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 : 181 ( 1 unt; 43 typ; 0 def)
% Number of atoms : 5987 ( 125 equ; 0 cnn)
% Maximal formula atoms : 132 ( 33 avg)
% Number of connectives : 11357 ( 10 ~; 1 |; 117 &;10446 @)
% ( 18 <=>; 765 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 18 avg;10446 nst)
% Number of types : 1 ( 0 usr)
% Number of type conns : 85 ( 85 >; 0 *; 0 +; 0 <<)
% Number of symbols : 120 ( 117 usr; 76 con; 0-3 aty)
% Number of variables : 988 ( 44 ^ 944 !; 0 ?; 988 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2Efmapal_2EAP__SND,type,
c_2Efmapal_2EAP__SND: del > del > del > $i ).
thf(mem_c_2Efmapal_2EAP__SND,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : ( 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 ) ) ) ) ).
thf(tp_c_2Efmapal_2EFMAPAL,type,
c_2Efmapal_2EFMAPAL: del > del > $i ).
thf(mem_c_2Efmapal_2EFMAPAL,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ).
thf(tp_c_2Efmapal_2EOFU,type,
c_2Efmapal_2EOFU: del > del > $i ).
thf(mem_c_2Efmapal_2EOFU,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ).
thf(tp_c_2Efmapal_2EOPTION__FLAT,type,
c_2Efmapal_2EOPTION__FLAT: del > $i ).
thf(mem_c_2Efmapal_2EOPTION__FLAT,axiom,
! [A_27z: del] : ( mem @ ( c_2Efmapal_2EOPTION__FLAT @ A_27z ) @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27z ) ) ) @ ( ty_2Elist_2Elist @ A_27z ) ) ) ).
thf(tp_c_2Efmapal_2EOPTION__UPDATE,type,
c_2Efmapal_2EOPTION__UPDATE: del > del > $i ).
thf(mem_c_2Efmapal_2EOPTION__UPDATE,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ).
thf(tp_c_2Efmapal_2EORL,type,
c_2Efmapal_2EORL: del > del > $i ).
thf(mem_c_2Efmapal_2EORL,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ).
thf(tp_c_2Efmapal_2EORL__bt,type,
c_2Efmapal_2EORL__bt: del > del > $i ).
thf(mem_c_2Efmapal_2EORL__bt,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ).
thf(tp_c_2Efmapal_2EORL__bt__lb,type,
c_2Efmapal_2EORL__bt__lb: del > del > $i ).
thf(mem_c_2Efmapal_2EORL__bt__lb,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ).
thf(tp_c_2Efmapal_2EORL__bt__lb__ub,type,
c_2Efmapal_2EORL__bt__lb__ub: del > del > $i ).
thf(mem_c_2Efmapal_2EORL__bt__lb__ub,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ).
thf(tp_c_2Efmapal_2EORL__bt__ub,type,
c_2Efmapal_2EORL__bt__ub: del > del > $i ).
thf(mem_c_2Efmapal_2EORL__bt__ub,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ).
thf(tp_c_2Efmapal_2EORL__sublists,type,
c_2Efmapal_2EORL__sublists: del > del > $i ).
thf(mem_c_2Efmapal_2EORL__sublists,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ).
thf(tp_c_2Efmapal_2EORWL,type,
c_2Efmapal_2EORWL: del > del > $i ).
thf(mem_c_2Efmapal_2EORWL,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ).
thf(tp_c_2Efmapal_2EUFO,type,
c_2Efmapal_2EUFO: del > del > $i ).
thf(mem_c_2Efmapal_2EUFO,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Eassocv,type,
c_2Efmapal_2Eassocv: del > del > $i ).
thf(mem_c_2Efmapal_2Eassocv,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ).
thf(tp_c_2Efmapal_2Ebl__to__fmap,type,
c_2Efmapal_2Ebl__to__fmap: del > del > $i ).
thf(mem_c_2Efmapal_2Ebl__to__fmap,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ).
thf(tp_c_2Efmapal_2Ebt__map,type,
c_2Efmapal_2Ebt__map: del > del > $i ).
thf(mem_c_2Efmapal_2Ebt__map,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ).
thf(tp_c_2Efmapal_2Ebt__rplacv__cn,type,
c_2Efmapal_2Ebt__rplacv__cn: del > del > $i ).
thf(mem_c_2Efmapal_2Ebt__rplacv__cn,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Ebt__to__fmap__lb,type,
c_2Efmapal_2Ebt__to__fmap__lb: del > del > $i ).
thf(mem_c_2Efmapal_2Ebt__to__fmap__lb,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Ebt__to__fmap__lb__ub,type,
c_2Efmapal_2Ebt__to__fmap__lb__ub: del > del > $i ).
thf(mem_c_2Efmapal_2Ebt__to__fmap__lb__ub,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Ebt__to__fmap__ub,type,
c_2Efmapal_2Ebt__to__fmap__ub: del > del > $i ).
thf(mem_c_2Efmapal_2Ebt__to__fmap__ub,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Ebt__to__orl,type,
c_2Efmapal_2Ebt__to__orl: del > del > $i ).
thf(mem_c_2Efmapal_2Ebt__to__orl,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Ebt__to__orl__ac,type,
c_2Efmapal_2Ebt__to__orl__ac: del > del > $i ).
thf(mem_c_2Efmapal_2Ebt__to__orl__ac,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Ebt__to__orl__lb,type,
c_2Efmapal_2Ebt__to__orl__lb: del > del > $i ).
thf(mem_c_2Efmapal_2Ebt__to__orl__lb,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Ebt__to__orl__lb__ac,type,
c_2Efmapal_2Ebt__to__orl__lb__ac: del > del > $i ).
thf(mem_c_2Efmapal_2Ebt__to__orl__lb__ac,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Ebt__to__orl__lb__ub,type,
c_2Efmapal_2Ebt__to__orl__lb__ub: del > del > $i ).
thf(mem_c_2Efmapal_2Ebt__to__orl__lb__ub,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Ebt__to__orl__lb__ub__ac,type,
c_2Efmapal_2Ebt__to__orl__lb__ub__ac: del > del > $i ).
thf(mem_c_2Efmapal_2Ebt__to__orl__lb__ub__ac,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux,type,
c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux: del > del > $i ).
thf(mem_c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Ebt__to__orl__ub,type,
c_2Efmapal_2Ebt__to__orl__ub: del > del > $i ).
thf(mem_c_2Efmapal_2Ebt__to__orl__ub,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Ebt__to__orl__ub__ac,type,
c_2Efmapal_2Ebt__to__orl__ub__ac: del > del > $i ).
thf(mem_c_2Efmapal_2Ebt__to__orl__ub__ac,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Ediff__merge,type,
c_2Efmapal_2Ediff__merge: del > del > $i ).
thf(mem_c_2Efmapal_2Ediff__merge,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Efmap,type,
c_2Efmapal_2Efmap: del > del > $i ).
thf(mem_c_2Efmapal_2Efmap,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ).
thf(tp_c_2Efmapal_2Eincr__build,type,
c_2Efmapal_2Eincr__build: del > del > $i ).
thf(mem_c_2Efmapal_2Eincr__build,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Eincr__flat,type,
c_2Efmapal_2Eincr__flat: del > del > $i ).
thf(mem_c_2Efmapal_2Eincr__flat,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Eincr__merge,type,
c_2Efmapal_2Eincr__merge: del > del > $i ).
thf(mem_c_2Efmapal_2Eincr__merge,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Eincr__sort,type,
c_2Efmapal_2Eincr__sort: del > del > $i ).
thf(mem_c_2Efmapal_2Eincr__sort,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Einter__merge,type,
c_2Efmapal_2Einter__merge: del > del > $i ).
