ITP001 Axioms: ITP060^5.ax
%------------------------------------------------------------------------------
% File : ITP060^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : Decode^2.ax [Gau20]
% : HL4060^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 120 ( 6 unt; 29 typ; 0 def)
% Number of atoms : 3856 ( 67 equ; 0 cnn)
% Maximal formula atoms : 108 ( 32 avg)
% Number of connectives : 5178 ( 1 ~; 0 |; 28 &;4964 @)
% ( 5 <=>; 180 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 12 avg;4964 nst)
% Number of types : 6 ( 5 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 101 ( 100 usr; 81 con; 0-2 aty)
% Number of variables : 354 ( 90 ^ 264 !; 0 ?; 354 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2EDecode_2Edec2enc,type,
c_2EDecode_2Edec2enc: del > $i ).
thf(mem_c_2EDecode_2Edec2enc,axiom,
! [A_27a: del] : ( mem @ ( c_2EDecode_2Edec2enc @ A_27a ) @ ( arr @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) ).
thf(stp_c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o,type,
tp__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o: $tType ).
thf(stp_inj_c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o,type,
inj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o: tp__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o > $i ).
thf(stp_surj_c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o,type,
surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o: $i > tp__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o ).
thf(stp_inj_surj_c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o,axiom,
! [X: tp__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ ( inj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o,axiom,
! [X: tp__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o] : ( mem @ ( inj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ X ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) )
=> ( X
= ( inj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ X ) ) ) ) ).
thf(stp_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o,type,
tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o: $tType ).
thf(stp_inj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o,type,
inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o > $i ).
thf(stp_surj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o,type,
surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o: $i > tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o ).
thf(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o,axiom,
! [X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o,axiom,
! [X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o] : ( mem @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ X ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) )
=> ( X
= ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ X ) ) ) ) ).
thf(tp_c_2EDecode_2Edec__bnum,type,
c_2EDecode_2Edec__bnum: $i ).
thf(mem_c_2EDecode_2Edec__bnum,axiom,
mem @ c_2EDecode_2Edec__bnum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ).
thf(tp_c_2EDecode_2Edecode__blist,type,
c_2EDecode_2Edecode__blist: del > $i ).
thf(mem_c_2EDecode_2Edecode__blist,axiom,
! [A_27a: del] : ( mem @ ( c_2EDecode_2Edecode__blist @ A_27a ) @ ( arr @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ) ) ) ).
thf(tp_c_2EDecode_2Edecode__bnum,type,
c_2EDecode_2Edecode__bnum: $i ).
thf(mem_c_2EDecode_2Edecode__bnum,axiom,
mem @ c_2EDecode_2Edecode__bnum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ) ).
thf(stp_c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o,type,
tp__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o: $tType ).
thf(stp_inj_c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o,type,
inj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o: tp__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o > $i ).
thf(stp_surj_c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o,type,
surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o: $i > tp__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o ).
thf(stp_inj_surj_c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o,axiom,
! [X: tp__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o @ ( inj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o,axiom,
! [X: tp__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o] : ( mem @ ( inj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o @ X ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Elist_2Elist @ bool ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Elist_2Elist @ bool ) ) ) )
=> ( X
= ( inj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o @ ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o @ X ) ) ) ) ).
thf(tp_c_2EDecode_2Edecode__bool,type,
c_2EDecode_2Edecode__bool: $i ).
thf(mem_c_2EDecode_2Edecode__bool,axiom,
mem @ c_2EDecode_2Edecode__bool @ ( arr @ ( arr @ bool @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ).
thf(tp_c_2EDecode_2Edecode__list,type,
c_2EDecode_2Edecode__list: del > $i ).
thf(mem_c_2EDecode_2Edecode__list,axiom,
! [A_27a: del] : ( mem @ ( c_2EDecode_2Edecode__list @ A_27a ) @ ( arr @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) @ ( arr @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ) ) ).
thf(tp_c_2EDecode_2Edecode__num,type,
c_2EDecode_2Edecode__num: $i ).
thf(mem_c_2EDecode_2Edecode__num,axiom,
mem @ c_2EDecode_2Edecode__num @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ).
thf(tp_c_2EDecode_2Edecode__option,type,
c_2EDecode_2Edecode__option: del > $i ).
thf(mem_c_2EDecode_2Edecode__option,axiom,
! [A_27a: del] : ( mem @ ( c_2EDecode_2Edecode__option @ A_27a ) @ ( arr @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) @ ( arr @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ) ) ).
thf(tp_c_2EDecode_2Edecode__prod,type,
c_2EDecode_2Edecode__prod: del > del > $i ).
thf(mem_c_2EDecode_2Edecode__prod,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EDecode_2Edecode__prod @ A_27a @ A_27b ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) @ ( arr @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( arr @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ) ) ) ).
thf(tp_c_2EDecode_2Edecode__sum,type,
c_2EDecode_2Edecode__sum: del > del > $i ).
thf(mem_c_2EDecode_2Edecode__sum,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EDecode_2Edecode__sum @ A_27a @ A_27b ) @ ( arr @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ bool ) @ ( arr @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( arr @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ) ) ) ).
thf(tp_c_2EDecode_2Edecode__tree,type,
c_2EDecode_2Edecode__tree: del > $i ).
thf(mem_c_2EDecode_2Edecode__tree,axiom,
! [A_27a: del] : ( mem @ ( c_2EDecode_2Edecode__tree @ A_27a ) @ ( arr @ ( arr @ ( ty_2EEncode_2Etree @ A_27a ) @ bool ) @ ( arr @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2EEncode_2Etree @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o,type,
tp__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o: $tType ).
thf(stp_inj_c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o,type,
inj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o: tp__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o > $i ).
thf(stp_surj_c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o,type,
surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o: $i > tp__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o ).
thf(stp_inj_surj_c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o,axiom,
! [X: tp__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o @ ( inj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o,axiom,
! [X: tp__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o] : ( mem @ ( inj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o @ X ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Eone_2Eone @ ( ty_2Elist_2Elist @ bool ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Eone_2Eone @ ( ty_2Elist_2Elist @ bool ) ) ) )
=> ( X
= ( inj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o @ ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o @ X ) ) ) ) ).
