ITP001 Axioms: ITP049^5.ax
%------------------------------------------------------------------------------
% File : ITP049^5 : 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 : llist^2.ax [Gau20]
% : HL4049^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 277 ( 10 unt; 30 typ; 0 def)
% Number of atoms : 5196 ( 321 equ; 0 cnn)
% Maximal formula atoms : 80 ( 18 avg)
% Number of connectives : 9888 ( 14 ~; 18 |; 196 &;9051 @)
% ( 64 <=>; 545 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 11 avg;9051 nst)
% Number of types : 1 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 116 ( 113 usr; 85 con; 0-2 aty)
% Number of variables : 1013 ( 116 ^ 833 !; 64 ?;1013 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_ty_2Ellist_2Ellist,type,
ty_2Ellist_2Ellist: del > del ).
thf(tp_c_2Ellist_2ELAPPEND,type,
c_2Ellist_2ELAPPEND: del > $i ).
thf(mem_c_2Ellist_2ELAPPEND,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) ) ).
thf(tp_c_2Ellist_2ELCONS,type,
c_2Ellist_2ELCONS: del > $i ).
thf(mem_c_2Ellist_2ELCONS,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2ELCONS @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) ) ).
thf(tp_c_2Ellist_2ELDROP,type,
c_2Ellist_2ELDROP: del > $i ).
thf(mem_c_2Ellist_2ELDROP,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Eoption_2Eoption @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) ) ) ).
thf(tp_c_2Ellist_2ELFILTER,type,
c_2Ellist_2ELFILTER: del > $i ).
thf(mem_c_2Ellist_2ELFILTER,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2ELFILTER @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) ) ).
thf(tp_c_2Ellist_2ELFINITE,type,
c_2Ellist_2ELFINITE: del > $i ).
thf(mem_c_2Ellist_2ELFINITE,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2ELFINITE @ A_27a ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool ) ) ).
thf(tp_c_2Ellist_2ELFLATTEN,type,
c_2Ellist_2ELFLATTEN: del > $i ).
thf(mem_c_2Ellist_2ELFLATTEN,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2ELFLATTEN @ A_27a ) @ ( arr @ ( ty_2Ellist_2Ellist @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) ).
thf(tp_c_2Ellist_2ELGENLIST,type,
c_2Ellist_2ELGENLIST: del > $i ).
thf(mem_c_2Ellist_2ELGENLIST,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) ) ).
thf(tp_c_2Ellist_2ELHD,type,
c_2Ellist_2ELHD: del > $i ).
thf(mem_c_2Ellist_2ELHD,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2ELHD @ A_27a ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ).
thf(tp_c_2Ellist_2ELLENGTH,type,
c_2Ellist_2ELLENGTH: del > $i ).
thf(mem_c_2Ellist_2ELLENGTH,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2Ellist_2ELMAP,type,
c_2Ellist_2ELMAP: del > del > $i ).
thf(mem_c_2Ellist_2ELMAP,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ellist_2ELMAP @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27b ) ) ) ) ).
thf(tp_c_2Ellist_2ELNIL,type,
c_2Ellist_2ELNIL: del > $i ).
thf(mem_c_2Ellist_2ELNIL,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2ELNIL @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27a ) ) ).
thf(tp_c_2Ellist_2ELNTH,type,
c_2Ellist_2ELNTH: del > $i ).
thf(mem_c_2Ellist_2ELNTH,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ).
thf(tp_c_2Ellist_2ELPREFIX,type,
c_2Ellist_2ELPREFIX: del > $i ).
thf(mem_c_2Ellist_2ELPREFIX,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool ) ) ) ).
thf(tp_c_2Ellist_2ELREPEAT,type,
c_2Ellist_2ELREPEAT: del > $i ).
thf(mem_c_2Ellist_2ELREPEAT,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2ELREPEAT @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) ).
thf(tp_c_2Ellist_2ELTAKE,type,
c_2Ellist_2ELTAKE: del > $i ).
thf(mem_c_2Ellist_2ELTAKE,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ).
thf(tp_c_2Ellist_2ELTL,type,
c_2Ellist_2ELTL: del > $i ).
thf(mem_c_2Ellist_2ELTL,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2ELTL @ A_27a ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Eoption_2Eoption @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) ) ).
thf(tp_c_2Ellist_2ELTL__HD,type,
c_2Ellist_2ELTL__HD: del > $i ).
thf(mem_c_2Ellist_2ELTL__HD,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2ELTL__HD @ A_27a ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) ) ).
thf(tp_c_2Ellist_2ELUNFOLD,type,
c_2Ellist_2ELUNFOLD: del > del > $i ).
thf(mem_c_2Ellist_2ELUNFOLD,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( arr @ A_27b @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) ) ).
thf(tp_c_2Ellist_2ELUNZIP,type,
c_2Ellist_2ELUNZIP: del > del > $i ).
thf(mem_c_2Ellist_2ELUNZIP,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ellist_2ELUNZIP @ A_27a @ A_27b ) @ ( arr @ ( ty_2Ellist_2Ellist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27b ) ) ) ) ).
thf(tp_c_2Ellist_2ELZIP,type,
c_2Ellist_2ELZIP: del > del > $i ).
thf(mem_c_2Ellist_2ELZIP,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ellist_2ELZIP @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27b ) ) @ ( ty_2Ellist_2Ellist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) ).
thf(tp_c_2Ellist_2Eevery,type,
c_2Ellist_2Eevery: del > $i ).
thf(mem_c_2Ellist_2Eevery,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2Eevery @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool ) ) ) ).
thf(tp_c_2Ellist_2Eexists,type,
c_2Ellist_2Eexists: del > $i ).
thf(mem_c_2Ellist_2Eexists,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2Eexists @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool ) ) ) ).
thf(tp_c_2Ellist_2EfromList,type,
c_2Ellist_2EfromList: del > $i ).
thf(mem_c_2Ellist_2EfromList,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2EfromList @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) ).
thf(tp_c_2Ellist_2Elinear__order__to__list__f,type,
c_2Ellist_2Elinear__order__to__list__f: del > $i ).
thf(mem_c_2Ellist_2Elinear__order__to__list__f,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2Elinear__order__to__list__f @ A_27a ) @ ( arr @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ A_27a ) ) ) ) ).
thf(tp_c_2Ellist_2Ellength__rel,type,
c_2Ellist_2Ellength__rel: del > $i ).
thf(mem_c_2Ellist_2Ellength__rel,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2Ellength__rel @ A_27a ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).
thf(tp_c_2Ellist_2Ellist__abs,type,
c_2Ellist_2Ellist__abs: del > $i ).
thf(mem_c_2Ellist_2Ellist__abs,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2Ellist__abs @ A_27a ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) ).
thf(tp_c_2Ellist_2Ellist__rep,type,
c_2Ellist_2Ellist__rep: del > $i ).
thf(mem_c_2Ellist_2Ellist__rep,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2Ellist__rep @ A_27a ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ).
thf(tp_c_2Ellist_2Elrep__ok,type,
c_2Ellist_2Elrep__ok: del > $i ).
thf(mem_c_2Ellist_2Elrep__ok,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2Elrep__ok @ A_27a ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ bool ) ) ).
thf(tp_c_2Ellist_2EtoList,type,
c_2Ellist_2EtoList: del > $i ).
thf(mem_c_2Ellist_2EtoList,axiom,
! [A_27a: del] : ( mem @ ( c_2Ellist_2EtoList @ A_27a ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ).
thf(ax_thm_2Ellist_2Elrep__ok__def,axiom,
! [A_27a: del] :
( ( c_2Ellist_2Elrep__ok @ A_27a )
= ( lam @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) )
@ ^ [V0a0: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ bool ) )
@ ( lam @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ bool )
@ ^ [V1lrep__ok_27: $i] :
( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1lrep__ok_27 @ V0a0 ) )
@ ( ap @ ( c_2Ebool_2E_21 @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
@ ( lam @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) )
@ ^ [V2a0: $i] :
( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V1lrep__ok_27 @ V2a0 ) )
@ ( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) @ V2a0 )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3n: $i] : ( c_2Eoption_2ENONE @ A_27a ) ) ) )
@ ( ap @ ( c_2Ebool_2E_3F @ A_27a )
@ ( lam @ A_27a
@ ^ [V4h: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
@ ( lam @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) )
@ ^ [V5t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) @ V2a0 )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6n: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V6n ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V4h ) ) @ ( ap @ V5t @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V6n ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
@ ( ap @ V1lrep__ok_27 @ V5t ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Elrep__ok__rules,axiom,
! [A_27a: del] :
( ( p
@ ( ap @ ( c_2Ellist_2Elrep__ok @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V0n: $i] : ( c_2Eoption_2ENONE @ A_27a ) ) ) )
& ! [V1h: $i] :
( ( mem @ V1h @ A_27a )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2Elrep__ok @ A_27a ) @ V2t ) )
=> ( p
@ ( ap @ ( c_2Ellist_2Elrep__ok @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3n: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3n ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1h ) ) @ ( ap @ V2t @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V3n ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Elrep__ok__coind,axiom,
! [A_27a: del,V0lrep__ok_27: $i] :
( ( mem @ V0lrep__ok_27 @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ bool ) )
=> ( ! [V1a0: $i] :
( ( mem @ V1a0 @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
=> ( ( p @ ( ap @ V0lrep__ok_27 @ V1a0 ) )
=> ( ( V1a0
= ( lam @ ty_2Enum_2Enum
@ ^ [V2n: $i] : ( c_2Eoption_2ENONE @ A_27a ) ) )
| ? [V3h: $i] :
( ( mem @ V3h @ A_27a )
& ? [V4t: $i] :
( ( mem @ V4t @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
& ( V1a0
= ( lam @ ty_2Enum_2Enum
@ ^ [V5n: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V5n ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3h ) ) @ ( ap @ V4t @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V5n ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ( p @ ( ap @ V0lrep__ok_27 @ V4t ) ) ) ) ) ) )
=> ! [V6a0: $i] :
( ( mem @ V6a0 @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
=> ( ( p @ ( ap @ V0lrep__ok_27 @ V6a0 ) )
=> ( p @ ( ap @ ( c_2Ellist_2Elrep__ok @ A_27a ) @ V6a0 ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Elrep__ok__cases,axiom,
! [A_27a: del,V0a0: $i] :
( ( mem @ V0a0 @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2Elrep__ok @ A_27a ) @ V0a0 ) )
<=> ( ( V0a0
= ( lam @ ty_2Enum_2Enum
@ ^ [V1n: $i] : ( c_2Eoption_2ENONE @ A_27a ) ) )
| ? [V2h: $i] :
( ( mem @ V2h @ A_27a )
& ? [V3t: $i] :
( ( mem @ V3t @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
& ( V0a0
= ( lam @ ty_2Enum_2Enum
@ ^ [V4n: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V4n ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2h ) ) @ ( ap @ V3t @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V4n ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ( p @ ( ap @ ( c_2Ellist_2Elrep__ok @ A_27a ) @ V3t ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Elrep__ok__alt,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2Elrep__ok @ A_27a ) @ V0f ) )
<=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( ap @ V0f @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
=> ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ).
thf(ax_thm_2Ellist_2Ellist__TY__DEF,axiom,
! [A_27a: del] :
? [V0rep: $i] :
( ( mem @ V0rep @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2Elrep__ok @ A_27a ) ) @ V0rep ) ) ) ).
thf(ax_thm_2Ellist_2Ellist__absrep,axiom,
! [A_27a: del] :
( ! [V0a: $i] :
( ( mem @ V0a @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2Ellist__abs @ A_27a ) @ ( ap @ ( c_2Ellist_2Ellist__rep @ A_27a ) @ V0a ) )
= V0a ) )
& ! [V1r: $i] :
( ( mem @ V1r @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2Elrep__ok @ A_27a ) @ V1r ) )
<=> ( ( ap @ ( c_2Ellist_2Ellist__rep @ A_27a ) @ ( ap @ ( c_2Ellist_2Ellist__abs @ A_27a ) @ V1r ) )
= V1r ) ) ) ) ).
thf(conj_thm_2Ellist_2Elrep__ok__MAP,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ A_27a ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ( ( p
@ ( ap @ ( c_2Ellist_2Elrep__ok @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2n: $i] : ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27b @ A_27a ) @ V0f ) @ ( ap @ V1g @ V2n ) ) ) ) )
<=> ( p @ ( ap @ ( c_2Ellist_2Elrep__ok @ A_27b ) @ V1g ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Elrep__ok__FUNPOW__BIND,axiom,
! [A_27a: del,V0g: $i] :
( ( mem @ V0g @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
=> ! [V1fz: $i] :
( ( mem @ V1fz @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ( p
@ ( ap @ ( c_2Ellist_2Elrep__ok @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2n: $i] :
( ap
@ ( ap
@ ( ap @ ( c_2Earithmetic_2EFUNPOW @ ( ty_2Eoption_2Eoption @ A_27a ) )
@ ( lam @ ( ty_2Eoption_2Eoption @ A_27a )
@ ^ [V3m: $i] : ( ap @ ( ap @ ( c_2Eoption_2EOPTION__BIND @ A_27a @ A_27a ) @ V3m ) @ V0g ) ) )
@ V2n )
@ V1fz ) ) ) ) ) ) ).
thf(ax_thm_2Ellist_2ELNIL,axiom,
! [A_27a: del] :
( ( c_2Ellist_2ELNIL @ A_27a )
= ( ap @ ( c_2Ellist_2Ellist__abs @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V0n: $i] : ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ).