thf(mem_c_2Efmapal_2Einter__merge,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Elist__rplacv__cn,type,
c_2Efmapal_2Elist__rplacv__cn: del > del > $i ).
thf(mem_c_2Efmapal_2Elist__rplacv__cn,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Emerge,type,
c_2Efmapal_2Emerge: del > del > $i ).
thf(mem_c_2Efmapal_2Emerge,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Emerge__out,type,
c_2Efmapal_2Emerge__out: del > del > $i ).
thf(mem_c_2Efmapal_2Emerge__out,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ) ) ).
thf(tp_c_2Efmapal_2Eoptry,type,
c_2Efmapal_2Eoptry: del > $i ).
thf(mem_c_2Efmapal_2Eoptry,axiom,
! [A_27z: del] : ( mem @ ( c_2Efmapal_2Eoptry @ A_27z ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27z ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27z ) @ ( ty_2Eoption_2Eoption @ A_27z ) ) ) ) ).
thf(tp_c_2Efmapal_2Eoptry__list,type,
c_2Efmapal_2Eoptry__list: del > del > $i ).
thf(mem_c_2Efmapal_2Eoptry__list,axiom,
! [A_27g: del,A_27z: del] : ( 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 ) ) ) ) ).
thf(tp_c_2Efmapal_2Eunlookup,type,
c_2Efmapal_2Eunlookup: del > del > $i ).
thf(mem_c_2Efmapal_2Eunlookup,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ).
thf(tp_c_2Efmapal_2Evcossa,type,
c_2Efmapal_2Evcossa: del > del > $i ).
thf(mem_c_2Efmapal_2Evcossa,axiom,
! [A_27a: del,A_27b: del] : ( 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 ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORL__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ bool ) ) )
=> ( ( ! [V1cmp: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ( p @ ( ap @ ( ap @ V0P @ V1cmp ) @ ( c_2Elist_2ENIL @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) )
& ! [V2cmp: $i] :
( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V3a: $i] :
( ( mem @ V3a @ A_27a )
=> ! [V4b: $i] :
( ( mem @ V4b @ A_27b )
=> ! [V5l: $i] :
( ( 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: $i] :
( ( mem @ V6v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V7v1: $i] :
( ( mem @ V7v1 @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( p @ ( ap @ ( ap @ V0P @ V6v ) @ V7v1 ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORL,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0cmp: $i] :
( ( 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: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V2cmp: $i] :
( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V3b: $i] :
( ( mem @ V3b @ A_27b )
=> ! [V4a: $i] :
( ( 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: $i] :
( ( mem @ V5p @ A_27a )
=> ! [V6q: $i] :
( ( 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 ) ) )
=> ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V2cmp ) @ V4a ) @ V5p ) )
= fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Efmapal_2Eoptry,axiom,
! [A_27z: del] :
( ! [V0p: $i] :
( ( mem @ V0p @ A_27z )
=> ! [V1q: $i] :
( ( 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: $i] :
( ( mem @ V2q @ ( ty_2Eoption_2Eoption @ A_27z ) )
=> ( ( ap @ ( ap @ ( c_2Efmapal_2Eoptry @ A_27z ) @ ( c_2Eoption_2ENONE @ A_27z ) ) @ V2q )
= V2q ) ) ) ).
thf(conj_thm_2Efmapal_2Eoptry__list__ind,axiom,
! [A_27g: del,A_27z: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( arr @ A_27z @ ( ty_2Eoption_2Eoption @ A_27g ) ) @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ A_27z ) ) @ bool ) ) )
=> ( ( ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27z @ ( ty_2Eoption_2Eoption @ A_27g ) ) )
=> ( p @ ( ap @ ( ap @ V0P @ V1f ) @ ( c_2Elist_2ENIL @ ( ty_2Eoption_2Eoption @ A_27z ) ) ) ) )
& ! [V2f: $i] :
( ( mem @ V2f @ ( arr @ A_27z @ ( ty_2Eoption_2Eoption @ A_27g ) ) )
=> ! [V3l: $i] :
( ( 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: $i] :
( ( mem @ V4f @ ( arr @ A_27z @ ( ty_2Eoption_2Eoption @ A_27g ) ) )
=> ! [V5z: $i] :
( ( mem @ V5z @ A_27z )
=> ! [V6l: $i] :
( ( 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: $i] :
( ( mem @ V7v @ ( arr @ A_27z @ ( ty_2Eoption_2Eoption @ A_27g ) ) )
=> ! [V8v1: $i] :
( ( mem @ V8v1 @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ A_27z ) ) )
=> ( p @ ( ap @ ( ap @ V0P @ V7v ) @ V8v1 ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Eoptry__list,axiom,
! [A_27g: del,A_27z: del] :
( ! [V0f: $i] :
( ( 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: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ A_27z ) ) )
=> ! [V2f: $i] :
( ( 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: $i] :
( ( mem @ V3z @ A_27z )
=> ! [V4l: $i] :
( ( mem @ V4l @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ A_27z ) ) )
=> ! [V5f: $i] :
( ( 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 ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Eassocv__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( arr @ A_27a @ bool ) ) )
=> ( ( ! [V1a: $i] :
( ( mem @ V1a @ A_27a )
=> ( p @ ( ap @ ( ap @ V0P @ ( c_2Elist_2ENIL @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V1a ) ) )
& ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ! [V3y: $i] :
( ( mem @ V3y @ A_27b )
=> ! [V4l: $i] :
( ( mem @ V4l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V5a: $i] :
( ( 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: $i] :
( ( mem @ V6v @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V7v1: $i] :
( ( mem @ V7v1 @ A_27a )
=> ( p @ ( ap @ ( ap @ V0P @ V6v ) @ V7v1 ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Eassocv,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0a: $i] :
( ( 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: $i] :
( ( mem @ V1y @ A_27b )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V4a: $i] :
( ( 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 ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Efmapal_2Evcossa,axiom,
! [A_27a: del,A_27b: del,V0a: $i] :
( ( mem @ V0a @ A_27a )
=> ! [V1l: $i] :
( ( 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 ) ) ) ) ).
