ITP001 Axioms: ITP079^7.ax
%------------------------------------------------------------------------------
% File : ITP079^7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : Coder.ax [Gau19]
% : HL4079^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 101 ( 19 unt; 65 typ; 0 def)
% Number of atoms : 116 ( 19 equ; 1 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1467 ( 1 ~; 1 |; 8 &;1432 @)
% ( 8 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg;1432 nst)
% Number of types : 4 ( 3 usr)
% Number of type conns : 441 ( 441 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 62 usr; 1 con; 0-6 aty)
% Number of variables : 186 ( 4 ^ 119 !; 2 ?; 186 :)
% ( 61 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2EEncode_2Etree,type,
tyop_2EEncode_2Etree: $tType > $tType ).
thf(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: $tType > $tType > $tType ).
thf(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
thf(tyop_2Eone_2Eone,type,
tyop_2Eone_2Eone: $tType ).
thf(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: $tType > $tType ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: $tType > $tType > $tType ).
thf(tyop_2Esum_2Esum,type,
tyop_2Esum_2Esum: $tType > $tType > $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Epair_2E_2C,type,
c_2Epair_2E_2C:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ).
thf(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Emin_2E_3D,type,
c_2Emin_2E_3D:
!>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
thf(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Emin_2E_40,type,
c_2Emin_2E_40:
!>[A_27a: $tType] : ( ( A_27a > $o ) > A_27a ) ).
thf(c_2Elist_2EEVERY,type,
c_2Elist_2EEVERY:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2ECoder_2Eblist__coder,type,
c_2ECoder_2Eblist__coder:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27b > ( tyop_2Elist_2Elist @ A_27c ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > ( tyop_2Epair_2Eprod @ ( ( tyop_2Elist_2Elist @ A_27a ) > $o ) @ ( tyop_2Epair_2Eprod @ ( ( tyop_2Elist_2Elist @ A_27b ) > ( tyop_2Elist_2Elist @ A_27c ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ) ).
thf(c_2ECoder_2Ebnum__coder,type,
c_2ECoder_2Ebnum__coder: tyop_2Enum_2Enum > ( tyop_2Enum_2Enum > $o ) > ( tyop_2Epair_2Eprod @ ( tyop_2Enum_2Enum > $o ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ).
thf(c_2ECoder_2Ebool__coder,type,
c_2ECoder_2Ebool__coder: ( $o > $o ) > ( tyop_2Epair_2Eprod @ ( $o > $o ) @ ( tyop_2Epair_2Eprod @ ( $o > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ).
thf(c_2ECoder_2Edecode,type,
c_2ECoder_2Edecode:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > ( tyop_2Elist_2Elist @ $o ) > A_27a ) ).
thf(c_2EDecode_2Edecode__blist,type,
c_2EDecode_2Edecode__blist:
!>[A_27a: $tType] : ( ( ( tyop_2Elist_2Elist @ A_27a ) > $o ) > tyop_2Enum_2Enum > ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ).
thf(c_2EDecode_2Edecode__bnum,type,
c_2EDecode_2Edecode__bnum: tyop_2Enum_2Enum > ( tyop_2Enum_2Enum > $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) ).
thf(c_2EDecode_2Edecode__bool,type,
c_2EDecode_2Edecode__bool: ( $o > $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Elist_2Elist @ $o ) ) ) ).
thf(c_2EDecode_2Edecode__list,type,
c_2EDecode_2Edecode__list:
!>[A_27a: $tType] : ( ( ( tyop_2Elist_2Elist @ A_27a ) > $o ) > ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ).
thf(c_2EDecode_2Edecode__num,type,
c_2EDecode_2Edecode__num: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) ).
thf(c_2EDecode_2Edecode__option,type,
c_2EDecode_2Edecode__option:
!>[A_27a: $tType] : ( ( ( tyop_2Eoption_2Eoption @ A_27a ) > $o ) > ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ).
thf(c_2EDecode_2Edecode__prod,type,
c_2EDecode_2Edecode__prod:
!>[A_27a: $tType,A_27b: $tType] : ( ( ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o ) > ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ).
