ITP001 Axioms: ITP107+5.ax
%------------------------------------------------------------------------------
% File : ITP107+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 : fmapal+2.ax [Gau20]
% : HL4107+5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 180 ( 3 unt; 0 def)
% Number of atoms : 1473 ( 167 equ)
% Maximal formula atoms : 34 ( 8 avg)
% Number of connectives : 1303 ( 10 ~; 1 |; 117 &)
% ( 18 <=>;1157 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 12 avg)
% Maximal term depth : 21 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 154 ( 154 usr; 9 con; 0-10 aty)
% Number of variables : 1173 (1173 !; 0 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(mem_c_2Efmapal_2EAP__SND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> mem(c_2Efmapal_2EAP__SND(A_27a,A_27b,A_27c),arr(arr(A_27b,A_27c),arr(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27a,A_27c)))) ) ) ) ).
fof(mem_c_2Efmapal_2EFMAPAL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2EFMAPAL(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Efinite__map_2Efmap(A_27a,A_27b)))) ) ) ).
fof(mem_c_2Efmapal_2EOFU,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2EOFU(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),ty_2Efinite__map_2Efmap(A_27a,A_27b))))) ) ) ).
fof(mem_c_2Efmapal_2EOPTION__FLAT,axiom,
! [A_27z] :
( ne(A_27z)
=> mem(c_2Efmapal_2EOPTION__FLAT(A_27z),arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),ty_2Elist_2Elist(A_27z))) ) ).
fof(mem_c_2Efmapal_2EOPTION__UPDATE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2EOPTION__UPDATE(A_27a,A_27b),arr(arr(A_27a,ty_2Eoption_2Eoption(A_27b)),arr(arr(A_27a,ty_2Eoption_2Eoption(A_27b)),arr(A_27a,ty_2Eoption_2Eoption(A_27b))))) ) ) ).
fof(mem_c_2Efmapal_2EORL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2EORL(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),bool))) ) ) ).
fof(mem_c_2Efmapal_2EORL__bt,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2EORL__bt(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),bool))) ) ) ).
fof(mem_c_2Efmapal_2EORL__bt__lb,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2EORL__bt__lb(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(A_27a,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),bool)))) ) ) ).
fof(mem_c_2Efmapal_2EORL__bt__lb__ub,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2EORL__bt__lb__ub(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(A_27a,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(A_27a,bool))))) ) ) ).
fof(mem_c_2Efmapal_2EORL__bt__ub,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2EORL__bt__ub(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(A_27a,bool)))) ) ) ).
fof(mem_c_2Efmapal_2EORL__sublists,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2EORL__sublists(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),bool))) ) ) ).
fof(mem_c_2Efmapal_2EORWL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2EORWL(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),bool)))) ) ) ).
fof(mem_c_2Efmapal_2EUFO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2EUFO(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),arr(ty_2Efinite__map_2Efmap(A_27a,A_27b),ty_2Efinite__map_2Efmap(A_27a,A_27b))))) ) ) ).
fof(mem_c_2Efmapal_2Eassocv,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Eassocv(A_27a,A_27b),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),arr(A_27a,ty_2Eoption_2Eoption(A_27b)))) ) ) ).
fof(mem_c_2Efmapal_2Ebl__to__fmap,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Ebl__to__fmap(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Eenumeral_2Ebl(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Efinite__map_2Efmap(A_27a,A_27b)))) ) ) ).
fof(mem_c_2Efmapal_2Ebt__map,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Ebt__map(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(ty_2Eenumeral_2Ebt(A_27a),ty_2Eenumeral_2Ebt(A_27b)))) ) ) ).
fof(mem_c_2Efmapal_2Ebt__rplacv__cn,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Ebt__rplacv__cn(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Epair_2Eprod(A_27a,A_27b),arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b))),ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b))))))) ) ) ).
fof(mem_c_2Efmapal_2Ebt__to__fmap__lb,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Ebt__to__fmap__lb(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(A_27a,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Efinite__map_2Efmap(A_27a,A_27b))))) ) ) ).
fof(mem_c_2Efmapal_2Ebt__to__fmap__lb__ub,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Ebt__to__fmap__lb__ub(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(A_27a,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(A_27a,ty_2Efinite__map_2Efmap(A_27a,A_27b)))))) ) ) ).
fof(mem_c_2Efmapal_2Ebt__to__fmap__ub,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Ebt__to__fmap__ub(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(A_27a,ty_2Efinite__map_2Efmap(A_27a,A_27b))))) ) ) ).
fof(mem_c_2Efmapal_2Ebt__to__orl,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Ebt__to__orl(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))) ) ) ).
fof(mem_c_2Efmapal_2Ebt__to__orl__ac,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Ebt__to__orl__ac(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))) ) ) ).
fof(mem_c_2Efmapal_2Ebt__to__orl__lb,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Ebt__to__orl__lb(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(A_27a,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))) ) ) ).
fof(mem_c_2Efmapal_2Ebt__to__orl__lb__ac,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Ebt__to__orl__lb__ac(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(A_27a,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))))) ) ) ).
fof(mem_c_2Efmapal_2Ebt__to__orl__lb__ub,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Ebt__to__orl__lb__ub(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(A_27a,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))))) ) ) ).
fof(mem_c_2Efmapal_2Ebt__to__orl__lb__ub__ac,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Ebt__to__orl__lb__ub__ac(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(A_27a,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(A_27a,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))))) ) ) ).
fof(mem_c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux(A_27a,A_27b),arr(arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),bool)),arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))) ) ) ).
fof(mem_c_2Efmapal_2Ebt__to__orl__ub,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Ebt__to__orl__ub(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))) ) ) ).
fof(mem_c_2Efmapal_2Ebt__to__orl__ub__ac,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Ebt__to__orl__ub__ac(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(A_27a,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))))) ) ) ).
fof(mem_c_2Efmapal_2Ediff__merge,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Ediff__merge(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))) ) ) ).
fof(mem_c_2Efmapal_2Efmap,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Efmap(A_27a,A_27b),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Efinite__map_2Efmap(A_27a,A_27b))) ) ) ).
fof(mem_c_2Efmapal_2Eincr__build,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Eincr__build(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))))) ) ) ).
fof(mem_c_2Efmapal_2Eincr__flat,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Eincr__flat(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))) ) ) ).
fof(mem_c_2Efmapal_2Eincr__merge,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Eincr__merge(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))))) ) ) ).
fof(mem_c_2Efmapal_2Eincr__sort,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Eincr__sort(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))) ) ) ).
fof(mem_c_2Efmapal_2Einter__merge,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Einter__merge(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))) ) ) ).
fof(mem_c_2Efmapal_2Elist__rplacv__cn,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Elist__rplacv__cn(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27a,A_27b),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),arr(arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))) ) ) ).
fof(mem_c_2Efmapal_2Emerge,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Emerge(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))) ) ) ).
fof(mem_c_2Efmapal_2Emerge__out,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Emerge__out(A_27a,A_27b),arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))) ) ) ).
fof(mem_c_2Efmapal_2Eoptry,axiom,
! [A_27z] :
( ne(A_27z)
=> mem(c_2Efmapal_2Eoptry(A_27z),arr(ty_2Eoption_2Eoption(A_27z),arr(ty_2Eoption_2Eoption(A_27z),ty_2Eoption_2Eoption(A_27z)))) ) ).
fof(mem_c_2Efmapal_2Eoptry__list,axiom,
! [A_27g] :
( ne(A_27g)
=> ! [A_27z] :
( ne(A_27z)
=> mem(c_2Efmapal_2Eoptry__list(A_27g,A_27z),arr(arr(A_27z,ty_2Eoption_2Eoption(A_27g)),arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(A_27z)),ty_2Eoption_2Eoption(A_27g)))) ) ) ).
fof(mem_c_2Efmapal_2Eunlookup,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Eunlookup(A_27a,A_27b),arr(arr(A_27a,ty_2Eoption_2Eoption(A_27b)),ty_2Efinite__map_2Efmap(A_27a,A_27b))) ) ) ).
fof(mem_c_2Efmapal_2Evcossa,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Efmapal_2Evcossa(A_27a,A_27b),arr(A_27a,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Eoption_2Eoption(A_27b)))) ) ) ).
fof(conj_thm_2Efmapal_2EORL__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),bool)))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> p(ap(ap(V0P,V1cmp),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)))) )
& ! [V2cmp] :
( mem(V2cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V3a] :
( mem(V3a,A_27a)
=> ! [V4b] :
( mem(V4b,A_27b)
=> ! [V5l] :
( mem(V5l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( p(ap(ap(V0P,V2cmp),V5l))
=> p(ap(ap(V0P,V2cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3a),V4b)),V5l))) ) ) ) ) ) )
=> ! [V6v] :
( mem(V6v,ty_2Etoto_2Etoto(A_27a))
=> ! [V7v1] :
( mem(V7v1,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(V0P,V6v),V7v1)) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EORL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ( p(ap(ap(c_2Efmapal_2EORL(A_27a,A_27b),V0cmp),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))))
<=> $true ) )
& ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V2cmp] :
( mem(V2cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V3b] :
( mem(V3b,A_27b)
=> ! [V4a] :
( mem(V4a,A_27a)
=> ( p(ap(ap(c_2Efmapal_2EORL(A_27a,A_27b),V2cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4a),V3b)),V1l)))
<=> ( p(ap(ap(c_2Efmapal_2EORL(A_27a,A_27b),V2cmp),V1l))
& ! [V5p] :
( mem(V5p,A_27a)
=> ! [V6q] :
( mem(V6q,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),V5p),V6q)),ap(c_2Elist_2ELIST__TO__SET(ty_2Epair_2Eprod(A_27a,A_27b)),V1l)))
=> ap(ap(ap(c_2Etoto_2Eapto(A_27a),V2cmp),V4a),V5p) = c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Efmapal_2Eoptry,axiom,
! [A_27z] :
( ne(A_27z)
=> ( ! [V0p] :
( mem(V0p,A_27z)
=> ! [V1q] :
( mem(V1q,ty_2Eoption_2Eoption(A_27z))
=> ap(ap(c_2Efmapal_2Eoptry(A_27z),ap(c_2Eoption_2ESOME(A_27z),V0p)),V1q) = ap(c_2Eoption_2ESOME(A_27z),V0p) ) )
& ! [V2q] :
( mem(V2q,ty_2Eoption_2Eoption(A_27z))
=> ap(ap(c_2Efmapal_2Eoptry(A_27z),c_2Eoption_2ENONE(A_27z)),V2q) = V2q ) ) ) ).
fof(conj_thm_2Efmapal_2Eoptry__list__ind,axiom,
! [A_27g] :
( ne(A_27g)
=> ! [A_27z] :
( ne(A_27z)
=> ! [V0P] :
( mem(V0P,arr(arr(A_27z,ty_2Eoption_2Eoption(A_27g)),arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(A_27z)),bool)))
=> ( ( ! [V1f] :
( mem(V1f,arr(A_27z,ty_2Eoption_2Eoption(A_27g)))
=> p(ap(ap(V0P,V1f),c_2Elist_2ENIL(ty_2Eoption_2Eoption(A_27z)))) )
& ! [V2f] :
( mem(V2f,arr(A_27z,ty_2Eoption_2Eoption(A_27g)))
=> ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(ty_2Eoption_2Eoption(A_27z)))
=> ( p(ap(ap(V0P,V2f),V3l))
=> p(ap(ap(V0P,V2f),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(A_27z)),c_2Eoption_2ENONE(A_27z)),V3l))) ) ) )
& ! [V4f] :
( mem(V4f,arr(A_27z,ty_2Eoption_2Eoption(A_27g)))
=> ! [V5z] :
( mem(V5z,A_27z)
=> ! [V6l] :
( mem(V6l,ty_2Elist_2Elist(ty_2Eoption_2Eoption(A_27z)))
=> ( p(ap(ap(V0P,V4f),V6l))
=> p(ap(ap(V0P,V4f),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(A_27z)),ap(c_2Eoption_2ESOME(A_27z),V5z)),V6l))) ) ) ) ) )
=> ! [V7v] :
( mem(V7v,arr(A_27z,ty_2Eoption_2Eoption(A_27g)))
=> ! [V8v1] :
( mem(V8v1,ty_2Elist_2Elist(ty_2Eoption_2Eoption(A_27z)))
=> p(ap(ap(V0P,V7v),V8v1)) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Eoptry__list,axiom,
! [A_27g] :
( ne(A_27g)
=> ! [A_27z] :
( ne(A_27z)
=> ( ! [V0f] :
( mem(V0f,arr(A_27z,ty_2Eoption_2Eoption(A_27g)))
=> ap(ap(c_2Efmapal_2Eoptry__list(A_27g,A_27z),V0f),c_2Elist_2ENIL(ty_2Eoption_2Eoption(A_27z))) = c_2Eoption_2ENONE(A_27g) )
& ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Eoption_2Eoption(A_27z)))
=> ! [V2f] :
( mem(V2f,arr(A_27z,ty_2Eoption_2Eoption(A_27g)))
=> ap(ap(c_2Efmapal_2Eoptry__list(A_27g,A_27z),V2f),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(A_27z)),c_2Eoption_2ENONE(A_27z)),V1l)) = ap(ap(c_2Efmapal_2Eoptry__list(A_27g,A_27z),V2f),V1l) ) )
& ! [V3z] :
( mem(V3z,A_27z)
=> ! [V4l] :
( mem(V4l,ty_2Elist_2Elist(ty_2Eoption_2Eoption(A_27z)))
=> ! [V5f] :
( mem(V5f,arr(A_27z,ty_2Eoption_2Eoption(A_27g)))
=> ap(ap(c_2Efmapal_2Eoptry__list(A_27g,A_27z),V5f),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(A_27z)),ap(c_2Eoption_2ESOME(A_27z),V3z)),V4l)) = ap(ap(c_2Efmapal_2Eoptry(A_27g),ap(V5f,V3z)),ap(ap(c_2Efmapal_2Eoptry__list(A_27g,A_27z),V5f),V4l)) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Eassocv__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),arr(A_27a,bool)))
=> ( ( ! [V1a] :
( mem(V1a,A_27a)
=> p(ap(ap(V0P,c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))),V1a)) )
& ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27b)
=> ! [V4l] :
( mem(V4l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V5a] :
( mem(V5a,A_27a)
=> ( ( V5a != V2x
=> p(ap(ap(V0P,V4l),V5a)) )
=> p(ap(ap(V0P,ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)),V4l)),V5a)) ) ) ) ) ) )
=> ! [V6v] :
( mem(V6v,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V7v1] :
( mem(V7v1,A_27a)
=> p(ap(ap(V0P,V6v),V7v1)) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Eassocv,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0a] :
( mem(V0a,A_27a)
=> ap(ap(c_2Efmapal_2Eassocv(A_27a,A_27b),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))),V0a) = c_2Eoption_2ENONE(A_27b) )
& ! [V1y] :
( mem(V1y,A_27b)
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V4a] :
( mem(V4a,A_27a)
=> ap(ap(c_2Efmapal_2Eassocv(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),V2x),V1y)),V3l)),V4a) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27b)),ap(ap(c_2Emin_2E_3D(A_27a),V4a),V2x)),ap(c_2Eoption_2ESOME(A_27b),V1y)),ap(ap(c_2Efmapal_2Eassocv(A_27a,A_27b),V3l),V4a)) ) ) ) ) ) ) ) ).
