ITP001 Axioms: ITP030+5.ax
%------------------------------------------------------------------------------
% File : ITP030+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 : list+2.ax [Gau20]
% : HL4030+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 622 ( 11 unt; 0 def)
% Number of atoms : 3821 ( 738 equ)
% Maximal formula atoms : 36 ( 6 avg)
% Number of connectives : 3251 ( 52 ~; 25 |; 411 &)
% ( 187 <=>;2576 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 10 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 233 ( 233 usr; 28 con; 0-6 aty)
% Number of variables : 2692 (2598 !; 94 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(ne_ty_2Elist_2Elist,axiom,
! [A0] :
( ne(A0)
=> ne(ty_2Elist_2Elist(A0)) ) ).
fof(mem_c_2Elist_2EALL__DISTINCT,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EALL__DISTINCT(A_27a),arr(ty_2Elist_2Elist(A_27a),bool)) ) ).
fof(mem_c_2Elist_2EAPPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EAPPEND(A_27a),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))) ) ).
fof(mem_c_2Elist_2ECONS,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2ECONS(A_27a),arr(A_27a,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))) ) ).
fof(mem_c_2Elist_2EDROP,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EDROP(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))) ) ).
fof(mem_c_2Elist_2EEL,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EEL(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),A_27a))) ) ).
fof(mem_c_2Elist_2EEVERY,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EEVERY(A_27a),arr(arr(A_27a,bool),arr(ty_2Elist_2Elist(A_27a),bool))) ) ).
fof(mem_c_2Elist_2EEVERYi,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EEVERYi(A_27a),arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),bool))) ) ).
fof(mem_c_2Elist_2EEXISTS,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EEXISTS(A_27a),arr(arr(A_27a,bool),arr(ty_2Elist_2Elist(A_27a),bool))) ) ).
fof(mem_c_2Elist_2EFILTER,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EFILTER(A_27a),arr(arr(A_27a,bool),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))) ) ).
fof(mem_c_2Elist_2EFIND,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EFIND(A_27a),arr(arr(A_27a,bool),arr(ty_2Elist_2Elist(A_27a),ty_2Eoption_2Eoption(A_27a)))) ) ).
fof(mem_c_2Elist_2EFLAT,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EFLAT(A_27a),arr(ty_2Elist_2Elist(ty_2Elist_2Elist(A_27a)),ty_2Elist_2Elist(A_27a))) ) ).
fof(mem_c_2Elist_2EFOLDL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Elist_2EFOLDL(A_27a,A_27b),arr(arr(A_27b,arr(A_27a,A_27b)),arr(A_27b,arr(ty_2Elist_2Elist(A_27a),A_27b)))) ) ) ).
fof(mem_c_2Elist_2EFOLDL2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> mem(c_2Elist_2EFOLDL2(A_27a,A_27b,A_27c),arr(arr(A_27a,arr(A_27b,arr(A_27c,A_27a))),arr(A_27a,arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27c),A_27a))))) ) ) ) ).
fof(mem_c_2Elist_2EFOLDR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Elist_2EFOLDR(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,A_27b)),arr(A_27b,arr(ty_2Elist_2Elist(A_27a),A_27b)))) ) ) ).
fof(mem_c_2Elist_2EFRONT,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EFRONT(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))) ) ).
fof(mem_c_2Elist_2EGENLIST,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EGENLIST(A_27a),arr(arr(ty_2Enum_2Enum,A_27a),arr(ty_2Enum_2Enum,ty_2Elist_2Elist(A_27a)))) ) ).
fof(mem_c_2Elist_2EGENLIST__AUX,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EGENLIST__AUX(A_27a),arr(arr(ty_2Enum_2Enum,A_27a),arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))))) ) ).
fof(mem_c_2Elist_2EHD,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EHD(A_27a),arr(ty_2Elist_2Elist(A_27a),A_27a)) ) ).
fof(mem_c_2Elist_2EINDEX__FIND,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EINDEX__FIND(A_27a),arr(ty_2Enum_2Enum,arr(arr(A_27a,bool),arr(ty_2Elist_2Elist(A_27a),ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)))))) ) ).
fof(mem_c_2Elist_2EINDEX__OF,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EINDEX__OF(A_27a),arr(A_27a,arr(ty_2Elist_2Elist(A_27a),ty_2Eoption_2Eoption(ty_2Enum_2Enum)))) ) ).
fof(mem_c_2Elist_2ELAST,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2ELAST(A_27a),arr(ty_2Elist_2Elist(A_27a),A_27a)) ) ).
fof(mem_c_2Elist_2ELEN,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2ELEN(A_27a),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ) ).
fof(mem_c_2Elist_2ELENGTH,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2ELENGTH(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Enum_2Enum)) ) ).
fof(mem_c_2Elist_2ELIST__APPLY,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Elist_2ELIST__APPLY(A_27a,A_27b),arr(ty_2Elist_2Elist(arr(A_27b,A_27a)),arr(ty_2Elist_2Elist(A_27b),ty_2Elist_2Elist(A_27a)))) ) ) ).
fof(mem_c_2Elist_2ELIST__BIND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Elist_2ELIST__BIND(A_27a,A_27b),arr(ty_2Elist_2Elist(A_27b),arr(arr(A_27b,ty_2Elist_2Elist(A_27a)),ty_2Elist_2Elist(A_27a)))) ) ) ).
fof(mem_c_2Elist_2ELIST__GUARD,axiom,
mem(c_2Elist_2ELIST__GUARD,arr(bool,ty_2Elist_2Elist(ty_2Eone_2Eone))) ).
fof(mem_c_2Elist_2ELIST__IGNORE__BIND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Elist_2ELIST__IGNORE__BIND(A_27a,A_27b),arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))) ) ) ).
fof(mem_c_2Elist_2ELIST__LIFT2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> mem(c_2Elist_2ELIST__LIFT2(A_27a,A_27b,A_27c),arr(arr(A_27b,arr(A_27c,A_27a)),arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27c),ty_2Elist_2Elist(A_27a))))) ) ) ) ).
fof(mem_c_2Elist_2ELIST__REL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Elist_2ELIST__REL(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27b),bool)))) ) ) ).
fof(mem_c_2Elist_2ELIST__TO__SET,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2ELIST__TO__SET(A_27a),arr(ty_2Elist_2Elist(A_27a),arr(A_27a,bool))) ) ).
fof(mem_c_2Elist_2ELLEX,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2ELLEX(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),bool)))) ) ).
fof(mem_c_2Elist_2ELRC,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2ELRC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),arr(A_27a,arr(A_27a,bool))))) ) ).
fof(mem_c_2Elist_2ELUPDATE,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2ELUPDATE(A_27a),arr(A_27a,arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))))) ) ).
fof(mem_c_2Elist_2EMAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Elist_2EMAP(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)))) ) ) ).
fof(mem_c_2Elist_2EMAP2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> mem(c_2Elist_2EMAP2(A_27a,A_27b,A_27c),arr(arr(A_27b,arr(A_27c,A_27a)),arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27c),ty_2Elist_2Elist(A_27a))))) ) ) ) ).
fof(mem_c_2Elist_2ENIL,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2ENIL(A_27a),ty_2Elist_2Elist(A_27a)) ) ).
fof(mem_c_2Elist_2ENULL,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2ENULL(A_27a),arr(ty_2Elist_2Elist(A_27a),bool)) ) ).
fof(mem_c_2Elist_2EOPT__MMAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Elist_2EOPT__MMAP(A_27a,A_27b),arr(arr(A_27b,ty_2Eoption_2Eoption(A_27a)),arr(ty_2Elist_2Elist(A_27b),ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27a))))) ) ) ).
fof(mem_c_2Elist_2EPAD__LEFT,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EPAD__LEFT(A_27a),arr(A_27a,arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))))) ) ).
fof(mem_c_2Elist_2EPAD__RIGHT,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EPAD__RIGHT(A_27a),arr(A_27a,arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))))) ) ).
fof(mem_c_2Elist_2EREV,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EREV(A_27a),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))) ) ).
fof(mem_c_2Elist_2EREVERSE,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EREVERSE(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))) ) ).
fof(mem_c_2Elist_2ESET__TO__LIST,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2ESET__TO__LIST(A_27a),arr(arr(A_27a,bool),ty_2Elist_2Elist(A_27a))) ) ).
fof(mem_c_2Elist_2ESHORTLEX,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2ESHORTLEX(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),bool)))) ) ).
fof(mem_c_2Elist_2ESNOC,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2ESNOC(A_27a),arr(A_27a,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))) ) ).
fof(mem_c_2Elist_2ESUM,axiom,
mem(c_2Elist_2ESUM,arr(ty_2Elist_2Elist(ty_2Enum_2Enum),ty_2Enum_2Enum)) ).
fof(mem_c_2Elist_2ESUM__ACC,axiom,
mem(c_2Elist_2ESUM__ACC,arr(ty_2Elist_2Elist(ty_2Enum_2Enum),arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) ).
fof(mem_c_2Elist_2ETAKE,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2ETAKE(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))) ) ).
fof(mem_c_2Elist_2ETL,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2ETL(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))) ) ).
fof(mem_c_2Elist_2EUNIQUE,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EUNIQUE(A_27a),arr(A_27a,arr(ty_2Elist_2Elist(A_27a),bool))) ) ).
fof(mem_c_2Elist_2EUNZIP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Elist_2EUNZIP(A_27a,A_27b),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)))) ) ) ).
fof(mem_c_2Elist_2EZIP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Elist_2EZIP(A_27a,A_27b),arr(ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))) ) ) ).
fof(mem_c_2Elist_2EdropWhile,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EdropWhile(A_27a),arr(arr(A_27a,bool),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))) ) ).
fof(mem_c_2Elist_2EisPREFIX,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EisPREFIX(A_27a),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),bool))) ) ).
fof(mem_c_2Elist_2Elist__CASE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Elist_2Elist__CASE(A_27a,A_27b),arr(ty_2Elist_2Elist(A_27a),arr(A_27b,arr(arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b)),A_27b)))) ) ) ).
fof(mem_c_2Elist_2Elist__size,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2Elist__size(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(ty_2Elist_2Elist(A_27a),ty_2Enum_2Enum))) ) ).
fof(mem_c_2Elist_2Enub,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2Enub(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))) ) ).
fof(mem_c_2Elist_2EoEL,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EoEL(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),ty_2Eoption_2Eoption(A_27a)))) ) ).
fof(mem_c_2Elist_2EoHD,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Elist_2EoHD(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Eoption_2Eoption(A_27a))) ) ).
fof(mem_c_2Elist_2EsplitAtPki,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Elist_2EsplitAtPki(A_27a,A_27b),arr(arr(ty_2Enum_2Enum,arr(A_27b,bool)),arr(arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27b),A_27a)),arr(ty_2Elist_2Elist(A_27b),A_27a)))) ) ) ).
fof(lameq_f380,axiom,
! [A_27a,V7a0] :
( mem(V7a0,A_27a)
=> ! [V8a1] : ap(f380(A_27a,V7a0),V8a1) = ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),ap(c_2Enum_2ESUC,c_2Enum_2E0)),V7a0),ap(ap(c_2Eind__type_2EFCONS(ty_2Eind__type_2Erecspace(A_27a)),V8a1),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(A_27a)))) ) ).
fof(lameq_f381,axiom,
! [A_27a,V7a0] : ap(f381(A_27a),V7a0) = f380(A_27a,V7a0) ).
fof(lameq_f382,axiom,
! [A_27a,V5a0] :
( mem(V5a0,A_27a)
=> ! [V3a0_27] :
( mem(V3a0_27,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V2_27list_27] :
( mem(V2_27list_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V6a1] : ap(f382(A_27a,V5a0,V3a0_27,V2_27list_27),V6a1) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(A_27a)),V3a0_27),ap(ap(f381(A_27a),V5a0),V6a1))),ap(V2_27list_27,V6a1)) ) ) ) ).
fof(lameq_f383,axiom,
! [A_27a,V2_27list_27] :
( mem(V2_27list_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V3a0_27] :
( mem(V3a0_27,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V5a0] : ap(f383(A_27a,V2_27list_27,V3a0_27),V5a0) = ap(c_2Ebool_2E_3F(ty_2Eind__type_2Erecspace(A_27a)),f382(A_27a,V5a0,V3a0_27,V2_27list_27)) ) ) ).
fof(lameq_f384,axiom,
! [A_27a,V2_27list_27] :
( mem(V2_27list_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V3a0_27] : ap(f384(A_27a,V2_27list_27),V3a0_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(A_27a)),V3a0_27),ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),c_2Enum_2E0),c_2Ebool_2EARB(A_27a)),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(A_27a))))),ap(c_2Ebool_2E_3F(A_27a),f383(A_27a,V2_27list_27,V3a0_27)))),ap(V2_27list_27,V3a0_27)) ) ).
fof(lameq_f385,axiom,
! [A_27a,V1a0_27] :
( mem(V1a0_27,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V2_27list_27] : ap(f385(A_27a,V1a0_27),V2_27list_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(ty_2Eind__type_2Erecspace(A_27a)),f384(A_27a,V2_27list_27))),ap(V2_27list_27,V1a0_27)) ) ).
fof(lameq_f386,axiom,
! [A_27a,V1a0_27] : ap(f386(A_27a),V1a0_27) = ap(c_2Ebool_2E_21(arr(ty_2Eind__type_2Erecspace(A_27a),bool)),f385(A_27a,V1a0_27)) ).
fof(ax_thm_2Elist_2Elist__TY__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ? [V0rep] :
( mem(V0rep,arr(ty_2Elist_2Elist(A_27a),ty_2Eind__type_2Erecspace(A_27a)))
& p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Eind__type_2Erecspace(A_27a),ty_2Elist_2Elist(A_27a)),f386(A_27a)),V0rep)) ) ) ).
fof(ax_thm_2Elist_2Elist__case__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0v] :
( mem(V0v,A_27b)
=> ! [V1f] :
( mem(V1f,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b)))
=> ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,A_27b),c_2Elist_2ENIL(A_27a)),V0v),V1f) = V0v ) )
& ! [V2a0] :
( mem(V2a0,A_27a)
=> ! [V3a1] :
( mem(V3a1,ty_2Elist_2Elist(A_27a))
=> ! [V4v] :
( mem(V4v,A_27b)
=> ! [V5f] :
( mem(V5f,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b)))
=> ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,A_27b),ap(ap(c_2Elist_2ECONS(A_27a),V2a0),V3a1)),V4v),V5f) = ap(ap(V5f,V2a0),V3a1) ) ) ) ) ) ) ) ).
fof(ax_thm_2Elist_2Elist__size__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ap(ap(c_2Elist_2Elist__size(A_27a),V0f),c_2Elist_2ENIL(A_27a)) = c_2Enum_2E0 )
& ! [V1f] :
( mem(V1f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V2a0] :
( mem(V2a0,A_27a)
=> ! [V3a1] :
( mem(V3a1,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2Elist__size(A_27a),V1f),ap(ap(c_2Elist_2ECONS(A_27a),V2a0),V3a1)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2B,ap(V1f,V2a0)),ap(ap(c_2Elist_2Elist__size(A_27a),V1f),V3a1))) ) ) ) ) ) ).
fof(conj_thm_2Elist_2Edatatype__list,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0list] :
( mem(V0list,arr(ty_2Elist_2Elist(A_27a),arr(arr(A_27a,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))),bool)))
=> p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(V0list,c_2Elist_2ENIL(A_27a)),c_2Elist_2ECONS(A_27a)))) ) ) ).
fof(conj_thm_2Elist_2Elist__11,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a0] :
( mem(V0a0,A_27a)
=> ! [V1a1] :
( mem(V1a1,ty_2Elist_2Elist(A_27a))
=> ! [V2a0_27] :
( mem(V2a0_27,A_27a)
=> ! [V3a1_27] :
( mem(V3a1_27,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2ECONS(A_27a),V0a0),V1a1) = ap(ap(c_2Elist_2ECONS(A_27a),V2a0_27),V3a1_27)
<=> ( V0a0 = V2a0_27
& V1a1 = V3a1_27 ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2Elist__distinct,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a1] :
( mem(V0a1,ty_2Elist_2Elist(A_27a))
=> ! [V1a0] :
( mem(V1a0,A_27a)
=> c_2Elist_2ENIL(A_27a) != ap(ap(c_2Elist_2ECONS(A_27a),V1a0),V0a1) ) ) ) ).
fof(conj_thm_2Elist_2Elist__Axiom,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f0] :
( mem(V0f0,A_27b)
=> ! [V1f1] :
( mem(V1f1,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),arr(A_27b,A_27b))))
=> ? [V2fn] :
( mem(V2fn,arr(ty_2Elist_2Elist(A_27a),A_27b))
& ap(V2fn,c_2Elist_2ENIL(A_27a)) = V0f0
& ! [V3a0] :
( mem(V3a0,A_27a)
=> ! [V4a1] :
( mem(V4a1,ty_2Elist_2Elist(A_27a))
=> ap(V2fn,ap(ap(c_2Elist_2ECONS(A_27a),V3a0),V4a1)) = ap(ap(ap(V1f1,V3a0),V4a1),ap(V2fn,V4a1)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2Elist__case__cong,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0v_27] :
( mem(V0v_27,A_27b)
=> ! [V1f_27] :
( mem(V1f_27,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b)))
=> ! [V2M] :
( mem(V2M,ty_2Elist_2Elist(A_27a))
=> ! [V3M_27] :
( mem(V3M_27,ty_2Elist_2Elist(A_27a))
=> ! [V4v] :
( mem(V4v,A_27b)
=> ! [V5f] :
( mem(V5f,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b)))
=> ( ( V2M = V3M_27
& ( V3M_27 = c_2Elist_2ENIL(A_27a)
=> V4v = V0v_27 )
& ! [V6a0] :
( mem(V6a0,A_27a)
=> ! [V7a1] :
( mem(V7a1,ty_2Elist_2Elist(A_27a))
=> ( V3M_27 = ap(ap(c_2Elist_2ECONS(A_27a),V6a0),V7a1)
=> ap(ap(V5f,V6a0),V7a1) = ap(ap(V1f_27,V6a0),V7a1) ) ) ) )
=> ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,A_27b),V2M),V4v),V5f) = ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,A_27b),V3M_27),V0v_27),V1f_27) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2Elist__case__eq,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,ty_2Elist_2Elist(A_27a))
=> ! [V1v] :
( mem(V1v,A_27b)
=> ! [V2f] :
( mem(V2f,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b)))
=> ! [V3v_27] :
( mem(V3v_27,A_27b)
=> ( ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,A_27b),V0x),V1v),V2f) = V3v_27
<=> ( ( V0x = c_2Elist_2ENIL(A_27a)
& V1v = V3v_27 )
| ? [V4a] :
( mem(V4a,A_27a)
& ? [V5l] :
( mem(V5l,ty_2Elist_2Elist(A_27a))
& V0x = ap(ap(c_2Elist_2ECONS(A_27a),V4a),V5l)
& ap(ap(V2f,V4a),V5l) = V3v_27 ) ) ) ) ) ) ) ) ) ) ).
fof(lameq_f387,axiom,
! [A_27b,A_27a,V1f] :
( mem(V1f,arr(A_27b,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b))))
=> ! [V2fn1] :
( mem(V2fn1,arr(ty_2Elist_2Elist(A_27a),A_27b))
=> ! [V3h] :
( mem(V3h,A_27a)
=> ! [V4t] : ap(f387(A_27b,A_27a,V1f,V2fn1,V3h),V4t) = ap(ap(c_2Emin_2E_3D(A_27b),ap(V2fn1,ap(ap(c_2Elist_2ECONS(A_27a),V3h),V4t))),ap(ap(ap(V1f,ap(V2fn1,V4t)),V3h),V4t)) ) ) ) ).
fof(lameq_f388,axiom,
! [A_27b,A_27a,V2fn1] :
( mem(V2fn1,arr(ty_2Elist_2Elist(A_27a),A_27b))
=> ! [V1f] :
( mem(V1f,arr(A_27b,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b))))
=> ! [V3h] : ap(f388(A_27b,A_27a,V2fn1,V1f),V3h) = ap(c_2Ebool_2E_21(ty_2Elist_2Elist(A_27a)),f387(A_27b,A_27a,V1f,V2fn1,V3h)) ) ) ).
fof(lameq_f389,axiom,
! [A_27b,A_27a,V0x] :
( mem(V0x,A_27b)
=> ! [V1f] :
( mem(V1f,arr(A_27b,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b))))
=> ! [V2fn1] : ap(f389(A_27b,A_27a,V0x,V1f),V2fn1) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27b),ap(V2fn1,c_2Elist_2ENIL(A_27a))),V0x)),ap(c_2Ebool_2E_21(A_27a),f388(A_27b,A_27a,V2fn1,V1f))) ) ) ).
fof(conj_thm_2Elist_2Elist__Axiom__old,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,A_27b)
=> ! [V1f] :
( mem(V1f,arr(A_27b,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b))))
=> p(ap(c_2Ebool_2E_3F_21(arr(ty_2Elist_2Elist(A_27a),A_27b)),f389(A_27b,A_27a,V0x,V1f))) ) ) ) ) ).
fof(ax_thm_2Elist_2ENULL__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ( p(ap(c_2Elist_2ENULL(A_27a),c_2Elist_2ENIL(A_27a)))
<=> $true )
& ! [V0h] :
( mem(V0h,A_27a)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(A_27a))
=> ( p(ap(c_2Elist_2ENULL(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)))
<=> $false ) ) ) ) ) ).
fof(ax_thm_2Elist_2EHD,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,A_27a)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2EHD(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)) = V0h ) ) ) ).
fof(ax_thm_2Elist_2ETL__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ap(c_2Elist_2ETL(A_27a),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a)
& ! [V0h] :
( mem(V0h,A_27a)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ETL(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)) = V1t ) ) ) ) ).
fof(conj_thm_2Elist_2ETL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,A_27a)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ETL(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)) = V1t ) ) ) ).
fof(ax_thm_2Elist_2ESUM,axiom,
( ap(c_2Elist_2ESUM,c_2Elist_2ENIL(ty_2Enum_2Enum)) = c_2Enum_2E0
& ! [V0h] :
( mem(V0h,ty_2Enum_2Enum)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),V0h),V1t)) = ap(ap(c_2Earithmetic_2E_2B,V0h),ap(c_2Elist_2ESUM,V1t)) ) ) ) ).
fof(ax_thm_2Elist_2EAPPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EAPPEND(A_27a),c_2Elist_2ENIL(A_27a)),V0l) = V0l )
& ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ! [V3h] :
( mem(V3h,A_27a)
=> ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V3h),V1l1)),V2l2) = ap(ap(c_2Elist_2ECONS(A_27a),V3h),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),V2l2)) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EFLAT,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ap(c_2Elist_2EFLAT(A_27a),c_2Elist_2ENIL(ty_2Elist_2Elist(A_27a))) = c_2Elist_2ENIL(A_27a)
& ! [V0h] :
( mem(V0h,ty_2Elist_2Elist(A_27a))
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27a)))
=> ap(c_2Elist_2EFLAT(A_27a),ap(ap(c_2Elist_2ECONS(ty_2Elist_2Elist(A_27a)),V0h),V1t)) = ap(ap(c_2Elist_2EAPPEND(A_27a),V0h),ap(c_2Elist_2EFLAT(A_27a),V1t)) ) ) ) ) ).
fof(ax_thm_2Elist_2ELENGTH,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ap(c_2Elist_2ELENGTH(A_27a),c_2Elist_2ENIL(A_27a)) = c_2Enum_2E0
& ! [V0h] :
( mem(V0h,A_27a)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)) = ap(c_2Enum_2ESUC,ap(c_2Elist_2ELENGTH(A_27a),V1t)) ) ) ) ) ).
fof(ax_thm_2Elist_2EMAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27b) )
& ! [V1f] :
( mem(V1f,arr(A_27a,A_27b))
=> ! [V2h] :
( mem(V2h,A_27a)
=> ! [V3t] :
( mem(V3t,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)) = ap(ap(c_2Elist_2ECONS(A_27b),ap(V1f,V2h)),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V3t)) ) ) ) ) ) ) ).
fof(ax_thm_2Elist_2ELIST__TO__SET__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0x] :
( mem(V0x,A_27a)
=> ( p(ap(ap(c_2Elist_2ELIST__TO__SET(A_27a),c_2Elist_2ENIL(A_27a)),V0x))
<=> $false ) )
& ! [V1h] :
( mem(V1h,A_27a)
=> ! [V2t] :
( mem(V2t,ty_2Elist_2Elist(A_27a))
=> ! [V3x] :
( mem(V3x,A_27a)
=> ( p(ap(ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t)),V3x))
<=> ( V3x = V1h
| p(ap(ap(c_2Elist_2ELIST__TO__SET(A_27a),V2t),V3x)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__TO__SET,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0h] :
( mem(V0h,A_27b)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(A_27b))
=> ( ap(c_2Elist_2ELIST__TO__SET(A_27a),c_2Elist_2ENIL(A_27a)) = c_2Epred__set_2EEMPTY(A_27a)
& ap(c_2Elist_2ELIST__TO__SET(A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V0h),V1t)) = ap(ap(c_2Epred__set_2EINSERT(A_27b),V0h),ap(c_2Elist_2ELIST__TO__SET(A_27b),V1t)) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EFILTER,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ap(ap(c_2Elist_2EFILTER(A_27a),V0P),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a) )
& ! [V1P] :
( mem(V1P,arr(A_27a,bool))
=> ! [V2h] :
( mem(V2h,A_27a)
=> ! [V3t] :
( mem(V3t,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EFILTER(A_27a),V1P),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(V1P,V2h)),ap(ap(c_2Elist_2ECONS(A_27a),V2h),ap(ap(c_2Elist_2EFILTER(A_27a),V1P),V3t))),ap(ap(c_2Elist_2EFILTER(A_27a),V1P),V3t)) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EFOLDR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0f] :
( mem(V0f,arr(A_27a,arr(A_27b,A_27b)))
=> ! [V1e] :
( mem(V1e,A_27b)
=> ap(ap(ap(c_2Elist_2EFOLDR(A_27a,A_27b),V0f),V1e),c_2Elist_2ENIL(A_27a)) = V1e ) )
& ! [V2f] :
( mem(V2f,arr(A_27a,arr(A_27b,A_27b)))
=> ! [V3e] :
( mem(V3e,A_27b)
=> ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5l] :
( mem(V5l,ty_2Elist_2Elist(A_27a))
=> ap(ap(ap(c_2Elist_2EFOLDR(A_27a,A_27b),V2f),V3e),ap(ap(c_2Elist_2ECONS(A_27a),V4x),V5l)) = ap(ap(V2f,V4x),ap(ap(ap(c_2Elist_2EFOLDR(A_27a,A_27b),V2f),V3e),V5l)) ) ) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EFOLDL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0f] :
( mem(V0f,arr(A_27b,arr(A_27a,A_27b)))
=> ! [V1e] :
( mem(V1e,A_27b)
=> ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),V0f),V1e),c_2Elist_2ENIL(A_27a)) = V1e ) )
& ! [V2f] :
( mem(V2f,arr(A_27b,arr(A_27a,A_27b)))
=> ! [V3e] :
( mem(V3e,A_27b)
=> ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5l] :
( mem(V5l,ty_2Elist_2Elist(A_27a))
=> ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),V2f),V3e),ap(ap(c_2Elist_2ECONS(A_27a),V4x),V5l)) = ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),V2f),ap(ap(V2f,V3e),V4x)),V5l) ) ) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EEVERY__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),c_2Elist_2ENIL(A_27a)))
<=> $true ) )
& ! [V1P] :
( mem(V1P,arr(A_27a,bool))
=> ! [V2h] :
( mem(V2h,A_27a)
=> ! [V3t] :
( mem(V3t,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V1P),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)))
<=> ( p(ap(V1P,V2h))
& p(ap(ap(c_2Elist_2EEVERY(A_27a),V1P),V3t)) ) ) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EEXISTS__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ( p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),c_2Elist_2ENIL(A_27a)))
<=> $false ) )
& ! [V1P] :
( mem(V1P,arr(A_27a,bool))
=> ! [V2h] :
( mem(V2h,A_27a)
=> ! [V3t] :
( mem(V3t,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEXISTS(A_27a),V1P),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)))
<=> ( p(ap(V1P,V2h))
| p(ap(ap(c_2Elist_2EEXISTS(A_27a),V1P),V3t)) ) ) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EEL,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EEL(A_27a),c_2Enum_2E0),V0l) = ap(c_2Elist_2EHD(A_27a),V0l) )
& ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Enum_2ESUC,V2n)),V1l) = ap(ap(c_2Elist_2EEL(A_27a),V2n),ap(c_2Elist_2ETL(A_27a),V1l)) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP2__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0P] :
( mem(V0P,arr(arr(A_27b,arr(A_27c,A_27a)),arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27c),bool))))
=> ( ( ! [V1f] :
( mem(V1f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V2h1] :
( mem(V2h1,A_27b)
=> ! [V3t1] :
( mem(V3t1,ty_2Elist_2Elist(A_27b))
=> ! [V4h2] :
( mem(V4h2,A_27c)
=> ! [V5t2] :
( mem(V5t2,ty_2Elist_2Elist(A_27c))
=> ( p(ap(ap(ap(V0P,V1f),V3t1),V5t2))
=> p(ap(ap(ap(V0P,V1f),ap(ap(c_2Elist_2ECONS(A_27b),V2h1),V3t1)),ap(ap(c_2Elist_2ECONS(A_27c),V4h2),V5t2))) ) ) ) ) ) )
& ! [V6f] :
( mem(V6f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V7y] :
( mem(V7y,ty_2Elist_2Elist(A_27c))
=> p(ap(ap(ap(V0P,V6f),c_2Elist_2ENIL(A_27b)),V7y)) ) )
& ! [V8f] :
( mem(V8f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V9v4] :
( mem(V9v4,A_27b)
=> ! [V10v5] :
( mem(V10v5,ty_2Elist_2Elist(A_27b))
=> p(ap(ap(ap(V0P,V8f),ap(ap(c_2Elist_2ECONS(A_27b),V9v4),V10v5)),c_2Elist_2ENIL(A_27c))) ) ) ) )
=> ! [V11v] :
( mem(V11v,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V12v1] :
( mem(V12v1,ty_2Elist_2Elist(A_27b))
=> ! [V13v2] :
( mem(V13v2,ty_2Elist_2Elist(A_27c))
=> p(ap(ap(ap(V0P,V11v),V12v1),V13v2)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP2__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ( ! [V0t2] :
( mem(V0t2,ty_2Elist_2Elist(A_27c))
=> ! [V1t1] :
( mem(V1t1,ty_2Elist_2Elist(A_27b))
=> ! [V2h2] :
( mem(V2h2,A_27c)
=> ! [V3h1] :
( mem(V3h1,A_27b)
=> ! [V4f] :
( mem(V4f,arr(A_27b,arr(A_27c,A_27a)))
=> ap(ap(ap(c_2Elist_2EMAP2(A_27a,A_27b,A_27c),V4f),ap(ap(c_2Elist_2ECONS(A_27b),V3h1),V1t1)),ap(ap(c_2Elist_2ECONS(A_27c),V2h2),V0t2)) = ap(ap(c_2Elist_2ECONS(A_27a),ap(ap(V4f,V3h1),V2h2)),ap(ap(ap(c_2Elist_2EMAP2(A_27a,A_27b,A_27c),V4f),V1t1),V0t2)) ) ) ) ) )
& ! [V5y] :
( mem(V5y,ty_2Elist_2Elist(A_27c))
=> ! [V6f] :
( mem(V6f,arr(A_27b,arr(A_27c,A_27a)))
=> ap(ap(ap(c_2Elist_2EMAP2(A_27a,A_27b,A_27c),V6f),c_2Elist_2ENIL(A_27b)),V5y) = c_2Elist_2ENIL(A_27a) ) )
& ! [V7v5] :
( mem(V7v5,ty_2Elist_2Elist(A_27b))
=> ! [V8v4] :
( mem(V8v4,A_27b)
=> ! [V9f] :
( mem(V9f,arr(A_27b,arr(A_27c,A_27a)))
=> ap(ap(ap(c_2Elist_2EMAP2(A_27a,A_27b,A_27c),V9f),ap(ap(c_2Elist_2ECONS(A_27b),V8v4),V7v5)),c_2Elist_2ENIL(A_27c)) = c_2Elist_2ENIL(A_27a) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [A_27e] :
( ne(A_27e)
=> ! [A_27f] :
( ne(A_27f)
=> ( ! [V0f] :
( mem(V0f,arr(A_27a,arr(A_27b,A_27c)))
=> ap(ap(ap(c_2Elist_2EMAP2(A_27c,A_27a,A_27b),V0f),c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27b)) = c_2Elist_2ENIL(A_27c) )
& ! [V1f] :
( mem(V1f,arr(A_27d,arr(A_27e,A_27f)))
=> ! [V2h1] :
( mem(V2h1,A_27d)
=> ! [V3t1] :
( mem(V3t1,ty_2Elist_2Elist(A_27d))
=> ! [V4h2] :
( mem(V4h2,A_27e)
=> ! [V5t2] :
( mem(V5t2,ty_2Elist_2Elist(A_27e))
=> ap(ap(ap(c_2Elist_2EMAP2(A_27f,A_27d,A_27e),V1f),ap(ap(c_2Elist_2ECONS(A_27d),V2h1),V3t1)),ap(ap(c_2Elist_2ECONS(A_27e),V4h2),V5t2)) = ap(ap(c_2Elist_2ECONS(A_27f),ap(ap(V1f,V2h1),V4h2)),ap(ap(ap(c_2Elist_2EMAP2(A_27f,A_27d,A_27e),V1f),V3t1),V5t2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP2__NIL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V1x] :
( mem(V1x,ty_2Elist_2Elist(A_27b))
=> ap(ap(ap(c_2Elist_2EMAP2(A_27a,A_27b,A_27c),V0f),V1x),c_2Elist_2ENIL(A_27c)) = c_2Elist_2ENIL(A_27a) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__MAP2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27a,arr(A_27b,A_27c)))
=> ! [V1xs] :
( mem(V1xs,ty_2Elist_2Elist(A_27a))
=> ! [V2ys] :
( mem(V2ys,ty_2Elist_2Elist(A_27b))
=> ap(c_2Elist_2ELENGTH(A_27c),ap(ap(ap(c_2Elist_2EMAP2(A_27c,A_27a,A_27b),V0f),V1xs),V2ys)) = ap(ap(c_2Earithmetic_2EMIN,ap(c_2Elist_2ELENGTH(A_27a),V1xs)),ap(c_2Elist_2ELENGTH(A_27b),V2ys)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEL__MAP2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27a,arr(A_27b,A_27c)))
=> ! [V1ts] :
( mem(V1ts,ty_2Elist_2Elist(A_27a))
=> ! [V2tt] :
( mem(V2tt,ty_2Elist_2Elist(A_27b))
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(ap(c_2Earithmetic_2EMIN,ap(c_2Elist_2ELENGTH(A_27a),V1ts)),ap(c_2Elist_2ELENGTH(A_27b),V2tt))))
=> ap(ap(c_2Elist_2EEL(A_27c),V3n),ap(ap(ap(c_2Elist_2EMAP2(A_27c,A_27a,A_27b),V0f),V1ts),V2tt)) = ap(ap(V0f,ap(ap(c_2Elist_2EEL(A_27a),V3n),V1ts)),ap(ap(c_2Elist_2EEL(A_27b),V3n),V2tt)) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EINDEX__FIND__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0i] :
( mem(V0i,ty_2Enum_2Enum)
=> ! [V1P] :
( mem(V1P,arr(A_27a,bool))
=> ap(ap(ap(c_2Elist_2EINDEX__FIND(A_27a),V0i),V1P),c_2Elist_2ENIL(A_27a)) = c_2Eoption_2ENONE(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)) ) )
& ! [V2i] :
( mem(V2i,ty_2Enum_2Enum)
=> ! [V3P] :
( mem(V3P,arr(A_27a,bool))
=> ! [V4h] :
( mem(V4h,A_27a)
=> ! [V5t] :
( mem(V5t,ty_2Elist_2Elist(A_27a))
=> ap(ap(ap(c_2Elist_2EINDEX__FIND(A_27a),V2i),V3P),ap(ap(c_2Elist_2ECONS(A_27a),V4h),V5t)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a))),ap(V3P,V4h)),ap(c_2Eoption_2ESOME(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,A_27a),V2i),V4h))),ap(ap(ap(c_2Elist_2EINDEX__FIND(A_27a),ap(c_2Enum_2ESUC,V2i)),V3P),V5t)) ) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EFIND__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ap(c_2Elist_2EFIND(A_27a),V0P) = ap(ap(c_2Ecombin_2Eo(ty_2Elist_2Elist(A_27a),ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a))),ap(c_2Eoption_2EOPTION__MAP(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a),A_27a),c_2Epair_2ESND(ty_2Enum_2Enum,A_27a))),ap(ap(c_2Elist_2EINDEX__FIND(A_27a),c_2Enum_2E0),V0P)) ) ) ).
