ITP001 Axioms: ITP060^7.ax
%------------------------------------------------------------------------------
% File : ITP060^7 : 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 : Decode.ax [Gau19]
% : HL4060^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 149 ( 24 unt; 80 typ; 0 def)
% Number of atoms : 329 ( 58 equ; 2 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 2988 ( 2 ~; 1 |; 29 &;2903 @)
% ( 12 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg;2903 nst)
% Number of types : 4 ( 3 usr)
% Number of type conns : 314 ( 314 >; 0 *; 0 +; 0 <<)
% Number of symbols : 79 ( 77 usr; 5 con; 0-6 aty)
% Number of variables : 407 ( 90 ^ 253 !; 1 ?; 407 :)
% ( 63 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2EEncode_2Etree,type,
tyop_2EEncode_2Etree: $tType > $tType ).
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_2Eone_2Eone,type,
tyop_2Eone_2Eone: $tType ).
thf(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: $tType > $tType ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: $tType > $tType > $tType ).
thf(tyop_2Esum_2Esum,type,
tyop_2Esum_2Esum: $tType > $tType > $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Earithmetic_2E_2A,type,
c_2Earithmetic_2E_2A: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
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_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_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_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_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_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_2Elist_2EEVERY,type,
c_2Elist_2EEVERY:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).
thf(c_2Earithmetic_2EEXP,type,
c_2Earithmetic_2EEXP: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
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_2Esum_2EINL,type,
c_2Esum_2EINL:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ).
thf(c_2Esum_2EINR,type,
c_2Esum_2EINR:
!>[A_27a: $tType,A_27b: $tType] : ( A_27b > ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ).
thf(c_2Ecombin_2EK,type,
c_2Ecombin_2EK:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > A_27a ) ).
thf(c_2Elist_2ENIL,type,
c_2Elist_2ENIL:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist @ A_27a ) ).
thf(c_2Eoption_2ENONE,type,
c_2Eoption_2ENONE:
!>[A_27a: $tType] : ( tyop_2Eoption_2Eoption @ A_27a ) ).
thf(c_2Earithmetic_2ENUMERAL,type,
c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2EEncode_2ENode,type,
c_2EEncode_2ENode:
!>[A_27a: $tType] : ( A_27a > ( tyop_2Elist_2Elist @ ( tyop_2EEncode_2Etree @ A_27a ) ) > ( tyop_2EEncode_2Etree @ 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_2Eoption_2ESOME,type,
c_2Eoption_2ESOME:
!>[A_27a: $tType] : ( A_27a > ( tyop_2Eoption_2Eoption @ A_27a ) ) ).
thf(c_2Enum_2ESUC,type,
c_2Enum_2ESUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ET,type,
c_2Ebool_2ET: $o ).
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_2Earithmetic_2EZERO,type,
c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2EDecode_2Edec2enc,type,
c_2EDecode_2Edec2enc:
!>[A_27a: $tType] : ( ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > A_27a > ( tyop_2Elist_2Elist @ $o ) ) ).
thf(c_2EDecode_2Edec__bnum,type,
c_2EDecode_2Edec__bnum: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) ).
thf(c_2EDecode_2Edecode__blist,type,
c_2EDecode_2Edecode__blist:
!>[A_27a: $tType] : ( ( ( tyop_2Elist_2Elist @ A_27a ) > $o ) > tyop_2Enum_2Enum > ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ).
thf(c_2EDecode_2Edecode__bnum,type,
c_2EDecode_2Edecode__bnum: tyop_2Enum_2Enum > ( tyop_2Enum_2Enum > $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) ).
thf(c_2EDecode_2Edecode__bool,type,
c_2EDecode_2Edecode__bool: ( $o > $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Elist_2Elist @ $o ) ) ) ).
thf(c_2EDecode_2Edecode__list,type,
c_2EDecode_2Edecode__list:
!>[A_27a: $tType] : ( ( ( tyop_2Elist_2Elist @ A_27a ) > $o ) > ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ).
thf(c_2EDecode_2Edecode__num,type,
c_2EDecode_2Edecode__num: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) ).
thf(c_2EDecode_2Edecode__option,type,
c_2EDecode_2Edecode__option:
!>[A_27a: $tType] : ( ( ( tyop_2Eoption_2Eoption @ A_27a ) > $o ) > ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ).
thf(c_2EDecode_2Edecode__prod,type,
c_2EDecode_2Edecode__prod:
!>[A_27a: $tType,A_27b: $tType] : ( ( ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o ) > ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ).
thf(c_2EDecode_2Edecode__sum,type,
c_2EDecode_2Edecode__sum:
!>[A_27a: $tType,A_27b: $tType] : ( ( ( tyop_2Esum_2Esum @ A_27a @ A_27b ) > $o ) > ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ).
thf(c_2EDecode_2Edecode__tree,type,
c_2EDecode_2Edecode__tree:
!>[A_27a: $tType] : ( ( ( tyop_2EEncode_2Etree @ A_27a ) > $o ) > ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2EEncode_2Etree @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ).
thf(c_2EDecode_2Edecode__unit,type,
c_2EDecode_2Edecode__unit: ( tyop_2Eone_2Eone > $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Eone_2Eone @ ( tyop_2Elist_2Elist @ $o ) ) ) ).
thf(c_2EDecode_2Eenc2dec,type,
c_2EDecode_2Eenc2dec:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ).
thf(c_2EEncode_2Eencode__blist,type,
c_2EEncode_2Eencode__blist:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Enum_2Enum > ( A_27b > ( tyop_2Elist_2Elist @ A_27a ) ) > ( tyop_2Elist_2Elist @ A_27b ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2EEncode_2Eencode__bnum,type,
c_2EEncode_2Eencode__bnum: tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2EEncode_2Eencode__bool,type,
c_2EEncode_2Eencode__bool: $o > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2EEncode_2Eencode__list,type,
c_2EEncode_2Eencode__list:
!>[A_27a: $tType] : ( ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ $o ) ) ).
thf(c_2EEncode_2Eencode__num,type,
c_2EEncode_2Eencode__num: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2EEncode_2Eencode__option,type,
c_2EEncode_2Eencode__option:
!>[A_27a: $tType] : ( ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) > ( tyop_2Eoption_2Eoption @ A_27a ) > ( tyop_2Elist_2Elist @ $o ) ) ).
thf(c_2EEncode_2Eencode__prod,type,
c_2EEncode_2Eencode__prod:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) > ( A_27b > ( tyop_2Elist_2Elist @ $o ) ) > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > ( tyop_2Elist_2Elist @ $o ) ) ).
thf(c_2EEncode_2Eencode__sum,type,
c_2EEncode_2Eencode__sum:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) > ( A_27b > ( tyop_2Elist_2Elist @ $o ) ) > ( tyop_2Esum_2Esum @ A_27a @ A_27b ) > ( tyop_2Elist_2Elist @ $o ) ) ).
thf(c_2EEncode_2Eencode__tree,type,
c_2EEncode_2Eencode__tree:
!>[A_27a: $tType] : ( ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) > ( tyop_2EEncode_2Etree @ A_27a ) > ( tyop_2Elist_2Elist @ $o ) ) ).