thf(ax_thm_2Efmapal_2EOPTION__UPDATE,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27b ) ) )
=> ! [V2x: $i] :
( ( 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 ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Emerge__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( 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: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V2l: $i] :
( ( 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: $i] :
( ( mem @ V3cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V4v4: $i] :
( ( mem @ V4v4 @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
=> ! [V5v5: $i] :
( ( 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: $i] :
( ( mem @ V6cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V7a1: $i] :
( ( mem @ V7a1 @ A_27a )
=> ! [V8b1: $i] :
( ( mem @ V8b1 @ A_27b )
=> ! [V9l1: $i] :
( ( mem @ V9l1 @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V10a2: $i] :
( ( mem @ V10a2 @ A_27a )
=> ! [V11b2: $i] :
( ( mem @ V11b2 @ A_27b )
=> ! [V12l2: $i] :
( ( mem @ V12l2 @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V6cmp ) @ V7a1 ) @ V10a2 ) )
= fo__c_2EternaryComparisons_2EEQUAL )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V6cmp ) @ V9l1 ) @ V12l2 ) ) )
& ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V6cmp ) @ V7a1 ) @ V10a2 ) )
= fo__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 ) ) )
& ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V6cmp ) @ V7a1 ) @ V10a2 ) )
= fo__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: $i] :
( ( mem @ V13v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V14v1: $i] :
( ( mem @ V14v1 @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V15v2: $i] :
( ( mem @ V15v2 @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V13v ) @ V14v1 ) @ V15v2 ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Emerge,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V1cmp: $i] :
( ( 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: $i] :
( ( mem @ V2v5 @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V3v4: $i] :
( ( mem @ V3v4 @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
=> ! [V4cmp: $i] :
( ( 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: $i] :
( ( mem @ V5l2 @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V6l1: $i] :
( ( mem @ V6l1 @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V7cmp: $i] :
( ( mem @ V7cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V8b2: $i] :
( ( mem @ V8b2 @ A_27b )
=> ! [V9b1: $i] :
( ( mem @ V9b1 @ A_27b )
=> ! [V10a2: $i] :
( ( mem @ V10a2 @ A_27a )
=> ! [V11a1: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Eincr__merge__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( 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: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V2l: $i] :
( ( 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: $i] :
( ( mem @ V3cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V4l: $i] :
( ( mem @ V4l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V5lol: $i] :
( ( 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: $i] :
( ( mem @ V6cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V7l: $i] :
( ( mem @ V7l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V8m: $i] :
( ( mem @ V8m @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V9lol: $i] :
( ( 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: $i] :
( ( mem @ V10v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V11v1: $i] :
( ( mem @ V11v1 @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V12v2: $i] :
( ( 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 ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Eincr__merge,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V1cmp: $i] :
( ( 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: $i] :
( ( mem @ V2lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V4cmp: $i] :
( ( 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: $i] :
( ( mem @ V5m @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V6lol: $i] :
( ( mem @ V6lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) )
=> ! [V7l: $i] :
( ( mem @ V7l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V8cmp: $i] :
( ( 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 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORL__sublists__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( 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: $i] :
( ( 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: $i] :
( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V3lol: $i] :
( ( 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: $i] :
( ( mem @ V4cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V5m: $i] :
( ( mem @ V5m @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V6lol: $i] :
( ( 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: $i] :
( ( mem @ V7v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V8v1: $i] :
( ( mem @ V8v1 @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) )
=> ( p @ ( ap @ ( ap @ V0P @ V7v ) @ V8v1 ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORL__sublists,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0cmp: $i] :
( ( 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: $i] :
( ( mem @ V1lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) )
=> ! [V2cmp: $i] :
( ( 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: $i] :
( ( mem @ V3m @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V4lol: $i] :
( ( mem @ V4lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) )
=> ! [V5cmp: $i] :
( ( 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 ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Efmapal_2Eincr__build,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0cmp: $i] :
( ( 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: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V2ab: $i] :
( ( mem @ V2ab @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
=> ! [V3l: $i] :
( ( 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 ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Emerge__out__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( 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: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V2l: $i] :
( ( 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: $i] :
( ( mem @ V3cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V4l: $i] :
( ( mem @ V4l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V5lol: $i] :
( ( 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: $i] :
( ( mem @ V6cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V7l: $i] :
( ( mem @ V7l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V8m: $i] :
( ( mem @ V8m @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V9lol: $i] :
( ( 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: $i] :
( ( mem @ V10v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V11v1: $i] :
( ( mem @ V11v1 @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V12v2: $i] :
( ( 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 ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Emerge__out,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0l: $i] :
( ( mem @ V0l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V1cmp: $i] :
( ( 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: $i] :
( ( mem @ V2lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V4cmp: $i] :
( ( 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: $i] :
( ( mem @ V5m @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V6lol: $i] :
( ( mem @ V6lol @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) )
=> ! [V7l: $i] :
( ( mem @ V7l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V8cmp: $i] :
( ( 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 ) ) ) ) ) ) ) ).
thf(ax_thm_2Efmapal_2Eincr__flat,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1lol: $i] :
( ( 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 ) ) ) ) ).
thf(ax_thm_2Efmapal_2Eincr__sort,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1l: $i] :
( ( 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 ) ) ) ) ) ).
thf(ax_thm_2Efmapal_2EOPTION__FLAT__primitive,axiom,
! [A_27z: del] :
( ( 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 ) ) )
@ ( lam @ ( 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 ) )
@ ^ [V0R: $i] :
( 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 ) ) ) )
@ ( lam @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27z ) ) )
@ ^ [V1l: $i] : ( 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 ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Elist_2Elist @ A_27z ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27z )
@ ^ [V2a: $i] :
( ap @ ( c_2Ebool_2E_21 @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27z ) ) ) )
@ ( lam @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27z ) ) )
@ ^ [V3l: $i] : ( 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 ) ) ) ) ) ) ) ) ) ) )
@ ( lam @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27z ) ) ) @ ( ty_2Elist_2Elist @ A_27z ) )
@ ^ [V4OPTION__FLAT: $i] :
( lam @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27z ) ) )
@ ^ [V5a_27: $i] :
( 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 ) ) )
@ ( lam @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27z ) )
@ ^ [V6v: $i] :
( lam @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27z ) ) )
@ ^ [V7l: $i] :
( 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 ) ) )
@ ( lam @ ( ty_2Elist_2Elist @ A_27z )
@ ^ [V8a: $i] : ( ap @ ( c_2Ecombin_2EI @ ( ty_2Elist_2Elist @ A_27z ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27z ) @ V8a ) @ ( ap @ V4OPTION__FLAT @ V7l ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EOPTION__FLAT__ind,axiom,
! [A_27z: del,V0P: $i] :
( ( 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: $i] :
( ( 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: $i] :
( ( mem @ V2a @ ( ty_2Elist_2Elist @ A_27z ) )
=> ! [V3l: $i] :
( ( 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: $i] :
( ( mem @ V4v @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27z ) ) ) )
=> ( p @ ( ap @ V0P @ V4v ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EOPTION__FLAT,axiom,
! [A_27z: del] :
( ( ( ap @ ( c_2Efmapal_2EOPTION__FLAT @ A_27z ) @ ( c_2Elist_2ENIL @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27z ) ) ) )
= ( c_2Elist_2ENIL @ A_27z ) )
& ! [V0l: $i] :
( ( 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: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ ( ty_2Eoption_2Eoption @ ( ty_2Elist_2Elist @ A_27z ) ) ) )
=> ! [V2a: $i] :
( ( 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 ) ) ) ) ) ) ).
thf(ax_thm_2Efmapal_2Eunlookup,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( 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 ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__fmap__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ bool ) ) )
=> ( ( ! [V1cmp: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ( p @ ( ap @ ( ap @ V0P @ V1cmp ) @ ( c_2Eenumeral_2Ent @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) )
& ! [V2cmp: $i] :
( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V4x: $i] :
( ( mem @ V4x @ A_27a )
=> ! [V5v: $i] :
( ( mem @ V5v @ A_27b )
=> ! [V6r: $i] :
( ( 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: $i] :
( ( mem @ V7v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V8v1: $i] :
( ( mem @ V8v1 @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( p @ ( ap @ ( ap @ V0P @ V7v ) @ V8v1 ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__fmap,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0cmp: $i] :
( ( 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: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2v: $i] :
( ( mem @ V2v @ A_27b )
=> ! [V3r: $i] :
( ( mem @ V3r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V4l: $i] :
( ( mem @ V4l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V5cmp: $i] :
( ( 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 )
@ ( lam @ A_27a
@ ^ [V6y: $i] : ( 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 ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) )
@ ( 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 )
@ ( lam @ A_27a
@ ^ [V7z: $i] : ( 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 ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EFAPPLY__nt,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1x: $i] :
( ( 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 ) ) ) ) ).