thf(ax_thm_2Ellist_2ELCONS,axiom,
! [A_27a: del,V0h: $i] :
( ( mem @ V0h @ A_27a )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V0h ) @ V1t )
= ( ap @ ( c_2Ellist_2Ellist__abs @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2n: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V2n ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0h ) ) @ ( ap @ ( ap @ ( c_2Ellist_2Ellist__rep @ A_27a ) @ V1t ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V2n ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Ellist__rep__LCONS,axiom,
! [A_27a: del,V0h: $i] :
( ( mem @ V0h @ A_27a )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2Ellist__rep @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V0h ) @ V1t ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2n: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V2n ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0h ) ) @ ( ap @ ( ap @ ( c_2Ellist_2Ellist__rep @ A_27a ) @ V1t ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V2n ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Ellist__rep__LNIL,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Ellist_2Ellist__rep @ A_27a ) @ ( c_2Ellist_2ELNIL @ A_27a ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V0n: $i] : ( c_2Eoption_2ENONE @ A_27a ) ) ) ).
thf(ax_thm_2Ellist_2ELTL__HD__def,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELTL__HD @ A_27a ) @ V0ll )
= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2Ellist__rep @ A_27a ) @ V0ll ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) )
@ ( lam @ A_27a
@ ^ [V1h: $i] : ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ ( ap @ ( c_2Ellist_2Ellist__abs @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Ellist_2Ellist__rep @ A_27a ) @ V0ll ) ) @ c_2Enum_2ESUC ) ) ) @ V1h ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTL__HD__LNIL,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Ellist_2ELTL__HD @ A_27a ) @ ( c_2Ellist_2ELNIL @ A_27a ) )
= ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) ).
thf(conj_thm_2Ellist_2ELTL__HD__LCONS,axiom,
! [A_27a: del,V0h: $i] :
( ( mem @ V0h @ A_27a )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELTL__HD @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V0h ) @ V1t ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ V1t ) @ V0h ) ) ) ) ) ).
thf(ax_thm_2Ellist_2ELHD,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ V0ll )
= ( ap @ ( ap @ ( c_2Ellist_2Ellist__rep @ A_27a ) @ V0ll ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
thf(ax_thm_2Ellist_2ELTL,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ V0ll )
= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ ( ty_2Eoption_2Eoption @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) @ ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ V0ll ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Ellist_2Ellist @ A_27a ) ) )
@ ( lam @ A_27a
@ ^ [V1v: $i] :
( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) )
@ ( ap @ ( c_2Ellist_2Ellist__abs @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2n: $i] : ( ap @ ( ap @ ( c_2Ellist_2Ellist__rep @ A_27a ) @ V0ll ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V2n ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTL__HD__HD,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ V0ll )
= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ A_27a ) @ ( c_2Epair_2ESND @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( ap @ ( c_2Ellist_2ELTL__HD @ A_27a ) @ V0ll ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTL__HD__TL,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ V0ll )
= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Epair_2EFST @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( ap @ ( c_2Ellist_2ELTL__HD @ A_27a ) @ V0ll ) ) ) ) ).
thf(conj_thm_2Ellist_2ELHD__LCONS,axiom,
! [A_27a: del,V0h: $i] :
( ( mem @ V0h @ A_27a )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V0h ) @ V1t ) )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0h ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTL__LCONS,axiom,
! [A_27a: del,V0h: $i] :
( ( mem @ V0h @ A_27a )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V0h ) @ V1t ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V1t ) ) ) ) ).
thf(conj_thm_2Ellist_2ELHDTL__CONS__THM,axiom,
! [A_27a: del,V0h: $i] :
( ( mem @ V0h @ A_27a )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V0h ) @ V1t ) )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0h ) )
& ( ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V0h ) @ V1t ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V1t ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Ellist__CASES,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( V0l
= ( c_2Ellist_2ELNIL @ A_27a ) )
| ? [V1h: $i] :
( ( mem @ V1h @ A_27a )
& ? [V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ A_27a ) )
& ( V0l
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ V2t ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTL__HD__11,axiom,
! [A_27a: del,V0ll1: $i] :
( ( mem @ V0ll1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1ll2: $i] :
( ( mem @ V1ll2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( ap @ ( c_2Ellist_2ELTL__HD @ A_27a ) @ V0ll1 )
= ( ap @ ( c_2Ellist_2ELTL__HD @ A_27a ) @ V1ll2 ) )
=> ( V0ll1 = V1ll2 ) ) ) ) ).
thf(conj_thm_2Ellist_2ELHD__THM,axiom,
! [A_27a: del,A_27b: del] :
( ( ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ ( c_2Ellist_2ELNIL @ A_27a ) )
= ( c_2Eoption_2ENONE @ A_27a ) )
& ! [V0h: $i] :
( ( mem @ V0h @ A_27b )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Ellist_2Ellist @ A_27b ) )
=> ( ( ap @ ( c_2Ellist_2ELHD @ A_27b ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V0h ) @ V1t ) )
= ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V0h ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTL__THM,axiom,
! [A_27a: del,A_27b: del] :
( ( ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ ( c_2Ellist_2ELNIL @ A_27a ) )
= ( c_2Eoption_2ENONE @ ( ty_2Ellist_2Ellist @ A_27a ) ) )
& ! [V0h: $i] :
( ( mem @ V0h @ A_27b )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Ellist_2Ellist @ A_27b ) )
=> ( ( ap @ ( c_2Ellist_2ELTL @ A_27b ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V0h ) @ V1t ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27b ) ) @ V1t ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELCONS__NOT__NIL,axiom,
! [A_27a: del,V0h: $i] :
( ( mem @ V0h @ A_27a )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V0h ) @ V1t )
!= ( c_2Ellist_2ELNIL @ A_27a ) )
& ( ( c_2Ellist_2ELNIL @ A_27a )
!= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V0h ) @ V1t ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELCONS__11,axiom,
! [A_27a: del,V0h1: $i] :
( ( mem @ V0h1 @ A_27a )
=> ! [V1t1: $i] :
( ( mem @ V1t1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2h2: $i] :
( ( mem @ V2h2 @ A_27a )
=> ! [V3t2: $i] :
( ( mem @ V3t2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V0h1 ) @ V1t1 )
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V2h2 ) @ V3t2 ) )
<=> ( ( V0h1 = V2h2 )
& ( V1t1 = V3t2 ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTL__HD__iff,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2h: $i] :
( ( mem @ V2h @ A_27a )
=> ( ( ( ( ap @ ( c_2Ellist_2ELTL__HD @ A_27a ) @ V0x )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ V1t ) @ V2h ) ) )
<=> ( V0x
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V2h ) @ V1t ) ) )
& ( ( ( ap @ ( c_2Ellist_2ELTL__HD @ A_27a ) @ V0x )
= ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) )
<=> ( V0x
= ( c_2Ellist_2ELNIL @ A_27a ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELHD__EQ__NONE,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ V0ll )
= ( c_2Eoption_2ENONE @ A_27a ) )
<=> ( V0ll
= ( c_2Ellist_2ELNIL @ A_27a ) ) )
& ( ( ( c_2Eoption_2ENONE @ A_27a )
= ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ V0ll ) )
<=> ( V0ll
= ( c_2Ellist_2ELNIL @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTL__EQ__NONE,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ V0ll )
= ( c_2Eoption_2ENONE @ ( ty_2Ellist_2Ellist @ A_27a ) ) )
<=> ( V0ll
= ( c_2Ellist_2ELNIL @ A_27a ) ) )
& ( ( ( c_2Eoption_2ENONE @ ( ty_2Ellist_2Ellist @ A_27a ) )
= ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ V0ll ) )
<=> ( V0ll
= ( c_2Ellist_2ELNIL @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELHDTL__EQ__SOME,axiom,
! [A_27a: del,V0h: $i] :
( ( mem @ V0h @ A_27a )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2ll: $i] :
( ( mem @ V2ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( V2ll
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V0h ) @ V1t ) )
<=> ( ( ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ V2ll )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0h ) )
& ( ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ V2ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V1t ) ) ) ) ) ) ) ).
thf(ax_thm_2Ellist_2ELNTH,axiom,
! [A_27a: del] :
( ! [V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0ll )
= ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ V0ll ) ) )
& ! [V1n: tp__ty_2Enum_2Enum,V2ll: $i] :
( ( mem @ V2ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ V2ll )
= ( ap @ ( c_2Eoption_2EOPTION__JOIN @ A_27a ) @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ V2ll ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELNTH__THM,axiom,
! [A_27a: del,A_27b: del,A_27c: del] :
( ! [V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( c_2Ellist_2ELNIL @ A_27a ) )
= ( c_2Eoption_2ENONE @ A_27a ) )
& ! [V1h: $i] :
( ( mem @ V1h @ A_27b )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V1h ) @ V2t ) )
= ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V1h ) ) ) )
& ! [V3n: tp__ty_2Enum_2Enum,V4h: $i] :
( ( mem @ V4h @ A_27c )
=> ! [V5t: $i] :
( ( mem @ V5t @ ( ty_2Ellist_2Ellist @ A_27c ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27c ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27c ) @ V4h ) @ V5t ) )
= ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V5t ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELNTH__rep,axiom,
! [A_27a: del,V0i: tp__ty_2Enum_2Enum,V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ V1ll )
= ( ap @ ( ap @ ( c_2Ellist_2Ellist__rep @ A_27a ) @ V1ll ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) ) ) ).
thf(conj_thm_2Ellist_2ELNTH__EQ,axiom,
! [A_27a: del,V0ll1: $i] :
( ( mem @ V0ll1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1ll2: $i] :
( ( mem @ V1ll2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( V0ll1 = V1ll2 )
<=> ! [V2n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V0ll1 )
= ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V1ll2 ) ) ) ) ) ).
thf(ax_thm_2Ellist_2ELUNFOLD__def,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) ) )
=> ! [V1z: $i] :
( ( mem @ V1z @ A_27b )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V0f ) @ V1z )
= ( ap @ ( c_2Ellist_2Ellist__abs @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2n: $i] :
( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ ( c_2Epair_2ESND @ A_27b @ A_27a ) )
@ ( ap
@ ( ap
@ ( ap @ ( c_2Earithmetic_2EFUNPOW @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) )
@ ( lam @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) )
@ ^ [V3m: $i] : ( ap @ ( ap @ ( c_2Eoption_2EOPTION__BIND @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V3m ) @ ( ap @ ( c_2Epair_2EUNCURRY @ A_27b @ A_27a @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27b @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Ecombin_2EK @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) @ A_27a ) ) @ V0f ) ) ) ) )
@ V2n )
@ ( ap @ V0f @ V1z ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELUNFOLD,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27b @ A_27a ) @ V0f ) @ V1x )
= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Ellist_2Ellist @ A_27b ) ) @ ( ap @ V0f @ V1x ) ) @ ( c_2Ellist_2ELNIL @ A_27b ) )
@ ( lam @ ( ty_2Epair_2Eprod @ A_27a @ A_27b )
@ ^ [V2v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Ellist_2Ellist @ A_27b ) @ A_27a @ A_27b ) @ V2v )
@ ( lam @ A_27a
@ ^ [V3v1: $i] :
( lam @ A_27b
@ ^ [V4v2: $i] : ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V4v2 ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27b @ A_27a ) @ V0f ) @ V3v1 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELUNFOLD__UNIQUE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27a @ ( ty_2Ellist_2Ellist @ A_27b ) ) )
=> ( ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( ap @ V1g @ V2x )
= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Ellist_2Ellist @ A_27b ) ) @ ( ap @ V0f @ V2x ) ) @ ( c_2Ellist_2ELNIL @ A_27b ) )
@ ( lam @ ( ty_2Epair_2Eprod @ A_27a @ A_27b )
@ ^ [V3v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Ellist_2Ellist @ A_27b ) @ A_27a @ A_27b ) @ V3v )
@ ( lam @ A_27a
@ ^ [V4v1: $i] :
( lam @ A_27b
@ ^ [V5v2: $i] : ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V5v2 ) @ ( ap @ V1g @ V4v1 ) ) ) ) ) ) ) ) )
=> ! [V6y: $i] :
( ( mem @ V6y @ A_27a )
=> ( ( ap @ V1g @ V6y )
= ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27b @ A_27a ) @ V0f ) @ V6y ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELUNFOLD__LTL__HD,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL__HD @ A_27a ) ) @ V0ll )
= V0ll ) ) ).