thf(stp_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o,type,
tp__c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o: $tType ).
thf(stp_inj_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o,type,
inj__c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o: tp__c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o > $i ).
thf(stp_surj_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o,type,
surj__c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o: $i > tp__c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o ).
thf(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o,axiom,
! [X: tp__c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o @ ( inj__c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o,axiom,
! [X: tp__c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o] : ( mem @ ( inj__c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o @ X ) @ ( ty_2Epair_2Eprod @ ty_2Eone_2Eone @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Epair_2Eprod @ ty_2Eone_2Eone @ ( ty_2Elist_2Elist @ bool ) ) )
=> ( X
= ( inj__c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o @ ( surj__c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o @ X ) ) ) ) ).
thf(tp_c_2EDecode_2Edecode__unit,type,
c_2EDecode_2Edecode__unit: $i ).
thf(mem_c_2EDecode_2Edecode__unit,axiom,
mem @ c_2EDecode_2Edecode__unit @ ( arr @ ( arr @ ty_2Eone_2Eone @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Eone_2Eone @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ).
thf(tp_c_2EDecode_2Eenc2dec,type,
c_2EDecode_2Eenc2dec: del > $i ).
thf(mem_c_2EDecode_2Eenc2dec,axiom,
! [A_27a: del] : ( mem @ ( c_2EDecode_2Eenc2dec @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ) ) ).
thf(tp_c_2EDecode_2Ewf__decoder,type,
c_2EDecode_2Ewf__decoder: del > $i ).
thf(mem_c_2EDecode_2Ewf__decoder,axiom,
! [A_27a: del] : ( mem @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ bool ) ) ) ).
thf(ax_thm_2EDecode_2Ewf__decoder__def,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1d: $i] :
( ( mem @ V1d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p ) @ V1d ) )
<=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( p
@ ( ap
@ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V0p @ V2x ) )
@ ( ap @ ( c_2Ebool_2E_3F @ ( ty_2Elist_2Elist @ bool ) )
@ ( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V3a: $i] :
( ap @ ( c_2Ebool_2E_21 @ ( ty_2Elist_2Elist @ bool ) )
@ ( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V4b: $i] :
( ap @ ( c_2Ebool_2E_21 @ ( ty_2Elist_2Elist @ bool ) )
@ ( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V5c: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ V1d @ V4b ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ V2x ) @ V5c ) ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Elist_2Elist @ bool ) ) @ V4b ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ V3a ) @ V5c ) ) ) ) ) ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Elist_2Elist @ bool ) )
@ ( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V6a: $i] :
( ap @ ( c_2Ebool_2E_21 @ ( ty_2Elist_2Elist @ bool ) )
@ ( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V7b: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ V1d @ V6a ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ V2x ) @ V7b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EDecode_2Eenc2dec__def,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) )
=> ! [V2l: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ A_27a ) @ V0p ) @ V1e ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) )
= ( ap
@ ( ap
@ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( ap @ ( c_2Ebool_2E_3F @ A_27a )
@ ( lam @ A_27a
@ ^ [V3x: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( ty_2Elist_2Elist @ bool ) )
@ ( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0p @ V3x ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Elist_2Elist @ bool ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( ap @ V1e @ V3x ) ) @ V4t ) ) ) ) ) ) ) )
@ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) )
@ ( ap @ ( c_2Emin_2E_40 @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) )
@ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ ( ty_2Elist_2Elist @ bool ) @ bool )
@ ( lam @ A_27a
@ ^ [V5x: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V6t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0p @ V5x ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Elist_2Elist @ bool ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( ap @ V1e @ V5x ) ) @ V6t ) ) ) ) ) ) ) ) )
@ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ) ) ).
thf(ax_thm_2EDecode_2Edec2enc__def,axiom,
! [A_27a: del,V0d: $i] :
( ( mem @ V0d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27a ) @ V0d ) @ V1x ) )
= ( surj__c_ty_2Elist_2Elist_o
@ ( ap @ ( c_2Emin_2E_40 @ ( ty_2Elist_2Elist @ bool ) )
@ ( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V2l: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ V0d @ V2l ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ V1x ) @ ( c_2Elist_2ENIL @ bool ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Eenc2dec__none,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) )
=> ! [V2l: tp__c_ty_2Elist_2Elist_o] :
( ( ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ A_27a ) @ V0p ) @ V1e ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) )
= ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) )
<=> ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ! [V4t: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ V0p @ V3x ) )
=> ( V2l
!= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( ap @ V1e @ V3x ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V4t ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Eenc2dec__some,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) )
=> ! [V2l: tp__c_ty_2Elist_2Elist_o,V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ! [V4t: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ ( c_2EEncode_2Ewf__encoder @ A_27a ) @ V0p ) @ V1e ) )
=> ( ( ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ A_27a ) @ V0p ) @ V1e ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ V3x ) @ ( inj__c_ty_2Elist_2Elist_o @ V4t ) ) ) )
<=> ( ( p @ ( ap @ V0p @ V3x ) )
& ( V2l
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( ap @ V1e @ V3x ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V4t ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Eenc2dec__some__alt,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) )
=> ! [V2l: tp__c_ty_2Elist_2Elist_o,V3x: $i] :
( ( mem @ V3x @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EEncode_2Ewf__encoder @ A_27a ) @ V0p ) @ V1e ) )
=> ( ( ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ A_27a ) @ V0p ) @ V1e ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) @ V3x ) )
<=> ( ( p @ ( ap @ V0p @ ( ap @ ( c_2Epair_2EFST @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ V3x ) ) )
& ( V2l
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( ap @ V1e @ ( ap @ ( c_2Epair_2EFST @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ V3x ) ) ) @ ( ap @ ( c_2Epair_2ESND @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ V3x ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Ewf__enc2dec,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EEncode_2Ewf__encoder @ A_27a ) @ V0p ) @ V1e ) )
=> ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p ) @ ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ A_27a ) @ V0p ) @ V1e ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edec2enc__some,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1d: $i] :
( ( mem @ V1d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ! [V3l: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p ) @ V1d ) )
=> ( ( ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27a ) @ V1d ) @ V2x ) )
= V3l )
& ( p @ ( ap @ V0p @ V2x ) ) )
<=> ( ( ap @ V1d @ ( inj__c_ty_2Elist_2Elist_o @ V3l ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ V2x ) @ ( c_2Elist_2ENIL @ bool ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edecode__dec2enc,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1d: $i] :
( ( mem @ V1d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p ) @ V1d ) )
& ( p @ ( ap @ V0p @ V2x ) ) )
=> ( ( ap @ V1d @ ( ap @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27a ) @ V1d ) @ V2x ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ V2x ) @ ( c_2Elist_2ENIL @ bool ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edecode__dec2enc__append,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1d: $i] :
( ( mem @ V1d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ! [V3t: tp__c_ty_2Elist_2Elist_o] :
( ( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p ) @ V1d ) )
& ( p @ ( ap @ V0p @ V2x ) ) )
=> ( ( ap @ V1d @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( ap @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27a ) @ V1d ) @ V2x ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V3t ) ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ V2x ) @ ( inj__c_ty_2Elist_2Elist_o @ V3t ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Ewf__dec2enc,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1d: $i] :
( ( mem @ V1d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p ) @ V1d ) )
=> ( p @ ( ap @ ( ap @ ( c_2EEncode_2Ewf__encoder @ A_27a ) @ V0p ) @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27a ) @ V1d ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edec2enc__enc2dec,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2EEncode_2Ewf__encoder @ A_27a ) @ V0p ) @ V1e ) )
& ( p @ ( ap @ V0p @ V2x ) ) )
=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27a ) @ ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ A_27a ) @ V0p ) @ V1e ) ) @ V2x ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ V1e @ V2x ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Eenc2dec__dec2enc,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1d: $i] :
( ( mem @ V1d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p ) @ V1d ) )
=> ( ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ A_27a ) @ V0p ) @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27a ) @ V1d ) )
= V1d ) ) ) ) ).