thf(c_2EDecode_2Edecode__sum,type,
c_2EDecode_2Edecode__sum:
!>[A_27a: $tType,A_27b: $tType] : ( ( ( tyop_2Esum_2Esum @ A_27a @ A_27b ) > $o ) > ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ).
thf(c_2EDecode_2Edecode__tree,type,
c_2EDecode_2Edecode__tree:
!>[A_27a: $tType] : ( ( ( tyop_2EEncode_2Etree @ A_27a ) > $o ) > ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2EEncode_2Etree @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ).
thf(c_2EDecode_2Edecode__unit,type,
c_2EDecode_2Edecode__unit: ( tyop_2Eone_2Eone > $o ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Eone_2Eone @ ( tyop_2Elist_2Elist @ $o ) ) ) ).
thf(c_2ECoder_2Edecoder,type,
c_2ECoder_2Edecoder:
!>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > ( tyop_2Elist_2Elist @ $o ) > A_27a ) ).
thf(c_2ECoder_2Edomain,type,
c_2ECoder_2Edomain:
!>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > A_27a > $o ) ).
thf(c_2EDecode_2Eenc2dec,type,
c_2EDecode_2Eenc2dec:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) > ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ).
thf(c_2EEncode_2Eencode__blist,type,
c_2EEncode_2Eencode__blist:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Enum_2Enum > ( A_27b > ( tyop_2Elist_2Elist @ A_27a ) ) > ( tyop_2Elist_2Elist @ A_27b ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2EEncode_2Eencode__bnum,type,
c_2EEncode_2Eencode__bnum: tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2EEncode_2Eencode__bool,type,
c_2EEncode_2Eencode__bool: $o > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2EEncode_2Eencode__list,type,
c_2EEncode_2Eencode__list:
!>[A_27a: $tType] : ( ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ $o ) ) ).
thf(c_2EEncode_2Eencode__num,type,
c_2EEncode_2Eencode__num: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2EEncode_2Eencode__option,type,
c_2EEncode_2Eencode__option:
!>[A_27a: $tType] : ( ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) > ( tyop_2Eoption_2Eoption @ A_27a ) > ( tyop_2Elist_2Elist @ $o ) ) ).
thf(c_2EEncode_2Eencode__prod,type,
c_2EEncode_2Eencode__prod:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) > ( A_27b > ( tyop_2Elist_2Elist @ $o ) ) > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > ( tyop_2Elist_2Elist @ $o ) ) ).
thf(c_2EEncode_2Eencode__sum,type,
c_2EEncode_2Eencode__sum:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) > ( A_27b > ( tyop_2Elist_2Elist @ $o ) ) > ( tyop_2Esum_2Esum @ A_27a @ A_27b ) > ( tyop_2Elist_2Elist @ $o ) ) ).
thf(c_2EEncode_2Eencode__tree,type,
c_2EEncode_2Eencode__tree:
!>[A_27a: $tType] : ( ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) > ( tyop_2EEncode_2Etree @ A_27a ) > ( tyop_2Elist_2Elist @ $o ) ) ).
thf(c_2EEncode_2Eencode__unit,type,
c_2EEncode_2Eencode__unit: tyop_2Eone_2Eone > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2ECoder_2Eencoder,type,
c_2ECoder_2Eencoder:
!>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > A_27a > ( tyop_2Elist_2Elist @ $o ) ) ).
thf(c_2EEncode_2Elift__blist,type,
c_2EEncode_2Elift__blist:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).
thf(c_2EEncode_2Elift__option,type,
c_2EEncode_2Elift__option:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2Eoption_2Eoption @ A_27a ) > $o ) ).
thf(c_2EEncode_2Elift__prod,type,
c_2EEncode_2Elift__prod:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > $o ) > ( A_27b > $o ) > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o ) ).
