axiom,
! [A_27a: $tType] :
( ( ( c_2Erich__list_2ETL__T @ A_27a @ ( c_2Elist_2ENIL @ A_27a ) )
= ( c_2Elist_2ENIL @ A_27a ) )
& ! [V0h: A_27a,V1t: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ETL__T @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V0h @ V1t ) )
= V1t ) ) ).
thf(thm_2Erich__list_2ELASTN__def,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1xs: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ELASTN @ A_27a @ V0n @ V1xs )
= ( c_2Elist_2EREVERSE @ A_27a @ ( c_2Elist_2ETAKE @ A_27a @ V0n @ ( c_2Elist_2EREVERSE @ A_27a @ V1xs ) ) ) ) ).
thf(thm_2Erich__list_2EBUTLASTN__def,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1xs: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0n @ V1xs )
= ( c_2Elist_2EREVERSE @ A_27a @ ( c_2Elist_2EDROP @ A_27a @ V0n @ ( c_2Elist_2EREVERSE @ A_27a @ V1xs ) ) ) ) ).
thf(thm_2Erich__list_2EIS__SUBLIST,axiom,
! [A_27a: $tType] :
( ! [V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EIS__SUBLIST @ A_27a @ V0l @ ( c_2Elist_2ENIL @ A_27a ) )
= c_2Ebool_2ET )
& ! [V1x: A_27a,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EIS__SUBLIST @ A_27a @ ( c_2Elist_2ENIL @ A_27a ) @ ( c_2Elist_2ECONS @ A_27a @ V1x @ V2l ) )
= c_2Ebool_2EF )
& ! [V3x1: A_27a,V4l1: tyop_2Elist_2Elist @ A_27a,V5x2: A_27a,V6l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EIS__SUBLIST @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V3x1 @ V4l1 ) @ ( c_2Elist_2ECONS @ A_27a @ V5x2 @ V6l2 ) )
<=> ( ( ( V3x1 = V5x2 )
& ( c_2Elist_2EisPREFIX @ A_27a @ V6l2 @ V4l1 ) )
| ( c_2Erich__list_2EIS__SUBLIST @ A_27a @ V4l1 @ ( c_2Elist_2ECONS @ A_27a @ V5x2 @ V6l2 ) ) ) ) ) ).
thf(thm_2Erich__list_2ESEG,axiom,
! [A_27a: $tType] :
( ! [V0k: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ESEG @ A_27a @ c_2Enum_2E0 @ V0k @ V1l )
= ( c_2Elist_2ENIL @ A_27a ) )
& ! [V2m: tyop_2Enum_2Enum,V3x: A_27a,V4l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Enum_2ESUC @ V2m ) @ c_2Enum_2E0 @ ( c_2Elist_2ECONS @ A_27a @ V3x @ V4l ) )
= ( c_2Elist_2ECONS @ A_27a @ V3x @ ( c_2Erich__list_2ESEG @ A_27a @ V2m @ c_2Enum_2E0 @ V4l ) ) )
& ! [V5m: tyop_2Enum_2Enum,V6k: tyop_2Enum_2Enum,V7x: A_27a,V8l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Enum_2ESUC @ V5m ) @ ( c_2Enum_2ESUC @ V6k ) @ ( c_2Elist_2ECONS @ A_27a @ V7x @ V8l ) )
= ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Enum_2ESUC @ V5m ) @ V6k @ V8l ) ) ) ).
thf(thm_2Erich__list_2EIS__SUFFIX,axiom,
! [A_27a: $tType] :
( ! [V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EIS__SUFFIX @ A_27a @ V0l @ ( c_2Elist_2ENIL @ A_27a ) )
= c_2Ebool_2ET )
& ! [V1x: A_27a,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EIS__SUFFIX @ A_27a @ ( c_2Elist_2ENIL @ A_27a ) @ ( c_2Elist_2ESNOC @ A_27a @ V1x @ V2l ) )
= c_2Ebool_2EF )
& ! [V3x1: A_27a,V4l1: tyop_2Elist_2Elist @ A_27a,V5x2: A_27a,V6l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EIS__SUFFIX @ A_27a @ ( c_2Elist_2ESNOC @ A_27a @ V3x1 @ V4l1 ) @ ( c_2Elist_2ESNOC @ A_27a @ V5x2 @ V6l2 ) )
<=> ( ( V3x1 = V5x2 )
& ( c_2Erich__list_2EIS__SUFFIX @ A_27a @ V4l1 @ V6l2 ) ) ) ) ).
thf(thm_2Erich__list_2EEL__REPLICATE,axiom,
! [A_27a: $tType,V0n1: tyop_2Enum_2Enum,V1n2: tyop_2Enum_2Enum,V2x: A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n1 @ V1n2 )
=> ( ( c_2Elist_2EEL @ A_27a @ V0n1 @ ( c_2Erich__list_2EREPLICATE @ A_27a @ V1n2 @ V2x ) )
= V2x ) ) ).
thf(thm_2Erich__list_2EREPLICATE__GENLIST,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1x: A_27a] :
( ( c_2Erich__list_2EREPLICATE @ A_27a @ V0n @ V1x )
= ( c_2Elist_2EGENLIST @ A_27a @ ( c_2Ecombin_2EK @ A_27a @ tyop_2Enum_2Enum @ V1x ) @ V0n ) ) ).
thf(thm_2Erich__list_2ELIST__TO__SET__EQ__SING,axiom,
! [A_27a: $tType,V0x: A_27a,V1ls: tyop_2Elist_2Elist @ A_27a] :
( ( ( c_2Elist_2ELIST__TO__SET @ A_27a @ V1ls )
= ( c_2Epred__set_2EINSERT @ A_27a @ V0x @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) )
<=> ( ( (~)
@ ( V1ls
= ( c_2Elist_2ENIL @ A_27a ) ) )
& ( c_2Elist_2EEVERY @ A_27a @ ( c_2Emin_2E_3D @ A_27a @ V0x ) @ V1ls ) ) ) ).
thf(thm_2Erich__list_2ELIST__ELEM__COUNT__MEM,axiom,
! [A_27a: $tType,V0e: A_27a,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3E @ ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27a @ V0e @ V1l ) @ c_2Enum_2E0 )
= ( c_2Ebool_2EIN @ A_27a @ V0e @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V1l ) ) ) ).
thf(thm_2Erich__list_2ELIST__ELEM__COUNT__THM,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] :
( ! [V0e: A_27a] :
( ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27a @ V0e @ ( c_2Elist_2ENIL @ A_27a ) )
= c_2Enum_2E0 )
& ! [V1e: A_27b,V2l1: tyop_2Elist_2Elist @ A_27b,V3l2: tyop_2Elist_2Elist @ A_27b] :
( ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27b @ V1e @ ( c_2Elist_2EAPPEND @ A_27b @ V2l1 @ V3l2 ) )
= ( c_2Earithmetic_2E_2B @ ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27b @ V1e @ V2l1 ) @ ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27b @ V1e @ V3l2 ) ) )
& ! [V4e: A_27c,V5h: A_27c,V6l: tyop_2Elist_2Elist @ A_27c] :
( ( V5h = V4e )
=> ( ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27c @ V4e @ ( c_2Elist_2ECONS @ A_27c @ V5h @ V6l ) )
= ( c_2Enum_2ESUC @ ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27c @ V4e @ V6l ) ) ) )
& ! [V7e: A_27d,V8h: A_27d,V9l: tyop_2Elist_2Elist @ A_27d] :
( ( (~) @ ( V8h = V7e ) )
=> ( ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27d @ V7e @ ( c_2Elist_2ECONS @ A_27d @ V8h @ V9l ) )
= ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27d @ V7e @ V9l ) ) ) ) ).
thf(thm_2Erich__list_2EMEM__LAST__FRONT,axiom,
! [A_27a: $tType,V0e: A_27a,V1l: tyop_2Elist_2Elist @ A_27a,V2h: A_27a] :
( ( ( c_2Ebool_2EIN @ A_27a @ V0e @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V1l ) )
& ( (~)
@ ( V0e
= ( c_2Elist_2ELAST @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V2h @ V1l ) ) ) ) )
=> ( c_2Ebool_2EIN @ A_27a @ V0e @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ ( c_2Elist_2EFRONT @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V2h @ V1l ) ) ) ) ) ).
thf(thm_2Erich__list_2EDROP__CONS__EL,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Elist_2EDROP @ A_27a @ V0n @ V1l )
= ( c_2Elist_2ECONS @ A_27a @ ( c_2Elist_2EEL @ A_27a @ V0n @ V1l ) @ ( c_2Elist_2EDROP @ A_27a @ ( c_2Enum_2ESUC @ V0n ) @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2EMEM__LAST,axiom,
! [A_27a: $tType,V0e: A_27a,V1l: tyop_2Elist_2Elist @ A_27a] : ( c_2Ebool_2EIN @ A_27a @ ( c_2Elist_2ELAST @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V0e @ V1l ) ) @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V0e @ V1l ) ) ) ).
thf(thm_2Erich__list_2EEL__FRONT,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Elist_2ELENGTH @ A_27a @ ( c_2Elist_2EFRONT @ A_27a @ V0l ) ) )
& ( (~) @ ( c_2Elist_2ENULL @ A_27a @ V0l ) ) )
=> ( ( c_2Elist_2EEL @ A_27a @ V1n @ ( c_2Elist_2EFRONT @ A_27a @ V0l ) )
= ( c_2Elist_2EEL @ A_27a @ V1n @ V0l ) ) ) ).
thf(thm_2Erich__list_2EFRONT__APPEND,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27a,V2e: A_27a] :
( ( c_2Elist_2EFRONT @ A_27a @ ( c_2Elist_2EAPPEND @ A_27a @ V0l1 @ ( c_2Elist_2ECONS @ A_27a @ V2e @ V1l2 ) ) )
= ( c_2Elist_2EAPPEND @ A_27a @ V0l1 @ ( c_2Elist_2EFRONT @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V2e @ V1l2 ) ) ) ) ).
thf(thm_2Erich__list_2EMEM__FRONT,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a,V1e: A_27a,V2y: A_27a] :
( ( c_2Ebool_2EIN @ A_27a @ V2y @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ ( c_2Elist_2EFRONT @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V1e @ V0l ) ) ) )
=> ( c_2Ebool_2EIN @ A_27a @ V2y @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V1e @ V0l ) ) ) ) ).
thf(thm_2Erich__list_2ESPLITP__EVERY,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEVERY @ A_27a
@ ^ [V2x: A_27a] : ( c_2Ebool_2E_7E @ ( V0P @ V2x ) )
@ V1l )
=> ( ( c_2Erich__list_2ESPLITP @ A_27a @ V0P @ V1l )
= ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ).
thf(thm_2Erich__list_2EFOLDL__MAP2,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f: A_27a > A_27b > A_27a,V1e: A_27a,V2g: A_27c > A_27b,V3l: tyop_2Elist_2Elist @ A_27c] :
( ( c_2Elist_2EFOLDL @ A_27b @ A_27a @ V0f @ V1e @ ( c_2Elist_2EMAP @ A_27c @ A_27b @ V2g @ V3l ) )
= ( c_2Elist_2EFOLDL @ A_27c @ A_27a
@ ^ [V4x: A_27a,V5y: A_27c] : ( V0f @ V4x @ ( V2g @ V5y ) )
@ V1e
@ V3l ) ) ).
thf(thm_2Erich__list_2EAPPEND__SNOC1,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1x: A_27a,V2l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EAPPEND @ A_27a @ ( c_2Elist_2ESNOC @ A_27a @ V1x @ V0l1 ) @ V2l2 )
= ( c_2Elist_2EAPPEND @ A_27a @ V0l1 @ ( c_2Elist_2ECONS @ A_27a @ V1x @ V2l2 ) ) ) ).
thf(thm_2Erich__list_2EAPPEND__ASSOC__CONS,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1h: A_27a,V2l2: tyop_2Elist_2Elist @ A_27a,V3l3: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EAPPEND @ A_27a @ ( c_2Elist_2EAPPEND @ A_27a @ V0l1 @ ( c_2Elist_2ECONS @ A_27a @ V1h @ V2l2 ) ) @ V3l3 )
= ( c_2Elist_2EAPPEND @ A_27a @ V0l1 @ ( c_2Elist_2ECONS @ A_27a @ V1h @ ( c_2Elist_2EAPPEND @ A_27a @ V2l2 @ V3l3 ) ) ) ) ).
thf(thm_2Erich__list_2EZIP__APPEND,axiom,
! [A_27a: $tType,A_27b: $tType,V0a: tyop_2Elist_2Elist @ A_27a,V1b: tyop_2Elist_2Elist @ A_27b,V2c: tyop_2Elist_2Elist @ A_27a,V3d: tyop_2Elist_2Elist @ A_27b] :
( ( ( ( c_2Elist_2ELENGTH @ A_27a @ V0a )
= ( c_2Elist_2ELENGTH @ A_27b @ V1b ) )
& ( ( c_2Elist_2ELENGTH @ A_27a @ V2c )
= ( c_2Elist_2ELENGTH @ A_27b @ V3d ) ) )
=> ( ( c_2Elist_2EAPPEND @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Elist_2EZIP @ A_27a @ A_27b @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) @ V0a @ V1b ) ) @ ( c_2Elist_2EZIP @ A_27a @ A_27b @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) @ V2c @ V3d ) ) )
= ( c_2Elist_2EZIP @ A_27a @ A_27b @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EAPPEND @ A_27a @ V0a @ V2c ) @ ( c_2Elist_2EAPPEND @ A_27b @ V1b @ V3d ) ) ) ) ) ).
thf(thm_2Erich__list_2EEL__TAKE,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1x: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V1x @ V0n )
=> ( ( c_2Elist_2EEL @ A_27a @ V1x @ ( c_2Elist_2ETAKE @ A_27a @ V0n @ V2l ) )
= ( c_2Elist_2EEL @ A_27a @ V1x @ V2l ) ) ) ).
thf(thm_2Erich__list_2EZIP__TAKE,axiom,
! [A_27a: $tType,A_27b: $tType,V0n: tyop_2Enum_2Enum,V1a: tyop_2Elist_2Elist @ A_27a,V2b: tyop_2Elist_2Elist @ A_27b] :
( ( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1a ) )
& ( ( c_2Elist_2ELENGTH @ A_27a @ V1a )
= ( c_2Elist_2ELENGTH @ A_27b @ V2b ) ) )
=> ( ( c_2Elist_2EZIP @ A_27a @ A_27b @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2ETAKE @ A_27a @ V0n @ V1a ) @ ( c_2Elist_2ETAKE @ A_27b @ V0n @ V2b ) ) )
= ( c_2Elist_2ETAKE @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V0n @ ( c_2Elist_2EZIP @ A_27a @ A_27b @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) @ V1a @ V2b ) ) ) ) ) ).
thf(thm_2Erich__list_2EZIP__TAKE__LEQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0n: tyop_2Enum_2Enum,V1a: tyop_2Elist_2Elist @ A_27a,V2b: tyop_2Elist_2Elist @ A_27b] :
( ( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1a ) )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Elist_2ELENGTH @ A_27a @ V1a ) @ ( c_2Elist_2ELENGTH @ A_27b @ V2b ) ) )
=> ( ( c_2Elist_2EZIP @ A_27a @ A_27b @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2ETAKE @ A_27a @ V0n @ V1a ) @ ( c_2Elist_2ETAKE @ A_27b @ V0n @ V2b ) ) )
= ( c_2Elist_2ETAKE @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V0n @ ( c_2Elist_2EZIP @ A_27a @ A_27b @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) @ V1a @ ( c_2Elist_2ETAKE @ A_27b @ ( c_2Elist_2ELENGTH @ A_27a @ V1a ) @ V2b ) ) ) ) ) ) ).
thf(thm_2Erich__list_2ESNOC__EL__TAKE,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Elist_2ESNOC @ A_27a @ ( c_2Elist_2EEL @ A_27a @ V0n @ V1l ) @ ( c_2Elist_2ETAKE @ A_27a @ V0n @ V1l ) )
= ( c_2Elist_2ETAKE @ A_27a @ ( c_2Enum_2ESUC @ V0n ) @ V1l ) ) ) ).
thf(thm_2Erich__list_2EEL__DROP,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2B @ V0m @ V1n ) @ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) )
=> ( ( c_2Elist_2EEL @ A_27a @ V0m @ ( c_2Elist_2EDROP @ A_27a @ V1n @ V2l ) )
= ( c_2Elist_2EEL @ A_27a @ ( c_2Earithmetic_2E_2B @ V0m @ V1n ) @ V2l ) ) ) ).
thf(thm_2Erich__list_2ECOUNT__LIST__ADD,axiom,
! [V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
( ( c_2Erich__list_2ECOUNT__LIST @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) )
= ( c_2Elist_2EAPPEND @ tyop_2Enum_2Enum @ ( c_2Erich__list_2ECOUNT__LIST @ V0n )
@ ( c_2Elist_2EMAP @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum
@ ^ [V2n_27: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B @ V2n_27 @ V0n )
@ ( c_2Erich__list_2ECOUNT__LIST @ V1m ) ) ) ) ).
thf(thm_2Erich__list_2ECOUNT__LIST__COUNT,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Elist_2ELIST__TO__SET @ tyop_2Enum_2Enum @ ( c_2Erich__list_2ECOUNT__LIST @ V0n ) )
= ( c_2Epred__set_2Ecount @ V0n ) ) ).
thf(thm_2Erich__list_2ECOUNT__LIST__SNOC,axiom,
( ( ( c_2Erich__list_2ECOUNT__LIST @ c_2Enum_2E0 )
= ( c_2Elist_2ENIL @ tyop_2Enum_2Enum ) )
& ! [V0n: tyop_2Enum_2Enum] :
( ( c_2Erich__list_2ECOUNT__LIST @ ( c_2Enum_2ESUC @ V0n ) )
= ( c_2Elist_2ESNOC @ tyop_2Enum_2Enum @ V0n @ ( c_2Erich__list_2ECOUNT__LIST @ V0n ) ) ) ) ).
thf(thm_2Erich__list_2EMEM__COUNT__LIST,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Ebool_2EIN @ tyop_2Enum_2Enum @ V0m @ ( c_2Elist_2ELIST__TO__SET @ tyop_2Enum_2Enum @ ( c_2Erich__list_2ECOUNT__LIST @ V1n ) ) )
= ( c_2Eprim__rec_2E_3C @ V0m @ V1n ) ) ).
thf(thm_2Erich__list_2EEL__COUNT__LIST,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0m @ V1n )
=> ( ( c_2Elist_2EEL @ tyop_2Enum_2Enum @ V0m @ ( c_2Erich__list_2ECOUNT__LIST @ V1n ) )
= V0m ) ) ).
thf(thm_2Erich__list_2ELENGTH__COUNT__LIST,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Elist_2ELENGTH @ tyop_2Enum_2Enum @ ( c_2Erich__list_2ECOUNT__LIST @ V0n ) )
= V0n ) ).
thf(thm_2Erich__list_2ECOUNT__LIST__GENLIST,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Erich__list_2ECOUNT__LIST @ V0n )
= ( c_2Elist_2EGENLIST @ tyop_2Enum_2Enum @ ( c_2Ecombin_2EI @ tyop_2Enum_2Enum ) @ V0n ) ) ).
thf(thm_2Erich__list_2Elongest__prefix__PAIR,axiom,
! [A_27a: $tType,V0ys: tyop_2Elist_2Elist @ A_27a,V1y: A_27a,V2xs: tyop_2Elist_2Elist @ A_27a,V3x: A_27a] :
( ( ( c_2Erich__list_2Elongest__prefix @ A_27a @ ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) @ ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27a ) @ V0ys @ ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) )
= ( c_2Elist_2ENIL @ A_27a ) )
& ( ( c_2Erich__list_2Elongest__prefix @ A_27a @ ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27a ) @ V2xs @ ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) )
= ( c_2Elist_2ENIL @ A_27a ) )
& ( ( c_2Erich__list_2Elongest__prefix @ A_27a @ ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS @ A_27a @ V3x @ V2xs ) @ ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS @ A_27a @ V1y @ V0ys ) @ ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Emin_2E_3D @ A_27a @ V3x @ V1y ) @ ( c_2Elist_2ECONS @ A_27a @ V3x @ ( c_2Erich__list_2Elongest__prefix @ A_27a @ ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27a ) @ V2xs @ ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27a ) @ V0ys @ ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ).
thf(thm_2Erich__list_2Ecommon__prefixes__PAIR,axiom,
! [A_27a: $tType,A_27b: $tType,V0ys: tyop_2Elist_2Elist @ A_27b,V1xs: tyop_2Elist_2Elist @ A_27b,V2x: tyop_2Elist_2Elist @ A_27a,V3b: A_27b,V4a: A_27b] :
( ( ( c_2Erich__list_2Ecommon__prefixes @ A_27a @ ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) @ ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27a ) @ V2x @ ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) )
= ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27a ) ) ) )
& ( ( c_2Erich__list_2Ecommon__prefixes @ A_27a @ ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27a ) @ V2x @ ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) )
= ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27a ) ) ) )
& ( ( c_2Erich__list_2Ecommon__prefixes @ A_27b @ ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2ECONS @ A_27b @ V4a @ V1xs ) @ ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2ECONS @ A_27b @ V3b @ V0ys ) @ ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27b ) ) ) ) )
= ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2ENIL @ A_27b ) @ ( c_2Ebool_2ECOND @ ( ( tyop_2Elist_2Elist @ A_27b ) > $o ) @ ( c_2Emin_2E_3D @ A_27b @ V4a @ V3b ) @ ( c_2Epred__set_2EIMAGE @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2ECONS @ A_27b @ V4a ) @ ( c_2Erich__list_2Ecommon__prefixes @ A_27b @ ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27b ) @ V1xs @ ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27b ) @ V0ys @ ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27b ) ) ) ) ) ) @ ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27b ) ) ) ) ) ) ).