fof(ax_thm_2Efmapal_2Evcossa,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0a] :
( mem(V0a,A_27a)
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ap(ap(c_2Efmapal_2Evcossa(A_27a,A_27b),V0a),V1l) = ap(ap(c_2Efmapal_2Eassocv(A_27a,A_27b),V1l),V0a) ) ) ) ) ).
fof(ax_thm_2Efmapal_2EOPTION__UPDATE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Eoption_2Eoption(A_27b)))
=> ! [V1g] :
( mem(V1g,arr(A_27a,ty_2Eoption_2Eoption(A_27b)))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ap(ap(ap(c_2Efmapal_2EOPTION__UPDATE(A_27a,A_27b),V0f),V1g),V2x) = ap(ap(c_2Efmapal_2Eoptry(A_27b),ap(V0f,V2x)),ap(V1g,V2x)) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Emerge__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),bool))))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(V0P,V1cmp),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))),V2l)) ) )
& ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V4v4] :
( mem(V4v4,ty_2Epair_2Eprod(A_27a,A_27b))
=> ! [V5v5] :
( mem(V5v5,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(V0P,V3cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),V4v4),V5v5)),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)))) ) ) )
& ! [V6cmp] :
( mem(V6cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V7a1] :
( mem(V7a1,A_27a)
=> ! [V8b1] :
( mem(V8b1,A_27b)
=> ! [V9l1] :
( mem(V9l1,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V10a2] :
( mem(V10a2,A_27a)
=> ! [V11b2] :
( mem(V11b2,A_27b)
=> ! [V12l2] :
( mem(V12l2,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ( ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V6cmp),V7a1),V10a2) = c_2EternaryComparisons_2EEQUAL
=> p(ap(ap(ap(V0P,V6cmp),V9l1),V12l2)) )
& ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V6cmp),V7a1),V10a2) = c_2EternaryComparisons_2EGREATER
=> p(ap(ap(ap(V0P,V6cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V7a1),V8b1)),V9l1)),V12l2)) )
& ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V6cmp),V7a1),V10a2) = c_2EternaryComparisons_2ELESS
=> p(ap(ap(ap(V0P,V6cmp),V9l1),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V10a2),V11b2)),V12l2))) ) )
=> p(ap(ap(ap(V0P,V6cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V7a1),V8b1)),V9l1)),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V10a2),V11b2)),V12l2))) ) ) ) ) ) ) ) ) )
=> ! [V13v] :
( mem(V13v,ty_2Etoto_2Etoto(A_27a))
=> ! [V14v1] :
( mem(V14v1,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V15v2] :
( mem(V15v2,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(V0P,V13v),V14v1),V15v2)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Emerge,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(c_2Efmapal_2Emerge(A_27a,A_27b),V1cmp),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))),V0l) = V0l ) )
& ! [V2v5] :
( mem(V2v5,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V3v4] :
( mem(V3v4,ty_2Epair_2Eprod(A_27a,A_27b))
=> ! [V4cmp] :
( mem(V4cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(c_2Efmapal_2Emerge(A_27a,A_27b),V4cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),V3v4),V2v5)),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))) = ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),V3v4),V2v5) ) ) )
& ! [V5l2] :
( mem(V5l2,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V6l1] :
( mem(V6l1,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V7cmp] :
( mem(V7cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V8b2] :
( mem(V8b2,A_27b)
=> ! [V9b1] :
( mem(V9b1,A_27b)
=> ! [V10a2] :
( mem(V10a2,A_27a)
=> ! [V11a1] :
( mem(V11a1,A_27a)
=> ap(ap(ap(c_2Efmapal_2Emerge(A_27a,A_27b),V7cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V11a1),V9b1)),V6l1)),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V10a2),V8b2)),V5l2)) = ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V7cmp),V11a1),V10a2)),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V11a1),V9b1)),ap(ap(ap(c_2Efmapal_2Emerge(A_27a,A_27b),V7cmp),V6l1),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V10a2),V8b2)),V5l2)))),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V11a1),V9b1)),ap(ap(ap(c_2Efmapal_2Emerge(A_27a,A_27b),V7cmp),V6l1),V5l2))),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V10a2),V8b2)),ap(ap(ap(c_2Efmapal_2Emerge(A_27a,A_27b),V7cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V11a1),V9b1)),V6l1)),V5l2))) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Eincr__merge__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),bool))))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(V0P,V1cmp),V2l),c_2Elist_2ENIL(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))) ) )
& ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V4l] :
( mem(V4l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V5lol] :
( mem(V5lol,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))
=> p(ap(ap(ap(V0P,V3cmp),V4l),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),c_2Eoption_2ENONE(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),V5lol))) ) ) )
& ! [V6cmp] :
( mem(V6cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V7l] :
( mem(V7l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V8m] :
( mem(V8m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V9lol] :
( mem(V9lol,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))
=> ( p(ap(ap(ap(V0P,V6cmp),ap(ap(ap(c_2Efmapal_2Emerge(A_27a,A_27b),V6cmp),V7l),V8m)),V9lol))
=> p(ap(ap(ap(V0P,V6cmp),V7l),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),ap(c_2Eoption_2ESOME(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),V8m)),V9lol))) ) ) ) ) ) )
=> ! [V10v] :
( mem(V10v,ty_2Etoto_2Etoto(A_27a))
=> ! [V11v1] :
( mem(V11v1,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V12v2] :
( mem(V12v2,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))
=> p(ap(ap(ap(V0P,V10v),V11v1),V12v2)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Eincr__merge,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(c_2Efmapal_2Eincr__merge(A_27a,A_27b),V1cmp),V0l),c_2Elist_2ENIL(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))) = ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),ap(c_2Eoption_2ESOME(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),V0l)),c_2Elist_2ENIL(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))) ) )
& ! [V2lol] :
( mem(V2lol,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))
=> ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V4cmp] :
( mem(V4cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(c_2Efmapal_2Eincr__merge(A_27a,A_27b),V4cmp),V3l),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),c_2Eoption_2ENONE(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),V2lol)) = ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),ap(c_2Eoption_2ESOME(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),V3l)),V2lol) ) ) )
& ! [V5m] :
( mem(V5m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V6lol] :
( mem(V6lol,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))
=> ! [V7l] :
( mem(V7l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V8cmp] :
( mem(V8cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(c_2Efmapal_2Eincr__merge(A_27a,A_27b),V8cmp),V7l),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),ap(c_2Eoption_2ESOME(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),V5m)),V6lol)) = ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),c_2Eoption_2ENONE(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),ap(ap(ap(c_2Efmapal_2Eincr__merge(A_27a,A_27b),V8cmp),ap(ap(ap(c_2Efmapal_2Emerge(A_27a,A_27b),V8cmp),V7l),V5m)),V6lol)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EORL__sublists__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),bool)))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> p(ap(ap(V0P,V1cmp),c_2Elist_2ENIL(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))) )
& ! [V2cmp] :
( mem(V2cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V3lol] :
( mem(V3lol,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))
=> ( p(ap(ap(V0P,V2cmp),V3lol))
=> p(ap(ap(V0P,V2cmp),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),c_2Eoption_2ENONE(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),V3lol))) ) ) )
& ! [V4cmp] :
( mem(V4cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V5m] :
( mem(V5m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V6lol] :
( mem(V6lol,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))
=> ( p(ap(ap(V0P,V4cmp),V6lol))
=> p(ap(ap(V0P,V4cmp),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),ap(c_2Eoption_2ESOME(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),V5m)),V6lol))) ) ) ) ) )
=> ! [V7v] :
( mem(V7v,ty_2Etoto_2Etoto(A_27a))
=> ! [V8v1] :
( mem(V8v1,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))
=> p(ap(ap(V0P,V7v),V8v1)) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EORL__sublists,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ( p(ap(ap(c_2Efmapal_2EORL__sublists(A_27a,A_27b),V0cmp),c_2Elist_2ENIL(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))))
<=> $true ) )
& ! [V1lol] :
( mem(V1lol,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))
=> ! [V2cmp] :
( mem(V2cmp,ty_2Etoto_2Etoto(A_27a))
=> ( p(ap(ap(c_2Efmapal_2EORL__sublists(A_27a,A_27b),V2cmp),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),c_2Eoption_2ENONE(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),V1lol)))
<=> p(ap(ap(c_2Efmapal_2EORL__sublists(A_27a,A_27b),V2cmp),V1lol)) ) ) )
& ! [V3m] :
( mem(V3m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V4lol] :
( mem(V4lol,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))
=> ! [V5cmp] :
( mem(V5cmp,ty_2Etoto_2Etoto(A_27a))
=> ( p(ap(ap(c_2Efmapal_2EORL__sublists(A_27a,A_27b),V5cmp),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),ap(c_2Eoption_2ESOME(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),V3m)),V4lol)))
<=> ( p(ap(ap(c_2Efmapal_2EORL(A_27a,A_27b),V5cmp),V3m))
& p(ap(ap(c_2Efmapal_2EORL__sublists(A_27a,A_27b),V5cmp),V4lol)) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Efmapal_2Eincr__build,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(c_2Efmapal_2Eincr__build(A_27a,A_27b),V0cmp),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))) = c_2Elist_2ENIL(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))) )
& ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V2ab] :
( mem(V2ab,ty_2Epair_2Eprod(A_27a,A_27b))
=> ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ap(ap(c_2Efmapal_2Eincr__build(A_27a,A_27b),V1cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),V2ab),V3l)) = ap(ap(ap(c_2Efmapal_2Eincr__merge(A_27a,A_27b),V1cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),V2ab),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)))),ap(ap(c_2Efmapal_2Eincr__build(A_27a,A_27b),V1cmp),V3l)) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Emerge__out__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),bool))))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(V0P,V1cmp),V2l),c_2Elist_2ENIL(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))) ) )
& ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V4l] :
( mem(V4l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V5lol] :
( mem(V5lol,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))
=> ( p(ap(ap(ap(V0P,V3cmp),V4l),V5lol))
=> p(ap(ap(ap(V0P,V3cmp),V4l),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),c_2Eoption_2ENONE(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),V5lol))) ) ) ) )
& ! [V6cmp] :
( mem(V6cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V7l] :
( mem(V7l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V8m] :
( mem(V8m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V9lol] :
( mem(V9lol,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))
=> ( p(ap(ap(ap(V0P,V6cmp),ap(ap(ap(c_2Efmapal_2Emerge(A_27a,A_27b),V6cmp),V7l),V8m)),V9lol))
=> p(ap(ap(ap(V0P,V6cmp),V7l),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),ap(c_2Eoption_2ESOME(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),V8m)),V9lol))) ) ) ) ) ) )
=> ! [V10v] :
( mem(V10v,ty_2Etoto_2Etoto(A_27a))
=> ! [V11v1] :
( mem(V11v1,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V12v2] :
( mem(V12v2,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))
=> p(ap(ap(ap(V0P,V10v),V11v1),V12v2)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Emerge__out,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(c_2Efmapal_2Emerge__out(A_27a,A_27b),V1cmp),V0l),c_2Elist_2ENIL(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))) = V0l ) )
& ! [V2lol] :
( mem(V2lol,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))
=> ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V4cmp] :
( mem(V4cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(c_2Efmapal_2Emerge__out(A_27a,A_27b),V4cmp),V3l),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),c_2Eoption_2ENONE(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),V2lol)) = ap(ap(ap(c_2Efmapal_2Emerge__out(A_27a,A_27b),V4cmp),V3l),V2lol) ) ) )
& ! [V5m] :
( mem(V5m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V6lol] :
( mem(V6lol,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))
=> ! [V7l] :
( mem(V7l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V8cmp] :
( mem(V8cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(c_2Efmapal_2Emerge__out(A_27a,A_27b),V8cmp),V7l),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),ap(c_2Eoption_2ESOME(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),V5m)),V6lol)) = ap(ap(ap(c_2Efmapal_2Emerge__out(A_27a,A_27b),V8cmp),ap(ap(ap(c_2Efmapal_2Emerge(A_27a,A_27b),V8cmp),V7l),V5m)),V6lol) ) ) ) ) ) ) ) ).
fof(ax_thm_2Efmapal_2Eincr__flat,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1lol] :
( mem(V1lol,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))
=> ap(ap(c_2Efmapal_2Eincr__flat(A_27a,A_27b),V0cmp),V1lol) = ap(ap(ap(c_2Efmapal_2Emerge__out(A_27a,A_27b),V0cmp),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))),V1lol) ) ) ) ) ).
fof(ax_thm_2Efmapal_2Eincr__sort,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ap(ap(c_2Efmapal_2Eincr__sort(A_27a,A_27b),V0cmp),V1l) = ap(ap(ap(c_2Efmapal_2Emerge__out(A_27a,A_27b),V0cmp),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(c_2Efmapal_2Eincr__build(A_27a,A_27b),V0cmp),V1l)) ) ) ) ) ).
fof(lameq_f2617,axiom,
! [A_27z,V0R] :
( mem(V0R,arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),bool)))
=> ! [V1l] : ap(f2617(A_27z,V0R),V1l) = ap(ap(V0R,V1l),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),c_2Eoption_2ENONE(ty_2Elist_2Elist(A_27z))),V1l)) ) ).
fof(lameq_f2618,axiom,
! [A_27z,V0R] :
( mem(V0R,arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),bool)))
=> ! [V2a] :
( mem(V2a,ty_2Elist_2Elist(A_27z))
=> ! [V3l] : ap(f2618(A_27z,V0R,V2a),V3l) = ap(ap(V0R,V3l),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),ap(c_2Eoption_2ESOME(ty_2Elist_2Elist(A_27z)),V2a)),V3l)) ) ) ).
fof(lameq_f2619,axiom,
! [A_27z,V0R] :
( mem(V0R,arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),bool)))
=> ! [V2a] : ap(f2619(A_27z,V0R),V2a) = ap(c_2Ebool_2E_21(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z)))),f2618(A_27z,V0R,V2a)) ) ).
fof(lameq_f2620,axiom,
! [A_27z,V0R] : ap(f2620(A_27z),V0R) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Erelation_2EWF(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z)))),V0R)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_21(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z)))),f2617(A_27z,V0R))),ap(c_2Ebool_2E_21(ty_2Elist_2Elist(A_27z)),f2619(A_27z,V0R)))) ).