thf(c_2EEncode_2Elift__sum,type,
c_2EEncode_2Elift__sum:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > $o ) > ( A_27b > $o ) > ( tyop_2Esum_2Esum @ A_27a @ A_27b ) > $o ) ).
thf(c_2EEncode_2Elift__tree,type,
c_2EEncode_2Elift__tree:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2EEncode_2Etree @ A_27a ) > $o ) ).
thf(c_2ECoder_2Elist__coder,type,
c_2ECoder_2Elist__coder:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27b > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > ( tyop_2Epair_2Eprod @ ( ( tyop_2Elist_2Elist @ A_27a ) > $o ) @ ( tyop_2Epair_2Eprod @ ( ( tyop_2Elist_2Elist @ A_27b ) > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ) ).
thf(c_2ECoder_2Enum__coder,type,
c_2ECoder_2Enum__coder: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Epair_2Eprod @ ( tyop_2Enum_2Enum > $o ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ).
thf(c_2Eoption_2Eoption__CASE,type,
c_2Eoption_2Eoption__CASE:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Eoption_2Eoption @ A_27a ) > A_27b > ( A_27a > A_27b ) > A_27b ) ).
thf(c_2ECoder_2Eoption__coder,type,
c_2ECoder_2Eoption__coder:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27b > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > ( tyop_2Epair_2Eprod @ ( ( tyop_2Eoption_2Eoption @ A_27a ) > $o ) @ ( tyop_2Epair_2Eprod @ ( ( tyop_2Eoption_2Eoption @ A_27b ) > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ) ).
thf(c_2Epair_2Epair__CASE,type,
c_2Epair_2Epair__CASE:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) > ( A_27b > A_27c > A_27a ) > A_27a ) ).
thf(c_2ECoder_2Eprod__coder,type,
c_2ECoder_2Eprod__coder:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27c > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > ( tyop_2Epair_2Eprod @ ( A_27b > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27d > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > ( tyop_2Epair_2Eprod @ ( ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o ) @ ( tyop_2Epair_2Eprod @ ( ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ) ).
thf(c_2ECoder_2Esum__coder,type,
c_2ECoder_2Esum__coder:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27c > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > ( tyop_2Epair_2Eprod @ ( A_27b > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27d > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > ( tyop_2Epair_2Eprod @ ( ( tyop_2Esum_2Esum @ A_27a @ A_27b ) > $o ) @ ( tyop_2Epair_2Eprod @ ( ( tyop_2Esum_2Esum @ A_27c @ A_27d ) > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ) ).
thf(c_2ECoder_2Etree__coder,type,
c_2ECoder_2Etree__coder:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27b > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > ( tyop_2Epair_2Eprod @ ( ( tyop_2EEncode_2Etree @ A_27a ) > $o ) @ ( tyop_2Epair_2Eprod @ ( ( tyop_2EEncode_2Etree @ A_27b ) > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2EEncode_2Etree @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ) ).
thf(c_2ECoder_2Eunit__coder,type,
c_2ECoder_2Eunit__coder: ( tyop_2Eone_2Eone > $o ) > ( tyop_2Epair_2Eprod @ ( tyop_2Eone_2Eone > $o ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eone_2Eone > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Eone_2Eone @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) ).
thf(c_2ECoder_2Ewf__coder,type,
c_2ECoder_2Ewf__coder:
!>[A_27a: $tType] : ( ( tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) ) > $o ) ).
thf(c_2EEncode_2Ewf__encoder,type,
c_2EEncode_2Ewf__encoder:
!>[A_27a: $tType] : ( ( A_27a > $o ) > ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) > $o ) ).
thf(c_2EEncode_2Ewf__pred,type,
c_2EEncode_2Ewf__pred:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2EEncode_2Ewf__pred__bnum,type,
c_2EEncode_2Ewf__pred__bnum: tyop_2Enum_2Enum > ( tyop_2Enum_2Enum > $o ) > $o ).
thf(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $o > $o ).
thf(logicdef_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(logicdef_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(logicdef_2E_7E,axiom,
! [V0: $o] :
( ( c_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(logicdef_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0: A_27a,V1: A_27a] :
( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
<=> ( V0 = V1 ) ) ).