thf(thm_2Erich__list_2Elongest__prefix__SING,axiom,
! [A_27a: $tType,V0s: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2Elongest__prefix @ A_27a @ ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27a ) @ V0s @ ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27a ) ) ) )
= V0s ) ).
thf(thm_2Erich__list_2Elongest__prefix__EMPTY,axiom,
! [A_27a: $tType] :
( ( c_2Erich__list_2Elongest__prefix @ A_27a @ ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27a ) ) )
= ( c_2Elist_2ENIL @ A_27a ) ) ).
thf(thm_2Erich__list_2ENIL__IN__common__prefixes,axiom,
! [A_27a: $tType,V0s: ( tyop_2Elist_2Elist @ A_27a ) > $o] : ( c_2Ebool_2EIN @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a @ V0s ) ) ).
thf(thm_2Erich__list_2Elongest__prefix__NIL,axiom,
! [A_27a: $tType,V0s: ( tyop_2Elist_2Elist @ A_27a ) > $o] :
( ( c_2Ebool_2EIN @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) @ V0s )
=> ( ( c_2Erich__list_2Elongest__prefix @ A_27a @ V0s )
= ( c_2Elist_2ENIL @ A_27a ) ) ) ).
thf(thm_2Erich__list_2Ecommon__prefixes__NIL,axiom,
! [A_27a: $tType,V0s: ( tyop_2Elist_2Elist @ A_27a ) > $o] :
( ( c_2Ebool_2EIN @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) @ V0s )
=> ( ( c_2Erich__list_2Ecommon__prefixes @ A_27a @ V0s )
= ( c_2Epred__set_2EINSERT @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) @ ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) ).
thf(thm_2Erich__list_2Elongest__prefix__UNIQUE,axiom,
! [A_27a: $tType,V0y: tyop_2Elist_2Elist @ A_27a,V1x: tyop_2Elist_2Elist @ A_27a,V2s: ( tyop_2Elist_2Elist @ A_27a ) > $o] :
( ( ( (~)
@ ( V2s
= ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27a ) ) ) )
& ( c_2Epred__set_2Eis__measure__maximal @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ELENGTH @ A_27a ) @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a @ V2s ) @ V1x )
& ( c_2Epred__set_2Eis__measure__maximal @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ELENGTH @ A_27a ) @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a @ V2s ) @ V0y ) )
=> ( V1x = V0y ) ) ).
thf(thm_2Erich__list_2Etwo__common__prefixes,axiom,
! [A_27a: $tType,V0s: ( tyop_2Elist_2Elist @ A_27a ) > $o,V1p2: tyop_2Elist_2Elist @ A_27a,V2p1: tyop_2Elist_2Elist @ A_27a] :
( ( ( (~)
@ ( V0s
= ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27a ) ) ) )
& ( c_2Ebool_2EIN @ ( tyop_2Elist_2Elist @ A_27a ) @ V2p1 @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a @ V0s ) )
& ( c_2Ebool_2EIN @ ( tyop_2Elist_2Elist @ A_27a ) @ V1p2 @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a @ V0s ) ) )
=> ( ( c_2Elist_2EisPREFIX @ A_27a @ V2p1 @ V1p2 )
| ( c_2Elist_2EisPREFIX @ A_27a @ V1p2 @ V2p1 ) ) ) ).
thf(thm_2Erich__list_2Ecommon__prefixes__NONEMPTY,axiom,
! [A_27a: $tType,V0s: ( tyop_2Elist_2Elist @ A_27a ) > $o] :
( (~)
@ ( ( c_2Erich__list_2Ecommon__prefixes @ A_27a @ V0s )
= ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ).
thf(thm_2Erich__list_2EFINITE__common__prefixes,axiom,
! [A_27a: $tType,V0s: ( tyop_2Elist_2Elist @ A_27a ) > $o] :
( ( (~)
@ ( V0s
= ( c_2Epred__set_2EEMPTY @ ( tyop_2Elist_2Elist @ A_27a ) ) ) )
=> ( c_2Epred__set_2EFINITE @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Erich__list_2Ecommon__prefixes @ A_27a @ V0s ) ) ) ).
thf(thm_2Erich__list_2EFINITE__prefix,axiom,
! [A_27a: $tType,V0b: tyop_2Elist_2Elist @ A_27a] :
( c_2Epred__set_2EFINITE @ ( tyop_2Elist_2Elist @ A_27a )
@ ( c_2Epred__set_2EGSPEC @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a )
@ ^ [V1a: tyop_2Elist_2Elist @ A_27a] : ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ $o @ V1a @ ( c_2Elist_2EisPREFIX @ A_27a @ V1a @ V0b ) ) ) ) ).
thf(thm_2Erich__list_2Ecommon__prefixes__BIGINTER,axiom,
! [A_27a: $tType,V0s: ( tyop_2Elist_2Elist @ A_27a ) > $o] :
( ( c_2Erich__list_2Ecommon__prefixes @ A_27a @ V0s )
= ( c_2Epred__set_2EBIGINTER @ ( tyop_2Elist_2Elist @ A_27a )
@ ( c_2Epred__set_2EIMAGE @ ( tyop_2Elist_2Elist @ A_27a ) @ ( ( tyop_2Elist_2Elist @ A_27a ) > $o )
@ ^ [V1l: tyop_2Elist_2Elist @ A_27a] :
( c_2Epred__set_2EGSPEC @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a )
@ ^ [V2p: tyop_2Elist_2Elist @ A_27a] : ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ $o @ V2p @ ( c_2Elist_2EisPREFIX @ A_27a @ V2p @ V1l ) ) )
@ V0s ) ) ) ).
thf(thm_2Erich__list_2Eprefixes__is__prefix__total,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a,V1l1: tyop_2Elist_2Elist @ A_27a,V2l2: tyop_2Elist_2Elist @ A_27a] :
( ( ( c_2Elist_2EisPREFIX @ A_27a @ V1l1 @ V0l )
& ( c_2Elist_2EisPREFIX @ A_27a @ V2l2 @ V0l ) )
=> ( ( c_2Elist_2EisPREFIX @ A_27a @ V1l1 @ V2l2 )
| ( c_2Elist_2EisPREFIX @ A_27a @ V2l2 @ V1l1 ) ) ) ).
thf(thm_2Erich__list_2EIS__PREFIX__APPEND3,axiom,
! [A_27a: $tType,V0c: tyop_2Elist_2Elist @ A_27a,V1a: tyop_2Elist_2Elist @ A_27a] : ( c_2Elist_2EisPREFIX @ A_27a @ V1a @ ( c_2Elist_2EAPPEND @ A_27a @ V1a @ V0c ) ) ).
thf(thm_2Erich__list_2EIS__PREFIX__APPENDS,axiom,
! [A_27a: $tType,V0a: tyop_2Elist_2Elist @ A_27a,V1b: tyop_2Elist_2Elist @ A_27a,V2c: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EisPREFIX @ A_27a @ ( c_2Elist_2EAPPEND @ A_27a @ V0a @ V1b ) @ ( c_2Elist_2EAPPEND @ A_27a @ V0a @ V2c ) )
= ( c_2Elist_2EisPREFIX @ A_27a @ V1b @ V2c ) ) ).
thf(thm_2Erich__list_2EIS__PREFIX__APPEND2,axiom,
! [A_27a: $tType,V0a: tyop_2Elist_2Elist @ A_27a,V1b: tyop_2Elist_2Elist @ A_27a,V2c: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EisPREFIX @ A_27a @ V0a @ ( c_2Elist_2EAPPEND @ A_27a @ V1b @ V2c ) )
=> ( ( c_2Elist_2EisPREFIX @ A_27a @ V0a @ V1b )
| ( c_2Elist_2EisPREFIX @ A_27a @ V1b @ V0a ) ) ) ).
thf(thm_2Erich__list_2EIS__PREFIX__APPEND1,axiom,
! [A_27a: $tType,V0a: tyop_2Elist_2Elist @ A_27a,V1b: tyop_2Elist_2Elist @ A_27a,V2c: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EisPREFIX @ A_27a @ ( c_2Elist_2EAPPEND @ A_27a @ V0a @ V1b ) @ V2c )
=> ( c_2Elist_2EisPREFIX @ A_27a @ V0a @ V2c ) ) ).
thf(thm_2Erich__list_2EIS__PREFIX__SNOC,axiom,
! [A_27a: $tType,V0x: A_27a,V1y: tyop_2Elist_2Elist @ A_27a,V2z: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EisPREFIX @ A_27a @ V2z @ ( c_2Elist_2ESNOC @ A_27a @ V0x @ V1y ) )
<=> ( ( c_2Elist_2EisPREFIX @ A_27a @ V2z @ V1y )
| ( V2z
= ( c_2Elist_2ESNOC @ A_27a @ V0x @ V1y ) ) ) ) ).
thf(thm_2Erich__list_2EIS__PREFIX__LENGTH__ANTI,axiom,
! [A_27a: $tType,V0x: tyop_2Elist_2Elist @ A_27a,V1y: tyop_2Elist_2Elist @ A_27a] :
( ( ( c_2Elist_2EisPREFIX @ A_27a @ V0x @ V1y )
& ( ( c_2Elist_2ELENGTH @ A_27a @ V0x )
= ( c_2Elist_2ELENGTH @ A_27a @ V1y ) ) )
<=> ( V0x = V1y ) ) ).
thf(thm_2Erich__list_2EIS__PREFIX__LENGTH,axiom,
! [A_27a: $tType,V0x: tyop_2Elist_2Elist @ A_27a,V1y: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EisPREFIX @ A_27a @ V0x @ V1y )
=> ( c_2Earithmetic_2E_3C_3D @ ( c_2Elist_2ELENGTH @ A_27a @ V0x ) @ ( c_2Elist_2ELENGTH @ A_27a @ V1y ) ) ) ).
thf(thm_2Erich__list_2EIS__PREFIX__BUTLAST,axiom,
! [A_27a: $tType,V0x: A_27a,V1y: tyop_2Elist_2Elist @ A_27a] : ( c_2Elist_2EisPREFIX @ A_27a @ ( c_2Elist_2EFRONT @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V0x @ V1y ) ) @ ( c_2Elist_2ECONS @ A_27a @ V0x @ V1y ) ) ).
thf(thm_2Erich__list_2EIS__PREFIX__TRANS,axiom,
! [A_27a: $tType,V0x: tyop_2Elist_2Elist @ A_27a,V1y: tyop_2Elist_2Elist @ A_27a,V2z: tyop_2Elist_2Elist @ A_27a] :
( ( ( c_2Elist_2EisPREFIX @ A_27a @ V1y @ V0x )
& ( c_2Elist_2EisPREFIX @ A_27a @ V2z @ V1y ) )
=> ( c_2Elist_2EisPREFIX @ A_27a @ V2z @ V0x ) ) ).
thf(thm_2Erich__list_2EIS__PREFIX__ANTISYM,axiom,
! [A_27a: $tType,V0x: tyop_2Elist_2Elist @ A_27a,V1y: tyop_2Elist_2Elist @ A_27a] :
( ( ( c_2Elist_2EisPREFIX @ A_27a @ V0x @ V1y )
& ( c_2Elist_2EisPREFIX @ A_27a @ V1y @ V0x ) )
=> ( V0x = V1y ) ) ).
thf(thm_2Erich__list_2EIS__PREFIX__REFL,axiom,
! [A_27a: $tType,V0x: tyop_2Elist_2Elist @ A_27a] : ( c_2Elist_2EisPREFIX @ A_27a @ V0x @ V0x ) ).
thf(thm_2Erich__list_2EIS__PREFIX__NIL,axiom,
! [A_27a: $tType,V0x: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EisPREFIX @ A_27a @ ( c_2Elist_2ENIL @ A_27a ) @ V0x )
& ( ( c_2Elist_2EisPREFIX @ A_27a @ V0x @ ( c_2Elist_2ENIL @ A_27a ) )
<=> ( V0x
= ( c_2Elist_2ENIL @ A_27a ) ) ) ) ).
thf(thm_2Erich__list_2EOR__EL__FOLDR,axiom,
! [V0l: tyop_2Elist_2Elist @ $o] :
( ( c_2Erich__list_2EOR__EL @ V0l )
= ( c_2Elist_2EFOLDR @ $o @ $o @ c_2Ebool_2E_5C_2F @ c_2Ebool_2EF @ V0l ) ) ).
thf(thm_2Erich__list_2EOR__EL__FOLDL,axiom,
! [V0l: tyop_2Elist_2Elist @ $o] :
( ( c_2Erich__list_2EOR__EL @ V0l )
= ( c_2Elist_2EFOLDL @ $o @ $o @ c_2Ebool_2E_5C_2F @ c_2Ebool_2EF @ V0l ) ) ).
thf(thm_2Erich__list_2EAND__EL__FOLDR,axiom,
! [V0l: tyop_2Elist_2Elist @ $o] :
( ( c_2Erich__list_2EAND__EL @ V0l )
= ( c_2Elist_2EFOLDR @ $o @ $o @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET @ V0l ) ) ).
thf(thm_2Erich__list_2EAND__EL__FOLDL,axiom,
! [V0l: tyop_2Elist_2Elist @ $o] :
( ( c_2Erich__list_2EAND__EL @ V0l )
= ( c_2Elist_2EFOLDL @ $o @ $o @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET @ V0l ) ) ).
thf(thm_2Erich__list_2EDROP__LENGTH__NIL,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EDROP @ A_27a @ ( c_2Elist_2ELENGTH @ A_27a @ V0l ) @ V0l )
= ( c_2Elist_2ENIL @ A_27a ) ) ).
thf(thm_2Erich__list_2ETAKE__TAKE,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0m @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ! [V2n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V2n @ V0m )
=> ( ( c_2Elist_2ETAKE @ A_27a @ V2n @ ( c_2Elist_2ETAKE @ A_27a @ V0m @ V1l ) )
= ( c_2Elist_2ETAKE @ A_27a @ V2n @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2ETAKE__TAKE__T,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a,V2n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V2n @ V0m )
=> ( ( c_2Elist_2ETAKE @ A_27a @ V2n @ ( c_2Elist_2ETAKE @ A_27a @ V0m @ V1l ) )
= ( c_2Elist_2ETAKE @ A_27a @ V2n @ V1l ) ) ) ).
thf(thm_2Erich__list_2EEVERY__BUTLASTN,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEVERY @ A_27a @ V0P @ V1l )
=> ! [V2m: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V2m @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( c_2Elist_2EEVERY @ A_27a @ V0P @ ( c_2Erich__list_2EBUTLASTN @ A_27a @ V2m @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2EEVERY__LASTN,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEVERY @ A_27a @ V0P @ V1l )
=> ! [V2m: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V2m @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( c_2Elist_2EEVERY @ A_27a @ V0P @ ( c_2Erich__list_2ELASTN @ A_27a @ V2m @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2EBUTLASTN__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ! [V2f: A_27a > A_27b] :
( ( c_2Erich__list_2EBUTLASTN @ A_27b @ V0n @ ( c_2Elist_2EMAP @ A_27a @ A_27b @ V2f @ V1l ) )
= ( c_2Elist_2EMAP @ A_27a @ A_27b @ V2f @ ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0n @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2ELASTN__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ! [V2f: A_27a > A_27b] :
( ( c_2Erich__list_2ELASTN @ A_27b @ V0n @ ( c_2Elist_2EMAP @ A_27a @ A_27b @ V2f @ V1l ) )
= ( c_2Elist_2EMAP @ A_27a @ A_27b @ V2f @ ( c_2Erich__list_2ELASTN @ A_27a @ V0n @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2ELASTN__APPEND1,axiom,
! [A_27a: $tType,V0l2: tyop_2Elist_2Elist @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Elist_2ELENGTH @ A_27a @ V0l2 ) @ V1n )
=> ! [V2l1: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ELASTN @ A_27a @ V1n @ ( c_2Elist_2EAPPEND @ A_27a @ V2l1 @ V0l2 ) )
= ( c_2Elist_2EAPPEND @ A_27a @ ( c_2Erich__list_2ELASTN @ A_27a @ ( c_2Earithmetic_2E_2D @ V1n @ ( c_2Elist_2ELENGTH @ A_27a @ V0l2 ) ) @ V2l1 ) @ V0l2 ) ) ) ).
thf(thm_2Erich__list_2ELASTN__APPEND2,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l2 ) )
=> ! [V2l1: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ELASTN @ A_27a @ V0n @ ( c_2Elist_2EAPPEND @ A_27a @ V2l1 @ V1l2 ) )
= ( c_2Erich__list_2ELASTN @ A_27a @ V0n @ V1l2 ) ) ) ).
thf(thm_2Erich__list_2EBUTLASTN__APPEND1,axiom,
! [A_27a: $tType,V0l2: tyop_2Elist_2Elist @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Elist_2ELENGTH @ A_27a @ V0l2 ) @ V1n )
=> ! [V2l1: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EBUTLASTN @ A_27a @ V1n @ ( c_2Elist_2EAPPEND @ A_27a @ V2l1 @ V0l2 ) )
= ( c_2Erich__list_2EBUTLASTN @ A_27a @ ( c_2Earithmetic_2E_2D @ V1n @ ( c_2Elist_2ELENGTH @ A_27a @ V0l2 ) ) @ V2l1 ) ) ) ).
thf(thm_2Erich__list_2EBUTLASTN__1,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( (~)
@ ( V0l
= ( c_2Elist_2ENIL @ A_27a ) ) )
=> ( ( c_2Erich__list_2EBUTLASTN @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0l )
= ( c_2Elist_2EFRONT @ A_27a @ V0l ) ) ) ).
thf(thm_2Erich__list_2ELASTN__1,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( (~)
@ ( V0l
= ( c_2Elist_2ENIL @ A_27a ) ) )
=> ( ( c_2Erich__list_2ELASTN @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0l )
= ( c_2Elist_2ECONS @ A_27a @ ( c_2Elist_2ELAST @ A_27a @ V0l ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ).
thf(thm_2Erich__list_2EBUTLASTN__LASTN,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( ( c_2Earithmetic_2E_3C_3D @ V0m @ V1n )
& ( c_2Earithmetic_2E_3C_3D @ V1n @ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) ) )
=> ( ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0m @ ( c_2Erich__list_2ELASTN @ A_27a @ V1n @ V2l ) )
= ( c_2Erich__list_2ELASTN @ A_27a @ ( c_2Earithmetic_2E_2D @ V1n @ V0m ) @ ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0m @ V2l ) ) ) ) ).
thf(thm_2Erich__list_2ELASTN__BUTLASTN,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) @ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) )
=> ( ( c_2Erich__list_2ELASTN @ A_27a @ V0n @ ( c_2Erich__list_2EBUTLASTN @ A_27a @ V1m @ V2l ) )
= ( c_2Erich__list_2EBUTLASTN @ A_27a @ V1m @ ( c_2Erich__list_2ELASTN @ A_27a @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) @ V2l ) ) ) ) ).
thf(thm_2Erich__list_2EBUTLASTN__LASTN__NIL,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0n @ ( c_2Erich__list_2ELASTN @ A_27a @ V0n @ V1l ) )
= ( c_2Elist_2ENIL @ A_27a ) ) ) ).
thf(thm_2Erich__list_2ELAST__LASTN__LAST,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V0n )
=> ( ( c_2Elist_2ELAST @ A_27a @ ( c_2Erich__list_2ELASTN @ A_27a @ V0n @ V1l ) )
= ( c_2Elist_2ELAST @ A_27a @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2EBUTLASTN__LENGTH__CONS,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a,V1x: A_27a] :
( ( c_2Erich__list_2EBUTLASTN @ A_27a @ ( c_2Elist_2ELENGTH @ A_27a @ V0l ) @ ( c_2Elist_2ECONS @ A_27a @ V1x @ V0l ) )
= ( c_2Elist_2ECONS @ A_27a @ V1x @ ( c_2Elist_2ENIL @ A_27a ) ) ) ).
thf(thm_2Erich__list_2EBUTLASTN__CONS,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ! [V2x: A_27a] :
( ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0n @ ( c_2Elist_2ECONS @ A_27a @ V2x @ V1l ) )
= ( c_2Elist_2ECONS @ A_27a @ V2x @ ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0n @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2ELASTN__LENGTH__APPEND,axiom,
! [A_27a: $tType,V0l2: tyop_2Elist_2Elist @ A_27a,V1l1: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ELASTN @ A_27a @ ( c_2Elist_2ELENGTH @ A_27a @ V0l2 ) @ ( c_2Elist_2EAPPEND @ A_27a @ V1l1 @ V0l2 ) )
= V0l2 ) ).