thf(conj_thm_2Efmapal_2EFAPPLY__node,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V3a: $i] :
( ( mem @ V3a @ A_27a )
=> ! [V4b: $i] :
( ( mem @ V4b @ A_27b )
=> ! [V5r: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Efmapal_2Ebt__to__fmap__lb,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1lb: $i] :
( ( mem @ V1lb @ A_27a )
=> ! [V2t: $i] :
( ( 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 )
@ ( lam @ A_27a
@ ^ [V3x: $i] : ( 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 ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Efmapal_2Ebt__to__fmap__ub,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V2ub: $i] :
( ( 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 )
@ ( lam @ A_27a
@ ^ [V3x: $i] : ( 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 ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Efmapal_2Ebt__to__fmap__lb__ub,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1lb: $i] :
( ( mem @ V1lb @ A_27a )
=> ! [V2t: $i] :
( ( mem @ V2t @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V3ub: $i] :
( ( 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 )
@ ( lam @ A_27a
@ ^ [V4x: $i] : ( 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 ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2EternaryComparisons_2Eordering ) @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V0cmp ) @ V4x ) @ V3ub ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Efmapal_2Ebt__map,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0f: $i] :
( ( 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: $i] :
( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Eenumeral_2Ebt @ A_27a ) )
=> ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ! [V4r: $i] :
( ( 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 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__FST__FDOM,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1t: $i] :
( ( 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 ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__orl__lb__ub__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( 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: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V2lb: $i] :
( ( mem @ V2lb @ A_27a )
=> ! [V3ub: $i] :
( ( mem @ V3ub @ A_27a )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V1cmp ) @ V2lb ) @ ( c_2Eenumeral_2Ent @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V3ub ) ) ) ) )
& ! [V4cmp: $i] :
( ( mem @ V4cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V5lb: $i] :
( ( mem @ V5lb @ A_27a )
=> ! [V6l: $i] :
( ( mem @ V6l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V7x: $i] :
( ( mem @ V7x @ A_27a )
=> ! [V8y: $i] :
( ( mem @ V8y @ A_27b )
=> ! [V9r: $i] :
( ( mem @ V9r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V10ub: $i] :
( ( mem @ V10ub @ A_27a )
=> ( ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V4cmp ) @ V5lb ) @ V7x ) )
!= fo__c_2EternaryComparisons_2ELESS )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V4cmp ) @ V5lb ) @ V9r ) @ V10ub ) ) )
& ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V4cmp ) @ V5lb ) @ V7x ) )
= fo__c_2EternaryComparisons_2ELESS )
& ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V4cmp ) @ V7x ) @ V10ub ) )
!= fo__c_2EternaryComparisons_2ELESS ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V4cmp ) @ V5lb ) @ V6l ) @ V10ub ) ) )
& ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V4cmp ) @ V5lb ) @ V7x ) )
= fo__c_2EternaryComparisons_2ELESS )
& ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V4cmp ) @ V7x ) @ V10ub ) )
= fo__c_2EternaryComparisons_2ELESS ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V4cmp ) @ V5lb ) @ V6l ) @ V7x ) ) )
& ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V4cmp ) @ V5lb ) @ V7x ) )
= fo__c_2EternaryComparisons_2ELESS )
& ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V4cmp ) @ V7x ) @ V10ub ) )
= fo__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: $i] :
( ( mem @ V11v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V12v1: $i] :
( ( mem @ V12v1 @ A_27a )
=> ! [V13v2: $i] :
( ( mem @ V13v2 @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V14v3: $i] :
( ( mem @ V14v3 @ A_27a )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V11v ) @ V12v1 ) @ V13v2 ) @ V14v3 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__orl__lb__ub,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0ub: $i] :
( ( mem @ V0ub @ A_27a )
=> ! [V1lb: $i] :
( ( mem @ V1lb @ A_27a )
=> ! [V2cmp: $i] :
( ( 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: $i] :
( ( mem @ V3y @ A_27b )
=> ! [V4x: $i] :
( ( mem @ V4x @ A_27a )
=> ! [V5ub: $i] :
( ( mem @ V5ub @ A_27a )
=> ! [V6r: $i] :
( ( mem @ V6r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V7lb: $i] :
( ( mem @ V7lb @ A_27a )
=> ! [V8l: $i] :
( ( mem @ V8l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V9cmp: $i] :
( ( 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 ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__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 ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__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 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__orl__lb__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ bool ) ) ) )
=> ( ( ! [V1cmp: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V2lb: $i] :
( ( mem @ V2lb @ A_27a )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V1cmp ) @ V2lb ) @ ( c_2Eenumeral_2Ent @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) ) )
& ! [V3cmp: $i] :
( ( mem @ V3cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V4lb: $i] :
( ( mem @ V4lb @ A_27a )
=> ! [V5l: $i] :
( ( mem @ V5l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V6x: $i] :
( ( mem @ V6x @ A_27a )
=> ! [V7y: $i] :
( ( mem @ V7y @ A_27b )
=> ! [V8r: $i] :
( ( mem @ V8r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V3cmp ) @ V4lb ) @ V6x ) )
!= fo__c_2EternaryComparisons_2ELESS )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V3cmp ) @ V4lb ) @ V8r ) ) )
& ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V3cmp ) @ V4lb ) @ V6x ) )
= fo__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: $i] :
( ( mem @ V9v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V10v1: $i] :
( ( mem @ V10v1 @ A_27a )
=> ! [V11v2: $i] :
( ( mem @ V11v2 @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V9v ) @ V10v1 ) @ V11v2 ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__orl__lb,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0lb: $i] :
( ( mem @ V0lb @ A_27a )
=> ! [V1cmp: $i] :
( ( 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: $i] :
( ( mem @ V2y @ A_27b )
=> ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ! [V4r: $i] :
( ( mem @ V4r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V5lb: $i] :
( ( mem @ V5lb @ A_27a )
=> ! [V6l: $i] :
( ( mem @ V6l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V7cmp: $i] :
( ( 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 ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__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 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__orl__ub__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( arr @ A_27a @ bool ) ) ) )
=> ( ( ! [V1cmp: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V2ub: $i] :
( ( mem @ V2ub @ A_27a )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V1cmp ) @ ( c_2Eenumeral_2Ent @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V2ub ) ) ) )
& ! [V3cmp: $i] :
( ( mem @ V3cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V4l: $i] :
( ( mem @ V4l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V5x: $i] :
( ( mem @ V5x @ A_27a )
=> ! [V6y: $i] :
( ( mem @ V6y @ A_27b )
=> ! [V7r: $i] :
( ( mem @ V7r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V8ub: $i] :
( ( mem @ V8ub @ A_27a )
=> ( ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V3cmp ) @ V5x ) @ V8ub ) )
!= fo__c_2EternaryComparisons_2ELESS )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V3cmp ) @ V4l ) @ V8ub ) ) )
& ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V3cmp ) @ V5x ) @ V8ub ) )
= fo__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: $i] :
( ( mem @ V9v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V10v1: $i] :
( ( mem @ V10v1 @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V11v2: $i] :
( ( mem @ V11v2 @ A_27a )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V9v ) @ V10v1 ) @ V11v2 ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__orl__ub,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0ub: $i] :
( ( mem @ V0ub @ A_27a )
=> ! [V1cmp: $i] :
( ( 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: $i] :
( ( mem @ V2y @ A_27b )
=> ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ! [V4ub: $i] :
( ( mem @ V4ub @ A_27a )
=> ! [V5r: $i] :
( ( mem @ V5r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V6l: $i] :
( ( mem @ V6l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V7cmp: $i] :
( ( 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 ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__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 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__orl__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ bool ) ) )
=> ( ( ! [V1cmp: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ( p @ ( ap @ ( ap @ V0P @ V1cmp ) @ ( c_2Eenumeral_2Ent @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) )
& ! [V2cmp: $i] :
( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V4x: $i] :
( ( mem @ V4x @ A_27a )
=> ! [V5y: $i] :
( ( mem @ V5y @ A_27b )
=> ! [V6r: $i] :
( ( 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: $i] :
( ( mem @ V7v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V8v1: $i] :
( ( mem @ V8v1 @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( p @ ( ap @ ( ap @ V0P @ V7v ) @ V8v1 ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__orl,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ! [V3y: $i] :
( ( mem @ V3y @ A_27b )
=> ! [V4r: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Efmapal_2Efmap,axiom,
! [A_27a: del,A_27b: del,V0l: $i] :
( ( 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 ) ) ) ) ).