fof(ax_thm_2Elist_2EINDEX__OF__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ap(c_2Elist_2EINDEX__OF(A_27a),V0x) = ap(ap(c_2Ecombin_2Eo(ty_2Elist_2Elist(A_27a),ty_2Eoption_2Eoption(ty_2Enum_2Enum),ty_2Eoption_2Eoption(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a))),ap(c_2Eoption_2EOPTION__MAP(ty_2Epair_2Eprod(ty_2Enum_2Enum,A_27a),ty_2Enum_2Enum),c_2Epair_2EFST(ty_2Enum_2Enum,A_27a))),ap(ap(c_2Elist_2EINDEX__FIND(A_27a),c_2Enum_2E0),ap(c_2Emin_2E_3D(A_27a),V0x))) ) ) ).
fof(conj_thm_2Elist_2ENULL,axiom,
! [A_27a] :
( ne(A_27a)
=> ( p(ap(c_2Elist_2ENULL(A_27a),c_2Elist_2ENIL(A_27a)))
& ! [V0h] :
( mem(V0h,A_27a)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(A_27a))
=> ~ p(ap(c_2Elist_2ENULL(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t))) ) ) ) ) ).
fof(conj_thm_2Elist_2Elist__INDUCT0,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool))
=> ( ( p(ap(V0P,c_2Elist_2ENIL(A_27a)))
& ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(V0P,V1l))
=> ! [V2a] :
( mem(V2a,A_27a)
=> p(ap(V0P,ap(ap(c_2Elist_2ECONS(A_27a),V2a),V1l))) ) ) ) )
=> ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(A_27a))
=> p(ap(V0P,V3l)) ) ) ) ) ).
fof(conj_thm_2Elist_2Elist__INDUCT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool))
=> ( ( p(ap(V0P,c_2Elist_2ENIL(A_27a)))
& ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(A_27a))
=> ( p(ap(V0P,V1t))
=> ! [V2h] :
( mem(V2h,A_27a)
=> p(ap(V0P,ap(ap(c_2Elist_2ECONS(A_27a),V2h),V1t))) ) ) ) )
=> ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(A_27a))
=> p(ap(V0P,V3l)) ) ) ) ) ).
fof(conj_thm_2Elist_2Elist__induction,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool))
=> ( ( p(ap(V0P,c_2Elist_2ENIL(A_27a)))
& ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(A_27a))
=> ( p(ap(V0P,V1t))
=> ! [V2h] :
( mem(V2h,A_27a)
=> p(ap(V0P,ap(ap(c_2Elist_2ECONS(A_27a),V2h),V1t))) ) ) ) )
=> ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(A_27a))
=> p(ap(V0P,V3l)) ) ) ) ) ).
fof(conj_thm_2Elist_2Elist__CASES,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( V0l = c_2Elist_2ENIL(A_27a)
| ? [V1h] :
( mem(V1h,A_27a)
& ? [V2t] :
( mem(V2t,ty_2Elist_2Elist(A_27a))
& V0l = ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t) ) ) ) ) ) ).
fof(conj_thm_2Elist_2Elist__nchotomy,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( V0l = c_2Elist_2ENIL(A_27a)
| ? [V1h] :
( mem(V1h,A_27a)
& ? [V2t] :
( mem(V2t,ty_2Elist_2Elist(A_27a))
& V0l = ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t) ) ) ) ) ) ).
fof(conj_thm_2Elist_2Elist__case__compute,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0b] :
( mem(V0b,A_27b)
=> ! [V1f] :
( mem(V1f,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),A_27b)))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,A_27b),V2l),V0b),V1f) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(c_2Elist_2ENULL(A_27a),V2l)),V0b),ap(ap(V1f,ap(c_2Elist_2EHD(A_27a),V2l)),ap(c_2Elist_2ETL(A_27a),V2l))) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ECONS__11,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a0] :
( mem(V0a0,A_27a)
=> ! [V1a1] :
( mem(V1a1,ty_2Elist_2Elist(A_27a))
=> ! [V2a0_27] :
( mem(V2a0_27,A_27a)
=> ! [V3a1_27] :
( mem(V3a1_27,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2ECONS(A_27a),V0a0),V1a1) = ap(ap(c_2Elist_2ECONS(A_27a),V2a0_27),V3a1_27)
<=> ( V0a0 = V2a0_27
& V1a1 = V3a1_27 ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ENOT__NIL__CONS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a1] :
( mem(V0a1,ty_2Elist_2Elist(A_27a))
=> ! [V1a0] :
( mem(V1a0,A_27a)
=> c_2Elist_2ENIL(A_27a) != ap(ap(c_2Elist_2ECONS(A_27a),V1a0),V0a1) ) ) ) ).
fof(conj_thm_2Elist_2ENOT__CONS__NIL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a1] :
( mem(V0a1,ty_2Elist_2Elist(A_27a))
=> ! [V1a0] :
( mem(V1a0,A_27a)
=> ap(ap(c_2Elist_2ECONS(A_27a),V1a0),V0a1) != c_2Elist_2ENIL(A_27a) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__NOT__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ( V0l1 != V1l2
=> ! [V2h1] :
( mem(V2h1,A_27a)
=> ! [V3h2] :
( mem(V3h2,A_27a)
=> ap(ap(c_2Elist_2ECONS(A_27a),V2h1),V0l1) != ap(ap(c_2Elist_2ECONS(A_27a),V3h2),V1l2) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ENOT__EQ__LIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h1] :
( mem(V0h1,A_27a)
=> ! [V1h2] :
( mem(V1h2,A_27a)
=> ( V0h1 != V1h2
=> ! [V2l1] :
( mem(V2l1,ty_2Elist_2Elist(A_27a))
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2ECONS(A_27a),V0h1),V2l1) != ap(ap(c_2Elist_2ECONS(A_27a),V1h2),V3l2) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEQ__LIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h1] :
( mem(V0h1,A_27a)
=> ! [V1h2] :
( mem(V1h2,A_27a)
=> ( V0h1 = V1h2
=> ! [V2l1] :
( mem(V2l1,ty_2Elist_2Elist(A_27a))
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(A_27a))
=> ( V2l1 = V3l2
=> ap(ap(c_2Elist_2ECONS(A_27a),V0h1),V2l1) = ap(ap(c_2Elist_2ECONS(A_27a),V1h2),V3l2) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ECONS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( ~ p(ap(c_2Elist_2ENULL(A_27a),V0l))
=> ap(ap(c_2Elist_2ECONS(A_27a),ap(c_2Elist_2EHD(A_27a),V0l)),ap(c_2Elist_2ETL(A_27a),V0l)) = V0l ) ) ) ).
fof(conj_thm_2Elist_2EAPPEND__NIL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EAPPEND(A_27a),V0l),c_2Elist_2ENIL(A_27a)) = V0l ) ) ).
fof(conj_thm_2Elist_2EAPPEND__ASSOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ! [V2l3] :
( mem(V2l3,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l2),V2l3)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)),V2l3) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__APPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ELENGTH(A_27a),V0l1)),ap(c_2Elist_2ELENGTH(A_27a),V1l2)) ) ) ) ).
fof(conj_thm_2Elist_2EMAP__APPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),V2l2)) = ap(ap(c_2Elist_2EAPPEND(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1l1)),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V2l2)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP__ID,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EMAP(A_27a,A_27a),i(A_27a)),V0l) = V0l
& ap(ap(c_2Elist_2EMAP(A_27a,A_27a),c_2Ecombin_2EI(A_27a)),V0l) = V0l ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1f] :
( mem(V1f,arr(A_27a,A_27b))
=> ap(c_2Elist_2ELENGTH(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V0l)) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP__EQ__NIL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1f] :
( mem(V1f,arr(A_27a,A_27b))
=> ( ( ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V0l) = c_2Elist_2ENIL(A_27b)
<=> V0l = c_2Elist_2ENIL(A_27a) )
& ( c_2Elist_2ENIL(A_27b) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V0l)
<=> V0l = c_2Elist_2ENIL(A_27a) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP__EQ__CONS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ! [V2h] :
( mem(V2h,A_27b)
=> ! [V3t] :
( mem(V3t,ty_2Elist_2Elist(A_27b))
=> ( ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1l) = ap(ap(c_2Elist_2ECONS(A_27b),V2h),V3t)
<=> ? [V4x0] :
( mem(V4x0,A_27a)
& ? [V5t0] :
( mem(V5t0,ty_2Elist_2Elist(A_27a))
& V1l = ap(ap(c_2Elist_2ECONS(A_27a),V4x0),V5t0)
& V2h = ap(V0f,V4x0)
& V3t = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V5t0) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP__EQ__SING,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ! [V2x] :
( mem(V2x,A_27b)
=> ( ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1l) = ap(ap(c_2Elist_2ECONS(A_27b),V2x),c_2Elist_2ENIL(A_27b))
<=> ? [V3x0] :
( mem(V3x0,A_27a)
& V1l = ap(ap(c_2Elist_2ECONS(A_27a),V3x0),c_2Elist_2ENIL(A_27a))
& V2x = ap(V0f,V3x0) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP__EQ__f,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f1] :
( mem(V0f1,arr(A_27a,A_27b))
=> ! [V1f2] :
( mem(V1f2,arr(A_27a,A_27b))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f1),V2l) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f2),V2l)
<=> ! [V3e] :
( mem(V3e,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2l)))
=> ap(V0f1,V3e) = ap(V1f2,V3e) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP__o,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27b,A_27c))
=> ! [V1g] :
( mem(V1g,arr(A_27a,A_27b))
=> ap(c_2Elist_2EMAP(A_27a,A_27c),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),V0f),V1g)) = ap(ap(c_2Ecombin_2Eo(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27c),ty_2Elist_2Elist(A_27b)),ap(c_2Elist_2EMAP(A_27b,A_27c),V0f)),ap(c_2Elist_2EMAP(A_27a,A_27b),V1g)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP__MAP__o,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27b,A_27c))
=> ! [V1g] :
( mem(V1g,arr(A_27a,A_27b))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EMAP(A_27b,A_27c),V0f),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1g),V2l)) = ap(ap(c_2Elist_2EMAP(A_27a,A_27c),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),V0f),V1g)),V2l) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEL__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Elist_2ELENGTH(A_27a),V1l)))
=> ! [V2f] :
( mem(V2f,arr(A_27a,A_27b))
=> ap(ap(c_2Elist_2EEL(A_27b),V0n),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V2f),V1l)) = ap(V2f,ap(ap(c_2Elist_2EEL(A_27a),V0n),V1l)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEL__APPEND__EQN,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2EEL(A_27a),V2n),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(c_2Elist_2ELENGTH(A_27a),V0l1))),ap(ap(c_2Elist_2EEL(A_27a),V2n),V0l1)),ap(ap(c_2Elist_2EEL(A_27a),ap(ap(c_2Earithmetic_2E_2D,V2n),ap(c_2Elist_2ELENGTH(A_27a),V0l1))),V1l2)) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP__TL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1f] :
( mem(V1f,arr(A_27a,A_27b))
=> ( ~ p(ap(c_2Elist_2ENULL(A_27a),V0l))
=> ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),ap(c_2Elist_2ETL(A_27a),V0l)) = ap(c_2Elist_2ETL(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V0l)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY__EL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1P] :
( mem(V1P,arr(A_27a,bool))
=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V1P),V0l))
<=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(c_2Elist_2ELENGTH(A_27a),V0l)))
=> p(ap(V1P,ap(ap(c_2Elist_2EEL(A_27a),V2n),V0l))) ) ) ) ) ) ) ).
fof(lameq_f390,axiom,
! [A_27a,V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q] :
( mem(V1Q,arr(A_27a,bool))
=> ! [V3x] : ap(f390(A_27a,V0P,V1Q),V3x) = ap(ap(c_2Ebool_2E_2F_5C,ap(V0P,V3x)),ap(V1Q,V3x)) ) ) ).
fof(conj_thm_2Elist_2EEVERY__CONJ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q] :
( mem(V1Q,arr(A_27a,bool))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),f390(A_27a,V0P,V1Q)),V2l))
<=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V2l))
& p(ap(ap(c_2Elist_2EEVERY(A_27a),V1Q),V2l)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY__MEM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V1l))
<=> ! [V2e] :
( mem(V2e,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l)))
=> p(ap(V0P,V2e)) ) ) ) ) ) ) ).
fof(lameq_f391,axiom,
! [A_27b,A_27a,V1f] :
( mem(V1f,arr(A_27a,A_27b))
=> ! [V0P] :
( mem(V0P,arr(A_27b,bool))
=> ! [V3x] : ap(f391(A_27b,A_27a,V1f,V0P),V3x) = ap(V0P,ap(V1f,V3x)) ) ) ).
fof(conj_thm_2Elist_2EEVERY__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(A_27b,bool))
=> ! [V1f] :
( mem(V1f,arr(A_27a,A_27b))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEVERY(A_27b),V0P),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V2l)))
<=> p(ap(ap(c_2Elist_2EEVERY(A_27a),f391(A_27b,A_27a,V1f,V0P)),V2l)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY__SIMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0c] :
( mem(V0c,bool)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),k(A_27a,V0c)),V1l))
<=> ( V1l = c_2Elist_2ENIL(A_27a)
| p(V0c) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMONO__EVERY,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q] :
( mem(V1Q,arr(A_27a,bool))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ( ! [V3x] :
( mem(V3x,A_27a)
=> ( p(ap(V0P,V3x))
=> p(ap(V1Q,V3x)) ) )
=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V2l))
=> p(ap(ap(c_2Elist_2EEVERY(A_27a),V1Q),V2l)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEXISTS__MEM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),V1l))
<=> ? [V2e] :
( mem(V2e,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l)))
& p(ap(V0P,V2e)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEXISTS__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(A_27b,bool))
=> ! [V1f] :
( mem(V1f,arr(A_27a,A_27b))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEXISTS(A_27b),V0P),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V2l)))
<=> p(ap(ap(c_2Elist_2EEXISTS(A_27a),f391(A_27b,A_27a,V1f,V0P)),V2l)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEXISTS__SIMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0c] :
( mem(V0c,bool)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEXISTS(A_27a),k(A_27a,V0c)),V1l))
<=> ( V1l != c_2Elist_2ENIL(A_27a)
& p(V0c) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMONO__EXISTS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q] :
( mem(V1Q,arr(A_27a,bool))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ( ! [V3x] :
( mem(V3x,A_27a)
=> ( p(ap(V0P,V3x))
=> p(ap(V1Q,V3x)) ) )
=> ( p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),V2l))
=> p(ap(ap(c_2Elist_2EEXISTS(A_27a),V1Q),V2l)) ) ) ) ) ) ) ).
fof(lameq_f392,axiom,
! [A_27a,V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V2x] : ap(f392(A_27a,V0P),V2x) = ap(c_2Ebool_2E_7E,ap(V0P,V2x)) ) ).
fof(conj_thm_2Elist_2EEVERY__NOT__EXISTS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V1l))
<=> ~ p(ap(ap(c_2Elist_2EEXISTS(A_27a),f392(A_27a,V0P)),V1l)) ) ) ) ) ).
fof(conj_thm_2Elist_2EEXISTS__NOT__EVERY,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),V1l))
<=> ~ p(ap(ap(c_2Elist_2EEVERY(A_27a),f392(A_27a,V0P)),V1l)) ) ) ) ) ).
fof(conj_thm_2Elist_2EMEM__APPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0e] :
( mem(V0e,A_27a)
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),V2l2))))
<=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l1)))
| p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2l2))) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMEM__FILTER,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1L] :
( mem(V1L,ty_2Elist_2Elist(A_27a))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1L))))
<=> ( p(ap(V0P,V2x))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1L))) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMEM__FLAT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1L] :
( mem(V1L,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27a)))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Elist_2EFLAT(A_27a),V1L))))
<=> ? [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
& p(ap(ap(c_2Ebool_2EIN(ty_2Elist_2Elist(A_27a)),V2l),ap(c_2Elist_2ELIST__TO__SET(ty_2Elist_2Elist(A_27a)),V1L)))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2l))) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EFLAT__APPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27a)))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27a)))
=> ap(c_2Elist_2EFLAT(A_27a),ap(ap(c_2Elist_2EAPPEND(ty_2Elist_2Elist(A_27a)),V0l1),V1l2)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(c_2Elist_2EFLAT(A_27a),V0l1)),ap(c_2Elist_2EFLAT(A_27a),V1l2)) ) ) ) ).
fof(conj_thm_2Elist_2EFLAT__compute,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0t] :
( mem(V0t,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27b)))
=> ! [V1h] :
( mem(V1h,A_27c)
=> ! [V2t1] :
( mem(V2t1,ty_2Elist_2Elist(A_27c))
=> ! [V3t2] :
( mem(V3t2,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27c)))
=> ( ap(c_2Elist_2EFLAT(A_27a),c_2Elist_2ENIL(ty_2Elist_2Elist(A_27a))) = c_2Elist_2ENIL(A_27a)
& ap(c_2Elist_2EFLAT(A_27b),ap(ap(c_2Elist_2ECONS(ty_2Elist_2Elist(A_27b)),c_2Elist_2ENIL(A_27b)),V0t)) = ap(c_2Elist_2EFLAT(A_27b),V0t)
& ap(c_2Elist_2EFLAT(A_27c),ap(ap(c_2Elist_2ECONS(ty_2Elist_2Elist(A_27c)),ap(ap(c_2Elist_2ECONS(A_27c),V1h),V2t1)),V3t2)) = ap(ap(c_2Elist_2ECONS(A_27c),V1h),ap(c_2Elist_2EFLAT(A_27c),ap(ap(c_2Elist_2ECONS(ty_2Elist_2Elist(A_27c)),V2t1),V3t2))) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY__APPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),V2l2)))
<=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V1l1))
& p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V2l2)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEXISTS__APPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),V2l2)))
<=> ( p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),V1l1))
| p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),V2l2)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ENOT__EVERY,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( ~ p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V1l))
<=> p(ap(ap(c_2Elist_2EEXISTS(A_27a),ap(ap(c_2Ecombin_2Eo(A_27a,bool,bool),c_2Ebool_2E_7E),V0P)),V1l)) ) ) ) ) ).
fof(conj_thm_2Elist_2ENOT__EXISTS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( ~ p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),V1l))
<=> p(ap(ap(c_2Elist_2EEVERY(A_27a),ap(ap(c_2Ecombin_2Eo(A_27a,bool,bool),c_2Ebool_2E_7E),V0P)),V1l)) ) ) ) ) ).
fof(conj_thm_2Elist_2EMEM__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1f] :
( mem(V1f,arr(A_27a,A_27b))
=> ! [V2x] :
( mem(V2x,A_27b)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27b),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V0l))))
<=> ? [V3y] :
( mem(V3y,A_27a)
& V2x = ap(V1f,V3y)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__NIL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = c_2Enum_2E0
<=> V0l = c_2Elist_2ENIL(A_27a) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__NIL__SYM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( c_2Enum_2E0 = ap(c_2Elist_2ELENGTH(A_27a),V0l)
<=> V0l = c_2Elist_2ENIL(A_27a) ) ) ) ).
fof(conj_thm_2Elist_2ENULL__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(c_2Elist_2ENULL(A_27a),V0l))
<=> V0l = c_2Elist_2ENIL(A_27a) ) ) ) ).
fof(conj_thm_2Elist_2ENULL__LENGTH,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(c_2Elist_2ENULL(A_27a),V0l))
<=> ap(c_2Elist_2ELENGTH(A_27a),V0l) = c_2Enum_2E0 ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__CONS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(c_2Enum_2ESUC,V1n)
<=> ? [V2h] :
( mem(V2h,A_27a)
& ? [V3l_27] :
( mem(V3l_27,ty_2Elist_2Elist(A_27a))
& ap(c_2Elist_2ELENGTH(A_27a),V3l_27) = V1n
& V0l = ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3l_27) ) ) ) ) ) ) ).
fof(lameq_f393,axiom,
! [A_27a,V4l] :
( mem(V4l,ty_2Elist_2Elist(A_27a))
=> ! [V0P] :
( mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool))
=> ! [V5x] : ap(f393(A_27a,V4l,V0P),V5x) = ap(V0P,ap(ap(c_2Elist_2ECONS(A_27a),V5x),V4l)) ) ) ).
fof(lameq_f394,axiom,
! [A_27a,V0P] :
( mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool))
=> ! [V4l] : ap(f394(A_27a,V0P),V4l) = ap(c_2Ebool_2E_21(A_27a),f393(A_27a,V4l,V0P)) ) ).
fof(conj_thm_2Elist_2ELENGTH__EQ__CONS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V2l) = ap(c_2Enum_2ESUC,V1n)
=> p(ap(V0P,V2l)) ) )
<=> ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V3l) = V1n
=> p(ap(f394(A_27a,V0P),V3l)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__EQ__SUM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1n1] :
( mem(V1n1,ty_2Enum_2Enum)
=> ! [V2n2] :
( mem(V2n2,ty_2Enum_2Enum)
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = ap(ap(c_2Earithmetic_2E_2B,V1n1),V2n2)
<=> ? [V3l1] :
( mem(V3l1,ty_2Elist_2Elist(A_27a))
& ? [V4l2] :
( mem(V4l2,ty_2Elist_2Elist(A_27a))
& ap(c_2Elist_2ELENGTH(A_27a),V3l1) = V1n1
& ap(c_2Elist_2ELENGTH(A_27a),V4l2) = V2n2
& V0l = ap(ap(c_2Elist_2EAPPEND(A_27a),V3l1),V4l2) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__EQ__NUM,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = c_2Enum_2E0
<=> V0l = c_2Elist_2ENIL(A_27a) ) )
& ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( ap(c_2Elist_2ELENGTH(A_27a),V1l) = ap(c_2Enum_2ESUC,V2n)
<=> ? [V3h] :
( mem(V3h,A_27a)
& ? [V4l_27] :
( mem(V4l_27,ty_2Elist_2Elist(A_27a))
& ap(c_2Elist_2ELENGTH(A_27a),V4l_27) = V2n
& V1l = ap(ap(c_2Elist_2ECONS(A_27a),V3h),V4l_27) ) ) ) ) )
& ! [V5l] :
( mem(V5l,ty_2Elist_2Elist(A_27a))
=> ! [V6n1] :
( mem(V6n1,ty_2Enum_2Enum)
=> ! [V7n2] :
( mem(V7n2,ty_2Enum_2Enum)
=> ( ap(c_2Elist_2ELENGTH(A_27a),V5l) = ap(ap(c_2Earithmetic_2E_2B,V6n1),V7n2)
<=> ? [V8l1] :
( mem(V8l1,ty_2Elist_2Elist(A_27a))
& ? [V9l2] :
( mem(V9l2,ty_2Elist_2Elist(A_27a))
& ap(c_2Elist_2ELENGTH(A_27a),V8l1) = V6n1
& ap(c_2Elist_2ELENGTH(A_27a),V9l2) = V7n2
& V5l = ap(ap(c_2Elist_2EAPPEND(A_27a),V8l1),V9l2) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__EQ__NUM__compute,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = c_2Enum_2E0
<=> V0l = c_2Elist_2ENIL(A_27a) ) )
& ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( ap(c_2Elist_2ELENGTH(A_27a),V1l) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V2n))
<=> ? [V3h] :
( mem(V3h,A_27a)
& ? [V4l_27] :
( mem(V4l_27,ty_2Elist_2Elist(A_27a))
& ap(c_2Elist_2ELENGTH(A_27a),V4l_27) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V2n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))
& V1l = ap(ap(c_2Elist_2ECONS(A_27a),V3h),V4l_27) ) ) ) ) )
& ! [V5l] :
( mem(V5l,ty_2Elist_2Elist(A_27a))
=> ! [V6n] :
( mem(V6n,ty_2Enum_2Enum)
=> ( ap(c_2Elist_2ELENGTH(A_27a),V5l) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V6n))
<=> ? [V7h] :
( mem(V7h,A_27a)
& ? [V8l_27] :
( mem(V8l_27,ty_2Elist_2Elist(A_27a))
& ap(c_2Elist_2ELENGTH(A_27a),V8l_27) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n))
& V5l = ap(ap(c_2Elist_2ECONS(A_27a),V7h),V8l_27) ) ) ) ) )
& ! [V9l] :
( mem(V9l,ty_2Elist_2Elist(A_27a))
=> ! [V10n1] :
( mem(V10n1,ty_2Enum_2Enum)
=> ! [V11n2] :
( mem(V11n2,ty_2Enum_2Enum)
=> ( ap(c_2Elist_2ELENGTH(A_27a),V9l) = ap(ap(c_2Earithmetic_2E_2B,V10n1),V11n2)
<=> ? [V12l1] :
( mem(V12l1,ty_2Elist_2Elist(A_27a))
& ? [V13l2] :
( mem(V13l2,ty_2Elist_2Elist(A_27a))
& ap(c_2Elist_2ELENGTH(A_27a),V12l1) = V10n1
& ap(c_2Elist_2ELENGTH(A_27a),V13l2) = V11n2
& V9l = ap(ap(c_2Elist_2EAPPEND(A_27a),V12l1),V13l2) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__EQ__NIL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool))
=> ( ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V1l) = c_2Enum_2E0
=> p(ap(V0P,V1l)) ) )
<=> p(ap(V0P,c_2Elist_2ENIL(A_27a))) ) ) ) ).
fof(conj_thm_2Elist_2ECONS__ACYCLIC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ( V0l != ap(ap(c_2Elist_2ECONS(A_27a),V1x),V0l)
& ap(ap(c_2Elist_2ECONS(A_27a),V1x),V0l) != V0l ) ) ) ) ).
fof(conj_thm_2Elist_2EAPPEND__eq__NIL,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ( c_2Elist_2ENIL(A_27a) = ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)
<=> ( V0l1 = c_2Elist_2ENIL(A_27a)
& V1l2 = c_2Elist_2ENIL(A_27a) ) ) ) )
& ! [V2l1] :
( mem(V2l1,ty_2Elist_2Elist(A_27a))
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EAPPEND(A_27a),V2l1),V3l2) = c_2Elist_2ENIL(A_27a)
<=> ( V2l1 = c_2Elist_2ENIL(A_27a)
& V3l2 = c_2Elist_2ENIL(A_27a) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP__EQ__APPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ! [V2l1] :
( mem(V2l1,ty_2Elist_2Elist(A_27b))
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(A_27b))
=> ( ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1l) = ap(ap(c_2Elist_2EAPPEND(A_27b),V2l1),V3l2)
<=> ? [V4l10] :
( mem(V4l10,ty_2Elist_2Elist(A_27a))
& ? [V5l20] :
( mem(V5l20,ty_2Elist_2Elist(A_27a))
& V1l = ap(ap(c_2Elist_2EAPPEND(A_27a),V4l10),V5l20)
& V2l1 = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V4l10)
& V3l2 = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V5l20) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EAPPEND__EQ__SING,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ! [V2e] :
( mem(V2e,A_27a)
=> ( ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2) = ap(ap(c_2Elist_2ECONS(A_27a),V2e),c_2Elist_2ENIL(A_27a))
<=> ( ( V0l1 = ap(ap(c_2Elist_2ECONS(A_27a),V2e),c_2Elist_2ENIL(A_27a))
& V1l2 = c_2Elist_2ENIL(A_27a) )
| ( V0l1 = c_2Elist_2ENIL(A_27a)
& V1l2 = ap(ap(c_2Elist_2ECONS(A_27a),V2e),c_2Elist_2ENIL(A_27a)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EAPPEND__11,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ! [V2l3] :
( mem(V2l3,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2) = ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V2l3)
<=> V1l2 = V2l3 ) ) ) )
& ! [V3l1] :
( mem(V3l1,ty_2Elist_2Elist(A_27a))
=> ! [V4l2] :
( mem(V4l2,ty_2Elist_2Elist(A_27a))
=> ! [V5l3] :
( mem(V5l3,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EAPPEND(A_27a),V4l2),V3l1) = ap(ap(c_2Elist_2EAPPEND(A_27a),V5l3),V3l1)
<=> V4l2 = V5l3 ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EAPPEND__LENGTH__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l1_27] :
( mem(V1l1_27,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27a),V1l1_27)
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ! [V3l2_27] :
( mem(V3l2_27,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V2l2) = ap(c_2Elist_2ELENGTH(A_27a),V3l2_27)
=> ( ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V2l2) = ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1_27),V3l2_27)
<=> ( V0l1 = V1l1_27
& V2l2 = V3l2_27 ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EAPPEND__11__LENGTH,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ! [V2l1_27] :
( mem(V2l1_27,ty_2Elist_2Elist(A_27a))
=> ! [V3l2_27] :
( mem(V3l2_27,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27a),V2l1_27)
=> ( ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2) = ap(ap(c_2Elist_2EAPPEND(A_27a),V2l1_27),V3l2_27)
<=> ( V0l1 = V2l1_27
& V1l2 = V3l2_27 ) ) ) ) ) ) )
& ! [V4l1] :
( mem(V4l1,ty_2Elist_2Elist(A_27a))
=> ! [V5l2] :
( mem(V5l2,ty_2Elist_2Elist(A_27a))
=> ! [V6l1_27] :
( mem(V6l1_27,ty_2Elist_2Elist(A_27a))
=> ! [V7l2_27] :
( mem(V7l2_27,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V5l2) = ap(c_2Elist_2ELENGTH(A_27a),V7l2_27)
=> ( ap(ap(c_2Elist_2EAPPEND(A_27a),V4l1),V5l2) = ap(ap(c_2Elist_2EAPPEND(A_27a),V6l1_27),V7l2_27)
<=> ( V4l1 = V6l1_27
& V5l2 = V7l2_27 ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EAPPEND__EQ__SELF,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2) = V0l1
<=> V1l2 = c_2Elist_2ENIL(A_27a) ) ) )
& ! [V2l1] :
( mem(V2l1,ty_2Elist_2Elist(A_27a))
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EAPPEND(A_27a),V2l1),V3l2) = V3l2
<=> V2l1 = c_2Elist_2ENIL(A_27a) ) ) )
& ! [V4l1] :
( mem(V4l1,ty_2Elist_2Elist(A_27a))
=> ! [V5l2] :
( mem(V5l2,ty_2Elist_2Elist(A_27a))
=> ( V4l1 = ap(ap(c_2Elist_2EAPPEND(A_27a),V4l1),V5l2)
<=> V5l2 = c_2Elist_2ENIL(A_27a) ) ) )
& ! [V6l1] :
( mem(V6l1,ty_2Elist_2Elist(A_27a))
=> ! [V7l2] :
( mem(V7l2,ty_2Elist_2Elist(A_27a))
=> ( V7l2 = ap(ap(c_2Elist_2EAPPEND(A_27a),V6l1),V7l2)
<=> V6l1 = c_2Elist_2ENIL(A_27a) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMEM__SPLIT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l)))
<=> ? [V2l1] :
( mem(V2l1,ty_2Elist_2Elist(A_27a))
& ? [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(A_27a))
& V1l = ap(ap(c_2Elist_2EAPPEND(A_27a),V2l1),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V3l2)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__EQ__REWRITE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ( V0l1 = V1l2
<=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27a),V1l2)
& ! [V2x] :
( mem(V2x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2x),ap(c_2Elist_2ELENGTH(A_27a),V0l1)))
=> ap(ap(c_2Elist_2EEL(A_27a),V2x),V0l1) = ap(ap(c_2Elist_2EEL(A_27a),V2x),V1l2) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27a),V1l2)
& ! [V2x] :
( mem(V2x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2x),ap(c_2Elist_2ELENGTH(A_27a),V0l1)))
=> ap(ap(c_2Elist_2EEL(A_27a),V2x),V0l1) = ap(ap(c_2Elist_2EEL(A_27a),V2x),V1l2) ) ) )
=> V0l1 = V1l2 ) ) ) ) ).