fof(lameq_f2621,axiom,
! [A_27z,V4OPTION__FLAT] :
( mem(V4OPTION__FLAT,arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),ty_2Elist_2Elist(A_27z)))
=> ! [V7l] :
( mem(V7l,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))))
=> ! [V8a] : ap(f2621(A_27z,V4OPTION__FLAT,V7l),V8a) = ap(c_2Ecombin_2EI(ty_2Elist_2Elist(A_27z)),ap(ap(c_2Elist_2EAPPEND(A_27z),V8a),ap(V4OPTION__FLAT,V7l))) ) ) ).
fof(lameq_f2622,axiom,
! [A_27z,V6v] :
( mem(V6v,ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z)))
=> ! [V4OPTION__FLAT] :
( mem(V4OPTION__FLAT,arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),ty_2Elist_2Elist(A_27z)))
=> ! [V7l] : ap(f2622(A_27z,V6v,V4OPTION__FLAT),V7l) = ap(ap(ap(c_2Eoption_2Eoption__CASE(ty_2Elist_2Elist(A_27z),ty_2Elist_2Elist(A_27z)),V6v),ap(c_2Ecombin_2EI(ty_2Elist_2Elist(A_27z)),ap(V4OPTION__FLAT,V7l))),f2621(A_27z,V4OPTION__FLAT,V7l)) ) ) ).
fof(lameq_f2623,axiom,
! [A_27z,V4OPTION__FLAT] :
( mem(V4OPTION__FLAT,arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),ty_2Elist_2Elist(A_27z)))
=> ! [V6v] : ap(f2623(A_27z,V4OPTION__FLAT),V6v) = f2622(A_27z,V6v,V4OPTION__FLAT) ) ).
fof(lameq_f2624,axiom,
! [A_27z,V4OPTION__FLAT] :
( mem(V4OPTION__FLAT,arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),ty_2Elist_2Elist(A_27z)))
=> ! [V5a_27] : ap(f2624(A_27z,V4OPTION__FLAT),V5a_27) = ap(ap(ap(c_2Elist_2Elist__CASE(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z)),ty_2Elist_2Elist(A_27z)),V5a_27),ap(c_2Ecombin_2EI(ty_2Elist_2Elist(A_27z)),c_2Elist_2ENIL(A_27z))),f2623(A_27z,V4OPTION__FLAT)) ) ).
fof(lameq_f2625,axiom,
! [A_27z,V4OPTION__FLAT] : ap(f2625(A_27z),V4OPTION__FLAT) = f2624(A_27z,V4OPTION__FLAT) ).
fof(ax_thm_2Efmapal_2EOPTION__FLAT__primitive,axiom,
! [A_27z] :
( ne(A_27z)
=> c_2Efmapal_2EOPTION__FLAT(A_27z) = ap(ap(c_2Erelation_2EWFREC(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),ty_2Elist_2Elist(A_27z)),ap(c_2Emin_2E_40(arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),bool))),f2620(A_27z))),f2625(A_27z)) ) ).
fof(conj_thm_2Efmapal_2EOPTION__FLAT__ind,axiom,
! [A_27z] :
( ne(A_27z)
=> ! [V0P] :
( mem(V0P,arr(ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),bool))
=> ( ( p(ap(V0P,c_2Elist_2ENIL(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z)))))
& ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))))
=> ( p(ap(V0P,V1l))
=> p(ap(V0P,ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),c_2Eoption_2ENONE(ty_2Elist_2Elist(A_27z))),V1l))) ) )
& ! [V2a] :
( mem(V2a,ty_2Elist_2Elist(A_27z))
=> ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))))
=> ( p(ap(V0P,V3l))
=> p(ap(V0P,ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),ap(c_2Eoption_2ESOME(ty_2Elist_2Elist(A_27z)),V2a)),V3l))) ) ) ) )
=> ! [V4v] :
( mem(V4v,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))))
=> p(ap(V0P,V4v)) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EOPTION__FLAT,axiom,
! [A_27z] :
( ne(A_27z)
=> ( ap(c_2Efmapal_2EOPTION__FLAT(A_27z),c_2Elist_2ENIL(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z)))) = c_2Elist_2ENIL(A_27z)
& ! [V0l] :
( mem(V0l,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))))
=> ap(c_2Efmapal_2EOPTION__FLAT(A_27z),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),c_2Eoption_2ENONE(ty_2Elist_2Elist(A_27z))),V0l)) = ap(c_2Efmapal_2EOPTION__FLAT(A_27z),V0l) )
& ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))))
=> ! [V2a] :
( mem(V2a,ty_2Elist_2Elist(A_27z))
=> ap(c_2Efmapal_2EOPTION__FLAT(A_27z),ap(ap(c_2Elist_2ECONS(ty_2Eoption_2Eoption(ty_2Elist_2Elist(A_27z))),ap(c_2Eoption_2ESOME(ty_2Elist_2Elist(A_27z)),V2a)),V1l)) = ap(ap(c_2Elist_2EAPPEND(A_27z),V2a),ap(c_2Efmapal_2EOPTION__FLAT(A_27z),V1l)) ) ) ) ) ).
fof(ax_thm_2Efmapal_2Eunlookup,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Eoption_2Eoption(A_27b)))
=> ap(c_2Efmapal_2Eunlookup(A_27a,A_27b),V0f) = ap(ap(c_2Efinite__map_2EFUN__FMAP(A_27a,A_27b),ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,ty_2Eoption_2Eoption(A_27b)),c_2Eoption_2ETHE(A_27b)),V0f)),ap(ap(c_2Ecombin_2Eo(A_27a,bool,ty_2Eoption_2Eoption(A_27b)),c_2Eoption_2EIS__SOME(A_27b)),V0f)) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__fmap__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),bool)))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> p(ap(ap(V0P,V1cmp),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b)))) )
& ! [V2cmp] :
( mem(V2cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V3l] :
( mem(V3l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5v] :
( mem(V5v,A_27b)
=> ! [V6r] :
( mem(V6r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ( p(ap(ap(V0P,V2cmp),V3l))
& p(ap(ap(V0P,V2cmp),V6r)) )
=> p(ap(ap(V0P,V2cmp),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V3l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4x),V5v)),V6r))) ) ) ) ) ) ) )
=> ! [V7v] :
( mem(V7v,ty_2Etoto_2Etoto(A_27a))
=> ! [V8v1] :
( mem(V8v1,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(V0P,V7v),V8v1)) ) ) ) ) ) ) ).
fof(lameq_f2626,axiom,
! [A_27a,V1x] :
( mem(V1x,A_27a)
=> ! [V5cmp] :
( mem(V5cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V6y] : ap(f2626(A_27a,V1x,V5cmp),V6y) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V6y),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V5cmp),V6y),V1x)),c_2EternaryComparisons_2ELESS)) ) ) ).
fof(lameq_f2627,axiom,
! [A_27a,V5cmp] :
( mem(V5cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V7z] : ap(f2627(A_27a,V5cmp,V1x),V7z) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V7z),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V5cmp),V1x),V7z)),c_2EternaryComparisons_2ELESS)) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__fmap,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V0cmp),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))) = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) )
& ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2v] :
( mem(V2v,A_27b)
=> ! [V3r] :
( mem(V3r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V4l] :
( mem(V4l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V5cmp] :
( mem(V5cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V5cmp),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V4l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2v)),V3r)) = ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V5cmp),V4l)),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f2626(A_27a,V1x,V5cmp)))),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2v)))),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V5cmp),V3r)),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f2627(A_27a,V5cmp,V1x)))) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EFAPPLY__nt,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V0cmp),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b)))),V1x) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),V1x) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EFAPPLY__node,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2l] :
( mem(V2l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V3a] :
( mem(V3a,A_27a)
=> ! [V4b] :
( mem(V4b,A_27b)
=> ! [V5r] :
( mem(V5r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V0cmp),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V2l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3a),V4b)),V5r))),V1x) = ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(A_27b),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0cmp),V1x),V3a)),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V0cmp),V2l)),V1x)),V4b),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V0cmp),V5r)),V1x)) ) ) ) ) ) ) ) ) ).
fof(lameq_f2628,axiom,
! [A_27a,V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1lb] :
( mem(V1lb,A_27a)
=> ! [V3x] : ap(f2628(A_27a,V0cmp,V1lb),V3x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V3x),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0cmp),V1lb),V3x)),c_2EternaryComparisons_2ELESS)) ) ) ).
fof(ax_thm_2Efmapal_2Ebt__to__fmap__lb,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1lb] :
( mem(V1lb,A_27a)
=> ! [V2t] :
( mem(V2t,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ap(ap(ap(c_2Efmapal_2Ebt__to__fmap__lb(A_27a,A_27b),V0cmp),V1lb),V2t) = ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V0cmp),V2t)),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f2628(A_27a,V0cmp,V1lb))) ) ) ) ) ) ).
fof(lameq_f2629,axiom,
! [A_27a,V2ub] :
( mem(V2ub,A_27a)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V3x] : ap(f2629(A_27a,V2ub,V0cmp),V3x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V3x),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0cmp),V3x),V2ub)),c_2EternaryComparisons_2ELESS)) ) ) ).
fof(ax_thm_2Efmapal_2Ebt__to__fmap__ub,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1t] :
( mem(V1t,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V2ub] :
( mem(V2ub,A_27a)
=> ap(ap(ap(c_2Efmapal_2Ebt__to__fmap__ub(A_27a,A_27b),V0cmp),V1t),V2ub) = ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V0cmp),V1t)),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f2629(A_27a,V2ub,V0cmp))) ) ) ) ) ) ).
fof(lameq_f2630,axiom,
! [A_27a,V3ub] :
( mem(V3ub,A_27a)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1lb] :
( mem(V1lb,A_27a)
=> ! [V4x] : ap(f2630(A_27a,V3ub,V0cmp,V1lb),V4x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V4x),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0cmp),V1lb),V4x)),c_2EternaryComparisons_2ELESS)),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0cmp),V4x),V3ub)),c_2EternaryComparisons_2ELESS))) ) ) ) ).
fof(ax_thm_2Efmapal_2Ebt__to__fmap__lb__ub,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1lb] :
( mem(V1lb,A_27a)
=> ! [V2t] :
( mem(V2t,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V3ub] :
( mem(V3ub,A_27a)
=> ap(ap(ap(ap(c_2Efmapal_2Ebt__to__fmap__lb__ub(A_27a,A_27b),V0cmp),V1lb),V2t),V3ub) = ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V0cmp),V2t)),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f2630(A_27a,V3ub,V0cmp,V1lb))) ) ) ) ) ) ) ).
fof(ax_thm_2Efmapal_2Ebt__map,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ap(ap(c_2Efmapal_2Ebt__map(A_27a,A_27b),V0f),c_2Eenumeral_2Ent(A_27a)) = c_2Eenumeral_2Ent(A_27b) )
& ! [V1f] :
( mem(V1f,arr(A_27a,A_27b))
=> ! [V2l] :
( mem(V2l,ty_2Eenumeral_2Ebt(A_27a))
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4r] :
( mem(V4r,ty_2Eenumeral_2Ebt(A_27a))
=> ap(ap(c_2Efmapal_2Ebt__map(A_27a,A_27b),V1f),ap(ap(ap(c_2Eenumeral_2Enode(A_27a),V2l),V3x),V4r)) = ap(ap(ap(c_2Eenumeral_2Enode(A_27b),ap(ap(c_2Efmapal_2Ebt__map(A_27a,A_27b),V1f),V2l)),ap(V1f,V3x)),ap(ap(c_2Efmapal_2Ebt__map(A_27a,A_27b),V1f),V4r)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__FST__FDOM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1t] :
( mem(V1t,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V0cmp),V1t)) = ap(ap(c_2Eenumeral_2EENUMERAL(A_27a),V0cmp),ap(ap(c_2Efmapal_2Ebt__map(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V1t)) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__orl__lb__ub__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(A_27a,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(A_27a,bool)))))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V2lb] :
( mem(V2lb,A_27a)
=> ! [V3ub] :
( mem(V3ub,A_27a)
=> p(ap(ap(ap(ap(V0P,V1cmp),V2lb),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))),V3ub)) ) ) )
& ! [V4cmp] :
( mem(V4cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V5lb] :
( mem(V5lb,A_27a)
=> ! [V6l] :
( mem(V6l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V7x] :
( mem(V7x,A_27a)
=> ! [V8y] :
( mem(V8y,A_27b)
=> ! [V9r] :
( mem(V9r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V10ub] :
( mem(V10ub,A_27a)
=> ( ( ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V4cmp),V5lb),V7x) != c_2EternaryComparisons_2ELESS
=> p(ap(ap(ap(ap(V0P,V4cmp),V5lb),V9r),V10ub)) )
& ( ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V4cmp),V5lb),V7x) = c_2EternaryComparisons_2ELESS
& ap(ap(ap(c_2Etoto_2Eapto(A_27a),V4cmp),V7x),V10ub) != c_2EternaryComparisons_2ELESS )
=> p(ap(ap(ap(ap(V0P,V4cmp),V5lb),V6l),V10ub)) )
& ( ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V4cmp),V5lb),V7x) = c_2EternaryComparisons_2ELESS
& ap(ap(ap(c_2Etoto_2Eapto(A_27a),V4cmp),V7x),V10ub) = c_2EternaryComparisons_2ELESS )
=> p(ap(ap(ap(ap(V0P,V4cmp),V5lb),V6l),V7x)) )
& ( ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V4cmp),V5lb),V7x) = c_2EternaryComparisons_2ELESS
& ap(ap(ap(c_2Etoto_2Eapto(A_27a),V4cmp),V7x),V10ub) = c_2EternaryComparisons_2ELESS )
=> p(ap(ap(ap(ap(V0P,V4cmp),V7x),V9r),V10ub)) ) )
=> p(ap(ap(ap(ap(V0P,V4cmp),V5lb),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V6l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V7x),V8y)),V9r)),V10ub)) ) ) ) ) ) ) ) ) )
=> ! [V11v] :
( mem(V11v,ty_2Etoto_2Etoto(A_27a))
=> ! [V12v1] :
( mem(V12v1,A_27a)
=> ! [V13v2] :
( mem(V13v2,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V14v3] :
( mem(V14v3,A_27a)
=> p(ap(ap(ap(ap(V0P,V11v),V12v1),V13v2),V14v3)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__orl__lb__ub,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0ub] :
( mem(V0ub,A_27a)
=> ! [V1lb] :
( mem(V1lb,A_27a)
=> ! [V2cmp] :
( mem(V2cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ub(A_27a,A_27b),V2cmp),V1lb),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))),V0ub) = c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)) ) ) )
& ! [V3y] :
( mem(V3y,A_27b)
=> ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5ub] :
( mem(V5ub,A_27a)
=> ! [V6r] :
( mem(V6r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V7lb] :
( mem(V7lb,A_27a)
=> ! [V8l] :
( mem(V8l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V9cmp] :
( mem(V9cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ub(A_27a,A_27b),V9cmp),V7lb),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V8l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4x),V3y)),V6r)),V5ub) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V9cmp),V7lb),V4x)),c_2EternaryComparisons_2ELESS)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V9cmp),V4x),V5ub)),c_2EternaryComparisons_2ELESS)),ap(ap(c_2Elist_2EAPPEND(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Elist_2EAPPEND(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ub(A_27a,A_27b),V9cmp),V7lb),V8l),V4x)),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4x),V3y)),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))))),ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ub(A_27a,A_27b),V9cmp),V4x),V6r),V5ub))),ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ub(A_27a,A_27b),V9cmp),V7lb),V8l),V5ub))),ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ub(A_27a,A_27b),V9cmp),V7lb),V6r),V5ub)) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__orl__lb__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(A_27a,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),bool))))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V2lb] :