thf(conj_thm_2Ellist_2ELTL__HD__LUNFOLD,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27b )
=> ( ( ap @ ( c_2Ellist_2ELTL__HD @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V0f ) @ V1x ) )
= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_23_23 @ A_27b @ A_27a @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V0f ) ) @ ( c_2Ecombin_2EI @ A_27a ) ) ) @ ( ap @ V0f @ V1x ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELNTH__LUNFOLD,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27b )
=> ! [V2n: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V0f ) @ V1x ) )
= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ ( c_2Epair_2ESND @ A_27b @ A_27a ) ) @ ( ap @ V0f @ V1x ) ) )
& ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V0f ) @ V1x ) )
= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ V0f @ V1x ) ) @ ( c_2Eoption_2ENONE @ A_27a ) )
@ ( lam @ ( ty_2Epair_2Eprod @ A_27b @ A_27a )
@ ^ [V3v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ A_27a ) @ A_27b @ A_27a ) @ V3v )
@ ( lam @ A_27b
@ ^ [V4tx: $i] :
( lam @ A_27a
@ ^ [V5hx: $i] : ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V0f ) @ V4tx ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELNTH__LUNFOLD__compute,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27b )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V0f ) @ V1x ) )
= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ ( c_2Epair_2ESND @ A_27b @ A_27a ) ) @ ( ap @ V0f @ V1x ) ) )
& ! [V2n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V0f ) @ V1x ) )
= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ V0f @ V1x ) ) @ ( c_2Eoption_2ENONE @ A_27a ) )
@ ( lam @ ( ty_2Epair_2Eprod @ A_27b @ A_27a )
@ ^ [V3v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ A_27a ) @ A_27b @ A_27a ) @ V3v )
@ ( lam @ A_27b
@ ^ [V4tx: $i] :
( lam @ A_27a
@ ^ [V5hx: $i] : ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V0f ) @ V4tx ) ) ) ) ) ) ) )
& ! [V6n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V0f ) @ V1x ) )
= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ V0f @ V1x ) ) @ ( c_2Eoption_2ENONE @ A_27a ) )
@ ( lam @ ( ty_2Epair_2Eprod @ A_27b @ A_27a )
@ ^ [V7v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ A_27a ) @ A_27b @ A_27a ) @ V7v )
@ ( lam @ A_27b
@ ^ [V8tx: $i] :
( lam @ A_27a
@ ^ [V9hx: $i] : ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V0f ) @ V8tx ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELHD__LUNFOLD,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27b )
=> ( ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V0f ) @ V1x ) )
= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ ( c_2Epair_2ESND @ A_27b @ A_27a ) ) @ ( ap @ V0f @ V1x ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTL__LUNFOLD,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27b )
=> ( ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V0f ) @ V1x ) )
= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27b ) @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V0f ) ) @ ( c_2Epair_2EFST @ A_27b @ A_27a ) ) ) @ ( ap @ V0f @ V1x ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Ellist__Axiom__1,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) )
=> ? [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27a @ ( ty_2Ellist_2Ellist @ A_27b ) ) )
& ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( ap @ V1g @ V2x )
= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Ellist_2Ellist @ A_27b ) ) @ ( ap @ V0f @ V2x ) ) @ ( c_2Ellist_2ELNIL @ A_27b ) )
@ ( lam @ ( ty_2Epair_2Eprod @ A_27a @ A_27b )
@ ^ [V3v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Ellist_2Ellist @ A_27b ) @ A_27a @ A_27b ) @ V3v )
@ ( lam @ A_27a
@ ^ [V4a: $i] :
( lam @ A_27b
@ ^ [V5b: $i] : ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V5b ) @ ( ap @ V1g @ V4a ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Ellist__Axiom__1ue,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) )
=> ( p
@ ( ap @ ( c_2Ebool_2E_3F_21 @ ( arr @ A_27a @ ( ty_2Ellist_2Ellist @ A_27b ) ) )
@ ( lam @ ( arr @ A_27a @ ( ty_2Ellist_2Ellist @ A_27b ) )
@ ^ [V1g: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x: $i] :
( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Ellist_2Ellist @ A_27b ) ) @ ( ap @ V1g @ V2x ) )
@ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Ellist_2Ellist @ A_27b ) ) @ ( ap @ V0f @ V2x ) ) @ ( c_2Ellist_2ELNIL @ A_27b ) )
@ ( lam @ ( ty_2Epair_2Eprod @ A_27a @ A_27b )
@ ^ [V3v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Ellist_2Ellist @ A_27b ) @ A_27a @ A_27b ) @ V3v )
@ ( lam @ A_27a
@ ^ [V4a: $i] :
( lam @ A_27b
@ ^ [V5b: $i] : ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V5b ) @ ( ap @ V1g @ V4a ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Ellist__ue__Axiom,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) )
=> ( p
@ ( ap @ ( c_2Ebool_2E_3F_21 @ ( arr @ A_27a @ ( ty_2Ellist_2Ellist @ A_27b ) ) )
@ ( lam @ ( arr @ A_27a @ ( ty_2Ellist_2Ellist @ A_27b ) )
@ ^ [V1g: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27b ) ) @ ( ap @ ( c_2Ellist_2ELHD @ A_27b ) @ ( ap @ V1g @ V2x ) ) ) @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ ( c_2Epair_2ESND @ A_27a @ A_27b ) ) @ ( ap @ V0f @ V2x ) ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V3x: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ ( ty_2Ellist_2Ellist @ A_27b ) ) ) @ ( ap @ ( c_2Ellist_2ELTL @ A_27b ) @ ( ap @ V1g @ V3x ) ) ) @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Ellist_2Ellist @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Ellist_2Ellist @ A_27b ) @ A_27a ) @ V1g ) @ ( c_2Epair_2EFST @ A_27a @ A_27b ) ) ) @ ( ap @ V0f @ V3x ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Ellist__Axiom,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) )
=> ? [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27a @ ( ty_2Ellist_2Ellist @ A_27b ) ) )
& ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( ap @ ( c_2Ellist_2ELHD @ A_27b ) @ ( ap @ V1g @ V2x ) )
= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ ( c_2Epair_2ESND @ A_27a @ A_27b ) ) @ ( ap @ V0f @ V2x ) ) ) )
& ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ( ( ap @ ( c_2Ellist_2ELTL @ A_27b ) @ ( ap @ V1g @ V3x ) )
= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Ellist_2Ellist @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ ( ty_2Ellist_2Ellist @ A_27b ) @ A_27a ) @ V1g ) @ ( c_2Epair_2EFST @ A_27a @ A_27b ) ) ) @ ( ap @ V0f @ V3x ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELUNFOLD__BISIMULATION,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f1: $i] :
( ( mem @ V0f1 @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) )
=> ! [V1f2: $i] :
( ( mem @ V1f2 @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27c @ A_27b ) ) ) )
=> ! [V2x1: $i] :
( ( mem @ V2x1 @ A_27a )
=> ! [V3x2: $i] :
( ( mem @ V3x2 @ A_27c )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27b @ A_27a ) @ V0f1 ) @ V2x1 )
= ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27b @ A_27c ) @ V1f2 ) @ V3x2 ) )
<=> ? [V4R: $i] :
( ( mem @ V4R @ ( arr @ A_27a @ ( arr @ A_27c @ bool ) ) )
& ( p @ ( ap @ ( ap @ V4R @ V2x1 ) @ V3x2 ) )
& ! [V5y1: $i] :
( ( mem @ V5y1 @ A_27a )
=> ! [V6y2: $i] :
( ( mem @ V6y2 @ A_27c )
=> ( ( p @ ( ap @ ( ap @ V4R @ V5y1 ) @ V6y2 ) )
=> ( ( ( ( ap @ V0f1 @ V5y1 )
= ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
& ( ( ap @ V1f2 @ V6y2 )
= ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ A_27c @ A_27b ) ) ) )
| ? [V7h: $i] :
( ( mem @ V7h @ A_27b )
& ? [V8t1: $i] :
( ( mem @ V8t1 @ A_27a )
& ? [V9t2: $i] :
( ( mem @ V9t2 @ A_27c )
& ( ( ap @ V0f1 @ V5y1 )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V8t1 ) @ V7h ) ) )
& ( ( ap @ V1f2 @ V6y2 )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27c @ A_27b ) @ V9t2 ) @ V7h ) ) )
& ( p @ ( ap @ ( ap @ V4R @ V8t1 ) @ V9t2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELLIST__BISIMULATION0,axiom,
! [A_27a: del,V0ll1: $i] :
( ( mem @ V0ll1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1ll2: $i] :
( ( mem @ V1ll2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( V0ll1 = V1ll2 )
<=> ? [V2R: $i] :
( ( mem @ V2R @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool ) ) )
& ( p @ ( ap @ ( ap @ V2R @ V0ll1 ) @ V1ll2 ) )
& ! [V3ll3: $i] :
( ( mem @ V3ll3 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V4ll4: $i] :
( ( mem @ V4ll4 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ V2R @ V3ll3 ) @ V4ll4 ) )
=> ( ( ( V3ll3
= ( c_2Ellist_2ELNIL @ A_27a ) )
& ( V4ll4
= ( c_2Ellist_2ELNIL @ A_27a ) ) )
| ? [V5h: $i] :
( ( mem @ V5h @ A_27a )
& ? [V6t1: $i] :
( ( mem @ V6t1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
& ? [V7t2: $i] :
( ( mem @ V7t2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
& ( V3ll3
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V5h ) @ V6t1 ) )
& ( V4ll4
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V5h ) @ V7t2 ) )
& ( p @ ( ap @ ( ap @ V2R @ V6t1 ) @ V7t2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELLIST__BISIMULATION,axiom,
! [A_27a: del,V0ll1: $i] :
( ( mem @ V0ll1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1ll2: $i] :
( ( mem @ V1ll2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( V0ll1 = V1ll2 )
<=> ? [V2R: $i] :
( ( mem @ V2R @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool ) ) )
& ( p @ ( ap @ ( ap @ V2R @ V0ll1 ) @ V1ll2 ) )
& ! [V3ll3: $i] :
( ( mem @ V3ll3 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V4ll4: $i] :
( ( mem @ V4ll4 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ V2R @ V3ll3 ) @ V4ll4 ) )
=> ( ( ( V3ll3
= ( c_2Ellist_2ELNIL @ A_27a ) )
& ( V4ll4
= ( c_2Ellist_2ELNIL @ A_27a ) ) )
| ( ( ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ V3ll3 )
= ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ V4ll4 ) )
& ( p @ ( ap @ ( ap @ V2R @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ V3ll3 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ V4ll4 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELLIST__STRONG__BISIMULATION,axiom,
! [A_27a: del,V0ll1: $i] :
( ( mem @ V0ll1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1ll2: $i] :
( ( mem @ V1ll2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( V0ll1 = V1ll2 )
<=> ? [V2R: $i] :
( ( mem @ V2R @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool ) ) )
& ( p @ ( ap @ ( ap @ V2R @ V0ll1 ) @ V1ll2 ) )
& ! [V3ll3: $i] :
( ( mem @ V3ll3 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V4ll4: $i] :
( ( mem @ V4ll4 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ V2R @ V3ll3 ) @ V4ll4 ) )
=> ( ( V3ll3 = V4ll4 )
| ? [V5h: $i] :
( ( mem @ V5h @ A_27a )
& ? [V6t1: $i] :
( ( mem @ V6t1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
& ? [V7t2: $i] :
( ( mem @ V7t2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
& ( V3ll3
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V5h ) @ V6t1 ) )
& ( V4ll4
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V5h ) @ V7t2 ) )
& ( p @ ( ap @ ( ap @ V2R @ V6t1 ) @ V7t2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ellist_2ELTAKE,axiom,
! [A_27a: del] :
( ! [V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) )
& ! [V1n: tp__ty_2Enum_2Enum,V2ll: $i] :
( ( mem @ V2ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ V2ll )
= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ V2ll ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) )
@ ( lam @ A_27a
@ ^ [V3hd: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ V2ll ) ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V4tl: $i] : ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V3hd ) @ V4tl ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__LUNFOLD,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27b )
=> ! [V2n: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V0f ) @ V1x ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) )
& ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V0f ) @ V1x ) )
= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ V0f @ V1x ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ A_27b @ A_27a )
@ ^ [V3v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) @ A_27b @ A_27a ) @ V3v )
@ ( lam @ A_27b
@ ^ [V4tx: $i] :
( lam @ A_27a
@ ^ [V5hx: $i] : ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V5hx ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V0f ) @ V4tx ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__THM,axiom,
! [A_27a: del,A_27b: del,A_27c: del] :
( ! [V0l: $i] :
( ( mem @ V0l @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0l )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) )
& ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27b ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( c_2Ellist_2ELNIL @ A_27b ) )
= ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27b ) ) )
& ! [V2n: tp__ty_2Enum_2Enum,V3h: $i] :
( ( mem @ V3h @ A_27c )
=> ! [V4t: $i] :
( ( mem @ V4t @ ( ty_2Ellist_2Ellist @ A_27c ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27c ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27c ) @ V3h ) @ V4t ) )
= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Elist_2Elist @ A_27c ) @ ( ty_2Elist_2Elist @ A_27c ) ) @ ( ap @ ( c_2Elist_2ECONS @ A_27c ) @ V3h ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V4t ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__SNOC__LNTH,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ V1ll )
= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ll ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V2l: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ll ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) )
@ ( lam @ A_27a
@ ^ [V3e: $i] : ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V2l ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V3e ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__EQ__NONE__LNTH,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ll )
= ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ll )
= ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__NIL__EQ__SOME,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1m: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( c_2Ellist_2ELNIL @ A_27a ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V0l ) )
<=> ( ( V1m = fo__c_2Enum_2E0 )
& ( V0l
= ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__NIL__EQ__NONE,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( c_2Ellist_2ELNIL @ A_27a ) )
= ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__EQ,axiom,
! [A_27a: del,V0ll1: $i] :
( ( mem @ V0ll1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1ll2: $i] :
( ( mem @ V1ll2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( V0ll1 = V1ll2 )
<=> ! [V2n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V0ll1 )
= ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V1ll2 ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__CONS__EQ__NONE,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1h: $i] :
( ( mem @ V1h @ A_27a )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ V2t ) )
= ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) )
<=> ? [V3n: tp__ty_2Enum_2Enum] :
( ( V0m
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
& ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V2t )
= ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__CONS__EQ__SOME,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1h: $i] :
( ( mem @ V1h @ A_27a )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ V2t ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V3l ) )
<=> ( ( ( V0m = fo__c_2Enum_2E0 )
& ( V3l
= ( c_2Elist_2ENIL @ A_27a ) ) )
| ? [V4n: tp__ty_2Enum_2Enum,V5l_27: $i] :
( ( mem @ V5l_27 @ ( ty_2Elist_2Elist @ A_27a ) )
& ( V0m
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) )
& ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) @ V2t )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V5l_27 ) )
& ( V3l
= ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V1h ) @ V5l_27 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__EQ__SOME__CONS,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V2x ) )
=> ! [V3h: $i] :
( ( mem @ V3h @ A_27a )
=> ? [V4y: $i] :
( ( mem @ V4y @ ( ty_2Elist_2Elist @ A_27a ) )
& ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V3h ) @ V1l ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V4y ) ) ) ) ) ) ) ).