thf(c_2EEncode_2Eencode__unit,type,
c_2EEncode_2Eencode__unit: tyop_2Eone_2Eone > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2EEncode_2Elift__blist,type,
c_2EEncode_2Elift__blist:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).
thf(c_2EEncode_2Elift__option,type,
c_2EEncode_2Elift__option:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2Eoption_2Eoption @ A_27a ) > $o ) ).
thf(c_2EEncode_2Elift__prod,type,
c_2EEncode_2Elift__prod:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > $o ) > ( A_27b > $o ) > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o ) ).
thf(c_2EEncode_2Elift__sum,type,
c_2EEncode_2Elift__sum:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > $o ) > ( A_27b > $o ) > ( tyop_2Esum_2Esum @ A_27a @ A_27b ) > $o ) ).
thf(c_2EEncode_2Elift__tree,type,
c_2EEncode_2Elift__tree:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2EEncode_2Etree @ A_27a ) > $o ) ).
thf(c_2Elist_2Elist__CASE,type,
c_2Elist_2Elist__CASE:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > A_27b > ( A_27a > ( tyop_2Elist_2Elist @ A_27a ) > A_27b ) > A_27b ) ).
thf(c_2Earithmetic_2Enum__CASE,type,
c_2Earithmetic_2Enum__CASE:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > A_27a > ( tyop_2Enum_2Enum > A_27a ) > A_27a ) ).
thf(c_2Eone_2Eone,type,
c_2Eone_2Eone: tyop_2Eone_2Eone ).
thf(c_2Eoption_2Eoption__CASE,type,
c_2Eoption_2Eoption__CASE:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Eoption_2Eoption @ A_27a ) > A_27b > ( A_27a > A_27b ) > A_27b ) ).
thf(c_2Epair_2Epair__CASE,type,
c_2Epair_2Epair__CASE:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) > ( A_27b > A_27c > A_27a ) > A_27a ) ).
thf(c_2EDecode_2Ewf__decoder,type,
c_2EDecode_2Ewf__decoder:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > $o ) ).
thf(c_2EEncode_2Ewf__encoder,type,
c_2EEncode_2Ewf__encoder:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) > $o ) ).
thf(c_2EEncode_2Ewf__pred__bnum,type,
c_2EEncode_2Ewf__pred__bnum: tyop_2Enum_2Enum > ( tyop_2Enum_2Enum > $o ) > $o ).
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_2EDecode_2Ewf__decoder__def,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p @ V1d )
<=> ! [V2x: A_27a] :
( c_2Ebool_2ECOND @ $o @ ( V0p @ V2x )
@ ( c_2Ebool_2E_3F @ ( tyop_2Elist_2Elist @ $o )
@ ^ [V3a: tyop_2Elist_2Elist @ $o] :
( c_2Ebool_2E_21 @ ( tyop_2Elist_2Elist @ $o )
@ ^ [V4b: tyop_2Elist_2Elist @ $o] :
( c_2Ebool_2E_21 @ ( tyop_2Elist_2Elist @ $o )
@ ^ [V5c: tyop_2Elist_2Elist @ $o] : ( c_2Emin_2E_3D @ $o @ ( c_2Emin_2E_3D @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( V1d @ V4b ) @ ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ A_27a @ ( tyop_2Elist_2Elist @ $o ) @ V2x @ V5c ) ) ) @ ( c_2Emin_2E_3D @ ( tyop_2Elist_2Elist @ $o ) @ V4b @ ( c_2Elist_2EAPPEND @ $o @ V3a @ V5c ) ) ) ) ) )
@ ( c_2Ebool_2E_21 @ ( tyop_2Elist_2Elist @ $o )
@ ^ [V6a: tyop_2Elist_2Elist @ $o] :
( c_2Ebool_2E_21 @ ( tyop_2Elist_2Elist @ $o )
@ ^ [V7b: tyop_2Elist_2Elist @ $o] : ( c_2Ebool_2E_7E @ ( c_2Emin_2E_3D @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( V1d @ V6a ) @ ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ A_27a @ ( tyop_2Elist_2Elist @ $o ) @ V2x @ V7b ) ) ) ) ) ) ) ) ).
thf(thm_2EDecode_2Eenc2dec__def,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1e: A_27a > ( tyop_2Elist_2Elist @ $o ),V2l: tyop_2Elist_2Elist @ $o] :
( ( c_2EDecode_2Eenc2dec @ A_27a @ V0p @ V1e @ V2l )
= ( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ( c_2Ebool_2E_3F @ A_27a
@ ^ [V3x: A_27a] :
( c_2Ebool_2E_3F @ ( tyop_2Elist_2Elist @ $o )
@ ^ [V4t: tyop_2Elist_2Elist @ $o] : ( c_2Ebool_2E_2F_5C @ ( V0p @ V3x ) @ ( c_2Emin_2E_3D @ ( tyop_2Elist_2Elist @ $o ) @ V2l @ ( c_2Elist_2EAPPEND @ $o @ ( V1e @ V3x ) @ V4t ) ) ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) )
@ ( c_2Emin_2E_40 @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) )
@ ( c_2Epair_2EUNCURRY @ A_27a @ ( tyop_2Elist_2Elist @ $o ) @ $o
@ ^ [V5x: A_27a,V6t: tyop_2Elist_2Elist @ $o] : ( c_2Ebool_2E_2F_5C @ ( V0p @ V5x ) @ ( c_2Emin_2E_3D @ ( tyop_2Elist_2Elist @ $o ) @ V2l @ ( c_2Elist_2EAPPEND @ $o @ ( V1e @ V5x ) @ V6t ) ) ) ) ) )
@ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ).
thf(thm_2EDecode_2Edec2enc__def,axiom,
! [A_27a: $tType,V0d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ),V1x: A_27a] :
( ( c_2EDecode_2Edec2enc @ A_27a @ V0d @ V1x )
= ( c_2Emin_2E_40 @ ( tyop_2Elist_2Elist @ $o )
@ ^ [V2l: tyop_2Elist_2Elist @ $o] : ( c_2Emin_2E_3D @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( V0d @ V2l ) @ ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ A_27a @ ( tyop_2Elist_2Elist @ $o ) @ V1x @ ( c_2Elist_2ENIL @ $o ) ) ) ) ) ) ).
thf(thm_2EDecode_2Edecode__unit__def,axiom,
! [V0p: tyop_2Eone_2Eone > $o] :
( ( c_2EDecode_2Edecode__unit @ V0p )
= ( c_2EDecode_2Eenc2dec @ tyop_2Eone_2Eone @ V0p @ c_2EEncode_2Eencode__unit ) ) ).
thf(thm_2EDecode_2Edecode__bool__def,axiom,
! [V0p: $o > $o] :
( ( c_2EDecode_2Edecode__bool @ V0p )
= ( c_2EDecode_2Eenc2dec @ $o @ V0p @ c_2EEncode_2Eencode__bool ) ) ).
thf(thm_2EDecode_2Edecode__prod__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0p: ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o,V1d1: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ),V2d2: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2EDecode_2Edecode__prod @ A_27a @ A_27b @ V0p @ V1d1 @ V2d2 )
= ( c_2EDecode_2Eenc2dec @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V0p @ ( c_2EEncode_2Eencode__prod @ A_27a @ A_27b @ ( c_2EDecode_2Edec2enc @ A_27a @ V1d1 ) @ ( c_2EDecode_2Edec2enc @ A_27b @ V2d2 ) ) ) ) ).