( mem(V2lb,A_27a)
=> p(ap(ap(ap(V0P,V1cmp),V2lb),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b)))) ) )
& ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V4lb] :
( mem(V4lb,A_27a)
=> ! [V5l] :
( mem(V5l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V6x] :
( mem(V6x,A_27a)
=> ! [V7y] :
( mem(V7y,A_27b)
=> ! [V8r] :
( mem(V8r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ( ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V3cmp),V4lb),V6x) != c_2EternaryComparisons_2ELESS
=> p(ap(ap(ap(V0P,V3cmp),V4lb),V8r)) )
& ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V3cmp),V4lb),V6x) = c_2EternaryComparisons_2ELESS
=> p(ap(ap(ap(V0P,V3cmp),V6x),V8r)) ) )
=> p(ap(ap(ap(V0P,V3cmp),V4lb),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V5l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V6x),V7y)),V8r))) ) ) ) ) ) ) ) )
=> ! [V9v] :
( mem(V9v,ty_2Etoto_2Etoto(A_27a))
=> ! [V10v1] :
( mem(V10v1,A_27a)
=> ! [V11v2] :
( mem(V11v2,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(V0P,V9v),V10v1),V11v2)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__orl__lb,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0lb] :
( mem(V0lb,A_27a)
=> ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb(A_27a,A_27b),V1cmp),V0lb),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))) = c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)) ) )
& ! [V2y] :
( mem(V2y,A_27b)
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4r] :
( mem(V4r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V5lb] :
( mem(V5lb,A_27a)
=> ! [V6l] :
( mem(V6l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V7cmp] :
( mem(V7cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb(A_27a,A_27b),V7cmp),V5lb),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V6l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3x),V2y)),V4r)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V7cmp),V5lb),V3x)),c_2EternaryComparisons_2ELESS)),ap(ap(c_2Elist_2EAPPEND(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Elist_2EAPPEND(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ub(A_27a,A_27b),V7cmp),V5lb),V6l),V3x)),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3x),V2y)),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))))),ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb(A_27a,A_27b),V7cmp),V3x),V4r))),ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb(A_27a,A_27b),V7cmp),V5lb),V4r)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__orl__ub__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(A_27a,bool))))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V2ub] :
( mem(V2ub,A_27a)
=> p(ap(ap(ap(V0P,V1cmp),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))),V2ub)) ) )
& ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V4l] :
( mem(V4l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V5x] :
( mem(V5x,A_27a)
=> ! [V6y] :
( mem(V6y,A_27b)
=> ! [V7r] :
( mem(V7r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V8ub] :
( mem(V8ub,A_27a)
=> ( ( ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V3cmp),V5x),V8ub) != c_2EternaryComparisons_2ELESS
=> p(ap(ap(ap(V0P,V3cmp),V4l),V8ub)) )
& ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V3cmp),V5x),V8ub) = c_2EternaryComparisons_2ELESS
=> p(ap(ap(ap(V0P,V3cmp),V4l),V5x)) ) )
=> p(ap(ap(ap(V0P,V3cmp),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V4l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V5x),V6y)),V7r)),V8ub)) ) ) ) ) ) ) ) )
=> ! [V9v] :
( mem(V9v,ty_2Etoto_2Etoto(A_27a))
=> ! [V10v1] :
( mem(V10v1,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V11v2] :
( mem(V11v2,A_27a)
=> p(ap(ap(ap(V0P,V9v),V10v1),V11v2)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__orl__ub,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0ub] :
( mem(V0ub,A_27a)
=> ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(c_2Efmapal_2Ebt__to__orl__ub(A_27a,A_27b),V1cmp),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))),V0ub) = c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)) ) )
& ! [V2y] :
( mem(V2y,A_27b)
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4ub] :
( mem(V4ub,A_27a)
=> ! [V5r] :
( mem(V5r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V6l] :
( mem(V6l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V7cmp] :
( mem(V7cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(c_2Efmapal_2Ebt__to__orl__ub(A_27a,A_27b),V7cmp),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V6l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3x),V2y)),V5r)),V4ub) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V7cmp),V3x),V4ub)),c_2EternaryComparisons_2ELESS)),ap(ap(c_2Elist_2EAPPEND(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Elist_2EAPPEND(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(ap(c_2Efmapal_2Ebt__to__orl__ub(A_27a,A_27b),V7cmp),V6l),V3x)),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3x),V2y)),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))))),ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ub(A_27a,A_27b),V7cmp),V3x),V5r),V4ub))),ap(ap(ap(c_2Efmapal_2Ebt__to__orl__ub(A_27a,A_27b),V7cmp),V6l),V4ub)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__orl__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),bool)))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> p(ap(ap(V0P,V1cmp),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b)))) )
& ! [V2cmp] :
( mem(V2cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V3l] :
( mem(V3l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5y] :
( mem(V5y,A_27b)
=> ! [V6r] :
( mem(V6r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(V0P,V2cmp),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V3l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4x),V5y)),V6r))) ) ) ) ) ) )
=> ! [V7v] :
( mem(V7v,ty_2Etoto_2Etoto(A_27a))
=> ! [V8v1] :
( mem(V8v1,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(V0P,V7v),V8v1)) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__orl,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1l] :
( mem(V1l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27b)
=> ! [V4r] :
( mem(V4r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ap(ap(c_2Efmapal_2Ebt__to__orl(A_27a,A_27b),V0cmp),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))) = c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))
& ap(ap(c_2Efmapal_2Ebt__to__orl(A_27a,A_27b),V0cmp),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V1l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)),V4r)) = ap(ap(c_2Elist_2EAPPEND(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Elist_2EAPPEND(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(ap(c_2Efmapal_2Ebt__to__orl__ub(A_27a,A_27b),V0cmp),V1l),V2x)),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))))),ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb(A_27a,A_27b),V0cmp),V2x),V4r)) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Efmapal_2Efmap,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_2Efmapal_2Efmap(A_27a,A_27b),V0l) = ap(ap(c_2Efinite__map_2EFUPDATE__LIST(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),ap(c_2Elist_2EREVERSE(ty_2Epair_2Eprod(A_27a,A_27b)),V0l)) ) ) ) ).
fof(lameq_f2631,axiom,
! [A_27a,A_27b,V1bt__to__orl__lb__ub__ac__tupled] :
( mem(V1bt__to__orl__lb__ub__ac__tupled,arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V5lb] :
( mem(V5lb,A_27a)
=> ! [V10m] :
( mem(V10m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V9ub] :
( mem(V9ub,A_27a)
=> ! [V13r] :
( mem(V13r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V11l] :
( mem(V11l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V14x] :
( mem(V14x,A_27a)
=> ! [V15y] : ap(f2631(A_27a,A_27b,V1bt__to__orl__lb__ub__ac__tupled,V5lb,V10m,V9ub,V13r,V3cmp,V11l,V14x),V15y) = ap(c_2Ecombin_2EI(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V3cmp),V5lb),V14x)),c_2EternaryComparisons_2ELESS)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V3cmp),V14x),V9ub)),c_2EternaryComparisons_2ELESS)),ap(V1bt__to__orl__lb__ub__ac__tupled,ap(ap(c_2Epair_2E_2C(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),V3cmp),ap(ap(c_2Epair_2E_2C(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))),V5lb),ap(ap(c_2Epair_2E_2C(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),V11l),ap(ap(c_2Epair_2E_2C(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),V14x),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V14x),V15y)),ap(V1bt__to__orl__lb__ub__ac__tupled,ap(ap(c_2Epair_2E_2C(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),V3cmp),ap(ap(c_2Epair_2E_2C(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))),V14x),ap(ap(c_2Epair_2E_2C(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),V13r),ap(ap(c_2Epair_2E_2C(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),V9ub),V10m)))))))))))),ap(V1bt__to__orl__lb__ub__ac__tupled,ap(ap(c_2Epair_2E_2C(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),V3cmp),ap(ap(c_2Epair_2E_2C(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))),V5lb),ap(ap(c_2Epair_2E_2C(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),V11l),ap(ap(c_2Epair_2E_2C(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),V9ub),V10m))))))),ap(V1bt__to__orl__lb__ub__ac__tupled,ap(ap(c_2Epair_2E_2C(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),V3cmp),ap(ap(c_2Epair_2E_2C(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))),V5lb),ap(ap(c_2Epair_2E_2C(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),V13r),ap(ap(c_2Epair_2E_2C(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),V9ub),V10m))))))) ) ) ) ) ) ) ) ) ).
fof(lameq_f2632,axiom,
! [A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled] :
( mem(V1bt__to__orl__lb__ub__ac__tupled,arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V5lb] :
( mem(V5lb,A_27a)
=> ! [V10m] :
( mem(V10m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V9ub] :
( mem(V9ub,A_27a)
=> ! [V13r] :
( mem(V13r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V11l] :
( mem(V11l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V14x] : ap(f2632(A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled,V5lb,V10m,V9ub,V13r,V3cmp,V11l),V14x) = f2631(A_27a,A_27b,V1bt__to__orl__lb__ub__ac__tupled,V5lb,V10m,V9ub,V13r,V3cmp,V11l,V14x) ) ) ) ) ) ) ) ).
fof(lameq_f2633,axiom,
! [A_27b,A_27a,V11l] :
( mem(V11l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V9ub] :
( mem(V9ub,A_27a)
=> ! [V10m] :
( mem(V10m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V5lb] :
( mem(V5lb,A_27a)
=> ! [V1bt__to__orl__lb__ub__ac__tupled] :
( mem(V1bt__to__orl__lb__ub__ac__tupled,arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V12v9] :
( mem(V12v9,ty_2Epair_2Eprod(A_27a,A_27b))
=> ! [V13r] : ap(f2633(A_27b,A_27a,V11l,V3cmp,V9ub,V10m,V5lb,V1bt__to__orl__lb__ub__ac__tupled,V12v9),V13r) = ap(ap(c_2Epair_2Epair__CASE(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),A_27a,A_27b),V12v9),f2632(A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled,V5lb,V10m,V9ub,V13r,V3cmp,V11l)) ) ) ) ) ) ) ) ).
fof(lameq_f2634,axiom,
! [A_27b,A_27a,V11l] :
( mem(V11l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V9ub] :
( mem(V9ub,A_27a)
=> ! [V10m] :
( mem(V10m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V5lb] :
( mem(V5lb,A_27a)
=> ! [V1bt__to__orl__lb__ub__ac__tupled] :
( mem(V1bt__to__orl__lb__ub__ac__tupled,arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V12v9] : ap(f2634(A_27b,A_27a,V11l,V3cmp,V9ub,V10m,V5lb,V1bt__to__orl__lb__ub__ac__tupled),V12v9) = f2633(A_27b,A_27a,V11l,V3cmp,V9ub,V10m,V5lb,V1bt__to__orl__lb__ub__ac__tupled,V12v9) ) ) ) ) ) ) ).
fof(lameq_f2635,axiom,
! [A_27b,A_27a,V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V9ub] :
( mem(V9ub,A_27a)
=> ! [V10m] :
( mem(V10m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V5lb] :
( mem(V5lb,A_27a)
=> ! [V1bt__to__orl__lb__ub__ac__tupled] :
( mem(V1bt__to__orl__lb__ub__ac__tupled,arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V11l] : ap(f2635(A_27b,A_27a,V3cmp,V9ub,V10m,V5lb,V1bt__to__orl__lb__ub__ac__tupled),V11l) = f2634(A_27b,A_27a,V11l,V3cmp,V9ub,V10m,V5lb,V1bt__to__orl__lb__ub__ac__tupled) ) ) ) ) ) ).
fof(lameq_f2636,axiom,
! [A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled] :
( mem(V1bt__to__orl__lb__ub__ac__tupled,arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V5lb] :
( mem(V5lb,A_27a)
=> ! [V9ub] :
( mem(V9ub,A_27a)
=> ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V7v4] :
( mem(V7v4,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V10m] : ap(f2636(A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled,V5lb,V9ub,V3cmp,V7v4),V10m) = ap(ap(ap(c_2Eenumeral_2Ebt__CASE(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),V7v4),ap(c_2Ecombin_2EI(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),V10m)),f2635(A_27b,A_27a,V3cmp,V9ub,V10m,V5lb,V1bt__to__orl__lb__ub__ac__tupled)) ) ) ) ) ) ).
fof(lameq_f2637,axiom,
! [A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled] :
( mem(V1bt__to__orl__lb__ub__ac__tupled,arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V5lb] :
( mem(V5lb,A_27a)
=> ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V7v4] :
( mem(V7v4,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V9ub] : ap(f2637(A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled,V5lb,V3cmp,V7v4),V9ub) = f2636(A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled,V5lb,V9ub,V3cmp,V7v4) ) ) ) ) ).
fof(lameq_f2638,axiom,
! [A_27b,A_27a,V7v4] :
( mem(V7v4,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V5lb] :
( mem(V5lb,A_27a)
=> ! [V1bt__to__orl__lb__ub__ac__tupled] :
( mem(V1bt__to__orl__lb__ub__ac__tupled,arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V8v5] : ap(f2638(A_27b,A_27a,V7v4,V3cmp,V5lb,V1bt__to__orl__lb__ub__ac__tupled),V8v5) = ap(ap(c_2Epair_2Epair__CASE(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),V8v5),f2637(A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled,V5lb,V3cmp,V7v4)) ) ) ) ) ).
fof(lameq_f2639,axiom,
! [A_27b,A_27a,V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V5lb] :
( mem(V5lb,A_27a)
=> ! [V1bt__to__orl__lb__ub__ac__tupled] :
( mem(V1bt__to__orl__lb__ub__ac__tupled,arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V7v4] : ap(f2639(A_27b,A_27a,V3cmp,V5lb,V1bt__to__orl__lb__ub__ac__tupled),V7v4) = f2638(A_27b,A_27a,V7v4,V3cmp,V5lb,V1bt__to__orl__lb__ub__ac__tupled) ) ) ) ).