thf(ax_thm_2Ellist_2ELMAP,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELMAP @ A_27a @ A_27b ) @ V0f ) @ ( c_2Ellist_2ELNIL @ A_27a ) )
= ( c_2Ellist_2ELNIL @ A_27b ) ) )
& ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
=> ! [V2h: $i] :
( ( mem @ V2h @ A_27a )
=> ! [V3t: $i] :
( ( mem @ V3t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELMAP @ A_27a @ A_27b ) @ V1f ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V2h ) @ V3t ) )
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ ( ap @ V1f @ V2h ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELMAP @ A_27a @ A_27b ) @ V1f ) @ V3t ) ) ) ) ) ) ) ).
thf(ax_thm_2Ellist_2ELAPPEND,axiom,
! [A_27a: del] :
( ! [V0x: $i] :
( ( mem @ V0x @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) @ V0x )
= V0x ) )
& ! [V1h: $i] :
( ( mem @ V1h @ A_27a )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V3x: $i] :
( ( mem @ V3x @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ V2t ) ) @ V3x )
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V2t ) @ V3x ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELMAP__APPEND,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1ll1: $i] :
( ( mem @ V1ll1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2ll2: $i] :
( ( mem @ V2ll2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELMAP @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V1ll1 ) @ V2ll2 ) )
= ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27b ) @ ( ap @ ( ap @ ( c_2Ellist_2ELMAP @ A_27a @ A_27b ) @ V0f ) @ V1ll1 ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELMAP @ A_27a @ A_27b ) @ V0f ) @ V2ll2 ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELAPPEND__EQ__LNIL,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V0l1 ) @ V1l2 )
= ( c_2Ellist_2ELNIL @ A_27a ) )
<=> ( ( V0l1
= ( c_2Ellist_2ELNIL @ A_27a ) )
& ( V1l2
= ( c_2Ellist_2ELNIL @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELAPPEND__ASSOC,axiom,
! [A_27a: del,V0ll1: $i] :
( ( mem @ V0ll1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1ll2: $i] :
( ( mem @ V1ll2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2ll3: $i] :
( ( mem @ V2ll3 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V0ll1 ) @ V1ll2 ) ) @ V2ll3 )
= ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V0ll1 ) @ ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V1ll2 ) @ V2ll3 ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELMAP__MAP,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27c @ A_27a ) )
=> ! [V2ll: $i] :
( ( mem @ V2ll @ ( ty_2Ellist_2Ellist @ A_27c ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELMAP @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Ellist_2ELMAP @ A_27c @ A_27a ) @ V1g ) @ V2ll ) )
= ( ap @ ( ap @ ( c_2Ellist_2ELMAP @ A_27c @ A_27b ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27c @ A_27b @ A_27a ) @ V0f ) @ V1g ) ) @ V2ll ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELAPPEND__NIL__2ND,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V0ll ) @ ( c_2Ellist_2ELNIL @ A_27a ) )
= V0ll ) ) ).
thf(conj_thm_2Ellist_2ELHD__LAPPEND,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V0l1 ) @ V1l2 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V0l1 ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) ) @ ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ V1l2 ) ) @ ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ V0l1 ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTL__LAPPEND,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V0l1 ) @ V1l2 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V0l1 ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) ) @ ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ V1l2 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ V0l1 ) ) ) @ V1l2 ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__LAPPEND1,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l1 ) ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V1l1 ) @ V2l2 ) )
= ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l1 ) ) ) ) ) ).
thf(ax_thm_2Ellist_2ELFINITE__def,axiom,
! [A_27a: del] :
( ( c_2Ellist_2ELFINITE @ A_27a )
= ( lam @ ( ty_2Ellist_2Ellist @ A_27a )
@ ^ [V0a0: $i] :
( ap @ ( c_2Ebool_2E_21 @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool ) )
@ ( lam @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool )
@ ^ [V1LFINITE_27: $i] :
( ap
@ ( ap @ c_2Emin_2E_3D_3D_3E
@ ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Ellist_2Ellist @ A_27a ) )
@ ( lam @ ( ty_2Ellist_2Ellist @ A_27a )
@ ^ [V2a0: $i] :
( ap
@ ( ap @ c_2Emin_2E_3D_3D_3E
@ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V2a0 ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) )
@ ( ap @ ( c_2Ebool_2E_3F @ A_27a )
@ ( lam @ A_27a
@ ^ [V3h: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( ty_2Ellist_2Ellist @ A_27a ) )
@ ( lam @ ( ty_2Ellist_2Ellist @ A_27a )
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V2a0 ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V3h ) @ V4t ) ) ) @ ( ap @ V1LFINITE_27 @ V4t ) ) ) ) ) ) ) )
@ ( ap @ V1LFINITE_27 @ V2a0 ) ) ) ) )
@ ( ap @ V1LFINITE_27 @ V0a0 ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__rules,axiom,
! [A_27a: del] :
( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) )
& ! [V0h: $i] :
( ( mem @ V0h @ A_27a )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V1t ) )
=> ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V0h ) @ V1t ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__ind,axiom,
! [A_27a: del,V0LFINITE_27: $i] :
( ( mem @ V0LFINITE_27 @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool ) )
=> ( ( ( p @ ( ap @ V0LFINITE_27 @ ( c_2Ellist_2ELNIL @ A_27a ) ) )
& ! [V1h: $i] :
( ( mem @ V1h @ A_27a )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ V0LFINITE_27 @ V2t ) )
=> ( p @ ( ap @ V0LFINITE_27 @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ V2t ) ) ) ) ) ) )
=> ! [V3a0: $i] :
( ( mem @ V3a0 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V3a0 ) )
=> ( p @ ( ap @ V0LFINITE_27 @ V3a0 ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__strongind,axiom,
! [A_27a: del,V0LFINITE_27: $i] :
( ( mem @ V0LFINITE_27 @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool ) )
=> ( ( ( p @ ( ap @ V0LFINITE_27 @ ( c_2Ellist_2ELNIL @ A_27a ) ) )
& ! [V1h: $i] :
( ( mem @ V1h @ A_27a )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V2t ) )
& ( p @ ( ap @ V0LFINITE_27 @ V2t ) ) )
=> ( p @ ( ap @ V0LFINITE_27 @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ V2t ) ) ) ) ) ) )
=> ! [V3a0: $i] :
( ( mem @ V3a0 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V3a0 ) )
=> ( p @ ( ap @ V0LFINITE_27 @ V3a0 ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__cases,axiom,
! [A_27a: del,V0a0: $i] :
( ( mem @ V0a0 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V0a0 ) )
<=> ( ( V0a0
= ( c_2Ellist_2ELNIL @ A_27a ) )
| ? [V1h: $i] :
( ( mem @ V1h @ A_27a )
& ? [V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ A_27a ) )
& ( V0a0
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ V2t ) )
& ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V2t ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__THM,axiom,
! [A_27a: del,A_27b: del] :
( ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) )
<=> $true )
& ! [V0h: $i] :
( ( mem @ V0h @ A_27b )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Ellist_2Ellist @ A_27b ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27b ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V0h ) @ V1t ) ) )
<=> ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27b ) @ V1t ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V0ll ) )
<=> ? [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V0ll )
= ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ).
thf(ax_thm_2Ellist_2Ellength__rel__def,axiom,
! [A_27a: del] :
( ( c_2Ellist_2Ellength__rel @ A_27a )
= ( lam @ ( ty_2Ellist_2Ellist @ A_27a )
@ ^ [V0a0: $i] :
( lam @ ty_2Enum_2Enum
@ ^ [V1a1: $i] :
( ap @ ( c_2Ebool_2E_21 @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) )
@ ( lam @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ bool ) )
@ ^ [V2llength__rel_27: $i] :
( ap
@ ( ap @ c_2Emin_2E_3D_3D_3E
@ ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Ellist_2Ellist @ A_27a ) )
@ ( lam @ ( ty_2Ellist_2Ellist @ A_27a )
@ ^ [V3a0: $i] :
( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4a1: $i] :
( ap
@ ( ap @ c_2Emin_2E_3D_3D_3E
@ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V3a0 ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V4a1 ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
@ ( ap @ ( c_2Ebool_2E_3F @ A_27a )
@ ( lam @ A_27a
@ ^ [V5h: $i] :
( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6n: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( ty_2Ellist_2Ellist @ A_27a ) )
@ ( lam @ ( ty_2Ellist_2Ellist @ A_27a )
@ ^ [V7t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V3a0 ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V5h ) @ V7t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V4a1 ) @ ( ap @ c_2Enum_2ESUC @ V6n ) ) ) @ ( ap @ ( ap @ V2llength__rel_27 @ V7t ) @ V6n ) ) ) ) ) ) ) ) ) ) )
@ ( ap @ ( ap @ V2llength__rel_27 @ V3a0 ) @ V4a1 ) ) ) ) ) ) )
@ ( ap @ ( ap @ V2llength__rel_27 @ V0a0 ) @ V1a1 ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Ellength__rel__rules,axiom,
! [A_27a: del] :
( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Ellength__rel @ A_27a ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V0h: $i] :
( ( mem @ V0h @ A_27a )
=> ! [V1n: tp__ty_2Enum_2Enum,V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Ellength__rel @ A_27a ) @ V2t ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ellist_2Ellength__rel @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V0h ) @ V2t ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Ellength__rel__ind,axiom,
! [A_27a: del,V0llength__rel_27: $i] :
( ( mem @ V0llength__rel_27 @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) )
=> ( ( ( p @ ( ap @ ( ap @ V0llength__rel_27 @ ( c_2Ellist_2ELNIL @ A_27a ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V1h: $i] :
( ( mem @ V1h @ A_27a )
=> ! [V2n: tp__ty_2Enum_2Enum,V3t: $i] :
( ( mem @ V3t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ V0llength__rel_27 @ V3t ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
=> ( p @ ( ap @ ( ap @ V0llength__rel_27 @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ V3t ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) )
=> ! [V4a0: $i] :
( ( mem @ V4a0 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V5a1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Ellength__rel @ A_27a ) @ V4a0 ) @ ( inj__ty_2Enum_2Enum @ V5a1 ) ) )
=> ( p @ ( ap @ ( ap @ V0llength__rel_27 @ V4a0 ) @ ( inj__ty_2Enum_2Enum @ V5a1 ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Ellength__rel__strongind,axiom,
! [A_27a: del,V0llength__rel_27: $i] :
( ( mem @ V0llength__rel_27 @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) )
=> ( ( ( p @ ( ap @ ( ap @ V0llength__rel_27 @ ( c_2Ellist_2ELNIL @ A_27a ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V1h: $i] :
( ( mem @ V1h @ A_27a )
=> ! [V2n: tp__ty_2Enum_2Enum,V3t: $i] :
( ( mem @ V3t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Ellength__rel @ A_27a ) @ V3t ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
& ( p @ ( ap @ ( ap @ V0llength__rel_27 @ V3t ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
=> ( p @ ( ap @ ( ap @ V0llength__rel_27 @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ V3t ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) )
=> ! [V4a0: $i] :
( ( mem @ V4a0 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V5a1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Ellength__rel @ A_27a ) @ V4a0 ) @ ( inj__ty_2Enum_2Enum @ V5a1 ) ) )
=> ( p @ ( ap @ ( ap @ V0llength__rel_27 @ V4a0 ) @ ( inj__ty_2Enum_2Enum @ V5a1 ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Ellength__rel__cases,axiom,
! [A_27a: del,V0a0: $i] :
( ( mem @ V0a0 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1a1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Ellength__rel @ A_27a ) @ V0a0 ) @ ( inj__ty_2Enum_2Enum @ V1a1 ) ) )
<=> ( ( ( V0a0
= ( c_2Ellist_2ELNIL @ A_27a ) )
& ( V1a1 = fo__c_2Enum_2E0 ) )
| ? [V2h: $i] :
( ( mem @ V2h @ A_27a )
& ? [V3n: tp__ty_2Enum_2Enum,V4t: $i] :
( ( mem @ V4t @ ( ty_2Ellist_2Ellist @ A_27a ) )
& ( V0a0
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V2h ) @ V4t ) )
& ( V1a1
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ellist_2Ellength__rel @ A_27a ) @ V4t ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ellist_2ELLENGTH,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V0ll ) )
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum
@ ( ap
@ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) ) @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V0ll ) )
@ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum )
@ ( ap @ ( c_2Emin_2E_40 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1n: $i] : ( ap @ ( ap @ ( c_2Ellist_2Ellength__rel @ A_27a ) @ V0ll ) @ V1n ) ) ) ) )
@ ( c_2Eoption_2ENONE @ ty_2Enum_2Enum ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELLENGTH__THM,axiom,
! [A_27a: del,A_27b: del] :
( ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) )
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ! [V0h: $i] :
( ( mem @ V0h @ A_27b )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Ellist_2Ellist @ A_27b ) )
=> ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27b ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V0h ) @ V1t ) ) )
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ c_2Enum_2ESUC ) @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27b ) @ V1t ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELLENGTH__0,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V0x ) )
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
<=> ( V0x
= ( c_2Ellist_2ELNIL @ A_27a ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__HAS__LENGTH,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V0ll ) )
=> ? [V1n: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V0ll ) )
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ENOT__LFINITE__NO__LENGTH,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ~ ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V0ll ) )
=> ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V0ll ) )
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( c_2Eoption_2ENONE @ ty_2Enum_2Enum ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__LLENGTH,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V0ll ) )
<=> ? [V1n: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V0ll ) )
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__INDUCTION,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool ) )
=> ( ( ( p @ ( ap @ V0P @ ( c_2Ellist_2ELNIL @ A_27a ) ) )
& ! [V1h: $i] :
( ( mem @ V1h @ A_27a )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ V0P @ V2t ) )
=> ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ V2t ) ) ) ) ) ) )
=> ! [V3a0: $i] :
( ( mem @ V3a0 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V3a0 ) )
=> ( p @ ( ap @ V0P @ V3a0 ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__STRONG__INDUCTION,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool ) )
=> ( ( ( p @ ( ap @ V0P @ ( c_2Ellist_2ELNIL @ A_27a ) ) )
& ! [V1h: $i] :
( ( mem @ V1h @ A_27a )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V2t ) )
& ( p @ ( ap @ V0P @ V2t ) ) )
=> ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ V2t ) ) ) ) ) ) )
=> ! [V3a0: $i] :
( ( mem @ V3a0 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V3a0 ) )
=> ( p @ ( ap @ V0P @ V3a0 ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__MAP,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27b ) @ ( ap @ ( ap @ ( c_2Ellist_2ELMAP @ A_27a @ A_27b ) @ V0f ) @ V1ll ) ) )
<=> ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V1ll ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__APPEND,axiom,
! [A_27a: del,V0ll1: $i] :
( ( mem @ V0ll1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1ll2: $i] :
( ( mem @ V1ll2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V0ll1 ) @ V1ll2 ) ) )
<=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V0ll1 ) )
& ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V1ll2 ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__LNTH__EL,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2m: tp__ty_2Enum_2Enum,V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V3l ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ V1ll )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ V3l ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ENOT__LFINITE__APPEND,axiom,
! [A_27a: del,V0ll1: $i] :
( ( mem @ V0ll1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1ll2: $i] :
( ( mem @ V1ll2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ~ ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V0ll1 ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V0ll1 ) @ V1ll2 )
= V0ll1 ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__LAPPEND__IMP__NIL,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V0ll ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V0ll ) @ V1l2 )
= V0ll )
=> ( V1l2
= ( c_2Ellist_2ELNIL @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELLENGTH__MAP,axiom,
! [A_27a: del,A_27b: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
=> ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27b ) @ ( ap @ ( ap @ ( c_2Ellist_2ELMAP @ A_27a @ A_27b ) @ V1f ) @ V0ll ) ) )
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V0ll ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELLENGTH__APPEND,axiom,
! [A_27a: del,V0ll1: $i] :
( ( mem @ V0ll1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1ll2: $i] :
( ( mem @ V1ll2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V0ll1 ) @ V1ll2 ) ) )
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V0ll1 ) ) @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V1ll2 ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Eoption_2ETHE @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V0ll1 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V1ll2 ) ) ) ) ) @ ( c_2Eoption_2ENONE @ ty_2Enum_2Enum ) ) ) ) ) ) ).