thf(thm_2EDecode_2Edecode__sum__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0p: ( tyop_2Esum_2Esum @ A_27a @ A_27b ) > $o,V1d1: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ),V2d2: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2EDecode_2Edecode__sum @ A_27a @ A_27b @ V0p @ V1d1 @ V2d2 )
= ( c_2EDecode_2Eenc2dec @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0p @ ( c_2EEncode_2Eencode__sum @ A_27a @ A_27b @ ( c_2EDecode_2Edec2enc @ A_27a @ V1d1 ) @ ( c_2EDecode_2Edec2enc @ A_27b @ V2d2 ) ) ) ) ).
thf(thm_2EDecode_2Edecode__option__def,axiom,
! [A_27a: $tType,V0p: ( tyop_2Eoption_2Eoption @ A_27a ) > $o,V1d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2EDecode_2Edecode__option @ A_27a @ V0p @ V1d )
= ( c_2EDecode_2Eenc2dec @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V0p @ ( c_2EEncode_2Eencode__option @ A_27a @ ( c_2EDecode_2Edec2enc @ A_27a @ V1d ) ) ) ) ).
thf(thm_2EDecode_2Edecode__list__def,axiom,
! [A_27a: $tType,V0p: ( tyop_2Elist_2Elist @ A_27a ) > $o,V1d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2EDecode_2Edecode__list @ A_27a @ V0p @ V1d )
= ( c_2EDecode_2Eenc2dec @ ( tyop_2Elist_2Elist @ A_27a ) @ V0p @ ( c_2EEncode_2Eencode__list @ A_27a @ ( c_2EDecode_2Edec2enc @ A_27a @ V1d ) ) ) ) ).
thf(thm_2EDecode_2Edecode__blist__def,axiom,
! [A_27a: $tType,V0p: ( tyop_2Elist_2Elist @ A_27a ) > $o,V1m: tyop_2Enum_2Enum,V2d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2EDecode_2Edecode__blist @ A_27a @ V0p @ V1m @ V2d )
= ( c_2EDecode_2Eenc2dec @ ( tyop_2Elist_2Elist @ A_27a ) @ V0p @ ( c_2EEncode_2Eencode__blist @ $o @ A_27a @ V1m @ ( c_2EDecode_2Edec2enc @ A_27a @ V2d ) ) ) ) ).
thf(thm_2EDecode_2Edecode__num__def,axiom,
! [V0p: tyop_2Enum_2Enum > $o] :
( ( c_2EDecode_2Edecode__num @ V0p )
= ( c_2EDecode_2Eenc2dec @ tyop_2Enum_2Enum @ V0p @ c_2EEncode_2Eencode__num ) ) ).
thf(thm_2EDecode_2Edecode__bnum__def,axiom,
! [V0m: tyop_2Enum_2Enum,V1p: tyop_2Enum_2Enum > $o] :
( ( c_2EDecode_2Edecode__bnum @ V0m @ V1p )
= ( c_2EDecode_2Eenc2dec @ tyop_2Enum_2Enum @ V1p @ ( c_2EEncode_2Eencode__bnum @ V0m ) ) ) ).
thf(thm_2EDecode_2Edec__bnum__def,axiom,
( ! [V0l: tyop_2Elist_2Elist @ $o] :
( ( c_2EDecode_2Edec__bnum @ c_2Enum_2E0 @ V0l )
= ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ c_2Enum_2E0 @ V0l ) ) )
& ! [V1m: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ $o] :
( ( c_2EDecode_2Edec__bnum @ ( c_2Enum_2ESUC @ V1m ) @ V2l )
= ( c_2Elist_2Elist__CASE @ $o @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V2l @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V3h: $o,V4t: tyop_2Elist_2Elist @ $o] :
( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( c_2EDecode_2Edec__bnum @ V1m @ V4t ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V5v: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ V5v
@ ^ [V6n: tyop_2Enum_2Enum,V7t_27: tyop_2Elist_2Elist @ $o] : ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V6n ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ V3h @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ c_2Enum_2E0 ) ) @ V7t_27 ) ) ) ) ) ) ) ).
thf(thm_2EDecode_2Edecode__tree__def,axiom,
! [A_27a: $tType,V0p: ( tyop_2EEncode_2Etree @ A_27a ) > $o,V1d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2EDecode_2Edecode__tree @ A_27a @ V0p @ V1d )
= ( c_2EDecode_2Eenc2dec @ ( tyop_2EEncode_2Etree @ A_27a ) @ V0p @ ( c_2EEncode_2Eencode__tree @ A_27a @ ( c_2EDecode_2Edec2enc @ A_27a @ V1d ) ) ) ) ).
thf(thm_2EDecode_2Eenc2dec__none,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1e: A_27a > ( tyop_2Elist_2Elist @ $o ),V2l: tyop_2Elist_2Elist @ $o] :
( ( ( c_2EDecode_2Eenc2dec @ A_27a @ V0p @ V1e @ V2l )
= ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) )
<=> ! [V3x: A_27a,V4t: tyop_2Elist_2Elist @ $o] :
( ( V0p @ V3x )
=> ( (~)
@ ( V2l
= ( c_2Elist_2EAPPEND @ $o @ ( V1e @ V3x ) @ V4t ) ) ) ) ) ).
thf(thm_2EDecode_2Eenc2dec__some,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1e: A_27a > ( tyop_2Elist_2Elist @ $o ),V2l: tyop_2Elist_2Elist @ $o,V3x: A_27a,V4t: tyop_2Elist_2Elist @ $o] :
( ( c_2EEncode_2Ewf__encoder @ A_27a @ V0p @ V1e )
=> ( ( ( c_2EDecode_2Eenc2dec @ A_27a @ V0p @ V1e @ V2l )
= ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ A_27a @ ( tyop_2Elist_2Elist @ $o ) @ V3x @ V4t ) ) )
<=> ( ( V0p @ V3x )
& ( V2l
= ( c_2Elist_2EAPPEND @ $o @ ( V1e @ V3x ) @ V4t ) ) ) ) ) ).
thf(thm_2EDecode_2Eenc2dec__some__alt,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1e: A_27a > ( tyop_2Elist_2Elist @ $o ),V2l: tyop_2Elist_2Elist @ $o,V3x: tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o )] :
( ( c_2EEncode_2Ewf__encoder @ A_27a @ V0p @ V1e )
=> ( ( ( c_2EDecode_2Eenc2dec @ A_27a @ V0p @ V1e @ V2l )
= ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) @ V3x ) )
<=> ( ( V0p @ ( c_2Epair_2EFST @ A_27a @ ( tyop_2Elist_2Elist @ $o ) @ V3x ) )
& ( V2l
= ( c_2Elist_2EAPPEND @ $o @ ( V1e @ ( c_2Epair_2EFST @ A_27a @ ( tyop_2Elist_2Elist @ $o ) @ V3x ) ) @ ( c_2Epair_2ESND @ A_27a @ ( tyop_2Elist_2Elist @ $o ) @ V3x ) ) ) ) ) ) ).