fof(lameq_f2640,axiom,
! [A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled] :
( mem(V1bt__to__orl__lb__ub__ac__tupled,arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V5lb] :
( mem(V5lb,A_27a)
=> ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V6v3] : ap(f2640(A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled,V5lb,V3cmp),V6v3) = ap(ap(c_2Epair_2Epair__CASE(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))),V6v3),f2639(A_27b,A_27a,V3cmp,V5lb,V1bt__to__orl__lb__ub__ac__tupled)) ) ) ) ).
fof(lameq_f2641,axiom,
! [A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled] :
( mem(V1bt__to__orl__lb__ub__ac__tupled,arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V5lb] : ap(f2641(A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled,V3cmp),V5lb) = f2640(A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled,V5lb,V3cmp) ) ) ).
fof(lameq_f2642,axiom,
! [A_27b,A_27a,V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1bt__to__orl__lb__ub__ac__tupled] :
( mem(V1bt__to__orl__lb__ub__ac__tupled,arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V4v1] : ap(f2642(A_27b,A_27a,V3cmp,V1bt__to__orl__lb__ub__ac__tupled),V4v1) = ap(ap(c_2Epair_2Epair__CASE(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))),V4v1),f2641(A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled,V3cmp)) ) ) ).
fof(lameq_f2643,axiom,
! [A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled] :
( mem(V1bt__to__orl__lb__ub__ac__tupled,arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V3cmp] : ap(f2643(A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled),V3cmp) = f2642(A_27b,A_27a,V3cmp,V1bt__to__orl__lb__ub__ac__tupled) ) ).
fof(lameq_f2644,axiom,
! [A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled] :
( mem(V1bt__to__orl__lb__ub__ac__tupled,arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V2a] : ap(f2644(A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled),V2a) = ap(ap(c_2Epair_2Epair__CASE(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),V2a),f2643(A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled)) ) ).
fof(lameq_f2645,axiom,
! [A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled] : ap(f2645(A_27b,A_27a),V1bt__to__orl__lb__ub__ac__tupled) = f2644(A_27b,A_27a,V1bt__to__orl__lb__ub__ac__tupled) ).
fof(ax_thm_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__AUX,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),arr(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),bool)))
=> ap(c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux(A_27a,A_27b),V0R) = ap(ap(c_2Erelation_2EWFREC(ty_2Epair_2Eprod(ty_2Etoto_2Etoto(A_27a),ty_2Epair_2Eprod(A_27a,ty_2Epair_2Eprod(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Epair_2Eprod(A_27a,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),V0R),f2645(A_27b,A_27a)) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__orl__lb__ub__ac__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(A_27a,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(A_27a,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),bool))))))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V2lb] :
( mem(V2lb,A_27a)
=> ! [V3ub] :
( mem(V3ub,A_27a)
=> ! [V4m] :
( mem(V4m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(ap(ap(V0P,V1cmp),V2lb),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))),V3ub),V4m)) ) ) ) )
& ! [V5cmp] :
( mem(V5cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V6lb] :
( mem(V6lb,A_27a)
=> ! [V7l] :
( mem(V7l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V8x] :
( mem(V8x,A_27a)
=> ! [V9y] :
( mem(V9y,A_27b)
=> ! [V10r] :
( mem(V10r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V11ub] :
( mem(V11ub,A_27a)
=> ! [V12m] :
( mem(V12m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ( ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V5cmp),V6lb),V8x) != c_2EternaryComparisons_2ELESS
=> p(ap(ap(ap(ap(ap(V0P,V5cmp),V6lb),V10r),V11ub),V12m)) )
& ( ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V5cmp),V6lb),V8x) = c_2EternaryComparisons_2ELESS
& ap(ap(ap(c_2Etoto_2Eapto(A_27a),V5cmp),V8x),V11ub) != c_2EternaryComparisons_2ELESS )
=> p(ap(ap(ap(ap(ap(V0P,V5cmp),V6lb),V7l),V11ub),V12m)) )
& ( ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V5cmp),V6lb),V8x) = c_2EternaryComparisons_2ELESS
& ap(ap(ap(c_2Etoto_2Eapto(A_27a),V5cmp),V8x),V11ub) = c_2EternaryComparisons_2ELESS )
=> p(ap(ap(ap(ap(ap(V0P,V5cmp),V6lb),V7l),V8x),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V8x),V9y)),ap(ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ub__ac(A_27a,A_27b),V5cmp),V8x),V10r),V11ub),V12m)))) )
& ( ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V5cmp),V6lb),V8x) = c_2EternaryComparisons_2ELESS
& ap(ap(ap(c_2Etoto_2Eapto(A_27a),V5cmp),V8x),V11ub) = c_2EternaryComparisons_2ELESS )
=> p(ap(ap(ap(ap(ap(V0P,V5cmp),V8x),V10r),V11ub),V12m)) ) )
=> p(ap(ap(ap(ap(ap(V0P,V5cmp),V6lb),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V7l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V8x),V9y)),V10r)),V11ub),V12m)) ) ) ) ) ) ) ) ) ) )
=> ! [V13v] :
( mem(V13v,ty_2Etoto_2Etoto(A_27a))
=> ! [V14v1] :
( mem(V14v1,A_27a)
=> ! [V15v2] :
( mem(V15v2,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V16v3] :
( mem(V16v3,A_27a)
=> ! [V17v4] :
( mem(V17v4,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(ap(ap(V0P,V13v),V14v1),V15v2),V16v3),V17v4)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__orl__lb__ub__ac,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0ub] :
( mem(V0ub,A_27a)
=> ! [V1m] :
( mem(V1m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V2lb] :
( mem(V2lb,A_27a)
=> ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ub__ac(A_27a,A_27b),V3cmp),V2lb),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))),V0ub),V1m) = V1m ) ) ) )
& ! [V4y] :
( mem(V4y,A_27b)
=> ! [V5x] :
( mem(V5x,A_27a)
=> ! [V6ub] :
( mem(V6ub,A_27a)
=> ! [V7r] :
( mem(V7r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V8m] :
( mem(V8m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V9lb] :
( mem(V9lb,A_27a)
=> ! [V10l] :
( mem(V10l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V11cmp] :
( mem(V11cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ub__ac(A_27a,A_27b),V11cmp),V9lb),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V10l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V5x),V4y)),V7r)),V6ub),V8m) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V11cmp),V9lb),V5x)),c_2EternaryComparisons_2ELESS)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V11cmp),V5x),V6ub)),c_2EternaryComparisons_2ELESS)),ap(ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ub__ac(A_27a,A_27b),V11cmp),V9lb),V10l),V5x),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V5x),V4y)),ap(ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ub__ac(A_27a,A_27b),V11cmp),V5x),V7r),V6ub),V8m)))),ap(ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ub__ac(A_27a,A_27b),V11cmp),V9lb),V10l),V6ub),V8m))),ap(ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ub__ac(A_27a,A_27b),V11cmp),V9lb),V7r),V6ub),V8m)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__orl__lb__ac__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(A_27a,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),bool)))))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V2lb] :
( mem(V2lb,A_27a)
=> ! [V3m] :
( mem(V3m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(ap(V0P,V1cmp),V2lb),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))),V3m)) ) ) )
& ! [V4cmp] :
( mem(V4cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V5lb] :
( mem(V5lb,A_27a)
=> ! [V6l] :
( mem(V6l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V7x] :
( mem(V7x,A_27a)
=> ! [V8y] :
( mem(V8y,A_27b)
=> ! [V9r] :
( mem(V9r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V10m] :
( mem(V10m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ( ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V4cmp),V5lb),V7x) != c_2EternaryComparisons_2ELESS
=> p(ap(ap(ap(ap(V0P,V4cmp),V5lb),V9r),V10m)) )
& ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V4cmp),V5lb),V7x) = c_2EternaryComparisons_2ELESS
=> p(ap(ap(ap(ap(V0P,V4cmp),V7x),V9r),V10m)) ) )
=> p(ap(ap(ap(ap(V0P,V4cmp),V5lb),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V6l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V7x),V8y)),V9r)),V10m)) ) ) ) ) ) ) ) ) )
=> ! [V11v] :
( mem(V11v,ty_2Etoto_2Etoto(A_27a))
=> ! [V12v1] :
( mem(V12v1,A_27a)
=> ! [V13v2] :
( mem(V13v2,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V14v3] :
( mem(V14v3,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(ap(V0P,V11v),V12v1),V13v2),V14v3)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__orl__lb__ac,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0m] :
( mem(V0m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1lb] :
( mem(V1lb,A_27a)
=> ! [V2cmp] :
( mem(V2cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ac(A_27a,A_27b),V2cmp),V1lb),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))),V0m) = V0m ) ) )
& ! [V3y] :
( mem(V3y,A_27b)
=> ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5r] :
( mem(V5r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V6m] :
( mem(V6m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V7lb] :
( mem(V7lb,A_27a)
=> ! [V8l] :
( mem(V8l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V9cmp] :
( mem(V9cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ac(A_27a,A_27b),V9cmp),V7lb),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V8l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4x),V3y)),V5r)),V6m) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V9cmp),V7lb),V4x)),c_2EternaryComparisons_2ELESS)),ap(ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ub__ac(A_27a,A_27b),V9cmp),V7lb),V8l),V4x),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4x),V3y)),ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ac(A_27a,A_27b),V9cmp),V4x),V5r),V6m)))),ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ac(A_27a,A_27b),V9cmp),V7lb),V5r),V6m)) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__orl__ub__ac__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(A_27a,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),bool)))))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V2ub] :
( mem(V2ub,A_27a)
=> ! [V3m] :
( mem(V3m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(ap(V0P,V1cmp),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))),V2ub),V3m)) ) ) )
& ! [V4cmp] :
( mem(V4cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V5l] :
( mem(V5l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V6x] :
( mem(V6x,A_27a)
=> ! [V7y] :
( mem(V7y,A_27b)
=> ! [V8r] :
( mem(V8r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V9ub] :
( mem(V9ub,A_27a)
=> ! [V10m] :
( mem(V10m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ( ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V4cmp),V6x),V9ub) != c_2EternaryComparisons_2ELESS
=> p(ap(ap(ap(ap(V0P,V4cmp),V5l),V9ub),V10m)) )
& ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V4cmp),V6x),V9ub) = c_2EternaryComparisons_2ELESS
=> p(ap(ap(ap(ap(V0P,V4cmp),V5l),V6x),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V6x),V7y)),ap(ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ub__ac(A_27a,A_27b),V4cmp),V6x),V8r),V9ub),V10m)))) ) )
=> p(ap(ap(ap(ap(V0P,V4cmp),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V5l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V6x),V7y)),V8r)),V9ub),V10m)) ) ) ) ) ) ) ) ) )
=> ! [V11v] :
( mem(V11v,ty_2Etoto_2Etoto(A_27a))
=> ! [V12v1] :
( mem(V12v1,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V13v2] :
( mem(V13v2,A_27a)
=> ! [V14v3] :
( mem(V14v3,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(ap(V0P,V11v),V12v1),V13v2),V14v3)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__orl__ub__ac,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0ub] :
( mem(V0ub,A_27a)
=> ! [V1m] :
( mem(V1m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V2cmp] :
( mem(V2cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__ub__ac(A_27a,A_27b),V2cmp),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))),V0ub),V1m) = V1m ) ) )
& ! [V3y] :
( mem(V3y,A_27b)
=> ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5ub] :
( mem(V5ub,A_27a)
=> ! [V6r] :
( mem(V6r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V7m] :
( mem(V7m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V8l] :
( mem(V8l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V9cmp] :
( mem(V9cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__ub__ac(A_27a,A_27b),V9cmp),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V8l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4x),V3y)),V6r)),V5ub),V7m) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V9cmp),V4x),V5ub)),c_2EternaryComparisons_2ELESS)),ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__ub__ac(A_27a,A_27b),V9cmp),V8l),V4x),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4x),V3y)),ap(ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ub__ac(A_27a,A_27b),V9cmp),V4x),V6r),V5ub),V7m)))),ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__ub__ac(A_27a,A_27b),V9cmp),V8l),V5ub),V7m)) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__orl__ac__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),bool))))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V2m] :
( mem(V2m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(V0P,V1cmp),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))),V2m)) ) )
& ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V4l] :
( mem(V4l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V5x] :
( mem(V5x,A_27a)
=> ! [V6y] :
( mem(V6y,A_27b)
=> ! [V7r] :
( mem(V7r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V8m] :
( mem(V8m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(V0P,V3cmp),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V4l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V5x),V6y)),V7r)),V8m)) ) ) ) ) ) ) )
=> ! [V9v] :
( mem(V9v,ty_2Etoto_2Etoto(A_27a))
=> ! [V10v1] :
( mem(V10v1,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V11v2] :
( mem(V11v2,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(V0P,V9v),V10v1),V11v2)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__orl__ac,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1m] :
( mem(V1m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V2l] :
( mem(V2l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] :
( mem(V4y,A_27b)
=> ! [V5r] :
( mem(V5r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ap(ap(ap(c_2Efmapal_2Ebt__to__orl__ac(A_27a,A_27b),V0cmp),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))),V1m) = V1m
& ap(ap(ap(c_2Efmapal_2Ebt__to__orl__ac(A_27a,A_27b),V0cmp),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V2l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3x),V4y)),V5r)),V1m) = ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__ub__ac(A_27a,A_27b),V0cmp),V2l),V3x),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3x),V4y)),ap(ap(ap(ap(c_2Efmapal_2Ebt__to__orl__lb__ac(A_27a,A_27b),V0cmp),V3x),V5r),V1m))) ) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Efmapal_2EORWL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1f] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( p(ap(ap(ap(c_2Efmapal_2EORWL(A_27a,A_27b),V0cmp),V1f),V2l))
<=> ( V1f = ap(c_2Efmapal_2Efmap(A_27a,A_27b),V2l)
& p(ap(ap(c_2Efmapal_2EORL(A_27a,A_27b),V0cmp),V2l)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EORWL__bt__to__orl,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1t] :
( mem(V1t,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(c_2Efmapal_2EORWL(A_27a,A_27b),V0cmp),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V0cmp),V1t)),ap(ap(c_2Efmapal_2Ebt__to__orl(A_27a,A_27b),V0cmp),V1t))) ) ) ) ) ).
fof(lameq_f2646,axiom,
! [A_27b,A_27a,V2g] :
( mem(V2g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V3x] : ap(f2646(A_27b,A_27a,V2g,V0cmp),V3x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V3x),ap(ap(ap(c_2Eenumeral_2ELESS__ALL(A_27a),V0cmp),V3x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V2g))) ) ) ).
fof(ax_thm_2Efmapal_2EOFU,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1f] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2g] :
( mem(V2g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ap(ap(ap(c_2Efmapal_2EOFU(A_27a,A_27b),V0cmp),V1f),V2g) = ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V1f),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f2646(A_27b,A_27a,V2g,V0cmp)))),V2g) ) ) ) ) ) ).
fof(lameq_f2647,axiom,
! [A_27b,A_27a,V3y] :
( mem(V3y,A_27a)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1f] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V4z] : ap(f2647(A_27b,A_27a,V3y,V0cmp,V1f),V4z) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(A_27a),V4z),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),V1f))),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V0cmp),V4z),V3y)),c_2EternaryComparisons_2ELESS)) ) ) ) ).