fof(conj_thm_2Elist_2EFOLDL__EQ__FOLDR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(A_27a,arr(A_27a,A_27a)))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ! [V2e] :
( mem(V2e,A_27a)
=> ( ( p(ap(c_2Ecombin_2EASSOC(A_27a),V0f))
& p(ap(c_2Ecombin_2ECOMM(A_27a,A_27a),V0f)) )
=> ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27a),V0f),V2e),V1l) = ap(ap(ap(c_2Elist_2EFOLDR(A_27a,A_27a),V0f),V2e),V1l) ) ) ) ) ) ).
fof(lameq_f395,axiom,
! [A_27a,A_27b,V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] : ap(f395(A_27a,A_27b,V0f,V3x),V4y) = ap(ap(c_2Elist_2ECONS(A_27b),ap(V0f,V3x)),V4y) ) ) ).
fof(lameq_f396,axiom,
! [A_27b,A_27a,V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V3x] : ap(f396(A_27b,A_27a,V0f),V3x) = f395(A_27a,A_27b,V0f,V3x) ) ).
fof(conj_thm_2Elist_2EFOLDR__CONS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
=> ! [V2a] :
( mem(V2a,ty_2Elist_2Elist(A_27b))
=> ap(ap(ap(c_2Elist_2EFOLDR(A_27a,ty_2Elist_2Elist(A_27b)),f396(A_27b,A_27a,V0f)),V2a),V1ls) = ap(ap(c_2Elist_2EAPPEND(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1ls)),V2a) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__TL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Elist_2ELENGTH(A_27a),V0l)))
=> ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Elist_2ETL(A_27a),V0l)) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ) ).
fof(conj_thm_2Elist_2EFILTER__EQ__NIL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l) = c_2Elist_2ENIL(A_27a)
<=> p(ap(ap(c_2Elist_2EEVERY(A_27a),f392(A_27a,V0P)),V1l)) ) ) ) ) ).
fof(conj_thm_2Elist_2EFILTER__NEQ__NIL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l) != c_2Elist_2ENIL(A_27a)
<=> ? [V2x] :
( mem(V2x,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l)))
& p(ap(V0P,V2x)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EFILTER__EQ__ID,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l) = V1l
<=> p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V1l)) ) ) ) ) ).
fof(conj_thm_2Elist_2EFILTER__NEQ__ID,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l) != V1l
<=> ? [V2x] :
( mem(V2x,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l)))
& ~ p(ap(V0P,V2x)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EFILTER__EQ__CONS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ! [V2h] :
( mem(V2h,A_27a)
=> ! [V3lr] :
( mem(V3lr,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l) = ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3lr)
<=> ? [V4l1] :
( mem(V4l1,ty_2Elist_2Elist(A_27a))
& ? [V5l2] :
( mem(V5l2,ty_2Elist_2Elist(A_27a))
& V1l = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V4l1),ap(ap(c_2Elist_2ECONS(A_27a),V2h),c_2Elist_2ENIL(A_27a)))),V5l2)
& ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V4l1) = c_2Elist_2ENIL(A_27a)
& ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V5l2) = V3lr
& p(ap(V0P,V2h)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EFILTER__APPEND__DISTRIB,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1L] :
( mem(V1L,ty_2Elist_2Elist(A_27a))
=> ! [V2M] :
( mem(V2M,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EFILTER(A_27a),V0P),ap(ap(c_2Elist_2EAPPEND(A_27a),V1L),V2M)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1L)),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V2M)) ) ) ) ) ).
fof(conj_thm_2Elist_2EMEM,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0x] :
( mem(V0x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),c_2Elist_2ENIL(A_27a))))
<=> $false ) )
& ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2h] :
( mem(V2h,A_27a)
=> ! [V3t] :
( mem(V3t,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t))))
<=> ( V1x = V2h
| p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V3t))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EFILTER__EQ__APPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ! [V2l1] :
( mem(V2l1,ty_2Elist_2Elist(A_27a))
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l) = ap(ap(c_2Elist_2EAPPEND(A_27a),V2l1),V3l2)
<=> ? [V4l3] :
( mem(V4l3,ty_2Elist_2Elist(A_27a))
& ? [V5l4] :
( mem(V5l4,ty_2Elist_2Elist(A_27a))
& V1l = ap(ap(c_2Elist_2EAPPEND(A_27a),V4l3),V5l4)
& ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V4l3) = V2l1
& ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V5l4) = V3l2 ) ) ) ) ) ) ) ) ).
fof(lameq_f397,axiom,
! [A_27a,V1P2] :
( mem(V1P2,arr(A_27a,bool))
=> ! [V0P1] :
( mem(V0P1,arr(A_27a,bool))
=> ! [V3x] : ap(f397(A_27a,V1P2,V0P1),V3x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(V1P2,V3x)),ap(V0P1,V3x)) ) ) ).
fof(conj_thm_2Elist_2EEVERY__FILTER,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P1] :
( mem(V0P1,arr(A_27a,bool))
=> ! [V1P2] :
( mem(V1P2,arr(A_27a,bool))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P1),ap(ap(c_2Elist_2EFILTER(A_27a),V1P2),V2l)))
<=> p(ap(ap(c_2Elist_2EEVERY(A_27a),f397(A_27a,V1P2,V0P1)),V2l)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY__FILTER__IMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P1] :
( mem(V0P1,arr(A_27a,bool))
=> ! [V1P2] :
( mem(V1P2,arr(A_27a,bool))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P1),V2l))
=> p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P1),ap(ap(c_2Elist_2EFILTER(A_27a),V1P2),V2l))) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EFILTER__COND__REWRITE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EFILTER(A_27a),V0P),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a)
& ! [V2h] :
( mem(V2h,A_27a)
=> ( p(ap(V0P,V2h))
=> ap(ap(c_2Elist_2EFILTER(A_27a),V0P),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V1l)) = ap(ap(c_2Elist_2ECONS(A_27a),V2h),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l)) ) )
& ! [V3h] :
( mem(V3h,A_27a)
=> ( ~ p(ap(V0P,V3h))
=> ap(ap(c_2Elist_2EFILTER(A_27a),V0P),ap(ap(c_2Elist_2ECONS(A_27a),V3h),V1l)) = ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ENOT__NULL__MEM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( ~ p(ap(c_2Elist_2ENULL(A_27a),V0l))
<=> ? [V1e] :
( mem(V1e,A_27a)
& p(ap(ap(c_2Ebool_2EIN(A_27a),V1e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l))) ) ) ) ) ).
fof(conj_thm_2Elist_2EEL__compute,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2EEL(A_27a),V1n),V0l) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1n),c_2Enum_2E0)),ap(c_2Elist_2EHD(A_27a),V0l)),ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Eprim__rec_2EPRE,V1n)),ap(c_2Elist_2ETL(A_27a),V0l))) ) ) ) ).
fof(conj_thm_2Elist_2EEL__simp,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),V1l) = ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n)))),ap(c_2Elist_2ETL(A_27a),V1l))
& ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n))),V1l) = ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),ap(c_2Elist_2ETL(A_27a),V1l)) ) ) ) ) ).
fof(conj_thm_2Elist_2EEL__restricted,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,A_27b)
=> ! [V2ls] :
( mem(V2ls,ty_2Elist_2Elist(A_27b))
=> ( ap(c_2Elist_2EEL(A_27a),c_2Enum_2E0) = c_2Elist_2EHD(A_27a)
& ap(ap(c_2Elist_2EEL(A_27b),ap(c_2Enum_2ESUC,V0n)),ap(ap(c_2Elist_2ECONS(A_27b),V1l),V2ls)) = ap(ap(c_2Elist_2EEL(A_27b),V0n),V2ls) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEL__simp__restricted,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,A_27a)
=> ! [V2ls] :
( mem(V2ls,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),ap(ap(c_2Elist_2ECONS(A_27a),V1l),V2ls)) = ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n)))),V2ls)
& ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n))),ap(ap(c_2Elist_2ECONS(A_27a),V1l),V2ls)) = ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),V2ls) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ESUM__eq__0,axiom,
! [V0ls] :
( mem(V0ls,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ( ap(c_2Elist_2ESUM,V0ls) = c_2Enum_2E0
<=> ! [V1x] :
( mem(V1x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V1x),ap(c_2Elist_2ELIST__TO__SET(ty_2Enum_2Enum),V0ls)))
=> V1x = c_2Enum_2E0 ) ) ) ) ).
fof(conj_thm_2Elist_2ENULL__FILTER,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
=> ( p(ap(c_2Elist_2ENULL(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1ls)))
<=> ! [V2x] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1ls)))
=> ~ p(ap(V0P,V2x)) ) ) ) ) ) ) ).
fof(lameq_f398,axiom,
! [A_27a,V0L1] :
( mem(V0L1,ty_2Elist_2Elist(A_27a))
=> ! [V1L2] :
( mem(V1L2,ty_2Elist_2Elist(A_27a))
=> ! [V2h] : ap(f398(A_27a,V0L1,V1L2),V2h) = ap(ap(c_2Emin_2E_3D(ty_2Elist_2Elist(A_27a)),V1L2),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V0L1)) ) ) ).
fof(lameq_f399,axiom,
! [A_27a,V0L1] :
( mem(V0L1,ty_2Elist_2Elist(A_27a))
=> ! [V1L2] : ap(f399(A_27a,V0L1),V1L2) = ap(c_2Ebool_2E_3F(A_27a),f398(A_27a,V0L1,V1L2)) ) ).
fof(lameq_f400,axiom,
! [A_27a,V0L1] : ap(f400(A_27a),V0L1) = f399(A_27a,V0L1) ).
fof(conj_thm_2Elist_2EWF__LIST__PRED,axiom,
! [A_27a] :
( ne(A_27a)
=> p(ap(c_2Erelation_2EWF(ty_2Elist_2Elist(A_27a)),f400(A_27a))) ) ).
fof(conj_thm_2Elist_2ELIST__REL__rules,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27b)))
& ! [V1h1] :
( mem(V1h1,A_27a)
=> ! [V2h2] :
( mem(V2h2,A_27b)
=> ! [V3t1] :
( mem(V3t1,ty_2Elist_2Elist(A_27a))
=> ! [V4t2] :
( mem(V4t2,ty_2Elist_2Elist(A_27b))
=> ( ( p(ap(ap(V0R,V1h1),V2h2))
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V3t1),V4t2)) )
=> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1h1),V3t1)),ap(ap(c_2Elist_2ECONS(A_27b),V2h2),V4t2))) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__REL__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1LIST__REL_27] :
( mem(V1LIST__REL_27,arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27b),bool)))
=> ( ( p(ap(ap(V1LIST__REL_27,c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27b)))
& ! [V2h1] :
( mem(V2h1,A_27a)
=> ! [V3h2] :
( mem(V3h2,A_27b)
=> ! [V4t1] :
( mem(V4t1,ty_2Elist_2Elist(A_27a))
=> ! [V5t2] :
( mem(V5t2,ty_2Elist_2Elist(A_27b))
=> ( ( p(ap(ap(V0R,V2h1),V3h2))
& p(ap(ap(V1LIST__REL_27,V4t1),V5t2)) )
=> p(ap(ap(V1LIST__REL_27,ap(ap(c_2Elist_2ECONS(A_27a),V2h1),V4t1)),ap(ap(c_2Elist_2ECONS(A_27b),V3h2),V5t2))) ) ) ) ) ) )
=> ! [V6a0] :
( mem(V6a0,ty_2Elist_2Elist(A_27a))
=> ! [V7a1] :
( mem(V7a1,ty_2Elist_2Elist(A_27b))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V6a0),V7a1))
=> p(ap(ap(V1LIST__REL_27,V6a0),V7a1)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__REL__strongind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1LIST__REL_27] :
( mem(V1LIST__REL_27,arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27b),bool)))
=> ( ( p(ap(ap(V1LIST__REL_27,c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27b)))
& ! [V2h1] :
( mem(V2h1,A_27a)
=> ! [V3h2] :
( mem(V3h2,A_27b)
=> ! [V4t1] :
( mem(V4t1,ty_2Elist_2Elist(A_27a))
=> ! [V5t2] :
( mem(V5t2,ty_2Elist_2Elist(A_27b))
=> ( ( p(ap(ap(V0R,V2h1),V3h2))
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V4t1),V5t2))
& p(ap(ap(V1LIST__REL_27,V4t1),V5t2)) )
=> p(ap(ap(V1LIST__REL_27,ap(ap(c_2Elist_2ECONS(A_27a),V2h1),V4t1)),ap(ap(c_2Elist_2ECONS(A_27b),V3h2),V5t2))) ) ) ) ) ) )
=> ! [V6a0] :
( mem(V6a0,ty_2Elist_2Elist(A_27a))
=> ! [V7a1] :
( mem(V7a1,ty_2Elist_2Elist(A_27b))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V6a0),V7a1))
=> p(ap(ap(V1LIST__REL_27,V6a0),V7a1)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__REL__cases,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1a0] :
( mem(V1a0,ty_2Elist_2Elist(A_27a))
=> ! [V2a1] :
( mem(V2a1,ty_2Elist_2Elist(A_27b))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V1a0),V2a1))
<=> ( ( V1a0 = c_2Elist_2ENIL(A_27a)
& V2a1 = c_2Elist_2ENIL(A_27b) )
| ? [V3h1] :
( mem(V3h1,A_27a)
& ? [V4h2] :
( mem(V4h2,A_27b)
& ? [V5t1] :
( mem(V5t1,ty_2Elist_2Elist(A_27a))
& ? [V6t2] :
( mem(V6t2,ty_2Elist_2Elist(A_27b))
& V1a0 = ap(ap(c_2Elist_2ECONS(A_27a),V3h1),V5t1)
& V2a1 = ap(ap(c_2Elist_2ECONS(A_27b),V4h2),V6t2)
& p(ap(ap(V0R,V3h1),V4h2))
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V5t1),V6t2)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__REL__EL__EQN,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27b))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V1l1),V2l2))
<=> ( ap(c_2Elist_2ELENGTH(A_27a),V1l1) = ap(c_2Elist_2ELENGTH(A_27b),V2l2)
& ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(c_2Elist_2ELENGTH(A_27a),V1l1)))
=> p(ap(ap(V0R,ap(ap(c_2Elist_2EEL(A_27a),V3n),V1l1)),ap(ap(c_2Elist_2EEL(A_27b),V3n),V2l2))) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__REL__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1a] :
( mem(V1a,A_27a)
=> ! [V2as] :
( mem(V2as,ty_2Elist_2Elist(A_27a))
=> ! [V3b] :
( mem(V3b,A_27b)
=> ! [V4bs] :
( mem(V4bs,ty_2Elist_2Elist(A_27b))
=> ( ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27b)))
<=> $true )
& ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1a),V2as)),c_2Elist_2ENIL(A_27b)))
<=> $false )
& ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27b),V3b),V4bs)))
<=> $false )
& ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1a),V2as)),ap(ap(c_2Elist_2ECONS(A_27b),V3b),V4bs)))
<=> ( p(ap(ap(V0R,V1a),V3b))
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V2as),V4bs)) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__REL__mono,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27b,bool)))
=> ! [V1R2] :
( mem(V1R2,arr(A_27a,arr(A_27b,bool)))
=> ! [V2l1] :
( mem(V2l1,ty_2Elist_2Elist(A_27a))
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(A_27b))
=> ( ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5y] :
( mem(V5y,A_27b)
=> ( p(ap(ap(V0R1,V4x),V5y))
=> p(ap(ap(V1R2,V4x),V5y)) ) ) )
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R1),V2l1),V3l2))
=> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V1R2),V2l1),V3l2)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__REL__NIL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1y] :
( mem(V1y,ty_2Elist_2Elist(A_27b))
=> ! [V2x] :
( mem(V2x,ty_2Elist_2Elist(A_27a))
=> ( ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),c_2Elist_2ENIL(A_27a)),V1y))
<=> V1y = c_2Elist_2ENIL(A_27b) )
& ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V2x),c_2Elist_2ENIL(A_27b)))
<=> V2x = c_2Elist_2ENIL(A_27a) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__REL__CONS1,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1h] :
( mem(V1h,A_27a)
=> ! [V2t] :
( mem(V2t,ty_2Elist_2Elist(A_27a))
=> ! [V3xs] :
( mem(V3xs,ty_2Elist_2Elist(A_27b))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t)),V3xs))
<=> ? [V4h_27] :
( mem(V4h_27,A_27b)
& ? [V5t_27] :
( mem(V5t_27,ty_2Elist_2Elist(A_27b))
& V3xs = ap(ap(c_2Elist_2ECONS(A_27b),V4h_27),V5t_27)
& p(ap(ap(V0R,V1h),V4h_27))
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V2t),V5t_27)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__REL__CONS2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1xs] :
( mem(V1xs,ty_2Elist_2Elist(A_27a))
=> ! [V2h] :
( mem(V2h,A_27b)
=> ! [V3t] :
( mem(V3t,ty_2Elist_2Elist(A_27b))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V1xs),ap(ap(c_2Elist_2ECONS(A_27b),V2h),V3t)))
<=> ? [V4h_27] :
( mem(V4h_27,A_27a)
& ? [V5t_27] :
( mem(V5t_27,ty_2Elist_2Elist(A_27a))
& V1xs = ap(ap(c_2Elist_2ECONS(A_27a),V4h_27),V5t_27)
& p(ap(ap(V0R,V4h_27),V2h))
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V5t_27),V3t)) ) ) ) ) ) ) ) ) ) ).
fof(lameq_f401,axiom,
! [A_27a,A_27b,V0P] :
( mem(V0P,arr(A_27a,arr(A_27b,bool)))
=> ! [V4a] :
( mem(V4a,A_27a)
=> ! [V1Q] :
( mem(V1Q,arr(A_27a,arr(A_27b,bool)))
=> ! [V5b] : ap(f401(A_27a,A_27b,V0P,V4a,V1Q),V5b) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(V0P,V4a),V5b)),ap(ap(V1Q,V4a),V5b)) ) ) ) ).
fof(lameq_f402,axiom,
! [A_27b,A_27a,V0P] :
( mem(V0P,arr(A_27a,arr(A_27b,bool)))
=> ! [V1Q] :
( mem(V1Q,arr(A_27a,arr(A_27b,bool)))
=> ! [V4a] : ap(f402(A_27b,A_27a,V0P,V1Q),V4a) = f401(A_27a,A_27b,V0P,V4a,V1Q) ) ) ).
fof(lameq_f403,axiom,
! [A_27a,A_27b,V6a] :
( mem(V6a,A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,arr(A_27b,bool)))
=> ! [V7b] : ap(f403(A_27a,A_27b,V6a,V0P),V7b) = ap(ap(V0P,V6a),V7b) ) ) ).
fof(lameq_f404,axiom,
! [A_27b,A_27a,V0P] :
( mem(V0P,arr(A_27a,arr(A_27b,bool)))
=> ! [V6a] : ap(f404(A_27b,A_27a,V0P),V6a) = f403(A_27a,A_27b,V6a,V0P) ) ).
fof(lameq_f405,axiom,
! [A_27a,A_27b,V8a] :
( mem(V8a,A_27a)
=> ! [V1Q] :
( mem(V1Q,arr(A_27a,arr(A_27b,bool)))
=> ! [V9b] : ap(f405(A_27a,A_27b,V8a,V1Q),V9b) = ap(ap(V1Q,V8a),V9b) ) ) ).
fof(lameq_f406,axiom,
! [A_27b,A_27a,V1Q] :
( mem(V1Q,arr(A_27a,arr(A_27b,bool)))
=> ! [V8a] : ap(f406(A_27b,A_27a,V1Q),V8a) = f405(A_27a,A_27b,V8a,V1Q) ) ).
fof(conj_thm_2Elist_2ELIST__REL__CONJ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(A_27a,arr(A_27b,bool)))
=> ! [V1Q] :
( mem(V1Q,arr(A_27a,arr(A_27b,bool)))
=> ! [V2l1] :
( mem(V2l1,ty_2Elist_2Elist(A_27a))
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(A_27b))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),f402(A_27b,A_27a,V0P,V1Q)),V2l1),V3l2))
<=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),f404(A_27b,A_27a,V0P)),V2l1),V3l2))
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),f406(A_27b,A_27a,V1Q)),V2l1),V3l2)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__REL__MAP1,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1f] :
( mem(V1f,arr(A_27c,A_27a))
=> ! [V2l1] :
( mem(V2l1,ty_2Elist_2Elist(A_27c))
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(A_27b))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),ap(ap(c_2Elist_2EMAP(A_27c,A_27a),V1f),V2l1)),V3l2))
<=> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27c,A_27b),ap(ap(c_2Ecombin_2Eo(A_27c,arr(A_27b,bool),A_27a),V0R),V1f)),V2l1),V3l2)) ) ) ) ) ) ) ) ) ).
fof(lameq_f407,axiom,
! [A_27a,A_27b,V4a] :
( mem(V4a,A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V5b] : ap(f407(A_27a,A_27b,V4a,V0R),V5b) = ap(ap(V0R,V4a),V5b) ) ) ).
fof(lameq_f408,axiom,
! [A_27b,A_27a,V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V4a] : ap(f408(A_27b,A_27a,V0R),V4a) = f407(A_27a,A_27b,V4a,V0R) ) ).
fof(lameq_f409,axiom,
! [A_27b,A_27a,A_27c,V6a] :
( mem(V6a,A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V2f] :
( mem(V2f,arr(A_27c,A_27b))
=> ! [V7b] : ap(f409(A_27b,A_27a,A_27c,V6a,V0R,V2f),V7b) = ap(ap(V0R,V6a),ap(V2f,V7b)) ) ) ) ).
fof(lameq_f410,axiom,
! [A_27c,A_27b,A_27a,V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V2f] :
( mem(V2f,arr(A_27c,A_27b))
=> ! [V6a] : ap(f410(A_27c,A_27b,A_27a,V0R,V2f),V6a) = f409(A_27b,A_27a,A_27c,V6a,V0R,V2f) ) ) ).
fof(conj_thm_2Elist_2ELIST__REL__MAP2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2f] :
( mem(V2f,arr(A_27c,A_27b))
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(A_27c))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),f408(A_27b,A_27a,V0R)),V1l1),ap(ap(c_2Elist_2EMAP(A_27c,A_27b),V2f),V3l2)))
<=> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27c),f410(A_27c,A_27b,A_27a,V0R,V2f)),V1l1),V3l2)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__REL__LENGTH,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1x] :
( mem(V1x,ty_2Elist_2Elist(A_27a))
=> ! [V2y] :
( mem(V2y,ty_2Elist_2Elist(A_27b))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V1x),V2y))
=> ap(c_2Elist_2ELENGTH(A_27a),V1x) = ap(c_2Elist_2ELENGTH(A_27b),V2y) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__REL__SPLIT1,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(A_27a,arr(A_27b,bool)))
=> ! [V1xs2] :
( mem(V1xs2,ty_2Elist_2Elist(A_27a))
=> ! [V2xs1] :
( mem(V2xs1,ty_2Elist_2Elist(A_27a))
=> ! [V3zs] :
( mem(V3zs,ty_2Elist_2Elist(A_27b))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0P),ap(ap(c_2Elist_2EAPPEND(A_27a),V2xs1),V1xs2)),V3zs))
<=> ? [V4ys1] :
( mem(V4ys1,ty_2Elist_2Elist(A_27b))
& ? [V5ys2] :
( mem(V5ys2,ty_2Elist_2Elist(A_27b))
& V3zs = ap(ap(c_2Elist_2EAPPEND(A_27b),V4ys1),V5ys2)
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0P),V2xs1),V4ys1))
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0P),V1xs2),V5ys2)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__REL__SPLIT2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(A_27b,arr(A_27a,bool)))
=> ! [V1xs2] :
( mem(V1xs2,ty_2Elist_2Elist(A_27a))
=> ! [V2xs1] :
( mem(V2xs1,ty_2Elist_2Elist(A_27a))
=> ! [V3zs] :
( mem(V3zs,ty_2Elist_2Elist(A_27b))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27b,A_27a),V0P),V3zs),ap(ap(c_2Elist_2EAPPEND(A_27a),V2xs1),V1xs2)))
<=> ? [V4ys1] :
( mem(V4ys1,ty_2Elist_2Elist(A_27b))
& ? [V5ys2] :
( mem(V5ys2,ty_2Elist_2Elist(A_27b))
& V3zs = ap(ap(c_2Elist_2EAPPEND(A_27b),V4ys1),V5ys2)
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27b,A_27a),V0P),V4ys1),V2xs1))
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27b,A_27a),V0P),V5ys2),V1xs2)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2Elist__size__cong,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0M] :
( mem(V0M,ty_2Elist_2Elist(A_27a))
=> ! [V1N] :
( mem(V1N,ty_2Elist_2Elist(A_27a))
=> ! [V2f] :
( mem(V2f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V3f_27] :
( mem(V3f_27,arr(A_27a,ty_2Enum_2Enum))
=> ( ( V0M = V1N
& ! [V4x] :
( mem(V4x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1N)))
=> ap(V2f,V4x) = ap(V3f_27,V4x) ) ) )
=> ap(ap(c_2Elist_2Elist__size(A_27a),V2f),V0M) = ap(ap(c_2Elist_2Elist__size(A_27a),V3f_27),V1N) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EFOLDR__CONG,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1l_27] :
( mem(V1l_27,ty_2Elist_2Elist(A_27a))
=> ! [V2b] :
( mem(V2b,A_27b)
=> ! [V3b_27] :
( mem(V3b_27,A_27b)
=> ! [V4f] :
( mem(V4f,arr(A_27a,arr(A_27b,A_27b)))
=> ! [V5f_27] :
( mem(V5f_27,arr(A_27a,arr(A_27b,A_27b)))
=> ( ( V0l = V1l_27
& V2b = V3b_27
& ! [V6x] :
( mem(V6x,A_27a)
=> ! [V7a] :
( mem(V7a,A_27b)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V6x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l_27)))
=> ap(ap(V4f,V6x),V7a) = ap(ap(V5f_27,V6x),V7a) ) ) ) )
=> ap(ap(ap(c_2Elist_2EFOLDR(A_27a,A_27b),V4f),V2b),V0l) = ap(ap(ap(c_2Elist_2EFOLDR(A_27a,A_27b),V5f_27),V3b_27),V1l_27) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EFOLDL__CONG,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1l_27] :
( mem(V1l_27,ty_2Elist_2Elist(A_27a))
=> ! [V2b] :
( mem(V2b,A_27b)
=> ! [V3b_27] :
( mem(V3b_27,A_27b)
=> ! [V4f] :
( mem(V4f,arr(A_27b,arr(A_27a,A_27b)))
=> ! [V5f_27] :
( mem(V5f_27,arr(A_27b,arr(A_27a,A_27b)))
=> ( ( V0l = V1l_27
& V2b = V3b_27
& ! [V6x] :
( mem(V6x,A_27a)
=> ! [V7a] :
( mem(V7a,A_27b)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V6x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l_27)))
=> ap(ap(V4f,V7a),V6x) = ap(ap(V5f_27,V7a),V6x) ) ) ) )
=> ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),V4f),V2b),V0l) = ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),V5f_27),V3b_27),V1l_27) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP__CONG,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ! [V2f] :
( mem(V2f,arr(A_27a,A_27b))
=> ! [V3f_27] :
( mem(V3f_27,arr(A_27a,A_27b))
=> ( ( V0l1 = V1l2
& ! [V4x] :
( mem(V4x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2)))
=> ap(V2f,V4x) = ap(V3f_27,V4x) ) ) )
=> ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V2f),V0l1) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V3f_27),V1l2) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP2__CONG,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l1_27] :
( mem(V1l1_27,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27b))
=> ! [V3l2_27] :
( mem(V3l2_27,ty_2Elist_2Elist(A_27b))
=> ! [V4f] :
( mem(V4f,arr(A_27a,arr(A_27b,A_27c)))
=> ! [V5f_27] :
( mem(V5f_27,arr(A_27a,arr(A_27b,A_27c)))
=> ( ( V0l1 = V1l1_27
& V2l2 = V3l2_27
& ! [V6x] :
( mem(V6x,A_27a)
=> ! [V7y] :
( mem(V7y,A_27b)
=> ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V6x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l1_27)))
& p(ap(ap(c_2Ebool_2EIN(A_27b),V7y),ap(c_2Elist_2ELIST__TO__SET(A_27b),V3l2_27))) )
=> ap(ap(V4f,V6x),V7y) = ap(ap(V5f_27,V6x),V7y) ) ) ) )
=> ap(ap(ap(c_2Elist_2EMAP2(A_27c,A_27a,A_27b),V4f),V0l1),V2l2) = ap(ap(ap(c_2Elist_2EMAP2(A_27c,A_27a,A_27b),V5f_27),V1l1_27),V3l2_27) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEXISTS__CONG,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ! [V2P] :
( mem(V2P,arr(A_27a,bool))
=> ! [V3P_27] :
( mem(V3P_27,arr(A_27a,bool))
=> ( ( V0l1 = V1l2
& ! [V4x] :
( mem(V4x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2)))
=> ( p(ap(V2P,V4x))
<=> p(ap(V3P_27,V4x)) ) ) ) )
=> ( p(ap(ap(c_2Elist_2EEXISTS(A_27a),V2P),V0l1))
<=> p(ap(ap(c_2Elist_2EEXISTS(A_27a),V3P_27),V1l2)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY__CONG,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ! [V2P] :
( mem(V2P,arr(A_27a,bool))
=> ! [V3P_27] :
( mem(V3P_27,arr(A_27a,bool))
=> ( ( V0l1 = V1l2
& ! [V4x] :
( mem(V4x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2)))
=> ( p(ap(V2P,V4x))
<=> p(ap(V3P_27,V4x)) ) ) ) )
=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V2P),V0l1))
<=> p(ap(ap(c_2Elist_2EEVERY(A_27a),V3P_27),V1l2)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY__MONOTONIC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q] :
( mem(V1Q,arr(A_27a,bool))
=> ( ! [V2x] :
( mem(V2x,A_27a)
=> ( p(ap(V0P,V2x))
=> p(ap(V1Q,V2x)) ) )
=> ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V3l))
=> p(ap(ap(c_2Elist_2EEVERY(A_27a),V1Q),V3l)) ) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EZIP__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0l2] :
( mem(V0l2,ty_2Elist_2Elist(A_27b))
=> ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),c_2Elist_2ENIL(A_27a)),V0l2)) = c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)) )
& ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V1l1),c_2Elist_2ENIL(A_27b))) = c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)) )
& ! [V2x1] :
( mem(V2x1,A_27a)
=> ! [V3l1] :
( mem(V3l1,ty_2Elist_2Elist(A_27a))
=> ! [V4x2] :
( mem(V4x2,A_27b)
=> ! [V5l2] :
( mem(V5l2,ty_2Elist_2Elist(A_27b))
=> ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2ECONS(A_27a),V2x1),V3l1)),ap(ap(c_2Elist_2ECONS(A_27b),V4x2),V5l2))) = ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x1),V4x2)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V3l1),V5l2))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EZIP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ( ap(c_2Elist_2EZIP(A_27c,A_27d),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),ty_2Elist_2Elist(A_27d)),c_2Elist_2ENIL(A_27c)),c_2Elist_2ENIL(A_27d))) = c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27c,A_27d))
& ! [V0x1] :
( mem(V0x1,A_27a)
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2x2] :
( mem(V2x2,A_27b)
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(A_27b))
=> ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2ECONS(A_27a),V0x1),V1l1)),ap(ap(c_2Elist_2ECONS(A_27b),V2x2),V3l2))) = ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x1),V2x2)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V1l1),V3l2))) ) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EUNZIP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ap(c_2Elist_2EUNZIP(A_27a,A_27b),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))) = ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27b))
& ! [V0x] :
( mem(V0x,ty_2Epair_2Eprod(A_27a,A_27b))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ap(c_2Elist_2EUNZIP(A_27a,A_27b),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),V0x),V1l)) = ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2ECONS(A_27a),ap(c_2Epair_2EFST(A_27a,A_27b),V0x)),ap(c_2Epair_2EFST(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(c_2Elist_2EUNZIP(A_27a,A_27b),V1l)))),ap(ap(c_2Elist_2ECONS(A_27b),ap(c_2Epair_2ESND(A_27a,A_27b),V0x)),ap(c_2Epair_2ESND(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(c_2Elist_2EUNZIP(A_27a,A_27b),V1l)))) ) ) ) ) ) ).
fof(lameq_f411,axiom,
! [A_27a,A_27b,V0x] :
( mem(V0x,A_27a)
=> ! [V3L1] :
( mem(V3L1,ty_2Elist_2Elist(A_27a))
=> ! [V1y] :
( mem(V1y,A_27b)
=> ! [V4L2] : ap(f411(A_27a,A_27b,V0x,V3L1,V1y),V4L2) = ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V3L1)),ap(ap(c_2Elist_2ECONS(A_27b),V1y),V4L2)) ) ) ) ).