thf(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_21 @ A_27a @ V0f )
<=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_3F @ A_27a @ V0f )
<=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(thm_2ECoder_2Edecode__def,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ),V2l: tyop_2Elist_2Elist @ $o] :
( ( c_2ECoder_2Edecode @ A_27a @ V0p @ V1d @ V2l )
= ( c_2Eoption_2Eoption__CASE @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) @ A_27a @ ( V1d @ V2l )
@ ( c_2Emin_2E_40 @ A_27a
@ ^ [V3x: A_27a] : ( V0p @ V3x ) )
@ ^ [V4v: tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o )] :
( c_2Epair_2Epair__CASE @ A_27a @ A_27a @ ( tyop_2Elist_2Elist @ $o ) @ V4v
@ ^ [V5x: A_27a,V6v2: tyop_2Elist_2Elist @ $o] : V5x ) ) ) ).
thf(thm_2ECoder_2Ewf__coder__def,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1e: A_27a > ( tyop_2Elist_2Elist @ $o ),V2d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2ECoder_2Ewf__coder @ A_27a @ ( c_2Epair_2E_2C @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ V0p @ ( c_2Epair_2E_2C @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ V1e @ V2d ) ) )
<=> ( ( c_2EEncode_2Ewf__pred @ A_27a @ V0p )
& ( c_2EEncode_2Ewf__encoder @ A_27a @ V0p @ V1e )
& ( V2d
= ( c_2EDecode_2Eenc2dec @ A_27a @ V0p @ V1e ) ) ) ) ).
thf(thm_2ECoder_2Edomain__def,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1e: A_27a > ( tyop_2Elist_2Elist @ $o ),V2d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2ECoder_2Edomain @ A_27a @ ( c_2Epair_2E_2C @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ V0p @ ( c_2Epair_2E_2C @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ V1e @ V2d ) ) )
= V0p ) ).
thf(thm_2ECoder_2Eencoder__def,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1e: A_27a > ( tyop_2Elist_2Elist @ $o ),V2d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2ECoder_2Eencoder @ A_27a @ ( c_2Epair_2E_2C @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ V0p @ ( c_2Epair_2E_2C @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ V1e @ V2d ) ) )
= V1e ) ).
thf(thm_2ECoder_2Edecoder__def,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1e: A_27a > ( tyop_2Elist_2Elist @ $o ),V2d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2ECoder_2Edecoder @ A_27a @ ( c_2Epair_2E_2C @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ V0p @ ( c_2Epair_2E_2C @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ V1e @ V2d ) ) )
= ( c_2ECoder_2Edecode @ A_27a @ V0p @ V2d ) ) ).
thf(thm_2ECoder_2Eunit__coder__def,axiom,
! [V0p: tyop_2Eone_2Eone > $o] :
( ( c_2ECoder_2Eunit__coder @ V0p )
= ( c_2Epair_2E_2C @ ( tyop_2Eone_2Eone > $o ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eone_2Eone > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Eone_2Eone @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ V0p @ ( c_2Epair_2E_2C @ ( tyop_2Eone_2Eone > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Eone_2Eone @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ c_2EEncode_2Eencode__unit @ ( c_2EDecode_2Edecode__unit @ V0p ) ) ) ) ).
thf(thm_2ECoder_2Ebool__coder__def,axiom,
! [V0p: $o > $o] :
( ( c_2ECoder_2Ebool__coder @ V0p )
= ( c_2Epair_2E_2C @ ( $o > $o ) @ ( tyop_2Epair_2Eprod @ ( $o > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ V0p @ ( c_2Epair_2E_2C @ ( $o > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ $o @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ c_2EEncode_2Eencode__bool @ ( c_2EDecode_2Edecode__bool @ V0p ) ) ) ) ).