thf(ax_thm_2EDecode_2Edecode__unit__def,axiom,
! [V0p: $i] :
( ( mem @ V0p @ ( arr @ ty_2Eone_2Eone @ bool ) )
=> ( ( ap @ c_2EDecode_2Edecode__unit @ V0p )
= ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ ty_2Eone_2Eone ) @ V0p ) @ c_2EEncode_2Eencode__unit ) ) ) ).
thf(conj_thm_2EDecode_2Ewf__decode__unit,axiom,
! [V0p: $i] :
( ( mem @ V0p @ ( arr @ ty_2Eone_2Eone @ bool ) )
=> ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ ty_2Eone_2Eone ) @ V0p ) @ ( ap @ c_2EDecode_2Edecode__unit @ V0p ) ) ) ) ).
thf(conj_thm_2EDecode_2Edec2enc__decode__unit,axiom,
! [V0p: $i] :
( ( mem @ V0p @ ( arr @ ty_2Eone_2Eone @ bool ) )
=> ! [V1x: tp__ty_2Eone_2Eone] :
( ( p @ ( ap @ V0p @ ( inj__ty_2Eone_2Eone @ V1x ) ) )
=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2EDecode_2Edec2enc @ ty_2Eone_2Eone ) @ ( ap @ c_2EDecode_2Edecode__unit @ V0p ) ) @ ( inj__ty_2Eone_2Eone @ V1x ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ c_2EEncode_2Eencode__unit @ ( inj__ty_2Eone_2Eone @ V1x ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edecode__unit,axiom,
! [V0p: $i] :
( ( mem @ V0p @ ( arr @ ty_2Eone_2Eone @ bool ) )
=> ! [V1l: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2EDecode_2Edecode__unit @ V0p ) @ ( inj__c_ty_2Elist_2Elist_o @ V1l ) ) )
= ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Eone_2Eone_c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Eone_2Eone @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ V0p @ ( inj__ty_2Eone_2Eone @ fo__c_2Eone_2Eone ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ty_2Eone_2Eone @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Eone_2Eone @ ( ty_2Elist_2Elist @ bool ) ) @ ( inj__ty_2Eone_2Eone @ fo__c_2Eone_2Eone ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1l ) ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Eone_2Eone @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ) ) ).
thf(ax_thm_2EDecode_2Edecode__bool__def,axiom,
! [V0p: $i] :
( ( mem @ V0p @ ( arr @ bool @ bool ) )
=> ( ( ap @ c_2EDecode_2Edecode__bool @ V0p )
= ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ bool ) @ V0p ) @ c_2EEncode_2Eencode__bool ) ) ) ).
thf(conj_thm_2EDecode_2Ewf__decode__bool,axiom,
! [V0p: $i] :
( ( mem @ V0p @ ( arr @ bool @ bool ) )
=> ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ bool ) @ V0p ) @ ( ap @ c_2EDecode_2Edecode__bool @ V0p ) ) ) ) ).