thf(thm_2Erich__list_2EBUTLASTN__LENGTH__APPEND,axiom,
! [A_27a: $tType,V0l2: tyop_2Elist_2Elist @ A_27a,V1l1: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EBUTLASTN @ A_27a @ ( c_2Elist_2ELENGTH @ A_27a @ V0l2 ) @ ( c_2Elist_2EAPPEND @ A_27a @ V1l1 @ V0l2 ) )
= V1l1 ) ).
thf(thm_2Erich__list_2EBUTLASTN__APPEND2,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l1: tyop_2Elist_2Elist @ A_27a,V2l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V2l2 ) )
=> ( ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0n @ ( c_2Elist_2EAPPEND @ A_27a @ V1l1 @ V2l2 ) )
= ( c_2Elist_2EAPPEND @ A_27a @ V1l1 @ ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0n @ V2l2 ) ) ) ) ).
thf(thm_2Erich__list_2EAPPEND__TAKE__LASTN,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( ( c_2Earithmetic_2E_2B @ V0m @ V1n )
= ( c_2Elist_2ELENGTH @ A_27a @ V2l ) )
=> ( ( c_2Elist_2EAPPEND @ A_27a @ ( c_2Elist_2ETAKE @ A_27a @ V1n @ V2l ) @ ( c_2Erich__list_2ELASTN @ A_27a @ V0m @ V2l ) )
= V2l ) ) ).
thf(thm_2Erich__list_2EAPPEND__BUTLASTN__LASTN,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Elist_2EAPPEND @ A_27a @ ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0n @ V1l ) @ ( c_2Erich__list_2ELASTN @ A_27a @ V0n @ V1l ) )
= V1l ) ) ).
thf(thm_2Erich__list_2EBUTLASTN__BUTLASTN,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V1n @ V0m ) @ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) )
=> ( ( c_2Erich__list_2EBUTLASTN @ A_27a @ V1n @ ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0m @ V2l ) )
= ( c_2Erich__list_2EBUTLASTN @ A_27a @ ( c_2Earithmetic_2E_2B @ V1n @ V0m ) @ V2l ) ) ) ).
thf(thm_2Erich__list_2ELENGTH__BUTLASTN,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Elist_2ELENGTH @ A_27a @ ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0n @ V1l ) )
= ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) @ V0n ) ) ) ).
thf(thm_2Erich__list_2EBUTLASTN__FRONT,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0n @ ( c_2Elist_2EFRONT @ A_27a @ V1l ) )
= ( c_2Elist_2EFRONT @ A_27a @ ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0n @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2EBUTLASTN__SUC__FRONT,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Erich__list_2EBUTLASTN @ A_27a @ ( c_2Enum_2ESUC @ V0n ) @ V1l )
= ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0n @ ( c_2Elist_2EFRONT @ A_27a @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2EELL__compute,axiom,
! [A_27a: $tType] :
( ! [V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EELL @ A_27a @ c_2Enum_2E0 @ V0l )
= ( c_2Elist_2ELAST @ A_27a @ V0l ) )
& ! [V1n: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EELL @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V1n ) ) @ V2l )
= ( c_2Erich__list_2EELL @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V1n ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Elist_2EFRONT @ A_27a @ V2l ) ) )
& ! [V3n: tyop_2Enum_2Enum,V4l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EELL @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ V3n ) ) @ V4l )
= ( c_2Erich__list_2EELL @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V3n ) ) @ ( c_2Elist_2EFRONT @ A_27a @ V4l ) ) ) ) ).
thf(thm_2Erich__list_2EREPLICATE__compute,axiom,
! [A_27a: $tType] :
( ! [V0x: A_27a] :
( ( c_2Erich__list_2EREPLICATE @ A_27a @ c_2Enum_2E0 @ V0x )
= ( c_2Elist_2ENIL @ A_27a ) )
& ! [V1n: tyop_2Enum_2Enum,V2x: A_27a] :
( ( c_2Erich__list_2EREPLICATE @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V1n ) ) @ V2x )
= ( c_2Elist_2ECONS @ A_27a @ V2x @ ( c_2Erich__list_2EREPLICATE @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V1n ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2x ) ) )
& ! [V3n: tyop_2Enum_2Enum,V4x: A_27a] :
( ( c_2Erich__list_2EREPLICATE @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ V3n ) ) @ V4x )
= ( c_2Elist_2ECONS @ A_27a @ V4x @ ( c_2Erich__list_2EREPLICATE @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V3n ) ) @ V4x ) ) ) ) ).
thf(thm_2Erich__list_2ECOUNT__LIST__AUX__def__compute,axiom,
( ! [V0l: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
( ( c_2Erich__list_2ECOUNT__LIST__AUX @ c_2Enum_2E0 @ V0l )
= V0l )
& ! [V1n: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
( ( c_2Erich__list_2ECOUNT__LIST__AUX @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V1n ) ) @ V2l )
= ( c_2Erich__list_2ECOUNT__LIST__AUX @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V1n ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Elist_2ECONS @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V1n ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2l ) ) )
& ! [V3n: tyop_2Enum_2Enum,V4l: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
( ( c_2Erich__list_2ECOUNT__LIST__AUX @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ V3n ) ) @ V4l )
= ( c_2Erich__list_2ECOUNT__LIST__AUX @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V3n ) ) @ ( c_2Elist_2ECONS @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V3n ) ) @ V4l ) ) ) ) ).
thf(thm_2Erich__list_2ETAKE,axiom,
! [A_27a: $tType] :
( ! [V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2ETAKE @ A_27a @ c_2Enum_2E0 @ V0l )
= ( c_2Elist_2ENIL @ A_27a ) )
& ! [V1n: tyop_2Enum_2Enum,V2x: A_27a,V3l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2ETAKE @ A_27a @ ( c_2Enum_2ESUC @ V1n ) @ ( c_2Elist_2ECONS @ A_27a @ V2x @ V3l ) )
= ( c_2Elist_2ECONS @ A_27a @ V2x @ ( c_2Elist_2ETAKE @ A_27a @ V1n @ V3l ) ) ) ) ).
thf(thm_2Erich__list_2EDROP,axiom,
! [A_27a: $tType] :
( ! [V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EDROP @ A_27a @ c_2Enum_2E0 @ V0l )
= V0l )
& ! [V1n: tyop_2Enum_2Enum,V2x: A_27a,V3l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EDROP @ A_27a @ ( c_2Enum_2ESUC @ V1n ) @ ( c_2Elist_2ECONS @ A_27a @ V2x @ V3l ) )
= ( c_2Elist_2EDROP @ A_27a @ V1n @ V3l ) ) ) ).
thf(thm_2Erich__list_2EDROP__FUNPOW__TL,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EDROP @ A_27a @ V0n @ V1l )
= ( c_2Earithmetic_2EFUNPOW @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Erich__list_2ETL__T @ A_27a ) @ V0n @ V1l ) ) ).
thf(thm_2Erich__list_2ENOT__NULL__SNOC,axiom,
! [A_27a: $tType,V0x: A_27a,V1l: tyop_2Elist_2Elist @ A_27a] : ( (~) @ ( c_2Elist_2ENULL @ A_27a @ ( c_2Elist_2ESNOC @ A_27a @ V0x @ V1l ) ) ) ).
thf(thm_2Erich__list_2ELASTN,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ELASTN @ A_27a @ c_2Enum_2E0 @ V0l )
= ( c_2Elist_2ENIL @ A_27a ) )
& ! [V1n: tyop_2Enum_2Enum,V2x: A_27b,V3l: tyop_2Elist_2Elist @ A_27b] :
( ( c_2Erich__list_2ELASTN @ A_27b @ ( c_2Enum_2ESUC @ V1n ) @ ( c_2Elist_2ESNOC @ A_27b @ V2x @ V3l ) )
= ( c_2Elist_2ESNOC @ A_27b @ V2x @ ( c_2Erich__list_2ELASTN @ A_27b @ V1n @ V3l ) ) ) ) ).
thf(thm_2Erich__list_2EBUTLASTN,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EBUTLASTN @ A_27a @ c_2Enum_2E0 @ V0l )
= V0l )
& ! [V1n: tyop_2Enum_2Enum,V2x: A_27b,V3l: tyop_2Elist_2Elist @ A_27b] :
( ( c_2Erich__list_2EBUTLASTN @ A_27b @ ( c_2Enum_2ESUC @ V1n ) @ ( c_2Elist_2ESNOC @ A_27b @ V2x @ V3l ) )
= ( c_2Erich__list_2EBUTLASTN @ A_27b @ V1n @ V3l ) ) ) ).
thf(thm_2Erich__list_2ELENGTH__NOT__NULL,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Elist_2ELENGTH @ A_27a @ V0l ) )
<=> ( (~) @ ( c_2Elist_2ENULL @ A_27a @ V0l ) ) ) ).
thf(thm_2Erich__list_2ENOT__NIL__SNOC,axiom,
! [A_27a: $tType,V0x: A_27a,V1l: tyop_2Elist_2Elist @ A_27a] :
( (~)
@ ( ( c_2Elist_2ENIL @ A_27a )
= ( c_2Elist_2ESNOC @ A_27a @ V0x @ V1l ) ) ) ).
thf(thm_2Erich__list_2ENOT__SNOC__NIL,axiom,
! [A_27a: $tType,V0x: A_27a,V1l: tyop_2Elist_2Elist @ A_27a] :
( (~)
@ ( ( c_2Elist_2ESNOC @ A_27a @ V0x @ V1l )
= ( c_2Elist_2ENIL @ A_27a ) ) ) ).
thf(thm_2Erich__list_2ESNOC__EQ__LENGTH__EQ,axiom,
! [A_27a: $tType,V0x1: A_27a,V1l1: tyop_2Elist_2Elist @ A_27a,V2x2: A_27a,V3l2: tyop_2Elist_2Elist @ A_27a] :
( ( ( c_2Elist_2ESNOC @ A_27a @ V0x1 @ V1l1 )
= ( c_2Elist_2ESNOC @ A_27a @ V2x2 @ V3l2 ) )
=> ( ( c_2Elist_2ELENGTH @ A_27a @ V1l1 )
= ( c_2Elist_2ELENGTH @ A_27a @ V3l2 ) ) ) ).
thf(thm_2Erich__list_2ESNOC__REVERSE__CONS,axiom,
! [A_27a: $tType,V0x: A_27a,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2ESNOC @ A_27a @ V0x @ V1l )
= ( c_2Elist_2EREVERSE @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V0x @ ( c_2Elist_2EREVERSE @ A_27a @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2EFOLDR__SNOC,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b > A_27b,V1e: A_27b,V2x: A_27a,V3l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFOLDR @ A_27a @ A_27b @ V0f @ V1e @ ( c_2Elist_2ESNOC @ A_27a @ V2x @ V3l ) )
= ( c_2Elist_2EFOLDR @ A_27a @ A_27b @ V0f @ ( V0f @ V2x @ V1e ) @ V3l ) ) ).
thf(thm_2Erich__list_2EFOLDR__FOLDL,axiom,
! [A_27a: $tType,V0f: A_27a > A_27a > A_27a,V1e: A_27a] :
( ( c_2Ecombin_2EMONOID @ A_27a @ V0f @ V1e )
=> ! [V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFOLDR @ A_27a @ A_27a @ V0f @ V1e @ V2l )
= ( c_2Elist_2EFOLDL @ A_27a @ A_27a @ V0f @ V1e @ V2l ) ) ) ).
thf(thm_2Erich__list_2ELENGTH__FOLDR,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2ELENGTH @ A_27a @ V0l )
= ( c_2Elist_2EFOLDR @ A_27a @ tyop_2Enum_2Enum
@ ^ [V1x: A_27a,V2l_27: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC @ V2l_27 )
@ c_2Enum_2E0
@ V0l ) ) ).
thf(thm_2Erich__list_2ELENGTH__FOLDL,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2ELENGTH @ A_27a @ V0l )
= ( c_2Elist_2EFOLDL @ A_27a @ tyop_2Enum_2Enum
@ ^ [V1l_27: tyop_2Enum_2Enum,V2x: A_27a] : ( c_2Enum_2ESUC @ V1l_27 )
@ c_2Enum_2E0
@ V0l ) ) ).
thf(thm_2Erich__list_2EMAP__FOLDR,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EMAP @ A_27a @ A_27b @ V0f @ V1l )
= ( c_2Elist_2EFOLDR @ A_27a @ ( tyop_2Elist_2Elist @ A_27b )
@ ^ [V2x: A_27a,V3l_27: tyop_2Elist_2Elist @ A_27b] : ( c_2Elist_2ECONS @ A_27b @ ( V0f @ V2x ) @ V3l_27 )
@ ( c_2Elist_2ENIL @ A_27b )
@ V1l ) ) ).
thf(thm_2Erich__list_2EMAP__FOLDL,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EMAP @ A_27a @ A_27b @ V0f @ V1l )
= ( c_2Elist_2EFOLDL @ A_27a @ ( tyop_2Elist_2Elist @ A_27b )
@ ^ [V2l_27: tyop_2Elist_2Elist @ A_27b,V3x: A_27a] : ( c_2Elist_2ESNOC @ A_27b @ ( V0f @ V3x ) @ V2l_27 )
@ ( c_2Elist_2ENIL @ A_27b )
@ V1l ) ) ).
thf(thm_2Erich__list_2EFILTER__FOLDR,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFILTER @ A_27a @ V0P @ V1l )
= ( c_2Elist_2EFOLDR @ A_27a @ ( tyop_2Elist_2Elist @ A_27a )
@ ^ [V2x: A_27a,V3l_27: tyop_2Elist_2Elist @ A_27a] : ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ A_27a ) @ ( V0P @ V2x ) @ ( c_2Elist_2ECONS @ A_27a @ V2x @ V3l_27 ) @ V3l_27 )
@ ( c_2Elist_2ENIL @ A_27a )
@ V1l ) ) ).
thf(thm_2Erich__list_2EFILTER__SNOC,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1x: A_27a,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFILTER @ A_27a @ V0P @ ( c_2Elist_2ESNOC @ A_27a @ V1x @ V2l ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ A_27a ) @ ( V0P @ V1x ) @ ( c_2Elist_2ESNOC @ A_27a @ V1x @ ( c_2Elist_2EFILTER @ A_27a @ V0P @ V2l ) ) @ ( c_2Elist_2EFILTER @ A_27a @ V0P @ V2l ) ) ) ).
thf(thm_2Erich__list_2EFILTER__FOLDL,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFILTER @ A_27a @ V0P @ V1l )
= ( c_2Elist_2EFOLDL @ A_27a @ ( tyop_2Elist_2Elist @ A_27a )
@ ^ [V2l_27: tyop_2Elist_2Elist @ A_27a,V3x: A_27a] : ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ A_27a ) @ ( V0P @ V3x ) @ ( c_2Elist_2ESNOC @ A_27a @ V3x @ V2l_27 ) @ V2l_27 )
@ ( c_2Elist_2ENIL @ A_27a )
@ V1l ) ) ).
thf(thm_2Erich__list_2EFILTER__COMM,axiom,
! [A_27a: $tType,V0f1: A_27a > $o,V1f2: A_27a > $o,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFILTER @ A_27a @ V0f1 @ ( c_2Elist_2EFILTER @ A_27a @ V1f2 @ V2l ) )
= ( c_2Elist_2EFILTER @ A_27a @ V1f2 @ ( c_2Elist_2EFILTER @ A_27a @ V0f1 @ V2l ) ) ) ).
thf(thm_2Erich__list_2EFILTER__IDEM,axiom,
! [A_27a: $tType,V0f: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFILTER @ A_27a @ V0f @ ( c_2Elist_2EFILTER @ A_27a @ V0f @ V1l ) )
= ( c_2Elist_2EFILTER @ A_27a @ V0f @ V1l ) ) ).
thf(thm_2Erich__list_2EFILTER__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0f1: A_27a > $o,V1f2: A_27b > A_27a,V2l: tyop_2Elist_2Elist @ A_27b] :
( ( c_2Elist_2EFILTER @ A_27a @ V0f1 @ ( c_2Elist_2EMAP @ A_27b @ A_27a @ V1f2 @ V2l ) )
= ( c_2Elist_2EMAP @ A_27b @ A_27a @ V1f2 @ ( c_2Elist_2EFILTER @ A_27b @ ( c_2Ecombin_2Eo @ A_27b @ $o @ A_27a @ V0f1 @ V1f2 ) @ V2l ) ) ) ).
thf(thm_2Erich__list_2ELENGTH__FILTER__LEQ,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] : ( c_2Earithmetic_2E_3C_3D @ ( c_2Elist_2ELENGTH @ A_27a @ ( c_2Elist_2EFILTER @ A_27a @ V0P @ V1l ) ) @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) ) ).
thf(thm_2Erich__list_2EFILTER__EQ,axiom,
! [A_27a: $tType,V0P1: A_27a > $o,V1P2: A_27a > $o,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( ( c_2Elist_2EFILTER @ A_27a @ V0P1 @ V2l )
= ( c_2Elist_2EFILTER @ A_27a @ V1P2 @ V2l ) )
<=> ! [V3x: A_27a] :
( ( c_2Ebool_2EIN @ A_27a @ V3x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V2l ) )
=> ( ( V0P1 @ V3x )
= ( V1P2 @ V3x ) ) ) ) ).
thf(thm_2Erich__list_2ELENGTH__SEG,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1k: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V0n @ V1k ) @ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) )
=> ( ( c_2Elist_2ELENGTH @ A_27a @ ( c_2Erich__list_2ESEG @ A_27a @ V0n @ V1k @ V2l ) )
= V0n ) ) ).
thf(thm_2Erich__list_2EAPPEND__NIL,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EAPPEND @ A_27a @ V0l @ ( c_2Elist_2ENIL @ A_27a ) )
= V0l )
& ! [V1l: tyop_2Elist_2Elist @ A_27b] :
( ( c_2Elist_2EAPPEND @ A_27b @ ( c_2Elist_2ENIL @ A_27b ) @ V1l )
= V1l ) ) ).
thf(thm_2Erich__list_2EAPPEND__FOLDR,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EAPPEND @ A_27a @ V0l1 @ V1l2 )
= ( c_2Elist_2EFOLDR @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS @ A_27a ) @ V1l2 @ V0l1 ) ) ).
thf(thm_2Erich__list_2EAPPEND__FOLDL,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EAPPEND @ A_27a @ V0l1 @ V1l2 )
= ( c_2Elist_2EFOLDL @ A_27a @ ( tyop_2Elist_2Elist @ A_27a )
@ ^ [V2l_27: tyop_2Elist_2Elist @ A_27a,V3x: A_27a] : ( c_2Elist_2ESNOC @ A_27a @ V3x @ V2l_27 )
@ V0l1
@ V1l2 ) ) ).
thf(thm_2Erich__list_2EFOLDR__APPEND,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b > A_27b,V1e: A_27b,V2l1: tyop_2Elist_2Elist @ A_27a,V3l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFOLDR @ A_27a @ A_27b @ V0f @ V1e @ ( c_2Elist_2EAPPEND @ A_27a @ V2l1 @ V3l2 ) )
= ( c_2Elist_2EFOLDR @ A_27a @ A_27b @ V0f @ ( c_2Elist_2EFOLDR @ A_27a @ A_27b @ V0f @ V1e @ V3l2 ) @ V2l1 ) ) ).
thf(thm_2Erich__list_2EFOLDL__APPEND,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b > A_27a,V1e: A_27a,V2l1: tyop_2Elist_2Elist @ A_27b,V3l2: tyop_2Elist_2Elist @ A_27b] :
( ( c_2Elist_2EFOLDL @ A_27b @ A_27a @ V0f @ V1e @ ( c_2Elist_2EAPPEND @ A_27b @ V2l1 @ V3l2 ) )
= ( c_2Elist_2EFOLDL @ A_27b @ A_27a @ V0f @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a @ V0f @ V1e @ V2l1 ) @ V3l2 ) ) ).
thf(thm_2Erich__list_2ECONS__APPEND,axiom,
! [A_27a: $tType,V0x: A_27a,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2ECONS @ A_27a @ V0x @ V1l )
= ( c_2Elist_2EAPPEND @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V0x @ ( c_2Elist_2ENIL @ A_27a ) ) @ V1l ) ) ).
thf(thm_2Erich__list_2EASSOC__APPEND,axiom,
! [A_27a: $tType] : ( c_2Ecombin_2EASSOC @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND @ A_27a ) ) ).
thf(thm_2Erich__list_2EMONOID__APPEND__NIL,axiom,
! [A_27a: $tType] : ( c_2Ecombin_2EMONOID @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) ) ).
thf(thm_2Erich__list_2EFLAT__SNOC,axiom,
! [A_27a: $tType,V0x: tyop_2Elist_2Elist @ A_27a,V1l: tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ A_27a )] :
( ( c_2Elist_2EFLAT @ A_27a @ ( c_2Elist_2ESNOC @ ( tyop_2Elist_2Elist @ A_27a ) @ V0x @ V1l ) )
= ( c_2Elist_2EAPPEND @ A_27a @ ( c_2Elist_2EFLAT @ A_27a @ V1l ) @ V0x ) ) ).
thf(thm_2Erich__list_2EFLAT__FOLDR,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ A_27a )] :
( ( c_2Elist_2EFLAT @ A_27a @ V0l )
= ( c_2Elist_2EFOLDR @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) @ V0l ) ) ).