thf(thm_2EDecode_2Ewf__enc2dec,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1e: A_27a > ( tyop_2Elist_2Elist @ $o )] :
( ( c_2EEncode_2Ewf__encoder @ A_27a @ V0p @ V1e )
=> ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p @ ( c_2EDecode_2Eenc2dec @ A_27a @ V0p @ V1e ) ) ) ).
thf(thm_2EDecode_2Edec2enc__some,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ),V2x: A_27a,V3l: tyop_2Elist_2Elist @ $o] :
( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p @ V1d )
=> ( ( ( ( c_2EDecode_2Edec2enc @ A_27a @ V1d @ V2x )
= V3l )
& ( V0p @ V2x ) )
<=> ( ( V1d @ V3l )
= ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ A_27a @ ( tyop_2Elist_2Elist @ $o ) @ V2x @ ( c_2Elist_2ENIL @ $o ) ) ) ) ) ) ).
thf(thm_2EDecode_2Edecode__dec2enc,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ),V2x: A_27a] :
( ( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p @ V1d )
& ( V0p @ V2x ) )
=> ( ( V1d @ ( c_2EDecode_2Edec2enc @ A_27a @ V1d @ V2x ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ A_27a @ ( tyop_2Elist_2Elist @ $o ) @ V2x @ ( c_2Elist_2ENIL @ $o ) ) ) ) ) ).
thf(thm_2EDecode_2Edecode__dec2enc__append,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ),V2x: A_27a,V3t: tyop_2Elist_2Elist @ $o] :
( ( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p @ V1d )
& ( V0p @ V2x ) )
=> ( ( V1d @ ( c_2Elist_2EAPPEND @ $o @ ( c_2EDecode_2Edec2enc @ A_27a @ V1d @ V2x ) @ V3t ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ A_27a @ ( tyop_2Elist_2Elist @ $o ) @ V2x @ V3t ) ) ) ) ).
thf(thm_2EDecode_2Ewf__dec2enc,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p @ V1d )
=> ( c_2EEncode_2Ewf__encoder @ A_27a @ V0p @ ( c_2EDecode_2Edec2enc @ A_27a @ V1d ) ) ) ).
thf(thm_2EDecode_2Edec2enc__enc2dec,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1e: A_27a > ( tyop_2Elist_2Elist @ $o ),V2x: A_27a] :
( ( ( c_2EEncode_2Ewf__encoder @ A_27a @ V0p @ V1e )
& ( V0p @ V2x ) )
=> ( ( c_2EDecode_2Edec2enc @ A_27a @ ( c_2EDecode_2Eenc2dec @ A_27a @ V0p @ V1e ) @ V2x )
= ( V1e @ V2x ) ) ) ).
thf(thm_2EDecode_2Eenc2dec__dec2enc,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p @ V1d )
=> ( ( c_2EDecode_2Eenc2dec @ A_27a @ V0p @ ( c_2EDecode_2Edec2enc @ A_27a @ V1d ) )
= V1d ) ) ).
thf(thm_2EDecode_2Ewf__decode__unit,axiom,
! [V0p: tyop_2Eone_2Eone > $o] : ( c_2EDecode_2Ewf__decoder @ tyop_2Eone_2Eone @ V0p @ ( c_2EDecode_2Edecode__unit @ V0p ) ) ).
thf(thm_2EDecode_2Edec2enc__decode__unit,axiom,
! [V0p: tyop_2Eone_2Eone > $o,V1x: tyop_2Eone_2Eone] :
( ( V0p @ V1x )
=> ( ( c_2EDecode_2Edec2enc @ tyop_2Eone_2Eone @ ( c_2EDecode_2Edecode__unit @ V0p ) @ V1x )
= ( c_2EEncode_2Eencode__unit @ V1x ) ) ) ).
thf(thm_2EDecode_2Edecode__unit,axiom,
! [V0p: tyop_2Eone_2Eone > $o,V1l: tyop_2Elist_2Elist @ $o] :
( ( c_2EDecode_2Edecode__unit @ V0p @ V1l )
= ( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Eone_2Eone @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( V0p @ c_2Eone_2Eone ) @ ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Eone_2Eone @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ tyop_2Eone_2Eone @ ( tyop_2Elist_2Elist @ $o ) @ c_2Eone_2Eone @ V1l ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Eone_2Eone @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ).
thf(thm_2EDecode_2Ewf__decode__bool,axiom,
! [V0p: $o > $o] : ( c_2EDecode_2Ewf__decoder @ $o @ V0p @ ( c_2EDecode_2Edecode__bool @ V0p ) ) ).
thf(thm_2EDecode_2Edec2enc__decode__bool,axiom,
! [V0p: $o > $o,V1x: $o] :
( ( V0p @ V1x )
=> ( ( c_2EDecode_2Edec2enc @ $o @ ( c_2EDecode_2Edecode__bool @ V0p ) @ V1x )
= ( c_2EEncode_2Eencode__bool @ V1x ) ) ) ).
thf(thm_2EDecode_2Edecode__bool,axiom,
! [V0p: $o > $o,V1l: tyop_2Elist_2Elist @ $o] :
( ( c_2EDecode_2Edecode__bool @ V0p @ V1l )
= ( c_2Elist_2Elist__CASE @ $o @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V1l @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V2h: $o,V3t: tyop_2Elist_2Elist @ $o] : ( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( V0p @ V2h ) @ ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ $o @ ( tyop_2Elist_2Elist @ $o ) @ V2h @ V3t ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ).
thf(thm_2EDecode_2Ewf__decode__prod,axiom,
! [A_27a: $tType,A_27b: $tType,V0p1: A_27a > $o,V1p2: A_27b > $o,V2d1: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ),V3d2: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p1 @ V2d1 )
& ( c_2EDecode_2Ewf__decoder @ A_27b @ V1p2 @ V3d2 ) )
=> ( c_2EDecode_2Ewf__decoder @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2EEncode_2Elift__prod @ A_27a @ A_27b @ V0p1 @ V1p2 ) @ ( c_2EDecode_2Edecode__prod @ A_27a @ A_27b @ ( c_2EEncode_2Elift__prod @ A_27a @ A_27b @ V0p1 @ V1p2 ) @ V2d1 @ V3d2 ) ) ) ).
thf(thm_2EDecode_2Edec2enc__decode__prod,axiom,
! [A_27a: $tType,A_27b: $tType,V0p1: A_27a > $o,V1p2: A_27b > $o,V2d1: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ),V3d2: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ),V4x: tyop_2Epair_2Eprod @ A_27a @ A_27b] :
( ( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p1 @ V2d1 )
& ( c_2EDecode_2Ewf__decoder @ A_27b @ V1p2 @ V3d2 )
& ( c_2EEncode_2Elift__prod @ A_27a @ A_27b @ V0p1 @ V1p2 @ V4x ) )
=> ( ( c_2EDecode_2Edec2enc @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2EDecode_2Edecode__prod @ A_27a @ A_27b @ ( c_2EEncode_2Elift__prod @ A_27a @ A_27b @ V0p1 @ V1p2 ) @ V2d1 @ V3d2 ) @ V4x )
= ( c_2EEncode_2Eencode__prod @ A_27a @ A_27b @ ( c_2EDecode_2Edec2enc @ A_27a @ V2d1 ) @ ( c_2EDecode_2Edec2enc @ A_27b @ V3d2 ) @ V4x ) ) ) ).