thf(ax_thm_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__AUX,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( 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 )
@ ( lam @ ( 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 ) ) )
@ ^ [V1bt__to__orl__lb__ub__ac__tupled: $i] :
( lam @ ( 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 ) ) ) ) ) )
@ ^ [V2a: $i] :
( 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 )
@ ( lam @ ( ty_2Etoto_2Etoto @ A_27a )
@ ^ [V3cmp: $i] :
( lam @ ( 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 ) ) ) ) )
@ ^ [V4v1: $i] :
( 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 )
@ ( lam @ A_27a
@ ^ [V5lb: $i] :
( lam @ ( 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 ) ) ) )
@ ^ [V6v3: $i] :
( 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 )
@ ( lam @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
@ ^ [V7v4: $i] :
( lam @ ( ty_2Epair_2Eprod @ A_27a @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
@ ^ [V8v5: $i] :
( 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 )
@ ( lam @ A_27a
@ ^ [V9ub: $i] :
( lam @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
@ ^ [V10m: $i] :
( 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 ) )
@ ( lam @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
@ ^ [V11l: $i] :
( lam @ ( ty_2Epair_2Eprod @ A_27a @ A_27b )
@ ^ [V12v9: $i] :
( lam @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
@ ^ [V13r: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ A_27a @ A_27b ) @ V12v9 )
@ ( lam @ A_27a
@ ^ [V14x: $i] :
( lam @ A_27b
@ ^ [V15y: $i] : ( 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 ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__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 ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__orl__lb__ub__ac__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( 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: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V2lb: $i] :
( ( mem @ V2lb @ A_27a )
=> ! [V3ub: $i] :
( ( mem @ V3ub @ A_27a )
=> ! [V4m: $i] :
( ( 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: $i] :
( ( mem @ V5cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V6lb: $i] :
( ( mem @ V6lb @ A_27a )
=> ! [V7l: $i] :
( ( mem @ V7l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V8x: $i] :
( ( mem @ V8x @ A_27a )
=> ! [V9y: $i] :
( ( mem @ V9y @ A_27b )
=> ! [V10r: $i] :
( ( mem @ V10r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V11ub: $i] :
( ( mem @ V11ub @ A_27a )
=> ! [V12m: $i] :
( ( mem @ V12m @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V5cmp ) @ V6lb ) @ V8x ) )
!= fo__c_2EternaryComparisons_2ELESS )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V5cmp ) @ V6lb ) @ V10r ) @ V11ub ) @ V12m ) ) )
& ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V5cmp ) @ V6lb ) @ V8x ) )
= fo__c_2EternaryComparisons_2ELESS )
& ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V5cmp ) @ V8x ) @ V11ub ) )
!= fo__c_2EternaryComparisons_2ELESS ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V5cmp ) @ V6lb ) @ V7l ) @ V11ub ) @ V12m ) ) )
& ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V5cmp ) @ V6lb ) @ V8x ) )
= fo__c_2EternaryComparisons_2ELESS )
& ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V5cmp ) @ V8x ) @ V11ub ) )
= fo__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 ) ) ) ) )
& ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V5cmp ) @ V6lb ) @ V8x ) )
= fo__c_2EternaryComparisons_2ELESS )
& ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V5cmp ) @ V8x ) @ V11ub ) )
= fo__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: $i] :
( ( mem @ V13v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V14v1: $i] :
( ( mem @ V14v1 @ A_27a )
=> ! [V15v2: $i] :
( ( mem @ V15v2 @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V16v3: $i] :
( ( mem @ V16v3 @ A_27a )
=> ! [V17v4: $i] :
( ( mem @ V17v4 @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V13v ) @ V14v1 ) @ V15v2 ) @ V16v3 ) @ V17v4 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__orl__lb__ub__ac,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0ub: $i] :
( ( mem @ V0ub @ A_27a )
=> ! [V1m: $i] :
( ( mem @ V1m @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V2lb: $i] :
( ( mem @ V2lb @ A_27a )
=> ! [V3cmp: $i] :
( ( 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: $i] :
( ( mem @ V4y @ A_27b )
=> ! [V5x: $i] :
( ( mem @ V5x @ A_27a )
=> ! [V6ub: $i] :
( ( mem @ V6ub @ A_27a )
=> ! [V7r: $i] :
( ( mem @ V7r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V8m: $i] :
( ( mem @ V8m @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V9lb: $i] :
( ( mem @ V9lb @ A_27a )
=> ! [V10l: $i] :
( ( mem @ V10l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V11cmp: $i] :
( ( 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 ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__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 ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__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 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__orl__lb__ac__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( 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: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V2lb: $i] :
( ( mem @ V2lb @ A_27a )
=> ! [V3m: $i] :
( ( 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: $i] :
( ( mem @ V4cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V5lb: $i] :
( ( mem @ V5lb @ A_27a )
=> ! [V6l: $i] :
( ( mem @ V6l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V7x: $i] :
( ( mem @ V7x @ A_27a )
=> ! [V8y: $i] :
( ( mem @ V8y @ A_27b )
=> ! [V9r: $i] :
( ( mem @ V9r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V10m: $i] :
( ( mem @ V10m @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V4cmp ) @ V5lb ) @ V7x ) )
!= fo__c_2EternaryComparisons_2ELESS )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V4cmp ) @ V5lb ) @ V9r ) @ V10m ) ) )
& ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V4cmp ) @ V5lb ) @ V7x ) )
= fo__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: $i] :
( ( mem @ V11v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V12v1: $i] :
( ( mem @ V12v1 @ A_27a )
=> ! [V13v2: $i] :
( ( mem @ V13v2 @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V14v3: $i] :
( ( mem @ V14v3 @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V11v ) @ V12v1 ) @ V13v2 ) @ V14v3 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__orl__lb__ac,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0m: $i] :
( ( mem @ V0m @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V1lb: $i] :
( ( mem @ V1lb @ A_27a )
=> ! [V2cmp: $i] :
( ( 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: $i] :
( ( mem @ V3y @ A_27b )
=> ! [V4x: $i] :
( ( mem @ V4x @ A_27a )
=> ! [V5r: $i] :
( ( mem @ V5r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V6m: $i] :
( ( mem @ V6m @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V7lb: $i] :
( ( mem @ V7lb @ A_27a )
=> ! [V8l: $i] :
( ( mem @ V8l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V9cmp: $i] :
( ( 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 ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__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 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__orl__ub__ac__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( 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: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V2ub: $i] :
( ( mem @ V2ub @ A_27a )
=> ! [V3m: $i] :
( ( 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: $i] :
( ( mem @ V4cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V5l: $i] :
( ( mem @ V5l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V6x: $i] :
( ( mem @ V6x @ A_27a )
=> ! [V7y: $i] :
( ( mem @ V7y @ A_27b )
=> ! [V8r: $i] :
( ( mem @ V8r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V9ub: $i] :
( ( mem @ V9ub @ A_27a )
=> ! [V10m: $i] :
( ( mem @ V10m @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V4cmp ) @ V6x ) @ V9ub ) )
!= fo__c_2EternaryComparisons_2ELESS )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V4cmp ) @ V5l ) @ V9ub ) @ V10m ) ) )
& ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V4cmp ) @ V6x ) @ V9ub ) )
= fo__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: $i] :
( ( mem @ V11v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V12v1: $i] :
( ( mem @ V12v1 @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V13v2: $i] :
( ( mem @ V13v2 @ A_27a )
=> ! [V14v3: $i] :
( ( mem @ V14v3 @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V11v ) @ V12v1 ) @ V13v2 ) @ V14v3 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__orl__ub__ac,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0ub: $i] :
( ( mem @ V0ub @ A_27a )
=> ! [V1m: $i] :
( ( mem @ V1m @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V2cmp: $i] :
( ( 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: $i] :
( ( mem @ V3y @ A_27b )
=> ! [V4x: $i] :
( ( mem @ V4x @ A_27a )
=> ! [V5ub: $i] :
( ( mem @ V5ub @ A_27a )
=> ! [V6r: $i] :
( ( mem @ V6r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V7m: $i] :
( ( mem @ V7m @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V8l: $i] :
( ( mem @ V8l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V9cmp: $i] :
( ( 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 ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__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 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__orl__ac__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( 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: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V2m: $i] :
( ( 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: $i] :
( ( mem @ V3cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V4l: $i] :
( ( mem @ V4l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V5x: $i] :
( ( mem @ V5x @ A_27a )
=> ! [V6y: $i] :
( ( mem @ V6y @ A_27b )
=> ! [V7r: $i] :
( ( mem @ V7r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V8m: $i] :
( ( 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: $i] :
( ( mem @ V9v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V10v1: $i] :
( ( mem @ V10v1 @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V11v2: $i] :
( ( mem @ V11v2 @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V9v ) @ V10v1 ) @ V11v2 ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__orl__ac,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1m: $i] :
( ( mem @ V1m @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ! [V4y: $i] :
( ( mem @ V4y @ A_27b )
=> ! [V5r: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Efmapal_2EORWL,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( ty_2Efinite__map_2Efmap @ A_27a @ A_27b ) )
=> ! [V2l: $i] :
( ( 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 ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORWL__bt__to__orl,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1t: $i] :
( ( 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 ) ) ) ) ) ).