fof(lameq_f2648,axiom,
! [A_27b,A_27a,V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1f] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V3y] : ap(f2648(A_27b,A_27a,V0cmp,V1f),V3y) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V3y),ap(c_2Ebool_2E_21(A_27a),f2647(A_27b,A_27a,V3y,V0cmp,V1f))) ) ) ).
fof(ax_thm_2Efmapal_2EUFO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1f] :
( mem(V1f,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2g] :
( mem(V2g,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ap(ap(ap(c_2Efmapal_2EUFO(A_27a,A_27b),V0cmp),V1f),V2g) = ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V1f),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V2g),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f2648(A_27b,A_27a,V0cmp,V1f)))) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebl__to__fmap__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Eenumeral_2Ebl(ty_2Epair_2Eprod(A_27a,A_27b)),bool)))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> p(ap(ap(V0P,V1cmp),c_2Eenumeral_2Enbl(ty_2Epair_2Eprod(A_27a,A_27b)))) )
& ! [V2cmp] :
( mem(V2cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V3b] :
( mem(V3b,ty_2Eenumeral_2Ebl(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( p(ap(ap(V0P,V2cmp),V3b))
=> p(ap(ap(V0P,V2cmp),ap(c_2Eenumeral_2Ezerbl(ty_2Epair_2Eprod(A_27a,A_27b)),V3b))) ) ) )
& ! [V4cmp] :
( mem(V4cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V5x] :
( mem(V5x,A_27a)
=> ! [V6y] :
( mem(V6y,A_27b)
=> ! [V7t] :
( mem(V7t,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V8b] :
( mem(V8b,ty_2Eenumeral_2Ebl(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( p(ap(ap(V0P,V4cmp),V8b))
=> p(ap(ap(V0P,V4cmp),ap(ap(ap(c_2Eenumeral_2Eonebl(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V5x),V6y)),V7t),V8b))) ) ) ) ) ) ) )
=> ! [V9v] :
( mem(V9v,ty_2Etoto_2Etoto(A_27a))
=> ! [V10v1] :
( mem(V10v1,ty_2Eenumeral_2Ebl(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(V0P,V9v),V10v1)) ) ) ) ) ) ) ).
fof(lameq_f2649,axiom,
! [A_27a,V6cmp] :
( mem(V6cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V4x] :
( mem(V4x,A_27a)
=> ! [V8z] : ap(f2649(A_27a,V6cmp,V4x),V8z) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V8z),ap(ap(c_2Emin_2E_3D(ty_2EternaryComparisons_2Eordering),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V6cmp),V4x),V8z)),c_2EternaryComparisons_2ELESS)) ) ) ).
fof(conj_thm_2Efmapal_2Ebl__to__fmap,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(c_2Efmapal_2Ebl__to__fmap(A_27a,A_27b),V0cmp),c_2Eenumeral_2Enbl(ty_2Epair_2Eprod(A_27a,A_27b))) = c_2Efinite__map_2EFEMPTY(A_27a,A_27b) )
& ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V2b] :
( mem(V2b,ty_2Eenumeral_2Ebl(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ap(ap(c_2Efmapal_2Ebl__to__fmap(A_27a,A_27b),V1cmp),ap(c_2Eenumeral_2Ezerbl(ty_2Epair_2Eprod(A_27a,A_27b)),V2b)) = ap(ap(c_2Efmapal_2Ebl__to__fmap(A_27a,A_27b),V1cmp),V2b) ) )
& ! [V3y] :
( mem(V3y,A_27b)
=> ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5t] :
( mem(V5t,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V6cmp] :
( mem(V6cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V7b] :
( mem(V7b,ty_2Eenumeral_2Ebl(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ap(ap(c_2Efmapal_2Ebl__to__fmap(A_27a,A_27b),V6cmp),ap(ap(ap(c_2Eenumeral_2Eonebl(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4x),V3y)),V5t),V7b)) = ap(ap(ap(c_2Efmapal_2EOFU(A_27a,A_27b),V6cmp),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4x),V3y))),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V6cmp),V5t)),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f2649(A_27a,V6cmp,V4x))))),ap(ap(c_2Efmapal_2Ebl__to__fmap(A_27a,A_27b),V6cmp),V7b)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__to__orl__ID__IMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( p(ap(ap(c_2Efmapal_2EORL(A_27a,A_27b),V0cmp),V1l))
=> ap(ap(c_2Efmapal_2Ebt__to__orl(A_27a,A_27b),V0cmp),ap(c_2Eenumeral_2Elist__to__bt(ty_2Epair_2Eprod(A_27a,A_27b)),V1l)) = V1l ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Efmap__FDOM,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_2Efinite__map_2EFDOM(A_27a,A_27b),ap(c_2Efmapal_2Efmap(A_27a,A_27b),V0l)) = ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST(A_27a,A_27b)),V0l)) ) ) ) ).
fof(conj_thm_2Efmapal_2EORL__FUNION__IMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( p(ap(ap(c_2Efmapal_2EORL(A_27a,A_27b),V0cmp),V1l))
=> ! [V2m] :
( mem(V2m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( p(ap(ap(c_2Efmapal_2EORL(A_27a,A_27b),V0cmp),V2m))
=> ( p(ap(ap(c_2Efmapal_2EORL(A_27a,A_27b),V0cmp),ap(ap(ap(c_2Efmapal_2Emerge(A_27a,A_27b),V0cmp),V1l),V2m)))
& ap(c_2Efmapal_2Efmap(A_27a,A_27b),ap(ap(ap(c_2Efmapal_2Emerge(A_27a,A_27b),V0cmp),V1l),V2m)) = ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),ap(c_2Efmapal_2Efmap(A_27a,A_27b),V1l)),ap(c_2Efmapal_2Efmap(A_27a,A_27b),V2m)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EFMAPAL__FDOM__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V0cmp),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))))))
<=> $false ) ) )
& ! [V2cmp] :
( mem(V2cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4a] :
( mem(V4a,A_27a)
=> ! [V5b] :
( mem(V5b,A_27b)
=> ! [V6l] :
( mem(V6l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V7r] :
( mem(V7r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V2cmp),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V6l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4a),V5b)),V7r)))))
<=> p(ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(bool),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V2cmp),V3x),V4a)),ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V2cmp),V6l)))),c_2Ebool_2ET),ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V2cmp),V7r))))) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Einter__merge__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),arr(ty_2Elist_2Elist(A_27a),bool))))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> p(ap(ap(ap(V0P,V1cmp),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2ENIL(A_27a))) )
& ! [V2cmp] :
( mem(V2cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V3a] :
( mem(V3a,A_27a)
=> ! [V4b] :
( mem(V4b,A_27b)
=> ! [V5l] :
( mem(V5l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(V0P,V2cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3a),V4b)),V5l)),c_2Elist_2ENIL(A_27a))) ) ) ) )
& ! [V6cmp] :
( mem(V6cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V7y] :
( mem(V7y,A_27a)
=> ! [V8m] :
( mem(V8m,ty_2Elist_2Elist(A_27a))
=> p(ap(ap(ap(V0P,V6cmp),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(c_2Elist_2ECONS(A_27a),V7y),V8m))) ) ) )
& ! [V9cmp] :
( mem(V9cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V10a] :
( mem(V10a,A_27a)
=> ! [V11b] :
( mem(V11b,A_27b)
=> ! [V12l] :
( mem(V12l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V13y] :
( mem(V13y,A_27a)
=> ! [V14m] :
( mem(V14m,ty_2Elist_2Elist(A_27a))
=> ( ( ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V9cmp),V10a),V13y) = c_2EternaryComparisons_2EEQUAL
=> p(ap(ap(ap(V0P,V9cmp),V12l),V14m)) )
& ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V9cmp),V10a),V13y) = c_2EternaryComparisons_2EGREATER
=> p(ap(ap(ap(V0P,V9cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V10a),V11b)),V12l)),V14m)) )
& ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V9cmp),V10a),V13y) = c_2EternaryComparisons_2ELESS
=> p(ap(ap(ap(V0P,V9cmp),V12l),ap(ap(c_2Elist_2ECONS(A_27a),V13y),V14m))) ) )
=> p(ap(ap(ap(V0P,V9cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V10a),V11b)),V12l)),ap(ap(c_2Elist_2ECONS(A_27a),V13y),V14m))) ) ) ) ) ) ) ) )
=> ! [V15v] :
( mem(V15v,ty_2Etoto_2Etoto(A_27a))
=> ! [V16v1] :
( mem(V16v1,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V17v2] :
( mem(V17v2,ty_2Elist_2Elist(A_27a))
=> p(ap(ap(ap(V0P,V15v),V16v1),V17v2)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Einter__merge,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(c_2Efmapal_2Einter__merge(A_27a,A_27b),V0cmp),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)) )
& ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V2cmp] :
( mem(V2cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V3b] :
( mem(V3b,A_27b)
=> ! [V4a] :
( mem(V4a,A_27a)
=> ap(ap(ap(c_2Efmapal_2Einter__merge(A_27a,A_27b),V2cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4a),V3b)),V1l)),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)) ) ) ) )
& ! [V5y] :
( mem(V5y,A_27a)
=> ! [V6m] :
( mem(V6m,ty_2Elist_2Elist(A_27a))
=> ! [V7cmp] :
( mem(V7cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(c_2Efmapal_2Einter__merge(A_27a,A_27b),V7cmp),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(c_2Elist_2ECONS(A_27a),V5y),V6m)) = c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)) ) ) )
& ! [V8y] :
( mem(V8y,A_27a)
=> ! [V9m] :
( mem(V9m,ty_2Elist_2Elist(A_27a))
=> ! [V10l] :
( mem(V10l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V11cmp] :
( mem(V11cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V12b] :
( mem(V12b,A_27b)
=> ! [V13a] :
( mem(V13a,A_27a)
=> ap(ap(ap(c_2Efmapal_2Einter__merge(A_27a,A_27b),V11cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V13a),V12b)),V10l)),ap(ap(c_2Elist_2ECONS(A_27a),V8y),V9m)) = ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V11cmp),V13a),V8y)),ap(ap(ap(c_2Efmapal_2Einter__merge(A_27a,A_27b),V11cmp),V10l),ap(ap(c_2Elist_2ECONS(A_27a),V8y),V9m))),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V13a),V12b)),ap(ap(ap(c_2Efmapal_2Einter__merge(A_27a,A_27b),V11cmp),V10l),V9m))),ap(ap(ap(c_2Efmapal_2Einter__merge(A_27a,A_27b),V11cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V13a),V12b)),V10l)),V9m)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EORL__DRESTRICT__IMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( p(ap(ap(c_2Efmapal_2EORL(A_27a,A_27b),V0cmp),V1l))
=> ! [V2m] :
( mem(V2m,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Eenumeral_2EOL(A_27a),V0cmp),V2m))
=> ( p(ap(ap(c_2Efmapal_2EORL(A_27a,A_27b),V0cmp),ap(ap(ap(c_2Efmapal_2Einter__merge(A_27a,A_27b),V0cmp),V1l),V2m)))
& ap(c_2Efmapal_2Efmap(A_27a,A_27b),ap(ap(ap(c_2Efmapal_2Einter__merge(A_27a,A_27b),V0cmp),V1l),V2m)) = ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),ap(c_2Efmapal_2Efmap(A_27a,A_27b),V1l)),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2m)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ediff__merge__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),arr(ty_2Elist_2Elist(A_27a),bool))))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> p(ap(ap(ap(V0P,V1cmp),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2ENIL(A_27a))) )
& ! [V2cmp] :
( mem(V2cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V3a] :
( mem(V3a,A_27a)
=> ! [V4b] :
( mem(V4b,A_27b)
=> ! [V5l] :
( mem(V5l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(V0P,V2cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3a),V4b)),V5l)),c_2Elist_2ENIL(A_27a))) ) ) ) )
& ! [V6cmp] :
( mem(V6cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V7y] :
( mem(V7y,A_27a)
=> ! [V8m] :
( mem(V8m,ty_2Elist_2Elist(A_27a))
=> p(ap(ap(ap(V0P,V6cmp),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(c_2Elist_2ECONS(A_27a),V7y),V8m))) ) ) )
& ! [V9cmp] :
( mem(V9cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V10a] :
( mem(V10a,A_27a)
=> ! [V11b] :
( mem(V11b,A_27b)
=> ! [V12l] :
( mem(V12l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V13y] :
( mem(V13y,A_27a)
=> ! [V14m] :
( mem(V14m,ty_2Elist_2Elist(A_27a))
=> ( ( ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V9cmp),V10a),V13y) = c_2EternaryComparisons_2EEQUAL
=> p(ap(ap(ap(V0P,V9cmp),V12l),V14m)) )
& ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V9cmp),V10a),V13y) = c_2EternaryComparisons_2EGREATER
=> p(ap(ap(ap(V0P,V9cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V10a),V11b)),V12l)),V14m)) )
& ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V9cmp),V10a),V13y) = c_2EternaryComparisons_2ELESS
=> p(ap(ap(ap(V0P,V9cmp),V12l),ap(ap(c_2Elist_2ECONS(A_27a),V13y),V14m))) ) )
=> p(ap(ap(ap(V0P,V9cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V10a),V11b)),V12l)),ap(ap(c_2Elist_2ECONS(A_27a),V13y),V14m))) ) ) ) ) ) ) ) )
=> ! [V15v] :
( mem(V15v,ty_2Etoto_2Etoto(A_27a))
=> ! [V16v1] :
( mem(V16v1,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V17v2] :
( mem(V17v2,ty_2Elist_2Elist(A_27a))
=> p(ap(ap(ap(V0P,V15v),V16v1),V17v2)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ediff__merge,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(c_2Efmapal_2Ediff__merge(A_27a,A_27b),V0cmp),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)) )
& ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V2cmp] :
( mem(V2cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V3b] :
( mem(V3b,A_27b)
=> ! [V4a] :
( mem(V4a,A_27a)
=> ap(ap(ap(c_2Efmapal_2Ediff__merge(A_27a,A_27b),V2cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4a),V3b)),V1l)),c_2Elist_2ENIL(A_27a)) = ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4a),V3b)),V1l) ) ) ) )
& ! [V5y] :
( mem(V5y,A_27a)
=> ! [V6m] :
( mem(V6m,ty_2Elist_2Elist(A_27a))
=> ! [V7cmp] :
( mem(V7cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(c_2Efmapal_2Ediff__merge(A_27a,A_27b),V7cmp),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(c_2Elist_2ECONS(A_27a),V5y),V6m)) = c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)) ) ) )
& ! [V8y] :
( mem(V8y,A_27a)
=> ! [V9m] :
( mem(V9m,ty_2Elist_2Elist(A_27a))
=> ! [V10l] :
( mem(V10l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V11cmp] :
( mem(V11cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V12b] :
( mem(V12b,A_27b)
=> ! [V13a] :
( mem(V13a,A_27a)
=> ap(ap(ap(c_2Efmapal_2Ediff__merge(A_27a,A_27b),V11cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V13a),V12b)),V10l)),ap(ap(c_2Elist_2ECONS(A_27a),V8y),V9m)) = ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V11cmp),V13a),V8y)),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V13a),V12b)),ap(ap(ap(c_2Efmapal_2Ediff__merge(A_27a,A_27b),V11cmp),V10l),ap(ap(c_2Elist_2ECONS(A_27a),V8y),V9m)))),ap(ap(ap(c_2Efmapal_2Ediff__merge(A_27a,A_27b),V11cmp),V10l),V9m)),ap(ap(ap(c_2Efmapal_2Ediff__merge(A_27a,A_27b),V11cmp),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V13a),V12b)),V10l)),V9m)) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EORL__DRESTRICT__COMPL__IMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( p(ap(ap(c_2Efmapal_2EORL(A_27a,A_27b),V0cmp),V1l))