thf(thm_2EDecode_2Eencode__then__decode__prod,axiom,
! [A_27a: $tType,A_27b: $tType,V0p1: A_27a > $o,V1p2: A_27b > $o,V2e1: A_27a > ( tyop_2Elist_2Elist @ $o ),V3e2: A_27b > ( tyop_2Elist_2Elist @ $o ),V4l: tyop_2Epair_2Eprod @ A_27a @ A_27b,V5t: tyop_2Elist_2Elist @ $o] :
( ( ( c_2EEncode_2Ewf__encoder @ A_27a @ V0p1 @ V2e1 )
& ( c_2EEncode_2Ewf__encoder @ A_27b @ V1p2 @ V3e2 )
& ( c_2EEncode_2Elift__prod @ A_27a @ A_27b @ V0p1 @ V1p2 @ V4l ) )
=> ( ( c_2EDecode_2Edecode__prod @ A_27a @ A_27b @ ( c_2EEncode_2Elift__prod @ A_27a @ A_27b @ V0p1 @ V1p2 ) @ ( c_2EDecode_2Eenc2dec @ A_27a @ V0p1 @ V2e1 ) @ ( c_2EDecode_2Eenc2dec @ A_27b @ V1p2 @ V3e2 ) @ ( c_2Elist_2EAPPEND @ $o @ ( c_2EEncode_2Eencode__prod @ A_27a @ A_27b @ V2e1 @ V3e2 @ V4l ) @ V5t ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) @ V4l @ V5t ) ) ) ) ).
thf(thm_2EDecode_2Edecode__prod,axiom,
! [A_27a: $tType,A_27b: $tType,V0p2: A_27b > $o,V1p1: A_27a > $o,V2l: tyop_2Elist_2Elist @ $o,V3d2: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ),V4d1: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( ( c_2EDecode_2Ewf__decoder @ A_27a @ V1p1 @ V4d1 )
& ( c_2EDecode_2Ewf__decoder @ A_27b @ V0p2 @ V3d2 ) )
=> ( ( c_2EDecode_2Edecode__prod @ A_27a @ A_27b @ ( c_2EEncode_2Elift__prod @ A_27a @ A_27b @ V1p1 @ V0p2 ) @ V4d1 @ V3d2 @ V2l )
= ( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( V4d1 @ V2l ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V5v1: tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ A_27a @ ( tyop_2Elist_2Elist @ $o ) @ V5v1
@ ^ [V6x: A_27a,V7t: tyop_2Elist_2Elist @ $o] :
( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( V3d2 @ V7t ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V8v: tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ A_27b @ ( tyop_2Elist_2Elist @ $o ) @ V8v
@ ^ [V9y: A_27b,V10t_27: tyop_2Elist_2Elist @ $o] : ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ V6x @ V9y ) @ V10t_27 ) ) ) ) ) ) ) ) ).
thf(thm_2EDecode_2Ewf__decode__sum,axiom,
! [A_27a: $tType,A_27b: $tType,V0p1: A_27a > $o,V1p2: A_27b > $o,V2d1: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ),V3d2: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p1 @ V2d1 )
& ( c_2EDecode_2Ewf__decoder @ A_27b @ V1p2 @ V3d2 ) )
=> ( c_2EDecode_2Ewf__decoder @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2EEncode_2Elift__sum @ A_27a @ A_27b @ V0p1 @ V1p2 ) @ ( c_2EDecode_2Edecode__sum @ A_27a @ A_27b @ ( c_2EEncode_2Elift__sum @ A_27a @ A_27b @ V0p1 @ V1p2 ) @ V2d1 @ V3d2 ) ) ) ).
thf(thm_2EDecode_2Edec2enc__decode__sum,axiom,
! [A_27a: $tType,A_27b: $tType,V0p1: A_27a > $o,V1p2: A_27b > $o,V2d1: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ),V3d2: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ),V4x: tyop_2Esum_2Esum @ A_27a @ A_27b] :
( ( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p1 @ V2d1 )
& ( c_2EDecode_2Ewf__decoder @ A_27b @ V1p2 @ V3d2 )
& ( c_2EEncode_2Elift__sum @ A_27a @ A_27b @ V0p1 @ V1p2 @ V4x ) )
=> ( ( c_2EDecode_2Edec2enc @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2EDecode_2Edecode__sum @ A_27a @ A_27b @ ( c_2EEncode_2Elift__sum @ A_27a @ A_27b @ V0p1 @ V1p2 ) @ V2d1 @ V3d2 ) @ V4x )
= ( c_2EEncode_2Eencode__sum @ A_27a @ A_27b @ ( c_2EDecode_2Edec2enc @ A_27a @ V2d1 ) @ ( c_2EDecode_2Edec2enc @ A_27b @ V3d2 ) @ V4x ) ) ) ).
thf(thm_2EDecode_2Eencode__then__decode__sum,axiom,
! [A_27a: $tType,A_27b: $tType,V0p1: A_27a > $o,V1p2: A_27b > $o,V2e1: A_27a > ( tyop_2Elist_2Elist @ $o ),V3e2: A_27b > ( tyop_2Elist_2Elist @ $o ),V4l: tyop_2Esum_2Esum @ A_27a @ A_27b,V5t: tyop_2Elist_2Elist @ $o] :
( ( ( c_2EEncode_2Ewf__encoder @ A_27a @ V0p1 @ V2e1 )
& ( c_2EEncode_2Ewf__encoder @ A_27b @ V1p2 @ V3e2 )
& ( c_2EEncode_2Elift__sum @ A_27a @ A_27b @ V0p1 @ V1p2 @ V4l ) )
=> ( ( c_2EDecode_2Edecode__sum @ A_27a @ A_27b @ ( c_2EEncode_2Elift__sum @ A_27a @ A_27b @ V0p1 @ V1p2 ) @ ( c_2EDecode_2Eenc2dec @ A_27a @ V0p1 @ V2e1 ) @ ( c_2EDecode_2Eenc2dec @ A_27b @ V1p2 @ V3e2 ) @ ( c_2Elist_2EAPPEND @ $o @ ( c_2EEncode_2Eencode__sum @ A_27a @ A_27b @ V2e1 @ V3e2 @ V4l ) @ V5t ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) @ V4l @ V5t ) ) ) ) ).