thf(thm_2Erich__list_2EFLAT__FOLDL,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ A_27a )] :
( ( c_2Elist_2EFLAT @ A_27a @ V0l )
= ( c_2Elist_2EFOLDL @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) @ V0l ) ) ).
thf(thm_2Erich__list_2ELENGTH__FLAT,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ A_27a )] :
( ( c_2Elist_2ELENGTH @ A_27a @ ( c_2Elist_2EFLAT @ A_27a @ V0l ) )
= ( c_2Elist_2ESUM @ ( c_2Elist_2EMAP @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) ) ).
thf(thm_2Erich__list_2EREVERSE__FOLDR,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EREVERSE @ A_27a @ V0l )
= ( c_2Elist_2EFOLDR @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ESNOC @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) @ V0l ) ) ).
thf(thm_2Erich__list_2EREVERSE__FOLDL,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EREVERSE @ A_27a @ V0l )
= ( c_2Elist_2EFOLDL @ A_27a @ ( tyop_2Elist_2Elist @ A_27a )
@ ^ [V1l_27: tyop_2Elist_2Elist @ A_27a,V2x: A_27a] : ( c_2Elist_2ECONS @ A_27a @ V2x @ V1l_27 )
@ ( c_2Elist_2ENIL @ A_27a )
@ V0l ) ) ).
thf(thm_2Erich__list_2EALL__EL__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0P: A_27a > $o,V1f: A_27b > A_27a,V2l: tyop_2Elist_2Elist @ A_27b] :
( ( c_2Elist_2EEVERY @ A_27a @ V0P @ ( c_2Elist_2EMAP @ A_27b @ A_27a @ V1f @ V2l ) )
= ( c_2Elist_2EEVERY @ A_27b @ ( c_2Ecombin_2Eo @ A_27b @ $o @ A_27a @ V0P @ V1f ) @ V2l ) ) ).
thf(thm_2Erich__list_2EMEM__EXISTS,axiom,
! [A_27a: $tType,V0x: A_27a,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Ebool_2EIN @ A_27a @ V0x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V1l ) )
= ( c_2Elist_2EEXISTS @ A_27a @ ( c_2Emin_2E_3D @ A_27a @ V0x ) @ V1l ) ) ).
thf(thm_2Erich__list_2ESUM__FOLDR,axiom,
! [V0l: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
( ( c_2Elist_2ESUM @ V0l )
= ( c_2Elist_2EFOLDR @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Earithmetic_2E_2B @ c_2Enum_2E0 @ V0l ) ) ).
thf(thm_2Erich__list_2ESUM__FOLDL,axiom,
! [V0l: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
( ( c_2Elist_2ESUM @ V0l )
= ( c_2Elist_2EFOLDL @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Earithmetic_2E_2B @ c_2Enum_2E0 @ V0l ) ) ).
thf(thm_2Erich__list_2EIS__PREFIX,axiom,
! [A_27a: $tType] :
( ! [V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EisPREFIX @ A_27a @ ( c_2Elist_2ENIL @ A_27a ) @ V0l )
= c_2Ebool_2ET )
& ! [V1x: A_27a,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EisPREFIX @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V1x @ V2l ) @ ( c_2Elist_2ENIL @ A_27a ) )
= c_2Ebool_2EF )
& ! [V3x1: A_27a,V4l1: tyop_2Elist_2Elist @ A_27a,V5x2: A_27a,V6l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EisPREFIX @ A_27a @ ( c_2Elist_2ECONS @ A_27a @ V5x2 @ V6l2 ) @ ( c_2Elist_2ECONS @ A_27a @ V3x1 @ V4l1 ) )
<=> ( ( V3x1 = V5x2 )
& ( c_2Elist_2EisPREFIX @ A_27a @ V6l2 @ V4l1 ) ) ) ) ).
thf(thm_2Erich__list_2EIS__PREFIX__APPEND,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EisPREFIX @ A_27a @ V1l2 @ V0l1 )
<=> ? [V2l: tyop_2Elist_2Elist @ A_27a] :
( V0l1
= ( c_2Elist_2EAPPEND @ A_27a @ V1l2 @ V2l ) ) ) ).
thf(thm_2Erich__list_2EIS__SUFFIX__APPEND,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EIS__SUFFIX @ A_27a @ V0l1 @ V1l2 )
<=> ? [V2l: tyop_2Elist_2Elist @ A_27a] :
( V0l1
= ( c_2Elist_2EAPPEND @ A_27a @ V2l @ V1l2 ) ) ) ).
thf(thm_2Erich__list_2EIS__SUBLIST__APPEND,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EIS__SUBLIST @ A_27a @ V0l1 @ V1l2 )
<=> ? [V2l: tyop_2Elist_2Elist @ A_27a,V3l_27: tyop_2Elist_2Elist @ A_27a] :
( V0l1
= ( c_2Elist_2EAPPEND @ A_27a @ V2l @ ( c_2Elist_2EAPPEND @ A_27a @ V1l2 @ V3l_27 ) ) ) ) ).
thf(thm_2Erich__list_2EIS__PREFIX__IS__SUBLIST,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EisPREFIX @ A_27a @ V1l2 @ V0l1 )
=> ( c_2Erich__list_2EIS__SUBLIST @ A_27a @ V0l1 @ V1l2 ) ) ).
thf(thm_2Erich__list_2EIS__SUFFIX__IS__SUBLIST,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EIS__SUFFIX @ A_27a @ V0l1 @ V1l2 )
=> ( c_2Erich__list_2EIS__SUBLIST @ A_27a @ V0l1 @ V1l2 ) ) ).
thf(thm_2Erich__list_2EIS__PREFIX__REVERSE,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EisPREFIX @ A_27a @ ( c_2Elist_2EREVERSE @ A_27a @ V1l2 ) @ ( c_2Elist_2EREVERSE @ A_27a @ V0l1 ) )
= ( c_2Erich__list_2EIS__SUFFIX @ A_27a @ V0l1 @ V1l2 ) ) ).
thf(thm_2Erich__list_2EIS__SUFFIX__REVERSE,axiom,
! [A_27a: $tType,V0l2: tyop_2Elist_2Elist @ A_27a,V1l1: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EIS__SUFFIX @ A_27a @ ( c_2Elist_2EREVERSE @ A_27a @ V1l1 ) @ ( c_2Elist_2EREVERSE @ A_27a @ V0l2 ) )
= ( c_2Elist_2EisPREFIX @ A_27a @ V0l2 @ V1l1 ) ) ).
thf(thm_2Erich__list_2EIS__SUFFIX__CONS2__E,axiom,
! [A_27a: $tType,V0s: tyop_2Elist_2Elist @ A_27a,V1h: A_27a,V2t: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EIS__SUFFIX @ A_27a @ V0s @ ( c_2Elist_2ECONS @ A_27a @ V1h @ V2t ) )
=> ( c_2Erich__list_2EIS__SUFFIX @ A_27a @ V0s @ V2t ) ) ).
thf(thm_2Erich__list_2EIS__SUFFIX__REFL,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] : ( c_2Erich__list_2EIS__SUFFIX @ A_27a @ V0l @ V0l ) ).
thf(thm_2Erich__list_2EIS__SUBLIST__REVERSE,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EIS__SUBLIST @ A_27a @ ( c_2Elist_2EREVERSE @ A_27a @ V0l1 ) @ ( c_2Elist_2EREVERSE @ A_27a @ V1l2 ) )
= ( c_2Erich__list_2EIS__SUBLIST @ A_27a @ V0l1 @ V1l2 ) ) ).
thf(thm_2Erich__list_2EPREFIX__FOLDR,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EPREFIX @ A_27a @ V0P @ V1l )
= ( c_2Elist_2EFOLDR @ A_27a @ ( tyop_2Elist_2Elist @ A_27a )
@ ^ [V2x: A_27a,V3l_27: tyop_2Elist_2Elist @ A_27a] : ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ A_27a ) @ ( V0P @ V2x ) @ ( c_2Elist_2ECONS @ A_27a @ V2x @ V3l_27 ) @ ( c_2Elist_2ENIL @ A_27a ) )
@ ( c_2Elist_2ENIL @ A_27a )
@ V1l ) ) ).
thf(thm_2Erich__list_2EPREFIX,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0P: A_27a > $o] :
( ( c_2Erich__list_2EPREFIX @ A_27a @ V0P @ ( c_2Elist_2ENIL @ A_27a ) )
= ( c_2Elist_2ENIL @ A_27a ) )
& ! [V1P: A_27b > $o,V2x: A_27b,V3l: tyop_2Elist_2Elist @ A_27b] :
( ( c_2Erich__list_2EPREFIX @ A_27b @ V1P @ ( c_2Elist_2ECONS @ A_27b @ V2x @ V3l ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ A_27b ) @ ( V1P @ V2x ) @ ( c_2Elist_2ECONS @ A_27b @ V2x @ ( c_2Erich__list_2EPREFIX @ A_27b @ V1P @ V3l ) ) @ ( c_2Elist_2ENIL @ A_27b ) ) ) ) ).
thf(thm_2Erich__list_2EIS__PREFIX__PREFIX,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] : ( c_2Elist_2EisPREFIX @ A_27a @ ( c_2Erich__list_2EPREFIX @ A_27a @ V0P @ V1l ) @ V1l ) ).
thf(thm_2Erich__list_2ELENGTH__SCANL,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b > A_27a,V1e: A_27a,V2l: tyop_2Elist_2Elist @ A_27b] :
( ( c_2Elist_2ELENGTH @ A_27a @ ( c_2Erich__list_2ESCANL @ A_27b @ A_27a @ V0f @ V1e @ V2l ) )
= ( c_2Enum_2ESUC @ ( c_2Elist_2ELENGTH @ A_27b @ V2l ) ) ) ).
thf(thm_2Erich__list_2ELENGTH__SCANR,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b > A_27b,V1e: A_27b,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2ELENGTH @ A_27b @ ( c_2Erich__list_2ESCANR @ A_27a @ A_27b @ V0f @ V1e @ V2l ) )
= ( c_2Enum_2ESUC @ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) ) ) ).
thf(thm_2Erich__list_2ECOMM__MONOID__FOLDL,axiom,
! [A_27a: $tType,V0f: A_27a > A_27a > A_27a] :
( ( c_2Ecombin_2ECOMM @ A_27a @ A_27a @ V0f )
=> ! [V1e_27: A_27a] :
( ( c_2Ecombin_2EMONOID @ A_27a @ V0f @ V1e_27 )
=> ! [V2e: A_27a,V3l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFOLDL @ A_27a @ A_27a @ V0f @ V2e @ V3l )
= ( V0f @ V2e @ ( c_2Elist_2EFOLDL @ A_27a @ A_27a @ V0f @ V1e_27 @ V3l ) ) ) ) ) ).
thf(thm_2Erich__list_2ECOMM__MONOID__FOLDR,axiom,
! [A_27a: $tType,V0f: A_27a > A_27a > A_27a] :
( ( c_2Ecombin_2ECOMM @ A_27a @ A_27a @ V0f )
=> ! [V1e_27: A_27a] :
( ( c_2Ecombin_2EMONOID @ A_27a @ V0f @ V1e_27 )
=> ! [V2e: A_27a,V3l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFOLDR @ A_27a @ A_27a @ V0f @ V2e @ V3l )
= ( V0f @ V2e @ ( c_2Elist_2EFOLDR @ A_27a @ A_27a @ V0f @ V1e_27 @ V3l ) ) ) ) ) ).
thf(thm_2Erich__list_2EFCOMM__FOLDR__APPEND,axiom,
! [A_27a: $tType,A_27b: $tType,V0g: A_27a > A_27a > A_27a,V1f: A_27b > A_27a > A_27a] :
( ( c_2Ecombin_2EFCOMM @ A_27a @ A_27a @ A_27b @ V0g @ V1f )
=> ! [V2e: A_27a] :
( ( c_2Ecombin_2ELEFT__ID @ A_27a @ A_27a @ V0g @ V2e )
=> ! [V3l1: tyop_2Elist_2Elist @ A_27b,V4l2: tyop_2Elist_2Elist @ A_27b] :
( ( c_2Elist_2EFOLDR @ A_27b @ A_27a @ V1f @ V2e @ ( c_2Elist_2EAPPEND @ A_27b @ V3l1 @ V4l2 ) )
= ( V0g @ ( c_2Elist_2EFOLDR @ A_27b @ A_27a @ V1f @ V2e @ V3l1 ) @ ( c_2Elist_2EFOLDR @ A_27b @ A_27a @ V1f @ V2e @ V4l2 ) ) ) ) ) ).
thf(thm_2Erich__list_2EFCOMM__FOLDL__APPEND,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b > A_27a,V1g: A_27a > A_27a > A_27a] :
( ( c_2Ecombin_2EFCOMM @ A_27a @ A_27b @ A_27a @ V0f @ V1g )
=> ! [V2e: A_27a] :
( ( c_2Ecombin_2ERIGHT__ID @ A_27a @ A_27a @ V1g @ V2e )
=> ! [V3l1: tyop_2Elist_2Elist @ A_27b,V4l2: tyop_2Elist_2Elist @ A_27b] :
( ( c_2Elist_2EFOLDL @ A_27b @ A_27a @ V0f @ V2e @ ( c_2Elist_2EAPPEND @ A_27b @ V3l1 @ V4l2 ) )
= ( V1g @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a @ V0f @ V2e @ V3l1 ) @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a @ V0f @ V2e @ V4l2 ) ) ) ) ) ).
thf(thm_2Erich__list_2EFOLDL__SINGLE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b > A_27a,V1e: A_27a,V2x: A_27b] :
( ( c_2Elist_2EFOLDL @ A_27b @ A_27a @ V0f @ V1e @ ( c_2Elist_2ECONS @ A_27b @ V2x @ ( c_2Elist_2ENIL @ A_27b ) ) )
= ( V0f @ V1e @ V2x ) ) ).
thf(thm_2Erich__list_2EFOLDR__SINGLE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b > A_27b,V1e: A_27b,V2x: A_27a] :
( ( c_2Elist_2EFOLDR @ A_27a @ A_27b @ V0f @ V1e @ ( c_2Elist_2ECONS @ A_27a @ V2x @ ( c_2Elist_2ENIL @ A_27a ) ) )
= ( V0f @ V2x @ V1e ) ) ).
thf(thm_2Erich__list_2EFOLDR__CONS__NIL,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFOLDR @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) @ V0l )
= V0l ) ).
thf(thm_2Erich__list_2EFOLDL__SNOC__NIL,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFOLDL @ A_27a @ ( tyop_2Elist_2Elist @ A_27a )
@ ^ [V1xs: tyop_2Elist_2Elist @ A_27a,V2x: A_27a] : ( c_2Elist_2ESNOC @ A_27a @ V2x @ V1xs )
@ ( c_2Elist_2ENIL @ A_27a )
@ V0l )
= V0l ) ).
thf(thm_2Erich__list_2EFOLDR__FOLDL__REVERSE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b > A_27b,V1e: A_27b,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFOLDR @ A_27a @ A_27b @ V0f @ V1e @ V2l )
= ( c_2Elist_2EFOLDL @ A_27a @ A_27b
@ ^ [V3x: A_27b,V4y: A_27a] : ( V0f @ V4y @ V3x )
@ V1e
@ ( c_2Elist_2EREVERSE @ A_27a @ V2l ) ) ) ).
thf(thm_2Erich__list_2EFOLDL__FOLDR__REVERSE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b > A_27a,V1e: A_27a,V2l: tyop_2Elist_2Elist @ A_27b] :
( ( c_2Elist_2EFOLDL @ A_27b @ A_27a @ V0f @ V1e @ V2l )
= ( c_2Elist_2EFOLDR @ A_27b @ A_27a
@ ^ [V3x: A_27b,V4y: A_27a] : ( V0f @ V4y @ V3x )
@ V1e
@ ( c_2Elist_2EREVERSE @ A_27b @ V2l ) ) ) ).
thf(thm_2Erich__list_2EFOLDR__REVERSE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b > A_27b,V1e: A_27b,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFOLDR @ A_27a @ A_27b @ V0f @ V1e @ ( c_2Elist_2EREVERSE @ A_27a @ V2l ) )
= ( c_2Elist_2EFOLDL @ A_27a @ A_27b
@ ^ [V3x: A_27b,V4y: A_27a] : ( V0f @ V4y @ V3x )
@ V1e
@ V2l ) ) ).
thf(thm_2Erich__list_2EFOLDL__REVERSE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b > A_27a,V1e: A_27a,V2l: tyop_2Elist_2Elist @ A_27b] :
( ( c_2Elist_2EFOLDL @ A_27b @ A_27a @ V0f @ V1e @ ( c_2Elist_2EREVERSE @ A_27b @ V2l ) )
= ( c_2Elist_2EFOLDR @ A_27b @ A_27a
@ ^ [V3x: A_27b,V4y: A_27a] : ( V0f @ V4y @ V3x )
@ V1e
@ V2l ) ) ).
thf(thm_2Erich__list_2EFOLDR__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f: A_27a > A_27b > A_27b,V1e: A_27b,V2g: A_27c > A_27a,V3l: tyop_2Elist_2Elist @ A_27c] :
( ( c_2Elist_2EFOLDR @ A_27a @ A_27b @ V0f @ V1e @ ( c_2Elist_2EMAP @ A_27c @ A_27a @ V2g @ V3l ) )
= ( c_2Elist_2EFOLDR @ A_27c @ A_27b
@ ^ [V4x: A_27c,V5y: A_27b] : ( V0f @ ( V2g @ V4x ) @ V5y )
@ V1e
@ V3l ) ) ).
thf(thm_2Erich__list_2EFOLDL__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f: A_27a > A_27b > A_27a,V1e: A_27a,V2g: A_27c > A_27b,V3l: tyop_2Elist_2Elist @ A_27c] :
( ( c_2Elist_2EFOLDL @ A_27b @ A_27a @ V0f @ V1e @ ( c_2Elist_2EMAP @ A_27c @ A_27b @ V2g @ V3l ) )
= ( c_2Elist_2EFOLDL @ A_27c @ A_27a
@ ^ [V4x: A_27a,V5y: A_27c] : ( V0f @ V4x @ ( V2g @ V5y ) )
@ V1e
@ V3l ) ) ).
thf(thm_2Erich__list_2EEVERY__FOLDR,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEVERY @ A_27a @ V0P @ V1l )
= ( c_2Elist_2EFOLDR @ A_27a @ $o
@ ^ [V2x: A_27a,V3l_27: $o] : ( c_2Ebool_2E_2F_5C @ ( V0P @ V2x ) @ V3l_27 )
@ c_2Ebool_2ET
@ V1l ) ) ).
thf(thm_2Erich__list_2EEVERY__FOLDL,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEVERY @ A_27a @ V0P @ V1l )
= ( c_2Elist_2EFOLDL @ A_27a @ $o
@ ^ [V2l_27: $o,V3x: A_27a] : ( c_2Ebool_2E_2F_5C @ V2l_27 @ ( V0P @ V3x ) )
@ c_2Ebool_2ET
@ V1l ) ) ).
thf(thm_2Erich__list_2EEXISTS__FOLDR,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEXISTS @ A_27a @ V0P @ V1l )
= ( c_2Elist_2EFOLDR @ A_27a @ $o
@ ^ [V2x: A_27a,V3l_27: $o] : ( c_2Ebool_2E_5C_2F @ ( V0P @ V2x ) @ V3l_27 )
@ c_2Ebool_2EF
@ V1l ) ) ).
thf(thm_2Erich__list_2EEXISTS__FOLDL,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEXISTS @ A_27a @ V0P @ V1l )
= ( c_2Elist_2EFOLDL @ A_27a @ $o
@ ^ [V2l_27: $o,V3x: A_27a] : ( c_2Ebool_2E_5C_2F @ V2l_27 @ ( V0P @ V3x ) )
@ c_2Ebool_2EF
@ V1l ) ) ).
thf(thm_2Erich__list_2EEVERY__FOLDR__MAP,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEVERY @ A_27a @ V0P @ V1l )
= ( c_2Elist_2EFOLDR @ $o @ $o @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET @ ( c_2Elist_2EMAP @ A_27a @ $o @ V0P @ V1l ) ) ) ).
thf(thm_2Erich__list_2EEVERY__FOLDL__MAP,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEVERY @ A_27a @ V0P @ V1l )
= ( c_2Elist_2EFOLDL @ $o @ $o @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET @ ( c_2Elist_2EMAP @ A_27a @ $o @ V0P @ V1l ) ) ) ).
thf(thm_2Erich__list_2EEXISTS__FOLDR__MAP,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEXISTS @ A_27a @ V0P @ V1l )
= ( c_2Elist_2EFOLDR @ $o @ $o @ c_2Ebool_2E_5C_2F @ c_2Ebool_2EF @ ( c_2Elist_2EMAP @ A_27a @ $o @ V0P @ V1l ) ) ) ).
thf(thm_2Erich__list_2EEXISTS__FOLDL__MAP,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEXISTS @ A_27a @ V0P @ V1l )
= ( c_2Elist_2EFOLDL @ $o @ $o @ c_2Ebool_2E_5C_2F @ c_2Ebool_2EF @ ( c_2Elist_2EMAP @ A_27a @ $o @ V0P @ V1l ) ) ) ).