thf(thm_2ECoder_2Eprod__coder__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0p1: A_27a > $o,V1e1: A_27c > ( tyop_2Elist_2Elist @ $o ),V2d1: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ),V3p2: A_27b > $o,V4e2: A_27d > ( tyop_2Elist_2Elist @ $o ),V5d2: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2ECoder_2Eprod__coder @ A_27a @ A_27b @ A_27c @ A_27d @ ( c_2Epair_2E_2C @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27c > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ V0p1 @ ( c_2Epair_2E_2C @ ( A_27c > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ V1e1 @ V2d1 ) ) @ ( c_2Epair_2E_2C @ ( A_27b > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27d > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ V3p2 @ ( c_2Epair_2E_2C @ ( A_27d > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ V4e2 @ V5d2 ) ) )
= ( c_2Epair_2E_2C @ ( ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o ) @ ( tyop_2Epair_2Eprod @ ( ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ ( c_2EEncode_2Elift__prod @ A_27a @ A_27b @ V0p1 @ V3p2 ) @ ( c_2Epair_2E_2C @ ( ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ ( c_2EEncode_2Eencode__prod @ A_27c @ A_27d @ V1e1 @ V4e2 ) @ ( c_2EDecode_2Edecode__prod @ A_27a @ A_27b @ ( c_2EEncode_2Elift__prod @ A_27a @ A_27b @ V0p1 @ V3p2 ) @ V2d1 @ V5d2 ) ) ) ) ).
thf(thm_2ECoder_2Esum__coder__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0p1: A_27a > $o,V1e1: A_27c > ( tyop_2Elist_2Elist @ $o ),V2d1: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ),V3p2: A_27b > $o,V4e2: A_27d > ( tyop_2Elist_2Elist @ $o ),V5d2: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2ECoder_2Esum__coder @ A_27a @ A_27b @ A_27c @ A_27d @ ( c_2Epair_2E_2C @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27c > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ V0p1 @ ( c_2Epair_2E_2C @ ( A_27c > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ V1e1 @ V2d1 ) ) @ ( c_2Epair_2E_2C @ ( A_27b > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27d > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ V3p2 @ ( c_2Epair_2E_2C @ ( A_27d > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ V4e2 @ V5d2 ) ) )
= ( c_2Epair_2E_2C @ ( ( tyop_2Esum_2Esum @ A_27a @ A_27b ) > $o ) @ ( tyop_2Epair_2Eprod @ ( ( tyop_2Esum_2Esum @ A_27c @ A_27d ) > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ ( c_2EEncode_2Elift__sum @ A_27a @ A_27b @ V0p1 @ V3p2 ) @ ( c_2Epair_2E_2C @ ( ( tyop_2Esum_2Esum @ A_27c @ A_27d ) > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ ( c_2EEncode_2Eencode__sum @ A_27c @ A_27d @ V1e1 @ V4e2 ) @ ( c_2EDecode_2Edecode__sum @ A_27a @ A_27b @ ( c_2EEncode_2Elift__sum @ A_27a @ A_27b @ V0p1 @ V3p2 ) @ V2d1 @ V5d2 ) ) ) ) ).
thf(thm_2ECoder_2Eoption__coder__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0p: A_27a > $o,V1e: A_27b > ( tyop_2Elist_2Elist @ $o ),V2d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2ECoder_2Eoption__coder @ A_27a @ A_27b @ ( c_2Epair_2E_2C @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27b > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ V0p @ ( c_2Epair_2E_2C @ ( A_27b > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ V1e @ V2d ) ) )
= ( c_2Epair_2E_2C @ ( ( tyop_2Eoption_2Eoption @ A_27a ) > $o ) @ ( tyop_2Epair_2Eprod @ ( ( tyop_2Eoption_2Eoption @ A_27b ) > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ ( c_2EEncode_2Elift__option @ A_27a @ V0p ) @ ( c_2Epair_2E_2C @ ( ( tyop_2Eoption_2Eoption @ A_27b ) > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ ( c_2EEncode_2Eencode__option @ A_27b @ V1e ) @ ( c_2EDecode_2Edecode__option @ A_27a @ ( c_2EEncode_2Elift__option @ A_27a @ V0p ) @ V2d ) ) ) ) ).