fof(lameq_f412,axiom,
! [A_27b,A_27a,V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,A_27b)
=> ! [V3L1] : ap(f412(A_27b,A_27a,V0x,V1y),V3L1) = f411(A_27a,A_27b,V0x,V3L1,V1y) ) ) ).
fof(conj_thm_2Elist_2EUNZIP__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,A_27b)
=> ! [V2t] :
( mem(V2t,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ap(c_2Elist_2EUNZIP(A_27a,A_27b),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))) = ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27b))
& ap(c_2Elist_2EUNZIP(A_27a,A_27b),ap(ap(c_2Elist_2ECONS(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_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b))),ap(c_2Epair_2EUNCURRY(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b),ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b))),f412(A_27b,A_27a,V0x,V1y))),ap(c_2Elist_2EUNZIP(A_27a,A_27b),V2t)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EUNZIP__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0L] :
( mem(V0L,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ap(c_2Elist_2EUNZIP(A_27a,A_27b),V0L) = ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0L)),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND(A_27a,A_27b)),V0L)) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__ZIP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27b))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2)
=> ( ap(c_2Elist_2ELENGTH(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) = ap(c_2Elist_2ELENGTH(A_27a),V0l1)
& ap(c_2Elist_2ELENGTH(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) = ap(c_2Elist_2ELENGTH(A_27b),V1l2) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__UNZIP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0pl] :
( mem(V0pl,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Epair_2EFST(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(c_2Elist_2EUNZIP(A_27a,A_27b),V0pl))) = ap(c_2Elist_2ELENGTH(ty_2Epair_2Eprod(A_27a,A_27b)),V0pl)
& ap(c_2Elist_2ELENGTH(A_27b),ap(c_2Epair_2ESND(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(c_2Elist_2EUNZIP(A_27a,A_27b),V0pl))) = ap(c_2Elist_2ELENGTH(ty_2Epair_2Eprod(A_27a,A_27b)),V0pl) ) ) ) ) ).
fof(conj_thm_2Elist_2EZIP__UNZIP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ap(c_2Elist_2EZIP(A_27a,A_27b),ap(c_2Elist_2EUNZIP(A_27a,A_27b),V0l)) = V0l ) ) ) ).
fof(conj_thm_2Elist_2EUNZIP__ZIP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27b))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2)
=> ap(c_2Elist_2EUNZIP(A_27a,A_27b),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) = ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2) ) ) ) ) ) ).
fof(lameq_f413,axiom,
! [A_27c,A_27a,A_27b,V2f1] :
( mem(V2f1,arr(A_27a,A_27c))
=> ! [V4p] : ap(f413(A_27c,A_27a,A_27b,V2f1),V4p) = ap(ap(c_2Epair_2E_2C(A_27c,A_27b),ap(V2f1,ap(c_2Epair_2EFST(A_27a,A_27b),V4p))),ap(c_2Epair_2ESND(A_27a,A_27b),V4p)) ) ).
fof(lameq_f414,axiom,
! [A_27d,A_27a,A_27b,V3f2] :
( mem(V3f2,arr(A_27b,A_27d))
=> ! [V5p] : ap(f414(A_27d,A_27a,A_27b,V3f2),V5p) = ap(ap(c_2Epair_2E_2C(A_27a,A_27d),ap(c_2Epair_2EFST(A_27a,A_27b),V5p)),ap(V3f2,ap(c_2Epair_2ESND(A_27a,A_27b),V5p))) ) ).
fof(conj_thm_2Elist_2EZIP__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27b))
=> ! [V2f1] :
( mem(V2f1,arr(A_27a,A_27c))
=> ! [V3f2] :
( mem(V3f2,arr(A_27b,A_27d))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2)
=> ( ap(c_2Elist_2EZIP(A_27c,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27c),ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2EMAP(A_27a,A_27c),V2f1),V0l1)),V1l2)) = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27c,A_27b)),f413(A_27c,A_27a,A_27b,V2f1)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2)))
& ap(c_2Elist_2EZIP(A_27a,A_27d),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27d)),V0l1),ap(ap(c_2Elist_2EMAP(A_27b,A_27d),V3f2),V1l2))) = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27a,A_27d)),f414(A_27d,A_27a,A_27b,V3f2)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMEM__ZIP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27b))
=> ! [V2p] :
( mem(V2p,ty_2Epair_2Eprod(A_27a,A_27b))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2)
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),V2p),ap(c_2Elist_2ELIST__TO__SET(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2)))))
<=> ? [V3n] :
( mem(V3n,ty_2Enum_2Enum)
& p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(c_2Elist_2ELENGTH(A_27a),V0l1)))
& V2p = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),ap(ap(c_2Elist_2EEL(A_27a),V3n),V0l1)),ap(ap(c_2Elist_2EEL(A_27b),V3n),V1l2)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEL__ZIP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27b))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( ( ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2)
& p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(c_2Elist_2ELENGTH(A_27a),V0l1))) )
=> ap(ap(c_2Elist_2EEL(ty_2Epair_2Eprod(A_27a,A_27b)),V2n),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),ap(ap(c_2Elist_2EEL(A_27a),V2n),V0l1)),ap(ap(c_2Elist_2EEL(A_27b),V2n),V1l2)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP2__ZIP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27b))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2)
=> ! [V2f] :
( mem(V2f,arr(A_27a,arr(A_27b,A_27c)))
=> ap(ap(ap(c_2Elist_2EMAP2(A_27c,A_27a,A_27b),V2f),V0l1),V1l2) = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V2f)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP2__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27b))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2)
=> ! [V2f] :
( mem(V2f,arr(A_27a,arr(A_27b,A_27c)))
=> ap(ap(ap(c_2Elist_2EMAP2(A_27c,A_27a,A_27b),V2f),V0l1),V1l2) = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V2f)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP__ZIP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27b))
=> ! [V2f] :
( mem(V2f,arr(A_27a,A_27c))
=> ! [V3g] :
( mem(V3g,arr(A_27b,A_27d))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2)
=> ( ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) = V0l1
& ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND(A_27a,A_27b)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) = V1l2
& ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),ap(ap(c_2Ecombin_2Eo(ty_2Epair_2Eprod(A_27a,A_27b),A_27c,A_27a),V2f),c_2Epair_2EFST(A_27a,A_27b))),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) = ap(ap(c_2Elist_2EMAP(A_27a,A_27c),V2f),V0l1)
& ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27d),ap(ap(c_2Ecombin_2Eo(ty_2Epair_2Eprod(A_27a,A_27b),A_27d,A_27b),V3g),c_2Epair_2ESND(A_27a,A_27b))),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) = ap(ap(c_2Elist_2EMAP(A_27b,A_27d),V3g),V1l2) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMEM__EL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l)))
<=> ? [V2n] :
( mem(V2n,ty_2Enum_2Enum)
& p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(c_2Elist_2ELENGTH(A_27a),V0l)))
& V1x = ap(ap(c_2Elist_2EEL(A_27a),V2n),V0l) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ESUM__MAP__PLUS__ZIP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Enum_2Enum))
=> ! [V1g] :
( mem(V1g,arr(A_27a,ty_2Enum_2Enum))
=> ! [V2h] :
( mem(V2h,arr(A_27b,ty_2Enum_2Enum))
=> ! [V3ls1] :
( mem(V3ls1,ty_2Elist_2Elist(A_27a))
=> ! [V4ls2] :
( mem(V4ls2,ty_2Elist_2Elist(A_27b))
=> ( ( ap(c_2Elist_2ELENGTH(A_27a),V3ls1) = ap(c_2Elist_2ELENGTH(A_27b),V4ls2)
& ! [V5x] :
( mem(V5x,A_27a)
=> ! [V6y] :
( mem(V6y,A_27b)
=> ap(V0f,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V5x),V6y)) = ap(ap(c_2Earithmetic_2E_2B,ap(V1g,V5x)),ap(V2h,V6y)) ) ) )
=> ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Enum_2Enum),V0f),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V3ls1),V4ls2)))) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(A_27a,ty_2Enum_2Enum),V1g),V3ls1))),ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(A_27b,ty_2Enum_2Enum),V2h),V4ls2))) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__REL__EVERY__ZIP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27b))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V1l1),V2l2))
<=> ( ap(c_2Elist_2ELENGTH(A_27a),V1l1) = ap(c_2Elist_2ELENGTH(A_27b),V2l2)
& p(ap(ap(c_2Elist_2EEVERY(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),V0R)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V1l1),V2l2)))) ) ) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EREVERSE__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ap(c_2Elist_2EREVERSE(A_27a),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a)
& ! [V0h] :
( mem(V0h,A_27a)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2EREVERSE(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V1t)),ap(ap(c_2Elist_2ECONS(A_27a),V0h),c_2Elist_2ENIL(A_27a))) ) ) ) ) ).
fof(conj_thm_2Elist_2EREVERSE__APPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2EREVERSE(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V1l2)),ap(c_2Elist_2EREVERSE(A_27a),V0l1)) ) ) ) ).
fof(conj_thm_2Elist_2EREVERSE__REVERSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2EREVERSE(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V0l)) = V0l ) ) ).
fof(conj_thm_2Elist_2EREVERSE__11,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Elist_2EREVERSE(A_27a),V0l1) = ap(c_2Elist_2EREVERSE(A_27a),V1l2)
<=> V0l1 = V1l2 ) ) ) ) ).
fof(conj_thm_2Elist_2EMEM__REVERSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V0l))))
<=> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l))) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__REVERSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V0l)) = ap(c_2Elist_2ELENGTH(A_27a),V0l) ) ) ).
fof(conj_thm_2Elist_2EREVERSE__EQ__NIL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Elist_2EREVERSE(A_27a),V0l) = c_2Elist_2ENIL(A_27a)
<=> V0l = c_2Elist_2ENIL(A_27a) ) ) ) ).
fof(conj_thm_2Elist_2EREVERSE__EQ__SING,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1e] :
( mem(V1e,A_27a)
=> ( ap(c_2Elist_2EREVERSE(A_27a),V0l) = ap(ap(c_2Elist_2ECONS(A_27a),V1e),c_2Elist_2ENIL(A_27a))
<=> V0l = ap(ap(c_2Elist_2ECONS(A_27a),V1e),c_2Elist_2ENIL(A_27a)) ) ) ) ) ).
fof(conj_thm_2Elist_2EFILTER__REVERSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1P] :
( mem(V1P,arr(A_27a,bool))
=> ap(ap(c_2Elist_2EFILTER(A_27a),V1P),ap(c_2Elist_2EREVERSE(A_27a),V0l)) = ap(c_2Elist_2EREVERSE(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V1P),V0l)) ) ) ) ).
fof(ax_thm_2Elist_2ELAST__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,A_27a)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Elist_2Elist(A_27a)),V1t),c_2Elist_2ENIL(A_27a))),V0h),ap(c_2Elist_2ELAST(A_27a),V1t)) ) ) ) ).
fof(ax_thm_2Elist_2EFRONT__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,A_27a)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Elist_2Elist(A_27a)),V1t),c_2Elist_2ENIL(A_27a))),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),V0h),ap(c_2Elist_2EFRONT(A_27a),V1t))) ) ) ) ).
fof(conj_thm_2Elist_2ELAST__CONS,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0x] :
( mem(V0x,A_27a)
=> ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),c_2Elist_2ENIL(A_27a))) = V0x )
& ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ! [V3z] :
( mem(V3z,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V1x),ap(ap(c_2Elist_2ECONS(A_27a),V2y),V3z))) = ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V2y),V3z)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELAST__EL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0ls] :
( mem(V0ls,ty_2Elist_2Elist(A_27a))
=> ( V0ls != c_2Elist_2ENIL(A_27a)
=> ap(c_2Elist_2ELAST(A_27a),V0ls) = ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Eprim__rec_2EPRE,ap(c_2Elist_2ELENGTH(A_27a),V0ls))),V0ls) ) ) ) ).
fof(conj_thm_2Elist_2ELAST__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1f] :
( mem(V1f,arr(A_27a,A_27b))
=> ( V0l != c_2Elist_2ENIL(A_27a)
=> ap(c_2Elist_2ELAST(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V0l)) = ap(V1f,ap(c_2Elist_2ELAST(A_27a),V0l)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EFRONT__CONS,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0x] :
( mem(V0x,A_27a)
=> ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),c_2Elist_2ENIL(A_27a))) = c_2Elist_2ENIL(A_27a) )
& ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ! [V3z] :
( mem(V3z,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V1x),ap(ap(c_2Elist_2ECONS(A_27a),V2y),V3z))) = ap(ap(c_2Elist_2ECONS(A_27a),V1x),ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V2y),V3z))) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__FRONT__CONS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1xs] :
( mem(V1xs,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V1xs))) = ap(c_2Elist_2ELENGTH(A_27a),V1xs) ) ) ) ).
fof(conj_thm_2Elist_2EFRONT__CONS__EQ__NIL,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1xs] :
( mem(V1xs,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V1xs)) = c_2Elist_2ENIL(A_27a)
<=> V1xs = c_2Elist_2ENIL(A_27a) ) ) )
& ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3xs] :
( mem(V3xs,ty_2Elist_2Elist(A_27a))
=> ( c_2Elist_2ENIL(A_27a) = ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V2x),V3xs))
<=> V3xs = c_2Elist_2ENIL(A_27a) ) ) )
& ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5xs] :
( mem(V5xs,ty_2Elist_2Elist(A_27a))
=> ( p(ap(c_2Elist_2ENULL(A_27a),ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V4x),V5xs))))
<=> p(ap(c_2Elist_2ENULL(A_27a),V5xs)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EAPPEND__FRONT__LAST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( V0l != c_2Elist_2ENIL(A_27a)
=> ap(ap(c_2Elist_2EAPPEND(A_27a),ap(c_2Elist_2EFRONT(A_27a),V0l)),ap(ap(c_2Elist_2ECONS(A_27a),ap(c_2Elist_2ELAST(A_27a),V0l)),c_2Elist_2ENIL(A_27a))) = V0l ) ) ) ).
fof(conj_thm_2Elist_2ELAST__CONS__cond,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,A_27a)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Elist_2Elist(A_27a)),V1t),c_2Elist_2ENIL(A_27a))),V0h),ap(c_2Elist_2ELAST(A_27a),V1t)) ) ) ) ).
fof(conj_thm_2Elist_2ELAST__APPEND__CONS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0h] :
( mem(V0h,A_27a)
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V2l2))) = ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V2l2)) ) ) ) ) ).
fof(ax_thm_2Elist_2ETAKE__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2ETAKE(A_27a),V0n),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a) )
& ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3xs] :
( mem(V3xs,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2ETAKE(A_27a),V1n),ap(ap(c_2Elist_2ECONS(A_27a),V2x),V3xs)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1n),c_2Enum_2E0)),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),V2x),ap(ap(c_2Elist_2ETAKE(A_27a),ap(ap(c_2Earithmetic_2E_2D,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V3xs))) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EDROP__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2EDROP(A_27a),V0n),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a) )
& ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3xs] :
( mem(V3xs,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EDROP(A_27a),V1n),ap(ap(c_2Elist_2ECONS(A_27a),V2x),V3xs)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1n),c_2Enum_2E0)),ap(ap(c_2Elist_2ECONS(A_27a),V2x),V3xs)),ap(ap(c_2Elist_2EDROP(A_27a),ap(ap(c_2Earithmetic_2E_2D,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V3xs)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ETAKE__nil,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2ETAKE(A_27a),V0n),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a) ) ) ).
fof(conj_thm_2Elist_2ETAKE__cons,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2xs] :
( mem(V2xs,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ap(ap(c_2Elist_2ETAKE(A_27a),V0n),ap(ap(c_2Elist_2ECONS(A_27a),V1x),V2xs)) = ap(ap(c_2Elist_2ECONS(A_27a),V1x),ap(ap(c_2Elist_2ETAKE(A_27a),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2xs)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EDROP__nil,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2EDROP(A_27a),V0n),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a) ) ) ).
fof(conj_thm_2Elist_2EDROP__cons,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2xs] :
( mem(V2xs,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ap(ap(c_2Elist_2EDROP(A_27a),V0n),ap(ap(c_2Elist_2ECONS(A_27a),V1x),V2xs)) = ap(ap(c_2Elist_2EDROP(A_27a),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2xs) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ETAKE__0,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2ETAKE(A_27a),c_2Enum_2E0),V0l) = c_2Elist_2ENIL(A_27a) ) ) ).
fof(conj_thm_2Elist_2ETAKE__LENGTH__ID,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2ETAKE(A_27a),ap(c_2Elist_2ELENGTH(A_27a),V0l)),V0l) = V0l ) ) ).
fof(conj_thm_2Elist_2ELENGTH__TAKE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),ap(c_2Elist_2ELENGTH(A_27a),V1l)))
=> ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2ETAKE(A_27a),V0n),V1l)) = V0n ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP__TAKE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),ap(ap(c_2Elist_2ETAKE(A_27a),V1n),V2l)) = ap(ap(c_2Elist_2ETAKE(A_27b),V1n),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V2l)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ETAKE__APPEND1,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V2n),ap(c_2Elist_2ELENGTH(A_27a),V0l1)))
=> ap(ap(c_2Elist_2ETAKE(A_27a),V2n),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)) = ap(ap(c_2Elist_2ETAKE(A_27a),V2n),V0l1) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ETAKE__APPEND2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(A_27a),V0l1)),V2n))
=> ap(ap(c_2Elist_2ETAKE(A_27a),V2n),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)) = ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),ap(ap(c_2Elist_2ETAKE(A_27a),ap(ap(c_2Earithmetic_2E_2D,V2n),ap(c_2Elist_2ELENGTH(A_27a),V0l1))),V1l2)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EDROP__0,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EDROP(A_27a),c_2Enum_2E0),V0l) = V0l ) ) ).
fof(conj_thm_2Elist_2ETAKE__DROP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2ETAKE(A_27a),V0n),V1l)),ap(ap(c_2Elist_2EDROP(A_27a),V0n),V1l)) = V1l ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__DROP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EDROP(A_27a),V0n),V1l)) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Elist_2ELENGTH(A_27a),V1l)),V0n) ) ) ) ).
fof(conj_thm_2Elist_2EMEM__DROP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EDROP(A_27a),V2n),V1ls))))
<=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(c_2Elist_2ELENGTH(A_27a),V1ls)))
& V0x = ap(ap(c_2Elist_2EEL(A_27a),V2n),V1ls) )
| p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EDROP(A_27a),ap(c_2Enum_2ESUC,V2n)),V1ls)))) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EDROP__NIL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0ls] :
( mem(V0ls,ty_2Elist_2Elist(A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Elist_2EDROP(A_27a),V1n),V0ls) = c_2Elist_2ENIL(A_27a)
<=> p(ap(ap(c_2Earithmetic_2E_3E_3D,V1n),ap(c_2Elist_2ELENGTH(A_27a),V0ls))) ) ) ) ) ).
fof(conj_thm_2Elist_2EFOLDL2__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0P] :
( mem(V0P,arr(arr(A_27a,arr(A_27b,arr(A_27c,A_27a))),arr(A_27a,arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27c),bool)))))
=> ( ( ! [V1f] :
( mem(V1f,arr(A_27a,arr(A_27b,arr(A_27c,A_27a))))
=> ! [V2a] :
( mem(V2a,A_27a)
=> ! [V3b] :
( mem(V3b,A_27b)
=> ! [V4bs] :
( mem(V4bs,ty_2Elist_2Elist(A_27b))
=> ! [V5c] :
( mem(V5c,A_27c)
=> ! [V6cs] :
( mem(V6cs,ty_2Elist_2Elist(A_27c))
=> ( p(ap(ap(ap(ap(V0P,V1f),ap(ap(ap(V1f,V2a),V3b),V5c)),V4bs),V6cs))
=> p(ap(ap(ap(ap(V0P,V1f),V2a),ap(ap(c_2Elist_2ECONS(A_27b),V3b),V4bs)),ap(ap(c_2Elist_2ECONS(A_27c),V5c),V6cs))) ) ) ) ) ) ) )
& ! [V7f] :
( mem(V7f,arr(A_27a,arr(A_27b,arr(A_27c,A_27a))))
=> ! [V8a] :
( mem(V8a,A_27a)
=> ! [V9cs] :
( mem(V9cs,ty_2Elist_2Elist(A_27c))
=> p(ap(ap(ap(ap(V0P,V7f),V8a),c_2Elist_2ENIL(A_27b)),V9cs)) ) ) )
& ! [V10f] :
( mem(V10f,arr(A_27a,arr(A_27b,arr(A_27c,A_27a))))
=> ! [V11a] :
( mem(V11a,A_27a)
=> ! [V12v6] :
( mem(V12v6,A_27b)
=> ! [V13v7] :
( mem(V13v7,ty_2Elist_2Elist(A_27b))
=> p(ap(ap(ap(ap(V0P,V10f),V11a),ap(ap(c_2Elist_2ECONS(A_27b),V12v6),V13v7)),c_2Elist_2ENIL(A_27c))) ) ) ) ) )
=> ! [V14v] :
( mem(V14v,arr(A_27a,arr(A_27b,arr(A_27c,A_27a))))
=> ! [V15v1] :
( mem(V15v1,A_27a)
=> ! [V16v2] :
( mem(V16v2,ty_2Elist_2Elist(A_27b))
=> ! [V17v3] :
( mem(V17v3,ty_2Elist_2Elist(A_27c))
=> p(ap(ap(ap(ap(V0P,V14v),V15v1),V16v2),V17v3)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EFOLDL2__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ( ! [V0f] :
( mem(V0f,arr(A_27a,arr(A_27b,arr(A_27c,A_27a))))
=> ! [V1cs] :
( mem(V1cs,ty_2Elist_2Elist(A_27c))
=> ! [V2c] :
( mem(V2c,A_27c)
=> ! [V3bs] :
( mem(V3bs,ty_2Elist_2Elist(A_27b))
=> ! [V4b] :
( mem(V4b,A_27b)
=> ! [V5a] :
( mem(V5a,A_27a)
=> ap(ap(ap(ap(c_2Elist_2EFOLDL2(A_27a,A_27b,A_27c),V0f),V5a),ap(ap(c_2Elist_2ECONS(A_27b),V4b),V3bs)),ap(ap(c_2Elist_2ECONS(A_27c),V2c),V1cs)) = ap(ap(ap(ap(c_2Elist_2EFOLDL2(A_27a,A_27b,A_27c),V0f),ap(ap(ap(V0f,V5a),V4b),V2c)),V3bs),V1cs) ) ) ) ) ) )
& ! [V6f] :
( mem(V6f,arr(A_27a,arr(A_27b,arr(A_27c,A_27a))))
=> ! [V7cs] :
( mem(V7cs,ty_2Elist_2Elist(A_27c))
=> ! [V8a] :
( mem(V8a,A_27a)
=> ap(ap(ap(ap(c_2Elist_2EFOLDL2(A_27a,A_27b,A_27c),V6f),V8a),c_2Elist_2ENIL(A_27b)),V7cs) = V8a ) ) )
& ! [V9v7] :
( mem(V9v7,ty_2Elist_2Elist(A_27b))
=> ! [V10v6] :
( mem(V10v6,A_27b)
=> ! [V11f] :
( mem(V11f,arr(A_27a,arr(A_27b,arr(A_27c,A_27a))))
=> ! [V12a] :
( mem(V12a,A_27a)
=> ap(ap(ap(ap(c_2Elist_2EFOLDL2(A_27a,A_27b,A_27c),V11f),V12a),ap(ap(c_2Elist_2ECONS(A_27b),V10v6),V9v7)),c_2Elist_2ENIL(A_27c)) = V12a ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EFOLDL2__cong,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l1_27] :
( mem(V1l1_27,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27b))
=> ! [V3l2_27] :
( mem(V3l2_27,ty_2Elist_2Elist(A_27b))
=> ! [V4a] :
( mem(V4a,A_27c)
=> ! [V5a_27] :
( mem(V5a_27,A_27c)
=> ! [V6f] :
( mem(V6f,arr(A_27c,arr(A_27a,arr(A_27b,A_27c))))
=> ! [V7f_27] :
( mem(V7f_27,arr(A_27c,arr(A_27a,arr(A_27b,A_27c))))
=> ( ( V0l1 = V1l1_27
& V2l2 = V3l2_27
& V4a = V5a_27
& ! [V8z] :
( mem(V8z,A_27c)
=> ! [V9b] :
( mem(V9b,A_27a)
=> ! [V10c] :
( mem(V10c,A_27b)
=> ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V9b),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l1_27)))
& p(ap(ap(c_2Ebool_2EIN(A_27b),V10c),ap(c_2Elist_2ELIST__TO__SET(A_27b),V3l2_27))) )
=> ap(ap(ap(V6f,V8z),V9b),V10c) = ap(ap(ap(V7f_27,V8z),V9b),V10c) ) ) ) ) )
=> ap(ap(ap(ap(c_2Elist_2EFOLDL2(A_27c,A_27a,A_27b),V6f),V4a),V0l1),V2l2) = ap(ap(ap(ap(c_2Elist_2EFOLDL2(A_27c,A_27a,A_27b),V7f_27),V5a_27),V1l1_27),V3l2_27) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(lameq_f415,axiom,
! [A_27a,A_27b,A_27c,V2f] :
( mem(V2f,arr(A_27c,arr(A_27a,arr(A_27b,A_27c))))
=> ! [V4a] : ap(f415(A_27a,A_27b,A_27c,V2f),V4a) = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),ap(V2f,V4a)) ) ).
fof(conj_thm_2Elist_2EFOLDL2__FOLDL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27b))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2)
=> ! [V2f] :
( mem(V2f,arr(A_27c,arr(A_27a,arr(A_27b,A_27c))))
=> ! [V3a] :
( mem(V3a,A_27c)
=> ap(ap(ap(ap(c_2Elist_2EFOLDL2(A_27c,A_27a,A_27b),V2f),V3a),V0l1),V1l2) = ap(ap(ap(c_2Elist_2EFOLDL(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),f415(A_27a,A_27b,A_27c,V2f)),V3a),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY2__cong,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l1_27] :
( mem(V1l1_27,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27b))
=> ! [V3l2_27] :
( mem(V3l2_27,ty_2Elist_2Elist(A_27b))
=> ! [V4P] :
( mem(V4P,arr(A_27a,arr(A_27b,bool)))
=> ! [V5P_27] :
( mem(V5P_27,arr(A_27a,arr(A_27b,bool)))
=> ( ( V0l1 = V1l1_27
& V2l2 = V3l2_27
& ! [V6x] :
( mem(V6x,A_27a)
=> ! [V7y] :
( mem(V7y,A_27b)
=> ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V6x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l1_27)))
& p(ap(ap(c_2Ebool_2EIN(A_27b),V7y),ap(c_2Elist_2ELIST__TO__SET(A_27b),V3l2_27))) )
=> ( p(ap(ap(V4P,V6x),V7y))
<=> p(ap(ap(V5P_27,V6x),V7y)) ) ) ) ) )
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V4P),V0l1),V2l2))
<=> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V5P_27),V1l1_27),V3l2_27)) ) ) ) ) ) ) ) ) ) ) ).
fof(lameq_f416,axiom,
! [A_27b,A_27a,A_27c,V0f1] :
( mem(V0f1,arr(A_27a,A_27b))
=> ! [V4x] :
( mem(V4x,A_27a)
=> ! [V1f2] :
( mem(V1f2,arr(A_27c,A_27b))
=> ! [V5y] : ap(f416(A_27b,A_27a,A_27c,V0f1,V4x,V1f2),V5y) = ap(ap(c_2Emin_2E_3D(A_27b),ap(V0f1,V4x)),ap(V1f2,V5y)) ) ) ) ).
fof(lameq_f417,axiom,
! [A_27c,A_27b,A_27a,V0f1] :
( mem(V0f1,arr(A_27a,A_27b))
=> ! [V1f2] :
( mem(V1f2,arr(A_27c,A_27b))
=> ! [V4x] : ap(f417(A_27c,A_27b,A_27a,V0f1,V1f2),V4x) = f416(A_27b,A_27a,A_27c,V0f1,V4x,V1f2) ) ) ).
fof(conj_thm_2Elist_2EMAP__EQ__EVERY2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f1] :
( mem(V0f1,arr(A_27a,A_27b))
=> ! [V1f2] :
( mem(V1f2,arr(A_27c,A_27b))
=> ! [V2l1] :
( mem(V2l1,ty_2Elist_2Elist(A_27a))
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(A_27c))
=> ( ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f1),V2l1) = ap(ap(c_2Elist_2EMAP(A_27c,A_27b),V1f2),V3l2)
<=> ( ap(c_2Elist_2ELENGTH(A_27a),V2l1) = ap(c_2Elist_2ELENGTH(A_27c),V3l2)
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27c),f417(A_27c,A_27b,A_27a,V0f1,V1f2)),V2l1),V3l2)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY2__EVERY,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27b))
=> ! [V2f] :
( mem(V2f,arr(A_27a,arr(A_27b,bool)))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V2f),V0l1),V1l2))
<=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2)
& p(ap(ap(c_2Elist_2EEVERY(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),V2f)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2)))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY2__LENGTH,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(A_27a,arr(A_27b,bool)))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27b))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0P),V1l1),V2l2))
=> ap(c_2Elist_2ELENGTH(A_27a),V1l1) = ap(c_2Elist_2ELENGTH(A_27b),V2l2) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY2__mono,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27b,bool)))
=> ! [V1R2] :
( mem(V1R2,arr(A_27a,arr(A_27b,bool)))
=> ! [V2l1] :
( mem(V2l1,ty_2Elist_2Elist(A_27a))
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(A_27b))
=> ( ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5y] :
( mem(V5y,A_27b)
=> ( p(ap(ap(V0R1,V4x),V5y))
=> p(ap(ap(V1R2,V4x),V5y)) ) ) )
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R1),V2l1),V3l2))
=> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V1R2),V2l1),V3l2)) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EALL__DISTINCT,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),c_2Elist_2ENIL(A_27a)))
<=> $true )
& ! [V0h] :
( mem(V0h,A_27a)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(A_27a))
=> ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)))
<=> ( ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V0h),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1t)))
& p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V1t)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EALL__DISTINCT__FILTER,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0l))
<=> ! [V1x] :
( mem(V1x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l)))
=> ap(ap(c_2Elist_2EFILTER(A_27a),ap(c_2Emin_2E_3D(A_27a),V1x)),V0l) = ap(ap(c_2Elist_2ECONS(A_27a),V1x),c_2Elist_2ENIL(A_27a)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EFILTER__ALL__DISTINCT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V1l))
=> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l))) ) ) ) ) ).
fof(conj_thm_2Elist_2EALL__DISTINCT__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
=> ( p(ap(c_2Elist_2EALL__DISTINCT(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1ls)))
=> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V1ls)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEL__ALL__DISTINCT__EL__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0l))
<=> ! [V1n1] :
( mem(V1n1,ty_2Enum_2Enum)
=> ! [V2n2] :
( mem(V2n2,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V1n1),ap(c_2Elist_2ELENGTH(A_27a),V0l)))
& p(ap(ap(c_2Eprim__rec_2E_3C,V2n2),ap(c_2Elist_2ELENGTH(A_27a),V0l))) )
=> ( ap(ap(c_2Elist_2EEL(A_27a),V1n1),V0l) = ap(ap(c_2Elist_2EEL(A_27a),V2n2),V0l)
<=> V1n1 = V2n2 ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EALL__DISTINCT__EL__IMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1n1] :
( mem(V1n1,ty_2Enum_2Enum)
=> ! [V2n2] :
( mem(V2n2,ty_2Enum_2Enum)
=> ( ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0l))
& p(ap(ap(c_2Eprim__rec_2E_3C,V1n1),ap(c_2Elist_2ELENGTH(A_27a),V0l)))
& p(ap(ap(c_2Eprim__rec_2E_3C,V2n2),ap(c_2Elist_2ELENGTH(A_27a),V0l))) )
=> ( ap(ap(c_2Elist_2EEL(A_27a),V1n1),V0l) = ap(ap(c_2Elist_2EEL(A_27a),V2n2),V0l)
<=> V1n1 = V2n2 ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EALL__DISTINCT__APPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)))
<=> ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0l1))
& p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V1l2))
& ! [V2e] :
( mem(V2e,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l1)))
=> ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V2e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EALL__DISTINCT__SING,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),c_2Elist_2ENIL(A_27a)))) ) ) ).
fof(conj_thm_2Elist_2EALL__DISTINCT__ZIP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27b))
=> ( ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0l1))
& ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2) )
=> p(ap(c_2Elist_2EALL__DISTINCT(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2)))) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EALL__DISTINCT__ZIP__SWAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27b))
=> ( ( p(ap(c_2Elist_2EALL__DISTINCT(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))))
& ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2) )
=> p(ap(c_2Elist_2EALL__DISTINCT(ty_2Epair_2Eprod(A_27b,A_27a)),ap(c_2Elist_2EZIP(A_27b,A_27a),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27b),ty_2Elist_2Elist(A_27a)),V1l2),V0l1)))) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EALL__DISTINCT__REVERSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V0l)))
<=> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0l)) ) ) ) ).
fof(conj_thm_2Elist_2EALL__DISTINCT__FLAT__REVERSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0xs] :
( mem(V0xs,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27a)))
=> ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(c_2Elist_2EFLAT(A_27a),ap(c_2Elist_2EREVERSE(ty_2Elist_2Elist(A_27a)),V0xs))))
<=> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(c_2Elist_2EFLAT(A_27a),V0xs))) ) ) ) ).