thf(ax_thm_2Ellist_2EtoList,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2EtoList @ A_27a ) @ V0ll )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V0ll ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( ap @ ( c_2Eoption_2ETHE @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V0ll ) ) ) @ V0ll ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Ellist_2EtoList__THM,axiom,
! [A_27a: del,A_27b: del] :
( ( ( ap @ ( c_2Ellist_2EtoList @ A_27a ) @ ( c_2Ellist_2ELNIL @ A_27a ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) )
& ! [V0h: $i] :
( ( mem @ V0h @ A_27b )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Ellist_2Ellist @ A_27b ) )
=> ( ( ap @ ( c_2Ellist_2EtoList @ A_27b ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V0h ) @ V1t ) )
= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Elist_2Elist @ A_27b ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( ap @ ( c_2Elist_2ECONS @ A_27b ) @ V0h ) ) @ ( ap @ ( c_2Ellist_2EtoList @ A_27b ) @ V1t ) ) ) ) ) ) ).
thf(ax_thm_2Ellist_2EfromList__def,axiom,
! [A_27a: del] :
( ( ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) )
= ( c_2Ellist_2ELNIL @ A_27a ) )
& ! [V0h: $i] :
( ( mem @ V0h @ A_27a )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V0h ) @ V1t ) )
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V0h ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ V1t ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2EfromList__EQ__LNIL,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ V0l )
= ( c_2Ellist_2ELNIL @ A_27a ) )
<=> ( V0l
= ( c_2Elist_2ENIL @ A_27a ) ) ) ) ).
thf(conj_thm_2Ellist_2ELHD__fromList,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ V0l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( c_2Elist_2ENULL @ A_27a ) @ V0l ) ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ ( c_2Elist_2EHD @ A_27a ) @ V0l ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTL__fromList,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ V0l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) @ ( ap @ ( c_2Elist_2ENULL @ A_27a ) @ V0l ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ ( ap @ ( c_2Elist_2ETL @ A_27a ) @ V0l ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__fromList,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ V0l ) ) ) ) ).
thf(conj_thm_2Ellist_2ELLENGTH__fromList,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ V0l ) ) )
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__fromList,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ V0l ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V0l ) ) ) ).
thf(conj_thm_2Ellist_2Efrom__toList,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2EtoList @ A_27a ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ V0l ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V0l ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__toList,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V0ll ) )
=> ? [V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
& ( ( ap @ ( c_2Ellist_2EtoList @ A_27a ) @ V0ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__toList__SOME,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V0ll ) )
<=> ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( c_2Ellist_2EtoList @ A_27a ) @ V0ll ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Eto__fromList,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V0ll ) )
=> ( ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( c_2Ellist_2EtoList @ A_27a ) @ V0ll ) ) )
= V0ll ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__LAPPEND2,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l1 )
= ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V1l1 ) @ V2l2 ) )
= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( c_2Ellist_2EtoList @ A_27a ) @ V1l1 ) ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Eoption_2ETHE @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V1l1 ) ) ) ) @ V2l2 ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELNTH__fromList,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ V1l ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) @ ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ).
thf(conj_thm_2Ellist_2Elnth__fromList__some,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1l ) ) )
<=> ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ V1l ) )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ) ).
thf(ax_thm_2Ellist_2ELDROP,axiom,
! [A_27a: del] :
( ! [V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V0ll ) ) )
& ! [V1n: tp__ty_2Enum_2Enum,V2ll: $i] :
( ( mem @ V2ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ V2ll )
= ( ap @ ( c_2Eoption_2EOPTION__JOIN @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Eoption_2Eoption @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ V2ll ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELDROP__FUNPOW,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ll )
= ( ap
@ ( ap
@ ( ap @ ( c_2Earithmetic_2EFUNPOW @ ( ty_2Eoption_2Eoption @ ( ty_2Ellist_2Ellist @ A_27a ) ) )
@ ( lam @ ( ty_2Eoption_2Eoption @ ( ty_2Ellist_2Ellist @ A_27a ) )
@ ^ [V2m: $i] : ( ap @ ( ap @ ( c_2Eoption_2EOPTION__BIND @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V2m ) @ ( c_2Ellist_2ELTL @ A_27a ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V0n ) )
@ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V1ll ) ) ) ) ).
thf(conj_thm_2Ellist_2ELDROP__THM,axiom,
! [A_27a: del,A_27b: del,A_27c: del] :
( ! [V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V0ll ) ) )
& ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27b ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( c_2Ellist_2ELNIL @ A_27b ) )
= ( c_2Eoption_2ENONE @ ( ty_2Ellist_2Ellist @ A_27b ) ) )
& ! [V2n: tp__ty_2Enum_2Enum,V3h: $i] :
( ( mem @ V3h @ A_27c )
=> ! [V4t: $i] :
( ( mem @ V4t @ ( ty_2Ellist_2Ellist @ A_27c ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27c ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27c ) @ V3h ) @ V4t ) )
= ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V4t ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELDROP1__THM,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Ellist_2ELTL @ A_27a ) ) ).
thf(conj_thm_2Ellist_2ELNTH__HD__LDROP,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ll )
= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__BIND @ A_27a @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ll ) ) @ ( c_2Ellist_2ELHD @ A_27a ) ) ) ) ).
thf(conj_thm_2Ellist_2ENOT__LFINITE__TAKE,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ~ ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V0ll ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
? [V2y: $i] :
( ( mem @ V2y @ ( ty_2Elist_2Elist @ A_27a ) )
& ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V0ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V2y ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__TAKE,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V1ll ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Eoption_2ETHE @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V1ll ) ) ) ) )
=> ? [V2y: $i] :
( ( mem @ V2y @ ( ty_2Elist_2Elist @ A_27a ) )
& ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V2y ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ENOT__LFINITE__DROP,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ~ ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V0ll ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
? [V2y: $i] :
( ( mem @ V2y @ ( ty_2Ellist_2Ellist @ A_27a ) )
& ( ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V0ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V2y ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__DROP,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V1ll ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Eoption_2ETHE @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V1ll ) ) ) ) )
=> ? [V2y: $i] :
( ( mem @ V2y @ ( ty_2Ellist_2Ellist @ A_27a ) )
& ( ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V2y ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__DROP,axiom,
! [A_27a: del] :
( ! [V0n: tp__ty_2Enum_2Enum,V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ~ ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V1ll ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ll ) ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ll ) ) )
= V1ll ) ) )
& ! [V2n: tp__ty_2Enum_2Enum,V3ll: $i] :
( ( mem @ V3ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V3ll ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( c_2Eoption_2ETHE @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V3ll ) ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V3ll ) ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V3ll ) ) )
= V3ll ) ) ) ) ).
thf(conj_thm_2Ellist_2ELDROP__ADD,axiom,
! [A_27a: del,V0k1: tp__ty_2Enum_2Enum,V1k2: tp__ty_2Enum_2Enum,V2x: $i] :
( ( mem @ V2x @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0k1 ) ) @ ( inj__ty_2Enum_2Enum @ V1k2 ) ) ) @ V2x )
= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Eoption_2Eoption @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0k1 ) ) @ V2x ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Ellist_2Ellist @ A_27a ) ) )
@ ( lam @ ( ty_2Ellist_2Ellist @ A_27a )
@ ^ [V3ll: $i] : ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1k2 ) ) @ V3ll ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELDROP__SOME__LLENGTH,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V3m: tp__ty_2Enum_2Enum] :
( ( ( ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V2l ) )
& ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V1ll ) )
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) )
& ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V2l ) )
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V3m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__LNTH__NONE,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V0ll ) )
<=> ? [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V0ll )
= ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ).
thf(conj_thm_2Ellist_2Einfinite__lnth__some,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ~ ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V0ll ) )
<=> ! [V1n: tp__ty_2Enum_2Enum] :
? [V2x: $i] :
( ( mem @ V2x @ A_27a )
& ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V0ll )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2x ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELNTH__LAPPEND,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V1l1 ) @ V2l2 ) )
= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V1l1 ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l1 ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3m: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V3m ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l1 ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V3m ) ) @ V2l2 ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELNTH__ADD,axiom,
! [A_27a: del,V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum,V2ll: $i] :
( ( mem @ V2ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) @ V2ll )
= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__BIND @ A_27a @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ V2ll ) ) @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Elnth__some__down__closed,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2n1: tp__ty_2Enum_2Enum,V3n2: tp__ty_2Enum_2Enum] :
( ( ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n1 ) ) @ V0ll )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3n2 ) ) @ ( inj__ty_2Enum_2Enum @ V2n1 ) ) ) )
=> ? [V4y: $i] :
( ( mem @ V4y @ A_27a )
& ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V3n2 ) ) @ V0ll )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V4y ) ) ) ) ) ) ).