thf(thm_2ECoder_2Elist__coder__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0p: A_27a > $o,V1e: A_27b > ( tyop_2Elist_2Elist @ $o ),V2d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2ECoder_2Elist__coder @ A_27a @ A_27b @ ( c_2Epair_2E_2C @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27b > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ V0p @ ( c_2Epair_2E_2C @ ( A_27b > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ V1e @ V2d ) ) )
= ( c_2Epair_2E_2C @ ( ( tyop_2Elist_2Elist @ A_27a ) > $o ) @ ( tyop_2Epair_2Eprod @ ( ( tyop_2Elist_2Elist @ A_27b ) > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ ( c_2Elist_2EEVERY @ A_27a @ V0p ) @ ( c_2Epair_2E_2C @ ( ( tyop_2Elist_2Elist @ A_27b ) > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ ( c_2EEncode_2Eencode__list @ A_27b @ V1e ) @ ( c_2EDecode_2Edecode__list @ A_27a @ ( c_2Elist_2EEVERY @ A_27a @ V0p ) @ V2d ) ) ) ) ).
thf(thm_2ECoder_2Eblist__coder__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0m: tyop_2Enum_2Enum,V1p: A_27a > $o,V2e: A_27b > ( tyop_2Elist_2Elist @ A_27c ),V3d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2ECoder_2Eblist__coder @ A_27a @ A_27b @ A_27c @ V0m @ ( c_2Epair_2E_2C @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27b > ( tyop_2Elist_2Elist @ A_27c ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ V1p @ ( c_2Epair_2E_2C @ ( A_27b > ( tyop_2Elist_2Elist @ A_27c ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ V2e @ V3d ) ) )
= ( c_2Epair_2E_2C @ ( ( tyop_2Elist_2Elist @ A_27a ) > $o ) @ ( tyop_2Epair_2Eprod @ ( ( tyop_2Elist_2Elist @ A_27b ) > ( tyop_2Elist_2Elist @ A_27c ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ ( c_2EEncode_2Elift__blist @ A_27a @ V0m @ V1p ) @ ( c_2Epair_2E_2C @ ( ( tyop_2Elist_2Elist @ A_27b ) > ( tyop_2Elist_2Elist @ A_27c ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ ( c_2EEncode_2Eencode__blist @ A_27c @ A_27b @ V0m @ V2e ) @ ( c_2EDecode_2Edecode__blist @ A_27a @ ( c_2EEncode_2Elift__blist @ A_27a @ V0m @ V1p ) @ V0m @ V3d ) ) ) ) ).
thf(thm_2ECoder_2Enum__coder__def,axiom,
! [V0p: tyop_2Enum_2Enum > $o] :
( ( c_2ECoder_2Enum__coder @ V0p )
= ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > $o ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ V0p @ ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ c_2EEncode_2Eencode__num @ ( c_2EDecode_2Edecode__num @ V0p ) ) ) ) ).
thf(thm_2ECoder_2Ebnum__coder__def,axiom,
! [V0m: tyop_2Enum_2Enum,V1p: tyop_2Enum_2Enum > $o] :
( ( c_2ECoder_2Ebnum__coder @ V0m @ V1p )
= ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > $o ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ V1p @ ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ ( c_2EEncode_2Eencode__bnum @ V0m ) @ ( c_2EDecode_2Edecode__bnum @ V0m @ V1p ) ) ) ) ).