fof(ax_thm_2Elist_2ELRC__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( p(ap(ap(ap(ap(c_2Elist_2ELRC(A_27a),V0R),c_2Elist_2ENIL(A_27a)),V1x),V2y))
<=> V1x = V2y ) ) ) )
& ! [V3R] :
( mem(V3R,arr(A_27a,arr(A_27a,bool)))
=> ! [V4h] :
( mem(V4h,A_27a)
=> ! [V5t] :
( mem(V5t,ty_2Elist_2Elist(A_27a))
=> ! [V6x] :
( mem(V6x,A_27a)
=> ! [V7y] :
( mem(V7y,A_27a)
=> ( p(ap(ap(ap(ap(c_2Elist_2ELRC(A_27a),V3R),ap(ap(c_2Elist_2ECONS(A_27a),V4h),V5t)),V6x),V7y))
<=> ( V6x = V4h
& ? [V8z] :
( mem(V8z,A_27a)
& p(ap(ap(V3R,V6x),V8z))
& p(ap(ap(ap(ap(c_2Elist_2ELRC(A_27a),V3R),V5t),V8z),V7y)) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ENRC__LRC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V1n),V2x),V3y))
<=> ? [V4ls] :
( mem(V4ls,ty_2Elist_2Elist(A_27a))
& p(ap(ap(ap(ap(c_2Elist_2ELRC(A_27a),V0R),V4ls),V2x),V3y))
& ap(c_2Elist_2ELENGTH(A_27a),V4ls) = V1n ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELRC__MEM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ! [V4e] :
( mem(V4e,A_27a)
=> ( ( p(ap(ap(ap(ap(c_2Elist_2ELRC(A_27a),V0R),V1ls),V2x),V3y))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V4e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1ls))) )
=> ? [V5z] :
( mem(V5z,A_27a)
& ? [V6t] :
( mem(V6t,ty_2Elist_2Elist(A_27a))
& p(ap(ap(V0R,V4e),V5z))
& p(ap(ap(ap(ap(c_2Elist_2ELRC(A_27a),V0R),V6t),V5z),V3y)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELRC__MEM__right,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1h] :
( mem(V1h,A_27a)
=> ! [V2t] :
( mem(V2t,ty_2Elist_2Elist(A_27a))
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] :
( mem(V4y,A_27a)
=> ! [V5e] :
( mem(V5e,A_27a)
=> ( ( p(ap(ap(ap(ap(c_2Elist_2ELRC(A_27a),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t)),V3x),V4y))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V5e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2t))) )
=> ? [V6z] :
( mem(V6z,A_27a)
& ? [V7p] :
( mem(V7p,ty_2Elist_2Elist(A_27a))
& p(ap(ap(V0R,V6z),V5e))
& p(ap(ap(ap(ap(c_2Elist_2ELRC(A_27a),V0R),V7p),V3x),V6z)) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__TO__SET__APPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l1)),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2)) ) ) ) ).
fof(conj_thm_2Elist_2EUNION__APPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l1)),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2)) = ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__TO__SET__EQ__EMPTY,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( ( ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l) = c_2Epred__set_2EEMPTY(A_27a)
<=> V0l = c_2Elist_2ENIL(A_27a) )
& ( c_2Epred__set_2EEMPTY(A_27a) = ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l)
<=> V0l = c_2Elist_2ENIL(A_27a) ) ) ) ) ).
fof(conj_thm_2Elist_2EFINITE__LIST__TO__SET,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> p(ap(c_2Epred__set_2EFINITE(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l))) ) ) ).
fof(conj_thm_2Elist_2ESUM__IMAGE__LIST__TO__SET__upper__bound,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V0f),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1ls))),ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(A_27a,ty_2Enum_2Enum),V0f),V1ls)))) ) ) ) ).
fof(conj_thm_2Elist_2ESUM__MAP__MEM__bound,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2ls] :
( mem(V2ls,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2ls)))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(V0f,V1x)),ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(A_27a,ty_2Enum_2Enum),V0f),V2ls)))) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EINJ__MAP__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ( ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l1)),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2l2))),c_2Epred__set_2EUNIV(A_27b)))
& ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1l1) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V2l2) )
=> V1l1 = V2l2 ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EINJ__MAP__EQ__IFF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),ap(ap(c_2Epred__set_2EUNION(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l1)),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2l2))),c_2Epred__set_2EUNIV(A_27b)))
=> ( ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1l1) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V2l2)
<=> V1l1 = V2l2 ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ECARD__LIST__TO__SET,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0ls] :
( mem(V0ls,ty_2Elist_2Elist(A_27a))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Epred__set_2ECARD(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0ls))),ap(c_2Elist_2ELENGTH(A_27a),V0ls))) ) ) ).
fof(conj_thm_2Elist_2EALL__DISTINCT__CARD__LIST__TO__SET,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0ls] :
( mem(V0ls,ty_2Elist_2Elist(A_27a))
=> ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0ls))
=> ap(c_2Epred__set_2ECARD(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0ls)) = ap(c_2Elist_2ELENGTH(A_27a),V0ls) ) ) ) ).
fof(conj_thm_2Elist_2ECARD__LIST__TO__SET__ALL__DISTINCT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0ls] :
( mem(V0ls,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Epred__set_2ECARD(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0ls)) = ap(c_2Elist_2ELENGTH(A_27a),V0ls)
=> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0ls)) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__TO__SET__REVERSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0ls] :
( mem(V0ls,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V0ls)) = ap(c_2Elist_2ELIST__TO__SET(A_27a),V0ls) ) ) ).
fof(conj_thm_2Elist_2ELIST__TO__SET__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0h] :
( mem(V0h,A_27b)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(A_27b))
=> ( ap(c_2Elist_2ELIST__TO__SET(A_27a),c_2Elist_2ENIL(A_27a)) = c_2Epred__set_2EEMPTY(A_27a)
& ap(c_2Elist_2ELIST__TO__SET(A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V0h),V1t)) = ap(ap(c_2Epred__set_2EINSERT(A_27b),V0h),ap(c_2Elist_2ELIST__TO__SET(A_27b),V1t)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__TO__SET__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELIST__TO__SET(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1l)) = ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l)) ) ) ) ) ).
fof(lameq_f418,axiom,
! [A_27a,V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V2x] : ap(f418(A_27a,V0P),V2x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(V0P,V2x)) ) ).
fof(conj_thm_2Elist_2ELIST__TO__SET__FILTER,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l)) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f418(A_27a,V0P))),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l)) ) ) ) ).
fof(lameq_f419,axiom,
! [A_27a,V0R] :
( mem(V0R,arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool)))
=> ! [V1s] : ap(f419(A_27a,V0R),V1s) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Epred__set_2EFINITE(A_27a),V1s)),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V1s),c_2Epred__set_2EEMPTY(A_27a))))),ap(ap(V0R,ap(c_2Epred__set_2EREST(A_27a),V1s)),V1s)) ) ).
fof(lameq_f420,axiom,
! [A_27a,V0R] : ap(f420(A_27a),V0R) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Erelation_2EWF(arr(A_27a,bool)),V0R)),ap(c_2Ebool_2E_21(arr(A_27a,bool)),f419(A_27a,V0R))) ).
fof(lameq_f421,axiom,
! [A_27a,V2SET__TO__LIST] :
( mem(V2SET__TO__LIST,arr(arr(A_27a,bool),ty_2Elist_2Elist(A_27a)))
=> ! [V3a] : ap(f421(A_27a,V2SET__TO__LIST),V3a) = ap(c_2Ecombin_2EI(ty_2Elist_2Elist(A_27a)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(c_2Epred__set_2EFINITE(A_27a),V3a)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V3a),c_2Epred__set_2EEMPTY(A_27a))),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),ap(c_2Epred__set_2ECHOICE(A_27a),V3a)),ap(V2SET__TO__LIST,ap(c_2Epred__set_2EREST(A_27a),V3a))))),c_2Ebool_2EARB(ty_2Elist_2Elist(A_27a)))) ) ).
fof(lameq_f422,axiom,
! [A_27a,V2SET__TO__LIST] : ap(f422(A_27a),V2SET__TO__LIST) = f421(A_27a,V2SET__TO__LIST) ).
fof(ax_thm_2Elist_2ESET__TO__LIST__primitive__def,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Elist_2ESET__TO__LIST(A_27a) = ap(ap(c_2Erelation_2EWFREC(arr(A_27a,bool),ty_2Elist_2Elist(A_27a)),ap(c_2Emin_2E_40(arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))),f420(A_27a))),f422(A_27a)) ) ).
fof(conj_thm_2Elist_2ESET__TO__LIST__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
=> ap(c_2Elist_2ESET__TO__LIST(A_27a),V0s) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V0s),c_2Epred__set_2EEMPTY(A_27a))),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),ap(c_2Epred__set_2ECHOICE(A_27a),V0s)),ap(c_2Elist_2ESET__TO__LIST(A_27a),ap(c_2Epred__set_2EREST(A_27a),V0s)))) ) ) ) ).
fof(conj_thm_2Elist_2ESET__TO__LIST__IND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(arr(A_27a,bool),bool))
=> ( ! [V1s] :
( mem(V1s,arr(A_27a,bool))
=> ( ( ( p(ap(c_2Epred__set_2EFINITE(A_27a),V1s))
& V1s != c_2Epred__set_2EEMPTY(A_27a) )
=> p(ap(V0P,ap(c_2Epred__set_2EREST(A_27a),V1s))) )
=> p(ap(V0P,V1s)) ) )
=> ! [V2v] :
( mem(V2v,arr(A_27a,bool))
=> p(ap(V0P,V2v)) ) ) ) ) ).
fof(conj_thm_2Elist_2ESET__TO__LIST__EMPTY,axiom,
! [A_27a] :
( ne(A_27a)
=> ap(c_2Elist_2ESET__TO__LIST(A_27a),c_2Epred__set_2EEMPTY(A_27a)) = c_2Elist_2ENIL(A_27a) ) ).
fof(conj_thm_2Elist_2ESET__TO__LIST__INV,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
=> ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Elist_2ESET__TO__LIST(A_27a),V0s)) = V0s ) ) ) ).
fof(conj_thm_2Elist_2ESET__TO__LIST__CARD,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
=> ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Elist_2ESET__TO__LIST(A_27a),V0s)) = ap(c_2Epred__set_2ECARD(A_27a),V0s) ) ) ) ).
fof(conj_thm_2Elist_2ESET__TO__LIST__IN__MEM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s))
<=> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Elist_2ESET__TO__LIST(A_27a),V0s)))) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMEM__SET__TO__LIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Elist_2ESET__TO__LIST(A_27a),V0s))))
<=> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ESET__TO__LIST__SING,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ap(c_2Elist_2ESET__TO__LIST(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))) = ap(ap(c_2Elist_2ECONS(A_27a),V0x),c_2Elist_2ENIL(A_27a)) ) ) ).
fof(conj_thm_2Elist_2EALL__DISTINCT__SET__TO__LIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
=> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(c_2Elist_2ESET__TO__LIST(A_27a),V0s))) ) ) ) ).
fof(conj_thm_2Elist_2EITSET__eq__FOLDL__SET__TO__LIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
=> ! [V1f] :
( mem(V1f,arr(A_27a,arr(A_27b,A_27b)))
=> ! [V2a] :
( mem(V2a,A_27b)
=> ap(ap(ap(c_2Epred__set_2EITSET(A_27a,A_27b),V1f),V0s),V2a) = ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),ap(c_2Ecombin_2EC(A_27a,A_27b,A_27b),V1f)),V2a),ap(c_2Elist_2ESET__TO__LIST(A_27a),V0s)) ) ) ) ) ) ) ).
fof(lameq_f423,axiom,
! [A_27a,V1h] :
( mem(V1h,A_27a)
=> ! [V4h_27] :
( mem(V4h_27,A_27a)
=> ! [V2t] :
( mem(V2t,ty_2Elist_2Elist(A_27a))
=> ! [V5t_27] : ap(f423(A_27a,V1h,V4h_27,V2t),V5t_27) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),V1h),V4h_27)),ap(ap(c_2Elist_2EisPREFIX(A_27a),V2t),V5t_27)) ) ) ) ).
fof(lameq_f424,axiom,
! [A_27a,V1h] :
( mem(V1h,A_27a)
=> ! [V2t] :
( mem(V2t,ty_2Elist_2Elist(A_27a))
=> ! [V4h_27] : ap(f424(A_27a,V1h,V2t),V4h_27) = f423(A_27a,V1h,V4h_27,V2t) ) ) ).
fof(ax_thm_2Elist_2EisPREFIX,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EisPREFIX(A_27a),c_2Elist_2ENIL(A_27a)),V0l))
<=> $true ) )
& ! [V1h] :
( mem(V1h,A_27a)
=> ! [V2t] :
( mem(V2t,ty_2Elist_2Elist(A_27a))
=> ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EisPREFIX(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t)),V3l))
<=> p(ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,bool),V3l),c_2Ebool_2EF),f424(A_27a,V1h,V2t))) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EisPREFIX__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1h] :
( mem(V1h,A_27a)
=> ! [V2t] :
( mem(V2t,ty_2Elist_2Elist(A_27a))
=> ! [V3h1] :
( mem(V3h1,A_27a)
=> ! [V4t1] :
( mem(V4t1,ty_2Elist_2Elist(A_27a))
=> ! [V5h2] :
( mem(V5h2,A_27a)
=> ! [V6t2] :
( mem(V6t2,ty_2Elist_2Elist(A_27a))
=> ( ( p(ap(ap(c_2Elist_2EisPREFIX(A_27a),c_2Elist_2ENIL(A_27a)),V0l))
<=> $true )
& ( p(ap(ap(c_2Elist_2EisPREFIX(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t)),c_2Elist_2ENIL(A_27a)))
<=> $false )
& ( p(ap(ap(c_2Elist_2EisPREFIX(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V3h1),V4t1)),ap(ap(c_2Elist_2ECONS(A_27a),V5h2),V6t2)))
<=> ( V3h1 = V5h2
& p(ap(ap(c_2Elist_2EisPREFIX(A_27a),V4t1),V6t2)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EisPREFIX__NILR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EisPREFIX(A_27a),V0x),c_2Elist_2ENIL(A_27a)))
<=> V0x = c_2Elist_2ENIL(A_27a) ) ) ) ).
fof(conj_thm_2Elist_2EisPREFIX__CONSR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,ty_2Elist_2Elist(A_27a))
=> ! [V1y] :
( mem(V1y,A_27a)
=> ! [V2ys] :
( mem(V2ys,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EisPREFIX(A_27a),V0x),ap(ap(c_2Elist_2ECONS(A_27a),V1y),V2ys)))
<=> ( V0x = c_2Elist_2ENIL(A_27a)
| ? [V3xs] :
( mem(V3xs,ty_2Elist_2Elist(A_27a))
& V0x = ap(ap(c_2Elist_2ECONS(A_27a),V1y),V3xs)
& p(ap(ap(c_2Elist_2EisPREFIX(A_27a),V3xs),V2ys)) ) ) ) ) ) ) ) ).
fof(ax_thm_2Elist_2ESNOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0x] :
( mem(V0x,A_27a)
=> ap(ap(c_2Elist_2ESNOC(A_27a),V0x),c_2Elist_2ENIL(A_27a)) = ap(ap(c_2Elist_2ECONS(A_27a),V0x),c_2Elist_2ENIL(A_27a)) )
& ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2x_27] :
( mem(V2x_27,A_27a)
=> ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2ESNOC(A_27a),V1x),ap(ap(c_2Elist_2ECONS(A_27a),V2x_27),V3l)) = ap(ap(c_2Elist_2ECONS(A_27a),V2x_27),ap(ap(c_2Elist_2ESNOC(A_27a),V1x),V3l)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__SNOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2ESNOC(A_27a),V0x),V1l)) = ap(c_2Enum_2ESUC,ap(c_2Elist_2ELENGTH(A_27a),V1l)) ) ) ) ).
fof(conj_thm_2Elist_2ELAST__SNOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2ESNOC(A_27a),V0x),V1l)) = V0x ) ) ) ).
fof(conj_thm_2Elist_2EFRONT__SNOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ESNOC(A_27a),V0x),V1l)) = V1l ) ) ) ).
fof(conj_thm_2Elist_2ESNOC__APPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2ESNOC(A_27a),V0x),V1l) = ap(ap(c_2Elist_2EAPPEND(A_27a),V1l),ap(ap(c_2Elist_2ECONS(A_27a),V0x),c_2Elist_2ENIL(A_27a))) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__TO__SET__SNOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2ESNOC(A_27a),V0x),V1ls)) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1ls)) ) ) ) ).
fof(conj_thm_2Elist_2EMAP__SNOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),ap(ap(c_2Elist_2ESNOC(A_27a),V1x),V2l)) = ap(ap(c_2Elist_2ESNOC(A_27b),ap(V0f,V1x)),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V2l)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEL__SNOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Elist_2ELENGTH(A_27a),V1l)))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ap(ap(c_2Elist_2EEL(A_27a),V0n),ap(ap(c_2Elist_2ESNOC(A_27a),V2x),V1l)) = ap(ap(c_2Elist_2EEL(A_27a),V0n),V1l) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEL__LENGTH__SNOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Elist_2ELENGTH(A_27a),V0l)),ap(ap(c_2Elist_2ESNOC(A_27a),V1x),V0l)) = V1x ) ) ) ).
fof(conj_thm_2Elist_2EAPPEND__SNOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),ap(ap(c_2Elist_2ESNOC(A_27a),V1x),V2l2)) = ap(ap(c_2Elist_2ESNOC(A_27a),V1x),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V2l2)) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY__SNOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),ap(ap(c_2Elist_2ESNOC(A_27a),V1x),V2l)))
<=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V2l))
& p(ap(V0P,V1x)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEXISTS__SNOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),ap(ap(c_2Elist_2ESNOC(A_27a),V1x),V2l)))
<=> ( p(ap(V0P,V1x))
| p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),V2l)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMEM__SNOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0y] :
( mem(V0y,A_27a)
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0y),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2ESNOC(A_27a),V1x),V2l))))
<=> ( V0y = V1x
| p(ap(ap(c_2Ebool_2EIN(A_27a),V0y),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2l))) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ESNOC__11,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,ty_2Elist_2Elist(A_27a))
=> ! [V2a] :
( mem(V2a,A_27a)
=> ! [V3b] :
( mem(V3b,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2ESNOC(A_27a),V0x),V1y) = ap(ap(c_2Elist_2ESNOC(A_27a),V2a),V3b)
<=> ( V0x = V2a
& V1y = V3b ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EREVERSE__SNOC__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ap(c_2Elist_2EREVERSE(A_27b),c_2Elist_2ENIL(A_27b)) = c_2Elist_2ENIL(A_27b)
& ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2EREVERSE(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V1l)) = ap(ap(c_2Elist_2ESNOC(A_27a),V0x),ap(c_2Elist_2EREVERSE(A_27a),V1l)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EREVERSE__SNOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2EREVERSE(A_27a),ap(ap(c_2Elist_2ESNOC(A_27a),V0x),V1l)) = ap(ap(c_2Elist_2ECONS(A_27a),V0x),ap(c_2Elist_2EREVERSE(A_27a),V1l)) ) ) ) ).
fof(conj_thm_2Elist_2ESNOC__Axiom,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0e] :
( mem(V0e,A_27b)
=> ! [V1f] :
( mem(V1f,arr(A_27a,arr(ty_2Elist_2Elist(A_27a),arr(A_27b,A_27b))))
=> ? [V2fn] :
( mem(V2fn,arr(ty_2Elist_2Elist(A_27a),A_27b))
& ap(V2fn,c_2Elist_2ENIL(A_27a)) = V0e
& ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4l] :
( mem(V4l,ty_2Elist_2Elist(A_27a))
=> ap(V2fn,ap(ap(c_2Elist_2ESNOC(A_27a),V3x),V4l)) = ap(ap(ap(V1f,V3x),V4l),ap(V2fn,V4l)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ESNOC__INDUCT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool))
=> ( ( p(ap(V0P,c_2Elist_2ENIL(A_27a)))
& ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(V0P,V1l))
=> ! [V2x] :
( mem(V2x,A_27a)
=> p(ap(V0P,ap(ap(c_2Elist_2ESNOC(A_27a),V2x),V1l))) ) ) ) )
=> ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(A_27a))
=> p(ap(V0P,V3l)) ) ) ) ) ).
fof(conj_thm_2Elist_2ESNOC__CASES,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0ll] :
( mem(V0ll,ty_2Elist_2Elist(A_27a))
=> ( V0ll = c_2Elist_2ENIL(A_27a)
| ? [V1x] :
( mem(V1x,A_27a)
& ? [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
& V0ll = ap(ap(c_2Elist_2ESNOC(A_27a),V1x),V2l) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EGENLIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,A_27a))
=> ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),c_2Enum_2E0) = c_2Elist_2ENIL(A_27a) )
& ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2EGENLIST(A_27a),V1f),ap(c_2Enum_2ESUC,V2n)) = ap(ap(c_2Elist_2ESNOC(A_27a),ap(V1f,V2n)),ap(ap(c_2Elist_2EGENLIST(A_27a),V1f),V2n)) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__GENLIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),V1n)) = V1n ) ) ) ).
fof(ax_thm_2Elist_2EGENLIST__AUX,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V0f),c_2Enum_2E0),V1l) = V1l ) )
& ! [V2f] :
( mem(V2f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ! [V4l] :
( mem(V4l,ty_2Elist_2Elist(A_27a))
=> ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V2f),ap(c_2Enum_2ESUC,V3n)),V4l) = ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V2f),V3n),ap(ap(c_2Elist_2ECONS(A_27a),ap(V2f,V3n)),V4l)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EGENLIST__AUX__compute,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V0f),c_2Enum_2E0),V1l) = V1l ) )
& ! [V2f] :
( mem(V2f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ! [V4l] :
( mem(V4l,ty_2Elist_2Elist(A_27a))
=> ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V2f),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),V4l) = ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V2f),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Elist_2ECONS(A_27a),ap(V2f,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),V4l)) ) ) )
& ! [V5f] :
( mem(V5f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V6n] :
( mem(V6n,ty_2Enum_2Enum)
=> ! [V7l] :
( mem(V7l,ty_2Elist_2Elist(A_27a))
=> ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V5f),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V6n))),V7l) = ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V5f),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n))),ap(ap(c_2Elist_2ECONS(A_27a),ap(V5f,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n)))),V7l)) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EPAD__LEFT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0c] :
( mem(V0c,A_27a)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2s] :
( mem(V2s,ty_2Elist_2Elist(A_27a))
=> ap(ap(ap(c_2Elist_2EPAD__LEFT(A_27a),V0c),V1n),V2s) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),ap(c_2Ecombin_2EK(A_27a,ty_2Enum_2Enum),V0c)),ap(ap(c_2Earithmetic_2E_2D,V1n),ap(c_2Elist_2ELENGTH(A_27a),V2s)))),V2s) ) ) ) ) ).
fof(ax_thm_2Elist_2EPAD__RIGHT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0c] :
( mem(V0c,A_27a)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2s] :
( mem(V2s,ty_2Elist_2Elist(A_27a))
=> ap(ap(ap(c_2Elist_2EPAD__RIGHT(A_27a),V0c),V1n),V2s) = ap(ap(c_2Elist_2EAPPEND(A_27a),V2s),ap(ap(c_2Elist_2EGENLIST(A_27a),ap(c_2Ecombin_2EK(A_27a,ty_2Enum_2Enum),V0c)),ap(ap(c_2Earithmetic_2E_2D,V1n),ap(c_2Elist_2ELENGTH(A_27a),V2s)))) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP__GENLIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1g] :
( mem(V1g,arr(ty_2Enum_2Enum,A_27a))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),ap(ap(c_2Elist_2EGENLIST(A_27a),V1g),V2n)) = ap(ap(c_2Elist_2EGENLIST(A_27b),ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,A_27b,A_27a),V0f),V1g)),V2n) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEL__GENLIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V2x),V1n))
=> ap(ap(c_2Elist_2EEL(A_27a),V2x),ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),V1n)) = ap(V0f,V2x) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EHD__GENLIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(c_2Elist_2EHD(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),ap(c_2Enum_2ESUC,V1n))) = ap(V0f,c_2Enum_2E0) ) ) ) ).
fof(conj_thm_2Elist_2EHD__GENLIST__COR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,A_27a))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))
=> ap(c_2Elist_2EHD(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V1f),V0n)) = ap(V1f,c_2Enum_2E0) ) ) ) ) ).
fof(conj_thm_2Elist_2EGENLIST__FUN__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V2g] :
( mem(V2g,arr(ty_2Enum_2Enum,A_27a))
=> ( ap(ap(c_2Elist_2EGENLIST(A_27a),V1f),V0n) = ap(ap(c_2Elist_2EGENLIST(A_27a),V2g),V0n)
<=> ! [V3x] :
( mem(V3x,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V3x),V0n))
=> ap(V1f,V3x) = ap(V2g,V3x) ) ) ) ) ) ) ) ).
fof(lameq_f425,axiom,
! [A_27a,V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V3t] : ap(f425(A_27a,V2b,V0f),V3t) = ap(V0f,ap(ap(c_2Earithmetic_2E_2B,V3t),V2b)) ) ) ).
fof(conj_thm_2Elist_2EGENLIST__APPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V1a] :
( mem(V1a,ty_2Enum_2Enum)
=> ! [V2b] :
( mem(V2b,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),ap(ap(c_2Earithmetic_2E_2B,V1a),V2b)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),V2b)),ap(ap(c_2Elist_2EGENLIST(A_27a),f425(A_27a,V2b,V0f)),V1a)) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY__GENLIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),ap(ap(c_2Elist_2EGENLIST(A_27a),V1f),V2n)))
<=> ! [V3i] :
( mem(V3i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V3i),V2n))
=> p(ap(V0P,ap(V1f,V3i))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEXISTS__GENLIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Elist_2EEXISTS(A_27a),V0P),ap(ap(c_2Elist_2EGENLIST(A_27a),V1f),V2n)))
<=> ? [V3i] :
( mem(V3i,ty_2Enum_2Enum)
& p(ap(ap(c_2Eprim__rec_2E_3C,V3i),V2n))
& p(ap(V0P,ap(V1f,V3i))) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ETL__GENLIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(c_2Elist_2ETL(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),ap(c_2Enum_2ESUC,V1n))) = ap(ap(c_2Elist_2EGENLIST(A_27a),ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,A_27a,ty_2Enum_2Enum),V0f),c_2Enum_2ESUC)),V1n) ) ) ) ).
fof(lameq_f426,axiom,
! [A_27b,A_27a,V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,A_27b))
=> ! [V3x] : ap(f426(A_27b,A_27a,V0l,V1f),V3x) = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),ap(ap(c_2Elist_2EEL(A_27a),V3x),V0l)),ap(V1f,V3x)) ) ) ).
fof(conj_thm_2Elist_2EZIP__GENLIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,A_27b))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l) = V2n
=> ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l),ap(ap(c_2Elist_2EGENLIST(A_27b),V1f),V2n))) = ap(ap(c_2Elist_2EGENLIST(ty_2Epair_2Eprod(A_27a,A_27b)),f426(A_27b,A_27a,V0l,V1f)),V2n) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EGENLIST__CONS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),ap(c_2Enum_2ESUC,V1n)) = ap(ap(c_2Elist_2ECONS(A_27a),ap(V0f,c_2Enum_2E0)),ap(ap(c_2Elist_2EGENLIST(A_27a),ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,A_27a,ty_2Enum_2Enum),V0f),c_2Enum_2ESUC)),V1n)) ) ) ) ).
fof(conj_thm_2Elist_2ENULL__GENLIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,A_27a))
=> ( p(ap(c_2Elist_2ENULL(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V1f),V0n)))
<=> V0n = c_2Enum_2E0 ) ) ) ) ).
fof(conj_thm_2Elist_2EGENLIST__GENLIST__AUX,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),V1n) = ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V0f),V1n),c_2Elist_2ENIL(A_27a)) ) ) ) ).
fof(conj_thm_2Elist_2EGENLIST__NUMERALS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),c_2Enum_2E0) = c_2Elist_2ENIL(A_27a)
& ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),ap(c_2Earithmetic_2ENUMERAL,V1n)) = ap(ap(ap(c_2Elist_2EGENLIST__AUX(A_27a),V0f),ap(c_2Earithmetic_2ENUMERAL,V1n)),c_2Elist_2ENIL(A_27a)) ) ) ) ) ).
fof(conj_thm_2Elist_2EMEM__GENLIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V1f),V2n))))
<=> ? [V3m] :
( mem(V3m,ty_2Enum_2Enum)
& p(ap(ap(c_2Eprim__rec_2E_3C,V3m),V2n))
& V0x = ap(V1f,V3m) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EALL__DISTINCT__SNOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2ESNOC(A_27a),V0x),V1l)))
<=> ( ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l)))
& p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V1l)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EALL__DISTINCT__GENLIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),V1n)))
<=> ! [V2m1] :
( mem(V2m1,ty_2Enum_2Enum)
=> ! [V3m2] :
( mem(V3m2,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V2m1),V1n))
& p(ap(ap(c_2Eprim__rec_2E_3C,V3m2),V1n))
& ap(V0f,V2m1) = ap(V0f,V3m2) )
=> V2m1 = V3m2 ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EFOLDL__SNOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27b,arr(A_27a,A_27b)))
=> ! [V1e] :
( mem(V1e,A_27b)
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(A_27a))
=> ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),V0f),V1e),ap(ap(c_2Elist_2ESNOC(A_27a),V2x),V3l)) = ap(ap(V0f,ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),V0f),V1e),V3l)),V2x) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ESUM__SNOC,axiom,
! [V0x] :
( mem(V0x,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2ESNOC(ty_2Enum_2Enum),V0x),V1l)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ESUM,V1l)),V0x) ) ) ).
fof(conj_thm_2Elist_2ESUM__APPEND,axiom,
! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EAPPEND(ty_2Enum_2Enum),V0l1),V1l2)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ESUM,V0l1)),ap(c_2Elist_2ESUM,V1l2)) ) ) ).
fof(lameq_f427,axiom,
! [A_27a,V0f] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V2a] :
( mem(V2a,ty_2Enum_2Enum)
=> ! [V3e] : ap(f427(A_27a,V0f,V2a),V3e) = ap(ap(c_2Earithmetic_2E_2B,V2a),ap(V0f,V3e)) ) ) ).
fof(lameq_f428,axiom,
! [A_27a,V0f] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V2a] : ap(f428(A_27a,V0f),V2a) = f427(A_27a,V0f,V2a) ) ).
fof(conj_thm_2Elist_2ESUM__MAP__FOLDL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(A_27a,ty_2Enum_2Enum),V0f),V1ls)) = ap(ap(ap(c_2Elist_2EFOLDL(A_27a,ty_2Enum_2Enum),f428(A_27a,V0f)),c_2Enum_2E0),V1ls) ) ) ) ).
fof(conj_thm_2Elist_2ESUM__IMAGE__eq__SUM__MAP__SET__TO__LIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1f] :
( mem(V1f,arr(A_27a,ty_2Enum_2Enum))
=> ( p(ap(c_2Epred__set_2EFINITE(A_27a),V0s))
=> ap(ap(c_2Epred__set_2ESUM__IMAGE(A_27a),V1f),V0s) = ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(A_27a,ty_2Enum_2Enum),V1f),ap(c_2Elist_2ESET__TO__LIST(A_27a),V0s))) ) ) ) ) ).
fof(conj_thm_2Elist_2EEL__REVERSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Elist_2ELENGTH(A_27a),V1l)))
=> ap(ap(c_2Elist_2EEL(A_27a),V0n),ap(c_2Elist_2EREVERSE(A_27a),V1l)) = ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Eprim__rec_2EPRE,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Elist_2ELENGTH(A_27a),V1l)),V0n))),V1l) ) ) ) ) ).
fof(lameq_f429,axiom,
! [A_27a,V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V2m] : ap(f429(A_27a,V1n,V0f),V2m) = ap(V0f,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Eprim__rec_2EPRE,V1n)),V2m)) ) ) ).
fof(conj_thm_2Elist_2EREVERSE__GENLIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(c_2Elist_2EREVERSE(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),V1n)) = ap(ap(c_2Elist_2EGENLIST(A_27a),f429(A_27a,V1n,V0f)),V1n) ) ) ) ).
fof(lameq_f430,axiom,
! [A_27b,A_27a,V0f] :
( mem(V0f,arr(A_27a,arr(A_27b,bool)))
=> ! [V3s] :
( mem(V3s,arr(A_27b,bool))
=> ! [V4x] : ap(f430(A_27b,A_27a,V0f,V3s),V4x) = ap(ap(c_2Epred__set_2EUNION(A_27b),V3s),ap(V0f,V4x)) ) ) ).
fof(lameq_f431,axiom,
! [A_27a,A_27b,V0f] :
( mem(V0f,arr(A_27a,arr(A_27b,bool)))
=> ! [V3s] : ap(f431(A_27a,A_27b,V0f),V3s) = f430(A_27b,A_27a,V0f,V3s) ) ).
fof(conj_thm_2Elist_2EFOLDL__UNION__BIGUNION,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,arr(A_27b,bool)))
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
=> ! [V2s] :
( mem(V2s,arr(A_27b,bool))
=> ap(ap(ap(c_2Elist_2EFOLDL(A_27a,arr(A_27b,bool)),f431(A_27a,A_27b,V0f)),V2s),V1ls) = ap(ap(c_2Epred__set_2EUNION(A_27b),V2s),ap(c_2Epred__set_2EBIGUNION(A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,arr(A_27b,bool)),V0f),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1ls)))) ) ) ) ) ) ).
fof(lameq_f432,axiom,
! [A_27c,A_27a,A_27b,V0f] :
( mem(V0f,arr(A_27a,arr(A_27b,arr(A_27c,bool))))
=> ! [V4x] :
( mem(V4x,A_27a)
=> ! [V3s] :
( mem(V3s,arr(A_27c,bool))
=> ! [V5y] : ap(f432(A_27c,A_27a,A_27b,V0f,V4x,V3s),V5y) = ap(ap(c_2Epred__set_2EUNION(A_27c),V3s),ap(ap(V0f,V4x),V5y)) ) ) ) ).
fof(lameq_f433,axiom,
! [A_27b,A_27c,A_27a,V0f] :
( mem(V0f,arr(A_27a,arr(A_27b,arr(A_27c,bool))))
=> ! [V3s] :
( mem(V3s,arr(A_27c,bool))
=> ! [V4x] : ap(f433(A_27b,A_27c,A_27a,V0f,V3s),V4x) = f432(A_27c,A_27a,A_27b,V0f,V4x,V3s) ) ) ).