thf(conj_thm_2EDecode_2Edec2enc__decode__bool,axiom,
! [V0p: $i] :
( ( mem @ V0p @ ( arr @ bool @ bool ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ bool )
=> ( ( p @ ( ap @ V0p @ V1x ) )
=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2EDecode_2Edec2enc @ bool ) @ ( ap @ c_2EDecode_2Edecode__bool @ V0p ) ) @ V1x ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ c_2EEncode_2Eencode__bool @ V1x ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edecode__bool,axiom,
! [V0p: $i] :
( ( mem @ V0p @ ( arr @ bool @ bool ) )
=> ! [V1l: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2EDecode_2Edecode__bool @ V0p ) @ ( inj__c_ty_2Elist_2Elist_o @ V1l ) ) )
= ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_o_c_ty_2Elist_2Elist_o
@ ( ap @ ( ap @ ( ap @ ( c_2Elist_2Elist__CASE @ bool @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1l ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ bool
@ ^ [V2h: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V3t: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ V0p @ V2h ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Elist_2Elist @ bool ) ) @ V2h ) @ V3t ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EDecode_2Edecode__prod__def,axiom,
! [A_27a: del,A_27b: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) )
=> ! [V1d1: $i] :
( ( mem @ V1d1 @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V2d2: $i] :
( ( mem @ V2d2 @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__prod @ A_27a @ A_27b ) @ V0p ) @ V1d1 ) @ V2d2 )
= ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0p ) @ ( ap @ ( ap @ ( c_2EEncode_2Eencode__prod @ A_27a @ A_27b ) @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27a ) @ V1d1 ) ) @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27b ) @ V2d2 ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Ewf__decode__prod,axiom,
! [A_27a: del,A_27b: del,V0p1: $i] :
( ( mem @ V0p1 @ ( arr @ A_27a @ bool ) )
=> ! [V1p2: $i] :
( ( mem @ V1p2 @ ( arr @ A_27b @ bool ) )
=> ! [V2d1: $i] :
( ( mem @ V2d1 @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V3d2: $i] :
( ( mem @ V3d2 @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p1 ) @ V2d1 ) )
& ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27b ) @ V1p2 ) @ V3d2 ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2EEncode_2Elift__prod @ A_27a @ A_27b ) @ V0p1 ) @ V1p2 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__prod @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2EEncode_2Elift__prod @ A_27a @ A_27b ) @ V0p1 ) @ V1p2 ) ) @ V2d1 ) @ V3d2 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edec2enc__decode__prod,axiom,
! [A_27a: del,A_27b: del,V0p1: $i] :
( ( mem @ V0p1 @ ( arr @ A_27a @ bool ) )
=> ! [V1p2: $i] :
( ( mem @ V1p2 @ ( arr @ A_27b @ bool ) )
=> ! [V2d1: $i] :
( ( mem @ V2d1 @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V3d2: $i] :
( ( mem @ V3d2 @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V4x: $i] :
( ( mem @ V4x @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p1 ) @ V2d1 ) )
& ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27b ) @ V1p2 ) @ V3d2 ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2EEncode_2Elift__prod @ A_27a @ A_27b ) @ V0p1 ) @ V1p2 ) @ V4x ) ) )
=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2EDecode_2Edec2enc @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__prod @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2EEncode_2Elift__prod @ A_27a @ A_27b ) @ V0p1 ) @ V1p2 ) ) @ V2d1 ) @ V3d2 ) ) @ V4x ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ ( c_2EEncode_2Eencode__prod @ A_27a @ A_27b ) @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27a ) @ V2d1 ) ) @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27b ) @ V3d2 ) ) @ V4x ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Eencode__then__decode__prod,axiom,
! [A_27a: del,A_27b: del,V0p1: $i] :
( ( mem @ V0p1 @ ( arr @ A_27a @ bool ) )
=> ! [V1p2: $i] :
( ( mem @ V1p2 @ ( arr @ A_27b @ bool ) )
=> ! [V2e1: $i] :
( ( mem @ V2e1 @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) )
=> ! [V3e2: $i] :
( ( mem @ V3e2 @ ( arr @ A_27b @ ( ty_2Elist_2Elist @ bool ) ) )
=> ! [V4l: $i] :
( ( mem @ V4l @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
=> ! [V5t: tp__c_ty_2Elist_2Elist_o] :
( ( ( p @ ( ap @ ( ap @ ( c_2EEncode_2Ewf__encoder @ A_27a ) @ V0p1 ) @ V2e1 ) )
& ( p @ ( ap @ ( ap @ ( c_2EEncode_2Ewf__encoder @ A_27b ) @ V1p2 ) @ V3e2 ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2EEncode_2Elift__prod @ A_27a @ A_27b ) @ V0p1 ) @ V1p2 ) @ V4l ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__prod @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2EEncode_2Elift__prod @ A_27a @ A_27b ) @ V0p1 ) @ V1p2 ) ) @ ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ A_27a ) @ V0p1 ) @ V2e1 ) ) @ ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ A_27b ) @ V1p2 ) @ V3e2 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( ap @ ( ap @ ( ap @ ( c_2EEncode_2Eencode__prod @ A_27a @ A_27b ) @ V2e1 ) @ V3e2 ) @ V4l ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V5t ) ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) @ V4l ) @ ( inj__c_ty_2Elist_2Elist_o @ V5t ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edecode__prod,axiom,
! [A_27a: del,A_27b: del,V0p1: $i] :
( ( mem @ V0p1 @ ( arr @ A_27a @ bool ) )
=> ! [V1d1: $i] :
( ( mem @ V1d1 @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V2p2: $i] :
( ( mem @ V2p2 @ ( arr @ A_27b @ bool ) )
=> ! [V3d2: $i] :
( ( mem @ V3d2 @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V4l: tp__c_ty_2Elist_2Elist_o] :
( ( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p1 ) @ V1d1 ) )
& ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27b ) @ V2p2 ) @ V3d2 ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__prod @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2EEncode_2Elift__prod @ A_27a @ A_27b ) @ V0p1 ) @ V2p2 ) ) @ V1d1 ) @ V3d2 ) @ ( inj__c_ty_2Elist_2Elist_o @ V4l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ V1d1 @ ( inj__c_ty_2Elist_2Elist_o @ V4l ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V5v1: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ V5v1 )
@ ( lam @ A_27a
@ ^ [V6x: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V7t: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ A_27b @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ V3d2 @ V7t ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ A_27b @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V8v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ A_27b @ ( ty_2Elist_2Elist @ bool ) ) @ V8v )
@ ( lam @ A_27b
@ ^ [V9y: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V10t_27: $i] : ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V6x ) @ V9y ) ) @ V10t_27 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EDecode_2Edecode__sum__def,axiom,
! [A_27a: del,A_27b: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ bool ) )
=> ! [V1d1: $i] :
( ( mem @ V1d1 @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V2d2: $i] :
( ( mem @ V2d2 @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__sum @ A_27a @ A_27b ) @ V0p ) @ V1d1 ) @ V2d2 )
= ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ V0p ) @ ( ap @ ( ap @ ( c_2EEncode_2Eencode__sum @ A_27a @ A_27b ) @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27a ) @ V1d1 ) ) @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27b ) @ V2d2 ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Ewf__decode__sum,axiom,
! [A_27a: del,A_27b: del,V0p1: $i] :
( ( mem @ V0p1 @ ( arr @ A_27a @ bool ) )
=> ! [V1p2: $i] :
( ( mem @ V1p2 @ ( arr @ A_27b @ bool ) )
=> ! [V2d1: $i] :
( ( mem @ V2d1 @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V3d2: $i] :
( ( mem @ V3d2 @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p1 ) @ V2d1 ) )
& ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27b ) @ V1p2 ) @ V3d2 ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2EEncode_2Elift__sum @ A_27a @ A_27b ) @ V0p1 ) @ V1p2 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__sum @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2EEncode_2Elift__sum @ A_27a @ A_27b ) @ V0p1 ) @ V1p2 ) ) @ V2d1 ) @ V3d2 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edec2enc__decode__sum,axiom,
! [A_27a: del,A_27b: del,V0p1: $i] :
( ( mem @ V0p1 @ ( arr @ A_27a @ bool ) )
=> ! [V1p2: $i] :
( ( mem @ V1p2 @ ( arr @ A_27b @ bool ) )
=> ! [V2d1: $i] :