thf(ax_thm_2Efmapal_2EOFU,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( ty_2Efinite__map_2Efmap @ A_27a @ A_27b ) )
=> ! [V2g: $i] :
( ( 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 )
@ ( lam @ A_27a
@ ^ [V3x: $i] : ( 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 ) ) ) ) ) ) )
@ V2g ) ) ) ) ) ).
thf(ax_thm_2Efmapal_2EUFO,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( ty_2Efinite__map_2Efmap @ A_27a @ A_27b ) )
=> ! [V2g: $i] :
( ( 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 )
@ ( lam @ A_27a
@ ^ [V3y: $i] :
( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ bool ) @ V3y )
@ ( ap @ ( c_2Ebool_2E_21 @ A_27a )
@ ( lam @ A_27a
@ ^ [V4z: $i] : ( 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 ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebl__to__fmap__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebl @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ bool ) ) )
=> ( ( ! [V1cmp: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ( p @ ( ap @ ( ap @ V0P @ V1cmp ) @ ( c_2Eenumeral_2Enbl @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) )
& ! [V2cmp: $i] :
( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V3b: $i] :
( ( 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: $i] :
( ( mem @ V4cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V5x: $i] :
( ( mem @ V5x @ A_27a )
=> ! [V6y: $i] :
( ( mem @ V6y @ A_27b )
=> ! [V7t: $i] :
( ( mem @ V7t @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V8b: $i] :
( ( 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: $i] :
( ( mem @ V9v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V10v1: $i] :
( ( mem @ V10v1 @ ( ty_2Eenumeral_2Ebl @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( p @ ( ap @ ( ap @ V0P @ V9v ) @ V10v1 ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebl__to__fmap,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0cmp: $i] :
( ( 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: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V2b: $i] :
( ( 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: $i] :
( ( mem @ V3y @ A_27b )
=> ! [V4x: $i] :
( ( mem @ V4x @ A_27a )
=> ! [V5t: $i] :
( ( mem @ V5t @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V6cmp: $i] :
( ( mem @ V6cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V7b: $i] :
( ( 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 )
@ ( lam @ A_27a
@ ^ [V8z: $i] : ( 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 ) ) @ ( inj__ty_2EternaryComparisons_2Eordering @ fo__c_2EternaryComparisons_2ELESS ) ) ) ) ) ) ) )
@ ( ap @ ( ap @ ( c_2Efmapal_2Ebl__to__fmap @ A_27a @ A_27b ) @ V6cmp ) @ V7b ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__to__orl__ID__IMP,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1l: $i] :
( ( 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 ) ) ) ) ).
thf(conj_thm_2Efmapal_2Efmap__FDOM,axiom,
! [A_27a: del,A_27b: del,V0l: $i] :
( ( 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 ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORL__FUNION__IMP,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1l: $i] :
( ( 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: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EFMAPAL__FDOM__THM,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1x: $i] :
( ( 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: $i] :
( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ! [V4a: $i] :
( ( mem @ V4a @ A_27a )
=> ! [V5b: $i] :
( ( mem @ V5b @ A_27b )
=> ! [V6l: $i] :
( ( mem @ V6l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V7r: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Einter__merge__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( 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: $i] :
( ( 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: $i] :
( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V3a: $i] :
( ( mem @ V3a @ A_27a )
=> ! [V4b: $i] :
( ( mem @ V4b @ A_27b )
=> ! [V5l: $i] :
( ( 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: $i] :
( ( mem @ V6cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V7y: $i] :
( ( mem @ V7y @ A_27a )
=> ! [V8m: $i] :
( ( 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: $i] :
( ( mem @ V9cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V10a: $i] :
( ( mem @ V10a @ A_27a )
=> ! [V11b: $i] :
( ( mem @ V11b @ A_27b )
=> ! [V12l: $i] :
( ( mem @ V12l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V13y: $i] :
( ( mem @ V13y @ A_27a )
=> ! [V14m: $i] :
( ( mem @ V14m @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V9cmp ) @ V10a ) @ V13y ) )
= fo__c_2EternaryComparisons_2EEQUAL )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V9cmp ) @ V12l ) @ V14m ) ) )
& ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V9cmp ) @ V10a ) @ V13y ) )
= fo__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 ) ) )
& ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V9cmp ) @ V10a ) @ V13y ) )
= fo__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: $i] :
( ( mem @ V15v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V16v1: $i] :
( ( mem @ V16v1 @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V17v2: $i] :
( ( mem @ V17v2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V15v ) @ V16v1 ) @ V17v2 ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Einter__merge,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0cmp: $i] :
( ( 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: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V2cmp: $i] :
( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V3b: $i] :
( ( mem @ V3b @ A_27b )
=> ! [V4a: $i] :
( ( 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: $i] :
( ( mem @ V5y @ A_27a )
=> ! [V6m: $i] :
( ( mem @ V6m @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V7cmp: $i] :
( ( 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: $i] :
( ( mem @ V8y @ A_27a )
=> ! [V9m: $i] :
( ( mem @ V9m @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V10l: $i] :
( ( mem @ V10l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V11cmp: $i] :
( ( mem @ V11cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V12b: $i] :
( ( mem @ V12b @ A_27b )
=> ! [V13a: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORL__DRESTRICT__IMP,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1l: $i] :
( ( 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: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ediff__merge__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( 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: $i] :
( ( 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: $i] :
( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V3a: $i] :
( ( mem @ V3a @ A_27a )
=> ! [V4b: $i] :
( ( mem @ V4b @ A_27b )
=> ! [V5l: $i] :
( ( 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: $i] :
( ( mem @ V6cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V7y: $i] :
( ( mem @ V7y @ A_27a )
=> ! [V8m: $i] :
( ( 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: $i] :
( ( mem @ V9cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V10a: $i] :
( ( mem @ V10a @ A_27a )
=> ! [V11b: $i] :
( ( mem @ V11b @ A_27b )
=> ! [V12l: $i] :
( ( mem @ V12l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V13y: $i] :
( ( mem @ V13y @ A_27a )
=> ! [V14m: $i] :
( ( mem @ V14m @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V9cmp ) @ V10a ) @ V13y ) )
= fo__c_2EternaryComparisons_2EEQUAL )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V9cmp ) @ V12l ) @ V14m ) ) )
& ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V9cmp ) @ V10a ) @ V13y ) )
= fo__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 ) ) )
& ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V9cmp ) @ V10a ) @ V13y ) )
= fo__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: $i] :
( ( mem @ V15v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V16v1: $i] :
( ( mem @ V16v1 @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V17v2: $i] :
( ( mem @ V17v2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V15v ) @ V16v1 ) @ V17v2 ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ediff__merge,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0cmp: $i] :
( ( 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: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V2cmp: $i] :
( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V3b: $i] :
( ( mem @ V3b @ A_27b )
=> ! [V4a: $i] :
( ( 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: $i] :
( ( mem @ V5y @ A_27a )
=> ! [V6m: $i] :
( ( mem @ V6m @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V7cmp: $i] :
( ( 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: $i] :
( ( mem @ V8y @ A_27a )
=> ! [V9m: $i] :
( ( mem @ V9m @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V10l: $i] :
( ( mem @ V10l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V11cmp: $i] :
( ( mem @ V11cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V12b: $i] :
( ( mem @ V12b @ A_27b )
=> ! [V13a: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORL__DRESTRICT__COMPL__IMP,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1l: $i] :
( ( 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: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EFMAPAL__fmap,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1l: $i] :
( ( 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 ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORL__FMAPAL,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1l: $i] :
( ( 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 ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORWL__FUNION__THM,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1s: $i] :
( ( mem @ V1s @ ( ty_2Efinite__map_2Efmap @ A_27a @ A_27b ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V3t: $i] :
( ( mem @ V3t @ ( ty_2Efinite__map_2Efmap @ A_27a @ A_27b ) )
=> ! [V4m: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORWL__DRESTRICT__THM,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1s: $i] :
( ( mem @ V1s @ ( ty_2Efinite__map_2Efmap @ A_27a @ A_27b ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V3t: $i] :
( ( mem @ V3t @ ( arr @ A_27a @ bool ) )
=> ! [V4m: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORWL__DRESTRICT__COMPL__THM,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1s: $i] :
( ( mem @ V1s @ ( ty_2Efinite__map_2Efmap @ A_27a @ A_27b ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V3t: $i] :
( ( mem @ V3t @ ( arr @ A_27a @ bool ) )
=> ! [V4m: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Efmapal_2EAP__SND,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ A_27c ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ A_27a )
=> ! [V2b: $i] :
( ( 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 ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Eo__f__bt__map,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27b @ A_27c ) )
=> ! [V2t: $i] :
( ( 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 ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EFAPPLY__fmap__NIL,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( ( 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 ) ) ) ).
thf(conj_thm_2Efmapal_2EFAPPLY__fmap__CONS,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1y: $i] :
( ( mem @ V1y @ A_27a )
=> ! [V2z: $i] :
( ( mem @ V2z @ A_27b )
=> ! [V3l: $i] :
( ( 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 ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Eo__f__fmap,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ A_27c ) )
=> ! [V1l: $i] :
( ( 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 ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORL__bt__lb__ub__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( 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: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V2lb: $i] :
( ( mem @ V2lb @ A_27a )
=> ! [V3ub: $i] :
( ( mem @ V3ub @ A_27a )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V1cmp ) @ V2lb ) @ ( c_2Eenumeral_2Ent @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V3ub ) ) ) ) )
& ! [V4cmp: $i] :
( ( mem @ V4cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V5lb: $i] :
( ( mem @ V5lb @ A_27a )
=> ! [V6l: $i] :
( ( mem @ V6l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V7x: $i] :
( ( mem @ V7x @ A_27a )
=> ! [V8y: $i] :
( ( mem @ V8y @ A_27b )
=> ! [V9r: $i] :
( ( mem @ V9r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V10ub: $i] :
( ( 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: $i] :
( ( mem @ V11v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V12v1: $i] :
( ( mem @ V12v1 @ A_27a )
=> ! [V13v2: $i] :
( ( mem @ V13v2 @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V14v3: $i] :
( ( mem @ V14v3 @ A_27a )
=> ( p @ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V11v ) @ V12v1 ) @ V13v2 ) @ V14v3 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORL__bt__lb__ub,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0ub: $i] :
( ( mem @ V0ub @ A_27a )
=> ! [V1lb: $i] :
( ( mem @ V1lb @ A_27a )
=> ! [V2cmp: $i] :
( ( 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 ) )
<=> ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V2cmp ) @ V1lb ) @ V0ub ) )
= fo__c_2EternaryComparisons_2ELESS ) ) ) ) )
& ! [V3y: $i] :
( ( mem @ V3y @ A_27b )
=> ! [V4x: $i] :
( ( mem @ V4x @ A_27a )
=> ! [V5ub: $i] :
( ( mem @ V5ub @ A_27a )
=> ! [V6r: $i] :
( ( mem @ V6r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V7lb: $i] :
( ( mem @ V7lb @ A_27a )
=> ! [V8l: $i] :
( ( mem @ V8l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V9cmp: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORL__bt__lb__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ bool ) ) ) )
=> ( ( ! [V1cmp: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V2lb: $i] :
( ( mem @ V2lb @ A_27a )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V1cmp ) @ V2lb ) @ ( c_2Eenumeral_2Ent @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) ) )
& ! [V3cmp: $i] :
( ( mem @ V3cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V4lb: $i] :
( ( mem @ V4lb @ A_27a )
=> ! [V5l: $i] :
( ( mem @ V5l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V6x: $i] :
( ( mem @ V6x @ A_27a )
=> ! [V7y: $i] :
( ( mem @ V7y @ A_27b )
=> ! [V8r: $i] :
( ( 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: $i] :
( ( mem @ V9v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V10v1: $i] :
( ( mem @ V10v1 @ A_27a )
=> ! [V11v2: $i] :
( ( mem @ V11v2 @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V9v ) @ V10v1 ) @ V11v2 ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORL__bt__lb,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0lb: $i] :
( ( mem @ V0lb @ A_27a )
=> ! [V1cmp: $i] :
( ( 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: $i] :
( ( mem @ V2y @ A_27b )
=> ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ! [V4r: $i] :
( ( mem @ V4r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V5lb: $i] :
( ( mem @ V5lb @ A_27a )
=> ! [V6l: $i] :
( ( mem @ V6l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V7cmp: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORL__bt__ub__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( arr @ A_27a @ bool ) ) ) )
=> ( ( ! [V1cmp: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V2ub: $i] :
( ( mem @ V2ub @ A_27a )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V1cmp ) @ ( c_2Eenumeral_2Ent @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V2ub ) ) ) )
& ! [V3cmp: $i] :
( ( mem @ V3cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V4l: $i] :
( ( mem @ V4l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V5x: $i] :
( ( mem @ V5x @ A_27a )
=> ! [V6y: $i] :
( ( mem @ V6y @ A_27b )
=> ! [V7r: $i] :
( ( mem @ V7r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V8ub: $i] :
( ( 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: $i] :
( ( mem @ V9v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V10v1: $i] :
( ( mem @ V10v1 @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V11v2: $i] :
( ( mem @ V11v2 @ A_27a )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V9v ) @ V10v1 ) @ V11v2 ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORL__bt__ub,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0ub: $i] :
( ( mem @ V0ub @ A_27a )
=> ! [V1cmp: $i] :
( ( 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: $i] :
( ( mem @ V2y @ A_27b )
=> ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ! [V4ub: $i] :
( ( mem @ V4ub @ A_27a )
=> ! [V5r: $i] :
( ( mem @ V5r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V6l: $i] :