fof(lameq_f434,axiom,
! [A_27a,A_27b,A_27c,V0f] :
( mem(V0f,arr(A_27a,arr(A_27b,arr(A_27c,bool))))
=> ! [V3s] : ap(f434(A_27a,A_27b,A_27c,V0f),V3s) = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,arr(A_27c,bool)),f433(A_27b,A_27c,A_27a,V0f,V3s)) ) ).
fof(conj_thm_2Elist_2EFOLDL__UNION__BIGUNION__paired,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27a,arr(A_27b,arr(A_27c,bool))))
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V2s] :
( mem(V2s,arr(A_27c,bool))
=> ap(ap(ap(c_2Elist_2EFOLDL(ty_2Epair_2Eprod(A_27a,A_27b),arr(A_27c,bool)),f434(A_27a,A_27b,A_27c,V0f)),V2s),V1ls) = ap(ap(c_2Epred__set_2EUNION(A_27c),V2s),ap(c_2Epred__set_2EBIGUNION(A_27c),ap(ap(c_2Epred__set_2EIMAGE(ty_2Epair_2Eprod(A_27a,A_27b),arr(A_27c,bool)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,arr(A_27c,bool)),V0f)),ap(c_2Elist_2ELIST__TO__SET(ty_2Epair_2Eprod(A_27a,A_27b)),V1ls)))) ) ) ) ) ) ) ).
fof(lameq_f435,axiom,
! [A_27b,A_27a,V3x] :
( mem(V3x,A_27b)
=> ! [V1f] :
( mem(V1f,arr(A_27b,arr(ty_2Epair_2Eprod(A_27a,A_27a),A_27b)))
=> ! [V4y] : ap(f435(A_27b,A_27a,V3x,V1f),V4y) = ap(ap(V1f,V3x),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V4y),V4y)) ) ) ).
fof(lameq_f436,axiom,
! [A_27a,A_27b,V1f] :
( mem(V1f,arr(A_27b,arr(ty_2Epair_2Eprod(A_27a,A_27a),A_27b)))
=> ! [V3x] : ap(f436(A_27a,A_27b,V1f),V3x) = f435(A_27b,A_27a,V3x,V1f) ) ).
fof(conj_thm_2Elist_2EFOLDL__ZIP__SAME,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0ls] :
( mem(V0ls,ty_2Elist_2Elist(A_27a))
=> ! [V1f] :
( mem(V1f,arr(A_27b,arr(ty_2Epair_2Eprod(A_27a,A_27a),A_27b)))
=> ! [V2e] :
( mem(V2e,A_27b)
=> ap(ap(ap(c_2Elist_2EFOLDL(ty_2Epair_2Eprod(A_27a,A_27a),A_27b),V1f),V2e),ap(c_2Elist_2EZIP(A_27a,A_27a),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),V0ls),V0ls))) = ap(ap(ap(c_2Elist_2EFOLDL(A_27a,A_27b),f436(A_27a,A_27b,V1f)),V2e),V0ls) ) ) ) ) ) ).
fof(lameq_f437,axiom,
! [A_27b,A_27a,V1f] :
( mem(V1f,arr(ty_2Epair_2Eprod(A_27a,A_27a),A_27b))
=> ! [V2x] : ap(f437(A_27b,A_27a,V1f),V2x) = ap(V1f,ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V2x),V2x)) ) ).
fof(conj_thm_2Elist_2EMAP__ZIP__SAME,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0ls] :
( mem(V0ls,ty_2Elist_2Elist(A_27a))
=> ! [V1f] :
( mem(V1f,arr(ty_2Epair_2Eprod(A_27a,A_27a),A_27b))
=> ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27a),A_27b),V1f),ap(c_2Elist_2EZIP(A_27a,A_27a),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),V0ls),V0ls))) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),f437(A_27b,A_27a,V1f)),V0ls) ) ) ) ) ).
fof(conj_thm_2Elist_2EINFINITE__LIST__UNIV,axiom,
! [A_27a] :
( ne(A_27a)
=> ~ p(ap(c_2Epred__set_2EFINITE(ty_2Elist_2Elist(A_27a)),c_2Epred__set_2EUNIV(ty_2Elist_2Elist(A_27a)))) ) ).
fof(ax_thm_2Elist_2ELEN__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2ELEN(A_27a),c_2Elist_2ENIL(A_27a)),V0n) = V0n )
& ! [V1h] :
( mem(V1h,A_27a)
=> ! [V2t] :
( mem(V2t,ty_2Elist_2Elist(A_27a))
=> ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2ELEN(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t)),V3n) = ap(ap(c_2Elist_2ELEN(A_27a),V2t),ap(ap(c_2Earithmetic_2E_2B,V3n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EREV__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0acc] :
( mem(V0acc,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EREV(A_27a),c_2Elist_2ENIL(A_27a)),V0acc) = V0acc )
& ! [V1h] :
( mem(V1h,A_27a)
=> ! [V2t] :
( mem(V2t,ty_2Elist_2Elist(A_27a))
=> ! [V3acc] :
( mem(V3acc,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EREV(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t)),V3acc) = ap(ap(c_2Elist_2EREV(A_27a),V2t),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V3acc)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELEN__LENGTH__LEM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0L] :
( mem(V0L,ty_2Elist_2Elist(A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2ELEN(A_27a),V0L),V1n) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ELENGTH(A_27a),V0L)),V1n) ) ) ) ).
fof(conj_thm_2Elist_2EREV__REVERSE__LEM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0L1] :
( mem(V0L1,ty_2Elist_2Elist(A_27a))
=> ! [V1L2] :
( mem(V1L2,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EREV(A_27a),V0L1),V1L2) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V0L1)),V1L2) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__LEN,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0L] :
( mem(V0L,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELENGTH(A_27a),V0L) = ap(ap(c_2Elist_2ELEN(A_27a),V0L),c_2Enum_2E0) ) ) ).
fof(conj_thm_2Elist_2EREVERSE__REV,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0L] :
( mem(V0L,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2EREVERSE(A_27a),V0L) = ap(ap(c_2Elist_2EREV(A_27a),V0L),c_2Elist_2ENIL(A_27a)) ) ) ).
fof(ax_thm_2Elist_2ESUM__ACC__DEF,axiom,
( ! [V0acc] :
( mem(V0acc,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2ESUM__ACC,c_2Elist_2ENIL(ty_2Enum_2Enum)),V0acc) = V0acc )
& ! [V1h] :
( mem(V1h,ty_2Enum_2Enum)
=> ! [V2t] :
( mem(V2t,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ! [V3acc] :
( mem(V3acc,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2ESUM__ACC,ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),V1h),V2t)),V3acc) = ap(ap(c_2Elist_2ESUM__ACC,V2t),ap(ap(c_2Earithmetic_2E_2B,V1h),V3acc)) ) ) ) ) ).
fof(conj_thm_2Elist_2ESUM__ACC__SUM__LEM,axiom,
! [V0L] :
( mem(V0L,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2ESUM__ACC,V0L),V1n) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ESUM,V0L)),V1n) ) ) ).
fof(conj_thm_2Elist_2ESUM__SUM__ACC,axiom,
! [V0L] :
( mem(V0L,ty_2Elist_2Elist(ty_2Enum_2Enum))
=> ap(c_2Elist_2ESUM,V0L) = ap(ap(c_2Elist_2ESUM__ACC,V0L),c_2Enum_2E0) ) ).
fof(conj_thm_2Elist_2EEXISTS__LIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool))
=> ( ? [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
& p(ap(V0P,V1l)) )
<=> ( p(ap(V0P,c_2Elist_2ENIL(A_27a)))
| ? [V2h] :
( mem(V2h,A_27a)
& ? [V3t] :
( mem(V3t,ty_2Elist_2Elist(A_27a))
& p(ap(V0P,ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t))) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EFORALL__LIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool))
=> ( ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> p(ap(V0P,V1l)) )
<=> ( p(ap(V0P,c_2Elist_2ENIL(A_27a)))
& ! [V2h] :
( mem(V2h,A_27a)
=> ! [V3t] :
( mem(V3t,ty_2Elist_2Elist(A_27a))
=> p(ap(V0P,ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t))) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMEM__SPLIT__APPEND__first,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0e] :
( mem(V0e,A_27a)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l)))
<=> ? [V2pfx] :
( mem(V2pfx,ty_2Elist_2Elist(A_27a))
& ? [V3sfx] :
( mem(V3sfx,ty_2Elist_2Elist(A_27a))
& V1l = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V2pfx),ap(ap(c_2Elist_2ECONS(A_27a),V0e),c_2Elist_2ENIL(A_27a)))),V3sfx)
& ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2pfx))) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMEM__SPLIT__APPEND__last,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0e] :
( mem(V0e,A_27a)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l)))
<=> ? [V2pfx] :
( mem(V2pfx,ty_2Elist_2Elist(A_27a))
& ? [V3sfx] :
( mem(V3sfx,ty_2Elist_2Elist(A_27a))
& V1l = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V2pfx),ap(ap(c_2Elist_2ECONS(A_27a),V0e),c_2Elist_2ENIL(A_27a)))),V3sfx)
& ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V3sfx))) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EAPPEND__EQ__APPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ! [V2m1] :
( mem(V2m1,ty_2Elist_2Elist(A_27a))
=> ! [V3m2] :
( mem(V3m2,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2) = ap(ap(c_2Elist_2EAPPEND(A_27a),V2m1),V3m2)
<=> ( ? [V4l] :
( mem(V4l,ty_2Elist_2Elist(A_27a))
& V0l1 = ap(ap(c_2Elist_2EAPPEND(A_27a),V2m1),V4l)
& V3m2 = ap(ap(c_2Elist_2EAPPEND(A_27a),V4l),V1l2) )
| ? [V5l] :
( mem(V5l,ty_2Elist_2Elist(A_27a))
& V2m1 = ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V5l)
& V1l2 = ap(ap(c_2Elist_2EAPPEND(A_27a),V5l),V3m2) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EAPPEND__EQ__CONS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ! [V2h] :
( mem(V2h,A_27a)
=> ! [V3t] :
( mem(V3t,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2) = ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)
<=> ( ( V0l1 = c_2Elist_2ENIL(A_27a)
& V1l2 = ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t) )
| ? [V4lt] :
( mem(V4lt,ty_2Elist_2Elist(A_27a))
& V0l1 = ap(ap(c_2Elist_2ECONS(A_27a),V2h),V4lt)
& V3t = ap(ap(c_2Elist_2EAPPEND(A_27a),V4lt),V1l2) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EAPPEND__EQ__APPEND__MID,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1e] :
( mem(V1e,A_27a)
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ! [V3m1] :
( mem(V3m1,ty_2Elist_2Elist(A_27a))
=> ! [V4m2] :
( mem(V4m2,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),ap(ap(c_2Elist_2ECONS(A_27a),V1e),c_2Elist_2ENIL(A_27a)))),V2l2) = ap(ap(c_2Elist_2EAPPEND(A_27a),V3m1),V4m2)
<=> ( ? [V5l] :
( mem(V5l,ty_2Elist_2Elist(A_27a))
& V3m1 = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),ap(ap(c_2Elist_2ECONS(A_27a),V1e),c_2Elist_2ENIL(A_27a)))),V5l)
& V2l2 = ap(ap(c_2Elist_2EAPPEND(A_27a),V5l),V4m2) )
| ? [V6l] :
( mem(V6l,ty_2Elist_2Elist(A_27a))
& V0l1 = ap(ap(c_2Elist_2EAPPEND(A_27a),V3m1),V6l)
& V4m2 = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V6l),ap(ap(c_2Elist_2ECONS(A_27a),V1e),c_2Elist_2ENIL(A_27a)))),V2l2) ) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Elist_2ELUPDATE__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0e] :
( mem(V0e,A_27a)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V0e),V1n),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a) ) )
& ! [V2e] :
( mem(V2e,A_27a)
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4l] :
( mem(V4l,ty_2Elist_2Elist(A_27a))
=> ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V2e),c_2Enum_2E0),ap(ap(c_2Elist_2ECONS(A_27a),V3x),V4l)) = ap(ap(c_2Elist_2ECONS(A_27a),V2e),V4l) ) ) )
& ! [V5e] :
( mem(V5e,A_27a)
=> ! [V6n] :
( mem(V6n,ty_2Enum_2Enum)
=> ! [V7x] :
( mem(V7x,A_27a)
=> ! [V8l] :
( mem(V8l,ty_2Elist_2Elist(A_27a))
=> ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V5e),ap(c_2Enum_2ESUC,V6n)),ap(ap(c_2Elist_2ECONS(A_27a),V7x),V8l)) = ap(ap(c_2Elist_2ECONS(A_27a),V7x),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V5e),V6n),V8l)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELUPDATE__NIL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0xs] :
( mem(V0xs,ty_2Elist_2Elist(A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,A_27a)
=> ( ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V2x),V1n),V0xs) = c_2Elist_2ENIL(A_27a)
<=> V0xs = c_2Elist_2ENIL(A_27a) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELUPDATE__SEM,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0e] :
( mem(V0e,A_27a)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELENGTH(A_27a),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V0e),V1n),V2l)) = ap(c_2Elist_2ELENGTH(A_27a),V2l) ) ) )
& ! [V3e] :
( mem(V3e,A_27a)
=> ! [V4n] :
( mem(V4n,ty_2Enum_2Enum)
=> ! [V5l] :
( mem(V5l,ty_2Elist_2Elist(A_27a))
=> ! [V6p] :
( mem(V6p,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V6p),ap(c_2Elist_2ELENGTH(A_27a),V5l)))
=> ap(ap(c_2Elist_2EEL(A_27a),V6p),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V3e),V4n),V5l)) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V6p),V4n)),V3e),ap(ap(c_2Elist_2EEL(A_27a),V6p),V5l)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEL__LUPDATE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0ys] :
( mem(V0ys,ty_2Elist_2Elist(A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2i] :
( mem(V2i,ty_2Enum_2Enum)
=> ! [V3k] :
( mem(V3k,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2EEL(A_27a),V2i),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V1x),V3k),V0ys)) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2i),V3k)),ap(ap(c_2Eprim__rec_2E_3C,V3k),ap(c_2Elist_2ELENGTH(A_27a),V0ys)))),V1x),ap(ap(c_2Elist_2EEL(A_27a),V2i),V0ys)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__LUPDATE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2ys] :
( mem(V2ys,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELENGTH(A_27a),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V0x),V1n),V2ys)) = ap(c_2Elist_2ELENGTH(A_27a),V2ys) ) ) ) ) ).
fof(conj_thm_2Elist_2ELUPDATE__LENGTH,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0xs] :
( mem(V0xs,ty_2Elist_2Elist(A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ! [V3ys] :
( mem(V3ys,ty_2Elist_2Elist(A_27a))
=> ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V1x),ap(c_2Elist_2ELENGTH(A_27a),V0xs)),ap(ap(c_2Elist_2EAPPEND(A_27a),V0xs),ap(ap(c_2Elist_2ECONS(A_27a),V2y),V3ys))) = ap(ap(c_2Elist_2EAPPEND(A_27a),V0xs),ap(ap(c_2Elist_2ECONS(A_27a),V1x),V3ys)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELUPDATE__SNOC,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0ys] :
( mem(V0ys,ty_2Elist_2Elist(A_27a))
=> ! [V1k] :
( mem(V1k,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V2x),V1k),ap(ap(c_2Elist_2ESNOC(A_27a),V3y),V0ys)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1k),ap(c_2Elist_2ELENGTH(A_27a),V0ys))),ap(ap(c_2Elist_2ESNOC(A_27a),V2x),V0ys)),ap(ap(c_2Elist_2ESNOC(A_27a),V3y),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V2x),V1k),V0ys))) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMEM__LUPDATE__E,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ! [V3i] :
( mem(V3i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V2y),V3i),V0l))))
=> ( V1x = V2y
| p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMEM__LUPDATE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ! [V3i] :
( mem(V3i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V2y),V3i),V0l))))
<=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V3i),ap(c_2Elist_2ELENGTH(A_27a),V0l)))
& V1x = V2y )
| ? [V4j] :
( mem(V4j,ty_2Enum_2Enum)
& p(ap(ap(c_2Eprim__rec_2E_3C,V4j),ap(c_2Elist_2ELENGTH(A_27a),V0l)))
& V3i != V4j
& ap(ap(c_2Elist_2EEL(A_27a),V4j),V0l) = V1x ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELUPDATE__compute,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0e] :
( mem(V0e,A_27a)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V0e),V1n),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a) ) )
& ! [V2e] :
( mem(V2e,A_27a)
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4l] :
( mem(V4l,ty_2Elist_2Elist(A_27a))
=> ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V2e),c_2Enum_2E0),ap(ap(c_2Elist_2ECONS(A_27a),V3x),V4l)) = ap(ap(c_2Elist_2ECONS(A_27a),V2e),V4l) ) ) )
& ! [V5e] :
( mem(V5e,A_27a)
=> ! [V6n] :
( mem(V6n,ty_2Enum_2Enum)
=> ! [V7x] :
( mem(V7x,A_27a)
=> ! [V8l] :
( mem(V8l,ty_2Elist_2Elist(A_27a))
=> ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V5e),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n))),ap(ap(c_2Elist_2ECONS(A_27a),V7x),V8l)) = ap(ap(c_2Elist_2ECONS(A_27a),V7x),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V5e),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V8l)) ) ) ) )
& ! [V9e] :
( mem(V9e,A_27a)
=> ! [V10n] :
( mem(V10n,ty_2Enum_2Enum)
=> ! [V11x] :
( mem(V11x,A_27a)
=> ! [V12l] :
( mem(V12l,ty_2Elist_2Elist(A_27a))
=> ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V9e),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V10n))),ap(ap(c_2Elist_2ECONS(A_27a),V11x),V12l)) = ap(ap(c_2Elist_2ECONS(A_27a),V11x),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V9e),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V10n))),V12l)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELUPDATE__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ! [V3f] :
( mem(V3f,arr(A_27a,A_27b))
=> ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V3f),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V0x),V1n),V2l)) = ap(ap(ap(c_2Elist_2ELUPDATE(A_27b),ap(V3f,V0x)),V1n),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V3f),V2l)) ) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EEVERYi__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,arr(A_27a,bool)))
=> ( p(ap(ap(c_2Elist_2EEVERYi(A_27a),V0P),c_2Elist_2ENIL(A_27a)))
<=> $true ) )
& ! [V1P] :
( mem(V1P,arr(ty_2Enum_2Enum,arr(A_27a,bool)))
=> ! [V2h] :
( mem(V2h,A_27a)
=> ! [V3t] :
( mem(V3t,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEVERYi(A_27a),V1P),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)))
<=> ( p(ap(ap(V1P,c_2Enum_2E0),V2h))
& p(ap(ap(c_2Elist_2EEVERYi(A_27a),ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,arr(A_27a,bool),ty_2Enum_2Enum),V1P),c_2Enum_2ESUC)),V3t)) ) ) ) ) ) ) ) ).
fof(lameq_f438,axiom,
! [A_27a,A_27b,V3k] :
( mem(V3k,arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27b),A_27a)))
=> ! [V4h] :
( mem(V4h,A_27b)
=> ! [V6p] :
( mem(V6p,ty_2Elist_2Elist(A_27b))
=> ! [V7s] : ap(f438(A_27a,A_27b,V3k,V4h,V6p),V7s) = ap(ap(V3k,ap(ap(c_2Elist_2ECONS(A_27b),V4h),V6p)),V7s) ) ) ) ).
fof(lameq_f439,axiom,
! [A_27a,A_27b,V3k] :
( mem(V3k,arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27b),A_27a)))
=> ! [V4h] :
( mem(V4h,A_27b)
=> ! [V6p] : ap(f439(A_27a,A_27b,V3k,V4h),V6p) = f438(A_27a,A_27b,V3k,V4h,V6p) ) ) ).
fof(ax_thm_2Elist_2EsplitAtPki__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,arr(A_27b,bool)))
=> ! [V1k] :
( mem(V1k,arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27b),A_27a)))
=> ap(ap(ap(c_2Elist_2EsplitAtPki(A_27a,A_27b),V0P),V1k),c_2Elist_2ENIL(A_27b)) = ap(ap(V1k,c_2Elist_2ENIL(A_27b)),c_2Elist_2ENIL(A_27b)) ) )
& ! [V2P] :
( mem(V2P,arr(ty_2Enum_2Enum,arr(A_27b,bool)))
=> ! [V3k] :
( mem(V3k,arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27b),A_27a)))
=> ! [V4h] :
( mem(V4h,A_27b)
=> ! [V5t] :
( mem(V5t,ty_2Elist_2Elist(A_27b))
=> ap(ap(ap(c_2Elist_2EsplitAtPki(A_27a,A_27b),V2P),V3k),ap(ap(c_2Elist_2ECONS(A_27b),V4h),V5t)) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(V2P,c_2Enum_2E0),V4h)),ap(ap(V3k,c_2Elist_2ENIL(A_27b)),ap(ap(c_2Elist_2ECONS(A_27b),V4h),V5t))),ap(ap(ap(c_2Elist_2EsplitAtPki(A_27a,A_27b),ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,arr(A_27b,bool),ty_2Enum_2Enum),V2P),c_2Enum_2ESUC)),f439(A_27a,A_27b,V3k,V4h)),V5t)) ) ) ) ) ) ) ) ).
fof(lameq_f440,axiom,
! [A_27a,V2P] :
( mem(V2P,arr(ty_2Enum_2Enum,arr(A_27a,bool)))
=> ! [V4i] : ap(f440(A_27a,V2P),V4i) = ap(ap(c_2Ecombin_2Eo(A_27a,bool,bool),c_2Ebool_2E_7E),ap(V2P,V4i)) ) ).
fof(conj_thm_2Elist_2EsplitAtPki__APPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ! [V2P] :
( mem(V2P,arr(ty_2Enum_2Enum,arr(A_27a,bool)))
=> ! [V3k] :
( mem(V3k,arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),A_27b)))
=> ( ( p(ap(ap(c_2Elist_2EEVERYi(A_27a),f440(A_27a,V2P)),V0l1))
& ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Elist_2ELENGTH(A_27a),V1l2)))
=> p(ap(ap(V2P,ap(c_2Elist_2ELENGTH(A_27a),V0l1)),ap(c_2Elist_2EHD(A_27a),V1l2))) ) )
=> ap(ap(ap(c_2Elist_2EsplitAtPki(A_27b,A_27a),V2P),V3k),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)) = ap(ap(V3k,V0l1),V1l2) ) ) ) ) ) ) ) ).
fof(lameq_f441,axiom,
! [A_27b,V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,arr(A_27b,bool)))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27b))
=> ! [V3i] : ap(f441(A_27b,V0P,V2l),V3i) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eprim__rec_2E_3C,V3i),ap(c_2Elist_2ELENGTH(A_27b),V2l))),ap(ap(V0P,V3i),ap(ap(c_2Elist_2EEL(A_27b),V3i),V2l))) ) ) ).
fof(lameq_f442,axiom,
! [A_27b,A_27a,V1k] :
( mem(V1k,arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27b),A_27a)))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27b))
=> ! [V4i] : ap(f442(A_27b,A_27a,V1k,V2l),V4i) = ap(ap(V1k,ap(ap(c_2Elist_2ETAKE(A_27b),V4i),V2l)),ap(ap(c_2Elist_2EDROP(A_27b),V4i),V2l)) ) ) ).
fof(conj_thm_2Elist_2EsplitAtPki__EQN,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Enum_2Enum,arr(A_27b,bool)))
=> ! [V1k] :
( mem(V1k,arr(ty_2Elist_2Elist(A_27b),arr(ty_2Elist_2Elist(A_27b),A_27a)))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27b))
=> ap(ap(ap(c_2Elist_2EsplitAtPki(A_27a,A_27b),V0P),V1k),V2l) = ap(ap(ap(c_2Eoption_2Eoption__CASE(ty_2Enum_2Enum,A_27a),ap(c_2Ewhile_2EOLEAST,f441(A_27b,V0P,V2l))),ap(ap(V1k,V2l),c_2Elist_2ENIL(A_27b))),f442(A_27b,A_27a,V1k,V2l)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ETAKE__LENGTH__TOO__LONG,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),V1n))
=> ap(ap(c_2Elist_2ETAKE(A_27a),V1n),V0l) = V0l ) ) ) ) ).
fof(conj_thm_2Elist_2EDROP__LENGTH__TOO__LONG,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),V0l)),V1n))
=> ap(ap(c_2Elist_2EDROP(A_27a),V1n),V0l) = c_2Elist_2ENIL(A_27a) ) ) ) ) ).
fof(conj_thm_2Elist_2ETAKE__splitAtPki,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2ETAKE(A_27a),V0n),V1l) = ap(ap(ap(c_2Elist_2EsplitAtPki(ty_2Elist_2Elist(A_27a),A_27a),ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,arr(A_27a,bool),bool),c_2Ecombin_2EK(bool,A_27a)),ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0n))),c_2Ecombin_2EK(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))),V1l) ) ) ) ).
fof(conj_thm_2Elist_2EDROP__splitAtPki,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EDROP(A_27a),V0n),V1l) = ap(ap(ap(c_2Elist_2EsplitAtPki(ty_2Elist_2Elist(A_27a),A_27a),ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,arr(A_27a,bool),bool),c_2Ecombin_2EK(bool,A_27a)),ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0n))),ap(c_2Ecombin_2EK(arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),ty_2Elist_2Elist(A_27a)),c_2Ecombin_2EI(ty_2Elist_2Elist(A_27a)))),V1l) ) ) ) ).
fof(ax_thm_2Elist_2ELIST__BIND__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27b))
=> ! [V1f] :
( mem(V1f,arr(A_27b,ty_2Elist_2Elist(A_27a)))
=> ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),V0l),V1f) = ap(c_2Elist_2EFLAT(A_27a),ap(ap(c_2Elist_2EMAP(A_27b,ty_2Elist_2Elist(A_27a)),V1f),V0l)) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__BIND__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27b,ty_2Elist_2Elist(A_27a)))
=> ! [V1h] :
( mem(V1h,A_27b)
=> ! [V2t] :
( mem(V2t,ty_2Elist_2Elist(A_27b))
=> ( ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),c_2Elist_2ENIL(A_27b)),V0f) = c_2Elist_2ENIL(A_27a)
& ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V1h),V2t)),V0f) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(V0f,V1h)),ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),V2t),V0f)) ) ) ) ) ) ) ).
fof(ax_thm_2Elist_2ELIST__IGNORE__BIND__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0m1] :
( mem(V0m1,ty_2Elist_2Elist(A_27b))
=> ! [V1m2] :
( mem(V1m2,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2ELIST__IGNORE__BIND(A_27a,A_27b),V0m1),V1m2) = ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),V0m1),ap(c_2Ecombin_2EK(ty_2Elist_2Elist(A_27a),A_27b),V1m2)) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__BIND__ID,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27a)))
=> ( ap(ap(c_2Elist_2ELIST__BIND(A_27a,ty_2Elist_2Elist(A_27a)),V0l),i(ty_2Elist_2Elist(A_27a))) = ap(c_2Elist_2EFLAT(A_27a),V0l)
& ap(ap(c_2Elist_2ELIST__BIND(A_27a,ty_2Elist_2Elist(A_27a)),V0l),c_2Ecombin_2EI(ty_2Elist_2Elist(A_27a))) = ap(c_2Elist_2EFLAT(A_27a),V0l) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__BIND__APPEND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27b))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27b))
=> ! [V2f] :
( mem(V2f,arr(A_27b,ty_2Elist_2Elist(A_27a)))
=> ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),ap(ap(c_2Elist_2EAPPEND(A_27b),V0l1),V1l2)),V2f) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),V0l1),V2f)),ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),V1l2),V2f)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__BIND__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27c,A_27b))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27c))
=> ! [V2g] :
( mem(V2g,arr(A_27b,ty_2Elist_2Elist(A_27a)))
=> ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),ap(ap(c_2Elist_2EMAP(A_27c,A_27b),V0f),V1l)),V2g) = ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27c),V1l),ap(ap(c_2Ecombin_2Eo(A_27c,ty_2Elist_2Elist(A_27a),A_27b),V2g),V0f)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP__LIST__BIND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27b,A_27a))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27c))
=> ! [V2g] :
( mem(V2g,arr(A_27c,ty_2Elist_2Elist(A_27b)))
=> ap(ap(c_2Elist_2EMAP(A_27b,A_27a),V0f),ap(ap(c_2Elist_2ELIST__BIND(A_27b,A_27c),V1l),V2g)) = ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27c),V1l),ap(ap(c_2Ecombin_2Eo(A_27c,ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(c_2Elist_2EMAP(A_27b,A_27a),V0f)),V2g)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__BIND__LIST__BIND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27c))
=> ! [V1g] :
( mem(V1g,arr(A_27c,ty_2Elist_2Elist(A_27b)))
=> ! [V2f] :
( mem(V2f,arr(A_27b,ty_2Elist_2Elist(A_27a)))
=> ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),ap(ap(c_2Elist_2ELIST__BIND(A_27b,A_27c),V0l),V1g)),V2f) = ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27c),V0l),ap(ap(c_2Ecombin_2Eo(A_27c,ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(ap(c_2Ecombin_2EC(ty_2Elist_2Elist(A_27b),arr(A_27b,ty_2Elist_2Elist(A_27a)),ty_2Elist_2Elist(A_27a)),c_2Elist_2ELIST__BIND(A_27a,A_27b)),V2f)),V1g)) ) ) ) ) ) ) ).
fof(ax_thm_2Elist_2ELIST__GUARD__def,axiom,
! [V0b] :
( mem(V0b,bool)
=> ap(c_2Elist_2ELIST__GUARD,V0b) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Eone_2Eone)),V0b),ap(ap(c_2Elist_2ECONS(ty_2Eone_2Eone),c_2Eone_2Eone),c_2Elist_2ENIL(ty_2Eone_2Eone))),c_2Elist_2ENIL(ty_2Eone_2Eone)) ) ).
fof(conj_thm_2Elist_2ESINGL__LIST__APPLY__L,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,A_27b)
=> ! [V1f] :
( mem(V1f,arr(A_27b,ty_2Elist_2Elist(A_27a)))
=> ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V0x),c_2Elist_2ENIL(A_27b))),V1f) = ap(V1f,V0x) ) ) ) ) ).
fof(lameq_f443,axiom,
! [A_27a,V1x] : ap(f443(A_27a),V1x) = ap(ap(c_2Elist_2ECONS(A_27a),V1x),c_2Elist_2ENIL(A_27a)) ).
fof(conj_thm_2Elist_2ESINGL__LIST__APPLY__R,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2ELIST__BIND(A_27a,A_27a),V0l),f443(A_27a)) = V0l ) ) ).
fof(ax_thm_2Elist_2ELIST__APPLY__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0fs] :
( mem(V0fs,ty_2Elist_2Elist(arr(A_27b,A_27a)))
=> ! [V1xs] :
( mem(V1xs,ty_2Elist_2Elist(A_27b))
=> ap(ap(c_2Elist_2ELIST__APPLY(A_27a,A_27b),V0fs),V1xs) = ap(ap(c_2Elist_2ELIST__BIND(A_27a,arr(A_27b,A_27a)),V0fs),ap(ap(c_2Ecombin_2EC(arr(A_27b,A_27a),ty_2Elist_2Elist(A_27b),ty_2Elist_2Elist(A_27a)),c_2Elist_2EMAP(A_27b,A_27a)),V1xs)) ) ) ) ) ).
fof(ax_thm_2Elist_2ELIST__LIFT2__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27b,arr(A_27c,A_27a)))
=> ! [V1xs] :
( mem(V1xs,ty_2Elist_2Elist(A_27b))
=> ! [V2ys] :
( mem(V2ys,ty_2Elist_2Elist(A_27c))
=> ap(ap(ap(c_2Elist_2ELIST__LIFT2(A_27a,A_27b,A_27c),V0f),V1xs),V2ys) = ap(ap(c_2Elist_2ELIST__APPLY(A_27a,A_27c),ap(ap(c_2Elist_2EMAP(A_27b,arr(A_27c,A_27a)),V0f),V1xs)),V2ys) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ESINGL__APPLY__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27b,A_27a))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27b))
=> ap(ap(c_2Elist_2ELIST__APPLY(A_27a,A_27b),ap(ap(c_2Elist_2ECONS(arr(A_27b,A_27a)),V0f),c_2Elist_2ENIL(arr(A_27b,A_27a)))),V1l) = ap(ap(c_2Elist_2EMAP(A_27b,A_27a),V0f),V1l) ) ) ) ) ).
fof(conj_thm_2Elist_2ESINGL__SINGL__APPLY,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27b,A_27a))
=> ! [V1x] :
( mem(V1x,A_27b)
=> ap(ap(c_2Elist_2ELIST__APPLY(A_27a,A_27b),ap(ap(c_2Elist_2ECONS(arr(A_27b,A_27a)),V0f),c_2Elist_2ENIL(arr(A_27b,A_27a)))),ap(ap(c_2Elist_2ECONS(A_27b),V1x),c_2Elist_2ENIL(A_27b))) = ap(ap(c_2Elist_2ECONS(A_27a),ap(V0f,V1x)),c_2Elist_2ENIL(A_27a)) ) ) ) ) ).
fof(lameq_f444,axiom,
! [A_27a,A_27b,V1x] :
( mem(V1x,A_27b)
=> ! [V2f] : ap(f444(A_27a,A_27b,V1x),V2f) = ap(V2f,V1x) ) ).