( ( mem @ V2d1 @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V3d2: $i] :
( ( mem @ V3d2 @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V4x: $i] :
( ( mem @ V4x @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p1 ) @ V2d1 ) )
& ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27b ) @ V1p2 ) @ V3d2 ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2EEncode_2Elift__sum @ A_27a @ A_27b ) @ V0p1 ) @ V1p2 ) @ V4x ) ) )
=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2EDecode_2Edec2enc @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__sum @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2EEncode_2Elift__sum @ A_27a @ A_27b ) @ V0p1 ) @ V1p2 ) ) @ V2d1 ) @ V3d2 ) ) @ V4x ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ ( c_2EEncode_2Eencode__sum @ A_27a @ A_27b ) @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27a ) @ V2d1 ) ) @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27b ) @ V3d2 ) ) @ V4x ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Eencode__then__decode__sum,axiom,
! [A_27a: del,A_27b: del,V0p1: $i] :
( ( mem @ V0p1 @ ( arr @ A_27a @ bool ) )
=> ! [V1p2: $i] :
( ( mem @ V1p2 @ ( arr @ A_27b @ bool ) )
=> ! [V2e1: $i] :
( ( mem @ V2e1 @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) )
=> ! [V3e2: $i] :
( ( mem @ V3e2 @ ( arr @ A_27b @ ( ty_2Elist_2Elist @ bool ) ) )
=> ! [V4l: $i] :
( ( mem @ V4l @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
=> ! [V5t: tp__c_ty_2Elist_2Elist_o] :
( ( ( p @ ( ap @ ( ap @ ( c_2EEncode_2Ewf__encoder @ A_27a ) @ V0p1 ) @ V2e1 ) )
& ( p @ ( ap @ ( ap @ ( c_2EEncode_2Ewf__encoder @ A_27b ) @ V1p2 ) @ V3e2 ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2EEncode_2Elift__sum @ A_27a @ A_27b ) @ V0p1 ) @ V1p2 ) @ V4l ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__sum @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2EEncode_2Elift__sum @ A_27a @ A_27b ) @ V0p1 ) @ V1p2 ) ) @ ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ A_27a ) @ V0p1 ) @ V2e1 ) ) @ ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ A_27b ) @ V1p2 ) @ V3e2 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( ap @ ( ap @ ( ap @ ( c_2EEncode_2Eencode__sum @ A_27a @ A_27b ) @ V2e1 ) @ V3e2 ) @ V4l ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V5t ) ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) @ V4l ) @ ( inj__c_ty_2Elist_2Elist_o @ V5t ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edecode__sum,axiom,
! [A_27a: del,A_27b: del,V0p1: $i] :
( ( mem @ V0p1 @ ( arr @ A_27a @ bool ) )
=> ! [V1d1: $i] :
( ( mem @ V1d1 @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V2p2: $i] :
( ( mem @ V2p2 @ ( arr @ A_27b @ bool ) )
=> ! [V3d2: $i] :
( ( mem @ V3d2 @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V4l: tp__c_ty_2Elist_2Elist_o] :
( ( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p1 ) @ V1d1 ) )
& ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27b ) @ V2p2 ) @ V3d2 ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__sum @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2EEncode_2Elift__sum @ A_27a @ A_27b ) @ V0p1 ) @ V2p2 ) ) @ V1d1 ) @ V3d2 ) @ ( inj__c_ty_2Elist_2Elist_o @ V4l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2Elist__CASE @ bool @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V4l ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ bool
@ ^ [V5v1: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V6t: $i] :
( ap
@ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ V5v1 )
@ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ V1d1 @ V6t ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V7v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ V7v )
@ ( lam @ A_27a
@ ^ [V8x: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V9t_27: $i] : ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( c_2Esum_2EINL @ A_27a @ A_27b ) @ V8x ) ) @ V9t_27 ) ) ) ) ) ) ) )
@ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ A_27b @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ V3d2 @ V6t ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ A_27b @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V10v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ A_27b @ ( ty_2Elist_2Elist @ bool ) ) @ V10v )
@ ( lam @ A_27b
@ ^ [V11x: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V12t_27: $i] : ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( c_2Esum_2EINR @ A_27a @ A_27b ) @ V11x ) ) @ V12t_27 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EDecode_2Edecode__option__def,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) )
=> ! [V1d: $i] :
( ( mem @ V1d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ( ( ap @ ( ap @ ( c_2EDecode_2Edecode__option @ A_27a ) @ V0p ) @ V1d )
= ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V0p ) @ ( ap @ ( c_2EEncode_2Eencode__option @ A_27a ) @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27a ) @ V1d ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Ewf__decode__option,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1d: $i] :
( ( mem @ V1d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p ) @ V1d ) )
=> ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( c_2EEncode_2Elift__option @ A_27a ) @ V0p ) ) @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__option @ A_27a ) @ ( ap @ ( c_2EEncode_2Elift__option @ A_27a ) @ V0p ) ) @ V1d ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edec2enc__decode__option,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1d: $i] :
( ( mem @ V1d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p ) @ V1d ) )
& ( p @ ( ap @ ( ap @ ( c_2EEncode_2Elift__option @ A_27a ) @ V0p ) @ V2x ) ) )
=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2EDecode_2Edec2enc @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__option @ A_27a ) @ ( ap @ ( c_2EEncode_2Elift__option @ A_27a ) @ V0p ) ) @ V1d ) ) @ V2x ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2EEncode_2Eencode__option @ A_27a ) @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27a ) @ V1d ) ) @ V2x ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Eencode__then__decode__option,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ! [V3t: tp__c_ty_2Elist_2Elist_o] :
( ( ( p @ ( ap @ ( ap @ ( c_2EEncode_2Ewf__encoder @ A_27a ) @ V0p ) @ V1e ) )
& ( p @ ( ap @ ( ap @ ( c_2EEncode_2Elift__option @ A_27a ) @ V0p ) @ V2l ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__option @ A_27a ) @ ( ap @ ( c_2EEncode_2Elift__option @ A_27a ) @ V0p ) ) @ ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ A_27a ) @ V0p ) @ V1e ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( ap @ ( ap @ ( c_2EEncode_2Eencode__option @ A_27a ) @ V1e ) @ V2l ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V3t ) ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) @ V2l ) @ ( inj__c_ty_2Elist_2Elist_o @ V3t ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edecode__option,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1d: $i] :
( ( mem @ V1d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V2l: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p ) @ V1d ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__option @ A_27a ) @ ( ap @ ( c_2EEncode_2Elift__option @ A_27a ) @ V0p ) ) @ V1d ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2Elist__CASE @ bool @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ bool
@ ^ [V3v1: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V4t: $i] :
( ap
@ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ V3v1 )
@ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ V1d @ V4t ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V5v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ V5v )
@ ( lam @ A_27a
@ ^ [V6x: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V7t_27: $i] : ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V6x ) ) @ V7t_27 ) ) ) ) ) ) ) )
@ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ V4t ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EDecode_2Edecode__list__def,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) )
=> ! [V1d: $i] :
( ( mem @ V1d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ( ( ap @ ( ap @ ( c_2EDecode_2Edecode__list @ A_27a ) @ V0p ) @ V1d )
= ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ ( ty_2Elist_2Elist @ A_27a ) ) @ V0p ) @ ( ap @ ( c_2EEncode_2Eencode__list @ A_27a ) @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27a ) @ V1d ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Ewf__decode__list,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1d: $i] :