thf(thm_2EDecode_2Edecode__sum,axiom,
! [A_27a: $tType,A_27b: $tType,V0p2: A_27b > $o,V1p1: A_27a > $o,V2l: tyop_2Elist_2Elist @ $o,V3d2: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ),V4d1: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( ( c_2EDecode_2Ewf__decoder @ A_27a @ V1p1 @ V4d1 )
& ( c_2EDecode_2Ewf__decoder @ A_27b @ V0p2 @ V3d2 ) )
=> ( ( c_2EDecode_2Edecode__sum @ A_27a @ A_27b @ ( c_2EEncode_2Elift__sum @ A_27a @ A_27b @ V1p1 @ V0p2 ) @ V4d1 @ V3d2 @ V2l )
= ( c_2Elist_2Elist__CASE @ $o @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V2l @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V5v1: $o,V6t: tyop_2Elist_2Elist @ $o] :
( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V5v1
@ ( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( V4d1 @ V6t ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V7v: tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ A_27a @ ( tyop_2Elist_2Elist @ $o ) @ V7v
@ ^ [V8x: A_27a,V9t_27: tyop_2Elist_2Elist @ $o] : ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Esum_2EINL @ A_27a @ A_27b @ V8x ) @ V9t_27 ) ) ) )
@ ( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( V3d2 @ V6t ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V10v: tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ A_27b @ ( tyop_2Elist_2Elist @ $o ) @ V10v
@ ^ [V11x: A_27b,V12t_27: tyop_2Elist_2Elist @ $o] : ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Esum_2EINR @ A_27a @ A_27b @ V11x ) @ V12t_27 ) ) ) ) ) ) ) ) ).
thf(thm_2EDecode_2Ewf__decode__option,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p @ V1d )
=> ( c_2EDecode_2Ewf__decoder @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2EEncode_2Elift__option @ A_27a @ V0p ) @ ( c_2EDecode_2Edecode__option @ A_27a @ ( c_2EEncode_2Elift__option @ A_27a @ V0p ) @ V1d ) ) ) ).
thf(thm_2EDecode_2Edec2enc__decode__option,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ),V2x: tyop_2Eoption_2Eoption @ A_27a] :
( ( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p @ V1d )
& ( c_2EEncode_2Elift__option @ A_27a @ V0p @ V2x ) )
=> ( ( c_2EDecode_2Edec2enc @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2EDecode_2Edecode__option @ A_27a @ ( c_2EEncode_2Elift__option @ A_27a @ V0p ) @ V1d ) @ V2x )
= ( c_2EEncode_2Eencode__option @ A_27a @ ( c_2EDecode_2Edec2enc @ A_27a @ V1d ) @ V2x ) ) ) ).
thf(thm_2EDecode_2Eencode__then__decode__option,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1e: A_27a > ( tyop_2Elist_2Elist @ $o ),V2l: tyop_2Eoption_2Eoption @ A_27a,V3t: tyop_2Elist_2Elist @ $o] :
( ( ( c_2EEncode_2Ewf__encoder @ A_27a @ V0p @ V1e )
& ( c_2EEncode_2Elift__option @ A_27a @ V0p @ V2l ) )
=> ( ( c_2EDecode_2Edecode__option @ A_27a @ ( c_2EEncode_2Elift__option @ A_27a @ V0p ) @ ( c_2EDecode_2Eenc2dec @ A_27a @ V0p @ V1e ) @ ( c_2Elist_2EAPPEND @ $o @ ( c_2EEncode_2Eencode__option @ A_27a @ V1e @ V2l ) @ V3t ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) @ V2l @ V3t ) ) ) ) ).
thf(thm_2EDecode_2Edecode__option,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1l: tyop_2Elist_2Elist @ $o,V2d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p @ V2d )
=> ( ( c_2EDecode_2Edecode__option @ A_27a @ ( c_2EEncode_2Elift__option @ A_27a @ V0p ) @ V2d @ V1l )
= ( c_2Elist_2Elist__CASE @ $o @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V1l @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V3v1: $o,V4t: tyop_2Elist_2Elist @ $o] :
( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V3v1
@ ( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( V2d @ V4t ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V5v: tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ A_27a @ ( tyop_2Elist_2Elist @ $o ) @ V5v
@ ^ [V6x: A_27a,V7t_27: tyop_2Elist_2Elist @ $o] : ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Eoption_2ESOME @ A_27a @ V6x ) @ V7t_27 ) ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Eoption_2ENONE @ A_27a ) @ V4t ) ) ) ) ) ) ).
thf(thm_2EDecode_2Ewf__decode__list,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p @ V1d )
=> ( c_2EDecode_2Ewf__decoder @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EEVERY @ A_27a @ V0p ) @ ( c_2EDecode_2Edecode__list @ A_27a @ ( c_2Elist_2EEVERY @ A_27a @ V0p ) @ V1d ) ) ) ).
thf(thm_2EDecode_2Edec2enc__decode__list,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ),V2x: tyop_2Elist_2Elist @ A_27a] :
( ( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p @ V1d )
& ( c_2Elist_2EEVERY @ A_27a @ V0p @ V2x ) )
=> ( ( c_2EDecode_2Edec2enc @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EDecode_2Edecode__list @ A_27a @ ( c_2Elist_2EEVERY @ A_27a @ V0p ) @ V1d ) @ V2x )
= ( c_2EEncode_2Eencode__list @ A_27a @ ( c_2EDecode_2Edec2enc @ A_27a @ V1d ) @ V2x ) ) ) ).
thf(thm_2EDecode_2Eencode__then__decode__list,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1e: A_27a > ( tyop_2Elist_2Elist @ $o ),V2l: tyop_2Elist_2Elist @ A_27a,V3t: tyop_2Elist_2Elist @ $o] :
( ( ( c_2EEncode_2Ewf__encoder @ A_27a @ V0p @ V1e )
& ( c_2Elist_2EEVERY @ A_27a @ V0p @ V2l ) )
=> ( ( c_2EDecode_2Edecode__list @ A_27a @ ( c_2Elist_2EEVERY @ A_27a @ V0p ) @ ( c_2EDecode_2Eenc2dec @ A_27a @ V0p @ V1e ) @ ( c_2Elist_2EAPPEND @ $o @ ( c_2EEncode_2Eencode__list @ A_27a @ V1e @ V2l ) @ V3t ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) @ V2l @ V3t ) ) ) ) ).
thf(thm_2EDecode_2Edecode__list,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1l: tyop_2Elist_2Elist @ $o,V2d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p @ V2d )
=> ( ( c_2EDecode_2Edecode__list @ A_27a @ ( c_2Elist_2EEVERY @ A_27a @ V0p ) @ V2d @ V1l )
= ( c_2Elist_2Elist__CASE @ $o @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V1l @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V3v2: $o,V4t: tyop_2Elist_2Elist @ $o] :
( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V3v2
@ ( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( V2d @ V4t ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V5v1: tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ A_27a @ ( tyop_2Elist_2Elist @ $o ) @ V5v1
@ ^ [V6x: A_27a,V7t_27: tyop_2Elist_2Elist @ $o] :
( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( c_2EDecode_2Edecode__list @ A_27a @ ( c_2Elist_2EEVERY @ A_27a @ V0p ) @ V2d @ V7t_27 ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V8v: tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) @ V8v
@ ^ [V9xs: tyop_2Elist_2Elist @ A_27a,V10t_27_27: tyop_2Elist_2Elist @ $o] : ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Elist_2ECONS @ A_27a @ V6x @ V9xs ) @ V10t_27_27 ) ) ) ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Elist_2ENIL @ A_27a ) @ V4t ) ) ) ) ) ) ).
thf(thm_2EDecode_2Ewf__decode__blist,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1p: A_27a > $o,V2d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2EDecode_2Ewf__decoder @ A_27a @ V1p @ V2d )
=> ( c_2EDecode_2Ewf__decoder @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EEncode_2Elift__blist @ A_27a @ V0m @ V1p ) @ ( c_2EDecode_2Edecode__blist @ A_27a @ ( c_2EEncode_2Elift__blist @ A_27a @ V0m @ V1p ) @ V0m @ V2d ) ) ) ).