thf(thm_2Erich__list_2EFOLDR__FILTER,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b > A_27b,V1e: A_27b,V2P: A_27a > $o,V3l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFOLDR @ A_27a @ A_27b @ V0f @ V1e @ ( c_2Elist_2EFILTER @ A_27a @ V2P @ V3l ) )
= ( c_2Elist_2EFOLDR @ A_27a @ A_27b
@ ^ [V4x: A_27a,V5y: A_27b] : ( c_2Ebool_2ECOND @ A_27b @ ( V2P @ V4x ) @ ( V0f @ V4x @ V5y ) @ V5y )
@ V1e
@ V3l ) ) ).
thf(thm_2Erich__list_2EFOLDL__FILTER,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b > A_27a,V1e: A_27a,V2P: A_27b > $o,V3l: tyop_2Elist_2Elist @ A_27b] :
( ( c_2Elist_2EFOLDL @ A_27b @ A_27a @ V0f @ V1e @ ( c_2Elist_2EFILTER @ A_27b @ V2P @ V3l ) )
= ( c_2Elist_2EFOLDL @ A_27b @ A_27a
@ ^ [V4x: A_27a,V5y: A_27b] : ( c_2Ebool_2ECOND @ A_27a @ ( V2P @ V5y ) @ ( V0f @ V4x @ V5y ) @ V4x )
@ V1e
@ V3l ) ) ).
thf(thm_2Erich__list_2EASSOC__FOLDR__FLAT,axiom,
! [A_27a: $tType,V0f: A_27a > A_27a > A_27a] :
( ( c_2Ecombin_2EASSOC @ A_27a @ V0f )
=> ! [V1e: A_27a] :
( ( c_2Ecombin_2ELEFT__ID @ A_27a @ A_27a @ V0f @ V1e )
=> ! [V2l: tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ A_27a )] :
( ( c_2Elist_2EFOLDR @ A_27a @ A_27a @ V0f @ V1e @ ( c_2Elist_2EFLAT @ A_27a @ V2l ) )
= ( c_2Elist_2EFOLDR @ A_27a @ A_27a @ V0f @ V1e @ ( c_2Elist_2EMAP @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a @ ( c_2Elist_2EFOLDR @ A_27a @ A_27a @ V0f @ V1e ) @ V2l ) ) ) ) ) ).
thf(thm_2Erich__list_2EASSOC__FOLDL__FLAT,axiom,
! [A_27a: $tType,V0f: A_27a > A_27a > A_27a] :
( ( c_2Ecombin_2EASSOC @ A_27a @ V0f )
=> ! [V1e: A_27a] :
( ( c_2Ecombin_2ERIGHT__ID @ A_27a @ A_27a @ V0f @ V1e )
=> ! [V2l: tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ A_27a )] :
( ( c_2Elist_2EFOLDL @ A_27a @ A_27a @ V0f @ V1e @ ( c_2Elist_2EFLAT @ A_27a @ V2l ) )
= ( c_2Elist_2EFOLDL @ A_27a @ A_27a @ V0f @ V1e @ ( c_2Elist_2EMAP @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a @ ( c_2Elist_2EFOLDL @ A_27a @ A_27a @ V0f @ V1e ) @ V2l ) ) ) ) ) ).
thf(thm_2Erich__list_2EMAP__FLAT,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b,V1l: tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ A_27a )] :
( ( c_2Elist_2EMAP @ A_27a @ A_27b @ V0f @ ( c_2Elist_2EFLAT @ A_27a @ V1l ) )
= ( c_2Elist_2EFLAT @ A_27b @ ( c_2Elist_2EMAP @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EMAP @ A_27a @ A_27b @ V0f ) @ V1l ) ) ) ).
thf(thm_2Erich__list_2EFILTER__FLAT,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ A_27a )] :
( ( c_2Elist_2EFILTER @ A_27a @ V0P @ ( c_2Elist_2EFLAT @ A_27a @ V1l ) )
= ( c_2Elist_2EFLAT @ A_27a @ ( c_2Elist_2EMAP @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EFILTER @ A_27a @ V0P ) @ V1l ) ) ) ).
thf(thm_2Erich__list_2EEXISTS__DISJ,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1Q: A_27a > $o,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEXISTS @ A_27a
@ ^ [V3x: A_27a] : ( c_2Ebool_2E_5C_2F @ ( V0P @ V3x ) @ ( V1Q @ V3x ) )
@ V2l )
<=> ( ( c_2Elist_2EEXISTS @ A_27a @ V0P @ V2l )
| ( c_2Elist_2EEXISTS @ A_27a @ V1Q @ V2l ) ) ) ).
thf(thm_2Erich__list_2EMEM__FOLDR,axiom,
! [A_27a: $tType,V0y: A_27a,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Ebool_2EIN @ A_27a @ V0y @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V1l ) )
= ( c_2Elist_2EFOLDR @ A_27a @ $o
@ ^ [V2x: A_27a,V3l_27: $o] : ( c_2Ebool_2E_5C_2F @ ( c_2Emin_2E_3D @ A_27a @ V0y @ V2x ) @ V3l_27 )
@ c_2Ebool_2EF
@ V1l ) ) ).
thf(thm_2Erich__list_2EMEM__FOLDL,axiom,
! [A_27a: $tType,V0y: A_27a,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Ebool_2EIN @ A_27a @ V0y @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V1l ) )
= ( c_2Elist_2EFOLDL @ A_27a @ $o
@ ^ [V2l_27: $o,V3x: A_27a] : ( c_2Ebool_2E_5C_2F @ V2l_27 @ ( c_2Emin_2E_3D @ A_27a @ V0y @ V3x ) )
@ c_2Ebool_2EF
@ V1l ) ) ).
thf(thm_2Erich__list_2ENULL__FOLDR,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2ENULL @ A_27a @ V0l )
= ( c_2Elist_2EFOLDR @ A_27a @ $o
@ ^ [V1x: A_27a,V2l_27: $o] : c_2Ebool_2EF
@ c_2Ebool_2ET
@ V0l ) ) ).
thf(thm_2Erich__list_2ENULL__FOLDL,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2ENULL @ A_27a @ V0l )
= ( c_2Elist_2EFOLDL @ A_27a @ $o
@ ^ [V1x: $o,V2l_27: A_27a] : c_2Ebool_2EF
@ c_2Ebool_2ET
@ V0l ) ) ).
thf(thm_2Erich__list_2EMAP__REVERSE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EMAP @ A_27a @ A_27b @ V0f @ ( c_2Elist_2EREVERSE @ A_27a @ V1l ) )
= ( c_2Elist_2EREVERSE @ A_27b @ ( c_2Elist_2EMAP @ A_27a @ A_27b @ V0f @ V1l ) ) ) ).
thf(thm_2Erich__list_2ESEG__LENGTH__ID,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Elist_2ELENGTH @ A_27a @ V0l ) @ c_2Enum_2E0 @ V0l )
= V0l ) ).
thf(thm_2Erich__list_2ESEG__SUC__CONS,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a,V3x: A_27a] :
( ( c_2Erich__list_2ESEG @ A_27a @ V0m @ ( c_2Enum_2ESUC @ V1n ) @ ( c_2Elist_2ECONS @ A_27a @ V3x @ V2l ) )
= ( c_2Erich__list_2ESEG @ A_27a @ V0m @ V1n @ V2l ) ) ).
thf(thm_2Erich__list_2ESEG__0__SNOC,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a,V2x: A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0m @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Erich__list_2ESEG @ A_27a @ V0m @ c_2Enum_2E0 @ ( c_2Elist_2ESNOC @ A_27a @ V2x @ V1l ) )
= ( c_2Erich__list_2ESEG @ A_27a @ V0m @ c_2Enum_2E0 @ V1l ) ) ) ).
thf(thm_2Erich__list_2EBUTLASTN__SEG,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0n @ V1l )
= ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) @ V0n ) @ c_2Enum_2E0 @ V1l ) ) ) ).
thf(thm_2Erich__list_2ELASTN__CONS,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ! [V2x: A_27a] :
( ( c_2Erich__list_2ELASTN @ A_27a @ V0n @ ( c_2Elist_2ECONS @ A_27a @ V2x @ V1l ) )
= ( c_2Erich__list_2ELASTN @ A_27a @ V0n @ V1l ) ) ) ).
thf(thm_2Erich__list_2ELENGTH__LASTN,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Elist_2ELENGTH @ A_27a @ ( c_2Erich__list_2ELASTN @ A_27a @ V0n @ V1l ) )
= V0n ) ) ).
thf(thm_2Erich__list_2ELASTN__LENGTH__ID,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ELASTN @ A_27a @ ( c_2Elist_2ELENGTH @ A_27a @ V0l ) @ V0l )
= V0l ) ).
thf(thm_2Erich__list_2ELASTN__LASTN,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a,V1n: tyop_2Enum_2Enum,V2m: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V2m @ ( c_2Elist_2ELENGTH @ A_27a @ V0l ) )
=> ( ( c_2Earithmetic_2E_3C_3D @ V1n @ V2m )
=> ( ( c_2Erich__list_2ELASTN @ A_27a @ V1n @ ( c_2Erich__list_2ELASTN @ A_27a @ V2m @ V0l ) )
= ( c_2Erich__list_2ELASTN @ A_27a @ V1n @ V0l ) ) ) ) ).
thf(thm_2Erich__list_2ETAKE__SNOC,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ! [V2x: A_27a] :
( ( c_2Elist_2ETAKE @ A_27a @ V0n @ ( c_2Elist_2ESNOC @ A_27a @ V2x @ V1l ) )
= ( c_2Elist_2ETAKE @ A_27a @ V0n @ V1l ) ) ) ).
thf(thm_2Erich__list_2EBUTLASTN__LENGTH__NIL,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EBUTLASTN @ A_27a @ ( c_2Elist_2ELENGTH @ A_27a @ V0l ) @ V0l )
= ( c_2Elist_2ENIL @ A_27a ) ) ).
thf(thm_2Erich__list_2EDROP__APPEND,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l1: tyop_2Elist_2Elist @ A_27a,V2l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EDROP @ A_27a @ V0n @ ( c_2Elist_2EAPPEND @ A_27a @ V1l1 @ V2l2 ) )
= ( c_2Elist_2EAPPEND @ A_27a @ ( c_2Elist_2EDROP @ A_27a @ V0n @ V1l1 ) @ ( c_2Elist_2EDROP @ A_27a @ ( c_2Earithmetic_2E_2D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l1 ) ) @ V2l2 ) ) ) ).
thf(thm_2Erich__list_2EDROP__APPEND1,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l1: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l1 ) )
=> ! [V2l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EDROP @ A_27a @ V0n @ ( c_2Elist_2EAPPEND @ A_27a @ V1l1 @ V2l2 ) )
= ( c_2Elist_2EAPPEND @ A_27a @ ( c_2Elist_2EDROP @ A_27a @ V0n @ V1l1 ) @ V2l2 ) ) ) ).
thf(thm_2Erich__list_2EDROP__APPEND2,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Elist_2ELENGTH @ A_27a @ V0l1 ) @ V1n )
=> ! [V2l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EDROP @ A_27a @ V1n @ ( c_2Elist_2EAPPEND @ A_27a @ V0l1 @ V2l2 ) )
= ( c_2Elist_2EDROP @ A_27a @ ( c_2Earithmetic_2E_2D @ V1n @ ( c_2Elist_2ELENGTH @ A_27a @ V0l1 ) ) @ V2l2 ) ) ) ).
thf(thm_2Erich__list_2EDROP__DROP__T,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EDROP @ A_27a @ V0n @ ( c_2Elist_2EDROP @ A_27a @ V1m @ V2l ) )
= ( c_2Elist_2EDROP @ A_27a @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) @ V2l ) ) ).
thf(thm_2Erich__list_2EDROP__DROP,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) @ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) )
=> ( ( c_2Elist_2EDROP @ A_27a @ V0n @ ( c_2Elist_2EDROP @ A_27a @ V1m @ V2l ) )
= ( c_2Elist_2EDROP @ A_27a @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) @ V2l ) ) ) ).
thf(thm_2Erich__list_2ELASTN__SEG,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Erich__list_2ELASTN @ A_27a @ V0n @ V1l )
= ( c_2Erich__list_2ESEG @ A_27a @ V0n @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) @ V0n ) @ V1l ) ) ) ).
thf(thm_2Erich__list_2ETAKE__SEG,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Elist_2ETAKE @ A_27a @ V0n @ V1l )
= ( c_2Erich__list_2ESEG @ A_27a @ V0n @ c_2Enum_2E0 @ V1l ) ) ) ).
thf(thm_2Erich__list_2EDROP__SEG,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Elist_2EDROP @ A_27a @ V0n @ V1l )
= ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) @ V0n ) @ V0n @ V1l ) ) ) ).
thf(thm_2Erich__list_2EDROP__SNOC,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ! [V2x: A_27a] :
( ( c_2Elist_2EDROP @ A_27a @ V0n @ ( c_2Elist_2ESNOC @ A_27a @ V2x @ V1l ) )
= ( c_2Elist_2ESNOC @ A_27a @ V2x @ ( c_2Elist_2EDROP @ A_27a @ V0n @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2EAPPEND__BUTLASTN__DROP,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( ( c_2Earithmetic_2E_2B @ V0m @ V1n )
= ( c_2Elist_2ELENGTH @ A_27a @ V2l ) )
=> ( ( c_2Elist_2EAPPEND @ A_27a @ ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0m @ V2l ) @ ( c_2Elist_2EDROP @ A_27a @ V1n @ V2l ) )
= V2l ) ) ).
thf(thm_2Erich__list_2ESEG__SEG,axiom,
! [A_27a: $tType,V0n1: tyop_2Enum_2Enum,V1m1: tyop_2Enum_2Enum,V2n2: tyop_2Enum_2Enum,V3m2: tyop_2Enum_2Enum,V4l: tyop_2Elist_2Elist @ A_27a] :
( ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V0n1 @ V1m1 ) @ ( c_2Elist_2ELENGTH @ A_27a @ V4l ) )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V2n2 @ V3m2 ) @ V0n1 ) )
=> ( ( c_2Erich__list_2ESEG @ A_27a @ V2n2 @ V3m2 @ ( c_2Erich__list_2ESEG @ A_27a @ V0n1 @ V1m1 @ V4l ) )
= ( c_2Erich__list_2ESEG @ A_27a @ V2n2 @ ( c_2Earithmetic_2E_2B @ V1m1 @ V3m2 ) @ V4l ) ) ) ).
thf(thm_2Erich__list_2ESEG__APPEND1,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum,V2l1: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) @ ( c_2Elist_2ELENGTH @ A_27a @ V2l1 ) )
=> ! [V3l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ESEG @ A_27a @ V0n @ V1m @ ( c_2Elist_2EAPPEND @ A_27a @ V2l1 @ V3l2 ) )
= ( c_2Erich__list_2ESEG @ A_27a @ V0n @ V1m @ V2l1 ) ) ) ).
thf(thm_2Erich__list_2ESEG__APPEND2,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1m: tyop_2Enum_2Enum,V2n: tyop_2Enum_2Enum,V3l2: tyop_2Elist_2Elist @ A_27a] :
( ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Elist_2ELENGTH @ A_27a @ V0l1 ) @ V1m )
& ( c_2Earithmetic_2E_3C_3D @ V2n @ ( c_2Elist_2ELENGTH @ A_27a @ V3l2 ) ) )
=> ( ( c_2Erich__list_2ESEG @ A_27a @ V2n @ V1m @ ( c_2Elist_2EAPPEND @ A_27a @ V0l1 @ V3l2 ) )
= ( c_2Erich__list_2ESEG @ A_27a @ V2n @ ( c_2Earithmetic_2E_2D @ V1m @ ( c_2Elist_2ELENGTH @ A_27a @ V0l1 ) ) @ V3l2 ) ) ) ).
thf(thm_2Erich__list_2ESEG__TAKE__DROP,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) @ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) )
=> ( ( c_2Erich__list_2ESEG @ A_27a @ V0n @ V1m @ V2l )
= ( c_2Elist_2ETAKE @ A_27a @ V0n @ ( c_2Elist_2EDROP @ A_27a @ V1m @ V2l ) ) ) ) ).
thf(thm_2Erich__list_2ESEG__APPEND,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1l1: tyop_2Elist_2Elist @ A_27a,V2n: tyop_2Enum_2Enum,V3l2: tyop_2Elist_2Elist @ A_27a] :
( ( ( c_2Eprim__rec_2E_3C @ V0m @ ( c_2Elist_2ELENGTH @ A_27a @ V1l1 ) )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Elist_2ELENGTH @ A_27a @ V1l1 ) @ ( c_2Earithmetic_2E_2B @ V2n @ V0m ) )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V2n @ V0m ) @ ( c_2Earithmetic_2E_2B @ ( c_2Elist_2ELENGTH @ A_27a @ V1l1 ) @ ( c_2Elist_2ELENGTH @ A_27a @ V3l2 ) ) ) )
=> ( ( c_2Erich__list_2ESEG @ A_27a @ V2n @ V0m @ ( c_2Elist_2EAPPEND @ A_27a @ V1l1 @ V3l2 ) )
= ( c_2Elist_2EAPPEND @ A_27a @ ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ A_27a @ V1l1 ) @ V0m ) @ V0m @ V1l1 ) @ ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2B @ V2n @ V0m ) @ ( c_2Elist_2ELENGTH @ A_27a @ V1l1 ) ) @ c_2Enum_2E0 @ V3l2 ) ) ) ) ).
thf(thm_2Erich__list_2ESEG__LENGTH__SNOC,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a,V1x: A_27a] :
( ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Elist_2ELENGTH @ A_27a @ V0l ) @ ( c_2Elist_2ESNOC @ A_27a @ V1x @ V0l ) )
= ( c_2Elist_2ECONS @ A_27a @ V1x @ ( c_2Elist_2ENIL @ A_27a ) ) ) ).
thf(thm_2Erich__list_2ESEG__SNOC,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) @ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) )
=> ! [V3x: A_27a] :
( ( c_2Erich__list_2ESEG @ A_27a @ V0n @ V1m @ ( c_2Elist_2ESNOC @ A_27a @ V3x @ V2l ) )
= ( c_2Erich__list_2ESEG @ A_27a @ V0n @ V1m @ V2l ) ) ) ).
thf(thm_2Erich__list_2EELL__SEG,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Erich__list_2EELL @ A_27a @ V0n @ V1l )
= ( c_2Elist_2EHD @ A_27a @ ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Eprim__rec_2EPRE @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) @ V0n ) ) @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2ESNOC__FOLDR,axiom,
! [A_27a: $tType,V0x: A_27a,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2ESNOC @ A_27a @ V0x @ V1l )
= ( c_2Elist_2EFOLDR @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS @ A_27a ) @ ( c_2Elist_2ECONS @ A_27a @ V0x @ ( c_2Elist_2ENIL @ A_27a ) ) @ V1l ) ) ).
thf(thm_2Erich__list_2EMEM__FOLDR__MAP,axiom,
! [A_27a: $tType,V0x: A_27a,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Ebool_2EIN @ A_27a @ V0x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V1l ) )
= ( c_2Elist_2EFOLDR @ $o @ $o @ c_2Ebool_2E_5C_2F @ c_2Ebool_2EF @ ( c_2Elist_2EMAP @ A_27a @ $o @ ( c_2Emin_2E_3D @ A_27a @ V0x ) @ V1l ) ) ) ).
thf(thm_2Erich__list_2EMEM__FOLDL__MAP,axiom,
! [A_27a: $tType,V0x: A_27a,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Ebool_2EIN @ A_27a @ V0x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V1l ) )
= ( c_2Elist_2EFOLDL @ $o @ $o @ c_2Ebool_2E_5C_2F @ c_2Ebool_2EF @ ( c_2Elist_2EMAP @ A_27a @ $o @ ( c_2Emin_2E_3D @ A_27a @ V0x ) @ V1l ) ) ) ).
thf(thm_2Erich__list_2EFILTER__FILTER,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1Q: A_27a > $o,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFILTER @ A_27a @ V0P @ ( c_2Elist_2EFILTER @ A_27a @ V1Q @ V2l ) )
= ( c_2Elist_2EFILTER @ A_27a
@ ^ [V3x: A_27a] : ( c_2Ebool_2E_2F_5C @ ( V0P @ V3x ) @ ( V1Q @ V3x ) )
@ V2l ) ) ).
thf(thm_2Erich__list_2EFCOMM__FOLDR__FLAT,axiom,
! [A_27a: $tType,A_27b: $tType,V0g: A_27a > A_27a > A_27a,V1f: A_27b > A_27a > A_27a] :
( ( c_2Ecombin_2EFCOMM @ A_27a @ A_27a @ A_27b @ V0g @ V1f )
=> ! [V2e: A_27a] :
( ( c_2Ecombin_2ELEFT__ID @ A_27a @ A_27a @ V0g @ V2e )
=> ! [V3l: tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ A_27b )] :
( ( c_2Elist_2EFOLDR @ A_27b @ A_27a @ V1f @ V2e @ ( c_2Elist_2EFLAT @ A_27b @ V3l ) )
= ( c_2Elist_2EFOLDR @ A_27a @ A_27a @ V0g @ V2e @ ( c_2Elist_2EMAP @ ( tyop_2Elist_2Elist @ A_27b ) @ A_27a @ ( c_2Elist_2EFOLDR @ A_27b @ A_27a @ V1f @ V2e ) @ V3l ) ) ) ) ) ).