=> ! [V2m] :
( mem(V2m,ty_2Elist_2Elist(A_27a))
=> ( p(ap(ap(c_2Eenumeral_2EOL(A_27a),V0cmp),V2m))
=> ( p(ap(ap(c_2Efmapal_2EORL(A_27a,A_27b),V0cmp),ap(ap(ap(c_2Efmapal_2Ediff__merge(A_27a,A_27b),V0cmp),V1l),V2m)))
& ap(c_2Efmapal_2Efmap(A_27a,A_27b),ap(ap(ap(c_2Efmapal_2Ediff__merge(A_27a,A_27b),V0cmp),V1l),V2m)) = ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),ap(c_2Efmapal_2Efmap(A_27a,A_27b),V1l)),ap(c_2Epred__set_2ECOMPL(A_27a),ap(c_2Elist_2ELIST__TO__SET(A_27a),V2m))) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EFMAPAL__fmap,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ap(c_2Efmapal_2Efmap(A_27a,A_27b),V1l) = ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V0cmp),ap(c_2Eenumeral_2Elist__to__bt(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Efmapal_2Eincr__sort(A_27a,A_27b),V0cmp),V1l))) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EORL__FMAPAL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( p(ap(ap(c_2Efmapal_2EORL(A_27a,A_27b),V0cmp),V1l))
=> ap(c_2Efmapal_2Efmap(A_27a,A_27b),V1l) = ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V0cmp),ap(c_2Eenumeral_2Elist__to__bt(ty_2Epair_2Eprod(A_27a,A_27b)),V1l)) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EORWL__FUNION__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1s] :
( mem(V1s,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V3t] :
( mem(V3t,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V4m] :
( mem(V4m,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ( p(ap(ap(ap(c_2Efmapal_2EORWL(A_27a,A_27b),V0cmp),V1s),V2l))
& p(ap(ap(ap(c_2Efmapal_2EORWL(A_27a,A_27b),V0cmp),V3t),V4m)) )
=> p(ap(ap(ap(c_2Efmapal_2EORWL(A_27a,A_27b),V0cmp),ap(ap(c_2Efinite__map_2EFUNION(A_27a,A_27b),V1s),V3t)),ap(ap(ap(c_2Efmapal_2Emerge(A_27a,A_27b),V0cmp),V2l),V4m))) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EORWL__DRESTRICT__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1s] :
( mem(V1s,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V3t] :
( mem(V3t,arr(A_27a,bool))
=> ! [V4m] :
( mem(V4m,ty_2Elist_2Elist(A_27a))
=> ( ( p(ap(ap(ap(c_2Efmapal_2EORWL(A_27a,A_27b),V0cmp),V1s),V2l))
& p(ap(ap(ap(c_2Eenumeral_2EOWL(A_27a),V0cmp),V3t),V4m)) )
=> p(ap(ap(ap(c_2Efmapal_2EORWL(A_27a,A_27b),V0cmp),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V1s),V3t)),ap(ap(ap(c_2Efmapal_2Einter__merge(A_27a,A_27b),V0cmp),V2l),V4m))) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EORWL__DRESTRICT__COMPL__THM,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1s] :
( mem(V1s,ty_2Efinite__map_2Efmap(A_27a,A_27b))
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V3t] :
( mem(V3t,arr(A_27a,bool))
=> ! [V4m] :
( mem(V4m,ty_2Elist_2Elist(A_27a))
=> ( ( p(ap(ap(ap(c_2Efmapal_2EORWL(A_27a,A_27b),V0cmp),V1s),V2l))
& p(ap(ap(ap(c_2Eenumeral_2EOWL(A_27a),V0cmp),V3t),V4m)) )
=> p(ap(ap(ap(c_2Efmapal_2EORWL(A_27a,A_27b),V0cmp),ap(ap(c_2Efinite__map_2EDRESTRICT(A_27a,A_27b),V1s),ap(c_2Epred__set_2ECOMPL(A_27a),V3t))),ap(ap(ap(c_2Efmapal_2Ediff__merge(A_27a,A_27b),V0cmp),V2l),V4m))) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Efmapal_2EAP__SND,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27b,A_27c))
=> ! [V1a] :
( mem(V1a,A_27a)
=> ! [V2b] :
( mem(V2b,A_27b)
=> ap(ap(c_2Efmapal_2EAP__SND(A_27a,A_27b,A_27c),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1a),V2b)) = ap(ap(c_2Epair_2E_2C(A_27a,A_27c),V1a),ap(V0f,V2b)) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Eo__f__bt__map,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1f] :
( mem(V1f,arr(A_27b,A_27c))
=> ! [V2t] :
( mem(V2t,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27b,A_27c),V1f),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V0cmp),V2t)) = ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27c),V0cmp),ap(ap(c_2Efmapal_2Ebt__map(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27a,A_27c)),ap(c_2Efmapal_2EAP__SND(A_27a,A_27b,A_27c),V1f)),V2t)) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EFAPPLY__fmap__NIL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(c_2Efmapal_2Efmap(A_27a,A_27b),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)))),V0x) = ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),c_2Efinite__map_2EFEMPTY(A_27a,A_27b)),V0x) ) ) ) ).
fof(conj_thm_2Efmapal_2EFAPPLY__fmap__CONS,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1y] :
( mem(V1y,A_27a)
=> ! [V2z] :
( mem(V2z,A_27b)
=> ! [V3l] :
( mem(V3l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(c_2Efmapal_2Efmap(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),V1y),V2z)),V3l))),V0x) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(ap(c_2Emin_2E_3D(A_27a),V0x),V1y)),V2z),ap(ap(c_2Efinite__map_2EFAPPLY(A_27a,A_27b),ap(c_2Efmapal_2Efmap(A_27a,A_27b),V3l)),V0x)) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Eo__f__fmap,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [A_27c] :
( ne(A_27c)
=> ! [V0f] :
( mem(V0f,arr(A_27b,A_27c))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ap(ap(c_2Efinite__map_2Eo__f(A_27a,A_27b,A_27c),V0f),ap(c_2Efmapal_2Efmap(A_27a,A_27b),V1l)) = ap(c_2Efmapal_2Efmap(A_27a,A_27c),ap(ap(c_2Elist_2EMAP(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27a,A_27c)),ap(c_2Efmapal_2EAP__SND(A_27a,A_27b,A_27c),V0f)),V1l)) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EORL__bt__lb__ub__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(A_27a,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(A_27a,bool)))))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V2lb] :
( mem(V2lb,A_27a)
=> ! [V3ub] :
( mem(V3ub,A_27a)
=> p(ap(ap(ap(ap(V0P,V1cmp),V2lb),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))),V3ub)) ) ) )
& ! [V4cmp] :
( mem(V4cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V5lb] :
( mem(V5lb,A_27a)
=> ! [V6l] :
( mem(V6l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V7x] :
( mem(V7x,A_27a)
=> ! [V8y] :
( mem(V8y,A_27b)
=> ! [V9r] :
( mem(V9r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V10ub] :
( mem(V10ub,A_27a)
=> ( ( p(ap(ap(ap(ap(V0P,V4cmp),V5lb),V6l),V7x))
& p(ap(ap(ap(ap(V0P,V4cmp),V7x),V9r),V10ub)) )
=> p(ap(ap(ap(ap(V0P,V4cmp),V5lb),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V6l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V7x),V8y)),V9r)),V10ub)) ) ) ) ) ) ) ) ) )
=> ! [V11v] :
( mem(V11v,ty_2Etoto_2Etoto(A_27a))
=> ! [V12v1] :
( mem(V12v1,A_27a)
=> ! [V13v2] :
( mem(V13v2,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V14v3] :
( mem(V14v3,A_27a)
=> p(ap(ap(ap(ap(V0P,V11v),V12v1),V13v2),V14v3)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EORL__bt__lb__ub,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0ub] :
( mem(V0ub,A_27a)
=> ! [V1lb] :
( mem(V1lb,A_27a)
=> ! [V2cmp] :
( mem(V2cmp,ty_2Etoto_2Etoto(A_27a))
=> ( p(ap(ap(ap(ap(c_2Efmapal_2EORL__bt__lb__ub(A_27a,A_27b),V2cmp),V1lb),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))),V0ub))
<=> ap(ap(ap(c_2Etoto_2Eapto(A_27a),V2cmp),V1lb),V0ub) = c_2EternaryComparisons_2ELESS ) ) ) )
& ! [V3y] :
( mem(V3y,A_27b)
=> ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5ub] :
( mem(V5ub,A_27a)
=> ! [V6r] :
( mem(V6r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V7lb] :
( mem(V7lb,A_27a)
=> ! [V8l] :
( mem(V8l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V9cmp] :
( mem(V9cmp,ty_2Etoto_2Etoto(A_27a))
=> ( p(ap(ap(ap(ap(c_2Efmapal_2EORL__bt__lb__ub(A_27a,A_27b),V9cmp),V7lb),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V8l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4x),V3y)),V6r)),V5ub))
<=> ( p(ap(ap(ap(ap(c_2Efmapal_2EORL__bt__lb__ub(A_27a,A_27b),V9cmp),V7lb),V8l),V4x))
& p(ap(ap(ap(ap(c_2Efmapal_2EORL__bt__lb__ub(A_27a,A_27b),V9cmp),V4x),V6r),V5ub)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EORL__bt__lb__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(A_27a,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),bool))))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V2lb] :
( mem(V2lb,A_27a)
=> p(ap(ap(ap(V0P,V1cmp),V2lb),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b)))) ) )
& ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V4lb] :
( mem(V4lb,A_27a)
=> ! [V5l] :
( mem(V5l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V6x] :
( mem(V6x,A_27a)
=> ! [V7y] :
( mem(V7y,A_27b)
=> ! [V8r] :
( mem(V8r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( p(ap(ap(ap(V0P,V3cmp),V6x),V8r))
=> p(ap(ap(ap(V0P,V3cmp),V4lb),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V5l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V6x),V7y)),V8r))) ) ) ) ) ) ) ) )
=> ! [V9v] :
( mem(V9v,ty_2Etoto_2Etoto(A_27a))
=> ! [V10v1] :
( mem(V10v1,A_27a)
=> ! [V11v2] :
( mem(V11v2,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(V0P,V9v),V10v1),V11v2)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EORL__bt__lb,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0lb] :
( mem(V0lb,A_27a)
=> ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ( p(ap(ap(ap(c_2Efmapal_2EORL__bt__lb(A_27a,A_27b),V1cmp),V0lb),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))))
<=> $true ) ) )
& ! [V2y] :
( mem(V2y,A_27b)
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4r] :
( mem(V4r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V5lb] :
( mem(V5lb,A_27a)
=> ! [V6l] :
( mem(V6l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V7cmp] :
( mem(V7cmp,ty_2Etoto_2Etoto(A_27a))
=> ( p(ap(ap(ap(c_2Efmapal_2EORL__bt__lb(A_27a,A_27b),V7cmp),V5lb),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V6l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3x),V2y)),V4r)))
<=> ( p(ap(ap(ap(ap(c_2Efmapal_2EORL__bt__lb__ub(A_27a,A_27b),V7cmp),V5lb),V6l),V3x))
& p(ap(ap(ap(c_2Efmapal_2EORL__bt__lb(A_27a,A_27b),V7cmp),V3x),V4r)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EORL__bt__ub__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(A_27a,bool))))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V2ub] :
( mem(V2ub,A_27a)
=> p(ap(ap(ap(V0P,V1cmp),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))),V2ub)) ) )
& ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V4l] :
( mem(V4l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V5x] :
( mem(V5x,A_27a)
=> ! [V6y] :
( mem(V6y,A_27b)
=> ! [V7r] :
( mem(V7r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V8ub] :
( mem(V8ub,A_27a)
=> ( p(ap(ap(ap(V0P,V3cmp),V4l),V5x))
=> p(ap(ap(ap(V0P,V3cmp),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V4l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V5x),V6y)),V7r)),V8ub)) ) ) ) ) ) ) ) )
=> ! [V9v] :
( mem(V9v,ty_2Etoto_2Etoto(A_27a))
=> ! [V10v1] :
( mem(V10v1,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V11v2] :
( mem(V11v2,A_27a)
=> p(ap(ap(ap(V0P,V9v),V10v1),V11v2)) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EORL__bt__ub,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0ub] :
( mem(V0ub,A_27a)
=> ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ( p(ap(ap(ap(c_2Efmapal_2EORL__bt__ub(A_27a,A_27b),V1cmp),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))),V0ub))
<=> $true ) ) )
& ! [V2y] :
( mem(V2y,A_27b)
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4ub] :
( mem(V4ub,A_27a)
=> ! [V5r] :
( mem(V5r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V6l] :
( mem(V6l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V7cmp] :
( mem(V7cmp,ty_2Etoto_2Etoto(A_27a))
=> ( p(ap(ap(ap(c_2Efmapal_2EORL__bt__ub(A_27a,A_27b),V7cmp),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V6l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3x),V2y)),V5r)),V4ub))
<=> ( p(ap(ap(ap(c_2Efmapal_2EORL__bt__ub(A_27a,A_27b),V7cmp),V6l),V3x))
& p(ap(ap(ap(ap(c_2Efmapal_2EORL__bt__lb__ub(A_27a,A_27b),V7cmp),V3x),V5r),V4ub)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EORL__bt__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),bool)))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> p(ap(ap(V0P,V1cmp),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b)))) )
& ! [V2cmp] :
( mem(V2cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V3l] :
( mem(V3l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5y] :
( mem(V5y,A_27b)
=> ! [V6r] :
( mem(V6r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(V0P,V2cmp),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V3l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4x),V5y)),V6r))) ) ) ) ) ) )
=> ! [V7v] :
( mem(V7v,ty_2Etoto_2Etoto(A_27a))
=> ! [V8v1] :
( mem(V8v1,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(V0P,V7v),V8v1)) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2EORL__bt,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1l] :
( mem(V1l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27b)
=> ! [V4r] :
( mem(V4r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( ( p(ap(ap(c_2Efmapal_2EORL__bt(A_27a,A_27b),V0cmp),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))))
<=> $true )
& ( p(ap(ap(c_2Efmapal_2EORL__bt(A_27a,A_27b),V0cmp),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V1l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)),V4r)))
<=> ( p(ap(ap(ap(c_2Efmapal_2EORL__bt__ub(A_27a,A_27b),V0cmp),V1l),V2x))
& p(ap(ap(ap(c_2Efmapal_2EORL__bt__lb(A_27a,A_27b),V0cmp),V2x),V4r)) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebetter__bt__to__orl,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1t] :
( mem(V1t,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ap(ap(c_2Efmapal_2Ebt__to__orl(A_27a,A_27b),V0cmp),V1t) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(c_2Efmapal_2EORL__bt(A_27a,A_27b),V0cmp),V1t)),ap(ap(c_2Eenumeral_2Ebt__to__list__ac(ty_2Epair_2Eprod(A_27a,A_27b)),V1t),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)))),ap(ap(ap(c_2Efmapal_2Ebt__to__orl__ac(A_27a,A_27b),V0cmp),V1t),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)))) ) ) ) ) ).