( ( mem @ V1d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p ) @ V1d ) )
=> ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0p ) ) @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__list @ A_27a ) @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0p ) ) @ V1d ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edec2enc__decode__list,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1d: $i] :
( ( mem @ V1d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p ) @ V1d ) )
& ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0p ) @ V2x ) ) )
=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2EDecode_2Edec2enc @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__list @ A_27a ) @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0p ) ) @ V1d ) ) @ V2x ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2EEncode_2Eencode__list @ A_27a ) @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27a ) @ V1d ) ) @ V2x ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Eencode__then__decode__list,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1e: $i] :
( ( mem @ V1e @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V3t: tp__c_ty_2Elist_2Elist_o] :
( ( ( p @ ( ap @ ( ap @ ( c_2EEncode_2Ewf__encoder @ A_27a ) @ V0p ) @ V1e ) )
& ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0p ) @ V2l ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__list @ A_27a ) @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0p ) ) @ ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ A_27a ) @ V0p ) @ V1e ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( ap @ ( ap @ ( c_2EEncode_2Eencode__list @ A_27a ) @ V1e ) @ V2l ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V3t ) ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) @ V2l ) @ ( inj__c_ty_2Elist_2Elist_o @ V3t ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edecode__list,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1d: $i] :
( ( mem @ V1d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V2l: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p ) @ V1d ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__list @ A_27a ) @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0p ) ) @ V1d ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2Elist__CASE @ bool @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ bool
@ ^ [V3v2: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V4t: $i] :
( ap
@ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ V3v2 )
@ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ V1d @ V4t ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V5v1: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ V5v1 )
@ ( lam @ A_27a
@ ^ [V6x: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V7t_27: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__list @ A_27a ) @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V0p ) ) @ V1d ) @ V7t_27 ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V8v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) @ V8v )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V9xs: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V10t_27_27: $i] : ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V6x ) @ V9xs ) ) @ V10t_27_27 ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ V4t ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EDecode_2Edecode__blist__def,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) )
=> ! [V1m: tp__ty_2Enum_2Enum,V2d: $i] :
( ( mem @ V2d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__blist @ A_27a ) @ V0p ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V2d )
= ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ ( ty_2Elist_2Elist @ A_27a ) ) @ V0p ) @ ( ap @ ( ap @ ( c_2EEncode_2Eencode__blist @ bool @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27a ) @ V2d ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Ewf__decode__blist,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1p: $i] :
( ( mem @ V1p @ ( arr @ A_27a @ bool ) )
=> ! [V2d: $i] :
( ( mem @ V2d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V1p ) @ V2d ) )
=> ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2EEncode_2Elift__blist @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1p ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__blist @ A_27a ) @ ( ap @ ( ap @ ( c_2EEncode_2Elift__blist @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1p ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V2d ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edec2enc__decode__blist,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1p: $i] :
( ( mem @ V1p @ ( arr @ A_27a @ bool ) )
=> ! [V2d: $i] :
( ( mem @ V2d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V1p ) @ V2d ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2EEncode_2Elift__blist @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1p ) @ V3l ) ) )
=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2EDecode_2Edec2enc @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__blist @ A_27a ) @ ( ap @ ( ap @ ( c_2EEncode_2Elift__blist @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1p ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V2d ) ) @ V3l ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ ( c_2EEncode_2Eencode__blist @ bool @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27a ) @ V2d ) ) @ V3l ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Eencode__then__decode__blist,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1p: $i] :
( ( mem @ V1p @ ( arr @ A_27a @ bool ) )
=> ! [V2e: $i] :
( ( mem @ V2e @ ( arr @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V4t: tp__c_ty_2Elist_2Elist_o] :
( ( ( p @ ( ap @ ( ap @ ( c_2EEncode_2Ewf__encoder @ A_27a ) @ V1p ) @ V2e ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2EEncode_2Elift__blist @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1p ) @ V3l ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__blist @ A_27a ) @ ( ap @ ( ap @ ( c_2EEncode_2Elift__blist @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1p ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ A_27a ) @ V1p ) @ V2e ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( ap @ ( ap @ ( ap @ ( c_2EEncode_2Eencode__blist @ bool @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V2e ) @ V3l ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V4t ) ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) @ V3l ) @ ( inj__c_ty_2Elist_2Elist_o @ V4t ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edecode__blist,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1d: $i] :
( ( mem @ V1d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V2m: tp__ty_2Enum_2Enum,V3l: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p ) @ V1d ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__blist @ A_27a ) @ ( ap @ ( ap @ ( c_2EEncode_2Elift__blist @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ V0p ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ V1d ) @ ( inj__c_ty_2Elist_2Elist_o @ V3l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Earithmetic_2Enum__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V3l ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4n: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ V1d @ ( inj__c_ty_2Elist_2Elist_o @ V3l ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V5v1: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ V5v1 )
@ ( lam @ A_27a
@ ^ [V6x: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V7t: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__blist @ A_27a ) @ ( ap @ ( ap @ ( c_2EEncode_2Elift__blist @ A_27a ) @ V4n ) @ V0p ) ) @ V4n ) @ V1d ) @ V7t ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V8v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) @ V8v )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V9xs: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V10t_27: $i] : ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V6x ) @ V9xs ) ) @ V10t_27 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EDecode_2Edecode__num__def,axiom,
! [V0p: $i] :
( ( mem @ V0p @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2EDecode_2Edecode__num @ V0p )
= ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ ty_2Enum_2Enum ) @ V0p ) @ c_2EEncode_2Eencode__num ) ) ) ).