thf(thm_2ECoder_2Etree__coder__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0p: A_27a > $o,V1e: A_27b > ( tyop_2Elist_2Elist @ $o ),V2d: ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) )] :
( ( c_2ECoder_2Etree__coder @ A_27a @ A_27b @ ( c_2Epair_2E_2C @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27b > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ V0p @ ( c_2Epair_2E_2C @ ( A_27b > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ V1e @ V2d ) ) )
= ( c_2Epair_2E_2C @ ( ( tyop_2EEncode_2Etree @ A_27a ) > $o ) @ ( tyop_2Epair_2Eprod @ ( ( tyop_2EEncode_2Etree @ A_27b ) > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2EEncode_2Etree @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ ( c_2EEncode_2Elift__tree @ A_27a @ V0p ) @ ( c_2Epair_2E_2C @ ( ( tyop_2EEncode_2Etree @ A_27b ) > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2EEncode_2Etree @ A_27a ) @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ ( c_2EEncode_2Eencode__tree @ A_27b @ V1e ) @ ( c_2EDecode_2Edecode__tree @ A_27a @ ( c_2EEncode_2Elift__tree @ A_27a @ V0p ) @ V2d ) ) ) ) ).
thf(thm_2ECoder_2Edecode__encode,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1e: A_27a > ( tyop_2Elist_2Elist @ $o ),V2x: A_27a] :
( ( ( c_2EEncode_2Ewf__encoder @ A_27a @ V0p @ V1e )
& ( V0p @ V2x ) )
=> ( ( c_2ECoder_2Edecode @ A_27a @ V0p @ ( c_2EDecode_2Eenc2dec @ A_27a @ V0p @ V1e ) @ ( V1e @ V2x ) )
= V2x ) ) ).
thf(thm_2ECoder_2Ewf__coder,axiom,
! [A_27a: $tType,V0c: tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) )] :
( ( c_2ECoder_2Ewf__coder @ A_27a @ V0c )
=> ! [V1x: A_27a] :
( ( c_2ECoder_2Edomain @ A_27a @ V0c @ V1x )
=> ( ( c_2ECoder_2Edecoder @ A_27a @ V0c @ ( c_2ECoder_2Eencoder @ A_27a @ V0c @ V1x ) )
= V1x ) ) ) ).
thf(thm_2ECoder_2Ewf__coder__closed,axiom,
! [A_27a: $tType,V0c: tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) )] :
( ( c_2ECoder_2Ewf__coder @ A_27a @ V0c )
=> ! [V1l: tyop_2Elist_2Elist @ $o] : ( c_2ECoder_2Edomain @ A_27a @ V0c @ ( c_2ECoder_2Edecoder @ A_27a @ V0c @ V1l ) ) ) ).
thf(thm_2ECoder_2Ewf__coder__op,axiom,
! [A_27a: $tType,V0p: A_27a > $o,V1e: A_27a > ( tyop_2Elist_2Elist @ $o ),V2f: A_27a > ( tyop_2Elist_2Elist @ $o )] :
( ( ? [V3x: A_27a] : ( V0p @ V3x )
& ( c_2EEncode_2Ewf__encoder @ A_27a @ V0p @ V1e )
& ! [V4x: A_27a] :
( ( V0p @ V4x )
=> ( ( V1e @ V4x )
= ( V2f @ V4x ) ) ) )
=> ( c_2ECoder_2Ewf__coder @ A_27a @ ( c_2Epair_2E_2C @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ) @ V0p @ ( c_2Epair_2E_2C @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) @ V1e @ ( c_2EDecode_2Eenc2dec @ A_27a @ V0p @ V2f ) ) ) ) ) ).
thf(thm_2ECoder_2Ewf__coder__unit,axiom,
! [V0p: tyop_2Eone_2Eone > $o] :
( ( c_2EEncode_2Ewf__pred @ tyop_2Eone_2Eone @ V0p )
=> ( c_2ECoder_2Ewf__coder @ tyop_2Eone_2Eone @ ( c_2ECoder_2Eunit__coder @ V0p ) ) ) ).
thf(thm_2ECoder_2Ewf__coder__bool,axiom,
! [V0p: $o > $o] :
( ( c_2EEncode_2Ewf__pred @ $o @ V0p )
=> ( c_2ECoder_2Ewf__coder @ $o @ ( c_2ECoder_2Ebool__coder @ V0p ) ) ) ).