fof(lameq_f2650,axiom,
! [A_27b,A_27a,V7z] :
( mem(V7z,A_27b)
=> ! [V6w] :
( mem(V6w,A_27a)
=> ! [V9cn] :
( mem(V9cn,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V10m] : ap(f2650(A_27b,A_27a,V7z,V6w,V9cn),V10m) = ap(V9cn,ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V6w),V7z)),V10m)) ) ) ) ).
fof(conj_thm_2Efmapal_2Elist__rplacv__cn__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),arr(arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),bool))))
=> ( ( ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27b)
=> ! [V3cn] :
( mem(V3cn,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> p(ap(ap(ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))),V3cn)) ) ) )
& ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5y] :
( mem(V5y,A_27b)
=> ! [V6w] :
( mem(V6w,A_27a)
=> ! [V7z] :
( mem(V7z,A_27b)
=> ! [V8l] :
( mem(V8l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V9cn] :
( mem(V9cn,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ( ( V4x != V6w
=> p(ap(ap(ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4x),V5y)),V8l),f2650(A_27b,A_27a,V7z,V6w,V9cn))) )
=> p(ap(ap(ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4x),V5y)),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V6w),V7z)),V8l)),V9cn)) ) ) ) ) ) ) ) )
=> ! [V11v] :
( mem(V11v,A_27a)
=> ! [V12v1] :
( mem(V12v1,A_27b)
=> ! [V13v2] :
( mem(V13v2,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V14v3] :
( mem(V14v3,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> p(ap(ap(ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V11v),V12v1)),V13v2),V14v3)) ) ) ) ) ) ) ) ) ).
fof(lameq_f2651,axiom,
! [A_27b,A_27a,V3z] :
( mem(V3z,A_27b)
=> ! [V6w] :
( mem(V6w,A_27a)
=> ! [V8cn] :
( mem(V8cn,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V9m] : ap(f2651(A_27b,A_27a,V3z,V6w,V8cn),V9m) = ap(V8cn,ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V6w),V3z)),V9m)) ) ) ) ).
fof(conj_thm_2Efmapal_2Elist__rplacv__cn,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0y] :
( mem(V0y,A_27b)
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2cn] :
( mem(V2cn,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ap(ap(ap(c_2Efmapal_2Elist__rplacv__cn(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V0y)),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))),V2cn) = c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)) ) ) )
& ! [V3z] :
( mem(V3z,A_27b)
=> ! [V4y] :
( mem(V4y,A_27b)
=> ! [V5x] :
( mem(V5x,A_27a)
=> ! [V6w] :
( mem(V6w,A_27a)
=> ! [V7l] :
( mem(V7l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V8cn] :
( mem(V8cn,arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ap(ap(ap(c_2Efmapal_2Elist__rplacv__cn(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V5x),V4y)),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V6w),V3z)),V7l)),V8cn) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(c_2Emin_2E_3D(A_27a),V5x),V6w)),ap(V8cn,ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V5x),V4y)),V7l))),ap(ap(ap(c_2Efmapal_2Elist__rplacv__cn(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V5x),V4y)),V7l),f2651(A_27b,A_27a,V3z,V6w,V8cn))) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Efmap__FDOM__rec,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0x] :
( mem(V0x,A_27a)
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(c_2Efmapal_2Efmap(A_27a,A_27b),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b))))))
<=> $false ) )
& ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2w] :
( mem(V2w,A_27a)
=> ! [V3z] :
( mem(V3z,A_27b)
=> ! [V4l] :
( mem(V4l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(c_2Efmapal_2Efmap(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),V2w),V3z)),V4l)))))
<=> ( V1x = V2w
| p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(c_2Efmapal_2Efmap(A_27a,A_27b),V4l)))) ) ) ) ) ) ) ) ) ) ).
fof(lameq_f2652,axiom,
! [A_27b,A_27a,V1y] :
( mem(V1y,A_27b)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ! [V2l] :
( mem(V2l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V3ans] : ap(f2652(A_27b,A_27a,V1y,V0x,V2l),V3ans) = ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b))),V3ans),c_2Elist_2ENIL(ty_2Epair_2Eprod(A_27a,A_27b)))),ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(c_2Efmapal_2Efmap(A_27a,A_27b),V2l))))),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(c_2Efmapal_2Efmap(A_27a,A_27b),V2l)))),ap(ap(c_2Emin_2E_3D(ty_2Efinite__map_2Efmap(A_27a,A_27b)),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(c_2Efmapal_2Efmap(A_27a,A_27b),V2l)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y))),ap(c_2Efmapal_2Efmap(A_27a,A_27b),V3ans)))) ) ) ) ).
fof(conj_thm_2Efmapal_2Elist__rplacv__thm,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_2ELET(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)),bool),f2652(A_27b,A_27a,V1y,V0x,V2l)),ap(ap(ap(c_2Efmapal_2Elist__rplacv__cn(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)),V2l),i(ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))))) ) ) ) ) ) ).
fof(lameq_f2653,axiom,
! [A_27b,A_27a,V10z] :
( mem(V10z,A_27b)
=> ! [V9w] :
( mem(V9w,A_27a)
=> ! [V8l] :
( mem(V8l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V12cn] :
( mem(V12cn,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V13m] : ap(f2653(A_27b,A_27a,V10z,V9w,V8l,V12cn),V13m) = ap(V12cn,ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V8l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V9w),V10z)),V13m)) ) ) ) ) ).
fof(lameq_f2654,axiom,
! [A_27b,A_27a,V11r] :
( mem(V11r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V10z] :
( mem(V10z,A_27b)
=> ! [V9w] :
( mem(V9w,A_27a)
=> ! [V12cn] :
( mem(V12cn,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V14m] : ap(f2654(A_27b,A_27a,V11r,V10z,V9w,V12cn),V14m) = ap(V12cn,ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V14m),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V9w),V10z)),V11r)) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__rplacv__cn__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0P] :
( mem(V0P,arr(ty_2Etoto_2Etoto(A_27a),arr(ty_2Epair_2Eprod(A_27a,A_27b),arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),arr(arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b))),bool)))))
=> ( ( ! [V1cmp] :
( mem(V1cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V2x] :
( mem(V2x,A_27a)
=> ! [V3y] :
( mem(V3y,A_27b)
=> ! [V4cn] :
( mem(V4cn,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b))))
=> p(ap(ap(ap(ap(V0P,V1cmp),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))),V4cn)) ) ) ) )
& ! [V5cmp] :
( mem(V5cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V6x] :
( mem(V6x,A_27a)
=> ! [V7y] :
( mem(V7y,A_27b)
=> ! [V8l] :
( mem(V8l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V9w] :
( mem(V9w,A_27a)
=> ! [V10z] :
( mem(V10z,A_27b)
=> ! [V11r] :
( mem(V11r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V12cn] :
( mem(V12cn,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ( ( ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V5cmp),V6x),V9w) = c_2EternaryComparisons_2EGREATER
=> p(ap(ap(ap(ap(V0P,V5cmp),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V6x),V7y)),V11r),f2653(A_27b,A_27a,V10z,V9w,V8l,V12cn))) )
& ( ap(ap(ap(c_2Etoto_2Eapto(A_27a),V5cmp),V6x),V9w) = c_2EternaryComparisons_2ELESS
=> p(ap(ap(ap(ap(V0P,V5cmp),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V6x),V7y)),V8l),f2654(A_27b,A_27a,V11r,V10z,V9w,V12cn))) ) )
=> p(ap(ap(ap(ap(V0P,V5cmp),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V6x),V7y)),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V8l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V9w),V10z)),V11r)),V12cn)) ) ) ) ) ) ) ) ) ) )
=> ! [V15v] :
( mem(V15v,ty_2Etoto_2Etoto(A_27a))
=> ! [V16v1] :
( mem(V16v1,A_27a)
=> ! [V17v2] :
( mem(V17v2,A_27b)
=> ! [V18v3] :
( mem(V18v3,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V19v4] :
( mem(V19v4,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b))))
=> p(ap(ap(ap(ap(V0P,V15v),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V16v1),V17v2)),V18v3),V19v4)) ) ) ) ) ) ) ) ) ) ).
fof(lameq_f2655,axiom,
! [A_27b,A_27a,V8r] :
( mem(V8r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V4z] :
( mem(V4z,A_27b)
=> ! [V7w] :
( mem(V7w,A_27a)
=> ! [V10cn] :
( mem(V10cn,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V12m] : ap(f2655(A_27b,A_27a,V8r,V4z,V7w,V10cn),V12m) = ap(V10cn,ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V12m),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V7w),V4z)),V8r)) ) ) ) ) ).
fof(lameq_f2656,axiom,
! [A_27b,A_27a,V4z] :
( mem(V4z,A_27b)
=> ! [V7w] :
( mem(V7w,A_27a)
=> ! [V9l] :
( mem(V9l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V10cn] :
( mem(V10cn,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V13m] : ap(f2656(A_27b,A_27a,V4z,V7w,V9l,V10cn),V13m) = ap(V10cn,ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V9l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V7w),V4z)),V13m)) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__rplacv__cn,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0y] :
( mem(V0y,A_27b)
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2cn] :
( mem(V2cn,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V3cmp] :
( mem(V3cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(ap(c_2Efmapal_2Ebt__rplacv__cn(A_27a,A_27b),V3cmp),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V0y)),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b))),V2cn) = c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b)) ) ) ) )
& ! [V4z] :
( mem(V4z,A_27b)
=> ! [V5y] :
( mem(V5y,A_27b)
=> ! [V6x] :
( mem(V6x,A_27a)
=> ! [V7w] :
( mem(V7w,A_27a)
=> ! [V8r] :
( mem(V8r,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V9l] :
( mem(V9l,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V10cn] :
( mem(V10cn,arr(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b))))
=> ! [V11cmp] :
( mem(V11cmp,ty_2Etoto_2Etoto(A_27a))
=> ap(ap(ap(ap(c_2Efmapal_2Ebt__rplacv__cn(A_27a,A_27b),V11cmp),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V6x),V5y)),ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V9l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V7w),V4z)),V8r)),V10cn) = ap(ap(ap(ap(c_2EternaryComparisons_2Eordering__CASE(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b))),ap(ap(ap(c_2Etoto_2Eapto(A_27a),V11cmp),V6x),V7w)),ap(ap(ap(ap(c_2Efmapal_2Ebt__rplacv__cn(A_27a,A_27b),V11cmp),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V6x),V5y)),V9l),f2655(A_27b,A_27a,V8r,V4z,V7w,V10cn))),ap(V10cn,ap(ap(ap(c_2Eenumeral_2Enode(ty_2Epair_2Eprod(A_27a,A_27b)),V9l),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V6x),V5y)),V8r))),ap(ap(ap(ap(c_2Efmapal_2Ebt__rplacv__cn(A_27a,A_27b),V11cmp),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V6x),V5y)),V8r),f2656(A_27b,A_27a,V4z,V7w,V9l,V10cn))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(lameq_f2657,axiom,
! [A_27b,A_27a,V2y] :
( mem(V2y,A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V3t] :
( mem(V3t,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V4ans] : ap(f2657(A_27b,A_27a,V2y,V0cmp,V3t,V1x),V4ans) = ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b))),V4ans),c_2Eenumeral_2Ent(ty_2Epair_2Eprod(A_27a,A_27b)))),ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V0cmp),V3t))))),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Efinite__map_2EFDOM(A_27a,A_27b),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V0cmp),V3t)))),ap(ap(c_2Emin_2E_3D(ty_2Efinite__map_2Efmap(A_27a,A_27b)),ap(ap(c_2Efinite__map_2EFUPDATE(A_27a,A_27b),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V0cmp),V3t)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y))),ap(ap(c_2Efmapal_2EFMAPAL(A_27a,A_27b),V0cmp),V4ans)))) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Ebt__rplacv__thm,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27b)
=> ! [V3t] :
( mem(V3t,ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(c_2Ebool_2ELET(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)),bool),f2657(A_27b,A_27a,V2y,V0cmp,V3t,V1x)),ap(ap(ap(ap(c_2Efmapal_2Ebt__rplacv__cn(A_27a,A_27b),V0cmp),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)),V3t),i(ty_2Eenumeral_2Ebt(ty_2Epair_2Eprod(A_27a,A_27b)))))) ) ) ) ) ) ) ).
fof(lameq_f2658,axiom,
! [A_27b,A_27a,V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V2x] : ap(f2658(A_27b,A_27a,V0f),V2x) = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),ap(V0f,V2x)) ) ).
fof(conj_thm_2Efmapal_2EFUN__fmap__thm,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_2Efmapal_2Efmap(A_27a,A_27b),ap(ap(c_2Elist_2EMAP(A_27a,ty_2Epair_2Eprod(A_27a,A_27b)),f2658(A_27b,A_27a,V0f)),V1l)) = ap(ap(c_2Efinite__map_2EFUN__FMAP(A_27a,A_27b),V0f),ap(c_2Elist_2ELIST__TO__SET(A_27a),V1l)) ) ) ) ) ).
fof(conj_thm_2Efmapal_2Efmap__ORWL__thm,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0cmp] :
( mem(V0cmp,ty_2Etoto_2Etoto(A_27a))
=> ! [V1l] :
( mem(V1l,ty_2Elist_2Elist(ty_2Epair_2Eprod(A_27a,A_27b)))
=> p(ap(ap(ap(c_2Efmapal_2EORWL(A_27a,A_27b),V0cmp),ap(c_2Efmapal_2Efmap(A_27a,A_27b),V1l)),ap(ap(c_2Efmapal_2Eincr__sort(A_27a,A_27b),V0cmp),V1l))) ) ) ) ) ).
%------------------------------------------------------------------------------