thf(conj_thm_2EDecode_2Ewf__decode__num,axiom,
! [V0p: $i] :
( ( mem @ V0p @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ ty_2Enum_2Enum ) @ V0p ) @ ( ap @ c_2EDecode_2Edecode__num @ V0p ) ) ) ) ).
thf(conj_thm_2EDecode_2Edec2enc__decode__num,axiom,
! [V0p: $i] :
( ( mem @ V0p @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1x: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0p @ ( inj__ty_2Enum_2Enum @ V1x ) ) )
=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2EDecode_2Edec2enc @ ty_2Enum_2Enum ) @ ( ap @ c_2EDecode_2Edecode__num @ V0p ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ c_2EEncode_2Eencode__num @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edecode__num__total,axiom,
! [V0l: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2EDecode_2Edecode__num @ ( ap @ ( c_2Ecombin_2EK @ bool @ ty_2Enum_2Enum ) @ c_2Ebool_2ET ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0l ) ) )
= ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o
@ ( ap @ ( ap @ ( ap @ ( c_2Elist_2Elist__CASE @ bool @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0l ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ bool
@ ^ [V1v4: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V2t_27: $i] :
( ap
@ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ V1v4 )
@ ( ap @ ( ap @ ( ap @ ( c_2Elist_2Elist__CASE @ bool @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ V2t_27 ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ bool
@ ^ [V3v8: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V4t: $i] :
( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ V3v8 ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V4t ) ) )
@ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ ( ap @ c_2EDecode_2Edecode__num @ ( ap @ ( c_2Ecombin_2EK @ bool @ ty_2Enum_2Enum ) @ c_2Ebool_2ET ) ) @ V4t ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V5v1: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ V5v1 )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6v: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V7t_27: $i] : ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V6v ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V7t_27 ) ) ) ) ) ) ) ) ) ) ) )
@ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ ( ap @ c_2EDecode_2Edecode__num @ ( ap @ ( c_2Ecombin_2EK @ bool @ ty_2Enum_2Enum ) @ c_2Ebool_2ET ) ) @ V2t_27 ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V8v1: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ V8v1 )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9v: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V10t_27: $i] : ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V9v ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V10t_27 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edecode__num,axiom,
! [V0p: $i] :
( ( mem @ V0p @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1l: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2EDecode_2Edecode__num @ V0p ) @ ( inj__c_ty_2Elist_2Elist_o @ V1l ) ) )
= ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o
@ ( ap @ ( ap @ ( ap @ ( c_2Elist_2Elist__CASE @ bool @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1l ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ bool
@ ^ [V2v4: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V3t_27: $i] :
( ap
@ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ V2v4 )
@ ( ap @ ( ap @ ( ap @ ( c_2Elist_2Elist__CASE @ bool @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ V3t_27 ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ bool
@ ^ [V4v8: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V5t: $i] :
( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ V4v8 ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ V0p @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V5t ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
@ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ ( ap @ c_2EDecode_2Edecode__num @ ( ap @ ( c_2Ecombin_2EK @ bool @ ty_2Enum_2Enum ) @ c_2Ebool_2ET ) ) @ V5t ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V6v1: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ V6v1 )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7v: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V8t_27: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ V0p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V7v ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V7v ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V8t_27 ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ ( ap @ c_2EDecode_2Edecode__num @ ( ap @ ( c_2Ecombin_2EK @ bool @ ty_2Enum_2Enum ) @ c_2Ebool_2ET ) ) @ V3t_27 ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V9v1: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ V9v1 )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10v: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V11t_27: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ V0p @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V10v ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V10v ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V11t_27 ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EDecode_2Edecode__bnum__def,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1p: $i] :
( ( mem @ V1p @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2EDecode_2Edecode__bnum @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1p )
= ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ ty_2Enum_2Enum ) @ V1p ) @ ( ap @ c_2EEncode_2Eencode__bnum @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ) ).