thf(thm_2ECoder_2Ewf__coder__prod,axiom,
! [A_27a: $tType,A_27b: $tType,V0c1: tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ),V1c2: tyop_2Epair_2Eprod @ ( A_27b > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27b > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ) ) )] :
( ( ( c_2ECoder_2Ewf__coder @ A_27a @ V0c1 )
& ( c_2ECoder_2Ewf__coder @ A_27b @ V1c2 ) )
=> ( c_2ECoder_2Ewf__coder @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2ECoder_2Eprod__coder @ A_27a @ A_27b @ A_27a @ A_27b @ V0c1 @ V1c2 ) ) ) ).
thf(thm_2ECoder_2Ewf__coder__sum,axiom,
! [A_27a: $tType,A_27b: $tType,V0c1: tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) ),V1c2: tyop_2Epair_2Eprod @ ( A_27b > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27b > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Elist_2Elist @ $o ) ) ) ) )] :
( ( ( c_2ECoder_2Ewf__coder @ A_27a @ V0c1 )
& ( c_2ECoder_2Ewf__coder @ A_27b @ V1c2 ) )
=> ( c_2ECoder_2Ewf__coder @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2ECoder_2Esum__coder @ A_27a @ A_27b @ A_27a @ A_27b @ V0c1 @ V1c2 ) ) ) ).
thf(thm_2ECoder_2Ewf__coder__option,axiom,
! [A_27a: $tType,V0c: tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) )] :
( ( c_2ECoder_2Ewf__coder @ A_27a @ V0c )
=> ( c_2ECoder_2Ewf__coder @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2ECoder_2Eoption__coder @ A_27a @ A_27a @ V0c ) ) ) ).
thf(thm_2ECoder_2Ewf__coder__list,axiom,
! [A_27a: $tType,V0c: tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) )] :
( ( c_2ECoder_2Ewf__coder @ A_27a @ V0c )
=> ( c_2ECoder_2Ewf__coder @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2ECoder_2Elist__coder @ A_27a @ A_27a @ V0c ) ) ) ).
thf(thm_2ECoder_2Ewf__coder__blist,axiom,
! [A_27a: $tType,V0m: tyop_2Enum_2Enum,V1c: tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) )] :
( ( c_2ECoder_2Ewf__coder @ A_27a @ V1c )
=> ( c_2ECoder_2Ewf__coder @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2ECoder_2Eblist__coder @ A_27a @ A_27a @ $o @ V0m @ V1c ) ) ) ).
thf(thm_2ECoder_2Ewf__coder__num,axiom,
! [V0p: tyop_2Enum_2Enum > $o] :
( ( c_2EEncode_2Ewf__pred @ tyop_2Enum_2Enum @ V0p )
=> ( c_2ECoder_2Ewf__coder @ tyop_2Enum_2Enum @ ( c_2ECoder_2Enum__coder @ V0p ) ) ) ).
thf(thm_2ECoder_2Ewf__coder__bnum,axiom,
! [V0m: tyop_2Enum_2Enum,V1p: tyop_2Enum_2Enum > $o] :
( ( c_2EEncode_2Ewf__pred__bnum @ V0m @ V1p )
=> ( c_2ECoder_2Ewf__coder @ tyop_2Enum_2Enum @ ( c_2ECoder_2Ebnum__coder @ V0m @ V1p ) ) ) ).
thf(thm_2ECoder_2Ewf__coder__tree,axiom,
! [A_27a: $tType,V0c: tyop_2Epair_2Eprod @ ( A_27a > $o ) @ ( tyop_2Epair_2Eprod @ ( A_27a > ( tyop_2Elist_2Elist @ $o ) ) @ ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ $o ) ) ) ) )] :
( ( c_2ECoder_2Ewf__coder @ A_27a @ V0c )
=> ( c_2ECoder_2Ewf__coder @ ( tyop_2EEncode_2Etree @ A_27a ) @ ( c_2ECoder_2Etree__coder @ A_27a @ A_27a @ V0c ) ) ) ).
%------------------------------------------------------------------------------