thf(ax_thm_2Ellist_2Eexists__def,axiom,
! [A_27a: del] :
( ( c_2Ellist_2Eexists @ A_27a )
= ( lam @ ( arr @ A_27a @ bool )
@ ^ [V0P: $i] :
( lam @ ( ty_2Ellist_2Ellist @ A_27a )
@ ^ [V1a0: $i] :
( ap @ ( c_2Ebool_2E_21 @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool ) )
@ ( lam @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool )
@ ^ [V2exists_27: $i] :
( ap
@ ( ap @ c_2Emin_2E_3D_3D_3E
@ ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Ellist_2Ellist @ A_27a ) )
@ ( lam @ ( ty_2Ellist_2Ellist @ A_27a )
@ ^ [V3a0: $i] :
( ap
@ ( ap @ c_2Emin_2E_3D_3D_3E
@ ( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ ( c_2Ebool_2E_3F @ A_27a )
@ ( lam @ A_27a
@ ^ [V4h: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( ty_2Ellist_2Ellist @ A_27a ) )
@ ( lam @ ( ty_2Ellist_2Ellist @ A_27a )
@ ^ [V5t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V3a0 ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V4h ) @ V5t ) ) ) @ ( ap @ V0P @ V4h ) ) ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_3F @ A_27a )
@ ( lam @ A_27a
@ ^ [V6h: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( ty_2Ellist_2Ellist @ A_27a ) )
@ ( lam @ ( ty_2Ellist_2Ellist @ A_27a )
@ ^ [V7t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V3a0 ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V6h ) @ V7t ) ) ) @ ( ap @ V2exists_27 @ V7t ) ) ) ) ) ) ) )
@ ( ap @ V2exists_27 @ V3a0 ) ) ) ) )
@ ( ap @ V2exists_27 @ V1a0 ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Eexists__rules,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ( ! [V1h: $i] :
( ( mem @ V1h @ A_27a )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ V0P @ V1h ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ V0P ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ V2t ) ) ) ) ) )
& ! [V3h: $i] :
( ( mem @ V3h @ A_27a )
=> ! [V4t: $i] :
( ( mem @ V4t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ V0P ) @ V4t ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ V0P ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V3h ) @ V4t ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Eexists__ind,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1exists_27: $i] :
( ( mem @ V1exists_27 @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool ) )
=> ( ( ! [V2h: $i] :
( ( mem @ V2h @ A_27a )
=> ! [V3t: $i] :
( ( mem @ V3t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ V0P @ V2h ) )
=> ( p @ ( ap @ V1exists_27 @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V2h ) @ V3t ) ) ) ) ) )
& ! [V4h: $i] :
( ( mem @ V4h @ A_27a )
=> ! [V5t: $i] :
( ( mem @ V5t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ V1exists_27 @ V5t ) )
=> ( p @ ( ap @ V1exists_27 @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V4h ) @ V5t ) ) ) ) ) ) )
=> ! [V6a0: $i] :
( ( mem @ V6a0 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ V0P ) @ V6a0 ) )
=> ( p @ ( ap @ V1exists_27 @ V6a0 ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Eexists__strongind,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1exists_27: $i] :
( ( mem @ V1exists_27 @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool ) )
=> ( ( ! [V2h: $i] :
( ( mem @ V2h @ A_27a )
=> ! [V3t: $i] :
( ( mem @ V3t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ V0P @ V2h ) )
=> ( p @ ( ap @ V1exists_27 @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V2h ) @ V3t ) ) ) ) ) )
& ! [V4h: $i] :
( ( mem @ V4h @ A_27a )
=> ! [V5t: $i] :
( ( mem @ V5t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ V0P ) @ V5t ) )
& ( p @ ( ap @ V1exists_27 @ V5t ) ) )
=> ( p @ ( ap @ V1exists_27 @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V4h ) @ V5t ) ) ) ) ) ) )
=> ! [V6a0: $i] :
( ( mem @ V6a0 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ V0P ) @ V6a0 ) )
=> ( p @ ( ap @ V1exists_27 @ V6a0 ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Eexists__cases,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1a0: $i] :
( ( mem @ V1a0 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ V0P ) @ V1a0 ) )
<=> ( ? [V2h: $i] :
( ( mem @ V2h @ A_27a )
& ? [V3t: $i] :
( ( mem @ V3t @ ( ty_2Ellist_2Ellist @ A_27a ) )
& ( V1a0
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V2h ) @ V3t ) )
& ( p @ ( ap @ V0P @ V2h ) ) ) )
| ? [V4h: $i] :
( ( mem @ V4h @ A_27a )
& ? [V5t: $i] :
( ( mem @ V5t @ ( ty_2Ellist_2Ellist @ A_27a ) )
& ( V1a0
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V4h ) @ V5t ) )
& ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ V0P ) @ V5t ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Eexists__thm,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1h: $i] :
( ( mem @ V1h @ A_27a )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ V0P ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) )
<=> $false )
& ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ V0P ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ V2t ) ) )
<=> ( ( p @ ( ap @ V0P @ V1h ) )
| ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ V0P ) @ V2t ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Eexists__LNTH,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ V0P ) @ V1l ) )
<=> ? [V2n: tp__ty_2Enum_2Enum,V3e: $i] :
( ( mem @ V3e @ A_27a )
& ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3e )
= ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V1l ) )
& ( p @ ( ap @ V0P @ V3e ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2EMONO__exists,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ( ( p @ ( ap @ V0P @ V3x ) )
=> ( p @ ( ap @ V1Q @ V3x ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ V0P ) @ V2l ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ V1Q ) @ V2l ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Eexists__strong__ind,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool ) )
=> ( ( ! [V2h: $i] :
( ( mem @ V2h @ A_27a )
=> ! [V3t: $i] :
( ( mem @ V3t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ V0P @ V2h ) )
=> ( p @ ( ap @ V1Q @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V2h ) @ V3t ) ) ) ) ) )
& ! [V4h: $i] :
( ( mem @ V4h @ A_27a )
=> ! [V5t: $i] :
( ( mem @ V5t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( p @ ( ap @ V1Q @ V5t ) )
& ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ V0P ) @ V5t ) ) )
=> ( p @ ( ap @ V1Q @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V4h ) @ V5t ) ) ) ) ) ) )
=> ! [V6a0: $i] :
( ( mem @ V6a0 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ V0P ) @ V6a0 ) )
=> ( p @ ( ap @ V1Q @ V6a0 ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Eexists__LDROP,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ V0P ) @ V1ll ) )
<=> ? [V2n: tp__ty_2Enum_2Enum,V3a: $i] :
( ( mem @ V3a @ A_27a )
& ? [V4t: $i] :
( ( mem @ V4t @ ( ty_2Ellist_2Ellist @ A_27a ) )
& ( ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V1ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V3a ) @ V4t ) ) )
& ( p @ ( ap @ V0P @ V3a ) ) ) ) ) ) ) ).
thf(ax_thm_2Ellist_2Eevery__def,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eevery @ A_27a ) @ V0P ) @ V1ll ) )
<=> ~ ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ bool @ bool ) @ c_2Ebool_2E_7E ) @ V0P ) ) @ V1ll ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Eevery__coind,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool ) )
=> ( ! [V2h: $i] :
( ( mem @ V2h @ A_27a )
=> ! [V3t: $i] :
( ( mem @ V3t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ V1Q @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V2h ) @ V3t ) ) )
=> ( ( p @ ( ap @ V0P @ V2h ) )
& ( p @ ( ap @ V1Q @ V3t ) ) ) ) ) )
=> ! [V4ll: $i] :
( ( mem @ V4ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ V1Q @ V4ll ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eevery @ A_27a ) @ V0P ) @ V4ll ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Eevery__thm,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1h: $i] :
( ( mem @ V1h @ A_27a )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eevery @ A_27a ) @ V0P ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) )
<=> $true )
& ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eevery @ A_27a ) @ V0P ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ V2t ) ) )
<=> ( ( p @ ( ap @ V0P @ V1h ) )
& ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eevery @ A_27a ) @ V0P ) @ V2t ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELL__ALL__THM,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1h: $i] :
( ( mem @ V1h @ A_27a )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eevery @ A_27a ) @ V0P ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) )
<=> $true )
& ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eevery @ A_27a ) @ V0P ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ V2t ) ) )
<=> ( ( p @ ( ap @ V0P @ V1h ) )
& ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eevery @ A_27a ) @ V0P ) @ V2t ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2EMONO__every,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ( ( p @ ( ap @ V0P @ V3x ) )
=> ( p @ ( ap @ V1Q @ V3x ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eevery @ A_27a ) @ V0P ) @ V2l ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eevery @ A_27a ) @ V1Q ) @ V2l ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Eevery__strong__coind,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ ( arr @ ( ty_2Ellist_2Ellist @ A_27a ) @ bool ) )
=> ( ( ! [V2h: $i] :
( ( mem @ V2h @ A_27a )
=> ! [V3t: $i] :
( ( mem @ V3t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ V1Q @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V2h ) @ V3t ) ) )
=> ( p @ ( ap @ V0P @ V2h ) ) ) ) )
& ! [V4h: $i] :
( ( mem @ V4h @ A_27a )
=> ! [V5t: $i] :
( ( mem @ V5t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ V1Q @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V4h ) @ V5t ) ) )
=> ( ( p @ ( ap @ V1Q @ V5t ) )
| ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eevery @ A_27a ) @ V0P ) @ V5t ) ) ) ) ) ) )
=> ! [V6ll: $i] :
( ( mem @ V6ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ V1Q @ V6ll ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eevery @ A_27a ) @ V0P ) @ V6ll ) ) ) ) ) ) ) ).
thf(ax_thm_2Ellist_2ELFILTER,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELFILTER @ A_27a ) @ V0P ) @ V1ll )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Ellist_2Eexists @ A_27a ) @ V0P ) @ V1ll ) ) ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ V0P @ ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ V1ll ) ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ V1ll ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELFILTER @ A_27a ) @ V0P ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ V1ll ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELFILTER @ A_27a ) @ V0P ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ V1ll ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFILTER__THM,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELFILTER @ A_27a ) @ V0P ) @ ( c_2Ellist_2ELNIL @ A_27a ) )
= ( c_2Ellist_2ELNIL @ A_27a ) ) )
& ! [V1P: $i] :
( ( mem @ V1P @ ( arr @ A_27b @ bool ) )
=> ! [V2h: $i] :
( ( mem @ V2h @ A_27b )
=> ! [V3t: $i] :
( ( mem @ V3t @ ( ty_2Ellist_2Ellist @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELFILTER @ A_27b ) @ V1P ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V2h ) @ V3t ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Ellist_2Ellist @ A_27b ) ) @ ( ap @ V1P @ V2h ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V2h ) @ ( ap @ ( ap @ ( c_2Ellist_2ELFILTER @ A_27b ) @ V1P ) @ V3t ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELFILTER @ A_27b ) @ V1P ) @ V3t ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFILTER__NIL,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eevery @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ bool @ bool ) @ c_2Ebool_2E_7E ) @ V0P ) ) @ V1ll ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELFILTER @ A_27a ) @ V0P ) @ V1ll )
= ( c_2Ellist_2ELNIL @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFILTER__EQ__NIL,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELFILTER @ A_27a ) @ V0P ) @ V1ll )
= ( c_2Ellist_2ELNIL @ A_27a ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eevery @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27a @ bool @ bool ) @ c_2Ebool_2E_7E ) @ V0P ) ) @ V1ll ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFILTER__APPEND,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1ll1: $i] :
( ( mem @ V1ll1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2ll2: $i] :
( ( mem @ V2ll2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V1ll1 ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELFILTER @ A_27a ) @ V0P ) @ ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V1ll1 ) @ V2ll2 ) )
= ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELFILTER @ A_27a ) @ V0P ) @ V1ll1 ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELFILTER @ A_27a ) @ V0P ) @ V2ll2 ) ) ) ) ) ) ) ).
thf(ax_thm_2Ellist_2ELFLATTEN,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ ( ty_2Ellist_2Ellist @ A_27a ) ) )
=> ( ( ap @ ( c_2Ellist_2ELFLATTEN @ A_27a ) @ V0ll )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2Eevery @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) ) @ V0ll ) ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( c_2Ellist_2ELHD @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V0ll ) ) ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) ) @ ( ap @ ( c_2Ellist_2ELFLATTEN @ A_27a ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Ellist_2Ellist @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) @ ( ap @ ( c_2Ellist_2ELTL @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V0ll ) ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( c_2Ellist_2ELHD @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V0ll ) ) ) ) ) @ ( ap @ ( c_2Ellist_2ELFLATTEN @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( c_2Ellist_2ELHD @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V0ll ) ) ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Ellist_2Ellist @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) @ ( ap @ ( c_2Ellist_2ELTL @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V0ll ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFLATTEN__THM,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Ellist_2Ellist @ ( ty_2Ellist_2Ellist @ A_27c ) ) )
=> ( ( ( ap @ ( c_2Ellist_2ELFLATTEN @ A_27a ) @ ( c_2Ellist_2ELNIL @ ( ty_2Ellist_2Ellist @ A_27a ) ) )
= ( c_2Ellist_2ELNIL @ A_27a ) )
& ! [V1tl: $i] :
( ( mem @ V1tl @ A_27b )
=> ( ( ap @ ( c_2Ellist_2ELFLATTEN @ A_27c ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ ( ty_2Ellist_2Ellist @ A_27c ) ) @ ( c_2Ellist_2ELNIL @ A_27c ) ) @ V0t ) )
= ( ap @ ( c_2Ellist_2ELFLATTEN @ A_27c ) @ V0t ) ) )
& ! [V2h: $i] :
( ( mem @ V2h @ A_27d )
=> ! [V3t: $i] :
( ( mem @ V3t @ ( ty_2Ellist_2Ellist @ A_27d ) )
=> ! [V4tl: $i] :
( ( mem @ V4tl @ ( ty_2Ellist_2Ellist @ ( ty_2Ellist_2Ellist @ A_27d ) ) )
=> ( ( ap @ ( c_2Ellist_2ELFLATTEN @ A_27d ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ ( ty_2Ellist_2Ellist @ A_27d ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27d ) @ V2h ) @ V3t ) ) @ V4tl ) )
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27d ) @ V2h ) @ ( ap @ ( c_2Ellist_2ELFLATTEN @ A_27d ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ ( ty_2Ellist_2Ellist @ A_27d ) ) @ V3t ) @ V4tl ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFLATTEN__APPEND,axiom,
! [A_27a: del,V0h: $i] :
( ( mem @ V0h @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Ellist_2Ellist @ ( ty_2Ellist_2Ellist @ A_27a ) ) )
=> ( ( ap @ ( c_2Ellist_2ELFLATTEN @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V0h ) @ V1t ) )
= ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V0h ) @ ( ap @ ( c_2Ellist_2ELFLATTEN @ A_27a ) @ V1t ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFLATTEN__EQ__NIL,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ ( ty_2Ellist_2Ellist @ A_27a ) ) )
=> ( ( ( ap @ ( c_2Ellist_2ELFLATTEN @ A_27a ) @ V0ll )
= ( c_2Ellist_2ELNIL @ A_27a ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ellist_2Eevery @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) ) @ V0ll ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFLATTEN__SINGLETON,axiom,
! [A_27a: del,V0h: $i] :
( ( mem @ V0h @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELFLATTEN @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V0h ) @ ( c_2Ellist_2ELNIL @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) )
= V0h ) ) ).