thf(thm_2Erich__list_2EFCOMM__FOLDL__FLAT,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b > A_27a,V1g: A_27a > A_27a > A_27a] :
( ( c_2Ecombin_2EFCOMM @ A_27a @ A_27b @ A_27a @ V0f @ V1g )
=> ! [V2e: A_27a] :
( ( c_2Ecombin_2ERIGHT__ID @ A_27a @ A_27a @ V1g @ V2e )
=> ! [V3l: tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ A_27b )] :
( ( c_2Elist_2EFOLDL @ A_27b @ A_27a @ V0f @ V2e @ ( c_2Elist_2EFLAT @ A_27b @ V3l ) )
= ( c_2Elist_2EFOLDL @ A_27a @ A_27a @ V1g @ V2e @ ( c_2Elist_2EMAP @ ( tyop_2Elist_2Elist @ A_27b ) @ A_27a @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a @ V0f @ V2e ) @ V3l ) ) ) ) ) ).
thf(thm_2Erich__list_2EFOLDR__MAP__REVERSE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27a > A_27a] :
( ! [V1a: A_27a,V2b: A_27a,V3c: A_27a] :
( ( V0f @ V1a @ ( V0f @ V2b @ V3c ) )
= ( V0f @ V2b @ ( V0f @ V1a @ V3c ) ) )
=> ! [V4e: A_27a,V5g: A_27b > A_27a,V6l: tyop_2Elist_2Elist @ A_27b] :
( ( c_2Elist_2EFOLDR @ A_27a @ A_27a @ V0f @ V4e @ ( c_2Elist_2EMAP @ A_27b @ A_27a @ V5g @ ( c_2Elist_2EREVERSE @ A_27b @ V6l ) ) )
= ( c_2Elist_2EFOLDR @ A_27a @ A_27a @ V0f @ V4e @ ( c_2Elist_2EMAP @ A_27b @ A_27a @ V5g @ V6l ) ) ) ) ).
thf(thm_2Erich__list_2EFOLDR__FILTER__REVERSE,axiom,
! [A_27a: $tType,V0f: A_27a > A_27a > A_27a] :
( ! [V1a: A_27a,V2b: A_27a,V3c: A_27a] :
( ( V0f @ V1a @ ( V0f @ V2b @ V3c ) )
= ( V0f @ V2b @ ( V0f @ V1a @ V3c ) ) )
=> ! [V4e: A_27a,V5P: A_27a > $o,V6l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFOLDR @ A_27a @ A_27a @ V0f @ V4e @ ( c_2Elist_2EFILTER @ A_27a @ V5P @ ( c_2Elist_2EREVERSE @ A_27a @ V6l ) ) )
= ( c_2Elist_2EFOLDR @ A_27a @ A_27a @ V0f @ V4e @ ( c_2Elist_2EFILTER @ A_27a @ V5P @ V6l ) ) ) ) ).
thf(thm_2Erich__list_2ECOMM__ASSOC__FOLDR__REVERSE,axiom,
! [A_27a: $tType,V0f: A_27a > A_27a > A_27a] :
( ( c_2Ecombin_2ECOMM @ A_27a @ A_27a @ V0f )
=> ( ( c_2Ecombin_2EASSOC @ A_27a @ V0f )
=> ! [V1e: A_27a,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFOLDR @ A_27a @ A_27a @ V0f @ V1e @ ( c_2Elist_2EREVERSE @ A_27a @ V2l ) )
= ( c_2Elist_2EFOLDR @ A_27a @ A_27a @ V0f @ V1e @ V2l ) ) ) ) ).
thf(thm_2Erich__list_2ECOMM__ASSOC__FOLDL__REVERSE,axiom,
! [A_27a: $tType,V0f: A_27a > A_27a > A_27a] :
( ( c_2Ecombin_2ECOMM @ A_27a @ A_27a @ V0f )
=> ( ( c_2Ecombin_2EASSOC @ A_27a @ V0f )
=> ! [V1e: A_27a,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EFOLDL @ A_27a @ A_27a @ V0f @ V1e @ ( c_2Elist_2EREVERSE @ A_27a @ V2l ) )
= ( c_2Elist_2EFOLDL @ A_27a @ A_27a @ V0f @ V1e @ V2l ) ) ) ) ).
thf(thm_2Erich__list_2EELL__LAST,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( (~) @ ( c_2Elist_2ENULL @ A_27a @ V0l ) )
=> ( ( c_2Erich__list_2EELL @ A_27a @ c_2Enum_2E0 @ V0l )
= ( c_2Elist_2ELAST @ A_27a @ V0l ) ) ) ).
thf(thm_2Erich__list_2EELL__0__SNOC,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a,V1x: A_27a] :
( ( c_2Erich__list_2EELL @ A_27a @ c_2Enum_2E0 @ ( c_2Elist_2ESNOC @ A_27a @ V1x @ V0l ) )
= V1x ) ).
thf(thm_2Erich__list_2EELL__SNOC,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V0n )
=> ! [V1x: A_27a,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EELL @ A_27a @ V0n @ ( c_2Elist_2ESNOC @ A_27a @ V1x @ V2l ) )
= ( c_2Erich__list_2EELL @ A_27a @ ( c_2Eprim__rec_2EPRE @ V0n ) @ V2l ) ) ) ).
thf(thm_2Erich__list_2EELL__SUC__SNOC,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1x: A_27a,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EELL @ A_27a @ ( c_2Enum_2ESUC @ V0n ) @ ( c_2Elist_2ESNOC @ A_27a @ V1x @ V2l ) )
= ( c_2Erich__list_2EELL @ A_27a @ V0n @ V2l ) ) ).
thf(thm_2Erich__list_2EELL__CONS,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ! [V2x: A_27a] :
( ( c_2Erich__list_2EELL @ A_27a @ V0n @ ( c_2Elist_2ECONS @ A_27a @ V2x @ V1l ) )
= ( c_2Erich__list_2EELL @ A_27a @ V0n @ V1l ) ) ) ).
thf(thm_2Erich__list_2EELL__LENGTH__CONS,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a,V1x: A_27a] :
( ( c_2Erich__list_2EELL @ A_27a @ ( c_2Elist_2ELENGTH @ A_27a @ V0l ) @ ( c_2Elist_2ECONS @ A_27a @ V1x @ V0l ) )
= V1x ) ).
thf(thm_2Erich__list_2EELL__LENGTH__SNOC,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a,V1x: A_27a] :
( ( c_2Erich__list_2EELL @ A_27a @ ( c_2Elist_2ELENGTH @ A_27a @ V0l ) @ ( c_2Elist_2ESNOC @ A_27a @ V1x @ V0l ) )
= ( c_2Ebool_2ECOND @ A_27a @ ( c_2Elist_2ENULL @ A_27a @ V0l ) @ V1x @ ( c_2Elist_2EHD @ A_27a @ V0l ) ) ) ).
thf(thm_2Erich__list_2EELL__APPEND2,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l2 ) )
=> ! [V2l1: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EELL @ A_27a @ V0n @ ( c_2Elist_2EAPPEND @ A_27a @ V2l1 @ V1l2 ) )
= ( c_2Erich__list_2EELL @ A_27a @ V0n @ V1l2 ) ) ) ).
thf(thm_2Erich__list_2EELL__APPEND1,axiom,
! [A_27a: $tType,V0l2: tyop_2Elist_2Elist @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Elist_2ELENGTH @ A_27a @ V0l2 ) @ V1n )
=> ! [V2l1: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EELL @ A_27a @ V1n @ ( c_2Elist_2EAPPEND @ A_27a @ V2l1 @ V0l2 ) )
= ( c_2Erich__list_2EELL @ A_27a @ ( c_2Earithmetic_2E_2D @ V1n @ ( c_2Elist_2ELENGTH @ A_27a @ V0l2 ) ) @ V2l1 ) ) ) ).
thf(thm_2Erich__list_2EELL__PRE__LENGTH,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( (~)
@ ( V0l
= ( c_2Elist_2ENIL @ A_27a ) ) )
=> ( ( c_2Erich__list_2EELL @ A_27a @ ( c_2Eprim__rec_2EPRE @ ( c_2Elist_2ELENGTH @ A_27a @ V0l ) ) @ V0l )
= ( c_2Elist_2EHD @ A_27a @ V0l ) ) ) ).
thf(thm_2Erich__list_2EEL__PRE__LENGTH,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( (~)
@ ( V0l
= ( c_2Elist_2ENIL @ A_27a ) ) )
=> ( ( c_2Elist_2EEL @ A_27a @ ( c_2Eprim__rec_2EPRE @ ( c_2Elist_2ELENGTH @ A_27a @ V0l ) ) @ V0l )
= ( c_2Elist_2ELAST @ A_27a @ V0l ) ) ) ).
thf(thm_2Erich__list_2EEL__ELL,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Elist_2EEL @ A_27a @ V0n @ V1l )
= ( c_2Erich__list_2EELL @ A_27a @ ( c_2Eprim__rec_2EPRE @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) @ V0n ) ) @ V1l ) ) ) ).
thf(thm_2Erich__list_2EEL__LENGTH__APPEND,axiom,
! [A_27a: $tType,V0l2: tyop_2Elist_2Elist @ A_27a,V1l1: tyop_2Elist_2Elist @ A_27a] :
( ( (~) @ ( c_2Elist_2ENULL @ A_27a @ V0l2 ) )
=> ( ( c_2Elist_2EEL @ A_27a @ ( c_2Elist_2ELENGTH @ A_27a @ V1l1 ) @ ( c_2Elist_2EAPPEND @ A_27a @ V1l1 @ V0l2 ) )
= ( c_2Elist_2EHD @ A_27a @ V0l2 ) ) ) ).
thf(thm_2Erich__list_2EELL__EL,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Erich__list_2EELL @ A_27a @ V0n @ V1l )
= ( c_2Elist_2EEL @ A_27a @ ( c_2Eprim__rec_2EPRE @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) @ V0n ) ) @ V1l ) ) ) ).
thf(thm_2Erich__list_2EELL__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a,V2f: A_27a > A_27b] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Erich__list_2EELL @ A_27b @ V0n @ ( c_2Elist_2EMAP @ A_27a @ A_27b @ V2f @ V1l ) )
= ( V2f @ ( c_2Erich__list_2EELL @ A_27a @ V0n @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2ELENGTH__FRONT,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a] :
( ( (~)
@ ( V0l
= ( c_2Elist_2ENIL @ A_27a ) ) )
=> ( ( c_2Elist_2ELENGTH @ A_27a @ ( c_2Elist_2EFRONT @ A_27a @ V0l ) )
= ( c_2Eprim__rec_2EPRE @ ( c_2Elist_2ELENGTH @ A_27a @ V0l ) ) ) ) ).
thf(thm_2Erich__list_2EDROP__LENGTH__APPEND,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EDROP @ A_27a @ ( c_2Elist_2ELENGTH @ A_27a @ V0l1 ) @ ( c_2Elist_2EAPPEND @ A_27a @ V0l1 @ V1l2 ) )
= V1l2 ) ).
thf(thm_2Erich__list_2ETAKE__APPEND,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l1: tyop_2Elist_2Elist @ A_27a,V2l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2ETAKE @ A_27a @ V0n @ ( c_2Elist_2EAPPEND @ A_27a @ V1l1 @ V2l2 ) )
= ( c_2Elist_2EAPPEND @ A_27a @ ( c_2Elist_2ETAKE @ A_27a @ V0n @ V1l1 ) @ ( c_2Elist_2ETAKE @ A_27a @ ( c_2Earithmetic_2E_2D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l1 ) ) @ V2l2 ) ) ) ).
thf(thm_2Erich__list_2ETAKE__APPEND1,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l1: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l1 ) )
=> ! [V2l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2ETAKE @ A_27a @ V0n @ ( c_2Elist_2EAPPEND @ A_27a @ V1l1 @ V2l2 ) )
= ( c_2Elist_2ETAKE @ A_27a @ V0n @ V1l1 ) ) ) ).
thf(thm_2Erich__list_2ETAKE__APPEND2,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Elist_2ELENGTH @ A_27a @ V0l1 ) @ V1n )
=> ! [V2l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2ETAKE @ A_27a @ V1n @ ( c_2Elist_2EAPPEND @ A_27a @ V0l1 @ V2l2 ) )
= ( c_2Elist_2EAPPEND @ A_27a @ V0l1 @ ( c_2Elist_2ETAKE @ A_27a @ ( c_2Earithmetic_2E_2D @ V1n @ ( c_2Elist_2ELENGTH @ A_27a @ V0l1 ) ) @ V2l2 ) ) ) ) ).
thf(thm_2Erich__list_2ETAKE__LENGTH__APPEND,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2ETAKE @ A_27a @ ( c_2Elist_2ELENGTH @ A_27a @ V0l1 ) @ ( c_2Elist_2EAPPEND @ A_27a @ V0l1 @ V1l2 ) )
= V0l1 ) ).
thf(thm_2Erich__list_2EREVERSE__FLAT,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ A_27a )] :
( ( c_2Elist_2EREVERSE @ A_27a @ ( c_2Elist_2EFLAT @ A_27a @ V0l ) )
= ( c_2Elist_2EFLAT @ A_27a @ ( c_2Elist_2EREVERSE @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EREVERSE @ A_27a ) @ V0l ) ) ) ) ).
thf(thm_2Erich__list_2EMAP__FILTER,axiom,
! [A_27a: $tType,V0f: A_27a > A_27a,V1P: A_27a > $o,V2l: tyop_2Elist_2Elist @ A_27a] :
( ! [V3x: A_27a] :
( ( V1P @ ( V0f @ V3x ) )
= ( V1P @ V3x ) )
=> ( ( c_2Elist_2EMAP @ A_27a @ A_27a @ V0f @ ( c_2Elist_2EFILTER @ A_27a @ V1P @ V2l ) )
= ( c_2Elist_2EFILTER @ A_27a @ V1P @ ( c_2Elist_2EMAP @ A_27a @ A_27a @ V0f @ V2l ) ) ) ) ).
thf(thm_2Erich__list_2EFLAT__REVERSE,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ A_27a )] :
( ( c_2Elist_2EFLAT @ A_27a @ ( c_2Elist_2EREVERSE @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l ) )
= ( c_2Elist_2EREVERSE @ A_27a @ ( c_2Elist_2EFLAT @ A_27a @ ( c_2Elist_2EMAP @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EREVERSE @ A_27a ) @ V0l ) ) ) ) ).
thf(thm_2Erich__list_2EFLAT__FLAT,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ A_27a ) )] :
( ( c_2Elist_2EFLAT @ A_27a @ ( c_2Elist_2EFLAT @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l ) )
= ( c_2Elist_2EFLAT @ A_27a @ ( c_2Elist_2EMAP @ ( tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EFLAT @ A_27a ) @ V0l ) ) ) ).
thf(thm_2Erich__list_2EEVERY__REVERSE,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEVERY @ A_27a @ V0P @ ( c_2Elist_2EREVERSE @ A_27a @ V1l ) )
= ( c_2Elist_2EEVERY @ A_27a @ V0P @ V1l ) ) ).
thf(thm_2Erich__list_2EEXISTS__REVERSE,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEXISTS @ A_27a @ V0P @ ( c_2Elist_2EREVERSE @ A_27a @ V1l ) )
= ( c_2Elist_2EEXISTS @ A_27a @ V0P @ V1l ) ) ).
thf(thm_2Erich__list_2EEVERY__SEG,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEVERY @ A_27a @ V0P @ V1l )
=> ! [V2m: tyop_2Enum_2Enum,V3k: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V2m @ V3k ) @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( c_2Elist_2EEVERY @ A_27a @ V0P @ ( c_2Erich__list_2ESEG @ A_27a @ V2m @ V3k @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2EEVERY__TAKE,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEVERY @ A_27a @ V0P @ V1l )
=> ! [V2m: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V2m @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( c_2Elist_2EEVERY @ A_27a @ V0P @ ( c_2Elist_2ETAKE @ A_27a @ V2m @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2EEVERY__DROP,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEVERY @ A_27a @ V0P @ V1l )
=> ! [V2m: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V2m @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( c_2Elist_2EEVERY @ A_27a @ V0P @ ( c_2Elist_2EDROP @ A_27a @ V2m @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2EEXISTS__SEG,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1k: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V0m @ V1k ) @ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) )
=> ! [V3P: A_27a > $o] :
( ( c_2Elist_2EEXISTS @ A_27a @ V3P @ ( c_2Erich__list_2ESEG @ A_27a @ V0m @ V1k @ V2l ) )
=> ( c_2Elist_2EEXISTS @ A_27a @ V3P @ V2l ) ) ) ).
thf(thm_2Erich__list_2EEXISTS__TAKE__IMP,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a,V1m: tyop_2Enum_2Enum,V2P: A_27a > $o] :
( ( c_2Elist_2EEXISTS @ A_27a @ V2P @ ( c_2Elist_2ETAKE @ A_27a @ V1m @ V0l ) )
=> ( c_2Elist_2EEXISTS @ A_27a @ V2P @ V0l ) ) ).
thf(thm_2Erich__list_2EEXISTS__DROP__IMP,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a,V1m: tyop_2Enum_2Enum,V2P: A_27a > $o] :
( ( c_2Elist_2EEXISTS @ A_27a @ V2P @ ( c_2Elist_2EDROP @ A_27a @ V1m @ V0l ) )
=> ( c_2Elist_2EEXISTS @ A_27a @ V2P @ V0l ) ) ).
thf(thm_2Erich__list_2EEXISTS__TAKE,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0m @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ! [V2P: A_27a > $o] :
( ( c_2Elist_2EEXISTS @ A_27a @ V2P @ ( c_2Elist_2ETAKE @ A_27a @ V0m @ V1l ) )
=> ( c_2Elist_2EEXISTS @ A_27a @ V2P @ V1l ) ) ) ).
thf(thm_2Erich__list_2EEXISTS__DROP,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0m @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ! [V2P: A_27a > $o] :
( ( c_2Elist_2EEXISTS @ A_27a @ V2P @ ( c_2Elist_2EDROP @ A_27a @ V0m @ V1l ) )
=> ( c_2Elist_2EEXISTS @ A_27a @ V2P @ V1l ) ) ) ).
thf(thm_2Erich__list_2EEXISTS__LASTN,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0m @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ! [V2P: A_27a > $o] :
( ( c_2Elist_2EEXISTS @ A_27a @ V2P @ ( c_2Erich__list_2ELASTN @ A_27a @ V0m @ V1l ) )
=> ( c_2Elist_2EEXISTS @ A_27a @ V2P @ V1l ) ) ) ).
thf(thm_2Erich__list_2EEXISTS__BUTLASTN,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0m @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ! [V2P: A_27a > $o] :
( ( c_2Elist_2EEXISTS @ A_27a @ V2P @ ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0m @ V1l ) )
=> ( c_2Elist_2EEXISTS @ A_27a @ V2P @ V1l ) ) ) ).
thf(thm_2Erich__list_2EMEM__SEG,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) @ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) )
=> ! [V3x: A_27a] :
( ( c_2Ebool_2EIN @ A_27a @ V3x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ ( c_2Erich__list_2ESEG @ A_27a @ V0n @ V1m @ V2l ) ) )
=> ( c_2Ebool_2EIN @ A_27a @ V3x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V2l ) ) ) ) ).
thf(thm_2Erich__list_2EMEM__TAKE__IMP,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a,V1m: tyop_2Enum_2Enum,V2x: A_27a] :
( ( c_2Ebool_2EIN @ A_27a @ V2x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ ( c_2Elist_2ETAKE @ A_27a @ V1m @ V0l ) ) )
=> ( c_2Ebool_2EIN @ A_27a @ V2x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V0l ) ) ) ).
thf(thm_2Erich__list_2EMEM__DROP__IMP,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a,V1m: tyop_2Enum_2Enum,V2x: A_27a] :
( ( c_2Ebool_2EIN @ A_27a @ V2x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ ( c_2Elist_2EDROP @ A_27a @ V1m @ V0l ) ) )
=> ( c_2Ebool_2EIN @ A_27a @ V2x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V0l ) ) ) ).