( ( mem @ V6l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V7cmp: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORL__bt__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Etoto_2Etoto @ A_27a ) @ ( arr @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ bool ) ) )
=> ( ( ! [V1cmp: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ( p @ ( ap @ ( ap @ V0P @ V1cmp ) @ ( c_2Eenumeral_2Ent @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) )
& ! [V2cmp: $i] :
( ( mem @ V2cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V4x: $i] :
( ( mem @ V4x @ A_27a )
=> ! [V5y: $i] :
( ( mem @ V5y @ A_27b )
=> ! [V6r: $i] :
( ( 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: $i] :
( ( mem @ V7v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V8v1: $i] :
( ( mem @ V8v1 @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ( p @ ( ap @ ( ap @ V0P @ V7v ) @ V8v1 ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EORL__bt,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1l: $i] :
( ( mem @ V1l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ! [V3y: $i] :
( ( mem @ V3y @ A_27b )
=> ! [V4r: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebetter__bt__to__orl,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1t: $i] :
( ( 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 ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Elist__rplacv__cn__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( 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: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2y: $i] :
( ( mem @ V2y @ A_27b )
=> ! [V3cn: $i] :
( ( 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: $i] :
( ( mem @ V4x @ A_27a )
=> ! [V5y: $i] :
( ( mem @ V5y @ A_27b )
=> ! [V6w: $i] :
( ( mem @ V6w @ A_27a )
=> ! [V7z: $i] :
( ( mem @ V7z @ A_27b )
=> ! [V8l: $i] :
( ( mem @ V8l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V9cn: $i] :
( ( 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 )
@ ( lam @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
@ ^ [V10m: $i] : ( 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 ) ) ) ) ) )
=> ( 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: $i] :
( ( mem @ V11v @ A_27a )
=> ! [V12v1: $i] :
( ( mem @ V12v1 @ A_27b )
=> ! [V13v2: $i] :
( ( mem @ V13v2 @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V14v3: $i] :
( ( 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 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Elist__rplacv__cn,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0y: $i] :
( ( mem @ V0y @ A_27b )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2cn: $i] :
( ( 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: $i] :
( ( mem @ V3z @ A_27b )
=> ! [V4y: $i] :
( ( mem @ V4y @ A_27b )
=> ! [V5x: $i] :
( ( mem @ V5x @ A_27a )
=> ! [V6w: $i] :
( ( mem @ V6w @ A_27a )
=> ! [V7l: $i] :
( ( mem @ V7l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V8cn: $i] :
( ( 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 )
@ ( lam @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
@ ^ [V9m: $i] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Efmap__FDOM__rec,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0x: $i] :
( ( 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: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2w: $i] :
( ( mem @ V2w @ A_27a )
=> ! [V3z: $i] :
( ( mem @ V3z @ A_27b )
=> ! [V4l: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Elist__rplacv__thm,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1y: $i] :
( ( mem @ V1y @ A_27b )
=> ! [V2l: $i] :
( ( 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 )
@ ( lam @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
@ ^ [V3ans: $i] : ( 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 ) ) ) ) ) )
@ ( 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 )
@ ( lam @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
@ ^ [V4m: $i] : V4m ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__rplacv__cn__ind,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( 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: $i] :
( ( mem @ V1cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ! [V3y: $i] :
( ( mem @ V3y @ A_27b )
=> ! [V4cn: $i] :
( ( 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: $i] :
( ( mem @ V5cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V6x: $i] :
( ( mem @ V6x @ A_27a )
=> ! [V7y: $i] :
( ( mem @ V7y @ A_27b )
=> ! [V8l: $i] :
( ( mem @ V8l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V9w: $i] :
( ( mem @ V9w @ A_27a )
=> ! [V10z: $i] :
( ( mem @ V10z @ A_27b )
=> ! [V11r: $i] :
( ( mem @ V11r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V12cn: $i] :
( ( mem @ V12cn @ ( arr @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) )
=> ( ( ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V5cmp ) @ V6x ) @ V9w ) )
= fo__c_2EternaryComparisons_2EGREATER )
=> ( p
@ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V5cmp ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V6x ) @ V7y ) ) @ V11r )
@ ( lam @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
@ ^ [V13m: $i] : ( 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 ) ) ) ) ) )
& ( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2Etoto_2Eapto @ A_27a ) @ V5cmp ) @ V6x ) @ V9w ) )
= fo__c_2EternaryComparisons_2ELESS )
=> ( p
@ ( ap @ ( ap @ ( ap @ ( ap @ V0P @ V5cmp ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V6x ) @ V7y ) ) @ V8l )
@ ( lam @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
@ ^ [V14m: $i] : ( 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 ) ) ) ) ) ) )
=> ( 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: $i] :
( ( mem @ V15v @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V16v1: $i] :
( ( mem @ V16v1 @ A_27a )
=> ! [V17v2: $i] :
( ( mem @ V17v2 @ A_27b )
=> ! [V18v3: $i] :
( ( mem @ V18v3 @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V19v4: $i] :
( ( 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 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__rplacv__cn,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0y: $i] :
( ( mem @ V0y @ A_27b )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2cn: $i] :
( ( mem @ V2cn @ ( arr @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) )
=> ! [V3cmp: $i] :
( ( 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: $i] :
( ( mem @ V4z @ A_27b )
=> ! [V5y: $i] :
( ( mem @ V5y @ A_27b )
=> ! [V6x: $i] :
( ( mem @ V6x @ A_27a )
=> ! [V7w: $i] :
( ( mem @ V7w @ A_27a )
=> ! [V8r: $i] :
( ( mem @ V8r @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V9l: $i] :
( ( mem @ V9l @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) )
=> ! [V10cn: $i] :
( ( mem @ V10cn @ ( arr @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) ) ) )
=> ! [V11cmp: $i] :
( ( 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 )
@ ( lam @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
@ ^ [V12m: $i] : ( 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 ) ) ) ) )
@ ( 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 )
@ ( lam @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
@ ^ [V13m: $i] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Ebt__rplacv__thm,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2y: $i] :
( ( mem @ V2y @ A_27b )
=> ! [V3t: $i] :
( ( 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 )
@ ( lam @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
@ ^ [V4ans: $i] : ( 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 ) ) ) ) ) )
@ ( 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 )
@ ( lam @ ( ty_2Eenumeral_2Ebt @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) )
@ ^ [V5m: $i] : V5m ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2EFUN__fmap__thm,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1l: $i] :
( ( 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 ) )
@ ( lam @ A_27a
@ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ A_27a @ A_27b ) @ V2x ) @ ( ap @ V0f @ V2x ) ) ) )
@ V1l ) )
= ( ap @ ( ap @ ( c_2Efinite__map_2EFUN__FMAP @ A_27a @ A_27b ) @ V0f ) @ ( ap @ ( c_2Elist_2ELIST__TO__SET @ A_27a ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2Efmapal_2Efmap__ORWL__thm,axiom,
! [A_27a: del,A_27b: del,V0cmp: $i] :
( ( mem @ V0cmp @ ( ty_2Etoto_2Etoto @ A_27a ) )
=> ! [V1l: $i] :
( ( 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 ) ) ) ) ) ).
%------------------------------------------------------------------------------