thf(ax_thm_2Ellist_2ELZIP__THM,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELZIP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27b ) ) @ V0l1 ) @ ( c_2Ellist_2ELNIL @ A_27b ) ) )
= ( c_2Ellist_2ELNIL @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) )
& ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Ellist_2Ellist @ A_27b ) )
=> ( ( ap @ ( c_2Ellist_2ELZIP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) @ V1l2 ) )
= ( c_2Ellist_2ELNIL @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) )
& ! [V2h1: $i] :
( ( mem @ V2h1 @ A_27a )
=> ! [V3h2: $i] :
( ( mem @ V3h2 @ A_27b )
=> ! [V4t1: $i] :
( ( mem @ V4t1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V5t2: $i] :
( ( mem @ V5t2 @ ( ty_2Ellist_2Ellist @ A_27b ) )
=> ( ( ap @ ( c_2Ellist_2ELZIP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V2h1 ) @ V4t1 ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V3h2 ) @ V5t2 ) ) )
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V2h1 ) @ V3h2 ) ) @ ( ap @ ( c_2Ellist_2ELZIP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27b ) ) @ V4t1 ) @ V5t2 ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ellist_2ELUNZIP__THM,axiom,
! [A_27a: del,A_27b: del] :
( ( ( ap @ ( c_2Ellist_2ELUNZIP @ A_27a @ A_27b ) @ ( c_2Ellist_2ELNIL @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
= ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) @ ( c_2Ellist_2ELNIL @ A_27b ) ) )
& ! [V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1y: $i] :
( ( mem @ V1y @ A_27b )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( ( ap @ ( c_2Ellist_2ELUNZIP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V0x ) @ V1y ) ) @ V2t ) )
= ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27b ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27b ) ) )
@ ( ap @ ( c_2Epair_2EUNCURRY @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27b ) @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27b ) ) )
@ ( lam @ ( ty_2Ellist_2Ellist @ A_27a )
@ ^ [V3ll1: $i] :
( lam @ ( ty_2Ellist_2Ellist @ A_27b )
@ ^ [V4ll2: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V0x ) @ V3ll1 ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V1y ) @ V4ll2 ) ) ) ) ) )
@ ( ap @ ( c_2Ellist_2ELUNZIP @ A_27a @ A_27b ) @ V2t ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELZIP__LUNZIP,axiom,
! [A_27a: del,A_27b: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( ( ap @ ( c_2Ellist_2ELZIP @ A_27a @ A_27b ) @ ( ap @ ( c_2Ellist_2ELUNZIP @ A_27a @ A_27b ) @ V0ll ) )
= V0ll ) ) ).
thf(conj_thm_2Ellist_2ELUNFOLD__THM,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2v1: $i] :
( ( mem @ V2v1 @ A_27a )
=> ! [V3v2: $i] :
( ( mem @ V3v2 @ A_27b )
=> ( ( ( ( ap @ V0f @ V1x )
= ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27b @ A_27a ) @ V0f ) @ V1x )
= ( c_2Ellist_2ELNIL @ A_27b ) ) )
& ( ( ( ap @ V0f @ V1x )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V2v1 ) @ V3v2 ) ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27b @ A_27a ) @ V0f ) @ V1x )
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V3v2 ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27b @ A_27a ) @ V0f ) @ V2v1 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELLIST__EQ,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( ty_2Ellist_2Ellist @ A_27b ) ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27a @ ( ty_2Ellist_2Ellist @ A_27b ) ) )
=> ( ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( ( ( ap @ V0f @ V2x )
= ( c_2Ellist_2ELNIL @ A_27b ) )
& ( ( ap @ V1g @ V2x )
= ( c_2Ellist_2ELNIL @ A_27b ) ) )
| ? [V3h: $i] :
( ( mem @ V3h @ A_27b )
& ? [V4y: $i] :
( ( mem @ V4y @ A_27a )
& ( ( ap @ V0f @ V2x )
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V3h ) @ ( ap @ V0f @ V4y ) ) )
& ( ( ap @ V1g @ V2x )
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V3h ) @ ( ap @ V1g @ V4y ) ) ) ) ) ) )
=> ! [V5x: $i] :
( ( mem @ V5x @ A_27a )
=> ( ( ap @ V0f @ V5x )
= ( ap @ V1g @ V5x ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELUNFOLD__EQ,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ ( ty_2Ellist_2Ellist @ A_27b ) @ bool ) ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) )
=> ! [V2s: $i] :
( ( mem @ V2s @ A_27a )
=> ! [V3ll: $i] :
( ( mem @ V3ll @ ( ty_2Ellist_2Ellist @ A_27b ) )
=> ( ( ( p @ ( ap @ ( ap @ V0R @ V2s ) @ V3ll ) )
& ! [V4s: $i] :
( ( mem @ V4s @ A_27a )
=> ! [V5ll: $i] :
( ( mem @ V5ll @ ( ty_2Ellist_2Ellist @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ V0R @ V4s ) @ V5ll ) )
=> ( ( ( ( ap @ V1f @ V4s )
= ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
& ( V5ll
= ( c_2Ellist_2ELNIL @ A_27b ) ) )
| ? [V6s_27: $i] :
( ( mem @ V6s_27 @ A_27a )
& ? [V7x: $i] :
( ( mem @ V7x @ A_27b )
& ? [V8ll_27: $i] :
( ( mem @ V8ll_27 @ ( ty_2Ellist_2Ellist @ A_27b ) )
& ( ( ap @ V1f @ V4s )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V6s_27 ) @ V7x ) ) )
& ( ( ap @ ( c_2Ellist_2ELHD @ A_27b ) @ V5ll )
= ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V7x ) )
& ( ( ap @ ( c_2Ellist_2ELTL @ A_27b ) @ V5ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27b ) ) @ V8ll_27 ) )
& ( p @ ( ap @ ( ap @ V0R @ V6s_27 ) @ V8ll_27 ) ) ) ) ) ) ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27b @ A_27a ) @ V1f ) @ V2s )
= V3ll ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELMAP__LUNFOLD,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27c @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27c @ A_27a ) ) ) )
=> ! [V2s: $i] :
( ( mem @ V2s @ A_27c )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELMAP @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27c ) @ V1g ) @ V2s ) )
= ( ap
@ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27b @ A_27c )
@ ( lam @ A_27c
@ ^ [V3s: $i] :
( ap
@ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Epair_2Eprod @ A_27c @ A_27a ) @ ( ty_2Epair_2Eprod @ A_27c @ A_27b ) )
@ ( ap @ ( c_2Epair_2EUNCURRY @ A_27c @ A_27a @ ( ty_2Epair_2Eprod @ A_27c @ A_27b ) )
@ ( lam @ A_27c
@ ^ [V4x: $i] :
( lam @ A_27a
@ ^ [V5y: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27c @ A_27b ) @ V4x ) @ ( ap @ V0f @ V5y ) ) ) ) ) )
@ ( ap @ V1g @ V3s ) ) ) )
@ V2s ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELNTH__LDROP,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2x ) )
=> ( ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2x ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELAPPEND__fromList,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ V0l1 ) ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ V1l2 ) )
= ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V0l1 ) @ V1l2 ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__LENGTH,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V2l ) )
=> ( V0n
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2l ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__TAKE__LESS,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V3m: tp__ty_2Enum_2Enum] :
( ( ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V2l ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3m ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) @ V1ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) @ V2l ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__LLENGTH__NONE,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum,V2m: tp__ty_2Enum_2Enum] :
( ( ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V0ll ) )
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ V0ll )
= ( c_2Eoption_2ENONE @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__LLENGTH__SOME,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V0ll ) )
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
=> ? [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ A_27a ) )
& ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V0ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V2l ) )
& ( ( ap @ ( c_2Ellist_2EtoList @ A_27a ) @ V0ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V2l ) ) ) ) ) ).
thf(conj_thm_2Ellist_2EtoList__LAPPEND__APPEND,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( ap @ ( c_2Ellist_2EtoList @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V0l1 ) @ V1l2 ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V2x ) )
=> ( V2x
= ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( c_2Ellist_2EtoList @ A_27a ) @ V0l1 ) ) ) @ ( ap @ ( c_2Eoption_2ETHE @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( c_2Ellist_2EtoList @ A_27a ) @ V1l2 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELNTH__LLENGTH__NONE,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1x: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
( ( ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V0l ) )
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ V0l )
= ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ).
thf(conj_thm_2Ellist_2ELNTH__NONE__MONO,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2l: $i] :
( ( mem @ V2l @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ V2l )
= ( c_2Eoption_2ENONE @ A_27a ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2l )
= ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ).
thf(ax_thm_2Ellist_2Elinear__order__to__list__f__def,axiom,
! [A_27a: del,V0lo: $i] :
( ( mem @ V0lo @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
=> ( ( ap @ ( c_2Ellist_2Elinear__order__to__list__f @ A_27a ) @ V0lo )
= ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( arr @ A_27a @ bool ) @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ A_27a ) ) )
@ ( lam @ ( arr @ A_27a @ bool )
@ ^ [V1min: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( arr @ A_27a @ bool ) ) @ V1min ) @ ( c_2Epred__set_2EEMPTY @ A_27a ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ A_27a ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ A_27a ) @ ( ap @ ( ap @ ( c_2Eset__relation_2Errestrict @ A_27a ) @ V0lo ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDIFF @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27a ) @ V0lo ) ) @ ( ap @ ( c_2Eset__relation_2Erange @ A_27a @ A_27a ) @ V0lo ) ) ) @ V1min ) ) ) @ ( ap @ ( c_2Epred__set_2ECHOICE @ A_27a ) @ V1min ) ) ) ) ) )
@ ( ap @ ( ap @ ( c_2Eset__relation_2Eminimal__elements @ A_27a ) @ ( ap @ ( ap @ ( c_2Epred__set_2EUNION @ A_27a ) @ ( ap @ ( c_2Eset__relation_2Edomain @ A_27a @ A_27a ) @ V0lo ) ) @ ( ap @ ( c_2Eset__relation_2Erange @ A_27a @ A_27a ) @ V0lo ) ) ) @ V0lo ) ) ) ) ).
thf(conj_thm_2Ellist_2Elinear__order__to__llist__eq,axiom,
! [A_27a: del,V0lo: $i] :
( ( mem @ V0lo @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
=> ! [V1X: $i] :
( ( mem @ V1X @ ( arr @ A_27a @ bool ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Elinear__order @ A_27a ) @ V0lo ) @ V1X ) )
& ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27a ) @ V0lo ) @ V1X ) ) )
=> ? [V2ll: $i] :
( ( mem @ V2ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
& ( V1X
= ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
@ ( lam @ A_27a
@ ^ [V3x: $i] :
( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V3x )
@ ( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4i: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ V4i ) @ V2ll ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3x ) ) ) ) ) ) ) )
& ( V0lo
= ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) )
@ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27a @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
@ ( lam @ A_27a
@ ^ [V5x: $i] :
( lam @ A_27a
@ ^ [V6y: $i] :
( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V5x ) @ V6y ) )
@ ( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7i: $i] :
( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8j: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ V7i ) @ V8j ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ V7i ) @ V2ll ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V5x ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ V8j ) @ V2ll ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V6y ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ! [V9i: tp__ty_2Enum_2Enum,V10j: tp__ty_2Enum_2Enum,V11x: $i] :
( ( mem @ V11x @ A_27a )
=> ( ( ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V9i ) ) @ V2ll )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V11x ) )
& ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V10j ) ) @ V2ll )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V11x ) ) )
=> ( V9i = V10j ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Elinear__order__to__llist,axiom,
! [A_27a: del,V0lo: $i] :
( ( mem @ V0lo @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
=> ! [V1X: $i] :
( ( mem @ V1X @ ( arr @ A_27a @ bool ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Elinear__order @ A_27a ) @ V0lo ) @ V1X ) )
& ( p @ ( ap @ ( ap @ ( c_2Eset__relation_2Efinite__prefixes @ A_27a @ A_27a ) @ V0lo ) @ V1X ) ) )
=> ? [V2ll: $i] :
( ( mem @ V2ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
& ( V1X
= ( ap @ ( c_2Epred__set_2EGSPEC @ A_27a @ A_27a )
@ ( lam @ A_27a
@ ^ [V3x: $i] :
( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V3x )
@ ( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4i: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ V4i ) @ V2ll ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3x ) ) ) ) ) ) ) )
& ( p
@ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) ) @ V0lo )
@ ( ap @ ( c_2Epred__set_2EGSPEC @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) )
@ ( ap @ ( c_2Epair_2EUNCURRY @ A_27a @ A_27a @ ( ty_2Epair_2Eprod @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) )
@ ( lam @ A_27a
@ ^ [V5x: $i] :
( lam @ A_27a
@ ^ [V6y: $i] :
( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Epair_2Eprod @ A_27a @ A_27a ) @ bool ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27a ) @ V5x ) @ V6y ) )
@ ( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7i: $i] :
( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8j: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ V7i ) @ V8j ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ V7i ) @ V2ll ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V5x ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ V8j ) @ V2ll ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V6y ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ! [V9i: tp__ty_2Enum_2Enum,V10j: tp__ty_2Enum_2Enum,V11x: $i] :
( ( mem @ V11x @ A_27a )
=> ( ( ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V9i ) ) @ V2ll )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V11x ) )
& ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V10j ) ) @ V2ll )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V11x ) ) )
=> ( V9i = V10j ) ) ) ) ) ) ) ).
thf(ax_thm_2Ellist_2ELPREFIX__def,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ V0l1 ) @ V1l2 ) )
<=> ( p
@ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) @ ( ap @ ( c_2Ellist_2EtoList @ A_27a ) @ V0l1 ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V0l1 ) @ V1l2 ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V2xs: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) @ ( ap @ ( c_2Ellist_2EtoList @ A_27a ) @ V1l2 ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2xs ) ) @ V1l2 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V2xs ) ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V3ys: $i] : ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V2xs ) @ V3ys ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELPREFIX__LNIL,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) @ V0ll ) )
& ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ V0ll ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) )
<=> ( V0ll
= ( c_2Ellist_2ELNIL @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELPREFIX__LCONS,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1h: $i] :
( ( mem @ V1h @ A_27a )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ V0ll ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ V2t ) ) )
<=> ( ( V0ll
= ( c_2Ellist_2ELNIL @ A_27a ) )
| ? [V3l: $i] :
( ( mem @ V3l @ ( ty_2Ellist_2Ellist @ A_27a ) )
& ( V0ll
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ V3l ) )
& ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ V3l ) @ V2t ) ) ) ) ) ) ) )
& ! [V4h: $i] :
( ( mem @ V4h @ A_27b )
=> ! [V5t: $i] :
( ( mem @ V5t @ ( ty_2Ellist_2Ellist @ A_27b ) )
=> ! [V6ll: $i] :
( ( mem @ V6ll @ ( ty_2Ellist_2Ellist @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27b ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V4h ) @ V5t ) ) @ V6ll ) )
<=> ? [V7l: $i] :
( ( mem @ V7l @ ( ty_2Ellist_2Ellist @ A_27b ) )
& ( V6ll
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27b ) @ V4h ) @ V7l ) )
& ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27b ) @ V5t ) @ V7l ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELPREFIX__LUNFOLD,axiom,
! [A_27a: del,A_27b: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27b @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) ) ) )
=> ! [V2n: $i] :
( ( mem @ V2n @ A_27b )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ V0ll ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V1f ) @ V2n ) ) )
<=> ( p
@ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Epair_2Eprod @ A_27b @ A_27a ) @ bool ) @ ( ap @ V1f @ V2n ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V0ll ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) )
@ ( lam @ ( ty_2Epair_2Eprod @ A_27b @ A_27a )
@ ^ [V3v: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ bool @ A_27b @ A_27a ) @ V3v )
@ ( lam @ A_27b
@ ^ [V4n: $i] :
( lam @ A_27a
@ ^ [V5x: $i] :
( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V6h: $i] :
( ap @ ( c_2Ebool_2E_21 @ ( ty_2Ellist_2Ellist @ A_27a ) )
@ ( lam @ ( ty_2Ellist_2Ellist @ A_27a )
@ ^ [V7t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V0ll ) @ ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V6h ) @ V7t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A_27a ) @ V6h ) @ V5x ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ V7t ) @ ( ap @ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ A_27b ) @ V1f ) @ V4n ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELPREFIX__REFL,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ V0ll ) @ V0ll ) ) ) ).