thf(ax_thm_2EDecode_2Edec__bnum__def,axiom,
( ! [V0l: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2EDecode_2Edec__bnum @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0l ) ) )
= ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0l ) ) ) ) )
& ! [V1m: tp__ty_2Enum_2Enum,V2l: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2EDecode_2Edec__bnum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) ) )
= ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o
@ ( ap @ ( ap @ ( ap @ ( c_2Elist_2Elist__CASE @ bool @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ bool
@ ^ [V3h: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V4t: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ ( ap @ c_2EDecode_2Edec__bnum @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V4t ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V5v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ V5v )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6n: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V7t_27: $i] : ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V6n ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ V3h ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ V7t_27 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edec__bnum__def__compute,axiom,
( ! [V0l: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2EDecode_2Edec__bnum @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0l ) ) )
= ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0l ) ) ) ) )
& ! [V1m: tp__ty_2Enum_2Enum,V2l: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2EDecode_2Edec__bnum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) ) )
= ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o
@ ( ap @ ( ap @ ( ap @ ( c_2Elist_2Elist__CASE @ bool @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ bool
@ ^ [V3h: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V4t: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ ( ap @ c_2EDecode_2Edec__bnum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V4t ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V5v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ V5v )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6n: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V7t_27: $i] : ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V6n ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ V3h ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ V7t_27 ) ) ) ) ) ) ) ) ) ) ) )
& ! [V8m: tp__ty_2Enum_2Enum,V9l: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2EDecode_2Edec__bnum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V8m ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V9l ) ) )
= ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o
@ ( ap @ ( ap @ ( ap @ ( c_2Elist_2Elist__CASE @ bool @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V9l ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ bool
@ ^ [V10h: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V11t: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ ( ap @ c_2EDecode_2Edec__bnum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V8m ) ) ) ) @ V11t ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V12v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ V12v )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V13n: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V14t_27: $i] : ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ V13n ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ V10h ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ V14t_27 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edec__bnum__lt,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1l: tp__c_ty_2Elist_2Elist_o,V2n: tp__ty_2Enum_2Enum,V3t: tp__c_ty_2Elist_2Elist_o] :
( ( ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2EDecode_2Edec__bnum @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1l ) ) )
= ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V3t ) ) ) ) )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edec__bnum__inj,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1l: tp__c_ty_2Elist_2Elist_o,V2n: tp__ty_2Enum_2Enum,V3t: tp__c_ty_2Elist_2Elist_o] :
( ( ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2EDecode_2Edec__bnum @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1l ) ) )
= ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V3t ) ) ) ) )
=> ( V1l
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( ap @ ( ap @ c_2EEncode_2Eencode__bnum @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V3t ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Ewf__decode__bnum,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1p: $i] :
( ( mem @ V1p @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ c_2EEncode_2Ewf__pred__bnum @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1p ) )
=> ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ ty_2Enum_2Enum ) @ V1p ) @ ( ap @ ( ap @ c_2EDecode_2Edecode__bnum @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1p ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edec2enc__decode__bnum,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1p: $i] :
( ( mem @ V1p @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2x: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2EEncode_2Ewf__pred__bnum @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1p ) )
& ( p @ ( ap @ V1p @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) )
=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2EDecode_2Edec2enc @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2EDecode_2Edecode__bnum @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1p ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2EEncode_2Eencode__bnum @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edecode__bnum,axiom,
! [V0m: tp__ty_2Enum_2Enum,V1p: $i] :
( ( mem @ V1p @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2l: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ c_2EEncode_2Ewf__pred__bnum @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1p ) )
=> ( ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2EDecode_2Edecode__bnum @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V1p ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) ) )
= ( surj__c_ty_2Eoption_2Eoption_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_c_ty_2Elist_2Elist_o
@ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ ( ap @ c_2EDecode_2Edec__bnum @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V3v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ V3v )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4n: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V5t: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ V1p @ V4n ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) @ V4n ) @ V5t ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EDecode_2Edecode__tree__def,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ ( ty_2EEncode_2Etree @ A_27a ) @ bool ) )
=> ! [V1d: $i] :
( ( mem @ V1d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ( ( ap @ ( ap @ ( c_2EDecode_2Edecode__tree @ A_27a ) @ V0p ) @ V1d )
= ( ap @ ( ap @ ( c_2EDecode_2Eenc2dec @ ( ty_2EEncode_2Etree @ A_27a ) ) @ V0p ) @ ( ap @ ( c_2EEncode_2Eencode__tree @ A_27a ) @ ( ap @ ( c_2EDecode_2Edec2enc @ A_27a ) @ V1d ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Ewf__decode__tree,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1d: $i] :
( ( mem @ V1d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p ) @ V1d ) )
=> ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ ( ty_2EEncode_2Etree @ A_27a ) ) @ ( ap @ ( c_2EEncode_2Elift__tree @ A_27a ) @ V0p ) ) @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__tree @ A_27a ) @ ( ap @ ( c_2EEncode_2Elift__tree @ A_27a ) @ V0p ) ) @ V1d ) ) ) ) ) ) ).
thf(conj_thm_2EDecode_2Edecode__tree,axiom,
! [A_27a: del,V0p: $i] :
( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
=> ! [V1d: $i] :
( ( mem @ V1d @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) ) ) )
=> ! [V2l: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ ( c_2EDecode_2Ewf__decoder @ A_27a ) @ V0p ) @ V1d ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__tree @ A_27a ) @ ( ap @ ( c_2EEncode_2Elift__tree @ A_27a ) @ V0p ) ) @ V1d ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2EEncode_2Etree @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ V1d @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ( ty_2EEncode_2Etree @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V3v1: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2EEncode_2Etree @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ A_27a @ ( ty_2Elist_2Elist @ bool ) ) @ V3v1 )
@ ( lam @ A_27a
@ ^ [V4a: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V5t: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ ( ty_2EEncode_2Etree @ A_27a ) ) @ ( ty_2Elist_2Elist @ bool ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2EEncode_2Etree @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__list @ ( ty_2EEncode_2Etree @ A_27a ) ) @ ( ap @ ( c_2Elist_2EEVERY @ ( ty_2EEncode_2Etree @ A_27a ) ) @ ( ap @ ( c_2EEncode_2Elift__tree @ A_27a ) @ V0p ) ) ) @ ( ap @ ( ap @ ( c_2EDecode_2Edecode__tree @ A_27a ) @ ( ap @ ( c_2EEncode_2Elift__tree @ A_27a ) @ V0p ) ) @ V1d ) ) @ V5t ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ( ty_2EEncode_2Etree @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ ( ty_2EEncode_2Etree @ A_27a ) ) @ ( ty_2Elist_2Elist @ bool ) )
@ ^ [V6v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2EEncode_2Etree @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ty_2Elist_2Elist @ ( ty_2EEncode_2Etree @ A_27a ) ) @ ( ty_2Elist_2Elist @ bool ) ) @ V6v )
@ ( lam @ ( ty_2Elist_2Elist @ ( ty_2EEncode_2Etree @ A_27a ) )
@ ^ [V7ts: $i] :
( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V8t_27: $i] : ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2EEncode_2Etree @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2EEncode_2Etree @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ ( c_2EEncode_2ENode @ A_27a ) @ V4a ) @ V7ts ) ) @ V8t_27 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------