fof(conj_thm_2Elist_2ESINGL__APPLY__PERMUTE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0fs] :
( mem(V0fs,ty_2Elist_2Elist(arr(A_27b,A_27a)))
=> ! [V1x] :
( mem(V1x,A_27b)
=> ap(ap(c_2Elist_2ELIST__APPLY(A_27a,A_27b),V0fs),ap(ap(c_2Elist_2ECONS(A_27b),V1x),c_2Elist_2ENIL(A_27b))) = ap(ap(c_2Elist_2ELIST__APPLY(A_27a,arr(A_27b,A_27a)),ap(ap(c_2Elist_2ECONS(arr(arr(A_27b,A_27a),A_27a)),f444(A_27a,A_27b,V1x)),c_2Elist_2ENIL(arr(arr(A_27b,A_27a),A_27a)))),V0fs) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP__FLAT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27b,A_27a))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27b)))
=> ap(ap(c_2Elist_2EMAP(A_27b,A_27a),V0f),ap(c_2Elist_2EFLAT(A_27b),V1l)) = ap(c_2Elist_2EFLAT(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Elist_2Elist(A_27b),ty_2Elist_2Elist(A_27a)),ap(c_2Elist_2EMAP(A_27b,A_27a),V0f)),V1l)) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__APPLY__o,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0fs] :
( mem(V0fs,ty_2Elist_2Elist(arr(A_27c,A_27a)))
=> ! [V1gs] :
( mem(V1gs,ty_2Elist_2Elist(arr(A_27b,A_27c)))
=> ! [V2xs] :
( mem(V2xs,ty_2Elist_2Elist(A_27b))
=> ap(ap(c_2Elist_2ELIST__APPLY(A_27a,A_27b),ap(ap(c_2Elist_2ELIST__APPLY(arr(A_27b,A_27a),arr(A_27b,A_27c)),ap(ap(c_2Elist_2ELIST__APPLY(arr(arr(A_27b,A_27c),arr(A_27b,A_27a)),arr(A_27c,A_27a)),ap(ap(c_2Elist_2ECONS(arr(arr(A_27c,A_27a),arr(arr(A_27b,A_27c),arr(A_27b,A_27a)))),c_2Ecombin_2Eo(A_27b,A_27a,A_27c)),c_2Elist_2ENIL(arr(arr(A_27c,A_27a),arr(arr(A_27b,A_27c),arr(A_27b,A_27a)))))),V0fs)),V1gs)),V2xs) = ap(ap(c_2Elist_2ELIST__APPLY(A_27a,A_27c),V0fs),ap(ap(c_2Elist_2ELIST__APPLY(A_27c,A_27b),V1gs),V2xs)) ) ) ) ) ) ) ).
fof(lameq_f445,axiom,
! [A_27a,V6h2] :
( mem(V6h2,A_27a)
=> ! [V2R] :
( mem(V2R,arr(A_27a,arr(A_27a,bool)))
=> ! [V3h1] :
( mem(V3h1,A_27a)
=> ! [V4t1] :
( mem(V4t1,ty_2Elist_2Elist(A_27a))
=> ! [V7t2] : ap(f445(A_27a,V6h2,V2R,V3h1,V4t1),V7t2) = ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(A_27a),V4t1)),ap(c_2Elist_2ELENGTH(A_27a),V7t2))),c_2Ebool_2ET),ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Elist_2ELENGTH(A_27a),V4t1)),ap(c_2Elist_2ELENGTH(A_27a),V7t2))),ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(V2R,V3h1),V6h2)),c_2Ebool_2ET),ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(A_27a),V3h1),V6h2)),ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V2R),V4t1),V7t2)),c_2Ebool_2EF))),c_2Ebool_2EF)) ) ) ) ) ).
fof(lameq_f446,axiom,
! [A_27a,V2R] :
( mem(V2R,arr(A_27a,arr(A_27a,bool)))
=> ! [V3h1] :
( mem(V3h1,A_27a)
=> ! [V4t1] :
( mem(V4t1,ty_2Elist_2Elist(A_27a))
=> ! [V6h2] : ap(f446(A_27a,V2R,V3h1,V4t1),V6h2) = f445(A_27a,V6h2,V2R,V3h1,V4t1) ) ) ) ).
fof(ax_thm_2Elist_2ESHORTLEX__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),c_2Elist_2ENIL(A_27a)),V1l2))
<=> V1l2 != c_2Elist_2ENIL(A_27a) ) ) )
& ! [V2R] :
( mem(V2R,arr(A_27a,arr(A_27a,bool)))
=> ! [V3h1] :
( mem(V3h1,A_27a)
=> ! [V4t1] :
( mem(V4t1,ty_2Elist_2Elist(A_27a))
=> ! [V5l2] :
( mem(V5l2,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V2R),ap(ap(c_2Elist_2ECONS(A_27a),V3h1),V4t1)),V5l2))
<=> p(ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,bool),V5l2),c_2Ebool_2EF),f446(A_27a,V2R,V3h1,V4t1))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ESHORTLEX__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1h1] :
( mem(V1h1,A_27a)
=> ! [V2t1] :
( mem(V2t1,ty_2Elist_2Elist(A_27a))
=> ! [V3h2] :
( mem(V3h2,A_27a)
=> ! [V4t2] :
( mem(V4t2,ty_2Elist_2Elist(A_27a))
=> ( ~ p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27a)))
& ~ p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1h1),V2t1)),c_2Elist_2ENIL(A_27a)))
& p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),V3h2),V4t2)))
& ( p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1h1),V2t1)),ap(ap(c_2Elist_2ECONS(A_27a),V3h2),V4t2)))
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(A_27a),V2t1)),ap(c_2Elist_2ELENGTH(A_27a),V4t2)))
| ( ap(c_2Elist_2ELENGTH(A_27a),V2t1) = ap(c_2Elist_2ELENGTH(A_27a),V4t2)
& ( p(ap(ap(V0R,V1h1),V3h2))
| ( V1h1 = V3h2
& p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),V2t1),V4t2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ESHORTLEX__MONO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1R2] :
( mem(V1R2,arr(A_27a,arr(A_27a,bool)))
=> ! [V2x] :
( mem(V2x,ty_2Elist_2Elist(A_27a))
=> ! [V3y] :
( mem(V3y,ty_2Elist_2Elist(A_27a))
=> ( ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5y] :
( mem(V5y,A_27a)
=> ( p(ap(ap(V0R1,V4x),V5y))
=> p(ap(ap(V1R2,V4x),V5y)) ) ) )
=> ( p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R1),V2x),V3y))
=> p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V1R2),V2x),V3y)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ESHORTLEX__NIL2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ~ p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),V1l),c_2Elist_2ENIL(A_27a))) ) ) ) ).
fof(conj_thm_2Elist_2ESHORTLEX__transitive,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R))
=> p(ap(c_2Erelation_2Etransitive(ty_2Elist_2Elist(A_27a)),ap(c_2Elist_2ESHORTLEX(A_27a),V0R))) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__LT__SHORTLEX,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Elist_2ELENGTH(A_27a),V1l1)),ap(c_2Elist_2ELENGTH(A_27a),V2l2)))
=> p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),V1l1),V2l2)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ESHORTLEX__LENGTH__LE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),V1l1),V2l2))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),V1l1)),ap(c_2Elist_2ELENGTH(A_27a),V2l2))) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ESHORTLEX__total,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Erelation_2Etotal(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)))
=> p(ap(c_2Erelation_2Etotal(ty_2Elist_2Elist(A_27a)),ap(c_2Erelation_2ERC(ty_2Elist_2Elist(A_27a)),ap(c_2Elist_2ESHORTLEX(A_27a),V0R)))) ) ) ) ).
fof(conj_thm_2Elist_2EWF__SHORTLEX__same__lengths,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Erelation_2EWF(A_27a),V0R))
=> ! [V1l] :
( mem(V1l,ty_2Enum_2Enum)
=> ! [V2s] :
( mem(V2s,arr(ty_2Elist_2Elist(A_27a),bool))
=> ( ( ! [V3d] :
( mem(V3d,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Elist_2Elist(A_27a)),V3d),V2s))
=> ap(c_2Elist_2ELENGTH(A_27a),V3d) = V1l ) )
& ? [V4a] :
( mem(V4a,ty_2Elist_2Elist(A_27a))
& p(ap(ap(c_2Ebool_2EIN(ty_2Elist_2Elist(A_27a)),V4a),V2s)) ) )
=> ? [V5b] :
( mem(V5b,ty_2Elist_2Elist(A_27a))
& p(ap(ap(c_2Ebool_2EIN(ty_2Elist_2Elist(A_27a)),V5b),V2s))
& ! [V6c] :
( mem(V6c,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(ap(c_2Elist_2ESHORTLEX(A_27a),V0R),V6c),V5b))
=> ~ p(ap(ap(c_2Ebool_2EIN(ty_2Elist_2Elist(A_27a)),V6c),V2s)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EWF__SHORTLEX,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Erelation_2EWF(A_27a),V0R))
=> p(ap(c_2Erelation_2EWF(ty_2Elist_2Elist(A_27a)),ap(c_2Elist_2ESHORTLEX(A_27a),V0R))) ) ) ) ).
fof(lameq_f447,axiom,
! [A_27a,V4t1] :
( mem(V4t1,ty_2Elist_2Elist(A_27a))
=> ! [V3h1] :
( mem(V3h1,A_27a)
=> ! [V2R] :
( mem(V2R,arr(A_27a,arr(A_27a,bool)))
=> ! [V6h2] :
( mem(V6h2,A_27a)
=> ! [V7t2] : ap(f447(A_27a,V4t1,V3h1,V2R,V6h2),V7t2) = ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(V2R,V3h1),V6h2)),c_2Ebool_2ET),ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(A_27a),V3h1),V6h2)),ap(ap(ap(c_2Elist_2ELLEX(A_27a),V2R),V4t1),V7t2)),c_2Ebool_2EF)) ) ) ) ) ).
fof(lameq_f448,axiom,
! [A_27a,V4t1] :
( mem(V4t1,ty_2Elist_2Elist(A_27a))
=> ! [V3h1] :
( mem(V3h1,A_27a)
=> ! [V2R] :
( mem(V2R,arr(A_27a,arr(A_27a,bool)))
=> ! [V6h2] : ap(f448(A_27a,V4t1,V3h1,V2R),V6h2) = f447(A_27a,V4t1,V3h1,V2R,V6h2) ) ) ) ).
fof(ax_thm_2Elist_2ELLEX__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R),c_2Elist_2ENIL(A_27a)),V1l2))
<=> V1l2 != c_2Elist_2ENIL(A_27a) ) ) )
& ! [V2R] :
( mem(V2R,arr(A_27a,arr(A_27a,bool)))
=> ! [V3h1] :
( mem(V3h1,A_27a)
=> ! [V4t1] :
( mem(V4t1,ty_2Elist_2Elist(A_27a))
=> ! [V5l2] :
( mem(V5l2,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V2R),ap(ap(c_2Elist_2ECONS(A_27a),V3h1),V4t1)),V5l2))
<=> p(ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,bool),V5l2),c_2Ebool_2EF),f448(A_27a,V4t1,V3h1,V2R))) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELLEX__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1h1] :
( mem(V1h1,A_27a)
=> ! [V2t1] :
( mem(V2t1,ty_2Elist_2Elist(A_27a))
=> ! [V3h2] :
( mem(V3h2,A_27a)
=> ! [V4t2] :
( mem(V4t2,ty_2Elist_2Elist(A_27a))
=> ( ~ p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R),c_2Elist_2ENIL(A_27a)),c_2Elist_2ENIL(A_27a)))
& ~ p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1h1),V2t1)),c_2Elist_2ENIL(A_27a)))
& p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),V3h2),V4t2)))
& ( p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R),ap(ap(c_2Elist_2ECONS(A_27a),V1h1),V2t1)),ap(ap(c_2Elist_2ECONS(A_27a),V3h2),V4t2)))
<=> ( p(ap(ap(V0R,V1h1),V3h2))
| ( V1h1 = V3h2
& p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R),V2t1),V4t2)) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELLEX__MONO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27a,bool)))
=> ! [V1R2] :
( mem(V1R2,arr(A_27a,arr(A_27a,bool)))
=> ! [V2x] :
( mem(V2x,ty_2Elist_2Elist(A_27a))
=> ! [V3y] :
( mem(V3y,ty_2Elist_2Elist(A_27a))
=> ( ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5y] :
( mem(V5y,A_27a)
=> ( p(ap(ap(V0R1,V4x),V5y))
=> p(ap(ap(V1R2,V4x),V5y)) ) ) )
=> ( p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R1),V2x),V3y))
=> p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V1R2),V2x),V3y)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELLEX__CONG,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ! [V3R_27] :
( mem(V3R_27,arr(A_27a,arr(A_27a,bool)))
=> ! [V4l1_27] :
( mem(V4l1_27,ty_2Elist_2Elist(A_27a))
=> ! [V5l2_27] :
( mem(V5l2_27,ty_2Elist_2Elist(A_27a))
=> ( ( V1l1 = V4l1_27
& V2l2 = V5l2_27
& ! [V6a] :
( mem(V6a,A_27a)
=> ! [V7b] :
( mem(V7b,A_27a)
=> ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V6a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V4l1_27)))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V7b),ap(c_2Elist_2ELIST__TO__SET(A_27a),V5l2_27))) )
=> ( p(ap(ap(V0R,V6a),V7b))
<=> p(ap(ap(V3R_27,V6a),V7b)) ) ) ) ) )
=> ( p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R),V1l1),V2l2))
<=> p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V3R_27),V4l1_27),V5l2_27)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELLEX__NIL2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ~ p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R),V1l),c_2Elist_2ENIL(A_27a))) ) ) ) ).
fof(conj_thm_2Elist_2ELLEX__transitive,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Erelation_2Etransitive(A_27a),V0R))
=> p(ap(c_2Erelation_2Etransitive(ty_2Elist_2Elist(A_27a)),ap(c_2Elist_2ELLEX(A_27a),V0R))) ) ) ) ).
fof(conj_thm_2Elist_2ELLEX__total,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ( p(ap(c_2Erelation_2Etotal(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)))
=> p(ap(c_2Erelation_2Etotal(ty_2Elist_2Elist(A_27a)),ap(c_2Erelation_2ERC(ty_2Elist_2Elist(A_27a)),ap(c_2Elist_2ELLEX(A_27a),V0R)))) ) ) ) ).
fof(conj_thm_2Elist_2ELLEX__not__WF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ( ? [V1a] :
( mem(V1a,A_27a)
& ? [V2b] :
( mem(V2b,A_27a)
& p(ap(ap(V0R,V1a),V2b)) ) )
=> ~ p(ap(c_2Erelation_2EWF(ty_2Elist_2Elist(A_27a)),ap(c_2Elist_2ELLEX(A_27a),V0R))) ) ) ) ).
fof(conj_thm_2Elist_2ELLEX__EL__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(ap(c_2Elist_2ELLEX(A_27a),V0R),V1l1),V2l2))
<=> ? [V3n] :
( mem(V3n,ty_2Enum_2Enum)
& p(ap(ap(c_2Earithmetic_2E_3C_3D,V3n),ap(c_2Elist_2ELENGTH(A_27a),V1l1)))
& p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(c_2Elist_2ELENGTH(A_27a),V2l2)))
& ap(ap(c_2Elist_2ETAKE(A_27a),V3n),V1l1) = ap(ap(c_2Elist_2ETAKE(A_27a),V3n),V2l2)
& ( p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(c_2Elist_2ELENGTH(A_27a),V1l1)))
=> p(ap(ap(V0R,ap(ap(c_2Elist_2EEL(A_27a),V3n),V1l1)),ap(ap(c_2Elist_2EEL(A_27a),V3n),V2l2))) ) ) ) ) ) ) ) ).
fof(ax_thm_2Elist_2Enub__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ap(c_2Elist_2Enub(A_27a),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a)
& ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2Enub(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),V1l)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l))),ap(c_2Elist_2Enub(A_27a),V1l)),ap(ap(c_2Elist_2ECONS(A_27a),V0x),ap(c_2Elist_2Enub(A_27a),V1l))) ) ) ) ) ).
fof(conj_thm_2Elist_2Enub__set,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Elist_2Enub(A_27a),V0l)) = ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l) ) ) ).
fof(conj_thm_2Elist_2Eall__distinct__nub,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(c_2Elist_2Enub(A_27a),V0l))) ) ) ).
fof(lameq_f449,axiom,
! [A_27a,V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ! [V2x] : ap(f449(A_27a,V1l2),V2x) = ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2))) ) ).
fof(conj_thm_2Elist_2Enub__append,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2Enub(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(c_2Elist_2Enub(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),f449(A_27a,V1l2)),V0l1))),ap(c_2Elist_2Enub(A_27a),V1l2)) ) ) ) ).
fof(lameq_f450,axiom,
! [A_27a,V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V2x] : ap(f450(A_27a,V0l1),V2x) = ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l1))) ) ).
fof(conj_thm_2Elist_2Elist__to__set__diff,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l2)),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0l1)) = ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),f450(A_27a,V0l1)),V1l2)) ) ) ) ).
fof(conj_thm_2Elist_2Elength__nub__append,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Elist_2Enub(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2))) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Elist_2Enub(A_27a),V0l1))),ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Elist_2Enub(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),f450(A_27a,V0l1)),V1l2)))) ) ) ) ).
fof(conj_thm_2Elist_2EALL__DISTINCT__DROP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0ls] :
( mem(V0ls,ty_2Elist_2Elist(A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0ls))
=> p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2EDROP(A_27a),V1n),V0ls))) ) ) ) ) ).
fof(lameq_f451,axiom,
! [A_27a,A_27b,V1f] :
( mem(V1f,arr(A_27b,A_27a))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] : ap(f451(A_27a,A_27b,V1f,V2x),V3y) = ap(ap(c_2Emin_2E_3D(A_27a),V2x),ap(V1f,V3y)) ) ) ).
fof(lameq_f452,axiom,
! [A_27b,A_27a,V1f] :
( mem(V1f,arr(A_27b,A_27a))
=> ! [V2x] : ap(f452(A_27b,A_27a,V1f),V2x) = ap(c_2Ebool_2E_3F(A_27b),f451(A_27a,A_27b,V1f,V2x)) ) ).
fof(conj_thm_2Elist_2EEXISTS__LIST__EQ__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0ls] :
( mem(V0ls,ty_2Elist_2Elist(A_27a))
=> ! [V1f] :
( mem(V1f,arr(A_27b,A_27a))
=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),f452(A_27b,A_27a,V1f)),V0ls))
=> ? [V4l] :
( mem(V4l,ty_2Elist_2Elist(A_27b))
& V0ls = ap(ap(c_2Elist_2EMAP(A_27b,A_27a),V1f),V4l) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__TO__SET__FLAT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0ls] :
( mem(V0ls,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27a)))
=> ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Elist_2EFLAT(A_27a),V0ls)) = ap(c_2Epred__set_2EBIGUNION(A_27a),ap(c_2Elist_2ELIST__TO__SET(arr(A_27a,bool)),ap(ap(c_2Elist_2EMAP(ty_2Elist_2Elist(A_27a),arr(A_27a,bool)),c_2Elist_2ELIST__TO__SET(A_27a)),V0ls))) ) ) ).
fof(conj_thm_2Elist_2EMEM__APPEND__lemma,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a] :
( mem(V0a,ty_2Elist_2Elist(A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Elist_2Elist(A_27a))
=> ! [V2c] :
( mem(V2c,ty_2Elist_2Elist(A_27a))
=> ! [V3d] :
( mem(V3d,ty_2Elist_2Elist(A_27a))
=> ! [V4x] :
( mem(V4x,A_27a)
=> ( ( ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0a),ap(ap(c_2Elist_2ECONS(A_27a),V4x),c_2Elist_2ENIL(A_27a)))),V1b) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V2c),ap(ap(c_2Elist_2ECONS(A_27a),V4x),c_2Elist_2ENIL(A_27a)))),V3d)
& ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1b)))
& ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0a))) )
=> ( V0a = V2c
& V1b = V3d ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY2__REVERSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27b))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),V1l1),V2l2))
=> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R),ap(c_2Elist_2EREVERSE(A_27a),V1l1)),ap(c_2Elist_2EREVERSE(A_27b),V2l2))) ) ) ) ) ) ) ).
fof(lameq_f453,axiom,
! [A_27a,V0f] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V1g] :
( mem(V1g,arr(A_27a,ty_2Enum_2Enum))
=> ! [V3x] : ap(f453(A_27a,V0f,V1g),V3x) = ap(ap(c_2Earithmetic_2E_2B,ap(V0f,V3x)),ap(V1g,V3x)) ) ) ).
fof(conj_thm_2Elist_2ESUM__MAP__PLUS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V1g] :
( mem(V1g,arr(A_27a,ty_2Enum_2Enum))
=> ! [V2ls] :
( mem(V2ls,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(A_27a,ty_2Enum_2Enum),f453(A_27a,V0f,V1g)),V2ls)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(A_27a,ty_2Enum_2Enum),V0f),V2ls))),ap(c_2Elist_2ESUM,ap(ap(c_2Elist_2EMAP(A_27a,ty_2Enum_2Enum),V1g),V2ls))) ) ) ) ) ).
fof(conj_thm_2Elist_2ETAKE__LENGTH__ID__rwt,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ( V1m = ap(c_2Elist_2ELENGTH(A_27a),V0l)
=> ap(ap(c_2Elist_2ETAKE(A_27a),V1m),V0l) = V0l ) ) ) ) ).
fof(conj_thm_2Elist_2EZIP__DROP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0a] :
( mem(V0a,ty_2Elist_2Elist(A_27a))
=> ! [V1b] :
( mem(V1b,ty_2Elist_2Elist(A_27b))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V2n),ap(c_2Elist_2ELENGTH(A_27a),V0a)))
& ap(c_2Elist_2ELENGTH(A_27a),V0a) = ap(c_2Elist_2ELENGTH(A_27b),V1b) )
=> ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),ap(ap(c_2Elist_2EDROP(A_27a),V2n),V0a)),ap(ap(c_2Elist_2EDROP(A_27b),V2n),V1b))) = ap(ap(c_2Elist_2EDROP(ty_2Epair_2Eprod(A_27a,A_27b)),V2n),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0a),V1b))) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EGENLIST__EL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0ls] :
( mem(V0ls,ty_2Elist_2Elist(A_27a))
=> ! [V1f] :
( mem(V1f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ( ( V2n = ap(c_2Elist_2ELENGTH(A_27a),V0ls)
& ! [V3i] :
( mem(V3i,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V3i),V2n))
=> ap(V1f,V3i) = ap(ap(c_2Elist_2EEL(A_27a),V3i),V0ls) ) ) )
=> ap(ap(c_2Elist_2EGENLIST(A_27a),V1f),V2n) = V0ls ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY2__trans,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ( ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ! [V3z] :
( mem(V3z,A_27a)
=> ( ( p(ap(ap(V0R,V1x),V2y))
& p(ap(ap(V0R,V2y),V3z)) )
=> p(ap(ap(V0R,V1x),V3z)) ) ) ) )
=> ! [V4x] :
( mem(V4x,ty_2Elist_2Elist(A_27a))
=> ! [V5y] :
( mem(V5y,ty_2Elist_2Elist(A_27a))
=> ! [V6z] :
( mem(V6z,ty_2Elist_2Elist(A_27a))
=> ( ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27a),V0R),V4x),V5y))
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27a),V0R),V5y),V6z)) )
=> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27a),V0R),V4x),V6z)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY2__sym,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R1] :
( mem(V0R1,arr(A_27a,arr(A_27b,bool)))
=> ! [V1R2] :
( mem(V1R2,arr(A_27b,arr(A_27a,bool)))
=> ( ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27b)
=> ( p(ap(ap(V0R1,V2x),V3y))
=> p(ap(ap(V1R2,V3y),V2x)) ) ) )
=> ! [V4x] :
( mem(V4x,ty_2Elist_2Elist(A_27a))
=> ! [V5y] :
( mem(V5y,ty_2Elist_2Elist(A_27b))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0R1),V4x),V5y))
=> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27b,A_27a),V1R2),V5y),V4x)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY2__LUPDATE__same,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(A_27a,arr(A_27b,bool)))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27b))
=> ! [V3v1] :
( mem(V3v1,A_27a)
=> ! [V4v2] :
( mem(V4v2,A_27b)
=> ! [V5n] :
( mem(V5n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(V0P,V3v1),V4v2))
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0P),V1l1),V2l2)) )
=> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0P),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V3v1),V5n),V1l1)),ap(ap(ap(c_2Elist_2ELUPDATE(A_27b),V4v2),V5n),V2l2))) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY2__refl,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0ls] :
( mem(V0ls,ty_2Elist_2Elist(A_27a))
=> ! [V1R] :
( mem(V1R,arr(A_27a,arr(A_27a,bool)))
=> ( ! [V2x] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0ls)))
=> p(ap(ap(V1R,V2x),V2x)) ) )
=> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27a),V1R),V0ls),V0ls)) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY2__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [A_27e] :
( ne(A_27e)
=> ! [A_27f] :
( ne(A_27f)
=> ! [A_27g] :
( ne(A_27g)
=> ! [A_27h] :
( ne(A_27h)
=> ( ! [V0P] :
( mem(V0P,arr(A_27a,arr(A_27b,bool)))
=> ! [V1ys] :
( mem(V1ys,ty_2Elist_2Elist(A_27b))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0P),c_2Elist_2ENIL(A_27a)),V1ys))
<=> V1ys = c_2Elist_2ENIL(A_27b) ) ) )
& ! [V2P] :
( mem(V2P,arr(A_27c,arr(A_27d,bool)))
=> ! [V3yys] :
( mem(V3yys,ty_2Elist_2Elist(A_27d))
=> ! [V4x] :
( mem(V4x,A_27c)
=> ! [V5xs] :
( mem(V5xs,ty_2Elist_2Elist(A_27c))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27c,A_27d),V2P),ap(ap(c_2Elist_2ECONS(A_27c),V4x),V5xs)),V3yys))
<=> ? [V6y] :
( mem(V6y,A_27d)
& ? [V7ys] :
( mem(V7ys,ty_2Elist_2Elist(A_27d))
& V3yys = ap(ap(c_2Elist_2ECONS(A_27d),V6y),V7ys)
& p(ap(ap(V2P,V4x),V6y))
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27c,A_27d),V2P),V5xs),V7ys)) ) ) ) ) ) ) )
& ! [V8P] :
( mem(V8P,arr(A_27e,arr(A_27f,bool)))
=> ! [V9xs] :
( mem(V9xs,ty_2Elist_2Elist(A_27e))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27e,A_27f),V8P),V9xs),c_2Elist_2ENIL(A_27f)))
<=> V9xs = c_2Elist_2ENIL(A_27e) ) ) )
& ! [V10P] :
( mem(V10P,arr(A_27g,arr(A_27h,bool)))
=> ! [V11xxs] :
( mem(V11xxs,ty_2Elist_2Elist(A_27g))
=> ! [V12y] :
( mem(V12y,A_27h)
=> ! [V13ys] :
( mem(V13ys,ty_2Elist_2Elist(A_27h))
=> ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27g,A_27h),V10P),V11xxs),ap(ap(c_2Elist_2ECONS(A_27h),V12y),V13ys)))
<=> ? [V14x] :
( mem(V14x,A_27g)
& ? [V15xs] :
( mem(V15xs,ty_2Elist_2Elist(A_27g))
& V11xxs = ap(ap(c_2Elist_2ECONS(A_27g),V14x),V15xs)
& p(ap(ap(V10P,V14x),V12y))
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27g,A_27h),V10P),V15xs),V13ys)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__REL__trans,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ! [V3l3] :
( mem(V3l3,ty_2Elist_2Elist(A_27a))
=> ( ( ! [V4n] :
( mem(V4n,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V4n),ap(c_2Elist_2ELENGTH(A_27a),V1l1)))
& p(ap(ap(V0R,ap(ap(c_2Elist_2EEL(A_27a),V4n),V1l1)),ap(ap(c_2Elist_2EEL(A_27a),V4n),V2l2)))
& p(ap(ap(V0R,ap(ap(c_2Elist_2EEL(A_27a),V4n),V2l2)),ap(ap(c_2Elist_2EEL(A_27a),V4n),V3l3))) )
=> p(ap(ap(V0R,ap(ap(c_2Elist_2EEL(A_27a),V4n),V1l1)),ap(ap(c_2Elist_2EEL(A_27a),V4n),V3l3))) ) )
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27a),V0R),V1l1),V2l2))
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27a),V0R),V2l2),V3l3)) )
=> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27a),V0R),V1l1),V3l3)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ESWAP__REVERSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ( V0l1 = ap(c_2Elist_2EREVERSE(A_27a),V1l2)
<=> V1l2 = ap(c_2Elist_2EREVERSE(A_27a),V0l1) ) ) ) ) ).
fof(conj_thm_2Elist_2ESWAP__REVERSE__SYM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27a))
=> ( ap(c_2Elist_2EREVERSE(A_27a),V0l1) = V1l2
<=> V0l1 = ap(c_2Elist_2EREVERSE(A_27a),V1l2) ) ) ) ) ).
fof(conj_thm_2Elist_2EBIGUNION__IMAGE__set__SUBSET,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27b,arr(A_27a,bool)))
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27b))
=> ! [V2s] :
( mem(V2s,arr(A_27a,bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Epred__set_2EBIGUNION(A_27a),ap(ap(c_2Epred__set_2EIMAGE(A_27b,arr(A_27a,bool)),V0f),ap(c_2Elist_2ELIST__TO__SET(A_27b),V1ls)))),V2s))
<=> ! [V3x] :
( mem(V3x,A_27b)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27b),V3x),ap(c_2Elist_2ELIST__TO__SET(A_27b),V1ls)))
=> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(V0f,V3x)),V2s)) ) ) ) ) ) ) ) ) ).
fof(lameq_f454,axiom,
! [A_27a,A_27b,V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V2n] : ap(f454(A_27a,A_27b,V1ls,V0f),V2n) = ap(V0f,ap(ap(c_2Elist_2EEL(A_27a),V2n),V1ls)) ) ) ).
fof(conj_thm_2Elist_2EIMAGE__EL__count__LENGTH,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,A_27b),f454(A_27a,A_27b,V1ls,V0f)),ap(c_2Epred__set_2Ecount,ap(c_2Elist_2ELENGTH(A_27a),V1ls))) = ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V0f),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1ls)) ) ) ) ) ).
fof(conj_thm_2Elist_2EGENLIST__EL__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EGENLIST(A_27b),f454(A_27a,A_27b,V1ls,V0f)),ap(c_2Elist_2ELENGTH(A_27a),V1ls)) = ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1ls) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__FILTER__LEQ__MONO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q] :
( mem(V1Q,arr(A_27a,bool))
=> ( ! [V2x] :
( mem(V2x,A_27a)
=> ( p(ap(V0P,V2x))
=> p(ap(V1Q,V2x)) ) )
=> ! [V3ls] :
( mem(V3ls,ty_2Elist_2Elist(A_27a))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V3ls))),ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V1Q),V3ls)))) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__EQ__MAP__PAIR,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ( ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0l1) = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V1l2)
& ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND(A_27a,A_27b)),V0l1) = ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND(A_27a,A_27b)),V1l2) )
=> V0l1 = V1l2 ) ) ) ) ) ).
fof(conj_thm_2Elist_2ETAKE__SUM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2ETAKE(A_27a),ap(ap(c_2Earithmetic_2E_2B,V0n),V1m)),V2l) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2ETAKE(A_27a),V0n),V2l)),ap(ap(c_2Elist_2ETAKE(A_27a),V1m),ap(ap(c_2Elist_2EDROP(A_27a),V0n),V2l))) ) ) ) ) ).
fof(conj_thm_2Elist_2EALL__DISTINCT__FILTER__EL__IMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(A_27a))
=> ! [V2n1] :
( mem(V2n1,ty_2Enum_2Enum)
=> ! [V3n2] :
( mem(V3n2,ty_2Enum_2Enum)
=> ( ( p(ap(c_2Elist_2EALL__DISTINCT(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),V0P),V1l)))
& p(ap(ap(c_2Eprim__rec_2E_3C,V2n1),ap(c_2Elist_2ELENGTH(A_27a),V1l)))
& p(ap(ap(c_2Eprim__rec_2E_3C,V3n2),ap(c_2Elist_2ELENGTH(A_27a),V1l)))
& p(ap(V0P,ap(ap(c_2Elist_2EEL(A_27a),V2n1),V1l)))
& ap(ap(c_2Elist_2EEL(A_27a),V2n1),V1l) = ap(ap(c_2Elist_2EEL(A_27a),V3n2),V1l) )
=> V2n1 = V3n2 ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EFLAT__EQ__NIL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0ls] :
( mem(V0ls,ty_2Elist_2Elist(ty_2Elist_2Elist(A_27a)))
=> ( ap(c_2Elist_2EFLAT(A_27a),V0ls) = c_2Elist_2ENIL(A_27a)
<=> p(ap(ap(c_2Elist_2EEVERY(ty_2Elist_2Elist(A_27a)),ap(c_2Emin_2E_3D(ty_2Elist_2Elist(A_27a)),c_2Elist_2ENIL(A_27a))),V0ls)) ) ) ) ).