thf(thm_2EDecode_2Edec2enc__decode__blist,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1p: A_27a > $o,V2d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ),V3l: tyop_2Elist_2Elist @ A_27a] :
( ( ( c_2EDecode_2Ewf__decoder @ A_27a @ V1p @ V2d )
& ( c_2EEncode_2Elift__blist @ A_27a @ V0m @ V1p @ V3l ) )
=> ( ( c_2EDecode_2Edec2enc @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2EDecode_2Edecode__blist @ A_27a @ ( c_2EEncode_2Elift__blist @ A_27a @ V0m @ V1p ) @ V0m @ V2d ) @ V3l )
= ( c_2EEncode_2Eencode__blist @ $o @ A_27a @ V0m @ ( c_2EDecode_2Edec2enc @ A_27a @ V2d ) @ V3l ) ) ) ).
thf(thm_2EDecode_2Eencode__then__decode__blist,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1p: A_27a > $o,V2e: A_27a > ( tyop_2Elist_2Elist @ $o ),V3l: tyop_2Elist_2Elist @ A_27a,V4t: tyop_2Elist_2Elist @ $o] :
( ( ( c_2EEncode_2Ewf__encoder @ A_27a @ V1p @ V2e )
& ( c_2EEncode_2Elift__blist @ A_27a @ V0m @ V1p @ V3l ) )
=> ( ( c_2EDecode_2Edecode__blist @ A_27a @ ( c_2EEncode_2Elift__blist @ A_27a @ V0m @ V1p ) @ V0m @ ( c_2EDecode_2Eenc2dec @ A_27a @ V1p @ V2e ) @ ( c_2Elist_2EAPPEND @ $o @ ( c_2EEncode_2Eencode__blist @ $o @ A_27a @ V0m @ V2e @ V3l ) @ V4t ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) @ V3l @ V4t ) ) ) ) ).
thf(thm_2EDecode_2Edecode__blist,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1m: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ $o,V3d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p @ V3d )
=> ( ( c_2EDecode_2Edecode__blist @ A_27a @ ( c_2EEncode_2Elift__blist @ A_27a @ V1m @ V0p ) @ V1m @ V3d @ V2l )
= ( c_2Earithmetic_2Enum__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V1m @ ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Elist_2ENIL @ A_27a ) @ V2l ) )
@ ^ [V4n: tyop_2Enum_2Enum] :
( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( V3d @ V2l ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V5v1: tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ A_27a @ ( tyop_2Elist_2Elist @ $o ) @ V5v1
@ ^ [V6x: A_27a,V7t: tyop_2Elist_2Elist @ $o] :
( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( c_2EDecode_2Edecode__blist @ A_27a @ ( c_2EEncode_2Elift__blist @ A_27a @ V4n @ V0p ) @ V4n @ V3d @ V7t ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V8v: tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) @ V8v
@ ^ [V9xs: tyop_2Elist_2Elist @ A_27a,V10t_27: tyop_2Elist_2Elist @ $o] : ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Elist_2ECONS @ A_27a @ V6x @ V9xs ) @ V10t_27 ) ) ) ) ) ) ) ) ) ).
thf(thm_2EDecode_2Ewf__decode__num,axiom,
! [V0p: tyop_2Enum_2Enum > $o] : ( c_2EDecode_2Ewf__decoder @ tyop_2Enum_2Enum @ V0p @ ( c_2EDecode_2Edecode__num @ V0p ) ) ).
thf(thm_2EDecode_2Edec2enc__decode__num,axiom,
! [V0p: tyop_2Enum_2Enum > $o,V1x: tyop_2Enum_2Enum] :
( ( V0p @ V1x )
=> ( ( c_2EDecode_2Edec2enc @ tyop_2Enum_2Enum @ ( c_2EDecode_2Edecode__num @ V0p ) @ V1x )
= ( c_2EEncode_2Eencode__num @ V1x ) ) ) ).
thf(thm_2EDecode_2Edecode__num__total,axiom,
! [V0l: tyop_2Elist_2Elist @ $o] :
( ( c_2EDecode_2Edecode__num @ ( c_2Ecombin_2EK @ $o @ tyop_2Enum_2Enum @ c_2Ebool_2ET ) @ V0l )
= ( c_2Elist_2Elist__CASE @ $o @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V0l @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V1v4: $o,V2t_27: tyop_2Elist_2Elist @ $o] :
( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V1v4
@ ( c_2Elist_2Elist__CASE @ $o @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V2t_27 @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V3v8: $o,V4t: tyop_2Elist_2Elist @ $o] :
( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V3v8 @ ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ c_2Enum_2E0 @ V4t ) )
@ ( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( c_2EDecode_2Edecode__num @ ( c_2Ecombin_2EK @ $o @ tyop_2Enum_2Enum @ c_2Ebool_2ET ) @ V4t ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V5v1: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ V5v1
@ ^ [V6v: tyop_2Enum_2Enum,V7t_27: tyop_2Elist_2Elist @ $o] : ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V6v ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V7t_27 ) ) ) ) ) )
@ ( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( c_2EDecode_2Edecode__num @ ( c_2Ecombin_2EK @ $o @ tyop_2Enum_2Enum @ c_2Ebool_2ET ) @ V2t_27 ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V8v1: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ V8v1
@ ^ [V9v: tyop_2Enum_2Enum,V10t_27: tyop_2Elist_2Elist @ $o] : ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V9v ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ V10t_27 ) ) ) ) ) ) ) ).
thf(thm_2EDecode_2Edecode__num,axiom,
! [V0p: tyop_2Enum_2Enum > $o,V1l: tyop_2Elist_2Elist @ $o] :
( ( c_2EDecode_2Edecode__num @ V0p @ V1l )
= ( c_2Elist_2Elist__CASE @ $o @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V1l @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V2v4: $o,V3t_27: tyop_2Elist_2Elist @ $o] :
( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V2v4
@ ( c_2Elist_2Elist__CASE @ $o @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V3t_27 @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V4v8: $o,V5t: tyop_2Elist_2Elist @ $o] :
( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V4v8 @ ( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( V0p @ c_2Enum_2E0 ) @ ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ c_2Enum_2E0 @ V5t ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) )
@ ( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( c_2EDecode_2Edecode__num @ ( c_2Ecombin_2EK @ $o @ tyop_2Enum_2Enum @ c_2Ebool_2ET ) @ V5t ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V6v1: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ V6v1
@ ^ [V7v: tyop_2Enum_2Enum,V8t_27: tyop_2Elist_2Elist @ $o] : ( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( V0p @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V7v ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V7v ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V8t_27 ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ) )
@ ( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( c_2EDecode_2Edecode__num @ ( c_2Ecombin_2EK @ $o @ tyop_2Enum_2Enum @ c_2Ebool_2ET ) @ V3t_27 ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V9v1: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ V9v1
@ ^ [V10v: tyop_2Enum_2Enum,V11t_27: tyop_2Elist_2Elist @ $o] : ( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( V0p @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V10v ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V10v ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ V11t_27 ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ) ) ) ).