thf(thm_2Erich__list_2EMEM__TAKE,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0m @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ! [V2x: A_27a] :
( ( c_2Ebool_2EIN @ A_27a @ V2x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ ( c_2Elist_2ETAKE @ A_27a @ V0m @ V1l ) ) )
=> ( c_2Ebool_2EIN @ A_27a @ V2x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2EMEM__DROP,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0m @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ! [V2x: A_27a] :
( ( c_2Ebool_2EIN @ A_27a @ V2x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ ( c_2Elist_2EDROP @ A_27a @ V0m @ V1l ) ) )
=> ( c_2Ebool_2EIN @ A_27a @ V2x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2EMEM__BUTLASTN,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0m @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ! [V2x: A_27a] :
( ( c_2Ebool_2EIN @ A_27a @ V2x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0m @ V1l ) ) )
=> ( c_2Ebool_2EIN @ A_27a @ V2x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2EMEM__LASTN,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0m @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ! [V2x: A_27a] :
( ( c_2Ebool_2EIN @ A_27a @ V2x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ ( c_2Erich__list_2ELASTN @ A_27a @ V0m @ V1l ) ) )
=> ( c_2Ebool_2EIN @ A_27a @ V2x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2EZIP__SNOC,axiom,
! [A_27a: $tType,A_27b: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27b] :
( ( ( c_2Elist_2ELENGTH @ A_27a @ V0l1 )
= ( c_2Elist_2ELENGTH @ A_27b @ V1l2 ) )
=> ! [V2x1: A_27a,V3x2: A_27b] :
( ( c_2Elist_2EZIP @ A_27a @ A_27b @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2ESNOC @ A_27a @ V2x1 @ V0l1 ) @ ( c_2Elist_2ESNOC @ A_27b @ V3x2 @ V1l2 ) ) )
= ( c_2Elist_2ESNOC @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ V2x1 @ V3x2 ) @ ( c_2Elist_2EZIP @ A_27a @ A_27b @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) @ V0l1 @ V1l2 ) ) ) ) ) ).
thf(thm_2Erich__list_2EUNZIP__SNOC,axiom,
! [A_27a: $tType,A_27b: $tType,V0x: tyop_2Epair_2Eprod @ A_27a @ A_27b,V1l: tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b )] :
( ( c_2Elist_2EUNZIP @ A_27a @ A_27b @ ( c_2Elist_2ESNOC @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V0x @ V1l ) )
= ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2ESNOC @ A_27a @ ( c_2Epair_2EFST @ A_27a @ A_27b @ V0x ) @ ( c_2Epair_2EFST @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EUNZIP @ A_27a @ A_27b @ V1l ) ) ) @ ( c_2Elist_2ESNOC @ A_27b @ ( c_2Epair_2ESND @ A_27a @ A_27b @ V0x ) @ ( c_2Epair_2ESND @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EUNZIP @ A_27a @ A_27b @ V1l ) ) ) ) ) ).
thf(thm_2Erich__list_2ELENGTH__UNZIP__FST,axiom,
! [A_27a: $tType,A_27b: $tType,V0l: tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b )] :
( ( c_2Elist_2ELENGTH @ A_27a @ ( c_2Erich__list_2EUNZIP__FST @ A_27a @ A_27b @ V0l ) )
= ( c_2Elist_2ELENGTH @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V0l ) ) ).
thf(thm_2Erich__list_2ELENGTH__UNZIP__SND,axiom,
! [A_27a: $tType,A_27b: $tType,V0l: tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b )] :
( ( c_2Elist_2ELENGTH @ A_27b @ ( c_2Erich__list_2EUNZIP__SND @ A_27b @ A_27a @ V0l ) )
= ( c_2Elist_2ELENGTH @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V0l ) ) ).
thf(thm_2Erich__list_2ESUM__REVERSE,axiom,
! [V0l: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
( ( c_2Elist_2ESUM @ ( c_2Elist_2EREVERSE @ tyop_2Enum_2Enum @ V0l ) )
= ( c_2Elist_2ESUM @ V0l ) ) ).
thf(thm_2Erich__list_2ESUM__FLAT,axiom,
! [V0l: tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum )] :
( ( c_2Elist_2ESUM @ ( c_2Elist_2EFLAT @ tyop_2Enum_2Enum @ V0l ) )
= ( c_2Elist_2ESUM @ ( c_2Elist_2EMAP @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum @ c_2Elist_2ESUM @ V0l ) ) ) ).
thf(thm_2Erich__list_2EEL__APPEND1,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l1: tyop_2Elist_2Elist @ A_27a,V2l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l1 ) )
=> ( ( c_2Elist_2EEL @ A_27a @ V0n @ ( c_2Elist_2EAPPEND @ A_27a @ V1l1 @ V2l2 ) )
= ( c_2Elist_2EEL @ A_27a @ V0n @ V1l1 ) ) ) ).
thf(thm_2Erich__list_2EEL__APPEND2,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Elist_2ELENGTH @ A_27a @ V0l1 ) @ V1n )
=> ! [V2l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEL @ A_27a @ V1n @ ( c_2Elist_2EAPPEND @ A_27a @ V0l1 @ V2l2 ) )
= ( c_2Elist_2EEL @ A_27a @ ( c_2Earithmetic_2E_2D @ V1n @ ( c_2Elist_2ELENGTH @ A_27a @ V0l1 ) ) @ V2l2 ) ) ) ).
thf(thm_2Erich__list_2ELUPDATE__APPEND2,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27a,V2n: tyop_2Enum_2Enum,V3x: A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Elist_2ELENGTH @ A_27a @ V0l1 ) @ V2n )
=> ( ( c_2Elist_2ELUPDATE @ A_27a @ V3x @ V2n @ ( c_2Elist_2EAPPEND @ A_27a @ V0l1 @ V1l2 ) )
= ( c_2Elist_2EAPPEND @ A_27a @ V0l1 @ ( c_2Elist_2ELUPDATE @ A_27a @ V3x @ ( c_2Earithmetic_2E_2D @ V2n @ ( c_2Elist_2ELENGTH @ A_27a @ V0l1 ) ) @ V1l2 ) ) ) ) ).
thf(thm_2Erich__list_2ELUPDATE__APPEND1,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27a,V2n: tyop_2Enum_2Enum,V3x: A_27a] :
( ( c_2Eprim__rec_2E_3C @ V2n @ ( c_2Elist_2ELENGTH @ A_27a @ V0l1 ) )
=> ( ( c_2Elist_2ELUPDATE @ A_27a @ V3x @ V2n @ ( c_2Elist_2EAPPEND @ A_27a @ V0l1 @ V1l2 ) )
= ( c_2Elist_2EAPPEND @ A_27a @ ( c_2Elist_2ELUPDATE @ A_27a @ V3x @ V2n @ V0l1 ) @ V1l2 ) ) ) ).
thf(thm_2Erich__list_2Eis__prefix__el,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l1: tyop_2Elist_2Elist @ A_27a,V2l2: tyop_2Elist_2Elist @ A_27a] :
( ( ( c_2Elist_2EisPREFIX @ A_27a @ V1l1 @ V2l2 )
& ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l1 ) )
& ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V2l2 ) ) )
=> ( ( c_2Elist_2EEL @ A_27a @ V0n @ V1l1 )
= ( c_2Elist_2EEL @ A_27a @ V0n @ V2l2 ) ) ) ).
thf(thm_2Erich__list_2EEL__CONS,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V0n )
=> ! [V1x: A_27a,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEL @ A_27a @ V0n @ ( c_2Elist_2ECONS @ A_27a @ V1x @ V2l ) )
= ( c_2Elist_2EEL @ A_27a @ ( c_2Eprim__rec_2EPRE @ V0n ) @ V2l ) ) ) ).
thf(thm_2Erich__list_2ESEG1,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0n @ V1l )
= ( c_2Elist_2ECONS @ A_27a @ ( c_2Elist_2EEL @ A_27a @ V0n @ V1l ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ).
thf(thm_2Erich__list_2EEL__SEG,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Elist_2EEL @ A_27a @ V0n @ V1l )
= ( c_2Elist_2EHD @ A_27a @ ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0n @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2ESEG__CONS,axiom,
! [A_27a: $tType,V0j: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2h: A_27a,V3t: tyop_2Elist_2Elist @ A_27a] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V0j )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V1n @ V0j ) @ ( c_2Earithmetic_2E_2B @ ( c_2Elist_2ELENGTH @ A_27a @ V3t ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
=> ( ( c_2Erich__list_2ESEG @ A_27a @ V1n @ V0j @ ( c_2Elist_2ECONS @ A_27a @ V2h @ V3t ) )
= ( c_2Erich__list_2ESEG @ A_27a @ V1n @ ( c_2Earithmetic_2E_2D @ V0j @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V3t ) ) ) ).
thf(thm_2Erich__list_2ESEG__SUC__EL,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1i: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2B @ V1i @ V0n ) @ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) )
=> ( ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Enum_2ESUC @ V0n ) @ V1i @ V2l )
= ( c_2Elist_2ECONS @ A_27a @ ( c_2Elist_2EEL @ A_27a @ V1i @ V2l ) @ ( c_2Erich__list_2ESEG @ A_27a @ V0n @ ( c_2Earithmetic_2E_2B @ V1i @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V2l ) ) ) ) ).
thf(thm_2Erich__list_2ETAKE__SEG__DROP,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1i: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V1i @ V0n ) @ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) )
=> ( ( c_2Elist_2EAPPEND @ A_27a @ ( c_2Elist_2EAPPEND @ A_27a @ ( c_2Elist_2ETAKE @ A_27a @ V1i @ V2l ) @ ( c_2Erich__list_2ESEG @ A_27a @ V0n @ V1i @ V2l ) ) @ ( c_2Elist_2EDROP @ A_27a @ ( c_2Earithmetic_2E_2B @ V1i @ V0n ) @ V2l ) )
= V2l ) ) ).
thf(thm_2Erich__list_2EEL__MEM,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( c_2Ebool_2EIN @ A_27a @ ( c_2Elist_2EEL @ A_27a @ V0n @ V1l ) @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V1l ) ) ) ).
thf(thm_2Erich__list_2ETL__SNOC,axiom,
! [A_27a: $tType,V0x: A_27a,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2ETL @ A_27a @ ( c_2Elist_2ESNOC @ A_27a @ V0x @ V1l ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ENULL @ A_27a @ V1l ) @ ( c_2Elist_2ENIL @ A_27a ) @ ( c_2Elist_2ESNOC @ A_27a @ V0x @ ( c_2Elist_2ETL @ A_27a @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2EEL__REVERSE__ELL,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Elist_2EEL @ A_27a @ V0n @ ( c_2Elist_2EREVERSE @ A_27a @ V1l ) )
= ( c_2Erich__list_2EELL @ A_27a @ V0n @ V1l ) ) ) ).
thf(thm_2Erich__list_2EELL__LENGTH__APPEND,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27a] :
( ( (~) @ ( c_2Elist_2ENULL @ A_27a @ V0l1 ) )
=> ( ( c_2Erich__list_2EELL @ A_27a @ ( c_2Elist_2ELENGTH @ A_27a @ V1l2 ) @ ( c_2Elist_2EAPPEND @ A_27a @ V0l1 @ V1l2 ) )
= ( c_2Elist_2ELAST @ A_27a @ V0l1 ) ) ) ).
thf(thm_2Erich__list_2EELL__MEM,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( c_2Ebool_2EIN @ A_27a @ ( c_2Erich__list_2EELL @ A_27a @ V0n @ V1l ) @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V1l ) ) ) ).
thf(thm_2Erich__list_2EELL__REVERSE,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Erich__list_2EELL @ A_27a @ V0n @ ( c_2Elist_2EREVERSE @ A_27a @ V1l ) )
= ( c_2Erich__list_2EELL @ A_27a @ ( c_2Eprim__rec_2EPRE @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) @ V0n ) ) @ V1l ) ) ) ).
thf(thm_2Erich__list_2EELL__REVERSE__EL,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Eprim__rec_2E_3C @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Erich__list_2EELL @ A_27a @ V0n @ ( c_2Elist_2EREVERSE @ A_27a @ V1l ) )
= ( c_2Elist_2EEL @ A_27a @ V0n @ V1l ) ) ) ).
thf(thm_2Erich__list_2ETAKE__BUTLASTN,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Elist_2ETAKE @ A_27a @ V0n @ V1l )
= ( c_2Erich__list_2EBUTLASTN @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) @ V0n ) @ V1l ) ) ) ).
thf(thm_2Erich__list_2EBUTLASTN__TAKE,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0n @ V1l )
= ( c_2Elist_2ETAKE @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) @ V0n ) @ V1l ) ) ) ).
thf(thm_2Erich__list_2ELASTN__DROP,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Erich__list_2ELASTN @ A_27a @ V0n @ V1l )
= ( c_2Elist_2EDROP @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) @ V0n ) @ V1l ) ) ) ).
thf(thm_2Erich__list_2EDROP__LASTN,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Elist_2EDROP @ A_27a @ V0n @ V1l )
= ( c_2Erich__list_2ELASTN @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) @ V0n ) @ V1l ) ) ) ).
thf(thm_2Erich__list_2ESEG__LASTN__BUTLASTN,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) @ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) )
=> ( ( c_2Erich__list_2ESEG @ A_27a @ V0n @ V1m @ V2l )
= ( c_2Erich__list_2ELASTN @ A_27a @ V0n @ ( c_2Erich__list_2EBUTLASTN @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) ) @ V2l ) ) ) ) ).
thf(thm_2Erich__list_2EDROP__REVERSE,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Elist_2EDROP @ A_27a @ V0n @ ( c_2Elist_2EREVERSE @ A_27a @ V1l ) )
= ( c_2Elist_2EREVERSE @ A_27a @ ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0n @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2EBUTLASTN__REVERSE,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Erich__list_2EBUTLASTN @ A_27a @ V0n @ ( c_2Elist_2EREVERSE @ A_27a @ V1l ) )
= ( c_2Elist_2EREVERSE @ A_27a @ ( c_2Elist_2EDROP @ A_27a @ V0n @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2ELASTN__REVERSE,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Erich__list_2ELASTN @ A_27a @ V0n @ ( c_2Elist_2EREVERSE @ A_27a @ V1l ) )
= ( c_2Elist_2EREVERSE @ A_27a @ ( c_2Elist_2ETAKE @ A_27a @ V0n @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2ETAKE__REVERSE,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V0n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l ) )
=> ( ( c_2Elist_2ETAKE @ A_27a @ V0n @ ( c_2Elist_2EREVERSE @ A_27a @ V1l ) )
= ( c_2Elist_2EREVERSE @ A_27a @ ( c_2Erich__list_2ELASTN @ A_27a @ V0n @ V1l ) ) ) ) ).
thf(thm_2Erich__list_2ESEG__REVERSE,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) @ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) )
=> ( ( c_2Erich__list_2ESEG @ A_27a @ V0n @ V1m @ ( c_2Elist_2EREVERSE @ A_27a @ V2l ) )
= ( c_2Elist_2EREVERSE @ A_27a @ ( c_2Erich__list_2ESEG @ A_27a @ V0n @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) ) @ V2l ) ) ) ) ).
thf(thm_2Erich__list_2ELENGTH__REPLICATE,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1x: A_27a] :
( ( c_2Elist_2ELENGTH @ A_27a @ ( c_2Erich__list_2EREPLICATE @ A_27a @ V0n @ V1x ) )
= V0n ) ).
thf(thm_2Erich__list_2EMEM__REPLICATE,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V0n )
=> ! [V1x: A_27a] : ( c_2Ebool_2EIN @ A_27a @ V1x @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ ( c_2Erich__list_2EREPLICATE @ A_27a @ V0n @ V1x ) ) ) ) ).
thf(thm_2Erich__list_2EEVERY__REPLICATE,axiom,
! [A_27a: $tType,V0f: A_27a > $o,V1n: tyop_2Enum_2Enum,V2x: A_27a] :
( ( c_2Elist_2EEVERY @ A_27a @ V0f @ ( c_2Erich__list_2EREPLICATE @ A_27a @ V1n @ V2x ) )
<=> ( ( V1n = c_2Enum_2E0 )
| ( V0f @ V2x ) ) ) ).
thf(thm_2Erich__list_2EALL__DISTINCT__DROP,axiom,
! [A_27a: $tType,V0ls: tyop_2Elist_2Elist @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Elist_2EALL__DISTINCT @ A_27a @ V0ls )
=> ( c_2Elist_2EALL__DISTINCT @ A_27a @ ( c_2Elist_2EDROP @ A_27a @ V1n @ V0ls ) ) ) ).
thf(thm_2Erich__list_2EMAP__SND__FILTER__NEQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0z: A_27a,V1ls: tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a )] :
( ( c_2Elist_2EMAP @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a @ ( c_2Epair_2ESND @ A_27b @ A_27a )
@ ( c_2Elist_2EFILTER @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a )
@ ( c_2Epair_2EUNCURRY @ A_27b @ A_27a @ $o
@ ^ [V2x: A_27b,V3y: A_27a] : ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ A_27a @ V3y @ V0z ) ) )
@ V1ls ) )
= ( c_2Elist_2EFILTER @ A_27a
@ ^ [V4y: A_27a] : ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ A_27a @ V0z @ V4y ) )
@ ( c_2Elist_2EMAP @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a @ ( c_2Epair_2ESND @ A_27b @ A_27a ) @ V1ls ) ) ) ).
thf(thm_2Erich__list_2EMEM__SING__APPEND,axiom,
! [A_27a: $tType,V0d: tyop_2Elist_2Elist @ A_27a,V1b: A_27a] :
( ! [V2a: tyop_2Elist_2Elist @ A_27a,V3c: tyop_2Elist_2Elist @ A_27a] :
( (~)
@ ( V0d
= ( c_2Elist_2EAPPEND @ A_27a @ ( c_2Elist_2EAPPEND @ A_27a @ V2a @ ( c_2Elist_2ECONS @ A_27a @ V1b @ ( c_2Elist_2ENIL @ A_27a ) ) ) @ V3c ) ) )
<=> ( (~) @ ( c_2Ebool_2EIN @ A_27a @ V1b @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V0d ) ) ) ) ).
thf(thm_2Erich__list_2EEL__LENGTH__APPEND__rwt,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l2: tyop_2Elist_2Elist @ A_27a,V2l1: tyop_2Elist_2Elist @ A_27a] :
( ( ( (~) @ ( c_2Elist_2ENULL @ A_27a @ V1l2 ) )
& ( V0n
= ( c_2Elist_2ELENGTH @ A_27a @ V2l1 ) ) )
=> ( ( c_2Elist_2EEL @ A_27a @ V0n @ ( c_2Elist_2EAPPEND @ A_27a @ V2l1 @ V1l2 ) )
= ( c_2Elist_2EHD @ A_27a @ V1l2 ) ) ) ).
thf(thm_2Erich__list_2EMAP__FST__funs,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0funs: tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) )] :
( ( c_2Elist_2EMAP @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ A_27a
@ ( c_2Epair_2EUNCURRY @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27a
@ ^ [V1x: A_27a] :
( c_2Epair_2EUNCURRY @ A_27b @ A_27c @ A_27a
@ ^ [V2y: A_27b,V3z: A_27c] : V1x ) )
@ V0funs )
= ( c_2Elist_2EMAP @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ A_27a @ ( c_2Epair_2EFST @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ V0funs ) ) ).
thf(thm_2Erich__list_2ETAKE__PRE__LENGTH,axiom,
! [A_27a: $tType,V0ls: tyop_2Elist_2Elist @ A_27a] :
( ( (~)
@ ( V0ls
= ( c_2Elist_2ENIL @ A_27a ) ) )
=> ( ( c_2Elist_2ETAKE @ A_27a @ ( c_2Eprim__rec_2EPRE @ ( c_2Elist_2ELENGTH @ A_27a @ V0ls ) ) @ V0ls )
= ( c_2Elist_2EFRONT @ A_27a @ V0ls ) ) ) ).
thf(thm_2Erich__list_2EDROP__LENGTH__NIL__rwt,axiom,
! [A_27a: $tType,V0l: tyop_2Elist_2Elist @ A_27a,V1m: tyop_2Enum_2Enum] :
( ( V1m
= ( c_2Elist_2ELENGTH @ A_27a @ V0l ) )
=> ( ( c_2Elist_2EDROP @ A_27a @ V1m @ V0l )
= ( c_2Elist_2ENIL @ A_27a ) ) ) ).
thf(thm_2Erich__list_2EDROP__EL__CONS,axiom,
! [A_27a: $tType,V0ls: tyop_2Elist_2Elist @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Elist_2ELENGTH @ A_27a @ V0ls ) )
=> ( ( c_2Elist_2EDROP @ A_27a @ V1n @ V0ls )
= ( c_2Elist_2ECONS @ A_27a @ ( c_2Elist_2EEL @ A_27a @ V1n @ V0ls ) @ ( c_2Elist_2EDROP @ A_27a @ ( c_2Earithmetic_2E_2B @ V1n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0ls ) ) ) ) ).
thf(thm_2Erich__list_2ETAKE__EL__SNOC,axiom,
! [A_27a: $tType,V0ls: tyop_2Elist_2Elist @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V1n @ ( c_2Elist_2ELENGTH @ A_27a @ V0ls ) )
=> ( ( c_2Elist_2ETAKE @ A_27a @ ( c_2Earithmetic_2E_2B @ V1n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0ls )
= ( c_2Elist_2ESNOC @ A_27a @ ( c_2Elist_2EEL @ A_27a @ V1n @ V0ls ) @ ( c_2Elist_2ETAKE @ A_27a @ V1n @ V0ls ) ) ) ) ).
thf(thm_2Erich__list_2EREVERSE__DROP,axiom,
! [A_27a: $tType,V0ls: tyop_2Elist_2Elist @ A_27a,V1n: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V1n @ ( c_2Elist_2ELENGTH @ A_27a @ V0ls ) )
=> ( ( c_2Elist_2EREVERSE @ A_27a @ ( c_2Elist_2EDROP @ A_27a @ V1n @ V0ls ) )
= ( c_2Elist_2EREVERSE @ A_27a @ ( c_2Erich__list_2ELASTN @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Elist_2ELENGTH @ A_27a @ V0ls ) @ V1n ) @ V0ls ) ) ) ) ).