fof(conj_thm_2Elist_2EALL__DISTINCT__MAP__INJ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0ls] :
( mem(V0ls,ty_2Elist_2Elist(A_27a))
=> ! [V1f] :
( mem(V1f,arr(A_27a,A_27b))
=> ( ( ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27a)
=> ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0ls)))
& p(ap(ap(c_2Ebool_2EIN(A_27a),V3y),ap(c_2Elist_2ELIST__TO__SET(A_27a),V0ls)))
& ap(V1f,V2x) = ap(V1f,V3y) )
=> V2x = V3y ) ) )
& p(ap(c_2Elist_2EALL__DISTINCT(A_27a),V0ls)) )
=> p(ap(c_2Elist_2EALL__DISTINCT(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V0ls))) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__o__REVERSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27b,ty_2Elist_2Elist(A_27c)))
=> ( ap(ap(c_2Ecombin_2Eo(ty_2Elist_2Elist(A_27a),ty_2Enum_2Enum,ty_2Elist_2Elist(A_27a)),c_2Elist_2ELENGTH(A_27a)),c_2Elist_2EREVERSE(A_27a)) = c_2Elist_2ELENGTH(A_27a)
& ap(ap(c_2Ecombin_2Eo(A_27b,ty_2Enum_2Enum,ty_2Elist_2Elist(A_27c)),c_2Elist_2ELENGTH(A_27c)),ap(ap(c_2Ecombin_2Eo(A_27b,ty_2Elist_2Elist(A_27c),ty_2Elist_2Elist(A_27c)),c_2Elist_2EREVERSE(A_27c)),V0f)) = ap(ap(c_2Ecombin_2Eo(A_27b,ty_2Enum_2Enum,ty_2Elist_2Elist(A_27c)),c_2Elist_2ELENGTH(A_27c)),V0f) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EREVERSE__o__REVERSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Elist_2Elist(A_27b)))
=> ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Elist_2Elist(A_27b),ty_2Elist_2Elist(A_27b)),c_2Elist_2EREVERSE(A_27b)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Elist_2Elist(A_27b),ty_2Elist_2Elist(A_27b)),c_2Elist_2EREVERSE(A_27b)),V0f)) = V0f ) ) ) ).
fof(conj_thm_2Elist_2EGENLIST__PLUS__APPEND,axiom,
! [V0a] :
( mem(V0a,ty_2Enum_2Enum)
=> ! [V1n1] :
( mem(V1n1,ty_2Enum_2Enum)
=> ! [V2n2] :
( mem(V2n2,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2EAPPEND(ty_2Enum_2Enum),ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),ap(c_2Earithmetic_2E_2B,V0a)),V1n1)),ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,V1n1),V0a))),V2n2)) = ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),ap(c_2Earithmetic_2E_2B,V0a)),ap(ap(c_2Earithmetic_2E_2B,V1n1),V2n2)) ) ) ) ).
fof(conj_thm_2Elist_2ELIST__TO__SET__GENLIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f] :
( mem(V0f,arr(ty_2Enum_2Enum,A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EGENLIST(A_27a),V0f),V1n)) = ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,A_27a),V0f),ap(c_2Epred__set_2Ecount,V1n)) ) ) ) ).
fof(conj_thm_2Elist_2EMEM__ZIP__MEM__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0ps] :
( mem(V0ps,ty_2Epair_2Eprod(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)))
=> ! [V1p] :
( mem(V1p,ty_2Epair_2Eprod(A_27a,A_27b))
=> ( ( ap(c_2Elist_2ELENGTH(A_27a),ap(c_2Epair_2EFST(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0ps)) = ap(c_2Elist_2ELENGTH(A_27b),ap(c_2Epair_2ESND(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0ps))
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),V1p),ap(c_2Elist_2ELIST__TO__SET(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Elist_2EZIP(A_27a,A_27b),V0ps)))) )
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),ap(c_2Epair_2EFST(A_27a,A_27b),V1p)),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(c_2Epair_2EFST(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0ps))))
& p(ap(ap(c_2Ebool_2EIN(A_27b),ap(c_2Epair_2ESND(A_27a,A_27b),V1p)),ap(c_2Elist_2ELIST__TO__SET(A_27b),ap(c_2Epair_2ESND(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0ps)))) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EDISJOINT__GENLIST__PLUS,axiom,
! [V0x] :
( mem(V0x,arr(ty_2Enum_2Enum,bool))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2a] :
( mem(V2a,ty_2Enum_2Enum)
=> ! [V3b] :
( mem(V3b,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Epred__set_2EDISJOINT(ty_2Enum_2Enum),V0x),ap(c_2Elist_2ELIST__TO__SET(ty_2Enum_2Enum),ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),ap(c_2Earithmetic_2E_2B,V1n)),ap(ap(c_2Earithmetic_2E_2B,V2a),V3b)))))
=> ( p(ap(ap(c_2Epred__set_2EDISJOINT(ty_2Enum_2Enum),V0x),ap(c_2Elist_2ELIST__TO__SET(ty_2Enum_2Enum),ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),ap(c_2Earithmetic_2E_2B,V1n)),V2a))))
& p(ap(ap(c_2Epred__set_2EDISJOINT(ty_2Enum_2Enum),V0x),ap(c_2Elist_2ELIST__TO__SET(ty_2Enum_2Enum),ap(ap(c_2Elist_2EGENLIST(ty_2Enum_2Enum),ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,V1n),V2a))),V3b)))) ) ) ) ) ) ) ).
fof(lameq_f455,axiom,
! [A_27a,A_27c,A_27b,V0P] :
( mem(V0P,arr(A_27a,arr(A_27b,bool)))
=> ! [V1f] :
( mem(V1f,arr(A_27c,A_27a))
=> ! [V6x] :
( mem(V6x,A_27c)
=> ! [V7y] : ap(f455(A_27a,A_27c,A_27b,V0P,V1f,V6x),V7y) = ap(ap(V0P,ap(V1f,V6x)),V7y) ) ) ) ).
fof(lameq_f456,axiom,
! [A_27b,A_27a,A_27c,V0P] :
( mem(V0P,arr(A_27a,arr(A_27b,bool)))
=> ! [V1f] :
( mem(V1f,arr(A_27c,A_27a))
=> ! [V6x] : ap(f456(A_27b,A_27a,A_27c,V0P,V1f),V6x) = f455(A_27a,A_27c,A_27b,V0P,V1f,V6x) ) ) ).
fof(lameq_f457,axiom,
! [A_27d,A_27c,A_27b,V8x] :
( mem(V8x,A_27c)
=> ! [V4Q] :
( mem(V4Q,arr(A_27c,arr(A_27d,bool)))
=> ! [V5g] :
( mem(V5g,arr(A_27b,A_27d))
=> ! [V9y] : ap(f457(A_27d,A_27c,A_27b,V8x,V4Q,V5g),V9y) = ap(ap(V4Q,V8x),ap(V5g,V9y)) ) ) ) ).
fof(lameq_f458,axiom,
! [A_27b,A_27d,A_27c,V4Q] :
( mem(V4Q,arr(A_27c,arr(A_27d,bool)))
=> ! [V5g] :
( mem(V5g,arr(A_27b,A_27d))
=> ! [V8x] : ap(f458(A_27b,A_27d,A_27c,V4Q,V5g),V8x) = f457(A_27d,A_27c,A_27b,V8x,V4Q,V5g) ) ) ).
fof(conj_thm_2Elist_2EEVERY2__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [A_27d] :
( ne(A_27d)
=> ! [V0P] :
( mem(V0P,arr(A_27a,arr(A_27b,bool)))
=> ! [V1f] :
( mem(V1f,arr(A_27c,A_27a))
=> ! [V2l1] :
( mem(V2l1,ty_2Elist_2Elist(A_27c))
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(A_27b))
=> ! [V4Q] :
( mem(V4Q,arr(A_27c,arr(A_27d,bool)))
=> ! [V5g] :
( mem(V5g,arr(A_27b,A_27d))
=> ( ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0P),ap(ap(c_2Elist_2EMAP(A_27c,A_27a),V1f),V2l1)),V3l2))
<=> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27c,A_27b),f456(A_27b,A_27a,A_27c,V0P,V1f)),V2l1),V3l2)) )
& ( p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27c,A_27d),V4Q),V2l1),ap(ap(c_2Elist_2EMAP(A_27b,A_27d),V5g),V3l2)))
<=> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27c,A_27b),f458(A_27b,A_27d,A_27c,V4Q,V5g)),V2l1),V3l2)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2Eexists__list__GENLIST,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool))
=> ( ? [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
& p(ap(V0P,V1ls)) )
<=> ? [V2n] :
( mem(V2n,ty_2Enum_2Enum)
& ? [V3f] :
( mem(V3f,arr(ty_2Enum_2Enum,A_27a))
& p(ap(V0P,ap(ap(c_2Elist_2EGENLIST(A_27a),V3f),V2n))) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY__MEM__MONO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1Q] :
( mem(V1Q,arr(A_27a,bool))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(A_27a))
=> ( ( ! [V3x] :
( mem(V3x,A_27a)
=> ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2l)))
& p(ap(V0P,V3x)) )
=> p(ap(V1Q,V3x)) ) )
& p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V2l)) )
=> p(ap(ap(c_2Elist_2EEVERY(A_27a),V1Q),V2l)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEVERY2__MEM__MONO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(A_27a,arr(A_27b,bool)))
=> ! [V1Q] :
( mem(V1Q,arr(A_27a,arr(A_27b,bool)))
=> ! [V2l1] :
( mem(V2l1,ty_2Elist_2Elist(A_27a))
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(A_27b))
=> ( ( ! [V4x] :
( mem(V4x,ty_2Epair_2Eprod(A_27a,A_27b))
=> ( ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),V4x),ap(c_2Elist_2ELIST__TO__SET(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V2l1),V3l2)))))
& p(ap(ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),V0P),V4x)) )
=> p(ap(ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),V1Q),V4x)) ) )
& p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V0P),V2l1),V3l2)) )
=> p(ap(ap(ap(c_2Elist_2ELIST__REL(A_27a,A_27b),V1Q),V2l1),V3l2)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2Emem__exists__set,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,A_27b)
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)),ap(c_2Elist_2ELIST__TO__SET(ty_2Epair_2Eprod(A_27a,A_27b)),V2l)))
=> ? [V3z] :
( mem(V3z,ty_2Epair_2Eprod(A_27a,A_27b))
& V0x = ap(c_2Epair_2EFST(A_27a,A_27b),V3z)
& p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),V3z),ap(c_2Elist_2ELIST__TO__SET(ty_2Epair_2Eprod(A_27a,A_27b)),V2l))) ) ) ) ) ) ) ) ).
fof(lameq_f459,axiom,
! [A_27a,A_27b,V2P] :
( mem(V2P,arr(A_27b,bool))
=> ! [V3x] : ap(f459(A_27a,A_27b,V2P),V3x) = ap(V2P,ap(c_2Epair_2ESND(A_27a,A_27b),V3x)) ) ).
fof(conj_thm_2Elist_2Eevery__zip__snd,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27b))
=> ! [V2P] :
( mem(V2P,arr(A_27b,bool))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2)
=> ( p(ap(ap(c_2Elist_2EEVERY(ty_2Epair_2Eprod(A_27a,A_27b)),f459(A_27a,A_27b,V2P)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))))
<=> p(ap(ap(c_2Elist_2EEVERY(A_27b),V2P),V1l2)) ) ) ) ) ) ) ) ).
fof(lameq_f460,axiom,
! [A_27b,A_27a,V2P] :
( mem(V2P,arr(A_27a,bool))
=> ! [V3x] : ap(f460(A_27b,A_27a,V2P),V3x) = ap(V2P,ap(c_2Epair_2EFST(A_27a,A_27b),V3x)) ) ).
fof(conj_thm_2Elist_2Eevery__zip__fst,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27b))
=> ! [V2P] :
( mem(V2P,arr(A_27a,bool))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2)
=> ( p(ap(ap(c_2Elist_2EEVERY(ty_2Epair_2Eprod(A_27a,A_27b)),f460(A_27b,A_27a,V2P)),ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2))))
<=> p(ap(ap(c_2Elist_2EEVERY(A_27a),V2P),V0l1)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2Eel__append3,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Elist_2ELENGTH(A_27a),V0l1)),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),ap(ap(c_2Elist_2ECONS(A_27a),V1x),c_2Elist_2ENIL(A_27a)))),V2l2)) = V1x ) ) ) ) ).
fof(conj_thm_2Elist_2Elupdate__append,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2l1] :
( mem(V2l1,ty_2Elist_2Elist(A_27a))
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Elist_2ELENGTH(A_27a),V2l1)))
=> ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V0x),V1n),ap(ap(c_2Elist_2EAPPEND(A_27a),V2l1),V3l2)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V0x),V1n),V2l1)),V3l2) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2Elupdate__append2,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0v] :
( mem(V0v,A_27a)
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3l2] :
( mem(V3l2,ty_2Elist_2Elist(A_27a))
=> ! [V4l3] :
( mem(V4l3,A_27b)
=> ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V0v),ap(c_2Elist_2ELENGTH(A_27a),V1l1)),ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),ap(ap(c_2Elist_2ECONS(A_27a),V2x),c_2Elist_2ENIL(A_27a)))),V3l2)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),ap(ap(c_2Elist_2ECONS(A_27a),V0v),c_2Elist_2ENIL(A_27a)))),V3l2) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EHD__REVERSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,ty_2Elist_2Elist(A_27a))
=> ( V0x != c_2Elist_2ENIL(A_27a)
=> ap(c_2Elist_2EHD(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V0x)) = ap(c_2Elist_2ELAST(A_27a),V0x) ) ) ) ).
fof(conj_thm_2Elist_2ELAST__REVERSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0ls] :
( mem(V0ls,ty_2Elist_2Elist(A_27a))
=> ( V0ls != c_2Elist_2ENIL(A_27a)
=> ap(c_2Elist_2ELAST(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V0ls)) = ap(c_2Elist_2EHD(A_27a),V0ls) ) ) ) ).
fof(conj_thm_2Elist_2ENOT__NIL__EQ__LENGTH__NOT__0,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,ty_2Elist_2Elist(A_27a))
=> ( V0x != c_2Elist_2ENIL(A_27a)
<=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Elist_2ELENGTH(A_27a),V0x))) ) ) ) ).
fof(conj_thm_2Elist_2Elast__drop,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Elist_2ELENGTH(A_27a),V0l)))
=> ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2EDROP(A_27a),V1n),V0l)) = ap(c_2Elist_2ELAST(A_27a),V0l) ) ) ) ) ).
fof(ax_thm_2Elist_2EdropWhile__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a) )
& ! [V1P] :
( mem(V1P,arr(A_27a,bool))
=> ! [V2h] :
( mem(V2h,A_27a)
=> ! [V3t] :
( mem(V3t,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EdropWhile(A_27a),V1P),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(V1P,V2h)),ap(ap(c_2Elist_2EdropWhile(A_27a),V1P),V3t)),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EdropWhile__splitAtPki,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ap(c_2Elist_2EdropWhile(A_27a),V0P) = ap(ap(c_2Elist_2EsplitAtPki(ty_2Elist_2Elist(A_27a),A_27a),ap(c_2Ecombin_2EC(A_27a,ty_2Enum_2Enum,bool),ap(ap(c_2Ecombin_2Eo(A_27a,arr(ty_2Enum_2Enum,bool),bool),c_2Ecombin_2EK(bool,ty_2Enum_2Enum)),ap(ap(c_2Ecombin_2Eo(A_27a,bool,bool),c_2Ebool_2E_7E),V0P)))),ap(c_2Ecombin_2EK(arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),ty_2Elist_2Elist(A_27a)),c_2Ecombin_2EI(ty_2Elist_2Elist(A_27a)))) ) ) ).
fof(conj_thm_2Elist_2EdropWhile__eq__nil,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
=> ( ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),V1ls) = c_2Elist_2ENIL(A_27a)
<=> p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V1ls)) ) ) ) ) ).
fof(conj_thm_2Elist_2EMEM__dropWhile__IMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),V1ls))))
=> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1ls))) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EHD__dropWhile,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEXISTS(A_27a),ap(ap(c_2Ecombin_2Eo(A_27a,bool,bool),c_2Ebool_2E_7E),V0P)),V1ls))
=> ~ p(ap(V0P,ap(c_2Elist_2EHD(A_27a),ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),V1ls)))) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__dropWhile__LESS__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),V1ls))),ap(c_2Elist_2ELENGTH(A_27a),V1ls))) ) ) ) ).
fof(conj_thm_2Elist_2EdropWhile__APPEND__EVERY,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V1l1))
=> ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),V2l2)) = ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),V2l2) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EdropWhile__APPEND__EXISTS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1l1] :
( mem(V1l1,ty_2Elist_2Elist(A_27a))
=> ! [V2l2] :
( mem(V2l2,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EEXISTS(A_27a),ap(ap(c_2Ecombin_2Eo(A_27a,bool,bool),c_2Ebool_2E_7E),V0P)),V1l1))
=> ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),V2l2)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),V1l1)),V2l2) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EEL__LENGTH__dropWhile__REVERSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
=> ! [V2k] :
( mem(V2k,ty_2Enum_2Enum)
=> ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EdropWhile(A_27a),V0P),ap(c_2Elist_2EREVERSE(A_27a),V1ls)))),V2k))
& p(ap(ap(c_2Eprim__rec_2E_3C,V2k),ap(c_2Elist_2ELENGTH(A_27a),V1ls))) )
=> p(ap(V0P,ap(ap(c_2Elist_2EEL(A_27a),V2k),V1ls))) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELENGTH__TAKE__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1xs] :
( mem(V1xs,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2ETAKE(A_27a),V0n),V1xs)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,V0n),ap(c_2Elist_2ELENGTH(A_27a),V1xs))),V0n),ap(c_2Elist_2ELENGTH(A_27a),V1xs)) ) ) ) ).
fof(conj_thm_2Elist_2EIMP__EVERY__LUPDATE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1xs] :
( mem(V1xs,ty_2Elist_2Elist(A_27a))
=> ! [V2h] :
( mem(V2h,A_27a)
=> ! [V3i] :
( mem(V3i,ty_2Enum_2Enum)
=> ( ( p(ap(V0P,V2h))
& p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V1xs)) )
=> p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V2h),V3i),V1xs))) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EMAP__APPEND__MAP__EQ,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f1] :
( mem(V0f1,arr(A_27a,A_27c))
=> ! [V1g1] :
( mem(V1g1,arr(A_27b,A_27c))
=> ! [V2f2] :
( mem(V2f2,arr(A_27a,A_27c))
=> ! [V3g2] :
( mem(V3g2,arr(A_27b,A_27c))
=> ! [V4xs] :
( mem(V4xs,ty_2Elist_2Elist(A_27a))
=> ! [V5ys] :
( mem(V5ys,ty_2Elist_2Elist(A_27b))
=> ( ap(ap(c_2Elist_2EAPPEND(A_27c),ap(ap(c_2Elist_2EMAP(A_27a,A_27c),V0f1),V4xs)),ap(ap(c_2Elist_2EMAP(A_27b,A_27c),V1g1),V5ys)) = ap(ap(c_2Elist_2EAPPEND(A_27c),ap(ap(c_2Elist_2EMAP(A_27a,A_27c),V2f2),V4xs)),ap(ap(c_2Elist_2EMAP(A_27b,A_27c),V3g2),V5ys))
<=> ( ap(ap(c_2Elist_2EMAP(A_27a,A_27c),V0f1),V4xs) = ap(ap(c_2Elist_2EMAP(A_27a,A_27c),V2f2),V4xs)
& ap(ap(c_2Elist_2EMAP(A_27b,A_27c),V1g1),V5ys) = ap(ap(c_2Elist_2EMAP(A_27b,A_27c),V3g2),V5ys) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELUPDATE__SOME__MAP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0xs] :
( mem(V0xs,ty_2Elist_2Elist(ty_2Eoption_2Eoption(A_27a)))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2f] :
( mem(V2f,arr(A_27a,A_27b))
=> ! [V3h] :
( mem(V3h,A_27a)
=> ap(ap(ap(c_2Elist_2ELUPDATE(ty_2Eoption_2Eoption(A_27b)),ap(c_2Eoption_2ESOME(A_27b),ap(V2f,V3h))),V1n),ap(ap(c_2Elist_2EMAP(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27b)),ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V2f)),V0xs)) = ap(ap(c_2Elist_2EMAP(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27b)),ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V2f)),ap(ap(ap(c_2Elist_2ELUPDATE(ty_2Eoption_2Eoption(A_27a)),ap(c_2Eoption_2ESOME(A_27a),V3h)),V1n),V0xs)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EZIP__EQ__NIL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(A_27a))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(A_27b))
=> ( ap(c_2Elist_2ELENGTH(A_27a),V0l1) = ap(c_2Elist_2ELENGTH(A_27b),V1l2)
=> ( ap(c_2Elist_2EZIP(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)),V0l1),V1l2)) = c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))
<=> ( V0l1 = c_2Elist_2ENIL(A_27a)
& V1l2 = c_2Elist_2ENIL(A_27b) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELUPDATE__SAME,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1ls] :
( mem(V1ls,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Elist_2ELENGTH(A_27a),V1ls)))
=> ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),ap(ap(c_2Elist_2EEL(A_27a),V0n),V1ls)),V0n),V1ls) = V1ls ) ) ) ) ).
fof(ax_thm_2Elist_2EUNIQUE__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0e] :
( mem(V0e,A_27a)
=> ! [V1L] :
( mem(V1L,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EUNIQUE(A_27a),V0e),V1L))
<=> ? [V2L1] :
( mem(V2L1,ty_2Elist_2Elist(A_27a))
& ? [V3L2] :
( mem(V3L2,ty_2Elist_2Elist(A_27a))
& ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V2L1),ap(ap(c_2Elist_2ECONS(A_27a),V0e),c_2Elist_2ENIL(A_27a)))),V3L2) = V1L
& ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2L1)))
& ~ p(ap(ap(c_2Ebool_2EIN(A_27a),V0e),ap(c_2Elist_2ELIST__TO__SET(A_27a),V3L2))) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EUNIQUE__FILTER,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0e] :
( mem(V0e,A_27a)
=> ! [V1L] :
( mem(V1L,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EUNIQUE(A_27a),V0e),V1L))
<=> ap(ap(c_2Elist_2EFILTER(A_27a),ap(c_2Emin_2E_3D(A_27a),V0e)),V1L) = ap(ap(c_2Elist_2ECONS(A_27a),V0e),c_2Elist_2ENIL(A_27a)) ) ) ) ) ).
fof(conj_thm_2Elist_2EUNIQUE__LENGTH__FILTER,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0e] :
( mem(V0e,A_27a)
=> ! [V1L] :
( mem(V1L,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Elist_2EUNIQUE(A_27a),V0e),V1L))
<=> ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2EFILTER(A_27a),ap(c_2Emin_2E_3D(A_27a),V0e)),V1L)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ) ) ).
fof(lameq_f461,axiom,
! [A_27a,V4h] :
( mem(V4h,A_27a)
=> ! [V5t] : ap(f461(A_27a,V4h),V5t) = ap(c_2Eoption_2ESOME(ty_2Elist_2Elist(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),V4h),V5t)) ) ).
fof(lameq_f462,axiom,
! [A_27b,A_27a,V1f] :
( mem(V1f,arr(A_27b,ty_2Eoption_2Eoption(A_27a)))
=> ! [V3t0] :
( mem(V3t0,ty_2Elist_2Elist(A_27b))
=> ! [V4h] : ap(f462(A_27b,A_27a,V1f,V3t0),V4h) = ap(ap(c_2Eoption_2EOPTION__BIND(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)),ap(ap(c_2Elist_2EOPT__MMAP(A_27a,A_27b),V1f),V3t0)),f461(A_27a,V4h)) ) ) ).
fof(ax_thm_2Elist_2EOPT__MMAP__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0f] :
( mem(V0f,arr(A_27b,ty_2Eoption_2Eoption(A_27a)))
=> ap(ap(c_2Elist_2EOPT__MMAP(A_27a,A_27b),V0f),c_2Elist_2ENIL(A_27b)) = ap(c_2Eoption_2ESOME(ty_2Elist_2Elist(A_27a)),c_2Elist_2ENIL(A_27a)) )
& ! [V1f] :
( mem(V1f,arr(A_27b,ty_2Eoption_2Eoption(A_27a)))
=> ! [V2h0] :
( mem(V2h0,A_27b)
=> ! [V3t0] :
( mem(V3t0,ty_2Elist_2Elist(A_27b))
=> ap(ap(c_2Elist_2EOPT__MMAP(A_27a,A_27b),V1f),ap(ap(c_2Elist_2ECONS(A_27b),V2h0),V3t0)) = ap(ap(c_2Eoption_2EOPTION__BIND(ty_2Elist_2Elist(A_27a),A_27a),ap(V1f,V2h0)),f462(A_27b,A_27a,V1f,V3t0)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EOPT__MMAP__cong,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f1] :
( mem(V0f1,arr(A_27a,ty_2Eoption_2Eoption(A_27b)))
=> ! [V1f2] :
( mem(V1f2,arr(A_27a,ty_2Eoption_2Eoption(A_27b)))
=> ! [V2x1] :
( mem(V2x1,ty_2Elist_2Elist(A_27a))
=> ! [V3x2] :
( mem(V3x2,ty_2Elist_2Elist(A_27a))
=> ( ( V2x1 = V3x2
& ! [V4a] :
( mem(V4a,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V3x2)))
=> ap(V0f1,V4a) = ap(V1f2,V4a) ) ) )
=> ap(ap(c_2Elist_2EOPT__MMAP(A_27b,A_27a),V0f1),V2x1) = ap(ap(c_2Elist_2EOPT__MMAP(A_27b,A_27a),V1f2),V3x2) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ELAST__compute,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0x] :
( mem(V0x,A_27a)
=> ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0x),c_2Elist_2ENIL(A_27a))) = V0x )
& ! [V1h1] :
( mem(V1h1,A_27b)
=> ! [V2h2] :
( mem(V2h2,A_27b)
=> ! [V3t] :
( mem(V3t,ty_2Elist_2Elist(A_27b))
=> ap(c_2Elist_2ELAST(A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V1h1),ap(ap(c_2Elist_2ECONS(A_27b),V2h2),V3t))) = ap(c_2Elist_2ELAST(A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V2h2),V3t)) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2ETAKE__compute,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ( ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2ETAKE(A_27a),c_2Enum_2E0),V0l) = c_2Elist_2ENIL(A_27a) )
& ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2ETAKE(A_27b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1n))),c_2Elist_2ENIL(A_27b)) = c_2Elist_2ENIL(A_27b) )
& ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2ETAKE(A_27b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V2n))),c_2Elist_2ENIL(A_27b)) = c_2Elist_2ENIL(A_27b) )
& ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ! [V4h] :
( mem(V4h,A_27c)
=> ! [V5t] :
( mem(V5t,ty_2Elist_2Elist(A_27c))
=> ap(ap(c_2Elist_2ETAKE(A_27c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),ap(ap(c_2Elist_2ECONS(A_27c),V4h),V5t)) = ap(ap(c_2Elist_2ECONS(A_27c),V4h),ap(ap(c_2Elist_2ETAKE(A_27c),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V5t)) ) ) )
& ! [V6n] :
( mem(V6n,ty_2Enum_2Enum)
=> ! [V7h] :
( mem(V7h,A_27c)
=> ! [V8t] :
( mem(V8t,ty_2Elist_2Elist(A_27c))
=> ap(ap(c_2Elist_2ETAKE(A_27c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V6n))),ap(ap(c_2Elist_2ECONS(A_27c),V7h),V8t)) = ap(ap(c_2Elist_2ECONS(A_27c),V7h),ap(ap(c_2Elist_2ETAKE(A_27c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n))),V8t)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EDROP__compute,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ( ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EDROP(A_27a),c_2Enum_2E0),V0l) = V0l )
& ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2EDROP(A_27b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1n))),c_2Elist_2ENIL(A_27b)) = c_2Elist_2ENIL(A_27b) )
& ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2EDROP(A_27b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V2n))),c_2Elist_2ENIL(A_27b)) = c_2Elist_2ENIL(A_27b) )
& ! [V3n] :
( mem(V3n,ty_2Enum_2Enum)
=> ! [V4h] :
( mem(V4h,A_27c)
=> ! [V5t] :
( mem(V5t,ty_2Elist_2Elist(A_27c))
=> ap(ap(c_2Elist_2EDROP(A_27c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),ap(ap(c_2Elist_2ECONS(A_27c),V4h),V5t)) = ap(ap(c_2Elist_2EDROP(A_27c),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V5t) ) ) )
& ! [V6n] :
( mem(V6n,ty_2Enum_2Enum)
=> ! [V7h] :
( mem(V7h,A_27c)
=> ! [V8t] :
( mem(V8t,ty_2Elist_2Elist(A_27c))
=> ap(ap(c_2Elist_2EDROP(A_27c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V6n))),ap(ap(c_2Elist_2ECONS(A_27c),V7h),V8t)) = ap(ap(c_2Elist_2EDROP(A_27c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6n))),V8t) ) ) ) ) ) ) ) ).
fof(lameq_f463,axiom,
! [A_27a,V1h] : ap(f463(A_27a),V1h) = k(ty_2Elist_2Elist(A_27a),ap(c_2Eoption_2ESOME(A_27a),V1h)) ).
fof(ax_thm_2Elist_2EoHD__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ap(c_2Elist_2EoHD(A_27a),V0l) = ap(ap(ap(c_2Elist_2Elist__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V0l),c_2Eoption_2ENONE(A_27a)),f463(A_27a)) ) ) ).
fof(conj_thm_2Elist_2EoHD__thm,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0h] :
( mem(V0h,A_27b)
=> ! [V1t] :
( mem(V1t,ty_2Elist_2Elist(A_27b))
=> ( ap(c_2Elist_2EoHD(A_27a),c_2Elist_2ENIL(A_27a)) = c_2Eoption_2ENONE(A_27a)
& ap(c_2Elist_2EoHD(A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V0h),V1t)) = ap(c_2Eoption_2ESOME(A_27b),V0h) ) ) ) ) ) ).
fof(ax_thm_2Elist_2EoEL__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2EoEL(A_27a),V0n),c_2Elist_2ENIL(A_27a)) = c_2Eoption_2ENONE(A_27a) )
& ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3xs] :
( mem(V3xs,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EoEL(A_27a),V1n),ap(ap(c_2Elist_2ECONS(A_27a),V2x),V3xs)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1n),c_2Enum_2E0)),ap(c_2Eoption_2ESOME(A_27a),V2x)),ap(ap(c_2Elist_2EoEL(A_27a),ap(ap(c_2Earithmetic_2E_2D,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V3xs)) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EoEL__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0xs] :
( mem(V0xs,ty_2Elist_2Elist(A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ap(ap(c_2Elist_2EoEL(A_27a),V1n),V0xs) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Elist_2ELENGTH(A_27a),V0xs))),ap(c_2Eoption_2ESOME(A_27a),ap(ap(c_2Elist_2EEL(A_27a),V1n),V0xs))),c_2Eoption_2ENONE(A_27a)) ) ) ) ).
fof(conj_thm_2Elist_2EoEL__EQ__EL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0xs] :
( mem(V0xs,ty_2Elist_2Elist(A_27a))
=> ! [V1n] :
( mem(V1n,ty_2Enum_2Enum)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( ap(ap(c_2Elist_2EoEL(A_27a),V1n),V0xs) = ap(c_2Eoption_2ESOME(A_27a),V2y)
<=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Elist_2ELENGTH(A_27a),V0xs)))
& V2y = ap(ap(c_2Elist_2EEL(A_27a),V1n),V0xs) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EoEL__DROP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2xs] :
( mem(V2xs,ty_2Elist_2Elist(A_27a))
=> ap(ap(c_2Elist_2EoEL(A_27a),V0n),ap(ap(c_2Elist_2EDROP(A_27a),V1m),V2xs)) = ap(ap(c_2Elist_2EoEL(A_27a),ap(ap(c_2Earithmetic_2E_2B,V1m),V0n)),V2xs) ) ) ) ) ).
fof(conj_thm_2Elist_2EoEL__TAKE__E,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0n] :
( mem(V0n,ty_2Enum_2Enum)
=> ! [V1m] :
( mem(V1m,ty_2Enum_2Enum)
=> ! [V2xs] :
( mem(V2xs,ty_2Elist_2Elist(A_27a))
=> ! [V3x] :
( mem(V3x,A_27a)
=> ( ap(ap(c_2Elist_2EoEL(A_27a),V0n),ap(ap(c_2Elist_2ETAKE(A_27a),V1m),V2xs)) = ap(c_2Eoption_2ESOME(A_27a),V3x)
=> ap(ap(c_2Elist_2EoEL(A_27a),V0n),V2xs) = ap(c_2Eoption_2ESOME(A_27a),V3x) ) ) ) ) ) ) ).
fof(conj_thm_2Elist_2EoEL__LUPDATE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0xs] :
( mem(V0xs,ty_2Elist_2Elist(A_27a))
=> ! [V1i] :
( mem(V1i,ty_2Enum_2Enum)
=> ! [V2n] :
( mem(V2n,ty_2Enum_2Enum)
=> ! [V3x] :
( mem(V3x,A_27a)
=> ap(ap(c_2Elist_2EoEL(A_27a),V2n),ap(ap(ap(c_2Elist_2ELUPDATE(A_27a),V3x),V1i),V0xs)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1i),V2n))),ap(ap(c_2Elist_2EoEL(A_27a),V2n),V0xs)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Eprim__rec_2E_3C,V1i),ap(c_2Elist_2ELENGTH(A_27a),V0xs))),ap(c_2Eoption_2ESOME(A_27a),V3x)),c_2Eoption_2ENONE(A_27a))) ) ) ) ) ) ).
fof(lameq_f464,axiom,
! [A_27b,A_27a,V1b] :
( mem(V1b,A_27b)
=> ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V2f] : ap(f464(A_27b,A_27a,V1b,V0l),V2f) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(c_2Elist_2ENULL(A_27a),V0l)),V1b),ap(ap(V2f,ap(c_2Elist_2EHD(A_27a),V0l)),ap(c_2Elist_2ETL(A_27a),V0l))) ) ) ).
fof(lameq_f465,axiom,
! [A_27a,A_27b,V0l] :
( mem(V0l,ty_2Elist_2Elist(A_27a))
=> ! [V1b] : ap(f465(A_27a,A_27b,V0l),V1b) = f464(A_27b,A_27a,V1b,V0l) ) ).
fof(lameq_f466,axiom,
! [A_27b,A_27a,V0l] : ap(f466(A_27b,A_27a),V0l) = f465(A_27a,A_27b,V0l) ).
fof(conj_thm_2Elist_2Elazy__list__case__compute,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> c_2Elist_2Elist__CASE(A_27a,A_27b) = f466(A_27b,A_27a) ) ) ).
%------------------------------------------------------------------------------