thf(conj_thm_2Ellist_2ELPREFIX__ANTISYM,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ V0l1 ) @ V1l2 ) )
& ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ V1l2 ) @ V0l1 ) ) )
=> ( V0l1 = V1l2 ) ) ) ) ).
thf(conj_thm_2Ellist_2ELPREFIX__TRANS,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2l3: $i] :
( ( mem @ V2l3 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ V0l1 ) @ V1l2 ) )
& ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ V1l2 ) @ V2l3 ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ V0l1 ) @ V2l3 ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELPREFIX__fromList,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ V0l ) ) @ V1ll ) )
<=> ( p
@ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ( ty_2Elist_2Elist @ A_27a ) @ bool ) @ ( ap @ ( c_2Ellist_2EtoList @ A_27a ) @ V1ll ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) @ V1ll ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V0l ) ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27a )
@ ^ [V2ys: $i] : ( ap @ ( ap @ ( c_2Elist_2EisPREFIX @ A_27a ) @ V0l ) @ V2ys ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Eprefixes__lprefix__total,axiom,
! [A_27a: del,V0ll: $i] :
( ( mem @ V0ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ V1l1 ) @ V0ll ) )
& ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ V2l2 ) @ V0ll ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ V1l1 ) @ V2l2 ) )
| ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ V2l2 ) @ V1l1 ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTAKE__IMP__LDROP,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2l1: $i] :
( ( mem @ V2l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELTAKE @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Elist_2Elist @ A_27a ) ) @ V2l1 ) )
=> ? [V3l2: $i] :
( ( mem @ V3l2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
& ( ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V3l2 ) )
& ( ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ V2l1 ) ) @ V3l2 )
= V1ll ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELDROP__EQ__LNIL,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1ll: $i] :
( ( mem @ V1ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ll )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELNIL @ A_27a ) ) )
<=> ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ V1ll ) )
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELPREFIX__APPEND,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ellist_2ELPREFIX @ A_27a ) @ V0l1 ) @ V1l2 ) )
<=> ? [V2ll: $i] :
( ( mem @ V2ll @ ( ty_2Ellist_2Ellist @ A_27a ) )
& ( V1l2
= ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V0l1 ) @ V2ll ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ENOT__LFINITE__DROP__LFINITE,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ~ ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V1l ) )
& ( ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V2t ) ) )
=> ~ ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ V2t ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELDROP__APPEND1,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ! [V3l2: $i] :
( ( mem @ V3l2 @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l1 )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ V2l ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V1l1 ) @ V3l2 ) )
= ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V2l ) @ V3l2 ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELDROP__fromList,axiom,
! [A_27a: del,V0ls: $i] :
( ( mem @ V0ls @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ V0ls ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0ls ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V0ls ) ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELDROP__SUC,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1ls: $i] :
( ( mem @ V1ls @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ V1ls )
= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__BIND @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELDROP @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1ls ) ) @ ( c_2Ellist_2ELTL @ A_27a ) ) ) ) ).
thf(ax_thm_2Ellist_2ELGENLIST__def,axiom,
! [A_27a: del] :
( ! [V0f: $i] :
( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ V0f ) @ ( c_2Eoption_2ENONE @ ty_2Enum_2Enum ) )
= ( ap
@ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1n: $i] : ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V1n ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ V0f @ V1n ) ) ) ) )
@ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ! [V2f: $i] :
( ( mem @ V2f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V3lim: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ V2f ) @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V3lim ) ) )
= ( ap
@ ( ap @ ( c_2Ellist_2ELUNFOLD @ A_27a @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4n: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ A_27a ) ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V4n ) @ ( inj__ty_2Enum_2Enum @ V3lim ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V4n ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ V2f @ V4n ) ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ A_27a ) ) ) ) )
@ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELHD__LGENLIST,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V1limopt: tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum] :
( ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ V0f ) @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V1limopt ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) ) @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V1limopt ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTL__LGENLIST,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V1limopt: tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum] :
( ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ V0f ) @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V1limopt ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) ) @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V1limopt ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( c_2Eoption_2ENONE @ ( ty_2Ellist_2Ellist @ A_27a ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ A_27a @ ty_2Enum_2Enum ) @ V0f ) @ c_2Enum_2ESUC ) ) @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ c_2Eprim__rec_2EPRE ) @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V1limopt ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2Enumopt__BISIMULATION,axiom,
! [V0mopt: tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum,V1nopt: tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum] :
( ( V0mopt = V1nopt )
<=> ? [V2R: $i] :
( ( mem @ V2R @ ( arr @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) @ bool ) ) )
& ( p @ ( ap @ ( ap @ V2R @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V0mopt ) ) @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V1nopt ) ) )
& ! [V3m: tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum,V4n: tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ V2R @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V3m ) ) @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V4n ) ) )
=> ( ( ( V3m
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ( V4n
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
| ( ( V3m
!= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ( V4n
!= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ( p @ ( ap @ ( ap @ V2R @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ c_2Eprim__rec_2EPRE ) @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V3m ) ) ) @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ c_2Eprim__rec_2EPRE ) @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V4n ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELGENLIST__EQ__LNIL,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V1n: tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum] :
( ( ( ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ V0f ) @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V1n ) )
= ( c_2Ellist_2ELNIL @ A_27a ) )
<=> ( V1n
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
& ( ( ( c_2Ellist_2ELNIL @ A_27a )
= ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ V0f ) @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V1n ) ) )
<=> ( V1n
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELFINITE__LGENLIST,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V1n: tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum] :
( ( p @ ( ap @ ( c_2Ellist_2ELFINITE @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ V0f ) @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V1n ) ) ) )
<=> ( V1n
!= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( c_2Eoption_2ENONE @ ty_2Enum_2Enum ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTL__HD__LTL__LHD,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELTL__HD @ A_27a ) @ V0l )
= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__BIND @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ A_27a ) @ ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ V0l ) )
@ ( lam @ A_27a
@ ^ [V1h: $i] :
( ap @ ( ap @ ( c_2Eoption_2EOPTION__BIND @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ V0l ) )
@ ( lam @ ( ty_2Ellist_2Ellist @ A_27a )
@ ^ [V2t: $i] : ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Epair_2Eprod @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ V2t ) @ V1h ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELGENLIST__SOME,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ V0f ) @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( c_2Ellist_2ELNIL @ A_27a ) )
& ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ V0f ) @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ A_27a @ ty_2Enum_2Enum ) @ V0f ) @ c_2Enum_2ESUC ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELGENLIST__SOME__compute,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ V0f ) @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( c_2Ellist_2ELNIL @ A_27a ) )
& ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ V0f ) @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ A_27a @ ty_2Enum_2Enum ) @ V0f ) @ c_2Enum_2ESUC ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ! [V2n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ V0f ) @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) )
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ A_27a @ ty_2Enum_2Enum ) @ V0f ) @ c_2Enum_2ESUC ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELNTH__LGENLIST,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1f: $i] :
( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V2lim: tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ V1f ) @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V2lim ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ ty_2Enum_2Enum @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V2lim ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ V1f @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3lim0: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V3lim0 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ V1f @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELNTH__LMAP,axiom,
! [A_27a: del,A_27b: del,V0n: tp__ty_2Enum_2Enum,V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELMAP @ A_27a @ A_27b ) @ V1f ) @ V2l ) )
= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ V1f ) @ ( ap @ ( ap @ ( c_2Ellist_2ELNTH @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V2l ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELLENGTH__LGENLIST,axiom,
! [A_27a: del,V0limopt: tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum,V1f: $i] :
( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ V1f ) @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V0limopt ) ) ) )
= V0limopt ) ) ).
thf(conj_thm_2Ellist_2ELMAP__LGENLIST,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ A_27a ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ ty_2Enum_2Enum @ A_27b ) )
=> ! [V2limopt: tp__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ellist_2ELMAP @ A_27b @ A_27a ) @ V0f ) @ ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27b ) @ V1g ) @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V2limopt ) ) )
= ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ A_27a @ A_27b ) @ V0f ) @ V1g ) ) @ ( inj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ V2limopt ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELGENLIST__EQ__CONS,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V1h: $i] :
( ( mem @ V1h @ A_27a )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( ty_2Ellist_2Ellist @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ V0f ) @ ( c_2Eoption_2ENONE @ ty_2Enum_2Enum ) )
= ( ap @ ( ap @ ( c_2Ellist_2ELCONS @ A_27a ) @ V1h ) @ V2t ) )
<=> ( ( V1h
= ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ( V2t
= ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ A_27a @ ty_2Enum_2Enum ) @ V0f ) @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( c_2Eoption_2ENONE @ ty_2Enum_2Enum ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ellist_2ELREPEAT__def,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELREPEAT @ A_27a ) @ V0l )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Ellist_2Ellist @ A_27a ) ) @ ( ap @ ( c_2Elist_2ENULL @ A_27a ) @ V0l ) ) @ ( c_2Ellist_2ELNIL @ A_27a ) )
@ ( ap
@ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1n: $i] : ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ V1n ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V0l ) ) ) @ V0l ) ) )
@ ( c_2Eoption_2ENONE @ ty_2Enum_2Enum ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELGENLIST__CHUNK__GENLIST,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ V0f ) @ ( c_2Eoption_2ENONE @ ty_2Enum_2Enum ) )
= ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EGENLIST @ A_27a ) @ V0f ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( ap @ ( ap @ ( c_2Ellist_2ELGENLIST @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ A_27a @ ty_2Enum_2Enum ) @ V0f ) @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( c_2Eoption_2ENONE @ ty_2Enum_2Enum ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELREPEAT__thm,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELREPEAT @ A_27a ) @ V0l )
= ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ V0l ) ) @ ( ap @ ( c_2Ellist_2ELREPEAT @ A_27a ) @ V0l ) ) ) ) ).
thf(conj_thm_2Ellist_2ELREPEAT__NIL,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Ellist_2ELREPEAT @ A_27a ) @ ( c_2Elist_2ENIL @ A_27a ) )
= ( c_2Ellist_2ELNIL @ A_27a ) ) ).
thf(conj_thm_2Ellist_2ELREPEAT__EQ__LNIL,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( ( ap @ ( c_2Ellist_2ELREPEAT @ A_27a ) @ V0l )
= ( c_2Ellist_2ELNIL @ A_27a ) )
<=> ( V0l
= ( c_2Elist_2ENIL @ A_27a ) ) )
& ( ( ( c_2Ellist_2ELNIL @ A_27a )
= ( ap @ ( c_2Ellist_2ELREPEAT @ A_27a ) @ V0l ) )
<=> ( V0l
= ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELHD__LREPEAT,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ ( ap @ ( c_2Ellist_2ELREPEAT @ A_27a ) @ V0l ) )
= ( ap @ ( c_2Ellist_2ELHD @ A_27a ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ V0l ) ) ) ) ).
thf(conj_thm_2Ellist_2ELTL__LREPEAT,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ ( ap @ ( c_2Ellist_2ELREPEAT @ A_27a ) @ V0l ) )
= ( ap
@ ( ap @ ( c_2Eoption_2EOPTION__MAP @ ( ty_2Ellist_2Ellist @ A_27a ) @ ( ty_2Ellist_2Ellist @ A_27a ) )
@ ( lam @ ( ty_2Ellist_2Ellist @ A_27a )
@ ^ [V1t: $i] : ( ap @ ( ap @ ( c_2Ellist_2ELAPPEND @ A_27a ) @ V1t ) @ ( ap @ ( c_2Ellist_2ELREPEAT @ A_27a ) @ V0l ) ) ) )
@ ( ap @ ( c_2Ellist_2ELTL @ A_27a ) @ ( ap @ ( c_2Ellist_2EfromList @ A_27a ) @ V0l ) ) ) ) ) ).
thf(conj_thm_2Ellist_2ELLENGTH__LREPEAT,axiom,
! [A_27a: del,V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( c_2Ellist_2ELLENGTH @ A_27a ) @ ( ap @ ( c_2Ellist_2ELREPEAT @ A_27a ) @ V0l ) ) )
= ( surj__c_ty_2Eoption_2Eoption_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ ty_2Enum_2Enum ) ) @ ( ap @ ( c_2Elist_2ENULL @ A_27a ) @ V0l ) ) @ ( ap @ ( c_2Eoption_2ESOME @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( c_2Eoption_2ENONE @ ty_2Enum_2Enum ) ) ) ) ) ).
%------------------------------------------------------------------------------