thf(thm_2Erich__list_2ELENGTH__FILTER__LESS,axiom,
! [A_27a: $tType,V0P: A_27a > $o,V1ls: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EEXISTS @ A_27a @ ( c_2Ecombin_2Eo @ A_27a @ $o @ $o @ c_2Ebool_2E_7E @ V0P ) @ V1ls )
=> ( c_2Eprim__rec_2E_3C @ ( c_2Elist_2ELENGTH @ A_27a @ ( c_2Elist_2EFILTER @ A_27a @ V0P @ V1ls ) ) @ ( c_2Elist_2ELENGTH @ A_27a @ V1ls ) ) ) ).
thf(thm_2Erich__list_2EEVERY2__APPEND,axiom,
! [A_27a: $tType,A_27b: $tType,V0l4: tyop_2Elist_2Elist @ A_27b,V1l3: tyop_2Elist_2Elist @ A_27a,V2l2: tyop_2Elist_2Elist @ A_27b,V3l1: tyop_2Elist_2Elist @ A_27a,V4R: A_27a > A_27b > $o] :
( ( ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V4R @ V3l1 @ V2l2 )
& ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V4R @ V1l3 @ V0l4 ) )
<=> ( ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V4R @ ( c_2Elist_2EAPPEND @ A_27a @ V3l1 @ V1l3 ) @ ( c_2Elist_2EAPPEND @ A_27b @ V2l2 @ V0l4 ) )
& ( ( c_2Elist_2ELENGTH @ A_27a @ V3l1 )
= ( c_2Elist_2ELENGTH @ A_27b @ V2l2 ) )
& ( ( c_2Elist_2ELENGTH @ A_27a @ V1l3 )
= ( c_2Elist_2ELENGTH @ A_27b @ V0l4 ) ) ) ) ).
thf(thm_2Erich__list_2ELIST__REL__APPEND__IMP,axiom,
! [A_27a: $tType,A_27b: $tType,V0P: A_27a > A_27b > $o,V1xs: tyop_2Elist_2Elist @ A_27a,V2ys: tyop_2Elist_2Elist @ A_27b,V3xs1: tyop_2Elist_2Elist @ A_27a,V4ys1: tyop_2Elist_2Elist @ A_27b] :
( ( ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V0P @ ( c_2Elist_2EAPPEND @ A_27a @ V1xs @ V3xs1 ) @ ( c_2Elist_2EAPPEND @ A_27b @ V2ys @ V4ys1 ) )
& ( ( c_2Elist_2ELENGTH @ A_27a @ V1xs )
= ( c_2Elist_2ELENGTH @ A_27b @ V2ys ) ) )
=> ( ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V0P @ V1xs @ V2ys )
& ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V0P @ V3xs1 @ V4ys1 ) ) ) ).
thf(thm_2Erich__list_2EEVERY2__APPEND__suff,axiom,
! [A_27a: $tType,A_27b: $tType,V0l4: tyop_2Elist_2Elist @ A_27b,V1l3: tyop_2Elist_2Elist @ A_27a,V2l2: tyop_2Elist_2Elist @ A_27b,V3l1: tyop_2Elist_2Elist @ A_27a,V4R: A_27a > A_27b > $o] :
( ( ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V4R @ V3l1 @ V2l2 )
& ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V4R @ V1l3 @ V0l4 ) )
=> ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V4R @ ( c_2Elist_2EAPPEND @ A_27a @ V3l1 @ V1l3 ) @ ( c_2Elist_2EAPPEND @ A_27b @ V2l2 @ V0l4 ) ) ) ).
thf(thm_2Erich__list_2EEVERY2__DROP,axiom,
! [A_27a: $tType,A_27b: $tType,V0R: A_27a > A_27b > $o,V1l1: tyop_2Elist_2Elist @ A_27a,V2l2: tyop_2Elist_2Elist @ A_27b,V3n: tyop_2Enum_2Enum] :
( ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V0R @ V1l1 @ V2l2 )
=> ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V0R @ ( c_2Elist_2EDROP @ A_27a @ V3n @ V1l1 ) @ ( c_2Elist_2EDROP @ A_27b @ V3n @ V2l2 ) ) ) ).
thf(thm_2Erich__list_2EEVERY2__TAKE,axiom,
! [A_27a: $tType,A_27b: $tType,V0P: A_27a > A_27b > $o,V1xs: tyop_2Elist_2Elist @ A_27a,V2ys: tyop_2Elist_2Elist @ A_27b,V3n: tyop_2Enum_2Enum] :
( ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V0P @ V1xs @ V2ys )
=> ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V0P @ ( c_2Elist_2ETAKE @ A_27a @ V3n @ V1xs ) @ ( c_2Elist_2ETAKE @ A_27b @ V3n @ V2ys ) ) ) ).
thf(thm_2Erich__list_2ELIST__REL__APPEND__SING,axiom,
! [A_27a: $tType,A_27b: $tType,V0x2: A_27b,V1x1: A_27a,V2l2: tyop_2Elist_2Elist @ A_27b,V3l1: tyop_2Elist_2Elist @ A_27a,V4R: A_27a > A_27b > $o] :
( ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V4R @ ( c_2Elist_2EAPPEND @ A_27a @ V3l1 @ ( c_2Elist_2ECONS @ A_27a @ V1x1 @ ( c_2Elist_2ENIL @ A_27a ) ) ) @ ( c_2Elist_2EAPPEND @ A_27b @ V2l2 @ ( c_2Elist_2ECONS @ A_27b @ V0x2 @ ( c_2Elist_2ENIL @ A_27b ) ) ) )
<=> ( ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V4R @ V3l1 @ V2l2 )
& ( V4R @ V1x1 @ V0x2 ) ) ) ).
thf(thm_2Erich__list_2ELIST__REL__GENLIST,axiom,
! [A_27a: $tType,A_27b: $tType,V0l: tyop_2Enum_2Enum,V1g: tyop_2Enum_2Enum > A_27b,V2f: tyop_2Enum_2Enum > A_27a,V3P: A_27a > A_27b > $o] :
( ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V3P @ ( c_2Elist_2EGENLIST @ A_27a @ V2f @ V0l ) @ ( c_2Elist_2EGENLIST @ A_27b @ V1g @ V0l ) )
<=> ! [V4i: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V4i @ V0l )
=> ( V3P @ ( V2f @ V4i ) @ ( V1g @ V4i ) ) ) ) ).
thf(thm_2Erich__list_2EALL__DISTINCT__MEM__ZIP__MAP,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b,V1x: tyop_2Epair_2Eprod @ A_27a @ A_27b,V2ls: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EALL__DISTINCT @ A_27a @ V2ls )
=> ( ( c_2Ebool_2EIN @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V1x @ ( c_2Elist_2ELIST__TO__SET @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Elist_2EZIP @ A_27a @ A_27b @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) @ V2ls @ ( c_2Elist_2EMAP @ A_27a @ A_27b @ V0f @ V2ls ) ) ) ) )
<=> ( ( c_2Ebool_2EIN @ A_27a @ ( c_2Epair_2EFST @ A_27a @ A_27b @ V1x ) @ ( c_2Elist_2ELIST__TO__SET @ A_27a @ V2ls ) )
& ( ( c_2Epair_2ESND @ A_27a @ A_27b @ V1x )
= ( V0f @ ( c_2Epair_2EFST @ A_27a @ A_27b @ V1x ) ) ) ) ) ) ).
thf(thm_2Erich__list_2EREVERSE__ZIP,axiom,
! [A_27a: $tType,A_27b: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27b] :
( ( ( c_2Elist_2ELENGTH @ A_27a @ V0l1 )
= ( c_2Elist_2ELENGTH @ A_27b @ V1l2 ) )
=> ( ( c_2Elist_2EREVERSE @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Elist_2EZIP @ A_27a @ A_27b @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) @ V0l1 @ V1l2 ) ) )
= ( c_2Elist_2EZIP @ A_27a @ A_27b @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EREVERSE @ A_27a @ V0l1 ) @ ( c_2Elist_2EREVERSE @ A_27b @ V1l2 ) ) ) ) ) ).
thf(thm_2Erich__list_2EEVERY2__REVERSE1,axiom,
! [A_27a: $tType,A_27b: $tType,V0R: A_27a > A_27b > $o,V1l1: tyop_2Elist_2Elist @ A_27a,V2l2: tyop_2Elist_2Elist @ A_27b] :
( ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V0R @ V1l1 @ ( c_2Elist_2EREVERSE @ A_27b @ V2l2 ) )
= ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V0R @ ( c_2Elist_2EREVERSE @ A_27a @ V1l1 ) @ V2l2 ) ) ).
thf(thm_2Erich__list_2ELIST__REL__REVERSE__EQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0l2: tyop_2Elist_2Elist @ A_27b,V1l1: tyop_2Elist_2Elist @ A_27a,V2R: A_27a > A_27b > $o] :
( ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V2R @ ( c_2Elist_2EREVERSE @ A_27a @ V1l1 ) @ ( c_2Elist_2EREVERSE @ A_27b @ V0l2 ) )
= ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V2R @ V1l1 @ V0l2 ) ) ).
thf(thm_2Erich__list_2Eevery__count__list,axiom,
! [V0P: tyop_2Enum_2Enum > $o,V1n: tyop_2Enum_2Enum] :
( ( c_2Elist_2EEVERY @ tyop_2Enum_2Enum @ V0P @ ( c_2Erich__list_2ECOUNT__LIST @ V1n ) )
<=> ! [V2m: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V2m @ V1n )
=> ( V0P @ V2m ) ) ) ).
thf(thm_2Erich__list_2Ecount__list__sub1,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( (~) @ ( V0n = c_2Enum_2E0 ) )
=> ( ( c_2Erich__list_2ECOUNT__LIST @ V0n )
= ( c_2Elist_2ECONS @ tyop_2Enum_2Enum @ c_2Enum_2E0 @ ( c_2Elist_2EMAP @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ c_2Enum_2ESUC @ ( c_2Erich__list_2ECOUNT__LIST @ ( c_2Earithmetic_2E_2D @ V0n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(thm_2Erich__list_2Eel__map__count,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1f: tyop_2Enum_2Enum > A_27a,V2m: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0n @ V2m )
=> ( ( c_2Elist_2EEL @ A_27a @ V0n @ ( c_2Elist_2EMAP @ tyop_2Enum_2Enum @ A_27a @ V1f @ ( c_2Erich__list_2ECOUNT__LIST @ V2m ) ) )
= ( V1f @ V0n ) ) ) ).
thf(thm_2Erich__list_2EZIP__COUNT__LIST,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1l1: tyop_2Elist_2Elist @ A_27a] :
( ( V0n
= ( c_2Elist_2ELENGTH @ A_27a @ V1l1 ) )
=> ( ( c_2Elist_2EZIP @ A_27a @ tyop_2Enum_2Enum @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ V1l1 @ ( c_2Erich__list_2ECOUNT__LIST @ V0n ) ) )
= ( c_2Elist_2EGENLIST @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum )
@ ^ [V2n: tyop_2Enum_2Enum] : ( c_2Epair_2E_2C @ A_27a @ tyop_2Enum_2Enum @ ( c_2Elist_2EEL @ A_27a @ V2n @ V1l1 ) @ V2n )
@ ( c_2Elist_2ELENGTH @ A_27a @ V1l1 ) ) ) ) ).
thf(thm_2Erich__list_2Emap__replicate,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b,V1n: tyop_2Enum_2Enum,V2x: A_27a] :
( ( c_2Elist_2EMAP @ A_27a @ A_27b @ V0f @ ( c_2Erich__list_2EREPLICATE @ A_27a @ V1n @ V2x ) )
= ( c_2Erich__list_2EREPLICATE @ A_27b @ V1n @ ( V0f @ V2x ) ) ) ).
thf(thm_2Erich__list_2EREPLICATE__NIL,axiom,
! [A_27a: $tType,V0y: A_27a,V1x: tyop_2Enum_2Enum] :
( ( ( c_2Erich__list_2EREPLICATE @ A_27a @ V1x @ V0y )
= ( c_2Elist_2ENIL @ A_27a ) )
<=> ( V1x = c_2Enum_2E0 ) ) ).
thf(thm_2Erich__list_2EREPLICATE__APPEND,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum,V2a: A_27a] :
( ( c_2Elist_2EAPPEND @ A_27a @ ( c_2Erich__list_2EREPLICATE @ A_27a @ V0n @ V2a ) @ ( c_2Erich__list_2EREPLICATE @ A_27a @ V1m @ V2a ) )
= ( c_2Erich__list_2EREPLICATE @ A_27a @ ( c_2Earithmetic_2E_2B @ V0n @ V1m ) @ V2a ) ) ).
thf(thm_2Erich__list_2EDROP__REPLICATE,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum,V2a: A_27a] :
( ( c_2Elist_2EDROP @ A_27a @ V0n @ ( c_2Erich__list_2EREPLICATE @ A_27a @ V1m @ V2a ) )
= ( c_2Erich__list_2EREPLICATE @ A_27a @ ( c_2Earithmetic_2E_2D @ V1m @ V0n ) @ V2a ) ) ).
thf(thm_2Erich__list_2ELIST__REL__REPLICATE__same,axiom,
! [A_27a: $tType,A_27b: $tType,V0y: A_27b,V1x: A_27a,V2n: tyop_2Enum_2Enum,V3P: A_27a > A_27b > $o] :
( ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V3P @ ( c_2Erich__list_2EREPLICATE @ A_27a @ V2n @ V1x ) @ ( c_2Erich__list_2EREPLICATE @ A_27b @ V2n @ V0y ) )
<=> ( ( c_2Earithmetic_2E_3E @ V2n @ c_2Enum_2E0 )
=> ( V3P @ V1x @ V0y ) ) ) ).
thf(thm_2Erich__list_2Etake__drop__partition,axiom,
! [A_27a: $tType,V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Earithmetic_2E_3C_3D @ V1m @ V0n )
=> ( ( c_2Elist_2EAPPEND @ A_27a @ ( c_2Elist_2ETAKE @ A_27a @ V1m @ V2l ) @ ( c_2Elist_2ETAKE @ A_27a @ ( c_2Earithmetic_2E_2D @ V0n @ V1m ) @ ( c_2Elist_2EDROP @ A_27a @ V1m @ V2l ) ) )
= ( c_2Elist_2ETAKE @ A_27a @ V0n @ V2l ) ) ) ).
thf(thm_2Erich__list_2Eall__distinct__count__list,axiom,
! [V0n: tyop_2Enum_2Enum] : ( c_2Elist_2EALL__DISTINCT @ tyop_2Enum_2Enum @ ( c_2Erich__list_2ECOUNT__LIST @ V0n ) ) ).
thf(thm_2Erich__list_2Elist__rel__lastn,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b > $o,V1l1: tyop_2Elist_2Elist @ A_27a,V2l2: tyop_2Elist_2Elist @ A_27b,V3n: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ V3n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l1 ) )
& ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V0f @ V1l1 @ V2l2 ) )
=> ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V0f @ ( c_2Erich__list_2ELASTN @ A_27a @ V3n @ V1l1 ) @ ( c_2Erich__list_2ELASTN @ A_27b @ V3n @ V2l2 ) ) ) ).
thf(thm_2Erich__list_2Elist__rel__butlastn,axiom,
! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b > $o,V1l1: tyop_2Elist_2Elist @ A_27a,V2l2: tyop_2Elist_2Elist @ A_27b,V3n: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ V3n @ ( c_2Elist_2ELENGTH @ A_27a @ V1l1 ) )
& ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V0f @ V1l1 @ V2l2 ) )
=> ( c_2Elist_2ELIST__REL @ A_27a @ A_27b @ V0f @ ( c_2Erich__list_2EBUTLASTN @ A_27a @ V3n @ V1l1 ) @ ( c_2Erich__list_2EBUTLASTN @ A_27b @ V3n @ V2l2 ) ) ) ).
thf(thm_2Erich__list_2EUNIQUE__LIST__ELEM__COUNT,axiom,
! [A_27a: $tType,V0e: A_27a,V1L: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Elist_2EUNIQUE @ A_27a @ V0e @ V1L )
<=> ( ( c_2Erich__list_2ELIST__ELEM__COUNT @ A_27a @ V0e @ V1L )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Erich__list_2ECOUNT__LIST__compute,axiom,
! [V0n: tyop_2Enum_2Enum] :
( ( c_2Erich__list_2ECOUNT__LIST @ V0n )
= ( c_2Erich__list_2ECOUNT__LIST__AUX @ V0n @ ( c_2Elist_2ENIL @ tyop_2Enum_2Enum ) ) ) ).
thf(thm_2Erich__list_2ESPLITP__compute,axiom,
! [A_27a: $tType] :
( ( c_2Erich__list_2ESPLITP @ A_27a )
= ( c_2Erich__list_2ESPLITP__AUX @ A_27a @ ( c_2Elist_2ENIL @ A_27a ) ) ) ).
thf(thm_2Erich__list_2EIS__SUFFIX__compute,axiom,
! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EIS__SUFFIX @ A_27a @ V0l1 @ V1l2 )
= ( c_2Elist_2EisPREFIX @ A_27a @ ( c_2Elist_2EREVERSE @ A_27a @ V1l2 ) @ ( c_2Elist_2EREVERSE @ A_27a @ V0l1 ) ) ) ).
thf(thm_2Erich__list_2ESEG__compute,axiom,
! [A_27a: $tType] :
( ! [V0k: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ESEG @ A_27a @ c_2Enum_2E0 @ V0k @ V1l )
= ( c_2Elist_2ENIL @ A_27a ) )
& ! [V2m: tyop_2Enum_2Enum,V3x: A_27a,V4l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V2m ) ) @ c_2Enum_2E0 @ ( c_2Elist_2ECONS @ A_27a @ V3x @ V4l ) )
= ( c_2Elist_2ECONS @ A_27a @ V3x @ ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V2m ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 @ V4l ) ) )
& ! [V5m: tyop_2Enum_2Enum,V6x: A_27a,V7l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ V5m ) ) @ c_2Enum_2E0 @ ( c_2Elist_2ECONS @ A_27a @ V6x @ V7l ) )
= ( c_2Elist_2ECONS @ A_27a @ V6x @ ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V5m ) ) @ c_2Enum_2E0 @ V7l ) ) )
& ! [V8m: tyop_2Enum_2Enum,V9k: tyop_2Enum_2Enum,V10x: A_27a,V11l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V8m ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V9k ) ) @ ( c_2Elist_2ECONS @ A_27a @ V10x @ V11l ) )
= ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V8m ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V9k ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V11l ) )
& ! [V12m: tyop_2Enum_2Enum,V13k: tyop_2Enum_2Enum,V14x: A_27a,V15l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ V12m ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V13k ) ) @ ( c_2Elist_2ECONS @ A_27a @ V14x @ V15l ) )
= ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ V12m ) ) @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V13k ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V15l ) )
& ! [V16m: tyop_2Enum_2Enum,V17k: tyop_2Enum_2Enum,V18x: A_27a,V19l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V16m ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ V17k ) ) @ ( c_2Elist_2ECONS @ A_27a @ V18x @ V19l ) )
= ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V16m ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V17k ) ) @ V19l ) )
& ! [V20m: tyop_2Enum_2Enum,V21k: tyop_2Enum_2Enum,V22x: A_27a,V23l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ V20m ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ V21k ) ) @ ( c_2Elist_2ECONS @ A_27a @ V22x @ V23l ) )
= ( c_2Erich__list_2ESEG @ A_27a @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ V20m ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V21k ) ) @ V23l ) ) ) ).
thf(thm_2Erich__list_2EBUTLASTN__compute,axiom,
! [A_27a: $tType,V0longer_20than_20list: $o,V1n: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2EBUTLASTN @ A_27a @ V1n @ V2l )
= ( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ A_27a )
@ ^ [V3m: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Earithmetic_2E_3C_3D @ V1n @ V3m ) @ ( c_2Elist_2ETAKE @ A_27a @ ( c_2Earithmetic_2E_2D @ V3m @ V1n ) @ V2l ) @ ( c_2Ecombin_2EFAIL @ ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) @ $o @ ( c_2Erich__list_2EBUTLASTN @ A_27a ) @ V0longer_20than_20list @ V1n @ V2l ) )
@ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) ) ) ).
thf(thm_2Erich__list_2ELASTN__compute,axiom,
! [A_27a: $tType,V0longer_20than_20list: $o,V1n: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ A_27a] :
( ( c_2Erich__list_2ELASTN @ A_27a @ V1n @ V2l )
= ( c_2Ebool_2ELET @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ A_27a )
@ ^ [V3m: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Earithmetic_2E_3C_3D @ V1n @ V3m ) @ ( c_2Elist_2EDROP @ A_27a @ ( c_2Earithmetic_2E_2D @ V3m @ V1n ) @ V2l ) @ ( c_2Ecombin_2EFAIL @ ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) @ $o @ ( c_2Erich__list_2ELASTN @ A_27a ) @ V0longer_20than_20list @ V1n @ V2l ) )
@ ( c_2Elist_2ELENGTH @ A_27a @ V2l ) ) ) ).
%------------------------------------------------------------------------------