thf(thm_2EDecode_2Edec__bnum__def__compute,axiom,
( ! [V0l: tyop_2Elist_2Elist @ $o] :
( ( c_2EDecode_2Edec__bnum @ c_2Enum_2E0 @ V0l )
= ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ c_2Enum_2E0 @ V0l ) ) )
& ! [V1m: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ $o] :
( ( c_2EDecode_2Edec__bnum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V1m ) ) @ V2l )
= ( c_2Elist_2Elist__CASE @ $o @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V2l @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V3h: $o,V4t: tyop_2Elist_2Elist @ $o] :
( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( c_2EDecode_2Edec__bnum @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V1m ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V4t ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V5v: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ V5v
@ ^ [V6n: tyop_2Enum_2Enum,V7t_27: tyop_2Elist_2Elist @ $o] : ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V6n ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ V3h @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ c_2Enum_2E0 ) ) @ V7t_27 ) ) ) ) ) )
& ! [V8m: tyop_2Enum_2Enum,V9l: tyop_2Elist_2Elist @ $o] :
( ( c_2EDecode_2Edec__bnum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ V8m ) ) @ V9l )
= ( c_2Elist_2Elist__CASE @ $o @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ V9l @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V10h: $o,V11t: tyop_2Elist_2Elist @ $o] :
( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( c_2EDecode_2Edec__bnum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ V8m ) ) @ V11t ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V12v: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ V12v
@ ^ [V13n: tyop_2Enum_2Enum,V14t_27: tyop_2Elist_2Elist @ $o] : ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V13n ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ V10h @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ c_2Enum_2E0 ) ) @ V14t_27 ) ) ) ) ) ) ) ).
thf(thm_2EDecode_2Edec__bnum__lt,axiom,
! [V0m: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ $o,V2n: tyop_2Enum_2Enum,V3t: tyop_2Elist_2Elist @ $o] :
( ( ( c_2EDecode_2Edec__bnum @ V0m @ V1l )
= ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ V2n @ V3t ) ) )
=> ( c_2Eprim__rec_2E_3C @ V2n @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ V0m ) ) ) ).
thf(thm_2EDecode_2Edec__bnum__inj,axiom,
! [V0m: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ $o,V2n: tyop_2Enum_2Enum,V3t: tyop_2Elist_2Elist @ $o] :
( ( ( c_2EDecode_2Edec__bnum @ V0m @ V1l )
= ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ V2n @ V3t ) ) )
=> ( V1l
= ( c_2Elist_2EAPPEND @ $o @ ( c_2EEncode_2Eencode__bnum @ V0m @ V2n ) @ V3t ) ) ) ).
thf(thm_2EDecode_2Ewf__decode__bnum,axiom,
! [V0m: tyop_2Enum_2Enum,V1p: tyop_2Enum_2Enum > $o] :
( ( c_2EEncode_2Ewf__pred__bnum @ V0m @ V1p )
=> ( c_2EDecode_2Ewf__decoder @ tyop_2Enum_2Enum @ V1p @ ( c_2EDecode_2Edecode__bnum @ V0m @ V1p ) ) ) ).
thf(thm_2EDecode_2Edec2enc__decode__bnum,axiom,
! [V0m: tyop_2Enum_2Enum,V1p: tyop_2Enum_2Enum > $o,V2x: tyop_2Enum_2Enum] :
( ( ( c_2EEncode_2Ewf__pred__bnum @ V0m @ V1p )
& ( V1p @ V2x ) )
=> ( ( c_2EDecode_2Edec2enc @ tyop_2Enum_2Enum @ ( c_2EDecode_2Edecode__bnum @ V0m @ V1p ) @ V2x )
= ( c_2EEncode_2Eencode__bnum @ V0m @ V2x ) ) ) ).
thf(thm_2EDecode_2Edecode__bnum,axiom,
! [V0p: tyop_2Enum_2Enum > $o,V1m: tyop_2Enum_2Enum,V2l: tyop_2Elist_2Elist @ $o] :
( ( c_2EEncode_2Ewf__pred__bnum @ V1m @ V0p )
=> ( ( c_2EDecode_2Edecode__bnum @ V1m @ V0p @ V2l )
= ( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( c_2EDecode_2Edec__bnum @ V1m @ V2l ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V3v: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ V3v
@ ^ [V4n: tyop_2Enum_2Enum,V5t: tyop_2Elist_2Elist @ $o] : ( c_2Ebool_2ECOND @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( V0p @ V4n ) @ ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) @ V4n @ V5t ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ) ) ).
thf(thm_2EDecode_2Ewf__decode__tree,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p @ V1d )
=> ( c_2EDecode_2Ewf__decoder @ ( tyop_2EEncode_2Etree @ A_27a ) @ ( c_2EEncode_2Elift__tree @ A_27a @ V0p ) @ ( c_2EDecode_2Edecode__tree @ A_27a @ ( c_2EEncode_2Elift__tree @ A_27a @ V0p ) @ V1d ) ) ) ).
thf(thm_2EDecode_2Edecode__tree,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1l: tyop_2Elist_2Elist @ $o,V2d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2EDecode_2Ewf__decoder @ A_27a @ V0p @ V2d )
=> ( ( c_2EDecode_2Edecode__tree @ A_27a @ ( c_2EEncode_2Elift__tree @ A_27a @ V0p ) @ V2d @ V1l )
= ( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2EEncode_2Etree @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( V2d @ V1l ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ ( tyop_2EEncode_2Etree @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V3v1: tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2EEncode_2Etree @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ A_27a @ ( tyop_2Elist_2Elist @ $o ) @ V3v1
@ ^ [V4a: A_27a,V5t: tyop_2Elist_2Elist @ $o] :
( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ ( tyop_2EEncode_2Etree @ A_27a ) ) @ ( tyop_2Elist_2Elist @ $o ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2EEncode_2Etree @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( c_2EDecode_2Edecode__list @ ( tyop_2EEncode_2Etree @ A_27a ) @ ( c_2Elist_2EEVERY @ ( tyop_2EEncode_2Etree @ A_27a ) @ ( c_2EEncode_2Elift__tree @ A_27a @ V0p ) ) @ ( c_2EDecode_2Edecode__tree @ A_27a @ ( c_2EEncode_2Elift__tree @ A_27a @ V0p ) @ V2d ) @ V5t ) @ ( c_2Eoption_2ENONE @ ( tyop_2Epair_2Eprod @ ( tyop_2EEncode_2Etree @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) )
@ ^ [V6v: tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ ( tyop_2EEncode_2Etree @ A_27a ) ) @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2EEncode_2Etree @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2EEncode_2Etree @ A_27a ) ) @ ( tyop_2Elist_2Elist @ $o ) @ V6v
@ ^ [V7ts: tyop_2Elist_2Elist @ ( tyop_2EEncode_2Etree @ A_27a ),V8t_27: tyop_2Elist_2Elist @ $o] : ( c_2Eoption_2ESOME @ ( tyop_2Epair_2Eprod @ ( tyop_2EEncode_2Etree @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) @ ( c_2Epair_2E_2C @ ( tyop_2EEncode_2Etree @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) @ ( c_2EEncode_2ENode @ A_27a @ V4a @ V7ts ) @ V8t_27 ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------